LMFDB - Embedded newform 76.3.g.c.11.7

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			11.7
Character	$\chi$	$=$	76.11
Dual form			76.3.g.c.7.7

$q$-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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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	−0.119085	−	0.992884i	$-0.537996\pi$
$3$	−3.11547	−	1.79872i	−1.03849	−	0.599572i	−0.919405	+	0.393312i	$0.871329\pi$
$4$	−3.99160	−	0.259045i	−0.997901	−	0.0647611i
$5$	4.52938	−	7.84512i	0.905876	−	1.56902i	0.0861387	−	0.996283i	$-0.472547\pi$
$5$	4.52938	−	7.84512i	0.905876	−	1.56902i	0.819737	−	0.572740i	$-0.194119\pi$
$6$	3.79741	−	6.11112i	0.632902	−	1.01852i
$7$			2.81904i			0.402720i	0.979517	+	0.201360i	$0.0645361\pi$
$7$			2.81904i			0.402720i	−0.979517	+	0.201360i	$0.935464\pi$
$8$	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	$-0.821952\pi$
$11$		−	11.6740i		−	1.06128i	0.847599	−	0.530638i	$-0.178048\pi$
$12$	11.9698	+	7.98681i	0.997481	+	0.665567i
$13$	−2.20531	−	3.81970i	−0.169639	−	0.293823i	0.768654	−	0.639665i	$-0.220927\pi$
$13$	−2.20531	−	3.81970i	−0.169639	−	0.293823i	−0.938293	+	0.345841i	$0.887593\pi$
$14$	−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	0.432588	+	0.901592i	$0.357601\pi$
$17$	−9.59663	+	16.6219i	−0.564508	+	0.977756i	−0.997095	+	0.0761642i	$0.975733\pi$
$18$	−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	0.163343	−	0.986569i	$-0.447772\pi$
$23$	25.2864	−	14.5991i	1.09941	−	0.634744i	0.936066	+	0.351825i	$0.114439\pi$
$24$	−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	0.998371	+	0.0570486i	$0.0181690\pi$
$29$	15.9091	+	27.5555i	0.548591	+	0.950188i	−0.449780	+	0.893139i	$0.648498\pi$
$30$	−30.7425	−	57.4707i	−1.02475	−	1.91569i
$31$			23.9508i			0.772606i	0.922372	+	0.386303i	$0.126248\pi$
$31$			23.9508i			0.772606i	−0.922372	+	0.386303i	$0.873752\pi$
$32$	−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	−0.828879	−	0.559428i	$-0.811021\pi$
$41$	2.87159	−	4.97375i	0.0700389	−	0.121311i	0.898918	+	0.438117i	$0.144354\pi$
$42$	17.2275	+	10.7051i	0.410179	+	0.254883i
$43$	12.4494	+	7.18768i	0.289521	+	0.167155i	0.637726	−	0.770263i	$-0.279875\pi$
$43$	12.4494	+	7.18768i	0.289521	+	0.167155i	−0.348205	+	0.937419i	$0.613209\pi$
$44$	−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	−0.0596567	−	0.998219i	$-0.519001\pi$
$47$	36.4249	−	21.0299i	0.774998	−	0.447445i	0.834655	+	0.550774i	$0.185667\pi$
$48$	−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	0.977784	−	0.209616i	$-0.0672212\pi$
$53$	16.2901	+	28.2152i	0.307360	+	0.532362i	−0.670424	+	0.741978i	$0.733888\pi$
$54$	−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	0.420586	−	0.907253i	$-0.361824\pi$
$59$	−9.13465	−	5.27389i	−0.154825	−	0.0893880i	−0.575411	+	0.817865i	$0.695158\pi$
$60$	116.873	−	57.7289i	1.94788	−	0.962149i
$61$	−53.5230	−	92.7045i	−0.877426	−	1.51975i	−0.854156	−	0.520016i	$-0.825926\pi$
$61$	−53.5230	−	92.7045i	−0.877426	−	1.51975i	−0.0232694	−	0.999729i	$-0.507408\pi$
$62$	−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	0.659911	−	0.751344i	$-0.270594\pi$
$67$	109.917	−	63.4605i	1.64055	−	0.947172i	0.980638	−	0.195828i	$-0.0627394\pi$
$68$	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	0.527170	−	0.849760i	$-0.323253\pi$
$71$	3.89373	+	2.24805i	0.0548413	+	0.0316626i	−0.472329	+	0.881423i	$0.656586\pi$
$72$	28.7090	−	13.0413i	0.398736	−	0.181129i
$73$	−12.5643	+	21.7620i	−0.172114	+	0.298110i	−0.939159	−	0.343484i	$-0.888393\pi$
$73$	−12.5643	+	21.7620i	−0.172114	+	0.298110i	0.767045	+	0.641594i	$0.221726\pi$
$74$	−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	−0.0174777	−	0.999847i	$-0.505564\pi$
$79$	−70.4767	−	40.6897i	−0.892110	−	0.515060i	−0.874632	+	0.484788i	$0.838897\pi$
$80$	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	$0.315505\pi$
$83$			138.888i			1.67336i	−0.547696	+	0.836678i	$0.684495\pi$
$84$	−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	0.697673	−	0.716416i	$-0.254219\pi$
$89$	−24.1722	−	41.8675i	−0.271598	−	0.470421i	−0.969271	+	0.245995i	$0.920885\pi$
$90$	−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	−0.970346	−	0.241719i	$-0.922289\pi$
$97$	−26.7563	+	46.3434i	−0.275839	+	0.477767i	0.694508	+	0.719485i	$0.255622\pi$
$98$	−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	0.780606	−	0.625024i	$-0.214911\pi$
$101$	−15.2493	−	26.4126i	−0.150984	−	0.261511i	−0.931589	+	0.363513i	$0.881577\pi$
$102$	65.1358	+	121.766i	0.638586	+	1.19379i
$103$			56.0986i			0.544646i	0.962206	+	0.272323i	$0.0877920\pi$
$103$			56.0986i			0.544646i	−0.962206	+	0.272323i	$0.912208\pi$
$104$	−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	$0.0132060\pi$
$107$			8.87585i			0.0829519i	−0.999140	+	0.0414759i	$0.986794\pi$
$108$	4.71396	−	72.6372i	0.0436478	−	0.672567i
$109$	−2.29522	+	3.97543i	−0.0210570	+	0.0364718i	−0.876362	−	0.481653i	$-0.840036\pi$
$109$	−2.29522	+	3.97543i	−0.0210570	+	0.0364718i	0.855305	+	0.518125i	$0.173370\pi$
$110$	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	−0.948354	−	0.317214i	$-0.897253\pi$
$127$	−145.773	+	84.1618i	−1.14782	+	0.662691i	−0.199461	+	0.979906i	$0.563919\pi$
$128$	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	0.848012	−	0.529977i	$-0.177800\pi$
$131$	106.509	+	61.4929i	0.813044	+	0.469411i	−0.0349677	+	0.999388i	$0.511133\pi$
$132$	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	0.975721	−	0.219015i	$-0.0702844\pi$
$137$	40.8518	+	70.7574i	0.298188	+	0.516477i	−0.677533	+	0.735492i	$0.736951\pi$
$138$	6.80600	−	209.967i	0.0493188	−	1.52150i
$139$	−16.6104	+	9.59003i	−0.119499	+	0.0689930i	−0.558558	−	0.829465i	$-0.688645\pi$
$139$	−16.6104	+	9.59003i	−0.119499	+	0.0689930i	0.439059	+	0.898458i	$0.355312\pi$
$140$	−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	−0.733603	−	0.679578i	$-0.762163\pi$
$149$	33.0378	−	57.2232i	0.221730	−	0.384048i	0.955333	+	0.295530i	$0.0954962\pi$
$150$	−410.332	−	13.3007i	−2.73554	−	0.0886715i
$151$			12.6319i			0.0836552i	0.999125	+	0.0418276i	$0.0133180\pi$
$151$			12.6319i			0.0836552i	−0.999125	+	0.0418276i	$0.986682\pi$
$152$	−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	−0.785362	−	0.619037i	$-0.787523\pi$
$157$	22.5170	−	39.0005i	0.143420	−	0.248411i	0.928782	+	0.370625i	$0.120857\pi$
$158$	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	$-0.920311\pi$
$163$		−	80.7645i		−	0.495488i	0.968826	−	0.247744i	$-0.0796892\pi$
$164$	−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	0.0796954	−	0.996819i	$-0.474605\pi$
$167$	164.130	−	94.7605i	0.982814	−	0.567428i	0.903119	+	0.429391i	$0.141272\pi$
$168$	−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	−0.991616	−	0.129223i	$-0.958752\pi$
$173$	−66.4142	+	115.033i	−0.383897	+	0.664930i	0.607718	+	0.794153i	$0.292085\pi$
$174$	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	$-0.936262\pi$
$179$		−	71.2078i		−	0.397809i	0.980019	−	0.198904i	$-0.0637384\pi$
$180$	−142.522	−	9.24928i	−0.791787	−	0.0513849i
$181$	−74.3514	−	128.780i	−0.410781	−	0.711494i	0.584194	−	0.811614i	$-0.301411\pi$
$181$	−74.3514	−	128.780i	−0.410781	−	0.711494i	−0.994975	+	0.100120i	$0.968077\pi$
$182$	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	$0.136426\pi$
$191$			158.757i			0.831187i	−0.909550	+	0.415594i	$0.863574\pi$
$192$	173.393	+	151.471i	0.903089	+	0.788909i
$193$	−154.059	+	266.837i	−0.798231	+	1.38258i	0.122536	+	0.992464i	$0.460897\pi$
$193$	−154.059	+	266.837i	−0.798231	+	1.38258i	−0.920767	+	0.390113i	$0.872436\pi$
$194$	−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	−0.907426	−	0.420212i	$-0.861956\pi$
$199$	−198.448	+	114.574i	−0.997225	+	0.575748i	−0.0897989	+	0.995960i	$0.528622\pi$
$200$	−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	0.177607	−	0.984101i	$-0.443164\pi$
$211$	−123.613	−	71.3683i	−0.585846	−	0.338238i	−0.763453	+	0.645863i	$0.776498\pi$
$212$	−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	0.310466	−	0.950585i	$-0.399515\pi$
$223$	−79.7297	−	46.0319i	−0.357532	−	0.206421i	−0.667998	+	0.744163i	$0.732848\pi$
$224$	−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	$-0.974216\pi$
$227$		−	36.7352i		−	0.161829i	0.996721	−	0.0809145i	$-0.0257841\pi$
$228$	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	−0.995514	−	0.0946161i	$-0.969838\pi$
$233$	−96.8854	+	167.810i	−0.415817	+	0.720216i	0.579697	+	0.814832i	$0.303171\pi$
$234$	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	$-0.882565\pi$
$239$		−	172.376i		−	0.721238i	0.932713	−	0.360619i	$-0.117435\pi$
$240$	−481.465	+	200.156i	−2.00611	+	0.833982i
$241$	136.476	+	236.384i	0.566291	+	0.980845i	0.996928	+	0.0783202i	$0.0249556\pi$
$241$	136.476	+	236.384i	0.566291	+	0.980845i	−0.430637	+	0.902525i	$0.641711\pi$
$242$	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	−0.851094	−	0.525014i	$-0.824060\pi$
$251$	−206.313	+	119.115i	−0.821965	+	0.474562i	0.0291287	+	0.999576i	$0.490727\pi$
$252$	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	0.696540	−	0.717518i	$-0.254722\pi$
$257$	−70.1915	−	121.575i	−0.273119	−	0.473055i	−0.969659	+	0.244463i	$0.921388\pi$
$258$	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	0.208655	−	0.977989i	$-0.433091\pi$
$263$	−140.437	−	81.0814i	−0.533981	−	0.308294i	−0.742636	+	0.669695i	$0.766425\pi$
$264$	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	−0.561657	−	0.827370i	$-0.689836\pi$
$269$	117.202	−	203.000i	0.435695	−	0.754647i	0.997352	+	0.0727237i	$0.0231691\pi$
$270$	−174.011	+	280.033i	−0.644484	+	1.03716i
$271$	107.762	+	62.2163i	0.397645	+	0.229581i	0.685467	−	0.728103i	$-0.259598\pi$
$271$	107.762	+	62.2163i	0.397645	+	0.229581i	−0.287822	+	0.957684i	$0.592931\pi$
$272$	−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	0.997952	+	0.0639730i	$0.0203772\pi$
$281$	155.780	+	269.819i	0.554378	+	0.960211i	−0.443574	+	0.896238i	$0.646290\pi$
$282$	9.80399	−	302.456i	0.0347659	−	1.07254i
$283$	342.914	+	197.981i	1.21171	+	0.699581i	0.963132	−	0.269031i	$-0.0867034\pi$
$283$	342.914	+	197.981i	1.21171	+	0.699581i	0.248578	+	0.968612i	$0.420037\pi$
$284$	−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	−0.0905962	−	0.995888i	$-0.528877\pi$
$307$	−306.496	−	176.956i	−0.998358	−	0.576403i	−0.907762	+	0.419485i	$0.862211\pi$
$308$	−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	$0.304817\pi$
$311$			508.683i			1.63564i	−0.575475	+	0.817819i	$0.695183\pi$
$312$	126.336	+	12.3199i	0.404923	+	0.0394869i
$313$	−227.534	−	394.101i	−0.726946	−	1.25911i	−0.958168	−	0.286206i	$-0.907606\pi$
$313$	−227.534	−	394.101i	−0.726946	−	1.25911i	0.231222	−	0.972901i	$-0.425728\pi$
$314$	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	−0.757886	−	0.652387i	$-0.773768\pi$
$317$	−299.225	−	518.273i	−0.943927	−	1.63493i	−0.186041	−	0.982542i	$-0.559566\pi$
$318$	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	$0.140193\pi$
$331$			282.230i			0.852657i	−0.904568	+	0.426329i	$0.859807\pi$
$332$	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	−0.918438	−	0.395564i	$-0.870549\pi$
$337$	−39.3112	+	68.0891i	−0.116651	+	0.202045i	0.801788	+	0.597609i	$0.203882\pi$
$338$	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	0.707167	−	0.707047i	$-0.249973\pi$
$347$	155.605	+	89.8386i	0.448429	+	0.258901i	−0.258737	+	0.965948i	$0.583306\pi$
$348$	−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	0.946632	−	0.322316i	$-0.104461\pi$
$359$	409.552	+	236.455i	1.14081	+	0.658649i	0.194182	+	0.980966i	$0.437795\pi$
$360$	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	−0.564729	−	0.825276i	$-0.691019\pi$
$367$	−48.5847	+	28.0504i	−0.132383	+	0.0764316i	0.432346	+	0.901708i	$0.357686\pi$
$368$	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	$-0.822454\pi$
$379$		−	401.210i		−	1.05860i	0.848434	−	0.529301i	$-0.177546\pi$
$380$	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	0.594636	−	0.803995i	$-0.297296\pi$
$383$	74.9428	+	43.2682i	0.195673	+	0.112972i	−0.398963	+	0.916967i	$0.630630\pi$
$384$	−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	0.932502	+	0.361164i	$0.117621\pi$
$389$	303.042	+	524.884i	0.779028	+	1.34932i	−0.153474	+	0.988153i	$0.549046\pi$
$390$	−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	−0.953509	−	0.301366i	$-0.902558\pi$
$397$	−85.6583	+	148.365i	−0.215764	+	0.373714i	0.737745	+	0.675080i	$0.235891\pi$
$398$	−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	−0.650208	−	0.759756i	$-0.725318\pi$
$401$	133.478	−	231.191i	0.332864	−	0.576537i	0.983072	+	0.183219i	$0.0586517\pi$
$402$	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	0.931973	−	0.362529i	$-0.118087\pi$
$409$	62.1792	+	107.697i	0.152027	+	0.263319i	−0.779945	+	0.625848i	$0.784753\pi$
$410$	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	$-0.904003\pi$
$419$		−	248.914i		−	0.594068i	0.954867	−	0.297034i	$-0.0959974\pi$
$420$	162.740	+	329.470i	0.387477	+	0.784453i
$421$	−162.941	+	282.223i	−0.387034	+	0.670362i	−0.992049	−	0.125852i	$-0.959834\pi$
$421$	−162.941	+	282.223i	−0.387034	+	0.670362i	0.605015	+	0.796214i	$0.293167\pi$
$422$	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	0.0441038	−	0.999027i	$-0.485957\pi$
$431$	401.407	−	231.752i	0.931338	−	0.537708i	0.887235	+	0.461319i	$0.152623\pi$
$432$	−37.6326	+	288.718i	−0.0871124	+	0.668328i
$433$	138.967	+	240.698i	0.320940	+	0.555884i	0.980682	−	0.195608i	$-0.0626679\pi$
$433$	138.967	+	240.698i	0.320940	+	0.555884i	−0.659742	+	0.751492i	$0.729335\pi$
$434$	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	−0.998850	−	0.0479384i	$-0.984735\pi$
$439$	−675.968	−	390.271i	−1.53979	−	0.888999i	−0.540941	−	0.841061i	$-0.681932\pi$
$440$	−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	0.297273	−	0.954792i	$-0.403923\pi$
$443$	563.843	−	325.535i	1.27278	−	0.734842i	0.975511	+	0.219950i	$0.0705894\pi$
$444$	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	−0.817640	−	0.575730i	$-0.804718\pi$
$461$	41.3870	−	71.6845i	0.0897767	−	0.155498i	0.907417	+	0.420232i	$0.138051\pi$
$462$	124.971	−	201.114i	0.270501	−	0.435312i
$463$			211.533i			0.456874i	0.973559	+	0.228437i	$0.0733615\pi$
$463$			211.533i			0.456874i	−0.973559	+	0.228437i	$0.926639\pi$
$464$	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	$-0.811021\pi$
$467$		−	522.505i		−	1.11885i	0.828879	−	0.559427i	$-0.188979\pi$
$468$	−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	−0.875140	−	0.483869i	$-0.839231\pi$
$479$	−428.067	+	247.144i	−0.893668	+	0.515959i	−0.0185273	+	0.999828i	$0.505898\pi$
$480$	−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	$0.353054\pi$
$487$			872.042i			1.79064i	−0.445422	+	0.895321i	$0.646946\pi$
$488$	−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	0.531784	−	0.846880i	$-0.321522\pi$
$491$	31.5500	+	18.2154i	0.0642565	+	0.0370985i	−0.467528	+	0.883979i	$0.654855\pi$
$492$	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	0.560127	−	0.828407i	$-0.310752\pi$
$499$	61.2620	+	35.3696i	0.122769	+	0.0708810i	−0.437358	+	0.899288i	$0.644086\pi$
$500$	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	−0.246143	−	0.969233i	$-0.579163\pi$
$503$	236.493	−	136.539i	0.470166	−	0.271450i	0.716309	+	0.697783i	$0.245830\pi$
$504$	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	0.999524	−	0.0308545i	$-0.00982285\pi$
$509$	240.778	+	417.040i	0.473041	+	0.819331i	−0.526483	+	0.850186i	$0.676490\pi$
$510$	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	−0.520940	−	0.853593i	$-0.674418\pi$
$523$	−22.0583	+	12.7354i	−0.0421764	+	0.0243506i	0.478764	+	0.877944i	$0.341085\pi$
$524$	−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	0.995967	+	0.0897216i	$0.0285977\pi$
$541$	311.445	+	539.439i	0.575685	+	0.997115i	−0.420282	+	0.907393i	$0.638069\pi$
$542$	−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	−0.994353	−	0.106125i	$-0.966155\pi$
$547$	−765.593	+	442.015i	−1.39962	+	0.808072i	−0.405269	+	0.914197i	$0.632822\pi$
$548$	−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	0.997919	+	0.0644847i	$0.0205404\pi$
$557$	309.026	+	535.249i	0.554805	+	0.960950i	−0.443114	+	0.896465i	$0.646126\pi$
$558$	−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	$0.0480352\pi$
$563$			169.277i			0.300670i	−0.988635	+	0.150335i	$0.951965\pi$
$564$	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	$0.0492160\pi$
$571$			175.870i			0.308003i	−0.988071	+	0.154001i	$0.950784\pi$
$572$	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	0.935293	−	0.353874i	$-0.115136\pi$
$587$	643.631	+	371.601i	1.09648	+	0.633050i	0.161182	+	0.986925i	$0.448469\pi$
$588$	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	0.906178	+	0.422897i	$0.138987\pi$
$593$	485.862	+	841.537i	0.819328	+	1.41912i	−0.0868496	+	0.996221i	$0.527680\pi$
$594$	−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	−0.698241	−	0.715863i	$-0.746033\pi$
$599$	−256.016	+	147.811i	−0.427405	+	0.246762i	0.270836	+	0.962626i	$0.412700\pi$
$600$	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	$-0.901299\pi$
$607$		−	370.431i		−	0.610265i	0.952310	−	0.305133i	$-0.0987008\pi$
$608$	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	−0.974718	−	0.223441i	$-0.928271\pi$
$613$	−180.132	+	311.998i	−0.293854	+	0.508969i	0.680864	+	0.732410i	$0.261604\pi$
$614$	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	0.856646	−	0.515904i	$-0.172544\pi$
$617$	−11.3914	−	19.7305i	−0.0184626	−	0.0319782i	−0.875109	+	0.483926i	$0.839211\pi$
$618$	342.825	+	213.029i	0.554733	+	0.344708i
$619$		−	362.401i		−	0.585462i	−0.956195	−	0.292731i	$-0.905436\pi$
$619$		−	362.401i		−	0.585462i	0.956195	−	0.292731i	$-0.0945641\pi$
$620$	−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	0.133391	−	0.991063i	$-0.457413\pi$
$631$	667.833	−	385.574i	1.05837	−	0.611052i	0.924982	+	0.380011i	$0.124080\pi$
$632$	−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	−0.848216	−	0.529651i	$-0.822323\pi$
$641$	22.1679	−	38.3960i	0.0345834	−	0.0599001i	0.882799	+	0.469751i	$0.155656\pi$
$642$	54.2414	+	33.7053i	0.0844881	+	0.0525004i
$643$	−1034.78	−	597.433i	−1.60931	−	0.929133i	−0.989525	−	0.144358i	$-0.953888\pi$
$643$	−1034.78	−	597.433i	−1.60931	−	0.929133i	−0.619781	−	0.784775i	$-0.712778\pi$
$644$	−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	$-0.964532\pi$
$647$		−	143.888i		−	0.222393i	0.993798	−	0.111196i	$-0.0354683\pi$
$648$	−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	0.0719062	−	0.997411i	$-0.477092\pi$
$659$	640.313	−	369.685i	0.971643	−	0.560978i	0.899737	+	0.436433i	$0.143758\pi$
$660$	−673.929	−	1364.38i	−1.02110	−	2.06724i
$661$	−364.477	−	631.293i	−0.551403	−	0.955058i	−0.998174	−	0.0604096i	$-0.980759\pi$
$661$	−364.477	−	631.293i	−0.551403	−	0.955058i	0.446771	−	0.894649i	$-0.352574\pi$
$662$	−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	$0.230124\pi$
$683$			903.750i			1.32321i	−0.749854	+	0.661604i	$0.769876\pi$
$684$	−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	$0.0304595\pi$
$691$			132.044i			0.191091i	−0.995425	+	0.0955454i	$0.969540\pi$
$692$	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	−0.216371	−	0.976311i	$-0.569422\pi$
$701$	516.865	−	895.236i	0.737325	−	1.27708i	0.953696	−	0.300773i	$-0.0972445\pi$
$702$	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	0.931473	+	0.363811i	$0.118525\pi$
$709$	553.592	+	958.849i	0.780806	+	1.35240i	−0.150667	+	0.988585i	$0.548142\pi$
$710$	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	0.924080	−	0.382200i	$-0.124833\pi$
$719$	758.635	+	437.998i	1.05513	+	0.609177i	0.131045	+	0.991376i	$0.458167\pi$
$720$	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	−0.00251881	−	0.999997i	$-0.500802\pi$
$727$	−632.345	−	365.085i	−0.869801	−	0.502180i	−0.867282	+	0.497817i	$0.834135\pi$
$728$	−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	0.805759	−	0.592243i	$-0.201758\pi$
$739$	514.152	+	296.846i	0.695741	+	0.401686i	−0.110018	+	0.993930i	$0.535091\pi$
$740$	−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	0.532407	−	0.846489i	$-0.321288\pi$
$743$	48.6881	+	28.1101i	0.0655291	+	0.0378332i	−0.466877	+	0.884322i	$0.654621\pi$
$744$	−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	−0.418524	−	0.908206i	$-0.637452\pi$
$751$	119.216	−	68.8295i	0.158743	−	0.0916504i	0.577267	+	0.816555i	$0.304119\pi$
$752$	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	0.395212	+	0.918590i	$0.370671\pi$
$757$	−452.623	+	783.966i	−0.597916	+	1.03562i	−0.993128	+	0.117032i	$0.962662\pi$
$758$	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	−0.980439	−	0.196825i	$-0.936937\pi$
$769$	−508.059	−	879.984i	−0.660675	−	1.14432i	0.319764	−	0.947497i	$-0.396396\pi$
$770$	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	0.984499	+	0.175388i	$0.0561179\pi$
$773$	497.920	+	862.423i	0.644140	+	1.11568i	−0.340359	+	0.940295i	$0.610549\pi$
$774$	−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	$-0.816709\pi$
$787$		−	857.085i		−	1.08905i	0.838743	−	0.544527i	$-0.183291\pi$
$788$	−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	0.544506	−	0.838757i	$-0.316717\pi$
$811$	1251.49	−	722.548i	1.54314	−	0.890934i	0.998638	−	0.0521771i	$-0.0166160\pi$
$812$	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	−0.999075	−	0.0429941i	$-0.986310\pi$
$821$	−440.690	−	763.297i	−0.536772	−	0.929716i	0.462304	−	0.886722i	$-0.347023\pi$
$822$	587.538	+	19.0448i	0.714766	+	0.0231688i
$823$	−712.755	+	411.509i	−0.866045	+	0.500011i	−0.866032	−	0.499989i	$-0.833337\pi$
$823$	−712.755	+	411.509i	−0.866045	+	0.500011i	−1.29516e−5		1.00000i	$0.500004\pi$
$824$	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	−0.432098	−	0.901827i	$-0.642227\pi$
$827$	109.874	−	63.4355i	0.132858	−	0.0767056i	0.564956	+	0.825121i	$0.308893\pi$
$828$	−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	−0.0837647	−	0.996486i	$-0.526694\pi$
$839$	−829.460	−	478.889i	−0.988629	−	0.570785i	−0.904864	+	0.425700i	$0.860028\pi$
$840$	−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	−0.953708	−	0.300733i	$-0.902769\pi$
$853$	−184.599	+	319.736i	−0.216412	+	0.374837i	0.737296	+	0.675569i	$0.236102\pi$
$854$	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	−0.703239	−	0.710953i	$-0.748264\pi$
$857$	226.320	−	391.998i	0.264084	−	0.457407i	0.967323	+	0.253546i	$0.0815971\pi$
$858$	−12.0020	+	370.267i	−0.0139884	+	0.431546i
$859$	−838.651	+	484.196i	−0.976311	+	0.563674i	−0.901154	−	0.433498i	$-0.857279\pi$
$859$	−838.651	+	484.196i	−0.976311	+	0.563674i	−0.0751568	+	0.997172i	$0.523946\pi$
$860$	−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	$0.0996092\pi$
$863$			531.348i			0.615698i	−0.951435	+	0.307849i	$0.900391\pi$
$864$	−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	−0.508589	−	0.861010i	$-0.669833\pi$
$877$	430.925	−	746.383i	0.491362	−	0.851064i	0.999951	+	0.00994571i	$0.00316587\pi$
$878$	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	−0.671565	+	0.740946i	$0.734378\pi$
$883$	−1456.09	+	840.674i	−1.64903	+	0.952065i	−0.977460	+	0.211120i	$0.932289\pi$
$884$	−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	−0.824925	−	0.565242i	$-0.808783\pi$
$887$	−663.364	+	382.993i	−0.747874	+	0.431785i	0.0770515	+	0.997027i	$0.475449\pi$
$888$	−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	0.334099	−	0.942538i	$-0.391568\pi$
$907$	−285.807	−	165.011i	−0.315113	−	0.181930i	−0.649212	+	0.760608i	$0.724901\pi$
$908$	−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	$-0.801347\pi$
$911$		−	1064.70i		−	1.16871i	0.811497	−	0.584357i	$-0.198653\pi$
$912$	−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	$-0.805926\pi$
$919$		−	1052.48i		−	1.14525i	0.819818	−	0.572624i	$-0.194074\pi$
$920$	−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	0.0190598	+	0.999818i	$0.493933\pi$
$929$	−795.538	+	1377.91i	−0.856338	+	1.48322i	−0.875398	+	0.483403i	$0.839401\pi$
$930$	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	0.877552	−	0.479481i	$-0.159175\pi$
$937$	22.0506	+	38.1928i	0.0235332	+	0.0407607i	−0.854019	+	0.520242i	$0.825842\pi$
$938$	−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	−0.897266	−	0.441491i	$-0.854450\pi$
$941$	−781.948	−	1354.37i	−0.830975	−	1.43929i	0.0662905	−	0.997800i	$-0.478884\pi$
$942$	−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	0.994252	−	0.107061i	$-0.0341442\pi$
$947$	1324.53	+	764.719i	1.39866	+	0.807517i	0.404408	+	0.914579i	$0.367478\pi$
$948$	−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	−0.920162	−	0.391537i	$-0.871943\pi$
$953$	−115.313	+	199.728i	−0.121000	+	0.209578i	0.799162	+	0.601115i	$0.205277\pi$
$954$	−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	−0.348032	−	0.937483i	$-0.613150\pi$
$967$	−1289.91	−	744.731i	−1.33393	−	0.770146i	−0.985900	+	0.167337i	$0.946483\pi$
$968$	−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	0.913506	−	0.406826i	$-0.133364\pi$
$971$	988.417	+	570.663i	1.01794	+	0.587706i	0.104432	+	0.994532i	$0.466698\pi$
$972$	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	0.713672	−	0.700480i	$-0.247031\pi$
$983$	455.988	+	263.265i	0.463874	+	0.267818i	−0.249798	+	0.968298i	$0.580364\pi$
$984$	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	0.736212	−	0.676751i	$-0.236613\pi$
$991$	513.571	+	296.510i	0.518235	+	0.299203i	−0.217977	+	0.975954i	$0.569946\pi$
$992$	−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	0.590725	−	0.806873i	$-0.298842\pi$
$997$	−402.199	−	696.629i	−0.403409	−	0.698726i	−0.994135	+	0.108147i	$0.965508\pi$
$998$	−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.11.7	yes	28
4.3	odd	2	inner	76.3.g.c.11.4	yes	28
19.7	even	3	inner	76.3.g.c.7.4	✓	28
76.7	odd	6	inner	76.3.g.c.7.7	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.g.c.7.4	✓	28	19.7	even	3	inner
76.3.g.c.7.7	yes	28	76.7	odd	6	inner
76.3.g.c.11.4	yes	28	4.3	odd	2	inner
76.3.g.c.11.7	yes	28	1.1	even	1	trivial

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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