LMFDB - Embedded newform 230.4.l.a.33.34

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,4,Mod(7,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.7"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			33.34
Character	$\chi$	$=$	230.33
Dual form			230.4.l.a.7.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.99490 + 0.142678i) q^{2} +(1.66607 + 7.65881i) q^{3} +(3.95929 + 0.569259i) q^{4} +(-9.74326 - 5.48352i) q^{5} +(2.23091 + 15.5163i) q^{6} +(-16.4725 - 30.1671i) q^{7} +(7.81717 + 1.70052i) q^{8} +(-31.3215 + 14.3041i) q^{9} +(-18.6545 - 12.3292i) q^{10} +(-52.5357 - 45.5225i) q^{11} +(2.23661 + 31.2719i) q^{12} +(-9.25586 - 5.05408i) q^{13} +(-28.5568 - 62.5307i) q^{14} +(25.7643 - 83.7577i) q^{15} +(15.3519 + 4.50772i) q^{16} +(-19.7165 + 26.3381i) q^{17} +(-64.5244 + 24.0663i) q^{18} +(-16.0009 + 111.289i) q^{19} +(-35.4548 - 27.2572i) q^{20} +(203.600 - 176.420i) q^{21} +(-98.3086 - 98.3086i) q^{22} +(-102.370 + 41.0776i) q^{23} +62.7035i q^{24} +(64.8621 + 106.855i) q^{25} +(-17.7434 - 11.4030i) q^{26} +(-34.9145 - 46.6403i) q^{27} +(-48.0463 - 128.817i) q^{28} +(-42.1443 + 6.05944i) q^{29} +(63.3476 - 163.413i) q^{30} +(177.298 - 113.943i) q^{31} +(29.9824 + 11.1829i) q^{32} +(261.120 - 478.205i) q^{33} +(-43.0903 + 49.7289i) q^{34} +(-4.92617 + 384.253i) q^{35} +(-132.154 + 38.8038i) q^{36} +(-5.14274 + 13.7882i) q^{37} +(-47.7988 + 219.728i) q^{38} +(23.2873 - 79.3093i) q^{39} +(-66.8399 - 59.4342i) q^{40} +(21.2072 - 46.4373i) q^{41} +(431.333 - 322.892i) q^{42} +(-161.600 + 35.1540i) q^{43} +(-182.090 - 210.143i) q^{44} +(383.610 + 32.3840i) q^{45} +(-210.079 + 67.3400i) q^{46} +(298.302 - 298.302i) q^{47} +(-8.94643 + 125.087i) q^{48} +(-453.270 + 705.302i) q^{49} +(114.148 + 222.419i) q^{50} +(-234.568 - 107.123i) q^{51} +(-33.7695 - 25.2795i) q^{52} +(-90.6305 + 49.4880i) q^{53} +(-62.9965 - 98.0245i) q^{54} +(262.246 + 731.617i) q^{55} +(-77.4684 - 263.833i) q^{56} +(-878.999 + 62.8673i) q^{57} +(-84.9384 + 6.07491i) q^{58} +(-175.273 - 596.926i) q^{59} +(149.688 - 316.954i) q^{60} +(-329.333 - 512.452i) q^{61} +(369.950 - 202.008i) q^{62} +(947.455 + 709.256i) q^{63} +(58.2164 + 26.5866i) q^{64} +(62.4681 + 99.9979i) q^{65} +(589.138 - 916.717i) q^{66} +(19.5131 - 272.829i) q^{67} +(-93.0563 + 93.0563i) q^{68} +(-485.162 - 715.595i) q^{69} +(-64.6518 + 765.844i) q^{70} +(-182.495 - 210.610i) q^{71} +(-269.170 + 58.5544i) q^{72} +(-561.202 + 420.111i) q^{73} +(-12.2266 + 26.7724i) q^{74} +(-710.315 + 674.794i) q^{75} +(-126.704 + 431.516i) q^{76} +(-507.886 + 2334.72i) q^{77} +(57.7717 - 154.892i) q^{78} +(520.480 - 152.827i) q^{79} +(-124.859 - 128.102i) q^{80} +(-309.783 + 357.508i) q^{81} +(48.9319 - 89.6122i) q^{82} +(153.732 + 57.3391i) q^{83} +(906.538 - 582.596i) q^{84} +(336.528 - 148.503i) q^{85} +(-327.393 + 47.0720i) q^{86} +(-116.624 - 312.680i) q^{87} +(-333.269 - 445.195i) q^{88} +(-210.478 - 135.266i) q^{89} +(760.646 + 119.336i) q^{90} +362.475i q^{91} +(-428.696 + 104.363i) q^{92} +(1168.06 + 1168.06i) q^{93} +(637.646 - 552.523i) q^{94} +(766.155 - 996.575i) q^{95} +(-35.6945 + 248.261i) q^{96} +(897.926 - 334.909i) q^{97} +(-1004.86 + 1342.34i) q^{98} +(2296.66 + 674.359i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q + 16 q^{3} + 16 q^{6} + 64 q^{12} - 192 q^{13} + 1152 q^{16} + 144 q^{18} + 1660 q^{23} - 880 q^{25} - 304 q^{26} - 728 q^{27} - 352 q^{28} - 608 q^{31} - 3872 q^{33} - 688 q^{35} - 2816 q^{36} - 2376 q^{37}+ \cdots + 14352 q^{98}+O(q^{100}) $ 720 * q + 16 * q^3 + 16 * q^6 + 64 * q^12 - 192 * q^13 + 1152 * q^16 + 144 * q^18 + 1660 * q^23 - 880 * q^25 - 304 * q^26 - 728 * q^27 - 352 * q^28 - 608 * q^31 - 3872 * q^33 - 688 * q^35 - 2816 * q^36 - 2376 * q^37 + 2208 * q^41 + 256 * q^46 + 3640 * q^47 - 256 * q^48 - 272 * q^50 - 768 * q^52 + 2360 * q^55 - 3872 * q^56 - 7656 * q^57 + 2112 * q^61 + 1376 * q^62 + 10912 * q^66 + 1104 * q^70 + 22752 * q^71 - 128 * q^72 + 1296 * q^73 - 5396 * q^75 + 752 * q^77 - 6000 * q^78 - 3928 * q^81 - 80 * q^82 + 3060 * q^85 - 10472 * q^86 - 6760 * q^87 - 1104 * q^92 + 5288 * q^93 + 9392 * q^95 - 256 * q^96 + 25344 * q^97 + 14352 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{22}\right)$

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 $

$2$	1.99490	+	0.142678i	0.705305	+	0.0504444i
$2$	1.99490	+	0.142678i	0.705305	+	0.0504444i
$3$	1.66607	+	7.65881i	0.320636	+	1.47394i	0.801950	+	0.597391i	$0.203796\pi$
$3$	1.66607	+	7.65881i	0.320636	+	1.47394i	−0.481314	+	0.876548i	$0.659840\pi$
$4$	3.95929	+	0.569259i	0.494911	+	0.0711574i
$5$	−9.74326	−	5.48352i	−0.871463	−	0.490461i
$5$	−9.74326	−	5.48352i	−0.871463	−	0.490461i
$6$	2.23091	+	15.5163i	0.151794	+	1.05575i
$7$	−16.4725	−	30.1671i	−0.889430	−	1.62887i	−0.771850	−	0.635805i	$-0.780668\pi$
$7$	−16.4725	−	30.1671i	−0.889430	−	1.62887i	−0.117580	−	0.993063i	$-0.537514\pi$
$8$	7.81717	+	1.70052i	0.345474	+	0.0751532i
$9$	−31.3215	+	14.3041i	−1.16006	+	0.529780i
$10$	−18.6545	−	12.3292i	−0.589907	−	0.389885i
$11$	−52.5357	−	45.5225i	−1.44001	−	1.24778i	−0.919019	−	0.394214i	$-0.871017\pi$
$11$	−52.5357	−	45.5225i	−1.44001	−	1.24778i	−0.520992	−	0.853562i	$-0.674438\pi$
$12$	2.23661	+	31.2719i	0.0538044	+	0.752284i
$13$	−9.25586	−	5.05408i	−0.197470	−	0.107827i	0.377472	−	0.926021i	$-0.376794\pi$
$13$	−9.25586	−	5.05408i	−0.197470	−	0.107827i	−0.574942	+	0.818194i	$0.694975\pi$
$14$	−28.5568	−	62.5307i	−0.545152	−	1.19372i
$15$	25.7643	−	83.7577i	0.443487	−	1.44174i
$16$	15.3519	+	4.50772i	0.239873	+	0.0704331i
$17$	−19.7165	+	26.3381i	−0.281291	+	0.375760i	−0.918827	−	0.394660i	$-0.870863\pi$
$17$	−19.7165	+	26.3381i	−0.281291	+	0.375760i	0.637537	+	0.770420i	$0.279953\pi$
$18$	−64.5244	+	24.0663i	−0.844919	+	0.315138i
$19$	−16.0009	+	111.289i	−0.193203	+	1.34376i	0.630258	+	0.776386i	$0.282949\pi$
$19$	−16.0009	+	111.289i	−0.193203	+	1.34376i	−0.823461	+	0.567373i	$0.807960\pi$
$20$	−35.4548	−	27.2572i	−0.396397	−	0.304745i
$21$	203.600	−	176.420i	2.11567	−	1.83324i
$22$	−98.3086	−	98.3086i	−0.952703	−	0.952703i
$23$	−102.370	+	41.0776i	−0.928071	+	0.372404i
$23$	−102.370	+	41.0776i	−0.928071	+	0.372404i
$24$			62.7035i			0.533304i
$25$	64.8621	+	106.855i	0.518897	+	0.854837i
$26$	−17.7434	−	11.4030i	−0.133838	−	0.0860121i
$27$	−34.9145	−	46.6403i	−0.248863	−	0.332442i
$28$	−48.0463	−	128.817i	−0.324282	−	0.869434i
$29$	−42.1443	+	6.05944i	−0.269862	+	0.0388003i	−0.275917	−	0.961181i	$-0.588982\pi$
$29$	−42.1443	+	6.05944i	−0.269862	+	0.0388003i	0.00605528	+	0.999982i	$0.498073\pi$
$30$	63.3476	−	163.413i	0.385521	−	0.994497i
$31$	177.298	−	113.943i	1.02722	−	0.660151i	0.0854222	−	0.996345i	$-0.472776\pi$
$31$	177.298	−	113.943i	1.02722	−	0.660151i	0.941793	+	0.336194i	$0.109140\pi$
$32$	29.9824	+	11.1829i	0.165631	+	0.0617771i
$33$	261.120	−	478.205i	1.37743	−	2.52257i
$34$	−43.0903	+	49.7289i	−0.217351	+	0.250836i
$35$	−4.92617	+	384.253i	−0.0237907	+	1.85573i
$36$	−132.154	+	38.8038i	−0.611823	+	0.179647i
$37$	−5.14274	+	13.7882i	−0.0228503	+	0.0612640i	−0.947874	−	0.318645i	$-0.896772\pi$
$37$	−5.14274	+	13.7882i	−0.0228503	+	0.0612640i	0.925024	+	0.379909i	$0.124045\pi$
$38$	−47.7988	+	219.728i	−0.204052	+	0.938014i
$39$	23.2873	−	79.3093i	0.0956143	−	0.325632i
$40$	−66.8399	−	59.4342i	−0.264208	−	0.234934i
$41$	21.2072	−	46.4373i	0.0807807	−	0.176885i	−0.864932	−	0.501889i	$-0.832638\pi$
$41$	21.2072	−	46.4373i	0.0807807	−	0.176885i	0.945713	+	0.325004i	$0.105366\pi$
$42$	431.333	−	322.892i	1.58467	−	1.18627i
$43$	−161.600	+	35.1540i	−0.573112	+	0.124673i	−0.489776	−	0.871848i	$-0.662921\pi$
$43$	−161.600	+	35.1540i	−0.573112	+	0.124673i	−0.0833367	+	0.996521i	$0.526558\pi$
$44$	−182.090	−	210.143i	−0.623888	−	0.720005i
$45$	383.610	+	32.3840i	1.27078	+	0.107278i
$46$	−210.079	+	67.3400i	−0.673359	+	0.215842i
$47$	298.302	−	298.302i	0.925785	−	0.925785i	−0.0716455	−	0.997430i	$-0.522825\pi$
$47$	298.302	−	298.302i	0.925785	−	0.925785i	0.997430	+	0.0716455i	$0.0228250\pi$
$48$	−8.94643	+	125.087i	−0.0269022	+	0.376142i
$49$	−453.270	+	705.302i	−1.32149	+	2.05627i
$50$	114.148	+	222.419i	0.322859	+	0.629096i
$51$	−234.568	−	107.123i	−0.644040	−	0.294123i
$52$	−33.7695	−	25.2795i	−0.0900575	−	0.0674162i
$53$	−90.6305	+	49.4880i	−0.234888	+	0.128258i	−0.592383	−	0.805657i	$-0.701813\pi$
$53$	−90.6305	+	49.4880i	−0.234888	+	0.128258i	0.357495	+	0.933915i	$0.383631\pi$
$54$	−62.9965	−	98.0245i	−0.158754	−	0.247027i
$55$	262.246	+	731.617i	0.642931	+	1.79366i
$56$	−77.4684	−	263.833i	−0.184860	−	0.629575i
$57$	−878.999	+	62.8673i	−2.04257	+	0.146087i
$58$	−84.9384	+	6.07491i	−0.192292	+	0.0137530i
$59$	−175.273	−	596.926i	−0.386757	−	1.31717i	−0.891154	−	0.453700i	$-0.850104\pi$
$59$	−175.273	−	596.926i	−0.386757	−	1.31717i	0.504398	−	0.863471i	$-0.331715\pi$
$60$	149.688	−	316.954i	0.322077	−	0.681977i
$61$	−329.333	−	512.452i	−0.691258	−	1.07562i	−0.992521	−	0.122077i	$-0.961045\pi$
$61$	−329.333	−	512.452i	−0.691258	−	1.07562i	0.301263	−	0.953541i	$-0.402592\pi$
$62$	369.950	−	202.008i	0.757801	−	0.413791i
$63$	947.455	+	709.256i	1.89473	+	1.41838i
$64$	58.2164	+	26.5866i	0.113704	+	0.0519269i
$65$	62.4681	+	99.9979i	0.119203	+	0.190819i
$66$	589.138	−	916.717i	1.09876	−	1.70970i
$67$	19.5131	−	272.829i	0.0355808	−	0.497484i	−0.948149	−	0.317827i	$-0.897047\pi$
$67$	19.5131	−	272.829i	0.0355808	−	0.497484i	0.983729	−	0.179657i	$-0.0574987\pi$
$68$	−93.0563	+	93.0563i	−0.165952	+	0.165952i
$69$	−485.162	−	715.595i	−0.846473	−	1.24851i
$70$	−64.6518	+	765.844i	−0.110391	+	1.30766i
$71$	−182.495	−	210.610i	−0.305044	−	0.352040i	0.582444	−	0.812871i	$-0.302097\pi$
$71$	−182.495	−	210.610i	−0.305044	−	0.352040i	−0.887488	+	0.460832i	$0.847551\pi$
$72$	−269.170	+	58.5544i	−0.440584	+	0.0958431i
$73$	−561.202	+	420.111i	−0.899778	+	0.673565i	−0.945581	−	0.325385i	$-0.894506\pi$
$73$	−561.202	+	420.111i	−0.899778	+	0.673565i	0.0458039	+	0.998950i	$0.485415\pi$
$74$	−12.2266	+	26.7724i	−0.0192069	+	0.0420572i
$75$	−710.315	+	674.794i	−1.09360	+	1.03891i
$76$	−126.704	+	431.516i	−0.191237	+	0.651293i
$77$	−507.886	+	2334.72i	−0.751675	+	3.45540i
$78$	57.7717	−	154.892i	0.0838636	−	0.224847i
$79$	520.480	−	152.827i	0.741248	−	0.217650i	0.110758	−	0.993847i	$-0.464672\pi$
$79$	520.480	−	152.827i	0.741248	−	0.217650i	0.630490	+	0.776198i	$0.282854\pi$
$80$	−124.859	−	128.102i	−0.174496	−	0.179028i
$81$	−309.783	+	357.508i	−0.424942	+	0.490409i
$82$	48.9319	−	89.6122i	0.0658979	−	0.120683i
$83$	153.732	+	57.3391i	0.203305	+	0.0758287i	0.449054	−	0.893505i	$-0.351761\pi$
$83$	153.732	+	57.3391i	0.203305	+	0.0758287i	−0.245749	+	0.969333i	$0.579034\pi$
$84$	906.538	−	582.596i	1.17752	−	0.756744i
$85$	336.528	−	148.503i	0.429430	−	0.189499i
$86$	−327.393	+	47.0720i	−0.410508	+	0.0590222i
$87$	−116.624	−	312.680i	−0.143717	−	0.385320i
$88$	−333.269	−	445.195i	−0.403711	−	0.539295i
$89$	−210.478	−	135.266i	−0.250681	−	0.161103i	0.409266	−	0.912415i	$-0.365785\pi$
$89$	−210.478	−	135.266i	−0.250681	−	0.161103i	−0.659947	+	0.751312i	$0.729421\pi$
$90$	760.646	+	119.336i	0.890879	+	0.139768i
$91$			362.475i			0.417558i
$92$	−428.696	+	104.363i	−0.485812	+	0.118267i
$93$	1168.06	+	1168.06i	1.30238	+	1.30238i
$94$	637.646	−	552.523i	0.699661	−	0.606260i
$95$	766.155	−	996.575i	0.827430	−	1.07628i
$96$	−35.6945	+	248.261i	−0.0379485	+	0.263938i
$97$	897.926	−	334.909i	0.939903	−	0.350566i	0.167625	−	0.985851i	$-0.446390\pi$
$97$	897.926	−	334.909i	0.939903	−	0.350566i	0.772278	+	0.635285i	$0.219117\pi$
$98$	−1004.86	+	1342.34i	−1.03578	+	1.38364i
$99$	2296.66	+	674.359i	2.33154	+	0.684602i
$100$	195.980	+	459.991i	0.195980	+	0.459991i
$101$	−789.173	−	1728.05i	−0.777482	−	1.70245i	−0.709440	−	0.704766i	$-0.751052\pi$
$101$	−789.173	−	1728.05i	−0.777482	−	1.70245i	−0.0680419	−	0.997682i	$-0.521675\pi$
$102$	−452.656	−	247.169i	−0.439408	−	0.239935i
$103$	−16.4904	−	230.566i	−0.0157752	−	0.220566i	−0.999224	−	0.0393814i	$-0.987461\pi$
$103$	−16.4904	−	230.566i	−0.0157752	−	0.220566i	0.983449	−	0.181185i	$-0.0579933\pi$
$104$	−63.7601	−	55.2484i	−0.0601172	−	0.0520919i
$105$	−2951.13	+	602.464i	−2.74286	+	0.559947i
$106$	−187.860	+	85.7928i	−0.172138	+	0.0786126i
$107$	1858.31	+	404.251i	1.67897	+	0.365238i	0.948271	−	0.317461i	$-0.102830\pi$
$107$	1858.31	+	404.251i	1.67897	+	0.365238i	0.730700	+	0.682699i	$0.239194\pi$
$108$	−111.686	−	204.538i	−0.0995092	−	0.182237i
$109$	−94.0666	−	654.247i	−0.0826600	−	0.574913i	−0.988492	−	0.151275i	$-0.951662\pi$
$109$	−94.0666	−	654.247i	−0.0826600	−	0.574913i	0.905832	−	0.423638i	$-0.139247\pi$
$110$	418.769	+	1496.92i	0.362983	+	1.29751i
$111$	−114.170	−	16.4151i	−0.0976261	−	0.0140365i
$112$	−116.899	−	537.375i	−0.0986240	−	0.453367i
$113$	695.934	+	49.7742i	0.579363	+	0.0414368i	0.357946	−	0.933742i	$-0.383477\pi$
$113$	695.934	+	49.7742i	0.579363	+	0.0414368i	0.221417	+	0.975179i	$0.428932\pi$
$114$	−1762.49			−1.44800
$115$	1222.67	+	161.118i	0.991429	+	0.130646i
$116$	−170.311			−0.136319
$117$	362.202	+	25.9052i	0.286201	+	0.0204695i
$118$	−264.485	−	1215.82i	−0.206337	−	0.948518i
$119$	1119.32	+	160.934i	0.862252	+	0.123973i
$120$	343.836	−	610.936i	0.261565	−	0.464755i
$121$	498.286	+	3465.66i	0.374370	+	2.60380i
$122$	−583.871	−	1069.28i	−0.433289	−	0.793509i
$123$	390.987	+	85.0541i	0.286619	+	0.0623502i
$124$	766.836	−	350.202i	0.555354	−	0.253622i
$125$	−46.0289	−	1396.78i	−0.0329356	−	0.999457i
$126$	1788.89	+	1550.08i	1.26481	+	1.09597i
$127$	−3.07350	−	42.9732i	−0.00214747	−	0.0300256i	0.996265	−	0.0863439i	$-0.0275184\pi$
$127$	−3.07350	−	42.9732i	−0.00214747	−	0.0300256i	−0.998413	+	0.0563183i	$0.982064\pi$
$128$	112.343	+	61.3439i	0.0775766	+	0.0423600i
$129$	−538.476	−	1179.10i	−0.367521	−	0.804758i
$130$	110.350	+	208.399i	0.0744489	+	0.140598i
$131$	−1468.29	−	431.128i	−0.979274	−	0.287541i	−0.247349	−	0.968926i	$-0.579559\pi$
$131$	−1468.29	−	431.128i	−0.979274	−	0.287541i	−0.731925	+	0.681386i	$0.761378\pi$
$132$	1306.07	−	1744.70i	0.861203	−	1.15043i
$133$	3620.83	−	1350.50i	2.36065	−	0.880476i
$134$	77.8537	−	541.485i	0.0501906	−	0.349083i
$135$	84.4280	+	645.883i	0.0538252	+	0.411768i
$136$	−198.915	+	172.361i	−0.125418	+	0.108675i
$137$	−764.366	−	764.366i	−0.476673	−	0.476673i	0.427393	−	0.904066i	$-0.359432\pi$
$137$	−764.366	−	764.366i	−0.476673	−	0.476673i	−0.904066	+	0.427393i	$0.859432\pi$
$138$	−865.752	−	1496.76i	−0.534041	−	0.923283i
$139$			775.564i			0.473255i	0.971600	+	0.236628i	$0.0760421\pi$
$139$			775.564i			0.473255i	−0.971600	+	0.236628i	$0.923958\pi$
$140$	−238.243	+	1518.56i	−0.143823	+	0.916728i
$141$	2781.64	+	1787.65i	1.66139	+	1.06771i
$142$	−334.010	−	446.185i	−0.197391	−	0.263683i
$143$	256.189	+	686.869i	0.149815	+	0.401670i
$144$	−545.324	+	78.4057i	−0.315581	+	0.0453737i
$145$	443.850	+	172.060i	0.254205	+	0.0985437i
$146$	−1179.49	+	758.009i	−0.668595	+	0.429680i
$147$	−6156.96	−	2296.43i	−3.45454	−	1.28848i
$148$	−28.2106	+	51.6639i	−0.0156682	+	0.0286943i
$149$	−2186.15	+	2522.95i	−1.20199	+	1.38717i	−0.300833	+	0.953677i	$0.597265\pi$
$149$	−2186.15	+	2522.95i	−1.20199	+	1.38717i	−0.901157	+	0.433494i	$0.857281\pi$
$150$	−1513.29	+	1244.80i	−0.823730	+	0.677585i
$151$	−530.120	+	155.657i	−0.285699	+	0.0838887i	−0.421442	−	0.906855i	$-0.638476\pi$
$151$	−530.120	+	155.657i	−0.285699	+	0.0838887i	0.135743	+	0.990744i	$0.456658\pi$
$152$	−314.331	+	842.755i	−0.167734	+	0.449713i
$153$	240.808	−	1106.98i	0.127243	−	0.584926i
$154$	−1346.30	+	4585.07i	−0.704466	+	2.39919i
$155$	−2352.27	+	137.955i	−1.21896	+	0.0714889i
$156$	137.349	−	300.752i	0.0704917	−	0.154355i
$157$	−752.206	+	563.095i	−0.382373	+	0.286241i	−0.773123	−	0.634256i	$-0.781307\pi$
$157$	−752.206	+	563.095i	−0.382373	+	0.286241i	0.390750	+	0.920497i	$0.372216\pi$
$158$	1060.11	−	230.613i	0.533785	−	0.116118i
$159$	−530.016	−	611.671i	−0.264359	−	0.305086i
$160$	−230.805	−	273.366i	−0.114042	−	0.135072i
$161$	2925.48	+	2411.55i	1.43205	+	1.18048i
$162$	−668.995	+	668.995i	−0.324452	+	0.324452i
$163$	37.6365	−	526.227i	0.0180854	−	0.252867i	−0.980364	−	0.197197i	$-0.936816\pi$
$163$	37.6365	−	526.227i	0.0180854	−	0.252867i	0.998449	−	0.0556696i	$-0.0177293\pi$
$164$	110.400	−	171.786i	0.0525659	−	0.0817942i
$165$	−5166.40	+	3227.42i	−2.43760	+	1.52275i
$166$	298.500	+	136.320i	0.139567	+	0.0637380i
$167$	1410.00	+	1055.52i	0.653350	+	0.489092i	0.873787	−	0.486310i	$-0.161657\pi$
$167$	1410.00	+	1055.52i	0.653350	+	0.489092i	−0.220437	+	0.975401i	$0.570748\pi$
$168$	1891.58	−	1032.88i	0.868682	−	0.474336i
$169$	−1127.66	−	1754.67i	−0.513273	−	0.798668i
$170$	692.529	−	248.235i	0.312439	−	0.111993i
$171$	−1090.71	−	3714.62i	−0.487770	−	1.66119i
$172$	−659.834	+	47.1923i	−0.292511	+	0.0209208i
$173$	−669.375	+	47.8746i	−0.294171	+	0.0210395i	−0.217645	−	0.976028i	$-0.569837\pi$
$173$	−669.375	+	47.8746i	−0.294171	+	0.0210395i	−0.0765263	+	0.997068i	$0.524383\pi$
$174$	−188.040	−	640.406i	−0.0819270	−	0.279018i
$175$	2155.05	−	3716.86i	0.930895	−	1.60553i
$176$	−601.320	−	935.672i	−0.257535	−	0.400733i
$177$	4279.73	−	2336.91i	1.81742	−	0.992388i
$178$	−400.584	−	299.873i	−0.168680	−	0.126272i
$179$	−3507.69	−	1601.91i	−1.46467	−	0.668895i	−0.485934	−	0.873996i	$-0.661520\pi$
$179$	−3507.69	−	1601.91i	−1.46467	−	0.668895i	−0.978741	+	0.205101i	$0.934248\pi$
$180$	1500.39	+	346.591i	0.621291	+	0.143519i
$181$	−1450.18	+	2256.53i	−0.595532	+	0.926665i	0.404395	+	0.914584i	$0.367482\pi$
$181$	−1450.18	+	2256.53i	−0.595532	+	0.926665i	−0.999927	+	0.0120812i	$0.996154\pi$
$182$	−51.7174	+	723.103i	−0.0210634	+	0.294505i
$183$	3376.08	−	3376.08i	1.36375	−	1.36375i
$184$	−870.098	+	147.029i	−0.348611	+	0.0589081i
$185$	125.715	−	106.142i	0.0499608	−	0.0421822i
$186$	2163.50	+	2496.82i	0.852880	+	0.984276i
$187$	2234.79	−	486.149i	0.873926	−	0.190111i
$188$	1350.88	−	1011.25i	0.524057	−	0.392304i
$189$	−831.873	+	1821.55i	−0.320158	+	0.701048i
$190$	1670.60	−	1878.76i	0.637883	−	0.717365i
$191$	91.7793	−	312.571i	0.0347692	−	0.118413i	−0.940280	−	0.340402i	$-0.889437\pi$
$191$	91.7793	−	312.571i	0.0347692	−	0.118413i	0.975049	+	0.221989i	$0.0712550\pi$
$192$	−106.629	+	490.164i	−0.0400795	+	0.184242i
$193$	−580.196	+	1555.57i	−0.216391	+	0.580166i	−0.999109	−	0.0422105i	$-0.986560\pi$
$193$	−580.196	+	1555.57i	−0.216391	+	0.580166i	0.782718	+	0.622376i	$0.213833\pi$
$194$	1839.06	−	539.997i	0.680602	−	0.199843i
$195$	−661.789	+	645.035i	−0.243034	+	0.236882i
$196$	−2196.13	+	2534.46i	−0.800337	+	0.923639i
$197$	−315.050	+	576.970i	−0.113941	+	0.208667i	−0.928426	−	0.371517i	$-0.878838\pi$
$197$	−315.050	+	576.970i	−0.113941	+	0.208667i	0.814485	+	0.580184i	$0.197020\pi$
$198$	4485.39	+	1672.96i	1.60991	+	0.600467i
$199$	−301.217	+	193.580i	−0.107300	+	0.0689575i	−0.593190	−	0.805062i	$-0.702132\pi$
$199$	−301.217	+	193.580i	−0.107300	+	0.0689575i	0.485890	+	0.874020i	$0.338495\pi$
$200$	325.330	+	945.601i	0.115021	+	0.334320i
$201$	2122.06	−	305.106i	0.744670	−	0.107067i
$202$	−1327.77	−	3559.89i	−0.462483	−	1.23997i
$203$	877.016	+	1171.56i	0.303224	+	0.405060i
$204$	−867.739	−	557.662i	−0.297813	−	0.191393i
$205$	−461.267	+	336.161i	−0.157153	+	0.114529i
$206$		−	462.310i		−	0.156362i
$207$	2618.81	−	2750.92i	0.879323	−	0.923683i
$208$	−119.313	−	119.313i	−0.0397732	−	0.0397732i
$209$	5906.76	−	5118.24i	1.95492	−	1.69395i
$210$	−5973.17	+	780.796i	−1.96280	+	0.256572i
$211$	370.849	−	2579.31i	0.120997	−	0.841549i	−0.835434	−	0.549590i	$-0.814784\pi$
$211$	370.849	−	2579.31i	0.120997	−	0.841549i	0.956431	−	0.291959i	$-0.0943071\pi$
$212$	−387.004	+	144.345i	−0.125375	+	0.0467625i
$213$	1308.97	−	1748.58i	0.421077	−	0.562493i
$214$	3649.48	+	1071.58i	1.16576	+	0.342299i
$215$	1767.28	+	543.624i	0.560594	+	0.172441i
$216$	−193.620	−	423.968i	−0.0609915	−	0.133553i
$217$	−6357.85	−	3471.65i	−1.98893	−	1.08604i
$218$	−94.3069	−	1318.58i	−0.0292994	−	0.409659i
$219$	−4152.55	−	3598.21i	−1.28129	−	1.11025i
$220$	621.826	+	3045.97i	0.190561	+	0.933451i
$221$	315.608	−	144.133i	0.0960636	−	0.0438708i
$222$	−225.415	−	49.0361i	−0.0681481	−	0.0148247i
$223$	1577.03	+	2888.11i	0.473567	+	0.867273i	0.999856	+	0.0169674i	$0.00540114\pi$
$223$	1577.03	+	2888.11i	0.473567	+	0.867273i	−0.526289	+	0.850306i	$0.676417\pi$
$224$	−156.530	−	1088.69i	−0.0466902	−	0.324737i
$225$	−3560.04	−	2419.06i	−1.05483	−	0.716758i
$226$	1381.22	+	198.589i	0.406537	+	0.0584512i
$227$	−941.403	−	4327.56i	−0.275256	−	1.26533i	−0.882309	−	0.470670i	$-0.844012\pi$
$227$	−941.403	−	4327.56i	−0.275256	−	1.26533i	0.607053	−	0.794661i	$-0.292351\pi$
$228$	−3516.00	−	251.469i	−1.02128	−	0.0730436i
$229$	−3527.16			−1.01782			−0.508911	−	0.860819i	$-0.669952\pi$
$229$	−3527.16			−1.01782			−0.508911	+	0.860819i	$0.669952\pi$
$230$	2416.12	+	495.863i	0.692670	+	0.142158i
$231$	−18727.3			−5.33406
$232$	−339.754	−	24.2997i	−0.0961462	−	0.00687651i
$233$	−540.878	−	2486.38i	−0.152078	−	0.699090i	−0.988527	−	0.151045i	$-0.951736\pi$
$233$	−540.878	−	2486.38i	−0.152078	−	0.699090i	0.836449	−	0.548045i	$-0.184628\pi$
$234$	718.862	+	103.357i	0.200827	+	0.0288745i
$235$	−4542.18	+	1270.69i	−1.26085	+	0.352726i
$236$	−354.151	−	2463.18i	−0.0976834	−	0.679403i
$237$	2037.63	+	3731.64i	0.558473	+	1.02277i
$238$	2209.98	+	480.751i	0.601897	+	0.130935i
$239$	2640.86	−	1206.04i	0.714741	−	0.326411i	−0.0246421	−	0.999696i	$-0.507845\pi$
$239$	2640.86	−	1206.04i	0.714741	−	0.326411i	0.739383	+	0.673285i	$0.235117\pi$
$240$	773.086	−	1169.70i	0.207927	−	0.314599i
$241$	1295.89	+	1122.89i	0.346371	+	0.300132i	0.810620	−	0.585573i	$-0.199130\pi$
$241$	1295.89	+	1122.89i	0.346371	+	0.300132i	−0.464249	+	0.885705i	$0.653676\pi$
$242$	499.559	+	6984.75i	0.132698	+	1.85536i
$243$	−4634.84	−	2530.81i	−1.22356	−	0.668114i
$244$	−1012.20	−	2216.42i	−0.265573	−	0.581523i
$245$	8283.86	−	4386.42i	2.16015	−	1.14383i
$246$	767.847	+	225.460i	0.199009	+	0.0584342i
$247$	710.565	−	949.204i	0.183045	−	0.244520i
$248$	1579.73	−	589.209i	0.404488	−	0.150866i
$249$	−183.021	+	1272.94i	−0.0465802	+	0.323972i
$250$	107.468	−	2793.02i	0.0271874	−	0.706584i
$251$	−3363.63	+	2914.60i	−0.845859	+	0.732941i	−0.965647	−	0.259859i	$-0.916324\pi$
$251$	−3363.63	+	2914.60i	−0.845859	+	0.732941i	0.119788	+	0.992800i	$0.461779\pi$
$252$	3347.49	+	3347.49i	0.836795	+	0.836795i
$253$	7248.04	+	2502.09i	1.80111	+	0.621760i
$254$		−	86.1659i		−	0.0212855i
$255$	1698.04	+	2329.99i	0.417001	+	0.572194i
$256$	215.361	+	138.404i	0.0525783	+	0.0337901i
$257$	−2735.24	−	3653.86i	−0.663891	−	0.886854i	0.334567	−	0.942372i	$-0.391410\pi$
$257$	−2735.24	−	3653.86i	−0.663891	−	0.886854i	−0.998458	+	0.0555179i	$0.982319\pi$
$258$	−905.976	−	2429.02i	−0.218619	−	0.586139i
$259$	500.664	−	71.9846i	0.120115	−	0.0172699i
$260$	190.404	+	431.481i	0.0454168	+	0.102920i
$261$	1233.35	−	792.626i	0.292500	−	0.187978i
$262$	−2867.58	−	1069.55i	−0.676182	−	0.252203i
$263$	−3921.46	+	7181.61i	−0.919420	+	1.68379i	−0.211653	+	0.977345i	$0.567885\pi$
$263$	−3921.46	+	7181.61i	−0.919420	+	1.68379i	−0.707767	+	0.706446i	$0.750297\pi$
$264$	2854.42	−	3294.17i	0.665444	−	0.767963i
$265$	1154.40	+	14.7996i	0.267602	+	0.00343069i
$266$	7415.90	−	2177.51i	1.70939	−	0.501923i
$267$	685.305	−	1837.37i	0.157079	−	0.421144i
$268$	232.569	−	1069.10i	0.0530090	−	0.243678i
$269$	−1656.69	+	5642.16i	−0.375502	+	1.27884i	0.527628	+	0.849475i	$0.323081\pi$
$269$	−1656.69	+	5642.16i	−0.375502	+	1.27884i	−0.903130	+	0.429367i	$0.858737\pi$
$270$	76.2722	+	1300.52i	0.0171918	+	0.293137i
$271$	913.639	−	2000.59i	0.204796	−	0.448440i	−0.779166	−	0.626817i	$-0.784357\pi$
$271$	913.639	−	2000.59i	0.204796	−	0.448440i	0.983962	+	0.178377i	$0.0570846\pi$
$272$	−421.410	+	315.463i	−0.0939401	+	0.0703227i
$273$	−2776.13	+	603.910i	−0.615454	+	0.133884i
$274$	−1415.78	−	1633.89i	−0.312154	−	0.360245i
$275$	1456.71	−	8566.36i	0.319428	−	1.87844i
$276$	−1513.54	−	3109.43i	−0.330087	−	0.678136i
$277$	4333.11	−	4333.11i	0.939897	−	0.939897i	−0.0583969	−	0.998293i	$-0.518599\pi$
$277$	4333.11	−	4333.11i	0.939897	−	0.939897i	0.998293	+	0.0583969i	$0.0185989\pi$
$278$	−110.656	+	1547.18i	−0.0238731	+	0.333789i
$279$	−3923.41	+	6104.94i	−0.841893	+	1.31001i
$280$	−691.939	+	2995.39i	−0.147683	+	0.639318i
$281$	621.310	+	283.743i	0.131901	+	0.0602372i	0.480272	−	0.877119i	$-0.340538\pi$
$281$	621.310	+	283.743i	0.131901	+	0.0602372i	−0.348371	+	0.937357i	$0.613265\pi$
$282$	5294.04	+	3963.07i	1.11793	+	0.836870i
$283$	−1972.12	+	1076.86i	−0.414241	+	0.226193i	−0.672834	−	0.739794i	$-0.734923\pi$
$283$	−1972.12	+	1076.86i	−0.414241	+	0.226193i	0.258592	+	0.965987i	$0.416741\pi$
$284$	−602.657	−	937.752i	−0.125919	−	0.195934i
$285$	8909.05	+	4207.48i	1.85167	+	0.874489i
$286$	413.071	+	1406.79i	0.0854035	+	0.290858i
$287$	−1750.21	+	125.178i	−0.359971	+	0.0257457i
$288$	−1099.06	+	78.6060i	−0.224870	+	0.0160830i
$289$	1079.20	+	3675.40i	0.219661	+	0.748097i
$290$	860.889	+	406.572i	0.174321	+	0.0823266i
$291$	4061.02	+	6319.06i	0.818079	+	1.27296i
$292$	−2461.11	+	1343.87i	−0.493239	+	0.269329i
$293$	−3040.95	−	2276.43i	−0.606329	−	0.453892i	0.251479	−	0.967863i	$-0.419083\pi$
$293$	−3040.95	−	2276.43i	−0.606329	−	0.453892i	−0.857808	+	0.513971i	$0.828174\pi$
$294$	−11954.9	−	5459.61i	−2.37151	−	1.08303i
$295$	−1565.52	+	6777.12i	−0.308977	+	1.33756i
$296$	−63.6489	+	99.0396i	−0.0124984	+	0.0194478i
$297$	−288.923	+	4039.67i	−0.0564479	+	0.789245i
$298$	−4721.13	+	4721.13i	−0.917745	+	0.917745i
$299$	1155.13	+	137.178i	0.223422	+	0.0265324i
$300$	−3196.47	+	2267.35i	−0.615161	+	0.436352i
$301$	3722.45	+	4295.94i	0.712819	+	0.822637i
$302$	−1079.75	+	234.885i	−0.205737	+	0.0447552i
$303$	11920.0	−	8923.19i	2.26002	−	1.69183i
$304$	−747.304	+	1636.37i	−0.140989	+	0.308724i
$305$	398.735	+	6798.85i	0.0748575	+	1.27640i
$306$	638.330	−	2173.95i	0.119251	−	0.406132i
$307$	−668.491	+	3073.00i	−0.124276	+	0.571288i	0.872326	+	0.488924i	$0.162611\pi$
$307$	−668.491	+	3073.00i	−0.124276	+	0.571288i	−0.996602	+	0.0823638i	$0.973753\pi$
$308$	−3339.93	+	8954.69i	−0.617889	+	1.65663i
$309$	1738.39	−	510.436i	0.320043	−	0.0939732i
$310$	−4712.23	−	60.4114i	−0.863344	−	0.0110682i
$311$	5385.68	−	6215.41i	0.981974	−	1.13326i	−0.00910136	−	0.999959i	$-0.502897\pi$
$311$	5385.68	−	6215.41i	0.981974	−	1.13326i	0.991076	−	0.133300i	$-0.0425575\pi$
$312$	316.908	−	580.374i	0.0575045	−	0.105312i
$313$	9001.13	+	3357.25i	1.62548	+	0.606271i	0.986617	−	0.163053i	$-0.0521340\pi$
$313$	9001.13	+	3357.25i	1.62548	+	0.606271i	0.638859	+	0.769324i	$0.279407\pi$
$314$	−1580.92	+	1016.00i	−0.284129	+	0.182599i
$315$	−5342.08	−	12105.8i	−0.955530	−	2.16536i
$316$	2147.73	−	308.796i	0.382339	−	0.0549720i
$317$	598.374	+	1604.30i	0.106019	+	0.284248i	0.979117	−	0.203296i	$-0.0651654\pi$
$317$	598.374	+	1604.30i	0.106019	+	0.284248i	−0.873098	+	0.487544i	$0.837893\pi$
$318$	−970.060	−	1295.85i	−0.171064	−	0.228514i
$319$	2489.92	+	1600.18i	0.437018	+	0.280855i
$320$	−421.430	−	578.271i	−0.0736208	−	0.101020i
$321$			14906.0i			2.59181i
$322$	5491.97	+	5228.22i	0.950484	+	0.904837i
$323$	−2615.66	−	2615.66i	−0.450585	−	0.450585i
$324$	−1430.03	+	1239.13i	−0.245204	+	0.212471i
$325$	−60.3024	−	1316.85i	−0.0102922	−	0.224756i
$326$	150.162	−	1044.40i	0.0255114	−	0.177436i
$327$	4854.04	−	1810.46i	0.820883	−	0.306174i
$328$	244.748	−	326.945i	0.0412011	−	0.0550382i
$329$	−13912.7	−	4085.13i	−2.33140	−	0.684561i
$330$	−10767.0	+	5701.26i	−1.79606	+	0.951042i
$331$	−3125.66	−	6844.25i	−0.519039	−	1.13654i	−0.969802	−	0.243894i	$-0.921575\pi$
$331$	−3125.66	−	6844.25i	−0.519039	−	1.13654i	0.450763	−	0.892644i	$-0.351152\pi$
$332$	576.029	+	314.535i	0.0952219	+	0.0519951i
$333$	−36.1491	−	505.430i	−0.00594882	−	0.0831754i
$334$	2662.23	+	2306.83i	0.436139	+	0.377917i
$335$	−1686.19	+	2551.25i	−0.275004	+	0.416088i
$336$	3920.89	−	1790.61i	0.636613	−	0.290732i
$337$	5093.26	+	1107.97i	0.823286	+	0.179095i	0.604426	−	0.796661i	$-0.293403\pi$
$337$	5093.26	+	1107.97i	0.823286	+	0.179095i	0.218860	+	0.975756i	$0.429766\pi$
$338$	−1999.22	−	3661.30i	−0.321726	−	0.589197i
$339$	778.266	+	5412.96i	0.124689	+	0.867231i
$340$	1416.95	−	396.395i	0.226014	−	0.0632281i
$341$	−14501.4	−	2084.99i	−2.30292	−	0.331110i
$342$	−1645.87	−	7565.93i	−0.260229	−	1.19625i
$343$	16984.0	+	1214.72i	2.67362	+	0.191221i
$344$	−1323.04			−0.207365
$345$	803.082	+	9632.62i	0.125323	+	1.50320i
$346$	−1342.17			−0.208542
$347$	9522.67	+	681.075i	1.47321	+	0.105366i	0.784707	−	0.619867i	$-0.212814\pi$
$347$	9522.67	+	681.075i	1.47321	+	0.105366i	0.688503	+	0.725233i	$0.258268\pi$
$348$	−283.750	−	1304.38i	−0.0437086	−	0.200925i
$349$	157.926	+	22.7063i	0.0242223	+	0.00348264i	0.154415	−	0.988006i	$-0.450651\pi$
$349$	157.926	+	22.7063i	0.0242223	+	0.00348264i	−0.130193	+	0.991489i	$0.541560\pi$
$350$	4829.44	−	7107.30i	0.737555	−	1.08543i
$351$	87.4397	+	608.157i	0.0132968	+	0.0924815i
$352$	−1066.08	−	1952.37i	−0.161426	−	0.295630i
$353$	−11152.2	−	2426.02i	−1.68151	−	0.365790i	−0.732433	−	0.680839i	$-0.761615\pi$
$353$	−11152.2	−	2426.02i	−1.68151	−	0.365790i	−0.949075	+	0.315050i	$0.897979\pi$
$354$	8871.07	−	4051.28i	1.33190	−	0.608258i
$355$	623.208	+	3052.74i	0.0931731	+	0.456402i
$356$	−756.341	−	655.373i	−0.112601	−	0.0975695i
$357$	632.307	+	8840.80i	0.0937401	+	1.31066i
$358$	−6768.94	−	3696.12i	−0.999301	−	0.545659i
$359$	121.015	+	264.986i	0.0177909	+	0.0389567i	0.918319	−	0.395841i	$-0.129547\pi$
$359$	121.015	+	264.986i	0.0177909	+	0.0389567i	−0.900528	+	0.434798i	$0.856820\pi$
$360$	2943.68	+	905.489i	0.430960	+	0.132565i
$361$	−5548.02	−	1629.05i	−0.808867	−	0.237505i
$362$	−3214.93	+	4294.65i	−0.466777	+	0.623541i
$363$	−25712.6	+	9590.32i	−3.71780	+	1.38667i
$364$	−206.342	+	1435.14i	−0.0297123	+	0.206654i
$365$	7771.62	−	1015.88i	1.11448	−	0.145682i
$366$	7216.65	−	6253.26i	1.03066	−	0.893069i
$367$	−89.7047	−	89.7047i	−0.0127590	−	0.0127590i	0.700699	−	0.713457i	$-0.252872\pi$
$367$	−89.7047	−	89.7047i	−0.0127590	−	0.0127590i	−0.713457	+	0.700699i	$0.752872\pi$
$368$	−1756.74	+	169.164i	−0.248849	+	0.0239627i
$369$			1757.84i			0.247993i
$370$	265.933	−	193.806i	0.0373655	−	0.0272311i
$371$	2985.82	+	1918.87i	0.417832	+	0.268525i
$372$	3959.74	+	5289.59i	0.551890	+	0.737238i
$373$	3528.62	+	9460.60i	0.489826	+	1.31327i	0.913271	+	0.407353i	$0.133548\pi$
$373$	3528.62	+	9460.60i	0.489826	+	1.31327i	−0.423445	+	0.905922i	$0.639179\pi$
$374$	4527.56	−	650.965i	0.625975	−	0.0900016i
$375$	10621.0	−	2679.67i	1.46258	−	0.369007i
$376$	2839.15	−	1824.61i	0.389410	−	0.250258i
$377$	420.707	+	156.915i	0.0574735	+	0.0214365i
$378$	−1919.40	+	3515.12i	−0.261173	+	0.478303i
$379$	1211.62	−	1398.29i	0.164213	−	0.189512i	−0.667679	−	0.744449i	$-0.732712\pi$
$379$	1211.62	−	1398.29i	0.164213	−	0.189512i	0.831892	+	0.554937i	$0.187258\pi$
$380$	3600.74	−	3509.58i	0.486089	−	0.473784i
$381$	324.003	−	95.1358i	0.0435674	−	0.0127925i
$382$	227.688	−	610.455i	0.0304962	−	0.0817634i
$383$	2406.09	−	11060.6i	0.321007	−	1.47565i	−0.480147	−	0.877188i	$-0.659417\pi$
$383$	2406.09	−	11060.6i	0.321007	−	1.47565i	0.801154	−	0.598458i	$-0.204220\pi$
$384$	−282.650	+	962.617i	−0.0375623	+	0.127925i
$385$	17750.9	−	19962.7i	2.34979	−	2.64258i
$386$	−1379.38	+	3020.42i	−0.181888	+	0.398278i
$387$	4558.73	−	3412.62i	0.598794	−	0.448252i
$388$	3745.80	−	814.848i	0.490113	−	0.106618i
$389$	−2592.01	−	2991.34i	−0.337841	−	0.389889i	0.561254	−	0.827644i	$-0.310319\pi$
$389$	−2592.01	−	2991.34i	−0.337841	−	0.389889i	−0.899094	+	0.437755i	$0.855774\pi$
$390$	−1412.24	+	1192.36i	−0.183363	+	0.154814i
$391$	936.467	−	3506.14i	0.121123	−	0.453486i
$392$	−4742.67	+	4742.67i	−0.611074	+	0.611074i
$393$	855.656	−	11963.6i	0.109827	−	1.53559i
$394$	−710.815	+	1106.05i	−0.0908892	+	0.141426i
$395$	−5909.20	−	1365.03i	−0.752719	−	0.173879i
$396$	8709.23	+	3977.37i	1.10519	+	0.504724i
$397$	7176.21	+	5372.04i	0.907213	+	0.679132i	0.947397	−	0.320061i	$-0.103703\pi$
$397$	7176.21	+	5372.04i	0.907213	+	0.679132i	−0.0401835	+	0.999192i	$0.512794\pi$
$398$	−628.518	+	343.197i	−0.0791577	+	0.0432234i
$399$	16375.8	+	25481.3i	2.05468	+	3.19714i
$400$	514.085	+	1932.80i	0.0642606	+	0.241600i
$401$	−291.209	−	991.768i	−0.0362651	−	0.123508i	0.939371	−	0.342902i	$-0.111410\pi$
$401$	−291.209	−	991.768i	−0.0362651	−	0.123508i	−0.975636	+	0.219395i	$0.929592\pi$
$402$	4276.84	−	305.886i	0.530620	−	0.0379507i
$403$	−2216.92	+	158.557i	−0.274026	+	0.0195988i
$404$	−2140.86	−	7291.08i	−0.263642	−	0.897883i
$405$	4978.69	−	1784.60i	0.610847	−	0.218956i
$406$	1582.41	+	2462.27i	0.193432	+	0.300987i
$407$	897.851	−	490.264i	0.109348	−	0.0597088i
$408$	−1651.49	−	1236.29i	−0.200394	−	0.150013i
$409$	11849.2	+	5411.35i	1.43253	+	0.654215i	0.972333	−	0.233601i	$-0.0750509\pi$
$409$	11849.2	+	5411.35i	1.43253	+	0.654215i	0.460199	+	0.887816i	$0.347778\pi$
$410$	−968.146	+	604.795i	−0.116618	+	0.0728505i
$411$	4580.64	−	7127.62i	0.549748	−	0.855425i
$412$	65.9616	−	922.263i	0.00788761	−	0.110283i
$413$	−15120.3	+	15120.3i	−1.80151	+	1.80151i
$414$	5616.77	−	5114.18i	0.666786	−	0.607122i
$415$	−1183.43	−	1401.66i	−0.139982	−	0.165795i
$416$	−220.994	−	255.040i	−0.0260459	−	0.0300586i
$417$	−5939.90	+	1292.15i	−0.697549	+	0.151743i
$418$	12513.7	−	9367.63i	1.46427	−	1.09614i
$419$	−1351.59	+	2959.57i	−0.157588	+	0.345070i	−0.971913	−	0.235339i	$-0.924380\pi$
$419$	−1351.59	+	2959.57i	−0.157588	+	0.345070i	0.814325	+	0.580409i	$0.197107\pi$
$420$	−12027.3	+	705.371i	−1.39732	+	0.0819491i
$421$	−2148.52	+	7317.18i	−0.248723	+	0.847073i	0.736594	+	0.676336i	$0.236433\pi$
$421$	−2148.52	+	7317.18i	−0.248723	+	0.847073i	−0.985317	+	0.170737i	$0.945385\pi$
$422$	1107.82	−	5092.56i	0.127791	−	0.587445i
$423$	−5076.35	+	13610.2i	−0.583501	+	1.56443i
$424$	−792.630	+	232.737i	−0.0907866	+	0.0266573i
$425$	−4093.20	−	398.450i	−0.467175	−	0.0454769i
$426$	2860.76	−	3301.49i	0.325362	−	0.375488i
$427$	−10034.2	+	18376.3i	−1.13722	+	2.08265i
$428$	7127.47	+	2658.41i	0.804952	+	0.300231i
$429$	−4833.77	+	3106.48i	−0.544002	+	0.349609i
$430$	3448.00	+	1336.63i	0.386691	+	0.149902i
$431$	−10496.4	+	1509.16i	−1.17307	+	0.168663i	−0.701175	−	0.712989i	$-0.747341\pi$
$431$	−10496.4	+	1509.16i	−1.17307	+	0.168663i	−0.471900	+	0.881652i	$0.656432\pi$
$432$	−325.762	−	873.401i	−0.0362806	−	0.0972721i
$433$	−111.522	−	148.976i	−0.0123774	−	0.0165342i	0.794310	−	0.607513i	$-0.207833\pi$
$433$	−111.522	−	148.976i	−0.0123774	−	0.0165342i	−0.806687	+	0.590979i	$0.798742\pi$
$434$	−12188.0	−	7832.73i	−1.34802	−	0.866321i
$435$	−578.292	+	3686.03i	−0.0637402	+	0.406279i
$436$		−	2643.90i		−	0.290413i
$437$	−2933.47	−	12049.9i	−0.321114	−	1.31905i
$438$	−7770.56	−	7770.56i	−0.847698	−	0.847698i
$439$	9364.37	−	8114.28i	1.01808	−	0.882171i	0.0250091	−	0.999687i	$-0.492039\pi$
$439$	9364.37	−	8114.28i	1.01808	−	0.882171i	0.993071	+	0.117516i	$0.0374931\pi$
$440$	805.889	+	6165.14i	0.0873165	+	0.667980i
$441$	4108.43	−	28574.8i	0.443627	−	3.08549i
$442$	650.171	−	242.501i	0.0699672	−	0.0260964i
$443$	1598.01	−	2134.70i	0.171386	−	0.228945i	−0.706622	−	0.707592i	$-0.749782\pi$
$443$	1598.01	−	2134.70i	0.171386	−	0.228945i	0.878007	+	0.478647i	$0.158873\pi$
$444$	−442.685	−	129.984i	−0.0473174	−	0.0138936i
$445$	1309.01	+	2472.09i	0.139445	+	0.263345i
$446$	2733.94	+	5986.50i	0.290260	+	0.635581i
$447$	−22965.1	−	12539.9i	−2.43001	−	1.32688i
$448$	−156.930	−	2194.17i	−0.0165496	−	0.231394i
$449$	−6779.31	−	5874.31i	−0.712551	−	0.617429i	0.221252	−	0.975217i	$-0.428986\pi$
$449$	−6779.31	−	5874.31i	−0.712551	−	0.617429i	−0.933803	+	0.357787i	$0.883531\pi$
$450$	−6756.78	−	5333.73i	−0.707818	−	0.558743i
$451$	−3228.08	+	1474.21i	−0.337038	+	0.153920i
$452$	2727.07	+	593.237i	0.283784	+	0.0617335i
$453$	−2075.37	−	3800.75i	−0.215252	−	0.394205i
$454$	−1260.56	−	8767.38i	−0.130311	−	0.906330i
$455$	1987.64	−	3531.69i	0.204796	−	0.363886i
$456$	−6978.20	−	1003.31i	−0.716632	−	0.103036i
$457$	986.213	+	4533.55i	0.100948	+	0.464049i	0.999674	+	0.0255386i	$0.00813009\pi$
$457$	986.213	+	4533.55i	0.100948	+	0.464049i	−0.898726	+	0.438510i	$0.855506\pi$
$458$	−7036.35	−	503.250i	−0.717876	−	0.0513435i
$459$	1916.81			0.194921
$460$	4749.17	+	1333.93i	0.481372	+	0.135206i
$461$	−14053.9			−1.41986			−0.709931	−	0.704271i	$-0.751274\pi$
$461$	−14053.9			−1.41986			−0.709931	+	0.704271i	$0.751274\pi$
$462$	−37359.2	−	2671.98i	−3.76214	−	0.269073i
$463$	3.77954	+	17.3742i	0.000379373	+	0.00174395i	0.977336	−	0.211693i	$-0.0678978\pi$
$463$	3.77954	+	17.3742i	0.000379373	+	0.00174395i	−0.976957	+	0.213437i	$0.931534\pi$
$464$	−674.309	−	96.9510i	−0.0674655	−	0.00970008i
$465$	−4975.61	−	17785.7i	−0.496212	−	1.77375i
$466$	−724.248	−	5037.26i	−0.0719960	−	0.500743i
$467$	−2914.77	−	5338.00i	−0.288821	−	0.528936i	0.692475	−	0.721442i	$-0.256520\pi$
$467$	−2914.77	−	5338.00i	−0.288821	−	0.528936i	−0.981296	+	0.192506i	$0.938339\pi$
$468$	1419.31	+	308.753i	0.140188	+	0.0304959i
$469$	−8551.90	+	3905.52i	−0.841983	+	0.384521i
$470$	−9242.52	+	1886.83i	−0.907076	+	0.185177i
$471$	−5565.87	−	4822.85i	−0.544504	−	0.471816i
$472$	−355.056	−	4964.33i	−0.0346245	−	0.484114i
$473$	10090.1	+	5509.61i	0.980852	+	0.535586i
$474$	3532.45	+	7734.98i	0.342301	+	0.749535i
$475$	−12929.6	+	5508.66i	−1.24895	+	0.532115i
$476$	4340.10	+	1274.37i	0.417916	+	0.122711i
$477$	2130.81	−	2846.43i	0.204535	−	0.273226i
$478$	5440.34	−	2029.14i	0.520576	−	0.194165i
$479$	866.581	−	6027.20i	0.0826620	−	0.574926i	−0.905829	−	0.423644i	$-0.860751\pi$
$479$	866.581	−	6027.20i	0.0826620	−	0.574926i	0.988491	−	0.151282i	$-0.0483402\pi$
$480$	1709.12	−	2223.14i	0.162522	−	0.211400i
$481$	117.287	−	101.630i	0.0111182	−	0.00963394i
$482$	2424.95	+	2424.95i	0.229157	+	0.229157i
$483$	−13595.6	+	26423.5i	−1.28079	+	2.48926i
$484$			14005.2i			1.31529i
$485$	−10585.2	−	1660.69i	−0.991030	−	0.155480i
$486$	−8884.96	−	5710.02i	−0.829280	−	0.532946i
$487$	−2694.60	−	3599.57i	−0.250727	−	0.334932i	0.657465	−	0.753485i	$-0.271629\pi$
$487$	−2694.60	−	3599.57i	−0.250727	−	0.334932i	−0.908193	+	0.418552i	$0.862538\pi$
$488$	−1703.02	−	4565.96i	−0.157975	−	0.423548i
$489$	4092.98	−	588.481i	0.378509	−	0.0544214i
$490$	17151.4	−	7568.57i	1.58126	−	0.697782i
$491$	16960.9	−	10900.1i	1.55893	−	1.00186i	0.576088	−	0.817387i	$-0.304578\pi$
$491$	16960.9	−	10900.1i	1.55893	−	1.00186i	0.982838	−	0.184473i	$-0.0590580\pi$
$492$	1499.61	+	559.327i	0.137414	+	0.0512528i
$493$	671.342	−	1229.47i	0.0613301	−	0.112318i
$494$	1552.94	−	1792.19i	0.141437	−	0.163228i
$495$	−18679.0	−	19164.2i	−1.69608	−	1.74014i
$496$	3235.48	−	950.023i	0.292898	−	0.0860026i
$497$	−3347.35	+	8974.59i	−0.302111	+	0.809991i
$498$	−546.729	+	2513.27i	−0.0491958	+	0.226150i
$499$	4589.49	−	15630.4i	0.411731	−	1.40223i	−0.449165	−	0.893449i	$-0.648279\pi$
$499$	4589.49	−	15630.4i	0.411731	−	1.40223i	0.860897	−	0.508780i	$-0.169903\pi$
$500$	612.891	−	5556.47i	0.0548186	−	0.496986i
$501$	−5734.83	+	12557.5i	−0.511404	+	1.11982i
$502$	−7125.97	+	5334.44i	−0.633561	+	0.474278i
$503$	15068.2	−	3277.88i	1.33570	−	0.290563i	0.512680	−	0.858580i	$-0.328653\pi$
$503$	15068.2	−	3277.88i	1.33570	−	0.290563i	0.823017	+	0.568016i	$0.192289\pi$
$504$	6200.32	+	7155.55i	0.547984	+	0.632407i
$505$	−1786.67	+	21164.3i	−0.157437	+	1.86495i
$506$	14102.1	+	6025.57i	1.23897	+	0.529386i
$507$	11560.0	−	11560.0i	1.01261	−	1.01261i
$508$	12.2940	−	171.893i	0.00107374	−	0.0150128i
$509$	−4871.73	+	7580.56i	−0.424235	+	0.660123i	−0.985918	−	0.167230i	$-0.946518\pi$
$509$	−4871.73	+	7580.56i	−0.424235	+	0.660123i	0.561683	+	0.827353i	$0.310154\pi$
$510$	3054.99	+	4890.37i	0.265249	+	0.424607i
$511$	21917.9	+	10009.6i	1.89744	+	0.866531i
$512$	409.877	+	306.830i	0.0353793	+	0.0264846i
$513$	5749.21	−	3139.31i	0.494803	−	0.270183i
$514$	−4935.22	−	7679.36i	−0.423509	−	0.658992i
$515$	−1103.64	+	2336.89i	−0.0944316	+	0.199953i
$516$	−1460.77	−	4974.92i	−0.124625	−	0.424435i
$517$	−29251.0	+	2092.07i	−2.48831	+	0.177968i
$518$	1009.05	−	72.1684i	0.0855887	−	0.00612143i
$519$	−1481.89	−	5046.85i	−0.125333	−	0.426844i
$520$	318.275	+	887.929i	0.0268409	+	0.0748813i
$521$	−4451.90	−	6927.30i	−0.374360	−	0.582515i	0.602045	−	0.798462i	$-0.294353\pi$
$521$	−4451.90	−	6927.30i	−0.374360	−	0.582515i	−0.976405	+	0.215947i	$0.930716\pi$
$522$	2573.51	−	1405.24i	0.215784	−	0.117827i
$523$	2575.11	+	1927.70i	0.215300	+	0.161171i	0.701485	−	0.712685i	$-0.252521\pi$
$523$	2575.11	+	1927.70i	0.215300	+	0.161171i	−0.486185	+	0.873856i	$0.661612\pi$
$524$	−5567.95	−	2542.80i	−0.464192	−	0.211990i
$525$	32057.2	+	10312.6i	2.66493	+	0.857292i
$526$	−8847.59	+	13767.1i	−0.733409	+	1.14121i
$527$	−494.659	+	6916.23i	−0.0408874	+	0.571681i
$528$	6164.29	−	6164.29i	0.508080	−	0.508080i
$529$	8792.25	−	8410.24i	0.722631	−	0.691234i
$530$	2300.81	+	194.232i	0.188568	+	0.0159187i
$531$	14028.3	+	16189.5i	1.14647	+	1.32310i
$532$	15104.7	−	3285.83i	1.23096	−	0.267779i
$533$	−430.989	+	322.634i	−0.0350248	+	0.0262192i
$534$	1629.27	−	3567.61i	0.132033	−	0.289111i
$535$	−15889.3	−	14128.8i	−1.28403	−	1.14176i
$536$	616.490	−	2099.57i	0.0496797	−	0.169194i
$537$	6424.64	−	29533.6i	0.516283	−	2.37331i
$538$	−4109.95	+	11019.2i	−0.329354	+	0.883032i
$539$	55919.9	−	16419.6i	4.46872	−	1.31214i
$540$	−33.4002	+	2605.30i	−0.00266170	+	0.207619i
$541$	4033.05	−	4654.39i	0.320507	−	0.369885i	−0.572518	−	0.819892i	$-0.694033\pi$
$541$	4033.05	−	4654.39i	0.320507	−	0.369885i	0.893025	+	0.450007i	$0.148579\pi$
$542$	2108.06	−	3860.63i	0.167065	−	0.305956i
$543$	−19698.4	−	7347.14i	−1.55680	−	0.580655i
$544$	−885.681	+	569.193i	−0.0698038	+	0.0448602i
$545$	−2671.06	+	6890.32i	−0.209937	+	0.541557i
$546$	−5624.28	+	808.649i	−0.440837	+	0.0633828i
$547$	8359.85	+	22413.6i	0.653458	+	1.75199i	0.659158	+	0.752005i	$0.270913\pi$
$547$	8359.85	+	22413.6i	0.653458	+	1.75199i	−0.00569955	+	0.999984i	$0.501814\pi$
$548$	−2591.22	−	3461.46i	−0.201992	−	0.269829i
$549$	17645.4	+	11340.0i	1.37174	+	0.881564i
$550$	4128.23	−	16881.2i	0.320051	−	1.30876i
$551$		−	4787.15i		−	0.370126i
$552$	−2575.71	−	6418.96i	−0.198604	−	0.494944i
$553$	−13183.9	−	13183.9i	−1.01381	−	1.01381i
$554$	9262.38	−	8025.90i	0.710326	−	0.615501i
$555$	1022.37	+	785.987i	0.0781932	+	0.0601140i
$556$	−441.497	+	3070.68i	−0.0336756	+	0.234219i
$557$	−13324.5	+	4969.77i	−1.01360	+	0.378054i	−0.800729	−	0.599026i	$-0.795554\pi$
$557$	−13324.5	+	4969.77i	−1.01360	+	0.378054i	−0.212872	+	0.977080i	$0.568282\pi$
$558$	−8697.86	+	11619.0i	−0.659874	+	0.881489i
$559$	1673.42	+	491.361i	0.126616	+	0.0371777i
$560$	−1807.73	+	5876.80i	−0.136412	+	0.443464i
$561$	7446.65	+	16305.9i	0.560424	+	1.22716i
$562$	1198.97	+	654.687i	0.0899919	+	0.0491393i
$563$	−403.523	−	5641.99i	−0.0302069	−	0.422347i	−0.989945	−	0.141452i	$-0.954823\pi$
$563$	−403.523	−	5641.99i	−0.0302069	−	0.422347i	0.959738	−	0.280896i	$-0.0906315\pi$
$564$	9995.65	+	8661.28i	0.746264	+	0.646642i
$565$	−6507.73	−	4301.13i	−0.484570	−	0.320265i
$566$	−4087.83	+	1866.85i	−0.303577	+	0.138639i
$567$	15887.9	+	3456.19i	1.17677	+	0.255990i
$568$	−1068.45	−	1956.71i	−0.0789278	−	0.144545i
$569$	1971.33	+	13710.9i	0.145242	+	1.01018i	0.923874	+	0.382697i	$0.125005\pi$
$569$	1971.33	+	13710.9i	0.145242	+	1.01018i	−0.778632	+	0.627480i	$0.784086\pi$
$570$	17172.4	+	9664.64i	1.26188	+	0.710188i
$571$	−22402.1	−	3220.93i	−1.64185	−	0.236063i	−0.741415	−	0.671047i	$-0.765845\pi$
$571$	−22402.1	−	3220.93i	−1.64185	−	0.236063i	−0.900438	+	0.434984i	$0.856754\pi$
$572$	623.319	+	2865.35i	0.0455634	+	0.209452i
$573$	2546.84	+	182.153i	0.185682	+	0.0132802i
$574$	−3509.37			−0.255188
$575$	−11029.3	−	8274.33i	−0.799917	−	0.600110i
$576$	−2203.73			−0.159413
$577$	13835.8	+	989.553i	0.998249	+	0.0713962i	0.560890	−	0.827890i	$-0.310459\pi$
$577$	13835.8	+	989.553i	0.998249	+	0.0713962i	0.437360	+	0.899287i	$0.355914\pi$
$578$	1628.49	+	7486.05i	0.117191	+	0.538717i
$579$	−12880.4	−	1851.93i	−0.924512	−	0.132925i
$580$	1659.38	+	933.902i	0.118797	+	0.0668589i
$581$	−802.594	−	5582.16i	−0.0573102	−	0.398601i
$582$	7199.74	+	13185.3i	0.512782	+	0.939090i
$583$	7014.15	+	1525.84i	0.498279	+	0.108394i
$584$	−5101.42	+	2329.74i	−0.361470	+	0.165078i
$585$	−3386.97	−	2238.54i	−0.239374	−	0.158209i
$586$	−5741.61	−	4975.14i	−0.404751	−	0.350718i
$587$	4.68544	+	65.5110i	0.000329453	+	0.00460635i	0.997614	−	0.0690358i	$-0.0219923\pi$
$587$	4.68544	+	65.5110i	0.000329453	+	0.00460635i	−0.997285	+	0.0736422i	$0.976538\pi$
$588$	−23069.9	−	12597.1i	−1.61800	−	0.883497i
$589$	9843.60	+	21554.5i	0.688622	+	1.50787i
$590$	−4090.01	+	13296.3i	−0.285395	+	0.927799i
$591$	−4943.80	−	1451.63i	−0.344096	−	0.101036i
$592$	−141.104	+	188.493i	−0.00979619	+	0.0130862i
$593$	−231.169	+	86.2217i	−0.0160084	+	0.00597083i	−0.357456	−	0.933930i	$-0.616356\pi$
$593$	−231.169	+	86.2217i	−0.0160084	+	0.00597083i	0.341447	+	0.939901i	$0.389083\pi$
$594$	−1152.75	+	8017.54i	−0.0796260	+	0.553811i
$595$	−10023.4	−	7705.84i	−0.690617	−	0.530939i
$596$	−10091.8	+	8744.61i	−0.693585	+	0.600995i
$597$	−1984.44	−	1984.44i	−0.136043	−	0.136043i
$598$	2284.81	+	438.469i	0.156242	+	0.0299838i
$599$		−	1868.53i		−	0.127456i	−0.997967	−	0.0637281i	$-0.979701\pi$
$599$		−	1868.53i		−	0.127456i	0.997967	−	0.0637281i	$-0.0202990\pi$
$600$	−6700.16	+	4067.08i	−0.455888	+	0.276730i
$601$	−13961.8	−	8972.72i	−0.947612	−	0.608993i	−0.0270683	−	0.999634i	$-0.508617\pi$
$601$	−13961.8	−	8972.72i	−0.947612	−	0.608993i	−0.920543	+	0.390641i	$0.872254\pi$
$602$	6813.00	+	9101.10i	0.461258	+	0.616168i
$603$	3291.39	+	8824.56i	0.222282	+	0.595960i
$604$	−2187.50	+	314.516i	−0.147365	+	0.0211878i
$605$	14149.1	−	36499.1i	0.950811	−	2.45273i
$606$	25052.4	−	16100.2i	1.67934	−	1.07925i
$607$	−7784.25	−	2903.37i	−0.520515	−	0.194142i	0.0754541	−	0.997149i	$-0.475959\pi$
$607$	−7784.25	−	2903.37i	−0.520515	−	0.194142i	−0.595970	+	0.803007i	$0.703232\pi$
$608$	−1724.27	+	3157.77i	−0.115014	+	0.210632i
$609$	−7511.56	+	8668.80i	−0.499809	+	0.576810i
$610$	−174.610	+	13619.9i	−0.0115897	+	0.904025i
$611$	−4268.69	+	1253.40i	−0.282639	+	0.0829904i
$612$	1583.58	−	4245.75i	0.104596	−	0.280432i
$613$	2280.12	−	10481.6i	0.150234	−	0.690613i	−0.838983	−	0.544157i	$-0.816850\pi$
$613$	2280.12	−	10481.6i	0.150234	−	0.690613i	0.989217	−	0.146456i	$-0.0467867\pi$
$614$	−1772.03	+	6034.96i	−0.116471	+	0.396663i
$615$	−3343.09	−	2972.69i	−0.219198	−	0.194911i
$616$	−7940.47	+	17387.2i	−0.519368	+	1.13726i
$617$	4951.29	−	3706.49i	0.323065	−	0.241844i	−0.425418	−	0.904997i	$-0.639873\pi$
$617$	4951.29	−	3706.49i	0.323065	−	0.241844i	0.748484	+	0.663153i	$0.230782\pi$
$618$	3540.74	−	770.241i	0.230469	−	0.0501354i
$619$	−14916.0	−	17213.9i	−0.968535	−	1.11775i	−0.993008	−	0.118049i	$-0.962336\pi$
$619$	−14916.0	−	17213.9i	−0.968535	−	1.11775i	0.0244727	−	0.999700i	$-0.492209\pi$
$620$	−9391.82	−	792.848i	−0.608363	−	0.0513573i
$621$	5490.07	+	3340.36i	0.354765	+	0.215852i
$622$	11630.7	−	11630.7i	0.749758	−	0.749758i
$623$	−613.487	+	8577.67i	−0.0394524	+	0.551617i
$624$	715.009	−	1112.58i	0.0458706	−	0.0713761i
$625$	−7210.82	+	13861.6i	−0.461492	+	0.887144i
$626$	17477.4	+	7981.66i	1.11587	+	0.509602i
$627$	49040.7	+	36711.4i	3.12360	+	2.33830i
$628$	−3298.75	+	1801.25i	−0.209609	+	0.114455i
$629$	−261.759	−	407.305i	−0.0165930	−	0.0258192i
$630$	−8929.69	−	24912.2i	−0.564710	−	1.57544i
$631$	1319.83	+	4494.94i	0.0832675	+	0.283583i	0.990592	−	0.136848i	$-0.0436971\pi$
$631$	1319.83	+	4494.94i	0.0832675	+	0.283583i	−0.907325	+	0.420431i	$0.861879\pi$
$632$	4328.57	−	309.585i	0.272439	−	0.0194852i
$633$	20372.3	−	1457.06i	1.27919	−	0.0914894i
$634$	964.800	+	3285.81i	0.0604371	+	0.205830i
$635$	−205.698	+	435.552i	−0.0128549	+	0.0272195i
$636$	−1750.29	−	2723.50i	−0.109125	−	0.169801i
$637$	7760.06	−	4237.31i	0.482676	−	0.263561i
$638$	4738.84	+	3547.45i	0.294064	+	0.220133i
$639$	8728.59	+	3986.22i	0.540372	+	0.246780i
$640$	−758.206	−	1213.72i	−0.0468292	−	0.0749635i
$641$	−10112.0	+	15734.6i	−0.623088	+	0.969544i	0.375990	+	0.926624i	$0.377303\pi$
$641$	−10112.0	+	15734.6i	−0.623088	+	0.969544i	−0.999078	+	0.0429205i	$0.986334\pi$
$642$	−2126.76	+	29736.0i	−0.130742	+	1.82802i
$643$	−14668.9	+	14668.9i	−0.899667	+	0.899667i	−0.995406	−	0.0957393i	$-0.969478\pi$
$643$	−14668.9	+	14668.9i	−0.899667	+	0.899667i	0.0957393	+	0.995406i	$0.469478\pi$
$644$	10210.0	+	11213.4i	0.624737	+	0.686133i
$645$	−1219.09	+	14441.0i	−0.0744214	+	0.881572i
$646$	−4844.78	−	5591.18i	−0.295070	−	0.340529i
$647$	−17753.6	+	3862.06i	−1.07877	+	0.234673i	−0.716633	−	0.697451i	$-0.754318\pi$
$647$	−17753.6	+	3862.06i	−1.07877	+	0.234673i	−0.362140	+	0.932124i	$0.617954\pi$
$648$	−3029.57	+	2267.91i	−0.183662	+	0.137488i
$649$	−17965.4	+	39338.8i	−1.08660	+	2.37933i
$650$	67.5884	−	2635.59i	0.00407852	−	0.159041i
$651$	15996.1	−	54477.6i	0.963034	−	3.27979i
$652$	448.573	−	2062.06i	0.0269440	−	0.123860i
$653$	7343.14	−	19687.7i	0.440060	−	1.17985i	−0.507888	−	0.861423i	$-0.669574\pi$
$653$	7343.14	−	19687.7i	0.440060	−	1.17985i	0.947948	−	0.318424i	$-0.103154\pi$
$654$	9941.65	−	2919.13i	0.594418	−	0.174537i
$655$	11941.8	+	12252.0i	0.712374	+	0.730876i
$656$	534.897	−	617.304i	0.0318357	−	0.0367404i
$657$	11568.4	−	21186.0i	0.686952	−	1.25806i
$658$	−27171.6	−	10134.5i	−1.60982	−	0.600431i
$659$	12564.1	−	8074.45i	0.742682	−	0.477293i	−0.113778	−	0.993506i	$-0.536295\pi$
$659$	12564.1	−	8074.45i	0.742682	−	0.477293i	0.856460	+	0.516213i	$0.172659\pi$
$660$	−22292.5	+	9837.25i	−1.31475	+	0.580174i
$661$	−8523.65	+	1225.52i	−0.501560	+	0.0721135i	−0.388452	−	0.921469i	$-0.626990\pi$
$661$	−8523.65	+	1225.52i	−0.501560	+	0.0721135i	−0.113109	+	0.993583i	$0.536081\pi$
$662$	−5258.87	−	14099.6i	−0.308749	−	0.827788i
$663$	1629.71	+	2177.04i	0.0954643	+	0.127525i
$664$	1104.24	+	709.655i	0.0645376	+	0.0414758i
$665$	−42684.2	−	6696.62i	−2.48906	−	0.390502i
$666$		−	1013.44i		−	0.0589641i
$667$	4065.41	−	2351.49i	0.236002	−	0.136507i
$668$	4981.75	+	4981.75i	0.288547	+	0.288547i
$669$	−19492.0	+	16889.9i	−1.12647	+	0.976088i
$670$	−3727.79	+	4848.91i	−0.214951	+	0.279597i
$671$	−6026.33	+	41914.0i	−0.346712	+	2.41144i
$672$	8077.28	−	3012.67i	0.463673	−	0.172941i
$673$	−9768.83	+	13049.6i	−0.559526	+	0.747439i	−0.987718	−	0.156249i	$-0.950060\pi$
$673$	−9768.83	+	13049.6i	−0.559526	+	0.747439i	0.428192	+	0.903688i	$0.359151\pi$
$674$	10002.5	+	2936.99i	0.571634	+	0.167847i
$675$	2719.10	−	6755.96i	0.155049	−	0.385240i
$676$	−3465.87	−	7589.19i	−0.197193	−	0.431793i
$677$	10600.4	+	5788.26i	0.601782	+	0.328598i	0.751097	−	0.660192i	$-0.229525\pi$
$677$	10600.4	+	5788.26i	0.601782	+	0.328598i	−0.149315	+	0.988790i	$0.547707\pi$
$678$	780.254	+	10909.4i	0.0441968	+	0.617953i
$679$	−24894.3	−	21571.0i	−1.40700	−	1.21917i
$680$	2883.23	−	588.603i	0.162598	−	0.0331940i
$681$	31575.5	−	14420.1i	1.77676	−	0.811421i
$682$	−28631.5	−	6228.39i	−1.60756	−	0.349703i
$683$	5558.30	+	10179.3i	0.311394	+	0.570276i	0.985767	−	0.168115i	$-0.0537678\pi$
$683$	5558.30	+	10179.3i	0.311394	+	0.570276i	−0.674373	+	0.738391i	$0.735586\pi$
$684$	−2203.85	−	15328.1i	−0.123196	−	0.856850i
$685$	3256.00	+	11638.8i	0.181614	+	0.649192i
$686$	33708.2	+	4846.50i	1.87607	+	0.269738i
$687$	−5876.51	−	27013.9i	−0.326350	−	1.50021i
$688$	−2639.34	−	188.769i	−0.146255	−	0.0104604i
$689$	1088.98			0.0602131
$690$	227.705	+	19330.7i	0.0125632	+	1.06653i
$691$	9738.97			0.536162			0.268081	−	0.963396i	$-0.413611\pi$
$691$	9738.97			0.536162			0.268081	+	0.963396i	$0.413611\pi$
$692$	−2677.50	−	191.499i	−0.147086	−	0.0105198i
$693$	−17488.2	−	80391.7i	−0.958615	−	4.40668i
$694$	18899.6	+	2717.36i	1.03375	+	0.148630i
$695$	4252.82	−	7556.52i	0.232113	−	0.412425i
$696$	−379.948	−	2642.59i	−0.0206924	−	0.143919i
$697$	804.939	+	1474.14i	0.0437435	+	0.0801103i
$698$	311.807	+	67.8295i	0.0169084	+	0.00367820i
$699$	18141.6	−	8284.97i	0.981654	−	0.448307i
$700$	10648.3	−	13489.3i	0.574955	−	0.728355i
$701$	25094.6	+	21744.6i	1.35208	+	1.17159i	0.968769	+	0.247967i	$0.0797624\pi$
$701$	25094.6	+	21744.6i	1.35208	+	1.17159i	0.383313	+	0.923619i	$0.374783\pi$
$702$	87.6631	+	1225.69i	0.00471315	+	0.0658984i
$703$	−1452.19	−	792.954i	−0.0779093	−	0.0425417i
$704$	−1848.16	−	4046.90i	−0.0989418	−	0.216652i
$705$	−17299.6	−	32670.7i	−0.924170	−	1.74532i
$706$	−21901.5	−	6430.85i	−1.16752	−	0.342816i
$707$	−39130.5	+	52272.3i	−2.08155	+	2.78062i
$708$	18275.0	−	6816.21i	0.970078	−	0.361820i
$709$	1057.73	−	7356.65i	0.0560279	−	0.389682i	−0.942441	−	0.334372i	$-0.891476\pi$
$709$	1057.73	−	7356.65i	0.0560279	−	0.389682i	0.998469	−	0.0553108i	$-0.0176150\pi$
$710$	807.681	+	6178.84i	0.0426926	+	0.326603i
$711$	−14116.2	+	12231.7i	−0.744583	+	0.645185i
$712$	−1415.32	−	1415.32i	−0.0744963	−	0.0744963i
$713$	−13469.5	+	18947.3i	−0.707486	+	0.995205i
$714$			17726.8i			0.929142i
$715$	1270.34	−	8097.16i	0.0664450	−	0.423520i
$716$	−12976.0	−	8339.19i	−0.677286	−	0.435266i
$717$	13636.7	+	18216.5i	0.710282	+	0.948825i
$718$	203.606	+	545.889i	0.0105829	+	0.0283738i
$719$	−24204.3	+	3480.05i	−1.25545	+	0.180506i	−0.737761	−	0.675063i	$-0.764117\pi$
$719$	−24204.3	+	3480.05i	−1.25545	+	0.180506i	−0.517689	+	0.855569i	$0.673208\pi$
$720$	5743.17	+	2226.36i	0.297271	+	0.115238i
$721$	−6683.86	+	4295.45i	−0.345243	+	0.221874i
$722$	−10835.3	−	4041.37i	−0.558517	−	0.208316i
$723$	−6440.97	+	11795.8i	−0.331317	+	0.606762i
$724$	−7026.24	+	8108.71i	−0.360674	+	0.416240i
$725$	−3381.05	−	4110.29i	−0.173199	−	0.210555i
$726$	−52662.6	+	15463.1i	−2.69214	+	0.790483i
$727$	5569.64	−	14932.8i	0.284135	−	0.761796i	−0.713965	−	0.700182i	$-0.753102\pi$
$727$	5569.64	−	14932.8i	0.284135	−	0.761796i	0.998100	−	0.0616145i	$-0.0196249\pi$
$728$	−616.397	+	2833.53i	−0.0313808	+	0.144255i
$729$	8062.65	−	27458.9i	0.409625	−	1.39505i
$730$	15648.6	−	917.751i	0.793398	−	0.0465308i
$731$	2260.30	−	4949.36i	0.114364	−	0.250422i
$732$	15288.7	−	11445.0i	0.771977	−	0.577895i
$733$	32149.9	−	6993.78i	1.62003	−	0.352416i	0.691127	−	0.722734i	$-0.257115\pi$
$733$	32149.9	−	6993.78i	1.62003	−	0.352416i	0.928905	+	0.370317i	$0.120751\pi$
$734$	−166.153	−	191.751i	−0.00835535	−	0.00964259i
$735$	47396.3	+	56136.4i	2.37856	+	2.81718i
$736$	−3528.66	+	86.8167i	−0.176723	+	0.00434797i
$737$	−13445.0	+	13445.0i	−0.671985	+	0.671985i
$738$	−250.805	+	3506.72i	−0.0125099	+	0.174911i
$739$	−9440.18	+	14689.2i	−0.469909	+	0.731193i	−0.992613	−	0.121321i	$-0.961287\pi$
$739$	−9440.18	+	14689.2i	−0.469909	+	0.731193i	0.522704	+	0.852514i	$0.324923\pi$
$740$	558.164	−	348.681i	0.0277277	−	0.0173213i
$741$	8453.63	+	3860.64i	0.419098	+	0.191396i
$742$	5682.64	+	4253.97i	0.281154	+	0.210469i
$743$	−3970.01	+	2167.79i	−0.196023	+	0.107037i	−0.574263	−	0.818671i	$-0.694711\pi$
$743$	−3970.01	+	2167.79i	−0.196023	+	0.107037i	0.378240	+	0.925708i	$0.376530\pi$
$744$	7144.59	+	11117.2i	0.352061	+	0.547818i
$745$	35134.9	−	12594.0i	1.72784	−	0.619339i
$746$	5689.44	+	19376.5i	0.279229	+	0.950968i
$747$	−5635.31	+	403.045i	−0.276018	+	0.0197412i
$748$	9124.93	−	652.628i	0.446043	−	0.0319016i
$749$	−18415.9	−	62718.9i	−0.898402	−	3.05968i
$750$	21570.3	−	3830.30i	1.05018	−	0.186484i
$751$	−6437.66	−	10017.2i	−0.312801	−	0.486728i	0.648883	−	0.760888i	$-0.275236\pi$
$751$	−6437.66	−	10017.2i	−0.312801	−	0.486728i	−0.961684	+	0.274160i	$0.911600\pi$
$752$	5924.17	−	3234.84i	0.287277	−	0.156865i
$753$	−27926.5	−	20905.5i	−1.35152	−	1.01174i
$754$	816.881	+	373.057i	0.0394550	+	0.0180185i
$755$	6018.64	+	1390.31i	0.290120	+	0.0670181i
$756$	−4330.56	+	6738.48i	−0.208334	+	0.324175i
$757$	−1521.64	+	21275.3i	−0.0730581	+	1.02149i	0.820239	+	0.572020i	$0.193840\pi$
$757$	−1521.64	+	21275.3i	−0.0730581	+	1.02149i	−0.893298	+	0.449466i	$0.851614\pi$
$758$	2616.57	−	2616.57i	0.125380	−	0.125380i
$759$	−7087.30	+	59680.0i	−0.338936	+	2.85408i
$760$	7683.87	−	6487.53i	0.366741	−	0.309642i
$761$	−7348.98	−	8481.18i	−0.350066	−	0.403998i	0.553221	−	0.833035i	$-0.313399\pi$
$761$	−7348.98	−	8481.18i	−0.350066	−	0.403998i	−0.903287	+	0.429037i	$0.858853\pi$
$762$	659.928	−	143.559i	0.0313736	−	0.00682491i
$763$	−18187.2	+	13614.8i	−0.862938	+	0.645987i
$764$	541.315	−	1185.31i	0.0256336	−	0.0561298i
$765$	−8416.37	+	9465.07i	−0.397771	+	0.447334i
$766$	6378.04	−	21721.6i	0.300846	−	1.02459i
$767$	−1394.61	+	6410.91i	−0.0656537	+	0.301805i
$768$	−701.204	+	1880.00i	−0.0329460	+	0.0883316i
$769$	−7486.56	+	2198.25i	−0.351069	+	0.103083i	−0.452512	−	0.891758i	$-0.649472\pi$
$769$	−7486.56	+	2198.25i	−0.351069	+	0.103083i	0.101443	+	0.994841i	$0.467654\pi$
$770$	38259.6	−	37291.1i	1.79063	−	1.74529i
$771$	23427.1	−	27036.3i	1.09430	−	1.26289i
$772$	−3182.68	+	5828.64i	−0.148377	+	0.271733i
$773$	−6083.20	−	2268.92i	−0.283050	−	0.105572i	0.203930	−	0.978986i	$-0.434629\pi$
$773$	−6083.20	−	2268.92i	−0.283050	−	0.105572i	−0.486980	+	0.873413i	$0.661901\pi$
$774$	9581.14	−	6157.42i	0.444944	−	0.285948i
$775$	23675.2	+	11554.6i	1.09734	+	0.535551i
$776$	7588.77	−	1091.10i	0.351058	−	0.0504745i
$777$	1385.46	+	3714.56i	0.0639679	+	0.171505i
$778$	−4744.01	−	6337.25i	−0.218613	−	0.292033i
$779$	4828.62	+	3103.17i	0.222084	+	0.142725i
$780$	−2987.40	+	2177.15i	−0.137136	+	0.0999415i
$781$			19372.1i			0.887567i
$782$	2368.41	−	6860.79i	0.108305	−	0.313736i
$783$	1754.06	+	1754.06i	0.0800575	+	0.0800575i
$784$	−10137.9	+	8784.50i	−0.461819	+	0.400169i
$785$	10416.7	−	1361.64i	0.473614	−	0.0619095i
$786$	3413.90	−	23744.2i	0.154923	−	1.07752i
$787$	−22666.2	+	8454.04i	−1.02663	+	0.382915i	−0.805668	−	0.592367i	$-0.798194\pi$
$787$	−22666.2	+	8454.04i	−1.02663	+	0.382915i	−0.220966	+	0.975282i	$0.570921\pi$
$788$	−1575.82	+	2105.05i	−0.0712388	+	0.0951639i
$789$	−61536.0	−	18068.6i	−2.77660	−	0.815285i
$790$	−11593.5	−	3566.22i	−0.522125	−	0.160608i
$791$	−9962.21	−	21814.2i	−0.447807	−	0.980561i
$792$	16806.6	+	9177.10i	0.754036	+	0.411735i
$793$	458.284	+	6407.65i	0.0205223	+	0.286939i
$794$	13549.4	+	11740.6i	0.605604	+	0.524759i
$795$	1809.97	+	8866.02i	0.0807461	+	0.395529i
$796$	−1302.80	+	594.969i	−0.0580107	+	0.0264926i
$797$	−27750.9	−	6036.83i	−1.23336	−	0.268300i	−0.451792	−	0.892123i	$-0.649215\pi$
$797$	−27750.9	−	6036.83i	−1.23336	−	0.268300i	−0.781566	+	0.623823i	$0.785579\pi$
$798$	29032.5	+	53169.1i	1.28790	+	2.35861i
$799$	1975.25	+	13738.2i	0.0874586	+	0.608288i
$800$	749.781	+	3929.10i	0.0331359	+	0.173643i
$801$	8527.35	+	1226.05i	0.376154	+	0.0540827i
$802$	−439.431	−	2020.03i	−0.0193477	−	0.0889399i
$803$	48607.6	+	3476.49i	2.13615	+	0.152780i
$804$	8575.53			0.376164
$805$	−15279.9	−	39538.3i	−0.669001	−	1.73111i
$806$	−4445.17			−0.194261
$807$	−45972.4	−	3288.01i	−2.00533	−	0.143424i
$808$	−3230.52	−	14850.5i	−0.140655	−	0.646581i
$809$	−8317.76	−	1195.91i	−0.361480	−	0.0519729i	−0.0408176	−	0.999167i	$-0.512996\pi$
$809$	−8317.76	−	1195.91i	−0.361480	−	0.0519729i	−0.320662	+	0.947194i	$0.603905\pi$
$810$	10186.6	−	2849.75i	0.441879	−	0.123617i
$811$	180.131	+	1252.84i	0.00779933	+	0.0542455i	0.993349	−	0.115139i	$-0.0367312\pi$
$811$	180.131	+	1252.84i	0.00779933	+	0.0542455i	−0.985550	+	0.169384i	$0.945822\pi$
$812$	2805.44	+	5137.78i	0.121246	+	0.222045i
$813$	16844.3	+	3664.26i	0.726638	+	0.158070i
$814$	1861.08	−	849.925i	0.0801360	−	0.0365969i
$815$	−3252.28	+	4920.78i	−0.139782	+	0.211494i
$816$	−3118.17	−	2701.91i	−0.133772	−	0.115914i
$817$	−1326.50	−	18546.8i	−0.0568032	−	0.794212i
$818$	22865.9	+	12485.7i	0.977370	+	0.533685i
$819$	−5184.87	−	11353.3i	−0.221214	−	0.484391i
$820$	−2017.65	+	1068.37i	−0.0859261	+	0.0454991i
$821$	9372.81	+	2752.10i	0.398433	+	0.116990i	0.474809	−	0.880089i	$-0.342517\pi$
$821$	9372.81	+	2752.10i	0.398433	+	0.116990i	−0.0763768	+	0.997079i	$0.524335\pi$
$822$	10154.9	−	13565.4i	0.430892	−	0.575604i
$823$	13449.2	−	5016.30i	0.569636	−	0.212463i	−0.0481086	−	0.998842i	$-0.515319\pi$
$823$	13449.2	−	5016.30i	0.569636	−	0.212463i	0.617744	+	0.786379i	$0.288047\pi$
$824$	263.174	−	1830.42i	0.0111263	−	0.0773854i
$825$	68035.2	−	3115.53i	2.87113	−	0.131477i
$826$	−32320.9	+	28006.3i	−1.36149	+	1.17974i
$827$	2537.83	+	2537.83i	0.106710	+	0.106710i	0.758446	−	0.651736i	$-0.225959\pi$
$827$	2537.83	+	2537.83i	0.106710	+	0.106710i	−0.651736	+	0.758446i	$0.725959\pi$
$828$	11934.6	−	9400.91i	0.500913	−	0.394570i
$829$		−	43329.5i		−	1.81532i	−0.419711	−	0.907658i	$-0.637869\pi$
$829$		−	43329.5i		−	1.81532i	0.419711	−	0.907658i	$-0.362131\pi$
$830$	−2160.85	−	2965.03i	−0.0903663	−	0.123997i
$831$	40405.7	+	25967.2i	1.68671	+	1.08399i
$832$	−404.473	−	540.312i	−0.0168540	−	0.0225144i
$833$	−9639.43	−	25844.3i	−0.400944	−	1.07497i
$834$	−12033.9	+	1730.21i	−0.499640	+	0.0718373i
$835$	−7950.10	−	18016.0i	−0.329490	−	0.746668i
$836$	26300.2	−	16902.1i	1.08805	−	0.699248i
$837$	−11504.6	−	4290.99i	−0.475097	−	0.177202i
$838$	−3118.56	+	5711.21i	−0.128555	+	0.235430i
$839$	25676.9	−	29632.8i	1.05657	−	1.21935i	0.0816866	−	0.996658i	$-0.473969\pi$
$839$	25676.9	−	29632.8i	1.05657	−	1.21935i	0.974888	−	0.222694i	$-0.0714852\pi$
$840$	−24094.0	−	308.888i	−0.989668	−	0.0126877i
$841$	−21661.6	+	6360.43i	−0.888173	+	0.260791i
$842$	−5330.09	+	14290.5i	−0.218156	+	0.584898i
$843$	−1137.98	+	5231.23i	−0.0464938	+	0.213728i
$844$	2936.59	−	10001.1i	0.119765	−	0.407882i
$845$	1365.30	+	23279.8i	0.0555832	+	0.947750i
$846$	−12068.7	+	26426.8i	−0.490463	+	1.07396i
$847$	96340.7	−	72119.7i	3.90827	−	2.92569i
$848$	−1614.43	+	351.197i	−0.0653770	+	0.0142219i
$849$	−11533.2	−	13310.0i	−0.466215	−	0.538041i
$850$	−8108.69	−	1378.88i	−0.327207	−	0.0556414i
$851$	−39.9250	−	1622.75i	−0.00160824	−	0.0653669i
$852$	6178.00	−	6178.00i	0.248421	−	0.248421i
$853$	16.0728	−	224.728i	0.000645162	−	0.00902055i	−0.997119	−	0.0758487i	$-0.975833\pi$
$853$	16.0728	−	224.728i	0.000645162	−	0.00902055i	0.997764	+	0.0668282i	$0.0212879\pi$
$854$	−22639.3	+	35227.4i	−0.907142	+	1.41154i
$855$	−9742.10	+	42173.4i	−0.389676	+	1.68690i
$856$	13839.3	+	6320.21i	0.552591	+	0.252360i
$857$	16073.1	+	12032.1i	0.640659	+	0.479592i	0.869540	−	0.493863i	$-0.164416\pi$
$857$	16073.1	+	12032.1i	0.640659	+	0.479592i	−0.228880	+	0.973455i	$0.573506\pi$
$858$	−10086.1	+	5507.45i	−0.401323	+	0.219139i
$859$	−22500.3	−	35011.2i	−0.893714	−	1.39065i	−0.920390	−	0.391002i	$-0.872128\pi$
$859$	−22500.3	−	35011.2i	−0.893714	−	1.39065i	0.0266754	−	0.999644i	$-0.491508\pi$
$860$	6687.71	+	3158.40i	0.265173	+	0.125233i
$861$	−3874.69	−	13196.0i	−0.153367	−	0.522321i
$862$	−21154.7	+	1513.01i	−0.835884	+	0.0597836i
$863$	−2885.68	+	206.388i	−0.113823	+	0.00814081i	−0.128135	−	0.991757i	$-0.540899\pi$
$863$	−2885.68	+	206.388i	−0.113823	+	0.00814081i	0.0143113	+	0.999898i	$0.495444\pi$
$864$	−525.248	−	1788.83i	−0.0206821	−	0.0704367i
$865$	6784.41	+	3204.07i	0.266679	+	0.125944i
$866$	−201.220	−	313.105i	−0.00789577	−	0.0122861i
$867$	−26351.2	+	14388.8i	−1.03222	+	0.563634i
$868$	−23196.3	−	17364.5i	−0.907065	−	0.679021i
$869$	−34300.8	−	15664.7i	−1.33898	−	0.611493i
$870$	−1679.55	+	7270.76i	−0.0654508	+	0.283336i
$871$	−1559.51	+	2426.65i	−0.0606683	+	0.0944017i
$872$	377.227	−	5274.33i	0.0146497	−	0.204829i
$873$	−23333.9	+	23333.9i	−0.904618	+	0.904618i
$874$	−4132.73	−	24457.0i	−0.159945	−	0.946533i
$875$	−41378.7	+	24397.0i	−1.59869	+	0.942595i
$876$	−14392.8	−	16610.2i	−0.555124	−	0.640647i
$877$	13286.9	−	2890.39i	0.511593	−	0.111290i	0.0506438	−	0.998717i	$-0.483873\pi$
$877$	13286.9	−	2890.39i	0.511593	−	0.111290i	0.460949	+	0.887427i	$0.347509\pi$
$878$	19838.8	−	14851.1i	0.762558	−	0.570844i
$879$	12368.3	−	27082.8i	0.474599	−	1.03923i
$880$	728.041	+	12413.8i	0.0278889	+	0.475535i
$881$	11736.8	−	39971.9i	0.448834	−	1.52859i	−0.355653	−	0.934618i	$-0.615741\pi$
$881$	11736.8	−	39971.9i	0.448834	−	1.52859i	0.804487	−	0.593970i	$-0.202440\pi$
$882$	12272.9	−	56417.7i	0.468538	−	2.15384i
$883$	−4304.82	+	11541.7i	−0.164064	+	0.439873i	−0.992802	−	0.119763i	$-0.961786\pi$
$883$	−4304.82	+	11541.7i	−0.164064	+	0.439873i	0.828738	+	0.559636i	$0.189059\pi$
$884$	1331.63	−	391.002i	0.0506646	−	0.0148765i
$885$	−54512.9	−	698.863i	−2.07054	−	0.0265447i
$886$	3492.46	−	4030.51i	0.132428	−	0.152830i
$887$	−14423.2	+	26414.1i	−0.545979	+	0.999885i	0.448383	+	0.893842i	$0.352000\pi$
$887$	−14423.2	+	26414.1i	−0.545979	+	0.999885i	−0.994361	+	0.106044i	$0.966182\pi$
$888$	−864.569	−	322.468i	−0.0326723	−	0.0121862i
$889$	−1245.75	+	800.593i	−0.0469977	+	0.0302036i
$890$	2258.63	+	5118.35i	0.0850669	+	0.192773i
$891$	32549.3	−	4679.88i	1.22384	−	0.175962i
$892$	4599.81	+	12332.6i	0.172660	+	0.462921i
$893$	28424.6	+	37970.9i	1.06517	+	1.42290i
$894$	−44024.0	−	28292.5i	−1.64696	−	1.05844i
$895$	25392.2	+	34842.2i	0.948344	+	1.30128i
$896$		−	4399.54i		−	0.164038i
$897$	873.917	+	9075.49i	0.0325298	+	0.337817i
$898$	−12685.9	−	12685.9i	−0.471420	−	0.471420i
$899$	−6781.68	+	5876.35i	−0.251592	+	0.218006i
$900$	−12718.1	−	11604.3i	−0.471042	−	0.429790i
$901$	483.492	−	3362.76i	0.0178773	−	0.124339i
$902$	−6650.04	+	2480.34i	−0.245479	+	0.0915590i
$903$	−26699.9	+	35666.9i	−0.983962	+	1.31442i
$904$	5355.60	+	1572.54i	0.197040	+	0.0578563i
$905$	26503.2	−	14033.8i	0.973477	−	0.515470i
$906$	−3597.87	−	7878.24i	−0.131933	−	0.288893i
$907$	9113.96	+	4976.60i	0.333654	+	0.182189i	0.637339	−	0.770584i	$-0.280035\pi$
$907$	9113.96	+	4976.60i	0.333654	+	0.182189i	−0.303685	+	0.952773i	$0.598217\pi$
$908$	−1263.78	−	17669.9i	−0.0461894	−	0.645812i
$909$	49436.3	+	42836.8i	1.80385	+	1.56304i
$910$	4469.05	−	6761.79i	0.162799	−	0.246320i
$911$	2897.10	−	1323.06i	0.105363	−	0.0481175i	−0.362036	−	0.932164i	$-0.617918\pi$
$911$	2897.10	−	1323.06i	0.105363	−	0.0481175i	0.467399	+	0.884046i	$0.345191\pi$
$912$	−13777.7	−	2997.15i	−0.500246	−	0.108822i
$913$	−5466.21	−	10010.6i	−0.198144	−	0.362873i
$914$	1320.56	+	9184.70i	0.0477902	+	0.332388i
$915$	−51406.8	+	14381.2i	−1.85733	+	0.519594i
$916$	−13965.0	−	2007.87i	−0.503731	−	0.0724256i
$917$	11180.4	+	51395.7i	0.402629	+	1.85086i
$918$	3823.85	+	273.487i	0.137479	+	0.00983269i
$919$	29862.2			1.07189			0.535943	−	0.844254i	$-0.319956\pi$
$919$	29862.2			1.07189			0.535943	+	0.844254i	$0.319956\pi$
$920$	9283.82	+	3338.66i	0.332694	+	0.119644i
$921$	−24649.3			−0.881891
$922$	−28036.2	−	2005.19i	−1.00144	−	0.0716241i
$923$	624.704	+	2871.72i	0.0222778	+	0.102409i
$924$	−74146.8	−	10660.7i	−2.63988	−	0.379558i
$925$	−1806.90	+	344.807i	−0.0642277	+	0.0122564i
$926$	5.06088	+	35.1992i	0.000179601	+	0.00124916i
$927$	3814.53	+	6985.80i	0.135152	+	0.247512i
$928$	−1331.35	−	289.617i	−0.0470945	−	0.0102448i
$929$	−22433.6	+	10245.1i	−0.792272	+	0.361819i	−0.770090	−	0.637935i	$-0.779789\pi$
$929$	−22433.6	+	10245.1i	−0.792272	+	0.361819i	−0.0221825	+	0.999754i	$0.507061\pi$
$930$	−7388.23	−	36190.7i	−0.260505	−	1.27607i
$931$	−71239.5	−	61729.4i	−2.50782	−	2.17304i
$932$	−726.098	−	10152.2i	−0.0255195	−	0.356809i
$933$	56575.6	+	30892.6i	1.98521	+	1.08401i
$934$	−5053.07	−	11064.7i	−0.177025	−	0.387631i
$935$	−24440.0	−	7517.84i	−0.854837	−	0.262952i
$936$	2787.34	+	818.437i	0.0973367	+	0.0285806i
$937$	22086.7	−	29504.3i	0.770053	−	1.02867i	−0.228427	−	0.973561i	$-0.573358\pi$
$937$	22086.7	−	29504.3i	0.770053	−	1.02867i	0.998480	−	0.0551096i	$-0.0175508\pi$
$938$	−17617.4	+	6570.97i	−0.613252	+	0.228731i
$939$	−10716.0	+	74531.4i	−0.372421	+	2.59025i
$940$	−18707.2	+	2445.35i	−0.649106	+	0.0848494i
$941$	16146.1	−	13990.6i	0.559348	−	0.484678i	−0.328696	−	0.944436i	$-0.606609\pi$
$941$	16146.1	−	13990.6i	0.559348	−	0.484678i	0.888044	+	0.459758i	$0.152064\pi$
$942$	−10415.3	−	10415.3i	−0.360241	−	0.360241i
$943$	−263.448	+	5624.93i	−0.00909760	+	0.194245i
$944$		−	9954.02i		−	0.343195i
$945$	18093.6	−	13186.2i	0.622843	−	0.453913i
$946$	19342.7	+	12430.8i	0.664782	+	0.427230i
$947$	−7014.94	−	9370.86i	−0.240713	−	0.321554i	0.663874	−	0.747845i	$-0.268911\pi$
$947$	−7014.94	−	9370.86i	−0.240713	−	0.321554i	−0.904587	+	0.426290i	$0.859820\pi$
$948$	5943.28	+	15934.6i	0.203617	+	0.545918i
$949$	7317.68	−	1052.12i	0.250308	−	0.0359888i
$950$	−26579.2	+	9144.47i	−0.907731	+	0.312301i
$951$	−11290.1	+	7255.72i	−0.384971	+	0.247406i
$952$	8476.26	+	3161.48i	0.288568	+	0.107630i
$953$	13822.1	−	25313.2i	0.469822	−	0.860415i	−0.530100	−	0.847935i	$-0.677846\pi$
$953$	13822.1	−	25313.2i	0.469822	−	0.860415i	0.999922	−	0.0124798i	$-0.00397254\pi$
$954$	4656.88	−	5374.33i	0.158042	−	0.182390i
$955$	−2608.22	+	2542.19i	−0.0883770	+	0.0861396i
$956$	11142.5	−	3271.72i	0.376959	−	0.110685i
$957$	−8107.05	+	21735.9i	−0.273839	+	0.734190i
$958$	2588.70	−	11900.0i	0.0873037	−	0.401329i
$959$	−10467.7	+	35649.7i	−0.352470	+	1.20040i
$960$	3726.73	−	4191.09i	0.125291	−	0.140903i
$961$	6076.06	−	13304.7i	0.203956	−	0.446602i
$962$	248.477	−	186.008i	0.00832768	−	0.00623402i
$963$	−63987.7	+	13919.7i	−2.14120	+	0.465789i
$964$	4491.56	+	5183.54i	0.150066	+	0.173185i
$965$	14183.0	−	11974.8i	0.473125	−	0.399462i
$966$	−30891.9	+	50772.6i	−1.02892	+	1.69108i
$967$	−1190.51	+	1190.51i	−0.0395908	+	0.0395908i	−0.726625	−	0.687034i	$-0.758912\pi$
$967$	−1190.51	+	1190.51i	−0.0395908	+	0.0395908i	0.687034	+	0.726625i	$0.258912\pi$
$968$	−1998.24	+	27939.0i	−0.0663489	+	0.927679i
$969$	15674.9	−	24390.7i	0.519661	−	0.808609i
$970$	−20879.5	−	4823.19i	−0.691135	−	0.159653i
$971$	27315.7	+	12474.6i	0.902782	+	0.412287i	0.812049	−	0.583589i	$-0.198352\pi$
$971$	27315.7	+	12474.6i	0.902782	+	0.412287i	0.0907323	+	0.995875i	$0.471079\pi$
$972$	−16910.0	−	12658.6i	−0.558011	−	0.417722i
$973$	23396.5	−	12775.4i	0.770870	−	0.420927i
$974$	−4861.90	−	7565.26i	−0.159944	−	0.248877i
$975$	9985.03	−	2655.81i	0.327976	−	0.0872349i
$976$	−2745.89	−	9351.64i	−0.0900551	−	0.306699i
$977$	13858.8	−	991.203i	0.453821	−	0.0324579i	0.157442	−	0.987528i	$-0.449675\pi$
$977$	13858.8	−	991.203i	0.453821	−	0.0324579i	0.296379	+	0.955070i	$0.404221\pi$
$978$	8249.06	−	589.985i	0.269710	−	0.0192900i
$979$	4899.97	+	16687.8i	0.159963	+	0.544784i
$980$	35295.2	−	12651.4i	1.15047	−	0.412383i
$981$	12304.7	+	19146.5i	0.400468	+	0.623140i
$982$	35390.5	−	19324.7i	1.15006	−	0.627978i
$983$	−33182.5	−	24840.1i	−1.07666	−	0.805977i	−0.0947825	−	0.995498i	$-0.530216\pi$
$983$	−33182.5	−	24840.1i	−1.07666	−	0.805977i	−0.981877	+	0.189521i	$0.939306\pi$
$984$	2911.78	+	1329.77i	0.0943335	+	0.0430807i
$985$	6233.44	−	3893.99i	0.201638	−	0.125962i
$986$	1514.68	−	2356.89i	0.0489222	−	0.0761245i
$987$	8107.72	−	113361.i	0.261471	−	3.65584i
$988$	3353.67	−	3353.67i	0.107990	−	0.107990i
$989$	15099.0	−	10236.9i	0.485460	−	0.329134i
$990$	−34528.6	−	40895.8i	−1.10848	−	1.31288i
$991$	−23978.7	−	27672.9i	−0.768626	−	0.887041i	0.227608	−	0.973753i	$-0.426910\pi$
$991$	−23978.7	−	27672.9i	−0.768626	−	0.887041i	−0.996233	+	0.0867117i	$0.972364\pi$
$992$	6590.02	−	1433.57i	0.210921	−	0.0458830i
$993$	47211.2	−	35341.9i	1.50876	−	1.12945i
$994$	−7958.12	+	17425.9i	−0.253940	+	0.556051i
$995$	3996.33	−	234.375i	0.127329	−	0.00746752i
$996$	−1449.26	+	4935.73i	−0.0461060	+	0.157023i
$997$	4761.74	−	21889.4i	0.151260	−	0.695330i	−0.837576	−	0.546321i	$-0.816028\pi$
$997$	4761.74	−	21889.4i	0.151260	−	0.695330i	0.988836	−	0.149009i	$-0.0476083\pi$
$998$	11385.7	−	30526.3i	0.361131	−	0.968229i
$999$	822.643	−	241.550i	0.0260533	−	0.00764994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.l.a.33.34	yes	720
5.2	odd	4	inner	230.4.l.a.217.16	yes	720
23.7	odd	22	inner	230.4.l.a.53.16	yes	720
115.7	even	44	inner	230.4.l.a.7.34	✓	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.l.a.7.34	✓	720	115.7	even	44	inner
230.4.l.a.33.34	yes	720	1.1	even	1	trivial
230.4.l.a.53.16	yes	720	23.7	odd	22	inner
230.4.l.a.217.16	yes	720	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.99490 + 0.142678i) q^{2} +(1.66607 + 7.65881i) q^{3} +(3.95929 + 0.569259i) q^{4} +(-9.74326 - 5.48352i) q^{5} +(2.23091 + 15.5163i) q^{6} +(-16.4725 - 30.1671i) q^{7} +(7.81717 + 1.70052i) q^{8} +(-31.3215 + 14.3041i) q^{9} +(-18.6545 - 12.3292i) q^{10} +(-52.5357 - 45.5225i) q^{11} +(2.23661 + 31.2719i) q^{12} +(-9.25586 - 5.05408i) q^{13} +(-28.5568 - 62.5307i) q^{14} +(25.7643 - 83.7577i) q^{15} +(15.3519 + 4.50772i) q^{16} +(-19.7165 + 26.3381i) q^{17} +(-64.5244 + 24.0663i) q^{18} +(-16.0009 + 111.289i) q^{19} +(-35.4548 - 27.2572i) q^{20} +(203.600 - 176.420i) q^{21} +(-98.3086 - 98.3086i) q^{22} +(-102.370 + 41.0776i) q^{23} +62.7035i q^{24} +(64.8621 + 106.855i) q^{25} +(-17.7434 - 11.4030i) q^{26} +(-34.9145 - 46.6403i) q^{27} +(-48.0463 - 128.817i) q^{28} +(-42.1443 + 6.05944i) q^{29} +(63.3476 - 163.413i) q^{30} +(177.298 - 113.943i) q^{31} +(29.9824 + 11.1829i) q^{32} +(261.120 - 478.205i) q^{33} +(-43.0903 + 49.7289i) q^{34} +(-4.92617 + 384.253i) q^{35} +(-132.154 + 38.8038i) q^{36} +(-5.14274 + 13.7882i) q^{37} +(-47.7988 + 219.728i) q^{38} +(23.2873 - 79.3093i) q^{39} +(-66.8399 - 59.4342i) q^{40} +(21.2072 - 46.4373i) q^{41} +(431.333 - 322.892i) q^{42} +(-161.600 + 35.1540i) q^{43} +(-182.090 - 210.143i) q^{44} +(383.610 + 32.3840i) q^{45} +(-210.079 + 67.3400i) q^{46} +(298.302 - 298.302i) q^{47} +(-8.94643 + 125.087i) q^{48} +(-453.270 + 705.302i) q^{49} +(114.148 + 222.419i) q^{50} +(-234.568 - 107.123i) q^{51} +(-33.7695 - 25.2795i) q^{52} +(-90.6305 + 49.4880i) q^{53} +(-62.9965 - 98.0245i) q^{54} +(262.246 + 731.617i) q^{55} +(-77.4684 - 263.833i) q^{56} +(-878.999 + 62.8673i) q^{57} +(-84.9384 + 6.07491i) q^{58} +(-175.273 - 596.926i) q^{59} +(149.688 - 316.954i) q^{60} +(-329.333 - 512.452i) q^{61} +(369.950 - 202.008i) q^{62} +(947.455 + 709.256i) q^{63} +(58.2164 + 26.5866i) q^{64} +(62.4681 + 99.9979i) q^{65} +(589.138 - 916.717i) q^{66} +(19.5131 - 272.829i) q^{67} +(-93.0563 + 93.0563i) q^{68} +(-485.162 - 715.595i) q^{69} +(-64.6518 + 765.844i) q^{70} +(-182.495 - 210.610i) q^{71} +(-269.170 + 58.5544i) q^{72} +(-561.202 + 420.111i) q^{73} +(-12.2266 + 26.7724i) q^{74} +(-710.315 + 674.794i) q^{75} +(-126.704 + 431.516i) q^{76} +(-507.886 + 2334.72i) q^{77} +(57.7717 - 154.892i) q^{78} +(520.480 - 152.827i) q^{79} +(-124.859 - 128.102i) q^{80} +(-309.783 + 357.508i) q^{81} +(48.9319 - 89.6122i) q^{82} +(153.732 + 57.3391i) q^{83} +(906.538 - 582.596i) q^{84} +(336.528 - 148.503i) q^{85} +(-327.393 + 47.0720i) q^{86} +(-116.624 - 312.680i) q^{87} +(-333.269 - 445.195i) q^{88} +(-210.478 - 135.266i) q^{89} +(760.646 + 119.336i) q^{90} +362.475i q^{91} +(-428.696 + 104.363i) q^{92} +(1168.06 + 1168.06i) q^{93} +(637.646 - 552.523i) q^{94} +(766.155 - 996.575i) q^{95} +(-35.6945 + 248.261i) q^{96} +(897.926 - 334.909i) q^{97} +(-1004.86 + 1342.34i) q^{98} +(2296.66 + 674.359i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q + 16 q^{3} + 16 q^{6} + 64 q^{12} - 192 q^{13} + 1152 q^{16} + 144 q^{18} + 1660 q^{23} - 880 q^{25} - 304 q^{26} - 728 q^{27} - 352 q^{28} - 608 q^{31} - 3872 q^{33} - 688 q^{35} - 2816 q^{36} - 2376 q^{37}+ \cdots + 14352 q^{98}+O(q^{100}) \) 720 * q + 16 * q^3 + 16 * q^6 + 64 * q^12 - 192 * q^13 + 1152 * q^16 + 144 * q^18 + 1660 * q^23 - 880 * q^25 - 304 * q^26 - 728 * q^27 - 352 * q^28 - 608 * q^31 - 3872 * q^33 - 688 * q^35 - 2816 * q^36 - 2376 * q^37 + 2208 * q^41 + 256 * q^46 + 3640 * q^47 - 256 * q^48 - 272 * q^50 - 768 * q^52 + 2360 * q^55 - 3872 * q^56 - 7656 * q^57 + 2112 * q^61 + 1376 * q^62 + 10912 * q^66 + 1104 * q^70 + 22752 * q^71 - 128 * q^72 + 1296 * q^73 - 5396 * q^75 + 752 * q^77 - 6000 * q^78 - 3928 * q^81 - 80 * q^82 + 3060 * q^85 - 10472 * q^86 - 6760 * q^87 - 1104 * q^92 + 5288 * q^93 + 9392 * q^95 - 256 * q^96 + 25344 * q^97 + 14352 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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