LMFDB - Embedded newform 76.3.g.c.7.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,3,Mod(7,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("76.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	76.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.07085000914$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.7
Character	$\chi$	$=$	76.7
Dual form			76.3.g.c.11.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0647951 - 1.99895i) q^{2} +(-3.11547 + 1.79872i) q^{3} +(-3.99160 + 0.259045i) q^{4} +(4.52938 + 7.84512i) q^{5} +(3.79741 + 6.11112i) q^{6} -2.81904i q^{7} +(0.776454 + 7.96223i) q^{8} +(1.97077 - 3.41347i) q^{9} +O(q^{10})$	\(q+(-0.0647951 - 1.99895i) q^{2} +(-3.11547 + 1.79872i) q^{3} +(-3.99160 + 0.259045i) q^{4} +(4.52938 + 7.84512i) q^{5} +(3.79741 + 6.11112i) q^{6} -2.81904i q^{7} +(0.776454 + 7.96223i) q^{8} +(1.97077 - 3.41347i) q^{9} +(15.3885 - 9.56233i) q^{10} +11.6740i q^{11} +(11.9698 - 7.98681i) q^{12} +(-2.20531 + 3.81970i) q^{13} +(-5.63512 + 0.182660i) q^{14} +(-28.2223 - 16.2941i) q^{15} +(15.8658 - 2.06801i) q^{16} +(-9.59663 - 16.6219i) q^{17} +(-6.95104 - 3.71829i) q^{18} +(-9.06982 + 16.6955i) q^{19} +(-20.1117 - 30.1413i) q^{20} +(5.07066 + 8.78264i) q^{21} +(23.3358 - 0.756420i) q^{22} +(25.2864 + 14.5991i) q^{23} +(-16.7408 - 23.4095i) q^{24} +(-28.5306 + 49.4164i) q^{25} +(7.77829 + 4.16080i) q^{26} -18.1975i q^{27} +(0.730257 + 11.2525i) q^{28} +(15.9091 - 27.5555i) q^{29} +(-30.7425 + 57.4707i) q^{30} -23.9508i q^{31} +(-5.16187 - 31.5809i) q^{32} +(-20.9983 - 36.3701i) q^{33} +(-32.6044 + 20.2602i) q^{34} +(22.1157 - 12.7685i) q^{35} +(-6.98227 + 14.1357i) q^{36} +19.3382 q^{37} +(33.9611 + 17.0483i) q^{38} -15.8669i q^{39} +(-58.9478 + 42.1553i) q^{40} +(2.87159 + 4.97375i) q^{41} +(17.2275 - 10.7051i) q^{42} +(12.4494 - 7.18768i) q^{43} +(-3.02409 - 46.5981i) q^{44} +35.7054 q^{45} +(27.5445 - 51.4922i) q^{46} +(36.4249 + 21.0299i) q^{47} +(-45.7096 + 34.9809i) q^{48} +41.0530 q^{49} +(100.630 + 53.8292i) q^{50} +(59.7960 + 34.5232i) q^{51} +(7.81323 - 15.8180i) q^{52} +(16.2901 - 28.2152i) q^{53} +(-36.3759 + 1.17911i) q^{54} +(-91.5841 + 52.8761i) q^{55} +(22.4459 - 2.18885i) q^{56} +(-1.77365 - 68.3282i) q^{57} +(-56.1128 - 30.0161i) q^{58} +(-9.13465 + 5.27389i) q^{59} +(116.873 + 57.7289i) q^{60} +(-53.5230 + 92.7045i) q^{61} +(-47.8764 + 1.55189i) q^{62} +(-9.62270 - 5.55567i) q^{63} +(-62.7942 + 12.3646i) q^{64} -39.9547 q^{65} +(-71.3414 + 44.3311i) q^{66} +(109.917 + 63.4605i) q^{67} +(42.6117 + 63.8619i) q^{68} -105.039 q^{69} +(-26.9566 - 43.3809i) q^{70} +(3.89373 - 2.24805i) q^{71} +(28.7090 + 13.0413i) q^{72} +(-12.5643 - 21.7620i) q^{73} +(-1.25302 - 38.6562i) q^{74} -205.274i q^{75} +(31.8783 - 68.9911i) q^{76} +32.9096 q^{77} +(-31.7171 + 1.02810i) q^{78} +(-70.4767 + 40.6897i) q^{79} +(88.0859 + 115.102i) q^{80} +(50.4691 + 87.4150i) q^{81} +(9.75621 - 6.06245i) q^{82} -138.888i q^{83} +(-22.5152 - 33.7433i) q^{84} +(86.9336 - 150.573i) q^{85} +(-15.1745 - 24.4200i) q^{86} +114.464i q^{87} +(-92.9513 + 9.06434i) q^{88} +(-24.1722 + 41.8675i) q^{89} +(-2.31354 - 71.3733i) q^{90} +(10.7679 + 6.21685i) q^{91} +(-104.715 - 51.7236i) q^{92} +(43.0807 + 74.6179i) q^{93} +(39.6776 - 74.1742i) q^{94} +(-172.058 + 4.46625i) q^{95} +(72.8868 + 89.1047i) q^{96} +(-26.7563 - 46.3434i) q^{97} +(-2.66004 - 82.0629i) q^{98} +(39.8489 + 23.0068i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 5 q^{2} - 11 q^{4} + 6 q^{5} - 3 q^{6} - 62 q^{8} + 20 q^{9}+O(q^{10}) $ 28 * q - 5 * q^2 - 11 * q^4 + 6 * q^5 - 3 * q^6 - 62 * q^8 + 20 * q^9	$ 28 q - 5 q^{2} - 11 q^{4} + 6 q^{5} - 3 q^{6} - 62 q^{8} + 20 q^{9} + 26 q^{12} + 30 q^{13} - 30 q^{14} - 19 q^{16} + 38 q^{17} - 60 q^{18} - 44 q^{20} + 80 q^{21} + 45 q^{22} + 17 q^{24} - 16 q^{25} - 56 q^{26} + 54 q^{28} + 6 q^{29} + 96 q^{30} - 45 q^{32} - 176 q^{33} - 20 q^{34} + 30 q^{36} + 104 q^{37} - 258 q^{38} + 94 q^{40} - 2 q^{41} - 2 q^{42} + 201 q^{44} - 360 q^{45} + 164 q^{46} - 17 q^{48} - 20 q^{49} + 490 q^{50} - 102 q^{52} - 242 q^{53} - 13 q^{54} + 276 q^{56} - 254 q^{57} + 96 q^{58} + 10 q^{60} - 58 q^{61} - 36 q^{62} - 74 q^{64} - 260 q^{65} + 167 q^{66} + 396 q^{68} + 340 q^{69} + 60 q^{70} - 422 q^{72} - 82 q^{73} - 136 q^{74} + 123 q^{76} - 144 q^{77} + 224 q^{78} - 174 q^{80} + 410 q^{81} - 305 q^{82} + 252 q^{84} + 714 q^{85} + 166 q^{86} - 718 q^{88} + 150 q^{89} - 272 q^{90} - 588 q^{92} + 344 q^{93} - 488 q^{94} - 122 q^{96} + 94 q^{97} + 307 q^{98}+O(q^{100}) $ 28 * q - 5 * q^2 - 11 * q^4 + 6 * q^5 - 3 * q^6 - 62 * q^8 + 20 * q^9 + 26 * q^12 + 30 * q^13 - 30 * q^14 - 19 * q^16 + 38 * q^17 - 60 * q^18 - 44 * q^20 + 80 * q^21 + 45 * q^22 + 17 * q^24 - 16 * q^25 - 56 * q^26 + 54 * q^28 + 6 * q^29 + 96 * q^30 - 45 * q^32 - 176 * q^33 - 20 * q^34 + 30 * q^36 + 104 * q^37 - 258 * q^38 + 94 * q^40 - 2 * q^41 - 2 * q^42 + 201 * q^44 - 360 * q^45 + 164 * q^46 - 17 * q^48 - 20 * q^49 + 490 * q^50 - 102 * q^52 - 242 * q^53 - 13 * q^54 + 276 * q^56 - 254 * q^57 + 96 * q^58 + 10 * q^60 - 58 * q^61 - 36 * q^62 - 74 * q^64 - 260 * q^65 + 167 * q^66 + 396 * q^68 + 340 * q^69 + 60 * q^70 - 422 * q^72 - 82 * q^73 - 136 * q^74 + 123 * q^76 - 144 * q^77 + 224 * q^78 - 174 * q^80 + 410 * q^81 - 305 * q^82 + 252 * q^84 + 714 * q^85 + 166 * q^86 - 718 * q^88 + 150 * q^89 - 272 * q^90 - 588 * q^92 + 344 * q^93 - 488 * q^94 - 122 * q^96 + 94 * q^97 + 307 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.0647951	−	1.99895i	−0.0323976	−	0.999475i
$2$	−0.0647951	−	1.99895i	−0.0323976	−	0.999475i
$3$	−3.11547	+	1.79872i	−1.03849	+	0.599572i	−0.919405	−	0.393312i	$-0.871329\pi$
$3$	−3.11547	+	1.79872i	−1.03849	+	0.599572i	−0.119085	+	0.992884i	$0.537996\pi$
$4$	−3.99160	+	0.259045i	−0.997901	+	0.0647611i
$5$	4.52938	+	7.84512i	0.905876	+	1.56902i	0.819737	+	0.572740i	$0.194119\pi$
$5$	4.52938	+	7.84512i	0.905876	+	1.56902i	0.0861387	+	0.996283i	$0.472547\pi$
$6$	3.79741	+	6.11112i	0.632902	+	1.01852i
$7$		−	2.81904i		−	0.402720i	−0.979517	−	0.201360i	$-0.935464\pi$
$7$		−	2.81904i		−	0.402720i	0.979517	−	0.201360i	$-0.0645361\pi$
$8$	0.776454	+	7.96223i	0.0970567	+	0.995279i
$9$	1.97077	−	3.41347i	0.218974	−	0.379274i
$10$	15.3885	−	9.56233i	1.53885	−	0.956233i
$11$			11.6740i			1.06128i	0.847599	+	0.530638i	$0.178048\pi$
$11$			11.6740i			1.06128i	−0.847599	+	0.530638i	$0.821952\pi$
$12$	11.9698	−	7.98681i	0.997481	−	0.665567i
$13$	−2.20531	+	3.81970i	−0.169639	+	0.293823i	−0.938293	−	0.345841i	$-0.887593\pi$
$13$	−2.20531	+	3.81970i	−0.169639	+	0.293823i	0.768654	+	0.639665i	$0.220927\pi$
$14$	−5.63512	+	0.182660i	−0.402509	+	0.0130472i
$15$	−28.2223	−	16.2941i	−1.88149	−	1.08628i
$16$	15.8658	−	2.06801i	0.991612	−	0.129250i
$17$	−9.59663	−	16.6219i	−0.564508	−	0.977756i	−0.997095	−	0.0761642i	$-0.975733\pi$
$17$	−9.59663	−	16.6219i	−0.564508	−	0.977756i	0.432588	−	0.901592i	$-0.357601\pi$
$18$	−6.95104	−	3.71829i	−0.386169	−	0.206571i
$19$	−9.06982	+	16.6955i	−0.477359	+	0.878708i
$19$	−9.06982	+	16.6955i	−0.477359	+	0.878708i
$20$	−20.1117	−	30.1413i	−1.00559	−	1.50706i
$21$	5.07066	+	8.78264i	0.241460	+	0.418221i
$22$	23.3358	−	0.756420i	1.06072	−	0.0343827i
$23$	25.2864	+	14.5991i	1.09941	+	0.634744i	0.936066	−	0.351825i	$-0.114439\pi$
$23$	25.2864	+	14.5991i	1.09941	+	0.634744i	0.163343	+	0.986569i	$0.447772\pi$
$24$	−16.7408	−	23.4095i	−0.697534	−	0.975394i
$25$	−28.5306	+	49.4164i	−1.14122	+	1.97665i
$26$	7.77829	+	4.16080i	0.299165	+	0.160031i
$27$		−	18.1975i		−	0.673982i
$28$	0.730257	+	11.2525i	0.0260806	+	0.401875i
$29$	15.9091	−	27.5555i	0.548591	−	0.950188i	−0.449780	−	0.893139i	$-0.648498\pi$
$29$	15.9091	−	27.5555i	0.548591	−	0.950188i	0.998371	−	0.0570486i	$-0.0181690\pi$
$30$	−30.7425	+	57.4707i	−1.02475	+	1.91569i
$31$		−	23.9508i		−	0.772606i	−0.922372	−	0.386303i	$-0.873752\pi$
$31$		−	23.9508i		−	0.772606i	0.922372	−	0.386303i	$-0.126248\pi$
$32$	−5.16187	−	31.5809i	−0.161308	−	0.986904i
$33$	−20.9983	−	36.3701i	−0.636311	−	1.10212i
$34$	−32.6044	+	20.2602i	−0.958954	+	0.595888i
$35$	22.1157	−	12.7685i	0.631877	−	0.364815i
$36$	−6.98227	+	14.1357i	−0.193952	+	0.392659i
$37$	19.3382			0.522655			0.261327	−	0.965250i	$-0.415840\pi$
$37$	19.3382			0.522655			0.261327	+	0.965250i	$0.415840\pi$
$38$	33.9611	+	17.0483i	0.893712	+	0.448641i
$39$		−	15.8669i		−	0.406843i
$40$	−58.9478	+	42.1553i	−1.47369	+	1.05388i
$41$	2.87159	+	4.97375i	0.0700389	+	0.121311i	0.898918	−	0.438117i	$-0.144354\pi$
$41$	2.87159	+	4.97375i	0.0700389	+	0.121311i	−0.828879	+	0.559428i	$0.811021\pi$
$42$	17.2275	−	10.7051i	0.410179	−	0.254883i
$43$	12.4494	−	7.18768i	0.289521	−	0.167155i	−0.348205	−	0.937419i	$-0.613209\pi$
$43$	12.4494	−	7.18768i	0.289521	−	0.167155i	0.637726	+	0.770263i	$0.279875\pi$
$44$	−3.02409	−	46.5981i	−0.0687294	−	1.05905i
$45$	35.7054			0.793453
$46$	27.5445	−	51.4922i	0.598793	−	1.11940i
$47$	36.4249	+	21.0299i	0.774998	+	0.447445i	0.834655	−	0.550774i	$-0.185667\pi$
$47$	36.4249	+	21.0299i	0.774998	+	0.447445i	−0.0596567	+	0.998219i	$0.519001\pi$
$48$	−45.7096	+	34.9809i	−0.952284	+	0.728768i
$49$	41.0530			0.837816
$50$	100.630	+	53.8292i	2.01259	+	1.07658i
$51$	59.7960	+	34.5232i	1.17247	+	0.676926i
$52$	7.81323	−	15.8180i	0.150255	−	0.304192i
$53$	16.2901	−	28.2152i	0.307360	−	0.532362i	−0.670424	−	0.741978i	$-0.733888\pi$
$53$	16.2901	−	28.2152i	0.307360	−	0.532362i	0.977784	+	0.209616i	$0.0672212\pi$
$54$	−36.3759	+	1.17911i	−0.673628	+	0.0218354i
$55$	−91.5841	+	52.8761i	−1.66517	+	0.961384i
$56$	22.4459	−	2.18885i	0.400819	−	0.0390867i
$57$	−1.77365	−	68.3282i	−0.0311166	−	1.19874i
$58$	−56.1128	−	30.0161i	−0.967462	−	0.517520i
$59$	−9.13465	+	5.27389i	−0.154825	+	0.0893880i	−0.575411	−	0.817865i	$-0.695158\pi$
$59$	−9.13465	+	5.27389i	−0.154825	+	0.0893880i	0.420586	+	0.907253i	$0.361824\pi$
$60$	116.873	+	57.7289i	1.94788	+	0.962149i
$61$	−53.5230	+	92.7045i	−0.877426	+	1.51975i	−0.0232694	+	0.999729i	$0.507408\pi$
$61$	−53.5230	+	92.7045i	−0.877426	+	1.51975i	−0.854156	+	0.520016i	$0.825926\pi$
$62$	−47.8764	+	1.55189i	−0.772200	+	0.0250306i
$63$	−9.62270	−	5.55567i	−0.152741	−	0.0881852i
$64$	−62.7942	+	12.3646i	−0.981160	+	0.193197i
$65$	−39.9547			−0.614687
$66$	−71.3414	+	44.3311i	−1.08093	+	0.671684i
$67$	109.917	+	63.4605i	1.64055	+	0.947172i	0.980638	+	0.195828i	$0.0627394\pi$
$67$	109.917	+	63.4605i	1.64055	+	0.947172i	0.659911	+	0.751344i	$0.270594\pi$
$68$	42.6117	+	63.8619i	0.626643	+	0.939145i
$69$	−105.039			−1.52230
$70$	−26.9566	−	43.3809i	−0.385094	−	0.619727i
$71$	3.89373	−	2.24805i	0.0548413	−	0.0316626i	−0.472329	−	0.881423i	$-0.656586\pi$
$71$	3.89373	−	2.24805i	0.0548413	−	0.0316626i	0.527170	+	0.849760i	$0.323253\pi$
$72$	28.7090	+	13.0413i	0.398736	+	0.181129i
$73$	−12.5643	−	21.7620i	−0.172114	−	0.298110i	0.767045	−	0.641594i	$-0.221726\pi$
$73$	−12.5643	−	21.7620i	−0.172114	−	0.298110i	−0.939159	+	0.343484i	$0.888393\pi$
$74$	−1.25302	−	38.6562i	−0.0169327	−	0.522381i
$75$		−	205.274i		−	2.73698i
$76$	31.8783	−	68.9911i	0.419451	−	0.907778i
$77$	32.9096			0.427397
$78$	−31.7171	+	1.02810i	−0.406630	+	0.0131807i
$79$	−70.4767	+	40.6897i	−0.892110	+	0.515060i	−0.874632	−	0.484788i	$-0.838897\pi$
$79$	−70.4767	+	40.6897i	−0.892110	+	0.515060i	−0.0174777	+	0.999847i	$0.505564\pi$
$80$	88.0859	+	115.102i	1.10107	+	1.43878i
$81$	50.4691	+	87.4150i	0.623075	+	1.07920i
$82$	9.75621	−	6.06245i	0.118978	−	0.0739323i
$83$		−	138.888i		−	1.67336i	−0.547696	−	0.836678i	$-0.684495\pi$
$83$		−	138.888i		−	1.67336i	0.547696	−	0.836678i	$-0.315505\pi$
$84$	−22.5152	−	33.7433i	−0.268038	−	0.401706i
$85$	86.9336	−	150.573i	1.02275	−	1.77145i
$86$	−15.1745	−	24.4200i	−0.176447	−	0.283954i
$87$			114.464i			1.31568i
$88$	−92.9513	+	9.06434i	−1.05627	+	0.103004i
$89$	−24.1722	+	41.8675i	−0.271598	+	0.470421i	−0.969271	−	0.245995i	$-0.920885\pi$
$89$	−24.1722	+	41.8675i	−0.271598	+	0.470421i	0.697673	+	0.716416i	$0.254219\pi$
$90$	−2.31354	−	71.3733i	−0.0257059	−	0.793036i
$91$	10.7679	+	6.21685i	0.118329	+	0.0683170i
$92$	−104.715	−	51.7236i	−1.13821	−	0.562213i
$93$	43.0807	+	74.6179i	0.463233	+	0.802343i
$94$	39.6776	−	74.1742i	0.422102	−	0.789087i
$95$	−172.058	+	4.46625i	−1.81114	+	0.0470131i
$96$	72.8868	+	89.1047i	0.759237	+	0.928174i
$97$	−26.7563	−	46.3434i	−0.275839	−	0.477767i	0.694508	−	0.719485i	$-0.255622\pi$
$97$	−26.7563	−	46.3434i	−0.275839	−	0.477767i	−0.970346	+	0.241719i	$0.922289\pi$
$98$	−2.66004	−	82.0629i	−0.0271432	−	0.837377i
$99$	39.8489	+	23.0068i	0.402514	+	0.232392i
$100$	101.082	−	204.641i	1.01082	−	2.04641i
$101$	−15.2493	+	26.4126i	−0.150984	+	0.261511i	−0.931589	−	0.363513i	$-0.881577\pi$
$101$	−15.2493	+	26.4126i	−0.150984	+	0.261511i	0.780606	+	0.625024i	$0.214911\pi$
$102$	65.1358	−	121.766i	0.638586	−	1.19379i
$103$		−	56.0986i		−	0.544646i	−0.962206	−	0.272323i	$-0.912208\pi$
$103$		−	56.0986i		−	0.544646i	0.962206	−	0.272323i	$-0.0877920\pi$
$104$	−32.1257	−	14.5933i	−0.308901	−	0.140321i
$105$	−45.9339	+	79.5598i	−0.437465	+	0.757712i
$106$	−57.4563	−	30.7348i	−0.542041	−	0.289951i
$107$		−	8.87585i		−	0.0829519i	−0.999140	−	0.0414759i	$-0.986794\pi$
$107$		−	8.87585i		−	0.0829519i	0.999140	−	0.0414759i	$-0.0132060\pi$
$108$	4.71396	+	72.6372i	0.0436478	+	0.672567i
$109$	−2.29522	−	3.97543i	−0.0210570	−	0.0364718i	0.855305	−	0.518125i	$-0.173370\pi$
$109$	−2.29522	−	3.97543i	−0.0210570	−	0.0364718i	−0.876362	+	0.481653i	$0.840036\pi$
$110$	111.631	+	179.646i	1.01483	+	1.63315i
$111$	−60.2477	+	34.7840i	−0.542772	+	0.313369i
$112$	−5.82979	−	44.7263i	−0.0520517	−	0.399342i
$113$	174.766			1.54660			0.773301	−	0.634039i	$-0.218604\pi$
$113$	174.766			1.54660			0.773301	+	0.634039i	$0.218604\pi$
$114$	−136.470	+	7.97277i	−1.19710	+	0.0699366i
$115$			264.500i			2.30000i
$116$	−56.3649	+	114.112i	−0.485904	+	0.983721i
$117$	8.69228	+	15.0555i	0.0742930	+	0.128679i
$118$	11.1341	+	17.9180i	0.0943571	+	0.151847i
$119$	−46.8577	+	27.0533i	−0.393762	+	0.227339i
$120$	107.824	−	237.364i	0.898537	−	1.97803i
$121$	−15.2830			−0.126306
$122$	188.780	+	100.983i	1.54737	+	0.827729i
$123$	−17.8927	−	10.3304i	−0.145469	−	0.0839868i
$124$	6.20432	+	95.6020i	0.0500348	+	0.770984i
$125$	−290.434			−2.32347
$126$	−10.4820	+	19.5953i	−0.0831905	+	0.155518i
$127$	−145.773	−	84.1618i	−1.14782	−	0.662691i	−0.199461	−	0.979906i	$-0.563919\pi$
$127$	−145.773	−	84.1618i	−1.14782	−	0.662691i	−0.948354	+	0.317214i	$0.897253\pi$
$128$	28.7850	+	124.721i	0.224883	+	0.974386i
$129$	−25.8572	+	44.7860i	−0.200443	+	0.347178i
$130$	2.58887	+	79.8674i	0.0199144	+	0.614365i
$131$	106.509	−	61.4929i	0.813044	−	0.469411i	−0.0349677	−	0.999388i	$-0.511133\pi$
$131$	106.509	−	61.4929i	0.813044	−	0.469411i	0.848012	+	0.529977i	$0.177800\pi$
$132$	93.2383	+	139.735i	0.706350	+	1.05860i
$133$	47.0652	+	25.5682i	0.353874	+	0.192242i
$134$	119.732	−	223.830i	0.893525	−	1.67037i
$135$	142.762	−	82.4234i	1.05749	−	0.610544i
$136$	124.896	−	89.3167i	0.918351	−	0.656740i
$137$	40.8518	−	70.7574i	0.298188	−	0.516477i	−0.677533	−	0.735492i	$-0.736951\pi$
$137$	40.8518	−	70.7574i	0.298188	−	0.516477i	0.975721	+	0.219015i	$0.0702844\pi$
$138$	6.80600	+	209.967i	0.0493188	+	1.52150i
$139$	−16.6104	−	9.59003i	−0.119499	−	0.0689930i	0.439059	−	0.898458i	$-0.355312\pi$
$139$	−16.6104	−	9.59003i	−0.119499	−	0.0689930i	−0.558558	+	0.829465i	$0.688645\pi$
$140$	−84.9695	+	56.6958i	−0.606925	+	0.404970i
$141$	−151.308			−1.07310
$142$	−4.74603	−	7.63771i	−0.0334227	−	0.0537867i
$143$	−44.5913	−	25.7448i	−0.311827	−	0.180034i
$144$	24.2087	−	58.2329i	0.168116	−	0.404395i
$145$	288.234			1.98782
$146$	−42.6871	+	26.5255i	−0.292377	+	0.181682i
$147$	−127.899	+	73.8427i	−0.870064	+	0.502332i
$148$	−77.1905	+	5.00946i	−0.521558	+	0.0338477i
$149$	33.0378	+	57.2232i	0.221730	+	0.384048i	0.955333	−	0.295530i	$-0.0954962\pi$
$149$	33.0378	+	57.2232i	0.221730	+	0.384048i	−0.733603	+	0.679578i	$0.762163\pi$
$150$	−410.332	+	13.3007i	−2.73554	+	0.0886715i
$151$		−	12.6319i		−	0.0836552i	−0.999125	−	0.0418276i	$-0.986682\pi$
$151$		−	12.6319i		−	0.0836552i	0.999125	−	0.0418276i	$-0.0133180\pi$
$152$	−139.975	−	59.2528i	−0.920891	−	0.389821i
$153$	−75.6508			−0.494450
$154$	−2.13238	−	65.7846i	−0.0138466	−	0.427173i
$155$	187.897	−	108.482i	1.21224	−	0.699885i
$156$	4.11023	+	63.3343i	0.0263476	+	0.405989i
$157$	22.5170	+	39.0005i	0.143420	+	0.248411i	0.928782	−	0.370625i	$-0.120857\pi$
$157$	22.5170	+	39.0005i	0.143420	+	0.248411i	−0.785362	+	0.619037i	$0.787523\pi$
$158$	85.9033	+	138.243i	0.543692	+	0.874955i
$159$			117.205i			0.737137i
$160$	224.376	−	183.537i	1.40235	−	1.14711i
$161$	41.1555	−	71.2834i	0.255624	−	0.442754i
$162$	171.468	−	106.549i	1.05844	−	0.657711i
$163$			80.7645i			0.495488i	0.968826	+	0.247744i	$0.0796892\pi$
$163$			80.7645i			0.495488i	−0.968826	+	0.247744i	$0.920311\pi$
$164$	−12.7507	−	19.1094i	−0.0777481	−	0.116520i
$165$	190.218	−	329.468i	1.15284	−	1.99677i
$166$	−277.631	+	8.99930i	−1.67248	+	0.0542126i
$167$	164.130	+	94.7605i	0.982814	+	0.567428i	0.903119	−	0.429391i	$-0.141272\pi$
$167$	164.130	+	94.7605i	0.982814	+	0.567428i	0.0796954	+	0.996819i	$0.474605\pi$
$168$	−65.9923	+	47.1931i	−0.392811	+	0.280911i
$169$	74.7732	+	129.511i	0.442445	+	0.766338i
$170$	−306.622	−	164.019i	−1.80366	−	0.964820i
$171$	39.1149	+	63.8624i	0.228742	+	0.373464i
$172$	−47.8312	+	31.9153i	−0.278088	+	0.185554i
$173$	−66.4142	−	115.033i	−0.383897	−	0.664930i	0.607718	−	0.794153i	$-0.292085\pi$
$173$	−66.4142	−	115.033i	−0.383897	−	0.664930i	−0.991616	+	0.129223i	$0.958752\pi$
$174$	228.808	−	7.41672i	1.31499	−	0.0426249i
$175$	139.307	+	80.4288i	0.796039	+	0.459593i
$176$	24.1420	+	185.218i	0.137170	+	1.05237i
$177$	18.9725	−	32.8613i	0.107189	−	0.185657i
$178$	85.2572	+	45.6062i	0.478973	+	0.256215i
$179$			71.2078i			0.397809i	0.980019	+	0.198904i	$0.0637384\pi$
$179$			71.2078i			0.397809i	−0.980019	+	0.198904i	$0.936262\pi$
$180$	−142.522	+	9.24928i	−0.791787	+	0.0513849i
$181$	−74.3514	+	128.780i	−0.410781	+	0.711494i	−0.994975	−	0.100120i	$-0.968077\pi$
$181$	−74.3514	+	128.780i	−0.410781	+	0.711494i	0.584194	+	0.811614i	$0.301411\pi$
$182$	11.7295	−	21.9273i	0.0644476	−	0.120480i
$183$		−	385.091i		−	2.10432i
$184$	−96.6078	+	212.672i	−0.525042	+	1.15582i
$185$	87.5902	+	151.711i	0.473460	+	0.820058i
$186$	146.366	−	90.9510i	0.786914	−	0.488984i
$187$	194.044	−	112.031i	1.03767	−	0.599098i
$188$	−150.841	−	74.5075i	−0.802348	−	0.396316i
$189$	−51.2995			−0.271426
$190$	20.0764	+	343.647i	0.105665	+	1.80867i
$191$		−	158.757i		−	0.831187i	−0.909550	−	0.415594i	$-0.863574\pi$
$191$		−	158.757i		−	0.831187i	0.909550	−	0.415594i	$-0.136426\pi$
$192$	173.393	−	151.471i	0.903089	−	0.788909i
$193$	−154.059	−	266.837i	−0.798231	−	1.38258i	−0.920767	−	0.390113i	$-0.872436\pi$
$193$	−154.059	−	266.837i	−0.798231	−	1.38258i	0.122536	−	0.992464i	$-0.460897\pi$
$194$	−90.9044	+	56.4874i	−0.468579	+	0.291172i
$195$	124.478	−	71.8672i	0.638346	−	0.368550i
$196$	−163.867	+	10.6346i	−0.836058	+	0.0542579i
$197$	44.2927			0.224836			0.112418	−	0.993661i	$-0.464140\pi$
$197$	44.2927			0.224836			0.112418	+	0.993661i	$0.464140\pi$
$198$	43.4074	−	81.1467i	0.219229	−	0.409832i
$199$	−198.448	−	114.574i	−0.997225	−	0.575748i	−0.0897989	−	0.995960i	$-0.528622\pi$
$199$	−198.448	−	114.574i	−0.997225	−	0.575748i	−0.907426	+	0.420212i	$0.861956\pi$
$200$	−415.617	−	188.797i	−2.07809	−	0.943987i
$201$	−456.590			−2.27159
$202$	53.7856	+	28.7713i	0.266265	+	0.142432i
$203$	−77.6800	−	44.8485i	−0.382660	−	0.220929i
$204$	−247.625	−	122.313i	−1.21385	−	0.599575i
$205$	−26.0131	+	45.0560i	−0.126893	+	0.219785i
$206$	−112.138	+	3.63491i	−0.544360	+	0.0176452i
$207$	99.6672	−	57.5429i	0.481484	−	0.277985i
$208$	−27.0898	+	65.1632i	−0.130239	+	0.313285i
$209$	−194.903	−	105.881i	−0.932552	−	0.506610i
$210$	162.012	+	86.6644i	0.771487	+	0.412688i
$211$	−123.613	+	71.3683i	−0.585846	+	0.338238i	−0.763453	−	0.645863i	$-0.776498\pi$
$211$	−123.613	+	71.3683i	−0.585846	+	0.338238i	0.177607	+	0.984101i	$0.443164\pi$
$212$	−57.7145	+	116.844i	−0.272238	+	0.551150i
$213$	−8.08720	+	14.0074i	−0.0379681	+	0.0657627i
$214$	−17.7424	+	0.575112i	−0.0829083	+	0.00268744i
$215$	112.776	+	65.1114i	0.524541	+	0.302844i
$216$	144.893	−	14.1295i	0.670800	−	0.0654144i
$217$	−67.5183			−0.311144
$218$	−7.79797	+	4.84561i	−0.0357705	+	0.0222276i
$219$	78.2875	+	45.1993i	0.357477	+	0.206389i
$220$	351.870	−	234.785i	1.59941	−	1.06720i
$221$	84.6541			0.383050
$222$	73.4352	+	118.178i	0.330789	+	0.532334i
$223$	−79.7297	+	46.0319i	−0.357532	+	0.206421i	−0.667998	−	0.744163i	$-0.732848\pi$
$223$	−79.7297	+	46.0319i	−0.357532	+	0.206421i	0.310466	+	0.950585i	$0.399515\pi$
$224$	−89.0280	+	14.5515i	−0.397446	+	0.0649621i
$225$	112.454	+	194.776i	0.499796	+	0.865672i
$226$	−11.3240	−	349.349i	−0.0501062	−	1.54579i
$227$			36.7352i			0.161829i	0.996721	+	0.0809145i	$0.0257841\pi$
$227$			36.7352i			0.161829i	−0.996721	+	0.0809145i	$0.974216\pi$
$228$	24.7797	+	272.280i	0.108683	+	1.19421i
$229$	45.3630			0.198092			0.0990459	−	0.995083i	$-0.468421\pi$
$229$	45.3630			0.198092			0.0990459	+	0.995083i	$0.468421\pi$
$230$	528.722	−	17.1383i	2.29879	−	0.0745143i
$231$	−102.529	+	59.1950i	−0.443848	+	0.256255i
$232$	231.756	+	105.277i	0.998946	+	0.453779i
$233$	−96.8854	−	167.810i	−0.415817	−	0.720216i	0.579697	−	0.814832i	$-0.303171\pi$
$233$	−96.8854	−	167.810i	−0.415817	−	0.720216i	−0.995514	+	0.0946161i	$0.969838\pi$
$234$	29.5319	−	18.3510i	0.126205	−	0.0784229i
$235$			381.010i			1.62132i
$236$	35.0957	−	23.4176i	0.148711	−	0.0992270i
$237$	146.379	−	253.535i	0.617631	−	1.06977i
$238$	57.1144	+	91.9133i	0.239976	+	0.386190i
$239$			172.376i			0.721238i	0.932713	+	0.360619i	$0.117435\pi$
$239$			172.376i			0.721238i	−0.932713	+	0.360619i	$0.882565\pi$
$240$	−481.465	−	200.156i	−2.00611	−	0.833982i
$241$	136.476	−	236.384i	0.566291	−	0.980845i	−0.430637	−	0.902525i	$-0.641711\pi$
$241$	136.476	−	236.384i	0.566291	−	0.980845i	0.996928	−	0.0783202i	$-0.0249556\pi$
$242$	0.990263	+	30.5499i	0.00409200	+	0.126239i
$243$	−172.634	−	99.6703i	−0.710428	−	0.410166i
$244$	189.628	−	383.904i	0.777163	−	1.57338i
$245$	185.945	+	322.066i	0.758958	+	1.31455i
$246$	−19.4905	+	36.4360i	−0.0792298	+	0.148114i
$247$	−43.7699	−	71.4626i	−0.177206	−	0.289322i
$248$	190.702	−	18.5967i	0.768958	−	0.0749866i
$249$	249.821	+	432.703i	1.00330	+	1.73776i
$250$	18.8187	+	580.563i	0.0752748	+	2.32225i
$251$	−206.313	−	119.115i	−0.821965	−	0.474562i	0.0291287	−	0.999576i	$-0.490727\pi$
$251$	−206.313	−	119.115i	−0.821965	−	0.474562i	−0.851094	+	0.525014i	$0.824060\pi$
$252$	39.8492	+	19.6833i	0.158132	+	0.0781084i
$253$	−170.430	+	295.194i	−0.673638	+	1.16678i
$254$	−158.790	+	296.845i	−0.625157	+	1.16868i
$255$			625.476i			2.45285i
$256$	247.447	−	65.6211i	0.966589	−	0.256332i
$257$	−70.1915	+	121.575i	−0.273119	+	0.473055i	−0.969659	−	0.244463i	$-0.921388\pi$
$257$	−70.1915	+	121.575i	−0.273119	+	0.473055i	0.696540	+	0.717518i	$0.254722\pi$
$258$	91.2003	+	48.7853i	0.353490	+	0.189090i
$259$		−	54.5153i		−	0.210484i
$260$	159.483	−	10.3500i	0.613397	−	0.0398078i
$261$	−62.7064	−	108.611i	−0.240254	−	0.416133i
$262$	−129.822	−	208.921i	−0.495506	−	0.797410i
$263$	−140.437	+	81.0814i	−0.533981	+	0.308294i	−0.742636	−	0.669695i	$-0.766425\pi$
$263$	−140.437	+	81.0814i	−0.533981	+	0.308294i	0.208655	+	0.977989i	$0.433091\pi$
$264$	273.283	−	195.433i	1.03516	−	0.740276i
$265$	295.135			1.11372
$266$	48.0600	−	95.7377i	0.180677	−	0.359916i
$267$		−	173.916i		−	0.651370i
$268$	−455.183	−	224.836i	−1.69845	−	0.838939i
$269$	117.202	+	203.000i	0.435695	+	0.754647i	0.997352	−	0.0727237i	$-0.0231691\pi$
$269$	117.202	+	203.000i	0.435695	+	0.754647i	−0.561657	+	0.827370i	$0.689836\pi$
$270$	−174.011	−	280.033i	−0.644484	−	1.03716i
$271$	107.762	−	62.2163i	0.397645	−	0.229581i	−0.287822	−	0.957684i	$-0.592931\pi$
$271$	107.762	−	62.2163i	0.397645	−	0.229581i	0.685467	+	0.728103i	$0.259598\pi$
$272$	−186.632	−	243.873i	−0.686148	−	0.896592i
$273$	−44.7294			−0.163844
$274$	−144.087	−	77.0759i	−0.525867	−	0.281299i
$275$	−576.888	−	333.067i	−2.09778	−	1.21115i
$276$	419.273	−	27.2097i	1.51910	−	0.0985859i
$277$	240.837			0.869447			0.434724	−	0.900564i	$-0.356846\pi$
$277$	240.837			0.869447			0.434724	+	0.900564i	$0.356846\pi$
$278$	−18.0937	+	33.8248i	−0.0650853	+	0.121672i
$279$	−81.7552	−	47.2014i	−0.293029	−	0.169181i
$280$	118.838	+	166.176i	0.424420	+	0.593486i
$281$	155.780	−	269.819i	0.554378	−	0.960211i	−0.443574	−	0.896238i	$-0.646290\pi$
$281$	155.780	−	269.819i	0.554378	−	0.960211i	0.997952	−	0.0639730i	$-0.0203772\pi$
$282$	9.80399	+	302.456i	0.0347659	+	1.07254i
$283$	342.914	−	197.981i	1.21171	−	0.699581i	0.248578	−	0.968612i	$-0.420037\pi$
$283$	342.914	−	197.981i	1.21171	−	0.699581i	0.963132	+	0.269031i	$0.0867034\pi$
$284$	−14.9599	+	9.98196i	−0.0526757	+	0.0351478i
$285$	528.009	−	323.399i	1.85266	−	1.13473i
$286$	−48.5733	+	90.8040i	−0.169837	+	0.317496i
$287$	14.0212	−	8.09515i	0.0488544	−	0.0282061i
$288$	−117.973	−	44.6188i	−0.409629	−	0.154926i
$289$	−39.6907	+	68.7463i	−0.137338	+	0.237876i
$290$	−18.6762	−	576.166i	−0.0644006	−	1.98678i
$291$	166.717	+	96.2542i	0.572911	+	0.330770i
$292$	55.7891	+	83.6107i	0.191059	+	0.286338i
$293$	−455.316			−1.55398			−0.776990	−	0.629513i	$-0.783254\pi$
$293$	−455.316			−1.55398			−0.776990	+	0.629513i	$0.783254\pi$
$294$	155.895	+	250.880i	0.530256	+	0.853333i
$295$	−82.7486	−	47.7749i	−0.280504	−	0.161949i
$296$	15.0152	+	153.975i	0.0507272	+	0.520187i
$297$	212.438			0.715280
$298$	112.246	−	69.7487i	0.376663	−	0.234056i
$299$	−111.529	+	64.3910i	−0.373005	+	0.215355i
$300$	53.1750	+	819.371i	0.177250	+	2.73124i
$301$	−20.2624	−	35.0954i	−0.0673168	−	0.116596i
$302$	−25.2506	+	0.818488i	−0.0836113	+	0.00271023i
$303$		−	109.717i		−	0.362102i
$304$	−109.374	+	283.643i	−0.359782	+	0.933037i
$305$	−969.703			−3.17935
$306$	4.90181	+	151.222i	0.0160190	+	0.494190i
$307$	−306.496	+	176.956i	−0.998358	+	0.576403i	−0.907762	−	0.419485i	$-0.862211\pi$
$307$	−306.496	+	176.956i	−0.998358	+	0.576403i	−0.0905962	+	0.995888i	$0.528877\pi$
$308$	−131.362	+	8.52505i	−0.426500	+	0.0276787i
$309$	100.905	+	174.773i	0.326555	+	0.565610i
$310$	−229.025	−	368.567i	−0.738791	−	1.18893i
$311$		−	508.683i		−	1.63564i	−0.575475	−	0.817819i	$-0.695183\pi$
$311$		−	508.683i		−	1.63564i	0.575475	−	0.817819i	$-0.304817\pi$
$312$	126.336	−	12.3199i	0.404923	−	0.0394869i
$313$	−227.534	+	394.101i	−0.726946	+	1.25911i	0.231222	+	0.972901i	$0.425728\pi$
$313$	−227.534	+	394.101i	−0.726946	+	1.25911i	−0.958168	+	0.286206i	$0.907606\pi$
$314$	76.5012	−	47.5374i	0.243634	−	0.151393i
$315$		−	100.655i		−	0.319540i
$316$	270.774	−	180.674i	0.856881	−	0.571753i
$317$	−299.225	+	518.273i	−0.943927	+	1.63493i	−0.186041	+	0.982542i	$0.559566\pi$
$317$	−299.225	+	518.273i	−0.943927	+	1.63493i	−0.757886	+	0.652387i	$0.773768\pi$
$318$	234.287	−	7.59430i	0.736750	−	0.0238815i
$319$	321.683	+	185.724i	1.00841	+	0.582206i
$320$	−381.421	−	436.624i	−1.19194	−	1.36445i
$321$	15.9651	+	27.6524i	0.0497356	+	0.0861446i
$322$	−145.159	−	77.6490i	−0.450803	−	0.241146i
$323$	364.549	−	9.46287i	1.12864	−	0.0292968i
$324$	−224.097	−	335.852i	−0.691657	−	1.03658i
$325$	−125.837	−	217.956i	−0.387191	−	0.670635i
$326$	161.444	−	5.23315i	0.495228	−	0.0160526i
$327$	14.3013	+	8.25689i	0.0437350	+	0.0252504i
$328$	−37.3725	+	26.7262i	−0.113940	+	0.0814823i
$329$	59.2842	−	102.683i	0.180195	−	0.312107i
$330$	−670.915	−	358.889i	−2.03308	−	1.08754i
$331$		−	282.230i		−	0.852657i	−0.904568	−	0.426329i	$-0.859807\pi$
$331$		−	282.230i		−	0.852657i	0.904568	−	0.426329i	$-0.140193\pi$
$332$	35.9783	+	554.388i	0.108368	+	1.66984i
$333$	38.1111	−	66.0104i	0.114448	−	0.198229i
$334$	178.787	−	334.228i	0.535289	−	1.00068i
$335$			1149.75i			3.43208i
$336$	98.6126	+	128.857i	0.293490	+	0.383504i
$337$	−39.3112	−	68.0891i	−0.116651	−	0.202045i	0.801788	−	0.597609i	$-0.203882\pi$
$337$	−39.3112	−	68.0891i	−0.116651	−	0.202045i	−0.918438	+	0.395564i	$0.870549\pi$
$338$	254.041	−	157.860i	0.751601	−	0.467040i
$339$	−544.478	+	314.355i	−1.60613	+	0.927300i
$340$	−307.999	+	623.549i	−0.905880	+	1.83397i
$341$	279.602			0.819948
$342$	125.123	−	82.3267i	0.365857	−	0.240721i
$343$		−	253.863i		−	0.740126i
$344$	66.8963	+	93.5443i	0.194466	+	0.271931i
$345$	−475.760	−	824.041i	−1.37901	−	2.38852i
$346$	−225.642	+	140.212i	−0.652143	+	0.405238i
$347$	155.605	−	89.8386i	0.448429	−	0.258901i	−0.258737	−	0.965948i	$-0.583306\pi$
$347$	155.605	−	89.8386i	0.448429	−	0.258901i	0.707167	+	0.707047i	$0.249973\pi$
$348$	−29.6513	−	456.896i	−0.0852050	−	1.31292i
$349$	−93.3245			−0.267405			−0.133703	−	0.991021i	$-0.542687\pi$
$349$	−93.3245			−0.267405			−0.133703	+	0.991021i	$0.542687\pi$
$350$	151.747	−	283.679i	0.433562	−	0.810511i
$351$	69.5091	+	40.1311i	0.198032	+	0.114334i
$352$	368.677	−	60.2598i	1.04738	−	0.171193i
$353$	474.560			1.34436			0.672182	−	0.740386i	$-0.265357\pi$
$353$	474.560			1.34436			0.672182	+	0.740386i	$0.265357\pi$
$354$	−66.9174	−	35.7958i	−0.189032	−	0.101118i
$355$	35.2724	+	20.3645i	0.0993588	+	0.0573648i
$356$	85.6403	−	173.380i	0.240563	−	0.487022i
$357$	97.3225	−	168.567i	0.272612	−	0.472178i
$358$	142.341	−	4.61392i	0.397600	−	0.0128880i
$359$	409.552	−	236.455i	1.14081	−	0.658649i	0.194182	−	0.980966i	$-0.437795\pi$
$359$	409.552	−	236.455i	1.14081	−	0.658649i	0.946632	+	0.322316i	$0.104461\pi$
$360$	27.7236	+	284.294i	0.0770099	+	0.789707i
$361$	−196.477	−	302.850i	−0.544257	−	0.838919i
$362$	262.243	+	140.280i	0.724429	+	0.387515i
$363$	47.6137	−	27.4898i	0.131167	−	0.0757294i
$364$	−44.5916	−	22.0258i	−0.122504	−	0.0605105i
$365$	113.817	−	197.137i	0.311828	−	0.540101i
$366$	−769.777	+	24.9520i	−2.10322	+	0.0681749i
$367$	−48.5847	−	28.0504i	−0.132383	−	0.0764316i	0.432346	−	0.901708i	$-0.357686\pi$
$367$	−48.5847	−	28.0504i	−0.132383	−	0.0764316i	−0.564729	+	0.825276i	$0.691019\pi$
$368$	431.380	+	179.334i	1.17223	+	0.487321i
$369$	22.6370			0.0613468
$370$	297.587	−	184.919i	0.804288	−	0.499780i
$371$	−79.5399	−	45.9224i	−0.214393	−	0.123780i
$372$	−191.290	−	286.685i	−0.514221	−	0.770659i
$373$	−491.645			−1.31808			−0.659042	−	0.752106i	$-0.729038\pi$
$373$	−491.645			−1.31808			−0.659042	+	0.752106i	$0.729038\pi$
$374$	−236.518	−	380.625i	−0.632402	−	1.01771i
$375$	904.838	−	522.408i	2.41290	−	1.39309i
$376$	−139.163	+	306.352i	−0.370114	+	0.814767i
$377$	70.1691	+	121.536i	0.186125	+	0.322378i
$378$	3.32396	+	102.545i	0.00879355	+	0.271284i
$379$			401.210i			1.05860i	0.848434	+	0.529301i	$0.177546\pi$
$379$			401.210i			1.05860i	−0.848434	+	0.529301i	$0.822454\pi$
$380$	685.632	−	62.3983i	1.80430	−	0.164206i
$381$	605.533			1.58933
$382$	−317.347	+	10.2867i	−0.830751	+	0.0269285i
$383$	74.9428	−	43.2682i	0.195673	−	0.112972i	−0.398963	−	0.916967i	$-0.630630\pi$
$383$	74.9428	−	43.2682i	0.195673	−	0.112972i	0.594636	+	0.803995i	$0.297296\pi$
$384$	−314.017	−	336.790i	−0.817753	−	0.877056i
$385$	149.060	+	258.179i	0.387169	+	0.670596i
$386$	−523.412	+	325.245i	−1.35599	+	0.842604i
$387$		−	56.6609i		−	0.146411i
$388$	118.806	+	178.053i	0.306200	+	0.458900i
$389$	303.042	−	524.884i	0.779028	−	1.34932i	−0.153474	−	0.988153i	$-0.549046\pi$
$389$	303.042	−	524.884i	0.779028	−	1.34932i	0.932502	−	0.361164i	$-0.117621\pi$
$390$	−151.724	−	244.168i	−0.389037	−	0.626071i
$391$		−	560.409i		−	1.43327i
$392$	31.8757	+	326.873i	0.0813157	+	0.833861i
$393$	−221.217	+	383.158i	−0.562892	+	0.974958i
$394$	−2.86995	−	88.5389i	−0.00728414	−	0.224718i
$395$	−638.431	−	368.598i	−1.61628	−	0.933160i
$396$	−165.021	−	81.5113i	−0.416719	−	0.205837i
$397$	−85.6583	−	148.365i	−0.215764	−	0.373714i	0.737745	−	0.675080i	$-0.235891\pi$
$397$	−85.6583	−	148.365i	−0.215764	−	0.373714i	−0.953509	+	0.301366i	$0.902558\pi$
$398$	−216.169	+	404.111i	−0.543138	+	1.01535i
$399$	−192.620	+	4.99998i	−0.482757	+	0.0125313i
$400$	−350.467	+	843.031i	−0.876166	+	2.10758i
$401$	133.478	+	231.191i	0.332864	+	0.576537i	0.983072	−	0.183219i	$-0.0586517\pi$
$401$	133.478	+	231.191i	0.332864	+	0.576537i	−0.650208	+	0.759756i	$0.725318\pi$
$402$	29.5848	+	912.700i	0.0735940	+	2.27040i
$403$	91.4849	+	52.8188i	0.227010	+	0.131064i
$404$	54.0273	−	109.379i	0.133731	−	0.270740i
$405$	−457.187	+	791.871i	−1.12886	+	1.95524i
$406$	−84.6167	+	158.184i	−0.208416	+	0.389617i
$407$			225.755i			0.554681i
$408$	−228.453	+	502.915i	−0.559934	+	1.23264i
$409$	62.1792	−	107.697i	0.152027	−	0.263319i	−0.779945	−	0.625848i	$-0.784753\pi$
$409$	62.1792	−	107.697i	0.152027	−	0.263319i	0.931973	+	0.362529i	$0.118087\pi$
$410$	91.7502	+	49.0795i	0.223781	+	0.119706i
$411$			293.923i			0.715141i
$412$	14.5320	+	223.923i	0.0352719	+	0.543503i
$413$	14.8673	+	25.7510i	0.0359984	+	0.0623510i
$414$	−121.483	−	195.501i	−0.293438	−	0.472225i
$415$	1089.60	−	629.079i	2.62553	−	1.51585i
$416$	132.013	+	49.9288i	0.317340	+	0.120021i
$417$	68.9990			0.165465
$418$	−199.023	+	396.463i	−0.476131	+	0.948475i
$419$			248.914i			0.594068i	0.954867	+	0.297034i	$0.0959974\pi$
$419$			248.914i			0.594068i	−0.954867	+	0.297034i	$0.904003\pi$
$420$	162.740	−	329.470i	0.387477	−	0.784453i
$421$	−162.941	−	282.223i	−0.387034	−	0.670362i	0.605015	−	0.796214i	$-0.293167\pi$
$421$	−162.941	−	282.223i	−0.387034	−	0.670362i	−0.992049	+	0.125852i	$0.959834\pi$
$422$	150.671	+	242.473i	0.357041	+	0.574580i
$423$	143.570	−	82.8901i	0.339409	−	0.195958i
$424$	237.304	+	107.797i	0.559680	+	0.254239i
$425$	1095.19			2.57692
$426$	28.5242	+	15.2583i	0.0669582	+	0.0358176i
$427$	261.338	+	150.883i	0.612032	+	0.353357i
$428$	2.29924	+	35.4289i	0.00537206	+	0.0827777i
$429$	185.231			0.431773
$430$	122.847	−	229.653i	0.285691	−	0.534077i
$431$	401.407	+	231.752i	0.931338	+	0.537708i	0.887235	−	0.461319i	$-0.152623\pi$
$431$	401.407	+	231.752i	0.931338	+	0.537708i	0.0441038	+	0.999027i	$0.485957\pi$
$432$	−37.6326	−	288.718i	−0.0871124	−	0.668328i
$433$	138.967	−	240.698i	0.320940	−	0.555884i	−0.659742	−	0.751492i	$-0.729335\pi$
$433$	138.967	−	240.698i	0.320940	−	0.555884i	0.980682	+	0.195608i	$0.0626679\pi$
$434$	4.37485	+	134.966i	0.0100803	+	0.310981i
$435$	−897.985	+	518.452i	−2.06433	+	1.19184i
$436$	10.1914	+	15.2738i	0.0233748	+	0.0350316i
$437$	−473.082	+	289.757i	−1.08257	+	0.663059i
$438$	85.2785	−	159.421i	0.194700	−	0.363976i
$439$	−675.968	+	390.271i	−1.53979	+	0.888999i	−0.540941	+	0.841061i	$0.681932\pi$
$439$	−675.968	+	390.271i	−1.53979	+	0.888999i	−0.998850	+	0.0479384i	$0.984735\pi$
$440$	−492.123	−	688.158i	−1.11846	−	1.56400i
$441$	80.9058	−	140.133i	0.183460	−	0.317762i
$442$	−5.48517	−	169.219i	−0.0124099	−	0.382849i
$443$	563.843	+	325.535i	1.27278	+	0.734842i	0.975511	−	0.219950i	$-0.0705894\pi$
$443$	563.843	+	325.535i	1.27278	+	0.734842i	0.297273	+	0.954792i	$0.403923\pi$
$444$	231.474	−	154.451i	0.521338	−	0.347862i
$445$	−437.940			−0.984135
$446$	97.1816	+	156.393i	0.217896	+	0.350657i
$447$	−205.857	−	118.851i	−0.460529	−	0.265887i
$448$	34.8563	+	177.020i	0.0778043	+	0.395133i
$449$	170.370			0.379444			0.189722	−	0.981838i	$-0.439241\pi$
$449$	170.370			0.379444			0.189722	+	0.981838i	$0.439241\pi$
$450$	382.061	−	237.411i	0.849025	−	0.527579i
$451$	−58.0637	+	33.5231i	−0.128744	+	0.0743306i
$452$	−697.597	+	45.2722i	−1.54336	+	0.100160i
$453$	22.7213	+	39.3544i	0.0501574	+	0.0868751i
$454$	73.4318	−	2.38026i	0.161744	−	0.00524287i
$455$			112.634i			0.247547i
$456$	542.668	−	67.1759i	1.19006	−	0.147316i
$457$	131.115			0.286903			0.143451	−	0.989657i	$-0.454180\pi$
$457$	131.115			0.286903			0.143451	+	0.989657i	$0.454180\pi$
$458$	−2.93930	−	90.6784i	−0.00641769	−	0.197988i
$459$	−302.476	+	174.635i	−0.658990	+	0.380468i
$460$	−68.5172	−	1055.78i	−0.148950	−	2.29517i
$461$	41.3870	+	71.6845i	0.0897767	+	0.155498i	0.907417	−	0.420232i	$-0.138051\pi$
$461$	41.3870	+	71.6845i	0.0897767	+	0.155498i	−0.817640	+	0.575730i	$0.804718\pi$
$462$	124.971	+	201.114i	0.270501	+	0.435312i
$463$		−	211.533i		−	0.456874i	−0.973559	−	0.228437i	$-0.926639\pi$
$463$		−	211.533i		−	0.456874i	0.973559	−	0.228437i	$-0.0733615\pi$
$464$	195.426	−	470.089i	0.421178	−	1.01312i
$465$	−390.257	+	675.946i	−0.839263	+	1.45365i
$466$	−329.167	+	204.542i	−0.706367	+	0.438932i
$467$			522.505i			1.11885i	0.828879	+	0.559427i	$0.188979\pi$
$467$			522.505i			1.11885i	−0.828879	+	0.559427i	$0.811021\pi$
$468$	−38.5962	−	57.8438i	−0.0824705	−	0.123598i
$469$	178.898	−	309.860i	0.381445	−	0.660682i
$470$	761.620	−	24.6876i	1.62047	−	0.0525268i
$471$	−140.302	−	81.0033i	−0.297881	−	0.171982i
$472$	−49.0846	−	68.6373i	−0.103993	−	0.145418i
$473$	83.9092	+	145.335i	0.177398	+	0.307262i
$474$	−516.289	−	276.176i	−1.08922	−	0.582649i
$475$	−566.262	−	924.528i	−1.19213	−	1.94638i
$476$	180.029	−	120.124i	0.378213	−	0.252362i
$477$	−64.2078	−	111.211i	−0.134607	−	0.233147i
$478$	344.571	−	11.1691i	0.720860	−	0.0233664i
$479$	−428.067	−	247.144i	−0.893668	−	0.515959i	−0.0185273	−	0.999828i	$-0.505898\pi$
$479$	−428.067	−	247.144i	−0.893668	−	0.515959i	−0.875140	+	0.483869i	$0.839231\pi$
$480$	−368.905	+	975.394i	−0.768551	+	2.03207i
$481$	−42.6467	+	73.8663i	−0.0886626	+	0.153568i
$482$	−481.362	−	257.493i	−0.998677	−	0.534217i
$483$			296.108i			0.613061i
$484$	61.0036	−	3.95897i	0.126041	−	0.00817970i
$485$	242.379	−	419.813i	0.499751	−	0.865594i
$486$	−188.050	+	351.545i	−0.386934	+	0.723344i
$487$		−	872.042i		−	1.79064i	−0.445422	−	0.895321i	$-0.646946\pi$
$487$		−	872.042i		−	1.79064i	0.445422	−	0.895321i	$-0.353054\pi$
$488$	−779.693	−	354.181i	−1.59773	−	0.725782i
$489$	−145.273	−	251.619i	−0.297081	−	0.514559i
$490$	631.745	−	392.562i	1.28927	−	0.801148i
$491$	31.5500	−	18.2154i	0.0642565	−	0.0370985i	−0.467528	−	0.883979i	$-0.654855\pi$
$491$	31.5500	−	18.2154i	0.0642565	−	0.0370985i	0.531784	+	0.846880i	$0.321522\pi$
$492$	74.0967	+	36.5997i	0.150603	+	0.0743897i
$493$	−610.697			−1.23874
$494$	−140.014	+	92.1244i	−0.283429	+	0.186487i
$495$			416.826i			0.842072i
$496$	−49.5304	−	379.998i	−0.0998596	−	0.766125i
$497$	−6.33734	−	10.9766i	−0.0127512	−	0.0220857i
$498$	848.764	−	527.417i	1.70435	−	1.05907i
$499$	61.2620	−	35.3696i	0.122769	−	0.0708810i	−0.437358	−	0.899288i	$-0.644086\pi$
$499$	61.2620	−	35.3696i	0.122769	−	0.0708810i	0.560127	+	0.828407i	$0.310752\pi$
$500$	1159.30	−	75.2353i	2.31859	−	0.150471i
$501$	−681.789			−1.36086
$502$	−224.737	+	420.128i	−0.447683	+	0.836908i
$503$	236.493	+	136.539i	0.470166	+	0.271450i	0.716309	−	0.697783i	$-0.245830\pi$
$503$	236.493	+	136.539i	0.470166	+	0.271450i	−0.246143	+	0.969233i	$0.579163\pi$
$504$	36.7639	−	80.9319i	0.0729443	−	0.160579i
$505$	−276.280			−0.547089
$506$	601.122	+	321.555i	1.18799	+	0.635484i
$507$	−465.907	−	268.992i	−0.918950	−	0.530556i
$508$	603.668	+	298.179i	1.18832	+	0.586966i
$509$	240.778	−	417.040i	0.473041	−	0.819331i	−0.526483	−	0.850186i	$-0.676490\pi$
$509$	240.778	−	417.040i	0.473041	−	0.819331i	0.999524	+	0.0308545i	$0.00982285\pi$
$510$	1250.29	−	40.5278i	2.45156	−	0.0794662i
$511$	−61.3481	+	35.4193i	−0.120055	+	0.0693137i
$512$	−147.207	−	490.382i	−0.287513	−	0.957777i
$513$	303.816	+	165.048i	0.592233	+	0.321731i
$514$	247.571	+	132.432i	0.481655	+	0.257649i
$515$	440.100	−	254.092i	0.854563	−	0.493382i
$516$	91.6101	−	185.466i	0.177539	−	0.359430i
$517$	−245.504	+	425.225i	−0.474863	+	0.822486i
$518$	−108.973	+	3.53233i	−0.210373	+	0.00681916i
$519$	413.823	+	238.921i	0.797347	+	0.460348i
$520$	−31.0230	−	318.128i	−0.0596595	−	0.611785i
$521$	136.712			0.262403			0.131202	−	0.991356i	$-0.458116\pi$
$521$	136.712			0.262403			0.131202	+	0.991356i	$0.458116\pi$
$522$	−213.044	+	132.384i	−0.408131	+	0.253610i
$523$	−22.0583	−	12.7354i	−0.0421764	−	0.0243506i	0.478764	−	0.877944i	$-0.341085\pi$
$523$	−22.0583	−	12.7354i	−0.0421764	−	0.0243506i	−0.520940	+	0.853593i	$0.674418\pi$
$524$	−409.211	+	273.046i	−0.780938	+	0.521080i
$525$	−578.675			−1.10224
$526$	171.177	+	275.473i	0.325432	+	0.523713i
$527$	−398.106	+	229.847i	−0.755420	+	0.436142i
$528$	−408.368	−	533.616i	−0.773424	−	1.01064i
$529$	161.768	+	280.191i	0.305800	+	0.529661i
$530$	−19.1233	−	589.961i	−0.0360818	−	1.11313i
$531$			41.5744i			0.0782946i
$532$	−194.489	−	89.8662i	−0.365581	−	0.168921i
$533$	−25.3310			−0.0475253
$534$	−347.649	+	11.2689i	−0.651028	+	0.0211028i
$535$	69.6321	−	40.2021i	0.130153	−	0.0751441i
$536$	−419.942	+	924.457i	−0.783474	+	1.72473i
$537$	−128.083	−	221.846i	−0.238515	−	0.413121i
$538$	398.193	−	247.435i	0.740135	−	0.459915i
$539$			479.254i			0.889154i
$540$	−548.496	+	365.983i	−1.01573	+	0.677747i
$541$	311.445	−	539.439i	0.575685	−	0.997115i	−0.420282	−	0.907393i	$-0.638069\pi$
$541$	311.445	−	539.439i	0.575685	−	0.997115i	0.995967	−	0.0897216i	$-0.0285977\pi$
$542$	−131.350	−	211.379i	−0.242343	−	0.389999i
$543$		−	534.949i		−	0.985172i
$544$	−475.397	+	388.870i	−0.873892	+	0.714835i
$545$	20.7918	−	36.0125i	0.0381501	−	0.0660779i
$546$	2.89825	+	89.4119i	0.00530815	+	0.163758i
$547$	−765.593	−	442.015i	−1.39962	−	0.808072i	−0.405269	−	0.914197i	$-0.632822\pi$
$547$	−765.593	−	442.015i	−1.39962	−	0.808072i	−0.994353	+	0.106125i	$0.966155\pi$
$548$	−144.735	+	293.018i	−0.264115	+	0.534704i
$549$	210.962	+	365.398i	0.384267	+	0.665569i
$550$	−628.404	+	1174.75i	−1.14255	+	2.13591i
$551$	315.758	+	515.534i	0.573063	+	0.935633i
$552$	−81.5577	−	836.342i	−0.147749	−	1.51511i
$553$	114.706	+	198.677i	0.207425	+	0.359271i
$554$	−15.6051	−	481.421i	−0.0281680	−	0.868991i
$555$	−545.769	−	315.100i	−0.983368	−	0.567748i
$556$	68.7865	+	33.9768i	0.123717	+	0.0611093i
$557$	309.026	−	535.249i	0.554805	−	0.960950i	−0.443114	−	0.896465i	$-0.646126\pi$
$557$	309.026	−	535.249i	0.554805	−	0.960950i	0.997919	−	0.0644847i	$-0.0205404\pi$
$558$	−89.0559	+	166.483i	−0.159598	+	0.298357i
$559$			63.4041i			0.113424i
$560$	324.478	−	248.318i	0.579425	−	0.443425i
$561$	−403.025	+	698.061i	−0.718405	+	1.24431i
$562$	−549.449	−	293.914i	−0.977667	−	0.522979i
$563$		−	169.277i		−	0.300670i	−0.988635	−	0.150335i	$-0.951965\pi$
$563$		−	169.277i		−	0.300670i	0.988635	−	0.150335i	$-0.0480352\pi$
$564$	603.960	−	39.1954i	1.07085	−	0.0694954i
$565$	791.582	+	1371.06i	1.40103	+	2.42666i
$566$	−417.974	−	672.639i	−0.738470	−	1.18841i
$567$	246.426	−	142.274i	0.434615	−	0.250925i
$568$	20.9228	+	29.2573i	0.0368359	+	0.0515093i
$569$	−403.875			−0.709798			−0.354899	−	0.934905i	$-0.615485\pi$
$569$	−403.875			−0.709798			−0.354899	+	0.934905i	$0.615485\pi$
$570$	−680.671	−	1034.51i	−1.19416	−	1.81493i
$571$		−	175.870i		−	0.308003i	−0.988071	−	0.154001i	$-0.950784\pi$
$571$		−	175.870i		−	0.308003i	0.988071	−	0.154001i	$-0.0492160\pi$
$572$	184.660	+	91.2119i	0.322832	+	0.159461i
$573$	285.559	+	494.602i	0.498357	+	0.863180i
$574$	−17.0903	−	27.5032i	−0.0297740	−	0.0479149i
$575$	−1442.87	+	833.042i	−2.50934	+	1.44877i
$576$	−81.5466	+	238.714i	−0.141574	+	0.414434i
$577$	−386.929			−0.670587			−0.335293	−	0.942114i	$-0.608835\pi$
$577$	−386.929			−0.670587			−0.335293	+	0.942114i	$0.608835\pi$
$578$	139.992	+	74.8853i	0.242201	+	0.129559i
$579$	959.929	+	554.216i	1.65791	+	0.957194i
$580$	−1150.52	+	74.6655i	−1.98365	+	0.128734i
$581$	−391.532			−0.673894
$582$	181.605	−	339.496i	0.312036	−	0.583327i
$583$	329.385	+	190.171i	0.564983	+	0.326193i
$584$	163.519	−	116.937i	0.279998	−	0.200235i
$585$	−78.7413	+	136.384i	−0.134601	+	0.233135i
$586$	29.5023	+	910.154i	0.0503452	+	1.55316i
$587$	643.631	−	371.601i	1.09648	−	0.633050i	0.161182	−	0.986925i	$-0.448469\pi$
$587$	643.631	−	371.601i	1.09648	−	0.633050i	0.935293	+	0.353874i	$0.115136\pi$
$588$	491.395	−	327.883i	0.835706	−	0.557623i
$589$	399.869	+	217.229i	0.678895	+	0.368810i
$590$	−90.1380	+	168.506i	−0.152776	+	0.285603i
$591$	−137.992	+	79.6700i	−0.233490	+	0.134805i
$592$	306.816	−	39.9916i	0.518271	−	0.0675533i
$593$	485.862	−	841.537i	0.819328	−	1.41912i	−0.0868496	−	0.996221i	$-0.527680\pi$
$593$	485.862	−	841.537i	0.819328	−	1.41912i	0.906178	−	0.422897i	$-0.138987\pi$
$594$	−13.7650	−	424.653i	−0.0231733	−	0.714905i
$595$	−424.473	−	245.069i	−0.713399	−	0.411881i
$596$	−146.697	−	219.854i	−0.246136	−	0.368882i
$597$	824.344			1.38081
$598$	135.941	+	218.768i	0.227326	+	0.365832i
$599$	−256.016	−	147.811i	−0.427405	−	0.246762i	0.270836	−	0.962626i	$-0.412700\pi$
$599$	−256.016	−	147.811i	−0.427405	−	0.246762i	−0.698241	+	0.715863i	$0.746033\pi$
$600$	1634.44	−	159.385i	2.72406	−	0.265642i
$601$	790.283			1.31495			0.657474	−	0.753477i	$-0.271625\pi$
$601$	790.283			1.31495			0.657474	+	0.753477i	$0.271625\pi$
$602$	−68.8411	+	42.7775i	−0.114354	+	0.0710589i
$603$	433.240	−	250.132i	0.718475	−	0.414812i
$604$	3.27224	+	50.4217i	0.00541761	+	0.0834796i
$605$	−69.2225	−	119.897i	−0.114417	−	0.198177i
$606$	−219.319	+	7.10913i	−0.361912	+	0.0117312i
$607$			370.431i			0.610265i	0.952310	+	0.305133i	$0.0987008\pi$
$607$			370.431i			0.610265i	−0.952310	+	0.305133i	$0.901299\pi$
$608$	574.075	+	200.254i	0.944203	+	0.329365i
$609$	322.679			0.529851
$610$	62.8321	+	1938.39i	0.103003	+	3.17769i
$611$	−160.656	+	92.7549i	−0.262940	+	0.151808i
$612$	301.968	−	19.5969i	0.493412	−	0.0320211i
$613$	−180.132	−	311.998i	−0.293854	−	0.508969i	0.680864	−	0.732410i	$-0.261604\pi$
$613$	−180.132	−	311.998i	−0.293854	−	0.508969i	−0.974718	+	0.223441i	$0.928271\pi$
$614$	373.585	+	601.204i	0.608444	+	0.979160i
$615$		−	187.161i		−	0.304326i
$616$	25.5528	+	262.034i	0.0414818	+	0.425379i
$617$	−11.3914	+	19.7305i	−0.0184626	+	0.0319782i	−0.875109	−	0.483926i	$-0.839211\pi$
$617$	−11.3914	+	19.7305i	−0.0184626	+	0.0319782i	0.856646	+	0.515904i	$0.172544\pi$
$618$	342.825	−	213.029i	0.554733	−	0.344708i
$619$			362.401i			0.585462i	0.956195	+	0.292731i	$0.0945641\pi$
$619$			362.401i			0.585462i	−0.956195	+	0.292731i	$0.905436\pi$
$620$	−721.907	+	481.691i	−1.16437	+	0.776922i
$621$	265.667	−	460.150i	0.427806	−	0.740982i
$622$	−1016.83	+	32.9602i	−1.63478	+	0.0529907i
$623$	118.026	+	68.1424i	0.189448	+	0.109378i
$624$	−32.8128	−	251.741i	−0.0525846	−	0.403431i
$625$	−602.221	−	1043.08i	−0.963554	−	1.66892i
$626$	802.531	+	429.293i	1.28200	+	0.685772i
$627$	797.666	−	20.7056i	1.27219	−	0.0330233i
$628$	−99.9817	−	149.842i	−0.159207	−	0.238602i
$629$	−185.582	−	321.437i	−0.295043	−	0.511029i
$630$	−201.204	+	6.52195i	−0.319372	+	0.0103523i
$631$	667.833	+	385.574i	1.05837	+	0.611052i	0.924982	−	0.380011i	$-0.124080\pi$
$631$	667.833	+	385.574i	1.05837	+	0.611052i	0.133391	+	0.991063i	$0.457413\pi$
$632$	−378.703	−	529.558i	−0.599213	−	0.837908i
$633$	256.743	−	444.691i	0.405597	−	0.702514i
$634$	1055.39	+	564.554i	1.66465	+	0.890464i
$635$		−	1524.80i		−	2.40126i
$636$	−30.3613	−	467.835i	−0.0477378	−	0.735590i
$637$	−90.5345	+	156.810i	−0.142126	+	0.246170i
$638$	350.409	−	655.063i	0.549231	−	1.02674i
$639$		−	17.7215i		−	0.0277332i
$640$	−848.076	+	790.732i	−1.32512	+	1.23552i
$641$	22.1679	+	38.3960i	0.0345834	+	0.0599001i	0.882799	−	0.469751i	$-0.155656\pi$
$641$	22.1679	+	38.3960i	0.0345834	+	0.0599001i	−0.848216	+	0.529651i	$0.822323\pi$
$642$	54.2414	−	33.7053i	0.0844881	−	0.0525004i
$643$	−1034.78	+	597.433i	−1.60931	+	0.929133i	−0.619781	+	0.784775i	$0.712778\pi$
$643$	−1034.78	+	597.433i	−1.60931	+	0.929133i	−0.989525	+	0.144358i	$0.953888\pi$
$644$	−145.811	+	295.196i	−0.226414	+	0.458379i
$645$	−468.468			−0.726307
$646$	−42.5368	−	728.103i	−0.0658465	−	1.12709i
$647$			143.888i			0.222393i	0.993798	+	0.111196i	$0.0354683\pi$
$647$			143.888i			0.222393i	−0.993798	+	0.111196i	$0.964532\pi$
$648$	−656.831	+	469.720i	−1.01363	+	0.724876i
$649$	−61.5676	−	106.638i	−0.0948653	−	0.164312i
$650$	−427.530	+	265.665i	−0.657739	+	0.408715i
$651$	210.351	−	121.446i	0.323120	−	0.186553i
$652$	−20.9216	−	322.380i	−0.0320884	−	0.494448i
$653$	−604.063			−0.925058			−0.462529	−	0.886604i	$-0.653058\pi$
$653$	−604.063			−0.925058			−0.462529	+	0.886604i	$0.653058\pi$
$654$	15.5784	−	29.1227i	0.0238203	−	0.0445301i
$655$	964.837	+	557.049i	1.47303	+	0.850457i
$656$	55.8459	+	72.9740i	0.0851309	+	0.111241i
$657$	−99.0453			−0.150754
$658$	−209.100	−	111.853i	−0.317781	−	0.169989i
$659$	640.313	+	369.685i	0.971643	+	0.560978i	0.899737	−	0.436433i	$-0.143758\pi$
$659$	640.313	+	369.685i	0.971643	+	0.560978i	0.0719062	+	0.997411i	$0.477092\pi$
$660$	−673.929	+	1364.38i	−1.02110	+	2.06724i
$661$	−364.477	+	631.293i	−0.551403	+	0.955058i	0.446771	+	0.894649i	$0.352574\pi$
$661$	−364.477	+	631.293i	−0.551403	+	0.955058i	−0.998174	+	0.0604096i	$0.980759\pi$
$662$	−564.163	+	18.2871i	−0.852210	+	0.0276240i
$663$	−263.737	+	152.269i	−0.397794	+	0.229666i
$664$	1105.86	−	107.840i	1.66545	−	0.162410i
$665$	12.5905	+	485.040i	0.0189331	+	0.729383i
$666$	−134.421	−	71.9051i	−0.201833	−	0.107966i
$667$	804.570	−	464.519i	1.20625	−	0.696430i
$668$	−679.689	−	335.729i	−1.01750	−	0.502589i
$669$	165.597	−	286.822i	0.247529	−	0.428733i
$670$	2298.29	−	74.4980i	3.43028	−	0.111191i
$671$	−1082.24	−	624.829i	−1.61287	−	0.931190i
$672$	251.190	−	205.471i	0.373794	−	0.305760i
$673$	−630.954			−0.937525			−0.468762	−	0.883324i	$-0.655300\pi$
$673$	−630.954			−0.937525			−0.468762	+	0.883324i	$0.655300\pi$
$674$	−133.559	+	82.9930i	−0.198159	+	0.123135i
$675$	899.255	+	519.185i	1.33223	+	0.769163i
$676$	−332.014	−	497.587i	−0.491145	−	0.736076i
$677$	−1243.47			−1.83673			−0.918365	−	0.395734i	$-0.870490\pi$
$677$	−1243.47			−1.83673			−0.918365	+	0.395734i	$0.870490\pi$
$678$	663.659	+	1068.02i	0.978848	+	1.57525i
$679$	−130.644	+	75.4273i	−0.192406	+	0.111086i
$680$	1266.40	+	575.272i	1.86235	+	0.845988i
$681$	−66.0762	−	114.447i	−0.0970282	−	0.168058i
$682$	−18.1169	−	558.911i	−0.0265643	−	0.819517i
$683$		−	903.750i		−	1.32321i	−0.749854	−	0.661604i	$-0.769876\pi$
$683$		−	903.750i		−	1.32321i	0.749854	−	0.661604i	$-0.230124\pi$
$684$	−172.674	−	244.781i	−0.252448	−	0.357867i
$685$	740.133			1.08049
$686$	−507.460	+	16.4491i	−0.739737	+	0.0239783i
$687$	−141.327	+	81.5952i	−0.205716	+	0.118770i
$688$	182.656	−	139.784i	0.265488	−	0.203174i
$689$	71.8491	+	124.446i	0.104280	+	0.180619i
$690$	−1616.39	+	1004.41i	−2.34259	+	1.45567i
$691$		−	132.044i		−	0.191091i	−0.995425	−	0.0955454i	$-0.969540\pi$
$691$		−	132.044i		−	0.191091i	0.995425	−	0.0955454i	$-0.0304595\pi$
$692$	294.898	+	441.961i	0.426153	+	0.638672i
$693$	64.8571	−	112.336i	0.0935888	−	0.162101i
$694$	−189.665	−	305.225i	−0.273293	−	0.439806i
$695$		−	173.748i		−	0.249997i
$696$	−911.390	+	88.8761i	−1.30947	+	0.127696i
$697$	55.1153	−	95.4625i	0.0790750	−	0.136962i
$698$	6.04697	+	186.551i	0.00866329	+	0.267265i
$699$	603.687	+	348.539i	0.863643	+	0.498625i
$700$	−576.892	−	284.953i	−0.824132	−	0.407076i
$701$	516.865	+	895.236i	0.737325	+	1.27708i	0.953696	+	0.300773i	$0.0972445\pi$
$701$	516.865	+	895.236i	0.737325	+	1.27708i	−0.216371	+	0.976311i	$0.569422\pi$
$702$	75.7162	−	141.545i	0.107858	−	0.201632i
$703$	−175.394	+	322.861i	−0.249494	+	0.459261i
$704$	−144.345	−	733.062i	−0.205035	−	1.04128i
$705$	−685.329	−	1187.03i	−0.972098	−	1.68372i
$706$	−30.7492	−	948.622i	−0.0435541	−	1.34366i
$707$	74.4583	+	42.9885i	0.105316	+	0.0608041i
$708$	−67.2181	+	136.084i	−0.0949408	+	0.192209i
$709$	553.592	−	958.849i	0.780806	−	1.35240i	−0.150667	−	0.988585i	$-0.548142\pi$
$709$	553.592	−	958.849i	0.780806	−	1.35240i	0.931473	−	0.363811i	$-0.118525\pi$
$710$	38.4222	−	71.8273i	0.0541157	−	0.101165i
$711$			320.760i			0.451139i
$712$	−352.127	−	159.956i	−0.494560	−	0.224658i
$713$	349.660	−	605.629i	0.490407	−	0.849410i
$714$	−343.264	−	183.620i	−0.480762	−	0.257171i
$715$		−	466.432i		−	0.652353i
$716$	−18.4460	−	284.233i	−0.0257626	−	0.396974i
$717$	−310.056	−	537.032i	−0.432435	−	0.748999i
$718$	−499.199	−	803.353i	−0.695263	−	1.11888i
$719$	758.635	−	437.998i	1.05513	−	0.609177i	0.131045	−	0.991376i	$-0.458167\pi$
$719$	758.635	−	437.998i	1.05513	−	0.609177i	0.924080	+	0.382200i	$0.124833\pi$
$720$	566.494	−	73.8389i	0.786797	−	0.102554i
$721$	−158.144			−0.219340
$722$	−592.651	+	412.370i	−0.820846	+	0.571150i
$723$			981.928i			1.35813i
$724$	263.421	−	533.301i	0.363842	−	0.736603i
$725$	907.794	+	1572.34i	1.25213	+	2.16875i
$726$	−58.0358	−	93.3962i	−0.0799391	−	0.128645i
$727$	−632.345	+	365.085i	−0.869801	+	0.502180i	−0.867282	−	0.497817i	$-0.834135\pi$
$727$	−632.345	+	365.085i	−0.869801	+	0.502180i	−0.00251881	+	0.999997i	$0.500802\pi$
$728$	−41.1392	+	90.5636i	−0.0565099	+	0.124401i
$729$	−191.328			−0.262453
$730$	−401.442	−	214.741i	−0.549920	−	0.294166i
$731$	−238.945	−	137.955i	−0.326874	−	0.188721i
$732$	99.7556	+	1537.13i	0.136278	+	2.09990i
$733$	690.943			0.942624			0.471312	−	0.881967i	$-0.343781\pi$
$733$	690.943			0.942624			0.471312	+	0.881967i	$0.343781\pi$
$734$	−52.9233	+	98.9360i	−0.0721026	+	0.134790i
$735$	−1158.61	−	668.924i	−1.57634	−	0.910100i
$736$	330.529	−	873.927i	0.449088	−	1.18740i
$737$	−740.840	+	1283.17i	−1.00521	+	1.74107i
$738$	−1.46677	−	45.2502i	−0.00198749	−	0.0613146i
$739$	514.152	−	296.846i	0.695741	−	0.401686i	−0.110018	−	0.993930i	$-0.535091\pi$
$739$	514.152	−	296.846i	0.695741	−	0.401686i	0.805759	+	0.592243i	$0.201758\pi$
$740$	−388.925	−	582.879i	−0.525574	−	0.787674i
$741$	264.905	+	143.910i	0.357497	+	0.194210i
$742$	−86.6427	+	161.972i	−0.116769	+	0.218291i
$743$	48.6881	−	28.1101i	0.0655291	−	0.0378332i	−0.466877	−	0.884322i	$-0.654621\pi$
$743$	48.6881	−	28.1101i	0.0655291	−	0.0378332i	0.532407	+	0.846489i	$0.321288\pi$
$744$	−560.675	+	400.956i	−0.753595	+	0.538919i
$745$	−299.282	+	518.371i	−0.401720	+	0.695800i
$746$	31.8562	+	982.775i	0.0427027	+	1.31739i
$747$	−474.091	−	273.717i	−0.634660	−	0.366421i
$748$	−745.526	+	497.451i	−0.996692	+	0.665041i
$749$	−25.0214			−0.0334064
$750$	−1102.90	−	1774.88i	−1.47053	−	2.36650i
$751$	119.216	+	68.8295i	0.158743	+	0.0916504i	0.577267	−	0.816555i	$-0.304119\pi$
$751$	119.216	+	68.8295i	0.158743	+	0.0916504i	−0.418524	+	0.908206i	$0.637452\pi$
$752$	621.400	+	258.330i	0.826330	+	0.343523i
$753$	857.016			1.13814
$754$	238.399	−	148.139i	0.316179	−	0.196471i
$755$	99.0990	−	57.2149i	0.131257	−	0.0757813i
$756$	204.767	−	13.2889i	0.270856	−	0.0175779i
$757$	−452.623	−	783.966i	−0.597916	−	1.03562i	−0.993128	−	0.117032i	$-0.962662\pi$
$757$	−452.623	−	783.966i	−0.597916	−	1.03562i	0.395212	−	0.918590i	$-0.370671\pi$
$758$	802.000	−	25.9965i	1.05805	−	0.0342962i
$759$		−	1226.22i		−	1.61558i
$760$	−169.157	−	1366.50i	−0.222575	−	1.79803i
$761$	−1082.43			−1.42238			−0.711190	−	0.703000i	$-0.751844\pi$
$761$	−1082.43			−1.42238			−0.711190	+	0.703000i	$0.751844\pi$
$762$	−39.2356	−	1210.43i	−0.0514903	−	1.58849i
$763$	−11.2069	+	6.47031i	−0.0146879	+	0.00848009i
$764$	41.1251	+	633.694i	0.0538286	+	0.829443i
$765$	−342.651	−	593.490i	−0.447910	−	0.775803i
$766$	−91.3470	−	147.003i	−0.119252	−	0.191910i
$767$		−	46.5222i		−	0.0606548i
$768$	−652.879	+	649.527i	−0.850103	+	0.845738i
$769$	−508.059	+	879.984i	−0.660675	+	1.14432i	0.319764	+	0.947497i	$0.396396\pi$
$769$	−508.059	+	879.984i	−0.660675	+	1.14432i	−0.980439	+	0.196825i	$0.936937\pi$
$770$	506.429	−	314.692i	0.657701	−	0.408691i
$771$		−	505.018i		−	0.655017i
$772$	684.063	+	1025.20i	0.886093	+	1.32798i
$773$	497.920	−	862.423i	0.644140	−	1.11568i	−0.340359	−	0.940295i	$-0.610549\pi$
$773$	497.920	−	862.423i	0.644140	−	1.11568i	0.984499	−	0.175388i	$-0.0561179\pi$
$774$	−113.262	+	3.67135i	−0.146334	+	0.00474335i
$775$	1183.56	+	683.329i	1.52718	+	0.881715i
$776$	348.221	−	249.024i	0.448739	−	0.320907i
$777$	98.0576	+	169.841i	0.126200	+	0.218585i
$778$	−1068.85	−	571.756i	−1.37385	−	0.734905i
$779$	−109.084	+	2.83157i	−0.140031	+	0.00363488i
$780$	−478.248	+	319.110i	−0.613139	+	0.409116i
$781$	26.2438	+	45.4556i	0.0336028	+	0.0582017i
$782$	−1120.23	+	36.3118i	−1.43252	+	0.0464345i
$783$	−501.441	−	289.507i	−0.640409	−	0.369741i
$784$	651.338	−	84.8978i	0.830789	−	0.108288i
$785$	−203.976	+	353.297i	−0.259842	+	0.450059i
$786$	780.248	+	417.374i	0.992682	+	0.531010i
$787$			857.085i			1.08905i	0.838743	+	0.544527i	$0.183291\pi$
$787$			857.085i			1.08905i	−0.838743	+	0.544527i	$0.816709\pi$
$788$	−176.799	+	11.4738i	−0.224364	+	0.0145606i
$789$	291.685	−	505.213i	0.369689	−	0.640321i
$790$	−695.443	+	1300.08i	−0.880307	+	1.64566i
$791$		−	492.673i		−	0.622848i
$792$	−152.244	+	335.150i	−0.192228	+	0.423169i
$793$	−236.069	−	408.884i	−0.297691	−	0.515616i
$794$	−291.023	+	180.840i	−0.366528	+	0.227758i
$795$	−919.485	+	530.865i	−1.15659	+	0.667755i
$796$	821.804	+	405.927i	1.03242	+	0.509958i
$797$	501.545			0.629292			0.314646	−	0.949209i	$-0.398114\pi$
$797$	501.545			0.629292			0.314646	+	0.949209i	$0.398114\pi$
$798$	22.4756	+	384.714i	0.0281649	+	0.482098i
$799$		−	807.266i		−	1.01035i
$800$	1707.89	+	645.941i	2.13486	+	0.807426i
$801$	95.2754	+	165.022i	0.118946	+	0.206020i
$802$	453.491	−	281.797i	0.565451	−	0.351368i
$803$	254.051	−	146.676i	0.316377	−	0.182660i
$804$	1822.53	−	118.277i	2.26682	−	0.147111i
$805$	745.636			0.926256
$806$	99.6544	−	186.296i	0.123641	−	0.231137i
$807$	−730.279	−	421.627i	−0.904931	−	0.522462i
$808$	−222.144	−	100.911i	−0.274930	−	0.124889i
$809$	−232.866			−0.287844			−0.143922	−	0.989589i	$-0.545971\pi$
$809$	−232.866			−0.287844			−0.143922	+	0.989589i	$0.545971\pi$
$810$	1612.53	+	862.585i	1.99078	+	1.06492i
$811$	1251.49	+	722.548i	1.54314	+	0.890934i	0.998638	+	0.0521771i	$0.0166160\pi$
$811$	1251.49	+	722.548i	1.54314	+	0.890934i	0.544506	+	0.838757i	$0.316717\pi$
$812$	321.685	+	158.895i	0.396164	+	0.195684i
$813$	−223.819	+	387.666i	−0.275300	+	0.476834i
$814$	451.273	−	14.6278i	0.554390	−	0.0179703i
$815$	−633.607	+	365.813i	−0.777432	+	0.448851i
$816$	1020.11	+	424.080i	1.25013	+	0.519706i
$817$	7.08749	+	273.040i	0.00867502	+	0.334198i
$818$	−219.311	−	117.315i	−0.268106	−	0.143417i
$819$	42.4420	−	24.5039i	0.0518218	−	0.0299193i
$820$	92.1624	−	186.584i	0.112393	−	0.227542i
$821$	−440.690	+	763.297i	−0.536772	+	0.929716i	0.462304	+	0.886722i	$0.347023\pi$
$821$	−440.690	+	763.297i	−0.536772	+	0.929716i	−0.999075	+	0.0429941i	$0.986310\pi$
$822$	587.538	−	19.0448i	0.714766	−	0.0231688i
$823$	−712.755	−	411.509i	−0.866045	−	0.500011i	−1.29516e−5	−	1.00000i	$-0.500004\pi$
$823$	−712.755	−	411.509i	−0.866045	−	0.500011i	−0.866032	+	0.499989i	$0.833337\pi$
$824$	446.670	−	43.5579i	0.542075	−	0.0528616i
$825$	2396.37			2.90469
$826$	50.5116	−	31.3876i	0.0611520	−	0.0379995i
$827$	109.874	+	63.4355i	0.132858	+	0.0767056i	0.564956	−	0.825121i	$-0.308893\pi$
$827$	109.874	+	63.4355i	0.132858	+	0.0767056i	−0.432098	+	0.901827i	$0.642227\pi$
$828$	−382.926	+	255.506i	−0.462470	+	0.308583i
$829$	748.707			0.903144			0.451572	−	0.892235i	$-0.350863\pi$
$829$	748.707			0.903144			0.451572	+	0.892235i	$0.350863\pi$
$830$	−1328.10	−	2137.29i	−1.60012	−	2.57504i
$831$	−750.320	+	433.197i	−0.902912	+	0.521296i
$832$	91.2514	−	267.123i	0.109677	−	0.321061i
$833$	−393.971	−	682.377i	−0.472954	−	0.819180i
$834$	−4.47080	−	137.926i	−0.00536067	−	0.165378i
$835$			1716.82i			2.05608i
$836$	805.405	+	372.148i	0.963403	+	0.445153i
$837$	−435.845			−0.520722
$838$	497.567	−	16.1284i	0.593756	−	0.0192464i
$839$	−829.460	+	478.889i	−0.988629	+	0.570785i	−0.904864	−	0.425700i	$-0.860028\pi$
$839$	−829.460	+	478.889i	−0.988629	+	0.570785i	−0.0837647	+	0.996486i	$0.526694\pi$
$840$	−669.139	−	303.962i	−0.796594	−	0.361859i
$841$	−85.7019	−	148.440i	−0.101905	−	0.176504i
$842$	−553.591	+	343.998i	−0.657472	+	0.408549i
$843$			1120.82i			1.32956i
$844$	474.928	−	316.895i	0.562711	−	0.375468i
$845$	−677.353	+	1173.21i	−0.801601	+	1.38841i
$846$	−174.996	−	281.618i	−0.206851	−	0.332882i
$847$			43.0834i			0.0508659i
$848$	200.105	−	481.345i	0.235973	−	0.567623i
$849$	−712.225	+	1233.61i	−0.838899	+	1.45301i
$850$	−70.9629	−	2189.23i	−0.0834858	−	2.57556i
$851$	488.994	+	282.321i	0.574611	+	0.331752i
$852$	28.6524	−	58.0071i	0.0336295	−	0.0680835i
$853$	−184.599	−	319.736i	−0.216412	−	0.374837i	0.737296	−	0.675569i	$-0.236102\pi$
$853$	−184.599	−	319.736i	−0.216412	−	0.374837i	−0.953708	+	0.300733i	$0.902769\pi$
$854$	284.675	−	532.178i	0.333343	−	0.623159i
$855$	−323.841	+	596.118i	−0.378762	+	0.697214i
$856$	70.6716	−	6.89168i	0.0825602	−	0.00805103i
$857$	226.320	+	391.998i	0.264084	+	0.457407i	0.967323	−	0.253546i	$-0.0815971\pi$
$857$	226.320	+	391.998i	0.264084	+	0.457407i	−0.703239	+	0.710953i	$0.748264\pi$
$858$	−12.0020	−	370.267i	−0.0139884	−	0.431546i
$859$	−838.651	−	484.196i	−0.976311	−	0.563674i	−0.0751568	−	0.997172i	$-0.523946\pi$
$859$	−838.651	−	484.196i	−0.976311	−	0.563674i	−0.901154	+	0.433498i	$0.857279\pi$
$860$	−467.025	−	230.685i	−0.543052	−	0.268238i
$861$	−29.1218	+	50.4404i	−0.0338232	+	0.0585835i
$862$	437.252	−	817.409i	0.507253	−	0.948270i
$863$		−	531.348i		−	0.615698i	−0.951435	−	0.307849i	$-0.900391\pi$
$863$		−	531.348i		−	0.615698i	0.951435	−	0.307849i	$-0.0996092\pi$
$864$	−574.694	+	93.9331i	−0.665155	+	0.108719i
$865$	601.631	−	1042.05i	0.695527	−	1.20469i
$866$	−490.147	−	262.192i	−0.565990	−	0.302762i
$867$		−	285.569i		−	0.329376i
$868$	269.506	−	17.4902i	0.310491	−	0.0201500i
$869$	−475.013	−	822.747i	−0.546620	−	0.946774i
$870$	1094.54	+	1761.43i	1.25810	+	2.02464i
$871$	−484.800	+	279.900i	−0.556602	+	0.321354i
$872$	29.8712	−	21.3618i	0.0342559	−	0.0244974i
$873$	−210.922			−0.241606
$874$	609.863	+	926.893i	0.697783	+	1.06052i
$875$			818.745i			0.935709i
$876$	−324.201	−	160.138i	−0.370093	−	0.182806i
$877$	430.925	+	746.383i	0.491362	+	0.851064i	0.999951	−	0.00994571i	$-0.00316587\pi$
$877$	430.925	+	746.383i	0.491362	+	0.851064i	−0.508589	+	0.861010i	$0.669833\pi$
$878$	823.931	+	1325.94i	0.938418	+	1.51018i
$879$	1418.52	−	818.985i	1.61379	−	0.931723i
$880$	−1343.71	+	1028.32i	−1.52694	+	1.16854i
$881$	944.406			1.07197			0.535985	−	0.844227i	$-0.319940\pi$
$881$	944.406			1.07197			0.535985	+	0.844227i	$0.319940\pi$
$882$	−285.361	−	152.647i	−0.323539	−	0.173069i
$883$	−1456.09	−	840.674i	−1.64903	−	0.952065i	−0.977460	−	0.211120i	$-0.932289\pi$
$883$	−1456.09	−	840.674i	−1.64903	−	0.952065i	−0.671565	−	0.740946i	$-0.734378\pi$
$884$	−337.905	+	21.9292i	−0.382246	+	0.0248068i
$885$	343.734			0.388400
$886$	614.194	−	1148.19i	0.693222	−	1.29592i
$887$	−663.364	−	382.993i	−0.747874	−	0.431785i	0.0770515	−	0.997027i	$-0.475449\pi$
$887$	−663.364	−	382.993i	−0.747874	−	0.431785i	−0.824925	+	0.565242i	$0.808783\pi$
$888$	−323.738	−	452.698i	−0.364570	−	0.509795i
$889$	−237.256	+	410.939i	−0.266879	+	0.462248i
$890$	28.3764	+	875.420i	0.0318836	+	0.983618i
$891$	−1020.49	+	589.177i	−1.14533	+	0.661254i
$892$	306.325	−	204.395i	0.343413	−	0.229142i
$893$	−681.472	+	417.393i	−0.763126	+	0.467405i
$894$	−224.239	+	419.198i	−0.250827	+	0.468902i
$895$	−558.633	+	322.527i	−0.624171	+	0.360366i
$896$	351.595	−	81.1461i	0.392405	−	0.0905648i
$897$	231.643	−	401.217i	0.258241	−	0.447287i
$898$	−11.0392	−	340.562i	−0.0122931	−	0.379244i
$899$	−659.975	−	381.037i	−0.734121	−	0.423845i
$900$	−499.328	−	748.339i	−0.554809	−	0.831487i
$901$	−625.319			−0.694028
$902$	70.7732	+	113.894i	0.0784626	+	0.126269i
$903$	126.254	+	72.8925i	0.139816	+	0.0807226i
$904$	135.698	+	1391.53i	0.150108	+	1.53930i
$905$	−1347.06			−1.48847
$906$	77.1953	−	47.9687i	0.0852045	−	0.0529456i
$907$	−285.807	+	165.011i	−0.315113	+	0.181930i	−0.649212	−	0.760608i	$-0.724901\pi$
$907$	−285.807	+	165.011i	−0.315113	+	0.181930i	0.334099	+	0.942538i	$0.391568\pi$
$908$	−9.51605	−	146.632i	−0.0104802	−	0.161489i
$909$	60.1057	+	104.106i	0.0661229	+	0.114528i
$910$	225.150	−	7.29813i	0.247417	−	0.00801992i
$911$			1064.70i			1.16871i	0.811497	+	0.584357i	$0.198653\pi$
$911$			1064.70i			1.16871i	−0.811497	+	0.584357i	$0.801347\pi$
$912$	−169.443	−	1080.41i	−0.185793	−	1.18466i
$913$	1621.39			1.77589
$914$	−8.49559	−	262.092i	−0.00929495	−	0.286752i
$915$	3021.08	−	1744.22i	3.30173	−	1.90625i
$916$	−181.071	+	11.7510i	−0.197676	+	0.0128286i
$917$	−173.351	−	300.253i	−0.189041	−	0.327429i
$918$	368.685	+	593.320i	0.401618	+	0.646318i
$919$			1052.48i			1.14525i	0.819818	+	0.572624i	$0.194074\pi$
$919$			1052.48i			1.14525i	−0.819818	+	0.572624i	$0.805926\pi$
$920$	−2106.01	+	205.372i	−2.28914	+	0.223230i
$921$	636.586	−	1102.60i	0.691190	−	1.19718i
$922$	140.612	−	87.3754i	0.152508	−	0.0947673i
$923$			19.8305i			0.0214849i
$924$	393.920	−	262.843i	0.426320	−	0.284462i
$925$	−551.730	+	955.625i	−0.596465	+	1.03311i
$926$	−422.843	+	13.7063i	−0.456634	+	0.0148016i
$927$	−191.491	−	110.557i	−0.206570	−	0.119263i
$928$	−952.348	−	360.188i	−1.02624	−	0.388134i
$929$	−795.538	−	1377.91i	−0.856338	−	1.48322i	−0.875398	−	0.483403i	$-0.839401\pi$
$929$	−795.538	−	1377.91i	−0.856338	−	1.48322i	0.0190598	−	0.999818i	$-0.493933\pi$
$930$	1376.47	+	736.307i	1.48007	+	0.791728i
$931$	−372.344	+	685.399i	−0.399939	+	0.736196i
$932$	430.198	+	644.735i	0.461586	+	0.691775i
$933$	914.978	+	1584.79i	0.980683	+	1.69859i
$934$	1044.46	−	33.8558i	1.11827	−	0.0362482i
$935$	1757.80	+	1014.87i	1.88000	+	1.08542i
$936$	−113.126	+	80.8998i	−0.120861	+	0.0864315i
$937$	22.0506	−	38.1928i	0.0235332	−	0.0407607i	−0.854019	−	0.520242i	$-0.825842\pi$
$937$	22.0506	−	38.1928i	0.0235332	−	0.0407607i	0.877552	+	0.479481i	$0.159175\pi$
$938$	−630.987	−	337.530i	−0.672694	−	0.359840i
$939$		−	1637.08i		−	1.74343i
$940$	−98.6986	−	1520.84i	−0.104998	−	1.61792i
$941$	−781.948	+	1354.37i	−0.830975	+	1.43929i	0.0662905	+	0.997800i	$0.478884\pi$
$941$	−781.948	+	1354.37i	−0.830975	+	1.43929i	−0.897266	+	0.441491i	$0.854450\pi$
$942$	−152.831	+	285.705i	−0.162241	+	0.303296i
$943$			167.691i			0.177827i
$944$	−134.022	+	102.565i	−0.141973	+	0.108649i
$945$	−232.355	−	402.451i	−0.245878	−	0.425874i
$946$	285.080	−	177.147i	0.301353	−	0.187259i
$947$	1324.53	−	764.719i	1.39866	−	0.807517i	0.404408	−	0.914579i	$-0.367478\pi$
$947$	1324.53	−	764.719i	1.39866	−	0.807517i	0.994252	+	0.107061i	$0.0341442\pi$
$948$	−518.608	+	1049.93i	−0.547055	+	1.10752i
$949$	110.833			0.116789
$950$	−1811.40	+	1191.83i	−1.90673	+	1.25456i
$951$		−	2152.88i		−	2.26381i
$952$	−251.788	−	352.086i	−0.264483	−	0.369838i
$953$	−115.313	−	199.728i	−0.121000	−	0.209578i	0.799162	−	0.601115i	$-0.205277\pi$
$953$	−115.313	−	199.728i	−0.121000	−	0.209578i	−0.920162	+	0.391537i	$0.871943\pi$
$954$	−218.145	+	135.554i	−0.228664	+	0.142090i
$955$	1245.47	−	719.070i	1.30415	−	0.752953i
$956$	−44.6530	−	688.056i	−0.0467082	−	0.719724i
$957$	−1336.26			−1.39630
$958$	−466.293	+	871.698i	−0.486736	+	0.909914i
$959$	−199.468	−	115.163i	−0.207996	−	0.120086i
$960$	1973.67	+	674.221i	2.05590	+	0.702313i
$961$	387.360			0.403080
$962$	150.418	+	80.4625i	0.156360	+	0.0836409i
$963$	−30.2974	−	17.4922i	−0.0314615	−	0.0181643i
$964$	−483.525	+	978.904i	−0.501582	+	1.01546i
$965$	1395.58	−	2417.21i	1.44620	−	2.50489i
$966$	591.906	−	19.1864i	0.612739	−	0.0198617i
$967$	−1289.91	+	744.731i	−1.33393	+	0.770146i	−0.985900	−	0.167337i	$-0.946483\pi$
$967$	−1289.91	+	744.731i	−1.33393	+	0.770146i	−0.348032	+	0.937483i	$0.613150\pi$
$968$	−11.8665	−	121.687i	−0.0122588	−	0.125709i
$969$	−1118.72	+	685.202i	−1.15451	+	0.707123i
$970$	−854.891	−	457.302i	−0.881331	−	0.471446i
$971$	988.417	−	570.663i	1.01794	−	0.587706i	0.104432	−	0.994532i	$-0.466698\pi$
$971$	988.417	−	570.663i	1.01794	−	0.587706i	0.913506	+	0.406826i	$0.133364\pi$
$972$	714.906	+	353.124i	0.735500	+	0.363297i
$973$	−27.0347	+	46.8255i	−0.0277849	+	0.0481249i
$974$	−1743.17	+	56.5041i	−1.78970	+	0.0580124i
$975$	784.084	+	452.691i	0.804189	+	0.464299i
$976$	−657.471	+	1581.52i	−0.673638	+	1.62041i
$977$	1598.63			1.63626			0.818132	−	0.575030i	$-0.195010\pi$
$977$	1598.63			1.63626			0.818132	+	0.575030i	$0.195010\pi$
$978$	−493.562	+	306.696i	−0.504664	+	0.313595i
$979$	−488.762	−	282.187i	−0.499246	−	0.288240i
$980$	−825.646	−	1237.39i	−0.842496	−	1.26264i
$981$	−18.0933			−0.0184438
$982$	−38.4559	−	61.8865i	−0.0391608	−	0.0630209i
$983$	455.988	−	263.265i	0.463874	−	0.267818i	−0.249798	−	0.968298i	$-0.580364\pi$
$983$	455.988	−	263.265i	0.463874	−	0.267818i	0.713672	+	0.700480i	$0.247031\pi$
$984$	68.3599	−	150.487i	0.0694715	−	0.152934i
$985$	200.618	+	347.481i	0.203673	+	0.352773i
$986$	39.5702	+	1220.75i	0.0401320	+	1.23809i
$987$			426.542i			0.432160i
$988$	193.224	+	273.912i	0.195571	+	0.277239i
$989$	419.735			0.424403
$990$	833.214	−	27.0083i	0.841630	−	0.0272811i
$991$	513.571	−	296.510i	0.518235	−	0.299203i	−0.217977	−	0.975954i	$-0.569946\pi$
$991$	513.571	−	296.510i	0.518235	−	0.299203i	0.736212	+	0.676751i	$0.236613\pi$
$992$	−756.388	+	123.631i	−0.762488	+	0.124628i
$993$	507.651	+	879.277i	0.511230	+	0.885476i
$994$	−21.5310	+	13.3793i	−0.0216610	+	0.0134600i
$995$		−	2075.79i		−	2.08623i
$996$	−1109.28	−	1662.46i	−1.11373	−	1.66914i
$997$	−402.199	+	696.629i	−0.403409	+	0.698726i	−0.994135	−	0.108147i	$-0.965508\pi$
$997$	−402.199	+	696.629i	−0.403409	+	0.698726i	0.590725	+	0.806873i	$0.298842\pi$
$998$	−74.6716	−	120.168i	−0.0748212	−	0.120409i
$999$		−	351.908i		−	0.352260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.3.g.c.7.7	yes	28
4.3	odd	2	inner	76.3.g.c.7.4	✓	28
19.11	even	3	inner	76.3.g.c.11.4	yes	28
76.11	odd	6	inner	76.3.g.c.11.7	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.g.c.7.4	✓	28	4.3	odd	2	inner
76.3.g.c.7.7	yes	28	1.1	even	1	trivial
76.3.g.c.11.4	yes	28	19.11	even	3	inner
76.3.g.c.11.7	yes	28	76.11	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	76.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0647951 - 1.99895i) q^{2} +(-3.11547 + 1.79872i) q^{3} +(-3.99160 + 0.259045i) q^{4} +(4.52938 + 7.84512i) q^{5} +(3.79741 + 6.11112i) q^{6} -2.81904i q^{7} +(0.776454 + 7.96223i) q^{8} +(1.97077 - 3.41347i) q^{9} +O(q^{10})\)	\(q+(-0.0647951 - 1.99895i) q^{2} +(-3.11547 + 1.79872i) q^{3} +(-3.99160 + 0.259045i) q^{4} +(4.52938 + 7.84512i) q^{5} +(3.79741 + 6.11112i) q^{6} -2.81904i q^{7} +(0.776454 + 7.96223i) q^{8} +(1.97077 - 3.41347i) q^{9} +(15.3885 - 9.56233i) q^{10} +11.6740i q^{11} +(11.9698 - 7.98681i) q^{12} +(-2.20531 + 3.81970i) q^{13} +(-5.63512 + 0.182660i) q^{14} +(-28.2223 - 16.2941i) q^{15} +(15.8658 - 2.06801i) q^{16} +(-9.59663 - 16.6219i) q^{17} +(-6.95104 - 3.71829i) q^{18} +(-9.06982 + 16.6955i) q^{19} +(-20.1117 - 30.1413i) q^{20} +(5.07066 + 8.78264i) q^{21} +(23.3358 - 0.756420i) q^{22} +(25.2864 + 14.5991i) q^{23} +(-16.7408 - 23.4095i) q^{24} +(-28.5306 + 49.4164i) q^{25} +(7.77829 + 4.16080i) q^{26} -18.1975i q^{27} +(0.730257 + 11.2525i) q^{28} +(15.9091 - 27.5555i) q^{29} +(-30.7425 + 57.4707i) q^{30} -23.9508i q^{31} +(-5.16187 - 31.5809i) q^{32} +(-20.9983 - 36.3701i) q^{33} +(-32.6044 + 20.2602i) q^{34} +(22.1157 - 12.7685i) q^{35} +(-6.98227 + 14.1357i) q^{36} +19.3382 q^{37} +(33.9611 + 17.0483i) q^{38} -15.8669i q^{39} +(-58.9478 + 42.1553i) q^{40} +(2.87159 + 4.97375i) q^{41} +(17.2275 - 10.7051i) q^{42} +(12.4494 - 7.18768i) q^{43} +(-3.02409 - 46.5981i) q^{44} +35.7054 q^{45} +(27.5445 - 51.4922i) q^{46} +(36.4249 + 21.0299i) q^{47} +(-45.7096 + 34.9809i) q^{48} +41.0530 q^{49} +(100.630 + 53.8292i) q^{50} +(59.7960 + 34.5232i) q^{51} +(7.81323 - 15.8180i) q^{52} +(16.2901 - 28.2152i) q^{53} +(-36.3759 + 1.17911i) q^{54} +(-91.5841 + 52.8761i) q^{55} +(22.4459 - 2.18885i) q^{56} +(-1.77365 - 68.3282i) q^{57} +(-56.1128 - 30.0161i) q^{58} +(-9.13465 + 5.27389i) q^{59} +(116.873 + 57.7289i) q^{60} +(-53.5230 + 92.7045i) q^{61} +(-47.8764 + 1.55189i) q^{62} +(-9.62270 - 5.55567i) q^{63} +(-62.7942 + 12.3646i) q^{64} -39.9547 q^{65} +(-71.3414 + 44.3311i) q^{66} +(109.917 + 63.4605i) q^{67} +(42.6117 + 63.8619i) q^{68} -105.039 q^{69} +(-26.9566 - 43.3809i) q^{70} +(3.89373 - 2.24805i) q^{71} +(28.7090 + 13.0413i) q^{72} +(-12.5643 - 21.7620i) q^{73} +(-1.25302 - 38.6562i) q^{74} -205.274i q^{75} +(31.8783 - 68.9911i) q^{76} +32.9096 q^{77} +(-31.7171 + 1.02810i) q^{78} +(-70.4767 + 40.6897i) q^{79} +(88.0859 + 115.102i) q^{80} +(50.4691 + 87.4150i) q^{81} +(9.75621 - 6.06245i) q^{82} -138.888i q^{83} +(-22.5152 - 33.7433i) q^{84} +(86.9336 - 150.573i) q^{85} +(-15.1745 - 24.4200i) q^{86} +114.464i q^{87} +(-92.9513 + 9.06434i) q^{88} +(-24.1722 + 41.8675i) q^{89} +(-2.31354 - 71.3733i) q^{90} +(10.7679 + 6.21685i) q^{91} +(-104.715 - 51.7236i) q^{92} +(43.0807 + 74.6179i) q^{93} +(39.6776 - 74.1742i) q^{94} +(-172.058 + 4.46625i) q^{95} +(72.8868 + 89.1047i) q^{96} +(-26.7563 - 46.3434i) q^{97} +(-2.66004 - 82.0629i) q^{98} +(39.8489 + 23.0068i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 5 q^{2} - 11 q^{4} + 6 q^{5} - 3 q^{6} - 62 q^{8} + 20 q^{9}+O(q^{10}) \) 28 * q - 5 * q^2 - 11 * q^4 + 6 * q^5 - 3 * q^6 - 62 * q^8 + 20 * q^9	\( 28 q - 5 q^{2} - 11 q^{4} + 6 q^{5} - 3 q^{6} - 62 q^{8} + 20 q^{9} + 26 q^{12} + 30 q^{13} - 30 q^{14} - 19 q^{16} + 38 q^{17} - 60 q^{18} - 44 q^{20} + 80 q^{21} + 45 q^{22} + 17 q^{24} - 16 q^{25} - 56 q^{26} + 54 q^{28} + 6 q^{29} + 96 q^{30} - 45 q^{32} - 176 q^{33} - 20 q^{34} + 30 q^{36} + 104 q^{37} - 258 q^{38} + 94 q^{40} - 2 q^{41} - 2 q^{42} + 201 q^{44} - 360 q^{45} + 164 q^{46} - 17 q^{48} - 20 q^{49} + 490 q^{50} - 102 q^{52} - 242 q^{53} - 13 q^{54} + 276 q^{56} - 254 q^{57} + 96 q^{58} + 10 q^{60} - 58 q^{61} - 36 q^{62} - 74 q^{64} - 260 q^{65} + 167 q^{66} + 396 q^{68} + 340 q^{69} + 60 q^{70} - 422 q^{72} - 82 q^{73} - 136 q^{74} + 123 q^{76} - 144 q^{77} + 224 q^{78} - 174 q^{80} + 410 q^{81} - 305 q^{82} + 252 q^{84} + 714 q^{85} + 166 q^{86} - 718 q^{88} + 150 q^{89} - 272 q^{90} - 588 q^{92} + 344 q^{93} - 488 q^{94} - 122 q^{96} + 94 q^{97} + 307 q^{98}+O(q^{100}) \) 28 * q - 5 * q^2 - 11 * q^4 + 6 * q^5 - 3 * q^6 - 62 * q^8 + 20 * q^9 + 26 * q^12 + 30 * q^13 - 30 * q^14 - 19 * q^16 + 38 * q^17 - 60 * q^18 - 44 * q^20 + 80 * q^21 + 45 * q^22 + 17 * q^24 - 16 * q^25 - 56 * q^26 + 54 * q^28 + 6 * q^29 + 96 * q^30 - 45 * q^32 - 176 * q^33 - 20 * q^34 + 30 * q^36 + 104 * q^37 - 258 * q^38 + 94 * q^40 - 2 * q^41 - 2 * q^42 + 201 * q^44 - 360 * q^45 + 164 * q^46 - 17 * q^48 - 20 * q^49 + 490 * q^50 - 102 * q^52 - 242 * q^53 - 13 * q^54 + 276 * q^56 - 254 * q^57 + 96 * q^58 + 10 * q^60 - 58 * q^61 - 36 * q^62 - 74 * q^64 - 260 * q^65 + 167 * q^66 + 396 * q^68 + 340 * q^69 + 60 * q^70 - 422 * q^72 - 82 * q^73 - 136 * q^74 + 123 * q^76 - 144 * q^77 + 224 * q^78 - 174 * q^80 + 410 * q^81 - 305 * q^82 + 252 * q^84 + 714 * q^85 + 166 * q^86 - 718 * q^88 + 150 * q^89 - 272 * q^90 - 588 * q^92 + 344 * q^93 - 488 * q^94 - 122 * q^96 + 94 * q^97 + 307 * q^98

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