LMFDB - Embedded newform 114.4.h.b.107.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,4,Mod(65,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("114.65");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	114.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.72621774065$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} + 10 x^{18} - 183 x^{17} + 864 x^{16} - 495 x^{15} - 1530 x^{14} + \cdots + 205891132094649 $ x^20 - 5x^19 + 10x^18 - 183x^17 + 864x^16 - 495x^15 - 1530x^14 + 118935x^13 - 524961x^12 + 4026996x^11 - 36285408x^10 + 108728892x^9 - 382696569x^8 + 2340997605x^7 - 813104730x^6 - 7102708965x^5 + 334731302496x^4 - 1914244636149x^3 + 2824295364810x^2 - 38127987424935*x + 205891132094649
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.10
Root			$1.24390 + 5.04507i$ of defining polynomial
Character	$\chi$	$=$	114.107
Dual form			114.4.h.b.65.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(4.99111 - 1.44529i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-1.54776 + 0.893602i) q^{5} +(7.49442 + 7.19956i) q^{6} +19.7997 q^{7} -8.00000 q^{8} +(22.8223 - 14.4272i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(4.99111 - 1.44529i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-1.54776 + 0.893602i) q^{5} +(7.49442 + 7.19956i) q^{6} +19.7997 q^{7} -8.00000 q^{8} +(22.8223 - 14.4272i) q^{9} +(-3.09553 - 1.78720i) q^{10} +43.6809i q^{11} +(-4.97559 + 20.1803i) q^{12} +(21.5591 + 12.4472i) q^{13} +(19.7997 + 34.2940i) q^{14} +(-6.43355 + 6.69703i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(47.2760 - 27.2948i) q^{17} +(47.8109 + 25.1022i) q^{18} +(-49.7813 - 66.1878i) q^{19} -7.14882i q^{20} +(98.8222 - 28.6162i) q^{21} +(-75.6575 + 43.6809i) q^{22} +(-48.5966 - 28.0573i) q^{23} +(-39.9289 + 11.5623i) q^{24} +(-60.9029 + 105.487i) q^{25} +49.7887i q^{26} +(93.0571 - 104.992i) q^{27} +(-39.5993 + 68.5880i) q^{28} +(-81.7025 + 141.513i) q^{29} +(-18.0331 - 4.44620i) q^{30} -148.462i q^{31} +(16.0000 - 27.7128i) q^{32} +(63.1314 + 218.016i) q^{33} +(94.5520 + 54.5896i) q^{34} +(-30.6452 + 17.6930i) q^{35} +(4.33257 + 107.913i) q^{36} -54.7219i q^{37} +(64.8594 - 152.411i) q^{38} +(125.594 + 30.9660i) q^{39} +(12.3821 - 7.14882i) q^{40} +(-242.840 - 420.611i) q^{41} +(148.387 + 142.549i) q^{42} +(103.055 + 178.496i) q^{43} +(-151.315 - 87.3618i) q^{44} +(-22.4314 + 42.7239i) q^{45} -112.229i q^{46} +(-434.840 - 251.055i) q^{47} +(-59.9553 - 57.5965i) q^{48} +49.0265 q^{49} -243.612 q^{50} +(196.511 - 204.559i) q^{51} +(-86.2365 + 49.7887i) q^{52} +(194.161 - 336.297i) q^{53} +(274.909 + 56.1874i) q^{54} +(-39.0333 - 67.6077i) q^{55} -158.397 q^{56} +(-344.124 - 258.402i) q^{57} -326.810 q^{58} +(-202.865 - 351.373i) q^{59} +(-10.3321 - 35.6805i) q^{60} +(56.1634 - 97.2778i) q^{61} +(257.144 - 148.462i) q^{62} +(451.874 - 285.653i) q^{63} +64.0000 q^{64} -44.4913 q^{65} +(-314.483 + 327.363i) q^{66} +(535.858 + 309.378i) q^{67} +218.359i q^{68} +(-283.102 - 69.8008i) q^{69} +(-61.2904 - 35.3860i) q^{70} +(8.43173 + 14.6042i) q^{71} +(-182.578 + 115.417i) q^{72} +(-37.0392 - 64.1537i) q^{73} +(94.7811 - 54.7219i) q^{74} +(-151.514 + 614.519i) q^{75} +(328.844 - 40.0717i) q^{76} +864.867i q^{77} +(71.9589 + 248.501i) q^{78} +(-751.348 + 433.791i) q^{79} +(24.7642 + 14.2976i) q^{80} +(312.714 - 658.522i) q^{81} +(485.680 - 841.223i) q^{82} +494.978i q^{83} +(-98.5150 + 399.563i) q^{84} +(-48.7814 + 84.4919i) q^{85} +(-206.110 + 356.992i) q^{86} +(-203.259 + 824.389i) q^{87} -349.447i q^{88} +(-263.375 + 456.178i) q^{89} +(-96.4314 + 3.87159i) q^{90} +(426.864 + 246.450i) q^{91} +(194.387 - 112.229i) q^{92} +(-214.570 - 740.990i) q^{93} -1004.22i q^{94} +(136.195 + 57.9585i) q^{95} +(39.8047 - 161.442i) q^{96} +(167.160 - 96.5100i) q^{97} +(49.0265 + 84.9164i) q^{98} +(630.191 + 996.898i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} + q^{3} - 40 q^{4} - 8 q^{6} - 10 q^{7} - 160 q^{8} - 37 q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 + q^3 - 40 * q^4 - 8 * q^6 - 10 * q^7 - 160 * q^8 - 37 * q^9	\( 20 q + 20 q^{2} + q^{3} - 40 q^{4} - 8 q^{6} - 10 q^{7} - 160 q^{8} - 37 q^{9} - 20 q^{12} - 111 q^{13} - 10 q^{14} - 133 q^{15} - 160 q^{16} - 90 q^{17} - 10 q^{18} - 143 q^{19} + 191 q^{21} - 54 q^{22} - 8 q^{24} + 184 q^{25} - 524 q^{27} + 20 q^{28} - 96 q^{29} - 292 q^{30} + 320 q^{32} - 55 q^{33} - 180 q^{34} + 774 q^{35} + 128 q^{36} - 314 q^{38} + 1002 q^{39} + 537 q^{41} - 382 q^{42} + 571 q^{43} - 108 q^{44} + 1516 q^{45} - 126 q^{47} + 64 q^{48} + 558 q^{49} + 736 q^{50} - 757 q^{51} + 444 q^{52} + 126 q^{53} - 1388 q^{54} + 366 q^{55} + 80 q^{56} - 281 q^{57} - 384 q^{58} - 1383 q^{59} - 52 q^{60} + 149 q^{61} - 222 q^{62} + 1153 q^{63} + 1280 q^{64} + 3636 q^{65} + 32 q^{66} - 1626 q^{67} + 236 q^{69} + 1548 q^{70} - 1368 q^{71} + 296 q^{72} + 946 q^{73} + 474 q^{74} - 669 q^{75} - 56 q^{76} + 132 q^{78} - 2109 q^{79} + 311 q^{81} - 1074 q^{82} - 1528 q^{84} + 786 q^{85} - 1142 q^{86} - 816 q^{87} - 1938 q^{89} + 1234 q^{90} - 3459 q^{91} - 705 q^{93} + 2502 q^{95} + 160 q^{96} + 1791 q^{97} + 558 q^{98} - 2285 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 + q^3 - 40 * q^4 - 8 * q^6 - 10 * q^7 - 160 * q^8 - 37 * q^9 - 20 * q^12 - 111 * q^13 - 10 * q^14 - 133 * q^15 - 160 * q^16 - 90 * q^17 - 10 * q^18 - 143 * q^19 + 191 * q^21 - 54 * q^22 - 8 * q^24 + 184 * q^25 - 524 * q^27 + 20 * q^28 - 96 * q^29 - 292 * q^30 + 320 * q^32 - 55 * q^33 - 180 * q^34 + 774 * q^35 + 128 * q^36 - 314 * q^38 + 1002 * q^39 + 537 * q^41 - 382 * q^42 + 571 * q^43 - 108 * q^44 + 1516 * q^45 - 126 * q^47 + 64 * q^48 + 558 * q^49 + 736 * q^50 - 757 * q^51 + 444 * q^52 + 126 * q^53 - 1388 * q^54 + 366 * q^55 + 80 * q^56 - 281 * q^57 - 384 * q^58 - 1383 * q^59 - 52 * q^60 + 149 * q^61 - 222 * q^62 + 1153 * q^63 + 1280 * q^64 + 3636 * q^65 + 32 * q^66 - 1626 * q^67 + 236 * q^69 + 1548 * q^70 - 1368 * q^71 + 296 * q^72 + 946 * q^73 + 474 * q^74 - 669 * q^75 - 56 * q^76 + 132 * q^78 - 2109 * q^79 + 311 * q^81 - 1074 * q^82 - 1528 * q^84 + 786 * q^85 - 1142 * q^86 - 816 * q^87 - 1938 * q^89 + 1234 * q^90 - 3459 * q^91 - 705 * q^93 + 2502 * q^95 + 160 * q^96 + 1791 * q^97 + 558 * q^98 - 2285 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$	4.99111	−	1.44529i	0.960539	−	0.278146i
$3$	4.99111	−	1.44529i	0.960539	−	0.278146i
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	−1.54776	+	0.893602i	−0.138436	+	0.0799262i	−0.567619	−	0.823292i	$-0.692135\pi$
$5$	−1.54776	+	0.893602i	−0.138436	+	0.0799262i	0.429182	+	0.903218i	$0.358802\pi$
$6$	7.49442	+	7.19956i	0.509930	+	0.489868i
$7$	19.7997			1.06908			0.534541	−	0.845143i	$-0.320485\pi$
$7$	19.7997			1.06908			0.534541	+	0.845143i	$0.320485\pi$
$8$	−8.00000			−0.353553
$9$	22.8223	−	14.4272i	0.845270	−	0.534339i
$10$	−3.09553	−	1.78720i	−0.0978892	−	0.0565164i
$11$			43.6809i			1.19730i	0.801011	+	0.598649i	$0.204296\pi$
$11$			43.6809i			1.19730i	−0.801011	+	0.598649i	$0.795704\pi$
$12$	−4.97559	+	20.1803i	−0.119694	+	0.485462i
$13$	21.5591	+	12.4472i	0.459956	+	0.265556i	0.712026	−	0.702153i	$-0.247778\pi$
$13$	21.5591	+	12.4472i	0.459956	+	0.265556i	−0.252070	+	0.967709i	$0.581111\pi$
$14$	19.7997	+	34.2940i	0.377977	+	0.654676i
$15$	−6.43355	+	6.69703i	−0.110742	+	0.115278i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	47.2760	−	27.2948i	0.674478	−	0.389410i	−0.123294	−	0.992370i	$-0.539346\pi$
$17$	47.2760	−	27.2948i	0.674478	−	0.389410i	0.797771	+	0.602960i	$0.206012\pi$
$18$	47.8109	+	25.1022i	0.626063	+	0.328703i
$19$	−49.7813	−	66.1878i	−0.601084	−	0.799186i
$19$	−49.7813	−	66.1878i	−0.601084	−	0.799186i
$20$		−	7.14882i		−	0.0799262i
$21$	98.8222	−	28.6162i	1.02689	−	0.297360i
$22$	−75.6575	+	43.6809i	−0.733193	+	0.423309i
$23$	−48.5966	−	28.0573i	−0.440570	−	0.254363i	0.263270	−	0.964722i	$-0.415199\pi$
$23$	−48.5966	−	28.0573i	−0.440570	−	0.254363i	−0.703839	+	0.710359i	$0.748532\pi$
$24$	−39.9289	+	11.5623i	−0.339602	+	0.0983393i
$25$	−60.9029	+	105.487i	−0.487224	+	0.843896i
$26$			49.7887i			0.375552i
$27$	93.0571	−	104.992i	0.663291	−	0.748362i
$28$	−39.5993	+	68.5880i	−0.267270	+	0.462926i
$29$	−81.7025	+	141.513i	−0.523164	+	0.906147i	0.476472	+	0.879190i	$0.341915\pi$
$29$	−81.7025	+	141.513i	−0.523164	+	0.906147i	−0.999637	+	0.0269579i	$0.991418\pi$
$30$	−18.0331	−	4.44620i	−0.109746	−	0.0270587i
$31$		−	148.462i		−	0.860148i	−0.902794	−	0.430074i	$-0.858488\pi$
$31$		−	148.462i		−	0.860148i	0.902794	−	0.430074i	$-0.141512\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$	63.1314	+	218.016i	0.333023	+	1.15005i
$34$	94.5520	+	54.5896i	0.476928	+	0.275354i
$35$	−30.6452	+	17.6930i	−0.148000	+	0.0854476i
$36$	4.33257	+	107.913i	0.0200582	+	0.499598i
$37$		−	54.7219i		−	0.243141i	−0.992583	−	0.121571i	$-0.961207\pi$
$37$		−	54.7219i		−	0.243141i	0.992583	−	0.121571i	$-0.0387931\pi$
$38$	64.8594	−	152.411i	0.276884	−	0.650642i
$39$	125.594	+	30.9660i	0.515669	+	0.127142i
$40$	12.3821	−	7.14882i	0.0489446	−	0.0282582i
$41$	−242.840	−	420.611i	−0.925006	−	1.60216i	−0.791551	−	0.611103i	$-0.790726\pi$
$41$	−242.840	−	420.611i	−0.925006	−	1.60216i	−0.133455	−	0.991055i	$-0.542607\pi$
$42$	148.387	+	142.549i	0.545157	+	0.523709i
$43$	103.055	+	178.496i	0.365481	+	0.633032i	0.988853	−	0.148893i	$-0.0475710\pi$
$43$	103.055	+	178.496i	0.365481	+	0.633032i	−0.623372	+	0.781926i	$0.714238\pi$
$44$	−151.315	−	87.3618i	−0.518445	−	0.299325i
$45$	−22.4314	+	42.7239i	−0.0743083	+	0.141531i
$46$		−	112.229i		−	0.359724i
$47$	−434.840	−	251.055i	−1.34953	−	0.779151i	−0.361347	−	0.932432i	$-0.617683\pi$
$47$	−434.840	−	251.055i	−1.34953	−	0.779151i	−0.988183	+	0.153280i	$0.951016\pi$
$48$	−59.9553	−	57.5965i	−0.180288	−	0.173195i
$49$	49.0265			0.142934
$50$	−243.612			−0.689038
$51$	196.511	−	204.559i	0.539549	−	0.561646i
$52$	−86.2365	+	49.7887i	−0.229978	+	0.132778i
$53$	194.161	−	336.297i	0.503209	−	0.871583i	−0.496784	−	0.867874i	$-0.665486\pi$
$53$	194.161	−	336.297i	0.503209	−	0.871583i	0.999993	−	0.00370916i	$-0.00118067\pi$
$54$	274.909	+	56.1874i	0.692785	+	0.141595i
$55$	−39.0333	−	67.6077i	−0.0956955	−	0.165750i
$56$	−158.397			−0.377977
$57$	−344.124	−	258.402i	−0.799655	−	0.600460i
$58$	−326.810			−0.739866
$59$	−202.865	−	351.373i	−0.447640	−	0.775336i	0.550592	−	0.834775i	$-0.314402\pi$
$59$	−202.865	−	351.373i	−0.447640	−	0.775336i	−0.998232	+	0.0594389i	$0.981069\pi$
$60$	−10.3321	−	35.6805i	−0.0222311	−	0.0767722i
$61$	56.1634	−	97.2778i	0.117885	−	0.204183i	−0.801044	−	0.598605i	$-0.795722\pi$
$61$	56.1634	−	97.2778i	0.117885	−	0.204183i	0.918929	+	0.394422i	$0.129055\pi$
$62$	257.144	−	148.462i	0.526731	−	0.304108i
$63$	451.874	−	285.653i	0.903662	−	0.571252i
$64$	64.0000			0.125000
$65$	−44.4913			−0.0848995
$66$	−314.483	+	327.363i	−0.586519	+	0.610539i
$67$	535.858	+	309.378i	0.977097	+	0.564127i	0.901392	−	0.433003i	$-0.142546\pi$
$67$	535.858	+	309.378i	0.977097	+	0.564127i	0.0757043	+	0.997130i	$0.475880\pi$
$68$			218.359i			0.389410i
$69$	−283.102	−	69.8008i	−0.493934	−	0.121783i
$70$	−61.2904	−	35.3860i	−0.104652	−	0.0604206i
$71$	8.43173	+	14.6042i	0.0140938	+	0.0244112i	0.872986	−	0.487745i	$-0.162180\pi$
$71$	8.43173	+	14.6042i	0.0140938	+	0.0244112i	−0.858892	+	0.512156i	$0.828847\pi$
$72$	−182.578	+	115.417i	−0.298848	+	0.188917i
$73$	−37.0392	−	64.1537i	−0.0593850	−	0.102858i	0.834804	−	0.550547i	$-0.185581\pi$
$73$	−37.0392	−	64.1537i	−0.0593850	−	0.102858i	−0.894190	+	0.447689i	$0.852247\pi$
$74$	94.7811	−	54.7219i	0.148893	−	0.0859634i
$75$	−151.514	+	614.519i	−0.233271	+	0.946114i
$76$	328.844	−	40.0717i	0.496329	−	0.0604808i
$77$			864.867i			1.28001i
$78$	71.9589	+	248.501i	0.104458	+	0.360733i
$79$	−751.348	+	433.791i	−1.07004	+	0.617789i	−0.928193	−	0.372100i	$-0.878638\pi$
$79$	−751.348	+	433.791i	−1.07004	+	0.617789i	−0.141849	+	0.989888i	$0.545305\pi$
$80$	24.7642	+	14.2976i	0.0346091	+	0.0199816i
$81$	312.714	−	658.522i	0.428963	−	0.903322i
$82$	485.680	−	841.223i	0.654078	−	1.13290i
$83$			494.978i			0.654589i	0.944922	+	0.327295i	$0.106137\pi$
$83$			494.978i			0.654589i	−0.944922	+	0.327295i	$0.893863\pi$
$84$	−98.5150	+	399.563i	−0.127963	+	0.518998i
$85$	−48.7814	+	84.4919i	−0.0622481	+	0.107817i
$86$	−206.110	+	356.992i	−0.258434	+	0.447622i
$87$	−203.259	+	824.389i	−0.250479	+	1.01591i
$88$		−	349.447i		−	0.423309i
$89$	−263.375	+	456.178i	−0.313682	+	0.543312i	−0.979156	−	0.203108i	$-0.934896\pi$
$89$	−263.375	+	456.178i	−0.313682	+	0.543312i	0.665475	+	0.746420i	$0.268229\pi$
$90$	−96.4314	+	3.87159i	−0.112942	+	0.00453446i
$91$	426.864	+	246.450i	0.491730	+	0.283901i
$92$	194.387	−	112.229i	0.220285	−	0.127181i
$93$	−214.570	−	740.990i	−0.239246	−	0.826205i
$94$		−	1004.22i		−	1.10189i
$95$	136.195	+	57.9585i	0.147088	+	0.0625939i
$96$	39.8047	−	161.442i	0.0423183	−	0.171637i
$97$	167.160	−	96.5100i	0.174975	−	0.101022i	−0.409955	−	0.912106i	$-0.634455\pi$
$97$	167.160	−	96.5100i	0.174975	−	0.101022i	0.584930	+	0.811084i	$0.301122\pi$
$98$	49.0265	+	84.9164i	0.0505350	+	0.0875291i
$99$	630.191	+	996.898i	0.639764	+	1.01204i
$100$	−243.612	−	421.948i	−0.243612	−	0.421948i
$101$	82.3786	+	47.5613i	0.0811582	+	0.0468567i	0.540030	−	0.841646i	$-0.318413\pi$
$101$	82.3786	+	47.5613i	0.0811582	+	0.0468567i	−0.458872	+	0.888503i	$0.651746\pi$
$102$	550.817	+	135.808i	0.534696	+	0.131833i
$103$			1717.17i			1.64269i	0.570430	+	0.821346i	$0.306777\pi$
$103$			1717.17i			1.64269i	−0.570430	+	0.821346i	$0.693223\pi$
$104$	−172.473	−	99.5774i	−0.162619	−	0.0938881i
$105$	−127.382	+	132.599i	−0.118393	+	0.123241i
$106$	776.644			0.711645
$107$	1929.59			1.74337			0.871685	−	0.490067i	$-0.163028\pi$
$107$	1929.59			1.74337			0.871685	+	0.490067i	$0.163028\pi$
$108$	177.590	+	532.344i	0.158228	+	0.474304i
$109$	−737.137	+	425.586i	−0.647751	+	0.373979i	−0.787594	−	0.616194i	$-0.788674\pi$
$109$	−737.137	+	425.586i	−0.647751	+	0.373979i	0.139843	+	0.990174i	$0.455340\pi$
$110$	78.0667	−	135.215i	0.0676670	−	0.117203i
$111$	−79.0888	−	273.123i	−0.0676286	−	0.233547i
$112$	−158.397	−	274.352i	−0.133635	−	0.231463i
$113$	−1066.49			−0.887849			−0.443925	−	0.896064i	$-0.646414\pi$
$113$	−1066.49			−0.887849			−0.443925	+	0.896064i	$0.646414\pi$
$114$	103.442	−	854.442i	0.0849843	−	0.701981i
$115$	100.288			0.0813211
$116$	−326.810	−	566.051i	−0.261582	−	0.453074i
$117$	671.606	−	26.9641i	0.530684	−	0.0213063i
$118$	405.730	−	702.745i	0.316530	−	0.548245i
$119$	936.049	−	540.428i	0.721071	−	0.416311i
$120$	51.4684	−	53.5762i	0.0391533	−	0.0407568i
$121$	−577.020			−0.433524
$122$	224.653			0.166715
$123$	−1819.95	−	1748.34i	−1.33414	−	1.28165i
$124$	514.288	+	296.924i	0.372455	+	0.215037i
$125$		−	441.093i		−	0.315620i
$126$	946.639	+	497.015i	0.669312	+	0.351410i
$127$	1096.59	+	633.114i	0.766190	+	0.442360i	0.831514	−	0.555504i	$-0.187475\pi$
$127$	1096.59	+	633.114i	0.766190	+	0.442360i	−0.0653235	+	0.997864i	$0.520808\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$	772.335	+	741.949i	0.527134	+	0.506395i
$130$	−44.4913	−	77.0612i	−0.0300165	−	0.0519901i
$131$	−73.3412	+	42.3436i	−0.0489149	+	0.0282410i	−0.524258	−	0.851559i	$-0.675657\pi$
$131$	−73.3412	+	42.3436i	−0.0489149	+	0.0282410i	0.475343	+	0.879801i	$0.342324\pi$
$132$	−881.492	−	217.338i	−0.581243	−	0.143310i
$133$	−985.652	−	1310.50i	−0.642608	−	0.854394i
$134$			1237.51i			0.797796i
$135$	−50.2092	+	245.659i	−0.0320098	+	0.156615i
$136$	−378.208	+	218.359i	−0.238464	+	0.137677i
$137$	2607.91	+	1505.68i	1.62634	+	0.938968i	0.985172	+	0.171567i	$0.0548829\pi$
$137$	2607.91	+	1505.68i	1.62634	+	0.938968i	0.641167	+	0.767401i	$0.278450\pi$
$138$	−162.203	−	560.148i	−0.100056	−	0.345528i
$139$	−487.211	+	843.875i	−0.297300	+	0.514939i	−0.975517	−	0.219923i	$-0.929420\pi$
$139$	−487.211	+	843.875i	−0.297300	+	0.514939i	0.678217	+	0.734861i	$0.262753\pi$
$140$		−	141.544i		−	0.0854476i
$141$	−2533.18	−	624.573i	−1.51299	−	0.373039i
$142$	−16.8635	+	29.2084i	−0.00996584	+	0.0172613i
$143$	−543.703	+	941.722i	−0.317949	+	0.550705i
$144$	−382.487	−	200.818i	−0.221347	−	0.116214i
$145$		−	292.038i		−	0.167258i
$146$	74.0784	−	128.307i	0.0419916	−	0.0727315i
$147$	244.697	−	70.8574i	0.137294	−	0.0397566i
$148$	189.562	+	109.444i	0.105283	+	0.0607853i
$149$	−389.717	+	225.003i	−0.214274	+	0.123711i	−0.603296	−	0.797517i	$-0.706146\pi$
$149$	−389.717	+	225.003i	−0.214274	+	0.123711i	0.389022	+	0.921228i	$0.372813\pi$
$150$	−1215.89	+	352.089i	−0.661848	+	0.191653i
$151$			2386.57i			1.28620i	0.765781	+	0.643101i	$0.222353\pi$
$151$			2386.57i			1.28620i	−0.765781	+	0.643101i	$0.777647\pi$
$152$	398.250	+	529.502i	0.212515	+	0.282555i
$153$	685.160	−	1304.99i	0.362039	−	0.689556i
$154$	−1497.99	+	864.867i	−0.783842	+	0.452552i
$155$	132.666	+	229.784i	0.0687483	+	0.119076i
$156$	−358.457	+	373.137i	−0.183971	+	0.191506i
$157$	−1261.09	−	2184.27i	−0.641056	−	1.11034i	−0.985197	−	0.171424i	$-0.945163\pi$
$157$	−1261.09	−	2184.27i	−0.641056	−	1.11034i	0.344141	−	0.938918i	$-0.388170\pi$
$158$	−1502.70	−	867.582i	−0.756634	−	0.436843i
$159$	483.033	−	1959.11i	0.240925	−	0.977155i
$160$			57.1905i			0.0282582i
$161$	−962.197	−	555.525i	−0.471005	−	0.271935i
$162$	1453.31	−	116.885i	0.704831	−	0.0566875i
$163$	3414.90			1.64095			0.820477	−	0.571680i	$-0.193708\pi$
$163$	3414.90			1.64095			0.820477	+	0.571680i	$0.193708\pi$
$164$	1942.72			0.925006
$165$	−292.532	−	281.023i	−0.138022	−	0.132592i
$166$	−857.327	+	494.978i	−0.400852	+	0.231432i
$167$	1171.46	−	2029.02i	0.542815	−	0.940183i	−0.455926	−	0.890018i	$-0.650692\pi$
$167$	1171.46	−	2029.02i	0.542815	−	0.940183i	0.998741	−	0.0501653i	$-0.0159748\pi$
$168$	−790.578	+	228.929i	−0.363062	+	0.105133i
$169$	−788.636	−	1365.96i	−0.358960	−	0.621738i
$170$	−195.126			−0.0880321
$171$	−2091.02	−	792.355i	−0.935115	−	0.354345i
$172$	−824.438			−0.365481
$173$	−1576.81	−	2731.12i	−0.692964	−	1.20025i	−0.970862	−	0.239638i	$-0.922971\pi$
$173$	−1576.81	−	2731.12i	−0.692964	−	1.20025i	0.277898	−	0.960610i	$-0.410362\pi$
$174$	−1631.14	+	472.334i	−0.710670	+	0.205791i
$175$	−1205.86	+	2088.61i	−0.520882	+	0.902193i
$176$	605.260	−	349.447i	0.259223	−	0.149662i
$177$	−1520.36	−	1460.54i	−0.645632	−	0.620231i
$178$	−1053.50			−0.443613
$179$	−1065.56			−0.444937			−0.222468	−	0.974940i	$-0.571411\pi$
$179$	−1065.56			−0.444937			−0.222468	+	0.974940i	$0.571411\pi$
$180$	−103.137	−	163.152i	−0.0427077	−	0.0675592i
$181$	−3611.54	−	2085.12i	−1.48311	−	0.856276i	−0.483297	−	0.875456i	$-0.660561\pi$
$181$	−3611.54	−	2085.12i	−1.48311	−	0.856276i	−0.999816	+	0.0191808i	$0.993894\pi$
$182$			985.799i			0.401496i
$183$	139.723	−	566.696i	0.0564406	−	0.228915i
$184$	388.773	+	224.458i	0.155765	+	0.0899309i
$185$	48.8996	+	84.6966i	0.0194334	+	0.0336596i
$186$	1068.86	−	1112.64i	0.421359	−	0.438615i
$187$	1192.26	+	2065.06i	0.466240	+	0.807551i
$188$	1739.36	−	1004.22i	0.674765	−	0.389576i
$189$	1842.50	−	2078.81i	0.709112	−	0.800060i
$190$	35.8082	+	293.856i	0.0136726	+	0.112203i
$191$		−	1032.66i		−	0.391207i	−0.980683	−	0.195604i	$-0.937333\pi$
$191$		−	1032.66i		−	0.391207i	0.980683	−	0.195604i	$-0.0626666\pi$
$192$	319.431	−	92.4984i	0.120067	−	0.0347682i
$193$	503.266	−	290.561i	0.187699	−	0.108368i	−0.403206	−	0.915109i	$-0.632104\pi$
$193$	503.266	−	290.561i	0.187699	−	0.108368i	0.590905	+	0.806741i	$0.298771\pi$
$194$	334.321	+	193.020i	0.123726	+	0.0714332i
$195$	−222.061	+	64.3027i	−0.0815492	+	0.0236144i
$196$	−98.0531	+	169.833i	−0.0357336	+	0.0618925i
$197$			3806.21i			1.37656i	0.725447	+	0.688278i	$0.241633\pi$
$197$			3806.21i			1.37656i	−0.725447	+	0.688278i	$0.758367\pi$
$198$	−1096.49	+	2088.42i	−0.393555	+	0.749584i
$199$	671.546	−	1163.15i	0.239219	−	0.414340i	−0.721271	−	0.692653i	$-0.756442\pi$
$199$	671.546	−	1163.15i	0.239219	−	0.414340i	0.960490	+	0.278313i	$0.0897752\pi$
$200$	487.224	−	843.896i	0.172260	−	0.298362i
$201$	3121.66	+	769.669i	1.09545	+	0.270091i
$202$			190.245i			0.0662654i
$203$	−1617.68	+	2801.91i	−0.559305	+	0.968745i
$204$	315.591	+	1089.85i	0.108313	+	0.374043i
$205$	751.719	+	434.005i	0.256109	+	0.147865i
$206$	−2974.22	+	1717.17i	−1.00594	+	0.580779i
$207$	−1513.87	+	60.7801i	−0.508316	+	0.0204082i
$208$		−	398.309i		−	0.132778i
$209$	2891.14	−	2174.49i	0.956864	−	0.719677i
$210$	−357.050	−	88.0333i	−0.117328	−	0.0289280i
$211$	3772.23	−	2177.90i	1.23076	−	0.710581i	0.263573	−	0.964639i	$-0.415099\pi$
$211$	3772.23	−	2177.90i	1.23076	−	0.710581i	0.967189	+	0.254059i	$0.0817657\pi$
$212$	776.644	+	1345.19i	0.251604	+	0.435792i
$213$	63.1909	+	60.7047i	0.0203275	+	0.0195278i
$214$	1929.59	+	3342.15i	0.616374	+	1.06759i
$215$	−319.009	−	184.180i	−0.101192	−	0.0584231i
$216$	−744.457	+	839.938i	−0.234509	+	0.264586i
$217$		−	2939.50i		−	0.919567i
$218$	−1474.27	−	851.172i	−0.458029	−	0.264443i
$219$	−277.587	−	266.666i	−0.0856511	−	0.0822813i
$220$	312.267			0.0956955
$221$	1358.97			0.413640
$222$	393.974	−	410.109i	0.119107	−	0.123985i
$223$	−66.7736	+	38.5517i	−0.0200515	+	0.0115767i	−0.509992	−	0.860179i	$-0.670352\pi$
$223$	−66.7736	+	38.5517i	−0.0200515	+	0.0115767i	0.489941	+	0.871756i	$0.337018\pi$
$224$	316.795	−	548.704i	0.0944943	−	0.163669i
$225$	131.933	+	3286.11i	0.0390913	+	0.973663i
$226$	−1066.49	−	1847.22i	−0.313902	−	0.543694i
$227$	6041.70			1.76653			0.883264	−	0.468875i	$-0.155341\pi$
$227$	6041.70			1.76653			0.883264	+	0.468875i	$0.155341\pi$
$228$	1583.38	−	675.276i	0.459920	−	0.196146i
$229$	137.785			0.0397603			0.0198801	−	0.999802i	$-0.493672\pi$
$229$	137.785			0.0397603			0.0198801	+	0.999802i	$0.493672\pi$
$230$	100.288	+	173.704i	0.0287513	+	0.0497988i
$231$	1249.98	+	4316.64i	0.356029	+	1.22950i
$232$	653.620	−	1132.10i	0.184967	−	0.320372i
$233$	−4205.62	+	2428.12i	−1.18249	+	0.682709i	−0.956589	−	0.291441i	$-0.905865\pi$
$233$	−4205.62	+	2428.12i	−1.18249	+	0.682709i	−0.225899	+	0.974151i	$0.572532\pi$
$234$	718.309	+	1136.29i	0.200672	+	0.317443i
$235$	897.373			0.249098
$236$	1622.92			0.447640
$237$	−3123.11	+	3251.01i	−0.855981	+	0.891037i
$238$	1872.10	+	1080.86i	0.509874	+	0.294376i
$239$			5348.82i			1.44764i	0.689988	+	0.723821i	$0.257616\pi$
$239$			5348.82i			1.44764i	−0.689988	+	0.723821i	$0.742384\pi$
$240$	144.265	+	35.5696i	0.0388011	+	0.00956670i
$241$	4287.47	+	2475.37i	1.14598	+	0.661630i	0.947903	−	0.318558i	$-0.103199\pi$
$241$	4287.47	+	2475.37i	1.14598	+	0.661630i	0.198073	+	0.980187i	$0.436532\pi$
$242$	−577.020	−	999.428i	−0.153274	−	0.265478i
$243$	609.036	−	3738.71i	0.160781	−	0.986990i
$244$	224.653	+	389.111i	0.0589425	+	0.102091i
$245$	−75.8815	+	43.8102i	−0.0197873	+	0.0114242i
$246$	1208.27	−	4900.58i	0.313157	−	1.27012i
$247$	−249.390	−	2046.59i	−0.0642441	−	0.527212i
$248$			1187.70i			0.304108i
$249$	715.385	+	2470.49i	0.182071	+	0.628758i
$250$	763.995	−	441.093i	0.193277	−	0.111589i
$251$	−1635.42	−	944.213i	−0.411263	−	0.237443i	0.280069	−	0.959980i	$-0.409643\pi$
$251$	−1635.42	−	944.213i	−0.411263	−	0.237443i	−0.691332	+	0.722537i	$0.742976\pi$
$252$	85.7834	+	2136.64i	0.0214438	+	0.534110i
$253$	1225.57	−	2122.74i	0.304548	−	0.527493i
$254$			2532.45i			0.625592i
$255$	−121.358	+	492.211i	−0.0298029	+	0.120876i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	1570.88	−	2720.84i	0.381279	−	0.660394i	−0.609967	−	0.792427i	$-0.708817\pi$
$257$	1570.88	−	2720.84i	0.381279	−	0.660394i	0.991245	+	0.132033i	$0.0421505\pi$
$258$	−512.759	+	2079.67i	−0.123732	+	0.501840i
$259$		−	1083.47i		−	0.259938i
$260$	88.9826	−	154.122i	0.0212249	−	0.0367625i
$261$	176.991	+	4408.38i	0.0419749	+	1.04549i
$262$	−146.682	−	84.6872i	−0.0345881	−	0.0199694i
$263$	−1303.80	+	752.748i	−0.305687	+	0.176488i	−0.644995	−	0.764187i	$-0.723140\pi$
$263$	−1303.80	+	752.748i	−0.305687	+	0.176488i	0.339308	+	0.940675i	$0.389807\pi$
$264$	−505.051	−	1744.13i	−0.117742	−	0.406605i
$265$			694.011i			0.160878i
$266$	1284.19	−	3017.70i	0.296011	−	0.695589i
$267$	−655.223	+	2657.49i	−0.150183	+	0.609122i
$268$	−2143.43	+	1237.51i	−0.488548	+	0.282063i
$269$	2800.70	+	4850.95i	0.634802	+	1.09951i	0.986557	+	0.163417i	$0.0522515\pi$
$269$	2800.70	+	4850.95i	0.634802	+	1.09951i	−0.351756	+	0.936092i	$0.614415\pi$
$270$	−475.704	+	158.695i	−0.107224	+	0.0357698i
$271$	−3207.05	−	5554.77i	−0.718871	−	1.24512i	−0.961447	−	0.274989i	$-0.911326\pi$
$271$	−3207.05	−	5554.77i	−0.718871	−	1.24512i	0.242576	−	0.970132i	$-0.422008\pi$
$272$	−756.416	−	436.717i	−0.168619	−	0.0973524i
$273$	2486.71	+	613.117i	0.551292	+	0.135925i
$274$			6022.70i			1.32790i
$275$	−4607.77	−	2660.29i	−1.01040	−	0.583352i
$276$	808.001	−	841.092i	0.176217	−	0.183434i
$277$	−8056.67			−1.74758			−0.873788	−	0.486307i	$-0.838344\pi$
$277$	−8056.67			−1.74758			−0.873788	+	0.486307i	$0.838344\pi$
$278$	−1948.84			−0.420446
$279$	−2141.89	−	3388.24i	−0.459611	−	0.727057i
$280$	245.162	−	141.544i	0.0523258	−	0.0302103i
$281$	4571.80	−	7918.59i	0.970572	−	1.68108i	0.276737	−	0.960946i	$-0.410747\pi$
$281$	4571.80	−	7918.59i	0.970572	−	1.68108i	0.693835	−	0.720134i	$-0.255920\pi$
$282$	−1451.38	−	5012.17i	−0.306485	−	1.05840i
$283$	988.347	+	1711.87i	0.207601	+	0.359576i	0.950958	−	0.309319i	$-0.100101\pi$
$283$	988.347	+	1711.87i	0.207601	+	0.359576i	−0.743357	+	0.668895i	$0.766768\pi$
$284$	−67.4538			−0.0140938
$285$	763.532	+	92.4358i	0.158694	+	0.0192120i
$286$	−2174.81			−0.449648
$287$	−4808.15	−	8327.96i	−0.988907	−	1.71284i
$288$	−34.6606	−	863.304i	−0.00709164	−	0.176634i
$289$	−966.486	+	1674.00i	−0.196720	+	0.340729i
$290$	505.825	−	292.038i	0.102424	−	0.0591347i
$291$	694.830	−	723.286i	0.139971	−	0.145704i
$292$	296.313			0.0593850
$293$	−8686.57			−1.73200			−0.865998	−	0.500048i	$-0.833316\pi$
$293$	−8686.57			−1.73200			−0.865998	+	0.500048i	$0.833316\pi$
$294$	367.425	+	352.970i	0.0728867	+	0.0700191i
$295$	627.975	+	362.561i	0.123939	+	0.0715564i
$296$			437.775i			0.0859634i
$297$	4586.16	+	4064.82i	0.896012	+	0.794157i
$298$	−779.433	−	450.006i	−0.151515	−	0.0874770i
$299$	−698.468	−	1209.78i	−0.135095	−	0.233991i
$300$	−1825.73	−	1753.90i	−0.351362	−	0.337538i
$301$	2040.45	+	3534.16i	0.390729	+	0.676763i
$302$	−4133.67	+	2386.57i	−0.787635	+	0.454741i
$303$	479.900	+	118.323i	0.0909886	+	0.0224339i
$304$	−518.875	+	1219.29i	−0.0978932	+	0.230037i
$305$			200.751i			0.0376884i
$306$	2945.47	−	118.257i	0.550265	−	0.0220924i
$307$	8506.57	−	4911.27i	1.58142	−	0.913032i	0.586765	−	0.809757i	$-0.300401\pi$
$307$	8506.57	−	4911.27i	1.58142	−	0.913032i	0.994653	−	0.103275i	$-0.0329323\pi$
$308$	−2995.99	−	1729.73i	−0.554260	−	0.320002i
$309$	2481.80	+	8570.55i	0.456908	+	1.57787i
$310$	−265.332	+	459.569i	−0.0486124	+	0.0841992i
$311$			7820.35i			1.42589i	0.701221	+	0.712944i	$0.252639\pi$
$311$			7820.35i			1.42589i	−0.701221	+	0.712944i	$0.747361\pi$
$312$	−1004.75	−	247.728i	−0.182316	−	0.0449514i
$313$	61.5692	−	106.641i	0.0111185	−	0.0192578i	−0.860413	−	0.509598i	$-0.829794\pi$
$313$	61.5692	−	106.641i	0.0111185	−	0.0192578i	0.871531	+	0.490340i	$0.163127\pi$
$314$	2522.18	−	4368.54i	0.453295	−	0.785130i
$315$	−444.134	+	845.919i	−0.0794416	+	0.151308i
$316$		−	3470.33i		−	0.617789i
$317$	1121.92	−	1943.22i	0.198780	−	0.344297i	−0.749353	−	0.662170i	$-0.769635\pi$
$317$	1121.92	−	1943.22i	0.198780	−	0.344297i	0.948133	+	0.317874i	$0.102969\pi$
$318$	3876.31	−	1122.47i	0.683562	−	0.197941i
$319$	−6181.41	−	3568.84i	−1.08493	−	0.626384i
$320$	−99.0569	+	57.1905i	−0.0173045	+	0.00999078i
$321$	9630.79	−	2788.81i	1.67457	−	0.484911i
$322$		−	2222.10i		−	0.384574i
$323$	−4160.04	−	1770.33i	−0.716629	−	0.304964i
$324$	1655.76	+	2400.32i	0.283909	+	0.411577i
$325$	−2626.03	+	1516.14i	−0.448203	+	0.258770i
$326$	3414.90	+	5914.78i	0.580165	+	1.00487i
$327$	−3064.03	+	3189.52i	−0.518170	+	0.539391i
$328$	1942.72	+	3364.89i	0.327039	+	0.566448i
$329$	−8609.68	−	4970.80i	−1.44276	−	0.832976i
$330$	194.214	−	787.704i	0.0323974	−	0.131399i
$331$			2648.14i			0.439743i	0.975529	+	0.219871i	$0.0705637\pi$
$331$			2648.14i			0.439743i	−0.975529	+	0.219871i	$0.929436\pi$
$332$	−1714.65	−	989.956i	−0.283445	−	0.163647i
$333$	−789.482	−	1248.88i	−0.129920	−	0.205520i
$334$	4685.83			0.767656
$335$	−1105.84			−0.180354
$336$	−1187.10	−	1140.39i	−0.192742	−	0.185159i
$337$	−3879.45	+	2239.80i	−0.627084	+	0.362047i	−0.779622	−	0.626251i	$-0.784589\pi$
$337$	−3879.45	+	2239.80i	−0.627084	+	0.362047i	0.152538	+	0.988298i	$0.451255\pi$
$338$	1577.27	−	2731.91i	0.253823	−	0.439635i
$339$	−5322.97	+	1541.38i	−0.852814	+	0.246951i
$340$	−195.126	−	337.968i	−0.0311241	−	0.0539084i
$341$	6484.95			1.02985
$342$	−718.625	−	4414.12i	−0.113622	−	0.697918i
$343$	−5820.57			−0.916273
$344$	−824.438	−	1427.97i	−0.129217	−	0.223811i
$345$	500.549	−	144.945i	0.0781120	−	0.0226191i
$346$	3153.62	−	5462.23i	0.489999	−	0.848704i
$347$	826.384	−	477.113i	0.127846	−	0.0738120i	−0.434713	−	0.900569i	$-0.643150\pi$
$347$	826.384	−	477.113i	0.127846	−	0.0738120i	0.562559	+	0.826757i	$0.309817\pi$
$348$	−2449.25	−	2352.89i	−0.377280	−	0.362437i
$349$	6677.56			1.02419			0.512094	−	0.858930i	$-0.328870\pi$
$349$	6677.56			1.02419			0.512094	+	0.858930i	$0.328870\pi$
$350$	−4823.43			−0.736638
$351$	3313.09	−	1105.24i	0.503816	−	0.168073i
$352$	1210.52	+	698.894i	0.183298	+	0.105827i
$353$			4400.78i			0.663541i	0.943360	+	0.331770i	$0.107646\pi$
$353$			4400.78i			0.663541i	−0.943360	+	0.331770i	$0.892354\pi$
$354$	1009.37	−	4093.87i	0.151547	−	0.614652i
$355$	−26.1007	−	15.0692i	−0.00390219	−	0.00225293i
$356$	−1053.50	−	1824.71i	−0.156841	−	0.271656i
$357$	3890.85	−	4050.19i	0.576822	−	0.600445i
$358$	−1065.56	−	1845.60i	−0.157309	−	0.272467i
$359$	4830.68	−	2789.00i	0.710177	−	0.410021i	−0.100949	−	0.994892i	$-0.532188\pi$
$359$	4830.68	−	2789.00i	0.710177	−	0.410021i	0.811127	+	0.584871i	$0.198855\pi$
$360$	179.451	−	341.791i	0.0262720	−	0.0500388i
$361$	−1902.65	+	6589.83i	−0.277395	+	0.960756i
$362$		−	8340.49i		−	1.21096i
$363$	−2879.97	+	833.959i	−0.416416	+	0.120583i
$364$	−1707.45	+	985.799i	−0.245865	+	0.141950i
$365$	114.656	+	66.1966i	0.0164421	+	0.00949284i
$366$	1121.27	−	324.689i	0.160136	−	0.0463709i
$367$	−3603.08	+	6240.71i	−0.512477	+	0.887637i	0.487418	+	0.873169i	$0.337939\pi$
$367$	−3603.08	+	6240.71i	−0.512477	+	0.887637i	−0.999895	+	0.0144679i	$0.995395\pi$
$368$			897.833i			0.127181i
$369$	−11610.4	−	6095.82i	−1.63798	−	0.859989i
$370$	−97.7992	+	169.393i	−0.0137415	+	0.0238009i
$371$	3844.32	−	6658.56i	0.537971	−	0.931793i
$372$	2996.01	+	738.687i	0.417569	+	0.102955i
$373$		−	6108.19i		−	0.847909i	−0.905683	−	0.423955i	$-0.860642\pi$
$373$		−	6108.19i		−	0.847909i	0.905683	−	0.423955i	$-0.139358\pi$
$374$	−2384.52	+	4130.12i	−0.329681	+	0.571025i
$375$	−637.505	−	2201.54i	−0.0877884	−	0.303165i
$376$	3478.72	+	2008.44i	0.477131	+	0.275472i
$377$	−3522.87	+	2033.93i	−0.481265	+	0.277859i
$378$	5443.11	+	1112.49i	0.740643	+	0.151377i
$379$			7605.25i			1.03075i	0.856964	+	0.515377i	$0.172348\pi$
$379$			7605.25i			1.03075i	−0.856964	+	0.515377i	$0.827652\pi$
$380$	−473.165	+	355.877i	−0.0638759	+	0.0480424i
$381$	6388.20	+	1575.06i	0.858996	+	0.211792i
$382$	1788.62	−	1032.66i	0.239565	−	0.138313i
$383$	3599.17	+	6233.94i	0.480180	+	0.831696i	0.999741	−	0.0227369i	$-0.00723802\pi$
$383$	3599.17	+	6233.94i	0.480180	+	0.831696i	−0.519562	+	0.854433i	$0.673905\pi$
$384$	479.643	+	460.772i	0.0637413	+	0.0612335i
$385$	−772.847	−	1338.61i	−0.102306	−	0.177200i
$386$	1006.53	+	581.121i	0.132723	+	0.0766277i
$387$	4927.14	+	2586.90i	0.647185	+	0.339792i
$388$			772.080i			0.101022i
$389$	−3403.27	−	1964.88i	−0.443580	−	0.256101i	0.261535	−	0.965194i	$-0.415771\pi$
$389$	−3403.27	−	1964.88i	−0.443580	−	0.256101i	−0.705115	+	0.709093i	$0.749105\pi$
$390$	−333.436	−	320.318i	−0.0432928	−	0.0415895i
$391$	−3063.27			−0.396206
$392$	−392.212			−0.0505350
$393$	−304.855	+	317.340i	−0.0391296	+	0.0407321i
$394$	−6592.56	+	3806.21i	−0.842965	+	0.486686i
$395$	775.273	−	1342.81i	0.0987550	−	0.171049i
$396$	−4713.74	+	189.250i	−0.598167	+	0.0240156i
$397$	93.1436	+	161.329i	0.0117752	+	0.0203952i	0.871853	−	0.489768i	$-0.162918\pi$
$397$	93.1436	+	161.329i	0.0117752	+	0.0203952i	−0.860078	+	0.510163i	$0.829585\pi$
$398$	2686.18			0.338307
$399$	−6813.54	−	5116.28i	−0.854896	−	0.641940i
$400$	1948.89			0.243612
$401$	6038.88	+	10459.6i	0.752038	+	1.30257i	0.946834	+	0.321724i	$0.104262\pi$
$401$	6038.88	+	10459.6i	0.752038	+	1.30257i	−0.194796	+	0.980844i	$0.562404\pi$
$402$	1788.56	+	6176.55i	0.221903	+	0.766314i
$403$	1847.93	−	3200.71i	0.228417	−	0.395630i
$404$	−329.514	+	190.245i	−0.0405791	+	0.0234283i
$405$	104.449	+	1298.68i	0.0128151	+	0.159338i
$406$	−6470.73			−0.790977
$407$	2390.30			0.291113
$408$	−1572.09	+	1636.47i	−0.190759	+	0.198572i
$409$	−7550.66	−	4359.38i	−0.912851	−	0.527035i	−0.0315037	−	0.999504i	$-0.510030\pi$
$409$	−7550.66	−	4359.38i	−0.912851	−	0.527035i	−0.881347	+	0.472469i	$0.843363\pi$
$410$			1736.02i			0.209112i
$411$	15192.5	+	3745.82i	1.82333	+	0.449556i
$412$	−5948.43	−	3434.33i	−0.711307	−	0.410673i
$413$	−4016.66	−	6957.06i	−0.478564	−	0.828897i
$414$	−1619.15	−	2561.33i	−0.192214	−	0.304064i
$415$	−442.313	−	766.109i	−0.0523188	−	0.0906189i
$416$	689.892	−	398.309i	0.0813095	−	0.0469441i
$417$	−1212.08	+	4916.03i	−0.142340	+	0.577312i
$418$	6657.47	+	2833.12i	0.779013	+	0.331512i
$419$		−	6943.88i		−	0.809620i	−0.914401	−	0.404810i	$-0.867338\pi$
$419$		−	6943.88i		−	0.809620i	0.914401	−	0.404810i	$-0.132662\pi$
$420$	−204.572	−	706.462i	−0.0237669	−	0.0820758i
$421$	8589.47	−	4959.13i	0.994359	−	0.574094i	0.0877848	−	0.996139i	$-0.472021\pi$
$421$	8589.47	−	4959.13i	0.994359	−	0.574094i	0.906574	+	0.422046i	$0.138688\pi$
$422$	7544.45	+	4355.79i	0.870280	+	0.502456i
$423$	−13546.0	+	543.856i	−1.55705	+	0.0625135i
$424$	−1553.29	+	2690.37i	−0.177911	+	0.308151i
$425$			6649.34i			0.758919i
$426$	−41.9528	+	170.155i	−0.00477141	+	0.0193521i
$427$	1112.02	−	1926.07i	0.126029	−	0.218288i
$428$	−3859.18	+	6684.30i	−0.435842	+	0.754901i
$429$	−1352.62	+	5486.04i	−0.152227	+	0.617409i
$430$		−	736.720i		−	0.0826227i
$431$	−5959.02	+	10321.3i	−0.665977	+	1.15351i	0.313043	+	0.949739i	$0.398652\pi$
$431$	−5959.02	+	10321.3i	−0.665977	+	1.15351i	−0.979020	+	0.203766i	$0.934682\pi$
$432$	−2199.27	−	449.499i	−0.244936	−	0.0500614i
$433$	−5470.33	−	3158.30i	−0.607130	−	0.350527i	0.164711	−	0.986342i	$-0.447331\pi$
$433$	−5470.33	−	3158.30i	−0.607130	−	0.350527i	−0.771842	+	0.635815i	$0.780664\pi$
$434$	5091.36	−	2939.50i	0.563118	−	0.325116i
$435$	−422.079	−	1457.59i	−0.0465221	−	0.160658i
$436$		−	3404.69i		−	0.373979i
$437$	562.152	+	4613.23i	0.0615363	+	0.504990i
$438$	184.292	−	747.461i	0.0201046	−	0.0815412i
$439$	796.866	−	460.071i	0.0866340	−	0.0500182i	−0.456057	−	0.889950i	$-0.650739\pi$
$439$	796.866	−	460.071i	0.0866340	−	0.0500182i	0.542691	+	0.839932i	$0.317405\pi$
$440$	312.267	+	540.862i	0.0338335	+	0.0586013i
$441$	1118.90	−	707.314i	0.120818	−	0.0763755i
$442$	1358.97	+	2353.81i	0.146244	+	0.253302i
$443$	2995.90	+	1729.68i	0.321308	+	0.185507i	0.651975	−	0.758240i	$-0.273940\pi$
$443$	2995.90	+	1729.68i	0.321308	+	0.185507i	−0.330667	+	0.943747i	$0.607274\pi$
$444$	1104.30	+	272.274i	0.118036	+	0.0291026i
$445$		−	941.409i		−	0.100286i
$446$	−133.547	−	77.1035i	−0.0141786	−	0.00818600i
$447$	−1619.92	+	1686.27i	−0.171409	+	0.178429i
$448$	1267.18			0.133635
$449$	6385.47			0.671156			0.335578	−	0.942012i	$-0.391068\pi$
$449$	6385.47			0.671156			0.335578	+	0.942012i	$0.391068\pi$
$450$	−5559.78	+	3514.63i	−0.582423	+	0.368180i
$451$	18372.7	−	10607.5i	1.91826	−	1.10751i
$452$	2132.98	−	3694.43i	0.221962	−	0.384450i
$453$	3449.28	+	11911.6i	0.357752	+	1.23545i
$454$	6041.70	+	10464.5i	0.624562	+	1.08177i
$455$	−880.912			−0.0907644
$456$	2752.99	+	2067.22i	0.282721	+	0.212295i
$457$	824.213			0.0843655			0.0421828	−	0.999110i	$-0.486569\pi$
$457$	824.213			0.0843655			0.0421828	+	0.999110i	$0.486569\pi$
$458$	137.785	+	238.651i	0.0140574	+	0.0243481i
$459$	1533.62	−	7503.59i	0.155955	−	0.763045i
$460$	−200.576	+	347.409i	−0.0203303	+	0.0352131i
$461$	15429.1	−	8908.00i	1.55880	−	0.899971i	0.561423	−	0.827529i	$-0.310254\pi$
$461$	15429.1	−	8908.00i	1.55880	−	0.899971i	0.997373	−	0.0724425i	$-0.0230794\pi$
$462$	−6226.66	+	6481.67i	−0.627036	+	0.652716i
$463$	−6243.71			−0.626717			−0.313358	−	0.949635i	$-0.601454\pi$
$463$	−6243.71			−0.626717			−0.313358	+	0.949635i	$0.601454\pi$
$464$	2614.48			0.261582
$465$	994.255	+	955.138i	0.0991558	+	0.0952547i
$466$	−8411.25	−	4856.24i	−0.836145	−	0.482748i
$467$			14029.7i			1.39019i	0.718919	+	0.695094i	$0.244637\pi$
$467$			14029.7i			1.39019i	−0.718919	+	0.695094i	$0.755363\pi$
$468$	−1249.81	+	2380.44i	−0.123445	+	0.235119i
$469$	10609.8	+	6125.57i	1.04460	+	0.603098i
$470$	897.373	+	1554.29i	0.0880696	+	0.152541i
$471$	−9451.12	−	9079.29i	−0.924596	−	0.888220i
$472$	1622.92	+	2810.98i	0.158265	+	0.274123i
$473$	−7796.87	+	4501.52i	−0.757929	+	0.437590i
$474$	−8754.02	−	2158.37i	−0.848282	−	0.209150i
$475$	10013.8	−	1220.24i	0.967292	−	0.117871i
$476$			4323.43i			0.416311i
$477$	−420.608	−	10476.3i	−0.0403738	−	1.00561i
$478$	−9264.43	+	5348.82i	−0.886496	+	0.511819i
$479$	16233.4	+	9372.37i	1.54848	+	0.894018i	0.998258	+	0.0590022i	$0.0187919\pi$
$479$	16233.4	+	9372.37i	1.54848	+	0.894018i	0.550226	+	0.835016i	$0.314541\pi$
$480$	82.6567	+	285.444i	0.00785989	+	0.0271431i
$481$	681.133	−	1179.76i	0.0645675	−	0.111834i
$482$			9901.49i			0.935685i
$483$	−5605.32	−	1382.03i	−0.528056	−	0.130196i
$484$	1154.04	−	1998.86i	0.108381	−	0.187721i
$485$	−172.483	+	298.750i	−0.0161486	+	0.0279701i
$486$	7084.68	−	2683.83i	0.661250	−	0.250496i
$487$		−	3158.98i		−	0.293937i	−0.989141	−	0.146968i	$-0.953048\pi$
$487$		−	3158.98i		−	0.293937i	0.989141	−	0.146968i	$-0.0469516\pi$
$488$	−449.307	+	778.223i	−0.0416786	+	0.0721895i
$489$	17044.1	−	4935.51i	1.57620	−	0.456424i
$490$	−151.763	−	87.6204i	−0.0139917	−	0.00807814i
$491$	−503.147	+	290.492i	−0.0462458	+	0.0267000i	−0.522945	−	0.852367i	$-0.675167\pi$
$491$	−503.147	+	290.492i	−0.0462458	+	0.0267000i	0.476699	+	0.879067i	$0.341833\pi$
$492$	9696.33	−	2807.79i	0.888505	−	0.257286i
$493$			8920.22i			0.814901i
$494$	3295.40	−	2478.54i	0.300136	−	0.225739i
$495$	−1866.22	−	979.823i	−0.169455	−	0.0889692i
$496$	−2057.15	+	1187.70i	−0.186227	+	0.107518i
$497$	166.945	+	289.158i	0.0150674	+	0.0260976i
$498$	−3563.63	+	3709.57i	−0.320662	+	0.333795i
$499$	−1806.84	−	3129.54i	−0.162095	−	0.280757i	0.773525	−	0.633766i	$-0.218492\pi$
$499$	−1806.84	−	3129.54i	−0.162095	−	0.280757i	−0.935620	+	0.353009i	$0.885158\pi$
$500$	1527.99	+	882.185i	0.136668	+	0.0789050i
$501$	2914.35	−	11820.2i	0.259887	−	1.05406i
$502$		−	3776.85i		−	0.335795i
$503$	−16052.5	−	9267.93i	−1.42295	−	0.821543i	−0.426405	−	0.904533i	$-0.640220\pi$
$503$	−16052.5	−	9267.93i	−1.42295	−	0.821543i	−0.996550	+	0.0829891i	$0.973553\pi$
$504$	−3614.99	+	2285.22i	−0.319493	+	0.201968i
$505$	−170.004			−0.0149803
$506$	4902.27			0.430696
$507$	−5910.37	−	5677.83i	−0.517729	−	0.497360i
$508$	−4386.34	+	2532.45i	−0.383095	+	0.221180i
$509$	644.409	−	1116.15i	0.0561158	−	0.0971954i	−0.836603	−	0.547810i	$-0.815462\pi$
$509$	644.409	−	1116.15i	0.0561158	−	0.0971954i	0.892719	+	0.450614i	$0.148795\pi$
$510$	−973.893	+	282.013i	−0.0845583	+	0.0244857i
$511$	−733.363	−	1270.22i	−0.0634874	−	0.109963i
$512$	−512.000			−0.0441942
$513$	−11581.7	−	932.599i	−0.996774	−	0.0802636i
$514$	6283.51			0.539209
$515$	−1534.46	−	2657.77i	−0.131294	−	0.227408i
$516$	−4114.86	+	1191.55i	−0.351059	+	0.101657i
$517$	10966.3	−	18994.2i	0.932877	−	1.61579i
$518$	1876.63	−	1083.47i	0.159179	−	0.0919018i
$519$	−11817.3	−	11352.4i	−0.999463	−	0.960141i
$520$	355.930			0.0300165
$521$	9884.31			0.831170			0.415585	−	0.909554i	$-0.363577\pi$
$521$	9884.31			0.831170			0.415585	+	0.909554i	$0.363577\pi$
$522$	−7458.55	+	4714.94i	−0.625387	+	0.395340i
$523$	12293.2	+	7097.50i	1.02781	+	0.593407i	0.916357	−	0.400362i	$-0.131116\pi$
$523$	12293.2	+	7097.50i	1.02781	+	0.593407i	0.111455	+	0.993769i	$0.464449\pi$
$524$		−	338.749i		−	0.0282410i
$525$	−2999.93	+	12167.3i	−0.249386	+	1.01147i
$526$	−2607.59	−	1505.50i	−0.216153	−	0.124796i
$527$	−4052.25	−	7018.69i	−0.334950	−	0.580150i
$528$	2515.87	−	2618.90i	0.207366	−	0.215858i
$529$	−4509.08	−	7809.95i	−0.370599	−	0.641896i
$530$	−1202.06	+	694.011i	−0.0985174	+	0.0568791i
$531$	−9699.15	−	5092.36i	−0.792669	−	0.416176i
$532$	6511.00	−	793.407i	0.530616	−	0.0646589i
$533$		−	12090.7i		−	0.982563i
$534$	−5258.12	+	1522.61i	−0.426107	+	0.123389i
$535$	−2986.55	+	1724.29i	−0.241346	+	0.139341i
$536$	−4286.86	−	2475.02i	−0.345456	−	0.199449i
$537$	−5318.32	+	1540.04i	−0.427379	+	0.123757i
$538$	−5601.40	+	9701.91i	−0.448873	+	0.777470i
$539$			2141.52i			0.171135i
$540$	−750.571	−	665.248i	−0.0598137	−	0.0530143i
$541$	−8252.23	+	14293.3i	−0.655806	+	1.13589i	0.325885	+	0.945409i	$0.394338\pi$
$541$	−8252.23	+	14293.3i	−0.655806	+	1.13589i	−0.981691	+	0.190480i	$0.938996\pi$
$542$	6414.09	−	11109.5i	0.508319	−	0.880434i
$543$	−21039.2	−	5187.36i	−1.66276	−	0.409965i
$544$		−	1746.87i		−	0.137677i
$545$	760.609	−	1317.41i	0.0597815	−	0.103545i
$546$	1424.76	+	4920.23i	0.111674	+	0.385653i
$547$	−761.024	−	439.377i	−0.0594863	−	0.0343445i	0.469962	−	0.882687i	$-0.344268\pi$
$547$	−761.024	−	439.377i	−0.0594863	−	0.0343445i	−0.529448	+	0.848342i	$0.677601\pi$
$548$	−10431.6	+	6022.70i	−0.813170	+	0.469484i
$549$	−121.666	−	3030.38i	−0.00945824	−	0.235580i
$550$		−	10641.2i		−	0.824984i
$551$	13433.7	−	1636.98i	1.03865	−	0.126566i
$552$	2264.81	+	558.406i	0.174632	+	0.0430568i
$553$	−14876.4	+	8588.92i	−1.14396	+	0.660466i
$554$	−8056.67	−	13954.6i	−0.617861	−	1.07017i
$555$	366.474	+	352.056i	0.0280288	+	0.0269260i
$556$	−1948.84	−	3375.50i	−0.148650	−	0.257469i
$557$	4268.83	+	2464.61i	0.324733	+	0.187485i	0.653500	−	0.756926i	$-0.273300\pi$
$557$	4268.83	+	2464.61i	0.324733	+	0.187485i	−0.328767	+	0.944411i	$0.606633\pi$
$558$	3726.73	−	7098.10i	0.282733	−	0.538506i
$559$			5130.96i			0.388223i
$560$	490.323	+	283.088i	0.0369999	+	0.0213619i
$561$	8935.31	+	8583.77i	0.672458	+	0.646002i
$562$	18287.2			1.37260
$563$	−10992.4			−0.822869			−0.411435	−	0.911439i	$-0.634972\pi$
$563$	−10992.4			−0.822869			−0.411435	+	0.911439i	$0.634972\pi$
$564$	7229.94	−	7526.04i	0.539779	−	0.561885i
$565$	1650.68	−	953.018i	0.122911	−	0.0709624i
$566$	−1976.69	+	3423.74i	−0.146796	+	0.254259i
$567$	6191.63	−	13038.5i	0.458596	−	0.965725i
$568$	−67.4538	−	116.833i	−0.00498292	−	0.00863067i
$569$	3636.08			0.267895			0.133948	−	0.990988i	$-0.457235\pi$
$569$	3636.08			0.267895			0.133948	+	0.990988i	$0.457235\pi$
$570$	603.428	+	1414.91i	0.0443418	+	0.103972i
$571$	−4352.03			−0.318961			−0.159481	−	0.987201i	$-0.550982\pi$
$571$	−4352.03			−0.318961			−0.159481	+	0.987201i	$0.550982\pi$
$572$	−2174.81	−	3766.89i	−0.158975	−	0.275352i
$573$	−1492.49	−	5154.11i	−0.108813	−	0.375770i
$574$	9616.30	−	16655.9i	0.699263	−	1.21116i
$575$	5919.36	−	3417.54i	0.429312	−	0.247863i
$576$	1460.63	−	923.338i	0.105659	−	0.0667924i
$577$	−21071.5			−1.52031			−0.760154	−	0.649743i	$-0.774876\pi$
$577$	−21071.5			−1.52031			−0.760154	+	0.649743i	$0.774876\pi$
$578$	−3865.94			−0.278204
$579$	2091.91	−	2177.58i	0.150150	−	0.156299i
$580$	1011.65	+	584.076i	0.0724249	+	0.0418146i
$581$			9800.40i			0.699809i
$582$	1947.60	+	480.195i	0.138712	+	0.0342005i
$583$	14689.7	+	8481.13i	1.04355	+	0.602491i
$584$	296.313	+	513.230i	0.0209958	+	0.0363658i
$585$	−1015.39	+	641.883i	−0.0717630	+	0.0453651i
$586$	−8686.57	−	15045.6i	−0.612353	−	1.06063i
$587$	−4771.22	+	2754.67i	−0.335484	+	0.193692i	−0.658273	−	0.752779i	$-0.728713\pi$
$587$	−4771.22	+	2754.67i	−0.335484	+	0.193692i	0.322789	+	0.946471i	$0.395380\pi$
$588$	−243.936	+	989.369i	−0.0171084	+	0.0693893i
$589$	−9826.38	+	7390.63i	−0.687417	+	0.517021i
$590$			1450.25i			0.101196i
$591$	5501.07	+	18997.2i	0.382883	+	1.32224i
$592$	−758.249	+	437.775i	−0.0526416	+	0.0303926i
$593$	−11072.8	−	6392.89i	−0.766789	−	0.442706i	0.0649390	−	0.997889i	$-0.479315\pi$
$593$	−11072.8	−	6392.89i	−0.766789	−	0.442706i	−0.831728	+	0.555183i	$0.812648\pi$
$594$	−2454.31	+	12008.3i	−0.169532	+	0.829470i
$595$	−965.856	+	1672.91i	−0.0665483	+	0.115265i
$596$		−	1800.02i		−	0.123711i
$597$	1670.67	−	6775.99i	0.114533	−	0.464527i
$598$	1396.94	−	2419.56i	0.0955266	−	0.165457i
$599$	−341.333	+	591.205i	−0.0232829	+	0.0403272i	−0.877432	−	0.479701i	$-0.840745\pi$
$599$	−341.333	+	591.205i	−0.0232829	+	0.0403272i	0.854149	+	0.520028i	$0.174079\pi$
$600$	1212.11	−	4916.15i	0.0824739	−	0.334502i
$601$			13750.8i			0.933292i	0.884444	+	0.466646i	$0.154538\pi$
$601$			13750.8i			0.933292i	−0.884444	+	0.466646i	$0.845462\pi$
$602$	−4080.90	+	7068.32i	−0.276287	+	0.478544i
$603$	16692.9	−	670.200i	1.12735	−	0.0452615i
$604$	−8267.33	−	4773.15i	−0.556942	−	0.321551i
$605$	893.091	−	515.626i	0.0600154	−	0.0346499i
$606$	274.959	+	949.534i	0.0184314	+	0.0636505i
$607$			4960.87i			0.331722i	0.986149	+	0.165861i	$0.0530404\pi$
$607$			4960.87i			0.331722i	−0.986149	+	0.165861i	$0.946960\pi$
$608$	−2630.75	+	320.574i	−0.175479	+	0.0213832i
$609$	−4024.46	+	16322.6i	−0.267782	+	1.08609i
$610$	−347.711	+	200.751i	−0.0230793	+	0.0133249i
$611$	−6249.84	−	10825.0i	−0.413816	−	0.716751i
$612$	3150.29	+	4983.44i	0.208077	+	0.329156i
$613$	4980.41	+	8626.32i	0.328151	+	0.568375i	0.982145	−	0.188125i	$-0.0602411\pi$
$613$	4980.41	+	8626.32i	0.328151	+	0.568375i	−0.653994	+	0.756500i	$0.726908\pi$
$614$	17013.1	+	9822.54i	1.11823	+	0.645611i
$615$	4379.17	+	1079.72i	0.287130	+	0.0707941i
$616$		−	6918.93i		−	0.452552i
$617$	−12036.2	−	6949.13i	−0.785350	−	0.453422i	0.0529727	−	0.998596i	$-0.483130\pi$
$617$	−12036.2	−	6949.13i	−0.785350	−	0.453422i	−0.838323	+	0.545174i	$0.816464\pi$
$618$	−12362.8	+	12869.2i	−0.804703	+	0.837659i
$619$	−21701.2			−1.40912			−0.704559	−	0.709645i	$-0.748855\pi$
$619$	−21701.2			−1.40912			−0.704559	+	0.709645i	$0.748855\pi$
$620$	−1061.33			−0.0687483
$621$	−7468.06	+	2491.34i	−0.482581	+	0.160989i
$622$	−13545.2	+	7820.35i	−0.873175	+	0.504128i
$623$	−5214.73	+	9032.18i	−0.335351	+	0.580845i
$624$	−575.671	−	1988.01i	−0.0369316	−	0.127538i
$625$	−7218.71	−	12503.2i	−0.461997	−	0.800203i
$626$	246.277			0.0157240
$627$	11287.2	−	15031.6i	0.718930	−	0.957426i
$628$	10088.7			0.641056
$629$	−1493.62	−	2587.03i	−0.0946816	−	0.163993i
$630$	−1909.31	+	76.6562i	−0.120744	+	0.00484771i
$631$	−8102.98	+	14034.8i	−0.511212	+	0.885445i	0.488704	+	0.872450i	$0.337470\pi$
$631$	−8102.98	+	14034.8i	−0.511212	+	0.885445i	−0.999916	+	0.0129951i	$0.995863\pi$
$632$	6010.79	−	3470.33i	0.378317	−	0.218421i
$633$	15679.9	−	16322.1i	0.984550	−	1.02487i
$634$	4487.67			0.281117
$635$	−2263.01			−0.141425
$636$	5820.49	+	5591.50i	0.362889	+	0.348612i
$637$	1056.97	+	610.242i	0.0657436	+	0.0379571i
$638$		−	14275.3i		−	0.885841i
$639$	403.128	+	211.655i	0.0249570	+	0.0131032i
$640$	−198.114	−	114.381i	−0.0122362	−	0.00706455i
$641$	−4310.57	−	7466.13i	−0.265612	−	0.460053i	0.702112	−	0.712067i	$-0.252241\pi$
$641$	−4310.57	−	7466.13i	−0.265612	−	0.460053i	−0.967724	+	0.252013i	$0.918907\pi$
$642$	14461.2	+	13892.2i	0.888997	+	0.854021i
$643$	15084.9	+	26127.7i	0.925177	+	1.60245i	0.791276	+	0.611459i	$0.209417\pi$
$643$	15084.9	+	26127.7i	0.925177	+	1.60245i	0.133901	+	0.990995i	$0.457250\pi$
$644$	3848.79	−	2222.10i	0.235502	−	0.135967i
$645$	−1858.40	−	458.202i	−0.113449	−	0.0279716i
$646$	−1093.75	−	8975.73i	−0.0666146	−	0.546665i
$647$			25613.8i			1.55639i	0.628023	+	0.778195i	$0.283864\pi$
$647$			25613.8i			1.55639i	−0.628023	+	0.778195i	$0.716136\pi$
$648$	−2501.71	+	5268.17i	−0.151661	+	0.319373i
$649$	15348.3	−	8861.33i	0.928308	−	0.535959i
$650$	−5252.06	−	3032.28i	−0.316927	−	0.182978i
$651$	−4248.42	−	14671.3i	−0.255774	−	0.883280i
$652$	−6829.80	+	11829.6i	−0.410238	+	0.710554i
$653$			15090.9i			0.904367i	0.891925	+	0.452184i	$0.149355\pi$
$653$			15090.9i			0.904367i	−0.891925	+	0.452184i	$0.850645\pi$
$654$	−8588.44	−	2117.54i	−0.513509	−	0.126609i
$655$	75.6766	−	131.076i	0.00451440	−	0.00781917i
$656$	−3885.44	+	6729.78i	−0.231252	+	0.400539i
$657$	−1770.88	−	929.765i	−0.105157	−	0.0552110i
$658$		−	19883.2i		−	1.17801i
$659$	15307.9	−	26514.0i	0.904872	−	1.56728i	0.0837829	−	0.996484i	$-0.473300\pi$
$659$	15307.9	−	26514.0i	0.904872	−	1.56728i	0.821089	−	0.570800i	$-0.193367\pi$
$660$	1558.56	−	451.315i	0.0919193	−	0.0266173i
$661$	8424.27	+	4863.75i	0.495713	+	0.286200i	0.726941	−	0.686700i	$-0.240941\pi$
$661$	8424.27	+	4863.75i	0.495713	+	0.286200i	−0.231229	+	0.972899i	$0.574275\pi$
$662$	−4586.71	+	2648.14i	−0.269286	+	0.155472i
$663$	6782.78	−	1964.11i	0.397317	−	0.115052i
$664$		−	3959.82i		−	0.231432i
$665$	2696.62	+	1147.56i	0.157249	+	0.0669179i
$666$	1373.64	−	2616.30i	0.0799211	−	0.152222i
$667$	7940.93	−	4584.70i	0.460981	−	0.266147i
$668$	4685.83	+	8116.09i	0.271407	+	0.470091i
$669$	−277.556	+	288.923i	−0.0160402	+	0.0166972i
$670$	−1105.84	−	1915.38i	−0.0637648	−	0.110444i
$671$	4249.18	+	2453.27i	0.244468	+	0.141143i
$672$	788.120	−	3196.50i	0.0452417	−	0.183494i
$673$			241.165i			0.0138131i	0.999976	+	0.00690657i	$0.00219845\pi$
$673$			241.165i			0.0138131i	−0.999976	+	0.00690657i	$0.997802\pi$
$674$	−7758.90	−	4479.60i	−0.443415	−	0.256006i
$675$	5407.87	+	16210.7i	0.308369	+	0.924368i
$676$	6309.09			0.358960
$677$	7048.12			0.400120			0.200060	−	0.979784i	$-0.435886\pi$
$677$	7048.12			0.400120			0.200060	+	0.979784i	$0.435886\pi$
$678$	−7992.72	−	7678.26i	−0.452741	−	0.434929i
$679$	3309.72	−	1910.87i	0.187062	−	0.108000i
$680$	390.251	−	675.935i	0.0220080	−	0.0381190i
$681$	30154.8	−	8732.00i	1.69682	−	0.491352i
$682$	6484.95	+	11232.3i	0.364108	+	0.630654i
$683$	6871.75			0.384978			0.192489	−	0.981299i	$-0.438344\pi$
$683$	6871.75			0.384978			0.192489	+	0.981299i	$0.438344\pi$
$684$	6926.85	−	5658.81i	0.387214	−	0.316331i
$685$	−5381.90			−0.300193
$686$	−5820.57	−	10081.5i	−0.323951	−	0.561100i
$687$	687.701	−	199.139i	0.0381913	−	0.0110591i
$688$	1648.88	−	2855.94i	0.0913704	−	0.158258i
$689$	8371.89	−	4833.51i	0.462908	−	0.267260i
$690$	751.602	+	722.031i	0.0414681	+	0.0398366i
$691$	12405.4			0.682956			0.341478	−	0.939890i	$-0.389073\pi$
$691$	12405.4			0.682956			0.341478	+	0.939890i	$0.389073\pi$
$692$	12614.5			0.692964
$693$	12477.6	+	19738.2i	0.683959	+	1.08195i
$694$	1652.77	+	954.226i	0.0904009	+	0.0521930i
$695$		−	1741.49i		−	0.0950483i
$696$	1626.07	−	6595.11i	0.0885577	−	0.359177i
$697$	−22961.0	−	13256.6i	−1.24779	−	0.720413i
$698$	6677.56	+	11565.9i	0.362105	+	0.627184i
$699$	−17481.4	+	18197.3i	−0.945933	+	0.984673i
$700$	−4823.43	−	8354.43i	−0.260441	−	0.451097i
$701$	−19745.2	+	11399.9i	−1.06386	+	0.614220i	−0.926498	−	0.376301i	$-0.877196\pi$
$701$	−19745.2	+	11399.9i	−1.06386	+	0.614220i	−0.137363	+	0.990521i	$0.543863\pi$
$702$	5227.43	+	4633.19i	0.281049	+	0.249100i
$703$	−3621.92	+	2724.13i	−0.194315	+	0.146148i
$704$			2795.58i			0.149662i
$705$	4478.88	−	1296.96i	0.239269	−	0.0692856i
$706$	−7622.38	+	4400.78i	−0.406334	+	0.234597i
$707$	1631.07	+	941.697i	0.0867647	+	0.0500936i
$708$	8100.17	−	2345.59i	0.429976	−	0.124509i
$709$	10742.4	−	18606.4i	0.569027	−	0.985583i	−0.427636	−	0.903951i	$-0.640654\pi$
$709$	10742.4	−	18606.4i	0.569027	−	0.985583i	0.996663	−	0.0816318i	$-0.0260132\pi$
$710$		−	60.2769i		−	0.00318613i
$711$	−10889.1	+	20739.9i	−0.574365	+	1.09396i
$712$	2107.00	−	3649.43i	0.110903	−	0.192090i
$713$	−4165.44	+	7214.76i	−0.218790	+	0.378955i
$714$	10906.0	+	2688.95i	0.571634	+	0.140940i
$715$		−	1943.42i		−	0.101650i
$716$	2131.12	−	3691.21i	0.111234	−	0.192663i
$717$	7730.58	+	26696.5i	0.402655	+	1.39052i
$718$	9661.36	+	5577.99i	0.502171	+	0.289929i
$719$	−6253.02	+	3610.18i	−0.324337	+	0.187256i	−0.653324	−	0.757078i	$-0.726626\pi$
$719$	−6253.02	+	3610.18i	−0.324337	+	0.187256i	0.328987	+	0.944334i	$0.393293\pi$
$720$	771.451	−	30.9727i	0.0399309	−	0.00160318i
$721$			33999.3i			1.75617i
$722$	−13316.6	+	3294.34i	−0.686414	+	0.169810i
$723$	24976.8	+	6158.22i	1.28478	+	0.316773i
$724$	14446.1	−	8340.49i	0.741556	−	0.428138i
$725$	−9951.84	−	17237.1i	−0.509796	−	0.882993i
$726$	−4324.43	−	4154.29i	−0.221067	−	0.212369i
$727$	−13254.2	−	22956.9i	−0.676162	−	1.17115i	−0.976128	−	0.217196i	$-0.930309\pi$
$727$	−13254.2	−	22956.9i	−0.676162	−	1.17115i	0.299966	−	0.953950i	$-0.403025\pi$
$728$	−3414.91	−	1971.60i	−0.173853	−	0.100374i
$729$	−2363.75	−	19540.6i	−0.120091	−	0.992763i
$730$			264.786i			0.0134249i
$731$	9744.04	+	5625.72i	0.493018	+	0.284644i
$732$	1683.65	+	1617.41i	0.0850128	+	0.0816681i
$733$	−14547.5			−0.733048			−0.366524	−	0.930409i	$-0.619452\pi$
$733$	−14547.5			−0.733048			−0.366524	+	0.930409i	$0.619452\pi$
$734$	−14412.3			−0.724752
$735$	−315.414	+	328.332i	−0.0158289	+	0.0164772i
$736$	−1555.09	+	897.833i	−0.0778824	+	0.0449654i
$737$	−13513.9	+	23406.8i	−0.675428	+	1.16988i
$738$	−1052.12	−	26205.6i	−0.0524785	−	1.30710i
$739$	13769.2	+	23848.9i	0.685395	+	1.18714i	0.973312	+	0.229484i	$0.0737038\pi$
$739$	13769.2	+	23848.9i	0.685395	+	1.18714i	−0.287917	+	0.957655i	$0.592963\pi$
$740$	−391.197			−0.0194334
$741$	−4202.64	−	9854.30i	−0.208351	−	0.488538i
$742$	15377.3			0.760806
$743$	−18413.9	−	31893.9i	−0.909209	−	1.57480i	−0.815166	−	0.579227i	$-0.803354\pi$
$743$	−18413.9	−	31893.9i	−0.909209	−	1.57480i	−0.0940425	−	0.995568i	$-0.529979\pi$
$744$	1716.56	+	5927.92i	0.0845863	+	0.292108i
$745$	402.126	−	696.503i	0.0197755	−	0.0342522i
$746$	10579.7	−	6108.19i	0.519236	−	0.299781i
$747$	7141.13	+	11296.5i	0.349773	+	0.553305i
$748$	−9538.10			−0.466240
$749$	38205.2			1.86380
$750$	3175.67	−	3305.73i	0.154612	−	0.160944i
$751$	−13262.4	−	7657.04i	−0.644409	−	0.372050i	0.141902	−	0.989881i	$-0.454678\pi$
$751$	−13262.4	−	7657.04i	−0.644409	−	0.372050i	−0.786311	+	0.617831i	$0.788012\pi$
$752$			8033.75i			0.389576i
$753$	−9527.24	−	2349.01i	−0.461078	−	0.113682i
$754$	−7045.74	−	4067.86i	−0.340306	−	0.196476i
$755$	−2132.65	−	3693.85i	−0.102801	−	0.178057i
$756$	3516.21	+	10540.2i	0.169158	+	0.507069i
$757$	1431.64	+	2479.67i	0.0687369	+	0.119056i	0.898346	−	0.439290i	$-0.144770\pi$
$757$	1431.64	+	2479.67i	0.0687369	+	0.119056i	−0.829609	+	0.558345i	$0.811436\pi$
$758$	−13172.7	+	7605.25i	−0.631205	+	0.364426i
$759$	3048.96	−	12366.1i	0.145811	−	0.591387i
$760$	−1089.56	−	463.668i	−0.0520034	−	0.0221303i
$761$			9600.25i			0.457305i	0.973508	+	0.228652i	$0.0734319\pi$
$761$			9600.25i			0.457305i	−0.973508	+	0.228652i	$0.926568\pi$
$762$	3660.12	+	12639.8i	0.174006	+	0.600905i
$763$	−14595.1	+	8426.46i	−0.692499	+	0.399814i
$764$	3577.24	+	2065.32i	0.169398	+	0.0978018i
$765$	105.674	+	2632.08i	0.00499434	+	0.124396i
$766$	−7198.34	+	12467.9i	−0.339539	+	0.588098i
$767$		−	10100.4i		−	0.475494i
$768$	−318.438	+	1291.54i	−0.0149618	+	0.0606827i
$769$	5763.92	−	9983.40i	0.270289	−	0.468154i	−0.698647	−	0.715467i	$-0.746214\pi$
$769$	5763.92	−	9983.40i	0.270289	−	0.468154i	0.968936	+	0.247313i	$0.0795474\pi$
$770$	1545.69	−	2677.22i	0.0723415	−	0.125299i
$771$	3908.02	−	15850.4i	0.182547	−	0.740385i
$772$			2324.48i			0.108368i
$773$	−7489.26	+	12971.8i	−0.348474	+	0.603574i	−0.985979	−	0.166872i	$-0.946633\pi$
$773$	−7489.26	+	12971.8i	−0.348474	+	0.603574i	0.637505	+	0.770446i	$0.279967\pi$
$774$	446.492	+	11121.0i	0.0207349	+	0.516453i
$775$	15660.8	+	9041.78i	0.725875	+	0.419084i
$776$	−1337.28	+	772.080i	−0.0618629	+	0.0357166i
$777$	−1565.93	−	5407.74i	−0.0723005	−	0.249680i
$778$		−	7859.51i		−	0.362181i
$779$	−15750.5	+	37011.6i	−0.724414	+	1.70228i
$780$	221.371	−	897.846i	0.0101620	−	0.0412155i
$781$	−637.923	+	368.305i	−0.0292275	+	0.0168745i
$782$	−3063.27	−	5305.75i	−0.140080	−	0.242625i
$783$	7254.76	+	21746.9i	0.331116	+	0.992556i
$784$	−392.212	−	679.332i	−0.0178668	−	0.0309462i
$785$	3903.74	+	2253.82i	0.177491	+	0.102474i
$786$	−854.505	−	210.684i	−0.0387776	−	0.00956090i
$787$		−	19828.3i		−	0.898096i	−0.893508	−	0.449048i	$-0.851763\pi$
$787$		−	19828.3i		−	0.898096i	0.893508	−	0.449048i	$-0.148237\pi$
$788$	−13185.1	−	7612.43i	−0.596066	−	0.344139i
$789$	−5419.46	+	5641.41i	−0.244535	+	0.254549i
$790$	3101.09			0.139661
$791$	−21116.1			−0.949183
$792$	−5041.53	−	7975.18i	−0.226191	−	0.357810i
$793$	2421.67	−	1398.15i	0.108444	−	0.0626101i
$794$	−186.287	+	322.659i	−0.00832631	+	0.0144216i
$795$	1003.04	+	3463.88i	0.0447476	+	0.154530i
$796$	2686.18	+	4652.61i	0.119610	+	0.207170i
$797$	−11929.1			−0.530175			−0.265087	−	0.964224i	$-0.585401\pi$
$797$	−11929.1			−0.530175			−0.265087	+	0.964224i	$0.585401\pi$
$798$	2048.11	−	16917.7i	0.0908551	−	0.750475i
$799$	−27410.0			−1.21364
$800$	1948.89	+	3375.58i	0.0861298	+	0.149181i
$801$	570.545	+	14210.8i	0.0251675	+	0.626858i
$802$	−12077.8	+	20919.3i	−0.531771	+	0.921054i
$803$	2802.29	−	1617.90i	0.123152	−	0.0711016i
$804$	−8909.54	+	9274.42i	−0.390815	+	0.406821i
$805$	1985.67			0.0869388
$806$	7391.73			0.323031
$807$	20989.6	+	20163.8i	0.915575	+	0.879554i
$808$	−659.029	−	380.490i	−0.0286937	−	0.0165663i
$809$		−	35874.5i		−	1.55906i	−0.626365	−	0.779530i	$-0.715458\pi$
$809$		−	35874.5i		−	1.55906i	0.626365	−	0.779530i	$-0.284542\pi$
$810$	−2144.93	+	1479.59i	−0.0930433	+	0.0641821i
$811$	34412.8	+	19868.2i	1.49001	+	0.860257i	0.999935	−	0.0114235i	$-0.00363628\pi$
$811$	34412.8	+	19868.2i	1.49001	+	0.860257i	0.490074	+	0.871681i	$0.336970\pi$
$812$	−6470.73	−	11207.6i	−0.279653	−	0.484373i
$813$	−24034.9	−	23089.3i	−1.03683	−	0.996037i
$814$	2390.30	+	4140.12i	0.102924	+	0.178269i
$815$	−5285.46	+	3051.56i	−0.227167	+	0.131155i
$816$	−4406.54	−	1086.46i	−0.189044	−	0.0466101i
$817$	6684.07	−	15706.7i	0.286225	−	0.672593i
$818$		−	17437.5i		−	0.745340i
$819$	13297.6	−	533.880i	0.567344	−	0.0227781i
$820$	−3006.87	+	1736.02i	−0.128054	+	0.0739323i
$821$	−30142.6	−	17402.8i	−1.28134	−	0.739784i	−0.304249	−	0.952593i	$-0.598405\pi$
$821$	−30142.6	−	17402.8i	−1.28134	−	0.739784i	−0.977094	+	0.212809i	$0.931739\pi$
$822$	8704.54	+	30060.0i	0.369350	+	1.27550i
$823$	10882.6	−	18849.2i	0.460926	−	0.798348i	−0.538081	−	0.842893i	$-0.680851\pi$
$823$	10882.6	−	18849.2i	0.460926	−	0.798348i	0.999007	+	0.0445454i	$0.0141839\pi$
$824$		−	13737.3i		−	0.580779i
$825$	−26842.7	−	6618.27i	−1.13278	−	0.279295i
$826$	8033.32	−	13914.1i	0.338396	−	0.586119i
$827$	20626.9	−	35726.8i	0.867311	−	1.50223i	0.00257684	−	0.999997i	$-0.499180\pi$
$827$	20626.9	−	35726.8i	0.867311	−	1.50223i	0.864734	−	0.502230i	$-0.167487\pi$
$828$	2817.20	−	5365.77i	0.118242	−	0.225209i
$829$		−	15830.1i		−	0.663211i	−0.943418	−	0.331605i	$-0.892410\pi$
$829$		−	15830.1i		−	0.663211i	0.943418	−	0.331605i	$-0.107590\pi$
$830$	884.627	−	1532.22i	0.0369950	−	0.0640772i
$831$	−40211.7	+	11644.2i	−1.67861	+	0.486080i
$832$	1379.78	+	796.619i	0.0574945	+	0.0331945i
$833$	2317.78	−	1338.17i	0.0964061	−	0.0556601i
$834$	−9726.89	+	2816.64i	−0.403855	+	0.116945i
$835$			4187.27i			0.173541i
$836$	1750.37	+	14364.2i	0.0724136	+	0.594253i
$837$	−15587.4	−	13815.5i	−0.643702	−	0.570528i
$838$	12027.2	−	6943.88i	0.495789	−	0.286244i
$839$	−12291.2	−	21289.0i	−0.505769	−	0.876017i	−0.999978	−	0.00667405i	$-0.997876\pi$
$839$	−12291.2	−	21289.0i	−0.505769	−	0.876017i	0.494209	−	0.869343i	$-0.335458\pi$
$840$	1019.06	−	1060.79i	0.0418581	−	0.0435723i
$841$	−1156.09	−	2002.41i	−0.0474022	−	0.0821030i
$842$	17178.9	+	9918.27i	0.703118	+	0.405945i
$843$	11373.7	−	46130.1i	0.464687	−	1.88470i
$844$			17423.2i			0.710581i
$845$	2441.25	+	1409.45i	0.0993863	+	0.0573807i
$846$	−14488.0	−	22918.6i	−0.588781	−	0.931391i
$847$	−11424.8			−0.463472
$848$	−6213.15			−0.251604
$849$	7407.09	+	7115.67i	0.299424	+	0.287643i
$850$	−11517.0	+	6649.34i	−0.464741	+	0.268318i
$851$	−1535.35	+	2659.30i	−0.0618461	+	0.107121i
$852$	−336.669	+	97.4901i	−0.0135377	+	0.00392014i
$853$	−21539.1	−	37306.8i	−0.864576	−	1.49749i	−0.867467	−	0.497494i	$-0.834254\pi$
$853$	−21539.1	−	37306.8i	−0.864576	−	1.49749i	0.00289122	−	0.999996i	$-0.499080\pi$
$854$	4448.06			0.178231
$855$	3944.46	−	642.165i	0.157775	−	0.0256861i
$856$	−15436.7			−0.616374
$857$	−2181.43	−	3778.35i	−0.0869502	−	0.150602i	0.819270	−	0.573407i	$-0.194379\pi$
$857$	−2181.43	−	3778.35i	−0.0869502	−	0.150602i	−0.906221	+	0.422805i	$0.861045\pi$
$858$	−10854.7	+	3143.23i	−0.431905	+	0.125068i
$859$	−3194.53	+	5533.09i	−0.126887	+	0.219775i	−0.922469	−	0.386071i	$-0.873832\pi$
$859$	−3194.53	+	5533.09i	−0.126887	+	0.219775i	0.795582	+	0.605846i	$0.207165\pi$
$860$	1276.04	−	736.720i	0.0505959	−	0.0292116i
$861$	−36034.3	−	34616.6i	−1.42630	−	1.37019i
$862$	−23836.1			−0.941833
$863$	50392.1			1.98768			0.993839	−	0.110832i	$-0.0353514\pi$
$863$	50392.1			1.98768			0.993839	+	0.110832i	$0.0353514\pi$
$864$	−1420.72	−	4258.75i	−0.0559419	−	0.167692i
$865$	4881.07	+	2818.08i	0.191863	+	0.110772i
$866$		−	12633.2i		−	0.495720i
$867$	−2404.42	+	9751.97i	−0.0941850	+	0.382000i
$868$	10182.7	+	5879.00i	0.398184	+	0.229892i
$869$	−18948.4	−	32819.6i	−0.739678	−	1.28116i
$870$	2102.55	−	2188.66i	0.0819345	−	0.0852901i
$871$	7701.76	+	13339.8i	0.299614	+	0.518947i
$872$	5897.09	−	3404.69i	0.229015	−	0.132222i
$873$	2422.62	−	4614.23i	0.0939211	−	0.178887i
$874$	−7428.20	+	5586.91i	−0.287486	+	0.216224i
$875$		−	8733.48i		−	0.337424i
$876$	1478.93	−	428.258i	0.0570416	−	0.0165177i
$877$	30324.7	−	17508.0i	1.16761	−	0.674119i	0.214493	−	0.976725i	$-0.431190\pi$
$877$	30324.7	−	17508.0i	1.16761	−	0.674119i	0.953116	+	0.302606i	$0.0978567\pi$
$878$	1593.73	+	920.142i	0.0612595	+	0.0353682i
$879$	−43355.6	+	12554.6i	−1.66365	+	0.481747i
$880$	−624.533	+	1081.72i	−0.0239239	+	0.0414374i
$881$		−	10685.4i		−	0.408628i	−0.978905	−	0.204314i	$-0.934504\pi$
$881$		−	10685.4i		−	0.408628i	0.978905	−	0.204314i	$-0.0654964\pi$
$882$	2344.00	+	1230.67i	0.0894860	+	0.0469829i
$883$	−8122.70	+	14068.9i	−0.309570	+	0.536191i	−0.978268	−	0.207343i	$-0.933519\pi$
$883$	−8122.70	+	14068.9i	−0.309570	+	0.536191i	0.668698	+	0.743534i	$0.266852\pi$
$884$	−2717.95	+	4707.62i	−0.103410	+	0.179111i
$885$	3658.29	+	901.979i	0.138952	+	0.0342595i
$886$			6918.73i			0.262347i
$887$	359.122	−	622.017i	0.0135943	−	0.0235460i	−0.859148	−	0.511727i	$-0.829006\pi$
$887$	359.122	−	622.017i	0.0135943	−	0.0235460i	0.872743	+	0.488181i	$0.162339\pi$
$888$	632.711	+	2184.98i	0.0239103	+	0.0825712i
$889$	21712.0	+	12535.4i	0.819120	+	0.472919i
$890$	1630.57	−	941.409i	0.0614121	−	0.0354563i
$891$	28764.8	+	13659.6i	1.08155	+	0.513597i
$892$		−	308.414i		−	0.0115767i
$893$	5030.10	+	41278.9i	0.188495	+	1.54686i
$894$	−4540.62	−	1119.52i	−0.169867	−	0.0418819i
$895$	1649.24	−	952.187i	0.0615954	−	0.0355621i
$896$	1267.18	+	2194.82i	0.0472472	+	0.0818345i
$897$	−5234.61	−	5028.66i	−0.194848	−	0.187182i
$898$	6385.47	+	11060.0i	0.237289	+	0.410997i
$899$	21009.3	+	12129.7i	0.779421	+	0.449999i
$900$	−11647.3	−	6115.19i	−0.431381	−	0.226489i
$901$		−	21198.4i		−	0.783818i
$902$	36745.4	+	21214.9i	1.35642	+	0.783127i
$903$	15292.0	+	14690.3i	0.563549	+	0.541378i
$904$	8531.92			0.313902
$905$	7453.08			0.273755
$906$	−17182.3	+	17886.0i	−0.630070	+	0.655874i
$907$	23862.6	−	13777.1i	0.873588	−	0.504366i	0.00504887	−	0.999987i	$-0.498393\pi$
$907$	23862.6	−	13777.1i	0.873588	−	0.504366i	0.868539	+	0.495621i	$0.165060\pi$
$908$	−12083.4	+	20929.1i	−0.441632	+	0.764929i
$909$	2566.24	−	103.031i	0.0936379	−	0.00375944i
$910$	−880.912	−	1525.78i	−0.0320901	−	0.0555816i
$911$	−18830.7			−0.684840			−0.342420	−	0.939547i	$-0.611247\pi$
$911$	−18830.7			−0.684840			−0.342420	+	0.939547i	$0.611247\pi$
$912$	−827.534	+	6835.54i	−0.0300465	+	0.248188i
$913$	−21621.1			−0.783739
$914$	824.213	+	1427.58i	0.0298277	+	0.0516631i
$915$	290.143	+	1001.97i	0.0104829	+	0.0362012i
$916$	−275.570	+	477.302i	−0.00994007	+	0.0172167i
$917$	−1452.13	+	838.388i	−0.0522940	+	0.0301920i
$918$	14530.2	−	4847.28i	0.522406	−	0.174274i
$919$	29940.1			1.07468			0.537341	−	0.843365i	$-0.319429\pi$
$919$	29940.1			1.07468			0.537341	+	0.843365i	$0.319429\pi$
$920$	−802.306			−0.0287513
$921$	35359.0	−	36807.1i	1.26506	−	1.31687i
$922$	30858.2	+	17816.0i	1.10224	+	0.636376i
$923$			419.805i			0.0149708i
$924$	−17453.2	−	4303.22i	−0.621396	−	0.153210i
$925$	5772.45	+	3332.72i	0.205186	+	0.118464i
$926$	−6243.71	−	10814.4i	−0.221578	−	0.383784i
$927$	24773.8	+	39189.6i	0.877755	+	1.38852i
$928$	2614.48	+	4528.41i	0.0924833	+	0.160186i
$929$	−22666.3	+	13086.4i	−0.800493	+	0.462165i	−0.843644	−	0.536904i	$-0.819594\pi$
$929$	−22666.3	+	13086.4i	−0.800493	+	0.462165i	0.0431503	+	0.999069i	$0.486261\pi$
$930$	−660.092	+	2677.24i	−0.0232745	+	0.0943979i
$931$	−2440.60	−	3244.96i	−0.0859157	−	0.114231i
$932$		−	19424.9i		−	0.682709i
$933$	11302.6	+	39032.2i	0.396605	+	1.36962i
$934$	−24300.2	+	14029.7i	−0.851313	+	0.491506i
$935$	−3690.68	−	2130.82i	−0.129089	−	0.0745296i
$936$	−5372.85	+	215.713i	−0.187625	+	0.00753290i
$937$	26974.7	−	46721.6i	0.940475	−	1.62895i	0.175908	−	0.984407i	$-0.443714\pi$
$937$	26974.7	−	46721.6i	0.940475	−	1.62895i	0.764567	−	0.644544i	$-0.222953\pi$
$938$			24502.3i			0.852909i
$939$	153.172	−	621.242i	0.00532329	−	0.0215905i
$940$	−1794.75	+	3108.59i	−0.0622746	+	0.107863i
$941$	1604.89	−	2779.76i	0.0555984	−	0.0962992i	−0.836887	−	0.547376i	$-0.815627\pi$
$941$	1604.89	−	2779.76i	0.0555984	−	0.0962992i	0.892485	+	0.451077i	$0.148960\pi$
$942$	6274.66	−	25449.1i	0.217027	−	0.880230i
$943$			27253.7i			0.941149i
$944$	−3245.84	+	5621.96i	−0.111910	+	0.193834i
$945$	−994.124	+	4863.97i	−0.0342210	+	0.167434i
$946$	−15593.7	−	9003.05i	−0.535937	−	0.309423i
$947$	−19169.4	+	11067.5i	−0.657785	+	0.379772i	−0.791432	−	0.611257i	$-0.790664\pi$
$947$	−19169.4	+	11067.5i	−0.657785	+	0.379772i	0.133648	+	0.991029i	$0.457331\pi$
$948$	−5015.62	−	17320.8i	−0.171835	−	0.593410i
$949$		−	1844.13i		−	0.0630802i
$950$	12127.3	+	16124.1i	0.414170	+	0.550669i
$951$	2791.10	−	11320.3i	0.0951712	−	0.386000i
$952$	−7488.39	+	4323.43i	−0.254937	+	0.147188i
$953$	1147.36	+	1987.28i	0.0389995	+	0.0675492i	0.884866	−	0.465845i	$-0.154250\pi$
$953$	1147.36	+	1987.28i	0.0389995	+	0.0675492i	−0.845867	+	0.533394i	$0.820916\pi$
$954$	17724.8	−	11204.8i	0.601532	−	0.380260i
$955$	922.787	+	1598.31i	0.0312677	+	0.0541573i
$956$	−18528.9	−	10697.6i	−0.626848	−	0.361911i
$957$	−36010.1	−	8878.54i	−1.21634	−	0.299898i
$958$			37489.5i			1.26433i
$959$	51635.7	+	29811.9i	1.73869	+	1.00383i
$960$	−411.747	+	428.610i	−0.0138428	+	0.0144097i
$961$	7750.02			0.260146
$962$	2724.53			0.0913123
$963$	44037.7	−	27838.5i	1.47362	−	0.931551i
$964$	−17149.9	+	9901.49i	−0.572988	+	0.330815i
$965$	−519.291	+	899.439i	−0.0173229	+	0.0300041i
$966$	−3211.57	−	11090.7i	−0.106967	−	0.369398i
$967$	−27807.6	−	48164.2i	−0.924749	−	1.60171i	−0.791965	−	0.610566i	$-0.790942\pi$
$967$	−27807.6	−	48164.2i	−0.924749	−	1.60171i	−0.132784	−	0.991145i	$-0.542392\pi$
$968$	4616.16			0.153274
$969$	−23321.9	−	2823.43i	−0.773174	−	0.0936032i
$970$	−689.933			−0.0228375
$971$	24714.7	+	42807.1i	0.816821	+	1.41478i	0.908013	+	0.418942i	$0.137599\pi$
$971$	24714.7	+	42807.1i	0.816821	+	1.41478i	−0.0911923	+	0.995833i	$0.529068\pi$
$972$	11733.2	+	9587.19i	0.387184	+	0.316368i
$973$	−9646.62	+	16708.4i	−0.317838	+	0.550511i
$974$	5471.52	−	3158.98i	0.179999	−	0.103922i
$975$	−10915.5	+	11362.6i	−0.358541	+	0.373224i
$976$	−1797.23			−0.0589425
$977$	35406.9			1.15944			0.579718	−	0.814818i	$-0.303163\pi$
$977$	35406.9			1.15944			0.579718	+	0.814818i	$0.303163\pi$
$978$	25592.7	+	24585.8i	0.836772	+	0.803851i
$979$	−19926.3	−	11504.4i	−0.650507	−	0.375570i
$980$		−	350.482i		−	0.0114242i
$981$	−10683.1	+	20347.6i	−0.347693	+	0.662232i
$982$	−1006.29	−	580.984i	−0.0327007	−	0.0188798i
$983$	14106.4	+	24433.0i	0.457705	+	0.792768i	0.998839	−	0.0481679i	$-0.0153382\pi$
$983$	14106.4	+	24433.0i	0.457705	+	0.792768i	−0.541134	+	0.840936i	$0.682005\pi$
$984$	14559.6	+	13986.7i	0.471689	+	0.453131i
$985$	−3401.24	−	5891.12i	−0.110023	−	0.190565i
$986$	−15450.3	+	8920.22i	−0.499023	+	0.288111i
$987$	−50156.1	−	12366.3i	−1.61751	−	0.398809i
$988$	7588.37	+	3229.26i	0.244350	+	0.103984i
$989$		−	11565.7i		−	0.371860i
$990$	−169.115	−	4212.21i	−0.00542911	−	0.135225i
$991$	−4302.80	+	2484.22i	−0.137924	+	0.0796306i	−0.567374	−	0.823460i	$-0.692041\pi$
$991$	−4302.80	+	2484.22i	−0.137924	+	0.0796306i	0.429450	+	0.903091i	$0.358707\pi$
$992$	−4114.30	−	2375.39i	−0.131683	−	0.0760270i
$993$	3827.32	+	13217.1i	0.122312	+	0.422390i
$994$	−333.891	+	578.316i	−0.0106543	+	0.0184538i
$995$			2400.38i			0.0764796i
$996$	−9988.79	−	2462.81i	−0.317778	−	0.0783505i
$997$	20068.8	−	34760.2i	0.637498	−	1.10418i	−0.348482	−	0.937316i	$-0.613303\pi$
$997$	20068.8	−	34760.2i	0.637498	−	1.10418i	0.985980	−	0.166864i	$-0.0533640\pi$
$998$	3613.69	−	6259.09i	0.114618	−	0.198525i
$999$	−5745.38	−	5092.26i	−0.181958	−	0.161273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.4.h.b.107.10	yes	20
3.2	odd	2		114.4.h.a.107.8	yes	20
19.8	odd	6		114.4.h.a.65.8	✓	20
57.8	even	6	inner	114.4.h.b.65.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.h.a.65.8	✓	20	19.8	odd	6
114.4.h.a.107.8	yes	20	3.2	odd	2
114.4.h.b.65.10	yes	20	57.8	even	6	inner
114.4.h.b.107.10	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	114.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(4.99111 - 1.44529i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-1.54776 + 0.893602i) q^{5} +(7.49442 + 7.19956i) q^{6} +19.7997 q^{7} -8.00000 q^{8} +(22.8223 - 14.4272i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(4.99111 - 1.44529i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-1.54776 + 0.893602i) q^{5} +(7.49442 + 7.19956i) q^{6} +19.7997 q^{7} -8.00000 q^{8} +(22.8223 - 14.4272i) q^{9} +(-3.09553 - 1.78720i) q^{10} +43.6809i q^{11} +(-4.97559 + 20.1803i) q^{12} +(21.5591 + 12.4472i) q^{13} +(19.7997 + 34.2940i) q^{14} +(-6.43355 + 6.69703i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(47.2760 - 27.2948i) q^{17} +(47.8109 + 25.1022i) q^{18} +(-49.7813 - 66.1878i) q^{19} -7.14882i q^{20} +(98.8222 - 28.6162i) q^{21} +(-75.6575 + 43.6809i) q^{22} +(-48.5966 - 28.0573i) q^{23} +(-39.9289 + 11.5623i) q^{24} +(-60.9029 + 105.487i) q^{25} +49.7887i q^{26} +(93.0571 - 104.992i) q^{27} +(-39.5993 + 68.5880i) q^{28} +(-81.7025 + 141.513i) q^{29} +(-18.0331 - 4.44620i) q^{30} -148.462i q^{31} +(16.0000 - 27.7128i) q^{32} +(63.1314 + 218.016i) q^{33} +(94.5520 + 54.5896i) q^{34} +(-30.6452 + 17.6930i) q^{35} +(4.33257 + 107.913i) q^{36} -54.7219i q^{37} +(64.8594 - 152.411i) q^{38} +(125.594 + 30.9660i) q^{39} +(12.3821 - 7.14882i) q^{40} +(-242.840 - 420.611i) q^{41} +(148.387 + 142.549i) q^{42} +(103.055 + 178.496i) q^{43} +(-151.315 - 87.3618i) q^{44} +(-22.4314 + 42.7239i) q^{45} -112.229i q^{46} +(-434.840 - 251.055i) q^{47} +(-59.9553 - 57.5965i) q^{48} +49.0265 q^{49} -243.612 q^{50} +(196.511 - 204.559i) q^{51} +(-86.2365 + 49.7887i) q^{52} +(194.161 - 336.297i) q^{53} +(274.909 + 56.1874i) q^{54} +(-39.0333 - 67.6077i) q^{55} -158.397 q^{56} +(-344.124 - 258.402i) q^{57} -326.810 q^{58} +(-202.865 - 351.373i) q^{59} +(-10.3321 - 35.6805i) q^{60} +(56.1634 - 97.2778i) q^{61} +(257.144 - 148.462i) q^{62} +(451.874 - 285.653i) q^{63} +64.0000 q^{64} -44.4913 q^{65} +(-314.483 + 327.363i) q^{66} +(535.858 + 309.378i) q^{67} +218.359i q^{68} +(-283.102 - 69.8008i) q^{69} +(-61.2904 - 35.3860i) q^{70} +(8.43173 + 14.6042i) q^{71} +(-182.578 + 115.417i) q^{72} +(-37.0392 - 64.1537i) q^{73} +(94.7811 - 54.7219i) q^{74} +(-151.514 + 614.519i) q^{75} +(328.844 - 40.0717i) q^{76} +864.867i q^{77} +(71.9589 + 248.501i) q^{78} +(-751.348 + 433.791i) q^{79} +(24.7642 + 14.2976i) q^{80} +(312.714 - 658.522i) q^{81} +(485.680 - 841.223i) q^{82} +494.978i q^{83} +(-98.5150 + 399.563i) q^{84} +(-48.7814 + 84.4919i) q^{85} +(-206.110 + 356.992i) q^{86} +(-203.259 + 824.389i) q^{87} -349.447i q^{88} +(-263.375 + 456.178i) q^{89} +(-96.4314 + 3.87159i) q^{90} +(426.864 + 246.450i) q^{91} +(194.387 - 112.229i) q^{92} +(-214.570 - 740.990i) q^{93} -1004.22i q^{94} +(136.195 + 57.9585i) q^{95} +(39.8047 - 161.442i) q^{96} +(167.160 - 96.5100i) q^{97} +(49.0265 + 84.9164i) q^{98} +(630.191 + 996.898i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} + q^{3} - 40 q^{4} - 8 q^{6} - 10 q^{7} - 160 q^{8} - 37 q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 + q^3 - 40 * q^4 - 8 * q^6 - 10 * q^7 - 160 * q^8 - 37 * q^9	\( 20 q + 20 q^{2} + q^{3} - 40 q^{4} - 8 q^{6} - 10 q^{7} - 160 q^{8} - 37 q^{9} - 20 q^{12} - 111 q^{13} - 10 q^{14} - 133 q^{15} - 160 q^{16} - 90 q^{17} - 10 q^{18} - 143 q^{19} + 191 q^{21} - 54 q^{22} - 8 q^{24} + 184 q^{25} - 524 q^{27} + 20 q^{28} - 96 q^{29} - 292 q^{30} + 320 q^{32} - 55 q^{33} - 180 q^{34} + 774 q^{35} + 128 q^{36} - 314 q^{38} + 1002 q^{39} + 537 q^{41} - 382 q^{42} + 571 q^{43} - 108 q^{44} + 1516 q^{45} - 126 q^{47} + 64 q^{48} + 558 q^{49} + 736 q^{50} - 757 q^{51} + 444 q^{52} + 126 q^{53} - 1388 q^{54} + 366 q^{55} + 80 q^{56} - 281 q^{57} - 384 q^{58} - 1383 q^{59} - 52 q^{60} + 149 q^{61} - 222 q^{62} + 1153 q^{63} + 1280 q^{64} + 3636 q^{65} + 32 q^{66} - 1626 q^{67} + 236 q^{69} + 1548 q^{70} - 1368 q^{71} + 296 q^{72} + 946 q^{73} + 474 q^{74} - 669 q^{75} - 56 q^{76} + 132 q^{78} - 2109 q^{79} + 311 q^{81} - 1074 q^{82} - 1528 q^{84} + 786 q^{85} - 1142 q^{86} - 816 q^{87} - 1938 q^{89} + 1234 q^{90} - 3459 q^{91} - 705 q^{93} + 2502 q^{95} + 160 q^{96} + 1791 q^{97} + 558 q^{98} - 2285 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 + q^3 - 40 * q^4 - 8 * q^6 - 10 * q^7 - 160 * q^8 - 37 * q^9 - 20 * q^12 - 111 * q^13 - 10 * q^14 - 133 * q^15 - 160 * q^16 - 90 * q^17 - 10 * q^18 - 143 * q^19 + 191 * q^21 - 54 * q^22 - 8 * q^24 + 184 * q^25 - 524 * q^27 + 20 * q^28 - 96 * q^29 - 292 * q^30 + 320 * q^32 - 55 * q^33 - 180 * q^34 + 774 * q^35 + 128 * q^36 - 314 * q^38 + 1002 * q^39 + 537 * q^41 - 382 * q^42 + 571 * q^43 - 108 * q^44 + 1516 * q^45 - 126 * q^47 + 64 * q^48 + 558 * q^49 + 736 * q^50 - 757 * q^51 + 444 * q^52 + 126 * q^53 - 1388 * q^54 + 366 * q^55 + 80 * q^56 - 281 * q^57 - 384 * q^58 - 1383 * q^59 - 52 * q^60 + 149 * q^61 - 222 * q^62 + 1153 * q^63 + 1280 * q^64 + 3636 * q^65 + 32 * q^66 - 1626 * q^67 + 236 * q^69 + 1548 * q^70 - 1368 * q^71 + 296 * q^72 + 946 * q^73 + 474 * q^74 - 669 * q^75 - 56 * q^76 + 132 * q^78 - 2109 * q^79 + 311 * q^81 - 1074 * q^82 - 1528 * q^84 + 786 * q^85 - 1142 * q^86 - 816 * q^87 - 1938 * q^89 + 1234 * q^90 - 3459 * q^91 - 705 * q^93 + 2502 * q^95 + 160 * q^96 + 1791 * q^97 + 558 * q^98 - 2285 * q^99

Introduction

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