LMFDB - Embedded newform 114.4.h.a.107.8

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			107.8
Root			$1.24390 + 5.04507i$ of defining polynomial
Character	$\chi$	$=$	114.107
Dual form			114.4.h.a.65.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(3.74721 - 3.59978i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(1.54776 - 0.893602i) q^{5} +(-9.98221 - 2.89057i) q^{6} +19.7997 q^{7} +8.00000 q^{8} +(1.08314 - 26.9783i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(3.74721 - 3.59978i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(1.54776 - 0.893602i) q^{5} +(-9.98221 - 2.89057i) q^{6} +19.7997 q^{7} +8.00000 q^{8} +(1.08314 - 26.9783i) 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} +(2.58302 - 8.92013i) 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} +(74.1935 - 71.2745i) q^{21} +(-75.6575 + 43.6809i) q^{22} +(48.5966 + 28.0573i) q^{23} +(29.9777 - 28.7983i) 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} +(-157.242 - 163.681i) q^{33} +(94.5520 + 54.5896i) q^{34} +(30.6452 - 17.6930i) q^{35} +(91.2892 + 57.7086i) 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} +(-197.644 - 57.2324i) 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} +(-79.8577 - 23.1246i) q^{48} +49.0265 q^{49} +243.612 q^{50} +(-78.8977 + 272.463i) q^{51} +(-86.2365 + 49.7887i) q^{52} +(-194.161 + 336.297i) q^{53} +(-88.7948 + 266.172i) q^{54} +(-39.0333 - 67.6077i) q^{55} +158.397 q^{56} +(-424.802 - 68.8178i) q^{57} -326.810 q^{58} +(202.865 + 351.373i) q^{59} +(25.7342 + 26.7881i) q^{60} +(56.1634 - 97.2778i) q^{61} +(-257.144 + 148.462i) q^{62} +(21.4458 - 534.160i) q^{63} +64.0000 q^{64} +44.4913 q^{65} +(-126.263 + 436.032i) 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} +(8.66514 - 215.826i) 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} +(-179.228 - 186.569i) q^{78} +(-751.348 + 433.791i) q^{79} +(-24.7642 - 14.2976i) q^{80} +(-726.654 - 58.4426i) 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} +(-51.5686 + 81.5762i) q^{90} +(426.864 + 246.450i) q^{91} +(-194.387 + 112.229i) q^{92} +(-534.431 - 556.318i) 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} +(-1178.43 - 47.3126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} - 4 q^{3} - 40 q^{4} - 2 q^{6} - 10 q^{7} + 160 q^{8} + 32 q^{9}+O(q^{10}) $ 20 * q - 20 * q^2 - 4 * q^3 - 40 * q^4 - 2 * q^6 - 10 * q^7 + 160 * q^8 + 32 * q^9	\( 20 q - 20 q^{2} - 4 q^{3} - 40 q^{4} - 2 q^{6} - 10 q^{7} + 160 q^{8} + 32 q^{9} + 20 q^{12} - 111 q^{13} + 10 q^{14} + 13 q^{15} - 160 q^{16} + 90 q^{17} + 10 q^{18} - 143 q^{19} - 191 q^{21} - 54 q^{22} - 32 q^{24} + 184 q^{25} + 524 q^{27} + 20 q^{28} + 96 q^{29} - 292 q^{30} - 320 q^{32} + 16 q^{33} - 180 q^{34} - 774 q^{35} - 148 q^{36} + 314 q^{38} + 1002 q^{39} - 537 q^{41} - 382 q^{42} + 571 q^{43} + 108 q^{44} + 1516 q^{45} + 126 q^{47} - 16 q^{48} + 558 q^{49} - 736 q^{50} - 1493 q^{51} + 444 q^{52} - 126 q^{53} + 340 q^{54} + 366 q^{55} - 80 q^{56} - 877 q^{57} - 384 q^{58} + 1383 q^{59} + 532 q^{60} + 149 q^{61} + 222 q^{62} + 619 q^{63} + 1280 q^{64} - 3636 q^{65} + 110 q^{66} - 1626 q^{67} - 236 q^{69} + 1548 q^{70} + 1368 q^{71} + 256 q^{72} + 946 q^{73} - 474 q^{74} + 669 q^{75} - 56 q^{76} - 1872 q^{78} - 2109 q^{79} - 340 q^{81} - 1074 q^{82} + 1528 q^{84} + 786 q^{85} + 1142 q^{86} - 816 q^{87} + 1938 q^{89} - 1798 q^{90} - 3459 q^{91} + 663 q^{93} - 2502 q^{95} + 160 q^{96} + 1791 q^{97} - 558 q^{98} - 710 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 - 4 * q^3 - 40 * q^4 - 2 * q^6 - 10 * q^7 + 160 * q^8 + 32 * q^9 + 20 * q^12 - 111 * q^13 + 10 * q^14 + 13 * q^15 - 160 * q^16 + 90 * q^17 + 10 * q^18 - 143 * q^19 - 191 * q^21 - 54 * q^22 - 32 * q^24 + 184 * q^25 + 524 * q^27 + 20 * q^28 + 96 * q^29 - 292 * q^30 - 320 * q^32 + 16 * q^33 - 180 * q^34 - 774 * q^35 - 148 * 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 - 16 * q^48 + 558 * q^49 - 736 * q^50 - 1493 * q^51 + 444 * q^52 - 126 * q^53 + 340 * q^54 + 366 * q^55 - 80 * q^56 - 877 * q^57 - 384 * q^58 + 1383 * q^59 + 532 * q^60 + 149 * q^61 + 222 * q^62 + 619 * q^63 + 1280 * q^64 - 3636 * q^65 + 110 * q^66 - 1626 * q^67 - 236 * q^69 + 1548 * q^70 + 1368 * q^71 + 256 * q^72 + 946 * q^73 - 474 * q^74 + 669 * q^75 - 56 * q^76 - 1872 * q^78 - 2109 * q^79 - 340 * q^81 - 1074 * q^82 + 1528 * q^84 + 786 * q^85 + 1142 * q^86 - 816 * q^87 + 1938 * q^89 - 1798 * q^90 - 3459 * q^91 + 663 * q^93 - 2502 * q^95 + 160 * q^96 + 1791 * q^97 - 558 * q^98 - 710 * 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
$3$	3.74721	−	3.59978i	0.721151	−	0.692778i
$3$	3.74721	−	3.59978i	0.721151	−	0.692778i
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	1.54776	−	0.893602i	0.138436	−	0.0799262i	−0.429182	−	0.903218i	$-0.641198\pi$
$5$	1.54776	−	0.893602i	0.138436	−	0.0799262i	0.567619	+	0.823292i	$0.307865\pi$
$6$	−9.98221	−	2.89057i	−0.679204	−	0.196679i
$7$	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
$9$	1.08314	−	26.9783i	0.0401164	−	0.999195i
$10$	−3.09553	−	1.78720i	−0.0978892	−	0.0565164i
$11$		−	43.6809i		−	1.19730i	−0.801011	−	0.598649i	$-0.795704\pi$
$11$		−	43.6809i		−	1.19730i	0.801011	−	0.598649i	$-0.204296\pi$
$12$	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
$15$	2.58302	−	8.92013i	0.0444622	−	0.153544i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−47.2760	+	27.2948i	−0.674478	+	0.389410i	−0.797771	−	0.602960i	$-0.793988\pi$
$17$	−47.2760	+	27.2948i	−0.674478	+	0.389410i	0.123294	+	0.992370i	$0.460654\pi$
$18$	−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
$21$	74.1935	−	71.2745i	0.770969	−	0.740636i
$22$	−75.6575	+	43.6809i	−0.733193	+	0.423309i
$23$	48.5966	+	28.0573i	0.440570	+	0.254363i	0.703839	−	0.710359i	$-0.251468\pi$
$23$	48.5966	+	28.0573i	0.440570	+	0.254363i	−0.263270	+	0.964722i	$0.584801\pi$
$24$	29.9777	−	28.7983i	0.254965	−	0.244934i
$25$	−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	$-0.658085\pi$
$29$	81.7025	−	141.513i	0.523164	−	0.906147i	0.999637	−	0.0269579i	$-0.00858200\pi$
$30$	−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
$33$	−157.242	−	163.681i	−0.829462	−	0.863433i
$34$	94.5520	+	54.5896i	0.476928	+	0.275354i
$35$	30.6452	−	17.6930i	0.148000	−	0.0854476i
$36$	91.2892	+	57.7086i	0.422635	+	0.267170i
$37$		−	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	$0.209274\pi$
$41$	242.840	+	420.611i	0.925006	+	1.60216i	0.133455	+	0.991055i	$0.457393\pi$
$42$	−197.644	−	57.2324i	−0.726124	−	0.210265i
$43$	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	0.988183	−	0.153280i	$-0.0489837\pi$
$47$	434.840	+	251.055i	1.34953	+	0.779151i	0.361347	+	0.932432i	$0.382317\pi$
$48$	−79.8577	−	23.1246i	−0.240135	−	0.0695364i
$49$	49.0265			0.142934
$50$	243.612			0.689038
$51$	−78.8977	+	272.463i	−0.216625	+	0.748087i
$52$	−86.2365	+	49.7887i	−0.229978	+	0.132778i
$53$	−194.161	+	336.297i	−0.503209	+	0.871583i	0.496784	+	0.867874i	$0.334514\pi$
$53$	−194.161	+	336.297i	−0.503209	+	0.871583i	−0.999993	+	0.00370916i	$0.998819\pi$
$54$	−88.7948	+	266.172i	−0.223767	+	0.670767i
$55$	−39.0333	−	67.6077i	−0.0956955	−	0.165750i
$56$	158.397			0.377977
$57$	−424.802	−	68.8178i	−0.987131	−	0.159915i
$58$	−326.810			−0.739866
$59$	202.865	+	351.373i	0.447640	+	0.775336i	0.998232	−	0.0594389i	$-0.0189312\pi$
$59$	202.865	+	351.373i	0.447640	+	0.775336i	−0.550592	+	0.834775i	$0.685598\pi$
$60$	25.7342	+	26.7881i	0.0553712	+	0.0576388i
$61$	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
$63$	21.4458	−	534.160i	0.0428877	−	1.06822i
$64$	64.0000			0.125000
$65$	44.4913			0.0848995
$66$	−126.263	+	436.032i	−0.235483	+	0.813209i
$67$	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	0.858892	−	0.512156i	$-0.171153\pi$
$71$	−8.43173	−	14.6042i	−0.0140938	−	0.0244112i	−0.872986	+	0.487745i	$0.837820\pi$
$72$	8.66514	−	215.826i	0.0141833	−	0.353269i
$73$	−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
$78$	−179.228	−	186.569i	−0.260175	−	0.270830i
$79$	−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
$81$	−726.654	−	58.4426i	−0.996781	−	0.0801682i
$82$	485.680	−	841.223i	0.654078	−	1.13290i
$83$		−	494.978i		−	0.654589i	−0.944922	−	0.327295i	$-0.893863\pi$
$83$		−	494.978i		−	0.654589i	0.944922	−	0.327295i	$-0.106137\pi$
$84$	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	−0.665475	−	0.746420i	$-0.731771\pi$
$89$	263.375	−	456.178i	0.313682	−	0.543312i	0.979156	+	0.203108i	$0.0651042\pi$
$90$	−51.5686	+	81.5762i	−0.0603978	+	0.0955432i
$91$	426.864	+	246.450i	0.491730	+	0.283901i
$92$	−194.387	+	112.229i	−0.220285	+	0.127181i
$93$	−534.431	−	556.318i	−0.595892	−	0.620296i
$94$		−	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
$99$	−1178.43	−	47.3126i	−1.19633	−	0.0480313i
$100$	−243.612	−	421.948i	−0.243612	−	0.421948i
$101$	−82.3786	−	47.5613i	−0.0811582	−	0.0468567i	0.458872	−	0.888503i	$-0.348254\pi$
$101$	−82.3786	−	47.5613i	−0.0811582	−	0.0468567i	−0.540030	+	0.841646i	$0.681587\pi$
$102$	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
$105$	51.1430	−	176.616i	0.0475338	−	0.164152i
$106$	776.644			0.711645
$107$	−1929.59			−1.74337			−0.871685	−	0.490067i	$-0.836972\pi$
$107$	−1929.59			−1.74337			−0.871685	+	0.490067i	$0.836972\pi$
$108$	549.818	−	112.375i	0.489873	−	0.100123i
$109$	−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
$111$	−196.987	−	205.054i	−0.168443	−	0.175341i
$112$	−158.397	−	274.352i	−0.133635	−	0.231463i
$113$	1066.49			0.887849			0.443925	−	0.896064i	$-0.353586\pi$
$113$	1066.49			0.887849			0.443925	+	0.896064i	$0.353586\pi$
$114$	305.606	+	804.597i	0.251076	+	0.661030i
$115$	100.288			0.0813211
$116$	326.810	+	566.051i	0.261582	+	0.453074i
$117$	359.155	−	568.146i	0.283794	−	0.448933i
$118$	405.730	−	702.745i	0.316530	−	0.548245i
$119$	−936.049	+	540.428i	−0.721071	+	0.416311i
$120$	20.6642	−	71.3610i	0.0157198	−	0.0542862i
$121$	−577.020			−0.433524
$122$	−224.653			−0.166715
$123$	2424.08	+	701.947i	1.77701	+	0.514573i
$124$	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
$129$	1028.71	+	297.887i	0.702118	+	0.203314i
$130$	−44.4913	−	77.0612i	−0.0300165	−	0.0519901i
$131$	73.3412	−	42.3436i	0.0489149	−	0.0282410i	−0.475343	−	0.879801i	$-0.657676\pi$
$131$	73.3412	−	42.3436i	0.0489149	−	0.0282410i	0.524258	+	0.851559i	$0.324343\pi$
$132$	881.492	−	217.338i	0.581243	−	0.143310i
$133$	−985.652	−	1310.50i	−0.642608	−	0.854394i
$134$		−	1237.51i		−	0.797796i
$135$	−237.852	−	79.3473i	−0.151637	−	0.0505861i
$136$	−378.208	+	218.359i	−0.238464	+	0.137677i
$137$	−2607.91	−	1505.68i	−1.62634	−	0.938968i	−0.985172	−	0.171567i	$-0.945117\pi$
$137$	−2607.91	−	1505.68i	−1.62634	−	0.938968i	−0.641167	−	0.767401i	$-0.721550\pi$
$138$	−404.000	−	420.546i	−0.249209	−	0.259415i
$139$	−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
$147$	183.713	−	176.485i	0.103077	−	0.0990219i
$148$	189.562	+	109.444i	0.105283	+	0.0607853i
$149$	389.717	−	225.003i	0.214274	−	0.123711i	−0.389022	−	0.921228i	$-0.627187\pi$
$149$	389.717	−	225.003i	0.214274	−	0.123711i	0.603296	+	0.797517i	$0.293854\pi$
$150$	912.864	−	876.949i	0.496900	−	0.477351i
$151$			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
$156$	−143.918	+	497.001i	−0.0738631	+	0.255077i
$157$	−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
$162$	625.428	+	1317.04i	0.303323	+	0.638745i
$163$	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
$165$	−389.639	−	112.829i	−0.183839	−	0.0532346i
$166$	−857.327	+	494.978i	−0.400852	+	0.231432i
$167$	−1171.46	+	2029.02i	−0.542815	+	0.940183i	0.455926	+	0.890018i	$0.349308\pi$
$167$	−1171.46	+	2029.02i	−0.542815	+	0.940183i	−0.998741	+	0.0501653i	$0.984025\pi$
$168$	593.548	−	570.196i	0.272579	−	0.261854i
$169$	−788.636	−	1365.96i	−0.358960	−	0.621738i
$170$	195.126			0.0880321
$171$	−1839.55	+	1271.32i	−0.822656	+	0.568540i
$172$	−824.438			−0.365481
$173$	1576.81	+	2731.12i	0.692964	+	1.20025i	0.970862	+	0.239638i	$0.0770288\pi$
$173$	1576.81	+	2731.12i	0.692964	+	1.20025i	−0.277898	+	0.960610i	$0.589638\pi$
$174$	−1224.62	+	1176.44i	−0.533555	+	0.512563i
$175$	−1205.86	+	2088.61i	−0.520882	+	0.902193i
$176$	−605.260	+	349.447i	−0.259223	+	0.149662i
$177$	2025.04	+	586.396i	0.859952	+	0.249018i
$178$	−1053.50			−0.443613
$179$	1065.56			0.444937			0.222468	−	0.974940i	$-0.428589\pi$
$179$	1065.56			0.444937			0.222468	+	0.974940i	$0.428589\pi$
$180$	192.863	+	7.74319i	0.0798619	+	0.00320635i
$181$	−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
$186$	−429.141	+	1481.98i	−0.169173	+	0.584215i
$187$	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	$0.0626666\pi$
$191$			1032.66i			0.391207i	−0.980683	+	0.195604i	$0.937333\pi$
$192$	239.821	−	230.386i	0.0901438	−	0.0865973i
$193$	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
$195$	166.718	−	160.159i	0.0612253	−	0.0588165i
$196$	−98.0531	+	169.833i	−0.0357336	+	0.0618925i
$197$		−	3806.21i		−	1.37656i	−0.725447	−	0.688278i	$-0.758367\pi$
$197$		−	3806.21i		−	1.37656i	0.725447	−	0.688278i	$-0.241633\pi$
$198$	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
$204$	−786.043	−	818.235i	−0.269775	−	0.280823i
$205$	751.719	+	434.005i	0.256109	+	0.147865i
$206$	2974.22	−	1717.17i	1.00594	−	0.580779i
$207$	809.574	−	1280.66i	0.271832	−	0.430011i
$208$		−	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
$213$	−84.1673	−	24.3725i	−0.0270753	−	0.00784027i
$214$	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
$219$	−369.733	−	107.064i	−0.114083	−	0.0330354i
$220$	312.267			0.0956955
$221$	−1358.97			−0.413640
$222$	−158.178	+	546.246i	−0.0478207	+	0.165142i
$223$	−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
$225$	2779.89	+	1757.31i	0.823671	+	0.520685i
$226$	−1066.49	−	1847.22i	−0.313902	−	0.543694i
$227$	−6041.70			−1.76653			−0.883264	−	0.468875i	$-0.844659\pi$
$227$	−6041.70			−1.76653			−0.883264	+	0.468875i	$0.844659\pi$
$228$	1088.00	−	1333.92i	0.316028	−	0.387461i
$229$	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
$231$	−3113.33	−	3240.84i	−0.886763	−	0.923079i
$232$	653.620	−	1132.10i	0.184967	−	0.320372i
$233$	4205.62	−	2428.12i	1.18249	−	0.682709i	0.225899	−	0.974151i	$-0.427468\pi$
$233$	4205.62	−	2428.12i	1.18249	−	0.682709i	0.956589	+	0.291441i	$0.0941348\pi$
$234$	−1343.21	−	53.9282i	−0.375250	−	0.0150658i
$235$	897.373			0.249098
$236$	−1622.92			−0.447640
$237$	−1253.91	+	4330.20i	−0.343670	+	1.18682i
$238$	1872.10	+	1080.86i	0.509874	+	0.294376i
$239$		−	5348.82i		−	1.44764i	−0.689988	−	0.723821i	$-0.742384\pi$
$239$		−	5348.82i		−	1.44764i	0.689988	−	0.723821i	$-0.257616\pi$
$240$	−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
$243$	−2933.30	+	2396.80i	−0.774368	+	0.632735i
$244$	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
$249$	−1781.81	−	1854.79i	−0.453485	−	0.472057i
$250$	763.995	−	441.093i	0.193277	−	0.111589i
$251$	1635.42	+	944.213i	0.411263	+	0.237443i	0.691332	−	0.722537i	$-0.257024\pi$
$251$	1635.42	+	944.213i	0.411263	+	0.237443i	−0.280069	+	0.959980i	$0.590357\pi$
$252$	1807.49	+	1142.61i	0.451831	+	0.285626i
$253$	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	−0.991245	−	0.132033i	$-0.957849\pi$
$257$	−1570.88	+	2720.84i	−0.381279	+	0.660394i	0.609967	+	0.792427i	$0.291183\pi$
$258$	−512.759	−	2079.67i	−0.123732	−	0.501840i
$259$		−	1083.47i		−	0.259938i
$260$	−88.9826	+	154.122i	−0.0212249	+	0.0367625i
$261$	−3729.28	−	2357.47i	−0.884431	−	0.559095i
$262$	−146.682	−	84.6872i	−0.0345881	−	0.0199694i
$263$	1303.80	−	752.748i	0.305687	−	0.176488i	−0.339308	−	0.940675i	$-0.610193\pi$
$263$	1303.80	−	752.748i	0.305687	−	0.176488i	0.644995	+	0.764187i	$0.276860\pi$
$264$	−1257.93	−	1309.45i	−0.293259	−	0.305269i
$265$			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	$-0.947748\pi$
$269$	−2800.70	−	4850.95i	−0.634802	−	1.09951i	0.351756	−	0.936092i	$-0.385585\pi$
$270$	100.418	+	491.319i	0.0226343	+	0.110743i
$271$	−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
$276$	−324.407	+	1120.30i	−0.0707499	+	0.244325i
$277$	−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
$279$	−4005.25	−	160.806i	−0.859455	−	0.0345060i
$280$	245.162	−	141.544i	0.0523258	−	0.0302103i
$281$	−4571.80	+	7918.59i	−0.970572	+	1.68108i	−0.276737	+	0.960946i	$0.589253\pi$
$281$	−4571.80	+	7918.59i	−0.970572	+	1.68108i	−0.693835	+	0.720134i	$0.744080\pi$
$282$	−3614.97	−	3763.02i	−0.763363	−	0.794626i
$283$	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
$285$	−718.990	+	273.091i	−0.149436	+	0.0567596i
$286$	−2174.81			−0.449648
$287$	4808.15	+	8327.96i	0.988907	+	1.71284i
$288$	730.313	+	461.669i	0.149424	+	0.0944587i
$289$	−966.486	+	1674.00i	−0.196720	+	0.340729i
$290$	−505.825	+	292.038i	−0.102424	+	0.0591347i
$291$	278.969	−	963.384i	0.0561975	−	0.194071i
$292$	296.313			0.0593850
$293$	8686.57			1.73200			0.865998	−	0.500048i	$-0.166684\pi$
$293$	8686.57			1.73200			0.865998	+	0.500048i	$0.166684\pi$
$294$	−489.393	−	141.715i	−0.0970816	−	0.0281122i
$295$	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
$300$	−2431.78	−	704.178i	−0.467997	−	0.135519i
$301$	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
$306$	1575.15	−	2491.72i	0.294265	−	0.465497i
$307$	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
$309$	6181.42	+	6434.58i	1.13802	+	1.18463i
$310$	−265.332	+	459.569i	−0.0486124	+	0.0841992i
$311$		−	7820.35i		−	1.42589i	−0.701221	−	0.712944i	$-0.747361\pi$
$311$		−	7820.35i		−	1.42589i	0.701221	−	0.712944i	$-0.252639\pi$
$312$	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	−0.948133	−	0.317874i	$-0.897031\pi$
$317$	−1121.92	+	1943.22i	−0.198780	+	0.344297i	0.749353	+	0.662170i	$0.230365\pi$
$318$	2910.25	−	2795.75i	0.513203	−	0.493012i
$319$	−6181.41	−	3568.84i	−1.08493	−	0.626384i
$320$	99.0569	−	57.1905i	0.0173045	−	0.00999078i
$321$	−7230.58	+	6946.11i	−1.25723	+	1.20777i
$322$		−	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
$327$	−1230.19	+	4248.29i	−0.208041	+	0.718443i
$328$	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
$333$	−1476.30	−	59.2716i	−0.242945	−	0.00975394i
$334$	4685.83			0.767656
$335$	1105.84			0.180354
$336$	−1581.16	−	457.859i	−0.256724	−	0.0743400i
$337$	−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
$339$	3996.36	−	3839.13i	0.640273	−	0.615083i
$340$	−195.126	−	337.968i	−0.0311241	−	0.0539084i
$341$	−6484.95			−1.02985
$342$	4041.55	+	1914.88i	0.639011	+	0.302762i
$343$	−5820.57			−0.916273
$344$	824.438	+	1427.97i	0.129217	+	0.223811i
$345$	375.801	−	361.016i	0.0586447	−	0.0563375i
$346$	3153.62	−	5462.23i	0.489999	−	0.848704i
$347$	−826.384	+	477.113i	−0.127846	+	0.0738120i	−0.562559	−	0.826757i	$-0.690183\pi$
$347$	−826.384	+	477.113i	−0.127846	+	0.0738120i	0.434713	+	0.900569i	$0.356850\pi$
$348$	3262.29	+	944.668i	0.502520	+	0.145516i
$349$	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
$351$	−699.374	−	3421.84i	−0.106353	−	0.520354i
$352$	1210.52	+	698.894i	0.183298	+	0.105827i
$353$		−	4400.78i		−	0.663541i	−0.943360	−	0.331770i	$-0.892354\pi$
$353$		−	4400.78i		−	0.663541i	0.943360	−	0.331770i	$-0.107646\pi$
$354$	−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
$357$	−1562.15	+	5394.67i	−0.231590	+	0.799765i
$358$	−1065.56	−	1845.60i	−0.157309	−	0.272467i
$359$	−4830.68	+	2789.00i	−0.710177	+	0.410021i	−0.811127	−	0.584871i	$-0.801145\pi$
$359$	−4830.68	+	2789.00i	−0.710177	+	0.410021i	0.100949	+	0.994892i	$0.467812\pi$
$360$	−179.451	−	341.791i	−0.0262720	−	0.0500388i
$361$	−1902.65	+	6589.83i	−0.277395	+	0.960756i
$362$			8340.49i			1.21096i
$363$	−2162.21	+	2077.15i	−0.312636	+	0.300336i
$364$	−1707.45	+	985.799i	−0.245865	+	0.141950i
$365$	−114.656	−	66.1966i	−0.0164421	−	0.00949284i
$366$	−841.823	+	808.704i	−0.120226	+	0.115496i
$367$	−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
$375$	1587.84	+	1652.87i	0.218655	+	0.227610i
$376$	3478.72	+	2008.44i	0.477131	+	0.275472i
$377$	3522.87	−	2033.93i	0.481265	−	0.277859i
$378$	−1758.11	+	5270.11i	−0.239226	+	0.717104i
$379$			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	0.519562	−	0.854433i	$-0.326095\pi$
$383$	−3599.17	−	6233.94i	−0.480180	−	0.831696i	−0.999741	+	0.0227369i	$0.992762\pi$
$384$	−638.862	−	184.997i	−0.0849004	−	0.0245848i
$385$	−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	0.705115	−	0.709093i	$-0.250895\pi$
$389$	3403.27	+	1964.88i	0.443580	+	0.256101i	−0.261535	+	0.965194i	$0.584229\pi$
$390$	−444.121	−	128.605i	−0.0576640	−	0.0166979i
$391$	−3063.27			−0.396206
$392$	392.212			0.0505350
$393$	122.397	−	422.683i	0.0157102	−	0.0542532i
$394$	−6592.56	+	3806.21i	−0.842965	+	0.486686i
$395$	−775.273	+	1342.81i	−0.0987550	+	0.171049i
$396$	2520.76	−	3987.59i	0.319882	−	0.506020i
$397$	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
$399$	−8410.94	−	1362.57i	−1.05532	−	0.170962i
$400$	1948.89			0.243612
$401$	−6038.88	−	10459.6i	−0.752038	−	1.30257i	−0.946834	−	0.321724i	$-0.895738\pi$
$401$	−6038.88	−	10459.6i	−0.752038	−	1.30257i	0.194796	−	0.980844i	$-0.437596\pi$
$402$	−4454.77	−	4637.21i	−0.552696	−	0.575331i
$403$	1847.93	−	3200.71i	0.228417	−	0.395630i
$404$	329.514	−	190.245i	0.0405791	−	0.0234283i
$405$	−1176.91	+	558.884i	−0.144398	+	0.0685708i
$406$	−6470.73			−0.790977
$407$	−2390.30			−0.291113
$408$	−631.182	+	2179.70i	−0.0765886	+	0.264489i
$409$	−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
$414$	−3027.75	−	121.560i	−0.359434	−	0.0144308i
$415$	−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	$0.132662\pi$
$419$			6943.88i			0.809620i	−0.914401	+	0.404810i	$0.867338\pi$
$420$	509.528	+	530.395i	0.0591963	+	0.0616206i
$421$	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
$423$	7244.02	−	11459.3i	0.832662	−	1.31719i
$424$	−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	$-0.601348\pi$
$431$	5959.02	−	10321.3i	0.665977	−	1.15351i	0.979020	−	0.203766i	$-0.0653183\pi$
$432$	−710.359	+	2129.38i	−0.0791138	+	0.237152i
$433$	−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
$435$	−1051.27	−	1094.33i	−0.115873	−	0.120618i
$436$		−	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
$441$	53.1027	−	1322.65i	0.00573401	−	0.142819i
$442$	1358.97	+	2353.81i	0.146244	+	0.253302i
$443$	−2995.90	−	1729.68i	−0.321308	−	0.185507i	0.330667	−	0.943747i	$-0.392726\pi$
$443$	−2995.90	−	1729.68i	−0.321308	−	0.185507i	−0.651975	+	0.758240i	$0.726060\pi$
$444$	1104.30	−	272.274i	0.118036	−	0.0291026i
$445$		−	941.409i		−	0.100286i
$446$	133.547	+	77.1035i	0.0141786	+	0.00818600i
$447$	650.388	−	2246.03i	0.0688194	−	0.237659i
$448$	1267.18			0.133635
$449$	−6385.47			−0.671156			−0.335578	−	0.942012i	$-0.608932\pi$
$449$	−6385.47			−0.671156			−0.335578	+	0.942012i	$0.608932\pi$
$450$	263.866	−	6572.22i	0.0276417	−	0.688484i
$451$	18372.7	−	10607.5i	1.91826	−	1.10751i
$452$	−2132.98	+	3694.43i	−0.221962	+	0.384450i
$453$	8591.14	+	8942.99i	0.891053	+	0.927546i
$454$	6041.70	+	10464.5i	0.624562	+	1.08177i
$455$	880.912			0.0907644
$456$	−3398.42	−	550.543i	−0.349003	−	0.0565384i
$457$	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
$459$	7265.11	+	2423.64i	0.738794	+	0.246461i
$460$	−200.576	+	347.409i	−0.0203303	+	0.0352131i
$461$	−15429.1	+	8908.00i	−1.55880	+	0.899971i	−0.561423	+	0.827529i	$0.689746\pi$
$461$	−15429.1	+	8908.00i	−1.55880	+	0.899971i	−0.997373	+	0.0724425i	$0.976921\pi$
$462$	−2499.96	+	8633.28i	−0.251750	+	0.869387i
$463$	−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
$465$	−1324.30	−	383.481i	−0.132071	−	0.0382441i
$466$	−8411.25	−	4856.24i	−0.836145	−	0.482748i
$467$		−	14029.7i		−	1.39019i	−0.718919	−	0.695094i	$-0.755363\pi$
$467$		−	14029.7i		−	1.39019i	0.718919	−	0.695094i	$-0.244637\pi$
$468$	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
$471$	−12588.5	−	3645.27i	−1.23152	−	0.356614i
$472$	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
$477$	8862.40	+	5602.38i	0.850695	+	0.537768i
$478$	−9264.43	+	5348.82i	−0.886496	+	0.511819i
$479$	−16233.4	−	9372.37i	−1.54848	−	0.894018i	−0.998258	−	0.0590022i	$-0.981208\pi$
$479$	−16233.4	−	9372.37i	−1.54848	−	0.894018i	−0.550226	−	0.835016i	$-0.685459\pi$
$480$	205.873	+	214.305i	0.0195767	+	0.0203784i
$481$	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
$489$	12796.3	−	12292.9i	1.18337	−	1.13682i
$490$	−151.763	−	87.6204i	−0.0139917	−	0.00807814i
$491$	503.147	−	290.492i	0.0462458	−	0.0267000i	−0.476699	−	0.879067i	$-0.658167\pi$
$491$	503.147	−	290.492i	0.0462458	−	0.0267000i	0.522945	+	0.852367i	$0.324833\pi$
$492$	−7279.78	+	6993.37i	−0.667069	+	0.640824i
$493$			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
$498$	−1430.77	+	4940.98i	−0.128744	+	0.444599i
$499$	−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	0.996550	−	0.0829891i	$-0.0264467\pi$
$503$	16052.5	+	9267.93i	1.42295	+	0.821543i	0.426405	+	0.904533i	$0.359780\pi$
$504$	171.567	−	4273.28i	0.0151631	−	0.377673i
$505$	−170.004			−0.0149803
$506$	−4902.27			−0.430696
$507$	−7872.33	−	2279.61i	−0.689591	−	0.199686i
$508$	−4386.34	+	2532.45i	−0.383095	+	0.221180i
$509$	−644.409	+	1116.15i	−0.0561158	+	0.0971954i	−0.892719	−	0.450614i	$-0.851205\pi$
$509$	−644.409	+	1116.15i	−0.0561158	+	0.0971954i	0.836603	+	0.547810i	$0.184538\pi$
$510$	731.177	−	702.410i	0.0634844	−	0.0609867i
$511$	−733.363	−	1270.22i	−0.0634874	−	0.109963i
$512$	512.000			0.0441942
$513$	−2316.71	+	11385.9i	−0.199386	+	0.979921i
$514$	6283.51			0.539209
$515$	1534.46	+	2657.77i	0.131294	+	0.227408i
$516$	−3089.34	+	2967.80i	−0.263567	+	0.253198i
$517$	10966.3	−	18994.2i	0.932877	−	1.61579i
$518$	−1876.63	+	1083.47i	−0.159179	+	0.0919018i
$519$	15740.1	+	4557.89i	1.33124	+	0.385490i
$520$	355.930			0.0300165
$521$	−9884.31			−0.831170			−0.415585	−	0.909554i	$-0.636423\pi$
$521$	−9884.31			−0.831170			−0.415585	+	0.909554i	$0.636423\pi$
$522$	−353.982	+	8816.77i	−0.0296808	+	0.739271i
$523$	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
$528$	−1010.10	+	3488.26i	−0.0832558	+	0.287513i
$529$	−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
$534$	−3947.68	+	3792.37i	−0.319912	+	0.307325i
$535$	−2986.55	+	1724.29i	−0.241346	+	0.139341i
$536$	4286.86	+	2475.02i	0.345456	+	0.199449i
$537$	3992.87	−	3835.78i	0.320866	−	0.308243i
$538$	−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
$546$	−3548.66	−	3693.99i	−0.278148	−	0.289539i
$547$	−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
$549$	−2563.55	−	1620.56i	−0.199289	−	0.125981i
$550$		−	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
$555$	−488.126	−	141.348i	−0.0373330	−	0.0108106i
$556$	−1948.84	−	3375.50i	−0.148650	−	0.257469i
$557$	−4268.83	−	2464.61i	−0.324733	−	0.187485i	0.328767	−	0.944411i	$-0.393367\pi$
$557$	−4268.83	−	2464.61i	−0.324733	−	0.187485i	−0.653500	+	0.756926i	$0.726700\pi$
$558$	3726.73	+	7098.10i	0.282733	+	0.538506i
$559$			5130.96i			0.388223i
$560$	−490.323	−	283.088i	−0.0369999	−	0.0213619i
$561$	11901.4	+	3446.32i	0.895683	+	0.259365i
$562$	18287.2			1.37260
$563$	10992.4			0.822869			0.411435	−	0.911439i	$-0.365028\pi$
$563$	10992.4			0.822869			0.411435	+	0.911439i	$0.365028\pi$
$564$	−2902.77	+	10024.3i	−0.216717	+	0.748405i
$565$	1650.68	−	953.018i	0.122911	−	0.0709624i
$566$	1976.69	−	3423.74i	0.146796	−	0.254259i
$567$	−14387.5	−	1157.14i	−1.06564	−	0.0857063i
$568$	−67.4538	−	116.833i	−0.00498292	−	0.00863067i
$569$	−3636.08			−0.267895			−0.133948	−	0.990988i	$-0.542765\pi$
$569$	−3636.08			−0.267895			−0.133948	+	0.990988i	$0.542765\pi$
$570$	1192.00	+	972.236i	0.0875917	+	0.0714430i
$571$	−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
$573$	3717.35	+	3869.59i	0.271020	+	0.282119i
$574$	9616.30	−	16655.9i	0.699263	−	1.21116i
$575$	−5919.36	+	3417.54i	−0.429312	+	0.247863i
$576$	69.3211	−	1726.61i	0.00501455	−	0.124899i
$577$	−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
$579$	839.887	−	2900.44i	0.0602841	−	0.208183i
$580$	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
$585$	48.1904	−	1200.30i	0.00340586	−	0.0848311i
$586$	−8686.57	−	15045.6i	−0.612353	−	1.06063i
$587$	4771.22	−	2754.67i	0.335484	−	0.193692i	−0.322789	−	0.946471i	$-0.604620\pi$
$587$	4771.22	−	2754.67i	0.335484	−	0.193692i	0.658273	+	0.752779i	$0.271287\pi$
$588$	243.936	+	989.369i	0.0171084	+	0.0693893i
$589$	−9826.38	+	7390.63i	−0.687417	+	0.517021i
$590$		−	1450.25i		−	0.101196i
$591$	−13701.5	−	14262.7i	−0.953648	−	0.992704i
$592$	−758.249	+	437.775i	−0.0526416	+	0.0303926i
$593$	11072.8	+	6392.89i	0.766789	+	0.442706i	0.831728	−	0.555183i	$-0.187352\pi$
$593$	11072.8	+	6392.89i	0.766789	+	0.442706i	−0.0649390	+	0.997889i	$0.520685\pi$
$594$	11626.6	+	3878.64i	0.803108	+	0.267916i
$595$	−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	−0.854149	−	0.520028i	$-0.825921\pi$
$599$	341.333	−	591.205i	0.0232829	−	0.0403272i	0.877432	+	0.479701i	$0.159255\pi$
$600$	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
$603$	8926.89	−	14121.4i	0.602870	−	0.953679i
$604$	−8267.33	−	4773.15i	−0.556942	−	0.321551i
$605$	−893.091	+	515.626i	−0.0600154	+	0.0346499i
$606$	684.841	+	712.888i	0.0459072	+	0.0477873i
$607$			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
$612$	−5890.94	−	236.513i	−0.389096	−	0.0156217i
$613$	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	0.838323	−	0.545174i	$-0.183536\pi$
$617$	12036.2	+	6949.13i	0.785350	+	0.453422i	−0.0529727	+	0.998596i	$0.516870\pi$
$618$	4963.59	−	17141.1i	0.323082	−	1.11572i
$619$	−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
$621$	−1576.47	−	7713.20i	−0.101870	−	0.498422i
$622$	−13545.2	+	7820.35i	−0.873175	+	0.504128i
$623$	5214.73	−	9032.18i	0.335351	−	0.580845i
$624$	−1433.83	−	1492.55i	−0.0919856	−	0.0957528i
$625$	−7218.71	−	12503.2i	−0.461997	−	0.800203i
$626$	−246.277			−0.0157240
$627$	−3006.02	+	18555.7i	−0.191466	+	1.18189i
$628$	10088.7			0.641056
$629$	1493.62	+	2587.03i	0.0946816	+	0.163993i
$630$	−1021.04	+	1615.18i	−0.0645702	+	0.102143i
$631$	−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
$633$	6295.37	−	21740.2i	0.395290	−	1.36508i
$634$	4487.67			0.281117
$635$	2263.01			0.141425
$636$	−7752.63	−	2244.95i	−0.483352	−	0.139965i
$637$	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	0.967724	−	0.252013i	$-0.0810927\pi$
$641$	4310.57	+	7466.13i	0.265612	+	0.460053i	−0.702112	+	0.712067i	$0.747759\pi$
$642$	19261.6	+	5577.62i	1.18410	+	0.342884i
$643$	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	$-0.716136\pi$
$647$		−	25613.8i		−	1.55639i	0.628023	−	0.778195i	$-0.283864\pi$
$648$	−5813.23	−	467.541i	−0.352415	−	0.0283437i
$649$	15348.3	−	8861.33i	0.928308	−	0.535959i
$650$	5252.06	+	3032.28i	0.316927	+	0.182978i
$651$	−10581.6	−	11014.9i	−0.637056	−	0.663147i
$652$	−6829.80	+	11829.6i	−0.410238	+	0.710554i
$653$		−	15090.9i		−	0.904367i	−0.891925	−	0.452184i	$-0.850645\pi$
$653$		−	15090.9i		−	0.904367i	0.891925	−	0.452184i	$-0.149355\pi$
$654$	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	$0.526700\pi$
$659$	−15307.9	+	26514.0i	−0.904872	+	1.56728i	−0.821089	+	0.570800i	$0.806633\pi$
$660$	1170.13	−	1124.09i	0.0690109	−	0.0662958i
$661$	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
$663$	−5092.36	+	4892.01i	−0.298297	+	0.286561i
$664$		−	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
$669$	−111.437	+	384.832i	−0.00644004	+	0.0222398i
$670$	−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
$675$	16742.8	−	3421.98i	0.954710	−	0.195129i
$676$	6309.09			0.358960
$677$	−7048.12			−0.400120			−0.200060	−	0.979784i	$-0.564114\pi$
$677$	−7048.12			−0.400120			−0.200060	+	0.979784i	$0.564114\pi$
$678$	−10645.9	−	3082.77i	−0.603030	−	0.174621i
$679$	3309.72	−	1910.87i	0.187062	−	0.108000i
$680$	−390.251	+	675.935i	−0.0220080	+	0.0381190i
$681$	−22639.5	+	21748.8i	−1.27393	+	1.22381i
$682$	6484.95	+	11232.3i	0.364108	+	0.630654i
$683$	−6871.75			−0.384978			−0.192489	−	0.981299i	$-0.561656\pi$
$683$	−6871.75			−0.384978			−0.192489	+	0.981299i	$0.561656\pi$
$684$	−724.881	−	8915.04i	−0.0405212	−	0.498355i
$685$	−5381.90			−0.300193
$686$	5820.57	+	10081.5i	0.323951	+	0.561100i
$687$	516.310	−	495.997i	0.0286731	−	0.0275451i
$688$	1648.88	−	2855.94i	0.0913704	−	0.158258i
$689$	−8371.89	+	4833.51i	−0.462908	+	0.267260i
$690$	−1001.10	−	289.890i	−0.0552336	−	0.0159941i
$691$	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
$693$	−23332.6	−	936.774i	−1.27898	−	0.0513493i
$694$	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
$699$	7018.65	−	24238.0i	0.379785	−	1.31154i
$700$	−4823.43	−	8354.43i	−0.260441	−	0.451097i
$701$	19745.2	−	11399.9i	1.06386	−	0.614220i	0.137363	−	0.990521i	$-0.456137\pi$
$701$	19745.2	−	11399.9i	1.06386	−	0.614220i	0.926498	+	0.376301i	$0.122804\pi$
$702$	−5227.43	+	4633.19i	−0.281049	+	0.249100i
$703$	−3621.92	+	2724.13i	−0.194315	+	0.146148i
$704$		−	2795.58i		−	0.149662i
$705$	3362.64	−	3230.35i	0.179637	−	0.172570i
$706$	−7622.38	+	4400.78i	−0.406334	+	0.234597i
$707$	−1631.07	−	941.697i	−0.0867647	−	0.0500936i
$708$	−6081.42	+	5842.16i	−0.322816	+	0.310116i
$709$	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
$717$	−19254.6	−	20043.2i	−1.00290	−	1.04397i
$718$	9661.36	+	5577.99i	0.502171	+	0.289929i
$719$	6253.02	−	3610.18i	0.324337	−	0.187256i	−0.328987	−	0.944334i	$-0.606707\pi$
$719$	6253.02	−	3610.18i	0.324337	−	0.187256i	0.653324	+	0.757078i	$0.273374\pi$
$720$	−412.549	+	652.610i	−0.0213539	+	0.0337796i
$721$			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
$726$	5759.94	+	1667.92i	0.294451	+	0.0852648i
$727$	−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
$732$	2242.54	+	649.377i	0.113233	+	0.0327892i
$733$	−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
$735$	126.637	−	437.323i	0.00635519	−	0.0219468i
$736$	−1555.09	+	897.833i	−0.0778824	+	0.0449654i
$737$	13513.9	−	23406.8i	0.675428	−	1.16988i
$738$	−22168.7	−	14014.0i	−1.10575	−	0.698999i
$739$	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
$741$	−8301.78	−	6771.24i	−0.411570	−	0.335692i
$742$	15377.3			0.760806
$743$	18413.9	+	31893.9i	0.909209	+	1.57480i	0.815166	+	0.579227i	$0.196646\pi$
$743$	18413.9	+	31893.9i	0.909209	+	1.57480i	0.0940425	+	0.995568i	$0.470021\pi$
$744$	−4275.45	−	4450.55i	−0.210679	−	0.219308i
$745$	402.126	−	696.503i	0.0197755	−	0.0342522i
$746$	−10579.7	+	6108.19i	−0.519236	+	0.299781i
$747$	−13353.6	−	536.132i	−0.654062	−	0.0262597i
$748$	−9538.10			−0.466240
$749$	−38205.2			−1.86380
$750$	1275.01	−	4403.08i	0.0620757	−	0.214370i
$751$	−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
$756$	10886.2	−	2224.98i	0.523714	−	0.107039i
$757$	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	$-0.926568\pi$
$761$		−	9600.25i		−	0.457305i	0.973508	−	0.228652i	$-0.0734319\pi$
$762$	−9116.28	−	9489.64i	−0.433396	−	0.451146i
$763$	−14595.1	+	8426.46i	−0.692499	+	0.399814i
$764$	−3577.24	−	2065.32i	−0.169398	−	0.0978018i
$765$	2226.61	+	1407.56i	0.105233	+	0.0665232i
$766$	−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	−0.637505	−	0.770446i	$-0.720033\pi$
$773$	7489.26	−	12971.8i	0.348474	−	0.603574i	0.985979	+	0.166872i	$0.0533668\pi$
$774$	−9407.78	−	5947.15i	−0.436894	−	0.276183i
$775$	15660.8	+	9041.78i	0.725875	+	0.419084i
$776$	1337.28	−	772.080i	0.0618629	−	0.0357166i
$777$	−3900.27	−	4060.01i	−0.180079	−	0.187454i
$778$		−	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
$783$	−22460.8	+	4590.65i	−1.02514	+	0.209523i
$784$	−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
$789$	2175.87	−	7514.09i	0.0981789	−	0.339048i
$790$	3101.09			0.139661
$791$	21116.1			0.949183
$792$	−9427.48	−	378.501i	−0.422968	−	0.0169816i
$793$	2421.67	−	1398.15i	0.108444	−	0.0626101i
$794$	186.287	−	322.659i	0.00832631	−	0.0144216i
$795$	2498.29	+	2600.60i	0.111453	+	0.116017i
$796$	2686.18	+	4652.61i	0.119610	+	0.207170i
$797$	11929.1			0.530175			0.265087	−	0.964224i	$-0.414599\pi$
$797$	11929.1			0.530175			0.265087	+	0.964224i	$0.414599\pi$
$798$	6050.90	+	15930.8i	0.268421	+	0.706695i
$799$	−27410.0			−1.21364
$800$	−1948.89	−	3375.58i	−0.0861298	−	0.149181i
$801$	−12021.6	−	7599.50i	−0.530291	−	0.335225i
$802$	−12077.8	+	20919.3i	−0.531771	+	0.921054i
$803$	−2802.29	+	1617.90i	−0.123152	+	0.0711016i
$804$	−3577.12	+	12353.1i	−0.156909	+	0.541866i
$805$	1985.67			0.0869388
$806$	−7391.73			−0.323031
$807$	−27957.2	−	8095.63i	−1.21950	−	0.353135i
$808$	−659.029	−	380.490i	−0.0286937	−	0.0165663i
$809$			35874.5i			1.55906i	0.626365	+	0.779530i	$0.284542\pi$
$809$			35874.5i			1.55906i	−0.626365	+	0.779530i	$0.715458\pi$
$810$	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
$813$	−32013.4	−	9270.20i	−1.38101	−	0.399902i
$814$	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
$819$	7111.14	−	11249.1i	0.303398	−	0.479945i
$820$	−3006.87	+	1736.02i	−0.128054	+	0.0739323i
$821$	30142.6	+	17402.8i	1.28134	+	0.739784i	0.977094	−	0.212809i	$-0.0682612\pi$
$821$	30142.6	+	17402.8i	1.28134	+	0.739784i	0.304249	+	0.952593i	$0.401595\pi$
$822$	21680.4	+	22568.3i	0.919941	+	0.957617i
$823$	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	$0.500820\pi$
$827$	−20626.9	+	35726.8i	−0.867311	+	1.50223i	−0.864734	+	0.502230i	$0.832513\pi$
$828$	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
$831$	−30190.0	+	29002.3i	−1.26027	+	1.21068i
$832$	1379.78	+	796.619i	0.0574945	+	0.0331945i
$833$	−2317.78	+	1338.17i	−0.0964061	+	0.0556601i
$834$	7302.73	−	7015.42i	0.303205	−	0.291276i
$835$			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	$0.00212443\pi$
$839$	12291.2	+	21289.0i	0.505769	+	0.876017i	−0.494209	+	0.869343i	$0.664542\pi$
$840$	409.144	−	1412.92i	0.0168057	−	0.0580363i
$841$	−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
$846$	−27092.1	−	1087.71i	−1.10100	−	0.0442037i
$847$	−11424.8			−0.463472
$848$	6213.15			0.251604
$849$	9865.89	+	2856.89i	0.398818	+	0.115487i
$850$	−11517.0	+	6649.34i	−0.464741	+	0.268318i
$851$	1535.35	−	2659.30i	0.0618461	−	0.107121i
$852$	252.763	−	242.819i	0.0101638	−	0.00976390i
$853$	−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
$855$	−1711.14	+	3611.53i	−0.0684441	+	0.144458i
$856$	−15436.7			−0.616374
$857$	2181.43	+	3778.35i	0.0869502	+	0.150602i	0.906221	−	0.422805i	$-0.138955\pi$
$857$	2181.43	+	3778.35i	0.0869502	+	0.150602i	−0.819270	+	0.573407i	$0.805621\pi$
$858$	−8149.48	+	7828.86i	−0.324264	+	0.311507i
$859$	−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
$861$	47996.0	+	13898.3i	1.89977	+	0.550120i
$862$	−23836.1			−0.941833
$863$	−50392.1			−1.98768			−0.993839	−	0.110832i	$-0.964649\pi$
$863$	−50392.1			−1.98768			−0.993839	+	0.110832i	$0.964649\pi$
$864$	4398.54	−	898.998i	0.173196	−	0.0353988i
$865$	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
$870$	−844.158	+	2915.19i	−0.0328961	+	0.113602i
$871$	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
$876$	1110.35	−	1066.66i	0.0428256	−	0.0411407i
$877$	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
$879$	32550.4	−	31269.7i	1.24903	−	1.19989i
$880$	−624.533	+	1081.72i	−0.0239239	+	0.0414374i
$881$			10685.4i			0.408628i	0.978905	+	0.204314i	$0.0654964\pi$
$881$			10685.4i			0.408628i	−0.978905	+	0.204314i	$0.934504\pi$
$882$	−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	−0.872743	−	0.488181i	$-0.837661\pi$
$887$	−359.122	+	622.017i	−0.0135943	+	0.0235460i	0.859148	+	0.511727i	$0.170994\pi$
$888$	−1575.90	−	1640.43i	−0.0595536	−	0.0619926i
$889$	21712.0	+	12535.4i	0.819120	+	0.472919i
$890$	−1630.57	+	941.409i	−0.0614121	+	0.0354563i
$891$	−2552.82	+	31740.9i	−0.0959852	+	1.19344i
$892$		−	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
$897$	6972.25	+	2018.97i	0.259528	+	0.0751522i
$898$	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
$903$	20368.2	+	5898.07i	0.750621	+	0.217359i
$904$	8531.92			0.313902
$905$	−7453.08			−0.273755
$906$	6898.57	−	23823.3i	0.252969	−	0.873593i
$907$	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
$909$	−1372.35	+	2170.92i	−0.0500747	+	0.0792131i
$910$	−880.912	−	1525.78i	−0.0320901	−	0.0555816i
$911$	18830.7			0.684840			0.342420	−	0.939547i	$-0.388753\pi$
$911$	18830.7			0.684840			0.342420	+	0.939547i	$0.388753\pi$
$912$	2444.85	+	6436.78i	0.0887688	+	0.233709i
$913$	−21621.1			−0.783739
$914$	−824.213	−	1427.58i	−0.0298277	−	0.0516631i
$915$	−722.659	−	752.255i	−0.0261097	−	0.0271790i
$916$	−275.570	+	477.302i	−0.00994007	+	0.0172167i
$917$	1452.13	−	838.388i	0.0522940	−	0.0301920i
$918$	−3067.25	−	15007.2i	−0.110277	−	0.539554i
$919$	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
$921$	14196.4	−	49025.3i	0.507912	−	1.75401i
$922$	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
$927$	46326.1	+	1859.93i	1.64137	+	0.0658989i
$928$	2614.48	+	4528.41i	0.0924833	+	0.160186i
$929$	22666.3	−	13086.4i	0.800493	−	0.462165i	−0.0431503	−	0.999069i	$-0.513739\pi$
$929$	22666.3	−	13086.4i	0.800493	−	0.462165i	0.843644	+	0.536904i	$0.180406\pi$
$930$	660.092	+	2677.24i	0.0232745	+	0.0943979i
$931$	−2440.60	−	3244.96i	−0.0859157	−	0.114231i
$932$			19424.9i			0.682709i
$933$	−28151.6	−	29304.5i	−0.987825	−	1.02828i
$934$	−24300.2	+	14029.7i	−0.851313	+	0.491506i
$935$	3690.68	+	2130.82i	0.129089	+	0.0745296i
$936$	2873.24	−	4545.17i	0.100336	−	0.158722i
$937$	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	−0.892485	−	0.451077i	$-0.851040\pi$
$941$	−1604.89	+	2779.76i	−0.0555984	+	0.0962992i	0.836887	+	0.547376i	$0.184373\pi$
$942$	6274.66	+	25449.1i	0.217027	+	0.880230i
$943$			27253.7i			0.941149i
$944$	3245.84	−	5621.96i	0.111910	−	0.193834i
$945$	−4709.38	−	1571.05i	−0.162112	−	0.0540807i
$946$	−15593.7	−	9003.05i	−0.535937	−	0.309423i
$947$	19169.4	−	11067.5i	0.657785	−	0.379772i	−0.133648	−	0.991029i	$-0.542669\pi$
$947$	19169.4	−	11067.5i	0.657785	−	0.379772i	0.791432	+	0.611257i	$0.209336\pi$
$948$	−12492.4	−	13004.0i	−0.427991	−	0.445519i
$949$		−	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	0.845867	−	0.533394i	$-0.179084\pi$
$953$	−1147.36	−	1987.28i	−0.0389995	−	0.0675492i	−0.884866	+	0.465845i	$0.845750\pi$
$954$	841.216	−	20952.5i	0.0285486	−	0.711072i
$955$	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
$960$	165.313	−	570.888i	0.00555778	−	0.0191931i
$961$	7750.02			0.260146
$962$	−2724.53			−0.0913123
$963$	−2090.02	+	52057.0i	−0.0699377	+	1.74197i
$964$	−17149.9	+	9901.49i	−0.572988	+	0.330815i
$965$	519.291	−	899.439i	0.0173229	−	0.0300041i
$966$	−7999.07	−	8326.67i	−0.266424	−	0.277335i
$967$	−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
$969$	21961.3	−	8341.47i	0.728070	−	0.276539i
$970$	−689.933			−0.0228375
$971$	−24714.7	−	42807.1i	−0.816821	−	1.41478i	−0.908013	−	0.418942i	$-0.862401\pi$
$971$	−24714.7	−	42807.1i	−0.816821	−	1.41478i	0.0911923	−	0.995833i	$-0.470932\pi$
$972$	−2436.14	−	14954.9i	−0.0803903	−	0.493495i
$973$	−9646.62	+	16708.4i	−0.317838	+	0.550511i
$974$	−5471.52	+	3158.98i	−0.179999	+	0.103922i
$975$	−4382.51	+	15134.4i	−0.143951	+	0.497117i
$976$	−1797.23			−0.0589425
$977$	−35406.9			−1.15944			−0.579718	−	0.814818i	$-0.696837\pi$
$977$	−35406.9			−1.15944			−0.579718	+	0.814818i	$0.696837\pi$
$978$	−34088.2	−	9871.01i	−1.11454	−	0.322740i
$979$	−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	0.541134	−	0.840936i	$-0.317995\pi$
$983$	−14106.4	−	24433.0i	−0.457705	−	0.792768i	−0.998839	+	0.0481679i	$0.984662\pi$
$984$	19392.7	+	5615.58i	0.628268	+	0.181929i
$985$	−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
$990$	3563.32	+	2252.56i	0.114394	+	0.0723142i
$991$	−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
$993$	9532.72	+	9923.12i	0.304644	+	0.317121i
$994$	−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.a.107.8	yes	20
3.2	odd	2		114.4.h.b.107.10	yes	20
19.8	odd	6		114.4.h.b.65.10	yes	20
57.8	even	6	inner	114.4.h.a.65.8	✓	20

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

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)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(3.74721 - 3.59978i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(1.54776 - 0.893602i) q^{5} +(-9.98221 - 2.89057i) q^{6} +19.7997 q^{7} +8.00000 q^{8} +(1.08314 - 26.9783i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(3.74721 - 3.59978i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(1.54776 - 0.893602i) q^{5} +(-9.98221 - 2.89057i) q^{6} +19.7997 q^{7} +8.00000 q^{8} +(1.08314 - 26.9783i) 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} +(2.58302 - 8.92013i) 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} +(74.1935 - 71.2745i) q^{21} +(-75.6575 + 43.6809i) q^{22} +(48.5966 + 28.0573i) q^{23} +(29.9777 - 28.7983i) 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} +(-157.242 - 163.681i) q^{33} +(94.5520 + 54.5896i) q^{34} +(30.6452 - 17.6930i) q^{35} +(91.2892 + 57.7086i) 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} +(-197.644 - 57.2324i) 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} +(-79.8577 - 23.1246i) q^{48} +49.0265 q^{49} +243.612 q^{50} +(-78.8977 + 272.463i) q^{51} +(-86.2365 + 49.7887i) q^{52} +(-194.161 + 336.297i) q^{53} +(-88.7948 + 266.172i) q^{54} +(-39.0333 - 67.6077i) q^{55} +158.397 q^{56} +(-424.802 - 68.8178i) q^{57} -326.810 q^{58} +(202.865 + 351.373i) q^{59} +(25.7342 + 26.7881i) q^{60} +(56.1634 - 97.2778i) q^{61} +(-257.144 + 148.462i) q^{62} +(21.4458 - 534.160i) q^{63} +64.0000 q^{64} +44.4913 q^{65} +(-126.263 + 436.032i) 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} +(8.66514 - 215.826i) 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} +(-179.228 - 186.569i) q^{78} +(-751.348 + 433.791i) q^{79} +(-24.7642 - 14.2976i) q^{80} +(-726.654 - 58.4426i) 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} +(-51.5686 + 81.5762i) q^{90} +(426.864 + 246.450i) q^{91} +(-194.387 + 112.229i) q^{92} +(-534.431 - 556.318i) 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} +(-1178.43 - 47.3126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} - 4 q^{3} - 40 q^{4} - 2 q^{6} - 10 q^{7} + 160 q^{8} + 32 q^{9}+O(q^{10}) \) 20 * q - 20 * q^2 - 4 * q^3 - 40 * q^4 - 2 * q^6 - 10 * q^7 + 160 * q^8 + 32 * q^9	\( 20 q - 20 q^{2} - 4 q^{3} - 40 q^{4} - 2 q^{6} - 10 q^{7} + 160 q^{8} + 32 q^{9} + 20 q^{12} - 111 q^{13} + 10 q^{14} + 13 q^{15} - 160 q^{16} + 90 q^{17} + 10 q^{18} - 143 q^{19} - 191 q^{21} - 54 q^{22} - 32 q^{24} + 184 q^{25} + 524 q^{27} + 20 q^{28} + 96 q^{29} - 292 q^{30} - 320 q^{32} + 16 q^{33} - 180 q^{34} - 774 q^{35} - 148 q^{36} + 314 q^{38} + 1002 q^{39} - 537 q^{41} - 382 q^{42} + 571 q^{43} + 108 q^{44} + 1516 q^{45} + 126 q^{47} - 16 q^{48} + 558 q^{49} - 736 q^{50} - 1493 q^{51} + 444 q^{52} - 126 q^{53} + 340 q^{54} + 366 q^{55} - 80 q^{56} - 877 q^{57} - 384 q^{58} + 1383 q^{59} + 532 q^{60} + 149 q^{61} + 222 q^{62} + 619 q^{63} + 1280 q^{64} - 3636 q^{65} + 110 q^{66} - 1626 q^{67} - 236 q^{69} + 1548 q^{70} + 1368 q^{71} + 256 q^{72} + 946 q^{73} - 474 q^{74} + 669 q^{75} - 56 q^{76} - 1872 q^{78} - 2109 q^{79} - 340 q^{81} - 1074 q^{82} + 1528 q^{84} + 786 q^{85} + 1142 q^{86} - 816 q^{87} + 1938 q^{89} - 1798 q^{90} - 3459 q^{91} + 663 q^{93} - 2502 q^{95} + 160 q^{96} + 1791 q^{97} - 558 q^{98} - 710 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 - 4 * q^3 - 40 * q^4 - 2 * q^6 - 10 * q^7 + 160 * q^8 + 32 * q^9 + 20 * q^12 - 111 * q^13 + 10 * q^14 + 13 * q^15 - 160 * q^16 + 90 * q^17 + 10 * q^18 - 143 * q^19 - 191 * q^21 - 54 * q^22 - 32 * q^24 + 184 * q^25 + 524 * q^27 + 20 * q^28 + 96 * q^29 - 292 * q^30 - 320 * q^32 + 16 * q^33 - 180 * q^34 - 774 * q^35 - 148 * 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 - 16 * q^48 + 558 * q^49 - 736 * q^50 - 1493 * q^51 + 444 * q^52 - 126 * q^53 + 340 * q^54 + 366 * q^55 - 80 * q^56 - 877 * q^57 - 384 * q^58 + 1383 * q^59 + 532 * q^60 + 149 * q^61 + 222 * q^62 + 619 * q^63 + 1280 * q^64 - 3636 * q^65 + 110 * q^66 - 1626 * q^67 - 236 * q^69 + 1548 * q^70 + 1368 * q^71 + 256 * q^72 + 946 * q^73 - 474 * q^74 + 669 * q^75 - 56 * q^76 - 1872 * q^78 - 2109 * q^79 - 340 * q^81 - 1074 * q^82 + 1528 * q^84 + 786 * q^85 + 1142 * q^86 - 816 * q^87 + 1938 * q^89 - 1798 * q^90 - 3459 * q^91 + 663 * q^93 - 2502 * q^95 + 160 * q^96 + 1791 * q^97 - 558 * q^98 - 710 * q^99

Introduction

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