LMFDB - Embedded newform 242.4.c.n.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [242,4,Mod(3,242)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(242, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("242.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 242 = 2 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	242.c (of order $5$, degree $4$, not 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:	$14.2784622214$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 71x^{6} - 141x^{5} + 2911x^{4} + 2710x^{3} + 75340x^{2} + 169400x + 5856400 $ x^8 - x^7 + 71x^6 - 141x^5 + 2911x^4 + 2710x^3 + 75340x^2 + 169400x + 5856400
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.2
Root			$-2.53202 - 7.79275i$ of defining polynomial
Character	$\chi$	$=$	242.81
Dual form			242.4.c.n.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61803 - 1.17557i) q^{2} +(2.34103 - 7.20496i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-4.37525 + 3.17880i) q^{5} +(-12.2578 + 8.90583i) q^{6} +(6.84467 + 21.0657i) q^{7} +(2.47214 - 7.60845i) q^{8} +(-24.5876 - 17.8639i) q^{9} +O(q^{10})$	\(q+(-1.61803 - 1.17557i) q^{2} +(2.34103 - 7.20496i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-4.37525 + 3.17880i) q^{5} +(-12.2578 + 8.90583i) q^{6} +(6.84467 + 21.0657i) q^{7} +(2.47214 - 7.60845i) q^{8} +(-24.5876 - 17.8639i) q^{9} +10.8162 q^{10} +30.3030 q^{12} +(62.1543 + 45.1577i) q^{13} +(13.6893 - 42.1315i) q^{14} +(12.6606 + 38.9652i) q^{15} +(-12.9443 + 9.40456i) q^{16} +(47.9653 - 34.8488i) q^{17} +(18.7833 + 57.8089i) q^{18} +(-29.4377 + 90.6001i) q^{19} +(-17.5010 - 12.7152i) q^{20} +167.801 q^{21} +142.484 q^{23} +(-49.0313 - 35.6233i) q^{24} +(-29.5891 + 91.0660i) q^{25} +(-47.4817 - 146.134i) q^{26} +(-20.7889 + 15.1041i) q^{27} +(-71.6783 + 52.0773i) q^{28} +(6.30960 + 19.4190i) q^{29} +(25.3211 - 77.9303i) q^{30} +(-172.567 - 125.377i) q^{31} +32.0000 q^{32} -118.577 q^{34} +(-96.9109 - 70.4099i) q^{35} +(37.5665 - 115.618i) q^{36} +(-44.9859 - 138.452i) q^{37} +(154.138 - 111.988i) q^{38} +(470.865 - 342.104i) q^{39} +(13.3696 + 41.1473i) q^{40} +(-25.5967 + 78.7785i) q^{41} +(-271.508 - 197.262i) q^{42} +151.373 q^{43} +164.363 q^{45} +(-230.544 - 167.500i) q^{46} +(27.9241 - 85.9416i) q^{47} +(37.4566 + 115.279i) q^{48} +(-119.423 + 86.7656i) q^{49} +(154.931 - 112.564i) q^{50} +(-138.796 - 427.170i) q^{51} +(-94.9633 + 292.267i) q^{52} +(189.997 + 138.041i) q^{53} +51.3931 q^{54} +177.199 q^{56} +(583.855 + 424.196i) q^{57} +(12.6192 - 38.8379i) q^{58} +(93.4769 + 287.692i) q^{59} +(-132.583 + 96.3272i) q^{60} +(-120.770 + 87.7443i) q^{61} +(131.829 + 405.729i) q^{62} +(208.023 - 640.229i) q^{63} +(-51.7771 - 37.6183i) q^{64} -415.488 q^{65} +826.236 q^{67} +(191.861 + 139.395i) q^{68} +(333.560 - 1026.59i) q^{69} +(74.0333 + 227.851i) q^{70} +(727.278 - 528.399i) q^{71} +(-196.701 + 142.912i) q^{72} +(42.6423 + 131.240i) q^{73} +(-89.9719 + 276.905i) q^{74} +(586.858 + 426.377i) q^{75} -381.050 q^{76} -1164.04 q^{78} +(-246.312 - 178.956i) q^{79} +(26.7391 - 82.2945i) q^{80} +(-193.417 - 595.278i) q^{81} +(134.026 - 97.3755i) q^{82} +(-618.327 + 449.241i) q^{83} +(207.414 + 638.355i) q^{84} +(-99.0824 + 304.944i) q^{85} +(-244.926 - 177.949i) q^{86} +154.684 q^{87} -313.100 q^{89} +(-265.944 - 193.220i) q^{90} +(-525.855 + 1618.42i) q^{91} +(176.120 + 542.041i) q^{92} +(-1307.32 + 949.825i) q^{93} +(-146.213 + 106.230i) q^{94} +(-159.202 - 489.974i) q^{95} +(74.9131 - 230.559i) q^{96} +(471.257 + 342.388i) q^{97} +295.229 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 7 q^{3} - 8 q^{4} - 30 q^{5} + 6 q^{6} - 4 q^{7} - 16 q^{8} - 81 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 7 * q^3 - 8 * q^4 - 30 * q^5 + 6 * q^6 - 4 * q^7 - 16 * q^8 - 81 * q^9	\( 8 q - 4 q^{2} - 7 q^{3} - 8 q^{4} - 30 q^{5} + 6 q^{6} - 4 q^{7} - 16 q^{8} - 81 q^{9} + 100 q^{10} + 32 q^{12} + 48 q^{13} - 8 q^{14} - 279 q^{15} - 32 q^{16} + 109 q^{17} - 42 q^{18} - 288 q^{19} - 120 q^{20} + 50 q^{21} + 628 q^{23} + 24 q^{24} + 38 q^{25} - 14 q^{26} + 242 q^{27} + 4 q^{28} - 528 q^{29} - 558 q^{30} - 522 q^{31} + 256 q^{32} + 208 q^{34} + 17 q^{35} - 84 q^{36} - 406 q^{37} + 544 q^{38} + 1429 q^{39} + 40 q^{40} + 329 q^{41} - 1480 q^{42} - 1442 q^{43} + 2652 q^{45} - 1044 q^{46} + 666 q^{47} - 112 q^{48} - 114 q^{49} - 34 q^{50} - 1158 q^{51} - 28 q^{52} + 414 q^{53} + 1144 q^{54} + 48 q^{56} + 593 q^{57} - 1056 q^{58} - 888 q^{59} + 844 q^{60} + 302 q^{61} + 646 q^{62} + 2061 q^{63} - 128 q^{64} + 138 q^{65} + 578 q^{67} + 436 q^{68} + 1930 q^{69} + 1394 q^{70} + 1090 q^{71} - 648 q^{72} - 253 q^{73} - 812 q^{74} + 2763 q^{75} + 128 q^{76} - 4152 q^{78} + 674 q^{79} + 80 q^{80} - 230 q^{81} - 722 q^{82} + 428 q^{83} + 2860 q^{84} - 1046 q^{85} - 984 q^{86} - 2122 q^{87} - 2202 q^{89} - 1366 q^{90} - 2217 q^{91} + 832 q^{92} - 3721 q^{93} - 2138 q^{94} + 973 q^{95} - 224 q^{96} + 3012 q^{97} + 3292 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 7 * q^3 - 8 * q^4 - 30 * q^5 + 6 * q^6 - 4 * q^7 - 16 * q^8 - 81 * q^9 + 100 * q^10 + 32 * q^12 + 48 * q^13 - 8 * q^14 - 279 * q^15 - 32 * q^16 + 109 * q^17 - 42 * q^18 - 288 * q^19 - 120 * q^20 + 50 * q^21 + 628 * q^23 + 24 * q^24 + 38 * q^25 - 14 * q^26 + 242 * q^27 + 4 * q^28 - 528 * q^29 - 558 * q^30 - 522 * q^31 + 256 * q^32 + 208 * q^34 + 17 * q^35 - 84 * q^36 - 406 * q^37 + 544 * q^38 + 1429 * q^39 + 40 * q^40 + 329 * q^41 - 1480 * q^42 - 1442 * q^43 + 2652 * q^45 - 1044 * q^46 + 666 * q^47 - 112 * q^48 - 114 * q^49 - 34 * q^50 - 1158 * q^51 - 28 * q^52 + 414 * q^53 + 1144 * q^54 + 48 * q^56 + 593 * q^57 - 1056 * q^58 - 888 * q^59 + 844 * q^60 + 302 * q^61 + 646 * q^62 + 2061 * q^63 - 128 * q^64 + 138 * q^65 + 578 * q^67 + 436 * q^68 + 1930 * q^69 + 1394 * q^70 + 1090 * q^71 - 648 * q^72 - 253 * q^73 - 812 * q^74 + 2763 * q^75 + 128 * q^76 - 4152 * q^78 + 674 * q^79 + 80 * q^80 - 230 * q^81 - 722 * q^82 + 428 * q^83 + 2860 * q^84 - 1046 * q^85 - 984 * q^86 - 2122 * q^87 - 2202 * q^89 - 1366 * q^90 - 2217 * q^91 + 832 * q^92 - 3721 * q^93 - 2138 * q^94 + 973 * q^95 - 224 * q^96 + 3012 * q^97 + 3292 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/242\mathbb{Z}\right)^\times$.

$n$	$123$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.61803	−	1.17557i	−0.572061	−	0.415627i
$2$	−1.61803	−	1.17557i	−0.572061	−	0.415627i
$3$	2.34103	−	7.20496i	0.450532	−	1.38660i	−0.425769	−	0.904832i	$-0.639996\pi$
$3$	2.34103	−	7.20496i	0.450532	−	1.38660i	0.876301	−	0.481764i	$-0.160004\pi$
$4$	1.23607	+	3.80423i	0.154508	+	0.475528i
$5$	−4.37525	+	3.17880i	−0.391334	+	0.284321i	−0.766002	−	0.642838i	$-0.777757\pi$
$5$	−4.37525	+	3.17880i	−0.391334	+	0.284321i	0.374668	+	0.927159i	$0.377757\pi$
$6$	−12.2578	+	8.90583i	−0.834039	+	0.605965i
$7$	6.84467	+	21.0657i	0.369577	+	1.13744i	0.947065	+	0.321043i	$0.104033\pi$
$7$	6.84467	+	21.0657i	0.369577	+	1.13744i	−0.577487	+	0.816400i	$0.695967\pi$
$8$	2.47214	−	7.60845i	0.109254	−	0.336249i
$9$	−24.5876	−	17.8639i	−0.910652	−	0.661627i
$10$	10.8162			0.342038
$11$		0			0
$11$		0			0
$12$	30.3030			0.728977
$13$	62.1543	+	45.1577i	1.32604	+	0.963423i	0.999836	+	0.0181234i	$0.00576918\pi$
$13$	62.1543	+	45.1577i	1.32604	+	0.963423i	0.326203	+	0.945300i	$0.394231\pi$
$14$	13.6893	−	42.1315i	0.261331	−	0.804293i
$15$	12.6606	+	38.9652i	0.217929	+	0.670718i
$16$	−12.9443	+	9.40456i	−0.202254	+	0.146946i
$17$	47.9653	−	34.8488i	0.684311	−	0.497181i	−0.190474	−	0.981692i	$-0.561003\pi$
$17$	47.9653	−	34.8488i	0.684311	−	0.497181i	0.874785	+	0.484511i	$0.161003\pi$
$18$	18.7833	+	57.8089i	0.245959	+	0.756983i
$19$	−29.4377	+	90.6001i	−0.355446	+	1.09395i	0.600304	+	0.799772i	$0.295046\pi$
$19$	−29.4377	+	90.6001i	−0.355446	+	1.09395i	−0.955750	+	0.294180i	$0.904954\pi$
$20$	−17.5010	−	12.7152i	−0.195667	−	0.142160i
$21$	167.801			1.74368
$22$		0			0
$23$	142.484			1.29174			0.645868	−	0.763449i	$-0.276495\pi$
$23$	142.484			1.29174			0.645868	+	0.763449i	$0.276495\pi$
$24$	−49.0313	−	35.6233i	−0.417019	−	0.302982i
$25$	−29.5891	+	91.0660i	−0.236713	+	0.728528i
$26$	−47.4817	−	146.134i	−0.358151	−	1.10227i
$27$	−20.7889	+	15.1041i	−0.148179	+	0.107658i
$28$	−71.6783	+	52.0773i	−0.483783	+	0.351489i
$29$	6.30960	+	19.4190i	0.0404022	+	0.124345i	0.969223	−	0.246183i	$-0.0791766\pi$
$29$	6.30960	+	19.4190i	0.0404022	+	0.124345i	−0.928821	+	0.370529i	$0.879177\pi$
$30$	25.3211	−	77.9303i	0.154099	−	0.474269i
$31$	−172.567	−	125.377i	−0.999803	−	0.726399i	−0.0377570	−	0.999287i	$-0.512021\pi$
$31$	−172.567	−	125.377i	−0.999803	−	0.726399i	−0.962046	+	0.272888i	$0.912021\pi$
$32$	32.0000			0.176777
$33$		0			0
$34$	−118.577			−0.598110
$35$	−96.9109	−	70.4099i	−0.468027	−	0.340041i
$36$	37.5665	−	115.618i	0.173919	−	0.535268i
$37$	−44.9859	−	138.452i	−0.199882	−	0.615174i	−0.999885	−	0.0151777i	$-0.995169\pi$
$37$	−44.9859	−	138.452i	−0.199882	−	0.615174i	0.800003	−	0.599997i	$-0.204831\pi$
$38$	154.138	−	111.988i	0.658013	−	0.478074i
$39$	470.865	−	342.104i	1.93330	−	1.40463i
$40$	13.3696	+	41.1473i	0.0528478	+	0.162649i
$41$	−25.5967	+	78.7785i	−0.0975007	+	0.300076i	−0.987897	−	0.155109i	$-0.950427\pi$
$41$	−25.5967	+	78.7785i	−0.0975007	+	0.300076i	0.890397	+	0.455185i	$0.150427\pi$
$42$	−271.508	−	197.262i	−0.997492	−	0.724720i
$43$	151.373			0.536841			0.268420	−	0.963302i	$-0.413498\pi$
$43$	151.373			0.536841			0.268420	+	0.963302i	$0.413498\pi$
$44$		0			0
$45$	164.363			0.544483
$46$	−230.544	−	167.500i	−0.738953	−	0.536881i
$47$	27.9241	−	85.9416i	0.0866628	−	0.266721i	−0.898329	−	0.439324i	$-0.855218\pi$
$47$	27.9241	−	85.9416i	0.0866628	−	0.266721i	0.984991	+	0.172604i	$0.0552180\pi$
$48$	37.4566	+	115.279i	0.112633	+	0.346649i
$49$	−119.423	+	86.7656i	−0.348171	+	0.252961i
$50$	154.931	−	112.564i	0.438210	−	0.318378i
$51$	−138.796	−	427.170i	−0.381085	−	1.17286i
$52$	−94.9633	+	292.267i	−0.253251	+	0.779426i
$53$	189.997	+	138.041i	0.492416	+	0.357761i	0.806113	−	0.591762i	$-0.201567\pi$
$53$	189.997	+	138.041i	0.492416	+	0.357761i	−0.313697	+	0.949523i	$0.601567\pi$
$54$	51.3931			0.129513
$55$		0			0
$56$	177.199			0.422842
$57$	583.855	+	424.196i	1.35673	+	0.985721i
$58$	12.6192	−	38.8379i	0.0285687	−	0.0879253i
$59$	93.4769	+	287.692i	0.206265	+	0.634819i	0.999659	+	0.0261105i	$0.00831218\pi$
$59$	93.4769	+	287.692i	0.206265	+	0.634819i	−0.793394	+	0.608709i	$0.791688\pi$
$60$	−132.583	+	96.3272i	−0.285273	+	0.207263i
$61$	−120.770	+	87.7443i	−0.253491	+	0.184172i	−0.707273	−	0.706941i	$-0.750075\pi$
$61$	−120.770	+	87.7443i	−0.253491	+	0.184172i	0.453781	+	0.891113i	$0.350075\pi$
$62$	131.829	+	405.729i	0.270038	+	0.831090i
$63$	208.023	−	640.229i	0.416007	−	1.28034i
$64$	−51.7771	−	37.6183i	−0.101127	−	0.0734732i
$65$	−415.488			−0.792845
$66$		0			0
$67$	826.236			1.50658			0.753290	−	0.657689i	$-0.228466\pi$
$67$	826.236			1.50658			0.753290	+	0.657689i	$0.228466\pi$
$68$	191.861	+	139.395i	0.342155	+	0.248591i
$69$	333.560	−	1026.59i	0.581969	−	1.79112i
$70$	74.0333	+	227.851i	0.126410	+	0.389049i
$71$	727.278	−	528.399i	1.21566	−	0.883231i	0.219930	−	0.975516i	$-0.429417\pi$
$71$	727.278	−	528.399i	1.21566	−	0.883231i	0.995733	+	0.0922852i	$0.0294171\pi$
$72$	−196.701	+	142.912i	−0.321964	+	0.233921i
$73$	42.6423	+	131.240i	0.0683685	+	0.210417i	0.979404	−	0.201912i	$-0.0647155\pi$
$73$	42.6423	+	131.240i	0.0683685	+	0.210417i	−0.911035	+	0.412329i	$0.864716\pi$
$74$	−89.9719	+	276.905i	−0.141338	+	0.434994i
$75$	586.858	+	426.377i	0.903527	+	0.656451i
$76$	−381.050			−0.575124
$77$		0			0
$78$	−1164.04			−1.68977
$79$	−246.312	−	178.956i	−0.350788	−	0.254863i	0.398411	−	0.917207i	$-0.369562\pi$
$79$	−246.312	−	178.956i	−0.350788	−	0.254863i	−0.749200	+	0.662344i	$0.769562\pi$
$80$	26.7391	−	82.2945i	0.0373691	−	0.115010i
$81$	−193.417	−	595.278i	−0.265319	−	0.816568i
$82$	134.026	−	97.3755i	0.180496	−	0.131138i
$83$	−618.327	+	449.241i	−0.817713	+	0.594103i	−0.916056	−	0.401049i	$-0.868646\pi$
$83$	−618.327	+	449.241i	−0.817713	+	0.594103i	0.0983437	+	0.995153i	$0.468646\pi$
$84$	207.414	+	638.355i	0.269413	+	0.829169i
$85$	−99.0824	+	304.944i	−0.126435	+	0.389128i
$86$	−244.926	−	177.949i	−0.307106	−	0.223125i
$87$	154.684			0.190619
$88$		0			0
$89$	−313.100			−0.372905			−0.186452	−	0.982464i	$-0.559699\pi$
$89$	−313.100			−0.372905			−0.186452	+	0.982464i	$0.559699\pi$
$90$	−265.944	−	193.220i	−0.311478	−	0.226302i
$91$	−525.855	+	1618.42i	−0.605765	+	1.86435i
$92$	176.120	+	542.041i	0.199584	+	0.614257i
$93$	−1307.32	+	949.825i	−1.45767	+	1.05906i
$94$	−146.213	+	106.230i	−0.160433	+	0.116561i
$95$	−159.202	−	489.974i	−0.171935	−	0.529161i
$96$	74.9131	−	230.559i	0.0796436	−	0.245118i
$97$	471.257	+	342.388i	0.493287	+	0.358394i	0.806447	−	0.591306i	$-0.201388\pi$
$97$	471.257	+	342.388i	0.493287	+	0.358394i	−0.313160	+	0.949700i	$0.601388\pi$
$98$	295.229			0.304313
$99$		0			0
$100$	−383.010			−0.383010
$101$	−114.520	−	83.2036i	−0.112823	−	0.0819709i	0.529943	−	0.848033i	$-0.322213\pi$
$101$	−114.520	−	83.2036i	−0.112823	−	0.0819709i	−0.642766	+	0.766062i	$0.722213\pi$
$102$	−277.592	+	854.341i	−0.269468	+	0.829337i
$103$	260.001	+	800.200i	0.248725	+	0.765496i	0.995002	+	0.0998600i	$0.0318395\pi$
$103$	260.001	+	800.200i	0.248725	+	0.765496i	−0.746277	+	0.665636i	$0.768161\pi$
$104$	497.234	−	361.262i	0.468825	−	0.340622i
$105$	−734.172	+	533.408i	−0.682361	+	0.495764i
$106$	−145.145	−	446.709i	−0.132997	−	0.409323i
$107$	19.9106	−	61.2784i	0.0179890	−	0.0553646i	−0.941659	−	0.336568i	$-0.890734\pi$
$107$	19.9106	−	61.2784i	0.0179890	−	0.0553646i	0.959648	+	0.281204i	$0.0907337\pi$
$108$	−83.1558	−	60.4162i	−0.0740895	−	0.0538292i
$109$	−1559.04			−1.36999			−0.684995	−	0.728547i	$-0.740196\pi$
$109$	−1559.04			−1.36999			−0.684995	+	0.728547i	$0.740196\pi$
$110$		0			0
$111$	−1102.86			−0.943052
$112$	−286.713	−	208.309i	−0.241892	−	0.175745i
$113$	−691.933	+	2129.55i	−0.576032	+	1.77284i	0.0566082	+	0.998396i	$0.481971\pi$
$113$	−691.933	+	2129.55i	−0.576032	+	1.77284i	−0.632640	+	0.774446i	$0.718029\pi$
$114$	−446.026	−	1372.73i	−0.366440	−	1.12779i
$115$	−623.402	+	452.928i	−0.505500	+	0.367267i
$116$	−66.0750	+	48.0063i	−0.0528872	+	0.0384248i
$117$	−721.530	−	2220.64i	−0.570132	−	1.75469i
$118$	186.954	−	575.384i	0.145852	−	0.448885i
$119$	1062.42	+	771.895i	0.818421	+	0.594618i
$120$	327.763			0.249338
$121$		0			0
$122$	298.559			0.221559
$123$	507.673	+	368.846i	0.372157	+	0.270388i
$124$	263.658	−	811.457i	0.190945	−	0.587669i
$125$	−368.920	−	1135.42i	−0.263978	−	0.812441i
$126$	−1089.22	+	791.366i	−0.770124	+	0.559528i
$127$	884.624	−	642.717i	0.618092	−	0.449070i	−0.234163	−	0.972197i	$-0.575235\pi$
$127$	884.624	−	642.717i	0.618092	−	0.449070i	0.852255	+	0.523127i	$0.175235\pi$
$128$	39.5542	+	121.735i	0.0273135	+	0.0840623i
$129$	354.369	−	1090.64i	0.241864	−	0.744381i
$130$	672.273	+	488.435i	0.453556	+	0.329528i
$131$	2466.16			1.64481			0.822403	−	0.568906i	$-0.192633\pi$
$131$	2466.16			1.64481			0.822403	+	0.568906i	$0.192633\pi$
$132$		0			0
$133$	−2110.05			−1.37567
$134$	−1336.88	−	971.299i	−0.861856	−	0.626175i
$135$	42.9439	−	132.168i	0.0273780	−	0.0842607i
$136$	−146.569	−	451.092i	−0.0924130	−	0.284418i
$137$	787.405	−	572.083i	0.491040	−	0.356762i	−0.314544	−	0.949243i	$-0.601852\pi$
$137$	787.405	−	572.083i	0.491040	−	0.356762i	0.805584	+	0.592481i	$0.201852\pi$
$138$	−1746.54	+	1268.94i	−1.07736	+	0.782747i
$139$	390.301	+	1201.22i	0.238165	+	0.732995i	0.996686	+	0.0813469i	$0.0259222\pi$
$139$	390.301	+	1201.22i	0.238165	+	0.732995i	−0.758521	+	0.651648i	$0.774078\pi$
$140$	148.067	−	455.702i	0.0893851	−	0.275099i
$141$	−553.835	−	402.384i	−0.330789	−	0.240332i
$142$	−1797.93			−1.06253
$143$		0			0
$144$	486.271			0.281407
$145$	−89.3351	−	64.9057i	−0.0511647	−	0.0371733i
$146$	85.2846	−	262.479i	0.0483439	−	0.148787i
$147$	345.571	+	1063.56i	0.193892	+	0.596740i
$148$	471.099	−	342.273i	0.261649	−	0.190099i
$149$	−395.884	+	287.627i	−0.217665	+	0.158143i	−0.691275	−	0.722592i	$-0.742951\pi$
$149$	−395.884	+	287.627i	−0.217665	+	0.158143i	0.473610	+	0.880735i	$0.342951\pi$
$150$	−448.320	−	1379.79i	−0.244034	−	0.751060i
$151$	−527.731	+	1624.19i	−0.284412	+	0.875329i	0.702163	+	0.712017i	$0.252218\pi$
$151$	−527.731	+	1624.19i	−0.284412	+	0.875329i	−0.986574	+	0.163313i	$0.947782\pi$
$152$	616.552	+	447.951i	0.329006	+	0.239037i
$153$	−1801.89			−0.952118
$154$		0			0
$155$	1153.57			0.597787
$156$	1883.46	+	1368.41i	0.966651	+	0.702313i
$157$	791.617	−	2436.35i	0.402407	−	1.23848i	−0.520634	−	0.853780i	$-0.674304\pi$
$157$	791.617	−	2436.35i	0.402407	−	1.23848i	0.923041	−	0.384702i	$-0.125696\pi$
$158$	188.166	+	579.115i	0.0947447	+	0.291594i
$159$	1439.37	−	1045.76i	0.717920	−	0.521599i
$160$	−140.008	+	101.722i	−0.0691787	+	0.0502613i
$161$	975.255	+	3001.53i	0.477397	+	1.46928i
$162$	−386.835	+	1190.56i	−0.187609	+	0.577400i
$163$	−1469.25	−	1067.47i	−0.706013	−	0.512949i	0.175872	−	0.984413i	$-0.443726\pi$
$163$	−1469.25	−	1067.47i	−0.706013	−	0.512949i	−0.881885	+	0.471464i	$0.843726\pi$
$164$	−331.330			−0.157759
$165$		0			0
$166$	1528.59			0.714707
$167$	306.557	+	222.727i	0.142048	+	0.103204i	0.656540	−	0.754291i	$-0.272019\pi$
$167$	306.557	+	222.727i	0.142048	+	0.103204i	−0.514492	+	0.857495i	$0.672019\pi$
$168$	414.828	−	1276.71i	0.190504	−	0.586311i
$169$	1145.02	+	3524.02i	0.521176	+	1.60402i
$170$	518.802	−	376.932i	0.234061	−	0.170055i
$171$	2342.28	−	1701.76i	1.04748	−	0.761036i
$172$	187.107	+	575.857i	0.0829464	+	0.255283i
$173$	−15.6739	+	48.2395i	−0.00688826	+	0.0211999i	−0.954442	−	0.298398i	$-0.903548\pi$
$173$	−15.6739	+	48.2395i	−0.00688826	+	0.0211999i	0.947553	+	0.319598i	$0.103548\pi$
$174$	−250.284	−	181.842i	−0.109046	−	0.0792264i
$175$	−2120.90			−0.916142
$176$		0			0
$177$	2291.64			0.973167
$178$	506.606	+	368.071i	0.213324	+	0.154989i
$179$	6.44850	−	19.8465i	0.00269265	−	0.00828712i	−0.949701	−	0.313158i	$-0.898613\pi$
$179$	6.44850	−	19.8465i	0.00269265	−	0.00828712i	0.952394	+	0.304871i	$0.0986132\pi$
$180$	203.163	+	625.273i	0.0841273	+	0.258917i
$181$	142.511	−	103.540i	0.0585235	−	0.0425198i	−0.558139	−	0.829748i	$-0.688484\pi$
$181$	142.511	−	103.540i	0.0585235	−	0.0425198i	0.616662	+	0.787228i	$0.288484\pi$
$182$	2753.41	−	2000.47i	1.12141	−	0.814752i
$183$	349.468	+	1075.55i	0.141166	+	0.434465i
$184$	352.240	−	1084.08i	0.141127	−	0.434346i
$185$	636.937	+	462.762i	0.253127	+	0.183908i
$186$	3231.88			1.27405
$187$		0			0
$188$	361.457			0.140223
$189$	−460.471	−	334.552i	−0.177219	−	0.128757i
$190$	−318.405	+	979.949i	−0.121576	+	0.374173i
$191$	−358.219	−	1102.48i	−0.135706	−	0.417659i	0.859993	−	0.510305i	$-0.170468\pi$
$191$	−358.219	−	1102.48i	−0.135706	−	0.417659i	−0.995699	+	0.0926459i	$0.970468\pi$
$192$	−392.250	+	284.986i	−0.147439	+	0.107120i
$193$	−1039.54	+	755.267i	−0.387707	+	0.281686i	−0.764515	−	0.644606i	$-0.777022\pi$
$193$	−1039.54	+	755.267i	−0.387707	+	0.281686i	0.376808	+	0.926291i	$0.377022\pi$
$194$	−360.008	−	1107.99i	−0.133232	−	0.410047i
$195$	−972.671	+	2993.57i	−0.357202	+	1.09936i
$196$	−477.691	−	347.063i	−0.174085	−	0.126481i
$197$	2685.06			0.971078			0.485539	−	0.874215i	$-0.338623\pi$
$197$	2685.06			0.971078			0.485539	+	0.874215i	$0.338623\pi$
$198$		0			0
$199$	−1333.54			−0.475036			−0.237518	−	0.971383i	$-0.576334\pi$
$199$	−1333.54			−0.475036			−0.237518	+	0.971383i	$0.576334\pi$
$200$	619.723	+	450.255i	0.219105	+	0.159189i
$201$	1934.25	−	5953.00i	0.678763	−	2.08902i
$202$	87.4854	+	269.252i	0.0304725	+	0.0937848i
$203$	−365.887	+	265.833i	−0.126504	+	0.0919104i
$204$	1453.49	−	1056.02i	0.498847	−	0.362433i
$205$	−138.429	−	426.042i	−0.0471626	−	0.145151i
$206$	520.001	−	1600.40i	0.175875	−	0.541287i
$207$	−3503.34	−	2545.32i	−1.17632	−	0.854648i
$208$	−1229.23			−0.409768
$209$		0			0
$210$	1814.97			0.596405
$211$	−1317.22	−	957.013i	−0.429767	−	0.312244i	0.351789	−	0.936079i	$-0.385574\pi$
$211$	−1317.22	−	957.013i	−0.429767	−	0.312244i	−0.781556	+	0.623835i	$0.785574\pi$
$212$	−290.289	+	893.418i	−0.0940431	+	0.289435i
$213$	−2104.51	−	6477.01i	−0.676989	−	2.08356i
$214$	−104.253	+	75.7443i	−0.0333018	+	0.0241952i
$215$	−662.293	+	481.184i	−0.210084	+	0.152635i
$216$	63.5254	+	195.511i	0.0200109	+	0.0615872i
$217$	1460.00	−	4493.41i	0.456733	−	1.40568i
$218$	2522.58	+	1832.76i	0.783719	+	0.569405i
$219$	1045.40			0.322565
$220$		0			0
$221$	4554.94			1.38642
$222$	1784.46	+	1296.49i	0.539483	+	0.391958i
$223$	−812.157	+	2499.56i	−0.243884	+	0.750596i	0.751934	+	0.659238i	$0.229121\pi$
$223$	−812.157	+	2499.56i	−0.243884	+	0.750596i	−0.995818	+	0.0913586i	$0.970879\pi$
$224$	219.029	+	674.103i	0.0653327	+	0.201073i
$225$	2354.32	−	1710.52i	0.697577	−	0.506820i
$226$	3623.01	−	2632.27i	1.06637	−	0.774761i
$227$	−526.118	−	1619.23i	−0.153831	−	0.473444i	0.844209	−	0.536014i	$-0.180070\pi$
$227$	−526.118	−	1619.23i	−0.153831	−	0.473444i	−0.998041	+	0.0625696i	$0.980070\pi$
$228$	−892.052	+	2745.45i	−0.259112	+	0.797465i
$229$	−4365.41	−	3171.66i	−1.25971	−	0.915236i	−0.260971	−	0.965347i	$-0.584043\pi$
$229$	−4365.41	−	3171.66i	−1.25971	−	0.915236i	−0.998744	+	0.0501107i	$0.984043\pi$
$230$	1541.13			0.441823
$231$		0			0
$232$	163.346			0.0462251
$233$	−4897.94	−	3558.56i	−1.37714	−	1.00055i	−0.997141	−	0.0755682i	$-0.975923\pi$
$233$	−4897.94	−	3558.56i	−1.37714	−	1.00055i	−0.380003	−	0.924985i	$-0.624077\pi$
$234$	−1443.06	+	4441.28i	−0.403144	+	1.24075i
$235$	151.016	+	464.781i	0.0419201	+	0.129017i
$236$	−978.902	+	711.214i	−0.270005	+	0.196170i
$237$	−1866.00	+	1355.73i	−0.511433	+	0.371578i
$238$	−811.618	−	2497.90i	−0.221048	−	0.680315i
$239$	−969.263	+	2983.08i	−0.262328	+	0.807362i	0.729969	+	0.683480i	$0.239534\pi$
$239$	−969.263	+	2983.08i	−0.262328	+	0.807362i	−0.992297	+	0.123882i	$0.960466\pi$
$240$	−530.332	−	385.309i	−0.142637	−	0.103632i
$241$	6499.26			1.73715			0.868577	−	0.495555i	$-0.165035\pi$
$241$	6499.26			1.73715			0.868577	+	0.495555i	$0.165035\pi$
$242$		0			0
$243$	−5435.56			−1.43494
$244$	−483.078	−	350.977i	−0.126746	−	0.0920861i
$245$	246.693	−	759.242i	0.0643290	−	0.197984i
$246$	−387.828	−	1193.61i	−0.100516	−	0.309357i
$247$	−5920.98	+	4301.84i	−1.52527	+	1.10818i
$248$	−1380.53	+	1003.02i	−0.353484	+	0.256821i
$249$	1789.24	+	5506.71i	0.455375	+	1.40150i
$250$	−737.841	+	2270.84i	−0.186661	+	0.574482i
$251$	−4502.82	−	3271.49i	−1.13233	−	0.822687i	−0.146299	−	0.989240i	$-0.546736\pi$
$251$	−4502.82	−	3271.49i	−1.13233	−	0.822687i	−0.986032	+	0.166553i	$0.946736\pi$
$252$	2692.70			0.673113
$253$		0			0
$254$	−2186.91			−0.540232
$255$	1965.16	+	1427.77i	0.482600	+	0.350629i
$256$	79.1084	−	243.470i	0.0193136	−	0.0594410i
$257$	−1865.32	−	5740.87i	−0.452745	−	1.39341i	−0.873762	−	0.486354i	$-0.838327\pi$
$257$	−1865.32	−	5740.87i	−0.452745	−	1.39341i	0.421016	−	0.907053i	$-0.361673\pi$
$258$	−1855.50	+	1348.10i	−0.447746	+	0.325306i
$259$	2608.69	−	1895.32i	0.625853	−	0.454709i
$260$	−513.571	−	1580.61i	−0.122501	−	0.377020i
$261$	191.761	−	590.180i	0.0454778	−	0.139966i
$262$	−3990.33	−	2899.15i	−0.940930	−	0.683625i
$263$	708.442			0.166100			0.0830502	−	0.996545i	$-0.473534\pi$
$263$	708.442			0.166100			0.0830502	+	0.996545i	$0.473534\pi$
$264$		0			0
$265$	−1270.09			−0.294418
$266$	3414.13	+	2480.51i	0.786969	+	0.571766i
$267$	−732.977	+	2255.87i	−0.168006	+	0.517068i
$268$	1021.28	+	3143.19i	0.232779	+	0.716421i
$269$	3891.13	−	2827.07i	0.881958	−	0.640780i	−0.0518111	−	0.998657i	$-0.516499\pi$
$269$	3891.13	−	2827.07i	0.881958	−	0.640780i	0.933769	+	0.357877i	$0.116499\pi$
$270$	−224.857	+	163.368i	−0.0506829	+	0.0368233i
$271$	1619.52	+	4984.38i	0.363022	+	1.11727i	0.951210	+	0.308543i	$0.0998413\pi$
$271$	1619.52	+	4984.38i	0.363022	+	1.11727i	−0.588189	+	0.808724i	$0.700159\pi$
$272$	−293.138	+	902.185i	−0.0653459	+	0.201114i
$273$	10429.6	+	7577.53i	2.31219	+	1.67990i
$274$	−1946.57			−0.429185
$275$		0			0
$276$	4317.69			0.941646
$277$	−4319.95	−	3138.63i	−0.937041	−	0.680800i	0.0106653	−	0.999943i	$-0.496605\pi$
$277$	−4319.95	−	3138.63i	−0.937041	−	0.680800i	−0.947707	+	0.319143i	$0.896605\pi$
$278$	780.601	−	2402.44i	0.168408	−	0.518306i
$279$	2003.27	+	6165.44i	0.429867	+	1.32299i
$280$	−775.287	+	563.279i	−0.165472	+	0.120223i
$281$	−2653.55	+	1927.92i	−0.563337	+	0.409288i	−0.832679	−	0.553757i	$-0.813194\pi$
$281$	−2653.55	+	1927.92i	−0.563337	+	0.409288i	0.269342	+	0.963045i	$0.413194\pi$
$282$	423.092	+	1302.14i	0.0893431	+	0.274970i
$283$	1512.79	−	4655.89i	0.317760	−	0.977964i	−0.656844	−	0.754027i	$-0.728109\pi$
$283$	1512.79	−	4655.89i	0.317760	−	0.977964i	0.974604	−	0.223937i	$-0.0718911\pi$
$284$	2909.11	+	2113.59i	0.607831	+	0.441615i
$285$	−3902.95			−0.811195
$286$		0			0
$287$	−1834.73			−0.377354
$288$	−786.803	−	571.646i	−0.160982	−	0.116960i
$289$	−431.973	+	1329.48i	−0.0879244	+	0.270604i
$290$	68.2459	+	210.039i	0.0138191	+	0.0425308i
$291$	3570.12	−	2593.85i	0.719190	−	0.522522i
$292$	−446.556	+	324.442i	−0.0894956	+	0.0650224i
$293$	−2072.21	−	6377.59i	−0.413172	−	1.27161i	−0.913875	−	0.405995i	$-0.866925\pi$
$293$	−2072.21	−	6377.59i	−0.413172	−	1.27161i	0.500703	−	0.865619i	$-0.333075\pi$
$294$	691.141	−	2127.11i	0.137103	−	0.421959i
$295$	−1323.50	−	961.580i	−0.261211	−	0.189781i
$296$	−1164.62			−0.228690
$297$		0			0
$298$	978.680			0.190246
$299$	8855.99	+	6434.25i	1.71289	+	1.24449i
$300$	−896.639	+	2759.57i	−0.172558	+	0.531080i
$301$	1036.10	+	3188.78i	0.198404	+	0.610625i
$302$	2763.24	−	2007.61i	0.526511	−	0.382533i
$303$	−867.574	+	630.329i	−0.164491	+	0.119510i
$304$	−471.004	−	1449.60i	−0.0888616	−	0.273488i
$305$	249.475	−	767.805i	0.0468357	−	0.144146i
$306$	2915.52	+	2118.25i	0.544670	+	0.395726i
$307$	−9507.29			−1.76746			−0.883730	−	0.467998i	$-0.844975\pi$
$307$	−9507.29			−1.76746			−0.883730	+	0.467998i	$0.844975\pi$
$308$		0			0
$309$	6374.08			1.17349
$310$	−1866.52	−	1356.10i	−0.341971	−	0.248456i
$311$	1782.43	−	5485.77i	0.324992	−	1.00022i	−0.646452	−	0.762954i	$-0.723748\pi$
$311$	1782.43	−	5485.77i	0.324992	−	1.00022i	0.971444	−	0.237268i	$-0.0762520\pi$
$312$	−1438.84	−	4428.28i	−0.261084	−	0.803532i
$313$	−4836.10	+	3513.63i	−0.873331	+	0.634512i	−0.931479	−	0.363796i	$-0.881481\pi$
$313$	−4836.10	+	3513.63i	−0.873331	+	0.634512i	0.0581477	+	0.998308i	$0.481481\pi$
$314$	−4144.96	+	3011.49i	−0.744948	+	0.541236i
$315$	1125.01	+	3462.42i	0.201229	+	0.619318i
$316$	376.332	−	1158.23i	0.0669946	−	0.206188i
$317$	−4232.72	−	3075.25i	−0.749948	−	0.544869i	0.145863	−	0.989305i	$-0.453404\pi$
$317$	−4232.72	−	3075.25i	−0.749948	−	0.544869i	−0.895811	+	0.444436i	$0.853404\pi$
$318$	−3558.31			−0.627485
$319$		0			0
$320$	346.118			0.0604644
$321$	−394.897	−	286.910i	−0.0686636	−	0.0498870i
$322$	1950.51	−	6003.05i	0.337571	−	1.03894i
$323$	1745.32	+	5371.53i	0.300656	+	0.925324i
$324$	2025.49	−	1471.61i	0.347307	−	0.252333i
$325$	−5951.43	+	4323.96i	−1.01577	+	0.738001i
$326$	1122.40	+	3454.40i	0.190688	+	0.586876i
$327$	−3649.77	+	11232.8i	−0.617225	+	1.89962i
$328$	536.104	+	389.502i	0.0902481	+	0.0655691i
$329$	2001.55			0.335408
$330$		0			0
$331$	−3963.72			−0.658205			−0.329102	−	0.944294i	$-0.606746\pi$
$331$	−3963.72			−0.658205			−0.329102	+	0.944294i	$0.606746\pi$
$332$	−2473.31	−	1796.96i	−0.408856	−	0.297052i
$333$	−1367.21	+	4207.84i	−0.224993	+	0.692457i
$334$	−234.189	−	720.758i	−0.0383659	−	0.118078i
$335$	−3614.99	+	2626.44i	−0.589576	+	0.428352i
$336$	−2172.07	+	1578.10i	−0.352667	+	0.256227i
$337$	−1578.03	−	4856.66i	−0.255076	−	0.785043i	−0.993815	−	0.111051i	$-0.964578\pi$
$337$	−1578.03	−	4856.66i	−0.255076	−	0.785043i	0.738739	−	0.673992i	$-0.235422\pi$
$338$	2290.05	−	7048.05i	0.368527	−	1.13421i
$339$	13723.5	+	9970.70i	2.19870	+	1.59745i
$340$	−1282.55			−0.204576
$341$		0			0
$342$	−5790.43			−0.915528
$343$	3501.23	+	2543.79i	0.551162	+	0.400442i
$344$	374.214	−	1151.71i	0.0586520	−	0.180512i
$345$	1803.92	+	5551.91i	0.281507	+	0.866391i
$346$	82.0699	−	59.6272i	0.0127517	−	0.00926468i
$347$	6104.64	−	4435.28i	0.944422	−	0.686162i	−0.00505934	−	0.999987i	$-0.501610\pi$
$347$	6104.64	−	4435.28i	0.944422	−	0.686162i	0.949481	+	0.313825i	$0.101610\pi$
$348$	191.200	+	588.453i	0.0294523	+	0.0906447i
$349$	1006.38	−	3097.32i	0.154356	−	0.475059i	−0.843739	−	0.536754i	$-0.819650\pi$
$349$	1006.38	−	3097.32i	0.154356	−	0.475059i	0.998095	+	0.0616946i	$0.0196505\pi$
$350$	3431.69	+	2493.27i	0.524090	+	0.380773i
$351$	−1974.19			−0.300212
$352$		0			0
$353$	−6506.83			−0.981087			−0.490543	−	0.871417i	$-0.663202\pi$
$353$	−6506.83			−0.981087			−0.490543	+	0.871417i	$0.663202\pi$
$354$	−3707.96	−	2693.99i	−0.556711	−	0.404474i
$355$	−1502.35	+	4623.75i	−0.224609	+	0.691276i
$356$	−387.012	−	1191.10i	−0.0576169	−	0.177327i
$357$	8048.64	−	5847.68i	1.19322	−	0.866925i
$358$	−33.7648	+	24.5316i	−0.00498471	+	0.00362160i
$359$	−1256.53	−	3867.19i	−0.184727	−	0.568531i	0.815217	−	0.579156i	$-0.196618\pi$
$359$	−1256.53	−	3867.19i	−0.184727	−	0.568531i	−0.999944	+	0.0106250i	$0.996618\pi$
$360$	406.327	−	1250.55i	0.0594870	−	0.183082i
$361$	−1792.74	−	1302.51i	−0.261371	−	0.189897i
$362$	−352.307			−0.0511514
$363$		0			0
$364$	−6806.81			−0.980148
$365$	−603.755	−	438.654i	−0.0865808	−	0.0629046i
$366$	698.937	−	2151.11i	0.0998197	−	0.307213i
$367$	−430.236	−	1324.13i	−0.0611939	−	0.188335i	0.915786	−	0.401666i	$-0.131569\pi$
$367$	−430.236	−	1324.13i	−0.0611939	−	0.188335i	−0.976980	+	0.213331i	$0.931569\pi$
$368$	−1844.35	+	1340.00i	−0.261259	+	0.189816i
$369$	2036.65	−	1479.72i	0.287328	−	0.208756i
$370$	−486.577	−	1497.53i	−0.0683674	−	0.210413i
$371$	−1607.46	+	4947.26i	−0.224947	+	0.692315i
$372$	−5229.29	−	3799.30i	−0.728833	−	0.529528i
$373$	−9440.30			−1.31046			−0.655228	−	0.755431i	$-0.727428\pi$
$373$	−9440.30			−1.31046			−0.655228	+	0.755431i	$0.727428\pi$
$374$		0			0
$375$	−9044.32			−1.24546
$376$	−584.850	−	424.919i	−0.0802163	−	0.0582806i
$377$	−484.747	+	1491.90i	−0.0662222	+	0.203811i
$378$	351.769	+	1082.63i	0.0478652	+	0.147314i
$379$	−1043.92	+	758.449i	−0.141484	+	0.102794i	−0.656276	−	0.754521i	$-0.727869\pi$
$379$	−1043.92	+	758.449i	−0.141484	+	0.102794i	0.514792	+	0.857315i	$0.327869\pi$
$380$	1667.19	−	1211.28i	0.225066	−	0.163520i
$381$	−2559.82	−	7878.31i	−0.344208	−	1.05936i
$382$	−716.437	+	2204.97i	−0.0959584	+	0.295330i
$383$	4573.29	+	3322.69i	0.610141	+	0.443293i	0.849464	−	0.527647i	$-0.176925\pi$
$383$	4573.29	+	3322.69i	0.610141	+	0.443293i	−0.239323	+	0.970940i	$0.576925\pi$
$384$	969.696			0.128866
$385$		0			0
$386$	2569.88			0.338868
$387$	−3721.90	−	2704.12i	−0.488875	−	0.355188i
$388$	−720.016	+	2215.98i	−0.0942095	+	0.289947i
$389$	−3967.16	−	12209.7i	−0.517077	−	1.59140i	−0.779471	−	0.626439i	$-0.784512\pi$
$389$	−3967.16	−	12209.7i	−0.517077	−	1.59140i	0.262394	−	0.964961i	$-0.415488\pi$
$390$	5092.97	−	3700.26i	0.661263	−	0.480436i
$391$	6834.28	−	4965.39i	0.883950	−	0.642227i
$392$	364.923	+	1123.12i	0.0470189	+	0.144709i
$393$	5773.37	−	17768.6i	0.741038	−	2.28068i
$394$	−4344.51	−	3156.47i	−0.555516	−	0.403606i
$395$	1646.54			0.209738
$396$		0			0
$397$	7691.26			0.972326			0.486163	−	0.873868i	$-0.338396\pi$
$397$	7691.26			0.972326			0.486163	+	0.873868i	$0.338396\pi$
$398$	2157.71	+	1567.67i	0.271750	+	0.197438i
$399$	−4939.70	+	15202.8i	−0.619785	+	1.90750i
$400$	−473.426	−	1457.06i	−0.0591783	−	0.182132i
$401$	−6299.15	+	4576.60i	−0.784450	+	0.569936i	−0.906311	−	0.422611i	$-0.861114\pi$
$401$	−6299.15	+	4576.60i	−0.784450	+	0.569936i	0.121861	+	0.992547i	$0.461114\pi$
$402$	−10127.9	+	7358.32i	−1.25655	+	0.912934i
$403$	−5064.02	−	15585.4i	−0.625947	−	1.92647i
$404$	174.971	−	538.505i	0.0215473	−	0.0663159i
$405$	2738.52	+	1989.65i	0.335995	+	0.244115i
$406$	904.523			0.110568
$407$		0			0
$408$	−3593.23			−0.436008
$409$	−7167.80	−	5207.71i	−0.866564	−	0.629596i	0.0630988	−	0.998007i	$-0.479902\pi$
$409$	−7167.80	−	5207.71i	−0.866564	−	0.629596i	−0.929663	+	0.368412i	$0.879902\pi$
$410$	−276.859	+	852.084i	−0.0333490	+	0.102638i
$411$	−2278.50	−	7012.49i	−0.273455	−	0.841607i
$412$	−2722.76	+	1978.20i	−0.325585	+	0.236551i
$413$	−5420.63	+	3938.32i	−0.645839	+	0.469230i
$414$	2676.31	+	8236.84i	0.317714	+	0.977823i
$415$	1277.28	−	3931.07i	0.151083	−	0.464985i
$416$	1988.94	+	1445.05i	0.234413	+	0.170311i
$417$	9568.47			1.12367
$418$		0			0
$419$	9469.08			1.10405			0.552023	−	0.833829i	$-0.313856\pi$
$419$	9469.08			1.10405			0.552023	+	0.833829i	$0.313856\pi$
$420$	−2936.69	−	2133.63i	−0.341180	−	0.247882i
$421$	1600.07	−	4924.52i	0.185232	−	0.570086i	−0.814720	−	0.579854i	$-0.803109\pi$
$421$	1600.07	−	4924.52i	0.185232	−	0.570086i	0.999952	+	0.00976831i	$0.00310940\pi$
$422$	1006.26	+	3096.96i	0.116076	+	0.357246i
$423$	−2221.84	+	1614.26i	−0.255389	+	0.185551i
$424$	1519.97	−	1104.33i	0.174095	−	0.126488i
$425$	1754.29	+	5399.15i	0.200225	+	0.616229i
$426$	−4209.02	+	12954.0i	−0.478703	+	1.47330i
$427$	−2675.03	−	1943.52i	−0.303170	−	0.220266i
$428$	257.728			0.0291069
$429$		0			0
$430$	1637.28			0.183620
$431$	8465.20	+	6150.32i	0.946065	+	0.687357i	0.949873	−	0.312636i	$-0.101212\pi$
$431$	8465.20	+	6150.32i	0.946065	+	0.687357i	−0.00380775	+	0.999993i	$0.501212\pi$
$432$	127.051	−	391.022i	0.0141498	−	0.0435487i
$433$	4894.28	+	15063.1i	0.543197	+	1.67179i	0.725239	+	0.688497i	$0.241729\pi$
$433$	4894.28	+	15063.1i	0.543197	+	1.67179i	−0.182042	+	0.983291i	$0.558271\pi$
$434$	−7644.64	+	5554.16i	−0.845517	+	0.614304i
$435$	−676.780	+	491.709i	−0.0745957	+	0.0541969i
$436$	−1927.08	−	5930.94i	−0.211675	−	0.651469i
$437$	−4194.41	+	12909.1i	−0.459143	+	1.41310i
$438$	−1691.50	−	1228.94i	−0.184527	−	0.134067i
$439$	4824.70			0.524534			0.262267	−	0.964995i	$-0.415530\pi$
$439$	4824.70			0.524534			0.262267	+	0.964995i	$0.415530\pi$
$440$		0			0
$441$	4486.29			0.484429
$442$	−7370.05	−	5354.65i	−0.793116	−	0.576233i
$443$	1107.33	−	3408.00i	0.118760	−	0.365506i	−0.873953	−	0.486011i	$-0.838451\pi$
$443$	1107.33	−	3408.00i	0.118760	−	0.365506i	0.992713	+	0.120505i	$0.0384515\pi$
$444$	−1363.21	−	4195.52i	−0.145709	−	0.448448i
$445$	1369.89	−	995.282i	0.145930	−	0.106024i
$446$	4252.51	−	3089.63i	0.451484	−	0.328023i
$447$	1145.56	+	3525.68i	0.121215	+	0.373062i
$448$	438.059	−	1348.21i	0.0461972	−	0.142180i
$449$	6307.08	+	4582.36i	0.662917	+	0.481637i	0.867647	−	0.497181i	$-0.165632\pi$
$449$	6307.08	+	4582.36i	0.662917	+	0.481637i	−0.204730	+	0.978819i	$0.565632\pi$
$450$	−5820.21			−0.609705
$451$		0			0
$452$	−8956.57			−0.932039
$453$	10466.8	+	7604.57i	1.08559	+	0.788728i
$454$	−1052.24	+	3238.45i	−0.108775	+	0.334776i
$455$	−2843.88	−	8752.55i	−0.293018	−	0.901815i
$456$	4670.84	−	3393.57i	0.479676	−	0.348505i
$457$	2708.61	−	1967.92i	0.277250	−	0.201434i	−0.440467	−	0.897769i	$-0.645187\pi$
$457$	2708.61	−	1967.92i	0.277250	−	0.201434i	0.717717	+	0.696335i	$0.245187\pi$
$458$	3334.88	+	10263.7i	0.340237	+	1.04714i
$459$	−470.789	+	1448.94i	−0.0478748	+	0.147344i
$460$	−2493.61	−	1811.71i	−0.252750	−	0.183634i
$461$	−7171.96			−0.724580			−0.362290	−	0.932065i	$-0.618005\pi$
$461$	−7171.96			−0.724580			−0.362290	+	0.932065i	$0.618005\pi$
$462$		0			0
$463$	4034.74			0.404990			0.202495	−	0.979283i	$-0.435095\pi$
$463$	4034.74			0.404990			0.202495	+	0.979283i	$0.435095\pi$
$464$	−264.300	−	192.025i	−0.0264436	−	0.0192124i
$465$	2700.55	−	8311.43i	0.269322	−	0.828889i
$466$	3741.69	+	11515.7i	0.371954	+	1.14476i
$467$	9564.07	−	6948.70i	0.947692	−	0.688539i	−0.00256754	−	0.999997i	$-0.500817\pi$
$467$	9564.07	−	6948.70i	0.947692	−	0.688539i	0.950260	+	0.311458i	$0.100817\pi$
$468$	7555.96	−	5489.73i	0.746313	−	0.542228i
$469$	5655.32	+	17405.3i	0.556798	+	1.71365i
$470$	302.033	−	929.561i	0.0296420	−	0.0912287i
$471$	−15700.6	−	11407.1i	−1.53598	−	1.11595i
$472$	2419.98			0.235993
$473$		0			0
$474$	4613.00			0.447009
$475$	−7379.55	−	5361.56i	−0.712836	−	0.517905i
$476$	−1623.24	+	4995.81i	−0.156304	+	0.481056i
$477$	−2205.61	−	6788.18i	−0.211715	−	0.651592i
$478$	5075.12	−	3687.29i	0.485629	−	0.352830i
$479$	−7006.04	+	5090.19i	−0.668297	+	0.485546i	−0.869455	−	0.494013i	$-0.835530\pi$
$479$	−7006.04	+	5090.19i	−0.668297	+	0.485546i	0.201158	+	0.979559i	$0.435530\pi$
$480$	405.138	+	1246.89i	0.0385248	+	0.118567i
$481$	3456.13	−	10636.9i	0.327622	−	1.00832i
$482$	−10516.0	−	7640.34i	−0.993759	−	0.722008i
$483$	23909.0			2.25238
$484$		0			0
$485$	−3150.25			−0.294939
$486$	8794.92	+	6389.88i	0.820876	+	0.596401i
$487$	2295.27	−	7064.12i	0.213570	−	0.657301i	−0.785682	−	0.618631i	$-0.787688\pi$
$487$	2295.27	−	7064.12i	0.213570	−	0.657301i	0.999252	−	0.0386707i	$-0.0123123\pi$
$488$	369.039	+	1135.79i	0.0342328	+	0.105358i
$489$	−11130.6	+	8086.88i	−1.02933	+	0.747855i
$490$	−1291.70	+	938.475i	−0.119088	+	0.0865224i
$491$	1713.16	+	5272.55i	0.157462	+	0.484617i	0.998402	−	0.0565108i	$-0.0179975\pi$
$491$	1713.16	+	5272.55i	0.157462	+	0.484617i	−0.840940	+	0.541128i	$0.817998\pi$
$492$	−775.656	+	2387.22i	−0.0710757	+	0.218749i
$493$	979.369	+	711.554i	0.0894697	+	0.0650036i
$494$	14637.5			1.33314
$495$		0			0
$496$	3412.87			0.308956
$497$	16109.1	+	11703.9i	1.45391	+	1.05632i
$498$	3578.48	−	11013.4i	0.321999	−	0.991010i
$499$	6307.66	+	19413.0i	0.565871	+	1.74157i	0.665349	+	0.746533i	$0.268283\pi$
$499$	6307.66	+	19413.0i	0.565871	+	1.74157i	−0.0994775	+	0.995040i	$0.531717\pi$
$500$	3863.38	−	2806.91i	0.345552	−	0.251058i
$501$	2322.40	−	1687.32i	0.207100	−	0.150467i
$502$	3439.85	+	10586.8i	0.305832	+	0.941255i
$503$	56.4703	−	173.798i	0.00500574	−	0.0154061i	−0.948522	−	0.316710i	$-0.897422\pi$
$503$	56.4703	−	173.798i	0.00500574	−	0.0154061i	0.953528	+	0.301304i	$0.0974218\pi$
$504$	−4356.89	−	3165.46i	−0.385062	−	0.279764i
$505$	765.540			0.0674576
$506$		0			0
$507$	28071.0			2.45893
$508$	3538.50	+	2570.87i	0.309046	+	0.224535i
$509$	1469.47	−	4522.55i	0.127963	−	0.393828i	−0.866467	−	0.499235i	$-0.833614\pi$
$509$	1469.47	−	4522.55i	0.127963	−	0.393828i	0.994429	+	0.105407i	$0.0336145\pi$
$510$	−1501.25	−	4620.36i	−0.130346	−	0.401163i
$511$	−2472.78	+	1796.58i	−0.214069	+	0.155531i
$512$	−414.217	+	300.946i	−0.0357538	+	0.0259767i
$513$	−756.448	−	2328.11i	−0.0651033	−	0.200367i
$514$	−3730.64	+	11481.7i	−0.320139	+	0.985288i
$515$	−3681.24	−	2674.58i	−0.314981	−	0.228847i
$516$	4587.05			0.391344
$517$		0			0
$518$	−6449.03			−0.547016
$519$	310.870	+	225.860i	0.0262923	+	0.0191025i
$520$	−1027.14	+	3161.22i	−0.0866215	+	0.266593i
$521$	−3625.12	−	11157.0i	−0.304836	−	0.938189i	−0.979738	−	0.200282i	$-0.935814\pi$
$521$	−3625.12	−	11157.0i	−0.304836	−	0.938189i	0.674902	−	0.737907i	$-0.264186\pi$
$522$	−1004.07	+	729.503i	−0.0841899	+	0.0611676i
$523$	−278.172	+	202.104i	−0.0232574	+	0.0168975i	−0.599353	−	0.800485i	$-0.704575\pi$
$523$	−278.172	+	202.104i	−0.0232574	+	0.0168975i	0.576096	+	0.817382i	$0.304575\pi$
$524$	3048.34	+	9381.84i	0.254136	+	0.782151i
$525$	−4965.10	+	15281.0i	−0.412752	+	1.27032i
$526$	−1146.28	−	832.824i	−0.0950196	−	0.0690358i
$527$	−12646.4			−1.04533
$528$		0			0
$529$	8134.66			0.668584
$530$	2055.04	+	1493.08i	0.168425	+	0.122368i
$531$	2840.94	−	8743.53i	0.232178	−	0.714570i
$532$	−2608.16	−	8027.10i	−0.212553	−	0.654171i
$533$	−5148.40	+	3740.53i	−0.418390	+	0.303978i
$534$	3837.92	−	2788.41i	0.311017	−	0.225967i
$535$	107.678	+	331.400i	0.00870157	+	0.0267807i
$536$	2042.57	−	6286.38i	0.164600	−	0.506586i
$537$	−127.897	−	92.9225i	−0.0102778	−	0.00746723i
$538$	−9619.41			−0.770859
$539$		0			0
$540$	555.878			0.0442985
$541$	−13950.5	−	10135.6i	−1.10865	−	0.805480i	−0.126198	−	0.992005i	$-0.540278\pi$
$541$	−13950.5	−	10135.6i	−1.10865	−	0.805480i	−0.982450	+	0.186525i	$0.940278\pi$
$542$	3239.04	−	9968.75i	0.256695	−	0.790027i
$543$	−412.381	−	1269.18i	−0.0325911	−	0.100305i
$544$	1534.89	−	1115.16i	0.120970	−	0.0878900i
$545$	6821.19	−	4955.88i	0.536124	−	0.389517i
$546$	−7967.49	−	24521.4i	−0.624500	−	1.92201i
$547$	2361.88	−	7269.13i	0.184619	−	0.568200i	−0.815322	−	0.579008i	$-0.803440\pi$
$547$	2361.88	−	7269.13i	0.184619	−	0.568200i	0.999942	+	0.0108075i	$0.00344019\pi$
$548$	3149.62	+	2288.33i	0.245520	+	0.178381i
$549$	4536.89			0.352696
$550$		0			0
$551$	−1945.10			−0.150388
$552$	−6986.17	−	5075.75i	−0.538679	−	0.391373i
$553$	2083.92	−	6413.64i	0.160248	−	0.493193i
$554$	3300.15	+	10156.8i	0.253086	+	0.778919i
$555$	4825.28	−	3505.77i	0.369048	−	0.268129i
$556$	−4087.28	+	2969.58i	−0.311761	+	0.226508i
$557$	−8067.26	−	24828.5i	−0.613681	−	1.88872i	−0.419514	−	0.907749i	$-0.637799\pi$
$557$	−8067.26	−	24828.5i	−0.613681	−	1.88872i	−0.194168	−	0.980968i	$-0.562201\pi$
$558$	4006.55	−	12330.9i	0.303962	−	0.935498i
$559$	9408.47	+	6835.66i	0.711871	+	0.517205i
$560$	1916.62			0.144628
$561$		0			0
$562$	6559.94			0.492374
$563$	−14622.1	−	10623.6i	−1.09458	−	0.795258i	−0.114412	−	0.993433i	$-0.536498\pi$
$563$	−14622.1	−	10623.6i	−1.09458	−	0.795258i	−0.980167	+	0.198175i	$0.936498\pi$
$564$	846.184	−	2604.29i	0.0631751	−	0.194433i
$565$	−3742.04	−	11516.8i	−0.278635	−	0.857551i
$566$	−7921.07	+	5754.99i	−0.588246	+	0.427386i
$567$	11216.1	−	8148.96i	0.830743	−	0.603570i
$568$	−2222.36	−	6839.73i	−0.164170	−	0.505262i
$569$	−2411.93	+	7423.15i	−0.177703	+	0.546915i	−0.999747	−	0.0225104i	$-0.992834\pi$
$569$	−2411.93	+	7423.15i	−0.177703	+	0.546915i	0.822043	+	0.569425i	$0.192834\pi$
$570$	6315.10	+	4588.19i	0.464053	+	0.337154i
$571$	13039.6			0.955672			0.477836	−	0.878449i	$-0.341421\pi$
$571$	13039.6			0.955672			0.477836	+	0.878449i	$0.341421\pi$
$572$		0			0
$573$	−8781.96			−0.640264
$574$	2968.65	+	2156.85i	0.215869	+	0.156838i
$575$	−4215.98	+	12975.4i	−0.305771	+	0.941066i
$576$	601.064	+	1849.89i	0.0434798	+	0.133817i
$577$	7741.83	−	5624.77i	0.558573	−	0.405827i	−0.272364	−	0.962194i	$-0.587805\pi$
$577$	7741.83	−	5624.77i	0.558573	−	0.405827i	0.830936	+	0.556368i	$0.187805\pi$
$578$	2261.84	−	1643.32i	0.162768	−	0.118258i
$579$	3008.08	+	9257.93i	0.215910	+	0.664502i
$580$	136.492	−	420.079i	0.00977158	−	0.0300738i
$581$	−13695.8	−	9950.60i	−0.977966	−	0.710534i
$582$	−8825.83			−0.628595
$583$		0			0
$584$	1103.95			0.0782220
$585$	10215.8	+	7422.25i	0.722006	+	0.524568i
$586$	−4144.41	+	12755.2i	−0.292157	+	0.899167i
$587$	3005.81	+	9250.93i	0.211351	+	0.650471i	0.999393	+	0.0348493i	$0.0110951\pi$
$587$	3005.81	+	9250.93i	0.211351	+	0.650471i	−0.788042	+	0.615622i	$0.788905\pi$
$588$	−3618.86	+	2629.26i	−0.253809	+	0.184403i
$589$	16439.1	−	11943.7i	1.15002	−	0.835540i
$590$	1011.06	+	3111.74i	0.0705506	+	0.217132i
$591$	6285.81	−	19345.7i	0.437502	−	1.34649i
$592$	1884.40	+	1369.09i	0.130825	+	0.0950496i
$593$	−6926.77			−0.479677			−0.239838	−	0.970813i	$-0.577094\pi$
$593$	−6926.77			−0.479677			−0.239838	+	0.970813i	$0.577094\pi$
$594$		0			0
$595$	−7102.06			−0.489338
$596$	−1583.54	−	1150.51i	−0.108833	−	0.0790715i
$597$	−3121.86	+	9608.10i	−0.214019	+	0.658682i
$598$	−6765.37	−	20821.7i	−0.462636	−	1.42385i
$599$	17786.0	−	12922.3i	1.21321	−	0.881451i	0.217695	−	0.976017i	$-0.430146\pi$
$599$	17786.0	−	12922.3i	1.21321	−	0.881451i	0.995519	+	0.0945657i	$0.0301462\pi$
$600$	4694.86	−	3411.02i	0.319445	−	0.232090i
$601$	2275.37	+	7002.88i	0.154433	+	0.475297i	0.998103	−	0.0615656i	$-0.0196093\pi$
$601$	2275.37	+	7002.88i	0.154433	+	0.475297i	−0.843670	+	0.536863i	$0.819609\pi$
$602$	2072.19	−	6377.56i	0.140293	−	0.431777i
$603$	−20315.2	−	14759.8i	−1.37197	−	0.996794i
$604$	−6831.10			−0.460188
$605$		0			0
$606$	2144.76			0.143771
$607$	8226.41	+	5976.84i	0.550082	+	0.399658i	0.827816	−	0.561000i	$-0.189583\pi$
$607$	8226.41	+	5976.84i	0.550082	+	0.399658i	−0.277734	+	0.960658i	$0.589583\pi$
$608$	−942.008	+	2899.20i	−0.0628346	+	0.193385i
$609$	1058.76	+	3258.53i	0.0704485	+	0.216818i
$610$	−1306.27	+	949.060i	−0.0867037	+	0.0629939i
$611$	5616.53	−	4080.65i	0.371883	−	0.270189i
$612$	−2227.26	−	6854.79i	−0.147110	−	0.452759i
$613$	−7751.53	+	23856.8i	−0.510737	+	1.57189i	0.280171	+	0.959950i	$0.409609\pi$
$613$	−7751.53	+	23856.8i	−0.510737	+	1.57189i	−0.790908	+	0.611936i	$0.790391\pi$
$614$	15383.1	+	11176.5i	1.01110	+	0.734604i
$615$	−3393.68			−0.222515
$616$		0			0
$617$	−26335.5			−1.71836			−0.859178	−	0.511677i	$-0.829024\pi$
$617$	−26335.5			−1.71836			−0.859178	+	0.511677i	$0.829024\pi$
$618$	−10313.5	−	7493.18i	−0.671309	−	0.487735i
$619$	−7615.16	+	23437.0i	−0.494473	+	1.52183i	0.323303	+	0.946296i	$0.395207\pi$
$619$	−7615.16	+	23437.0i	−0.494473	+	1.52183i	−0.817776	+	0.575537i	$0.804793\pi$
$620$	1425.89	+	4388.44i	0.0923632	+	0.284265i
$621$	−2962.09	+	2152.08i	−0.191408	+	0.139066i
$622$	−9332.94	+	6780.78i	−0.601635	+	0.437113i
$623$	−2143.06	−	6595.67i	−0.137817	−	0.424157i
$624$	−2877.67	+	8856.56i	−0.184614	+	0.568183i
$625$	−4459.78	−	3240.22i	−0.285426	−	0.207374i
$626$	11955.5			0.763319
$627$		0			0
$628$	10246.9			0.651108
$629$	−6982.67	−	5073.20i	−0.442635	−	0.321593i
$630$	2250.02	−	6924.84i	0.142290	−	0.437924i
$631$	2303.82	+	7090.43i	0.145346	+	0.447331i	0.997055	−	0.0766847i	$-0.0244335\pi$
$631$	2303.82	+	7090.43i	0.145346	+	0.447331i	−0.851709	+	0.524015i	$0.824433\pi$
$632$	−1970.50	+	1431.65i	−0.124022	+	0.0901076i
$633$	−9978.89	+	7250.09i	−0.626580	+	0.455237i
$634$	3233.51	+	9951.73i	0.202554	+	0.623397i
$635$	−1827.38	+	5624.09i	−0.114200	+	0.351473i
$636$	5757.47	+	4183.05i	0.358960	+	0.260800i
$637$	−11340.8			−0.705397
$638$		0			0
$639$	−27321.3			−1.69141
$640$	−560.031	−	406.887i	−0.0345894	−	0.0251306i
$641$	−858.656	+	2642.67i	−0.0529093	+	0.162838i	−0.974020	−	0.226464i	$-0.927284\pi$
$641$	−858.656	+	2642.67i	−0.0529093	+	0.162838i	0.921110	+	0.389302i	$0.127284\pi$
$642$	301.675	+	928.460i	0.0185454	+	0.0570769i
$643$	−6114.32	+	4442.31i	−0.375000	+	0.272454i	−0.759281	−	0.650763i	$-0.774449\pi$
$643$	−6114.32	+	4442.31i	−0.375000	+	0.272454i	0.384281	+	0.923216i	$0.374449\pi$
$644$	−10213.0	+	7420.18i	−0.624921	+	0.454031i
$645$	1916.46	+	5898.27i	0.116993	+	0.360068i
$646$	3490.63	−	10743.1i	0.212596	−	0.654303i
$647$	22191.9	+	16123.4i	1.34846	+	0.979713i	0.999087	+	0.0427297i	$0.0136054\pi$
$647$	22191.9	+	16123.4i	1.34846	+	0.979713i	0.349373	+	0.936984i	$0.386395\pi$
$648$	−5007.30			−0.303557
$649$		0			0
$650$	14712.7			0.887817
$651$	−28956.9	−	21038.4i	−1.74334	−	1.26661i
$652$	2244.81	−	6908.81i	0.134837	−	0.414984i
$653$	87.9858	+	270.792i	0.00527282	+	0.0162281i	0.953658	−	0.300892i	$-0.0972843\pi$
$653$	87.9858	+	270.792i	0.00527282	+	0.0162281i	−0.948385	+	0.317120i	$0.897284\pi$
$654$	19110.4	−	13884.5i	1.14263	−	0.830166i
$655$	−10790.1	+	7839.44i	−0.643668	+	0.467652i
$656$	−409.547	−	1260.46i	−0.0243752	−	0.0750191i
$657$	1295.98	−	3988.62i	0.0769575	−	0.236851i
$658$	−3238.58	−	2352.97i	−0.191874	−	0.139405i
$659$	−20747.0			−1.22639			−0.613193	−	0.789933i	$-0.710115\pi$
$659$	−20747.0			−1.22639			−0.613193	+	0.789933i	$0.710115\pi$
$660$		0			0
$661$	−18908.8			−1.11266			−0.556328	−	0.830963i	$-0.687790\pi$
$661$	−18908.8			−1.11266			−0.556328	+	0.830963i	$0.687790\pi$
$662$	6413.43	+	4659.63i	0.376534	+	0.273568i
$663$	10663.3	−	32818.2i	0.624626	−	1.92240i
$664$	1889.44	+	5815.09i	0.110428	+	0.339863i
$665$	9231.98	−	6707.43i	0.538347	−	0.391132i
$666$	7158.81	−	5201.18i	0.416514	−	0.302615i
$667$	899.017	+	2766.89i	0.0521890	+	0.160621i
$668$	−468.377	+	1441.52i	−0.0271288	+	0.0834939i
$669$	16108.0	+	11703.1i	0.930897	+	0.676336i
$670$	8936.74			0.515308
$671$		0			0
$672$	5369.65			0.308242
$673$	24162.0	+	17554.7i	1.38392	+	1.00548i	0.996502	+	0.0835714i	$0.0266327\pi$
$673$	24162.0	+	17554.7i	1.38392	+	1.00548i	0.387417	+	0.921905i	$0.373367\pi$
$674$	−3156.05	+	9713.33i	−0.180366	+	0.555109i
$675$	−760.339	−	2340.08i	−0.0433562	−	0.133437i
$676$	−11990.9	+	8711.86i	−0.682229	+	0.495668i
$677$	−13980.4	+	10157.4i	−0.793665	+	0.576631i	−0.909049	−	0.416690i	$-0.863190\pi$
$677$	−13980.4	+	10157.4i	−0.793665	+	0.576631i	0.115384	+	0.993321i	$0.463190\pi$
$678$	−10483.8	−	32265.9i	−0.593847	−	1.82767i
$679$	−3987.06	+	12270.9i	−0.225345	+	0.693541i
$680$	2075.21	+	1507.73i	0.117030	+	0.0850275i
$681$	−12898.1			−0.725782
$682$		0			0
$683$	25104.0			1.40641			0.703204	−	0.710988i	$-0.251752\pi$
$683$	25104.0			1.40641			0.703204	+	0.710988i	$0.251752\pi$
$684$	9369.11	+	6807.06i	0.523738	+	0.380518i
$685$	−1626.55	+	5006.01i	−0.0907260	+	0.279226i
$686$	−2674.70	−	8231.88i	−0.148864	−	0.458155i
$687$	−33071.3	+	24027.7i	−1.83660	+	1.33437i
$688$	−1959.41	+	1423.60i	−0.108578	+	0.0788867i
$689$	5575.51	+	17159.6i	0.308287	+	0.948810i
$690$	3607.85	−	11103.8i	0.199056	−	0.612631i
$691$	21167.0	+	15378.7i	1.16531	+	0.846647i	0.990440	−	0.137944i	$-0.0440495\pi$
$691$	21167.0	+	15378.7i	1.16531	+	0.846647i	0.174870	+	0.984592i	$0.444050\pi$
$692$	−202.888			−0.0111454
$693$		0			0
$694$	−15091.5			−0.825455
$695$	−5526.11	−	4014.95i	−0.301608	−	0.219131i
$696$	382.400	−	1176.91i	0.0208259	−	0.0640955i
$697$	1517.58	+	4670.64i	0.0824714	+	0.253821i
$698$	−5269.47	+	3828.50i	−0.285748	+	0.207608i
$699$	−37105.5	+	26958.7i	−2.00781	+	1.45876i
$700$	−2621.58	−	8068.38i	−0.141552	−	0.435652i
$701$	469.534	−	1445.08i	0.0252982	−	0.0778600i	−0.937610	−	0.347688i	$-0.886967\pi$
$701$	469.534	−	1445.08i	0.0252982	−	0.0778600i	0.962909	+	0.269828i	$0.0869668\pi$
$702$	3194.30	+	2320.80i	0.171739	+	0.124776i
$703$	13868.1			0.744018
$704$		0			0
$705$	3702.26			0.197781
$706$	10528.3	+	7649.24i	0.561242	+	0.407766i
$707$	968.893	−	2981.95i	0.0515403	−	0.158625i
$708$	2832.63	+	8717.93i	0.150363	+	0.462768i
$709$	17583.1	−	12774.9i	0.931378	−	0.676686i	−0.0149520	−	0.999888i	$-0.504760\pi$
$709$	17583.1	−	12774.9i	0.931378	−	0.676686i	0.946330	+	0.323203i	$0.104760\pi$
$710$	7866.39	−	5715.26i	0.415803	−	0.302099i
$711$	2859.36	+	8800.21i	0.150822	+	0.464182i
$712$	−774.025	+	2382.20i	−0.0407413	+	0.125389i
$713$	−24588.0	−	17864.2i	−1.29148	−	0.938317i
$714$	−19897.3			−1.04291
$715$		0			0
$716$	83.4712			0.00435679
$717$	19223.9	+	13967.0i	1.00130	+	0.727486i
$718$	−2513.06	+	7734.39i	−0.130622	+	0.402012i
$719$	−4348.44	−	13383.1i	−0.225549	−	0.694167i	−0.998235	−	0.0593798i	$-0.981088\pi$
$719$	−4348.44	−	13383.1i	−0.225549	−	0.694167i	0.772687	−	0.634787i	$-0.218912\pi$
$720$	−2127.56	+	1545.76i	−0.110124	+	0.0800098i
$721$	−15077.2	+	10954.2i	−0.778784	+	0.565820i
$722$	1369.54	+	4215.00i	0.0705939	+	0.217266i
$723$	15215.0	−	46826.9i	0.782644	−	2.40873i
$724$	570.044	+	414.161i	0.0292618	+	0.0212599i
$725$	−1955.10			−0.100153
$726$		0			0
$727$	10409.2			0.531027			0.265513	−	0.964107i	$-0.414459\pi$
$727$	10409.2			0.531027			0.265513	+	0.964107i	$0.414459\pi$
$728$	11013.7	+	8001.89i	0.560705	+	0.407376i
$729$	−7502.56	+	23090.5i	−0.381170	+	1.17312i
$730$	461.228	+	1419.51i	0.0233847	+	0.0719706i
$731$	7260.64	−	5275.16i	0.367366	−	0.266907i
$732$	−3659.68	+	2658.91i	−0.184789	+	0.134257i
$733$	5993.34	+	18445.6i	0.302004	+	0.929474i	0.980778	+	0.195127i	$0.0625117\pi$
$733$	5993.34	+	18445.6i	0.302004	+	0.929474i	−0.678774	+	0.734348i	$0.737488\pi$
$734$	−860.473	+	2648.26i	−0.0432706	+	0.133173i
$735$	−4892.79	−	3554.82i	−0.245542	−	0.178397i
$736$	4559.48			0.228349
$737$		0			0
$738$	−5034.89			−0.251134
$739$	−5397.95	−	3921.84i	−0.268697	−	0.195220i	0.445275	−	0.895394i	$-0.353106\pi$
$739$	−5397.95	−	3921.84i	−0.268697	−	0.195220i	−0.713972	+	0.700174i	$0.753106\pi$
$740$	−973.154	+	2995.06i	−0.0483430	+	0.148785i
$741$	17133.4	+	52731.2i	0.849408	+	2.61421i
$742$	8416.78	−	6115.15i	0.416428	−	0.302553i
$743$	5311.34	−	3858.92i	0.262253	−	0.190538i	−0.448886	−	0.893589i	$-0.648179\pi$
$743$	5311.34	−	3858.92i	0.262253	−	0.190538i	0.711140	+	0.703050i	$0.248179\pi$
$744$	3994.82	+	12294.8i	0.196851	+	0.605845i
$745$	817.783	−	2516.88i	0.0402164	−	0.123773i
$746$	15274.7	+	11097.7i	0.749662	+	0.544661i
$747$	23228.4			1.13773
$748$		0			0
$749$	1427.16			0.0696223
$750$	14634.0	+	10632.2i	0.712478	+	0.517646i
$751$	5852.37	−	18011.8i	0.284362	−	0.875177i	−0.702227	−	0.711953i	$-0.747811\pi$
$751$	5852.37	−	18011.8i	0.284362	−	0.875177i	0.986589	−	0.163224i	$-0.0521893\pi$
$752$	446.786	+	1375.07i	0.0216657	+	0.0666801i
$753$	−34112.2	+	24784.0i	−1.65089	+	1.19944i
$754$	2538.17	−	1844.09i	0.122592	−	0.0890686i
$755$	−2854.02	−	8783.79i	−0.137574	−	0.423410i
$756$	703.538	−	2165.27i	0.0338458	−	0.104167i
$757$	8865.50	+	6441.16i	0.425657	+	0.309258i	0.779910	−	0.625892i	$-0.215265\pi$
$757$	8865.50	+	6441.16i	0.425657	+	0.309258i	−0.354253	+	0.935150i	$0.615265\pi$
$758$	2580.70			0.123661
$759$		0			0
$760$	−4121.52			−0.196715
$761$	−28673.3	−	20832.4i	−1.36584	−	0.992344i	−0.998049	−	0.0624371i	$-0.980113\pi$
$761$	−28673.3	−	20832.4i	−1.36584	−	0.992344i	−0.367795	−	0.929907i	$-0.619887\pi$
$762$	−5119.63	+	15756.6i	−0.243392	+	0.749084i
$763$	−10671.1	−	32842.3i	−0.506318	−	1.55829i
$764$	3751.31	−	2725.49i	0.177641	−	0.129064i
$765$	7883.70	−	5727.84i	0.372596	−	0.270707i
$766$	−3493.68	−	10752.4i	−0.164793	−	0.507182i
$767$	−7181.54	+	22102.5i	−0.338084	+	1.04052i
$768$	−1569.00	−	1139.95i	−0.0737193	−	0.0535602i
$769$	−4444.21			−0.208404			−0.104202	−	0.994556i	$-0.533229\pi$
$769$	−4444.21			−0.208404			−0.104202	+	0.994556i	$0.533229\pi$
$770$		0			0
$771$	−45729.5			−2.13607
$772$	−4158.15	−	3021.07i	−0.193854	−	0.140843i
$773$	3139.67	−	9662.90i	0.146088	−	0.449612i	−0.851061	−	0.525066i	$-0.824041\pi$
$773$	3139.67	−	9662.90i	0.146088	−	0.449612i	0.997149	+	0.0754539i	$0.0240406\pi$
$774$	2843.28	+	8750.70i	0.132041	+	0.406379i
$775$	16523.7	−	12005.2i	0.765869	−	0.556436i
$776$	3770.05	−	2739.11i	0.174403	−	0.126712i
$777$	−7548.70	−	23232.5i	−0.348531	−	1.07267i
$778$	−7934.32	+	24419.3i	−0.365629	+	1.12529i
$779$	−6383.83	−	4638.12i	−0.293613	−	0.213322i
$780$	−12590.5			−0.577965
$781$		0			0
$782$	−16895.3			−0.772600
$783$	−424.475	−	308.399i	−0.0193736	−	0.0140757i
$784$	729.846	−	2246.24i	0.0332474	−	0.102325i
$785$	4281.14	+	13176.0i	0.194650	+	0.599072i
$786$	−30229.8	+	21963.2i	−1.37183	+	0.996694i
$787$	−14780.8	+	10738.9i	−0.669477	+	0.486404i	−0.869850	−	0.493316i	$-0.835785\pi$
$787$	−14780.8	+	10738.9i	−0.669477	+	0.486404i	0.200373	+	0.979720i	$0.435785\pi$
$788$	3318.91	+	10214.6i	0.150040	+	0.461775i
$789$	1658.49	−	5104.30i	0.0748336	−	0.230314i
$790$	−2664.16	−	1935.63i	−0.119983	−	0.0871728i
$791$	−49596.6			−2.22939
$792$		0			0
$793$	−11468.7			−0.513575
$794$	−12444.7	−	9041.62i	−0.556230	−	0.404125i
$795$	−2973.32	+	9150.92i	−0.132645	+	0.408239i
$796$	−1648.35	−	5073.08i	−0.0733970	−	0.225893i
$797$	−14549.3	+	10570.7i	−0.646630	+	0.469804i	−0.862122	−	0.506701i	$-0.830865\pi$
$797$	−14549.3	+	10570.7i	−0.646630	+	0.469804i	0.215491	+	0.976506i	$0.430865\pi$
$798$	25864.6	−	18791.7i	1.14736	−	0.833609i
$799$	−1655.57	−	5095.33i	−0.0733041	−	0.225607i
$800$	−946.852	+	2914.11i	−0.0418454	+	0.128787i
$801$	7698.37	+	5593.19i	0.339586	+	0.246724i
$802$	15572.3			0.685634
$803$		0			0
$804$	25037.4			1.09826
$805$	−13808.2	−	10032.3i	−0.604567	−	0.439244i
$806$	−10128.0	+	31170.9i	−0.442611	+	1.36222i
$807$	−11259.7	−	34653.8i	−0.491152	−	1.51161i
$808$	−916.159	+	665.629i	−0.0398891	+	0.0289811i
$809$	4161.78	−	3023.71i	0.180866	−	0.131407i	−0.493669	−	0.869650i	$-0.664344\pi$
$809$	4161.78	−	3023.71i	0.180866	−	0.131407i	0.674534	+	0.738243i	$0.264344\pi$
$810$	−2092.04	−	6438.64i	−0.0907492	−	0.279297i
$811$	2551.24	−	7851.91i	0.110464	−	0.339973i	−0.880510	−	0.474027i	$-0.842800\pi$
$811$	2551.24	−	7851.91i	0.110464	−	0.339973i	0.990974	+	0.134055i	$0.0427997\pi$
$812$	−1463.55	−	1063.33i	−0.0632519	−	0.0459552i
$813$	39703.6			1.71275
$814$		0			0
$815$	9821.58			0.422129
$816$	5813.96	+	4224.09i	0.249423	+	0.181217i
$817$	−4456.08	+	13714.4i	−0.190818	+	0.587278i
$818$	5475.71	+	16852.5i	0.234051	+	0.720335i
$819$	41840.8	−	30399.1i	1.78515	−	1.29699i
$820$	1449.65	−	1053.23i	0.0617366	−	0.0448543i
$821$	−76.4045	−	235.149i	−0.00324791	−	0.00999604i	0.949419	−	0.314011i	$-0.101673\pi$
$821$	−76.4045	−	235.149i	−0.00324791	−	0.00999604i	−0.952667	+	0.304015i	$0.901673\pi$
$822$	−4556.99	+	14025.0i	−0.193362	+	0.595106i
$823$	−9542.21	−	6932.82i	−0.404156	−	0.293637i	0.367076	−	0.930191i	$-0.380359\pi$
$823$	−9542.21	−	6932.82i	−0.404156	−	0.293637i	−0.771232	+	0.636555i	$0.780359\pi$
$824$	6731.04			0.284571
$825$		0			0
$826$	13400.5			0.564484
$827$	−2242.32	−	1629.14i	−0.0942844	−	0.0685016i	0.539644	−	0.841893i	$-0.318559\pi$
$827$	−2242.32	−	1629.14i	−0.0942844	−	0.0685016i	−0.633929	+	0.773392i	$0.718559\pi$
$828$	5352.62	−	16473.7i	0.224658	−	0.691425i
$829$	−8435.56	−	25962.0i	−0.353413	−	1.08769i	−0.956924	−	0.290338i	$-0.906232\pi$
$829$	−8435.56	−	25962.0i	−0.353413	−	1.08769i	0.603512	−	0.797354i	$-0.293768\pi$
$830$	−6687.94	+	4859.08i	−0.279689	+	0.203206i
$831$	−32726.8	+	23777.4i	−1.36616	+	0.992575i
$832$	−1519.41	−	4676.27i	−0.0633127	−	0.194856i
$833$	−2704.46	+	8323.47i	−0.112490	+	0.346208i
$834$	−15482.1	−	11248.4i	−0.642808	−	0.467027i
$835$	−2049.26			−0.0849314
$836$		0			0
$837$	5481.18			0.226353
$838$	−15321.3	−	11131.6i	−0.631582	−	0.458871i
$839$	2705.36	−	8326.25i	0.111322	−	0.342615i	−0.879840	−	0.475270i	$-0.842350\pi$
$839$	2705.36	−	8326.25i	0.111322	−	0.342615i	0.991162	+	0.132655i	$0.0423503\pi$
$840$	2243.43	+	6904.57i	0.0921497	+	0.283608i
$841$	19393.8	−	14090.4i	0.795188	−	0.577738i
$842$	−8378.09	+	6087.04i	−0.342907	+	0.249137i
$843$	7678.52	+	23632.1i	0.313716	+	0.965518i
$844$	2012.53	−	6193.92i	0.0820782	−	0.252611i
$845$	−16211.9	−	11778.7i	−0.660009	−	0.479525i
$846$	5492.70			0.223218
$847$		0			0
$848$	−3757.58			−0.152165
$849$	−30004.0	−	21799.2i	−1.21288	−	0.881209i
$850$	3508.58	−	10798.3i	0.141580	−	0.435740i
$851$	−6409.77	−	19727.2i	−0.258195	−	0.794643i
$852$	22038.7	−	16012.1i	0.886190	−	0.643854i
$853$	33318.8	−	24207.5i	1.33741	−	0.971687i	0.337878	−	0.941190i	$-0.390291\pi$
$853$	33318.8	−	24207.5i	1.33741	−	0.971687i	0.999535	−	0.0304969i	$-0.00970897\pi$
$854$	2043.54	+	6289.36i	0.0818834	+	0.252011i
$855$	−4838.47	+	14891.3i	−0.193535	+	0.595638i
$856$	−417.012	−	302.977i	−0.0166509	−	0.0120976i
$857$	18020.0			0.718265			0.359132	−	0.933287i	$-0.383073\pi$
$857$	18020.0			0.718265			0.359132	+	0.933287i	$0.383073\pi$
$858$		0			0
$859$	6159.11			0.244640			0.122320	−	0.992491i	$-0.460967\pi$
$859$	6159.11			0.244640			0.122320	+	0.992491i	$0.460967\pi$
$860$	−2649.17	−	1924.74i	−0.105042	−	0.0763174i
$861$	−4295.16	+	13219.1i	−0.170010	+	0.523237i
$862$	−6466.83	−	19902.9i	−0.255523	−	0.786420i
$863$	−23407.0	+	17006.2i	−0.923270	+	0.670795i	−0.944336	−	0.328983i	$-0.893294\pi$
$863$	−23407.0	+	17006.2i	−0.923270	+	0.670795i	0.0210656	+	0.999778i	$0.493294\pi$
$864$	−665.246	+	483.330i	−0.0261946	+	0.0190315i
$865$	−84.7663	−	260.884i	−0.00333195	−	0.0102547i
$866$	9788.56	−	30126.1i	0.384098	−	1.18213i
$867$	8567.56	+	6224.70i	0.335605	+	0.243831i
$868$	18898.6			0.739009
$869$		0			0
$870$	1673.09			0.0651990
$871$	51354.1	+	37311.0i	1.99778	+	1.45147i
$872$	−3854.16	+	11861.9i	−0.149677	+	0.460658i
$873$	−5470.68	−	16837.0i	−0.212090	−	0.652745i
$874$	21962.2	−	15956.5i	0.849980	−	0.617546i
$875$	21393.3	−	15543.2i	0.826544	−	0.600519i
$876$	1292.19	+	3976.95i	0.0498391	+	0.153389i
$877$	13952.9	−	42942.7i	0.537237	−	1.65345i	−0.201528	−	0.979483i	$-0.564591\pi$
$877$	13952.9	−	42942.7i	0.537237	−	1.65345i	0.738765	−	0.673963i	$-0.235409\pi$
$878$	−7806.53	−	5671.78i	−0.300066	−	0.218010i
$879$	−50801.4			−1.94936
$880$		0			0
$881$	22263.5			0.851391			0.425696	−	0.904866i	$-0.360029\pi$
$881$	22263.5			0.851391			0.425696	+	0.904866i	$0.360029\pi$
$882$	−7258.97	−	5273.95i	−0.277123	−	0.201342i
$883$	11809.2	−	36345.1i	0.450071	−	1.38518i	−0.426754	−	0.904368i	$-0.640343\pi$
$883$	11809.2	−	36345.1i	0.450071	−	1.38518i	0.876825	−	0.480809i	$-0.159657\pi$
$884$	5630.22	+	17328.0i	0.214213	+	0.659281i
$885$	−10026.5	+	7284.68i	−0.380833	+	0.276691i
$886$	−5798.04	+	4212.52i	−0.219852	+	0.159732i
$887$	−14882.4	−	45803.4i	−0.563364	−	1.73385i	−0.672764	−	0.739857i	$-0.734893\pi$
$887$	−14882.4	−	45803.4i	−0.563364	−	1.73385i	0.109401	−	0.993998i	$-0.465107\pi$
$888$	−2726.42	+	8391.05i	−0.103032	+	0.317100i
$889$	19594.3	+	14236.1i	0.739224	+	0.537078i
$890$	−3386.55			−0.127548
$891$		0			0
$892$	−10512.8			−0.394612
$893$	6964.29	+	5059.85i	0.260975	+	0.189610i
$894$	2291.12	−	7051.36i	0.0857122	−	0.263795i
$895$	34.8742	+	107.332i	0.00130247	+	0.00400860i
$896$	−2293.71	+	1666.48i	−0.0855216	+	0.0621351i
$897$	67090.7	−	48744.3i	2.49732	−	1.81441i
$898$	−4818.18	−	14828.8i	−0.179048	−	0.551052i
$899$	1345.86	−	4142.14i	0.0499300	−	0.153669i
$900$	9417.29	+	6842.06i	0.348789	+	0.253410i
$901$	13923.8			0.514838
$902$		0			0
$903$	25400.6			0.936078
$904$	14492.0	+	10529.1i	0.533183	+	0.387380i
$905$	−294.386	+	906.028i	−0.0108130	+	0.0332789i
$906$	−7995.92	−	24608.9i	−0.293208	−	0.902402i
$907$	−6884.64	+	5001.98i	−0.252040	+	0.183118i	−0.706631	−	0.707583i	$-0.749786\pi$
$907$	−6884.64	+	5001.98i	−0.252040	+	0.183118i	0.454590	+	0.890701i	$0.349786\pi$
$908$	5509.58	−	4002.95i	0.201368	−	0.146302i
$909$	1329.43	+	4091.55i	0.0485086	+	0.149294i
$910$	−5687.75	+	17505.1i	−0.207195	+	0.637680i
$911$	−9128.51	−	6632.25i	−0.331988	−	0.241203i	0.409286	−	0.912406i	$-0.365778\pi$
$911$	−9128.51	−	6632.25i	−0.331988	−	0.241203i	−0.741274	+	0.671203i	$0.765778\pi$
$912$	−11547.0			−0.419252
$913$		0			0
$914$	−6696.04			−0.242325
$915$	−4947.98	−	3594.92i	−0.178771	−	0.129884i
$916$	6669.76	−	20527.4i	0.240584	−	0.740442i
$917$	16880.1	+	51951.5i	0.607883	+	1.87087i
$918$	2465.08	−	1790.99i	0.0886273	−	0.0643915i
$919$	21485.0	−	15609.8i	0.771191	−	0.560303i	−0.131131	−	0.991365i	$-0.541861\pi$
$919$	21485.0	−	15609.8i	0.771191	−	0.560303i	0.902322	+	0.431062i	$0.141861\pi$
$920$	1904.95	+	5862.82i	0.0682655	+	0.210100i
$921$	−22256.9	+	68499.7i	−0.796298	+	2.45075i
$922$	11604.5	+	8431.14i	0.414504	+	0.301155i
$923$	69064.7			2.46294
$924$		0			0
$925$	13939.4			0.495486
$926$	−6528.35	−	4743.13i	−0.231679	−	0.168325i
$927$	7901.93	−	24319.6i	0.279971	−	0.861663i
$928$	201.907	+	621.407i	0.00714217	+	0.0219813i
$929$	38762.5	−	28162.6i	1.36895	−	0.994602i	0.371134	−	0.928579i	$-0.378969\pi$
$929$	38762.5	−	28162.6i	1.36895	−	0.994602i	0.997818	−	0.0660230i	$-0.0210311\pi$
$930$	−14140.3	+	10273.5i	−0.498578	+	0.362238i
$931$	−4345.44	−	13373.9i	−0.152971	−	0.470796i
$932$	7483.38	−	23031.5i	0.263011	−	0.809465i
$933$	−35352.0	−	25684.7i	−1.24049	−	0.901265i
$934$	−23643.7			−0.828314
$935$		0			0
$936$	−18679.4			−0.652301
$937$	4626.72	+	3361.51i	0.161311	+	0.117199i	0.665512	−	0.746387i	$-0.268213\pi$
$937$	4626.72	+	3361.51i	0.161311	+	0.117199i	−0.504201	+	0.863586i	$0.668213\pi$
$938$	11310.6	−	34810.5i	0.393716	−	1.21173i
$939$	13994.1	+	43069.5i	0.486348	+	1.49683i
$940$	−1581.46	+	1149.00i	−0.0548741	+	0.0398684i
$941$	−8984.62	+	6527.71i	−0.311254	+	0.226140i	−0.732435	−	0.680837i	$-0.761616\pi$
$941$	−8984.62	+	6527.71i	−0.311254	+	0.226140i	0.421180	+	0.906977i	$0.361616\pi$
$942$	11994.2	+	36914.3i	0.414853	+	1.27679i
$943$	−3647.11	+	11224.7i	−0.125945	+	0.387620i
$944$	−3915.61	−	2844.86i	−0.135002	−	0.0980850i
$945$	3078.15			0.105960
$946$		0			0
$947$	39759.1			1.36430			0.682152	−	0.731210i	$-0.261044\pi$
$947$	39759.1			1.36430			0.682152	+	0.731210i	$0.261044\pi$
$948$	−7464.00	−	5422.91i	−0.255717	−	0.185789i
$949$	−3276.08	+	10082.7i	−0.112061	+	0.344889i
$950$	5637.47	+	17350.4i	0.192530	+	0.592547i
$951$	−32066.0	+	23297.3i	−1.09339	+	0.794394i
$952$	8499.38	−	6175.16i	0.289355	−	0.210229i
$953$	4923.25	+	15152.2i	0.167345	+	0.515035i	0.999201	−	0.0399561i	$-0.0127218\pi$
$953$	4923.25	+	15152.2i	0.167345	+	0.515035i	−0.831857	+	0.554991i	$0.812722\pi$
$954$	−4411.23	+	13576.4i	−0.149705	+	0.460745i
$955$	5071.87	+	3684.93i	0.171855	+	0.124860i
$956$	−12546.4			−0.424456
$957$		0			0
$958$	17319.9			0.584113
$959$	17440.9	+	12671.5i	0.587274	+	0.426679i
$960$	810.275	−	2493.77i	0.0272412	−	0.0838397i
$961$	4853.93	+	14938.9i	0.162933	+	0.501456i
$962$	−18096.5	+	13147.9i	−0.606503	+	0.440650i
$963$	−1584.23	+	1151.01i	−0.0530125	+	0.0385158i
$964$	8033.52	+	24724.6i	0.268405	+	0.826066i
$965$	2147.38	−	6608.96i	0.0716338	−	0.220466i
$966$	−38685.6	−	28106.7i	−1.28850	−	0.936148i
$967$	−14952.9			−0.497264			−0.248632	−	0.968598i	$-0.579981\pi$
$967$	−14952.9			−0.497264			−0.248632	+	0.968598i	$0.579981\pi$
$968$		0			0
$969$	42787.5			1.41851
$970$	5097.21	+	3703.34i	0.168723	+	0.122585i
$971$	8633.10	−	26569.9i	0.285324	−	0.878136i	−0.700978	−	0.713183i	$-0.747253\pi$
$971$	8633.10	−	26569.9i	0.285324	−	0.878136i	0.986301	−	0.164953i	$-0.0527472\pi$
$972$	−6718.72	−	20678.1i	−0.221711	−	0.682356i
$973$	−22633.1	+	16443.9i	−0.745720	+	0.541797i
$974$	−12018.2	+	8731.73i	−0.395367	+	0.287251i
$975$	17221.5	+	53002.4i	0.565671	+	1.74096i
$976$	738.078	−	2271.57i	0.0242063	−	0.0744992i
$977$	−26988.2	−	19608.1i	−0.883755	−	0.642086i	0.0504873	−	0.998725i	$-0.483923\pi$
$977$	−26988.2	−	19608.1i	−0.883755	−	0.642086i	−0.934242	+	0.356639i	$0.883923\pi$
$978$	27516.4			0.899671
$979$		0			0
$980$	3193.26			0.104087
$981$	38333.1	+	27850.6i	1.24758	+	0.906423i
$982$	3426.31	−	10545.1i	0.111342	−	0.342676i
$983$	3816.38	+	11745.6i	0.123829	+	0.381106i	0.993686	−	0.112198i	$-0.0357891\pi$
$983$	3816.38	+	11745.6i	0.123829	+	0.381106i	−0.869857	+	0.493304i	$0.835789\pi$
$984$	4061.39	−	2950.77i	0.131577	−	0.0955966i
$985$	−11747.8	+	8535.27i	−0.380016	+	0.276098i
$986$	−748.172	−	2302.64i	−0.0241649	−	0.0743721i
$987$	4685.71	−	14421.1i	0.151112	−	0.465075i
$988$	−23683.9	−	17207.4i	−0.762637	−	0.554088i
$989$	21568.2			0.693457
$990$		0			0
$991$	−30154.0			−0.966571			−0.483286	−	0.875463i	$-0.660557\pi$
$991$	−30154.0			−0.966571			−0.483286	+	0.875463i	$0.660557\pi$
$992$	−5522.13	−	4012.06i	−0.176742	−	0.128410i
$993$	−9279.21	+	28558.5i	−0.296543	+	0.912664i
$994$	−12306.2	−	37874.7i	−0.392686	−	1.20856i
$995$	5834.56	−	4239.06i	0.185898	−	0.135062i
$996$	−18737.1	+	13613.3i	−0.596093	+	0.433087i
$997$	−646.801	−	1990.65i	−0.0205460	−	0.0632342i	0.940258	−	0.340463i	$-0.110584\pi$
$997$	−646.801	−	1990.65i	−0.0205460	−	0.0632342i	−0.960804	+	0.277229i	$0.910584\pi$
$998$	12615.3	−	38826.0i	0.400131	−	1.23148i
$999$	3026.40	+	2198.81i	0.0958470	+	0.0696369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.4.c.n.81.2		8
11.2	odd	10		22.4.c.b.5.1	✓	8
11.3	even	5	inner	242.4.c.n.3.2		8
11.4	even	5		242.4.c.q.9.1		8
11.5	even	5		242.4.a.o.1.3		4
11.6	odd	10		242.4.a.n.1.3		4
11.7	odd	10		22.4.c.b.9.1	yes	8
11.8	odd	10		242.4.c.r.3.2		8
11.9	even	5		242.4.c.q.27.1		8
11.10	odd	2		242.4.c.r.81.2		8
33.2	even	10		198.4.f.d.181.2		8
33.5	odd	10		2178.4.a.bt.1.3		4
33.17	even	10		2178.4.a.by.1.3		4
33.29	even	10		198.4.f.d.163.2		8
44.7	even	10		176.4.m.b.97.2		8
44.27	odd	10		1936.4.a.bm.1.2		4
44.35	even	10		176.4.m.b.49.2		8
44.39	even	10		1936.4.a.bn.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.4.c.b.5.1	✓	8	11.2	odd	10
22.4.c.b.9.1	yes	8	11.7	odd	10
176.4.m.b.49.2		8	44.35	even	10
176.4.m.b.97.2		8	44.7	even	10
198.4.f.d.163.2		8	33.29	even	10
198.4.f.d.181.2		8	33.2	even	10
242.4.a.n.1.3		4	11.6	odd	10
242.4.a.o.1.3		4	11.5	even	5
242.4.c.n.3.2		8	11.3	even	5	inner
242.4.c.n.81.2		8	1.1	even	1	trivial
242.4.c.q.9.1		8	11.4	even	5
242.4.c.q.27.1		8	11.9	even	5
242.4.c.r.3.2		8	11.8	odd	10
242.4.c.r.81.2		8	11.10	odd	2
1936.4.a.bm.1.2		4	44.27	odd	10
1936.4.a.bn.1.2		4	44.39	even	10
2178.4.a.bt.1.3		4	33.5	odd	10
2178.4.a.by.1.3		4	33.17	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	242.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.61803 - 1.17557i) q^{2} +(2.34103 - 7.20496i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-4.37525 + 3.17880i) q^{5} +(-12.2578 + 8.90583i) q^{6} +(6.84467 + 21.0657i) q^{7} +(2.47214 - 7.60845i) q^{8} +(-24.5876 - 17.8639i) q^{9} +O(q^{10})\)	\(q+(-1.61803 - 1.17557i) q^{2} +(2.34103 - 7.20496i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-4.37525 + 3.17880i) q^{5} +(-12.2578 + 8.90583i) q^{6} +(6.84467 + 21.0657i) q^{7} +(2.47214 - 7.60845i) q^{8} +(-24.5876 - 17.8639i) q^{9} +10.8162 q^{10} +30.3030 q^{12} +(62.1543 + 45.1577i) q^{13} +(13.6893 - 42.1315i) q^{14} +(12.6606 + 38.9652i) q^{15} +(-12.9443 + 9.40456i) q^{16} +(47.9653 - 34.8488i) q^{17} +(18.7833 + 57.8089i) q^{18} +(-29.4377 + 90.6001i) q^{19} +(-17.5010 - 12.7152i) q^{20} +167.801 q^{21} +142.484 q^{23} +(-49.0313 - 35.6233i) q^{24} +(-29.5891 + 91.0660i) q^{25} +(-47.4817 - 146.134i) q^{26} +(-20.7889 + 15.1041i) q^{27} +(-71.6783 + 52.0773i) q^{28} +(6.30960 + 19.4190i) q^{29} +(25.3211 - 77.9303i) q^{30} +(-172.567 - 125.377i) q^{31} +32.0000 q^{32} -118.577 q^{34} +(-96.9109 - 70.4099i) q^{35} +(37.5665 - 115.618i) q^{36} +(-44.9859 - 138.452i) q^{37} +(154.138 - 111.988i) q^{38} +(470.865 - 342.104i) q^{39} +(13.3696 + 41.1473i) q^{40} +(-25.5967 + 78.7785i) q^{41} +(-271.508 - 197.262i) q^{42} +151.373 q^{43} +164.363 q^{45} +(-230.544 - 167.500i) q^{46} +(27.9241 - 85.9416i) q^{47} +(37.4566 + 115.279i) q^{48} +(-119.423 + 86.7656i) q^{49} +(154.931 - 112.564i) q^{50} +(-138.796 - 427.170i) q^{51} +(-94.9633 + 292.267i) q^{52} +(189.997 + 138.041i) q^{53} +51.3931 q^{54} +177.199 q^{56} +(583.855 + 424.196i) q^{57} +(12.6192 - 38.8379i) q^{58} +(93.4769 + 287.692i) q^{59} +(-132.583 + 96.3272i) q^{60} +(-120.770 + 87.7443i) q^{61} +(131.829 + 405.729i) q^{62} +(208.023 - 640.229i) q^{63} +(-51.7771 - 37.6183i) q^{64} -415.488 q^{65} +826.236 q^{67} +(191.861 + 139.395i) q^{68} +(333.560 - 1026.59i) q^{69} +(74.0333 + 227.851i) q^{70} +(727.278 - 528.399i) q^{71} +(-196.701 + 142.912i) q^{72} +(42.6423 + 131.240i) q^{73} +(-89.9719 + 276.905i) q^{74} +(586.858 + 426.377i) q^{75} -381.050 q^{76} -1164.04 q^{78} +(-246.312 - 178.956i) q^{79} +(26.7391 - 82.2945i) q^{80} +(-193.417 - 595.278i) q^{81} +(134.026 - 97.3755i) q^{82} +(-618.327 + 449.241i) q^{83} +(207.414 + 638.355i) q^{84} +(-99.0824 + 304.944i) q^{85} +(-244.926 - 177.949i) q^{86} +154.684 q^{87} -313.100 q^{89} +(-265.944 - 193.220i) q^{90} +(-525.855 + 1618.42i) q^{91} +(176.120 + 542.041i) q^{92} +(-1307.32 + 949.825i) q^{93} +(-146.213 + 106.230i) q^{94} +(-159.202 - 489.974i) q^{95} +(74.9131 - 230.559i) q^{96} +(471.257 + 342.388i) q^{97} +295.229 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 7 q^{3} - 8 q^{4} - 30 q^{5} + 6 q^{6} - 4 q^{7} - 16 q^{8} - 81 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 7 * q^3 - 8 * q^4 - 30 * q^5 + 6 * q^6 - 4 * q^7 - 16 * q^8 - 81 * q^9	\( 8 q - 4 q^{2} - 7 q^{3} - 8 q^{4} - 30 q^{5} + 6 q^{6} - 4 q^{7} - 16 q^{8} - 81 q^{9} + 100 q^{10} + 32 q^{12} + 48 q^{13} - 8 q^{14} - 279 q^{15} - 32 q^{16} + 109 q^{17} - 42 q^{18} - 288 q^{19} - 120 q^{20} + 50 q^{21} + 628 q^{23} + 24 q^{24} + 38 q^{25} - 14 q^{26} + 242 q^{27} + 4 q^{28} - 528 q^{29} - 558 q^{30} - 522 q^{31} + 256 q^{32} + 208 q^{34} + 17 q^{35} - 84 q^{36} - 406 q^{37} + 544 q^{38} + 1429 q^{39} + 40 q^{40} + 329 q^{41} - 1480 q^{42} - 1442 q^{43} + 2652 q^{45} - 1044 q^{46} + 666 q^{47} - 112 q^{48} - 114 q^{49} - 34 q^{50} - 1158 q^{51} - 28 q^{52} + 414 q^{53} + 1144 q^{54} + 48 q^{56} + 593 q^{57} - 1056 q^{58} - 888 q^{59} + 844 q^{60} + 302 q^{61} + 646 q^{62} + 2061 q^{63} - 128 q^{64} + 138 q^{65} + 578 q^{67} + 436 q^{68} + 1930 q^{69} + 1394 q^{70} + 1090 q^{71} - 648 q^{72} - 253 q^{73} - 812 q^{74} + 2763 q^{75} + 128 q^{76} - 4152 q^{78} + 674 q^{79} + 80 q^{80} - 230 q^{81} - 722 q^{82} + 428 q^{83} + 2860 q^{84} - 1046 q^{85} - 984 q^{86} - 2122 q^{87} - 2202 q^{89} - 1366 q^{90} - 2217 q^{91} + 832 q^{92} - 3721 q^{93} - 2138 q^{94} + 973 q^{95} - 224 q^{96} + 3012 q^{97} + 3292 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 7 * q^3 - 8 * q^4 - 30 * q^5 + 6 * q^6 - 4 * q^7 - 16 * q^8 - 81 * q^9 + 100 * q^10 + 32 * q^12 + 48 * q^13 - 8 * q^14 - 279 * q^15 - 32 * q^16 + 109 * q^17 - 42 * q^18 - 288 * q^19 - 120 * q^20 + 50 * q^21 + 628 * q^23 + 24 * q^24 + 38 * q^25 - 14 * q^26 + 242 * q^27 + 4 * q^28 - 528 * q^29 - 558 * q^30 - 522 * q^31 + 256 * q^32 + 208 * q^34 + 17 * q^35 - 84 * q^36 - 406 * q^37 + 544 * q^38 + 1429 * q^39 + 40 * q^40 + 329 * q^41 - 1480 * q^42 - 1442 * q^43 + 2652 * q^45 - 1044 * q^46 + 666 * q^47 - 112 * q^48 - 114 * q^49 - 34 * q^50 - 1158 * q^51 - 28 * q^52 + 414 * q^53 + 1144 * q^54 + 48 * q^56 + 593 * q^57 - 1056 * q^58 - 888 * q^59 + 844 * q^60 + 302 * q^61 + 646 * q^62 + 2061 * q^63 - 128 * q^64 + 138 * q^65 + 578 * q^67 + 436 * q^68 + 1930 * q^69 + 1394 * q^70 + 1090 * q^71 - 648 * q^72 - 253 * q^73 - 812 * q^74 + 2763 * q^75 + 128 * q^76 - 4152 * q^78 + 674 * q^79 + 80 * q^80 - 230 * q^81 - 722 * q^82 + 428 * q^83 + 2860 * q^84 - 1046 * q^85 - 984 * q^86 - 2122 * q^87 - 2202 * q^89 - 1366 * q^90 - 2217 * q^91 + 832 * q^92 - 3721 * q^93 - 2138 * q^94 + 973 * q^95 - 224 * q^96 + 3012 * q^97 + 3292 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more