LMFDB - Embedded newform 76.3.g.c.7.4

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			7.4
Character	$\chi$	$=$	76.7
Dual form			76.3.g.c.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69874 - 1.05559i) q^{2} +(3.11547 - 1.79872i) q^{3} +(1.77146 + 3.58635i) q^{4} +(4.52938 + 7.84512i) q^{5} +(-7.19109 - 0.233096i) q^{6} +2.81904i q^{7} +(0.776454 - 7.96223i) q^{8} +(1.97077 - 3.41347i) q^{9} +O(q^{10})$	\(q+(-1.69874 - 1.05559i) q^{2} +(3.11547 - 1.79872i) q^{3} +(1.77146 + 3.58635i) q^{4} +(4.52938 + 7.84512i) q^{5} +(-7.19109 - 0.233096i) q^{6} +2.81904i q^{7} +(0.776454 - 7.96223i) q^{8} +(1.97077 - 3.41347i) q^{9} +(0.586964 - 18.1080i) q^{10} -11.6740i q^{11} +(11.9698 + 7.98681i) q^{12} +(-2.20531 + 3.81970i) q^{13} +(2.97575 - 4.78883i) q^{14} +(28.2223 + 16.2941i) q^{15} +(-9.72384 + 12.7062i) 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} +(-12.3230 + 19.8312i) q^{22} +(-25.2864 - 14.5991i) q^{23} +(-11.9028 - 26.2027i) q^{24} +(-28.5306 + 49.4164i) q^{25} +(7.77829 - 4.16080i) q^{26} +18.1975i q^{27} +(-10.1101 + 4.99383i) q^{28} +(15.9091 - 27.5555i) q^{29} +(-30.7425 - 57.4707i) q^{30} +23.9508i q^{31} +(29.9308 - 11.3202i) q^{32} +(-20.9983 - 36.3701i) q^{33} +(-1.24363 + 38.3664i) q^{34} +(-22.1157 + 12.7685i) q^{35} +(15.7330 + 1.02103i) q^{36} +19.3382 q^{37} +(-33.0309 + 18.7873i) q^{38} +15.8669i q^{39} +(65.9815 - 29.9726i) q^{40} +(2.87159 + 4.97375i) q^{41} +(0.657108 - 20.2720i) q^{42} +(-12.4494 + 7.18768i) q^{43} +(41.8672 - 20.6801i) q^{44} +35.7054 q^{45} +(27.5445 + 51.4922i) q^{46} +(-36.4249 - 21.0299i) q^{47} +(-7.43951 + 57.0761i) q^{48} +41.0530 q^{49} +(100.630 - 53.8292i) q^{50} +(-59.7960 - 34.5232i) q^{51} +(-17.6054 - 1.14255i) q^{52} +(16.2901 - 28.2152i) q^{53} +(19.2091 - 30.9129i) 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} +(-8.44182 + 130.080i) q^{60} +(-53.5230 + 92.7045i) q^{61} +(25.2822 - 40.6862i) q^{62} +(9.62270 + 5.55567i) q^{63} +(-62.7942 - 12.3646i) q^{64} -39.9547 q^{65} +(-2.72117 + 83.9490i) q^{66} +(-109.917 - 63.4605i) q^{67} +(42.6117 - 63.8619i) q^{68} -105.039 q^{69} +(51.0472 + 1.65467i) q^{70} +(-3.89373 + 2.24805i) q^{71} +(-25.6486 - 18.3421i) q^{72} +(-12.5643 - 21.7620i) q^{73} +(-32.8507 - 20.4132i) q^{74} +205.274i q^{75} +(75.9426 + 2.95220i) q^{76} +32.9096 q^{77} +(16.7489 - 26.9538i) q^{78} +(70.4767 - 40.6897i) q^{79} +(-143.724 - 18.7336i) q^{80} +(50.4691 + 87.4150i) q^{81} +(0.372131 - 11.4803i) q^{82} +138.888i q^{83} +(-22.5152 + 33.7433i) q^{84} +(86.9336 - 150.573i) q^{85} +(28.7356 + 0.931453i) q^{86} -114.464i q^{87} +(-92.9513 - 9.06434i) q^{88} +(-24.1722 + 41.8675i) q^{89} +(-60.6543 - 37.6902i) q^{90} +(-10.7679 - 6.21685i) q^{91} +(7.56364 - 116.548i) 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} +(-69.7385 - 43.3351i) 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 $

$2$	−1.69874	−	1.05559i	−0.849372	−	0.527795i
$2$	−1.69874	−	1.05559i	−0.849372	−	0.527795i
$3$	3.11547	−	1.79872i	1.03849	−	0.599572i	0.119085	−	0.992884i	$-0.462004\pi$
$3$	3.11547	−	1.79872i	1.03849	−	0.599572i	0.919405	+	0.393312i	$0.128671\pi$
$4$	1.77146	+	3.58635i	0.442866	+	0.896588i
$5$	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	$0.472547\pi$
$6$	−7.19109	−	0.233096i	−1.19852	−	0.0388494i
$7$			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
$10$	0.586964	−	18.1080i	0.0586964	−	1.81080i
$11$		−	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	−0.938293	−	0.345841i	$-0.887593\pi$
$13$	−2.20531	+	3.81970i	−0.169639	+	0.293823i	0.768654	+	0.639665i	$0.220927\pi$
$14$	2.97575	−	4.78883i	0.212554	−	0.342059i
$15$	28.2223	+	16.2941i	1.88149	+	1.08628i
$16$	−9.72384	+	12.7062i	−0.607740	+	0.794136i
$17$	−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
$22$	−12.3230	+	19.8312i	−0.560136	+	0.901418i
$23$	−25.2864	−	14.5991i	−1.09941	−	0.634744i	−0.163343	−	0.986569i	$-0.552228\pi$
$23$	−25.2864	−	14.5991i	−1.09941	−	0.634744i	−0.936066	+	0.351825i	$0.885561\pi$
$24$	−11.9028	−	26.2027i	−0.495949	−	1.09178i
$25$	−28.5306	+	49.4164i	−1.14122	+	1.97665i
$26$	7.77829	−	4.16080i	0.299165	−	0.160031i
$27$			18.1975i			0.673982i
$28$	−10.1101	+	4.99383i	−0.361074	+	0.178351i
$29$	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	$0.126248\pi$
$31$			23.9508i			0.772606i	−0.922372	+	0.386303i	$0.873752\pi$
$32$	29.9308	−	11.3202i	0.935338	−	0.353755i
$33$	−20.9983	−	36.3701i	−0.636311	−	1.10212i
$34$	−1.24363	+	38.3664i	−0.0365774	+	1.12842i
$35$	−22.1157	+	12.7685i	−0.631877	+	0.364815i
$36$	15.7330	+	1.02103i	0.437029	+	0.0283620i
$37$	19.3382			0.522655			0.261327	−	0.965250i	$-0.415840\pi$
$37$	19.3382			0.522655			0.261327	+	0.965250i	$0.415840\pi$
$38$	−33.0309	+	18.7873i	−0.869233	+	0.494403i
$39$			15.8669i			0.406843i
$40$	65.9815	−	29.9726i	1.64954	−	0.749315i
$41$	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	$0.811021\pi$
$42$	0.657108	−	20.2720i	0.0156454	−	0.482666i
$43$	−12.4494	+	7.18768i	−0.289521	+	0.167155i	−0.637726	−	0.770263i	$-0.720125\pi$
$43$	−12.4494	+	7.18768i	−0.289521	+	0.167155i	0.348205	+	0.937419i	$0.386791\pi$
$44$	41.8672	−	20.6801i	0.951527	−	0.470002i
$45$	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	$-0.480999\pi$
$47$	−36.4249	−	21.0299i	−0.774998	−	0.447445i	−0.834655	+	0.550774i	$0.814333\pi$
$48$	−7.43951	+	57.0761i	−0.154990	+	1.18909i
$49$	41.0530			0.837816
$50$	100.630	−	53.8292i	2.01259	−	1.07658i
$51$	−59.7960	−	34.5232i	−1.17247	−	0.676926i
$52$	−17.6054	−	1.14255i	−0.338566	−	0.0219720i
$53$	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	$0.0672212\pi$
$54$	19.2091	−	30.9129i	0.355724	−	0.572461i
$55$	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	$-0.638176\pi$
$59$	9.13465	−	5.27389i	0.154825	−	0.0893880i	0.575411	+	0.817865i	$0.304842\pi$
$60$	−8.44182	+	130.080i	−0.140697	+	2.16799i
$61$	−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	$0.825926\pi$
$62$	25.2822	−	40.6862i	0.407777	−	0.656230i
$63$	9.62270	+	5.55567i	0.152741	+	0.0881852i
$64$	−62.7942	−	12.3646i	−0.981160	−	0.193197i
$65$	−39.9547			−0.614687
$66$	−2.72117	+	83.9490i	−0.0412299	+	1.27195i
$67$	−109.917	−	63.4605i	−1.64055	−	0.947172i	−0.980638	−	0.195828i	$-0.937261\pi$
$67$	−109.917	−	63.4605i	−1.64055	−	0.947172i	−0.659911	−	0.751344i	$-0.729406\pi$
$68$	42.6117	−	63.8619i	0.626643	−	0.939145i
$69$	−105.039			−1.52230
$70$	51.0472	+	1.65467i	0.729246	+	0.0236382i
$71$	−3.89373	+	2.24805i	−0.0548413	+	0.0316626i	−0.527170	−	0.849760i	$-0.676747\pi$
$71$	−3.89373	+	2.24805i	−0.0548413	+	0.0316626i	0.472329	+	0.881423i	$0.343414\pi$
$72$	−25.6486	−	18.3421i	−0.356231	−	0.254751i
$73$	−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	$0.888393\pi$
$74$	−32.8507	−	20.4132i	−0.443928	−	0.275854i
$75$			205.274i			2.73698i
$76$	75.9426	+	2.95220i	0.999245	+	0.0388448i
$77$	32.9096			0.427397
$78$	16.7489	−	26.9538i	0.214730	−	0.345561i
$79$	70.4767	−	40.6897i	0.892110	−	0.515060i	0.0174777	−	0.999847i	$-0.494436\pi$
$79$	70.4767	−	40.6897i	0.892110	−	0.515060i	0.874632	+	0.484788i	$0.161103\pi$
$80$	−143.724	−	18.7336i	−1.79655	−	0.234170i
$81$	50.4691	+	87.4150i	0.623075	+	1.07920i
$82$	0.372131	−	11.4803i	0.00453818	−	0.140004i
$83$			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
$86$	28.7356	+	0.931453i	0.334135	+	0.0108308i
$87$		−	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	$0.254219\pi$
$90$	−60.6543	−	37.6902i	−0.673937	−	0.418780i
$91$	−10.7679	−	6.21685i	−0.118329	−	0.0683170i
$92$	7.56364	−	116.548i	0.0822135	−	1.26682i
$93$	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	$0.922289\pi$
$98$	−69.7385	−	43.3351i	−0.711618	−	0.442195i
$99$	−39.8489	−	23.0068i	−0.402514	−	0.232392i
$100$	−227.765	−	14.7814i	−2.27765	−	0.147814i
$101$	−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	$0.0877920\pi$
$103$			56.0986i			0.544646i	−0.962206	+	0.272323i	$0.912208\pi$
$104$	28.7010	+	20.5250i	0.275972	+	0.197356i
$105$	−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	$0.986794\pi$
$108$	−65.2627	+	32.2362i	−0.604284	+	0.298483i
$109$	−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	$0.840036\pi$
$110$	−211.393	−	6.85223i	−1.92176	−	0.0622930i
$111$	60.2477	−	34.7840i	0.542772	−	0.313369i
$112$	−35.8192	−	27.4119i	−0.319815	−	0.244749i
$113$	174.766			1.54660			0.773301	−	0.634039i	$-0.218604\pi$
$113$	174.766			1.54660			0.773301	+	0.634039i	$0.218604\pi$
$114$	−69.1136	+	117.944i	−0.606259	+	1.03460i
$115$		−	264.500i		−	2.30000i
$116$	127.006	+	8.24235i	1.09488	+	0.0710548i
$117$	8.69228	+	15.0555i	0.0742930	+	0.128679i
$118$	−21.0845	−	0.683445i	−0.178682	−	0.00579191i
$119$	46.8577	−	27.0533i	0.393762	−	0.227339i
$120$	151.651	−	212.061i	1.26376	−	1.76717i
$121$	−15.2830			−0.126306
$122$	188.780	−	100.983i	1.54737	−	0.827729i
$123$	17.8927	+	10.3304i	0.145469	+	0.0839868i
$124$	−85.8959	+	42.4279i	−0.692709	+	0.342161i
$125$	−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	$-0.102747\pi$
$127$	145.773	+	84.1618i	1.14782	+	0.662691i	0.199461	+	0.979906i	$0.436081\pi$
$128$	93.6194	+	87.2892i	0.731402	+	0.681947i
$129$	−25.8572	+	44.7860i	−0.200443	+	0.347178i
$130$	67.8728	+	42.1757i	0.522098	+	0.324429i
$131$	−106.509	+	61.4929i	−0.813044	+	0.469411i	−0.848012	−	0.529977i	$-0.822200\pi$
$131$	−106.509	+	61.4929i	−0.813044	+	0.469411i	0.0349677	+	0.999388i	$0.488867\pi$
$132$	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
$136$	−139.798	+	63.5045i	−1.02793	+	0.466945i
$137$	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	$0.0702844\pi$
$138$	178.434	+	110.878i	1.29300	+	0.803462i
$139$	16.6104	+	9.59003i	0.119499	+	0.0689930i	0.558558	−	0.829465i	$-0.311355\pi$
$139$	16.6104	+	9.59003i	0.119499	+	0.0689930i	−0.439059	+	0.898458i	$0.644688\pi$
$140$	−84.9695	−	56.6958i	−0.606925	−	0.404970i
$141$	−151.308			−1.07310
$142$	8.98747	+	0.291325i	0.0632920	+	0.00205159i
$143$	44.5913	+	25.7448i	0.311827	+	0.180034i
$144$	24.2087	+	58.2329i	0.168116	+	0.404395i
$145$	288.234			1.98782
$146$	−1.62821	+	50.2309i	−0.0111521	+	0.344047i
$147$	127.899	−	73.8427i	0.870064	−	0.502332i
$148$	34.2570	+	69.3537i	0.231466	+	0.468606i
$149$	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	$0.762163\pi$
$150$	216.685	−	348.707i	1.44456	−	2.32472i
$151$			12.6319i			0.0836552i	0.999125	+	0.0418276i	$0.0133180\pi$
$151$			12.6319i			0.0836552i	−0.999125	+	0.0418276i	$0.986682\pi$
$152$	−125.891	−	85.1793i	−0.828229	−	0.560390i
$153$	−75.6508			−0.494450
$154$	−55.9050	−	34.7390i	−0.363019	−	0.225578i
$155$	−187.897	+	108.482i	−1.21224	+	0.699885i
$156$	−56.9042	+	28.1076i	−0.364771	+	0.180177i
$157$	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	$0.787523\pi$
$158$	−162.673	−	5.27299i	−1.02958	−	0.0333734i
$159$		−	117.205i		−	0.737137i
$160$	224.376	+	183.537i	1.40235	+	1.14711i
$161$	41.1555	−	71.2834i	0.255624	−	0.442754i
$162$	6.54030	−	201.770i	0.0403722	−	1.24550i
$163$		−	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
$166$	146.609	−	235.936i	0.883188	−	1.42130i
$167$	−164.130	−	94.7605i	−0.982814	−	0.567428i	−0.0796954	−	0.996819i	$-0.525395\pi$
$167$	−164.130	−	94.7605i	−0.982814	−	0.567428i	−0.903119	+	0.429391i	$0.858728\pi$
$168$	73.8665	−	33.5544i	0.439682	−	0.199729i
$169$	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	$0.958752\pi$
$174$	−120.827	+	194.445i	−0.694409	+	1.11750i
$175$	−139.307	−	80.4288i	−0.796039	−	0.459593i
$176$	148.332	+	113.516i	0.842797	+	0.644980i
$177$	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	$-0.0637384\pi$
$180$	63.2507	+	128.052i	0.351393	+	0.711400i
$181$	−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
$184$	−135.875	+	190.001i	−0.738452	+	1.03261i
$185$	87.5902	+	151.711i	0.473460	+	0.820058i
$186$	5.58284	−	172.232i	0.0300153	−	0.925980i
$187$	−194.044	+	112.031i	−1.03767	+	0.599098i
$188$	10.8954	−	167.886i	0.0579541	−	0.893012i
$189$	−51.2995			−0.271426
$190$	−296.998	−	174.036i	−1.56315	−	0.915979i
$191$			158.757i			0.831187i	0.909550	+	0.415594i	$0.136426\pi$
$191$			158.757i			0.831187i	−0.909550	+	0.415594i	$0.863574\pi$
$192$	−217.874	+	74.4275i	−1.13476	+	0.387643i
$193$	−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	$-0.460897\pi$
$194$	−3.46736	+	106.969i	−0.0178730	+	0.551388i
$195$	−124.478	+	71.8672i	−0.638346	+	0.368550i
$196$	72.7239	+	147.231i	0.371040	+	0.751176i
$197$	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	$-0.138044\pi$
$199$	198.448	+	114.574i	0.997225	+	0.575748i	0.0897989	+	0.995960i	$0.471378\pi$
$200$	371.312	+	265.536i	1.85656	+	1.32768i
$201$	−456.590			−2.27159
$202$	53.7856	−	28.7713i	0.266265	−	0.142432i
$203$	77.6800	+	44.8485i	0.382660	+	0.220929i
$204$	17.8861	−	275.606i	0.0876770	−	1.35101i
$205$	−26.0131	+	45.0560i	−0.126893	+	0.219785i
$206$	59.2171	−	95.2971i	0.287461	−	0.462607i
$207$	−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	$-0.556836\pi$
$211$	123.613	−	71.3683i	0.585846	−	0.338238i	0.763453	+	0.645863i	$0.223502\pi$
$212$	130.047	+	8.43970i	0.613429	+	0.0398099i
$213$	−8.08720	+	14.0074i	−0.0379681	+	0.0657627i
$214$	9.36925	−	15.0778i	0.0437815	−	0.0704570i
$215$	−112.776	−	65.1114i	−0.524541	−	0.302844i
$216$	144.893	+	14.1295i	0.670800	+	0.0654144i
$217$	−67.5183			−0.311144
$218$	−0.297438	+	9.17604i	−0.00136439	+	0.0420919i
$219$	−78.2875	−	45.1993i	−0.357477	−	0.206389i
$220$	351.870	+	234.785i	1.59941	+	1.06720i
$221$	84.6541			0.383050
$222$	−139.063	−	4.50767i	−0.626410	−	0.0203048i
$223$	79.7297	−	46.0319i	0.357532	−	0.206421i	−0.310466	−	0.950585i	$-0.600485\pi$
$223$	79.7297	−	46.0319i	0.357532	−	0.206421i	0.667998	+	0.744163i	$0.267152\pi$
$224$	31.9120	+	84.3762i	0.142464	+	0.376680i
$225$	112.454	+	194.776i	0.499796	+	0.865672i
$226$	−296.883	−	184.481i	−1.31364	−	0.816289i
$227$		−	36.7352i		−	0.161829i	−0.996721	−	0.0809145i	$-0.974216\pi$
$227$		−	36.7352i		−	0.161829i	0.996721	−	0.0809145i	$-0.0257841\pi$
$228$	241.907	−	127.402i	1.06100	−	0.558780i
$229$	45.3630			0.198092			0.0990459	−	0.995083i	$-0.468421\pi$
$229$	45.3630			0.198092			0.0990459	+	0.995083i	$0.468421\pi$
$230$	−279.203	+	449.317i	−1.21393	+	1.95355i
$231$	102.529	−	59.1950i	0.443848	−	0.256255i
$232$	−207.050	−	148.068i	−0.892458	−	0.638223i
$233$	−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	$0.969838\pi$
$234$	1.12644	−	34.7509i	0.00481383	−	0.148508i
$235$		−	381.010i		−	1.62132i
$236$	35.0957	+	23.4176i	0.148711	+	0.0992270i
$237$	146.379	−	253.535i	0.617631	−	1.06977i
$238$	−108.156	−	3.50585i	−0.454439	−	0.0147304i
$239$		−	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	−0.430637	−	0.902525i	$-0.641711\pi$
$241$	136.476	−	236.384i	0.566291	−	0.980845i	0.996928	−	0.0783202i	$-0.0249556\pi$
$242$	25.9619	+	16.1326i	0.107281	+	0.0666635i
$243$	172.634	+	99.6703i	0.710428	+	0.410166i
$244$	−427.285	−	27.7297i	−1.75117	−	0.113646i
$245$	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
$250$	493.373	+	306.579i	1.97349	+	1.22632i
$251$	206.313	+	119.115i	0.821965	+	0.474562i	0.851094	−	0.525014i	$-0.175940\pi$
$251$	206.313	+	119.115i	0.821965	+	0.474562i	−0.0291287	+	0.999576i	$0.509273\pi$
$252$	−2.87833	+	44.3521i	−0.0114220	+	0.176000i
$253$	−170.430	+	295.194i	−0.673638	+	1.16678i
$254$	−158.790	−	296.845i	−0.625157	−	1.16868i
$255$		−	625.476i		−	2.45285i
$256$	−66.8938	−	247.106i	−0.261304	−	0.965257i
$257$	−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
$260$	−70.7782	−	143.292i	−0.272224	−	0.551121i
$261$	−62.7064	−	108.611i	−0.240254	−	0.416133i
$262$	245.842	+	7.96888i	0.938330	+	0.0304156i
$263$	140.437	−	81.0814i	0.533981	−	0.308294i	−0.208655	−	0.977989i	$-0.566909\pi$
$263$	140.437	−	81.0814i	0.533981	−	0.308294i	0.742636	+	0.669695i	$0.233575\pi$
$264$	−305.891	+	138.953i	−1.15868	+	0.526339i
$265$	295.135			1.11372
$266$	−52.9622	−	93.1154i	−0.199106	−	0.350058i
$267$			173.916i			0.651370i
$268$	32.8782	−	506.618i	0.122680	−	1.89037i
$269$	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	$0.689836\pi$
$270$	329.521	+	10.6813i	1.22045	+	0.0395603i
$271$	−107.762	+	62.2163i	−0.397645	+	0.229581i	−0.685467	−	0.728103i	$-0.740402\pi$
$271$	−107.762	+	62.2163i	−0.397645	+	0.229581i	0.287822	+	0.957684i	$0.407069\pi$
$272$	304.516	+	39.6918i	1.11955	+	0.145926i
$273$	−44.7294			−0.163844
$274$	−144.087	+	77.0759i	−0.525867	+	0.281299i
$275$	576.888	+	333.067i	2.09778	+	1.21115i
$276$	−186.072	−	376.706i	−0.674174	−	1.36488i
$277$	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
$280$	84.4940	+	186.005i	0.301764	+	0.664302i
$281$	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	$-0.0203772\pi$
$282$	257.033	+	159.719i	0.911464	+	0.566378i
$283$	−342.914	+	197.981i	−1.21171	+	0.699581i	−0.963132	−	0.269031i	$-0.913297\pi$
$283$	−342.914	+	197.981i	−1.21171	+	0.699581i	−0.248578	+	0.968612i	$0.579963\pi$
$284$	−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
$288$	20.3457	−	124.477i	0.0706446	−	0.432213i
$289$	−39.6907	+	68.7463i	−0.137338	+	0.237876i
$290$	−489.636	−	304.257i	−1.68840	−	1.04916i
$291$	−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	$0.783254\pi$
$294$	−295.216	−	9.56930i	−1.00414	−	0.0325486i
$295$	82.7486	+	47.7749i	0.280504	+	0.161949i
$296$	15.0152	−	153.975i	0.0507272	−	0.520187i
$297$	212.438			0.715280
$298$	4.28138	−	132.082i	0.0143670	−	0.443228i
$299$	111.529	−	64.3910i	0.373005	−	0.215355i
$300$	−736.183	+	363.634i	−2.45394	+	1.21211i
$301$	−20.2624	−	35.0954i	−0.0673168	−	0.116596i
$302$	13.3341	−	21.4584i	0.0441528	−	0.0710544i
$303$			109.717i			0.362102i
$304$	123.942	+	277.587i	0.407704	+	0.913114i
$305$	−969.703			−3.17935
$306$	128.511	+	79.8562i	0.419972	+	0.260968i
$307$	306.496	−	176.956i	0.998358	−	0.576403i	0.0905962	−	0.995888i	$-0.471123\pi$
$307$	306.496	−	176.956i	0.998358	−	0.576403i	0.907762	+	0.419485i	$0.137789\pi$
$308$	58.2981	+	118.025i	0.189279	+	0.383199i
$309$	100.905	+	174.773i	0.326555	+	0.565610i
$310$	433.701	+	14.0582i	1.39904	+	0.0453491i
$311$			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	0.231222	+	0.972901i	$0.425728\pi$
$313$	−227.534	+	394.101i	−0.726946	+	1.25911i	−0.958168	+	0.286206i	$0.907606\pi$
$314$	2.91798	−	90.0206i	0.00929293	−	0.286690i
$315$			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	$0.773768\pi$
$318$	−123.720	+	199.101i	−0.389057	+	0.626104i
$319$	−321.683	−	185.724i	−1.00841	−	0.582206i
$320$	−187.417	−	548.632i	−0.585679	−	1.71448i
$321$	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
$326$	−85.2542	+	137.198i	−0.261516	+	0.420854i
$327$	−14.3013	−	8.25689i	−0.0437350	−	0.0252504i
$328$	41.8318	−	19.0024i	0.127536	−	0.0579342i
$329$	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	$0.859807\pi$
$332$	−498.103	+	246.036i	−1.50031	+	0.741071i
$333$	38.1111	−	66.0104i	0.114448	−	0.198229i
$334$	178.787	+	334.228i	0.535289	+	1.00068i
$335$		−	1149.75i		−	3.43208i
$336$	−160.900	−	20.9723i	−0.478869	−	0.0624176i
$337$	−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	$0.870549\pi$
$338$	9.68989	−	298.936i	0.0286683	−	0.884426i
$339$	544.478	−	314.355i	1.60613	−	0.927300i
$340$	694.009	+	45.0393i	2.04120	+	0.132469i
$341$	279.602			0.819948
$342$	−0.966261	+	149.775i	−0.00282533	+	0.437939i
$343$			253.863i			0.740126i
$344$	47.5635	+	104.706i	0.138266	+	0.304378i
$345$	−475.760	−	824.041i	−1.37901	−	2.38852i
$346$	−8.60664	+	265.518i	−0.0248747	+	0.767392i
$347$	−155.605	+	89.8386i	−0.448429	+	0.258901i	−0.707167	−	0.707047i	$-0.750027\pi$
$347$	−155.605	+	89.8386i	−0.448429	+	0.258901i	0.258737	+	0.965948i	$0.416694\pi$
$348$	410.509	−	202.769i	1.17962	−	0.582670i
$349$	−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
$352$	−132.152	−	349.413i	−0.375431	−	0.992651i
$353$	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
$356$	−192.972	−	12.5233i	−0.542055	−	0.0351779i
$357$	97.3225	−	168.567i	0.272612	−	0.472178i
$358$	−75.1662	+	120.964i	−0.209961	+	0.337888i
$359$	−409.552	+	236.455i	−1.14081	+	0.658649i	−0.946632	−	0.322316i	$-0.895539\pi$
$359$	−409.552	+	236.455i	−1.14081	+	0.658649i	−0.194182	+	0.980966i	$0.562205\pi$
$360$	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
$364$	3.22088	−	49.6304i	0.00884858	−	0.136347i
$365$	113.817	−	197.137i	0.311828	−	0.540101i
$366$	406.498	−	654.170i	1.11065	−	1.78735i
$367$	48.5847	+	28.0504i	0.132383	+	0.0764316i	0.564729	−	0.825276i	$-0.308981\pi$
$367$	48.5847	+	28.0504i	0.132383	+	0.0764316i	−0.432346	+	0.901708i	$0.642314\pi$
$368$	431.380	−	179.334i	1.17223	−	0.487321i
$369$	22.6370			0.0613468
$370$	11.3508	−	350.177i	0.0306779	−	0.946424i
$371$	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	$0.729038\pi$
$374$	447.890	+	14.5182i	1.19757	+	0.0388187i
$375$	−904.838	+	522.408i	−2.41290	+	1.39309i
$376$	−195.727	+	273.695i	−0.520552	+	0.727911i
$377$	70.1691	+	121.536i	0.186125	+	0.322378i
$378$	87.1448	+	54.1512i	0.230542	+	0.143257i
$379$		−	401.210i		−	1.05860i	−0.848434	−	0.529301i	$-0.822454\pi$
$379$		−	401.210i		−	1.05860i	0.848434	−	0.529301i	$-0.177546\pi$
$380$	320.813	+	609.150i	0.844244	+	1.60303i
$381$	605.533			1.58933
$382$	167.582	−	269.687i	0.438696	−	0.705987i
$383$	−74.9428	+	43.2682i	−0.195673	+	0.112972i	−0.594636	−	0.803995i	$-0.702704\pi$
$383$	−74.9428	+	43.2682i	−0.195673	+	0.112972i	0.398963	+	0.916967i	$0.369370\pi$
$384$	448.677	+	103.552i	1.16843	+	0.269667i
$385$	149.060	+	258.179i	0.387169	+	0.670596i
$386$	−19.9645	+	615.911i	−0.0517215	+	1.59562i
$387$			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	$-0.117621\pi$
$390$	287.318	+	9.31329i	0.736712	+	0.0238802i
$391$			560.409i			1.43327i
$392$	31.8757	−	326.873i	0.0813157	−	0.833861i
$393$	−221.217	+	383.158i	−0.562892	+	0.974958i
$394$	−75.2419	−	46.7549i	−0.190969	−	0.118667i
$395$	638.431	+	368.598i	1.61628	+	0.933160i
$396$	11.9196	−	183.668i	0.0300999	−	0.463808i
$397$	−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	$0.725318\pi$
$402$	775.629	+	481.971i	1.92943	+	1.19893i
$403$	−91.4849	−	52.8188i	−0.227010	−	0.131064i
$404$	−121.739	−	7.90051i	−0.301333	−	0.0195557i
$405$	−457.187	+	791.871i	−1.12886	+	1.95524i
$406$	−84.6167	−	158.184i	−0.208416	−	0.389617i
$407$		−	225.755i		−	0.554681i
$408$	−321.311	+	449.304i	−0.787527	+	1.10124i
$409$	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
$412$	−201.189	+	99.3765i	−0.488323	+	0.241205i
$413$	14.8673	+	25.7510i	0.0359984	+	0.0623510i
$414$	230.051	+	7.45700i	0.555678	+	0.0180121i
$415$	−1089.60	+	629.079i	−2.62553	+	1.51585i
$416$	−22.7670	+	139.291i	−0.0547284	+	0.334835i
$417$	68.9990			0.165465
$418$	219.324	+	385.603i	0.524697	+	0.922496i
$419$		−	248.914i		−	0.594068i	−0.954867	−	0.297034i	$-0.904003\pi$
$419$		−	248.914i		−	0.594068i	0.954867	−	0.297034i	$-0.0959974\pi$
$420$	−366.700	−	23.7978i	−0.873094	−	0.0566615i
$421$	−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	$0.959834\pi$
$422$	−285.323	−	9.24864i	−0.676121	−	0.0219162i
$423$	−143.570	+	82.8901i	−0.339409	+	0.195958i
$424$	−212.008	−	151.613i	−0.500018	−	0.357578i
$425$	1095.19			2.57692
$426$	28.5242	−	15.2583i	0.0669582	−	0.0358176i
$427$	−261.338	−	150.883i	−0.612032	−	0.353357i
$428$	−31.8319	+	15.7232i	−0.0743736	+	0.0367365i
$429$	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	$-0.514043\pi$
$431$	−401.407	−	231.752i	−0.931338	−	0.537708i	−0.887235	+	0.461319i	$0.847377\pi$
$432$	−231.221	−	176.950i	−0.535233	−	0.409606i
$433$	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	$0.0626679\pi$
$434$	114.696	+	71.2715i	0.264277	+	0.164220i
$435$	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	$-0.318068\pi$
$439$	675.968	−	390.271i	1.53979	−	0.888999i	0.998850	−	0.0479384i	$-0.0152651\pi$
$440$	−349.901	−	770.270i	−0.795230	−	1.75061i
$441$	80.9058	−	140.133i	0.183460	−	0.317762i
$442$	−143.806	−	89.3599i	−0.325352	−	0.202172i
$443$	−563.843	−	325.535i	−1.27278	−	0.734842i	−0.297273	−	0.954792i	$-0.596077\pi$
$443$	−563.843	−	325.535i	−1.27278	−	0.734842i	−0.975511	+	0.219950i	$0.929411\pi$
$444$	231.474	+	154.451i	0.521338	+	0.347862i
$445$	−437.940			−0.984135
$446$	−184.031	−	5.96529i	−0.412626	−	0.0133751i
$447$	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	$0.439241\pi$
$450$	14.5730	−	449.580i	0.0323843	−	0.999067i
$451$	58.0637	−	33.5231i	0.128744	−	0.0743306i
$452$	309.592	+	626.773i	0.684937	+	1.38667i
$453$	22.7213	+	39.3544i	0.0501574	+	0.0868751i
$454$	−38.7773	+	62.4037i	−0.0854125	+	0.137453i
$455$		−	112.634i		−	0.247547i
$456$	−545.422	−	38.9315i	−1.19610	−	0.0853761i
$457$	131.115			0.286903			0.143451	−	0.989657i	$-0.454180\pi$
$457$	131.115			0.286903			0.143451	+	0.989657i	$0.454180\pi$
$458$	−77.0602	−	47.8847i	−0.168254	−	0.104552i
$459$	302.476	−	174.635i	0.658990	−	0.380468i
$460$	948.589	−	468.551i	2.06215	−	1.01859i
$461$	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	$0.804718\pi$
$462$	−236.656	−	7.67110i	−0.512242	−	0.0166041i
$463$			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
$466$	−12.5554	+	387.338i	−0.0269429	+	0.831197i
$467$		−	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
$470$	−402.190	+	647.239i	−0.855724	+	1.37710i
$471$	140.302	+	81.0033i	0.297881	+	0.171982i
$472$	−34.8993	−	76.8271i	−0.0739393	−	0.162769i
$473$	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
$478$	−181.958	+	292.823i	−0.380666	+	0.612600i
$479$	428.067	+	247.144i	0.893668	+	0.515959i	0.875140	−	0.483869i	$-0.160769\pi$
$479$	428.067	+	247.144i	0.893668	+	0.515959i	0.0185273	+	0.999828i	$0.494102\pi$
$480$	1029.17	+	168.216i	2.14410	+	0.350451i
$481$	−42.6467	+	73.8663i	−0.0886626	+	0.153568i
$482$	−481.362	+	257.493i	−0.998677	+	0.534217i
$483$		−	296.108i		−	0.613061i
$484$	−27.0732	−	54.8102i	−0.0559364	−	0.113244i
$485$	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	$0.646946\pi$
$488$	696.576	+	498.143i	1.42741	+	1.02078i
$489$	−145.273	−	251.619i	−0.297081	−	0.514559i
$490$	24.0966	−	743.388i	0.0491768	−	1.51712i
$491$	−31.5500	+	18.2154i	−0.0642565	+	0.0370985i	−0.531784	−	0.846880i	$-0.678478\pi$
$491$	−31.5500	+	18.2154i	−0.0642565	+	0.0370985i	0.467528	+	0.883979i	$0.345145\pi$
$492$	−5.35205	+	82.4695i	−0.0108782	+	0.167621i
$493$	−610.697			−1.23874
$494$	1.08126	−	167.600i	0.00218878	−	0.339271i
$495$		−	416.826i		−	0.842072i
$496$	−304.323	−	232.894i	−0.613554	−	0.469544i
$497$	−6.33734	−	10.9766i	−0.0127512	−	0.0220857i
$498$	32.3744	−	998.760i	0.0650088	−	2.00554i
$499$	−61.2620	+	35.3696i	−0.122769	+	0.0708810i	−0.560127	−	0.828407i	$-0.689248\pi$
$499$	−61.2620	+	35.3696i	−0.122769	+	0.0708810i	0.437358	+	0.899288i	$0.355914\pi$
$500$	−514.493	−	1041.60i	−1.02899	−	2.08320i
$501$	−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	$-0.420837\pi$
$503$	−236.493	−	136.539i	−0.470166	−	0.271450i	−0.716309	+	0.697783i	$0.754170\pi$
$504$	51.7071	−	72.3045i	0.102593	−	0.143461i
$505$	−276.280			−0.547089
$506$	601.122	−	321.555i	1.18799	−	0.635484i
$507$	465.907	+	268.992i	0.918950	+	0.530556i
$508$	−43.6033	+	671.881i	−0.0858333	+	1.32260i
$509$	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	$0.00982285\pi$
$510$	−660.245	+	1062.52i	−1.29460	+	2.08338i
$511$	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
$516$	−206.423	−	13.3963i	−0.400045	−	0.0259619i
$517$	−245.504	+	425.225i	−0.474863	+	0.822486i
$518$	57.5457	−	92.6075i	0.111092	−	0.178779i
$519$	−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	$0.458116\pi$
$522$	−8.12614	+	250.694i	−0.0155673	+	0.480257i
$523$	22.0583	+	12.7354i	0.0421764	+	0.0243506i	0.520940	−	0.853593i	$-0.325582\pi$
$523$	22.0583	+	12.7354i	0.0421764	+	0.0243506i	−0.478764	+	0.877944i	$0.658915\pi$
$524$	−409.211	−	273.046i	−0.780938	−	0.521080i
$525$	−578.675			−1.10224
$526$	−324.155	−	10.5074i	−0.616265	−	0.0199760i
$527$	398.106	−	229.847i	0.755420	−	0.436142i
$528$	666.309	+	86.8491i	1.26195	+	0.164487i
$529$	161.768	+	280.191i	0.305800	+	0.529661i
$530$	−501.360	−	311.542i	−0.945961	−	0.587815i
$531$		−	41.5744i		−	0.0782946i
$532$	−8.32239	+	214.085i	−0.0156436	+	0.402416i
$533$	−25.3310			−0.0475253
$534$	183.584	−	295.438i	0.343789	−	0.553255i
$535$	−69.6321	+	40.2021i	−0.130153	+	0.0751441i
$536$	−590.632	+	825.909i	−1.10193	+	1.54087i
$537$	−128.083	−	221.846i	−0.238515	−	0.413121i
$538$	15.1883	−	468.562i	0.0282309	−	0.870933i
$539$		−	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	$-0.0285977\pi$
$542$	248.735	+	8.06263i	0.458920	+	0.0148757i
$543$			534.949i			0.985172i
$544$	−475.397	−	388.870i	−0.873892	−	0.714835i
$545$	20.7918	−	36.0125i	0.0381501	−	0.0660779i
$546$	75.9838	+	47.2159i	0.139165	+	0.0864760i
$547$	765.593	+	442.015i	1.39962	+	0.808072i	0.994353	−	0.106125i	$-0.0338445\pi$
$547$	765.593	+	442.015i	1.39962	+	0.808072i	0.405269	+	0.914197i	$0.367178\pi$
$548$	326.128	+	21.1649i	0.595124	+	0.0386220i
$549$	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
$554$	−409.120	−	254.225i	−0.738484	−	0.458890i
$555$	545.769	+	315.100i	0.983368	+	0.567748i
$556$	−4.96849	+	76.5592i	−0.00893613	+	0.137696i
$557$	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
$560$	52.8107	−	405.165i	0.0943048	−	0.723509i
$561$	−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	$0.951965\pi$
$564$	−268.036	−	542.642i	−0.475241	−	0.962131i
$565$	791.582	+	1371.06i	1.40103	+	2.42666i
$566$	791.510	+	25.6565i	1.39843	+	0.0453294i
$567$	−246.426	+	142.274i	−0.434615	+	0.250925i
$568$	14.8762	+	32.7483i	0.0261904	+	0.0576555i
$569$	−403.875			−0.709798			−0.354899	−	0.934905i	$-0.615485\pi$
$569$	−403.875			−0.709798			−0.354899	+	0.934905i	$0.615485\pi$
$570$	−1238.33	−	7.98898i	−2.17251	−	0.0140158i
$571$			175.870i			0.308003i	0.988071	+	0.154001i	$0.0492160\pi$
$571$			175.870i			0.308003i	−0.988071	+	0.154001i	$0.950784\pi$
$572$	−13.3381	+	205.526i	−0.0233184	+	0.359311i
$573$	285.559	+	494.602i	0.498357	+	0.863180i
$574$	32.3636	+	1.04905i	0.0563826	+	0.00182762i
$575$	1442.87	−	833.042i	2.50934	−	1.44877i
$576$	−165.959	+	189.978i	−0.288123	+	0.329823i
$577$	−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
$580$	510.596	+	1033.71i	0.880338	+	1.78226i
$581$	−391.532			−0.673894
$582$	181.605	+	339.496i	0.312036	+	0.583327i
$583$	−329.385	−	190.171i	−0.564983	−	0.326193i
$584$	−183.030	+	83.1428i	−0.313407	+	0.142368i
$585$	−78.7413	+	136.384i	−0.134601	+	0.233135i
$586$	773.465	+	480.627i	1.31991	+	0.820182i
$587$	−643.631	+	371.601i	−1.09648	+	0.633050i	−0.935293	−	0.353874i	$-0.884864\pi$
$587$	−643.631	+	371.601i	−1.09648	+	0.633050i	−0.161182	+	0.986925i	$0.551531\pi$
$588$	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
$592$	−188.042	+	245.715i	−0.317638	+	0.415059i
$593$	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	$-0.138987\pi$
$594$	−360.878	−	224.248i	−0.607539	−	0.377521i
$595$	424.473	+	245.069i	0.713399	+	0.411881i
$596$	−146.697	+	219.854i	−0.246136	+	0.368882i
$597$	824.344			1.38081
$598$	−257.429	−	8.34445i	−0.430483	−	0.0139539i
$599$	256.016	+	147.811i	0.427405	+	0.246762i	0.698241	−	0.715863i	$-0.253967\pi$
$599$	256.016	+	147.811i	0.427405	+	0.246762i	−0.270836	+	0.962626i	$0.587300\pi$
$600$	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	$0.271625\pi$
$602$	−2.62580	+	81.0069i	−0.00436180	+	0.134563i
$603$	−433.240	+	250.132i	−0.718475	+	0.414812i
$604$	−45.3026	+	22.3770i	−0.0750043	+	0.0370480i
$605$	−69.2225	−	119.897i	−0.114417	−	0.198177i
$606$	115.816	−	186.381i	0.191116	−	0.307559i
$607$		−	370.431i		−	0.610265i	−0.952310	−	0.305133i	$-0.901299\pi$
$607$		−	370.431i		−	0.610265i	0.952310	−	0.305133i	$-0.0987008\pi$
$608$	82.4721	−	602.381i	0.135645	−	0.990758i
$609$	322.679			0.529851
$610$	1647.28	+	1023.61i	2.70045	+	1.67805i
$611$	160.656	−	92.7549i	0.262940	−	0.151808i
$612$	−134.013	−	271.311i	−0.218975	−	0.443318i
$613$	−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	$0.928271\pi$
$614$	−707.451	−	22.9317i	−1.15220	−	0.0373481i
$615$			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	$0.172544\pi$
$618$	13.0764	−	403.410i	0.0211592	−	0.652767i
$619$		−	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
$622$	536.961	−	864.123i	0.863281	−	1.38927i
$623$	−118.026	−	68.1424i	−0.189448	−	0.109378i
$624$	−201.607	−	154.287i	−0.323089	−	0.247255i
$625$	−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
$630$	106.250	−	170.987i	0.168651	−	0.271408i
$631$	−667.833	−	385.574i	−1.05837	−	0.611052i	−0.133391	−	0.991063i	$-0.542587\pi$
$631$	−667.833	−	385.574i	−1.05837	−	0.611052i	−0.924982	+	0.380011i	$0.875920\pi$
$632$	−269.259	−	592.745i	−0.426043	−	0.937888i
$633$	256.743	−	444.691i	0.405597	−	0.702514i
$634$	1055.39	−	564.554i	1.66465	−	0.890464i
$635$			1524.80i			2.40126i
$636$	420.338	−	207.624i	0.660908	−	0.326453i
$637$	−90.5345	+	156.810i	−0.142126	+	0.246170i
$638$	350.409	+	655.063i	0.549231	+	1.02674i
$639$			17.7215i			0.0277332i
$640$	−260.756	+	1129.82i	−0.407432	+	1.76535i
$641$	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	$0.822323\pi$
$642$	2.06893	−	63.8270i	0.00322263	−	0.0994191i
$643$	1034.78	−	597.433i	1.60931	−	0.929133i	0.619781	−	0.784775i	$-0.287222\pi$
$643$	1034.78	−	597.433i	1.60931	−	0.929133i	0.989525	−	0.144358i	$-0.0461118\pi$
$644$	328.553	+	21.3222i	0.510175	+	0.0331090i
$645$	−468.468			−0.726307
$646$	629.265	+	368.739i	0.974094	+	0.570804i
$647$		−	143.888i		−	0.222393i	−0.993798	−	0.111196i	$-0.964532\pi$
$647$		−	143.888i		−	0.222393i	0.993798	−	0.111196i	$-0.0354683\pi$
$648$	735.205	−	333.973i	1.13458	−	0.515390i
$649$	−61.5676	−	106.638i	−0.0948653	−	0.164312i
$650$	−16.3073	+	503.085i	−0.0250881	+	0.773976i
$651$	−210.351	+	121.446i	−0.323120	+	0.186553i
$652$	289.650	−	143.071i	0.444249	−	0.219435i
$653$	−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
$656$	−91.1203	−	11.8769i	−0.138903	−	0.0181051i
$657$	−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	$-0.522908\pi$
$659$	−640.313	−	369.685i	−0.971643	−	0.560978i	−0.899737	+	0.436433i	$0.856242\pi$
$660$	1518.55	+	98.5500i	2.30084	+	0.149318i
$661$	−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	$0.980759\pi$
$662$	297.918	−	479.436i	0.450028	−	0.724223i
$663$	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
$668$	49.0944	−	756.492i	0.0734945	−	1.13247i
$669$	165.597	−	286.822i	0.247529	−	0.428733i
$670$	−1213.66	+	1953.13i	−1.81143	+	2.91511i
$671$	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	$0.655300\pi$
$674$	−5.09435	+	157.162i	−0.00755839	+	0.233179i
$675$	−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	$0.870490\pi$
$678$	−1256.76	−	40.7373i	−1.85363	−	0.0600845i
$679$	130.644	−	75.4273i	0.192406	−	0.111086i
$680$	−1131.40	−	809.098i	−1.66382	−	1.18985i
$681$	−66.0762	−	114.447i	−0.0970282	−	0.168058i
$682$	−474.972	−	295.145i	−0.696441	−	0.432764i
$683$			903.750i			1.32321i	0.749854	+	0.661604i	$0.230124\pi$
$683$			903.750i			1.32321i	−0.749854	+	0.661604i	$0.769876\pi$
$684$	159.742	−	253.410i	0.233541	−	0.370482i
$685$	740.133			1.08049
$686$	267.975	−	431.249i	0.390634	−	0.628642i
$687$	141.327	−	81.5952i	0.205716	−	0.118770i
$688$	29.7283	−	228.076i	0.0432098	−	0.331506i
$689$	71.8491	+	124.446i	0.104280	+	0.180619i
$690$	−61.6539	+	1902.04i	−0.0893535	+	2.75658i
$691$			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
$694$	359.166	+	11.6422i	0.517530	+	0.0167755i
$695$			173.748i			0.249997i
$696$	−911.390	−	88.8761i	−1.30947	−	0.127696i
$697$	55.1153	−	95.4625i	0.0790750	−	0.136962i
$698$	158.534	+	98.5123i	0.227127	+	0.141135i
$699$	−603.687	−	348.539i	−0.863643	−	0.498625i
$700$	41.6693	−	642.080i	0.0595276	−	0.917257i
$701$	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
$706$	−806.156	−	500.941i	−1.14186	−	0.709548i
$707$	−74.4583	−	42.9885i	−0.105316	−	0.0608041i
$708$	151.461	+	9.82944i	0.213928	+	0.0138834i
$709$	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
$712$	314.590	+	224.973i	0.441840	+	0.315973i
$713$	349.660	−	605.629i	0.490407	−	0.849410i
$714$	−343.264	+	183.620i	−0.480762	+	0.257171i
$715$			466.432i			0.652353i
$716$	255.376	−	126.142i	0.356671	−	0.176176i
$717$	−310.056	−	537.032i	−0.432435	−	0.748999i
$718$	945.324	+	30.6423i	1.31661	+	0.0426773i
$719$	−758.635	+	437.998i	−1.05513	+	0.609177i	−0.924080	−	0.382200i	$-0.875167\pi$
$719$	−758.635	+	437.998i	−1.05513	+	0.609177i	−0.131045	+	0.991376i	$0.541833\pi$
$720$	−347.193	+	453.679i	−0.482213	+	0.630109i
$721$	−158.144			−0.219340
$722$	14.0785	+	721.863i	0.0194993	+	0.999810i
$723$		−	981.928i		−	1.35813i
$724$	−593.563	−	38.5207i	−0.819838	−	0.0532053i
$725$	907.794	+	1572.34i	1.25213	+	2.16875i
$726$	109.901	+	3.56241i	0.151379	+	0.00490690i
$727$	632.345	−	365.085i	0.869801	−	0.502180i	0.00251881	−	0.999997i	$-0.499198\pi$
$727$	632.345	−	365.085i	0.869801	−	0.502180i	0.867282	+	0.497817i	$0.165865\pi$
$728$	−57.8608	+	80.9094i	−0.0794791	+	0.111139i
$729$	−191.328			−0.262453
$730$	−401.442	+	214.741i	−0.549920	+	0.294166i
$731$	238.945	+	137.955i	0.326874	+	0.188721i
$732$	−1381.07	+	682.174i	−1.88671	+	0.931931i
$733$	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
$736$	−922.107	−	150.717i	−1.25286	−	0.204779i
$737$	−740.840	+	1283.17i	−1.00521	+	1.74107i
$738$	−38.4544	−	23.8953i	−0.0521062	−	0.0323785i
$739$	−514.152	+	296.846i	−0.695741	+	0.401686i	−0.805759	−	0.592243i	$-0.798242\pi$
$739$	−514.152	+	296.846i	−0.695741	+	0.401686i	0.110018	+	0.993930i	$0.464909\pi$
$740$	−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	$-0.678712\pi$
$743$	−48.6881	+	28.1101i	−0.0655291	+	0.0378332i	0.466877	+	0.884322i	$0.345379\pi$
$744$	627.575	−	285.081i	0.843515	−	0.383173i
$745$	−299.282	+	518.371i	−0.401720	+	0.695800i
$746$	835.180	+	518.976i	1.11954	+	0.695678i
$747$	474.091	+	273.717i	0.634660	+	0.366421i
$748$	−745.526	−	497.451i	−0.996692	−	0.665041i
$749$	−25.0214			−0.0334064
$750$	2088.54	+	67.6990i	2.78472	+	0.0902654i
$751$	−119.216	−	68.8295i	−0.158743	−	0.0916504i	0.418524	−	0.908206i	$-0.362548\pi$
$751$	−119.216	−	68.8295i	−0.158743	−	0.0916504i	−0.577267	+	0.816555i	$0.695881\pi$
$752$	621.400	−	258.330i	0.826330	−	0.343523i
$753$	857.016			1.13814
$754$	9.09323	−	280.529i	0.0120600	−	0.372054i
$755$	−99.0990	+	57.2149i	−0.131257	+	0.0757813i
$756$	−90.8752	−	183.978i	−0.120205	−	0.243357i
$757$	−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	$-0.370671\pi$
$758$	−423.513	+	681.554i	−0.558725	+	0.899148i
$759$			1226.22i			1.61558i
$760$	98.0341	−	1373.44i	0.128992	−	1.80715i
$761$	−1082.43			−1.42238			−0.711190	−	0.703000i	$-0.751844\pi$
$761$	−1082.43			−1.42238			−0.711190	+	0.703000i	$0.751844\pi$
$762$	−1028.65	−	639.194i	−1.34993	−	0.838838i
$763$	11.2069	−	6.47031i	0.0146879	−	0.00848009i
$764$	−569.358	+	281.232i	−0.745233	+	0.368104i
$765$	−342.651	−	593.490i	−0.447910	−	0.775803i
$766$	172.982	+	5.60714i	0.225825	+	0.00732003i
$767$			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	$0.936937\pi$
$770$	19.3167	−	595.927i	0.0250867	−	0.773931i
$771$			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	$-0.0561179\pi$
$774$	59.8106	−	96.2524i	0.0772747	−	0.124357i
$775$	−1183.56	−	683.329i	−1.52718	−	0.881715i
$776$	−389.772	+	177.057i	−0.502283	+	0.228166i
$777$	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
$782$	591.562	−	951.992i	0.756473	−	1.21738i
$783$	501.441	+	289.507i	0.640409	+	0.369741i
$784$	−399.193	+	521.627i	−0.509175	+	0.665340i
$785$	−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	$-0.183291\pi$
$788$	78.4628	+	158.849i	0.0995721	+	0.201585i
$789$	291.685	−	505.213i	0.369689	−	0.640321i
$790$	−695.443	−	1300.08i	−0.880307	−	1.64566i
$791$			492.673i			0.622848i
$792$	−214.126	+	299.422i	−0.270361	+	0.378059i
$793$	−236.069	−	408.884i	−0.297691	−	0.515616i
$794$	−11.1005	+	342.454i	−0.0139805	+	0.431302i
$795$	919.485	−	530.865i	1.15659	−	0.667755i
$796$	−59.3595	+	914.667i	−0.0745722	+	1.14908i
$797$	501.545			0.629292			0.314646	−	0.949209i	$-0.398114\pi$
$797$	501.545			0.629292			0.314646	+	0.949209i	$0.398114\pi$
$798$	−332.490	−	194.834i	−0.416654	−	0.244153i
$799$			807.266i			1.01035i
$800$	−294.542	+	1802.04i	−0.368177	+	2.25255i
$801$	95.2754	+	165.022i	0.118946	+	0.206020i
$802$	17.2975	−	533.634i	0.0215680	−	0.665379i
$803$	−254.051	+	146.676i	−0.316377	+	0.182660i
$804$	−808.832	−	1637.49i	−1.00601	−	2.03668i
$805$	745.636			0.926256
$806$	99.6544	+	186.296i	0.123641	+	0.231137i
$807$	730.279	+	421.627i	0.904931	+	0.522462i
$808$	198.463	+	141.927i	0.245623	+	0.175652i
$809$	−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	$-0.983384\pi$
$811$	−1251.49	−	722.548i	−1.54314	−	0.890934i	−0.544506	−	0.838757i	$-0.683283\pi$
$812$	−23.2355	+	358.035i	−0.0286152	+	0.440930i
$813$	−223.819	+	387.666i	−0.275300	+	0.476834i
$814$	−238.305	+	383.500i	−0.292758	+	0.471130i
$815$	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
$820$	−207.668	−	13.4771i	−0.253253	−	0.0164355i
$821$	−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	$0.986310\pi$
$822$	−310.262	+	499.300i	−0.377448	+	0.607421i
$823$	712.755	+	411.509i	0.866045	+	0.500011i	0.866032	−	0.499989i	$-0.166663\pi$
$823$	712.755	+	411.509i	0.866045	+	0.500011i	1.29516e−5		1.00000i	$0.499996\pi$
$824$	446.670	+	43.5579i	0.542075	+	0.0528616i
$825$	2396.37			2.90469
$826$	1.92666	−	59.4381i	0.00233252	−	0.0719590i
$827$	−109.874	−	63.4355i	−0.132858	−	0.0767056i	0.432098	−	0.901827i	$-0.357773\pi$
$827$	−109.874	−	63.4355i	−0.132858	−	0.0767056i	−0.564956	+	0.825121i	$0.691107\pi$
$828$	−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	$0.350863\pi$
$830$	2514.99	+	81.5225i	3.03011	+	0.0982198i
$831$	750.320	−	433.197i	0.902912	−	0.521296i
$832$	185.710	−	212.588i	0.223209	−	0.255514i
$833$	−393.971	−	682.377i	−0.472954	−	0.819180i
$834$	−117.212	−	72.8346i	−0.140542	−	0.0873317i
$835$		−	1716.82i		−	2.05608i
$836$	34.4641	−	886.557i	0.0412250	−	1.06047i
$837$	−435.845			−0.520722
$838$	−262.751	+	422.842i	−0.313546	+	0.504585i
$839$	829.460	−	478.889i	0.988629	−	0.570785i	0.0837647	−	0.996486i	$-0.473306\pi$
$839$	829.460	−	478.889i	0.988629	−	0.570785i	0.904864	+	0.425700i	$0.139972\pi$
$840$	597.808	+	427.511i	0.711676	+	0.508941i
$841$	−85.7019	−	148.440i	−0.101905	−	0.176504i
$842$	−21.1156	+	651.423i	−0.0250779	+	0.773662i
$843$		−	1120.82i		−	1.32956i
$844$	474.928	+	316.895i	0.562711	+	0.375468i
$845$	−677.353	+	1173.21i	−0.801601	+	1.38841i
$846$	331.386	+	10.7418i	0.391710	+	0.0126971i
$847$		−	43.0834i		−	0.0508659i
$848$	200.105	+	481.345i	0.235973	+	0.567623i
$849$	−712.225	+	1233.61i	−0.838899	+	1.45301i
$850$	−1860.45	−	1156.07i	−2.18876	−	1.36008i
$851$	−488.994	−	282.321i	−0.574611	−	0.331752i
$852$	−64.5618	−	4.18989i	−0.0757768	−	0.00491771i
$853$	−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	$0.748264\pi$
$858$	−314.659	−	195.527i	−0.366736	−	0.227887i
$859$	838.651	+	484.196i	0.976311	+	0.563674i	0.901154	−	0.433498i	$-0.142721\pi$
$859$	838.651	+	484.196i	0.976311	+	0.563674i	0.0751568	+	0.997172i	$0.476054\pi$
$860$	33.7335	−	519.798i	0.0392250	−	0.604416i
$861$	−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	$0.900391\pi$
$864$	205.999	+	544.666i	0.238424	+	0.630401i
$865$	601.631	−	1042.05i	0.695527	−	1.20469i
$866$	−490.147	+	262.192i	−0.565990	+	0.302762i
$867$			285.569i			0.329376i
$868$	−119.606	−	242.144i	−0.137795	−	0.278968i
$869$	−475.013	−	822.747i	−0.546620	−	0.946774i
$870$	−2072.72	−	67.1863i	−2.38244	−	0.0772257i
$871$	484.800	−	279.900i	0.556602	−	0.321354i
$872$	−33.4354	+	15.1883i	−0.0383434	+	0.0174178i
$873$	−210.922			−0.241606
$874$	1109.51	+	7.15791i	1.26946	+	0.00818983i
$875$		−	818.745i		−	0.935709i
$876$	23.4173	−	360.835i	0.0267320	−	0.411912i
$877$	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	$0.669833\pi$
$878$	−1560.26	−	50.5753i	−1.77706	−	0.0576028i
$879$	−1418.52	+	818.985i	−1.61379	+	0.931723i
$880$	−218.696	+	1677.84i	−0.248518	+	1.90664i
$881$	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	$0.0677110\pi$
$883$	1456.09	+	840.674i	1.64903	+	0.952065i	0.671565	+	0.740946i	$0.265622\pi$
$884$	149.961	+	303.599i	0.169640	+	0.343438i
$885$	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	$-0.191217\pi$
$887$	663.364	+	382.993i	0.747874	+	0.431785i	−0.0770515	+	0.997027i	$0.524551\pi$
$888$	−230.179	−	506.714i	−0.259210	−	0.570624i
$889$	−237.256	+	410.939i	−0.266879	+	0.462248i
$890$	743.948	+	462.285i	0.835897	+	0.519421i
$891$	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
$896$	−246.072	+	263.917i	−0.274634	+	0.294550i
$897$	231.643	−	401.217i	0.258241	−	0.447287i
$898$	−289.415	−	179.841i	−0.322289	−	0.200268i
$899$	659.975	+	381.037i	0.734121	+	0.423845i
$900$	−499.328	+	748.339i	−0.554809	+	0.831487i
$901$	−625.319			−0.694028
$902$	−134.022	−	4.34427i	−0.148583	−	0.00481626i
$903$	−126.254	−	72.8925i	−0.139816	−	0.0807226i
$904$	135.698	−	1391.53i	0.150108	−	1.53930i
$905$	−1347.06			−1.48847
$906$	2.94446	−	90.8374i	0.00324995	−	0.100262i
$907$	285.807	−	165.011i	0.315113	−	0.181930i	−0.334099	−	0.942538i	$-0.608432\pi$
$907$	285.807	−	165.011i	0.315113	−	0.181930i	0.649212	+	0.760608i	$0.275099\pi$
$908$	131.745	−	65.0750i	0.145094	−	0.0716685i
$909$	60.1057	+	104.106i	0.0661229	+	0.114528i
$910$	−118.895	+	191.336i	−0.130654	+	0.210260i
$911$		−	1064.70i		−	1.16871i	−0.811497	−	0.584357i	$-0.801347\pi$
$911$		−	1064.70i		−	1.16871i	0.811497	−	0.584357i	$-0.198653\pi$
$912$	885.437	+	641.877i	0.970874	+	0.703812i
$913$	1621.39			1.77589
$914$	−222.730	−	138.403i	−0.243687	−	0.151426i
$915$	−3021.08	+	1744.22i	−3.30173	+	1.90625i
$916$	80.3589	+	162.688i	0.0877280	+	0.177607i
$917$	−173.351	−	300.253i	−0.189041	−	0.327429i
$918$	−698.172	−	22.6310i	−0.760536	−	0.0246525i
$919$		−	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
$922$	5.36336	−	165.461i	0.00581709	−	0.179459i
$923$		−	19.8305i		−	0.0214849i
$924$	393.920	+	262.843i	0.426320	+	0.284462i
$925$	−551.730	+	955.625i	−0.596465	+	1.03311i
$926$	223.292	−	359.340i	0.241136	−	0.388056i
$927$	191.491	+	110.557i	0.206570	+	0.119263i
$928$	164.242	−	1004.85i	0.176985	−	1.08281i
$929$	−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
$934$	−551.551	+	887.602i	−0.590525	+	0.950324i
$935$	−1757.80	−	1014.87i	−1.88000	−	1.08542i
$936$	126.624	−	57.5201i	0.135282	−	0.0614531i
$937$	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
$940$	1366.44	−	674.945i	1.45366	−	0.718027i
$941$	−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
$944$	−21.8129	+	167.349i	−0.0231069	+	0.177276i
$945$	−232.355	−	402.451i	−0.245878	−	0.425874i
$946$	10.8738	−	335.460i	0.0114945	−	0.354609i
$947$	−1324.53	+	764.719i	−1.39866	+	0.807517i	−0.994252	−	0.107061i	$-0.965856\pi$
$947$	−1324.53	+	764.719i	−1.39866	+	0.807517i	−0.404408	+	0.914579i	$0.632522\pi$
$948$	1168.57	+	75.8371i	1.23267	+	0.0799970i
$949$	110.833			0.116789
$950$	13.9885	−	2168.28i	0.0147247	−	2.28240i
$951$			2152.88i			2.26381i
$952$	−179.022	−	394.097i	−0.188048	−	0.413968i
$953$	−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	$0.871943\pi$
$954$	−8.32070	+	256.696i	−0.00872191	+	0.269074i
$955$	−1245.47	+	719.070i	−1.30415	+	0.752953i
$956$	618.201	−	305.358i	0.646654	−	0.319412i
$957$	−1336.26			−1.39630
$958$	−466.293	−	871.698i	−0.486736	−	0.909914i
$959$	199.468	+	115.163i	0.207996	+	0.120086i
$960$	−1570.73	−	1372.14i	−1.63617	−	1.42931i
$961$	387.360			0.403080
$962$	150.418	−	80.4625i	0.156360	−	0.0836409i
$963$	30.2974	+	17.4922i	0.0314615	+	0.0181643i
$964$	1089.52	+	70.7068i	1.13021	+	0.0733473i
$965$	1395.58	−	2417.21i	1.44620	−	2.50489i
$966$	−312.569	+	503.012i	−0.323570	+	0.520717i
$967$	1289.91	−	744.731i	1.33393	−	0.770146i	0.348032	−	0.937483i	$-0.386850\pi$
$967$	1289.91	−	744.731i	1.33393	−	0.770146i	0.985900	+	0.167337i	$0.0535166\pi$
$968$	−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	$-0.866636\pi$
$971$	−988.417	+	570.663i	−1.01794	+	0.587706i	−0.104432	+	0.994532i	$0.533302\pi$
$972$	−51.6381	+	795.689i	−0.0531256	+	0.818610i
$973$	−27.0347	+	46.8255i	−0.0277849	+	0.0481249i
$974$	920.519	−	1481.38i	0.945091	−	1.52092i
$975$	−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	$0.195010\pi$
$978$	−18.8259	+	580.785i	−0.0192494	+	0.593850i
$979$	488.762	+	282.187i	0.499246	+	0.288240i
$980$	−825.646	+	1237.39i	−0.842496	+	1.26264i
$981$	−18.0933			−0.0184438
$982$	72.8233	+	2.36054i	0.0741581	+	0.00240380i
$983$	−455.988	+	263.265i	−0.463874	+	0.267818i	−0.713672	−	0.700480i	$-0.752969\pi$
$983$	−455.988	+	263.265i	−0.463874	+	0.267818i	0.249798	+	0.968298i	$0.419636\pi$
$984$	96.1457	−	134.445i	0.0977090	−	0.136631i
$985$	200.618	+	347.481i	0.203673	+	0.352773i
$986$	1037.42	+	644.645i	1.05215	+	0.653798i
$987$		−	426.542i		−	0.432160i
$988$	−178.753	+	283.568i	−0.180924	+	0.287012i
$989$	419.735			0.424403
$990$	−439.997	+	708.080i	−0.444441	+	0.715232i
$991$	−513.571	+	296.510i	−0.518235	+	0.299203i	−0.736212	−	0.676751i	$-0.763387\pi$
$991$	−513.571	+	296.510i	−0.518235	+	0.299203i	0.217977	+	0.975954i	$0.430054\pi$
$992$	271.127	+	716.867i	0.273313	+	0.722648i
$993$	507.651	+	879.277i	0.511230	+	0.885476i
$994$	−0.821258	+	25.3361i	−0.000826215	+	0.0254890i
$995$			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	$0.298842\pi$
$998$	141.404	+	4.58356i	0.141688	+	0.00459274i
$999$			351.908i			0.352260i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.69874 - 1.05559i) q^{2} +(3.11547 - 1.79872i) q^{3} +(1.77146 + 3.58635i) q^{4} +(4.52938 + 7.84512i) q^{5} +(-7.19109 - 0.233096i) q^{6} +2.81904i q^{7} +(0.776454 - 7.96223i) q^{8} +(1.97077 - 3.41347i) q^{9} +O(q^{10})\)	\(q+(-1.69874 - 1.05559i) q^{2} +(3.11547 - 1.79872i) q^{3} +(1.77146 + 3.58635i) q^{4} +(4.52938 + 7.84512i) q^{5} +(-7.19109 - 0.233096i) q^{6} +2.81904i q^{7} +(0.776454 - 7.96223i) q^{8} +(1.97077 - 3.41347i) q^{9} +(0.586964 - 18.1080i) q^{10} -11.6740i q^{11} +(11.9698 + 7.98681i) q^{12} +(-2.20531 + 3.81970i) q^{13} +(2.97575 - 4.78883i) q^{14} +(28.2223 + 16.2941i) q^{15} +(-9.72384 + 12.7062i) 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} +(-12.3230 + 19.8312i) q^{22} +(-25.2864 - 14.5991i) q^{23} +(-11.9028 - 26.2027i) q^{24} +(-28.5306 + 49.4164i) q^{25} +(7.77829 - 4.16080i) q^{26} +18.1975i q^{27} +(-10.1101 + 4.99383i) q^{28} +(15.9091 - 27.5555i) q^{29} +(-30.7425 - 57.4707i) q^{30} +23.9508i q^{31} +(29.9308 - 11.3202i) q^{32} +(-20.9983 - 36.3701i) q^{33} +(-1.24363 + 38.3664i) q^{34} +(-22.1157 + 12.7685i) q^{35} +(15.7330 + 1.02103i) q^{36} +19.3382 q^{37} +(-33.0309 + 18.7873i) q^{38} +15.8669i q^{39} +(65.9815 - 29.9726i) q^{40} +(2.87159 + 4.97375i) q^{41} +(0.657108 - 20.2720i) q^{42} +(-12.4494 + 7.18768i) q^{43} +(41.8672 - 20.6801i) q^{44} +35.7054 q^{45} +(27.5445 + 51.4922i) q^{46} +(-36.4249 - 21.0299i) q^{47} +(-7.43951 + 57.0761i) q^{48} +41.0530 q^{49} +(100.630 - 53.8292i) q^{50} +(-59.7960 - 34.5232i) q^{51} +(-17.6054 - 1.14255i) q^{52} +(16.2901 - 28.2152i) q^{53} +(19.2091 - 30.9129i) 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} +(-8.44182 + 130.080i) q^{60} +(-53.5230 + 92.7045i) q^{61} +(25.2822 - 40.6862i) q^{62} +(9.62270 + 5.55567i) q^{63} +(-62.7942 - 12.3646i) q^{64} -39.9547 q^{65} +(-2.72117 + 83.9490i) q^{66} +(-109.917 - 63.4605i) q^{67} +(42.6117 - 63.8619i) q^{68} -105.039 q^{69} +(51.0472 + 1.65467i) q^{70} +(-3.89373 + 2.24805i) q^{71} +(-25.6486 - 18.3421i) q^{72} +(-12.5643 - 21.7620i) q^{73} +(-32.8507 - 20.4132i) q^{74} +205.274i q^{75} +(75.9426 + 2.95220i) q^{76} +32.9096 q^{77} +(16.7489 - 26.9538i) q^{78} +(70.4767 - 40.6897i) q^{79} +(-143.724 - 18.7336i) q^{80} +(50.4691 + 87.4150i) q^{81} +(0.372131 - 11.4803i) q^{82} +138.888i q^{83} +(-22.5152 + 33.7433i) q^{84} +(86.9336 - 150.573i) q^{85} +(28.7356 + 0.931453i) q^{86} -114.464i q^{87} +(-92.9513 - 9.06434i) q^{88} +(-24.1722 + 41.8675i) q^{89} +(-60.6543 - 37.6902i) q^{90} +(-10.7679 - 6.21685i) q^{91} +(7.56364 - 116.548i) 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} +(-69.7385 - 43.3351i) 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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