LMFDB - Embedded newform 87.4.i.a.13.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,4,Mod(4,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("87.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	87.i (of order $14$, degree $6$, 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:	$5.13316617050$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			13.12
Character	$\chi$	$=$	87.13
Dual form			87.4.i.a.67.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.999092 - 2.07464i) q^{2} +(-2.34549 - 1.87047i) q^{3} +(1.68199 + 2.10915i) q^{4} +(14.6253 + 7.04316i) q^{5} +(-6.22391 + 2.99728i) q^{6} +(-0.0111297 + 0.0139563i) q^{7} +(24.0157 - 5.48142i) q^{8} +(2.00269 + 8.77435i) q^{9} +O(q^{10})$	\(q+(0.999092 - 2.07464i) q^{2} +(-2.34549 - 1.87047i) q^{3} +(1.68199 + 2.10915i) q^{4} +(14.6253 + 7.04316i) q^{5} +(-6.22391 + 2.99728i) q^{6} +(-0.0111297 + 0.0139563i) q^{7} +(24.0157 - 5.48142i) q^{8} +(2.00269 + 8.77435i) q^{9} +(29.2240 - 23.3054i) q^{10} +(-1.96540 - 0.448589i) q^{11} -8.09311i q^{12} +(3.62769 - 15.8940i) q^{13} +(0.0178345 + 0.0370338i) q^{14} +(-21.1295 - 43.8758i) q^{15} +(7.81956 - 34.2597i) q^{16} -47.9733i q^{17} +(20.2045 + 4.61153i) q^{18} +(76.4298 - 60.9507i) q^{19} +(9.74449 + 42.6934i) q^{20} +(0.0522095 - 0.0119165i) q^{21} +(-2.89427 + 3.62930i) q^{22} +(-181.675 + 87.4899i) q^{23} +(-66.5815 - 32.0640i) q^{24} +(86.3565 + 108.288i) q^{25} +(-29.3498 - 23.4057i) q^{26} +(11.7149 - 24.3262i) q^{27} -0.0481560 q^{28} +(1.33642 + 156.164i) q^{29} -112.137 q^{30} +(-40.3008 + 83.6855i) q^{31} +(90.8087 + 72.4175i) q^{32} +(3.77076 + 4.72838i) q^{33} +(-99.5271 - 47.9297i) q^{34} +(-0.261072 + 0.125726i) q^{35} +(-15.1379 + 18.9823i) q^{36} +(113.110 - 25.8166i) q^{37} +(-50.0901 - 219.459i) q^{38} +(-38.2379 + 30.4937i) q^{39} +(389.843 + 88.9791i) q^{40} +63.3965i q^{41} +(0.0274398 - 0.120221i) q^{42} +(-180.543 - 374.902i) q^{43} +(-2.35964 - 4.89984i) q^{44} +(-32.5093 + 142.433i) q^{45} +464.319i q^{46} +(-473.642 - 108.106i) q^{47} +(-82.4225 + 65.7298i) q^{48} +(76.3246 + 334.400i) q^{49} +(310.935 - 70.9690i) q^{50} +(-89.7326 + 112.521i) q^{51} +(39.6245 - 19.0821i) q^{52} +(-250.046 - 120.416i) q^{53} +(-38.7637 - 48.6081i) q^{54} +(-25.5850 - 20.4034i) q^{55} +(-0.190788 + 0.396176i) q^{56} -293.272 q^{57} +(325.319 + 153.250i) q^{58} -554.244 q^{59} +(57.0011 - 118.364i) q^{60} +(-182.611 - 145.628i) q^{61} +(133.353 + 167.219i) q^{62} +(-0.144747 - 0.0697063i) q^{63} +(494.252 - 238.019i) q^{64} +(165.000 - 206.903i) q^{65} +(13.5770 - 3.09886i) q^{66} +(-150.831 - 660.832i) q^{67} +(101.183 - 80.6906i) q^{68} +(589.764 + 134.610i) q^{69} +0.667241i q^{70} +(77.9827 - 341.664i) q^{71} +(96.1919 + 199.745i) q^{72} +(71.8482 + 149.194i) q^{73} +(59.4471 - 260.455i) q^{74} -415.515i q^{75} +(257.108 + 58.6833i) q^{76} +(0.0281350 - 0.0224369i) q^{77} +(25.0602 + 109.796i) q^{78} +(-408.368 + 93.2074i) q^{79} +(355.660 - 445.984i) q^{80} +(-72.9785 + 35.1446i) q^{81} +(131.525 + 63.3389i) q^{82} +(718.775 + 901.315i) q^{83} +(0.112950 + 0.0900742i) q^{84} +(337.884 - 701.623i) q^{85} -958.163 q^{86} +(288.966 - 368.782i) q^{87} -49.6593 q^{88} +(-213.863 + 444.091i) q^{89} +(263.016 + 209.748i) q^{90} +(0.181445 + 0.227525i) q^{91} +(-490.104 - 236.022i) q^{92} +(251.057 - 120.902i) q^{93} +(-697.491 + 874.626i) q^{94} +(1547.09 - 353.114i) q^{95} +(-77.5365 - 339.710i) q^{96} +(221.126 - 176.342i) q^{97} +(770.013 + 175.751i) q^{98} -18.1435i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 52 q^{4} + 28 q^{5} + 12 q^{6} - 40 q^{7} + 144 q^{9}+O(q^{10}) $ 96 * q + 52 * q^4 + 28 * q^5 + 12 * q^6 - 40 * q^7 + 144 * q^9	\( 96 q + 52 q^{4} + 28 q^{5} + 12 q^{6} - 40 q^{7} + 144 q^{9} - 140 q^{11} + 304 q^{13} - 294 q^{15} - 692 q^{16} + 800 q^{20} - 528 q^{22} + 324 q^{23} - 54 q^{24} - 170 q^{25} - 1288 q^{26} - 956 q^{28} - 478 q^{29} + 1056 q^{30} - 616 q^{31} - 406 q^{32} + 72 q^{33} + 34 q^{34} + 1032 q^{35} - 468 q^{36} + 1792 q^{37} + 1912 q^{38} + 2688 q^{40} + 762 q^{42} - 1092 q^{43} + 1750 q^{44} + 630 q^{45} + 2772 q^{47} + 1848 q^{48} - 1304 q^{49} - 882 q^{50} - 192 q^{51} + 1304 q^{52} - 3066 q^{53} - 108 q^{54} - 1974 q^{55} - 4704 q^{56} - 1752 q^{57} - 6092 q^{58} - 640 q^{59} - 7812 q^{60} - 252 q^{61} - 532 q^{62} - 18 q^{63} - 454 q^{64} - 8346 q^{65} + 5628 q^{66} + 744 q^{67} + 5530 q^{68} + 2100 q^{69} + 3216 q^{71} + 2142 q^{72} + 6510 q^{73} + 5090 q^{74} + 6594 q^{76} - 8876 q^{77} - 2118 q^{78} + 7092 q^{80} - 1296 q^{81} - 10590 q^{82} + 572 q^{83} - 2520 q^{85} + 12680 q^{86} - 2238 q^{87} + 6472 q^{88} - 2800 q^{89} + 1576 q^{91} - 10418 q^{92} + 60 q^{93} - 17564 q^{94} + 1374 q^{96} + 11690 q^{97} + 22554 q^{98}+O(q^{100}) \) 96 * q + 52 * q^4 + 28 * q^5 + 12 * q^6 - 40 * q^7 + 144 * q^9 - 140 * q^11 + 304 * q^13 - 294 * q^15 - 692 * q^16 + 800 * q^20 - 528 * q^22 + 324 * q^23 - 54 * q^24 - 170 * q^25 - 1288 * q^26 - 956 * q^28 - 478 * q^29 + 1056 * q^30 - 616 * q^31 - 406 * q^32 + 72 * q^33 + 34 * q^34 + 1032 * q^35 - 468 * q^36 + 1792 * q^37 + 1912 * q^38 + 2688 * q^40 + 762 * q^42 - 1092 * q^43 + 1750 * q^44 + 630 * q^45 + 2772 * q^47 + 1848 * q^48 - 1304 * q^49 - 882 * q^50 - 192 * q^51 + 1304 * q^52 - 3066 * q^53 - 108 * q^54 - 1974 * q^55 - 4704 * q^56 - 1752 * q^57 - 6092 * q^58 - 640 * q^59 - 7812 * q^60 - 252 * q^61 - 532 * q^62 - 18 * q^63 - 454 * q^64 - 8346 * q^65 + 5628 * q^66 + 744 * q^67 + 5530 * q^68 + 2100 * q^69 + 3216 * q^71 + 2142 * q^72 + 6510 * q^73 + 5090 * q^74 + 6594 * q^76 - 8876 * q^77 - 2118 * q^78 + 7092 * q^80 - 1296 * q^81 - 10590 * q^82 + 572 * q^83 - 2520 * q^85 + 12680 * q^86 - 2238 * q^87 + 6472 * q^88 - 2800 * q^89 + 1576 * q^91 - 10418 * q^92 + 60 * q^93 - 17564 * q^94 + 1374 * q^96 + 11690 * q^97 + 22554 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{9}{14}\right)$	$1$

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 $

$2$	0.999092	−	2.07464i	0.353232	−	0.733494i	−0.646331	−	0.763058i	$-0.723697\pi$
$2$	0.999092	−	2.07464i	0.353232	−	0.733494i	0.999563	+	0.0295630i	$0.00941157\pi$
$3$	−2.34549	−	1.87047i	−0.451391	−	0.359972i
$3$	−2.34549	−	1.87047i	−0.451391	−	0.359972i
$4$	1.68199	+	2.10915i	0.210249	+	0.263644i
$5$	14.6253	+	7.04316i	1.30812	+	0.629960i	0.952463	−	0.304655i	$-0.0985411\pi$
$5$	14.6253	+	7.04316i	1.30812	+	0.629960i	0.355662	+	0.934615i	$0.384255\pi$
$6$	−6.22391	+	2.99728i	−0.423483	+	0.203939i
$7$	−0.0111297	+	0.0139563i	−0.000600950	+	0.000753567i	−0.782132	−	0.623113i	$-0.785868\pi$
$7$	−0.0111297	+	0.0139563i	−0.000600950	+	0.000753567i	0.781531	+	0.623867i	$0.214439\pi$
$8$	24.0157	−	5.48142i	1.06135	−	0.242247i
$9$	2.00269	+	8.77435i	0.0741736	+	0.324976i
$10$	29.2240	−	23.3054i	0.924144	−	0.736980i
$11$	−1.96540	−	0.448589i	−0.0538718	−	0.0122959i	0.195500	−	0.980704i	$-0.437367\pi$
$11$	−1.96540	−	0.448589i	−0.0538718	−	0.0122959i	−0.249372	+	0.968408i	$0.580224\pi$
$12$		−	8.09311i		−	0.194690i
$13$	3.62769	−	15.8940i	0.0773955	−	0.339092i	−0.921374	−	0.388676i	$-0.872933\pi$
$13$	3.62769	−	15.8940i	0.0773955	−	0.339092i	0.998770	+	0.0495843i	$0.0157897\pi$
$14$	0.0178345	+	0.0370338i	0.000340463	+	0.000706978i
$15$	−21.1295	−	43.8758i	−0.363707	−	0.755246i
$16$	7.81956	−	34.2597i	0.122181	−	0.535308i
$17$		−	47.9733i		−	0.684425i	−0.939623	−	0.342213i	$-0.888824\pi$
$17$		−	47.9733i		−	0.684425i	0.939623	−	0.342213i	$-0.111176\pi$
$18$	20.2045	+	4.61153i	0.264569	+	0.0603861i
$19$	76.4298	−	60.9507i	0.922852	−	0.735950i	−0.0418968	−	0.999122i	$-0.513340\pi$
$19$	76.4298	−	60.9507i	0.922852	−	0.735950i	0.964749	+	0.263172i	$0.0847686\pi$
$20$	9.74449	+	42.6934i	0.108947	+	0.477327i
$21$	0.0522095	−	0.0119165i	0.000542526	−	0.000123828i
$22$	−2.89427	+	3.62930i	−0.0280482	+	0.0351714i
$23$	−181.675	+	87.4899i	−1.64703	+	0.793170i	−0.647518	+	0.762050i	$0.724193\pi$
$23$	−181.675	+	87.4899i	−1.64703	+	0.793170i	−0.999516	+	0.0311193i	$0.990093\pi$
$24$	−66.5815	−	32.0640i	−0.566287	−	0.272710i
$25$	86.3565	+	108.288i	0.690852	+	0.866301i
$26$	−29.3498	−	23.4057i	−0.221383	−	0.176547i
$27$	11.7149	−	24.3262i	0.0835010	−	0.173392i
$28$	−0.0481560			−0.000325022
$29$	1.33642	+	156.164i	0.00855748	+	0.999963i
$29$	1.33642	+	156.164i	0.00855748	+	0.999963i
$30$	−112.137			−0.682442
$31$	−40.3008	+	83.6855i	−0.233492	+	0.484850i	−0.984487	−	0.175457i	$-0.943860\pi$
$31$	−40.3008	+	83.6855i	−0.233492	+	0.484850i	0.750995	+	0.660307i	$0.229574\pi$
$32$	90.8087	+	72.4175i	0.501652	+	0.400054i
$33$	3.77076	+	4.72838i	0.0198910	+	0.0249426i
$34$	−99.5271	−	47.9297i	−0.502022	−	0.241761i
$35$	−0.261072	+	0.125726i	−0.00126083	+	0.000607186i
$36$	−15.1379	+	18.9823i	−0.0700829	+	0.0878812i
$37$	113.110	−	25.8166i	0.502571	−	0.114709i	0.0362830	−	0.999342i	$-0.488448\pi$
$37$	113.110	−	25.8166i	0.502571	−	0.114709i	0.466288	+	0.884633i	$0.345591\pi$
$38$	−50.0901	−	219.459i	−0.213834	−	0.936868i
$39$	−38.2379	+	30.4937i	−0.156999	+	0.125203i
$40$	389.843	+	88.9791i	1.54099	+	0.351721i
$41$			63.3965i			0.241485i	0.992684	+	0.120742i	$0.0385275\pi$
$41$			63.3965i			0.241485i	−0.992684	+	0.120742i	$0.961473\pi$
$42$	0.0274398	−	0.120221i	0.000100811	−	0.000441680i
$43$	−180.543	−	374.902i	−0.640292	−	1.32958i	−0.928257	−	0.371939i	$-0.878693\pi$
$43$	−180.543	−	374.902i	−0.640292	−	1.32958i	0.287965	−	0.957641i	$-0.407021\pi$
$44$	−2.35964	−	4.89984i	−0.00808474	−	0.0167881i
$45$	−32.5093	+	142.433i	−0.107693	+	0.471836i
$46$			464.319i			1.48826i
$47$	−473.642	−	108.106i	−1.46995	−	0.335507i	−0.588776	−	0.808296i	$-0.700390\pi$
$47$	−473.642	−	108.106i	−1.46995	−	0.335507i	−0.881175	+	0.472789i	$0.843247\pi$
$48$	−82.4225	+	65.7298i	−0.247847	+	0.197652i
$49$	76.3246	+	334.400i	0.222521	+	0.974927i
$50$	310.935	−	70.9690i	0.879458	−	0.200731i
$51$	−89.7326	+	112.521i	−0.246374	+	0.308943i
$52$	39.6245	−	19.0821i	0.105672	−	0.0508888i
$53$	−250.046	−	120.416i	−0.648046	−	0.312082i	0.0808306	−	0.996728i	$-0.474243\pi$
$53$	−250.046	−	120.416i	−0.648046	−	0.312082i	−0.728876	+	0.684646i	$0.759957\pi$
$54$	−38.7637	−	48.6081i	−0.0976865	−	0.122495i
$55$	−25.5850	−	20.4034i	−0.0627251	−	0.0500216i
$56$	−0.190788	+	0.396176i	−0.000455271	+	0.000945380i
$57$	−293.272			−0.681488
$58$	325.319	+	153.250i	0.736490	+	0.346943i
$59$	−554.244			−1.22299			−0.611495	−	0.791248i	$-0.709432\pi$
$59$	−554.244			−1.22299			−0.611495	+	0.791248i	$0.709432\pi$
$60$	57.0011	−	118.364i	0.122647	−	0.254679i
$61$	−182.611	−	145.628i	−0.383295	−	0.305667i	0.412821	−	0.910812i	$-0.364544\pi$
$61$	−182.611	−	145.628i	−0.383295	−	0.305667i	−0.796115	+	0.605145i	$0.793115\pi$
$62$	133.353	+	167.219i	0.273158	+	0.342530i
$63$	−0.144747	−	0.0697063i	−0.000289466	−	0.000139399i
$64$	494.252	−	238.019i	0.965336	−	0.464882i
$65$	165.000	−	206.903i	0.314857	−	0.394818i
$66$	13.5770	−	3.09886i	0.0253214	−	0.00577945i
$67$	−150.831	−	660.832i	−0.275028	−	1.20498i	−0.903994	−	0.427544i	$-0.859379\pi$
$67$	−150.831	−	660.832i	−0.275028	−	1.20498i	0.628966	−	0.777432i	$-0.283478\pi$
$68$	101.183	−	80.6906i	0.180444	−	0.143900i
$69$	589.764	+	134.610i	1.02897	+	0.234857i
$70$			0.667241i			0.00113929i
$71$	77.9827	−	341.664i	0.130350	−	0.571100i	−0.866998	−	0.498312i	$-0.833953\pi$
$71$	77.9827	−	341.664i	0.130350	−	0.571100i	0.997347	−	0.0727877i	$-0.0231896\pi$
$72$	96.1919	+	199.745i	0.157449	+	0.326946i
$73$	71.8482	+	149.194i	0.115194	+	0.239204i	0.950592	−	0.310442i	$-0.100477\pi$
$73$	71.8482	+	149.194i	0.115194	+	0.239204i	−0.835398	+	0.549646i	$0.814763\pi$
$74$	59.4471	−	260.455i	0.0933862	−	0.409152i
$75$		−	415.515i		−	0.639727i
$76$	257.108	+	58.6833i	0.388057	+	0.0885715i
$77$	0.0281350	−	0.0224369i	4.16400e−5	−	3.32068e-5i
$78$	25.0602	+	109.796i	0.0363783	+	0.159384i
$79$	−408.368	+	93.2074i	−0.581583	+	0.132742i	−0.503183	−	0.864180i	$-0.667838\pi$
$79$	−408.368	+	93.2074i	−0.581583	+	0.132742i	−0.0783991	+	0.996922i	$0.524981\pi$
$80$	355.660	−	445.984i	0.497050	−	0.623281i
$81$	−72.9785	+	35.1446i	−0.100108	+	0.0482093i
$82$	131.525	+	63.3389i	0.177128	+	0.0853002i
$83$	718.775	+	901.315i	0.950552	+	1.19195i	0.981311	+	0.192427i	$0.0616359\pi$
$83$	718.775	+	901.315i	0.950552	+	1.19195i	−0.0307596	+	0.999527i	$0.509793\pi$
$84$	0.112950	+	0.0900742i	0.000146712	+	0.000116999i
$85$	337.884	−	701.623i	0.431160	−	0.895314i
$86$	−958.163			−1.20141
$87$	288.966	−	368.782i	0.356096	−	0.454455i
$88$	−49.6593			−0.0601557
$89$	−213.863	+	444.091i	−0.254712	+	0.528916i	−0.988638	−	0.150314i	$-0.951972\pi$
$89$	−213.863	+	444.091i	−0.254712	+	0.528916i	0.733926	+	0.679230i	$0.237686\pi$
$90$	263.016	+	209.748i	0.308048	+	0.245660i
$91$	0.181445	+	0.227525i	0.000209018	+	0.000262100i
$92$	−490.104	−	236.022i	−0.555401	−	0.267467i
$93$	251.057	−	120.902i	0.279929	−	0.134806i
$94$	−697.491	+	874.626i	−0.765327	+	0.959690i
$95$	1547.09	−	353.114i	1.67082	−	0.381355i
$96$	−77.5365	−	339.710i	−0.0824327	−	0.361161i
$97$	221.126	−	176.342i	0.231464	−	0.184586i	−0.500889	−	0.865511i	$-0.666994\pi$
$97$	221.126	−	176.342i	0.231464	−	0.184586i	0.732353	+	0.680925i	$0.238422\pi$
$98$	770.013	+	175.751i	0.793705	+	0.181158i
$99$		−	18.1435i		−	0.0184191i
$100$	−83.1439	+	364.277i	−0.0831439	+	0.364277i
$101$	30.1007	+	62.5048i	0.0296548	+	0.0615788i	0.915270	−	0.402841i	$-0.131977\pi$
$101$	30.1007	+	62.5048i	0.0296548	+	0.0615788i	−0.885615	+	0.464420i	$0.846263\pi$
$102$	143.789	+	298.581i	0.139581	+	0.289843i
$103$	181.124	−	793.556i	0.173269	−	0.759140i	−0.811370	−	0.584533i	$-0.801278\pi$
$103$	181.124	−	793.556i	0.173269	−	0.759140i	0.984638	−	0.174606i	$-0.0558653\pi$
$104$		−	401.589i		−	0.378645i
$105$	0.847509	+	0.193438i	0.000787699	+	0.000179787i
$106$	−499.637	+	398.447i	−0.457821	+	0.365100i
$107$	19.7289	+	86.4379i	0.0178249	+	0.0780959i	0.983058	−	0.183294i	$-0.0586762\pi$
$107$	19.7289	+	86.4379i	0.0178249	+	0.0780959i	−0.965233	+	0.261390i	$0.915819\pi$
$108$	71.0118	−	16.2080i	0.0632695	−	0.0144409i
$109$	−285.185	+	357.611i	−0.250603	+	0.314247i	−0.891182	−	0.453646i	$-0.850123\pi$
$109$	−285.185	+	357.611i	−0.250603	+	0.314247i	0.640579	+	0.767893i	$0.278695\pi$
$110$	−67.8913	+	32.6947i	−0.0588471	+	0.0283393i
$111$	−313.587	−	151.016i	−0.268148	−	0.129133i
$112$	0.391108	+	0.490434i	0.000329967	+	0.000413765i
$113$	1456.16	+	1161.25i	1.21225	+	0.966734i	0.999945	−	0.0104699i	$-0.00333274\pi$
$113$	1456.16	+	1161.25i	1.21225	+	0.966734i	0.212301	+	0.977204i	$0.431904\pi$
$114$	−293.006	+	608.433i	−0.240724	+	0.499868i
$115$	−3273.25			−2.65419
$116$	−327.125	+	265.485i	−0.261835	+	0.212497i
$117$	146.724			0.115937
$118$	−553.741	+	1149.85i	−0.432000	+	0.897056i
$119$	0.669528	+	0.533931i	0.000515761	+	0.000411305i
$120$	−747.942	−	937.889i	−0.568978	−	0.713476i
$121$	−1195.53	−	575.736i	−0.898218	−	0.432559i
$122$	−484.569	+	233.356i	−0.359597	+	0.173173i
$123$	118.581	−	148.696i	0.0869277	−	0.109004i
$124$	−244.291	+	55.7578i	−0.176919	+	0.0403806i
$125$	48.7822	+	213.729i	0.0349057	+	0.152932i
$126$	−0.289230	+	0.230653i	−0.000204497	+	0.000163081i
$127$	−1040.98	−	237.596i	−0.727338	−	0.166010i	−0.157209	−	0.987565i	$-0.550250\pi$
$127$	−1040.98	−	237.596i	−0.727338	−	0.166010i	−0.570129	+	0.821555i	$0.693107\pi$
$128$		−	334.007i		−	0.230643i
$129$	−277.779	+	1217.03i	−0.189590	+	0.830647i
$130$	−264.399	−	549.030i	−0.178379	−	0.370409i
$131$	1222.22	+	2537.96i	0.815156	+	1.69269i	0.716521	+	0.697566i	$0.245733\pi$
$131$	1222.22	+	2537.96i	0.815156	+	1.69269i	0.0986351	+	0.995124i	$0.468552\pi$
$132$	−3.63048	+	15.9062i	−0.00239388	+	0.0104883i
$133$			1.74504i			0.00113770i
$134$	−1521.68	−	347.313i	−0.980992	−	0.223905i
$135$	342.666	−	273.267i	0.218459	−	0.174216i
$136$	−262.962	−	1152.11i	−0.165800	−	0.726417i
$137$	−802.454	+	183.155i	−0.500425	+	0.114219i	−0.465280	−	0.885163i	$-0.654046\pi$
$137$	−802.454	+	183.155i	−0.500425	+	0.114219i	−0.0351449	+	0.999382i	$0.511189\pi$
$138$	868.495	−	1089.06i	0.535733	−	0.671788i
$139$	1702.12	−	819.696i	1.03865	−	0.500185i	0.164768	−	0.986332i	$-0.447312\pi$
$139$	1702.12	−	819.696i	1.03865	−	0.500185i	0.873877	+	0.486147i	$0.161598\pi$
$140$	−0.704294	−	0.339170i	−0.000425170	−	0.000204751i
$141$	908.715	+	1139.49i	0.542749	+	0.680586i
$142$	−630.917	−	503.140i	−0.372855	−	0.297342i
$143$	−14.2597	+	29.6106i	−0.00833887	+	0.0173158i
$144$	316.267			0.183025
$145$	−1080.34	+	2293.36i	−0.618742	+	1.31347i
$146$	381.307			0.216145
$147$	446.466	−	927.096i	0.250503	−	0.520174i
$148$	244.700	+	195.142i	0.135907	+	0.108382i
$149$	−1545.57	−	1938.08i	−0.849785	−	1.06560i	−0.997069	−	0.0765020i	$-0.975625\pi$
$149$	−1545.57	−	1938.08i	−0.849785	−	1.06560i	0.147285	−	0.989094i	$-0.452947\pi$
$150$	−862.043	−	415.138i	−0.469237	−	0.225972i
$151$	894.699	−	430.864i	0.482182	−	0.232207i	−0.176970	−	0.984216i	$-0.556630\pi$
$151$	894.699	−	430.864i	0.482182	−	0.232207i	0.659152	+	0.752009i	$0.270915\pi$
$152$	1501.42	−	1882.72i	0.801191	−	1.00466i
$153$	420.934	−	96.0755i	0.222422	−	0.0507663i
$154$	−0.0184390	−	0.0807865i	−9.64841e−6	−	4.22725e-5i
$155$	−1178.82	+	940.079i	−0.610873	+	0.487155i
$156$	−128.632	−	29.3593i	−0.0660177	−	0.0150681i
$157$		−	1986.72i		−	1.00992i	−0.863142	−	0.504961i	$-0.831507\pi$
$157$		−	1986.72i		−	1.00992i	0.863142	−	0.504961i	$-0.168493\pi$
$158$	−214.626	+	940.338i	−0.108068	+	0.473477i
$159$	361.247	+	750.137i	0.180181	+	0.374149i
$160$	818.054	+	1698.71i	0.404205	+	0.839341i
$161$	0.800961	−	3.50924i	0.000392078	−	0.00171781i
$162$			186.516i			0.0904575i
$163$	2413.05	+	550.763i	1.15954	+	0.264657i	0.758668	−	0.651478i	$-0.225851\pi$
$163$	2413.05	+	550.763i	1.15954	+	0.264657i	0.400870	+	0.916135i	$0.368708\pi$
$164$	−133.713	+	106.632i	−0.0636658	+	0.0507718i
$165$	21.8456	+	95.7120i	0.0103072	+	0.0451586i
$166$	2588.02	−	590.699i	1.21006	−	0.276188i
$167$	−234.049	+	293.488i	−0.108451	+	0.135993i	−0.833094	−	0.553131i	$-0.813433\pi$
$167$	−234.049	+	293.488i	−0.108451	+	0.135993i	0.724644	+	0.689124i	$0.242004\pi$
$168$	1.18853	−	0.572365i	0.000545815	−	0.000262851i
$169$	1739.97	+	837.926i	0.791976	+	0.381395i
$170$	−1118.03	−	1401.97i	−0.504408	−	0.632508i
$171$	687.868	+	548.556i	0.307617	+	0.245317i
$172$	487.051	−	1011.37i	0.215915	−	0.448351i
$173$	2761.18			1.21346			0.606729	−	0.794908i	$-0.292481\pi$
$173$	2761.18			1.21346			0.606729	+	0.794908i	$0.292481\pi$
$174$	−476.385	−	967.945i	−0.207555	−	0.421723i
$175$	−2.47242			−0.00106798
$176$	−30.7371	+	63.8262i	−0.0131642	+	0.0273357i
$177$	1299.98	+	1036.70i	0.552046	+	0.440242i
$178$	707.658	+	887.375i	0.297984	+	0.373660i
$179$	−472.034	−	227.320i	−0.197103	−	0.0949200i	0.332729	−	0.943023i	$-0.392031\pi$
$179$	−472.034	−	227.320i	−0.197103	−	0.0949200i	−0.529832	+	0.848103i	$0.677745\pi$
$180$	−355.092	+	171.003i	−0.147039	+	0.0708102i
$181$	−2059.64	+	2582.70i	−0.845809	+	1.06061i	0.151583	+	0.988444i	$0.451563\pi$
$181$	−2059.64	+	2582.70i	−0.845809	+	1.06061i	−0.997393	+	0.0721668i	$0.977009\pi$
$182$	0.653312	−	0.149114i	0.000266081	−	6.07312e-5i
$183$	155.922	+	683.137i	0.0629839	+	0.275951i
$184$	−3883.47	+	3096.97i	−1.55594	+	1.24082i
$185$	1836.09	+	419.076i	0.729687	+	0.166546i
$186$		−	641.644i		−	0.252944i
$187$	−21.5203	+	94.2866i	−0.00841562	+	0.0368712i
$188$	−568.649	−	1180.81i	−0.220601	−	0.458083i
$189$	0.209119	+	0.434240i	8.04823e−5	+	0.000167123i
$190$	813.105	−	3562.45i	0.310468	−	1.36025i
$191$		−	3273.79i		−	1.24022i	−0.784513	−	0.620112i	$-0.787087\pi$
$191$		−	3273.79i		−	1.24022i	0.784513	−	0.620112i	$-0.212913\pi$
$192$	−1604.47	−	366.211i	−0.603088	−	0.137651i
$193$	3596.02	−	2867.73i	1.34118	−	1.06955i	0.350037	−	0.936736i	$-0.386169\pi$
$193$	3596.02	−	2867.73i	1.34118	−	1.06955i	0.991141	−	0.132817i	$-0.0424023\pi$
$194$	−144.921	−	634.939i	−0.0536325	−	0.234979i
$195$	−774.013	+	176.663i	−0.284247	+	0.0648776i
$196$	−576.922	+	723.437i	−0.210249	+	0.263643i
$197$	2135.87	−	1028.58i	0.772460	−	0.371997i	−0.00576445	−	0.999983i	$-0.501835\pi$
$197$	2135.87	−	1028.58i	0.772460	−	0.371997i	0.778224	+	0.627986i	$0.216121\pi$
$198$	−37.6411	−	18.1270i	−0.0135103	−	0.00650621i
$199$	−2023.46	−	2537.34i	−0.720802	−	0.903857i	0.277581	−	0.960702i	$-0.410467\pi$
$199$	−2023.46	−	2537.34i	−0.720802	−	0.903857i	−0.998383	+	0.0568451i	$0.981896\pi$
$200$	2667.48	+	2127.24i	0.943097	+	0.752095i
$201$	−882.293	+	1832.10i	−0.309613	+	0.642918i
$202$	159.748			0.0556428
$203$	−2.19434	−	1.71942i	−0.000758683	−	0.000594479i
$204$	−388.253			−0.133251
$205$	−446.512	+	927.191i	−0.152126	+	0.315892i
$206$	−1465.38	−	1168.60i	−0.495621	−	0.395244i
$207$	−1131.50	−	1418.86i	−0.379928	−	0.476414i
$208$	−516.156	−	248.568i	−0.172062	−	0.0828609i
$209$	−177.557	+	85.5068i	−0.0587649	+	0.0282997i
$210$	1.24805	−	1.56501i	0.000410114	−	0.000514266i
$211$	5154.90	−	1176.57i	1.68189	−	0.383880i	0.728362	−	0.685193i	$-0.240282\pi$
$211$	5154.90	−	1176.57i	1.68189	−	0.383880i	0.953525	+	0.301313i	$0.0974248\pi$
$212$	−166.600	−	729.921i	−0.0539723	−	0.236468i
$213$	−821.981	+	655.508i	−0.264419	+	0.210867i
$214$	199.038	+	45.4291i	0.0635793	+	0.0145115i
$215$		−	6754.64i		−	2.14262i
$216$	147.998	−	648.424i	0.0466205	−	0.204258i
$217$	−0.719399	−	1.49385i	−0.000225051	−	0.000467323i
$218$	456.986	+	948.941i	0.141977	+	0.294818i
$219$	110.544	−	484.324i	0.0341089	−	0.149441i
$220$		−	88.2808i		−	0.0270541i
$221$	−762.486	−	174.032i	−0.232083	−	0.0529714i
$222$	−626.605	+	499.701i	−0.189437	+	0.151071i
$223$	1002.49	+	4392.18i	0.301038	+	1.31893i	0.868564	+	0.495577i	$0.165043\pi$
$223$	1002.49	+	4392.18i	0.301038	+	1.31893i	−0.567527	+	0.823355i	$0.692100\pi$
$224$	−2.02136	+	0.461361i	−0.000602935	+	0.000137616i
$225$	−777.208	+	974.588i	−0.230284	+	0.288767i
$226$	3864.00	−	1860.81i	1.13730	−	0.547694i
$227$	−3506.62	−	1688.70i	−1.02530	−	0.493757i	−0.155848	−	0.987781i	$-0.549811\pi$
$227$	−3506.62	−	1688.70i	−1.02530	−	0.493757i	−0.869448	+	0.494024i	$0.835525\pi$
$228$	−493.280	−	618.554i	−0.143282	−	0.179670i
$229$	1320.89	+	1053.37i	0.381165	+	0.303969i	0.795264	−	0.606263i	$-0.207332\pi$
$229$	1320.89	+	1053.37i	0.381165	+	0.303969i	−0.414099	+	0.910232i	$0.635903\pi$
$230$	−3270.28	+	6790.80i	−0.937546	+	1.94683i
$231$	−0.107958			−3.07494e−5
$232$	888.097	+	3743.06i	0.251321	+	1.05924i
$233$	−4386.21			−1.23326			−0.616631	−	0.787252i	$-0.711503\pi$
$233$	−4386.21			−1.23326			−0.616631	+	0.787252i	$0.711503\pi$
$234$	146.591	−	304.400i	0.0409528	−	0.0850394i
$235$	−6165.74	−	4917.01i	−1.71152	−	1.36490i
$236$	−932.233	−	1168.98i	−0.257132	−	0.322433i
$237$	1132.17	+	545.223i	0.310304	+	0.149435i
$238$	1.77663	−	0.855581i	0.000483874	−	0.000233021i
$239$	−3832.63	+	4805.97i	−1.03729	+	1.30072i	−0.0847197	+	0.996405i	$0.526999\pi$
$239$	−3832.63	+	4805.97i	−1.03729	+	1.30072i	−0.952571	+	0.304317i	$0.901572\pi$
$240$	−1668.40	+	380.801i	−0.448728	+	0.102419i
$241$	1236.32	+	5416.66i	0.330449	+	1.44779i	0.818264	+	0.574843i	$0.194937\pi$
$241$	1236.32	+	5416.66i	0.330449	+	1.44779i	−0.487815	+	0.872947i	$0.662206\pi$
$242$	−2388.88	+	1905.07i	−0.634559	+	0.506044i
$243$	236.907	+	54.0726i	0.0625417	+	0.0142747i
$244$		−	630.098i		−	0.165319i
$245$	−1238.97	+	5428.26i	−0.323080	+	1.41551i
$246$	−190.017	−	394.574i	−0.0492481	−	0.102265i
$247$	−691.485	−	1435.88i	−0.178130	−	0.369891i
$248$	−509.136	+	2230.67i	−0.130364	+	0.571160i
$249$		−	3458.48i		−	0.880209i
$250$	492.147	+	112.329i	0.124504	+	0.0284173i
$251$	4783.71	−	3814.88i	1.20297	−	0.959336i	0.203165	−	0.979144i	$-0.434877\pi$
$251$	4783.71	−	3814.88i	1.20297	−	0.959336i	0.999804	+	0.0198088i	$0.00630575\pi$
$252$	−0.0964414	−	0.422537i	−2.41081e−5	−	0.000105624i
$253$	396.310	−	90.4551i	0.0984814	−	0.0224777i
$254$	−1532.96	+	1922.27i	−0.378687	+	0.474858i
$255$	−2104.87	+	1013.65i	−0.516910	+	0.248931i
$256$	3261.07	+	1570.45i	0.796161	+	0.383411i
$257$	3700.74	+	4640.58i	0.898232	+	1.12635i	0.991422	+	0.130699i	$0.0417221\pi$
$257$	3700.74	+	4640.58i	0.898232	+	1.12635i	−0.0931902	+	0.995648i	$0.529706\pi$
$258$	2247.37	+	1792.22i	0.542306	+	0.432475i
$259$	−0.898580	+	1.86592i	−0.000215579	+	0.000447655i
$260$	713.918			0.170290
$261$	−1367.56	+	324.474i	−0.324329	+	0.0769519i
$262$	6486.44			1.52952
$263$	954.683	−	1982.42i	0.223834	−	0.464796i	−0.758564	−	0.651599i	$-0.774098\pi$
$263$	954.683	−	1982.42i	0.223834	−	0.464796i	0.982397	+	0.186803i	$0.0598128\pi$
$264$	116.476	+	92.8862i	0.0271537	+	0.0216544i
$265$	−2808.88	−	3522.23i	−0.651125	−	0.816485i
$266$	3.62032	+	1.74346i	0.000834497	+	0.000401873i
$267$	1332.27	−	641.588i	0.305370	−	0.147058i
$268$	1140.10	−	1429.64i	0.259860	−	0.325854i
$269$	−2707.35	+	617.935i	−0.613643	+	0.140060i	−0.518036	−	0.855359i	$-0.673337\pi$
$269$	−2707.35	+	617.935i	−0.613643	+	0.140060i	−0.0956075	+	0.995419i	$0.530479\pi$
$270$	−224.575	−	983.927i	−0.0506192	−	0.221777i
$271$	−1872.51	+	1493.28i	−0.419731	+	0.334724i	−0.810473	−	0.585776i	$-0.800790\pi$
$271$	−1872.51	+	1493.28i	−0.419731	+	0.334724i	0.390742	+	0.920500i	$0.372218\pi$
$272$	−1643.55	−	375.130i	−0.366379	−	0.0836235i
$273$		−	0.873046i		−	0.000193550i
$274$	−421.745	+	1847.79i	−0.0929875	+	0.407405i
$275$	−121.148	−	251.567i	−0.0265655	−	0.0551638i
$276$	708.065	+	1470.31i	0.154422	+	0.320661i
$277$	1629.35	−	7138.65i	0.353423	−	1.54845i	−0.415793	−	0.909459i	$-0.636496\pi$
$277$	1629.35	−	7138.65i	0.353423	−	1.54845i	0.769216	−	0.638989i	$-0.220647\pi$
$278$		−	4350.23i		−	0.938522i
$279$	−814.996	−	186.018i	−0.174884	−	0.0399161i
$280$	−5.58067	+	4.45043i	−0.00119110	+	0.000949873i
$281$	734.330	+	3217.31i	0.155895	+	0.683020i	0.991104	+	0.133088i	$0.0424892\pi$
$281$	734.330	+	3217.31i	0.155895	+	0.683020i	−0.835209	+	0.549932i	$0.814654\pi$
$282$	3271.92	−	746.795i	0.690923	−	0.157699i
$283$	−3232.52	+	4053.45i	−0.678987	+	0.851423i	−0.995260	−	0.0972449i	$-0.968997\pi$
$283$	−3232.52	+	4053.45i	−0.678987	+	0.851423i	0.316273	+	0.948668i	$0.397568\pi$
$284$	851.787	−	410.199i	0.177973	−	0.0857071i
$285$	−4289.19	−	2065.56i	−0.891472	−	0.429310i
$286$	47.1845	+	59.1675i	0.00975551	+	0.0122330i
$287$	−0.884778	−	0.705587i	−0.000181975	−	0.000145120i
$288$	−453.555	+	941.817i	−0.0927986	+	0.192698i
$289$	2611.56			0.531562
$290$	3678.52	+	4532.59i	0.744862	+	0.917804i
$291$	−848.494			−0.170926
$292$	−193.825	+	402.482i	−0.0388450	+	0.0806625i
$293$	2480.92	+	1978.47i	0.494666	+	0.394483i	0.838802	−	0.544437i	$-0.183257\pi$
$293$	2480.92	+	1978.47i	0.494666	+	0.394483i	−0.344136	+	0.938920i	$0.611828\pi$
$294$	−1477.33	−	1852.51i	−0.293059	−	0.367485i
$295$	−8105.97	−	3903.63i	−1.59982	−	0.770435i
$296$	2574.90	−	1240.00i	0.505618	−	0.243493i
$297$	−33.9368	+	42.5554i	−0.00663035	+	0.00831420i
$298$	−5564.98	+	1270.17i	−1.08178	+	0.246909i
$299$	731.501	+	3204.92i	0.141484	+	0.619883i
$300$	876.383	−	698.892i	0.168660	−	0.134502i
$301$	7.24163	+	1.65285i	0.00138671	+	0.000316508i
$302$		−	2286.65i		−	0.435701i
$303$	46.3123	−	202.907i	0.00878076	−	0.0384710i
$304$	−1490.51	−	3095.07i	−0.281206	−	0.583929i
$305$	−1645.06	−	3416.00i	−0.308839	−	0.641311i
$306$	221.230	−	969.274i	0.0413298	−	0.181077i
$307$			2709.49i			0.503709i	0.967765	+	0.251855i	$0.0810405\pi$
$307$			2709.49i			0.503709i	−0.967765	+	0.251855i	$0.918959\pi$
$308$	0.0946456	+	0.0216022i	1.75095e−5	+	3.99644e-6i
$309$	−1909.15	+	1522.49i	−0.351481	+	0.280297i
$310$	772.570	+	3384.85i	0.141545	+	0.620151i
$311$	5668.73	−	1293.85i	1.03358	−	0.235909i	0.328106	−	0.944641i	$-0.393590\pi$
$311$	5668.73	−	1293.85i	1.03358	−	0.235909i	0.705477	+	0.708732i	$0.250733\pi$
$312$	−751.161	+	941.926i	−0.136302	+	0.170917i
$313$	6022.39	−	2900.23i	1.08756	−	0.523741i	0.197833	−	0.980236i	$-0.436610\pi$
$313$	6022.39	−	2900.23i	1.08756	−	0.523741i	0.889726	+	0.456495i	$0.150895\pi$
$314$	−4121.73	−	1984.92i	−0.740773	−	0.356737i
$315$	−1.62601	−	2.03895i	−0.000290842	−	0.000364704i
$316$	−883.459	−	704.535i	−0.157274	−	0.125422i
$317$	−711.145	+	1476.71i	−0.126000	+	0.261641i	−0.954421	−	0.298465i	$-0.903525\pi$
$317$	−711.145	+	1476.71i	−0.126000	+	0.261641i	0.828421	+	0.560106i	$0.189240\pi$
$318$	1917.18			0.338082
$319$	67.4269	−	307.524i	0.0118344	−	0.0539750i
$320$	8904.99			1.55564
$321$	115.405	−	239.642i	0.0200664	−	0.0416682i
$322$	−6.48016	−	5.16775i	−0.00112151	−	0.000894372i
$323$	−2924.01	−	3666.59i	−0.503703	−	0.631623i
$324$	−196.874	−	94.8096i	−0.0337576	−	0.0162568i
$325$	2034.39	−	979.713i	0.347224	−	0.167214i
$326$	3553.49	−	4455.94i	0.603711	−	0.757029i
$327$	1337.80	−	305.344i	0.226240	−	0.0516378i
$328$	347.503	+	1522.51i	0.0584989	+	0.256300i
$329$	6.78026	−	5.40708i	0.00113619	−	0.000906085i
$330$	220.393	+	50.3033i	0.0367644	+	0.00839123i
$331$			7839.63i			1.30183i	0.759151	+	0.650914i	$0.225614\pi$
$331$			7839.63i			1.30183i	−0.759151	+	0.650914i	$0.774386\pi$
$332$	−692.035	+	3032.01i	−0.114399	+	0.501214i
$333$	453.047	+	940.762i	0.0745550	+	0.154815i
$334$	375.044	+	778.788i	0.0614417	+	0.127585i
$335$	2448.41	−	10727.2i	0.399316	−	1.74952i
$336$		−	1.88187i		−	0.000305548i
$337$	−9979.65	−	2277.79i	−1.61313	−	0.368187i	−0.681566	−	0.731756i	$-0.738701\pi$
$337$	−9979.65	−	2277.79i	−1.61313	−	0.368187i	−0.931567	+	0.363569i	$0.881558\pi$
$338$	3476.78	−	2772.64i	0.559503	−	0.446189i
$339$	−1243.33	−	5447.40i	−0.199199	−	0.872750i
$340$	2048.14	−	467.475i	0.326695	−	0.0745659i
$341$	116.748	−	146.397i	0.0185403	−	0.0232488i
$342$	1825.30	−	879.017i	0.288599	−	0.138982i
$343$	−11.0329	−	5.31317i	−0.00173680	−	0.000836396i
$344$	−6390.86	−	8013.89i	−1.00166	−	1.25605i
$345$	7677.38	+	6122.51i	1.19808	+	0.955434i
$346$	2758.67	−	5728.44i	0.428633	−	0.890065i
$347$	−9134.88			−1.41322			−0.706608	−	0.707605i	$-0.749776\pi$
$347$	−9134.88			−1.41322			−0.706608	+	0.707605i	$0.749776\pi$
$348$	1263.85	−	10.8158i	0.194683	−	0.00166606i
$349$	−7555.46			−1.15884			−0.579419	−	0.815030i	$-0.696720\pi$
$349$	−7555.46			−1.15884			−0.579419	+	0.815030i	$0.696720\pi$
$350$	−2.47017	+	5.12936i	−0.000377246	+	0.000783360i
$351$	−344.141	−	274.443i	−0.0523330	−	0.0417342i
$352$	−145.989	−	183.065i	−0.0221059	−	0.0277199i
$353$	6626.85	+	3191.32i	0.999183	+	0.481181i	0.860661	−	0.509178i	$-0.170051\pi$
$353$	6626.85	+	3191.32i	0.999183	+	0.481181i	0.138522	+	0.990359i	$0.455765\pi$
$354$	3449.56	−	1661.22i	0.517916	−	0.249415i
$355$	3546.92	−	4447.69i	0.530284	−	0.664955i
$356$	−1296.37	+	295.887i	−0.192998	+	0.0440506i
$357$	−0.571673	−	2.50466i	−8.47511e−5	−	0.000371319i
$358$	−943.212	+	752.186i	−0.139247	+	0.111045i
$359$	1874.26	+	427.788i	0.275543	+	0.0628908i	0.358059	−	0.933699i	$-0.383439\pi$
$359$	1874.26	+	427.788i	0.275543	+	0.0628908i	−0.0825166	+	0.996590i	$0.526296\pi$
$360$			3598.82i			0.526873i
$361$	600.250	−	2629.87i	0.0875127	−	0.383418i
$362$	3300.40	+	6853.35i	0.479185	+	0.995039i
$363$	1727.21	+	3586.58i	0.249738	+	0.518586i
$364$	−0.174695	+	0.765389i	−2.51552e−5	+	0.000110212i
$365$			2688.05i			0.385476i
$366$	1573.04	+	359.036i	0.224656	+	0.0512763i
$367$	2954.67	−	2356.27i	0.420252	−	0.335140i	−0.390424	−	0.920635i	$-0.627671\pi$
$367$	2954.67	−	2356.27i	0.420252	−	0.335140i	0.810676	+	0.585496i	$0.199100\pi$
$368$	1576.76	+	6908.26i	0.223355	+	0.978581i
$369$	−556.263	+	126.963i	−0.0784767	+	0.0179118i
$370$	2703.85	−	3390.53i	0.379910	−	0.476392i
$371$	4.46350	−	2.14951i	0.000624618	−	0.000300800i
$372$	677.276	+	326.159i	0.0943955	+	0.0454585i
$373$	3741.61	+	4691.83i	0.519392	+	0.651297i	0.970480	−	0.241182i	$-0.0775352\pi$
$373$	3741.61	+	4691.83i	0.519392	+	0.651297i	−0.451088	+	0.892480i	$0.648964\pi$
$374$	174.110	+	138.848i	0.0240722	+	0.0191969i
$375$	285.355	−	592.545i	0.0392951	−	0.0815971i
$376$	−11967.4			−1.64141
$377$	2486.91	+	545.274i	0.339742	+	0.0744909i
$378$	1.10982			0.000151013
$379$	−4684.56	+	9727.59i	−0.634907	+	1.31840i	0.296714	+	0.954966i	$0.404109\pi$
$379$	−4684.56	+	9727.59i	−0.634907	+	1.31840i	−0.931621	+	0.363431i	$0.881605\pi$
$380$	3346.96	+	2669.11i	0.451831	+	0.360323i
$381$	1997.19	+	2504.40i	0.268554	+	0.336757i
$382$	−6791.91	−	3270.81i	−0.909698	−	0.438087i
$383$	3784.79	−	1822.66i	0.504945	−	0.243169i	−0.164028	−	0.986456i	$-0.552449\pi$
$383$	3784.79	−	1822.66i	0.504945	−	0.243169i	0.668973	+	0.743287i	$0.266734\pi$
$384$	−624.750	+	783.412i	−0.0830251	+	0.104110i
$385$	0.569510	−	0.129987i	7.53893e−5	−	1.72071e-5i
$386$	−2356.74	−	10325.6i	−0.310764	−	1.36155i
$387$	2927.95	−	2334.96i	0.384589	−	0.306699i
$388$	743.865	+	169.782i	0.0973299	+	0.0222149i
$389$			1649.94i			0.215052i	0.994202	+	0.107526i	$0.0342929\pi$
$389$			1649.94i			0.215052i	−0.994202	+	0.107526i	$0.965707\pi$
$390$	−406.798	+	1782.30i	−0.0528179	+	0.231411i
$391$	4197.18	+	8715.53i	0.542865	+	1.12727i
$392$	3665.98	+	7612.48i	0.472346	+	0.980837i
$393$	1880.47	−	8238.88i	0.241367	−	1.05750i
$394$		−	5458.81i		−	0.697997i
$395$	−6628.98	−	1513.02i	−0.844405	−	0.192730i
$396$	38.2673	−	30.5171i	0.00485607	−	0.00387259i
$397$	1782.51	+	7809.69i	0.225344	+	0.987298i	0.953383	+	0.301762i	$0.0975748\pi$
$397$	1782.51	+	7809.69i	0.225344	+	0.987298i	−0.728039	+	0.685536i	$0.759568\pi$
$398$	−7285.69	+	1662.91i	−0.917585	+	0.209433i
$399$	3.26404	−	4.09298i	0.000409540	−	0.000513547i
$400$	4385.17	−	2111.79i	0.548147	−	0.263974i
$401$	−11231.1	−	5408.59i	−1.39863	−	0.673546i	−0.425750	−	0.904841i	$-0.639990\pi$
$401$	−11231.1	−	5408.59i	−1.39863	−	0.673546i	−0.972884	+	0.231294i	$0.925704\pi$
$402$	2919.45	+	3660.87i	0.362211	+	0.454199i
$403$	1183.90	+	944.126i	0.146338	+	0.116700i
$404$	−81.2028	+	168.619i	−0.00999998	+	0.0207652i
$405$	−1314.86			−0.161323
$406$	−5.75951	+	2.83460i	−0.000704039	+	0.000346500i
$407$	−233.887			−0.0284848
$408$	−1538.21	+	3194.13i	−0.186649	+	0.387581i
$409$	−5416.52	−	4319.53i	−0.654841	−	0.522218i	0.238761	−	0.971078i	$-0.423259\pi$
$409$	−5416.52	−	4319.53i	−0.654841	−	0.522218i	−0.893602	+	0.448860i	$0.851830\pi$
$410$	1477.48	+	1852.70i	0.177969	+	0.223167i
$411$	2224.74	+	1071.38i	0.267003	+	0.128582i
$412$	1978.38	−	952.736i	0.236572	−	0.113927i
$413$	6.16860	−	7.73517i	0.000734956	−	0.000921606i
$414$	−4074.10	+	929.886i	−0.483650	+	0.110390i
$415$	4164.17	+	18244.4i	0.492557	+	2.15803i
$416$	1480.43	−	1180.60i	0.174481	−	0.139144i
$417$	−5525.52	−	1261.16i	−0.648887	−	0.148104i
$418$			453.795i			0.0531001i
$419$	−1452.33	+	6363.08i	−0.169334	+	0.741902i	0.816931	+	0.576735i	$0.195673\pi$
$419$	−1452.33	+	6363.08i	−0.169334	+	0.741902i	−0.986266	+	0.165167i	$0.947184\pi$
$420$	1.01751	+	2.11288i	0.000118213	+	0.000245472i
$421$	−2273.39	−	4720.74i	−0.263179	−	0.546496i	0.726944	−	0.686696i	$-0.240940\pi$
$421$	−2273.39	−	4720.74i	−0.263179	−	0.546496i	−0.990123	+	0.140200i	$0.955225\pi$
$422$	2709.26	−	11870.1i	0.312523	−	1.36925i
$423$		−	4372.40i		−	0.502585i
$424$	−6665.07	−	1521.26i	−0.763407	−	0.174243i
$425$	5194.91	−	4142.80i	0.592918	−	0.472837i
$426$	538.705	+	2360.22i	0.0612685	+	0.268435i
$427$	4.06483	−	0.927772i	0.000460682	−	0.000105148i
$428$	−149.127	+	186.999i	−0.0168418	+	0.0211190i
$429$	88.8319	−	42.7792i	0.00999730	−	0.00481445i
$430$	−14013.4	−	6748.50i	−1.57160	−	0.756841i
$431$	−2847.95	−	3571.22i	−0.318285	−	0.399117i	0.596792	−	0.802396i	$-0.296442\pi$
$431$	−2847.95	−	3571.22i	−0.318285	−	0.399117i	−0.915077	+	0.403279i	$0.867870\pi$
$432$	−741.803	−	591.568i	−0.0826157	−	0.0658839i
$433$	2434.41	−	5055.11i	0.270186	−	0.561047i	−0.721091	−	0.692840i	$-0.756359\pi$
$433$	2434.41	−	5055.11i	0.270186	−	0.561047i	0.991277	+	0.131793i	$0.0420735\pi$
$434$	−3.81794			−0.000422274
$435$	6823.59	−	3358.30i	0.752106	−	0.370157i
$436$	−1233.93			−0.135538
$437$	−8552.78	+	17760.0i	−0.936235	+	1.94411i
$438$	−894.353	−	713.222i	−0.0975658	−	0.0778061i
$439$	−445.064	−	558.093i	−0.0483867	−	0.0606749i	0.757049	−	0.653358i	$-0.226640\pi$
$439$	−445.064	−	558.093i	−0.0483867	−	0.0606749i	−0.805436	+	0.592683i	$0.798069\pi$
$440$	−726.281	−	349.759i	−0.0786911	−	0.0378956i
$441$	−2781.29	+	1339.40i	−0.300323	+	0.144628i
$442$	−1122.85	+	1408.01i	−0.120833	+	0.151520i
$443$	−4360.77	+	995.318i	−0.467690	+	0.106747i	−0.449870	−	0.893094i	$-0.648530\pi$
$443$	−4360.77	+	995.318i	−0.467690	+	0.106747i	−0.0178198	+	0.999841i	$0.505673\pi$
$444$	−208.936	−	915.409i	−0.0223326	−	0.0978455i
$445$	−6255.61	+	4988.68i	−0.666391	+	0.531429i
$446$	10113.7	+	2308.39i	1.07377	+	0.245080i
$447$			7436.70i			0.786899i
$448$	−2.17904	+	9.54701i	−0.000229799	+	0.00100682i
$449$	−7626.53	−	15836.6i	−0.801599	−	1.66454i	−0.745870	−	0.666092i	$-0.767966\pi$
$449$	−7626.53	−	15836.6i	−0.801599	−	1.66454i	−0.0557296	−	0.998446i	$-0.517748\pi$
$450$	1245.41	+	2586.13i	0.130465	+	0.270914i
$451$	28.4390	−	124.599i	0.00296927	−	0.0130092i
$452$			5024.46i			0.522856i
$453$	−2904.43	−	662.917i	−0.301241	−	0.0687562i
$454$	−7006.86	+	5587.79i	−0.724335	+	0.577638i
$455$	1.05119	+	4.60556i	0.000108309	+	0.000474532i
$456$	−7043.13	+	1607.55i	−0.723300	+	0.165088i
$457$	11626.1	−	14578.6i	1.19003	−	1.49225i	0.361443	−	0.932394i	$-0.382284\pi$
$457$	11626.1	−	14578.6i	1.19003	−	1.49225i	0.828588	−	0.559859i	$-0.189145\pi$
$458$	3505.06	−	1687.95i	0.357599	−	0.172211i
$459$	−1167.01	−	562.000i	−0.118674	−	0.0571502i
$460$	−5505.57	−	6903.76i	−0.558040	−	0.699760i
$461$	6683.51	+	5329.92i	0.675232	+	0.538479i	0.899977	−	0.435938i	$-0.143583\pi$
$461$	6683.51	+	5329.92i	0.675232	+	0.538479i	−0.224745	+	0.974418i	$0.572155\pi$
$462$	−0.107860	+	0.223974i	−1.08617e−5	+	2.25545e-5i
$463$	−6626.86			−0.665176			−0.332588	−	0.943072i	$-0.607922\pi$
$463$	−6626.86			−0.665176			−0.332588	+	0.943072i	$0.607922\pi$
$464$	5360.59	+	1175.35i	0.536334	+	0.117595i
$465$	4523.31			0.451104
$466$	−4382.22	+	9099.78i	−0.435628	+	0.904591i
$467$	7509.76	+	5988.84i	0.744134	+	0.593427i	0.920429	−	0.390911i	$-0.127840\pi$
$467$	7509.76	+	5988.84i	0.744134	+	0.593427i	−0.176295	+	0.984337i	$0.556411\pi$
$468$	246.789	+	309.463i	0.0243757	+	0.0305661i
$469$	10.9014	+	5.24986i	0.00107331	+	0.000516878i
$470$	−16361.1	+	7879.11i	−1.60571	+	0.773269i
$471$	−3716.11	+	4659.85i	−0.363544	+	0.455870i
$472$	−13310.6	+	3038.05i	−1.29802	+	0.296266i
$473$	186.662	+	817.820i	0.0181453	+	0.0794998i
$474$	2262.28	−	1804.11i	0.219219	−	0.174821i
$475$	13200.4	+	3012.91i	1.27511	+	0.291035i
$476$			2.31020i			0.000222453i
$477$	555.806	−	2435.14i	0.0533513	−	0.233748i
$478$	6141.49	+	12752.9i	0.587667	+	1.22030i
$479$	−4575.75	−	9501.64i	−0.436474	−	0.906349i	−0.996940	−	0.0781708i	$-0.975092\pi$
$479$	−4575.75	−	9501.64i	−0.436474	−	0.906349i	0.560466	−	0.828178i	$-0.310622\pi$
$480$	1258.64	−	5514.45i	0.119685	−	0.524373i
$481$		−	1891.42i		−	0.179296i
$482$	12472.8	+	2846.83i	1.17867	+	0.269024i
$483$	−8.44257	+	6.73273i	−0.000795342	+	0.000634264i
$484$	−796.553	−	3489.93i	−0.0748078	−	0.327754i
$485$	4476.04	−	1021.63i	0.419065	−	0.0956489i
$486$	348.873	−	437.473i	0.0325622	−	0.0408317i
$487$	1030.39	−	496.209i	0.0958755	−	0.0461712i	−0.385331	−	0.922778i	$-0.625913\pi$
$487$	1030.39	−	496.209i	0.0958755	−	0.0461712i	0.481207	+	0.876607i	$0.340199\pi$
$488$	−5183.78	−	2496.38i	−0.480858	−	0.231569i
$489$	−4629.61	−	5805.35i	−0.428135	−	0.536865i
$490$	10023.8	+	7993.73i	0.924143	+	0.736980i
$491$	−3022.09	+	6275.44i	−0.277770	+	0.576795i	−0.992449	−	0.122657i	$-0.960858\pi$
$491$	−3022.09	+	6275.44i	−0.277770	+	0.576795i	0.714679	+	0.699452i	$0.246573\pi$
$492$	513.074			0.0470146
$493$	7491.70	−	64.1125i	0.684400	−	0.00585696i
$494$	−3669.79			−0.334234
$495$	127.787	−	265.353i	0.0116033	−	0.0240944i
$496$	2551.91	+	2035.08i	0.231016	+	0.184229i
$497$	3.90043	+	4.89099i	0.000352029	+	0.000441430i
$498$	−7175.08	−	3455.34i	−0.645628	−	0.310918i
$499$	9155.18	−	4408.90i	0.821327	−	0.395530i	0.0244715	−	0.999701i	$-0.492210\pi$
$499$	9155.18	−	4408.90i	0.821327	−	0.395530i	0.796855	+	0.604171i	$0.206495\pi$
$500$	−368.735	+	462.378i	−0.0329806	+	0.0413564i
$501$	1097.92	−	250.593i	0.0979071	−	0.0223467i
$502$	−3135.12	−	13735.9i	−0.278740	−	1.22124i
$503$	10992.8	−	8766.44i	0.974440	−	0.777090i	−0.000398966	−	1.00000i	$-0.500127\pi$
$503$	10992.8	−	8766.44i	0.974440	−	0.777090i	0.974839	+	0.222910i	$0.0715556\pi$
$504$	−3.85828	−	0.880627i	−0.000340995	−	7.78298e-5i
$505$			1126.16i			0.0992342i
$506$	208.289	−	912.572i	0.0182995	−	0.0801754i
$507$	−2513.78	−	5219.91i	−0.220199	−	0.457247i
$508$	−1249.79	−	2595.21i	−0.109154	−	0.226661i
$509$	−3503.92	+	15351.7i	−0.305125	+	1.33684i	0.557156	+	0.830408i	$0.311892\pi$
$509$	−3503.92	+	15351.7i	−0.305125	+	1.33684i	−0.862281	+	0.506431i	$0.830965\pi$
$510$			5379.57i			0.467081i
$511$	−2.88185	−	0.657763i	−0.000249482	−	5.69427e-5i
$512$	8605.33	−	6862.52i	0.742784	−	0.592350i
$513$	−587.332	−	2573.27i	−0.0505485	−	0.221467i
$514$	13324.9	−	3041.32i	1.14345	−	0.260986i
$515$	8238.14	−	10330.3i	0.704885	−	0.883898i
$516$	−3034.12	+	1461.15i	−0.258856	+	0.124658i
$517$	882.399	+	424.941i	0.0750636	+	0.0361487i
$518$	2.97334	+	3.72845i	0.000252203	+	0.000316253i
$519$	−6476.32	−	5164.70i	−0.547744	−	0.436811i
$520$	2828.46	−	5873.36i	0.238531	−	0.495315i
$521$	13970.0			1.17474			0.587369	−	0.809319i	$-0.300164\pi$
$521$	13970.0			1.17474			0.587369	+	0.809319i	$0.300164\pi$
$522$	−693.154	+	3161.37i	−0.0581198	+	0.265076i
$523$	13357.3			1.11677			0.558386	−	0.829581i	$-0.311421\pi$
$523$	13357.3			1.11677			0.558386	+	0.829581i	$0.311421\pi$
$524$	−3297.17	+	6846.65i	−0.274881	+	0.570796i
$525$	5.79904	+	4.62458i	0.000482078	+	0.000384444i
$526$	−3158.98	−	3961.24i	−0.261860	−	0.328362i
$527$	4014.67	+	1933.36i	0.331844	+	0.159808i
$528$	191.479	−	92.2113i	0.0157823	−	0.00760034i
$529$	17765.2	−	22276.8i	1.46011	−	1.83092i
$530$	−10113.7	+	2308.38i	−0.828886	+	0.189188i
$531$	−1109.98	−	4863.13i	−0.0907136	−	0.397442i
$532$	−3.68055	+	2.93514i	−0.000299947	+	0.000239200i
$533$	1007.62	+	229.983i	0.0818854	+	0.0186898i
$534$		−	3404.98i		−	0.275933i
$535$	−320.256	+	1403.13i	−0.0258801	+	0.113388i
$536$	−7244.60	−	15043.6i	−0.583804	−	1.21228i
$537$	681.959	+	1416.10i	0.0548021	+	0.113798i
$538$	−1422.90	+	6234.14i	−0.114025	+	0.499578i
$539$		−	691.467i		−	0.0552572i
$540$	1152.72	+	263.101i	0.0918616	+	0.0209668i
$541$	14000.2	−	11164.8i	1.11260	−	0.887270i	0.118205	−	0.992989i	$-0.462286\pi$
$541$	14000.2	−	11164.8i	1.11260	−	0.887270i	0.994396	+	0.105719i	$0.0337144\pi$
$542$	1227.20	+	5376.71i	0.0972559	+	0.426106i
$543$	9661.73	−	2205.23i	0.763581	−	0.174282i
$544$	3474.11	−	4356.39i	0.273807	−	0.343343i
$545$	−6689.62	+	3221.55i	−0.525783	+	0.253204i
$546$	−1.81125	−	0.872253i	−0.000141968	−	6.83681e-5i
$547$	3979.33	+	4989.93i	0.311049	+	0.390044i	0.912642	−	0.408759i	$-0.134038\pi$
$547$	3979.33	+	4989.93i	0.311049	+	0.390044i	−0.601593	+	0.798803i	$0.705467\pi$
$548$	−1736.02	−	1384.43i	−0.135327	−	0.107919i
$549$	912.074	−	1893.94i	0.0709041	−	0.147234i
$550$	−642.948			−0.0498461
$551$	9620.45	+	11854.1i	0.743820	+	0.916520i
$552$	14901.4			1.14900
$553$	3.24421	−	6.73667i	0.000249472	−	0.000518033i
$554$	−13182.2	−	10512.5i	−1.01094	−	0.806196i
$555$	−3522.67	−	4417.29i	−0.269422	−	0.337844i
$556$	4591.80	+	2211.30i	0.350244	+	0.168669i
$557$	−10425.4	+	5020.61i	−0.793067	+	0.381921i	−0.786135	−	0.618055i	$-0.787921\pi$
$557$	−10425.4	+	5020.61i	−0.793067	+	0.381921i	−0.00693242	+	0.999976i	$0.502207\pi$
$558$	−1200.17	+	1504.97i	−0.0910528	+	0.114177i
$559$	−6613.63	+	1509.52i	−0.500406	+	0.114214i
$560$	2.26586	+	9.92738i	0.000170982	+	0.000749122i
$561$	226.836	−	180.896i	0.0170713	−	0.0136139i
$562$	7408.41	+	1690.92i	0.556058	+	0.126917i
$563$			7592.70i			0.568373i	0.958769	+	0.284187i	$0.0917235\pi$
$563$			7592.70i			0.568373i	−0.958769	+	0.284187i	$0.908277\pi$
$564$	−874.910	+	3833.23i	−0.0653198	+	0.286185i
$565$	13117.9	+	27239.5i	0.976766	+	2.02828i
$566$	5179.85	+	10756.1i	0.384674	+	0.798784i
$567$	0.321745	−	1.40966i	2.38307e−5	−	0.000104409i
$568$		−	8632.76i		−	0.637716i
$569$	−6875.47	−	1569.28i	−0.506564	−	0.115620i	−0.0384016	−	0.999262i	$-0.512227\pi$
$569$	−6875.47	−	1569.28i	−0.506564	−	0.115620i	−0.468162	+	0.883642i	$0.655084\pi$
$570$	−8570.58	+	6834.81i	−0.629793	+	0.502243i
$571$	1633.91	+	7158.62i	0.119749	+	0.524657i	0.998847	+	0.0480141i	$0.0152892\pi$
$571$	1633.91	+	7158.62i	0.119749	+	0.524657i	−0.879097	+	0.476642i	$0.841854\pi$
$572$	−86.4379	+	19.7289i	−0.00631844	+	0.00144214i
$573$	−6123.52	+	7678.65i	−0.446446	+	0.559826i
$574$	−2.34781	+	1.13065i	−0.000170724	+	8.22165e-5i
$575$	−25162.8	−	12117.8i	−1.82498	−	0.878864i
$576$	3078.30	+	3860.06i	0.222678	+	0.279229i
$577$	−16967.4	−	13531.0i	−1.22420	−	0.976265i	−0.999999	−	0.00172154i	$-0.999452\pi$
$577$	−16967.4	−	13531.0i	−1.22420	−	0.976265i	−0.224199	−	0.974543i	$-0.571977\pi$
$578$	2609.19	−	5418.04i	0.187765	−	0.389898i
$579$	−13798.4			−0.990404
$580$	−6654.15	+	1578.80i	−0.476377	+	0.113027i
$581$	−20.5788			−0.00146945
$582$	−847.723	+	1760.32i	−0.0603767	+	0.125374i
$583$	437.422	+	348.832i	0.0310741	+	0.0247807i
$584$	2543.28	+	3189.17i	0.180208	+	0.225974i
$585$	2145.89	+	1033.40i	0.151661	+	0.0730359i
$586$	6583.28	−	3170.34i	0.464083	−	0.223491i
$587$	−10554.7	+	13235.2i	−0.742145	+	0.930620i	−0.999361	−	0.0357336i	$-0.988623\pi$
$587$	−10554.7	+	13235.2i	−0.742145	+	0.930620i	0.257216	+	0.966354i	$0.417195\pi$
$588$	2706.33	−	617.703i	0.189808	−	0.0433225i
$589$	2020.51	+	8852.43i	0.141347	+	0.619284i
$590$	−16197.2	+	12916.9i	−1.13022	+	0.901320i
$591$	−6933.61	−	1582.55i	−0.482590	−	0.110148i
$592$		−	4076.98i		−	0.283046i
$593$	2025.60	−	8874.75i	0.140273	−	0.614574i	−0.855098	−	0.518466i	$-0.826503\pi$
$593$	2025.60	−	8874.75i	0.140273	−	0.614574i	0.995371	−	0.0961083i	$-0.0306395\pi$
$594$	54.3810	+	112.923i	0.00375636	+	0.00780017i
$595$	6.03147	+	12.5245i	0.000415574	+	0.000862947i
$596$	1488.07	−	6519.67i	0.102271	−	0.448080i
$597$			9736.16i			0.667461i
$598$	7379.87	+	1684.41i	0.504658	+	0.115185i
$599$	14064.1	−	11215.8i	0.959341	−	0.765049i	−0.0126854	−	0.999920i	$-0.504038\pi$
$599$	14064.1	−	11215.8i	0.959341	−	0.765049i	0.972027	+	0.234870i	$0.0754666\pi$
$600$	−2277.61	−	9978.88i	−0.154972	−	0.678977i
$601$	−1296.09	+	295.825i	−0.0879680	+	0.0200781i	−0.266278	−	0.963896i	$-0.585794\pi$
$601$	−1296.09	+	295.825i	−0.0879680	+	0.0200781i	0.178310	+	0.983974i	$0.442937\pi$
$602$	10.6641	−	13.3724i	0.000721988	−	0.000905345i
$603$	5496.30	−	2646.88i	0.371189	−	0.178755i
$604$	2413.63	+	1162.34i	0.162598	+	0.0783031i
$605$	−13429.9	−	16840.6i	−0.902487	−	1.13168i
$606$	−374.688	−	298.804i	−0.0251166	−	0.0200298i
$607$	−12542.1	+	26043.9i	−0.838661	+	1.74150i	−0.187940	+	0.982180i	$0.560181\pi$
$607$	−12542.1	+	26043.9i	−0.838661	+	1.74150i	−0.650721	+	0.759317i	$0.725533\pi$
$608$	11354.4			0.757370
$609$	1.93070	+	8.13733i	0.000128466	+	0.000541447i
$610$	−8730.53			−0.579490
$611$	−3436.45	+	7135.87i	−0.227535	+	0.472482i
$612$	910.645	+	726.215i	0.0601481	+	0.0479665i
$613$	−13595.3	−	17048.0i	−0.895775	−	1.12327i	−0.991789	−	0.127886i	$-0.959181\pi$
$613$	−13595.3	−	17048.0i	−0.895775	−	1.12327i	0.0960142	−	0.995380i	$-0.469391\pi$
$614$	5621.21	+	2707.03i	0.369468	+	0.177926i
$615$	2781.57	−	1339.54i	0.182380	−	0.0878297i
$616$	0.552696	−	0.693058i	3.61505e−5	−	4.53314e-5i
$617$	21271.3	−	4855.04i	1.38793	−	0.316786i	0.537672	−	0.843154i	$-0.319304\pi$
$617$	21271.3	−	4855.04i	1.38793	−	0.316786i	0.850256	+	0.526369i	$0.176447\pi$
$618$	1251.21	+	5481.90i	0.0814417	+	0.356819i
$619$	−9720.07	+	7751.50i	−0.631151	+	0.503326i	−0.886019	−	0.463650i	$-0.846540\pi$
$619$	−9720.07	+	7751.50i	−0.631151	+	0.503326i	0.254867	+	0.966976i	$0.417968\pi$
$620$	−3965.53	−	905.107i	−0.256870	−	0.0586290i
$621$			5444.38i			0.351812i
$622$	2979.31	−	13053.2i	0.192057	−	0.841458i
$623$	−3.81761	−	7.92734i	−0.000245504	−	0.000509795i
$624$	745.703	+	1548.47i	0.0478398	+	0.0993403i
$625$	3060.66	−	13409.6i	0.195882	−	0.858216i
$626$		−	15391.9i		−	0.982720i
$627$	576.396	+	131.559i	0.0367130	+	0.00837950i
$628$	4190.30	−	3341.65i	0.266260	−	0.212335i
$629$	−1238.50	−	5426.24i	−0.0785094	−	0.343972i
$630$	−5.85461	+	1.33628i	−0.000370243	+	8.45055e-5i
$631$	−9395.70	+	11781.8i	−0.592768	+	0.743308i	−0.984231	−	0.176886i	$-0.943398\pi$
$631$	−9395.70	+	11781.8i	−0.592768	+	0.743308i	0.391463	+	0.920194i	$0.371969\pi$
$632$	−9296.34	+	4476.88i	−0.585108	+	0.281773i
$633$	−14291.5	−	6882.44i	−0.897374	−	0.432153i
$634$	2353.13	+	2950.73i	0.147405	+	0.184840i
$635$	−13551.2	−	10806.7i	−0.846869	−	0.675355i
$636$	−974.537	+	2023.65i	−0.0607593	+	0.126168i
$637$	5591.82			0.347812
$638$	−570.635	−	447.131i	−0.0354101	−	0.0277462i
$639$	3154.06			0.195262
$640$	2352.47	−	4884.95i	0.145296	−	0.301710i
$641$	−8778.39	−	7000.53i	−0.540914	−	0.431364i	0.314540	−	0.949244i	$-0.398150\pi$
$641$	−8778.39	−	7000.53i	−0.540914	−	0.431364i	−0.855453	+	0.517880i	$0.826721\pi$
$642$	−381.869	−	478.848i	−0.0234753	−	0.0294371i
$643$	6877.63	+	3312.09i	0.421815	+	0.203136i	0.632736	−	0.774368i	$-0.281932\pi$
$643$	6877.63	+	3312.09i	0.421815	+	0.203136i	−0.210921	+	0.977503i	$0.567646\pi$
$644$	8.74871	−	4.21316i	0.000535322	−	0.000257798i
$645$	−12634.3	+	15843.0i	−0.771282	+	0.967157i
$646$	−10528.2	+	2402.99i	−0.641216	+	0.146353i
$647$	4245.88	+	18602.4i	0.257995	+	1.13035i	0.923391	+	0.383860i	$0.125405\pi$
$647$	4245.88	+	18602.4i	0.257995	+	1.13035i	−0.665396	+	0.746490i	$0.731737\pi$
$648$	−1559.99	+	1244.05i	−0.0945711	+	0.0754179i
$649$	1089.31	+	248.628i	0.0658847	+	0.0150377i
$650$		−	5199.45i		−	0.313753i
$651$	−1.10685	+	4.84943i	−6.66373e−5	+	0.000291957i
$652$	2897.08	+	6015.86i	0.174016	+	0.361348i
$653$	−2889.83	−	6000.79i	−0.173182	−	0.359616i	0.796253	−	0.604963i	$-0.206812\pi$
$653$	−2889.83	−	6000.79i	−0.173182	−	0.359616i	−0.969435	+	0.245348i	$0.921098\pi$
$654$	703.107	−	3080.51i	0.0420392	−	0.184186i
$655$			45726.6i			2.72776i
$656$	2171.95	+	495.733i	0.129269	+	0.0295047i
$657$	−1165.19	+	929.211i	−0.0691910	+	0.0551780i
$658$	−4.44361	−	19.4687i	−0.000263268	−	0.00115345i
$659$	22271.6	−	5083.35i	1.31651	−	0.300484i	0.494111	−	0.869399i	$-0.335493\pi$
$659$	22271.6	−	5083.35i	1.31651	−	0.300484i	0.822397	+	0.568914i	$0.192636\pi$
$660$	−165.127	+	207.062i	−0.00973870	+	0.0122119i
$661$	−24249.9	+	11678.2i	−1.42695	+	0.687183i	−0.978428	−	0.206589i	$-0.933764\pi$
$661$	−24249.9	+	11678.2i	−1.42695	+	0.687183i	−0.448522	+	0.893772i	$0.648049\pi$
$662$	16264.4	+	7832.51i	0.954884	+	0.459848i
$663$	1462.88	+	1834.40i	0.0856919	+	0.107454i
$664$	22202.4	+	17705.8i	1.29762	+	1.03482i
$665$	−12.2906	+	25.5217i	−0.000716706	+	0.00148825i
$666$	2404.37			0.139891
$667$	−13905.6	−	28254.1i	−0.807235	−	1.64019i
$668$	−1012.68			−0.0586552
$669$	5864.11	−	12176.9i	0.338893	−	0.703719i
$670$	−19808.8	−	15797.0i	−1.14221	−	0.910882i
$671$	293.577	+	368.133i	0.0168903	+	0.0211798i
$672$	5.60404	+	2.69876i	0.000321697	+	0.000154921i
$673$	14960.4	−	7204.53i	0.856878	−	0.412651i	0.0467523	−	0.998907i	$-0.485113\pi$
$673$	14960.4	−	7204.53i	0.856878	−	0.412651i	0.810126	+	0.586256i	$0.199399\pi$
$674$	−14696.2	+	18428.4i	−0.839874	+	1.05317i
$675$	3645.88	−	832.147i	0.207896	−	0.0474509i
$676$	1159.30	+	5079.24i	0.0659594	+	0.288987i
$677$	−8895.44	+	7093.88i	−0.504992	+	0.402718i	−0.842576	−	0.538578i	$-0.818962\pi$
$677$	−8895.44	+	7093.88i	−0.504992	+	0.402718i	0.337584	+	0.941296i	$0.390390\pi$
$678$	−12543.6	−	2862.99i	−0.710521	−	0.162172i
$679$			5.04875i			0.000285351i
$680$	4268.62	−	18702.0i	0.240727	−	1.05469i
$681$	5066.09	+	10519.8i	0.285070	+	0.591955i
$682$	−187.079	−	388.473i	−0.0105038	−	0.0218114i
$683$	−3457.94	+	15150.2i	−0.193726	+	0.848767i	0.780852	+	0.624716i	$0.214785\pi$
$683$	−3457.94	+	15150.2i	−0.193726	+	0.848767i	−0.974577	+	0.224051i	$0.928072\pi$
$684$			2373.48i			0.132679i
$685$	−13026.1	−	2973.12i	−0.726572	−	0.165835i
$686$	−22.0458	+	17.5809i	−0.00122698	+	0.000978487i
$687$	−1127.83	−	4941.36i	−0.0626340	−	0.274417i
$688$	−14255.8	+	3253.79i	−0.789967	+	0.180305i
$689$	−2820.97	+	3537.39i	−0.155980	+	0.195593i
$690$	20372.4	−	9810.83i	1.12401	−	0.541292i
$691$	11673.3	+	5621.56i	0.642653	+	0.309485i	0.726678	−	0.686978i	$-0.241063\pi$
$691$	11673.3	+	5621.56i	0.642653	+	0.309485i	−0.0840251	+	0.996464i	$0.526778\pi$
$692$	4644.27	+	5823.73i	0.255128	+	0.319921i
$693$	0.253215	+	0.201932i	1.38800e−5	+	1.10689e-5i
$694$	−9126.59	+	18951.6i	−0.499194	+	1.03659i
$695$	30667.2			1.67377
$696$	4918.26	−	10440.5i	0.267854	−	0.568600i
$697$	3041.34			0.165278
$698$	−7548.60	+	15674.8i	−0.409339	+	0.850001i
$699$	10287.8	+	8204.27i	0.556683	+	0.443940i
$700$	−4.15858	−	5.21469i	−0.000224542	−	0.000281567i
$701$	180.054	+	86.7095i	0.00970121	+	0.00467186i	0.438728	−	0.898620i	$-0.355429\pi$
$701$	180.054	+	86.7095i	0.00970121	+	0.00467186i	−0.429027	+	0.903292i	$0.641143\pi$
$702$	−913.199	+	439.773i	−0.0490975	+	0.0236441i
$703$	7071.41	−	8867.27i	0.379379	−	0.475726i
$704$	−1078.18	+	246.086i	−0.0577205	+	0.0131743i
$705$	5264.58	+	23065.6i	0.281242	+	1.23220i
$706$	13241.7	−	10559.9i	0.705887	−	0.562926i
$707$	−1.20735	−	0.275569i	−6.42249e−5	−	1.46589e-5i
$708$			4485.55i			0.238104i
$709$	650.542	−	2850.21i	0.0344592	−	0.150976i	−0.954771	−	0.297341i	$-0.903900\pi$
$709$	650.542	−	2850.21i	0.0344592	−	0.150976i	0.989231	+	0.146365i	$0.0467574\pi$
$710$	−5683.65	−	11802.2i	−0.300427	−	0.623844i
$711$	−1635.67	−	3396.50i	−0.0862762	−	0.179154i
$712$	−2701.81	+	11837.4i	−0.142212	+	0.623070i
$713$		−	18729.4i		−	0.983764i
$714$	−5.76742	−	1.31638i	−0.000302297	−	6.89974e-5i
$715$	−417.105	+	332.630i	−0.0218166	+	0.0173981i
$716$	−314.506	−	1377.94i	−0.0164157	−	0.0719218i
$717$	17978.8	−	4103.55i	0.936447	−	0.213738i
$718$	2760.07	−	3461.01i	0.143461	−	0.179894i
$719$	13149.1	−	6332.28i	0.682029	−	0.328448i	−0.0605892	−	0.998163i	$-0.519298\pi$
$719$	13149.1	−	6332.28i	0.682029	−	0.328448i	0.742618	+	0.669715i	$0.233584\pi$
$720$	4625.50	+	2227.52i	0.239420	+	0.115298i
$721$	9.05921	+	11.3599i	0.000467937	+	0.000586775i
$722$	−4856.31	−	3872.78i	−0.250323	−	0.199626i
$723$	7231.92	−	15017.2i	0.372003	−	0.772471i
$724$	−8911.58			−0.457454
$725$	−16795.2	+	13630.5i	−0.860357	+	0.698240i
$726$	9166.49			0.468596
$727$	9549.00	−	19828.7i	0.487143	−	1.01156i	−0.502036	−	0.864847i	$-0.667416\pi$
$727$	9549.00	−	19828.7i	0.487143	−	1.01156i	0.989179	−	0.146715i	$-0.0468701\pi$
$728$	5.60469	+	4.46959i	0.000285335	+	0.000227547i
$729$	−454.524	−	569.955i	−0.0230922	−	0.0289567i
$730$	5576.72	+	2685.61i	0.282745	+	0.136163i
$731$	−17985.3	+	8661.25i	−0.909999	+	0.438232i
$732$	−1178.58	+	1477.89i	−0.0595103	+	0.0746236i
$733$	−11692.8	+	2668.80i	−0.589198	+	0.134480i	−0.506717	−	0.862112i	$-0.669141\pi$
$733$	−11692.8	+	2668.80i	−0.589198	+	0.134480i	−0.0824801	+	0.996593i	$0.526284\pi$
$734$	−1936.42	−	8483.99i	−0.0973766	−	0.426635i
$735$	13059.4	−	10414.5i	0.655378	−	0.522646i
$736$	−22833.4	−	5211.58i	−1.14355	−	0.261007i
$737$			1366.46i			0.0682960i
$738$	−292.355	+	1280.89i	−0.0145823	+	0.0638892i
$739$	7430.13	+	15428.8i	0.369853	+	0.768009i	0.999964	−	0.00849692i	$-0.00270469\pi$
$739$	7430.13	+	15428.8i	0.369853	+	0.768009i	−0.630110	+	0.776506i	$0.716990\pi$
$740$	2204.39	+	4577.47i	0.109507	+	0.227393i
$741$	−1063.90	+	4661.26i	−0.0527441	+	0.231087i
$742$		−	11.4077i		−	0.000564406i
$743$	−4294.80	−	980.261i	−0.212061	−	0.0484015i	0.115171	−	0.993346i	$-0.463258\pi$
$743$	−4294.80	−	980.261i	−0.212061	−	0.0484015i	−0.327231	+	0.944944i	$0.606116\pi$
$744$	5366.58	−	4279.70i	0.264447	−	0.210889i
$745$	−8954.15	−	39230.7i	−0.440342	−	1.92926i
$746$	13472.1	−	3074.91i	0.661189	−	0.150912i
$747$	−6468.97	+	8111.84i	−0.316851	+	0.397318i
$748$	−235.061	+	113.200i	−0.0114902	+	0.00553340i
$749$	−1.42593	−	0.686690i	−6.95624e−5	−	3.34995e-5i
$750$	−944.220	−	1184.01i	−0.0459707	−	0.0576455i
$751$	−11900.6	−	9490.42i	−0.578241	−	0.461132i	0.290171	−	0.956975i	$-0.406288\pi$
$751$	−11900.6	−	9490.42i	−0.578241	−	0.461132i	−0.868412	+	0.495843i	$0.834859\pi$
$752$	−7407.34	+	15381.5i	−0.359199	+	0.745885i
$753$	−18355.8			−0.888343
$754$	3615.90	−	4614.66i	0.174646	−	0.222886i
$755$	16119.9			0.777036
$756$	−0.564140	+	1.17145i	−2.71397e−5	+	5.63561e-5i
$757$	−27312.0	−	21780.6i	−1.31132	−	1.04575i	−0.995284	−	0.0969993i	$-0.969076\pi$
$757$	−27312.0	−	21780.6i	−1.31132	−	1.04575i	−0.316039	−	0.948746i	$-0.602353\pi$
$758$	15500.9	+	19437.5i	0.742768	+	0.931401i
$759$	−1098.74	−	529.123i	−0.0525449	−	0.0253043i
$760$	35218.9	−	16960.5i	1.68095	−	0.809505i
$761$	18099.8	−	22696.4i	0.862177	−	1.08114i	−0.133754	−	0.991015i	$-0.542703\pi$
$761$	18099.8	−	22696.4i	0.862177	−	1.08114i	0.995931	−	0.0901212i	$-0.0287255\pi$
$762$	7191.09	−	1641.32i	0.341871	−	0.0780299i
$763$	−1.81687	−	7.96023i	−8.62060e−5	−	0.000377693i
$764$	6904.90	−	5506.47i	0.326977	−	0.260756i
$765$	6832.96	+	1559.58i	0.322936	+	0.0737081i
$766$		−	9673.08i		−	0.456269i
$767$	−2010.63	+	8809.13i	−0.0946539	+	0.414706i
$768$	−4711.35	−	9783.22i	−0.221362	−	0.459664i
$769$	13295.3	+	27607.9i	0.623458	+	1.29462i	0.938412	+	0.345517i	$0.112297\pi$
$769$	13295.3	+	27607.9i	0.623458	+	1.29462i	−0.314954	+	0.949107i	$0.601989\pi$
$770$	0.299317	−	1.31139i	1.40086e−5	−	6.13758e-5i
$771$		−	17806.6i		−	0.831761i
$772$	12096.9	+	2761.05i	0.563962	+	0.128721i
$773$	−13687.2	+	10915.2i	−0.636862	+	0.507881i	−0.887864	−	0.460106i	$-0.847811\pi$
$773$	−13687.2	+	10915.2i	−0.636862	+	0.507881i	0.251002	+	0.967987i	$0.419240\pi$
$774$	−1918.90	−	8407.26i	−0.0891131	−	0.390430i
$775$	−12542.3	+	2862.71i	−0.581335	+	0.132686i
$776$	4343.89	−	5447.07i	0.200949	−	0.251983i
$777$	5.59776	−	2.69574i	0.000258454	−	0.000124465i
$778$	3423.02	+	1648.44i	0.157739	+	0.0759633i
$779$	3864.06	+	4845.38i	0.177721	+	0.222855i
$780$	−1674.49	−	1335.36i	−0.0768671	−	0.0612995i
$781$	−306.534	+	636.524i	−0.0140444	+	0.0291634i
$782$	22274.9			1.01861
$783$	3814.53	+	1796.93i	0.174100	+	0.0820141i
$784$	12053.3			0.549074
$785$	13992.8	−	29056.4i	0.636211	−	1.32111i
$786$	−15213.9	−	12132.7i	−0.690410	−	0.550584i
$787$	−22002.4	−	27590.2i	−0.996572	−	1.24966i	−0.968229	−	0.250064i	$-0.919548\pi$
$787$	−22002.4	−	27590.2i	−0.996572	−	1.24966i	−0.0283431	−	0.999598i	$-0.509023\pi$
$788$	5761.95	+	2774.81i	0.260483	+	0.125442i
$789$	−5947.26	+	2864.05i	−0.268350	+	0.129230i
$790$	−9761.92	+	12241.1i	−0.439638	+	0.551288i
$791$	−32.4134	+	7.39814i	−0.00145700	+	0.000332551i
$792$	−99.4521	−	435.728i	−0.00446196	−	0.0195491i
$793$	−2977.06	+	2374.12i	−0.133314	+	0.106315i
$794$	17983.2	+	4104.54i	0.803776	+	0.183457i
$795$			13515.3i			0.602941i
$796$	1948.19	−	8535.57i	0.0867484	−	0.380070i
$797$	−18209.4	−	37812.2i	−0.809298	−	1.68053i	−0.729770	−	0.683692i	$-0.760373\pi$
$797$	−18209.4	−	37812.2i	−0.809298	−	1.68053i	−0.0795279	−	0.996833i	$-0.525341\pi$
$798$	−5.23037	−	10.8610i	−0.000232021	−	0.000481797i
$799$	−5186.18	+	22722.1i	−0.229629	+	1.00607i
$800$			16087.2i			0.710960i
$801$	−4324.91	−	987.132i	−0.190778	−	0.0435438i
$802$	−22441.7	+	17896.7i	−0.988085	+	0.787972i
$803$	−74.2833	−	325.456i	−0.00326451	−	0.0143027i
$804$	−5348.18	+	1220.69i	−0.234597	+	0.0535452i
$805$	36.4304	−	45.6823i	0.00159504	−	0.00200011i
$806$	3141.54	−	1512.88i	0.137290	−	0.0661155i
$807$	7505.90	+	3614.65i	0.327410	+	0.157673i
$808$	1065.51	+	1336.10i	0.0463915	+	0.0581731i
$809$	−12295.6	−	9805.45i	−0.534353	−	0.426133i	0.318777	−	0.947830i	$-0.396728\pi$
$809$	−12295.6	−	9805.45i	−0.534353	−	0.426133i	−0.853131	+	0.521697i	$0.825299\pi$
$810$	−1313.67	+	2727.86i	−0.0569846	+	0.118330i
$811$	−2080.51			−0.0900820			−0.0450410	−	0.998985i	$-0.514342\pi$
$811$	−2080.51			−0.0900820			−0.0450410	+	0.998985i	$0.514342\pi$
$812$	−0.0643566	−	7.52023i	−2.78137e−6	−	0.000325010i
$813$	7185.11			0.309954
$814$	−233.674	+	485.230i	−0.0100618	+	0.0208935i
$815$	31412.4	+	25050.6i	1.35010	+	1.07667i
$816$	3153.27	+	3954.08i	0.135278	+	0.169633i
$817$	−36649.4	−	17649.4i	−1.56940	−	0.755783i
$818$	−14373.1	+	6921.70i	−0.614355	+	0.295858i
$819$	−1.63301	+	2.04772i	−6.96726e−5	+	8.73666e-5i
$820$	−2706.61	+	617.767i	−0.115267	+	0.0263090i
$821$	1579.25	+	6919.15i	0.0671331	+	0.294129i	0.997339	−	0.0729101i	$-0.0232286\pi$
$821$	1579.25	+	6919.15i	0.0671331	+	0.294129i	−0.930205	+	0.367039i	$0.880371\pi$
$822$	4445.43	−	3545.11i	0.188628	−	0.150426i
$823$	−843.110	−	192.434i	−0.0357096	−	0.00815048i	0.204629	−	0.978840i	$-0.434401\pi$
$823$	−843.110	−	192.434i	−0.0357096	−	0.00815048i	−0.240338	+	0.970689i	$0.577258\pi$
$824$		−	20050.6i		−	0.847690i
$825$	−186.396	+	816.653i	−0.00786601	+	0.0344633i
$826$	−9.88468	−	20.5257i	−0.000416382	−	0.000864627i
$827$	−1335.01	−	2772.17i	−0.0561339	−	0.116563i	0.871015	−	0.491257i	$-0.163462\pi$
$827$	−1335.01	−	2772.17i	−0.0561339	−	0.116563i	−0.927149	+	0.374693i	$0.877748\pi$
$828$	1089.41	−	4773.02i	0.0457242	−	0.200331i
$829$		−	29131.8i		−	1.22049i	−0.792211	−	0.610247i	$-0.791070\pi$
$829$		−	29131.8i		−	1.22049i	0.792211	−	0.610247i	$-0.208930\pi$
$830$	42011.0	+	9588.73i	1.75689	+	0.400999i
$831$	−17174.3	+	13696.0i	−0.716930	+	0.571732i
$832$	−1990.08	−	8719.09i	−0.0829248	−	0.363317i
$833$	16042.3	−	3661.54i	0.667265	−	0.152299i
$834$	−8136.96	+	10203.4i	−0.337842	+	0.423640i
$835$	−5490.11	+	2643.90i	−0.227537	+	0.109576i
$836$	−478.995	−	230.672i	−0.0198163	−	0.00954301i
$837$	1563.63	+	1960.73i	0.0645722	+	0.0809710i
$838$	11750.1	+	9370.36i	0.484367	+	0.386269i
$839$	−3678.86	+	7639.22i	−0.151380	+	0.314345i	−0.962844	−	0.270058i	$-0.912957\pi$
$839$	−3678.86	+	7639.22i	−0.151380	+	0.314345i	0.811464	+	0.584403i	$0.198671\pi$
$840$	21.4138			0.000879580
$841$	−24385.4	+	417.402i	−0.999854	+	0.0171143i
$842$	−12065.2			−0.493815
$843$	4295.51	−	8919.72i	0.175499	−	0.364427i
$844$	11152.1	+	8893.47i	0.454822	+	0.362708i
$845$	19545.9	+	24509.8i	0.795739	+	0.997826i
$846$	−9071.14	−	4368.43i	−0.368643	−	0.177529i
$847$	21.3411	−	10.2773i	0.000865746	−	0.000416921i
$848$	−6080.66	+	7624.90i	−0.246239	+	0.308774i
$849$	15163.7	−	3461.02i	0.612977	−	0.139908i
$850$	−3404.62	−	14916.6i	−0.137385	−	0.601923i
$851$	−18290.5	+	14586.2i	−0.736768	+	0.587553i
$852$	−2765.13	−	631.122i	−0.111187	−	0.0253778i
$853$			6859.48i			0.275339i	0.990478	+	0.137670i	$0.0439612\pi$
$853$			6859.48i			0.275339i	−0.990478	+	0.137670i	$0.956039\pi$
$854$	2.13635	−	9.35998i	8.56025e−5	−	0.000375049i
$855$	6196.69	+	12867.6i	0.247862	+	0.514691i
$856$	947.605	+	1967.72i	0.0378370	+	0.0785694i
$857$	−155.865	+	682.888i	−0.00621265	+	0.0272194i	−0.977939	−	0.208890i	$-0.933015\pi$
$857$	−155.865	+	682.888i	−0.00621265	+	0.0272194i	0.971727	+	0.236109i	$0.0758722\pi$
$858$		−	227.034i		−	0.00903359i
$859$	4709.24	+	1074.85i	0.187051	+	0.0426932i	0.315020	−	0.949085i	$-0.397989\pi$
$859$	4709.24	+	1074.85i	0.187051	+	0.0426932i	−0.127969	+	0.991778i	$0.540846\pi$
$860$	14246.5	−	11361.2i	0.564887	−	0.450482i
$861$	0.755463	+	3.30990i	2.99026e−5	+	0.000131012i
$862$	−10254.3	+	2340.49i	−0.405179	+	0.0924794i
$863$	1462.38	−	1833.76i	0.0576824	−	0.0723314i	−0.752153	−	0.658988i	$-0.770985\pi$
$863$	1462.38	−	1833.76i	0.0576824	−	0.0723314i	0.809836	+	0.586657i	$0.199556\pi$
$864$	2825.45	−	1360.67i	0.111254	−	0.0535773i
$865$	40383.0	+	19447.4i	1.58736	+	0.764430i
$866$	−8055.31	−	10101.0i	−0.316086	−	0.396360i
$867$	−6125.41	−	4884.85i	−0.239942	−	0.191347i
$868$	1.94072	−	4.02996i	7.58900e−5	−	0.000157587i
$869$	844.418			0.0329631
$870$	−149.862	−	17511.7i	−0.00583999	−	0.682417i
$871$	−11050.4			−0.429884
$872$	−4888.70	+	10151.5i	−0.189853	+	0.394235i
$873$	1990.14	+	1587.08i	0.0771546	+	0.0615287i
$874$	28300.6	+	35487.8i	1.09529	+	1.37345i
$875$	−3.52579	−	1.69793i	−0.000136221	−	6.56006e-5i
$876$	1207.44	−	581.475i	0.0465705	−	0.0224272i
$877$	17911.2	−	22460.0i	0.689646	−	0.864789i	−0.306556	−	0.951852i	$-0.599177\pi$
$877$	17911.2	−	22460.0i	0.689646	−	0.864789i	0.996203	+	0.0870633i	$0.0277482\pi$
$878$	−1602.50	+	365.760i	−0.0615965	+	0.0140590i
$879$	−2118.32	−	9280.99i	−0.0812848	−	0.356132i
$880$	−899.077	+	716.990i	−0.0344408	+	0.0274656i
$881$	13142.2	+	2999.62i	0.502579	+	0.114710i	0.466292	−	0.884631i	$-0.345590\pi$
$881$	13142.2	+	2999.62i	0.502579	+	0.114710i	0.0362872	+	0.999341i	$0.488447\pi$
$882$			7108.34i			0.271372i
$883$	−1922.57	+	8423.31i	−0.0732724	+	0.321027i	−0.998260	−	0.0589707i	$-0.981218\pi$
$883$	−1922.57	+	8423.31i	−0.0732724	+	0.321027i	0.924987	+	0.379998i	$0.124075\pi$
$884$	−915.433	−	1900.92i	−0.0348296	−	0.0723244i
$885$	11710.9	+	24317.9i	0.444811	+	0.923659i
$886$	−2291.89	+	10041.4i	−0.0869047	+	0.380754i
$887$		−	8625.76i		−	0.326522i	−0.986583	−	0.163261i	$-0.947799\pi$
$887$		−	8625.76i		−	0.326522i	0.986583	−	0.163261i	$-0.0522012\pi$
$888$	−8358.80	−	1907.84i	−0.315882	−	0.0720979i
$889$	14.9018	−	11.8838i	0.000562193	−	0.000448334i
$890$	4099.77	+	17962.3i	0.154410	+	0.676512i
$891$	159.197	−	36.3357i	0.00598575	−	0.00136621i
$892$	−7577.58	+	9501.98i	−0.284435	+	0.356670i
$893$	−42789.4	+	20606.3i	−1.60346	+	0.772188i
$894$	15428.4	+	7429.94i	0.577186	+	0.277958i
$895$	−5302.59	−	6649.23i	−0.198040	−	0.248334i
$896$	4.66149	+	3.71742i	0.000173805	+	0.000138605i
$897$	4278.97	−	8885.36i	0.159276	−	0.330740i
$898$	−40474.9			−1.50408
$899$	−13122.5	−	6181.70i	−0.486831	−	0.229334i
$900$	−3362.81			−0.124548
$901$	−5776.73	+	11995.5i	−0.213597	+	0.443539i
$902$	−230.085	−	183.487i	−0.00849334	−	0.00677321i
$903$	−13.8936	−	17.4220i	−0.000512015	−	0.000642046i
$904$	41335.9	+	19906.3i	1.52081	+	0.732384i
$905$	−48313.1	+	23266.4i	−1.77457	+	0.854586i
$906$	−4277.10	+	5363.32i	−0.156840	+	0.196671i
$907$	−25658.4	+	5856.35i	−0.939329	+	0.214396i	−0.664663	−	0.747144i	$-0.731425\pi$
$907$	−25658.4	+	5856.35i	−0.939329	+	0.214396i	−0.274667	+	0.961539i	$0.588568\pi$
$908$	−2336.38	−	10236.3i	−0.0853914	−	0.374124i
$909$	−488.157	+	389.292i	−0.0178120	+	0.0142046i
$910$	10.6051	+	2.42055i	0.000386325	+	8.81762e-5i
$911$		−	9945.06i		−	0.361684i	−0.983512	−	0.180842i	$-0.942118\pi$
$911$		−	9945.06i		−	0.361684i	0.983512	−	0.180842i	$-0.0578823\pi$
$912$	−2293.26	+	10047.4i	−0.0832647	+	0.364806i
$913$	−1008.36	−	2093.88i	−0.0365518	−	0.0759006i
$914$	−18629.8	−	38685.2i	−0.674201	−	1.39999i
$915$	−2531.05	+	11089.3i	−0.0914469	+	0.400655i
$916$			4557.71i			0.164401i
$917$	−49.0233	−	11.1893i	−0.00176542	−	0.000402946i
$918$	−2331.89	+	1859.62i	−0.0838387	+	0.0668591i
$919$	7717.36	+	33812.0i	0.277010	+	1.21366i	0.901552	+	0.432670i	$0.142428\pi$
$919$	7717.36	+	33812.0i	0.277010	+	1.21366i	−0.624542	+	0.780991i	$0.714714\pi$
$920$	−78609.3	+	17942.1i	−2.81703	+	0.642970i
$921$	5068.02	−	6355.09i	0.181321	−	0.227370i
$922$	17735.1	−	8540.76i	0.633485	−	0.305070i
$923$	−5147.50	−	2478.91i	−0.183567	−	0.0884011i
$924$	−0.181584	−	0.227700i	−6.46503e−6	−	8.10689e-6i
$925$	12563.4	+	10019.0i	0.446574	+	0.356131i
$926$	−6620.84	+	13748.3i	−0.234962	+	0.487903i
$927$	7325.68			0.259554
$928$	−11187.7	+	14277.8i	−0.395747	+	0.505057i
$929$	−28825.4			−1.01801			−0.509004	−	0.860764i	$-0.669986\pi$
$929$	−28825.4			−1.01801			−0.509004	+	0.860764i	$0.669986\pi$
$930$	4519.20	−	9384.22i	0.159345	−	0.330882i
$931$	26215.4	+	20906.1i	0.922851	+	0.735949i
$932$	−7377.56	−	9251.16i	−0.259292	−	0.325142i
$933$	−15716.1	−	7568.47i	−0.551470	−	0.265574i
$934$	19927.6	−	9596.63i	0.698127	−	0.336200i
$935$	−978.816	+	1227.40i	−0.0342361	+	0.0429307i
$936$	3523.69	−	804.259i	0.123051	−	0.0280855i
$937$	−6736.42	−	29514.2i	−0.234866	−	1.02901i	−0.945543	−	0.325496i	$-0.894469\pi$
$937$	−6736.42	−	29514.2i	−0.234866	−	1.02901i	0.710678	−	0.703518i	$-0.248388\pi$
$938$	21.7831	−	17.3714i	0.000758255	−	0.000604688i
$939$	−19550.3	−	4462.23i	−0.679446	−	0.155079i
$940$		−	21274.8i		−	0.738200i
$941$	230.813	−	1011.26i	0.00799607	−	0.0350331i	−0.970773	−	0.240002i	$-0.922852\pi$
$941$	230.813	−	1011.26i	0.00799607	−	0.0350331i	0.978769	+	0.204968i	$0.0657092\pi$
$942$	5954.76	+	12365.2i	0.205962	+	0.427685i
$943$	−5546.55	−	11517.5i	−0.191538	−	0.397733i
$944$	−4333.94	+	18988.3i	−0.149426	+	0.654677i
$945$			7.82374i			0.000269319i
$946$	1883.17	+	429.822i	0.0647222	+	0.0147724i
$947$	40444.8	−	32253.6i	1.38783	−	1.10676i	0.406673	−	0.913574i	$-0.366689\pi$
$947$	40444.8	−	32253.6i	1.38783	−	1.10676i	0.981162	−	0.193187i	$-0.0618824\pi$
$948$	754.337	+	3304.97i	0.0258436	+	0.113228i
$949$	2631.93	−	600.721i	0.0900275	−	0.0205482i
$950$	19439.1	−	24375.9i	0.663882	−	0.832482i
$951$	4430.12	−	2133.43i	0.151058	−	0.0727459i
$952$	19.0059	+	9.15275i	0.000647042	+	0.000311599i
$953$	3681.16	+	4616.02i	0.125125	+	0.156902i	0.840448	−	0.541892i	$-0.182292\pi$
$953$	3681.16	+	4616.02i	0.125125	+	0.156902i	−0.715323	+	0.698794i	$0.753720\pi$
$954$	−4496.74	−	3586.03i	−0.152607	−	0.121700i
$955$	23057.8	−	47880.0i	0.781291	−	1.62237i
$956$	−16583.0			−0.561016
$957$	−733.364	+	595.176i	−0.0247715	+	0.0201038i
$958$	−24284.0			−0.818979
$959$	6.37495	−	13.2377i	0.000214659	−	0.000445744i
$960$	−20886.6	−	16656.5i	−0.702200	−	0.559986i
$961$	13195.3	+	16546.3i	0.442928	+	0.555414i
$962$	−3924.00	−	1889.70i	−0.131512	−	0.0633330i
$963$	−718.925	+	346.216i	−0.0240572	+	0.0115853i
$964$	−9345.06	+	11718.3i	−0.312224	+	0.391517i
$965$	72790.7	−	16614.0i	2.42820	−	0.554221i
$966$	5.53305	+	24.2419i	0.000184289	+	0.000807422i
$967$	32575.1	−	25977.8i	1.08329	−	0.863897i	0.0920243	−	0.995757i	$-0.470666\pi$
$967$	32575.1	−	25977.8i	1.08329	−	0.863897i	0.991268	+	0.131860i	$0.0420948\pi$
$968$	−31867.3	−	7273.50i	−1.05811	−	0.241507i
$969$			14069.2i			0.466428i
$970$	2352.47	−	10306.9i	0.0778695	−	0.341168i
$971$	−8572.11	−	17800.2i	−0.283308	−	0.588295i	0.709946	−	0.704256i	$-0.248719\pi$
$971$	−8572.11	−	17800.2i	−0.283308	−	0.588295i	−0.993254	+	0.115961i	$0.963005\pi$
$972$	284.429	+	590.623i	0.00938586	+	0.0194899i
$973$	−7.50424	+	32.8782i	−0.000247251	+	0.00108328i
$974$		−	2633.44i		−	0.0866333i
$975$	−6604.18	−	1507.36i	−0.216926	−	0.0495120i
$976$	−6417.10	+	5117.47i	−0.210457	+	0.167834i
$977$	9457.69	+	41436.8i	0.309701	+	1.35689i	0.854991	+	0.518643i	$0.173563\pi$
$977$	9457.69	+	41436.8i	0.309701	+	1.35689i	−0.545290	+	0.838248i	$0.683580\pi$
$978$	−16669.4	+	3804.68i	−0.545019	+	0.124397i
$979$	619.540	−	776.878i	0.0202253	−	0.0253617i
$980$	−13532.9	+	6517.12i	−0.441116	+	0.212430i
$981$	−3708.94	−	1786.13i	−0.120711	−	0.0581312i
$982$	9999.90	+	12539.5i	0.324959	+	0.407485i
$983$	−46833.5	−	37348.4i	−1.51959	−	1.21183i	−0.906783	−	0.421597i	$-0.861470\pi$
$983$	−46833.5	−	37348.4i	−1.51959	−	1.21183i	−0.612805	−	0.790234i	$-0.709959\pi$
$984$	2032.74	−	4221.03i	0.0658551	−	0.136750i
$985$	38482.2			1.24482
$986$	7351.89	−	15606.6i	0.237456	−	0.504073i
$987$	−26.0168			−0.000839033
$988$	1865.42	−	3873.58i	0.0600677	−	0.124732i
$989$	65600.2	+	52314.4i	2.10917	+	1.68200i
$990$	−422.840	−	530.225i	−0.0135745	−	0.0170219i
$991$	−1028.43	−	495.265i	−0.0329658	−	0.0158755i	0.417328	−	0.908756i	$-0.362967\pi$
$991$	−1028.43	−	495.265i	−0.0329658	−	0.0158755i	−0.450294	+	0.892880i	$0.648681\pi$
$992$	−9719.96	+	4680.89i	−0.311098	+	0.149817i
$993$	14663.8	−	18387.8i	0.468622	−	0.587633i
$994$	14.0439	−	3.20543i	0.000448134	−	0.000102284i
$995$	−11722.8	−	51361.0i	−0.373505	−	1.63643i
$996$	7294.44	−	5817.12i	0.232061	−	0.185063i
$997$	−16481.5	−	3761.80i	−0.523545	−	0.119496i	−0.0474231	−	0.998875i	$-0.515101\pi$
$997$	−16481.5	−	3761.80i	−0.523545	−	0.119496i	−0.476122	+	0.879379i	$0.657958\pi$
$998$		−	23398.6i		−	0.742153i
$999$	697.047	−	3053.96i	0.0220757	−	0.0967198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.4.i.a.13.12	✓	96
29.9	even	14	inner	87.4.i.a.67.12	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.4.i.a.13.12	✓	96	1.1	even	1	trivial
87.4.i.a.67.12	yes	96	29.9	even	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	87.i (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.999092 - 2.07464i) q^{2} +(-2.34549 - 1.87047i) q^{3} +(1.68199 + 2.10915i) q^{4} +(14.6253 + 7.04316i) q^{5} +(-6.22391 + 2.99728i) q^{6} +(-0.0111297 + 0.0139563i) q^{7} +(24.0157 - 5.48142i) q^{8} +(2.00269 + 8.77435i) q^{9} +O(q^{10})\)	\(q+(0.999092 - 2.07464i) q^{2} +(-2.34549 - 1.87047i) q^{3} +(1.68199 + 2.10915i) q^{4} +(14.6253 + 7.04316i) q^{5} +(-6.22391 + 2.99728i) q^{6} +(-0.0111297 + 0.0139563i) q^{7} +(24.0157 - 5.48142i) q^{8} +(2.00269 + 8.77435i) q^{9} +(29.2240 - 23.3054i) q^{10} +(-1.96540 - 0.448589i) q^{11} -8.09311i q^{12} +(3.62769 - 15.8940i) q^{13} +(0.0178345 + 0.0370338i) q^{14} +(-21.1295 - 43.8758i) q^{15} +(7.81956 - 34.2597i) q^{16} -47.9733i q^{17} +(20.2045 + 4.61153i) q^{18} +(76.4298 - 60.9507i) q^{19} +(9.74449 + 42.6934i) q^{20} +(0.0522095 - 0.0119165i) q^{21} +(-2.89427 + 3.62930i) q^{22} +(-181.675 + 87.4899i) q^{23} +(-66.5815 - 32.0640i) q^{24} +(86.3565 + 108.288i) q^{25} +(-29.3498 - 23.4057i) q^{26} +(11.7149 - 24.3262i) q^{27} -0.0481560 q^{28} +(1.33642 + 156.164i) q^{29} -112.137 q^{30} +(-40.3008 + 83.6855i) q^{31} +(90.8087 + 72.4175i) q^{32} +(3.77076 + 4.72838i) q^{33} +(-99.5271 - 47.9297i) q^{34} +(-0.261072 + 0.125726i) q^{35} +(-15.1379 + 18.9823i) q^{36} +(113.110 - 25.8166i) q^{37} +(-50.0901 - 219.459i) q^{38} +(-38.2379 + 30.4937i) q^{39} +(389.843 + 88.9791i) q^{40} +63.3965i q^{41} +(0.0274398 - 0.120221i) q^{42} +(-180.543 - 374.902i) q^{43} +(-2.35964 - 4.89984i) q^{44} +(-32.5093 + 142.433i) q^{45} +464.319i q^{46} +(-473.642 - 108.106i) q^{47} +(-82.4225 + 65.7298i) q^{48} +(76.3246 + 334.400i) q^{49} +(310.935 - 70.9690i) q^{50} +(-89.7326 + 112.521i) q^{51} +(39.6245 - 19.0821i) q^{52} +(-250.046 - 120.416i) q^{53} +(-38.7637 - 48.6081i) q^{54} +(-25.5850 - 20.4034i) q^{55} +(-0.190788 + 0.396176i) q^{56} -293.272 q^{57} +(325.319 + 153.250i) q^{58} -554.244 q^{59} +(57.0011 - 118.364i) q^{60} +(-182.611 - 145.628i) q^{61} +(133.353 + 167.219i) q^{62} +(-0.144747 - 0.0697063i) q^{63} +(494.252 - 238.019i) q^{64} +(165.000 - 206.903i) q^{65} +(13.5770 - 3.09886i) q^{66} +(-150.831 - 660.832i) q^{67} +(101.183 - 80.6906i) q^{68} +(589.764 + 134.610i) q^{69} +0.667241i q^{70} +(77.9827 - 341.664i) q^{71} +(96.1919 + 199.745i) q^{72} +(71.8482 + 149.194i) q^{73} +(59.4471 - 260.455i) q^{74} -415.515i q^{75} +(257.108 + 58.6833i) q^{76} +(0.0281350 - 0.0224369i) q^{77} +(25.0602 + 109.796i) q^{78} +(-408.368 + 93.2074i) q^{79} +(355.660 - 445.984i) q^{80} +(-72.9785 + 35.1446i) q^{81} +(131.525 + 63.3389i) q^{82} +(718.775 + 901.315i) q^{83} +(0.112950 + 0.0900742i) q^{84} +(337.884 - 701.623i) q^{85} -958.163 q^{86} +(288.966 - 368.782i) q^{87} -49.6593 q^{88} +(-213.863 + 444.091i) q^{89} +(263.016 + 209.748i) q^{90} +(0.181445 + 0.227525i) q^{91} +(-490.104 - 236.022i) q^{92} +(251.057 - 120.902i) q^{93} +(-697.491 + 874.626i) q^{94} +(1547.09 - 353.114i) q^{95} +(-77.5365 - 339.710i) q^{96} +(221.126 - 176.342i) q^{97} +(770.013 + 175.751i) q^{98} -18.1435i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 52 q^{4} + 28 q^{5} + 12 q^{6} - 40 q^{7} + 144 q^{9}+O(q^{10}) \) 96 * q + 52 * q^4 + 28 * q^5 + 12 * q^6 - 40 * q^7 + 144 * q^9	\( 96 q + 52 q^{4} + 28 q^{5} + 12 q^{6} - 40 q^{7} + 144 q^{9} - 140 q^{11} + 304 q^{13} - 294 q^{15} - 692 q^{16} + 800 q^{20} - 528 q^{22} + 324 q^{23} - 54 q^{24} - 170 q^{25} - 1288 q^{26} - 956 q^{28} - 478 q^{29} + 1056 q^{30} - 616 q^{31} - 406 q^{32} + 72 q^{33} + 34 q^{34} + 1032 q^{35} - 468 q^{36} + 1792 q^{37} + 1912 q^{38} + 2688 q^{40} + 762 q^{42} - 1092 q^{43} + 1750 q^{44} + 630 q^{45} + 2772 q^{47} + 1848 q^{48} - 1304 q^{49} - 882 q^{50} - 192 q^{51} + 1304 q^{52} - 3066 q^{53} - 108 q^{54} - 1974 q^{55} - 4704 q^{56} - 1752 q^{57} - 6092 q^{58} - 640 q^{59} - 7812 q^{60} - 252 q^{61} - 532 q^{62} - 18 q^{63} - 454 q^{64} - 8346 q^{65} + 5628 q^{66} + 744 q^{67} + 5530 q^{68} + 2100 q^{69} + 3216 q^{71} + 2142 q^{72} + 6510 q^{73} + 5090 q^{74} + 6594 q^{76} - 8876 q^{77} - 2118 q^{78} + 7092 q^{80} - 1296 q^{81} - 10590 q^{82} + 572 q^{83} - 2520 q^{85} + 12680 q^{86} - 2238 q^{87} + 6472 q^{88} - 2800 q^{89} + 1576 q^{91} - 10418 q^{92} + 60 q^{93} - 17564 q^{94} + 1374 q^{96} + 11690 q^{97} + 22554 q^{98}+O(q^{100}) \) 96 * q + 52 * q^4 + 28 * q^5 + 12 * q^6 - 40 * q^7 + 144 * q^9 - 140 * q^11 + 304 * q^13 - 294 * q^15 - 692 * q^16 + 800 * q^20 - 528 * q^22 + 324 * q^23 - 54 * q^24 - 170 * q^25 - 1288 * q^26 - 956 * q^28 - 478 * q^29 + 1056 * q^30 - 616 * q^31 - 406 * q^32 + 72 * q^33 + 34 * q^34 + 1032 * q^35 - 468 * q^36 + 1792 * q^37 + 1912 * q^38 + 2688 * q^40 + 762 * q^42 - 1092 * q^43 + 1750 * q^44 + 630 * q^45 + 2772 * q^47 + 1848 * q^48 - 1304 * q^49 - 882 * q^50 - 192 * q^51 + 1304 * q^52 - 3066 * q^53 - 108 * q^54 - 1974 * q^55 - 4704 * q^56 - 1752 * q^57 - 6092 * q^58 - 640 * q^59 - 7812 * q^60 - 252 * q^61 - 532 * q^62 - 18 * q^63 - 454 * q^64 - 8346 * q^65 + 5628 * q^66 + 744 * q^67 + 5530 * q^68 + 2100 * q^69 + 3216 * q^71 + 2142 * q^72 + 6510 * q^73 + 5090 * q^74 + 6594 * q^76 - 8876 * q^77 - 2118 * q^78 + 7092 * q^80 - 1296 * q^81 - 10590 * q^82 + 572 * q^83 - 2520 * q^85 + 12680 * q^86 - 2238 * q^87 + 6472 * q^88 - 2800 * q^89 + 1576 * q^91 - 10418 * q^92 + 60 * q^93 - 17564 * q^94 + 1374 * q^96 + 11690 * q^97 + 22554 * q^98

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