LMFDB - Embedded newform 19.3.d.a.12.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,3,Mod(8,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("19.8");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	19.d (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:	$0.517712502285$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.6967728.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 $ x^6 - x^5 + 8x^4 + 5x^3 + 50x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			12.2
Root			$-1.13654 - 1.96854i$ of defining polynomial
Character	$\chi$	$=$	19.12
Dual form			19.3.d.a.8.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.583430 + 0.336844i) q^{2} +(2.49304 - 1.43936i) q^{3} +(-1.77307 + 3.07105i) q^{4} +(-1.55311 - 2.69006i) q^{5} +(-0.969676 + 1.67953i) q^{6} -8.15294 q^{7} -5.08374i q^{8} +(-0.356503 + 0.617481i) q^{9} +O(q^{10})$	\(q+(-0.583430 + 0.336844i) q^{2} +(2.49304 - 1.43936i) q^{3} +(-1.77307 + 3.07105i) q^{4} +(-1.55311 - 2.69006i) q^{5} +(-0.969676 + 1.67953i) q^{6} -8.15294 q^{7} -5.08374i q^{8} +(-0.356503 + 0.617481i) q^{9} +(1.81226 + 1.04631i) q^{10} +17.6991 q^{11} +10.2083i q^{12} +(5.33372 + 3.07942i) q^{13} +(4.75667 - 2.74626i) q^{14} +(-7.74391 - 4.47095i) q^{15} +(-5.37987 - 9.31820i) q^{16} +(-6.91657 - 11.9799i) q^{17} -0.480343i q^{18} +(3.11375 + 18.7431i) q^{19} +11.0151 q^{20} +(-20.3256 + 11.7350i) q^{21} +(-10.3262 + 5.96182i) q^{22} +(2.46968 - 4.27760i) q^{23} +(-7.31732 - 12.6740i) q^{24} +(7.67572 - 13.2947i) q^{25} -4.14914 q^{26} +27.9610i q^{27} +(14.4558 - 25.0381i) q^{28} +(-38.2711 - 22.0958i) q^{29} +6.02404 q^{30} +43.0049i q^{31} +(23.8881 + 13.7918i) q^{32} +(44.1245 - 25.4753i) q^{33} +(8.07067 + 4.65960i) q^{34} +(12.6624 + 21.9319i) q^{35} +(-1.26421 - 2.18968i) q^{36} -30.7849i q^{37} +(-8.13016 - 9.88645i) q^{38} +17.7296 q^{39} +(-13.6756 + 7.89559i) q^{40} +(-28.6795 + 16.5581i) q^{41} +(7.90571 - 13.6931i) q^{42} +(-15.7586 - 27.2946i) q^{43} +(-31.3818 + 54.3548i) q^{44} +2.21475 q^{45} +3.32758i q^{46} +(8.86404 - 15.3530i) q^{47} +(-26.8244 - 15.4871i) q^{48} +17.4704 q^{49} +10.3421i q^{50} +(-34.4866 - 19.9108i) q^{51} +(-18.9142 + 10.9201i) q^{52} +(14.6396 + 8.45218i) q^{53} +(-9.41847 - 16.3133i) q^{54} +(-27.4886 - 47.6116i) q^{55} +41.4474i q^{56} +(34.7408 + 42.2455i) q^{57} +29.7713 q^{58} +(20.3412 - 11.7440i) q^{59} +(27.4610 - 15.8546i) q^{60} +(-8.52643 + 14.7682i) q^{61} +(-14.4859 - 25.0903i) q^{62} +(2.90655 - 5.03429i) q^{63} +24.4562 q^{64} -19.1307i q^{65} +(-17.1624 + 29.7261i) q^{66} +(84.9924 + 49.0704i) q^{67} +49.0543 q^{68} -14.2190i q^{69} +(-14.7752 - 8.53048i) q^{70} +(-1.36156 + 0.786099i) q^{71} +(3.13911 + 1.81237i) q^{72} +(2.85534 + 4.94560i) q^{73} +(10.3697 + 17.9608i) q^{74} -44.1924i q^{75} +(-63.0820 - 23.6704i) q^{76} -144.300 q^{77} +(-10.3440 + 5.97209i) q^{78} +(41.9327 - 24.2099i) q^{79} +(-16.7110 + 28.9443i) q^{80} +(37.0373 + 64.1505i) q^{81} +(11.1550 - 19.3210i) q^{82} -74.2729 q^{83} -83.2280i q^{84} +(-21.4843 + 37.2120i) q^{85} +(18.3880 + 10.6163i) q^{86} -127.215 q^{87} -89.9776i q^{88} +(81.0798 + 46.8114i) q^{89} +(-1.29215 + 0.746024i) q^{90} +(-43.4855 - 25.1064i) q^{91} +(8.75783 + 15.1690i) q^{92} +(61.8994 + 107.213i) q^{93} +11.9432i q^{94} +(45.5841 - 37.4862i) q^{95} +79.4055 q^{96} +(-8.15700 + 4.70945i) q^{97} +(-10.1928 + 5.88480i) q^{98} +(-6.30978 + 10.9289i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 9 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 14 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 9 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 14 * q^9	$ 6 q - 3 q^{2} - 9 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 14 q^{9} - 60 q^{10} + 26 q^{11} + 30 q^{13} + 54 q^{14} - 18 q^{15} + q^{16} - 42 q^{17} + 25 q^{19} + 108 q^{20} - 102 q^{21} - 39 q^{22} + 8 q^{23} - 83 q^{24} - 17 q^{25} - 148 q^{26} + 32 q^{28} - 12 q^{29} + 304 q^{30} + 51 q^{32} + 123 q^{33} - 6 q^{34} - 38 q^{35} - 54 q^{36} - 14 q^{38} - 44 q^{39} - 96 q^{40} + 63 q^{41} - 92 q^{42} - 34 q^{43} - 69 q^{44} - 28 q^{45} + 58 q^{47} - 147 q^{48} + 18 q^{49} + 132 q^{51} + 162 q^{52} - 12 q^{53} + 29 q^{54} - 28 q^{55} - 16 q^{57} + 172 q^{58} - 147 q^{59} - 222 q^{60} + 58 q^{61} - 116 q^{62} + 86 q^{63} + 166 q^{64} + 11 q^{66} + 201 q^{67} - 84 q^{68} - 198 q^{70} - 102 q^{71} + 210 q^{72} + 7 q^{73} + 174 q^{74} - 173 q^{76} - 376 q^{77} + 450 q^{78} + 134 q^{80} + 253 q^{81} - 145 q^{82} + 146 q^{83} - 90 q^{85} - 270 q^{86} - 568 q^{87} - 72 q^{89} - 438 q^{90} - 216 q^{91} + 72 q^{92} - 160 q^{93} + 558 q^{95} + 126 q^{96} + 21 q^{97} + 411 q^{98} - 56 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 9 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 14 * q^9 - 60 * q^10 + 26 * q^11 + 30 * q^13 + 54 * q^14 - 18 * q^15 + q^16 - 42 * q^17 + 25 * q^19 + 108 * q^20 - 102 * q^21 - 39 * q^22 + 8 * q^23 - 83 * q^24 - 17 * q^25 - 148 * q^26 + 32 * q^28 - 12 * q^29 + 304 * q^30 + 51 * q^32 + 123 * q^33 - 6 * q^34 - 38 * q^35 - 54 * q^36 - 14 * q^38 - 44 * q^39 - 96 * q^40 + 63 * q^41 - 92 * q^42 - 34 * q^43 - 69 * q^44 - 28 * q^45 + 58 * q^47 - 147 * q^48 + 18 * q^49 + 132 * q^51 + 162 * q^52 - 12 * q^53 + 29 * q^54 - 28 * q^55 - 16 * q^57 + 172 * q^58 - 147 * q^59 - 222 * q^60 + 58 * q^61 - 116 * q^62 + 86 * q^63 + 166 * q^64 + 11 * q^66 + 201 * q^67 - 84 * q^68 - 198 * q^70 - 102 * q^71 + 210 * q^72 + 7 * q^73 + 174 * q^74 - 173 * q^76 - 376 * q^77 + 450 * q^78 + 134 * q^80 + 253 * q^81 - 145 * q^82 + 146 * q^83 - 90 * q^85 - 270 * q^86 - 568 * q^87 - 72 * q^89 - 438 * q^90 - 216 * q^91 + 72 * q^92 - 160 * q^93 + 558 * q^95 + 126 * q^96 + 21 * q^97 + 411 * q^98 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.583430	+	0.336844i	−0.291715	+	0.168422i	−0.638715	−	0.769443i	$-0.720534\pi$
$2$	−0.583430	+	0.336844i	−0.291715	+	0.168422i	0.347000	+	0.937865i	$0.387200\pi$
$3$	2.49304	−	1.43936i	0.831013	−	0.479786i	−0.0231863	−	0.999731i	$-0.507381\pi$
$3$	2.49304	−	1.43936i	0.831013	−	0.479786i	0.854199	+	0.519946i	$0.174048\pi$
$4$	−1.77307	+	3.07105i	−0.443268	+	0.767763i
$5$	−1.55311	−	2.69006i	−0.310621	−	0.538012i	0.667876	−	0.744273i	$-0.267204\pi$
$5$	−1.55311	−	2.69006i	−0.310621	−	0.538012i	−0.978497	+	0.206261i	$0.933870\pi$
$6$	−0.969676	+	1.67953i	−0.161613	+	0.279921i
$7$	−8.15294			−1.16471			−0.582353	−	0.812936i	$-0.697868\pi$
$7$	−8.15294			−1.16471			−0.582353	+	0.812936i	$0.697868\pi$
$8$		−	5.08374i		−	0.635468i
$9$	−0.356503	+	0.617481i	−0.0396114	+	0.0686090i
$10$	1.81226	+	1.04631i	0.181226	+	0.104631i
$11$	17.6991			1.60901			0.804504	−	0.593947i	$-0.202431\pi$
$11$	17.6991			1.60901			0.804504	+	0.593947i	$0.202431\pi$
$12$			10.2083i			0.850695i
$13$	5.33372	+	3.07942i	0.410286	+	0.236879i	0.690913	−	0.722938i	$-0.257209\pi$
$13$	5.33372	+	3.07942i	0.410286	+	0.236879i	−0.280627	+	0.959817i	$0.590542\pi$
$14$	4.75667	−	2.74626i	0.339762	−	0.196162i
$15$	−7.74391	−	4.47095i	−0.516261	−	0.298063i
$16$	−5.37987	−	9.31820i	−0.336242	−	0.582388i
$17$	−6.91657	−	11.9799i	−0.406857	−	0.704697i	0.587679	−	0.809094i	$-0.300042\pi$
$17$	−6.91657	−	11.9799i	−0.406857	−	0.704697i	−0.994536	+	0.104397i	$0.966709\pi$
$18$		−	0.480343i		−	0.0266857i
$19$	3.11375	+	18.7431i	0.163882	+	0.986480i
$19$	3.11375	+	18.7431i	0.163882	+	0.986480i
$20$	11.0151			0.550754
$21$	−20.3256	+	11.7350i	−0.967886	+	0.558809i
$22$	−10.3262	+	5.96182i	−0.469372	+	0.270992i
$23$	2.46968	−	4.27760i	0.107377	−	0.185983i	−0.807330	−	0.590101i	$-0.799088\pi$
$23$	2.46968	−	4.27760i	0.107377	−	0.185983i	0.914707	+	0.404118i	$0.132421\pi$
$24$	−7.31732	−	12.6740i	−0.304888	−	0.528082i
$25$	7.67572	−	13.2947i	0.307029	−	0.531790i
$26$	−4.14914			−0.159582
$27$			27.9610i			1.03559i
$28$	14.4558	−	25.0381i	0.516277	−	0.894218i
$29$	−38.2711	−	22.0958i	−1.31969	−	0.761925i	−0.336013	−	0.941857i	$-0.609079\pi$
$29$	−38.2711	−	22.0958i	−1.31969	−	0.761925i	−0.983679	+	0.179933i	$0.942412\pi$
$30$	6.02404			0.200801
$31$			43.0049i			1.38725i	0.720334	+	0.693627i	$0.243989\pi$
$31$			43.0049i			1.38725i	−0.720334	+	0.693627i	$0.756011\pi$
$32$	23.8881	+	13.7918i	0.746505	+	0.430995i
$33$	44.1245	−	25.4753i	1.33711	−	0.771979i
$34$	8.07067	+	4.65960i	0.237373	+	0.137047i
$35$	12.6624	+	21.9319i	0.361782	+	0.626625i
$36$	−1.26421	−	2.18968i	−0.0351170	−	0.0608244i
$37$		−	30.7849i		−	0.832024i	−0.909359	−	0.416012i	$-0.863428\pi$
$37$		−	30.7849i		−	0.832024i	0.909359	−	0.416012i	$-0.136572\pi$
$38$	−8.13016	−	9.88645i	−0.213951	−	0.260170i
$39$	17.7296			0.454604
$40$	−13.6756	+	7.89559i	−0.341889	+	0.197390i
$41$	−28.6795	+	16.5581i	−0.699501	+	0.403857i	−0.807161	−	0.590331i	$-0.798997\pi$
$41$	−28.6795	+	16.5581i	−0.699501	+	0.403857i	0.107661	+	0.994188i	$0.465664\pi$
$42$	7.90571	−	13.6931i	0.188231	−	0.326026i
$43$	−15.7586	−	27.2946i	−0.366478	−	0.634759i	0.622534	−	0.782593i	$-0.286103\pi$
$43$	−15.7586	−	27.2946i	−0.366478	−	0.634759i	−0.989012	+	0.147834i	$0.952770\pi$
$44$	−31.3818	+	54.3548i	−0.713222	+	1.23534i
$45$	2.21475			0.0492166
$46$			3.32758i			0.0723386i
$47$	8.86404	−	15.3530i	0.188597	−	0.326659i	−0.756186	−	0.654357i	$-0.772939\pi$
$47$	8.86404	−	15.3530i	0.188597	−	0.326659i	0.944783	+	0.327698i	$0.106273\pi$
$48$	−26.8244	−	15.4871i	−0.558842	−	0.322648i
$49$	17.4704			0.356539
$50$			10.3421i			0.206841i
$51$	−34.4866	−	19.9108i	−0.676207	−	0.390408i
$52$	−18.9142	+	10.9201i	−0.363734	+	0.210002i
$53$	14.6396	+	8.45218i	0.276219	+	0.159475i	0.631710	−	0.775204i	$-0.282353\pi$
$53$	14.6396	+	8.45218i	0.276219	+	0.159475i	−0.355492	+	0.934679i	$0.615687\pi$
$54$	−9.41847	−	16.3133i	−0.174416	−	0.302098i
$55$	−27.4886	−	47.6116i	−0.499792	−	0.865665i
$56$			41.4474i			0.740133i
$57$	34.7408	+	42.2455i	0.609487	+	0.741150i
$58$	29.7713			0.513299
$59$	20.3412	−	11.7440i	0.344766	−	0.199050i	−0.317612	−	0.948221i	$-0.602881\pi$
$59$	20.3412	−	11.7440i	0.344766	−	0.199050i	0.662377	+	0.749170i	$0.269548\pi$
$60$	27.4610	−	15.8546i	0.457684	−	0.264244i
$61$	−8.52643	+	14.7682i	−0.139777	+	0.242102i	−0.927412	−	0.374041i	$-0.877972\pi$
$61$	−8.52643	+	14.7682i	−0.139777	+	0.242102i	0.787635	+	0.616142i	$0.211305\pi$
$62$	−14.4859	−	25.0903i	−0.233644	−	0.404683i
$63$	2.90655	−	5.03429i	0.0461357	−	0.0799093i
$64$	24.4562			0.382128
$65$		−	19.1307i		−	0.294318i
$66$	−17.1624	+	29.7261i	−0.260036	+	0.450396i
$67$	84.9924	+	49.0704i	1.26854	+	0.732393i	0.974712	−	0.223464i	$-0.0717365\pi$
$67$	84.9924	+	49.0704i	1.26854	+	0.732393i	0.293831	+	0.955858i	$0.405070\pi$
$68$	49.0543			0.721387
$69$		−	14.2190i		−	0.206072i
$70$	−14.7752	−	8.53048i	−0.211075	−	0.121864i
$71$	−1.36156	+	0.786099i	−0.0191769	+	0.0110718i	−0.509558	−	0.860436i	$-0.670191\pi$
$71$	−1.36156	+	0.786099i	−0.0191769	+	0.0110718i	0.490381	+	0.871508i	$0.336858\pi$
$72$	3.13911	+	1.81237i	0.0435988	+	0.0251718i
$73$	2.85534	+	4.94560i	0.0391143	+	0.0677479i	0.884920	−	0.465743i	$-0.154213\pi$
$73$	2.85534	+	4.94560i	0.0391143	+	0.0677479i	−0.845806	+	0.533491i	$0.820880\pi$
$74$	10.3697	+	17.9608i	0.140131	+	0.242714i
$75$		−	44.1924i		−	0.589232i
$76$	−63.0820	−	23.6704i	−0.830026	−	0.311453i
$77$	−144.300			−1.87402
$78$	−10.3440	+	5.97209i	−0.132615	+	0.0765653i
$79$	41.9327	−	24.2099i	0.530794	−	0.306454i	−0.210546	−	0.977584i	$-0.567524\pi$
$79$	41.9327	−	24.2099i	0.530794	−	0.306454i	0.741340	+	0.671130i	$0.234191\pi$
$80$	−16.7110	+	28.9443i	−0.208888	+	0.361804i
$81$	37.0373	+	64.1505i	0.457250	+	0.791981i
$82$	11.1550	−	19.3210i	0.136037	−	0.235622i
$83$	−74.2729			−0.894854			−0.447427	−	0.894320i	$-0.647660\pi$
$83$	−74.2729			−0.894854			−0.447427	+	0.894320i	$0.647660\pi$
$84$		−	83.2280i		−	0.990809i
$85$	−21.4843	+	37.2120i	−0.252757	+	0.437788i
$86$	18.3880	+	10.6163i	0.213815	+	0.123446i
$87$	−127.215			−1.46224
$88$		−	89.9776i		−	1.02247i
$89$	81.0798	+	46.8114i	0.911008	+	0.525971i	0.880755	−	0.473571i	$-0.157035\pi$
$89$	81.0798	+	46.8114i	0.911008	+	0.525971i	0.0302530	+	0.999542i	$0.490369\pi$
$90$	−1.29215	+	0.746024i	−0.0143572	+	0.00828915i
$91$	−43.4855	−	25.1064i	−0.477863	−	0.275894i
$92$	8.75783	+	15.1690i	0.0951938	+	0.164881i
$93$	61.8994	+	107.213i	0.665585	+	1.15283i
$94$			11.9432i			0.127055i
$95$	45.5841	−	37.4862i	0.479833	−	0.394592i
$96$	79.4055			0.827140
$97$	−8.15700	+	4.70945i	−0.0840928	+	0.0485510i	−0.541457	−	0.840729i	$-0.682127\pi$
$97$	−8.15700	+	4.70945i	−0.0840928	+	0.0485510i	0.457364	+	0.889280i	$0.348794\pi$
$98$	−10.1928	+	5.88480i	−0.104008	+	0.0600489i
$99$	−6.30978	+	10.9289i	−0.0637351	+	0.110392i
$100$	27.2192	+	47.1451i	0.272192	+	0.471451i
$101$	66.5604	−	115.286i	0.659014	−	1.14145i	−0.321858	−	0.946788i	$-0.604307\pi$
$101$	66.5604	−	115.286i	0.659014	−	1.14145i	0.980871	−	0.194657i	$-0.0623595\pi$
$102$	26.8273			0.263013
$103$			92.7893i			0.900867i	0.892810	+	0.450433i	$0.148731\pi$
$103$			92.7893i			0.900867i	−0.892810	+	0.450433i	$0.851269\pi$
$104$	15.6550	−	27.1153i	0.150529	−	0.260724i
$105$	63.1356	+	36.4514i	0.601292	+	0.347156i
$106$	−11.3882			−0.107436
$107$		−	139.410i		−	1.30289i	−0.758695	−	0.651446i	$-0.774163\pi$
$107$		−	139.410i		−	1.30289i	0.758695	−	0.651446i	$-0.225837\pi$
$108$	−85.8696	−	49.5768i	−0.795089	−	0.459045i
$109$	−112.823	+	65.1381i	−1.03507	+	0.597597i	−0.918433	−	0.395577i	$-0.870545\pi$
$109$	−112.823	+	65.1381i	−1.03507	+	0.597597i	−0.116636	+	0.993175i	$0.537211\pi$
$110$	32.0753	+	18.5187i	0.291594	+	0.168352i
$111$	−44.3104	−	76.7479i	−0.399193	−	0.691422i
$112$	43.8617	+	75.9707i	0.391623	+	0.678310i
$113$			19.1195i			0.169199i	0.996415	+	0.0845997i	$0.0269612\pi$
$113$			19.1195i			0.169199i	−0.996415	+	0.0845997i	$0.973039\pi$
$114$	−34.4989	−	12.9451i	−0.302622	−	0.113554i
$115$	−15.3427			−0.133415
$116$	135.715	−	78.3550i	1.16996	−	0.675474i
$117$	−3.80297	+	2.19565i	−0.0325041	+	0.0187662i
$118$	−7.91177	+	13.7036i	−0.0670489	+	0.116132i
$119$	56.3904	+	97.6710i	0.473869	+	0.820765i
$120$	−22.7291	+	39.3680i	−0.189410	+	0.328067i
$121$	192.258			1.58891
$122$		−	11.4883i		−	0.0941663i
$123$	−47.6661	+	82.5601i	−0.387529	+	0.671221i
$124$	−132.070	−	76.2508i	−1.06508	−	0.614926i
$125$	−125.340			−1.00272
$126$			3.91621i			0.0310810i
$127$	−21.1332	−	12.2013i	−0.166403	−	0.0960730i	0.414486	−	0.910056i	$-0.363962\pi$
$127$	−21.1332	−	12.2013i	−0.166403	−	0.0960730i	−0.580889	+	0.813983i	$0.697295\pi$
$128$	−109.821	+	63.4052i	−0.857977	+	0.495353i
$129$	−78.5735	−	45.3644i	−0.609097	−	0.351662i
$130$	6.44405	+	11.1614i	0.0495696	+	0.0858571i
$131$	−38.0958	−	65.9839i	−0.290808	−	0.503694i	0.683193	−	0.730238i	$-0.260591\pi$
$131$	−38.0958	−	65.9839i	−0.290808	−	0.503694i	−0.974001	+	0.226544i	$0.927257\pi$
$132$			180.678i			1.36877i
$133$	−25.3862	−	152.812i	−0.190874	−	1.14896i
$134$	−66.1161			−0.493404
$135$	75.2166	−	43.4264i	0.557160	−	0.321677i
$136$	−60.9025	+	35.1620i	−0.447812	+	0.258544i
$137$	118.616	−	205.449i	0.865811	−	1.49963i	−0.000428189	−	1.00000i	$-0.500136\pi$
$137$	118.616	−	205.449i	0.865811	−	1.49963i	0.866239	−	0.499629i	$-0.166530\pi$
$138$	4.78957	+	8.29578i	0.0347070	+	0.0601144i
$139$	−10.0402	+	17.3902i	−0.0722320	+	0.125110i	−0.899879	−	0.436139i	$-0.856346\pi$
$139$	−10.0402	+	17.3902i	−0.0722320	+	0.125110i	0.827647	+	0.561249i	$0.189679\pi$
$140$	−89.8053			−0.641466
$141$		−	51.0341i		−	0.361944i
$142$	0.529585	−	0.917267i	0.00372947	−	0.00645963i
$143$	94.4020	+	54.5030i	0.660154	+	0.381140i
$144$	7.67175			0.0532761
$145$			137.269i			0.946680i
$146$	−3.33178	−	1.92361i	−0.0228204	−	0.0131754i
$147$	43.5544	−	25.1462i	0.296289	−	0.171062i
$148$	94.5419	+	54.5838i	0.638797	+	0.368810i
$149$	77.8489	+	134.838i	0.522476	+	0.904954i	0.999658	+	0.0261500i	$0.00832476\pi$
$149$	77.8489	+	134.838i	0.522476	+	0.904954i	−0.477182	+	0.878804i	$0.658342\pi$
$150$	14.8859	+	25.7832i	0.0992395	+	0.171888i
$151$		−	41.4678i		−	0.274621i	−0.990528	−	0.137310i	$-0.956154\pi$
$151$		−	41.4678i		−	0.274621i	0.990528	−	0.137310i	$-0.0438458\pi$
$152$	95.2852	−	15.8295i	0.626876	−	0.104142i
$153$	9.86311			0.0644648
$154$	84.1887	−	48.6064i	0.546680	−	0.315626i
$155$	115.686	−	66.7912i	0.746359	−	0.430911i
$156$	−31.4358	+	54.4484i	−0.201512	+	0.349028i
$157$	39.5539	+	68.5094i	0.251936	+	0.436366i	0.964059	−	0.265689i	$-0.0855994\pi$
$157$	39.5539	+	68.5094i	0.251936	+	0.436366i	−0.712123	+	0.702055i	$0.752266\pi$
$158$	−16.3099	+	28.2495i	−0.103227	+	0.178794i
$159$	48.6628			0.306055
$160$		−	85.6807i		−	0.535504i
$161$	−20.1351	+	34.8751i	−0.125063	+	0.216615i
$162$	−43.2173	−	24.9515i	−0.266774	−	0.154022i
$163$	−135.441			−0.830926			−0.415463	−	0.909610i	$-0.636380\pi$
$163$	−135.441			−0.830926			−0.415463	+	0.909610i	$0.636380\pi$
$164$		−	117.435i		−	0.716068i
$165$	−137.060	−	79.1317i	−0.830667	−	0.479586i
$166$	43.3330	−	25.0183i	0.261042	−	0.150713i
$167$	54.3880	+	31.4010i	0.325677	+	0.188030i	0.653920	−	0.756564i	$-0.273123\pi$
$167$	54.3880	+	31.4010i	0.325677	+	0.188030i	−0.328243	+	0.944593i	$0.606457\pi$
$168$	59.6576	+	103.330i	0.355105	+	0.615060i
$169$	−65.5343	−	113.509i	−0.387777	−	0.671649i
$170$		−	28.9474i		−	0.170279i
$171$	−12.6836	−	4.75929i	−0.0741730	−	0.0278321i
$172$	111.764			0.649793
$173$	−282.606	+	163.162i	−1.63356	+	0.943135i	−0.650574	+	0.759442i	$0.725472\pi$
$173$	−282.606	+	163.162i	−1.63356	+	0.943135i	−0.982984	+	0.183693i	$0.941195\pi$
$174$	74.2211	−	42.8516i	0.426558	−	0.246273i
$175$	−62.5797	+	108.391i	−0.357598	+	0.619378i
$176$	−95.2187	−	164.924i	−0.541015	−	0.937066i
$177$	33.8076	−	58.5564i	0.191003	−	0.330827i
$178$	−63.0725			−0.354340
$179$			266.546i			1.48909i	0.667575	+	0.744543i	$0.267332\pi$
$179$			266.546i			1.48909i	−0.667575	+	0.744543i	$0.732668\pi$
$180$	−3.92691	+	6.80161i	−0.0218162	+	0.0377867i
$181$	129.999	+	75.0548i	0.718225	+	0.414667i	0.814099	−	0.580726i	$-0.197231\pi$
$181$	129.999	+	75.0548i	0.718225	+	0.414667i	−0.0958743	+	0.995393i	$0.530565\pi$
$182$	33.8277			0.185866
$183$			49.0903i			0.268253i
$184$	−21.7462	−	12.5552i	−0.118186	−	0.0682347i
$185$	−82.8131	+	47.8122i	−0.447638	+	0.258444i
$186$	−72.2279	−	41.7008i	−0.388322	−	0.224198i
$187$	−122.417	−	212.032i	−0.654636	−	1.13386i
$188$	31.4332	+	54.4439i	0.167198	+	0.289595i
$189$		−	227.964i		−	1.20616i
$190$	−13.9681	+	37.2253i	−0.0735165	+	0.195923i
$191$	−99.5798			−0.521360			−0.260680	−	0.965425i	$-0.583947\pi$
$191$	−99.5798			−0.521360			−0.260680	+	0.965425i	$0.583947\pi$
$192$	60.9702	−	35.2012i	0.317553	−	0.183339i
$193$	−42.4195	+	24.4909i	−0.219790	+	0.126896i	−0.605853	−	0.795577i	$-0.707168\pi$
$193$	−42.4195	+	24.4909i	−0.219790	+	0.126896i	0.386063	+	0.922472i	$0.373835\pi$
$194$	3.17269	−	5.49527i	0.0163541	−	0.0283261i
$195$	−27.5359	−	47.6936i	−0.141210	−	0.244582i
$196$	−30.9763	+	53.6526i	−0.158042	+	0.273738i
$197$	−167.819			−0.851875			−0.425938	−	0.904753i	$-0.640056\pi$
$197$	−167.819			−0.851875			−0.425938	+	0.904753i	$0.640056\pi$
$198$		−	8.50163i		−	0.0429375i
$199$	46.2601	−	80.1249i	0.232463	−	0.402638i	−0.726069	−	0.687621i	$-0.758655\pi$
$199$	46.2601	−	80.1249i	0.232463	−	0.402638i	0.958532	+	0.284984i	$0.0919882\pi$
$200$	−67.5870	−	39.0214i	−0.337935	−	0.195107i
$201$	282.519			1.40557
$202$			89.6818i			0.443969i
$203$	312.022	+	180.146i	1.53705	+	0.887418i
$204$	122.294	−	70.6067i	0.599482	−	0.346111i
$205$	89.0847	+	51.4331i	0.434559	+	0.250893i
$206$	−31.2555	−	54.1361i	−0.151726	−	0.262796i
$207$	1.76089	+	3.04996i	0.00850673	+	0.0147341i
$208$		−	66.2676i		−	0.318594i
$209$	55.1106	+	331.736i	0.263687	+	1.58725i
$210$	−49.1136			−0.233874
$211$	−54.4067	+	31.4117i	−0.257852	+	0.148871i	−0.623354	−	0.781940i	$-0.714231\pi$
$211$	−54.4067	+	31.4117i	−0.257852	+	0.148871i	0.365502	+	0.930810i	$0.380897\pi$
$212$	−51.9142	+	29.9726i	−0.244878	+	0.141380i
$213$	−2.26295	+	3.91955i	−0.0106242	+	0.0184016i
$214$	46.9592	+	81.3357i	0.219436	+	0.380073i
$215$	−48.9495	+	84.7830i	−0.227672	+	0.394339i
$216$	142.146			0.658085
$217$		−	350.616i		−	1.61574i
$218$	43.8827	−	76.0071i	0.201297	−	0.348656i
$219$	14.2370	+	8.21971i	0.0650089	+	0.0375329i
$220$	194.957			0.886168
$221$		−	85.1962i		−	0.385503i
$222$	51.7041	+	29.8514i	0.232901	+	0.134466i
$223$	371.890	−	214.711i	1.66767	−	0.962830i	0.698781	−	0.715336i	$-0.253726\pi$
$223$	371.890	−	214.711i	1.66767	−	0.962830i	0.968889	−	0.247494i	$-0.0796071\pi$
$224$	−194.759	−	112.444i	−0.869458	−	0.501982i
$225$	5.47284	+	9.47923i	0.0243237	+	0.0421299i
$226$	−6.44029	−	11.1549i	−0.0284969	−	0.0493580i
$227$			246.184i			1.08451i	0.840213	+	0.542256i	$0.182430\pi$
$227$			246.184i			1.08451i	−0.840213	+	0.542256i	$0.817570\pi$
$228$	−191.336	+	31.7863i	−0.839194	+	0.139413i
$229$	−31.8783			−0.139207			−0.0696033	−	0.997575i	$-0.522173\pi$
$229$	−31.8783			−0.139207			−0.0696033	+	0.997575i	$0.522173\pi$
$230$	8.95138	−	5.16808i	0.0389190	−	0.0224699i
$231$	−359.744	+	207.699i	−1.55734	+	0.899128i
$232$	−112.329	+	194.560i	−0.484178	+	0.838622i
$233$	−184.933	−	320.313i	−0.793704	−	1.37474i	−0.923659	−	0.383216i	$-0.874817\pi$
$233$	−184.933	−	320.313i	−0.793704	−	1.37474i	0.129955	−	0.991520i	$-0.458517\pi$
$234$	1.47918	−	2.56201i	0.00632128	−	0.0109488i
$235$	−55.0672			−0.234329
$236$			83.2917i			0.352931i
$237$	69.6933	−	120.712i	0.294064	−	0.509335i
$238$	−65.7997	−	37.9895i	−0.276469	−	0.159620i
$239$	106.567			0.445887			0.222944	−	0.974831i	$-0.428433\pi$
$239$	106.567			0.445887			0.222944	+	0.974831i	$0.428433\pi$
$240$			96.2124i			0.400885i
$241$	−11.9695	−	6.91062i	−0.0496662	−	0.0286748i	0.474961	−	0.880007i	$-0.342462\pi$
$241$	−11.9695	−	6.91062i	−0.0496662	−	0.0286748i	−0.524627	+	0.851332i	$0.675795\pi$
$242$	−112.169	+	64.7607i	−0.463508	+	0.267606i
$243$	−33.2633	−	19.2046i	−0.136886	−	0.0790313i
$244$	−30.2359	−	52.3702i	−0.123918	−	0.214632i
$245$	−27.1334	−	46.9964i	−0.110749	−	0.191822i
$246$		−	64.2241i		−	0.261074i
$247$	−41.1101	+	109.559i	−0.166438	+	0.443559i
$248$	218.626			0.881555
$249$	−185.165	+	106.905i	−0.743635	+	0.429338i
$250$	73.1272	−	42.2200i	0.292509	−	0.168880i
$251$	61.3921	−	106.334i	0.244590	−	0.423642i	−0.717426	−	0.696635i	$-0.754680\pi$
$251$	61.3921	−	106.334i	0.244590	−	0.423642i	0.962016	+	0.272992i	$0.0880133\pi$
$252$	10.3070	+	17.8523i	0.0409010	+	0.0708425i
$253$	43.7110	−	75.7097i	0.172771	−	0.299248i
$254$	16.4397			0.0647231
$255$			123.695i			0.485077i
$256$	−6.19708	+	10.7337i	−0.0242073	+	0.0419283i
$257$	−343.131	−	198.107i	−1.33514	−	0.770843i	−0.349058	−	0.937101i	$-0.613498\pi$
$257$	−343.131	−	198.107i	−1.33514	−	0.770843i	−0.986082	+	0.166258i	$0.946832\pi$
$258$	61.1228			0.236910
$259$			250.987i			0.969062i
$260$	58.7514	+	33.9201i	0.225967	+	0.130462i
$261$	27.2875	−	15.7544i	0.104550	−	0.0603619i
$262$	44.4525	+	25.6647i	0.169666	+	0.0979568i
$263$	26.7480	+	46.3289i	0.101704	+	0.176156i	0.912387	−	0.409330i	$-0.134237\pi$
$263$	26.7480	+	46.3289i	0.101704	+	0.176156i	−0.810683	+	0.585485i	$0.800904\pi$
$264$	−129.510	−	224.318i	−0.490568	−	0.849688i
$265$		−	52.5085i		−	0.198145i
$266$	66.2847	+	80.6036i	0.249190	+	0.303021i
$267$	269.513			1.00941
$268$	−301.395	+	174.011i	−1.12461	+	0.649293i
$269$	316.357	−	182.649i	1.17605	−	0.678993i	0.220953	−	0.975285i	$-0.429083\pi$
$269$	316.357	−	182.649i	1.17605	−	0.678993i	0.955098	+	0.296292i	$0.0957500\pi$
$270$	−29.2558	+	50.6725i	−0.108355	+	0.187676i
$271$	−87.1835	−	151.006i	−0.321710	−	0.557219i	0.659131	−	0.752028i	$-0.270924\pi$
$271$	−87.1835	−	151.006i	−0.321710	−	0.557219i	−0.980841	+	0.194810i	$0.937591\pi$
$272$	−74.4204	+	128.900i	−0.273605	+	0.473897i
$273$	−144.548			−0.529480
$274$			159.820i			0.583286i
$275$	135.853	−	235.305i	0.494012	−	0.855654i
$276$	43.6672	+	25.2113i	0.158215	+	0.0913453i
$277$	93.2815			0.336756			0.168378	−	0.985722i	$-0.446147\pi$
$277$	93.2815			0.336756			0.168378	+	0.985722i	$0.446147\pi$
$278$		−	13.5280i		−	0.0486618i
$279$	−26.5547	−	15.3314i	−0.0951782	−	0.0549512i
$280$	111.496	−	64.3723i	0.398200	−	0.229901i
$281$	325.337	+	187.834i	1.15778	+	0.668447i	0.950772	−	0.309891i	$-0.100293\pi$
$281$	325.337	+	187.834i	1.15778	+	0.668447i	0.207013	+	0.978338i	$0.433626\pi$
$282$	17.1905	+	29.7748i	0.0609592	+	0.105584i
$283$	32.0728	+	55.5518i	0.113332	+	0.196296i	0.917112	−	0.398631i	$-0.130514\pi$
$283$	32.0728	+	55.5518i	0.113332	+	0.196296i	−0.803780	+	0.594927i	$0.797181\pi$
$284$		−	5.57524i		−	0.0196311i
$285$	59.6869	−	159.066i	0.209428	−	0.558128i
$286$	−73.4359			−0.256769
$287$	233.822	−	134.997i	0.814712	−	0.470374i
$288$	−17.0324	+	9.83366i	−0.0591402	+	0.0341446i
$289$	48.8221	−	84.5624i	0.168935	−	0.292603i
$290$	−46.2380	−	80.0866i	−0.159442	−	0.276161i
$291$	−13.5572	+	23.4817i	−0.0465882	+	0.0806931i
$292$	−20.2509			−0.0693524
$293$			111.814i			0.381618i	0.981627	+	0.190809i	$0.0611112\pi$
$293$			111.814i			0.381618i	−0.981627	+	0.190809i	$0.938889\pi$
$294$	−16.9406	+	29.3421i	−0.0576212	+	0.0998029i
$295$	−63.1840	−	36.4793i	−0.214183	−	0.123659i
$296$	−156.502			−0.528724
$297$			494.884i			1.66627i
$298$	−90.8387	−	52.4458i	−0.304828	−	0.175993i
$299$	26.3451	−	15.2104i	0.0881108	−	0.0508708i
$300$	135.717	+	78.3564i	0.452391	+	0.261188i
$301$	128.479	+	222.532i	0.426839	+	0.739308i
$302$	13.9681	+	24.1935i	0.0462521	+	0.0801110i
$303$		−	383.217i		−	1.26474i
$304$	157.901	−	129.850i	0.519410	−	0.427138i
$305$	52.9698			0.173671
$306$	−5.75444	+	3.32233i	−0.0188053	+	0.0108573i
$307$	−297.331	+	171.664i	−0.968503	+	0.559166i	−0.898780	−	0.438401i	$-0.855545\pi$
$307$	−297.331	+	171.664i	−0.968503	+	0.559166i	−0.0697237	+	0.997566i	$0.522212\pi$
$308$	255.854	−	443.151i	0.830694	−	1.43880i
$309$	133.557	+	231.327i	0.432223	+	0.748632i
$310$	−44.9963	+	77.9360i	−0.145150	+	0.251406i
$311$	−251.722			−0.809397			−0.404698	−	0.914450i	$-0.632624\pi$
$311$	−251.722			−0.809397			−0.404698	+	0.914450i	$0.632624\pi$
$312$		−	90.1325i		−	0.288886i
$313$	−243.143	+	421.136i	−0.776814	+	1.34548i	0.156955	+	0.987606i	$0.449832\pi$
$313$	−243.143	+	421.136i	−0.776814	+	1.34548i	−0.933769	+	0.357876i	$0.883501\pi$
$314$	−46.1539	−	26.6470i	−0.146987	−	0.0848630i
$315$	−18.0567			−0.0573229
$316$			171.703i			0.543365i
$317$	−240.229	−	138.696i	−0.757819	−	0.437527i	0.0706929	−	0.997498i	$-0.477479\pi$
$317$	−240.229	−	138.696i	−0.757819	−	0.437527i	−0.828512	+	0.559971i	$0.810812\pi$
$318$	−28.3913	+	16.3917i	−0.0892809	+	0.0515464i
$319$	−677.363	−	391.076i	−2.12340	−	1.22594i
$320$	−37.9830	−	65.7886i	−0.118697	−	0.205589i
$321$	−200.660	−	347.553i	−0.625109	−	1.08272i
$322$		−	27.1295i		−	0.0842532i
$323$	203.003	−	166.940i	0.628493	−	0.516843i
$324$	−262.679			−0.810738
$325$	81.8803	−	47.2736i	0.251939	−	0.145457i
$326$	79.0203	−	45.6224i	0.242394	−	0.139946i
$327$	−187.514	+	324.784i	−0.573437	+	0.993222i
$328$	84.1772	+	145.799i	0.256638	+	0.444510i
$329$	−72.2680	+	125.172i	−0.219660	+	0.380462i
$330$	106.620			0.323091
$331$			110.480i			0.333776i	0.985976	+	0.166888i	$0.0533719\pi$
$331$			110.480i			0.333776i	−0.985976	+	0.166888i	$0.946628\pi$
$332$	131.691	−	228.096i	0.396660	−	0.687036i
$333$	19.0091	+	10.9749i	0.0570843	+	0.0329577i
$334$	−42.3088			−0.126673
$335$		−	304.846i		−	0.909988i
$336$	218.698	+	126.265i	0.650887	+	0.375790i
$337$	23.9735	−	13.8411i	0.0711380	−	0.0410716i	−0.464009	−	0.885830i	$-0.653590\pi$
$337$	23.9735	−	13.8411i	0.0711380	−	0.0410716i	0.535147	+	0.844759i	$0.320256\pi$
$338$	76.4694	+	44.1496i	0.226241	+	0.130620i
$339$	27.5198	+	47.6658i	0.0811795	+	0.140607i
$340$	−76.1866	−	131.959i	−0.224078	−	0.388115i
$341$			761.147i			2.23210i
$342$	9.00312	−	1.49567i	0.0263249	−	0.00437330i
$343$	257.059			0.749443
$344$	−138.759	+	80.1125i	−0.403369	+	0.232885i
$345$	−38.2499	+	22.0836i	−0.110869	+	0.0640104i
$346$	109.920	−	190.388i	0.317689	−	0.550254i
$347$	−129.243	−	223.856i	−0.372459	−	0.645118i	0.617484	−	0.786583i	$-0.288152\pi$
$347$	−129.243	−	223.856i	−0.372459	−	0.645118i	−0.989943	+	0.141465i	$0.954819\pi$
$348$	225.562	−	390.684i	0.648165	−	1.12266i
$349$	502.852			1.44084			0.720419	−	0.693539i	$-0.243950\pi$
$349$	502.852			1.44084			0.720419	+	0.693539i	$0.243950\pi$
$350$		−	84.3183i		−	0.240909i
$351$	−86.1037	+	149.136i	−0.245310	+	0.424889i
$352$	422.798	+	244.103i	1.20113	+	0.693474i
$353$	54.1066			0.153277			0.0766383	−	0.997059i	$-0.475581\pi$
$353$	54.1066			0.153277			0.0766383	+	0.997059i	$0.475581\pi$
$354$			45.5514i			0.128676i
$355$	4.22930	+	2.44179i	0.0119135	+	0.00687828i
$356$	−287.521	+	166.000i	−0.807642	+	0.466292i
$357$	281.167	+	162.332i	0.787582	+	0.454711i
$358$	−89.7844	−	155.511i	−0.250794	−	0.434389i
$359$	218.686	+	378.775i	0.609152	+	1.05508i	0.991380	+	0.131015i	$0.0418236\pi$
$359$	218.686	+	378.775i	0.609152	+	1.05508i	−0.382228	+	0.924068i	$0.624843\pi$
$360$		−	11.2592i		−	0.0312756i
$361$	−341.609	+	116.723i	−0.946286	+	0.323332i
$362$	−101.127			−0.279356
$363$	479.306	−	276.727i	1.32040	−	0.762334i
$364$	154.206	−	89.0308i	0.423643	−	0.244590i
$365$	8.86930	−	15.3621i	0.0242994	−	0.0420879i
$366$	−16.5357	−	28.6407i	−0.0451796	−	0.0782534i
$367$	48.1329	−	83.3687i	0.131152	−	0.227163i	−0.792969	−	0.609262i	$-0.791466\pi$
$367$	48.1329	−	83.3687i	0.131152	−	0.227163i	0.924121	+	0.382100i	$0.124799\pi$
$368$	−53.1461			−0.144419
$369$		−	23.6121i		−	0.0639894i
$370$	32.2104	−	55.7901i	0.0870553	−	0.150784i
$371$	−119.356	−	68.9101i	−0.321714	−	0.185741i
$372$	−439.009			−1.18013
$373$		−	598.561i		−	1.60472i	−0.596840	−	0.802360i	$-0.703577\pi$
$373$		−	598.561i		−	1.60472i	0.596840	−	0.802360i	$-0.296423\pi$
$374$	142.843	+	82.4707i	0.381934	+	0.220510i
$375$	−312.478	+	180.409i	−0.833275	+	0.481091i
$376$	−78.0505	−	45.0625i	−0.207581	−	0.119847i
$377$	−136.085	−	235.706i	−0.360968	−	0.625214i
$378$	76.7882	+	133.001i	0.203143	+	0.351855i
$379$		−	161.020i		−	0.424855i	−0.977177	−	0.212427i	$-0.931863\pi$
$379$		−	161.020i		−	0.424855i	0.977177	−	0.212427i	$-0.0681369\pi$
$380$	34.2983	+	206.457i	0.0902586	+	0.543308i
$381$	−70.2479			−0.184378
$382$	58.0979	−	33.5428i	0.152089	−	0.0878084i
$383$	200.487	−	115.751i	0.523464	−	0.302222i	−0.214887	−	0.976639i	$-0.568938\pi$
$383$	200.487	−	115.751i	0.523464	−	0.302222i	0.738351	+	0.674417i	$0.235605\pi$
$384$	−182.525	+	316.143i	−0.475327	+	0.823290i
$385$	224.113	+	388.174i	0.582111	+	1.00825i
$386$	16.4992	−	28.5775i	0.0427440	−	0.0740348i
$387$	22.4719			0.0580670
$388$		−	33.4008i		−	0.0860845i
$389$	−40.5074	+	70.1609i	−0.104132	+	0.180362i	−0.913383	−	0.407101i	$-0.866540\pi$
$389$	−40.5074	+	70.1609i	−0.104132	+	0.180362i	0.809251	+	0.587463i	$0.199873\pi$
$390$	32.1306	+	18.5506i	0.0823860	+	0.0475656i
$391$	−68.3268			−0.174749
$392$		−	88.8151i		−	0.226569i
$393$	−189.949	−	109.667i	−0.483330	−	0.279051i
$394$	97.9109	−	56.5289i	0.248505	−	0.143474i
$395$	−130.252	−	75.2010i	−0.329752	−	0.190382i
$396$	−22.3754	−	38.7553i	−0.0565035	−	0.0978669i
$397$	341.051	+	590.718i	0.859071	+	1.48796i	0.872816	+	0.488050i	$0.162291\pi$
$397$	341.051	+	590.718i	0.859071	+	1.48796i	−0.0137446	+	0.999906i	$0.504375\pi$
$398$			62.3297i			0.156607i
$399$	−283.239	−	344.425i	−0.709873	−	0.863221i
$400$	−165.177			−0.412944
$401$	−82.6912	+	47.7418i	−0.206213	+	0.119057i	−0.599550	−	0.800337i	$-0.704654\pi$
$401$	−82.6912	+	47.7418i	−0.206213	+	0.119057i	0.393337	+	0.919394i	$0.371320\pi$
$402$	−164.830	+	95.1647i	−0.410025	+	0.236728i
$403$	−132.430	+	229.376i	−0.328611	+	0.569171i
$404$	236.033	+	408.821i	0.584240	+	1.01193i
$405$	115.046	−	199.265i	0.284063	−	0.492012i
$406$	−242.724			−0.597842
$407$		−	544.864i		−	1.33873i
$408$	−101.221	+	175.321i	−0.248092	+	0.429708i
$409$	−169.330	−	97.7625i	−0.414009	−	0.239028i	0.278502	−	0.960436i	$-0.410162\pi$
$409$	−169.330	−	97.7625i	−0.414009	−	0.239028i	−0.692511	+	0.721408i	$0.743495\pi$
$410$	−69.2996			−0.169023
$411$		−	682.924i		−	1.66162i
$412$	−284.961	−	164.522i	−0.691652	−	0.399326i
$413$	−165.840	+	95.7479i	−0.401550	+	0.231835i
$414$	−2.05472	−	1.18629i	−0.00496308	−	0.00286544i
$415$	115.354	+	199.798i	0.277961	+	0.481442i
$416$	84.9418	+	147.124i	0.204187	+	0.353662i
$417$			57.8060i			0.138624i
$418$	−143.896	−	174.981i	−0.344250	−	0.418615i
$419$	−388.318			−0.926773			−0.463387	−	0.886156i	$-0.653366\pi$
$419$	−388.318			−0.926773			−0.463387	+	0.886156i	$0.653366\pi$
$420$	−223.888	+	129.262i	−0.533067	+	0.307766i
$421$	225.968	−	130.463i	0.536742	−	0.309888i	−0.207015	−	0.978338i	$-0.566375\pi$
$421$	225.968	−	130.463i	0.536742	−	0.309888i	0.743758	+	0.668449i	$0.233042\pi$
$422$	21.1617	−	36.6531i	0.0501462	−	0.0868557i
$423$	6.32012	+	10.9468i	0.0149412	+	0.0258789i
$424$	42.9687	−	74.4239i	0.101341	−	0.175528i
$425$	−212.359			−0.499667
$426$		−	3.04904i		−	0.00715738i
$427$	69.5154	−	120.404i	0.162800	−	0.281977i
$428$	428.134	+	247.183i	1.00031	+	0.577531i
$429$	313.797			0.731462
$430$		−	65.9533i		−	0.153380i
$431$	496.682	+	286.760i	1.15239	+	0.665335i	0.949470	−	0.313859i	$-0.101622\pi$
$431$	496.682	+	286.760i	1.15239	+	0.665335i	0.202925	+	0.979194i	$0.434955\pi$
$432$	260.546	−	150.426i	0.603116	−	0.348209i
$433$	216.750	+	125.141i	0.500578	+	0.289009i	0.728952	−	0.684565i	$-0.240008\pi$
$433$	216.750	+	125.141i	0.500578	+	0.289009i	−0.228374	+	0.973573i	$0.573341\pi$
$434$	118.103	+	204.560i	0.272126	+	0.471337i
$435$	197.579	+	342.216i	0.454203	+	0.786704i
$436$		−	461.978i		−	1.05958i
$437$	87.8656	+	32.9700i	0.201065	+	0.0754463i
$438$	−11.0750			−0.0252854
$439$	406.897	−	234.922i	0.926872	−	0.535130i	0.0410511	−	0.999157i	$-0.486929\pi$
$439$	406.897	−	234.922i	0.926872	−	0.535130i	0.885821	+	0.464027i	$0.153596\pi$
$440$	−242.045	+	139.745i	−0.550102	+	0.317602i
$441$	−6.22826	+	10.7877i	−0.0141230	+	0.0244618i
$442$	28.6978	+	49.7060i	0.0649271	+	0.112457i
$443$	−360.119	+	623.744i	−0.812909	+	1.40800i	0.0979100	+	0.995195i	$0.468784\pi$
$443$	−360.119	+	623.744i	−0.812909	+	1.40800i	−0.910819	+	0.412805i	$0.864549\pi$
$444$	314.262			0.707798
$445$		−	290.812i		−	0.653511i
$446$	−144.648	+	250.538i	−0.324323	+	0.561744i
$447$	388.161	+	224.105i	0.868368	+	0.501353i
$448$	−199.390			−0.445066
$449$		−	726.910i		−	1.61895i	−0.587151	−	0.809477i	$-0.699751\pi$
$449$		−	726.910i		−	1.61895i	0.587151	−	0.809477i	$-0.300249\pi$
$450$	−6.38603	−	3.68698i	−0.0141912	−	0.00819329i
$451$	−507.601	+	293.064i	−1.12550	+	0.649809i
$452$	−58.7171	−	33.9003i	−0.129905	−	0.0750007i
$453$	−59.6869	−	103.381i	−0.131759	−	0.228214i
$454$	−82.9256	−	143.631i	−0.182655	−	0.316369i
$455$			155.971i			0.342794i
$456$	214.765	−	176.613i	0.470977	−	0.387309i
$457$	114.104			0.249681			0.124841	−	0.992177i	$-0.460158\pi$
$457$	114.104			0.249681			0.124841	+	0.992177i	$0.460158\pi$
$458$	18.5988	−	10.7380i	0.0406087	−	0.0234454i
$459$	334.968	−	193.394i	0.729778	−	0.421338i
$460$	27.2037	−	47.1182i	0.0591385	−	0.102431i
$461$	157.029	+	271.982i	0.340626	+	0.589982i	0.984549	−	0.175108i	$-0.0560276\pi$
$461$	157.029	+	271.982i	0.340626	+	0.589982i	−0.643923	+	0.765090i	$0.722694\pi$
$462$	139.924	−	242.355i	0.302865	−	0.524578i
$463$	402.830			0.870044			0.435022	−	0.900420i	$-0.356741\pi$
$463$	402.830			0.870044			0.435022	+	0.900420i	$0.356741\pi$
$464$			475.490i			1.02476i
$465$	192.273	−	333.026i	0.413490	−	0.716185i
$466$	215.791	+	124.587i	0.463071	+	0.267354i
$467$	−759.715			−1.62680			−0.813399	−	0.581706i	$-0.802386\pi$
$467$	−759.715			−1.62680			−0.813399	+	0.581706i	$0.802386\pi$
$468$		−	15.5722i		−	0.0332739i
$469$	−692.938	−	400.068i	−1.47748	−	0.853023i
$470$	32.1279	−	18.5490i	0.0683572	−	0.0394660i
$471$	197.219	+	113.864i	0.418724	+	0.241751i
$472$	−59.7033	−	103.409i	−0.126490	−	0.219087i
$473$	−278.912	−	483.090i	−0.589667	−	1.02133i
$474$			93.9029i			0.198107i
$475$	273.085	+	102.470i	0.574916	+	0.215727i
$476$	−399.937			−0.840204
$477$	−10.4381	+	6.02645i	−0.0218829	+	0.0126341i
$478$	−62.1744	+	35.8964i	−0.130072	+	0.0750971i
$479$	14.1426	−	24.4957i	0.0295253	−	0.0511393i	−0.850885	−	0.525352i	$-0.823934\pi$
$479$	14.1426	−	24.4957i	0.0295253	−	0.0511393i	0.880411	+	0.474212i	$0.157267\pi$
$480$	−123.325	−	213.605i	−0.256927	−	0.445011i
$481$	94.7997	−	164.198i	0.197089	−	0.341368i
$482$	9.31119			0.0193178
$483$			115.926i			0.240013i
$484$	−340.887	+	590.433i	−0.704311	+	1.21990i
$485$	25.3374	+	14.6285i	0.0522420	+	0.0301620i
$486$	25.8758			0.0532423
$487$			918.051i			1.88511i	0.334045	+	0.942557i	$0.391586\pi$
$487$			918.051i			1.88511i	−0.334045	+	0.942557i	$0.608414\pi$
$488$	75.0777	+	43.3461i	0.153848	+	0.0888241i
$489$	−337.660	+	194.948i	−0.690510	+	0.398666i
$490$	31.6609	+	18.2794i	0.0646141	+	0.0373050i
$491$	−20.5361	−	35.5696i	−0.0418250	−	0.0724431i	0.844355	−	0.535784i	$-0.179984\pi$
$491$	−20.5361	−	35.5696i	−0.0418250	−	0.0724431i	−0.886180	+	0.463341i	$0.846651\pi$
$492$	−169.031	−	292.770i	−0.343559	−	0.595062i
$493$			611.309i			1.23998i
$494$	−12.9194	−	77.7678i	−0.0261526	−	0.157425i
$495$	39.1990			0.0791899
$496$	400.728	−	231.361i	0.807920	−	0.466453i
$497$	11.1007	−	6.40901i	0.0223355	−	0.0128954i
$498$	72.0206	−	124.743i	0.144620	−	0.250489i
$499$	−324.374	−	561.832i	−0.650047	−	1.12592i	−0.983111	−	0.183011i	$-0.941416\pi$
$499$	−324.374	−	561.832i	−0.650047	−	1.12592i	0.333063	−	0.942904i	$-0.391918\pi$
$500$	222.237	−	384.926i	0.444474	−	0.769852i
$501$	180.789			0.360856
$502$			82.7181i			0.164777i
$503$	−205.525	+	355.979i	−0.408598	+	0.707712i	−0.994733	−	0.102501i	$-0.967315\pi$
$503$	−205.525	+	355.979i	−0.408598	+	0.707712i	0.586135	+	0.810213i	$0.300649\pi$
$504$	−25.5930	−	14.7761i	−0.0507798	−	0.0293177i
$505$	−413.501			−0.818815
$506$			58.8951i			0.116393i
$507$	−326.759	−	188.654i	−0.644495	−	0.372100i
$508$	74.9414	−	43.2675i	0.147523	−	0.0851722i
$509$	−19.2779	−	11.1301i	−0.0378740	−	0.0218666i	0.480943	−	0.876752i	$-0.340294\pi$
$509$	−19.2779	−	11.1301i	−0.0378740	−	0.0218666i	−0.518817	+	0.854885i	$0.673628\pi$
$510$	−41.6657	−	72.1671i	−0.0816974	−	0.141504i
$511$	−23.2794	−	40.3211i	−0.0455566	−	0.0789064i
$512$		−	515.592i		−	1.00701i
$513$	−524.076	+	87.0636i	−1.02159	+	0.169715i
$514$	266.924			0.519307
$515$	249.609	−	144.112i	0.484677	−	0.279828i
$516$	278.633	−	160.869i	0.539986	−	0.311761i
$517$	156.885	−	271.734i	0.303454	−	0.525597i
$518$	−84.5434	−	146.433i	−0.163211	−	0.282690i
$519$	−469.698	+	813.541i	−0.905006	+	1.56752i
$520$	−97.2555			−0.187030
$521$		−	87.1316i		−	0.167239i	−0.996498	−	0.0836196i	$-0.973352\pi$
$521$		−	87.1316i		−	0.167239i	0.996498	−	0.0836196i	$-0.0266481\pi$
$522$	−10.6136	+	18.3832i	−0.0203325	+	0.0352169i
$523$	−342.658	−	197.833i	−0.655177	−	0.378267i	0.135260	−	0.990810i	$-0.456813\pi$
$523$	−342.658	−	197.833i	−0.655177	−	0.378267i	−0.790437	+	0.612544i	$0.790146\pi$
$524$	270.187			0.515624
$525$			360.298i			0.686282i
$526$	−31.2112	−	18.0198i	−0.0593369	−	0.0342582i
$527$	515.192	−	297.446i	0.977594	−	0.564414i
$528$	−474.768	−	274.107i	−0.899182	−	0.519143i
$529$	252.301	+	436.999i	0.476940	+	0.826085i
$530$	17.6872	+	30.6350i	0.0333720	+	0.0578020i
$531$			16.7471i			0.0315387i
$532$	514.304	+	192.983i	0.966736	+	0.362751i
$533$	−203.958			−0.382661
$534$	−157.242	+	90.7838i	−0.294461	+	0.170007i
$535$	−375.020	+	216.518i	−0.700972	+	0.404706i
$536$	249.461	−	432.079i	0.465412	−	0.806118i
$537$	383.655	+	664.510i	0.714442	+	1.23745i
$538$	−123.048	+	213.126i	−0.228714	+	0.396145i
$539$	309.210			0.573674
$540$			307.992i			0.570356i
$541$	509.586	−	882.629i	0.941933	−	1.63148i	0.180155	−	0.983638i	$-0.442340\pi$
$541$	509.586	−	882.629i	0.941933	−	1.63148i	0.761778	−	0.647838i	$-0.224327\pi$
$542$	101.731	+	58.7344i	0.187696	+	0.108366i
$543$	432.122			0.795805
$544$		−	381.569i		−	0.701413i
$545$	350.451	+	202.333i	0.643029	+	0.371253i
$546$	84.3337	−	48.6901i	0.154457	−	0.0891760i
$547$	582.402	+	336.250i	1.06472	+	0.614717i	0.926734	−	0.375717i	$-0.122604\pi$
$547$	582.402	+	336.250i	1.06472	+	0.614717i	0.137986	+	0.990434i	$0.455937\pi$
$548$	420.630	+	728.553i	0.767573	+	1.32948i
$549$	−6.07939	−	10.5298i	−0.0110736	−	0.0191800i
$550$			183.045i			0.332809i
$551$	294.978	−	786.120i	0.535350	−	1.42672i
$552$	−72.2856			−0.130952
$553$	−341.875	+	197.382i	−0.618219	+	0.356929i
$554$	−54.4232	+	31.4213i	−0.0982369	+	0.0567171i
$555$	−137.638	+	238.395i	−0.247996	+	0.429541i
$556$	−35.6042	−	61.6683i	−0.0640363	−	0.110914i
$557$	108.576	−	188.060i	0.194931	−	0.337630i	−0.751947	−	0.659223i	$-0.770885\pi$
$557$	108.576	−	188.060i	0.194931	−	0.337630i	0.946878	+	0.321594i	$0.104219\pi$
$558$	20.6571			0.0370199
$559$		−	194.109i		−	0.347244i
$560$	136.244	−	235.981i	0.243293	−	0.421395i
$561$	−610.381	−	352.403i	−1.08802	−	0.628170i
$562$	−253.082			−0.450324
$563$			571.551i			1.01519i	0.861596	+	0.507594i	$0.169465\pi$
$563$			571.551i			1.01519i	−0.861596	+	0.507594i	$0.830535\pi$
$564$	156.728	+	90.4872i	0.277887	+	0.160438i
$565$	51.4327	−	29.6947i	0.0910313	−	0.0525570i
$566$	−37.4245	−	21.6071i	−0.0661211	−	0.0381750i
$567$	−301.963	−	523.015i	−0.532562	−	0.922425i
$568$	3.99632	+	6.92183i	0.00703578	+	0.0121863i
$569$		−	411.891i		−	0.723886i	−0.932200	−	0.361943i	$-0.882114\pi$
$569$		−	411.891i		−	0.723886i	0.932200	−	0.361943i	$-0.117886\pi$
$570$	18.7574	+	112.909i	0.0329077	+	0.198087i
$571$	746.121			1.30669			0.653346	−	0.757060i	$-0.273365\pi$
$571$	746.121			1.30669			0.653346	+	0.757060i	$0.273365\pi$
$572$	−334.763	+	193.276i	−0.585250	+	0.337894i
$573$	−248.256	+	143.331i	−0.433257	+	0.250141i
$574$	−90.9460	+	157.523i	−0.158443	+	0.274431i
$575$	−37.9131	−	65.6674i	−0.0659358	−	0.114204i
$576$	−8.71870	+	15.1012i	−0.0151366	+	0.0262174i
$577$	−877.551			−1.52089			−0.760443	−	0.649405i	$-0.775018\pi$
$577$	−877.551			−1.52089			−0.760443	+	0.649405i	$0.775018\pi$
$578$			65.7817i			0.113809i
$579$	−70.5023	+	122.114i	−0.121766	+	0.210904i
$580$	−421.559	−	243.387i	−0.726826	−	0.419633i
$581$	605.542			1.04224
$582$		−	18.2666i		−	0.0313858i
$583$	259.107	+	149.596i	0.444438	+	0.256597i
$584$	25.1421	−	14.5158i	0.0430516	−	0.0248558i
$585$	11.8128	+	6.82015i	0.0201929	+	0.0116584i
$586$	−37.6639	−	65.2358i	−0.0642728	−	0.111324i
$587$	−0.899138	−	1.55735i	−0.00153175	−	0.00265307i	0.865259	−	0.501326i	$-0.167154\pi$
$587$	−0.899138	−	1.55735i	−0.00153175	−	0.00265307i	−0.866790	+	0.498673i	$0.833821\pi$
$588$			178.344i			0.303306i
$589$	−806.046	+	133.907i	−1.36850	+	0.227346i
$590$	49.1513			0.0833072
$591$	−418.380	+	241.552i	−0.707919	+	0.408717i
$592$	−286.860	+	165.618i	−0.484560	+	0.279761i
$593$	−5.61476	+	9.72504i	−0.00946839	+	0.0163997i	−0.870721	−	0.491778i	$-0.836347\pi$
$593$	−5.61476	+	9.72504i	−0.00946839	+	0.0163997i	0.861252	+	0.508177i	$0.169681\pi$
$594$	−166.698	−	288.730i	−0.280637	−	0.486077i
$595$	175.160	−	303.387i	0.294387	−	0.509894i
$596$	−552.127			−0.926387
$597$		−	266.339i		−	0.446129i
$598$	−10.2470	+	17.7484i	−0.0171355	+	0.0296795i
$599$	−391.707	−	226.152i	−0.653934	−	0.377549i	0.136028	−	0.990705i	$-0.456566\pi$
$599$	−391.707	−	226.152i	−0.653934	−	0.377549i	−0.789962	+	0.613156i	$0.789900\pi$
$600$	−224.663			−0.374438
$601$			32.0350i			0.0533029i	0.999645	+	0.0266514i	$0.00848442\pi$
$601$			32.0350i			0.0533029i	−0.999645	+	0.0266514i	$0.991516\pi$
$602$	−149.917	−	86.5544i	−0.249031	−	0.143778i
$603$	−60.6001	+	34.9875i	−0.100498	+	0.0580223i
$604$	127.350	+	73.5253i	0.210844	+	0.121731i
$605$	−298.596	−	517.184i	−0.493548	−	0.854850i
$606$	129.084	+	223.580i	0.213010	+	0.368944i
$607$		−	161.891i		−	0.266706i	−0.991069	−	0.133353i	$-0.957426\pi$
$607$		−	161.891i		−	0.266706i	0.991069	−	0.133353i	$-0.0425745\pi$
$608$	−184.120	+	490.683i	−0.302829	+	0.807044i
$609$	1037.18			1.70308
$610$	−30.9042	+	17.8425i	−0.0506626	+	0.0292500i
$611$	94.5567	−	54.5923i	0.154757	−	0.0893491i
$612$	−17.4880	+	30.2901i	−0.0285752	+	0.0494937i
$613$	−9.10873	−	15.7768i	−0.0148593	−	0.0257370i	0.858500	−	0.512813i	$-0.171397\pi$
$613$	−9.10873	−	15.7768i	−0.0148593	−	0.0257370i	−0.873359	+	0.487076i	$0.838063\pi$
$614$	115.648	−	200.308i	0.188351	−	0.326234i
$615$	296.122			0.481500
$616$			733.582i			1.19088i
$617$	355.912	−	616.457i	0.576842	−	0.999120i	−0.418997	−	0.907988i	$-0.637618\pi$
$617$	355.912	−	616.457i	0.576842	−	0.999120i	0.995839	−	0.0911323i	$-0.0290486\pi$
$618$	−155.842	−	89.9756i	−0.252172	−	0.145592i
$619$	1039.82			1.67984			0.839918	−	0.542713i	$-0.182603\pi$
$619$	1039.82			1.67984			0.839918	+	0.542713i	$0.182603\pi$
$620$			473.702i			0.764036i
$621$	119.606	+	69.0545i	0.192602	+	0.111199i
$622$	146.862	−	84.7911i	0.236113	−	0.136320i
$623$	−661.038	−	381.651i	−1.06106	−	0.612601i
$624$	−95.3827	−	165.208i	−0.152857	−	0.264756i
$625$	2.77356	+	4.80394i	0.00443769	+	0.00768631i
$626$		−	327.604i		−	0.523330i
$627$	614.880	+	747.707i	0.980669	+	1.19252i
$628$	−280.528			−0.446701
$629$	−368.798	+	212.926i	−0.586325	+	0.338515i
$630$	10.5348	−	6.08228i	0.0167219	−	0.00965442i
$631$	−417.964	+	723.935i	−0.662383	+	1.14728i	0.317604	+	0.948223i	$0.397122\pi$
$631$	−417.964	+	723.935i	−0.662383	+	1.14728i	−0.979988	+	0.199058i	$0.936212\pi$
$632$	−123.077	−	213.175i	−0.194742	−	0.337302i
$633$	−90.4254	+	156.621i	−0.142852	+	0.247427i
$634$	186.876			0.294756
$635$			75.7994i			0.119369i
$636$	−86.2827	+	149.446i	−0.135665	+	0.234978i
$637$	93.1823	+	53.7988i	0.146283	+	0.0844566i
$638$	526.925			0.825902
$639$		−	1.12099i		−	0.00175428i
$640$	341.128	+	196.950i	0.533012	+	0.307735i
$641$	504.690	−	291.383i	0.787347	−	0.454575i	−0.0516806	−	0.998664i	$-0.516458\pi$
$641$	504.690	−	291.383i	0.787347	−	0.454575i	0.839028	+	0.544089i	$0.183124\pi$
$642$	234.142	+	135.182i	0.364708	+	0.210564i
$643$	−238.122	−	412.439i	−0.370330	−	0.641430i	0.619286	−	0.785165i	$-0.287422\pi$
$643$	−238.122	−	412.439i	−0.370330	−	0.641430i	−0.989616	+	0.143735i	$0.954089\pi$
$644$	−71.4021	−	123.672i	−0.110873	−	0.192037i
$645$			281.823i			0.436935i
$646$	−62.2054	+	165.778i	−0.0962932	+	0.256623i
$647$	−304.985			−0.471383			−0.235691	−	0.971828i	$-0.575735\pi$
$647$	−304.985			−0.471383			−0.235691	+	0.971828i	$0.575735\pi$
$648$	326.124	−	188.288i	0.503278	−	0.290568i
$649$	360.020	−	207.858i	0.554730	−	0.320274i
$650$	−31.8476	+	55.1617i	−0.0489963	+	0.0848642i
$651$	−504.662	−	874.100i	−0.775210	−	1.34270i
$652$	240.147	−	415.946i	0.368323	−	0.637954i
$653$	123.278			0.188787			0.0943937	−	0.995535i	$-0.469909\pi$
$653$	123.278			0.188787			0.0943937	+	0.995535i	$0.469909\pi$
$654$		−	252.651i		−	0.386317i
$655$	−118.334	+	204.960i	−0.180662	+	0.312916i
$656$	308.584	+	178.161i	0.470402	+	0.271587i
$657$	−4.07175			−0.00619749
$658$		−	97.3721i		−	0.147982i
$659$	749.625	+	432.796i	1.13752	+	0.656747i	0.945815	−	0.324706i	$-0.105265\pi$
$659$	749.625	+	432.796i	1.13752	+	0.656747i	0.191704	+	0.981453i	$0.438599\pi$
$660$	486.035	−	280.613i	0.736417	−	0.425171i
$661$	−572.988	−	330.815i	−0.866850	−	0.500476i	−0.000549974	−	1.00000i	$-0.500175\pi$
$661$	−572.988	−	330.815i	−0.866850	−	0.500476i	−0.866300	+	0.499524i	$0.833508\pi$
$662$	−37.2145	−	64.4573i	−0.0562152	−	0.0973676i
$663$	−122.628	−	212.398i	−0.184959	−	0.320358i
$664$			377.584i			0.568651i
$665$	−371.644	+	305.623i	−0.558864	+	0.459583i
$666$	−14.7873			−0.0222031
$667$	−189.034	+	109.139i	−0.283410	+	0.163627i
$668$	−192.868	+	111.352i	−0.288724	+	0.166695i
$669$	618.092	−	1070.57i	0.923904	−	1.60025i
$670$	102.685	+	177.856i	0.153262	+	0.265457i
$671$	−150.910	+	261.384i	−0.224903	+	0.389543i
$672$	−647.388			−0.963375
$673$			104.231i			0.154875i	0.996997	+	0.0774373i	$0.0246737\pi$
$673$			104.231i			0.154875i	−0.996997	+	0.0774373i	$0.975326\pi$
$674$	−9.32458	+	16.1506i	−0.0138347	+	0.0239624i
$675$	371.734	+	214.621i	0.550717	+	0.317956i
$676$	464.788			0.687557
$677$			863.985i			1.27620i	0.769955	+	0.638099i	$0.220279\pi$
$677$			863.985i			1.27620i	−0.769955	+	0.638099i	$0.779721\pi$
$678$	−32.1118	−	18.5398i	−0.0473626	−	0.0273448i
$679$	66.5036	−	38.3958i	0.0979434	−	0.0565476i
$680$	189.176	+	109.221i	0.278200	+	0.160619i
$681$	354.347	+	613.747i	0.520333	+	0.901244i
$682$	−256.388	−	444.076i	−0.375935	−	0.651138i
$683$			34.9808i			0.0512165i	0.999672	+	0.0256082i	$0.00815224\pi$
$683$			34.9808i			0.0512165i	−0.999672	+	0.0256082i	$0.991848\pi$
$684$	37.1050	−	30.5134i	0.0542470	−	0.0446102i
$685$	−736.894			−1.07576
$686$	−149.976	+	86.5886i	−0.218624	+	0.126222i
$687$	−79.4739	+	45.8843i	−0.115683	+	0.0667893i
$688$	−169.558	+	293.683i	−0.246451	+	0.426865i
$689$	52.0557	+	90.1631i	0.0755525	+	0.130861i
$690$	14.8774	−	25.7685i	0.0215615	−	0.0373456i
$691$	−346.797			−0.501876			−0.250938	−	0.968003i	$-0.580739\pi$
$691$	−346.797			−0.501876			−0.250938	+	0.968003i	$0.580739\pi$
$692$		−	1157.20i		−	1.67225i
$693$	51.4432	−	89.1023i	0.0742326	−	0.128575i
$694$	150.809	+	87.0696i	0.217304	+	0.125461i
$695$	62.3743			0.0897472
$696$			646.728i			0.929208i
$697$	396.728	+	229.051i	0.569193	+	0.328624i
$698$	−293.379	+	169.383i	−0.420314	+	0.242668i
$699$	−922.091	−	532.369i	−1.31916	−	0.761615i
$700$	−221.917	−	384.371i	−0.317024	−	0.549101i
$701$	−320.881	−	555.783i	−0.457748	−	0.792843i	0.541094	−	0.840962i	$-0.318010\pi$
$701$	−320.881	−	555.783i	−0.457748	−	0.792843i	−0.998842	+	0.0481197i	$0.984677\pi$
$702$		−	116.014i		−	0.165262i
$703$	577.005	−	95.8565i	0.820775	−	0.136354i
$704$	432.852			0.614847
$705$	−137.285	+	79.2614i	−0.194730	+	0.112427i
$706$	−31.5674	+	18.2255i	−0.0447131	+	0.0258151i
$707$	−542.663	+	939.920i	−0.767557	+	1.32945i
$708$	119.887	+	207.650i	0.169331	+	0.293290i
$709$	−277.968	+	481.454i	−0.392056	+	0.679061i	−0.992721	−	0.120440i	$-0.961569\pi$
$709$	−277.968	+	481.454i	−0.392056	+	0.679061i	0.600665	+	0.799501i	$0.294903\pi$
$710$	−3.29000			−0.00463381
$711$			34.5236i			0.0485563i
$712$	237.977	−	412.188i	0.334238	−	0.578916i
$713$	183.958	+	106.208i	0.258006	+	0.148960i
$714$	−218.722			−0.306333
$715$		−	338.596i		−	0.473561i
$716$	−818.578	−	472.606i	−1.14326	−	0.660064i
$717$	265.676	−	153.388i	0.370538	−	0.213930i
$718$	−255.176	−	147.326i	−0.355398	−	0.205189i
$719$	120.548	+	208.795i	0.167661	+	0.290397i	0.937597	−	0.347724i	$-0.113045\pi$
$719$	120.548	+	208.795i	0.167661	+	0.290397i	−0.769936	+	0.638121i	$0.779712\pi$
$720$	−11.9150	−	20.6375i	−0.0165487	−	0.0286632i
$721$		−	756.505i		−	1.04924i
$722$	159.988	−	183.168i	0.221590	−	0.253696i
$723$	−39.7874			−0.0550310
$724$	−460.994	+	266.155i	−0.636732	+	0.367618i
$725$	−587.516	+	339.203i	−0.810367	+	0.467866i
$726$	−186.428	+	322.902i	−0.256787	+	0.444769i
$727$	−495.032	−	857.420i	−0.680924	−	1.17939i	−0.974699	−	0.223520i	$-0.928245\pi$
$727$	−495.032	−	857.420i	−0.680924	−	1.17939i	0.293776	−	0.955874i	$-0.405088\pi$
$728$	−127.634	+	221.069i	−0.175322	+	0.303666i
$729$	−777.240			−1.06617
$730$			11.9503i			0.0163702i
$731$	−217.991	+	377.571i	−0.298209	+	0.516513i
$732$	−150.759	−	87.0406i	−0.205955	−	0.118908i
$733$	748.994			1.02182			0.510910	−	0.859634i	$-0.329309\pi$
$733$	748.994			1.02182			0.510910	+	0.859634i	$0.329309\pi$
$734$			64.8531i			0.0883557i
$735$	−135.289	−	78.1093i	−0.184067	−	0.106271i
$736$	117.992	−	68.1227i	0.160315	−	0.0925580i
$737$	1504.29	+	868.501i	2.04110	+	1.17843i
$738$	7.95358	+	13.7760i	0.0107772	+	0.0186667i
$739$	−123.521	−	213.945i	−0.167147	−	0.289506i	0.770269	−	0.637719i	$-0.220122\pi$
$739$	−123.521	−	213.945i	−0.167147	−	0.289506i	−0.937415	+	0.348213i	$0.886789\pi$
$740$		−	339.098i		−	0.458240i
$741$	55.2055	+	332.307i	0.0745014	+	0.448458i
$742$	92.8477			0.125132
$743$	278.718	−	160.918i	0.375126	−	0.216579i	−0.300570	−	0.953760i	$-0.597177\pi$
$743$	278.718	−	160.918i	0.375126	−	0.216579i	0.675695	+	0.737181i	$0.263843\pi$
$744$	545.043	−	314.680i	0.732584	−	0.422958i
$745$	241.815	−	418.836i	0.324584	−	0.562196i
$746$	201.621	+	349.218i	0.270270	+	0.468121i
$747$	26.4785	−	45.8621i	0.0354465	−	0.0613951i
$748$	868.217			1.16072
$749$			1136.60i			1.51749i
$750$	121.539	−	210.512i	0.162052	−	0.280683i
$751$	−165.099	−	95.3199i	−0.219839	−	0.126924i	0.386037	−	0.922483i	$-0.373844\pi$
$751$	−165.099	−	95.3199i	−0.219839	−	0.126924i	−0.605876	+	0.795559i	$0.707177\pi$
$752$	−190.749			−0.253656
$753$		−	353.461i		−	0.469403i
$754$	158.792	+	91.6786i	0.210599	+	0.121590i
$755$	−111.551	+	64.4038i	−0.147749	+	0.0853031i
$756$	700.090	+	404.197i	0.926044	+	0.534652i
$757$	292.845	+	507.222i	0.386849	+	0.670042i	0.992024	−	0.126050i	$-0.0402301\pi$
$757$	292.845	+	507.222i	0.386849	+	0.670042i	−0.605175	+	0.796093i	$0.706897\pi$
$758$	54.2385	+	93.9439i	0.0715548	+	0.123936i
$759$		−	251.663i		−	0.331572i
$760$	−190.570	−	231.738i	−0.250750	−	0.304918i
$761$	581.690			0.764376			0.382188	−	0.924085i	$-0.375171\pi$
$761$	581.690			0.764376			0.382188	+	0.924085i	$0.375171\pi$
$762$	40.9847	−	23.6626i	0.0537858	−	0.0310532i
$763$	919.835	−	531.067i	1.20555	−	0.696025i
$764$	176.562	−	305.815i	0.231102	−	0.400281i
$765$	−15.3185	−	26.5324i	−0.0200241	−	0.0346828i
$766$	−77.9799	+	135.065i	−0.101801	+	0.176325i
$767$	144.659			0.188603
$768$			35.6792i			0.0464573i
$769$	−642.973	+	1113.66i	−0.836116	+	1.44820i	0.0570025	+	0.998374i	$0.481846\pi$
$769$	−642.973	+	1113.66i	−0.836116	+	1.44820i	−0.893119	+	0.449821i	$0.851488\pi$
$770$	−261.508	−	150.982i	−0.339621	−	0.196080i
$771$	−1140.59			−1.47936
$772$		−	173.697i		−	0.224996i
$773$	−1069.34	−	617.384i	−1.38336	−	0.798686i	−0.390809	−	0.920472i	$-0.627805\pi$
$773$	−1069.34	−	617.384i	−1.38336	−	0.798686i	−0.992556	+	0.121786i	$0.961138\pi$
$774$	−13.1108	+	7.56952i	−0.0169390	+	0.00977974i
$775$	571.739	+	330.094i	0.737728	+	0.425927i
$776$	23.9416	+	41.4681i	0.0308526	+	0.0534383i
$777$	361.260	+	625.721i	0.464942	+	0.805304i
$778$		−	54.5786i		−	0.0701525i
$779$	−399.652	−	485.986i	−0.513032	−	0.623859i
$780$	195.293			0.250375
$781$	−24.0984	+	13.9132i	−0.0308558	+	0.0178146i
$782$	39.8639	−	23.0154i	0.0509768	−	0.0294315i
$783$	617.820	−	1070.10i	0.789043	−	1.36666i
$784$	−93.9885	−	162.793i	−0.119883	−	0.207644i
$785$	122.863	−	212.805i	0.156513	−	0.271089i
$786$	147.763			0.187993
$787$			543.258i			0.690289i	0.938550	+	0.345145i	$0.112170\pi$
$787$			543.258i			0.690289i	−0.938550	+	0.345145i	$0.887830\pi$
$788$	297.556	−	515.382i	0.377609	−	0.654038i
$789$	133.368	+	76.9999i	0.169034	+	0.0975918i
$790$	101.324			0.128258
$791$		−	155.880i		−	0.197068i
$792$	55.5595	+	32.0773i	0.0701508	+	0.0405016i
$793$	−90.9551	+	52.5130i	−0.114698	+	0.0662206i
$794$	−397.959	−	229.762i	−0.501208	−	0.289373i
$795$	−75.5785	−	130.906i	−0.0950673	−	0.164661i
$796$	164.045	+	284.134i	0.206087	+	0.356953i
$797$			942.119i			1.18208i	0.806642	+	0.591041i	$0.201283\pi$
$797$			942.119i			1.18208i	−0.806642	+	0.591041i	$0.798717\pi$
$798$	281.268	+	105.541i	0.352466	+	0.132257i
$799$	−245.235			−0.306928
$800$	366.718	−	211.724i	0.458397	−	0.264656i
$801$	−57.8103	+	33.3768i	−0.0721727	+	0.0416689i
$802$	32.1630	−	55.7080i	0.0401035	−	0.0694614i
$803$	50.5369	+	87.5325i	0.0629352	+	0.109007i
$804$	−500.927	+	867.631i	−0.623043	+	1.07914i
$805$	125.088			0.155389
$806$		−	178.433i		−	0.221381i
$807$	525.794	−	910.703i	0.651542	−	1.12850i
$808$	−586.084	−	338.376i	−0.725352	−	0.418782i
$809$	−374.800			−0.463288			−0.231644	−	0.972801i	$-0.574410\pi$
$809$	−374.800			−0.463288			−0.231644	+	0.972801i	$0.574410\pi$
$810$			155.010i			0.191370i
$811$	−145.337	−	83.9101i	−0.179207	−	0.103465i	0.407713	−	0.913110i	$-0.366326\pi$
$811$	−145.337	−	83.9101i	−0.179207	−	0.103465i	−0.586920	+	0.809645i	$0.699660\pi$
$812$	−1106.47	+	638.823i	−1.36265	+	0.786728i
$813$	−434.704	−	250.976i	−0.534691	−	0.308704i
$814$	183.534	+	317.890i	0.225472	+	0.390528i
$815$	210.354	+	364.344i	0.258103	+	0.447048i
$816$			428.470i			0.525086i
$817$	462.518	−	380.354i	0.566118	−	0.465549i
$818$	131.723			0.161030
$819$	31.0054	−	17.9010i	0.0378577	−	0.0218571i
$820$	−315.907	+	182.389i	−0.385253	+	0.222426i
$821$	−628.725	+	1088.98i	−0.765804	+	1.32641i	0.174016	+	0.984743i	$0.444325\pi$
$821$	−628.725	+	1088.98i	−0.765804	+	1.32641i	−0.939820	+	0.341669i	$0.889008\pi$
$822$	230.038	+	398.438i	0.279852	+	0.484718i
$823$	225.462	−	390.511i	0.273951	−	0.474497i	−0.695919	−	0.718120i	$-0.745003\pi$
$823$	225.462	−	390.511i	0.273951	−	0.474497i	0.969870	+	0.243623i	$0.0783361\pi$
$824$	471.717			0.572472
$825$		−	782.165i		−	0.948079i
$826$	64.5041	−	111.724i	0.0780922	−	0.135260i
$827$	−349.235	−	201.631i	−0.422292	−	0.243810i	0.273766	−	0.961796i	$-0.411731\pi$
$827$	−349.235	−	201.631i	−0.422292	−	0.243810i	−0.696057	+	0.717986i	$0.745064\pi$
$828$	−12.4888			−0.0150831
$829$		−	676.543i		−	0.816096i	−0.912961	−	0.408048i	$-0.866210\pi$
$829$		−	676.543i		−	0.816096i	0.912961	−	0.408048i	$-0.133790\pi$
$830$	−134.602	−	77.7123i	−0.162171	−	0.0936293i
$831$	232.554	−	134.265i	0.279849	−	0.161571i
$832$	130.442	+	75.3110i	0.156782	+	0.0905180i
$833$	−120.835	−	209.293i	−0.145060	−	0.251252i
$834$	−19.4716	−	33.7258i	−0.0233472	−	0.0404386i
$835$		−	195.076i		−	0.233624i
$836$	−1116.49	−	418.945i	−1.33552	−	0.501130i
$837$	−1202.46			−1.43663
$838$	226.556	−	130.802i	0.270354	−	0.156089i
$839$	−1311.19	+	757.016i	−1.56280	+	0.902284i	−0.565830	+	0.824522i	$0.691444\pi$
$839$	−1311.19	+	757.016i	−1.56280	+	0.902284i	−0.996972	+	0.0777621i	$0.975223\pi$
$840$	185.309	−	320.965i	0.220606	−	0.382101i
$841$	555.950	+	962.934i	0.661058	+	1.14499i
$842$	−87.8912	+	152.232i	−0.104384	+	0.180798i
$843$	1081.44			1.28285
$844$		−	222.781i		−	0.263959i
$845$	−203.563	+	352.582i	−0.240903	+	0.417257i
$846$	−7.37469	−	4.25778i	−0.00871713	−	0.00503284i
$847$	−1567.46			−1.85061
$848$		−	181.886i		−	0.214489i
$849$	159.918	+	92.3285i	0.188360	+	0.108750i
$850$	123.896	−	71.5316i	0.145761	−	0.0841549i
$851$	−131.686	−	76.0287i	−0.154742	−	0.0893404i
$852$	−8.02476	−	13.8993i	−0.00941873	−	0.0163137i
$853$	−533.457	−	923.975i	−0.625389	−	1.08321i	−0.988465	−	0.151447i	$-0.951607\pi$
$853$	−533.457	−	923.975i	−0.625389	−	1.08321i	0.363076	−	0.931760i	$-0.381727\pi$
$854$			93.6633i			0.109676i
$855$	6.89618	+	41.5113i	0.00806571	+	0.0485512i
$856$	−708.722			−0.827946
$857$	1171.55	−	676.397i	1.36704	−	0.789261i	0.376492	−	0.926420i	$-0.377130\pi$
$857$	1171.55	−	676.397i	1.36704	−	0.789261i	0.990549	+	0.137158i	$0.0437970\pi$
$858$	−183.079	+	105.701i	−0.213378	+	0.123194i
$859$	419.232	−	726.131i	0.488046	−	0.845321i	−0.511859	−	0.859069i	$-0.671043\pi$
$859$	419.232	−	726.131i	0.488046	−	0.845321i	0.999905	+	0.0137483i	$0.00437635\pi$
$860$	−173.582	−	300.653i	−0.201839	−	0.349596i
$861$	388.619	−	673.108i	0.451358	−	0.781774i
$862$	−386.372			−0.448228
$863$			61.7364i			0.0715369i	0.999360	+	0.0357685i	$0.0113879\pi$
$863$			61.7364i			0.0715369i	−0.999360	+	0.0357685i	$0.988612\pi$
$864$	−385.633	+	667.936i	−0.446334	+	0.773074i
$865$	877.833	+	506.817i	1.01484	+	0.585916i
$866$	−168.612			−0.194702
$867$		−	281.090i		−	0.324210i
$868$	1076.76	+	621.668i	1.24051	+	0.716208i
$869$	742.171	−	428.492i	0.854051	−	0.493087i
$870$	−230.547	−	133.106i	−0.264996	−	0.152996i
$871$	302.217	+	523.455i	0.346977	+	0.600982i
$872$	331.145	+	573.560i	0.379754	+	0.657753i
$873$		−	6.71573i		−	0.00769270i
$874$	−62.3692	+	10.3613i	−0.0713606	+	0.0118550i
$875$	1021.89			1.16788
$876$	−50.4863	+	29.1483i	−0.0576328	+	0.0332743i
$877$	−411.522	+	237.592i	−0.469239	+	0.270915i	−0.715921	−	0.698181i	$-0.753993\pi$
$877$	−411.522	+	237.592i	−0.469239	+	0.270915i	0.246682	+	0.969096i	$0.420660\pi$
$878$	−158.264	+	274.121i	−0.180255	+	0.312211i
$879$	160.940	+	278.757i	0.183095	+	0.317130i
$880$	−295.770	+	512.288i	−0.336102	+	0.582145i
$881$	1656.73			1.88051			0.940253	−	0.340477i	$-0.110588\pi$
$881$	1656.73			1.88051			0.940253	+	0.340477i	$0.110588\pi$
$882$		−	8.39179i		−	0.00951450i
$883$	3.24702	−	5.62400i	0.00367726	−	0.00636920i	−0.864181	−	0.503181i	$-0.832163\pi$
$883$	3.24702	−	5.62400i	0.00367726	−	0.00636920i	0.867858	+	0.496812i	$0.165496\pi$
$884$	261.642	+	151.059i	0.295975	+	0.170881i
$885$	−210.027			−0.237319
$886$		−	485.215i		−	0.547647i
$887$	−517.144	−	298.573i	−0.583026	−	0.336610i	0.179309	−	0.983793i	$-0.442614\pi$
$887$	−517.144	−	298.573i	−0.583026	−	0.336610i	−0.762335	+	0.647183i	$0.775947\pi$
$888$	−390.166	+	225.263i	−0.439377	+	0.253674i
$889$	172.298	+	99.4762i	0.193811	+	0.111897i
$890$	97.9583	+	169.669i	0.110065	+	0.190639i
$891$	655.526	+	1135.40i	0.735719	+	1.27430i
$892$			1522.79i			1.70717i
$893$	315.363	+	118.334i	0.353150	+	0.132513i
$894$	−301.953			−0.337755
$895$	717.025	−	413.975i	0.801145	−	0.462542i
$896$	895.364	−	516.939i	0.999291	−	0.576941i
$897$	43.7863	−	75.8401i	0.0488141	−	0.0845486i
$898$	244.855	+	424.101i	0.272667	+	0.472273i
$899$	950.228	−	1645.84i	1.05698	−	1.83075i
$900$	−38.8149			−0.0431277
$901$		−	233.840i		−	0.259534i
$902$	197.433	−	341.964i	0.218884	−	0.379118i
$903$	640.605	+	369.853i	0.709418	+	0.409583i
$904$	97.1988			0.107521
$905$		−	466.272i		−	0.515218i
$906$	69.6463	+	40.2103i	0.0768723	+	0.0443822i
$907$	−1415.50	+	817.238i	−1.56064	+	0.901034i	−0.563445	+	0.826154i	$0.690524\pi$
$907$	−1415.50	+	817.238i	−1.56064	+	0.901034i	−0.997192	+	0.0748809i	$0.976142\pi$
$908$	−756.045	−	436.503i	−0.832649	−	0.480730i
$909$	47.4580	+	82.1996i	0.0522090	+	0.0904286i
$910$	−52.5380	−	90.9984i	−0.0577340	−	0.0999983i
$911$		−	1326.40i		−	1.45598i	−0.685587	−	0.727991i	$-0.740454\pi$
$911$		−	1326.40i		−	1.45598i	0.685587	−	0.727991i	$-0.259546\pi$
$912$	206.752	−	550.997i	0.226702	−	0.604163i
$913$	−1314.56			−1.43983
$914$	−66.5719	+	38.4353i	−0.0728358	+	0.0420518i
$915$	132.056	−	76.2424i	0.144323	−	0.0833251i
$916$	56.5226	−	97.9000i	0.0617059	−	0.106878i
$917$	310.593	+	537.963i	0.338706	+	0.586655i
$918$	−130.287	+	225.664i	−0.141925	+	0.245821i
$919$	−1155.93			−1.25782			−0.628908	−	0.777479i	$-0.716498\pi$
$919$	−1155.93			−1.25782			−0.628908	+	0.777479i	$0.716498\pi$
$920$			77.9982i			0.0847807i
$921$	−494.171	+	855.930i	−0.536559	+	0.929348i
$922$	−183.231	−	105.788i	−0.198732	−	0.114738i
$923$	−9.68293			−0.0104907
$924$		−	1473.06i		−	1.59422i
$925$	−409.277	−	236.296i	−0.442461	−	0.255455i
$926$	−235.023	+	135.691i	−0.253805	+	0.146534i
$927$	−57.2957	−	33.0797i	−0.0618076	−	0.0356846i
$928$	−609.483	−	1055.66i	−0.656771	−	1.13756i
$929$	−24.9510	−	43.2164i	−0.0268579	−	0.0465192i	0.852284	−	0.523079i	$-0.175217\pi$
$929$	−24.9510	−	43.2164i	−0.0268579	−	0.0465192i	−0.879142	+	0.476560i	$0.841883\pi$
$930$			259.063i			0.278563i
$931$	54.3986	+	327.450i	0.0584303	+	0.351719i
$932$	1311.60			1.40729
$933$	−627.554	+	362.318i	−0.672619	+	0.388337i
$934$	443.241	−	255.905i	0.474562	−	0.273988i
$935$	−380.253	+	658.618i	−0.406688	+	0.704404i
$936$	11.1621	+	19.3333i	0.0119253	+	0.0206553i
$937$	261.663	−	453.214i	0.279256	−	0.483686i	−0.691944	−	0.721951i	$-0.743245\pi$
$937$	261.663	−	453.214i	0.279256	−	0.483686i	0.971200	+	0.238265i	$0.0765788\pi$
$938$	539.041			0.574670
$939$			1399.88i			1.49082i
$940$	97.6382	−	169.114i	0.103870	−	0.179909i
$941$	528.450	+	305.101i	0.561583	+	0.324230i	0.753781	−	0.657126i	$-0.228228\pi$
$941$	528.450	+	305.101i	0.561583	+	0.324230i	−0.192197	+	0.981356i	$0.561561\pi$
$942$	−153.418			−0.162864
$943$			163.573i			0.173460i
$944$	−218.865	−	126.362i	−0.231849	−	0.133858i
$945$	−613.237	+	354.052i	−0.648928	+	0.374659i
$946$	325.452	+	187.900i	0.344029	+	0.198625i
$947$	−727.100	−	1259.37i	−0.767794	−	1.32986i	−0.938757	−	0.344580i	$-0.888021\pi$
$947$	−727.100	−	1259.37i	−0.767794	−	1.32986i	0.170963	−	0.985277i	$-0.445312\pi$
$948$	247.143	+	428.063i	0.260699	+	0.451544i
$949$			35.1712i			0.0370614i
$950$	−193.843	+	32.2027i	−0.204045	+	0.0338975i
$951$	−798.533			−0.839677
$952$	496.534	−	286.674i	0.521569	−	0.301128i
$953$	1408.40	−	813.142i	1.47786	−	0.853244i	0.478176	−	0.878264i	$-0.341298\pi$
$953$	1408.40	−	813.142i	1.47786	−	0.853244i	0.999687	+	0.0250198i	$0.00796489\pi$
$954$	4.05994	−	7.03203i	0.00425571	−	0.00737110i
$955$	154.658	+	267.876i	0.161946	+	0.280498i
$956$	−188.951	+	327.273i	−0.197648	+	0.342336i
$957$	−2251.59			−2.35276
$958$			19.0554i			0.0198908i
$959$	−967.070	+	1675.01i	−1.00842	+	1.74663i
$960$	−189.386	−	109.342i	−0.197278	−	0.113898i
$961$	−888.421			−0.924475
$962$			127.731i			0.132776i
$963$	86.0828	+	49.6999i	0.0893902	+	0.0516095i
$964$	42.4457	−	24.5061i	0.0440309	−	0.0254212i
$965$	131.764	+	76.0739i	0.136543	+	0.0788331i
$966$	−39.0491	−	67.6350i	−0.0404235	−	0.0700155i
$967$	716.252	+	1240.59i	0.740695	+	1.28292i	0.952179	+	0.305540i	$0.0988370\pi$
$967$	716.252	+	1240.59i	0.740695	+	1.28292i	−0.211484	+	0.977381i	$0.567830\pi$
$968$		−	977.388i		−	1.00970i
$969$	265.808	−	708.383i	0.274312	−	0.731046i
$970$	−19.7101			−0.0203197
$971$	−870.744	+	502.724i	−0.896749	+	0.517738i	−0.876144	−	0.482049i	$-0.839893\pi$
$971$	−870.744	+	502.724i	−0.896749	+	0.517738i	−0.0206051	+	0.999788i	$0.506559\pi$
$972$	117.957	−	68.1023i	0.121355	−	0.0700641i
$973$	81.8575	−	141.781i	0.0841290	−	0.145716i
$974$	−309.239	−	535.618i	−0.317494	−	0.549916i
$975$	136.087	−	235.710i	0.139577	−	0.241754i
$976$	183.484			0.187996
$977$		−	1459.45i		−	1.49381i	−0.664931	−	0.746905i	$-0.731539\pi$
$977$		−	1459.45i		−	1.49381i	0.664931	−	0.746905i	$-0.268461\pi$
$978$	131.334	−	227.477i	0.134288	−	0.232594i
$979$	1435.04	+	828.519i	1.46582	+	0.846291i
$980$	192.438			0.196365
$981$		−	92.8877i		−	0.0946868i
$982$	23.9628	+	13.8349i	0.0244020	+	0.0140885i
$983$	447.660	−	258.456i	0.455401	−	0.262926i	−0.254707	−	0.967018i	$-0.581979\pi$
$983$	447.660	−	258.456i	0.455401	−	0.262926i	0.710109	+	0.704092i	$0.248646\pi$
$984$	419.714	+	242.322i	0.426539	+	0.246262i
$985$	260.641	+	451.444i	0.264611	+	0.458319i
$986$	−205.915	−	356.656i	−0.208839	−	0.361720i
$987$			416.078i			0.421558i
$988$	−263.571	−	320.508i	−0.266772	−	0.324401i
$989$	−155.674			−0.157406
$990$	−22.8699	+	13.2039i	−0.0231009	+	0.0133373i
$991$	−333.382	+	192.478i	−0.336410	+	0.194226i	−0.658683	−	0.752420i	$-0.728886\pi$
$991$	−333.382	+	192.478i	−0.336410	+	0.194226i	0.322274	+	0.946647i	$0.395553\pi$
$992$	−593.116	+	1027.31i	−0.597899	+	1.03559i
$993$	159.020	+	275.431i	0.160141	+	0.277373i
$994$	−4.31767	+	7.47842i	−0.00434373	+	0.00752357i
$995$	−287.388			−0.288832
$996$		−	758.203i		−	0.761248i
$997$	532.640	−	922.560i	0.534243	−	0.925336i	−0.464957	−	0.885333i	$-0.653930\pi$
$997$	532.640	−	922.560i	0.534243	−	0.925336i	0.999200	−	0.0400025i	$-0.0127366\pi$
$998$	378.499	+	218.526i	0.379257	+	0.218964i
$999$	860.775			0.861636

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.3.d.a.12.2	yes	6
3.2	odd	2		171.3.p.d.145.2		6
4.3	odd	2		304.3.r.b.145.1		6
19.2	odd	18		361.3.f.h.333.2		18
19.3	odd	18		361.3.f.h.127.2		18
19.4	even	9		361.3.f.h.116.2		18
19.5	even	9		361.3.f.i.262.2		18
19.6	even	9		361.3.f.h.299.2		18
19.7	even	3		361.3.b.b.360.3		6
19.8	odd	6	inner	19.3.d.a.8.2	✓	6
19.9	even	9		361.3.f.h.307.2		18
19.10	odd	18		361.3.f.i.307.2		18
19.11	even	3		361.3.d.c.293.2		6
19.12	odd	6		361.3.b.b.360.4		6
19.13	odd	18		361.3.f.i.299.2		18
19.14	odd	18		361.3.f.h.262.2		18
19.15	odd	18		361.3.f.i.116.2		18
19.16	even	9		361.3.f.i.127.2		18
19.17	even	9		361.3.f.i.333.2		18
19.18	odd	2		361.3.d.c.69.2		6
57.8	even	6		171.3.p.d.46.2		6
76.27	even	6		304.3.r.b.65.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.d.a.8.2	✓	6	19.8	odd	6	inner
19.3.d.a.12.2	yes	6	1.1	even	1	trivial
171.3.p.d.46.2		6	57.8	even	6
171.3.p.d.145.2		6	3.2	odd	2
304.3.r.b.65.1		6	76.27	even	6
304.3.r.b.145.1		6	4.3	odd	2
361.3.b.b.360.3		6	19.7	even	3
361.3.b.b.360.4		6	19.12	odd	6
361.3.d.c.69.2		6	19.18	odd	2
361.3.d.c.293.2		6	19.11	even	3
361.3.f.h.116.2		18	19.4	even	9
361.3.f.h.127.2		18	19.3	odd	18
361.3.f.h.262.2		18	19.14	odd	18
361.3.f.h.299.2		18	19.6	even	9
361.3.f.h.307.2		18	19.9	even	9
361.3.f.h.333.2		18	19.2	odd	18
361.3.f.i.116.2		18	19.15	odd	18
361.3.f.i.127.2		18	19.16	even	9
361.3.f.i.262.2		18	19.5	even	9
361.3.f.i.299.2		18	19.13	odd	18
361.3.f.i.307.2		18	19.10	odd	18
361.3.f.i.333.2		18	19.17	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	19.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.583430 + 0.336844i) q^{2} +(2.49304 - 1.43936i) q^{3} +(-1.77307 + 3.07105i) q^{4} +(-1.55311 - 2.69006i) q^{5} +(-0.969676 + 1.67953i) q^{6} -8.15294 q^{7} -5.08374i q^{8} +(-0.356503 + 0.617481i) q^{9} +O(q^{10})\)	\(q+(-0.583430 + 0.336844i) q^{2} +(2.49304 - 1.43936i) q^{3} +(-1.77307 + 3.07105i) q^{4} +(-1.55311 - 2.69006i) q^{5} +(-0.969676 + 1.67953i) q^{6} -8.15294 q^{7} -5.08374i q^{8} +(-0.356503 + 0.617481i) q^{9} +(1.81226 + 1.04631i) q^{10} +17.6991 q^{11} +10.2083i q^{12} +(5.33372 + 3.07942i) q^{13} +(4.75667 - 2.74626i) q^{14} +(-7.74391 - 4.47095i) q^{15} +(-5.37987 - 9.31820i) q^{16} +(-6.91657 - 11.9799i) q^{17} -0.480343i q^{18} +(3.11375 + 18.7431i) q^{19} +11.0151 q^{20} +(-20.3256 + 11.7350i) q^{21} +(-10.3262 + 5.96182i) q^{22} +(2.46968 - 4.27760i) q^{23} +(-7.31732 - 12.6740i) q^{24} +(7.67572 - 13.2947i) q^{25} -4.14914 q^{26} +27.9610i q^{27} +(14.4558 - 25.0381i) q^{28} +(-38.2711 - 22.0958i) q^{29} +6.02404 q^{30} +43.0049i q^{31} +(23.8881 + 13.7918i) q^{32} +(44.1245 - 25.4753i) q^{33} +(8.07067 + 4.65960i) q^{34} +(12.6624 + 21.9319i) q^{35} +(-1.26421 - 2.18968i) q^{36} -30.7849i q^{37} +(-8.13016 - 9.88645i) q^{38} +17.7296 q^{39} +(-13.6756 + 7.89559i) q^{40} +(-28.6795 + 16.5581i) q^{41} +(7.90571 - 13.6931i) q^{42} +(-15.7586 - 27.2946i) q^{43} +(-31.3818 + 54.3548i) q^{44} +2.21475 q^{45} +3.32758i q^{46} +(8.86404 - 15.3530i) q^{47} +(-26.8244 - 15.4871i) q^{48} +17.4704 q^{49} +10.3421i q^{50} +(-34.4866 - 19.9108i) q^{51} +(-18.9142 + 10.9201i) q^{52} +(14.6396 + 8.45218i) q^{53} +(-9.41847 - 16.3133i) q^{54} +(-27.4886 - 47.6116i) q^{55} +41.4474i q^{56} +(34.7408 + 42.2455i) q^{57} +29.7713 q^{58} +(20.3412 - 11.7440i) q^{59} +(27.4610 - 15.8546i) q^{60} +(-8.52643 + 14.7682i) q^{61} +(-14.4859 - 25.0903i) q^{62} +(2.90655 - 5.03429i) q^{63} +24.4562 q^{64} -19.1307i q^{65} +(-17.1624 + 29.7261i) q^{66} +(84.9924 + 49.0704i) q^{67} +49.0543 q^{68} -14.2190i q^{69} +(-14.7752 - 8.53048i) q^{70} +(-1.36156 + 0.786099i) q^{71} +(3.13911 + 1.81237i) q^{72} +(2.85534 + 4.94560i) q^{73} +(10.3697 + 17.9608i) q^{74} -44.1924i q^{75} +(-63.0820 - 23.6704i) q^{76} -144.300 q^{77} +(-10.3440 + 5.97209i) q^{78} +(41.9327 - 24.2099i) q^{79} +(-16.7110 + 28.9443i) q^{80} +(37.0373 + 64.1505i) q^{81} +(11.1550 - 19.3210i) q^{82} -74.2729 q^{83} -83.2280i q^{84} +(-21.4843 + 37.2120i) q^{85} +(18.3880 + 10.6163i) q^{86} -127.215 q^{87} -89.9776i q^{88} +(81.0798 + 46.8114i) q^{89} +(-1.29215 + 0.746024i) q^{90} +(-43.4855 - 25.1064i) q^{91} +(8.75783 + 15.1690i) q^{92} +(61.8994 + 107.213i) q^{93} +11.9432i q^{94} +(45.5841 - 37.4862i) q^{95} +79.4055 q^{96} +(-8.15700 + 4.70945i) q^{97} +(-10.1928 + 5.88480i) q^{98} +(-6.30978 + 10.9289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 9 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 14 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 9 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 14 * q^9	\( 6 q - 3 q^{2} - 9 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 14 q^{9} - 60 q^{10} + 26 q^{11} + 30 q^{13} + 54 q^{14} - 18 q^{15} + q^{16} - 42 q^{17} + 25 q^{19} + 108 q^{20} - 102 q^{21} - 39 q^{22} + 8 q^{23} - 83 q^{24} - 17 q^{25} - 148 q^{26} + 32 q^{28} - 12 q^{29} + 304 q^{30} + 51 q^{32} + 123 q^{33} - 6 q^{34} - 38 q^{35} - 54 q^{36} - 14 q^{38} - 44 q^{39} - 96 q^{40} + 63 q^{41} - 92 q^{42} - 34 q^{43} - 69 q^{44} - 28 q^{45} + 58 q^{47} - 147 q^{48} + 18 q^{49} + 132 q^{51} + 162 q^{52} - 12 q^{53} + 29 q^{54} - 28 q^{55} - 16 q^{57} + 172 q^{58} - 147 q^{59} - 222 q^{60} + 58 q^{61} - 116 q^{62} + 86 q^{63} + 166 q^{64} + 11 q^{66} + 201 q^{67} - 84 q^{68} - 198 q^{70} - 102 q^{71} + 210 q^{72} + 7 q^{73} + 174 q^{74} - 173 q^{76} - 376 q^{77} + 450 q^{78} + 134 q^{80} + 253 q^{81} - 145 q^{82} + 146 q^{83} - 90 q^{85} - 270 q^{86} - 568 q^{87} - 72 q^{89} - 438 q^{90} - 216 q^{91} + 72 q^{92} - 160 q^{93} + 558 q^{95} + 126 q^{96} + 21 q^{97} + 411 q^{98} - 56 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 9 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 14 * q^9 - 60 * q^10 + 26 * q^11 + 30 * q^13 + 54 * q^14 - 18 * q^15 + q^16 - 42 * q^17 + 25 * q^19 + 108 * q^20 - 102 * q^21 - 39 * q^22 + 8 * q^23 - 83 * q^24 - 17 * q^25 - 148 * q^26 + 32 * q^28 - 12 * q^29 + 304 * q^30 + 51 * q^32 + 123 * q^33 - 6 * q^34 - 38 * q^35 - 54 * q^36 - 14 * q^38 - 44 * q^39 - 96 * q^40 + 63 * q^41 - 92 * q^42 - 34 * q^43 - 69 * q^44 - 28 * q^45 + 58 * q^47 - 147 * q^48 + 18 * q^49 + 132 * q^51 + 162 * q^52 - 12 * q^53 + 29 * q^54 - 28 * q^55 - 16 * q^57 + 172 * q^58 - 147 * q^59 - 222 * q^60 + 58 * q^61 - 116 * q^62 + 86 * q^63 + 166 * q^64 + 11 * q^66 + 201 * q^67 - 84 * q^68 - 198 * q^70 - 102 * q^71 + 210 * q^72 + 7 * q^73 + 174 * q^74 - 173 * q^76 - 376 * q^77 + 450 * q^78 + 134 * q^80 + 253 * q^81 - 145 * q^82 + 146 * q^83 - 90 * q^85 - 270 * q^86 - 568 * q^87 - 72 * q^89 - 438 * q^90 - 216 * q^91 + 72 * q^92 - 160 * q^93 + 558 * q^95 + 126 * q^96 + 21 * q^97 + 411 * q^98 - 56 * q^99

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