LMFDB - Embedded newform 76.3.g.a.7.1

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 10x^{2} + 100 $ x^4 - 10*x^2 + 100
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.1
Root			$-2.73861 + 1.58114i$ of defining polynomial
Character	$\chi$	$=$	76.7
Dual form			76.3.g.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(-1.23861 + 0.715113i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-3.73861 - 6.47547i) q^{5} -2.86045i q^{6} -3.76593i q^{7} +8.00000 q^{8} +(-3.47723 + 6.02273i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(-1.23861 + 0.715113i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-3.73861 - 6.47547i) q^{5} -2.86045i q^{6} -3.76593i q^{7} +8.00000 q^{8} +(-3.47723 + 6.02273i) q^{9} +14.9545 q^{10} -14.0793i q^{11} +(4.95445 + 2.86045i) q^{12} +(-3.00000 + 5.19615i) q^{13} +(6.52277 + 3.76593i) q^{14} +(9.26139 + 5.34706i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-13.4772 - 23.3432i) q^{17} +(-6.95445 - 12.0455i) q^{18} +(-18.7158 - 3.27374i) q^{19} +(-14.9545 + 25.9019i) q^{20} +(2.69306 + 4.66452i) q^{21} +(24.3861 + 14.0793i) q^{22} +(21.6475 + 12.4982i) q^{23} +(-9.90890 + 5.72091i) q^{24} +(-15.4545 + 26.7679i) q^{25} +(-6.00000 - 10.3923i) q^{26} -22.8185i q^{27} +(-13.0455 + 7.53185i) q^{28} +(1.73861 - 3.01137i) q^{29} +(-18.5228 + 10.6941i) q^{30} +39.4565i q^{31} +(-16.0000 - 27.7128i) q^{32} +(10.0683 + 17.4388i) q^{33} +53.9089 q^{34} +(-24.3861 + 14.0793i) q^{35} +27.8178 q^{36} +3.38613 q^{37} +(24.3861 - 29.1430i) q^{38} -8.58136i q^{39} +(-29.9089 - 51.8037i) q^{40} +(-4.45445 - 7.71534i) q^{41} -10.7723 q^{42} +(45.3861 - 26.2037i) q^{43} +(-48.7723 + 28.1587i) q^{44} +52.0000 q^{45} +(-43.2950 + 24.9964i) q^{46} +(-19.1703 - 11.0680i) q^{47} -22.8836i q^{48} +34.8178 q^{49} +(-30.9089 - 53.5358i) q^{50} +(33.3861 + 19.2755i) q^{51} +24.0000 q^{52} +(41.9545 - 72.6672i) q^{53} +(39.5228 + 22.8185i) q^{54} +(-91.1703 + 52.6372i) q^{55} -30.1274i q^{56} +(25.5228 - 9.32905i) q^{57} +(3.47723 + 6.02273i) q^{58} +(22.2386 - 12.8395i) q^{59} -42.7765i q^{60} +(-13.7386 + 23.7960i) q^{61} +(-68.3406 - 39.4565i) q^{62} +(22.6812 + 13.0950i) q^{63} +64.0000 q^{64} +44.8634 q^{65} -40.2733 q^{66} +(-32.0109 - 18.4815i) q^{67} +(-53.9089 + 93.3730i) q^{68} -35.7505 q^{69} -56.3173i q^{70} +(-89.3406 + 51.5808i) q^{71} +(-27.8178 + 48.1819i) q^{72} +(4.45445 + 7.71534i) q^{73} +(-3.38613 + 5.86495i) q^{74} -44.2067i q^{75} +(26.0911 + 71.3811i) q^{76} -53.0217 q^{77} +(14.8634 + 8.58136i) q^{78} +(111.909 - 64.6106i) q^{79} +119.636 q^{80} +(-14.9772 - 25.9413i) q^{81} +17.8178 q^{82} -27.1743i q^{83} +(10.7723 - 18.6581i) q^{84} +(-100.772 + 174.543i) q^{85} +104.815i q^{86} +4.97322i q^{87} -112.635i q^{88} +(-64.2495 + 111.283i) q^{89} +(-52.0000 + 90.0666i) q^{90} +(19.5683 + 11.2978i) q^{91} -99.9856i q^{92} +(-28.2158 - 48.8713i) q^{93} +(38.3406 - 22.1359i) q^{94} +(48.7723 + 133.433i) q^{95} +(39.6356 + 22.8836i) q^{96} +(-53.0228 - 91.8381i) q^{97} +(-34.8178 + 60.3062i) q^{98} +(84.7961 + 48.9570i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} - 4 q^{5} + 32 q^{8} + 8 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 - 4 * q^5 + 32 * q^8 + 8 * q^9	$ 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} - 4 q^{5} + 32 q^{8} + 8 q^{9} + 16 q^{10} - 24 q^{12} - 12 q^{13} + 48 q^{14} + 48 q^{15} - 32 q^{16} - 32 q^{17} + 16 q^{18} - 42 q^{19} - 16 q^{20} - 44 q^{21} - 12 q^{22} - 12 q^{23} + 48 q^{24} - 18 q^{25} - 24 q^{26} - 96 q^{28} - 4 q^{29} - 96 q^{30} - 64 q^{32} + 106 q^{33} + 128 q^{34} + 12 q^{35} - 64 q^{36} - 96 q^{37} - 12 q^{38} - 32 q^{40} + 26 q^{41} + 176 q^{42} + 72 q^{43} + 24 q^{44} + 208 q^{45} + 24 q^{46} - 36 q^{49} - 36 q^{50} + 24 q^{51} + 96 q^{52} + 124 q^{53} + 180 q^{54} - 288 q^{55} + 124 q^{57} - 8 q^{58} + 78 q^{59} - 44 q^{61} - 120 q^{62} - 216 q^{63} + 256 q^{64} + 48 q^{65} - 424 q^{66} + 102 q^{67} - 128 q^{68} - 384 q^{69} - 204 q^{71} + 64 q^{72} - 26 q^{73} + 96 q^{74} + 192 q^{76} + 248 q^{77} - 72 q^{78} + 360 q^{79} + 128 q^{80} - 38 q^{81} - 104 q^{82} - 176 q^{84} - 184 q^{85} - 16 q^{89} - 208 q^{90} + 144 q^{91} - 80 q^{93} - 24 q^{95} - 192 q^{96} - 234 q^{97} + 36 q^{98} + 624 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 - 4 * q^5 + 32 * q^8 + 8 * q^9 + 16 * q^10 - 24 * q^12 - 12 * q^13 + 48 * q^14 + 48 * q^15 - 32 * q^16 - 32 * q^17 + 16 * q^18 - 42 * q^19 - 16 * q^20 - 44 * q^21 - 12 * q^22 - 12 * q^23 + 48 * q^24 - 18 * q^25 - 24 * q^26 - 96 * q^28 - 4 * q^29 - 96 * q^30 - 64 * q^32 + 106 * q^33 + 128 * q^34 + 12 * q^35 - 64 * q^36 - 96 * q^37 - 12 * q^38 - 32 * q^40 + 26 * q^41 + 176 * q^42 + 72 * q^43 + 24 * q^44 + 208 * q^45 + 24 * q^46 - 36 * q^49 - 36 * q^50 + 24 * q^51 + 96 * q^52 + 124 * q^53 + 180 * q^54 - 288 * q^55 + 124 * q^57 - 8 * q^58 + 78 * q^59 - 44 * q^61 - 120 * q^62 - 216 * q^63 + 256 * q^64 + 48 * q^65 - 424 * q^66 + 102 * q^67 - 128 * q^68 - 384 * q^69 - 204 * q^71 + 64 * q^72 - 26 * q^73 + 96 * q^74 + 192 * q^76 + 248 * q^77 - 72 * q^78 + 360 * q^79 + 128 * q^80 - 38 * q^81 - 104 * q^82 - 176 * q^84 - 184 * q^85 - 16 * q^89 - 208 * q^90 + 144 * q^91 - 80 * q^93 - 24 * q^95 - 192 * q^96 - 234 * q^97 + 36 * q^98 + 624 * q^99

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 $

$2$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$2$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$3$	−1.23861	+	0.715113i	−0.412871	+	0.238371i	−0.692023	−	0.721876i	$-0.743280\pi$
$3$	−1.23861	+	0.715113i	−0.412871	+	0.238371i	0.279152	+	0.960247i	$0.409947\pi$
$4$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$5$	−3.73861	−	6.47547i	−0.747723	−	1.29509i	−0.948912	−	0.315541i	$-0.897814\pi$
$5$	−3.73861	−	6.47547i	−0.747723	−	1.29509i	0.201189	−	0.979552i	$-0.435519\pi$
$6$		−	2.86045i		−	0.476742i
$7$		−	3.76593i		−	0.537989i	−0.963142	−	0.268995i	$-0.913309\pi$
$7$		−	3.76593i		−	0.537989i	0.963142	−	0.268995i	$-0.0866914\pi$
$8$	8.00000			1.00000
$9$	−3.47723	+	6.02273i	−0.386358	+	0.669192i
$10$	14.9545			1.49545
$11$		−	14.0793i		−	1.27994i	−0.768400	−	0.639970i	$-0.778947\pi$
$11$		−	14.0793i		−	1.27994i	0.768400	−	0.639970i	$-0.221053\pi$
$12$	4.95445	+	2.86045i	0.412871	+	0.238371i
$13$	−3.00000	+	5.19615i	−0.230769	+	0.399704i	−0.958035	−	0.286652i	$-0.907458\pi$
$13$	−3.00000	+	5.19615i	−0.230769	+	0.399704i	0.727265	+	0.686356i	$0.240791\pi$
$14$	6.52277	+	3.76593i	0.465912	+	0.268995i
$15$	9.26139	+	5.34706i	0.617426	+	0.356471i
$16$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$17$	−13.4772	−	23.3432i	−0.792778	−	1.37313i	−0.924241	−	0.381811i	$-0.875301\pi$
$17$	−13.4772	−	23.3432i	−0.792778	−	1.37313i	0.131463	−	0.991321i	$-0.458033\pi$
$18$	−6.95445	−	12.0455i	−0.386358	−	0.669192i
$19$	−18.7158	−	3.27374i	−0.985044	−	0.172302i
$19$	−18.7158	−	3.27374i	−0.985044	−	0.172302i
$20$	−14.9545	+	25.9019i	−0.747723	+	1.29509i
$21$	2.69306	+	4.66452i	0.128241	+	0.222120i
$22$	24.3861	+	14.0793i	1.10846	+	0.639970i
$23$	21.6475	+	12.4982i	0.941196	+	0.543400i	0.890335	−	0.455306i	$-0.150470\pi$
$23$	21.6475	+	12.4982i	0.941196	+	0.543400i	0.0508612	+	0.998706i	$0.483803\pi$
$24$	−9.90890	+	5.72091i	−0.412871	+	0.238371i
$25$	−15.4545	+	26.7679i	−0.618178	+	1.07072i
$26$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$27$		−	22.8185i		−	0.845129i
$28$	−13.0455	+	7.53185i	−0.465912	+	0.268995i
$29$	1.73861	−	3.01137i	0.0599522	−	0.103840i	−0.834492	−	0.551021i	$-0.814239\pi$
$29$	1.73861	−	3.01137i	0.0599522	−	0.103840i	0.894444	+	0.447181i	$0.147572\pi$
$30$	−18.5228	+	10.6941i	−0.617426	+	0.356471i
$31$			39.4565i			1.27279i	0.771364	+	0.636394i	$0.219575\pi$
$31$			39.4565i			1.27279i	−0.771364	+	0.636394i	$0.780425\pi$
$32$	−16.0000	−	27.7128i	−0.500000	−	0.866025i
$33$	10.0683	+	17.4388i	0.305101	+	0.528450i
$34$	53.9089			1.58556
$35$	−24.3861	+	14.0793i	−0.696747	+	0.402267i
$36$	27.8178			0.772717
$37$	3.38613			0.0915170			0.0457585	−	0.998953i	$-0.485430\pi$
$37$	3.38613			0.0915170			0.0457585	+	0.998953i	$0.485430\pi$
$38$	24.3861	−	29.1430i	0.641740	−	0.766922i
$39$		−	8.58136i		−	0.220035i
$40$	−29.9089	−	51.8037i	−0.747723	−	1.29509i
$41$	−4.45445	−	7.71534i	−0.108645	−	0.188179i	0.806576	−	0.591130i	$-0.201318\pi$
$41$	−4.45445	−	7.71534i	−0.108645	−	0.188179i	−0.915222	+	0.402951i	$0.867985\pi$
$42$	−10.7723			−0.256482
$43$	45.3861	−	26.2037i	1.05549	−	0.609388i	0.131310	−	0.991341i	$-0.458082\pi$
$43$	45.3861	−	26.2037i	1.05549	−	0.609388i	0.924182	+	0.381953i	$0.124748\pi$
$44$	−48.7723	+	28.1587i	−1.10846	+	0.639970i
$45$	52.0000			1.15556
$46$	−43.2950	+	24.9964i	−0.941196	+	0.543400i
$47$	−19.1703	−	11.0680i	−0.407879	−	0.235489i	0.281999	−	0.959415i	$-0.409002\pi$
$47$	−19.1703	−	11.0680i	−0.407879	−	0.235489i	−0.689878	+	0.723926i	$0.742336\pi$
$48$		−	22.8836i		−	0.476742i
$49$	34.8178			0.710567
$50$	−30.9089	−	53.5358i	−0.618178	−	1.07072i
$51$	33.3861	+	19.2755i	0.654630	+	0.377951i
$52$	24.0000			0.461538
$53$	41.9545	−	72.6672i	0.791593	−	1.37108i	−0.133387	−	0.991064i	$-0.542585\pi$
$53$	41.9545	−	72.6672i	0.791593	−	1.37108i	0.924980	−	0.380016i	$-0.124081\pi$
$54$	39.5228	+	22.8185i	0.731903	+	0.422565i
$55$	−91.1703	+	52.6372i	−1.65764	+	0.957040i
$56$		−	30.1274i		−	0.537989i
$57$	25.5228	−	9.32905i	0.447768	−	0.163667i
$58$	3.47723	+	6.02273i	0.0599522	+	0.103840i
$59$	22.2386	−	12.8395i	0.376926	−	0.217618i	−0.299554	−	0.954079i	$-0.596838\pi$
$59$	22.2386	−	12.8395i	0.376926	−	0.217618i	0.676480	+	0.736461i	$0.263505\pi$
$60$		−	42.7765i		−	0.712942i
$61$	−13.7386	+	23.7960i	−0.225223	+	0.390098i	−0.956386	−	0.292105i	$-0.905644\pi$
$61$	−13.7386	+	23.7960i	−0.225223	+	0.390098i	0.731163	+	0.682203i	$0.238978\pi$
$62$	−68.3406	−	39.4565i	−1.10227	−	0.636394i
$63$	22.6812	+	13.0950i	0.360018	+	0.207857i
$64$	64.0000			1.00000
$65$	44.8634			0.690205
$66$	−40.2733			−0.610201
$67$	−32.0109	−	18.4815i	−0.477774	−	0.275843i	0.241714	−	0.970347i	$-0.422290\pi$
$67$	−32.0109	−	18.4815i	−0.477774	−	0.275843i	−0.719488	+	0.694504i	$0.755624\pi$
$68$	−53.9089	+	93.3730i	−0.792778	+	1.37313i
$69$	−35.7505			−0.518123
$70$		−	56.3173i		−	0.804534i
$71$	−89.3406	+	51.5808i	−1.25832	+	0.726490i	−0.972747	−	0.231867i	$-0.925516\pi$
$71$	−89.3406	+	51.5808i	−1.25832	+	0.726490i	−0.285571	+	0.958358i	$0.592183\pi$
$72$	−27.8178	+	48.1819i	−0.386358	+	0.669192i
$73$	4.45445	+	7.71534i	0.0610199	+	0.105690i	0.894922	−	0.446224i	$-0.147231\pi$
$73$	4.45445	+	7.71534i	0.0610199	+	0.105690i	−0.833902	+	0.551913i	$0.813898\pi$
$74$	−3.38613	+	5.86495i	−0.0457585	+	0.0792560i
$75$		−	44.2067i		−	0.589423i
$76$	26.0911	+	71.3811i	0.343304	+	0.939224i
$77$	−53.0217			−0.688594
$78$	14.8634	+	8.58136i	0.190556	+	0.110017i
$79$	111.909	−	64.6106i	1.41657	−	0.817856i	0.420573	−	0.907259i	$-0.361829\pi$
$79$	111.909	−	64.6106i	1.41657	−	0.817856i	0.995996	+	0.0894026i	$0.0284958\pi$
$80$	119.636			1.49545
$81$	−14.9772	−	25.9413i	−0.184904	−	0.320263i
$82$	17.8178			0.217290
$83$		−	27.1743i		−	0.327401i	−0.986510	−	0.163701i	$-0.947657\pi$
$83$		−	27.1743i		−	0.327401i	0.986510	−	0.163701i	$-0.0523431\pi$
$84$	10.7723	−	18.6581i	0.128241	−	0.222120i
$85$	−100.772	+	174.543i	−1.18556	+	2.05344i
$86$			104.815i			1.21878i
$87$			4.97322i			0.0571635i
$88$		−	112.635i		−	1.27994i
$89$	−64.2495	+	111.283i	−0.721904	+	1.25037i	0.238331	+	0.971184i	$0.423400\pi$
$89$	−64.2495	+	111.283i	−0.721904	+	1.25037i	−0.960236	+	0.279191i	$0.909934\pi$
$90$	−52.0000	+	90.0666i	−0.577778	+	1.00074i
$91$	19.5683	+	11.2978i	0.215037	+	0.124151i
$92$		−	99.9856i		−	1.08680i
$93$	−28.2158	−	48.8713i	−0.303396	−	0.525497i
$94$	38.3406	−	22.1359i	0.407879	−	0.235489i
$95$	48.7723	+	133.433i	0.513392	+	1.40456i
$96$	39.6356	+	22.8836i	0.412871	+	0.238371i
$97$	−53.0228	−	91.8381i	−0.546627	−	0.946785i	−0.998503	−	0.0547042i	$-0.982578\pi$
$97$	−53.0228	−	91.8381i	−0.546627	−	0.946785i	0.451876	−	0.892081i	$-0.350755\pi$
$98$	−34.8178	+	60.3062i	−0.355284	+	0.615369i
$99$	84.7961	+	48.9570i	0.856526	+	0.494515i
$100$	123.636			1.23636
$101$	66.9425	−	115.948i	0.662797	−	1.14800i	−0.317080	−	0.948399i	$-0.602702\pi$
$101$	66.9425	−	115.948i	0.662797	−	1.14800i	0.979877	−	0.199600i	$-0.0639643\pi$
$102$	−66.7723	+	38.5510i	−0.654630	+	0.377951i
$103$		−	103.477i		−	1.00463i	−0.864684	−	0.502316i	$-0.832481\pi$
$103$		−	103.477i		−	1.00463i	0.864684	−	0.502316i	$-0.167519\pi$
$104$	−24.0000	+	41.5692i	−0.230769	+	0.399704i
$105$	20.1366	−	34.8777i	0.191778	−	0.332169i
$106$	83.9089	+	145.334i	0.791593	+	1.37108i
$107$		−	67.7867i		−	0.633520i	−0.948506	−	0.316760i	$-0.897405\pi$
$107$		−	67.7867i		−	0.633520i	0.948506	−	0.316760i	$-0.102595\pi$
$108$	−79.0455	+	45.6370i	−0.731903	+	0.422565i
$109$	24.8634	+	43.0646i	0.228104	+	0.395088i	0.957246	−	0.289274i	$-0.0934140\pi$
$109$	24.8634	+	43.0646i	0.228104	+	0.395088i	−0.729142	+	0.684362i	$0.760081\pi$
$110$		−	210.549i		−	1.91408i
$111$	−4.19410	+	2.42147i	−0.0377847	+	0.0218150i
$112$	52.1822	+	30.1274i	0.465912	+	0.268995i
$113$	−70.9089			−0.627512			−0.313756	−	0.949504i	$-0.601587\pi$
$113$	−70.9089			−0.627512			−0.313756	+	0.949504i	$0.601587\pi$
$114$	−9.36439	+	53.5358i	−0.0821438	+	0.469612i
$115$		−	186.904i		−	1.62525i
$116$	−13.9089			−0.119904
$117$	−20.8634	−	36.1364i	−0.178319	−	0.308858i
$118$			51.3579i			0.435236i
$119$	−87.9089	+	50.7542i	−0.738730	+	0.426506i
$120$	74.0911	+	42.7765i	0.617426	+	0.356471i
$121$	−77.2277			−0.638246
$122$	−27.4772	−	47.5920i	−0.225223	−	0.390098i
$123$	11.0347	+	6.37088i	0.0897128	+	0.0517957i
$124$	136.681	−	78.9129i	1.10227	−	0.636394i
$125$	44.1822			0.353458
$126$	−45.3623	+	26.1899i	−0.360018	+	0.207857i
$127$	−20.2039	−	11.6647i	−0.159086	−	0.0918484i	0.418343	−	0.908289i	$-0.362611\pi$
$127$	−20.2039	−	11.6647i	−0.159086	−	0.0918484i	−0.577430	+	0.816441i	$0.695944\pi$
$128$	−64.0000	+	110.851i	−0.500000	+	0.866025i
$129$	−37.4772	+	64.9125i	−0.290521	+	0.503197i
$130$	−44.8634	+	77.7056i	−0.345103	+	0.597735i
$131$	−23.9436	+	13.8238i	−0.182775	+	0.105525i	−0.588596	−	0.808427i	$-0.700319\pi$
$131$	−23.9436	+	13.8238i	−0.182775	+	0.105525i	0.405821	+	0.913953i	$0.366986\pi$
$132$	40.2733	−	69.7554i	0.305101	−	0.528450i
$133$	−12.3287	+	70.4825i	−0.0926968	+	0.529943i
$134$	64.0217	−	36.9630i	0.477774	−	0.275843i
$135$	−147.760	+	85.3095i	−1.09452	+	0.631922i
$136$	−107.818	−	186.746i	−0.792778	−	1.37313i
$137$	99.4089	−	172.181i	0.725612	−	1.25680i	−0.233109	−	0.972451i	$-0.574890\pi$
$137$	99.4089	−	172.181i	0.725612	−	1.25680i	0.958721	−	0.284347i	$-0.0917768\pi$
$138$	35.7505	−	61.9217i	0.259062	−	0.448708i
$139$	−232.738	−	134.371i	−1.67437	−	0.966699i	−0.965144	−	0.261718i	$-0.915711\pi$
$139$	−232.738	−	134.371i	−1.67437	−	0.966699i	−0.709227	−	0.704981i	$-0.750956\pi$
$140$	97.5445	+	56.3173i	0.696747	+	0.402267i
$141$	31.6594			0.224535
$142$		−	206.323i		−	1.45298i
$143$	73.1584	+	42.2380i	0.511597	+	0.295371i
$144$	−55.6356	−	96.3637i	−0.386358	−	0.669192i
$145$	−26.0000			−0.179310
$146$	−17.8178			−0.122040
$147$	−43.1258	+	24.8987i	−0.293373	+	0.169379i
$148$	−6.77226	−	11.7299i	−0.0457585	−	0.0792560i
$149$	36.2158	+	62.7277i	0.243059	+	0.420991i	0.961584	−	0.274510i	$-0.0885157\pi$
$149$	36.2158	+	62.7277i	0.243059	+	0.420991i	−0.718525	+	0.695501i	$0.755182\pi$
$150$	76.5683	+	44.2067i	0.510455	+	0.294712i
$151$			39.4565i			0.261301i	0.991428	+	0.130651i	$0.0417066\pi$
$151$			39.4565i			0.261301i	−0.991428	+	0.130651i	$0.958293\pi$
$152$	−149.727	−	26.1899i	−0.985044	−	0.172302i
$153$	187.453			1.22519
$154$	53.0217	−	91.8363i	0.344297	−	0.596340i
$155$	255.499	−	147.512i	1.64838	−	0.951693i
$156$	−29.7267	+	17.1627i	−0.190556	+	0.110017i
$157$	−50.9545	−	88.2557i	−0.324551	−	0.562138i	0.656871	−	0.754003i	$-0.271880\pi$
$157$	−50.9545	−	88.2557i	−0.324551	−	0.562138i	−0.981421	+	0.191865i	$0.938546\pi$
$158$			258.443i			1.63571i
$159$			120.009i			0.754772i
$160$	−119.636	+	207.215i	−0.747723	+	1.29509i
$161$	47.0673	−	81.5229i	0.292343	−	0.506354i
$162$	59.9089			0.369808
$163$			190.563i			1.16910i	0.811358	+	0.584550i	$0.198729\pi$
$163$			190.563i			1.16910i	−0.811358	+	0.584550i	$0.801271\pi$
$164$	−17.8178	+	30.8613i	−0.108645	+	0.188179i
$165$	75.2831	−	130.394i	0.456261	−	0.790268i
$166$	47.0673	+	27.1743i	0.283538	+	0.163701i
$167$	256.681	+	148.195i	1.53701	+	0.887395i	0.999012	+	0.0444508i	$0.0141538\pi$
$167$	256.681	+	148.195i	1.53701	+	0.887395i	0.538001	+	0.842944i	$0.319180\pi$
$168$	21.5445	+	37.3162i	0.128241	+	0.222120i
$169$	66.5000	+	115.181i	0.393491	+	0.681547i
$170$	−201.545	−	349.085i	−1.18556	−	2.05344i
$171$	84.7961	−	101.337i	0.495883	−	0.592614i
$172$	−181.545	−	104.815i	−1.05549	−	0.609388i
$173$	113.863	+	197.217i	0.658170	+	1.13998i	0.981089	+	0.193557i	$0.0620024\pi$
$173$	113.863	+	197.217i	0.658170	+	1.13998i	−0.322919	+	0.946426i	$0.604664\pi$
$174$	−8.61387	−	4.97322i	−0.0495050	−	0.0285817i
$175$	100.806	+	58.2003i	0.576034	+	0.332573i
$176$	195.089	+	112.635i	1.10846	+	0.639970i
$177$	−18.3634	+	31.8063i	−0.103748	+	0.179696i
$178$	−128.499	−	222.567i	−0.721904	−	1.25037i
$179$		−	262.287i		−	1.46529i	−0.680610	−	0.732646i	$-0.738285\pi$
$179$		−	262.287i		−	1.46529i	0.680610	−	0.732646i	$-0.261715\pi$
$180$	−104.000	−	180.133i	−0.577778	−	1.00074i
$181$	−39.9425	+	69.1825i	−0.220677	+	0.382224i	−0.955014	−	0.296562i	$-0.904160\pi$
$181$	−39.9425	+	69.1825i	−0.220677	+	0.382224i	0.734337	+	0.678785i	$0.237493\pi$
$182$	−39.1366	+	22.5956i	−0.215037	+	0.124151i
$183$		−	39.2987i		−	0.214747i
$184$	173.180	+	99.9856i	0.941196	+	0.543400i
$185$	−12.6594	−	21.9268i	−0.0684293	−	0.118523i
$186$	112.863			0.606792
$187$	−328.657	+	189.750i	−1.75753	+	1.01471i
$188$			88.5438i			0.470978i
$189$	−85.9327			−0.454670
$190$	−279.885	−	48.9570i	−1.47308	−	0.257669i
$191$			233.144i			1.22065i	0.792151	+	0.610325i	$0.208961\pi$
$191$			233.144i			1.22065i	−0.792151	+	0.610325i	$0.791039\pi$
$192$	−79.2712	+	45.7673i	−0.412871	+	0.238371i
$193$	61.4772	+	106.482i	0.318535	+	0.551719i	0.980183	−	0.198096i	$-0.0634759\pi$
$193$	61.4772	+	106.482i	0.318535	+	0.551719i	−0.661648	+	0.749815i	$0.730143\pi$
$194$	212.091			1.09325
$195$	−55.5683	+	32.0824i	−0.284966	+	0.164525i
$196$	−69.6356	−	120.612i	−0.355284	−	0.615369i
$197$	−154.158			−0.782530			−0.391265	−	0.920278i	$-0.627962\pi$
$197$	−154.158			−0.782530			−0.391265	+	0.920278i	$0.627962\pi$
$198$	−169.592	+	97.9141i	−0.856526	+	0.494515i
$199$	92.9762	+	53.6798i	0.467217	+	0.269748i	0.715074	−	0.699049i	$-0.246393\pi$
$199$	92.9762	+	53.6798i	0.467217	+	0.269748i	−0.247857	+	0.968797i	$0.579726\pi$
$200$	−123.636	+	214.143i	−0.618178	+	1.07072i
$201$	52.8654			0.263012
$202$	133.885	+	231.896i	0.662797	+	1.14800i
$203$	−11.3406	−	6.54749i	−0.0558649	−	0.0322536i
$204$		−	154.204i		−	0.755902i
$205$	−33.3069	+	57.6893i	−0.162473	+	0.281411i
$206$	179.228	+	103.477i	0.870038	+	0.502316i
$207$	−150.547	+	86.9181i	−0.727278	+	0.419894i
$208$	−48.0000	−	83.1384i	−0.230769	−	0.399704i
$209$	−46.0921	+	263.507i	−0.220537	+	1.26080i
$210$	40.2733	+	69.7554i	0.191778	+	0.332169i
$211$	117.226	−	67.6803i	0.555572	−	0.320760i	−0.195794	−	0.980645i	$-0.562729\pi$
$211$	117.226	−	67.6803i	0.555572	−	0.320760i	0.751366	+	0.659885i	$0.229395\pi$
$212$	−335.636			−1.58319
$213$	73.7723	−	127.777i	0.346349	−	0.599893i
$214$	117.410	+	67.7867i	0.548645	+	0.316760i
$215$	−339.362	−	195.931i	−1.57843	−	0.911307i
$216$		−	182.548i		−	0.845129i
$217$	148.590			0.684747
$218$	−99.4534			−0.456208
$219$	−11.0347	−	6.37088i	−0.0503867	−	0.0290908i
$220$	364.681	+	210.549i	1.65764	+	0.957040i
$221$	161.727			0.731795
$222$		−	9.68586i		−	0.0436300i
$223$	118.943	−	68.6715i	0.533375	−	0.307944i	−0.209015	−	0.977912i	$-0.567026\pi$
$223$	118.943	−	68.6715i	0.533375	−	0.307944i	0.742390	+	0.669968i	$0.233692\pi$
$224$	−104.364	+	60.2548i	−0.465912	+	0.268995i
$225$	−107.477	−	186.156i	−0.477677	−	0.827360i
$226$	70.9089	−	122.818i	0.313756	−	0.543442i
$227$			92.9922i			0.409657i	0.978798	+	0.204829i	$0.0656637\pi$
$227$			92.9922i			0.409657i	−0.978798	+	0.204829i	$0.934336\pi$
$228$	−83.3623	−	69.7554i	−0.365624	−	0.305945i
$229$	−164.182			−0.716953			−0.358476	−	0.933539i	$-0.616704\pi$
$229$	−164.182			−0.716953			−0.358476	+	0.933539i	$0.616704\pi$
$230$	323.727	+	186.904i	1.40751	+	0.812625i
$231$	65.6734	−	37.9166i	0.284300	−	0.164141i
$232$	13.9089	−	24.0909i	0.0599522	−	0.103840i
$233$	−27.2723	−	47.2369i	−0.117048	−	0.202734i	0.801548	−	0.597930i	$-0.204010\pi$
$233$	−27.2723	−	47.2369i	−0.117048	−	0.202734i	−0.918597	+	0.395196i	$0.870677\pi$
$234$	83.4534			0.356639
$235$			165.515i			0.704321i
$236$	−88.9545	−	51.3579i	−0.376926	−	0.217618i
$237$	−92.4079	+	160.055i	−0.389907	+	0.675338i
$238$		−	203.017i		−	0.853012i
$239$		−	285.524i		−	1.19466i	−0.801995	−	0.597331i	$-0.796228\pi$
$239$		−	285.524i		−	1.19466i	0.801995	−	0.597331i	$-0.203772\pi$
$240$	−148.182	+	85.5530i	−0.617426	+	0.356471i
$241$	87.8861	−	152.223i	0.364673	−	0.631632i	−0.624051	−	0.781384i	$-0.714514\pi$
$241$	87.8861	−	152.223i	0.364673	−	0.631632i	0.988724	+	0.149752i	$0.0478475\pi$
$242$	77.2277	−	133.762i	0.319123	−	0.552737i
$243$	214.954	+	124.104i	0.884586	+	0.510716i
$244$	109.909			0.450446
$245$	−130.170	−	225.462i	−0.531307	−	0.920251i
$246$	−22.0694	+	12.7418i	−0.0897128	+	0.0517957i
$247$	73.1584	−	87.4291i	0.296188	−	0.353964i
$248$			315.652i			1.27279i
$249$	19.4327	+	33.6584i	0.0780430	+	0.135174i
$250$	−44.1822	+	76.5258i	−0.176729	+	0.306103i
$251$	−140.124	−	80.9005i	−0.558262	−	0.322313i	0.194186	−	0.980965i	$-0.437794\pi$
$251$	−140.124	−	80.9005i	−0.558262	−	0.322313i	−0.752448	+	0.658652i	$0.771127\pi$
$252$		−	104.760i		−	0.415713i
$253$	175.966	−	304.783i	0.695519	−	1.20467i
$254$	40.4079	−	23.3295i	0.159086	−	0.0918484i
$255$		−	288.254i		−	1.13041i
$256$	−128.000	−	221.703i	−0.500000	−	0.866025i
$257$	154.862	−	268.229i	0.602577	−	1.04369i	−0.389852	−	0.920877i	$-0.627474\pi$
$257$	154.862	−	268.229i	0.602577	−	1.04369i	0.992429	−	0.122817i	$-0.0391927\pi$
$258$	−74.9545	−	129.825i	−0.290521	−	0.503197i
$259$		−	12.7519i		−	0.0492352i
$260$	−89.7267	−	155.411i	−0.345103	−	0.597735i
$261$	12.0911	+	20.9424i	0.0463260	+	0.0802391i
$262$		−	55.2953i		−	0.211051i
$263$	171.238	−	98.8641i	0.651093	−	0.375909i	−0.137782	−	0.990463i	$-0.543997\pi$
$263$	171.238	−	98.8641i	0.651093	−	0.375909i	0.788875	+	0.614554i	$0.210664\pi$
$264$	80.5466	+	139.511i	0.305101	+	0.528450i
$265$	−627.406			−2.36757
$266$	−109.751	−	91.8363i	−0.412596	−	0.345249i
$267$		−	183.783i		−	0.688325i
$268$			147.852i			0.551686i
$269$	77.6356	+	134.469i	0.288608	+	0.499884i	0.973478	−	0.228782i	$-0.0734742\pi$
$269$	77.6356	+	134.469i	0.288608	+	0.499884i	−0.684870	+	0.728666i	$0.740141\pi$
$270$		−	341.238i		−	1.26384i
$271$	−52.0098	+	30.0279i	−0.191918	+	0.110804i	−0.592880	−	0.805291i	$-0.702009\pi$
$271$	−52.0098	+	30.0279i	−0.191918	+	0.110804i	0.400962	+	0.916095i	$0.368676\pi$
$272$	431.271			1.58556
$273$	−32.3168			−0.118376
$274$	198.818	+	344.363i	0.725612	+	1.25680i
$275$	376.874	+	217.588i	1.37045	+	0.791231i
$276$	71.5010	+	123.843i	0.259062	+	0.448708i
$277$	399.430			1.44198			0.720992	−	0.692943i	$-0.243686\pi$
$277$	399.430			1.44198			0.720992	+	0.692943i	$0.243686\pi$
$278$	465.475	−	268.742i	1.67437	−	0.966699i
$279$	−237.636	−	137.199i	−0.851741	−	0.491753i
$280$	−195.089	+	112.635i	−0.696747	+	0.402267i
$281$	−228.999	+	396.638i	−0.814943	+	1.41152i	0.0944260	+	0.995532i	$0.469898\pi$
$281$	−228.999	+	396.638i	−0.814943	+	1.41152i	−0.909369	+	0.415991i	$0.863435\pi$
$282$	−31.6594	+	54.8357i	−0.112267	+	0.194453i
$283$	−362.237	+	209.137i	−1.27999	+	0.739001i	−0.976846	−	0.213944i	$-0.931369\pi$
$283$	−362.237	+	209.137i	−1.27999	+	0.739001i	−0.303142	+	0.952945i	$0.598036\pi$
$284$	357.362	+	206.323i	1.25832	+	0.726490i
$285$	−155.830	−	130.394i	−0.546771	−	0.457523i
$286$	−146.317	+	84.4760i	−0.511597	+	0.295371i
$287$	−29.0554	+	16.7751i	−0.101238	+	0.0584499i
$288$	222.542			0.772717
$289$	−218.771	+	378.923i	−0.756994	+	1.31115i
$290$	26.0000	−	45.0333i	0.0896552	−	0.155287i
$291$	131.349	+	75.8346i	0.451372	+	0.260600i
$292$	17.8178	−	30.8613i	0.0610199	−	0.105690i
$293$	−123.794			−0.422505			−0.211253	−	0.977432i	$-0.567754\pi$
$293$	−123.794			−0.422505			−0.211253	+	0.977432i	$0.567754\pi$
$294$		−	99.5947i		−	0.338758i
$295$	−166.283	−	96.0036i	−0.563672	−	0.325436i
$296$	27.0890			0.0915170
$297$	−321.269			−1.08171
$298$	−144.863			−0.486119
$299$	−129.885	+	74.9892i	−0.434398	+	0.250800i
$300$	−153.137	+	88.4135i	−0.510455	+	0.294712i
$301$	−98.6812	−	170.921i	−0.327844	−	0.567843i
$302$	−68.3406	−	39.4565i	−0.226293	−	0.130651i
$303$			191.486i			0.631967i
$304$	195.089	−	233.144i	0.641740	−	0.766922i
$305$	205.453			0.673618
$306$	−187.453	+	324.679i	−0.612593	+	1.06104i
$307$	146.783	−	84.7453i	0.478121	−	0.276043i	−0.241512	−	0.970398i	$-0.577643\pi$
$307$	146.783	−	84.7453i	0.478121	−	0.276043i	0.719633	+	0.694355i	$0.244310\pi$
$308$	106.043	+	183.673i	0.344297	+	0.596340i
$309$	73.9979	+	128.168i	0.239475	+	0.414784i
$310$			590.050i			1.90339i
$311$		−	407.488i		−	1.31025i	−0.755520	−	0.655125i	$-0.772616\pi$
$311$		−	407.488i		−	1.31025i	0.755520	−	0.655125i	$-0.227384\pi$
$312$		−	68.6509i		−	0.220035i
$313$	286.361	−	495.992i	0.914892	−	1.58464i	0.107833	−	0.994169i	$-0.465609\pi$
$313$	286.361	−	495.992i	0.914892	−	1.58464i	0.807059	−	0.590471i	$-0.201058\pi$
$314$	203.818			0.649101
$315$		−	195.828i		−	0.621677i
$316$	−447.636	−	258.443i	−1.41657	−	0.817856i
$317$	−264.453	+	458.047i	−0.834238	+	1.44494i	0.0604115	+	0.998174i	$0.480759\pi$
$317$	−264.453	+	458.047i	−0.834238	+	1.44494i	−0.894649	+	0.446769i	$0.852575\pi$
$318$	−207.861	−	120.009i	−0.653652	−	0.377386i
$319$	−42.3980	−	24.4785i	−0.132909	−	0.0767352i
$320$	−239.271	−	414.430i	−0.747723	−	1.29509i
$321$	48.4752	+	83.9614i	0.151013	+	0.261562i
$322$	94.1346	+	163.046i	0.292343	+	0.506354i
$323$	175.818	+	481.009i	0.544328	+	1.48919i
$324$	−59.9089	+	103.765i	−0.184904	+	0.320263i
$325$	−92.7267	−	160.607i	−0.285313	−	0.494177i
$326$	−330.065	−	190.563i	−1.01247	−	0.584550i
$327$	−61.5921	−	35.5602i	−0.188355	−	0.108747i
$328$	−35.6356	−	61.7227i	−0.108645	−	0.188179i
$329$	−41.6812	+	72.1939i	−0.126690	+	0.219434i
$330$	150.566	+	260.788i	0.456261	+	0.790268i
$331$		−	59.2704i		−	0.179065i	−0.995984	−	0.0895324i	$-0.971463\pi$
$331$		−	59.2704i		−	0.179065i	0.995984	−	0.0895324i	$-0.0285373\pi$
$332$	−94.1346	+	54.3486i	−0.283538	+	0.163701i
$333$	−11.7743	+	20.3937i	−0.0353583	+	0.0612425i
$334$	−513.362	+	296.390i	−1.53701	+	0.887395i
$335$			276.380i			0.825016i
$336$	−86.1780			−0.256482
$337$	−135.203	−	234.178i	−0.401196	−	0.694891i	0.592675	−	0.805442i	$-0.298072\pi$
$337$	−135.203	−	234.178i	−0.401196	−	0.694891i	−0.993870	+	0.110551i	$0.964739\pi$
$338$	−266.000			−0.786982
$339$	87.8287	−	50.7079i	0.259082	−	0.149581i
$340$	806.178			2.37111
$341$	555.521			1.62909
$342$	90.7246	+	248.208i	0.265277	+	0.725754i
$343$		−	315.652i		−	0.920267i
$344$	363.089	−	209.630i	1.05549	−	0.609388i
$345$	133.657	+	231.501i	0.387413	+	0.671018i
$346$	−455.453			−1.31634
$347$	−292.649	+	168.961i	−0.843368	+	0.486919i	−0.858407	−	0.512968i	$-0.828546\pi$
$347$	−292.649	+	168.961i	−0.843368	+	0.486919i	0.0150399	+	0.999887i	$0.495212\pi$
$348$	17.2277	−	9.94644i	0.0495050	−	0.0285817i
$349$	−156.729			−0.449080			−0.224540	−	0.974465i	$-0.572088\pi$
$349$	−156.729			−0.449080			−0.224540	+	0.974465i	$0.572088\pi$
$350$	−201.612	+	116.401i	−0.576034	+	0.332573i
$351$	118.568	+	68.4555i	0.337801	+	0.195030i
$352$	−390.178	+	225.269i	−1.10846	+	0.639970i
$353$	13.7723			0.0390149			0.0195074	−	0.999810i	$-0.493790\pi$
$353$	13.7723			0.0390149			0.0195074	+	0.999810i	$0.493790\pi$
$354$	−36.7267	−	63.6125i	−0.103748	−	0.179696i
$355$	668.020	+	385.681i	1.88175	+	1.08643i
$356$	513.996			1.44381
$357$	72.5901	−	125.730i	0.203334	−	0.352184i
$358$	454.295	+	262.287i	1.26898	+	0.732646i
$359$	−71.7148	+	41.4046i	−0.199763	+	0.115333i	−0.596545	−	0.802580i	$-0.703460\pi$
$359$	−71.7148	+	41.4046i	−0.199763	+	0.115333i	0.396782	+	0.917913i	$0.370127\pi$
$360$	416.000			1.15556
$361$	339.565	+	122.542i	0.940624	+	0.339451i
$362$	−79.8851	−	138.365i	−0.220677	−	0.382224i
$363$	95.6553	−	55.2266i	0.263513	−	0.152139i
$364$		−	90.3822i		−	0.248303i
$365$	33.3069	−	57.6893i	0.0912519	−	0.158053i
$366$	68.0673	+	39.2987i	0.185976	+	0.107373i
$367$	261.398	+	150.918i	0.712256	+	0.411221i	0.811896	−	0.583802i	$-0.198436\pi$
$367$	261.398	+	150.918i	0.712256	+	0.411221i	−0.0996397	+	0.995024i	$0.531769\pi$
$368$	−346.360	+	199.971i	−0.941196	+	0.543400i
$369$	61.9565			0.167904
$370$	50.6377			0.136859
$371$	−273.659	−	157.997i	−0.737626	−	0.425869i
$372$	−112.863	+	195.485i	−0.303396	+	0.525497i
$373$	301.909			0.809407			0.404704	−	0.914448i	$-0.367375\pi$
$373$	301.909			0.809407			0.404704	+	0.914448i	$0.367375\pi$
$374$		−	759.002i		−	2.02942i
$375$	−54.7246	+	31.5953i	−0.145932	+	0.0842541i
$376$	−153.362	−	88.5438i	−0.407879	−	0.235489i
$377$	10.4317	+	18.0682i	0.0276702	+	0.0479262i
$378$	85.9327	−	148.840i	0.227335	−	0.393756i
$379$			498.042i			1.31409i	0.753850	+	0.657047i	$0.228195\pi$
$379$			498.042i			1.31409i	−0.753850	+	0.657047i	$0.771805\pi$
$380$	364.681	−	435.818i	0.959687	−	1.14689i
$381$	33.3665			0.0875760
$382$	−403.818	−	233.144i	−1.05711	−	0.610325i
$383$	30.0771	−	17.3650i	0.0785303	−	0.0453395i	−0.460221	−	0.887805i	$-0.652230\pi$
$383$	30.0771	−	17.3650i	0.0785303	−	0.0453395i	0.538751	+	0.842465i	$0.318896\pi$
$384$		−	183.069i		−	0.476742i
$385$	198.228	+	343.341i	0.514877	+	0.891794i
$386$	−245.909			−0.637070
$387$			364.465i			0.941769i
$388$	−212.091	+	367.353i	−0.546627	+	0.946785i
$389$	−189.046	+	327.436i	−0.485978	+	0.841739i	−0.999870	−	0.0161159i	$-0.994870\pi$
$389$	−189.046	+	327.436i	−0.485978	+	0.841739i	0.513892	+	0.857855i	$0.328203\pi$
$390$		−	128.330i		−	0.329050i
$391$		−	673.764i		−	1.72318i
$392$	278.542			0.710567
$393$	19.7712	−	34.2448i	0.0503084	−	0.0871368i
$394$	154.158	−	267.010i	0.391265	−	0.677691i
$395$	−836.768	−	483.108i	−2.11840	−	1.22306i
$396$		−	391.656i		−	0.989031i
$397$	−80.5326	−	139.487i	−0.202853	−	0.351352i	0.746594	−	0.665280i	$-0.231688\pi$
$397$	−80.5326	−	139.487i	−0.202853	−	0.351352i	−0.949447	+	0.313929i	$0.898355\pi$
$398$	−185.952	+	107.360i	−0.467217	+	0.269748i
$399$	−35.1325	−	96.1169i	−0.0880514	−	0.240894i
$400$	−247.271	−	428.286i	−0.618178	−	1.07072i
$401$	−220.045	−	381.128i	−0.548739	−	0.950445i	−0.998361	−	0.0572256i	$-0.981775\pi$
$401$	−220.045	−	381.128i	−0.548739	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$402$	−52.8654	+	91.5656i	−0.131506	+	0.227775i
$403$	−205.022	−	118.369i	−0.508739	−	0.293720i
$404$	−535.540			−1.32559
$405$	−111.988	+	193.969i	−0.276514	+	0.478936i
$406$	22.6812	−	13.0950i	0.0558649	−	0.0322536i
$407$		−	47.6744i		−	0.117136i
$408$	267.089	+	154.204i	0.654630	+	0.377951i
$409$	110.068	−	190.644i	0.269116	−	0.466122i	−0.699518	−	0.714615i	$-0.746602\pi$
$409$	110.068	−	190.644i	0.269116	−	0.466122i	0.968634	+	0.248493i	$0.0799353\pi$
$410$	−66.6139	−	115.379i	−0.162473	−	0.281411i
$411$			284.355i			0.691860i
$412$	−358.455	+	206.954i	−0.870038	+	0.502316i
$413$	−48.3525	−	83.7490i	−0.117076	−	0.202782i
$414$		−	347.672i		−	0.839789i
$415$	−175.966	+	101.594i	−0.424015	+	0.244805i
$416$	192.000			0.461538
$417$	384.362			0.921732
$418$	−410.315	−	343.341i	−0.981614	−	0.821389i
$419$			431.538i			1.02992i	0.857213	+	0.514961i	$0.172194\pi$
$419$			431.538i			1.02992i	−0.857213	+	0.514961i	$0.827806\pi$
$420$	−161.093			−0.383555
$421$	27.0357	+	46.8272i	0.0642179	+	0.111229i	0.896347	−	0.443354i	$-0.146211\pi$
$421$	27.0357	+	46.8272i	0.0642179	+	0.111229i	−0.832129	+	0.554582i	$0.812878\pi$
$422$			270.721i			0.641519i
$423$	133.319	−	76.9717i	0.315175	−	0.181966i
$424$	335.636	−	581.338i	0.791593	−	1.37108i
$425$	833.132			1.96031
$426$	147.545	+	255.555i	0.346349	+	0.599893i
$427$	89.6139	+	51.7386i	0.209869	+	0.121168i
$428$	−234.820	+	135.573i	−0.548645	+	0.316760i
$429$	−120.820			−0.281631
$430$	678.725	−	391.862i	1.57843	−	0.911307i
$431$	708.564	+	409.090i	1.64400	+	0.949164i	0.979391	+	0.201973i	$0.0647353\pi$
$431$	708.564	+	409.090i	1.64400	+	0.949164i	0.664609	+	0.747191i	$0.268598\pi$
$432$	316.182	+	182.548i	0.731903	+	0.422565i
$433$	186.863	−	323.657i	0.431555	−	0.747475i	−0.565452	−	0.824781i	$-0.691298\pi$
$433$	186.863	−	323.657i	0.431555	−	0.747475i	0.997007	+	0.0773056i	$0.0246317\pi$
$434$	−148.590	+	257.366i	−0.342373	+	0.593008i
$435$	32.2039	−	18.5929i	0.0740320	−	0.0427424i
$436$	99.4534	−	172.258i	0.228104	−	0.395088i
$437$	−364.236	−	304.783i	−0.833491	−	0.697443i
$438$	22.0694	−	12.7418i	0.0503867	−	0.0290908i
$439$	234.784	−	135.553i	0.534816	−	0.308776i	−0.208159	−	0.978095i	$-0.566747\pi$
$439$	234.784	−	135.553i	0.534816	−	0.308776i	0.742975	+	0.669319i	$0.233414\pi$
$440$	−729.362	+	421.098i	−1.65764	+	0.957040i
$441$	−121.069	+	209.698i	−0.274534	+	0.475506i
$442$	−161.727	+	280.119i	−0.365898	+	0.633753i
$443$	−379.351	−	219.019i	−0.856324	−	0.494399i	0.00645570	−	0.999979i	$-0.497945\pi$
$443$	−379.351	−	219.019i	−0.856324	−	0.494399i	−0.862780	+	0.505580i	$0.831278\pi$
$444$	16.7764	+	9.68586i	0.0377847	+	0.0218150i
$445$	960.816			2.15914
$446$			274.686i			0.615888i
$447$	−89.7148	−	51.7969i	−0.200704	−	0.115877i
$448$		−	241.019i		−	0.537989i
$449$	−710.180			−1.58169			−0.790846	−	0.612015i	$-0.790359\pi$
$449$	−710.180			−1.58169			−0.790846	+	0.612015i	$0.790359\pi$
$450$	429.909			0.955353
$451$	−108.627	+	62.7157i	−0.240858	+	0.139059i
$452$	141.818	+	245.636i	0.313756	+	0.543442i
$453$	−28.2158	−	48.8713i	−0.0622866	−	0.107884i
$454$	−161.067	−	92.9922i	−0.354774	−	0.204829i
$455$		−	168.952i		−	0.371323i
$456$	204.182	−	74.6324i	0.447768	−	0.163667i
$457$	320.996			0.702398			0.351199	−	0.936301i	$-0.385774\pi$
$457$	320.996			0.702398			0.351199	+	0.936301i	$0.385774\pi$
$458$	164.182	−	284.372i	0.358476	−	0.620899i
$459$	−532.657	+	307.530i	−1.16047	+	0.670000i
$460$	−647.453	+	373.807i	−1.40751	+	0.812625i
$461$	−415.907	−	720.372i	−0.902184	−	1.56263i	−0.824653	−	0.565639i	$-0.808630\pi$
$461$	−415.907	−	720.372i	−0.902184	−	1.56263i	−0.0775307	−	0.996990i	$-0.524704\pi$
$462$			151.666i			0.328282i
$463$			231.176i			0.499299i	0.968336	+	0.249650i	$0.0803155\pi$
$463$			231.176i			0.499299i	−0.968336	+	0.249650i	$0.919685\pi$
$464$	27.8178	+	48.1819i	0.0599522	+	0.103840i
$465$	−210.976	+	365.421i	−0.453712	+	0.785853i
$466$	109.089			0.234097
$467$		−	327.762i		−	0.701846i	−0.936404	−	0.350923i	$-0.885868\pi$
$467$		−	327.762i		−	0.701846i	0.936404	−	0.350923i	$-0.114132\pi$
$468$	−83.4534	+	144.546i	−0.178319	+	0.308858i
$469$	−69.5999	+	120.551i	−0.148401	+	0.257037i
$470$	−286.681	−	165.515i	−0.609960	−	0.352161i
$471$	126.226	+	72.8764i	0.267995	+	0.154727i
$472$	177.909	−	102.716i	0.376926	−	0.217618i
$473$	−368.931	−	639.007i	−0.779980	−	1.35097i
$474$	−184.816	−	320.110i	−0.389907	−	0.675338i
$475$	376.874	−	450.390i	0.793419	−	0.948189i
$476$	351.636	+	203.017i	0.738730	+	0.426506i
$477$	291.770	+	505.361i	0.611678	+	1.05946i
$478$	494.542	+	285.524i	1.03461	+	0.597331i
$479$	−67.8178	−	39.1546i	−0.141582	−	0.0817424i	0.427536	−	0.903998i	$-0.359382\pi$
$479$	−67.8178	−	39.1546i	−0.141582	−	0.0817424i	−0.569118	+	0.822256i	$0.692715\pi$
$480$		−	342.212i		−	0.712942i
$481$	−10.1584	+	17.5948i	−0.0211193	+	0.0365797i
$482$	175.772	+	304.446i	0.364673	+	0.631632i
$483$			134.634i			0.278745i
$484$	154.455	+	267.525i	0.319123	+	0.552737i
$485$	−396.463	+	686.694i	−0.817450	+	1.41586i
$486$	−429.909	+	248.208i	−0.884586	+	0.510716i
$487$		−	13.2665i		−	0.0272413i	−0.999907	−	0.0136206i	$-0.995664\pi$
$487$		−	13.2665i		−	0.0272413i	0.999907	−	0.0136206i	$-0.00433572\pi$
$488$	−109.909	+	190.368i	−0.225223	+	0.390098i
$489$	−136.274	−	236.034i	−0.278680	−	0.482687i
$490$	520.681			1.06261
$491$	139.069	−	80.2917i	0.283237	−	0.163527i	−0.351651	−	0.936131i	$-0.614380\pi$
$491$	139.069	−	80.2917i	0.283237	−	0.163527i	0.634888	+	0.772604i	$0.281046\pi$
$492$		−	50.9670i		−	0.103591i
$493$	−93.7267			−0.190115
$494$	78.2733	+	214.143i	0.158448	+	0.433488i
$495$		−	732.126i		−	1.47904i
$496$	−546.725	−	315.652i	−1.10227	−	0.636394i
$497$	194.249	+	336.450i	0.390844	+	0.676962i
$498$	−77.7309			−0.156086
$499$	522.621	−	301.735i	1.04734	−	0.604680i	0.125434	−	0.992102i	$-0.459968\pi$
$499$	522.621	−	301.735i	1.04734	−	0.604680i	0.921902	+	0.387422i	$0.126634\pi$
$500$	−88.3644	−	153.052i	−0.176729	−	0.306103i
$501$	−423.905			−0.846117
$502$	280.247	−	161.801i	0.558262	−	0.322313i
$503$	220.170	+	127.115i	0.437714	+	0.252714i	0.702628	−	0.711558i	$-0.252010\pi$
$503$	220.170	+	127.115i	0.437714	+	0.252714i	−0.264913	+	0.964272i	$0.585343\pi$
$504$	181.449	+	104.760i	0.360018	+	0.207857i
$505$	−1001.09			−1.98235
$506$	351.933	+	609.565i	0.695519	+	1.20467i
$507$	−164.736	−	95.1101i	−0.324922	−	0.187594i
$508$			93.3180i			0.183697i
$509$	49.0455	−	84.9494i	0.0963567	−	0.166895i	−0.813817	−	0.581121i	$-0.802614\pi$
$509$	49.0455	−	84.9494i	0.0963567	−	0.166895i	0.910174	+	0.414226i	$0.135948\pi$
$510$	499.271	+	288.254i	0.978963	+	0.565205i
$511$	29.0554	−	16.7751i	0.0568598	−	0.0328280i
$512$	512.000			1.00000
$513$	−74.7019	+	427.067i	−0.145618	+	0.832489i
$514$	309.725	+	536.459i	0.602577	+	1.04369i
$515$	−670.063	+	386.861i	−1.30109	+	0.751187i
$516$	299.818			0.581042
$517$	−155.830	+	269.905i	−0.301411	+	0.522060i
$518$	22.0869	+	12.7519i	0.0426389	+	0.0246176i
$519$	−282.065	−	162.850i	−0.543478	−	0.313777i
$520$	358.907			0.690205
$521$	−491.317			−0.943026			−0.471513	−	0.881859i	$-0.656292\pi$
$521$	−491.317			−0.943026			−0.471513	+	0.881859i	$0.656292\pi$
$522$	−48.3644			−0.0926521
$523$	399.564	+	230.688i	0.763985	+	0.441087i	0.830725	−	0.556683i	$-0.187926\pi$
$523$	399.564	+	230.688i	0.763985	+	0.441087i	−0.0667397	+	0.997770i	$0.521260\pi$
$524$	95.7743	+	55.2953i	0.182775	+	0.105525i
$525$	−166.479			−0.317103
$526$			395.456i			0.751818i
$527$	921.041	−	531.763i	1.74771	−	1.00904i
$528$	−322.186			−0.610201
$529$	47.9099	+	82.9824i	0.0905670	+	0.156867i
$530$	627.406	−	1086.70i	1.18378	−	2.05037i
$531$			178.583i			0.336314i
$532$	268.816	−	98.2571i	0.505293	−	0.184694i
$533$	53.4534			0.100288
$534$	318.321	+	183.783i	0.596107	+	0.344162i
$535$	−438.950	+	253.428i	−0.820468	+	0.473697i
$536$	−256.087	−	147.852i	−0.477774	−	0.275843i
$537$	187.565	+	324.872i	0.349283	+	0.604977i
$538$	−310.542			−0.577216
$539$		−	490.212i		−	0.909484i
$540$	591.041	+	341.238i	1.09452	+	0.631922i
$541$	−38.1822	+	66.1335i	−0.0705771	+	0.122243i	−0.899154	−	0.437632i	$-0.855817\pi$
$541$	−38.1822	+	66.1335i	−0.0705771	+	0.122243i	0.828577	+	0.559875i	$0.189151\pi$
$542$		−	120.112i		−	0.221608i
$543$		−	114.254i		−	0.210412i
$544$	−431.271	+	746.984i	−0.792778	+	1.37313i
$545$	185.909	−	322.004i	0.341117	−	0.590832i
$546$	32.3168	−	55.9743i	0.0591882	−	0.102517i
$547$	181.521	+	104.801i	0.331848	+	0.191592i	0.656661	−	0.754186i	$-0.271968\pi$
$547$	181.521	+	104.801i	0.331848	+	0.191592i	−0.324813	+	0.945778i	$0.605302\pi$
$548$	−795.271			−1.45122
$549$	−95.5445	−	165.488i	−0.174034	−	0.301435i
$550$	−753.748	+	435.177i	−1.37045	+	0.791231i
$551$	−42.3980	+	50.6685i	−0.0769474	+	0.0919573i
$552$	−286.004			−0.518123
$553$	−243.319	−	421.441i	−0.439998	−	0.762099i
$554$	−399.430	+	691.832i	−0.720992	+	1.24879i
$555$	31.3602	+	18.1058i	0.0565049	+	0.0326231i
$556$			1074.97i			1.93340i
$557$	91.1801	−	157.929i	0.163699	−	0.283534i	−0.772494	−	0.635022i	$-0.780991\pi$
$557$	91.1801	−	157.929i	0.163699	−	0.283534i	0.936192	+	0.351488i	$0.114324\pi$
$558$	475.271	−	274.398i	0.851741	−	0.491753i
$559$			314.444i			0.562512i
$560$		−	450.539i		−	0.804534i
$561$	271.386	−	470.055i	0.483754	−	0.837887i
$562$	−457.998	−	793.276i	−0.814943	−	1.41152i
$563$			483.962i			0.859613i	0.902921	+	0.429807i	$0.141418\pi$
$563$			483.962i			0.859613i	−0.902921	+	0.429807i	$0.858582\pi$
$564$	−63.3188	−	109.671i	−0.112267	−	0.194453i
$565$	265.101	+	459.168i	0.469205	+	0.812687i
$566$		−	836.549i		−	1.47800i
$567$	−97.6931	+	56.4031i	−0.172298	+	0.0994764i
$568$	−714.725	+	412.646i	−1.25832	+	0.726490i
$569$	64.9586			0.114163			0.0570814	−	0.998370i	$-0.481821\pi$
$569$	64.9586			0.114163			0.0570814	+	0.998370i	$0.481821\pi$
$570$	381.679	−	139.511i	0.669612	−	0.244756i
$571$			553.718i			0.969733i	0.874588	+	0.484867i	$0.161132\pi$
$571$			553.718i			0.969733i	−0.874588	+	0.484867i	$0.838868\pi$
$572$		−	337.904i		−	0.590741i
$573$	−166.725	−	288.776i	−0.290968	−	0.503971i
$574$		−	67.1005i		−	0.116900i
$575$	−669.101	+	386.306i	−1.16365	+	0.671836i
$576$	−222.542	+	385.455i	−0.386358	+	0.669192i
$577$	−21.9979			−0.0381247			−0.0190623	−	0.999818i	$-0.506068\pi$
$577$	−21.9979			−0.0381247			−0.0190623	+	0.999818i	$0.506068\pi$
$578$	−437.542	−	757.846i	−0.756994	−	1.31115i
$579$	−152.293	−	87.9264i	−0.263028	−	0.151859i
$580$	52.0000	+	90.0666i	0.0896552	+	0.155287i
$581$	−102.336			−0.176138
$582$	−262.699	+	151.669i	−0.451372	+	0.260600i
$583$	−1023.11	−	590.691i	−1.75490	−	1.01319i
$584$	35.6356	+	61.7227i	0.0610199	+	0.105690i
$585$	−156.000	+	270.200i	−0.266667	+	0.461880i
$586$	123.794	−	214.417i	0.211253	−	0.365900i
$587$	838.432	−	484.069i	1.42833	−	0.824649i	0.431344	−	0.902188i	$-0.358040\pi$
$587$	838.432	−	484.069i	1.42833	−	0.824649i	0.996989	+	0.0775389i	$0.0247062\pi$
$588$	172.503	+	99.5947i	0.293373	+	0.169379i
$589$	129.170	−	738.461i	0.219304	−	1.25375i
$590$	332.566	−	192.007i	0.563672	−	0.325436i
$591$	190.943	−	110.241i	0.323084	−	0.186533i
$592$	−27.0890	+	46.9196i	−0.0457585	+	0.0792560i
$593$	64.8188	−	112.270i	0.109307	−	0.189325i	−0.806183	−	0.591666i	$-0.798470\pi$
$593$	64.8188	−	112.270i	0.109307	−	0.189325i	0.915490	+	0.402342i	$0.131804\pi$
$594$	321.269	−	556.454i	0.540857	−	0.936792i
$595$	657.315	+	379.501i	1.10473	+	0.637816i
$596$	144.863	−	250.911i	0.243059	−	0.420991i
$597$	−153.549			−0.257200
$598$		−	299.957i		−	0.501600i
$599$	−636.142	−	367.277i	−1.06201	−	0.613150i	−0.136020	−	0.990706i	$-0.543431\pi$
$599$	−636.142	−	367.277i	−1.06201	−	0.613150i	−0.925987	+	0.377556i	$0.876765\pi$
$600$		−	353.654i		−	0.589423i
$601$	964.041			1.60406			0.802031	−	0.597282i	$-0.203753\pi$
$601$	964.041			1.60406			0.802031	+	0.597282i	$0.203753\pi$
$602$	394.725			0.655689
$603$	222.618	−	128.529i	0.369184	−	0.213149i
$604$	136.681	−	78.9129i	0.226293	−	0.130651i
$605$	288.725	+	500.086i	0.477231	+	0.826588i
$606$	−331.664	−	191.486i	−0.547300	−	0.315984i
$607$			526.372i			0.867170i	0.901113	+	0.433585i	$0.142752\pi$
$607$			526.372i			0.867170i	−0.901113	+	0.433585i	$0.857248\pi$
$608$	208.729	+	571.048i	0.343304	+	0.939224i
$609$	18.7288			0.0307533
$610$	−205.453	+	355.856i	−0.336809	+	0.583370i
$611$	115.022	−	66.4078i	0.188252	−	0.108687i
$612$	−374.907	−	649.358i	−0.612593	−	1.06104i
$613$	38.9565	+	67.4747i	0.0635506	+	0.110073i	0.896050	−	0.443953i	$-0.146424\pi$
$613$	38.9565	+	67.4747i	0.0635506	+	0.110073i	−0.832500	+	0.554026i	$0.813091\pi$
$614$			338.981i			0.552086i
$615$		−	95.2729i		−	0.154915i
$616$	−424.174			−0.688594
$617$	98.9317	−	171.355i	0.160343	−	0.277722i	−0.774649	−	0.632392i	$-0.782073\pi$
$617$	98.9317	−	171.355i	0.160343	−	0.277722i	0.934992	+	0.354669i	$0.115407\pi$
$618$	−295.992			−0.478951
$619$			86.1017i			0.139098i	0.997579	+	0.0695490i	$0.0221560\pi$
$619$			86.1017i			0.139098i	−0.997579	+	0.0695490i	$0.977844\pi$
$620$	−1022.00	−	590.050i	−1.64838	−	0.951693i
$621$	285.190	−	493.963i	0.459243	−	0.795432i
$622$	705.790	+	407.488i	1.13471	+	0.655125i
$623$	419.085	+	241.959i	0.672688	+	0.388377i
$624$	118.907	+	68.6509i	0.190556	+	0.110017i
$625$	221.181	+	383.097i	0.353890	+	0.612955i
$626$	572.723	+	991.985i	0.914892	+	1.58464i
$627$	−131.347	−	359.344i	−0.209485	−	0.573116i
$628$	−203.818	+	353.023i	−0.324551	+	0.562138i
$629$	−45.6356	−	79.0432i	−0.0725526	−	0.125665i
$630$	339.184	+	195.828i	0.538388	+	0.310838i
$631$	−367.717	−	212.301i	−0.582753	−	0.336452i	0.179474	−	0.983763i	$-0.442560\pi$
$631$	−367.717	−	212.301i	−0.582753	−	0.336452i	−0.762227	+	0.647310i	$0.775894\pi$
$632$	895.271	−	516.885i	1.41657	−	0.817856i
$633$	−96.7981	+	167.659i	−0.152920	+	0.264865i
$634$	−528.907	−	916.093i	−0.834238	−	1.44494i
$635$			174.440i			0.274708i
$636$	415.723	−	240.018i	0.653652	−	0.377386i
$637$	−104.453	+	180.919i	−0.163977	+	0.284017i
$638$	84.7961	−	48.9570i	0.132909	−	0.0767352i
$639$		−	717.432i		−	1.12274i
$640$	957.085			1.49545
$641$	131.637	+	228.001i	0.205361	+	0.355696i	0.950248	−	0.311495i	$-0.100830\pi$
$641$	131.637	+	228.001i	0.205361	+	0.355696i	−0.744886	+	0.667191i	$0.767496\pi$
$642$	−193.901			−0.302026
$643$	−71.3256	+	41.1798i	−0.110926	+	0.0640433i	−0.554437	−	0.832226i	$-0.687066\pi$
$643$	−71.3256	+	41.1798i	−0.110926	+	0.0640433i	0.443510	+	0.896269i	$0.353733\pi$
$644$	−376.538			−0.584687
$645$	560.451			0.868917
$646$	−1008.95	−	176.484i	−1.56184	−	0.273195i
$647$			149.354i			0.230841i	0.993317	+	0.115421i	$0.0368216\pi$
$647$			149.354i			0.230841i	−0.993317	+	0.115421i	$0.963178\pi$
$648$	−119.818	−	207.531i	−0.184904	−	0.320263i
$649$	−180.771	−	313.105i	−0.278538	−	0.482442i
$650$	370.907			0.570626
$651$	−184.046	+	106.259i	−0.282712	+	0.163224i
$652$	660.130	−	381.126i	1.01247	−	0.584550i
$653$	335.540			0.513844			0.256922	−	0.966432i	$-0.417292\pi$
$653$	335.540			0.513844			0.256922	+	0.966432i	$0.417292\pi$
$654$	123.184	−	71.1205i	0.188355	−	0.108747i
$655$	179.032	+	103.364i	0.273331	+	0.157808i
$656$	142.542			0.217290
$657$	−61.9565			−0.0943022
$658$	−83.3623	−	144.388i	−0.126690	−	0.219434i
$659$	−741.636	−	428.184i	−1.12540	−	0.649747i	−0.182623	−	0.983183i	$-0.558459\pi$
$659$	−741.636	−	428.184i	−1.12540	−	0.649747i	−0.942773	+	0.333436i	$0.891792\pi$
$660$	−602.265			−0.912523
$661$	115.830	−	200.623i	0.175234	−	0.303514i	−0.765008	−	0.644021i	$-0.777265\pi$
$661$	115.830	−	200.623i	0.175234	−	0.303514i	0.940242	+	0.340506i	$0.110598\pi$
$662$	102.659	+	59.2704i	0.155075	+	0.0895324i
$663$	−200.317	+	115.653i	−0.302137	+	0.174439i
$664$		−	217.394i		−	0.327401i
$665$	502.499	−	183.673i	0.755638	−	0.276200i
$666$	−23.5487	−	40.7875i	−0.0353583	−	0.0612425i
$667$	75.2733	−	43.4591i	0.112854	−	0.0651560i
$668$		−	1185.56i		−	1.77479i
$669$	−98.2158	+	170.115i	−0.146810	+	0.254282i
$670$	−478.705	−	276.380i	−0.714485	−	0.412508i
$671$	335.032	+	193.431i	0.499302	+	0.288272i
$672$	86.1780	−	149.265i	0.128241	−	0.222120i
$673$	241.727			0.359178			0.179589	−	0.983742i	$-0.442523\pi$
$673$	241.727			0.359178			0.179589	+	0.983742i	$0.442523\pi$
$674$	540.812			0.802391
$675$	610.803	+	352.647i	0.904893	+	0.522440i
$676$	266.000	−	460.726i	0.393491	−	0.681547i
$677$	842.356			1.24425			0.622124	−	0.782919i	$-0.286270\pi$
$677$	842.356			1.24425			0.622124	+	0.782919i	$0.286270\pi$
$678$			202.832i			0.299162i
$679$	−345.856	+	199.680i	−0.509360	+	0.294079i
$680$	−806.178	+	1396.34i	−1.18556	+	2.05344i
$681$	−66.5000	−	115.181i	−0.0976505	−	0.169136i
$682$	−555.521	+	962.190i	−0.814546	+	1.41084i
$683$		−	469.540i		−	0.687467i	−0.939067	−	0.343734i	$-0.888308\pi$
$683$		−	469.540i		−	0.687467i	0.939067	−	0.343734i	$-0.111692\pi$
$684$	−520.634	−	91.0683i	−0.761160	−	0.133141i
$685$	−1486.61			−2.17023
$686$	546.725	+	315.652i	0.796975	+	0.460134i
$687$	203.358	−	117.409i	0.296009	−	0.170901i
$688$			838.518i			1.21878i
$689$	251.727	+	436.003i	0.365351	+	0.632806i
$690$	−534.629			−0.774825
$691$			627.366i			0.907910i	0.891025	+	0.453955i	$0.149987\pi$
$691$			627.366i			0.907910i	−0.891025	+	0.453955i	$0.850013\pi$
$692$	455.453	−	788.868i	0.658170	−	1.13998i
$693$	184.369	−	319.336i	0.266044	−	0.460802i
$694$		−	675.843i		−	0.973837i
$695$			2009.45i			2.89129i
$696$			39.7858i			0.0571635i
$697$	−120.067	+	207.963i	−0.172263	+	0.298368i
$698$	156.729	−	271.462i	0.224540	−	0.388914i
$699$	67.5595	+	39.0055i	0.0966517	+	0.0558019i
$700$		−	465.603i		−	0.665146i
$701$	440.075	+	762.232i	0.627782	+	1.08735i	0.987996	+	0.154480i	$0.0493703\pi$
$701$	440.075	+	762.232i	0.627782	+	1.08735i	−0.360214	+	0.932870i	$0.617296\pi$
$702$	−237.137	+	136.911i	−0.337801	+	0.195030i
$703$	−63.3742	−	11.0853i	−0.0901483	−	0.0157686i
$704$		−	901.078i		−	1.27994i
$705$	−118.362	−	205.010i	−0.167890	−	0.290794i
$706$	−13.7723	+	23.8542i	−0.0195074	+	0.0337879i
$707$	−436.651	−	252.101i	−0.617611	−	0.356578i
$708$	146.907			0.207496
$709$	533.689	−	924.376i	0.752735	−	1.30377i	−0.193758	−	0.981049i	$-0.562068\pi$
$709$	533.689	−	924.376i	0.752735	−	1.30377i	0.946493	−	0.322725i	$-0.104599\pi$
$710$	−1336.04	+	771.363i	−1.88175	+	1.08643i
$711$			898.663i			1.26394i
$712$	−513.996	+	890.267i	−0.721904	+	1.25037i
$713$	−493.135	+	854.134i	−0.691633	+	1.19794i
$714$	145.180	+	251.459i	0.203334	+	0.352184i
$715$		−	631.646i		−	0.883421i
$716$	−908.590	+	524.575i	−1.26898	+	0.732646i
$717$	204.182	+	353.654i	0.284773	+	0.493241i
$718$		−	165.618i		−	0.230666i
$719$	517.610	−	298.842i	0.719902	−	0.415636i	−0.0948144	−	0.995495i	$-0.530226\pi$
$719$	517.610	−	298.842i	0.719902	−	0.415636i	0.814717	+	0.579859i	$0.196892\pi$
$720$	−416.000	+	720.533i	−0.577778	+	1.00074i
$721$	−389.687			−0.540482
$722$	−551.814	+	465.603i	−0.764285	+	0.644879i
$723$			251.394i			0.347710i
$724$	319.540			0.441354
$725$	53.7386	+	93.0780i	0.0741222	+	0.128383i
$726$			220.906i			0.304279i
$727$	209.050	−	120.695i	0.287551	−	0.166018i	−0.349286	−	0.937016i	$-0.613576\pi$
$727$	209.050	−	120.695i	0.287551	−	0.166018i	0.636837	+	0.770998i	$0.280242\pi$
$728$	156.547	+	90.3822i	0.215037	+	0.124151i
$729$	−85.4037			−0.117152
$730$	66.6139	+	115.379i	0.0912519	+	0.158053i
$731$	−1223.36	−	706.306i	−1.67354	−	0.966219i
$732$	−136.135	+	78.5973i	−0.185976	+	0.107373i
$733$	201.525			0.274932			0.137466	−	0.990507i	$-0.456104\pi$
$733$	201.525			0.274932			0.137466	+	0.990507i	$0.456104\pi$
$734$	−522.796	+	301.836i	−0.712256	+	0.411221i
$735$	322.461	+	186.173i	0.438723	+	0.253297i
$736$		−	799.885i		−	1.08680i
$737$	−260.207	+	450.692i	−0.353062	+	0.611522i
$738$	−61.9565	+	107.312i	−0.0839519	+	0.145409i
$739$	258.757	−	149.394i	0.350145	−	0.202156i	−0.314604	−	0.949223i	$-0.601872\pi$
$739$	258.757	−	149.394i	0.350145	−	0.202156i	0.664749	+	0.747067i	$0.268538\pi$
$740$	−50.6377	+	87.7070i	−0.0684293	+	0.118523i
$741$	−28.0932	+	160.607i	−0.0379125	+	0.216744i
$742$	547.319	−	315.995i	0.737626	−	0.425869i
$743$	510.962	−	295.004i	0.687701	−	0.397045i	−0.115049	−	0.993360i	$-0.536702\pi$
$743$	510.962	−	295.004i	0.687701	−	0.397045i	0.802750	+	0.596315i	$0.203369\pi$
$744$	−225.727	−	390.970i	−0.303396	−	0.525497i
$745$	270.794	−	469.029i	0.363482	−	0.629569i
$746$	−301.909	+	522.922i	−0.404704	+	0.700967i
$747$	163.664	+	94.4912i	0.219094	+	0.126494i
$748$	1314.63	+	759.002i	1.75753	+	1.01471i
$749$	−255.280			−0.340827
$750$		−	126.381i		−	0.168508i
$751$	360.208	+	207.966i	0.479638	+	0.276919i	0.720266	−	0.693698i	$-0.244020\pi$
$751$	360.208	+	207.966i	0.479638	+	0.276919i	−0.240628	+	0.970617i	$0.577353\pi$
$752$	306.725	−	177.088i	0.407879	−	0.235489i
$753$	231.412			0.307320
$754$	−41.7267			−0.0553405
$755$	255.499	−	147.512i	0.338409	−	0.195381i
$756$	171.865	+	297.680i	0.227335	+	0.393756i
$757$	−94.9565	−	164.470i	−0.125438	−	0.217265i	0.796466	−	0.604683i	$-0.206700\pi$
$757$	−94.9565	−	164.470i	−0.125438	−	0.217265i	−0.921904	+	0.387418i	$0.873367\pi$
$758$	−862.634	−	498.042i	−1.13804	−	0.657047i
$759$			503.344i			0.663167i
$760$	390.178	+	1067.46i	0.513392	+	1.40456i
$761$	−418.493			−0.549925			−0.274962	−	0.961455i	$-0.588665\pi$
$761$	−418.493			−0.549925			−0.274962	+	0.961455i	$0.588665\pi$
$762$	−33.3665	+	57.7924i	−0.0437880	+	0.0758431i
$763$	162.178	−	93.6335i	0.212553	−	0.122718i
$764$	807.636	−	466.289i	1.05711	−	0.610325i
$765$	−700.816	−	1213.85i	−0.916099	−	1.58673i
$766$			69.4601i			0.0906790i
$767$			154.074i			0.200878i
$768$	317.085	+	183.069i	0.412871	+	0.238371i
$769$	−26.8157	+	46.4462i	−0.0348709	+	0.0603982i	−0.882934	−	0.469497i	$-0.844435\pi$
$769$	−26.8157	+	46.4462i	−0.0348709	+	0.0603982i	0.848063	+	0.529895i	$0.177769\pi$
$770$	−792.911			−1.02975
$771$			442.976i			0.574548i
$772$	245.909	−	425.927i	0.318535	−	0.551719i
$773$	−271.667	+	470.541i	−0.351445	+	0.608721i	−0.986503	−	0.163744i	$-0.947643\pi$
$773$	−271.667	+	470.541i	−0.351445	+	0.608721i	0.635058	+	0.772465i	$0.280976\pi$
$774$	−631.271	−	364.465i	−0.815596	−	0.470885i
$775$	−1056.17	−	609.778i	−1.36280	−	0.786810i
$776$	−424.182	−	734.705i	−0.546627	−	0.946785i
$777$	9.11906	+	15.7947i	0.0117362	+	0.0203278i
$778$	−378.091	−	654.873i	−0.485978	−	0.841739i
$779$	58.1108	+	158.982i	0.0745966	+	0.204084i
$780$	222.273	+	128.330i	0.284966	+	0.164525i
$781$	726.224	+	1257.86i	0.929864	+	1.61057i
$782$	1166.99	+	673.764i	1.49232	+	0.861591i
$783$	−68.7148	−	39.6725i	−0.0877584	−	0.0506673i
$784$	−278.542	+	482.450i	−0.355284	+	0.615369i
$785$	−380.998	+	659.908i	−0.485348	+	0.840647i
$786$	39.5424	+	68.4895i	0.0503084	+	0.0871368i
$787$		−	976.098i		−	1.24028i	−0.784492	−	0.620138i	$-0.787076\pi$
$787$		−	976.098i		−	1.24028i	0.784492	−	0.620138i	$-0.212924\pi$
$788$	308.317	+	534.020i	0.391265	+	0.677691i
$789$	−141.398	+	244.909i	−0.179212	+	0.310404i
$790$	1673.54	−	966.217i	2.11840	−	1.22306i
$791$			267.038i			0.337595i
$792$	678.369	+	391.656i	0.856526	+	0.494515i
$793$	−82.4317	−	142.776i	−0.103949	−	0.180045i
$794$	322.130			0.405706
$795$	777.113	−	448.666i	0.977500	−	0.564360i
$796$		−	429.439i		−	0.539496i
$797$	−596.606			−0.748564			−0.374282	−	0.927315i	$-0.622111\pi$
$797$	−596.606			−0.748564			−0.374282	+	0.927315i	$0.622111\pi$
$798$	201.612	+	35.2656i	0.252646	+	0.0441925i
$799$			596.662i			0.746761i
$800$	989.085			1.23636
$801$	−446.820	−	773.915i	−0.557828	−	0.966186i
$802$	880.178			1.09748
$803$	108.627	−	62.7157i	0.135276	−	0.0781018i
$804$	−105.731	−	183.131i	−0.131506	−	0.227775i
$805$	−703.865			−0.874367
$806$	410.043	−	236.739i	0.508739	−	0.293720i
$807$	−192.321	−	111.037i	−0.238316	−	0.137592i
$808$	535.540	−	927.583i	0.662797	−	1.14800i
$809$	718.128			0.887674			0.443837	−	0.896108i	$-0.353617\pi$
$809$	718.128			0.887674			0.443837	+	0.896108i	$0.353617\pi$
$810$	−223.976	−	387.938i	−0.276514	−	0.478936i
$811$	−548.471	−	316.660i	−0.676290	−	0.390456i	0.122166	−	0.992510i	$-0.461016\pi$
$811$	−548.471	−	316.660i	−0.676290	−	0.390456i	−0.798456	+	0.602054i	$0.794349\pi$
$812$			52.3799i			0.0645073i
$813$	42.9467	−	74.3859i	0.0528250	−	0.0914955i
$814$	82.5745	+	47.6744i	0.101443	+	0.0585681i
$815$	1233.99	−	712.442i	1.51409	−	0.874162i
$816$	−534.178	+	308.408i	−0.654630	+	0.377951i
$817$	−935.224	+	341.842i	−1.14470	+	0.418411i
$818$	220.137	+	381.288i	0.269116	+	0.466122i
$819$	−136.087	+	78.5698i	−0.166162	+	0.0959339i
$820$	266.455			0.324946
$821$	390.770	−	676.834i	0.475969	−	0.824402i	−0.523652	−	0.851932i	$-0.675431\pi$
$821$	390.770	−	676.834i	0.475969	−	0.824402i	0.999621	+	0.0275303i	$0.00876427\pi$
$822$	−492.517	−	284.355i	−0.599169	−	0.345930i
$823$	117.748	+	67.9821i	0.143072	+	0.0826028i	0.569827	−	0.821764i	$-0.307010\pi$
$823$	117.748	+	67.9821i	0.143072	+	0.0826028i	−0.426755	+	0.904367i	$0.640343\pi$
$824$		−	827.817i		−	1.00463i
$825$	−622.402			−0.754426
$826$	193.410			0.234152
$827$	−447.466	−	258.345i	−0.541072	−	0.312388i	0.204441	−	0.978879i	$-0.434462\pi$
$827$	−447.466	−	258.345i	−0.541072	−	0.312388i	−0.745513	+	0.666491i	$0.767796\pi$
$828$	602.186	+	347.672i	0.727278	+	0.419894i
$829$	−1147.72			−1.38447			−0.692233	−	0.721674i	$-0.743373\pi$
$829$	−1147.72			−1.38447			−0.692233	+	0.721674i	$0.743373\pi$
$830$		−	406.377i		−	0.489611i
$831$	−494.739	+	285.637i	−0.595353	+	0.343727i
$832$	−192.000	+	332.554i	−0.230769	+	0.399704i
$833$	−469.247	−	812.760i	−0.563322	−	0.975703i
$834$	−384.362	+	665.735i	−0.460866	+	0.798243i
$835$		−	2216.17i		−	2.65410i
$836$	1005.00	−	367.345i	1.20215	−	0.439408i
$837$	900.336			1.07567
$838$	−747.445	−	431.538i	−0.891939	−	0.514961i
$839$	166.461	−	96.1064i	0.198404	−	0.114549i	−0.397507	−	0.917599i	$-0.630124\pi$
$839$	166.461	−	96.1064i	0.198404	−	0.114549i	0.595911	+	0.803051i	$0.296791\pi$
$840$	161.093	−	279.022i	0.191778	−	0.332169i
$841$	414.454	+	717.856i	0.492811	+	0.853575i
$842$	−108.143			−0.128436
$843$		−	655.041i		−	0.777036i
$844$	−468.903	−	270.721i	−0.555572	−	0.320760i
$845$	497.236	−	861.237i	0.588444	−	1.01922i
$846$			307.887i			0.363932i
$847$			290.834i			0.343369i
$848$	671.271	+	1162.68i	0.791593	+	1.37108i
$849$	299.114	−	518.080i	0.352313	−	0.610224i
$850$	−833.132	+	1443.03i	−0.980156	+	1.69768i
$851$	73.3013	+	42.3205i	0.0861354	+	0.0497303i
$852$	−590.178			−0.692697
$853$	449.317	+	778.239i	0.526749	+	0.912356i	0.999514	+	0.0311674i	$0.00992250\pi$
$853$	449.317	+	778.239i	0.526749	+	0.912356i	−0.472765	+	0.881188i	$0.656744\pi$
$854$	−179.228	+	103.477i	−0.209869	+	0.121168i
$855$	−973.224	−	170.235i	−1.13827	−	0.199105i
$856$		−	542.293i		−	0.633520i
$857$	−62.9555	−	109.042i	−0.0734603	−	0.127237i	0.826955	−	0.562268i	$-0.190071\pi$
$857$	−62.9555	−	109.042i	−0.0734603	−	0.127237i	−0.900416	+	0.435031i	$0.856738\pi$
$858$	120.820	−	209.266i	0.140816	−	0.243900i
$859$	503.551	+	290.725i	0.586206	+	0.338446i	0.763596	−	0.645694i	$-0.223432\pi$
$859$	503.551	+	290.725i	0.586206	+	0.338446i	−0.177390	+	0.984141i	$0.556765\pi$
$860$			1567.45i			1.82261i
$861$	23.9922	−	41.5558i	0.0278656	−	0.0482646i
$862$	−1417.13	+	818.179i	−1.64400	+	0.949164i
$863$			1700.91i			1.97092i	0.169894	+	0.985462i	$0.445657\pi$
$863$			1700.91i			1.97092i	−0.169894	+	0.985462i	$0.554343\pi$
$864$	−632.364	+	365.096i	−0.731903	+	0.422565i
$865$	851.382	−	1474.64i	0.984257	−	1.70478i
$866$	373.727	+	647.314i	0.431555	+	0.747475i
$867$		−	625.785i		−	0.721782i
$868$	−297.180	−	514.731i	−0.342373	−	0.593008i
$869$	−909.675	−	1575.60i	−1.04681	−	1.81312i
$870$			74.3718i			0.0854848i
$871$	192.065	−	110.889i	0.220511	−	0.127312i
$872$	198.907	+	344.517i	0.228104	+	0.395088i
$873$	737.489			0.844775
$874$	892.135	−	326.092i	1.02075	−	0.373103i
$875$		−	166.387i		−	0.190156i
$876$			50.9670i			0.0581815i
$877$	−36.2417	−	62.7725i	−0.0413247	−	0.0715764i	0.844623	−	0.535361i	$-0.179824\pi$
$877$	−36.2417	−	62.7725i	−0.0413247	−	0.0715764i	−0.885948	+	0.463785i	$0.846491\pi$
$878$			542.211i			0.617552i
$879$	153.333	−	88.5267i	0.174440	−	0.100713i
$880$		−	1684.39i		−	1.91408i
$881$	201.998			0.229283			0.114641	−	0.993407i	$-0.463428\pi$
$881$	201.998			0.229283			0.114641	+	0.993407i	$0.463428\pi$
$882$	−242.139	−	419.397i	−0.274534	−	0.475506i
$883$	−752.052	−	434.198i	−0.851701	−	0.491730i	0.00952321	−	0.999955i	$-0.496969\pi$
$883$	−752.052	−	434.198i	−0.851701	−	0.491730i	−0.861225	+	0.508225i	$0.830302\pi$
$884$	−323.453	−	560.238i	−0.365898	−	0.633753i
$885$	274.614			0.310298
$886$	758.703	−	438.037i	0.856324	−	0.494399i
$887$	511.770	+	295.471i	0.576968	+	0.333112i	0.759927	−	0.650008i	$-0.225234\pi$
$887$	511.770	+	295.471i	0.576968	+	0.333112i	−0.182960	+	0.983120i	$0.558568\pi$
$888$	−33.5528	+	19.3717i	−0.0377847	+	0.0218150i
$889$	−43.9286	+	76.0865i	−0.0494135	+	0.0855866i
$890$	−960.816	+	1664.18i	−1.07957	+	1.86987i
$891$	−365.237	+	210.869i	−0.409918	+	0.236666i
$892$	−475.770	−	274.686i	−0.533375	−	0.307944i
$893$	322.554	+	269.905i	0.361203	+	0.302245i
$894$	179.430	−	103.594i	0.200704	−	0.115877i
$895$	−1698.43	+	980.591i	−1.89769	+	1.09563i
$896$	417.458	+	241.019i	0.465912	+	0.268995i
$897$	107.252	−	185.765i	0.119567	−	0.207096i
$898$	710.180	−	1230.07i	0.790846	−	1.36979i
$899$	118.818	+	68.5995i	0.132167	+	0.0763064i
$900$	−429.909	+	744.624i	−0.477677	+	0.827360i
$901$	−2261.72			−2.51023
$902$		−	250.863i		−	0.278118i
$903$	244.455	+	141.136i	0.270715	+	0.156297i
$904$	−567.271			−0.627512
$905$	597.319			0.660021
$906$	112.863			0.124573
$907$	−774.413	+	447.107i	−0.853818	+	0.492952i	−0.861937	−	0.507015i	$-0.830749\pi$
$907$	−774.413	+	447.107i	−0.853818	+	0.492952i	0.00811954	+	0.999967i	$0.497415\pi$
$908$	322.135	−	185.984i	0.354774	−	0.204829i
$909$	465.549	+	806.354i	0.512155	+	0.887078i
$910$	292.634	+	168.952i	0.321575	+	0.185662i
$911$		−	1132.77i		−	1.24343i	−0.783242	−	0.621717i	$-0.786436\pi$
$911$		−	1132.77i		−	1.24343i	0.783242	−	0.621717i	$-0.213564\pi$
$912$	−74.9151	+	428.286i	−0.0821438	+	0.469612i
$913$	−382.596			−0.419054
$914$	−320.996	+	555.981i	−0.351199	+	0.608294i
$915$	−254.477	+	146.922i	−0.278117	+	0.160571i
$916$	328.364	+	568.744i	0.358476	+	0.620899i
$917$	52.0595	+	90.1697i	0.0567716	+	0.0983312i
$918$		−	1230.12i		−	1.34000i
$919$		−	103.477i		−	0.112598i	−0.998414	−	0.0562988i	$-0.982070\pi$
$919$		−	103.477i		−	0.112598i	0.998414	−	0.0562988i	$-0.0179299\pi$
$920$		−	1495.23i		−	1.62525i
$921$	−121.205	+	209.933i	−0.131601	+	0.227940i
$922$	1663.63			1.80437
$923$		−	618.970i		−	0.670606i
$924$	−262.694	−	151.666i	−0.284300	−	0.164141i
$925$	−52.3307	+	90.6395i	−0.0565738	+	0.0979887i
$926$	−400.408	−	231.176i	−0.432406	−	0.249650i
$927$	623.215	+	359.814i	0.672293	+	0.388148i
$928$	−111.271			−0.119904
$929$	622.997	+	1079.06i	0.670610	+	1.16153i	0.977731	+	0.209861i	$0.0673010\pi$
$929$	622.997	+	1079.06i	0.670610	+	1.16153i	−0.307121	+	0.951670i	$0.599366\pi$
$930$	−421.952	−	730.843i	−0.453712	−	0.785853i
$931$	−651.644	−	113.985i	−0.699940	−	0.122432i
$932$	−109.089	+	188.948i	−0.117048	+	0.202734i
$933$	291.400	+	504.720i	0.312326	+	0.540964i
$934$	567.701	+	327.762i	0.607817	+	0.350923i
$935$	2457.45	+	1418.81i	2.62828	+	1.51744i
$936$	−166.907	−	289.091i	−0.178319	−	0.308858i
$937$	−831.676	+	1440.51i	−0.887594	+	1.53736i	−0.0448835	+	0.998992i	$0.514292\pi$
$937$	−831.676	+	1440.51i	−0.887594	+	1.53736i	−0.842711	+	0.538366i	$0.819042\pi$
$938$	−139.200	−	241.101i	−0.148401	−	0.257037i
$939$			819.123i			0.872336i
$940$	573.362	−	331.031i	0.609960	−	0.352161i
$941$	−156.636	+	271.301i	−0.166457	+	0.288311i	−0.937172	−	0.348869i	$-0.886566\pi$
$941$	−156.636	+	271.301i	−0.166457	+	0.288311i	0.770715	+	0.637180i	$0.219899\pi$
$942$	−252.451	+	145.753i	−0.267995	+	0.154727i
$943$		−	222.690i		−	0.236151i
$944$			410.863i			0.435236i
$945$	321.269	+	556.454i	0.339967	+	0.588841i
$946$	1475.72			1.55996
$947$	−918.950	+	530.556i	−0.970380	+	0.560249i	−0.899352	−	0.437225i	$-0.855961\pi$
$947$	−918.950	+	530.556i	−0.970380	+	0.560249i	−0.0710283	+	0.997474i	$0.522628\pi$
$948$	739.263			0.779813
$949$	−53.4534			−0.0563260
$950$	403.224	+	1103.15i	0.424446	+	1.16122i
$951$		−	756.457i		−	0.795433i
$952$	−703.271	+	406.034i	−0.738730	+	0.426506i
$953$	−649.318	−	1124.65i	−0.681341	−	1.18012i	−0.974572	−	0.224075i	$-0.928064\pi$
$953$	−649.318	−	1124.65i	−0.681341	−	1.18012i	0.293231	−	0.956042i	$-0.405269\pi$
$954$	−1167.08			−1.22336
$955$	1509.72	−	871.636i	1.58086	−	0.912708i
$956$	−989.085	+	571.048i	−1.03461	+	0.597331i
$957$	70.0197			0.0731658
$958$	135.636	−	78.3093i	0.141582	−	0.0817424i
$959$	−648.422	−	374.367i	−0.676144	−	0.390372i
$960$	592.729	+	342.212i	0.617426	+	0.356471i
$961$	−595.812			−0.619991
$962$	−20.3168	−	35.1897i	−0.0211193	−	0.0365797i
$963$	408.261	+	235.710i	0.423947	+	0.244766i
$964$	−703.089			−0.729345
$965$	459.679	−	796.188i	0.476351	−	0.825065i
$966$	−233.193	−	134.634i	−0.241400	−	0.139372i
$967$	312.980	−	180.699i	0.323661	−	0.186866i	−0.329362	−	0.944204i	$-0.606834\pi$
$967$	312.980	−	180.699i	0.323661	−	0.186866i	0.653023	+	0.757338i	$0.273500\pi$
$968$	−617.822			−0.638246
$969$	−561.746	−	470.055i	−0.579718	−	0.485092i
$970$	−792.926	−	1373.39i	−0.817450	−	1.41586i
$971$	1318.71	−	761.356i	1.35809	−	0.784095i	0.368726	−	0.929538i	$-0.379794\pi$
$971$	1318.71	−	761.356i	1.35809	−	0.784095i	0.989367	+	0.145443i	$0.0464609\pi$
$972$		−	992.832i		−	1.02143i
$973$	−506.032	+	876.472i	−0.520074	+	0.900794i
$974$	22.9783	+	13.2665i	0.0235916	+	0.0136206i
$975$	229.705	+	132.620i	0.235595	+	0.136021i
$976$	−219.818	−	380.736i	−0.225223	−	0.390098i
$977$	−12.6874			−0.0129861			−0.00649303	−	0.999979i	$-0.502067\pi$
$977$	−12.6874			−0.0129861			−0.00649303	+	0.999979i	$0.502067\pi$
$978$	545.097			0.557359
$979$	1566.80	+	904.590i	1.60040	+	0.923994i
$980$	−520.681	+	901.846i	−0.531307	+	0.920251i
$981$	−345.822			−0.352520
$982$			321.167i			0.327054i
$983$	−726.273	+	419.314i	−0.738833	+	0.426566i	−0.821645	−	0.570000i	$-0.806943\pi$
$983$	−726.273	+	419.314i	−0.738833	+	0.426566i	0.0828116	+	0.996565i	$0.473610\pi$
$984$	88.2774	+	50.9670i	0.0897128	+	0.0517957i
$985$	576.339	+	998.248i	0.585115	+	1.01345i
$986$	93.7267	−	162.339i	0.0950575	−	0.164644i
$987$		−	119.227i		−	0.120797i
$988$	−449.180	−	78.5698i	−0.454636	−	0.0795241i
$989$	1310.00			1.32457
$990$	1268.08	+	732.126i	1.28089	+	0.739521i
$991$	−1478.90	+	853.842i	−1.49233	+	0.861597i	−0.999961	−	0.00879022i	$-0.997202\pi$
$991$	−1478.90	+	853.842i	−1.49233	+	0.861597i	−0.492368	+	0.870387i	$0.663869\pi$
$992$	1093.45	−	631.303i	1.10227	−	0.636394i
$993$	42.3851	+	73.4131i	0.0426839	+	0.0739306i
$994$	−776.998			−0.781688
$995$		−	802.752i		−	0.806786i
$996$	77.7309	−	134.634i	0.0780430	−	0.135174i
$997$	329.734	−	571.117i	0.330727	−	0.572835i	−0.651928	−	0.758281i	$-0.726040\pi$
$997$	329.734	−	571.117i	0.330727	−	0.572835i	0.982655	+	0.185446i	$0.0593729\pi$
$998$			1206.94i			1.20936i
$999$		−	77.2663i		−	0.0773436i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.3.g.a.7.1	✓	4
4.3	odd	2		76.3.g.b.7.2	yes	4
19.11	even	3		76.3.g.b.11.2	yes	4
76.11	odd	6	inner	76.3.g.a.11.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.g.a.7.1	✓	4	1.1	even	1	trivial
76.3.g.a.11.1	yes	4	76.11	odd	6	inner
76.3.g.b.7.2	yes	4	4.3	odd	2
76.3.g.b.11.2	yes	4	19.11	even	3

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)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-1.23861 + 0.715113i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-3.73861 - 6.47547i) q^{5} -2.86045i q^{6} -3.76593i q^{7} +8.00000 q^{8} +(-3.47723 + 6.02273i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-1.23861 + 0.715113i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-3.73861 - 6.47547i) q^{5} -2.86045i q^{6} -3.76593i q^{7} +8.00000 q^{8} +(-3.47723 + 6.02273i) q^{9} +14.9545 q^{10} -14.0793i q^{11} +(4.95445 + 2.86045i) q^{12} +(-3.00000 + 5.19615i) q^{13} +(6.52277 + 3.76593i) q^{14} +(9.26139 + 5.34706i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-13.4772 - 23.3432i) q^{17} +(-6.95445 - 12.0455i) q^{18} +(-18.7158 - 3.27374i) q^{19} +(-14.9545 + 25.9019i) q^{20} +(2.69306 + 4.66452i) q^{21} +(24.3861 + 14.0793i) q^{22} +(21.6475 + 12.4982i) q^{23} +(-9.90890 + 5.72091i) q^{24} +(-15.4545 + 26.7679i) q^{25} +(-6.00000 - 10.3923i) q^{26} -22.8185i q^{27} +(-13.0455 + 7.53185i) q^{28} +(1.73861 - 3.01137i) q^{29} +(-18.5228 + 10.6941i) q^{30} +39.4565i q^{31} +(-16.0000 - 27.7128i) q^{32} +(10.0683 + 17.4388i) q^{33} +53.9089 q^{34} +(-24.3861 + 14.0793i) q^{35} +27.8178 q^{36} +3.38613 q^{37} +(24.3861 - 29.1430i) q^{38} -8.58136i q^{39} +(-29.9089 - 51.8037i) q^{40} +(-4.45445 - 7.71534i) q^{41} -10.7723 q^{42} +(45.3861 - 26.2037i) q^{43} +(-48.7723 + 28.1587i) q^{44} +52.0000 q^{45} +(-43.2950 + 24.9964i) q^{46} +(-19.1703 - 11.0680i) q^{47} -22.8836i q^{48} +34.8178 q^{49} +(-30.9089 - 53.5358i) q^{50} +(33.3861 + 19.2755i) q^{51} +24.0000 q^{52} +(41.9545 - 72.6672i) q^{53} +(39.5228 + 22.8185i) q^{54} +(-91.1703 + 52.6372i) q^{55} -30.1274i q^{56} +(25.5228 - 9.32905i) q^{57} +(3.47723 + 6.02273i) q^{58} +(22.2386 - 12.8395i) q^{59} -42.7765i q^{60} +(-13.7386 + 23.7960i) q^{61} +(-68.3406 - 39.4565i) q^{62} +(22.6812 + 13.0950i) q^{63} +64.0000 q^{64} +44.8634 q^{65} -40.2733 q^{66} +(-32.0109 - 18.4815i) q^{67} +(-53.9089 + 93.3730i) q^{68} -35.7505 q^{69} -56.3173i q^{70} +(-89.3406 + 51.5808i) q^{71} +(-27.8178 + 48.1819i) q^{72} +(4.45445 + 7.71534i) q^{73} +(-3.38613 + 5.86495i) q^{74} -44.2067i q^{75} +(26.0911 + 71.3811i) q^{76} -53.0217 q^{77} +(14.8634 + 8.58136i) q^{78} +(111.909 - 64.6106i) q^{79} +119.636 q^{80} +(-14.9772 - 25.9413i) q^{81} +17.8178 q^{82} -27.1743i q^{83} +(10.7723 - 18.6581i) q^{84} +(-100.772 + 174.543i) q^{85} +104.815i q^{86} +4.97322i q^{87} -112.635i q^{88} +(-64.2495 + 111.283i) q^{89} +(-52.0000 + 90.0666i) q^{90} +(19.5683 + 11.2978i) q^{91} -99.9856i q^{92} +(-28.2158 - 48.8713i) q^{93} +(38.3406 - 22.1359i) q^{94} +(48.7723 + 133.433i) q^{95} +(39.6356 + 22.8836i) q^{96} +(-53.0228 - 91.8381i) q^{97} +(-34.8178 + 60.3062i) q^{98} +(84.7961 + 48.9570i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} - 4 q^{5} + 32 q^{8} + 8 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 - 4 * q^5 + 32 * q^8 + 8 * q^9	\( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} - 4 q^{5} + 32 q^{8} + 8 q^{9} + 16 q^{10} - 24 q^{12} - 12 q^{13} + 48 q^{14} + 48 q^{15} - 32 q^{16} - 32 q^{17} + 16 q^{18} - 42 q^{19} - 16 q^{20} - 44 q^{21} - 12 q^{22} - 12 q^{23} + 48 q^{24} - 18 q^{25} - 24 q^{26} - 96 q^{28} - 4 q^{29} - 96 q^{30} - 64 q^{32} + 106 q^{33} + 128 q^{34} + 12 q^{35} - 64 q^{36} - 96 q^{37} - 12 q^{38} - 32 q^{40} + 26 q^{41} + 176 q^{42} + 72 q^{43} + 24 q^{44} + 208 q^{45} + 24 q^{46} - 36 q^{49} - 36 q^{50} + 24 q^{51} + 96 q^{52} + 124 q^{53} + 180 q^{54} - 288 q^{55} + 124 q^{57} - 8 q^{58} + 78 q^{59} - 44 q^{61} - 120 q^{62} - 216 q^{63} + 256 q^{64} + 48 q^{65} - 424 q^{66} + 102 q^{67} - 128 q^{68} - 384 q^{69} - 204 q^{71} + 64 q^{72} - 26 q^{73} + 96 q^{74} + 192 q^{76} + 248 q^{77} - 72 q^{78} + 360 q^{79} + 128 q^{80} - 38 q^{81} - 104 q^{82} - 176 q^{84} - 184 q^{85} - 16 q^{89} - 208 q^{90} + 144 q^{91} - 80 q^{93} - 24 q^{95} - 192 q^{96} - 234 q^{97} + 36 q^{98} + 624 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 - 4 * q^5 + 32 * q^8 + 8 * q^9 + 16 * q^10 - 24 * q^12 - 12 * q^13 + 48 * q^14 + 48 * q^15 - 32 * q^16 - 32 * q^17 + 16 * q^18 - 42 * q^19 - 16 * q^20 - 44 * q^21 - 12 * q^22 - 12 * q^23 + 48 * q^24 - 18 * q^25 - 24 * q^26 - 96 * q^28 - 4 * q^29 - 96 * q^30 - 64 * q^32 + 106 * q^33 + 128 * q^34 + 12 * q^35 - 64 * q^36 - 96 * q^37 - 12 * q^38 - 32 * q^40 + 26 * q^41 + 176 * q^42 + 72 * q^43 + 24 * q^44 + 208 * q^45 + 24 * q^46 - 36 * q^49 - 36 * q^50 + 24 * q^51 + 96 * q^52 + 124 * q^53 + 180 * q^54 - 288 * q^55 + 124 * q^57 - 8 * q^58 + 78 * q^59 - 44 * q^61 - 120 * q^62 - 216 * q^63 + 256 * q^64 + 48 * q^65 - 424 * q^66 + 102 * q^67 - 128 * q^68 - 384 * q^69 - 204 * q^71 + 64 * q^72 - 26 * q^73 + 96 * q^74 + 192 * q^76 + 248 * q^77 - 72 * q^78 + 360 * q^79 + 128 * q^80 - 38 * q^81 - 104 * q^82 - 176 * q^84 - 184 * q^85 - 16 * q^89 - 208 * q^90 + 144 * q^91 - 80 * q^93 - 24 * q^95 - 192 * q^96 - 234 * q^97 + 36 * q^98 + 624 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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