LMFDB - Embedded newform 33.4.e.b.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,4,Mod(4,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("33.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	33.e (of order $5$, degree $4$, 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:	$1.94706303019$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			16.2
Root			$-1.20316 + 0.874145i$ of defining polynomial
Character	$\chi$	$=$	33.16
Dual form			33.4.e.b.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0404346 - 0.124445i) q^{2} +(-2.42705 - 1.76336i) q^{3} +(6.45828 - 4.69222i) q^{4} +(2.06705 - 6.36172i) q^{5} +(-0.121304 + 0.373335i) q^{6} +(11.6029 - 8.43002i) q^{7} +(-1.69194 - 1.22926i) q^{8} +(2.78115 + 8.55951i) q^{9} +O(q^{10})$	\(q+(-0.0404346 - 0.124445i) q^{2} +(-2.42705 - 1.76336i) q^{3} +(6.45828 - 4.69222i) q^{4} +(2.06705 - 6.36172i) q^{5} +(-0.121304 + 0.373335i) q^{6} +(11.6029 - 8.43002i) q^{7} +(-1.69194 - 1.22926i) q^{8} +(2.78115 + 8.55951i) q^{9} -0.875265 q^{10} +(-28.3816 + 22.9234i) q^{11} -23.9486 q^{12} +(10.8178 + 33.2938i) q^{13} +(-1.51823 - 1.10306i) q^{14} +(-16.2348 + 11.7953i) q^{15} +(19.6502 - 60.4771i) q^{16} +(-21.6244 + 66.5530i) q^{17} +(0.952733 - 0.692201i) q^{18} +(45.0187 + 32.7080i) q^{19} +(-16.5010 - 50.7849i) q^{20} -43.0260 q^{21} +(4.00030 + 2.60506i) q^{22} -43.4430 q^{23} +(1.93879 + 5.96697i) q^{24} +(64.9283 + 47.1732i) q^{25} +(3.70583 - 2.69244i) q^{26} +(8.34346 - 25.6785i) q^{27} +(35.3795 - 108.887i) q^{28} +(168.156 - 122.172i) q^{29} +(2.12431 + 1.54340i) q^{30} +(-38.3253 - 117.953i) q^{31} -25.0514 q^{32} +(109.306 - 5.58930i) q^{33} +9.15657 q^{34} +(-29.6457 - 91.2399i) q^{35} +(58.1246 + 42.2300i) q^{36} +(-316.639 + 230.052i) q^{37} +(2.25003 - 6.92488i) q^{38} +(32.4534 - 99.8813i) q^{39} +(-11.3175 + 8.22268i) q^{40} +(340.499 + 247.387i) q^{41} +(1.73974 + 5.35438i) q^{42} -410.216 q^{43} +(-75.7352 + 281.219i) q^{44} +60.2020 q^{45} +(1.75660 + 5.40626i) q^{46} +(-177.304 - 128.819i) q^{47} +(-154.335 + 112.131i) q^{48} +(-42.4301 + 130.586i) q^{49} +(3.24511 - 9.98743i) q^{50} +(169.840 - 123.396i) q^{51} +(226.086 + 164.261i) q^{52} +(-109.401 - 336.701i) q^{53} -3.53293 q^{54} +(87.1660 + 227.940i) q^{55} -29.9941 q^{56} +(-51.5868 - 158.768i) q^{57} +(-22.0031 - 15.9862i) q^{58} +(-2.98246 + 2.16688i) q^{59} +(-49.5030 + 152.355i) q^{60} +(37.7322 - 116.128i) q^{61} +(-13.1290 + 9.53880i) q^{62} +(104.426 + 75.8702i) q^{63} +(-156.189 - 480.699i) q^{64} +234.167 q^{65} +(-5.11530 - 13.3766i) q^{66} -219.635 q^{67} +(172.625 + 531.285i) q^{68} +(105.438 + 76.6054i) q^{69} +(-10.1556 + 7.37851i) q^{70} +(332.200 - 1022.41i) q^{71} +(5.81636 - 17.9009i) q^{72} +(592.358 - 430.373i) q^{73} +(41.4320 + 30.1021i) q^{74} +(-74.4012 - 228.983i) q^{75} +444.216 q^{76} +(-136.066 + 505.237i) q^{77} -13.7420 q^{78} +(-85.3301 - 262.619i) q^{79} +(-344.121 - 250.018i) q^{80} +(-65.5304 + 47.6106i) q^{81} +(17.0181 - 52.3764i) q^{82} +(-117.512 + 361.666i) q^{83} +(-277.874 + 201.888i) q^{84} +(378.693 + 275.137i) q^{85} +(16.5869 + 51.0493i) q^{86} -623.557 q^{87} +(76.1988 - 3.89639i) q^{88} -1309.41 q^{89} +(-2.43425 - 7.49184i) q^{90} +(406.185 + 295.111i) q^{91} +(-280.567 + 203.844i) q^{92} +(-114.976 + 353.860i) q^{93} +(-8.86164 + 27.2733i) q^{94} +(301.135 - 218.787i) q^{95} +(60.8010 + 44.1745i) q^{96} +(242.603 + 746.654i) q^{97} +17.9665 q^{98} +(-275.147 - 179.180i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} - 6 q^{3} - 16 q^{4} + 9 q^{5} - 18 q^{6} + 3 q^{7} + 36 q^{8} - 18 q^{9}+O(q^{10}) $ 8 * q - 6 * q^2 - 6 * q^3 - 16 * q^4 + 9 * q^5 - 18 * q^6 + 3 * q^7 + 36 * q^8 - 18 * q^9	\( 8 q - 6 q^{2} - 6 q^{3} - 16 q^{4} + 9 q^{5} - 18 q^{6} + 3 q^{7} + 36 q^{8} - 18 q^{9} + 8 q^{10} - 87 q^{11} - 18 q^{12} + 171 q^{13} + 12 q^{14} - 63 q^{15} + 44 q^{16} + 36 q^{17} + 81 q^{18} + 324 q^{19} - 87 q^{20} - 66 q^{21} - 521 q^{22} - 84 q^{23} + 18 q^{24} + 263 q^{25} - 774 q^{26} - 54 q^{27} + 387 q^{28} + 393 q^{29} + 204 q^{30} + 15 q^{31} + 102 q^{32} - 216 q^{33} - 712 q^{34} + 1002 q^{35} - 144 q^{36} - 747 q^{37} - 36 q^{38} + 513 q^{39} + 41 q^{40} + 159 q^{41} + 396 q^{42} - 644 q^{43} + 219 q^{44} + 216 q^{45} + 753 q^{46} - 351 q^{47} - 423 q^{48} - 1967 q^{49} + 330 q^{50} + 63 q^{51} + 2871 q^{52} - 531 q^{53} - 162 q^{54} - 716 q^{55} + 1470 q^{56} - 453 q^{57} - 1205 q^{58} - 1002 q^{59} - 261 q^{60} + 1449 q^{61} + 99 q^{62} + 27 q^{63} - 1118 q^{64} - 954 q^{65} + 897 q^{66} - 518 q^{67} + 873 q^{68} + 693 q^{69} + 26 q^{70} + 429 q^{71} + 54 q^{72} + 2547 q^{73} + 468 q^{74} - 231 q^{75} - 2276 q^{76} - 2697 q^{77} + 1638 q^{78} + 2805 q^{79} - 1620 q^{80} - 162 q^{81} - 1631 q^{82} - 2553 q^{83} - 1509 q^{84} - 197 q^{85} - 1713 q^{86} - 3906 q^{87} + 2866 q^{88} + 1788 q^{89} - 648 q^{90} + 2885 q^{91} + 423 q^{92} + 45 q^{93} + 1159 q^{94} + 3009 q^{95} - 504 q^{96} + 9 q^{97} + 5550 q^{98} + 27 q^{99}+O(q^{100}) \) 8 * q - 6 * q^2 - 6 * q^3 - 16 * q^4 + 9 * q^5 - 18 * q^6 + 3 * q^7 + 36 * q^8 - 18 * q^9 + 8 * q^10 - 87 * q^11 - 18 * q^12 + 171 * q^13 + 12 * q^14 - 63 * q^15 + 44 * q^16 + 36 * q^17 + 81 * q^18 + 324 * q^19 - 87 * q^20 - 66 * q^21 - 521 * q^22 - 84 * q^23 + 18 * q^24 + 263 * q^25 - 774 * q^26 - 54 * q^27 + 387 * q^28 + 393 * q^29 + 204 * q^30 + 15 * q^31 + 102 * q^32 - 216 * q^33 - 712 * q^34 + 1002 * q^35 - 144 * q^36 - 747 * q^37 - 36 * q^38 + 513 * q^39 + 41 * q^40 + 159 * q^41 + 396 * q^42 - 644 * q^43 + 219 * q^44 + 216 * q^45 + 753 * q^46 - 351 * q^47 - 423 * q^48 - 1967 * q^49 + 330 * q^50 + 63 * q^51 + 2871 * q^52 - 531 * q^53 - 162 * q^54 - 716 * q^55 + 1470 * q^56 - 453 * q^57 - 1205 * q^58 - 1002 * q^59 - 261 * q^60 + 1449 * q^61 + 99 * q^62 + 27 * q^63 - 1118 * q^64 - 954 * q^65 + 897 * q^66 - 518 * q^67 + 873 * q^68 + 693 * q^69 + 26 * q^70 + 429 * q^71 + 54 * q^72 + 2547 * q^73 + 468 * q^74 - 231 * q^75 - 2276 * q^76 - 2697 * q^77 + 1638 * q^78 + 2805 * q^79 - 1620 * q^80 - 162 * q^81 - 1631 * q^82 - 2553 * q^83 - 1509 * q^84 - 197 * q^85 - 1713 * q^86 - 3906 * q^87 + 2866 * q^88 + 1788 * q^89 - 648 * q^90 + 2885 * q^91 + 423 * q^92 + 45 * q^93 + 1159 * q^94 + 3009 * q^95 - 504 * q^96 + 9 * q^97 + 5550 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.0404346	−	0.124445i	−0.0142958	−	0.0439980i	0.943654	−	0.330933i	$-0.107364\pi$
$2$	−0.0404346	−	0.124445i	−0.0142958	−	0.0439980i	−0.957950	+	0.286935i	$0.907364\pi$
$3$	−2.42705	−	1.76336i	−0.467086	−	0.339358i
$3$	−2.42705	−	1.76336i	−0.467086	−	0.339358i
$4$	6.45828	−	4.69222i	0.807286	−	0.586527i
$5$	2.06705	−	6.36172i	0.184883	−	0.569010i	−0.815064	−	0.579371i	$-0.803298\pi$
$5$	2.06705	−	6.36172i	0.184883	−	0.569010i	0.999946	+	0.0103613i	$0.00329816\pi$
$6$	−0.121304	+	0.373335i	−0.00825369	+	0.0254022i
$7$	11.6029	−	8.43002i	0.626500	−	0.455179i	−0.228686	−	0.973500i	$-0.573443\pi$
$7$	11.6029	−	8.43002i	0.626500	−	0.455179i	0.855186	+	0.518322i	$0.173443\pi$
$8$	−1.69194	−	1.22926i	−0.0747737	−	0.0543263i
$9$	2.78115	+	8.55951i	0.103006	+	0.317019i
$10$	−0.875265			−0.0276783
$11$	−28.3816	+	22.9234i	−0.777944	+	0.628333i
$11$	−28.3816	+	22.9234i	−0.777944	+	0.628333i
$12$	−23.9486			−0.576115
$13$	10.8178	+	33.2938i	0.230794	+	0.710310i	0.997652	+	0.0684930i	$0.0218191\pi$
$13$	10.8178	+	33.2938i	0.230794	+	0.710310i	−0.766858	+	0.641817i	$0.778181\pi$
$14$	−1.51823	−	1.10306i	−0.0289832	−	0.0210576i
$15$	−16.2348	+	11.7953i	−0.279454	+	0.203035i
$16$	19.6502	−	60.4771i	0.307034	−	0.944955i
$17$	−21.6244	+	66.5530i	−0.308511	+	0.949499i	0.669833	+	0.742512i	$0.266366\pi$
$17$	−21.6244	+	66.5530i	−0.308511	+	0.949499i	−0.978344	+	0.206987i	$0.933634\pi$
$18$	0.952733	−	0.692201i	0.0124756	−	0.00906408i
$19$	45.0187	+	32.7080i	0.543578	+	0.394933i	0.825412	−	0.564530i	$-0.190943\pi$
$19$	45.0187	+	32.7080i	0.543578	+	0.394933i	−0.281834	+	0.959463i	$0.590943\pi$
$20$	−16.5010	−	50.7849i	−0.184487	−	0.567792i
$21$	−43.0260			−0.447098
$22$	4.00030	+	2.60506i	0.0387667	+	0.0252454i
$23$	−43.4430			−0.393847			−0.196924	−	0.980419i	$-0.563095\pi$
$23$	−43.4430			−0.393847			−0.196924	+	0.980419i	$0.563095\pi$
$24$	1.93879	+	5.96697i	0.0164897	+	0.0507501i
$25$	64.9283	+	47.1732i	0.519426	+	0.377385i
$26$	3.70583	−	2.69244i	0.0279528	−	0.0203089i
$27$	8.34346	−	25.6785i	0.0594703	−	0.183031i
$28$	35.3795	−	108.887i	0.238789	−	0.734918i
$29$	168.156	−	122.172i	1.07675	−	0.782306i	0.0996377	−	0.995024i	$-0.468232\pi$
$29$	168.156	−	122.172i	1.07675	−	0.782306i	0.977114	+	0.212718i	$0.0682316\pi$
$30$	2.12431	+	1.54340i	0.0129282	+	0.00939286i
$31$	−38.3253	−	117.953i	−0.222046	−	0.683388i	−0.998578	−	0.0533101i	$-0.983023\pi$
$31$	−38.3253	−	117.953i	−0.222046	−	0.683388i	0.776532	−	0.630078i	$-0.216977\pi$
$32$	−25.0514			−0.138391
$33$	109.306	−	5.58930i	0.576597	−	0.0294840i
$34$	9.15657			0.0461864
$35$	−29.6457	−	91.2399i	−0.143172	−	0.440639i
$36$	58.1246	+	42.2300i	0.269095	+	0.195509i
$37$	−316.639	+	230.052i	−1.40690	+	1.02217i	−0.413133	+	0.910671i	$0.635566\pi$
$37$	−316.639	+	230.052i	−1.40690	+	1.02217i	−0.993764	+	0.111500i	$0.964434\pi$
$38$	2.25003	−	6.92488i	0.00960535	−	0.0295622i
$39$	32.4534	−	99.8813i	0.133249	−	0.410098i
$40$	−11.3175	+	8.22268i	−0.0447365	+	0.0325030i
$41$	340.499	+	247.387i	1.29700	+	0.942326i	0.999922	−	0.0125265i	$-0.00398742\pi$
$41$	340.499	+	247.387i	1.29700	+	0.942326i	0.297079	+	0.954853i	$0.403987\pi$
$42$	1.73974	+	5.35438i	0.00639162	+	0.0196714i
$43$	−410.216			−1.45482			−0.727410	−	0.686203i	$-0.759276\pi$
$43$	−410.216			−1.45482			−0.727410	+	0.686203i	$0.759276\pi$
$44$	−75.7352	+	281.219i	−0.259489	+	0.963530i
$45$	60.2020			0.199431
$46$	1.75660	+	5.40626i	0.00563036	+	0.0173285i
$47$	−177.304	−	128.819i	−0.550265	−	0.399791i	0.277618	−	0.960691i	$-0.410455\pi$
$47$	−177.304	−	128.819i	−0.550265	−	0.399791i	−0.827883	+	0.560901i	$0.810455\pi$
$48$	−154.335	+	112.131i	−0.464089	+	0.337181i
$49$	−42.4301	+	130.586i	−0.123703	+	0.380718i
$50$	3.24511	−	9.98743i	0.00917856	−	0.0282487i
$51$	169.840	−	123.396i	0.466321	−	0.338802i
$52$	226.086	+	164.261i	0.602933	+	0.438056i
$53$	−109.401	−	336.701i	−0.283535	−	0.872630i	−0.986834	−	0.161736i	$-0.948291\pi$
$53$	−109.401	−	336.701i	−0.283535	−	0.872630i	0.703299	−	0.710894i	$-0.251709\pi$
$54$	−3.53293			−0.00890316
$55$	87.1660	+	227.940i	0.213699	+	0.558826i
$56$	−29.9941			−0.0715738
$57$	−51.5868	−	158.768i	−0.119874	−	0.368935i
$58$	−22.0031	−	15.9862i	−0.0498129	−	0.0361912i
$59$	−2.98246	+	2.16688i	−0.00658106	+	0.00478142i	−0.591071	−	0.806620i	$-0.701295\pi$
$59$	−2.98246	+	2.16688i	−0.00658106	+	0.00478142i	0.584490	+	0.811401i	$0.301295\pi$
$60$	−49.5030	+	152.355i	−0.106514	+	0.327815i
$61$	37.7322	−	116.128i	0.0791985	−	0.243748i	−0.903616	−	0.428343i	$-0.859097\pi$
$61$	37.7322	−	116.128i	0.0791985	−	0.243748i	0.982815	+	0.184595i	$0.0590974\pi$
$62$	−13.1290	+	9.53880i	−0.0268934	+	0.0195392i
$63$	104.426	+	75.8702i	0.208833	+	0.151726i
$64$	−156.189	−	480.699i	−0.305056	−	0.938866i
$65$	234.167			0.446843
$66$	−5.11530	−	13.3766i	−0.00954015	−	0.0249476i
$67$	−219.635			−0.400487			−0.200244	−	0.979746i	$-0.564173\pi$
$67$	−219.635			−0.400487			−0.200244	+	0.979746i	$0.564173\pi$
$68$	172.625	+	531.285i	0.307851	+	0.947467i
$69$	105.438	+	76.6054i	0.183961	+	0.133655i
$70$	−10.1556	+	7.37851i	−0.0173405	+	0.0125986i
$71$	332.200	−	1022.41i	0.555280	−	1.70898i	−0.139921	−	0.990163i	$-0.544685\pi$
$71$	332.200	−	1022.41i	0.555280	−	1.70898i	0.695202	−	0.718815i	$-0.255315\pi$
$72$	5.81636	−	17.9009i	0.00952034	−	0.0293006i
$73$	592.358	−	430.373i	0.949729	−	0.690019i	−0.00101345	−	0.999999i	$-0.500323\pi$
$73$	592.358	−	430.373i	0.949729	−	0.690019i	0.950743	+	0.309981i	$0.100323\pi$
$74$	41.4320	+	30.1021i	0.0650862	+	0.0472879i
$75$	−74.4012	−	228.983i	−0.114548	−	0.352543i
$76$	444.216			0.670462
$77$	−136.066	+	505.237i	−0.201378	+	0.747754i
$78$	−13.7420			−0.0199484
$79$	−85.3301	−	262.619i	−0.121524	−	0.374012i	0.871728	−	0.489990i	$-0.163000\pi$
$79$	−85.3301	−	262.619i	−0.121524	−	0.374012i	−0.993252	+	0.115978i	$0.963000\pi$
$80$	−344.121	−	250.018i	−0.480923	−	0.349411i
$81$	−65.5304	+	47.6106i	−0.0898908	+	0.0653095i
$82$	17.0181	−	52.3764i	0.0229188	−	0.0705367i
$83$	−117.512	+	361.666i	−0.155406	+	0.478289i	−0.998202	−	0.0599436i	$-0.980908\pi$
$83$	−117.512	+	361.666i	−0.155406	+	0.478289i	0.842796	+	0.538233i	$0.180908\pi$
$84$	−277.874	+	201.888i	−0.360936	+	0.262235i
$85$	378.693	+	275.137i	0.483236	+	0.351092i
$86$	16.5869	+	51.0493i	0.0207978	+	0.0640091i
$87$	−623.557			−0.768417
$88$	76.1988	−	3.89639i	0.0923048	−	0.00471996i
$89$	−1309.41			−1.55952			−0.779761	−	0.626077i	$-0.784660\pi$
$89$	−1309.41			−1.55952			−0.779761	+	0.626077i	$0.784660\pi$
$90$	−2.43425	−	7.49184i	−0.00285102	−	0.00877455i
$91$	406.185	+	295.111i	0.467910	+	0.339956i
$92$	−280.567	+	203.844i	−0.317947	+	0.231002i
$93$	−114.976	+	353.860i	−0.128198	+	0.394554i
$94$	−8.86164	+	27.2733i	−0.00972350	+	0.0299258i
$95$	301.135	−	218.787i	0.325219	−	0.236285i
$96$	60.8010	+	44.1745i	0.0646404	+	0.0469640i
$97$	242.603	+	746.654i	0.253944	+	0.781559i	0.994036	+	0.109053i	$0.0347819\pi$
$97$	242.603	+	746.654i	0.253944	+	0.781559i	−0.740092	+	0.672506i	$0.765218\pi$
$98$	17.9665			0.0185193
$99$	−275.147	−	179.180i	−0.279326	−	0.181901i
$100$	640.672			0.640672
$101$	484.251	+	1490.37i	0.477077	+	1.46829i	0.843136	+	0.537701i	$0.180707\pi$
$101$	484.251	+	1490.37i	0.477077	+	1.46829i	−0.366059	+	0.930592i	$0.619293\pi$
$102$	−22.2235	−	16.1463i	−0.0215730	−	0.0156737i
$103$	128.981	−	93.7100i	0.123387	−	0.0896458i	−0.524380	−	0.851484i	$-0.675703\pi$
$103$	128.981	−	93.7100i	0.123387	−	0.0896458i	0.647767	+	0.761838i	$0.275703\pi$
$104$	22.6238	−	69.6288i	0.0213312	−	0.0656507i
$105$	−88.9370	+	273.720i	−0.0826606	+	0.254403i
$106$	−37.4771	+	27.2287i	−0.0343406	+	0.0249499i
$107$	−1594.63	−	1158.57i	−1.44074	−	1.04676i	−0.987888	−	0.155171i	$-0.950407\pi$
$107$	−1594.63	−	1158.57i	−1.44074	−	1.04676i	−0.452850	−	0.891586i	$-0.649593\pi$
$108$	−66.6048	−	204.989i	−0.0593431	−	0.182639i
$109$	−1306.85			−1.14838			−0.574192	−	0.818721i	$-0.694684\pi$
$109$	−1306.85			−1.14838			−0.574192	+	0.818721i	$0.694684\pi$
$110$	24.8415	−	20.0641i	0.0215322	−	0.0173912i
$111$	1174.16			1.00402
$112$	−281.823	−	867.363i	−0.237766	−	0.731769i
$113$	1060.53	+	770.518i	0.882884	+	0.641453i	0.934013	−	0.357239i	$-0.116282\pi$
$113$	1060.53	+	770.518i	0.882884	+	0.641453i	−0.0511286	+	0.998692i	$0.516282\pi$
$114$	−17.6720	+	12.8394i	−0.0145187	+	0.0105485i
$115$	−89.7988	+	276.372i	−0.0728155	+	0.224103i
$116$	512.739	−	1578.05i	0.410402	−	1.26309i
$117$	−254.892	+	185.190i	−0.201409	+	0.146332i
$118$	0.390252	+	0.283535i	0.000304454	+	0.000221199i
$119$	310.137	+	954.504i	0.238910	+	0.735288i
$120$	41.9678			0.0319260
$121$	280.036	−	1301.21i	0.210395	−	0.977616i
$122$	−15.9772			−0.0118566
$123$	−390.177	−	1200.84i	−0.286025	−	0.880295i
$124$	−800.979	−	581.945i	−0.580081	−	0.421453i
$125$	1110.76	−	807.017i	0.794798	−	0.577454i
$126$	5.21923	−	16.0631i	0.00369020	−	0.0113573i
$127$	−389.285	+	1198.10i	−0.271996	+	0.837117i	0.718003	+	0.696040i	$0.245056\pi$
$127$	−389.285	+	1198.10i	−0.271996	+	0.837117i	−0.989999	+	0.141077i	$0.954944\pi$
$128$	−215.641	+	156.673i	−0.148908	+	0.108188i
$129$	995.614	+	723.356i	0.679527	+	0.493705i
$130$	−9.46845	−	29.1409i	−0.00638798	−	0.0196602i
$131$	1789.88			1.19376			0.596881	−	0.802330i	$-0.296406\pi$
$131$	1789.88			1.19376			0.596881	+	0.802330i	$0.296406\pi$
$132$	679.702	−	548.984i	0.448185	−	0.361992i
$133$	798.078			0.520317
$134$	8.88085	+	27.3324i	0.00572529	+	0.0176206i
$135$	−146.113	−	106.158i	−0.0931514	−	0.0676784i
$136$	118.398	−	86.0214i	0.0746512	−	0.0542373i
$137$	226.156	−	696.035i	0.141035	−	0.434061i	−0.855445	−	0.517894i	$-0.826716\pi$
$137$	226.156	−	696.035i	0.141035	−	0.434061i	0.996480	+	0.0838331i	$0.0267162\pi$
$138$	5.26980	−	16.2188i	0.00325069	−	0.0100046i
$139$	−1359.71	+	987.889i	−0.829708	+	0.602818i	−0.919477	−	0.393145i	$-0.871387\pi$
$139$	−1359.71	+	987.889i	−0.829708	+	0.602818i	0.0897691	+	0.995963i	$0.471387\pi$
$140$	−619.578	−	450.150i	−0.374028	−	0.271747i
$141$	203.172	+	625.300i	0.121349	+	0.373473i
$142$	−140.666			−0.0831297
$143$	−1070.23	−	696.951i	−0.625856	−	0.407566i
$144$	572.304			0.331195
$145$	−429.641	−	1322.30i	−0.246067	−	0.757317i
$146$	−77.5096	−	56.3140i	−0.0439366	−	0.0319218i
$147$	333.250	−	242.120i	0.186980	−	0.135849i
$148$	−965.493	+	2971.48i	−0.536237	+	1.65037i
$149$	−390.773	+	1202.67i	−0.214855	+	0.661255i	0.784309	+	0.620370i	$0.213018\pi$
$149$	−390.773	+	1202.67i	−0.214855	+	0.661255i	−0.999164	+	0.0408845i	$0.986982\pi$
$150$	−25.4874	+	18.5177i	−0.0138736	+	0.0100798i
$151$	−543.143	−	394.616i	−0.292718	−	0.212672i	0.431728	−	0.902004i	$-0.357904\pi$
$151$	−543.143	−	394.616i	−0.292718	−	0.212672i	−0.724445	+	0.689332i	$0.757904\pi$
$152$	−35.9620	−	110.680i	−0.0191901	−	0.0590612i
$153$	−629.802			−0.332787
$154$	68.3759	−	3.49637i	0.0357785	−	0.00182952i
$155$	−829.607			−0.429907
$156$	−259.072	−	797.340i	−0.132964	−	0.409220i
$157$	−45.0659	−	32.7423i	−0.0229086	−	0.0166441i	0.576272	−	0.817258i	$-0.304507\pi$
$157$	−45.0659	−	32.7423i	−0.0229086	−	0.0166441i	−0.599181	+	0.800614i	$0.704507\pi$
$158$	−29.2313	+	21.2378i	−0.0147185	+	0.0106936i
$159$	−328.202	+	1010.10i	−0.163699	+	0.503813i
$160$	−51.7825	+	159.370i	−0.0255860	+	0.0787457i
$161$	−504.066	+	366.225i	−0.246745	+	0.179271i
$162$	8.57460	+	6.22981i	0.00415854	+	0.00302136i
$163$	235.921	+	726.091i	0.113367	+	0.348907i	0.991603	−	0.129320i	$-0.0412795\pi$
$163$	235.921	+	726.091i	0.113367	+	0.348907i	−0.878236	+	0.478227i	$0.841280\pi$
$164$	3359.83			1.59975
$165$	190.383	−	706.927i	0.0898260	−	0.333540i
$166$	49.7591			0.0232654
$167$	943.529	+	2903.88i	0.437200	+	1.34556i	0.890815	+	0.454366i	$0.150134\pi$
$167$	943.529	+	2903.88i	0.437200	+	1.34556i	−0.453615	+	0.891198i	$0.649866\pi$
$168$	72.7973	+	52.8903i	0.0334311	+	0.0242892i
$169$	785.960	−	571.034i	0.357743	−	0.259915i
$170$	18.9271	−	58.2516i	0.00853906	−	0.0262805i
$171$	−154.760	+	476.304i	−0.0692095	+	0.213005i
$172$	−2649.29	+	1924.82i	−1.17446	+	0.853292i
$173$	−3475.80	−	2525.32i	−1.52752	−	1.10981i	−0.957599	−	0.288105i	$-0.906975\pi$
$173$	−3475.80	−	2525.32i	−1.52752	−	1.10981i	−0.569918	−	0.821701i	$-0.693025\pi$
$174$	25.2133	+	77.5985i	0.0109851	+	0.0338088i
$175$	1151.03			0.497198
$176$	828.635	+	2166.89i	0.354890	+	0.928042i
$177$	11.0596			0.00469654
$178$	52.9456	+	162.950i	0.0222946	+	0.0686158i
$179$	−2050.48	−	1489.76i	−0.856203	−	0.622068i	0.0706466	−	0.997501i	$-0.477494\pi$
$179$	−2050.48	−	1489.76i	−0.856203	−	0.622068i	−0.926849	+	0.375434i	$0.877494\pi$
$180$	388.802	−	282.481i	0.160998	−	0.116972i
$181$	464.374	−	1429.20i	0.190700	−	0.586914i	−0.809300	−	0.587395i	$-0.800153\pi$
$181$	464.374	−	1429.20i	0.190700	−	0.586914i	1.00000		0.000481688i	$0.000153326\pi$
$182$	20.3011	−	62.4805i	0.00826824	−	0.0254470i
$183$	−296.352	+	215.312i	−0.119710	+	0.0869746i
$184$	73.5027	+	53.4028i	0.0294494	+	0.0213962i
$185$	809.018	+	2489.90i	0.321515	+	0.989520i
$186$	48.6851			0.0191923
$187$	−911.885	−	2384.59i	−0.356597	−	0.932505i
$188$	−1749.53			−0.678709
$189$	−119.662	−	368.282i	−0.0460536	−	0.141738i
$190$	−39.4033	−	28.6282i	−0.0150453	−	0.0109311i
$191$	3414.82	−	2481.01i	1.29365	−	0.939894i	0.293780	−	0.955873i	$-0.405087\pi$
$191$	3414.82	−	2481.01i	1.29365	−	0.939894i	0.999872	+	0.0159793i	$0.00508657\pi$
$192$	−468.566	+	1442.10i	−0.176124	+	0.542054i
$193$	1100.29	−	3386.36i	0.410368	−	1.26298i	−0.505962	−	0.862556i	$-0.668862\pi$
$193$	1100.29	−	3386.36i	0.410368	−	1.26298i	0.916329	−	0.400426i	$-0.131138\pi$
$194$	83.1078	−	60.3814i	0.0307567	−	0.0223460i
$195$	−568.335	−	412.919i	−0.208714	−	0.151640i
$196$	338.714	+	1042.46i	0.123438	+	0.379903i
$197$	1118.82			0.404632			0.202316	−	0.979320i	$-0.435153\pi$
$197$	1118.82			0.404632			0.202316	+	0.979320i	$0.435153\pi$
$198$	−11.1725	+	41.4857i	−0.00401009	+	0.0148902i
$199$	3755.04			1.33763			0.668813	−	0.743431i	$-0.266803\pi$
$199$	3755.04			1.33763			0.668813	+	0.743431i	$0.266803\pi$
$200$	−51.8662	−	159.628i	−0.0183375	−	0.0564370i
$201$	533.064	+	387.294i	0.187062	+	0.135909i
$202$	165.889	−	120.525i	0.0577817	−	0.0419808i
$203$	921.186	−	2835.12i	0.318495	−	0.980228i
$204$	517.875	−	1593.85i	0.177738	−	0.547020i
$205$	2277.64	−	1654.80i	0.775986	−	0.563787i
$206$	−16.8770	−	12.2619i	−0.00570815	−	0.00414721i
$207$	−120.822	−	371.850i	−0.0405685	−	0.124857i
$208$	2226.08			0.742072
$209$	−2027.48	+	103.674i	−0.671023	+	0.0343124i
$210$	37.6592			0.0123749
$211$	338.887	+	1042.99i	0.110569	+	0.340295i	0.990997	−	0.133884i	$-0.0427449\pi$
$211$	338.887	+	1042.99i	0.110569	+	0.340295i	−0.880428	+	0.474179i	$0.842745\pi$
$212$	−2286.41	−	1661.18i	−0.740715	−	0.538161i
$213$	−2609.13	+	1895.65i	−0.839319	+	0.609801i
$214$	−79.6997	+	245.290i	−0.0254587	+	0.0783538i
$215$	−847.936	+	2609.68i	−0.268971	+	0.827807i
$216$	−45.6823	+	33.1901i	−0.0143902	+	0.0104551i
$217$	−1439.04	−	1045.52i	−0.450176	−	0.327072i
$218$	52.8421	+	162.631i	0.0164171	+	0.0505265i
$219$	−2196.58			−0.677769
$220$	1632.49	+	1063.10i	0.500283	+	0.325792i
$221$	−2449.73			−0.745641
$222$	−47.4769	−	146.119i	−0.0143533	−	0.0441750i
$223$	4922.64	+	3576.51i	1.47823	+	1.07399i	0.978123	+	0.208029i	$0.0667050\pi$
$223$	4922.64	+	3576.51i	1.47823	+	1.07399i	0.500104	+	0.865965i	$0.333295\pi$
$224$	−290.670	+	211.184i	−0.0867017	+	0.0629925i
$225$	−223.204	+	686.950i	−0.0661344	+	0.203541i
$226$	53.0051	−	163.133i	0.0156011	−	0.0480152i
$227$	−1689.15	+	1227.24i	−0.493889	+	0.358832i	−0.806678	−	0.590991i	$-0.798737\pi$
$227$	−1689.15	+	1227.24i	−0.493889	+	0.358832i	0.312789	+	0.949823i	$0.398737\pi$
$228$	−1078.14	−	783.311i	−0.313163	−	0.227527i
$229$	−695.591	−	2140.81i	−0.200725	−	0.617767i	−0.999862	−	0.0166184i	$-0.994710\pi$
$229$	−695.591	−	2140.81i	−0.200725	−	0.617767i	0.799137	−	0.601149i	$-0.205290\pi$
$230$	38.0241			0.0109010
$231$	1221.15	−	986.303i	0.347817	−	0.280926i
$232$	−434.691			−0.123012
$233$	338.818	+	1042.78i	0.0952649	+	0.293195i	0.987323	−	0.158726i	$-0.0507387\pi$
$233$	338.818	+	1042.78i	0.0952649	+	0.293195i	−0.892058	+	0.451921i	$0.850739\pi$
$234$	33.3525	+	24.2320i	0.00931760	+	0.00676963i
$235$	−1186.01	+	861.684i	−0.329219	+	0.239192i
$236$	−9.09407	+	27.9887i	−0.00250836	+	0.00771994i
$237$	−255.990	+	787.857i	−0.0701618	+	0.215936i
$238$	106.243	−	77.1901i	0.0289358	−	0.0210231i
$239$	3309.49	+	2404.48i	0.895703	+	0.650766i	0.937359	−	0.348366i	$-0.113263\pi$
$239$	3309.49	+	2404.48i	0.895703	+	0.650766i	−0.0416560	+	0.999132i	$0.513263\pi$
$240$	394.327	+	1213.61i	0.106057	+	0.326410i
$241$	−6372.09			−1.70316			−0.851581	−	0.524223i	$-0.824356\pi$
$241$	−6372.09			−1.70316			−0.851581	+	0.524223i	$0.824356\pi$
$242$	−173.252	+	17.7648i	−0.0460209	+	0.00471885i
$243$	243.000			0.0641500
$244$	−301.211	−	927.033i	−0.0790290	−	0.243226i
$245$	743.049	+	539.857i	0.193762	+	0.140776i
$246$	−133.662	+	97.1112i	−0.0346422	+	0.0251691i
$247$	−601.969	+	1852.67i	−0.155070	+	0.477257i
$248$	−80.1516	+	246.681i	−0.0205227	+	0.0631624i
$249$	922.955	−	670.566i	0.234899	−	0.170664i
$250$	−145.343	−	105.598i	−0.0367691	−	0.0267143i
$251$	−23.3779	−	71.9497i	−0.00587888	−	0.0180933i	0.948074	−	0.318050i	$-0.103028\pi$
$251$	−23.3779	−	71.9497i	−0.00587888	−	0.0180933i	−0.953953	+	0.299956i	$0.903028\pi$
$252$	1030.42			0.257580
$253$	1232.98	−	995.860i	0.306391	−	0.247467i
$254$	164.838			0.0407198
$255$	−433.944	−	1335.54i	−0.106567	−	0.327980i
$256$	−3243.04	−	2356.21i	−0.791758	−	0.575246i
$257$	725.765	−	527.299i	0.176156	−	0.127985i	−0.496214	−	0.868200i	$-0.665277\pi$
$257$	725.765	−	527.299i	0.176156	−	0.127985i	0.672369	+	0.740216i	$0.265277\pi$
$258$	49.7608	−	153.148i	0.0120076	−	0.0369557i
$259$	−1734.60	+	5338.56i	−0.416150	+	1.28078i
$260$	1512.32	−	1098.76i	0.360730	−	0.262086i
$261$	1513.40	+	1099.55i	0.358917	+	0.260769i
$262$	−72.3733	−	222.742i	−0.0170658	−	0.0525231i
$263$	−2411.17			−0.565321			−0.282660	−	0.959220i	$-0.591217\pi$
$263$	−2411.17			−0.565321			−0.282660	+	0.959220i	$0.591217\pi$
$264$	−191.809	−	124.909i	−0.0447160	−	0.0291197i
$265$	−2368.13			−0.548956
$266$	−32.2700	−	99.3168i	−0.00743834	−	0.0228929i
$267$	3178.01	+	2308.96i	0.728431	+	0.529236i
$268$	−1418.46	+	1030.57i	−0.323307	+	0.234897i
$269$	605.489	−	1863.50i	0.137239	−	0.422378i	−0.858693	−	0.512491i	$-0.828723\pi$
$269$	605.489	−	1863.50i	0.137239	−	0.422378i	0.995932	+	0.0901127i	$0.0287227\pi$
$270$	−7.30274	+	22.4755i	−0.00164604	+	0.00506599i
$271$	32.4426	−	23.5709i	0.00727213	−	0.00528351i	−0.584143	−	0.811651i	$-0.698569\pi$
$271$	32.4426	−	23.5709i	0.00727213	−	0.00528351i	0.591415	+	0.806367i	$0.298569\pi$
$272$	3600.01	+	2615.56i	0.802510	+	0.583057i
$273$	−465.447	−	1432.50i	−0.103187	−	0.317578i
$274$	−95.7627			−0.0211140
$275$	−2924.14	+	149.524i	−0.641208	+	0.0327879i
$276$	1040.40			0.226901
$277$	−1031.67	−	3175.16i	−0.223780	−	0.688725i	−0.998413	−	0.0563135i	$-0.982065\pi$
$277$	−1031.67	−	3175.16i	−0.223780	−	0.688725i	0.774633	−	0.632411i	$-0.217935\pi$
$278$	177.917	+	129.265i	0.0383841	+	0.0278877i
$279$	903.034	−	656.092i	0.193775	−	0.140786i
$280$	−61.9994	+	190.814i	−0.0132328	+	0.0407262i
$281$	−121.136	+	372.818i	−0.0257166	+	0.0791475i	−0.963091	−	0.269176i	$-0.913249\pi$
$281$	−121.136	+	372.818i	−0.0257166	+	0.0791475i	0.937375	+	0.348323i	$0.113249\pi$
$282$	69.6002	−	50.5675i	0.0146973	−	0.0106782i
$283$	5304.54	+	3853.98i	1.11421	+	0.809524i	0.983322	−	0.181873i	$-0.0582160\pi$
$283$	5304.54	+	3853.98i	1.11421	+	0.809524i	0.130892	+	0.991397i	$0.458216\pi$
$284$	−2651.91	−	8161.75i	−0.554092	−	1.70532i
$285$	−1116.67			−0.232091
$286$	−43.4576	+	161.366i	−0.00898498	+	0.0333629i
$287$	6036.27			1.24150
$288$	−69.6718	−	214.428i	−0.0142550	−	0.0438725i
$289$	13.0094	+	9.45189i	0.00264796	+	0.00192385i
$290$	−147.181	+	106.933i	−0.0298027	+	0.0216529i
$291$	727.808	−	2239.96i	0.146615	−	0.451233i
$292$	1806.21	−	5558.94i	0.361988	−	1.11408i
$293$	4667.01	−	3390.78i	0.930545	−	0.676081i	−0.0155811	−	0.999879i	$-0.504960\pi$
$293$	4667.01	−	3390.78i	0.930545	−	0.676081i	0.946126	+	0.323798i	$0.104960\pi$
$294$	−43.6055	−	31.6813i	−0.00865009	−	0.00628466i
$295$	7.62022	+	23.4526i	0.00150395	+	0.00462869i
$296$	818.528			0.160730
$297$	351.838	+	920.059i	0.0687397	+	0.179755i
$298$	165.468			0.0321654
$299$	−469.957	−	1446.38i	−0.0908974	−	0.279754i
$300$	−1554.94	−	1129.73i	−0.299249	−	0.217417i
$301$	−4759.70	+	3458.13i	−0.911444	+	0.662203i
$302$	−27.1463	+	83.5476i	−0.00517249	+	0.0159193i
$303$	1452.75	−	4471.12i	0.275441	−	0.847719i
$304$	2862.71	−	2079.88i	0.540091	−	0.392399i
$305$	−660.778	−	480.083i	−0.124053	−	0.0901294i
$306$	25.4658	+	78.3757i	0.00475746	+	0.0146420i
$307$	−4161.46			−0.773638			−0.386819	−	0.922156i	$-0.626426\pi$
$307$	−4161.46			−0.773638			−0.386819	+	0.922156i	$0.626426\pi$
$308$	1491.93	+	3901.41i	0.276008	+	0.721765i
$309$	−478.287			−0.0880543
$310$	33.5448	+	103.240i	0.00614587	+	0.0189150i
$311$	1409.63	+	1024.15i	0.257018	+	0.186734i	0.708831	−	0.705378i	$-0.249223\pi$
$311$	1409.63	+	1024.15i	0.257018	+	0.186734i	−0.451813	+	0.892112i	$0.649223\pi$
$312$	−177.689	+	129.099i	−0.0322426	+	0.0234256i
$313$	1445.67	−	4449.33i	0.261068	−	0.803485i	−0.731505	−	0.681836i	$-0.761182\pi$
$313$	1445.67	−	4449.33i	0.261068	−	0.803485i	0.992573	−	0.121649i	$-0.0388182\pi$
$314$	−2.25239	+	6.93215i	−0.000404808	+	0.00124587i
$315$	698.520	−	507.505i	0.124943	−	0.0907766i
$316$	−1783.35	−	1295.68i	−0.317473	−	0.230657i
$317$	588.811	+	1812.18i	0.104325	+	0.321079i	0.989571	−	0.144043i	$-0.0460105\pi$
$317$	588.811	+	1812.18i	0.104325	+	0.321079i	−0.885247	+	0.465122i	$0.846010\pi$
$318$	138.973			0.0245069
$319$	−1971.94	+	7322.16i	−0.346104	+	1.28515i
$320$	−3380.93			−0.590623
$321$	1827.29	+	5623.81i	0.317723	+	0.977852i
$322$	65.9566	+	47.9203i	0.0114150	+	0.00829346i
$323$	−3150.32	+	2288.84i	−0.542688	+	0.394286i
$324$	−199.814	+	614.966i	−0.0342617	+	0.105447i
$325$	−868.191	+	2672.02i	−0.148180	+	0.456052i
$326$	80.8190	−	58.7184i	0.0137305	−	0.00997581i
$327$	3171.80	+	2304.45i	0.536394	+	0.389713i
$328$	−271.999	−	837.126i	−0.0457885	−	0.140922i
$329$	−3143.19			−0.526717
$330$	−95.6716	+	4.89212i	−0.0159592	+	0.000816068i
$331$	−8459.25			−1.40472			−0.702360	−	0.711822i	$-0.747870\pi$
$331$	−8459.25			−1.40472			−0.702360	+	0.711822i	$0.747870\pi$
$332$	938.088	+	2887.14i	0.155073	+	0.477266i
$333$	−2849.75	−	2070.47i	−0.468966	−	0.340724i
$334$	323.222	−	234.835i	0.0529519	−	0.0384718i
$335$	−453.996	+	1397.25i	−0.0740431	+	0.227881i
$336$	−845.470	+	2602.09i	−0.137274	+	0.422487i
$337$	2698.53	−	1960.60i	0.436197	−	0.316916i	−0.347925	−	0.937522i	$-0.613114\pi$
$337$	2698.53	−	1960.60i	0.436197	−	0.316916i	0.784122	+	0.620607i	$0.213114\pi$
$338$	−102.842	−	74.7193i	−0.0165500	−	0.0120242i
$339$	−1215.26	−	3740.17i	−0.194701	−	0.599228i
$340$	3736.71			0.596034
$341$	3791.63	+	2469.16i	0.602135	+	0.392119i
$342$	65.5313			0.0103612
$343$	2128.68	+	6551.41i	0.335097	+	1.03132i
$344$	694.058	+	504.263i	0.108782	+	0.0790350i
$345$	705.289	−	512.422i	0.110062	−	0.0799649i
$346$	−173.721	+	534.657i	−0.0269921	+	0.0830732i
$347$	2224.10	−	6845.07i	0.344080	−	1.05897i	−0.617994	−	0.786183i	$-0.712054\pi$
$347$	2224.10	−	6845.07i	0.344080	−	1.05897i	0.962074	−	0.272787i	$-0.0879455\pi$
$348$	−4027.11	+	2925.86i	−0.620332	+	0.450698i
$349$	4369.75	+	3174.81i	0.670221	+	0.486944i	0.870099	−	0.492877i	$-0.164055\pi$
$349$	4369.75	+	3174.81i	0.670221	+	0.486944i	−0.199878	+	0.979821i	$0.564055\pi$
$350$	−46.5415	−	143.240i	−0.00710784	−	0.0218757i
$351$	945.193			0.143734
$352$	711.000	−	574.263i	0.107660	−	0.0869555i
$353$	−3383.09			−0.510095			−0.255048	−	0.966928i	$-0.582091\pi$
$353$	−3383.09			−0.510095			−0.255048	+	0.966928i	$0.582091\pi$
$354$	−0.447189	−	1.37631i	−6.71408e−5	−	0.000206638i
$355$	−5817.60	−	4226.73i	−0.869764	−	0.631920i
$356$	−8456.56	+	6144.05i	−1.25898	+	0.914702i
$357$	930.412	−	2863.51i	0.137935	−	0.424519i
$358$	−102.483	+	315.410i	−0.0151296	+	0.0465641i
$359$	−14.1725	+	10.2969i	−0.00208356	+	0.00151379i	−0.588827	−	0.808259i	$-0.700410\pi$
$359$	−14.1725	+	10.2969i	−0.00208356	+	0.00151379i	0.586743	+	0.809773i	$0.300410\pi$
$360$	−101.858	−	74.0041i	−0.0149122	−	0.0108343i
$361$	−1162.68	−	3578.36i	−0.169511	−	0.521703i
$362$	−196.633			−0.0285492
$363$	−2974.15	+	2664.29i	−0.430035	+	0.385232i
$364$	4007.99			0.577131
$365$	−1513.48	−	4658.02i	−0.217039	−	0.667978i
$366$	38.7775	+	28.1735i	0.00553806	+	0.00402364i
$367$	3971.35	−	2885.36i	0.564858	−	0.410393i	−0.268376	−	0.963314i	$-0.586487\pi$
$367$	3971.35	−	2885.36i	0.564858	−	0.410393i	0.833234	+	0.552921i	$0.186487\pi$
$368$	−853.663	+	2627.30i	−0.120925	+	0.372168i
$369$	−1170.53	+	3602.53i	−0.165137	+	0.508239i
$370$	277.144	−	201.357i	0.0389406	−	0.0282920i
$371$	−4107.76	−	2984.46i	−0.574837	−	0.417643i
$372$	917.840	+	2824.82i	0.127924	+	0.393710i
$373$	8416.78			1.16838			0.584188	−	0.811618i	$-0.301413\pi$
$373$	8416.78			1.16838			0.584188	+	0.811618i	$0.301413\pi$
$374$	−259.878	+	209.900i	−0.0359305	+	0.0290205i
$375$	−4118.94			−0.567203
$376$	141.635	+	435.906i	0.0194262	+	0.0597876i
$377$	5886.66	+	4276.91i	0.804187	+	0.584276i
$378$	−40.9923	+	29.7827i	−0.00557783	+	0.00405253i
$379$	1992.17	−	6131.26i	0.270002	−	0.830981i	−0.720497	−	0.693459i	$-0.756086\pi$
$379$	1992.17	−	6131.26i	0.270002	−	0.830981i	0.990499	−	0.137522i	$-0.0439139\pi$
$380$	918.217	−	2825.98i	0.123957	−	0.381499i
$381$	3057.49	−	2221.39i	0.411128	−	0.298702i
$382$	−446.826	−	324.638i	−0.0598472	−	0.0434815i
$383$	−1465.70	−	4510.98i	−0.195546	−	0.601828i	−0.999970	−	0.00777244i	$-0.997526\pi$
$383$	−1465.70	−	4510.98i	−0.195546	−	0.601828i	0.804424	−	0.594056i	$-0.202474\pi$
$384$	799.642			0.106267
$385$	2932.92	+	1909.96i	0.388248	+	0.252833i
$386$	−465.906			−0.0614352
$387$	−1140.87	−	3511.24i	−0.149855	−	0.461206i
$388$	5070.26	+	3683.76i	0.663411	+	0.481996i
$389$	−2402.14	+	1745.26i	−0.313093	+	0.227476i	−0.733223	−	0.679989i	$-0.761985\pi$
$389$	−2402.14	+	1745.26i	−0.313093	+	0.227476i	0.420129	+	0.907464i	$0.361985\pi$
$390$	−28.4053	+	87.4226i	−0.00368810	+	0.0113508i
$391$	939.427	−	2891.26i	0.121506	−	0.373957i
$392$	232.314	−	168.786i	0.0299327	−	0.0217474i
$393$	−4344.14	−	3156.20i	−0.557590	−	0.405113i
$394$	−45.2390	−	139.231i	−0.00578454	−	0.0178030i
$395$	−1847.09			−0.235284
$396$	−2617.72	+	133.856i	−0.332186	+	0.0169862i
$397$	1573.89			0.198971			0.0994854	−	0.995039i	$-0.468280\pi$
$397$	1573.89			0.198971			0.0994854	+	0.995039i	$0.468280\pi$
$398$	−151.834	−	467.296i	−0.0191224	−	0.0588528i
$399$	−1936.97	−	1407.29i	−0.243033	−	0.176574i
$400$	4128.75	−	2999.71i	0.516094	−	0.374964i
$401$	−1143.43	+	3519.10i	−0.142394	+	0.438243i	−0.996667	−	0.0815818i	$-0.974003\pi$
$401$	−1143.43	+	3519.10i	−0.142394	+	0.438243i	0.854273	+	0.519825i	$0.174003\pi$
$402$	26.6425	−	81.9973i	0.00330550	−	0.0101733i
$403$	3512.51	−	2551.99i	0.434171	−	0.315443i
$404$	10120.6	+	7353.03i	1.24633	+	0.905513i
$405$	167.431	+	515.300i	0.0205425	+	0.0632233i
$406$	−390.064			−0.0476812
$407$	3713.18	−	13787.7i	0.452224	−	1.67919i
$408$	−439.045			−0.0532744
$409$	−984.737	−	3030.71i	−0.119052	−	0.366403i	0.873719	−	0.486431i	$-0.161702\pi$
$409$	−984.737	−	3030.71i	−0.119052	−	0.366403i	−0.992771	+	0.120028i	$0.961702\pi$
$410$	−298.027	−	216.529i	−0.0358988	−	0.0260820i
$411$	−1776.25	+	1290.52i	−0.213177	+	0.154882i
$412$	393.286	−	1210.41i	0.0470287	−	0.144739i
$413$	−16.3384	+	50.2843i	−0.00194663	+	0.00599112i
$414$	−41.3896	+	30.0713i	−0.00491349	+	0.00356986i
$415$	2057.92	+	1495.16i	0.243420	+	0.176855i
$416$	−271.001	−	834.055i	−0.0319397	−	0.0983003i
$417$	5042.09			0.592116
$418$	94.8822	+	248.118i	0.0111025	+	0.0290331i
$419$	7400.64			0.862875			0.431438	−	0.902143i	$-0.358006\pi$
$419$	7400.64			0.862875			0.431438	+	0.902143i	$0.358006\pi$
$420$	709.973	+	2185.07i	0.0824837	+	0.253859i
$421$	−1999.14	−	1452.46i	−0.231430	−	0.168144i	0.466027	−	0.884771i	$-0.345685\pi$
$421$	−1999.14	−	1452.46i	−0.231430	−	0.168144i	−0.697457	+	0.716627i	$0.745685\pi$
$422$	116.092	−	84.3457i	0.0133916	−	0.00972958i
$423$	609.517	−	1875.90i	0.0700608	−	0.215625i
$424$	−228.795	+	704.158i	−0.0262058	+	0.0806531i
$425$	−4543.55	+	3301.08i	−0.518575	+	0.376767i
$426$	341.403	+	248.044i	0.0388287	+	0.0282107i
$427$	−541.155	−	1665.50i	−0.0613310	−	0.188757i
$428$	−15734.8			−1.77704
$429$	1368.54	+	3578.74i	0.154018	+	0.402758i
$430$	359.047			0.0402670
$431$	−338.498	−	1041.79i	−0.0378303	−	0.116430i	0.930358	−	0.366652i	$-0.119496\pi$
$431$	−338.498	−	1041.79i	−0.0378303	−	0.116430i	−0.968188	+	0.250223i	$0.919496\pi$
$432$	−1389.01	−	1009.18i	−0.154696	−	0.112394i
$433$	73.0855	−	53.0997i	0.00811147	−	0.00589333i	−0.583722	−	0.811953i	$-0.698404\pi$
$433$	73.0855	−	53.0997i	0.00811147	−	0.00589333i	0.591834	+	0.806060i	$0.298404\pi$
$434$	−71.9229	+	221.356i	−0.00795487	+	0.0244826i
$435$	−1288.92	+	3966.90i	−0.142067	+	0.437237i
$436$	−8440.03	+	6132.04i	−0.927074	+	0.673558i
$437$	−1955.74	−	1420.93i	−0.214087	−	0.155543i
$438$	88.8181	+	273.354i	0.00968925	+	0.0298204i
$439$	−3930.60			−0.427329			−0.213664	−	0.976907i	$-0.568540\pi$
$439$	−3930.60			−0.427329			−0.213664	+	0.976907i	$0.568540\pi$
$440$	132.719	−	492.810i	0.0143798	−	0.0533950i
$441$	−1235.76			−0.133437
$442$	99.0539	+	304.857i	0.0106595	+	0.0328067i
$443$	−3212.40	−	2333.94i	−0.344527	−	0.250314i	0.402042	−	0.915621i	$-0.368300\pi$
$443$	−3212.40	−	2333.94i	−0.344527	−	0.250314i	−0.746570	+	0.665307i	$0.768300\pi$
$444$	7583.08	−	5509.43i	0.810534	−	0.588888i
$445$	−2706.62	+	8330.13i	−0.288328	+	0.887384i
$446$	246.034	−	757.213i	0.0261211	−	0.0803926i
$447$	3069.17	−	2229.88i	0.324758	−	0.235950i
$448$	−5864.55	−	4260.85i	−0.618469	−	0.449344i
$449$	5497.77	+	16920.4i	0.577852	+	1.77845i	0.626254	+	0.779619i	$0.284587\pi$
$449$	5497.77	+	16920.4i	0.577852	+	1.77845i	−0.0484019	+	0.998828i	$0.515413\pi$
$450$	94.5126			0.00990082
$451$	−15334.9	+	784.142i	−1.60109	+	0.0818709i
$452$	10464.6			1.08897
$453$	622.386	+	1915.51i	0.0645525	+	0.198672i
$454$	221.024	+	160.583i	0.0228484	+	0.0166003i
$455$	2717.02	−	1974.03i	0.279947	−	0.203393i
$456$	−107.886	+	332.039i	−0.0110794	+	0.0340990i
$457$	−3571.23	+	10991.1i	−0.365547	+	1.12504i	0.584091	+	0.811688i	$0.301451\pi$
$457$	−3571.23	+	10991.1i	−0.365547	+	1.12504i	−0.949638	+	0.313349i	$0.898549\pi$
$458$	−238.287	+	173.126i	−0.0243110	+	0.0176630i
$459$	1528.56	+	1110.56i	0.155440	+	0.112934i
$460$	716.853	+	2206.25i	0.0726596	+	0.223623i
$461$	−996.474			−0.100673			−0.0503367	−	0.998732i	$-0.516029\pi$
$461$	−996.474			−0.100673			−0.0503367	+	0.998732i	$0.516029\pi$
$462$	−172.117	−	112.085i	−0.0173325	−	0.0112872i
$463$	3950.65			0.396549			0.198275	−	0.980146i	$-0.436466\pi$
$463$	3950.65			0.396549			0.198275	+	0.980146i	$0.436466\pi$
$464$	−4084.34	−	12570.3i	−0.408644	−	1.25768i
$465$	2013.50	+	1462.89i	0.200804	+	0.145892i
$466$	116.068	−	84.3285i	0.0115381	−	0.00838292i
$467$	−5110.85	+	15729.6i	−0.506428	+	1.55862i	0.291929	+	0.956440i	$0.405703\pi$
$467$	−5110.85	+	15729.6i	−0.506428	+	1.55862i	−0.798357	+	0.602185i	$0.794297\pi$
$468$	−777.215	+	2392.02i	−0.0767666	+	0.236263i
$469$	−2548.41	+	1851.53i	−0.250905	+	0.182293i
$470$	155.188	+	112.751i	0.0152304	+	0.0110655i
$471$	51.6409	+	158.934i	0.00505199	+	0.0155484i
$472$	7.70979			0.000751847
$473$	11642.6	−	9403.53i	1.13177	−	0.914112i
$474$	108.396			0.0105038
$475$	1380.05	+	4247.34i	0.133307	+	0.410277i
$476$	6481.70	+	4709.23i	0.624135	+	0.453460i
$477$	2577.73	−	1872.83i	0.247434	−	0.179772i
$478$	165.408	−	509.074i	0.0158276	−	0.0487123i
$479$	−1492.05	+	4592.05i	−0.142324	+	0.438030i	−0.996657	−	0.0816967i	$-0.973966\pi$
$479$	−1492.05	+	4592.05i	−0.142324	+	0.438030i	0.854333	+	0.519726i	$0.173966\pi$
$480$	406.705	−	295.488i	0.0386739	−	0.0280982i
$481$	−11084.6	−	8053.46i	−1.05076	−	0.763423i
$482$	257.653	+	792.974i	0.0243481	+	0.0749357i
$483$	1869.18			0.176088
$484$	−4297.00	−	9717.56i	−0.403550	−	0.912618i
$485$	5251.48			0.491665
$486$	−9.82562	−	30.2401i	−0.000917076	−	0.00282247i
$487$	756.687	+	549.765i	0.0704081	+	0.0511545i	0.622433	−	0.782673i	$-0.286144\pi$
$487$	756.687	+	549.765i	0.0704081	+	0.0511545i	−0.552024	+	0.833828i	$0.686144\pi$
$488$	−206.592	+	150.098i	−0.0191639	+	0.0139234i
$489$	707.764	−	2178.27i	0.0654523	−	0.201441i
$490$	37.1376	−	114.298i	0.00342389	−	0.0105376i
$491$	−9774.71	+	7101.75i	−0.898425	+	0.652744i	−0.938061	−	0.346470i	$-0.887380\pi$
$491$	−9774.71	+	7101.75i	−0.898425	+	0.652744i	0.0396360	+	0.999214i	$0.487380\pi$
$492$	−8154.49	−	5924.58i	−0.747221	−	0.542888i
$493$	4494.68	+	13833.2i	0.410609	+	1.26372i
$494$	254.896			0.0232152
$495$	−1708.63	+	1380.03i	−0.155146	+	0.125309i
$496$	−7886.57			−0.713947
$497$	−4764.42	−	14663.4i	−0.430007	−	1.32343i
$498$	−120.768	−	87.7430i	−0.0108669	−	0.00789530i
$499$	1372.15	−	996.922i	0.123098	−	0.0894356i	−0.524533	−	0.851390i	$-0.675760\pi$
$499$	1372.15	−	996.922i	0.123098	−	0.0894356i	0.647631	+	0.761955i	$0.275760\pi$
$500$	3386.93	−	10423.9i	0.302936	−	0.932341i
$501$	2830.59	−	8711.65i	0.252418	−	0.776862i
$502$	−8.00851	+	5.81852i	−0.000712026	+	0.000517317i
$503$	−1799.33	−	1307.29i	−0.159499	−	0.115883i	0.505173	−	0.863018i	$-0.331429\pi$
$503$	−1799.33	−	1307.29i	−0.159499	−	0.115883i	−0.664672	+	0.747135i	$0.731429\pi$
$504$	−83.4183	−	256.735i	−0.00737251	−	0.0226903i
$505$	10482.3			0.923676
$506$	−173.785	−	113.171i	−0.0152682	−	0.00994284i
$507$	−2914.50			−0.255301
$508$	3107.62	+	9564.26i	0.271414	+	0.835326i
$509$	−3040.47	−	2209.03i	−0.264767	−	0.192364i	0.447479	−	0.894294i	$-0.352322\pi$
$509$	−3040.47	−	2209.03i	−0.264767	−	0.192364i	−0.712246	+	0.701930i	$0.752322\pi$
$510$	−148.655	+	108.004i	−0.0129070	+	0.00937747i
$511$	3245.03	−	9987.18i	0.280923	−	0.864593i
$512$	−821.028	+	2526.86i	−0.0708685	+	0.218111i
$513$	1215.50	−	883.115i	0.104612	−	0.0760049i
$514$	−94.9658	−	68.9967i	−0.00814934	−	0.00592085i
$515$	−329.547	−	1014.24i	−0.0281973	−	0.0867823i
$516$	9824.10			0.838143
$517$	7985.14	−	408.316i	0.679277	−	0.0347345i
$518$	734.495			0.0623009
$519$	3982.92	+	12258.2i	0.336861	+	1.03675i
$520$	−396.195	−	287.852i	−0.0334121	−	0.0242753i
$521$	11756.3	−	8541.48i	0.988588	−	0.718251i	0.0289765	−	0.999580i	$-0.490775\pi$
$521$	11756.3	−	8541.48i	0.988588	−	0.718251i	0.959611	+	0.281329i	$0.0907752\pi$
$522$	75.6399	−	232.796i	0.00634227	−	0.0195195i
$523$	5823.56	−	17923.1i	0.486896	−	1.49851i	−0.342320	−	0.939584i	$-0.611213\pi$
$523$	5823.56	−	17923.1i	0.486896	−	1.49851i	0.829216	−	0.558929i	$-0.188787\pi$
$524$	11559.6	−	8398.53i	0.963707	−	0.700174i
$525$	−2793.61	−	2029.67i	−0.232234	−	0.168728i
$526$	97.4949	+	300.059i	0.00808171	+	0.0248730i
$527$	8678.91			0.717380
$528$	1809.86	−	6720.33i	0.149174	−	0.553910i
$529$	−10279.7			−0.844884
$530$	95.7546	+	294.702i	0.00784776	+	0.0241529i
$531$	−26.8421	−	19.5019i	−0.00219369	−	0.00159381i
$532$	5154.21	−	3744.75i	0.420044	−	0.305180i
$533$	−4553.00	+	14012.7i	−0.370004	+	1.13876i
$534$	158.837	−	488.850i	0.0128718	−	0.0396154i
$535$	−10666.7	+	7749.80i	−0.861983	+	0.626267i
$536$	371.608	+	269.989i	0.0299459	+	0.0217570i
$537$	2349.64	+	7231.46i	0.188817	+	0.581118i
$538$	−256.386			−0.0205457
$539$	−1789.25	−	4678.90i	−0.142984	−	0.373904i
$540$	−1441.76			−0.114895
$541$	3327.59	+	10241.3i	0.264444	+	0.813874i	0.991821	+	0.127636i	$0.0407391\pi$
$541$	3327.59	+	10241.3i	0.264444	+	0.813874i	−0.727377	+	0.686238i	$0.759261\pi$
$542$	−4.24509	−	3.08424i	−0.000336425	−	0.000244427i
$543$	−3647.24	+	2649.88i	−0.288247	+	0.209424i
$544$	541.721	−	1667.25i	0.0426950	−	0.131402i
$545$	−2701.33	+	8313.84i	−0.212316	+	0.653442i
$546$	−159.447	+	115.845i	−0.0124976	+	0.00908006i
$547$	−11180.1	−	8122.79i	−0.873903	−	0.634928i	0.0577281	−	0.998332i	$-0.481614\pi$
$547$	−11180.1	−	8122.79i	−0.873903	−	0.634928i	−0.931632	+	0.363404i	$0.881614\pi$
$548$	−1805.37	−	5556.37i	−0.140733	−	0.433132i
$549$	1098.93			0.0854306
$550$	136.844	+	357.849i	0.0106092	+	0.0277431i
$551$	11566.2			0.894257
$552$	−84.2266	−	259.223i	−0.00649442	−	0.0199878i
$553$	−3203.96	−	2327.82i	−0.246377	−	0.179003i
$554$	−353.417	+	256.773i	−0.0271034	+	0.0196917i
$555$	2427.05	−	7469.71i	0.185627	−	0.571300i
$556$	−4146.02	+	12760.1i	−0.316242	+	0.973292i
$557$	−16061.9	+	11669.7i	−1.22184	+	0.887719i	−0.996252	−	0.0865030i	$-0.972431\pi$
$557$	−16061.9	+	11669.7i	−1.22184	+	0.887719i	−0.225589	+	0.974222i	$0.572431\pi$
$558$	−118.161	−	85.8492i	−0.00896445	−	0.00651306i
$559$	−4437.63	−	13657.6i	−0.335763	−	1.03337i
$560$	−6100.47			−0.460343
$561$	−1991.69	+	7395.50i	−0.149891	+	0.556574i
$562$	51.2934			0.00384997
$563$	−1236.21	−	3804.66i	−0.0925399	−	0.284809i	0.894065	−	0.447938i	$-0.147841\pi$
$563$	−1236.21	−	3804.66i	−0.0925399	−	0.284809i	−0.986605	+	0.163129i	$0.947841\pi$
$564$	4246.19	+	3085.04i	0.317015	+	0.230325i
$565$	7093.98	−	5154.08i	0.528223	−	0.383777i
$566$	265.121	−	815.958i	0.0196888	−	0.0605959i
$567$	−358.986	+	1104.85i	−0.0265891	+	0.0818327i
$568$	−1818.87	+	1321.49i	−0.134363	+	0.0976202i
$569$	−1788.40	−	1299.35i	−0.131764	−	0.0957322i	0.519951	−	0.854196i	$-0.325950\pi$
$569$	−1788.40	−	1299.35i	−0.131764	−	0.0957322i	−0.651715	+	0.758464i	$0.725950\pi$
$570$	45.1521	+	138.964i	0.00331792	+	0.0102115i
$571$	23778.7			1.74274			0.871372	−	0.490623i	$-0.163231\pi$
$571$	23778.7			1.74274			0.871372	+	0.490623i	$0.163231\pi$
$572$	−10182.1	+	520.658i	−0.744293	+	0.0380591i
$573$	−12662.8			−0.923208
$574$	−244.074	−	751.184i	−0.0177482	−	0.0546233i
$575$	−2820.68	−	2049.34i	−0.204575	−	0.148632i
$576$	3680.16	−	2673.80i	0.266216	−	0.193417i
$577$	−3253.36	+	10012.8i	−0.234730	+	0.722425i	0.762427	+	0.647074i	$0.224008\pi$
$577$	−3253.36	+	10012.8i	−0.234730	+	0.722425i	−0.997157	+	0.0753510i	$0.975992\pi$
$578$	0.650210	−	2.00114i	4.67910e−5	−	0.000144008i
$579$	−8641.83	+	6278.66i	−0.620280	+	0.450660i
$580$	−8979.26	−	6523.81i	−0.642833	−	0.467046i
$581$	1685.37	+	5187.02i	0.120346	+	0.370385i
$582$	−308.181			−0.0219493
$583$	10823.3	+	7048.28i	0.768876	+	0.500703i
$584$	−1531.27			−0.108501
$585$	651.253	+	2004.35i	0.0460274	+	0.141658i
$586$	−610.675	−	443.681i	−0.0430491	−	0.0312770i
$587$	−3998.49	+	2905.08i	−0.281151	+	0.204268i	−0.719419	−	0.694576i	$-0.755592\pi$
$587$	−3998.49	+	2905.08i	−0.281151	+	0.204268i	0.438268	+	0.898844i	$0.355592\pi$
$588$	1016.14	−	3127.37i	0.0712670	−	0.219337i
$589$	2132.66	−	6563.64i	0.149193	−	0.459168i
$590$	2.61044	−	1.89660i	0.000182153	−	0.000132342i
$591$	−2715.43	−	1972.88i	−0.188998	−	0.137315i
$592$	7690.85	+	23670.0i	0.533939	+	1.64330i
$593$	3015.99			0.208856			0.104428	−	0.994532i	$-0.466699\pi$
$593$	3015.99			0.208856			0.104428	+	0.994532i	$0.466699\pi$
$594$	100.270	−	80.9867i	0.00692617	−	0.00559415i
$595$	6713.36			0.462556
$596$	3119.49	+	9600.80i	0.214395	+	0.659839i
$597$	−9113.67	−	6621.47i	−0.624787	−	0.453934i
$598$	−160.992	+	116.968i	−0.0110091	+	0.00799860i
$599$	−7948.47	+	24462.9i	−0.542180	+	1.66866i	0.185422	+	0.982659i	$0.440635\pi$
$599$	−7948.47	+	24462.9i	−0.542180	+	1.66866i	−0.727602	+	0.686000i	$0.759365\pi$
$600$	−155.599	+	478.884i	−0.0105872	+	0.0325839i
$601$	19507.5	−	14173.0i	1.32401	−	0.961947i	0.324133	−	0.946012i	$-0.394928\pi$
$601$	19507.5	−	14173.0i	1.32401	−	0.961947i	0.999873	−	0.0159349i	$-0.00507245\pi$
$602$	622.804	+	452.493i	0.0421654	+	0.0306350i
$603$	−610.837	−	1879.96i	−0.0412524	−	0.126962i
$604$	−5359.40			−0.361044
$605$	−7699.08	−	4471.17i	−0.517375	−	0.300461i
$606$	−615.150			−0.0412356
$607$	−2140.96	−	6589.19i	−0.143161	−	0.440604i	0.853609	−	0.520914i	$-0.174409\pi$
$607$	−2140.96	−	6589.19i	−0.143161	−	0.440604i	−0.996770	+	0.0803101i	$0.974409\pi$
$608$	−1127.78	−	819.381i	−0.0752262	−	0.0546550i
$609$	−7235.09	+	5256.60i	−0.481413	+	0.349767i
$610$	−33.0256	+	101.642i	−0.00219208	+	0.00674653i
$611$	2370.83	−	7296.65i	0.156978	−	0.483128i
$612$	−4067.44	+	2955.17i	−0.268654	+	0.195189i
$613$	13240.1	+	9619.49i	0.872370	+	0.633814i	0.931222	−	0.364453i	$-0.118744\pi$
$613$	13240.1	+	9619.49i	0.872370	+	0.633814i	−0.0588522	+	0.998267i	$0.518744\pi$
$614$	168.267	+	517.873i	0.0110598	+	0.0340385i
$615$	−8445.94			−0.553778
$616$	851.283	−	687.567i	0.0556805	−	0.0449722i
$617$	11265.9			0.735087			0.367543	−	0.930006i	$-0.380199\pi$
$617$	11265.9			0.735087			0.367543	+	0.930006i	$0.380199\pi$
$618$	19.3393	+	59.5204i	0.00125881	+	0.00387421i
$619$	−2263.53	−	1644.55i	−0.146977	−	0.106785i	0.511867	−	0.859065i	$-0.328954\pi$
$619$	−2263.53	−	1644.55i	−0.146977	−	0.106785i	−0.658844	+	0.752280i	$0.728954\pi$
$620$	−5357.84	+	3892.70i	−0.347058	+	0.252152i
$621$	−362.465	+	1115.55i	−0.0234222	+	0.0720862i
$622$	70.4531	−	216.832i	0.00454166	−	0.0139778i
$623$	−15193.0	+	11038.4i	−0.977040	+	0.709861i
$624$	−5402.81	−	3925.37i	−0.346612	−	0.251828i
$625$	262.033	+	806.456i	0.0167701	+	0.0516132i
$626$	−612.152			−0.0390839
$627$	5103.62	+	3323.55i	0.325070	+	0.211690i
$628$	−444.682			−0.0282560
$629$	−8463.52	−	26048.0i	−0.536507	−	1.65120i
$630$	−91.4008	−	66.4066i	−0.00578015	−	0.00419953i
$631$	394.979	−	286.969i	0.0249190	−	0.0181047i	−0.575256	−	0.817973i	$-0.695098\pi$
$631$	394.979	−	286.969i	0.0249190	−	0.0181047i	0.600175	+	0.799869i	$0.295098\pi$
$632$	−178.455	+	549.228i	−0.0112319	+	0.0345682i
$633$	1016.66	−	3128.96i	0.0638368	−	0.196469i
$634$	201.708	−	146.549i	0.0126354	−	0.00918015i
$635$	6817.29	+	4953.05i	0.426041	+	0.309537i
$636$	2620.00	+	8063.52i	0.163348	+	0.502735i
$637$	−4806.71			−0.298978
$638$	990.941	−	50.6713i	0.0614918	−	0.00314435i
$639$	9675.20			0.598975
$640$	550.966	+	1695.70i	0.0340295	+	0.104732i
$641$	−5133.48	−	3729.69i	−0.316318	−	0.229819i	0.418284	−	0.908316i	$-0.362632\pi$
$641$	−5133.48	−	3729.69i	−0.316318	−	0.229819i	−0.734603	+	0.678497i	$0.762632\pi$
$642$	625.969	−	454.793i	0.0384814	−	0.0279584i
$643$	5753.88	−	17708.6i	0.352894	−	1.08610i	−0.604327	−	0.796737i	$-0.706558\pi$
$643$	5753.88	−	17708.6i	0.352894	−	1.08610i	0.957221	−	0.289359i	$-0.0934421\pi$
$644$	−1536.99	+	4730.37i	−0.0940465	+	0.289445i
$645$	6659.78	−	4838.61i	0.406556	−	0.295380i
$646$	412.216	+	299.493i	0.0251059	+	0.0182405i
$647$	−6786.89	−	20887.9i	−0.412396	−	1.26923i	−0.914559	−	0.404452i	$-0.867462\pi$
$647$	−6786.89	−	20887.9i	−0.412396	−	1.26923i	0.502163	−	0.864773i	$-0.332538\pi$
$648$	169.399			0.0102695
$649$	34.9747	−	129.868i	0.00211538	−	0.00785478i
$650$	367.624			0.0221837
$651$	1648.99	+	5075.06i	0.0992764	+	0.305541i
$652$	4930.62	+	3582.31i	0.296163	+	0.215175i
$653$	10213.3	−	7420.42i	0.612065	−	0.444691i	−0.238076	−	0.971247i	$-0.576517\pi$
$653$	10213.3	−	7420.42i	0.612065	−	0.444691i	0.850141	+	0.526555i	$0.176517\pi$
$654$	158.526	−	487.894i	0.00947840	−	0.0291715i
$655$	3699.78	−	11386.8i	0.220706	−	0.679263i
$656$	21652.1	−	15731.2i	1.28868	−	0.936280i
$657$	5331.22	+	3873.36i	0.316576	+	0.230006i
$658$	127.094	+	391.155i	0.00752984	+	0.0231745i
$659$	−151.172			−0.00893598			−0.00446799	−	0.999990i	$-0.501422\pi$
$659$	−151.172			−0.00893598			−0.00446799	+	0.999990i	$0.501422\pi$
$660$	−2087.51	−	5458.85i	−0.123115	−	0.321948i
$661$	−3426.10			−0.201603			−0.100802	−	0.994907i	$-0.532141\pi$
$661$	−3426.10			−0.201603			−0.100802	+	0.994907i	$0.532141\pi$
$662$	342.047	+	1052.71i	0.0200816	+	0.0618048i
$663$	5945.62	+	4319.74i	0.348279	+	0.253039i
$664$	643.406	−	467.462i	0.0376039	−	0.0273209i
$665$	1649.67	−	5077.15i	0.0961974	−	0.296065i
$666$	−142.431	+	438.356i	−0.00828690	+	0.0255045i
$667$	−7305.19	+	5307.53i	−0.424075	+	0.308109i
$668$	19719.2	+	14326.9i	1.14216	+	0.829824i
$669$	−5640.85	−	17360.7i	−0.325991	−	1.00330i
$670$	192.239			0.0110848
$671$	1591.14	+	4160.84i	0.0915428	+	0.239385i
$672$	1077.86			0.0618742
$673$	−7619.14	−	23449.3i	−0.436398	−	1.34310i	−0.891647	−	0.452732i	$-0.850450\pi$
$673$	−7619.14	−	23449.3i	−0.436398	−	1.34310i	0.455248	−	0.890364i	$-0.349550\pi$
$674$	−353.101	−	256.543i	−0.0201794	−	0.0146612i
$675$	1753.06	−	1273.68i	0.0999636	−	0.0726278i
$676$	2396.54	−	7375.79i	0.136353	−	0.419652i
$677$	340.547	−	1048.10i	0.0193328	−	0.0595001i	−0.940925	−	0.338616i	$-0.890041\pi$
$677$	340.547	−	1048.10i	0.0193328	−	0.0595001i	0.960257	+	0.279116i	$0.0900413\pi$
$678$	−416.307	+	302.465i	−0.0235814	+	0.0171329i
$679$	9109.21	+	6618.23i	0.514845	+	0.374056i
$680$	−302.509	−	931.028i	−0.0170598	−	0.0525048i
$681$	6263.72			0.352461
$682$	153.962	−	571.689i	0.00864443	−	0.0320984i
$683$	9464.22			0.530217			0.265109	−	0.964219i	$-0.414592\pi$
$683$	9464.22			0.530217			0.265109	+	0.964219i	$0.414592\pi$
$684$	1235.43	+	3802.27i	0.0690614	+	0.212549i
$685$	−3960.51	−	2877.48i	−0.220910	−	0.160500i
$686$	729.218	−	529.808i	0.0405855	−	0.0294871i
$687$	−2086.77	+	6422.43i	−0.115888	+	0.356668i
$688$	−8060.82	+	24808.6i	−0.446680	+	1.37474i
$689$	10026.6	−	7284.72i	0.554400	−	0.402795i
$690$	−92.2865	−	67.0500i	−0.00509172	−	0.00369935i
$691$	−3887.43	−	11964.3i	−0.214016	−	0.658672i	−0.999222	−	0.0394383i	$-0.987443\pi$
$691$	−3887.43	−	11964.3i	−0.214016	−	0.658672i	0.785206	−	0.619234i	$-0.212557\pi$
$692$	−34297.1			−1.88407
$693$	−4703.00	+	240.485i	−0.257795	+	0.0131822i
$694$	−941.765			−0.0515114
$695$	3474.09	+	10692.1i	0.189611	+	0.583562i
$696$	1055.02	+	766.515i	0.0574574	+	0.0417452i
$697$	−23827.4	+	17311.7i	−1.29488	+	0.940783i
$698$	218.400	−	672.165i	0.0118432	−	0.0364496i
$699$	1016.45	−	3128.33i	0.0550012	−	0.169276i
$700$	7433.67	−	5400.88i	0.401381	−	0.291620i
$701$	−9895.69	−	7189.64i	−0.533174	−	0.387374i	0.288370	−	0.957519i	$-0.406887\pi$
$701$	−9895.69	−	7189.64i	−0.533174	−	0.387374i	−0.821544	+	0.570146i	$0.806887\pi$
$702$	−38.2185	−	117.625i	−0.00205479	−	0.00632400i
$703$	−21779.2			−1.16845
$704$	15452.1	+	10062.7i	0.827237	+	0.538709i
$705$	4397.95			0.234945
$706$	136.794	+	421.009i	0.00729222	+	0.0224432i
$707$	18182.6	+	13210.4i	0.967224	+	0.702729i
$708$	71.4257	−	51.8938i	0.00379145	−	0.00275465i
$709$	−8803.85	+	27095.5i	−0.466341	+	1.43525i	0.390947	+	0.920413i	$0.372147\pi$
$709$	−8803.85	+	27095.5i	−0.466341	+	1.43525i	−0.857288	+	0.514837i	$0.827853\pi$
$710$	−290.763	+	894.877i	−0.0153692	+	0.0473016i
$711$	2010.57	−	1460.77i	0.106051	−	0.0770507i
$712$	2215.44	+	1609.61i	0.116611	+	0.0847230i
$713$	1664.97	+	5124.24i	0.0874523	+	0.269150i
$714$	−393.971			−0.0206498
$715$	−6646.04	+	5367.90i	−0.347619	+	0.280766i
$716$	−20232.9			−1.05606
$717$	−3792.33	−	11671.6i	−0.197528	−	0.607928i
$718$	1.85446	+	1.34735i	9.63899e−5	+	7.00314e-5i
$719$	−21391.9	+	15542.1i	−1.10957	+	0.806151i	−0.982596	−	0.185755i	$-0.940527\pi$
$719$	−21391.9	+	15542.1i	−1.10957	+	0.806151i	−0.126976	+	0.991906i	$0.540527\pi$
$720$	1182.98	−	3640.84i	0.0612321	−	0.188453i
$721$	706.577	−	2174.62i	0.0364970	−	0.112326i
$722$	−398.296	+	289.379i	−0.0205305	+	0.0149163i
$723$	15465.4	+	11236.3i	0.795524	+	0.577982i
$724$	−3707.04	−	11409.1i	−0.190292	−	0.585658i
$725$	16681.3			0.854523
$726$	451.817	+	262.389i	0.0230971	+	0.0134134i
$727$	−10380.5			−0.529559			−0.264780	−	0.964309i	$-0.585299\pi$
$727$	−10380.5			−0.529559			−0.264780	+	0.964309i	$0.585299\pi$
$728$	−324.471	−	998.618i	−0.0165188	−	0.0508396i
$729$	−589.773	−	428.495i	−0.0299636	−	0.0217698i
$730$	−518.470	+	376.691i	−0.0262869	+	0.0190986i
$731$	8870.66	−	27301.1i	0.448828	−	1.38135i
$732$	−903.634	+	2781.10i	−0.0456274	+	0.140427i
$733$	1899.30	−	1379.92i	0.0957058	−	0.0695344i	−0.538903	−	0.842368i	$-0.681161\pi$
$733$	1899.30	−	1379.92i	0.0957058	−	0.0695344i	0.634609	+	0.772833i	$0.281161\pi$
$734$	−519.649	−	377.547i	−0.0261316	−	0.0189857i
$735$	−851.459	−	2620.52i	−0.0427300	−	0.131509i
$736$	1088.31			0.0545048
$737$	6233.59	−	5034.77i	0.311557	−	0.251639i
$738$	495.647			0.0247222
$739$	11989.6	+	36900.1i	0.596811	+	1.83680i	0.545495	+	0.838114i	$0.316342\pi$
$739$	11989.6	+	36900.1i	0.596811	+	1.83680i	0.0513159	+	0.998682i	$0.483658\pi$
$740$	16908.0	+	12284.4i	0.839935	+	0.610248i
$741$	4727.92	−	3435.04i	0.234392	−	0.170296i
$742$	−205.306	+	631.866i	−0.0101577	+	0.0312622i
$743$	3775.96	−	11621.2i	0.186442	−	0.573809i	−0.813528	−	0.581525i	$-0.802456\pi$
$743$	3775.96	−	11621.2i	0.186442	−	0.573809i	0.999970	+	0.00771602i	$0.00245611\pi$
$744$	629.519	−	457.372i	0.0310205	−	0.0225377i
$745$	6843.34	+	4971.98i	0.336538	+	0.244509i
$746$	−340.330	−	1047.43i	−0.0167029	−	0.0514062i
$747$	−3422.50			−0.167634
$748$	−17078.2	−	11121.6i	−0.834815	−	0.543644i
$749$	−28269.2			−1.37908
$750$	166.548	+	512.581i	0.00810862	+	0.0249558i
$751$	8583.48	+	6236.26i	0.417065	+	0.303015i	0.776456	−	0.630172i	$-0.217016\pi$
$751$	8583.48	+	6236.26i	0.417065	+	0.303015i	−0.359391	+	0.933187i	$0.617016\pi$
$752$	−11274.6	+	8191.51i	−0.546734	+	0.397226i
$753$	−70.1336	+	215.849i	−0.00339417	+	0.0104462i
$754$	294.215	−	905.501i	0.0142105	−	0.0437353i
$755$	−3633.14	+	2639.63i	−0.175131	+	0.127240i
$756$	−2500.87	−	1816.99i	−0.120312	−	0.0874117i
$757$	−3944.61	−	12140.3i	−0.189391	−	0.582887i	0.810605	−	0.585593i	$-0.199138\pi$
$757$	−3944.61	−	12140.3i	−0.189391	−	0.582887i	−0.999996	+	0.00270668i	$0.999138\pi$
$758$	−843.558			−0.0404214
$759$	−4748.57	+	242.816i	−0.227091	+	0.0116122i
$760$	−778.448			−0.0371543
$761$	11176.9	+	34399.1i	0.532410	+	1.63859i	0.749181	+	0.662366i	$0.230447\pi$
$761$	11176.9	+	34399.1i	0.532410	+	1.63859i	−0.216771	+	0.976222i	$0.569553\pi$
$762$	−400.070	−	290.668i	−0.0190197	−	0.0138186i
$763$	−15163.3	+	11016.8i	−0.719462	+	0.522720i
$764$	10412.4	−	32046.2i	0.493074	−	1.51753i
$765$	−1301.83	+	4006.63i	−0.0615266	+	0.189359i
$766$	−502.103	+	364.799i	−0.0236837	+	0.0172072i
$767$	−104.407	−	75.8563i	−0.00491516	−	0.00357107i
$768$	3716.19	+	11437.3i	0.174605	+	0.537379i
$769$	−25178.7			−1.18071			−0.590356	−	0.807143i	$-0.701013\pi$
$769$	−25178.7			−1.18071			−0.590356	+	0.807143i	$0.701013\pi$
$770$	119.094	−	442.216i	0.00557381	−	0.0206966i
$771$	−2691.29			−0.125712
$772$	−8783.52	−	27032.9i	−0.409489	−	1.26028i
$773$	−26891.5	−	19537.8i	−1.25126	−	0.909091i	−0.252962	−	0.967476i	$-0.581405\pi$
$773$	−26891.5	−	19537.8i	−1.25126	−	0.909091i	−0.998294	+	0.0583858i	$0.981405\pi$
$774$	−390.826	+	283.952i	−0.0181498	+	0.0131866i
$775$	3075.83	−	9466.43i	0.142564	−	0.438767i
$776$	507.366	−	1561.51i	0.0234709	−	0.0722359i
$777$	13623.7	−	9898.23i	0.629021	−	0.457010i
$778$	314.318	+	228.365i	0.0144844	+	0.0105235i
$779$	7237.29	+	22274.1i	0.332866	+	1.02446i
$780$	−5607.97			−0.257433
$781$	14008.7	+	36632.8i	0.641830	+	1.67839i
$782$	−397.788			−0.0181904
$783$	−1734.21	−	5337.34i	−0.0791513	−	0.243603i
$784$	7063.72	+	5132.10i	0.321780	+	0.233787i
$785$	−301.451	+	219.017i	−0.0137060	+	0.00995802i
$786$	−217.120	+	668.227i	−0.00985294	+	0.0303242i
$787$	−1198.90	+	3689.82i	−0.0543024	+	0.167126i	−0.974530	−	0.224259i	$-0.928004\pi$
$787$	−1198.90	+	3689.82i	−0.0543024	+	0.167126i	0.920227	+	0.391385i	$0.128004\pi$
$788$	7225.65	−	5249.74i	0.326654	−	0.237328i
$789$	5852.04	+	4251.76i	0.264053	+	0.191846i
$790$	74.6865	+	229.861i	0.00336358	+	0.0103520i
$791$	18800.7			0.845102
$792$	245.272	+	641.388i	0.0110042	+	0.0287762i
$793$	4274.50			0.191415
$794$	−63.6398	−	195.863i	−0.00284445	−	0.00875431i
$795$	5747.58	+	4175.86i	0.256410	+	0.186292i
$796$	24251.1	−	17619.5i	1.07985	−	0.784554i
$797$	3037.48	−	9348.40i	0.134998	−	0.415480i	−0.860592	−	0.509295i	$-0.829906\pi$
$797$	3037.48	−	9348.40i	0.134998	−	0.415480i	0.995590	+	0.0938152i	$0.0299063\pi$
$798$	−96.8099	+	297.950i	−0.00429453	+	0.0132172i
$799$	12407.4	−	9014.48i	0.549363	−	0.399136i
$800$	−1626.54	−	1181.75i	−0.0718838	−	0.0522266i
$801$	−3641.68	−	11207.9i	−0.160640	−	0.494398i
$802$	484.169			0.0213174
$803$	−6946.48	+	25793.6i	−0.305275	+	1.13354i
$804$	5259.95			0.230727
$805$	1287.90	+	3963.73i	0.0563880	+	0.173544i
$806$	−459.610	−	333.926i	−0.0200857	−	0.0145931i
$807$	−4755.57	+	3455.12i	−0.207440	+	0.150714i
$808$	1012.74	−	3116.89i	0.0440940	−	0.135707i
$809$	4343.22	−	13367.0i	0.188751	−	0.580915i	−0.811242	−	0.584711i	$-0.801208\pi$
$809$	4343.22	−	13367.0i	0.188751	−	0.580915i	0.999993	+	0.00379534i	$0.00120810\pi$
$810$	57.3565	−	41.6719i	0.00248803	−	0.00180766i
$811$	7740.27	+	5623.64i	0.335139	+	0.243493i	0.742608	−	0.669726i	$-0.233589\pi$
$811$	7740.27	+	5623.64i	0.335139	+	0.243493i	−0.407469	+	0.913219i	$0.633589\pi$
$812$	−7353.71	−	22632.4i	−0.317814	−	0.978130i
$813$	−120.304			−0.00518972
$814$	−1865.95	+	95.4145i	−0.0803459	+	0.00410845i
$815$	5106.85			0.219491
$816$	−4125.24	−	12696.2i	−0.176976	−	0.544676i
$817$	−18467.4	−	13417.3i	−0.790809	−	0.574556i
$818$	−337.339	+	245.091i	−0.0144191	+	0.0104761i
$819$	−1396.34	+	4297.50i	−0.0595752	+	0.183354i
$820$	6944.95	−	21374.3i	0.295766	−	0.910274i
$821$	29189.7	−	21207.5i	1.24084	−	0.901520i	0.243182	−	0.969981i	$-0.421809\pi$
$821$	29189.7	−	21207.5i	1.24084	−	0.901520i	0.997654	+	0.0684608i	$0.0218088\pi$
$822$	232.421	+	168.864i	0.00986205	+	0.00716520i
$823$	−7651.20	−	23548.0i	−0.324063	−	0.997364i	−0.971862	−	0.235552i	$-0.924310\pi$
$823$	−7651.20	−	23548.0i	−0.324063	−	0.997364i	0.647798	−	0.761812i	$-0.275690\pi$
$824$	−333.421			−0.0140962
$825$	7360.70	+	4793.40i	0.310626	+	0.202284i
$826$	6.91827			0.000291426
$827$	8085.85	+	24885.7i	0.339991	+	1.04638i	0.964211	+	0.265136i	$0.0854168\pi$
$827$	8085.85	+	24885.7i	0.339991	+	1.04638i	−0.624220	+	0.781249i	$0.714583\pi$
$828$	−2525.10	−	1834.59i	−0.105982	−	0.0770007i
$829$	−5360.16	+	3894.39i	−0.224567	+	0.163158i	−0.694380	−	0.719608i	$-0.744321\pi$
$829$	−5360.16	+	3894.39i	−0.224567	+	0.163158i	0.469813	+	0.882766i	$0.344321\pi$
$830$	102.855	−	316.554i	0.00430137	−	0.0132382i
$831$	−3095.01	+	9525.47i	−0.129200	+	0.397635i
$832$	14314.7	−	10400.2i	0.596481	−	0.433369i
$833$	−7773.39	−	5647.70i	−0.323328	−	0.234911i
$834$	−203.875	−	627.463i	−0.00846477	−	0.0260519i
$835$	20424.0			0.846470
$836$	−12607.6	+	10182.9i	−0.521582	+	0.421273i
$837$	−3348.63			−0.138286
$838$	−299.242	−	920.972i	−0.0123355	−	0.0379648i
$839$	709.265	+	515.311i	0.0291854	+	0.0212044i	0.602282	−	0.798283i	$-0.294258\pi$
$839$	709.265	+	515.311i	0.0291854	+	0.0212044i	−0.573097	+	0.819488i	$0.694258\pi$
$840$	486.949	−	353.789i	0.0200016	−	0.0145320i
$841$	5813.71	−	17892.8i	0.238374	−	0.733640i
$842$	−99.9170	+	307.513i	−0.00408951	+	0.0125862i
$843$	951.413	−	691.242i	0.0388712	−	0.0282416i
$844$	7082.56	+	5145.78i	0.288853	+	0.209864i
$845$	−2008.14	−	6180.42i	−0.0817540	−	0.251613i
$846$	−258.092			−0.0104886
$847$	−7719.97	−	17458.5i	−0.313177	−	0.708244i
$848$	−22512.4			−0.911650
$849$	−6078.47	−	18707.6i	−0.245716	−	0.756235i
$850$	594.520	+	431.944i	0.0239904	+	0.0174301i
$851$	13755.8	−	9994.14i	0.554102	−	0.402579i
$852$	−7955.74	+	24485.3i	−0.319905	+	0.984567i
$853$	−5723.03	+	17613.7i	−0.229722	+	0.707012i	0.768056	+	0.640383i	$0.221224\pi$
$853$	−5723.03	+	17613.7i	−0.229722	+	0.707012i	−0.997778	+	0.0666287i	$0.978776\pi$
$854$	−185.382	+	134.688i	−0.00742816	+	0.00539688i
$855$	2710.21	+	1969.09i	0.108406	+	0.0787618i
$856$	1273.83	+	3920.45i	0.0508629	+	0.156540i
$857$	−8236.44			−0.328298			−0.164149	−	0.986436i	$-0.552488\pi$
$857$	−8236.44			−0.328298			−0.164149	+	0.986436i	$0.552488\pi$
$858$	390.020	−	315.013i	0.0155187	−	0.0125342i
$859$	30938.9			1.22890			0.614449	−	0.788957i	$-0.289379\pi$
$859$	30938.9			1.22890			0.614449	+	0.788957i	$0.289379\pi$
$860$	6768.97	+	20832.7i	0.268395	+	0.826036i
$861$	−14650.3	−	10644.1i	−0.579886	−	0.421312i
$862$	−115.958	+	84.2487i	−0.00458185	+	0.00332891i
$863$	−4465.48	+	13743.3i	−0.176138	+	0.542096i	−0.999684	−	0.0251537i	$-0.991992\pi$
$863$	−4465.48	+	13743.3i	−0.176138	+	0.542096i	0.823546	+	0.567249i	$0.191992\pi$
$864$	−209.015	+	643.283i	−0.00823015	+	0.0253298i
$865$	−23250.0	+	16892.1i	−0.913902	+	0.663989i
$866$	−9.56318	−	6.94806i	−0.000375254	−	0.000272638i
$867$	−14.9075	−	45.8805i	−0.000583949	−	0.00179721i
$868$	−14199.5			−0.555257
$869$	8441.93	+	5497.51i	0.329543	+	0.214603i
$870$	545.778			0.0212685
$871$	−2375.96	−	7312.46i	−0.0924299	−	0.284470i
$872$	2211.11	+	1606.47i	0.0858689	+	0.0623874i
$873$	−5716.28	+	4153.12i	−0.221611	+	0.161010i
$874$	−97.7480	+	300.837i	−0.00378304	+	0.0116430i
$875$	6084.94	−	18727.5i	0.235096	−	0.723550i
$876$	−14186.2	+	10306.9i	−0.547153	+	0.397530i
$877$	29441.4	+	21390.4i	1.13360	+	0.823608i	0.986215	−	0.165472i	$-0.0529146\pi$
$877$	29441.4	+	21390.4i	1.13360	+	0.823608i	0.147384	+	0.989079i	$0.452915\pi$
$878$	158.932	+	489.144i	0.00610901	+	0.0188016i
$879$	−17306.2			−0.664078
$880$	15498.0	−	792.482i	0.593678	−	0.0303574i
$881$	−48846.6			−1.86797			−0.933987	−	0.357306i	$-0.883695\pi$
$881$	−48846.6			−1.86797			−0.933987	+	0.357306i	$0.883695\pi$
$882$	49.9675	+	153.784i	0.00190759	+	0.00587095i
$883$	16773.1	+	12186.4i	0.639252	+	0.464443i	0.859593	−	0.510979i	$-0.170717\pi$
$883$	16773.1	+	12186.4i	0.639252	+	0.464443i	−0.220341	+	0.975423i	$0.570717\pi$
$884$	−15821.0	+	11494.7i	−0.601945	+	0.437339i
$885$	22.8606	−	70.3578i	0.000868308	−	0.00267238i
$886$	−160.555	+	494.139i	−0.00608800	+	0.0187369i
$887$	−35100.5	+	25502.0i	−1.32870	+	0.965359i	−0.328923	+	0.944357i	$0.606686\pi$
$887$	−35100.5	+	25502.0i	−1.32870	+	0.965359i	−0.999779	+	0.0210025i	$0.993314\pi$
$888$	−1986.61	−	1443.36i	−0.0750746	−	0.0545449i
$889$	5583.13	+	17183.1i	0.210632	+	0.648260i
$890$	1146.08			0.0431650
$891$	768.464	−	2853.45i	0.0288939	−	0.107288i
$892$	48573.6			1.82328
$893$	−3768.58	−	11598.5i	−0.141222	−	0.434635i
$894$	−401.598	−	291.778i	−0.0150240	−	0.0109156i
$895$	−13715.9	+	9965.19i	−0.512260	+	0.372178i
$896$	−1181.32	+	3635.72i	−0.0440458	+	0.135559i
$897$	−1409.87	+	4339.14i	−0.0524797	+	0.161516i
$898$	1883.36	−	1368.34i	0.0699872	−	0.0508486i
$899$	−20855.3	−	15152.3i	−0.773707	−	0.562131i
$900$	1781.81	+	5483.84i	0.0659928	+	0.203105i
$901$	24774.2			0.916034
$902$	717.643	+	1876.64i	0.0264910	+	0.0692743i
$903$	17650.0			0.650447
$904$	−847.174	−	2607.33i	−0.0311688	−	0.0959276i
$905$	−8132.27	−	5908.44i	−0.298703	−	0.217020i
$906$	213.210	−	154.906i	0.00781834	−	0.00568035i
$907$	−10209.6	+	31421.8i	−0.373763	+	1.15032i	0.570547	+	0.821265i	$0.306731\pi$
$907$	−10209.6	+	31421.8i	−0.373763	+	1.15032i	−0.944310	+	0.329058i	$0.893269\pi$
$908$	−5150.54	+	15851.7i	−0.188245	+	0.579359i
$909$	−11410.1	+	8289.90i	−0.416335	+	0.302485i
$910$	−355.520	−	258.300i	−0.0129510	−	0.00940942i
$911$	516.811	+	1590.58i	0.0187955	+	0.0578466i	0.960014	−	0.279951i	$-0.0903181\pi$
$911$	516.811	+	1590.58i	0.0187955	+	0.0578466i	−0.941219	+	0.337797i	$0.890318\pi$
$912$	−10615.5			−0.385433
$913$	−4955.42	−	12958.5i	−0.179628	−	0.469729i
$914$	1512.19			0.0547251
$915$	757.184	+	2330.37i	0.0273571	+	0.0841964i
$916$	−14537.5	−	10562.1i	−0.524379	−	0.380984i
$917$	20767.9	−	15088.8i	0.747892	−	0.543375i
$918$	76.3974	−	235.127i	0.00274672	−	0.00845354i
$919$	6171.40	−	18993.6i	0.221519	−	0.681765i	−0.777108	−	0.629368i	$-0.783314\pi$
$919$	6171.40	−	18993.6i	0.221519	−	0.681765i	0.998626	−	0.0523969i	$-0.0166861\pi$
$920$	491.668	−	357.218i	0.0176194	−	0.0128012i
$921$	10100.1	+	7338.13i	0.361356	+	0.262540i
$922$	40.2921	+	124.006i	0.00143921	+	0.00442942i
$923$	37633.5			1.34206
$924$	3258.59	−	12099.7i	0.116017	−	0.430792i
$925$	−31411.1			−1.11653
$926$	−159.743	−	491.639i	−0.00566899	−	0.0174474i
$927$	1160.83	+	843.390i	0.0411289	+	0.0298819i
$928$	−4212.54	+	3060.59i	−0.149012	+	0.108264i
$929$	−239.193	+	736.159i	−0.00844742	+	0.0259985i	−0.955191	−	0.295989i	$-0.904351\pi$
$929$	−239.193	+	736.159i	−0.00844742	+	0.0259985i	0.946744	+	0.321987i	$0.104351\pi$
$930$	100.635	−	309.721i	0.00354832	−	0.0109206i
$931$	−6181.36	+	4491.02i	−0.217600	+	0.158096i
$932$	7081.11	+	5144.73i	0.248873	+	0.180817i
$933$	−1615.29	−	4971.34i	−0.0566797	−	0.174442i
$934$	2164.12			0.0758161
$935$	−17055.0	+	872.100i	−0.596533	+	0.0305034i
$936$	658.909			0.0230097
$937$	−11510.1	−	35424.5i	−0.401301	−	1.23508i	−0.923944	−	0.382527i	$-0.875054\pi$
$937$	−11510.1	−	35424.5i	−0.401301	−	1.23508i	0.522643	−	0.852552i	$-0.324946\pi$
$938$	333.457	+	242.271i	0.0116074	+	0.00843328i
$939$	−11354.5	+	8249.50i	−0.394610	+	0.286701i
$940$	−3616.36	+	11130.0i	−0.125481	+	0.386192i
$941$	−14111.0	+	43429.3i	−0.488849	+	1.50452i	0.337479	+	0.941333i	$0.390426\pi$
$941$	−14111.0	+	43429.3i	−0.488849	+	1.50452i	−0.826328	+	0.563189i	$0.809574\pi$
$942$	17.6905	−	12.8529i	0.000611877	−	0.000444555i
$943$	−14792.3	−	10747.2i	−0.510820	−	0.371132i
$944$	72.4408	+	222.950i	0.00249761	+	0.00768686i
$945$	−2590.25			−0.0891651
$946$	−1640.99	−	1068.63i	−0.0563986	−	0.0367276i
$947$	19714.7			0.676497			0.338249	−	0.941057i	$-0.390166\pi$
$947$	19714.7			0.676497			0.338249	+	0.941057i	$0.390166\pi$
$948$	2043.54	+	6289.37i	0.0700117	+	0.215474i
$949$	20736.8	+	15066.1i	0.709319	+	0.515350i
$950$	472.759	−	343.480i	0.0161456	−	0.0117305i
$951$	1766.43	−	5436.53i	0.0602319	−	0.185375i
$952$	648.605	−	1996.20i	0.0220813	−	0.0679593i
$953$	30227.8	−	21961.8i	1.02747	−	0.746498i	0.0596665	−	0.998218i	$-0.480996\pi$
$953$	30227.8	−	21961.8i	1.02747	−	0.746498i	0.967800	+	0.251720i	$0.0809963\pi$
$954$	−337.294	−	245.059i	−0.0114469	−	0.00831663i
$955$	−8724.91	−	26852.5i	−0.295635	−	0.909871i
$956$	32656.0			1.10478
$957$	17697.6	−	14294.0i	0.597786	−	0.482822i
$958$	631.788			0.0213071
$959$	−3243.53	−	9982.55i	−0.109217	−	0.336135i
$960$	8205.68	+	5961.77i	0.275872	+	0.200433i
$961$	11657.3	−	8469.51i	0.391302	−	0.284298i
$962$	−554.010	+	1705.07i	−0.0185676	+	0.0571451i
$963$	5481.86	−	16871.4i	0.183438	−	0.564563i
$964$	−41152.7	+	29899.2i	−1.37494	+	0.998951i
$965$	−19268.7	−	13999.5i	−0.642779	−	0.467007i
$966$	−75.5796	−	232.610i	−0.00251732	−	0.00774752i
$967$	−55189.6			−1.83535			−0.917673	−	0.397337i	$-0.869934\pi$
$967$	−55189.6			−1.83535			−0.917673	+	0.397337i	$0.869934\pi$
$968$	−2073.33	+	1857.32i	−0.0688423	+	0.0616700i
$969$	11682.0			0.387286
$970$	−212.342	−	653.520i	−0.00702874	−	0.0216322i
$971$	−15338.2	−	11143.8i	−0.506926	−	0.368303i	0.304730	−	0.952439i	$-0.401434\pi$
$971$	−15338.2	−	11143.8i	−0.506926	−	0.368303i	−0.811656	+	0.584135i	$0.801434\pi$
$972$	1569.36	−	1140.21i	0.0517874	−	0.0376257i
$973$	−7448.73	+	22924.8i	−0.245422	+	0.755330i
$974$	37.8192	−	116.395i	0.00124415	−	0.00382911i
$975$	6818.86	−	4954.19i	0.223978	−	0.162729i
$976$	−6281.62	−	4563.86i	−0.206014	−	0.149678i
$977$	7393.34	+	22754.4i	0.242102	+	0.745114i	0.996100	+	0.0882365i	$0.0281231\pi$
$977$	7393.34	+	22754.4i	0.242102	+	0.745114i	−0.753997	+	0.656877i	$0.771877\pi$
$978$	−299.693			−0.00979871
$979$	37163.3	−	30016.2i	1.21322	−	0.979899i
$980$	7331.95			0.238990
$981$	−3634.56	−	11186.0i	−0.118290	−	0.364059i
$982$	1279.01	+	929.258i	0.0415631	+	0.0301974i
$983$	37475.9	−	27227.8i	1.21597	−	0.883451i	0.220207	−	0.975453i	$-0.429327\pi$
$983$	37475.9	−	27227.8i	1.21597	−	0.883451i	0.995759	+	0.0920022i	$0.0293267\pi$
$984$	−815.996	+	2511.38i	−0.0264360	+	0.0813616i
$985$	2312.65	−	7117.62i	0.0748094	−	0.230240i
$986$	1539.73	−	1118.68i	0.0497313	−	0.0361319i
$987$	7628.69	+	5542.57i	0.246022	+	0.178745i
$988$	4805.44	+	14789.6i	0.154738	+	0.476236i
$989$	17821.0			0.572977
$990$	240.826	+	156.830i	0.00773128	+	0.00503472i
$991$	17231.6			0.552351			0.276175	−	0.961107i	$-0.410933\pi$
$991$	17231.6			0.552351			0.276175	+	0.961107i	$0.410933\pi$
$992$	960.104	+	2954.89i	0.0307292	+	0.0945746i
$993$	20531.0	+	14916.7i	0.656126	+	0.476703i
$994$	−1632.14	+	1185.82i	−0.0520807	+	0.0378389i
$995$	7761.85	−	23888.5i	0.247304	−	0.761123i
$996$	2814.26	−	8661.41i	0.0895315	−	0.275550i
$997$	26124.4	−	18980.5i	0.829857	−	0.602926i	−0.0896621	−	0.995972i	$-0.528579\pi$
$997$	26124.4	−	18980.5i	0.829857	−	0.602926i	0.919519	+	0.393046i	$0.128579\pi$
$998$	−179.544	−	130.447i	−0.00569476	−	0.00413749i
$999$	3265.53	+	10050.3i	0.103420	+	0.318295i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.4.e.b.16.2	✓	8
3.2	odd	2		99.4.f.b.82.1		8
11.3	even	5		363.4.a.p.1.3		4
11.8	odd	10		363.4.a.t.1.2		4
11.9	even	5	inner	33.4.e.b.31.2	yes	8
33.8	even	10		1089.4.a.z.1.3		4
33.14	odd	10		1089.4.a.bg.1.2		4
33.20	odd	10		99.4.f.b.64.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.e.b.16.2	✓	8	1.1	even	1	trivial
33.4.e.b.31.2	yes	8	11.9	even	5	inner
99.4.f.b.64.1		8	33.20	odd	10
99.4.f.b.82.1		8	3.2	odd	2
363.4.a.p.1.3		4	11.3	even	5
363.4.a.t.1.2		4	11.8	odd	10
1089.4.a.z.1.3		4	33.8	even	10
1089.4.a.bg.1.2		4	33.14	odd	10

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0404346 - 0.124445i) q^{2} +(-2.42705 - 1.76336i) q^{3} +(6.45828 - 4.69222i) q^{4} +(2.06705 - 6.36172i) q^{5} +(-0.121304 + 0.373335i) q^{6} +(11.6029 - 8.43002i) q^{7} +(-1.69194 - 1.22926i) q^{8} +(2.78115 + 8.55951i) q^{9} +O(q^{10})\)	\(q+(-0.0404346 - 0.124445i) q^{2} +(-2.42705 - 1.76336i) q^{3} +(6.45828 - 4.69222i) q^{4} +(2.06705 - 6.36172i) q^{5} +(-0.121304 + 0.373335i) q^{6} +(11.6029 - 8.43002i) q^{7} +(-1.69194 - 1.22926i) q^{8} +(2.78115 + 8.55951i) q^{9} -0.875265 q^{10} +(-28.3816 + 22.9234i) q^{11} -23.9486 q^{12} +(10.8178 + 33.2938i) q^{13} +(-1.51823 - 1.10306i) q^{14} +(-16.2348 + 11.7953i) q^{15} +(19.6502 - 60.4771i) q^{16} +(-21.6244 + 66.5530i) q^{17} +(0.952733 - 0.692201i) q^{18} +(45.0187 + 32.7080i) q^{19} +(-16.5010 - 50.7849i) q^{20} -43.0260 q^{21} +(4.00030 + 2.60506i) q^{22} -43.4430 q^{23} +(1.93879 + 5.96697i) q^{24} +(64.9283 + 47.1732i) q^{25} +(3.70583 - 2.69244i) q^{26} +(8.34346 - 25.6785i) q^{27} +(35.3795 - 108.887i) q^{28} +(168.156 - 122.172i) q^{29} +(2.12431 + 1.54340i) q^{30} +(-38.3253 - 117.953i) q^{31} -25.0514 q^{32} +(109.306 - 5.58930i) q^{33} +9.15657 q^{34} +(-29.6457 - 91.2399i) q^{35} +(58.1246 + 42.2300i) q^{36} +(-316.639 + 230.052i) q^{37} +(2.25003 - 6.92488i) q^{38} +(32.4534 - 99.8813i) q^{39} +(-11.3175 + 8.22268i) q^{40} +(340.499 + 247.387i) q^{41} +(1.73974 + 5.35438i) q^{42} -410.216 q^{43} +(-75.7352 + 281.219i) q^{44} +60.2020 q^{45} +(1.75660 + 5.40626i) q^{46} +(-177.304 - 128.819i) q^{47} +(-154.335 + 112.131i) q^{48} +(-42.4301 + 130.586i) q^{49} +(3.24511 - 9.98743i) q^{50} +(169.840 - 123.396i) q^{51} +(226.086 + 164.261i) q^{52} +(-109.401 - 336.701i) q^{53} -3.53293 q^{54} +(87.1660 + 227.940i) q^{55} -29.9941 q^{56} +(-51.5868 - 158.768i) q^{57} +(-22.0031 - 15.9862i) q^{58} +(-2.98246 + 2.16688i) q^{59} +(-49.5030 + 152.355i) q^{60} +(37.7322 - 116.128i) q^{61} +(-13.1290 + 9.53880i) q^{62} +(104.426 + 75.8702i) q^{63} +(-156.189 - 480.699i) q^{64} +234.167 q^{65} +(-5.11530 - 13.3766i) q^{66} -219.635 q^{67} +(172.625 + 531.285i) q^{68} +(105.438 + 76.6054i) q^{69} +(-10.1556 + 7.37851i) q^{70} +(332.200 - 1022.41i) q^{71} +(5.81636 - 17.9009i) q^{72} +(592.358 - 430.373i) q^{73} +(41.4320 + 30.1021i) q^{74} +(-74.4012 - 228.983i) q^{75} +444.216 q^{76} +(-136.066 + 505.237i) q^{77} -13.7420 q^{78} +(-85.3301 - 262.619i) q^{79} +(-344.121 - 250.018i) q^{80} +(-65.5304 + 47.6106i) q^{81} +(17.0181 - 52.3764i) q^{82} +(-117.512 + 361.666i) q^{83} +(-277.874 + 201.888i) q^{84} +(378.693 + 275.137i) q^{85} +(16.5869 + 51.0493i) q^{86} -623.557 q^{87} +(76.1988 - 3.89639i) q^{88} -1309.41 q^{89} +(-2.43425 - 7.49184i) q^{90} +(406.185 + 295.111i) q^{91} +(-280.567 + 203.844i) q^{92} +(-114.976 + 353.860i) q^{93} +(-8.86164 + 27.2733i) q^{94} +(301.135 - 218.787i) q^{95} +(60.8010 + 44.1745i) q^{96} +(242.603 + 746.654i) q^{97} +17.9665 q^{98} +(-275.147 - 179.180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} - 6 q^{3} - 16 q^{4} + 9 q^{5} - 18 q^{6} + 3 q^{7} + 36 q^{8} - 18 q^{9}+O(q^{10}) \) 8 * q - 6 * q^2 - 6 * q^3 - 16 * q^4 + 9 * q^5 - 18 * q^6 + 3 * q^7 + 36 * q^8 - 18 * q^9	\( 8 q - 6 q^{2} - 6 q^{3} - 16 q^{4} + 9 q^{5} - 18 q^{6} + 3 q^{7} + 36 q^{8} - 18 q^{9} + 8 q^{10} - 87 q^{11} - 18 q^{12} + 171 q^{13} + 12 q^{14} - 63 q^{15} + 44 q^{16} + 36 q^{17} + 81 q^{18} + 324 q^{19} - 87 q^{20} - 66 q^{21} - 521 q^{22} - 84 q^{23} + 18 q^{24} + 263 q^{25} - 774 q^{26} - 54 q^{27} + 387 q^{28} + 393 q^{29} + 204 q^{30} + 15 q^{31} + 102 q^{32} - 216 q^{33} - 712 q^{34} + 1002 q^{35} - 144 q^{36} - 747 q^{37} - 36 q^{38} + 513 q^{39} + 41 q^{40} + 159 q^{41} + 396 q^{42} - 644 q^{43} + 219 q^{44} + 216 q^{45} + 753 q^{46} - 351 q^{47} - 423 q^{48} - 1967 q^{49} + 330 q^{50} + 63 q^{51} + 2871 q^{52} - 531 q^{53} - 162 q^{54} - 716 q^{55} + 1470 q^{56} - 453 q^{57} - 1205 q^{58} - 1002 q^{59} - 261 q^{60} + 1449 q^{61} + 99 q^{62} + 27 q^{63} - 1118 q^{64} - 954 q^{65} + 897 q^{66} - 518 q^{67} + 873 q^{68} + 693 q^{69} + 26 q^{70} + 429 q^{71} + 54 q^{72} + 2547 q^{73} + 468 q^{74} - 231 q^{75} - 2276 q^{76} - 2697 q^{77} + 1638 q^{78} + 2805 q^{79} - 1620 q^{80} - 162 q^{81} - 1631 q^{82} - 2553 q^{83} - 1509 q^{84} - 197 q^{85} - 1713 q^{86} - 3906 q^{87} + 2866 q^{88} + 1788 q^{89} - 648 q^{90} + 2885 q^{91} + 423 q^{92} + 45 q^{93} + 1159 q^{94} + 3009 q^{95} - 504 q^{96} + 9 q^{97} + 5550 q^{98} + 27 q^{99}+O(q^{100}) \) 8 * q - 6 * q^2 - 6 * q^3 - 16 * q^4 + 9 * q^5 - 18 * q^6 + 3 * q^7 + 36 * q^8 - 18 * q^9 + 8 * q^10 - 87 * q^11 - 18 * q^12 + 171 * q^13 + 12 * q^14 - 63 * q^15 + 44 * q^16 + 36 * q^17 + 81 * q^18 + 324 * q^19 - 87 * q^20 - 66 * q^21 - 521 * q^22 - 84 * q^23 + 18 * q^24 + 263 * q^25 - 774 * q^26 - 54 * q^27 + 387 * q^28 + 393 * q^29 + 204 * q^30 + 15 * q^31 + 102 * q^32 - 216 * q^33 - 712 * q^34 + 1002 * q^35 - 144 * q^36 - 747 * q^37 - 36 * q^38 + 513 * q^39 + 41 * q^40 + 159 * q^41 + 396 * q^42 - 644 * q^43 + 219 * q^44 + 216 * q^45 + 753 * q^46 - 351 * q^47 - 423 * q^48 - 1967 * q^49 + 330 * q^50 + 63 * q^51 + 2871 * q^52 - 531 * q^53 - 162 * q^54 - 716 * q^55 + 1470 * q^56 - 453 * q^57 - 1205 * q^58 - 1002 * q^59 - 261 * q^60 + 1449 * q^61 + 99 * q^62 + 27 * q^63 - 1118 * q^64 - 954 * q^65 + 897 * q^66 - 518 * q^67 + 873 * q^68 + 693 * q^69 + 26 * q^70 + 429 * q^71 + 54 * q^72 + 2547 * q^73 + 468 * q^74 - 231 * q^75 - 2276 * q^76 - 2697 * q^77 + 1638 * q^78 + 2805 * q^79 - 1620 * q^80 - 162 * q^81 - 1631 * q^82 - 2553 * q^83 - 1509 * q^84 - 197 * q^85 - 1713 * q^86 - 3906 * q^87 + 2866 * q^88 + 1788 * q^89 - 648 * q^90 + 2885 * q^91 + 423 * q^92 + 45 * q^93 + 1159 * q^94 + 3009 * q^95 - 504 * q^96 + 9 * q^97 + 5550 * q^98 + 27 * q^99

Introduction

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