LMFDB - Embedded newform 230.4.l.a.7.34

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			7.34
Character	$\chi$	$=$	230.7
Dual form			230.4.l.a.33.34

$q$-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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{19}{22}\right)$

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	−0.481314	−	0.876548i	$-0.659840\pi$
$3$	1.66607	−	7.65881i	0.320636	−	1.47394i	0.801950	−	0.597391i	$-0.203796\pi$
$4$	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	−0.117580	+	0.993063i	$0.537514\pi$
$7$	−16.4725	+	30.1671i	−0.889430	+	1.62887i	−0.771850	+	0.635805i	$0.780668\pi$
$8$	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	−0.520992	+	0.853562i	$0.674438\pi$
$11$	−52.5357	+	45.5225i	−1.44001	+	1.24778i	−0.919019	+	0.394214i	$0.871017\pi$
$12$	2.23661	−	31.2719i	0.0538044	−	0.752284i
$13$	−9.25586	+	5.05408i	−0.197470	+	0.107827i	−0.574942	−	0.818194i	$-0.694975\pi$
$13$	−9.25586	+	5.05408i	−0.197470	+	0.107827i	0.377472	+	0.926021i	$0.376794\pi$
$14$	−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	0.637537	−	0.770420i	$-0.279953\pi$
$17$	−19.7165	−	26.3381i	−0.281291	−	0.375760i	−0.918827	+	0.394660i	$0.870863\pi$
$18$	−64.5244	−	24.0663i	−0.844919	−	0.315138i
$19$	−16.0009	−	111.289i	−0.193203	−	1.34376i	−0.823461	−	0.567373i	$-0.807960\pi$
$19$	−16.0009	−	111.289i	−0.193203	−	1.34376i	0.630258	−	0.776386i	$-0.282949\pi$
$20$	−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	0.00605528	−	0.999982i	$-0.498073\pi$
$29$	−42.1443	−	6.05944i	−0.269862	−	0.0388003i	−0.275917	+	0.961181i	$0.588982\pi$
$30$	63.3476	+	163.413i	0.385521	+	0.994497i
$31$	177.298	+	113.943i	1.02722	+	0.660151i	0.941793	−	0.336194i	$-0.109140\pi$
$31$	177.298	+	113.943i	1.02722	+	0.660151i	0.0854222	+	0.996345i	$0.472776\pi$
$32$	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	0.925024	−	0.379909i	$-0.124045\pi$
$37$	−5.14274	−	13.7882i	−0.0228503	−	0.0612640i	−0.947874	+	0.318645i	$0.896772\pi$
$38$	−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	0.945713	−	0.325004i	$-0.105366\pi$
$41$	21.2072	+	46.4373i	0.0807807	+	0.176885i	−0.864932	+	0.501889i	$0.832638\pi$
$42$	431.333	+	322.892i	1.58467	+	1.18627i
$43$	−161.600	−	35.1540i	−0.573112	−	0.124673i	−0.0833367	−	0.996521i	$-0.526558\pi$
$43$	−161.600	−	35.1540i	−0.573112	−	0.124673i	−0.489776	+	0.871848i	$0.662921\pi$
$44$	−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	0.997430	−	0.0716455i	$-0.0228250\pi$
$47$	298.302	+	298.302i	0.925785	+	0.925785i	−0.0716455	+	0.997430i	$0.522825\pi$
$48$	−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	0.357495	−	0.933915i	$-0.383631\pi$
$53$	−90.6305	−	49.4880i	−0.234888	−	0.128258i	−0.592383	+	0.805657i	$0.701813\pi$
$54$	−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	0.504398	+	0.863471i	$0.331715\pi$
$59$	−175.273	+	596.926i	−0.386757	+	1.31717i	−0.891154	+	0.453700i	$0.850104\pi$
$60$	149.688	+	316.954i	0.322077	+	0.681977i
$61$	−329.333	+	512.452i	−0.691258	+	1.07562i	0.301263	+	0.953541i	$0.402592\pi$
$61$	−329.333	+	512.452i	−0.691258	+	1.07562i	−0.992521	+	0.122077i	$0.961045\pi$
$62$	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	0.983729	+	0.179657i	$0.0574987\pi$
$67$	19.5131	+	272.829i	0.0355808	+	0.497484i	−0.948149	+	0.317827i	$0.897047\pi$
$68$	−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	−0.887488	−	0.460832i	$-0.847551\pi$
$71$	−182.495	+	210.610i	−0.305044	+	0.352040i	0.582444	+	0.812871i	$0.302097\pi$
$72$	−269.170	−	58.5544i	−0.440584	−	0.0958431i
$73$	−561.202	−	420.111i	−0.899778	−	0.673565i	0.0458039	−	0.998950i	$-0.485415\pi$
$73$	−561.202	−	420.111i	−0.899778	−	0.673565i	−0.945581	+	0.325385i	$0.894506\pi$
$74$	−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	0.630490	−	0.776198i	$-0.282854\pi$
$79$	520.480	+	152.827i	0.741248	+	0.217650i	0.110758	+	0.993847i	$0.464672\pi$
$80$	−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	−0.245749	−	0.969333i	$-0.579034\pi$
$83$	153.732	−	57.3391i	0.203305	−	0.0758287i	0.449054	+	0.893505i	$0.351761\pi$
$84$	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	−0.659947	−	0.751312i	$-0.729421\pi$
$89$	−210.478	+	135.266i	−0.250681	+	0.161103i	0.409266	+	0.912415i	$0.365785\pi$
$90$	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	0.772278	−	0.635285i	$-0.219117\pi$
$97$	897.926	+	334.909i	0.939903	+	0.350566i	0.167625	+	0.985851i	$0.446390\pi$
$98$	−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	−0.0680419	+	0.997682i	$0.521675\pi$
$101$	−789.173	+	1728.05i	−0.777482	+	1.70245i	−0.709440	+	0.704766i	$0.751052\pi$
$102$	−452.656	+	247.169i	−0.439408	+	0.239935i
$103$	−16.4904	+	230.566i	−0.0157752	+	0.220566i	0.983449	+	0.181185i	$0.0579933\pi$
$103$	−16.4904	+	230.566i	−0.0157752	+	0.220566i	−0.999224	+	0.0393814i	$0.987461\pi$
$104$	−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	0.730700	−	0.682699i	$-0.239194\pi$
$107$	1858.31	−	404.251i	1.67897	−	0.365238i	0.948271	+	0.317461i	$0.102830\pi$
$108$	−111.686	+	204.538i	−0.0995092	+	0.182237i
$109$	−94.0666	+	654.247i	−0.0826600	+	0.574913i	0.905832	+	0.423638i	$0.139247\pi$
$109$	−94.0666	+	654.247i	−0.0826600	+	0.574913i	−0.988492	+	0.151275i	$0.951662\pi$
$110$	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	0.221417	−	0.975179i	$-0.428932\pi$
$113$	695.934	−	49.7742i	0.579363	−	0.0414368i	0.357946	+	0.933742i	$0.383477\pi$
$114$	−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	−0.998413	−	0.0563183i	$-0.982064\pi$
$127$	−3.07350	+	42.9732i	−0.00214747	+	0.0300256i	0.996265	+	0.0863439i	$0.0275184\pi$
$128$	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	−0.731925	−	0.681386i	$-0.761378\pi$
$131$	−1468.29	+	431.128i	−0.979274	+	0.287541i	−0.247349	+	0.968926i	$0.579559\pi$
$132$	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	−0.904066	−	0.427393i	$-0.859432\pi$
$137$	−764.366	+	764.366i	−0.476673	+	0.476673i	0.427393	+	0.904066i	$0.359432\pi$
$138$	−865.752	+	1496.76i	−0.534041	+	0.923283i
$139$		−	775.564i		−	0.473255i	−0.971600	−	0.236628i	$-0.923958\pi$
$139$		−	775.564i		−	0.473255i	0.971600	−	0.236628i	$-0.0760421\pi$
$140$	−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	−0.901157	−	0.433494i	$-0.857281\pi$
$149$	−2186.15	−	2522.95i	−1.20199	−	1.38717i	−0.300833	−	0.953677i	$-0.597265\pi$
$150$	−1513.29	−	1244.80i	−0.823730	−	0.677585i
$151$	−530.120	−	155.657i	−0.285699	−	0.0838887i	0.135743	−	0.990744i	$-0.456658\pi$
$151$	−530.120	−	155.657i	−0.285699	−	0.0838887i	−0.421442	+	0.906855i	$0.638476\pi$
$152$	−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	0.390750	−	0.920497i	$-0.372216\pi$
$157$	−752.206	−	563.095i	−0.382373	−	0.286241i	−0.773123	+	0.634256i	$0.781307\pi$
$158$	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	0.998449	+	0.0556696i	$0.0177293\pi$
$163$	37.6365	+	526.227i	0.0180854	+	0.252867i	−0.980364	+	0.197197i	$0.936816\pi$
$164$	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	−0.220437	−	0.975401i	$-0.570748\pi$
$167$	1410.00	−	1055.52i	0.653350	−	0.489092i	0.873787	+	0.486310i	$0.161657\pi$
$168$	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	−0.0765263	−	0.997068i	$-0.524383\pi$
$173$	−669.375	−	47.8746i	−0.294171	−	0.0210395i	−0.217645	+	0.976028i	$0.569837\pi$
$174$	−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	−0.978741	−	0.205101i	$-0.934248\pi$
$179$	−3507.69	+	1601.91i	−1.46467	+	0.668895i	−0.485934	+	0.873996i	$0.661520\pi$
$180$	1500.39	−	346.591i	0.621291	−	0.143519i
$181$	−1450.18	−	2256.53i	−0.595532	−	0.926665i	−0.999927	−	0.0120812i	$-0.996154\pi$
$181$	−1450.18	−	2256.53i	−0.595532	−	0.926665i	0.404395	−	0.914584i	$-0.367482\pi$
$182$	−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	0.975049	−	0.221989i	$-0.0712550\pi$
$191$	91.7793	+	312.571i	0.0347692	+	0.118413i	−0.940280	+	0.340402i	$0.889437\pi$
$192$	−106.629	−	490.164i	−0.0400795	−	0.184242i
$193$	−580.196	−	1555.57i	−0.216391	−	0.580166i	0.782718	−	0.622376i	$-0.213833\pi$
$193$	−580.196	−	1555.57i	−0.216391	−	0.580166i	−0.999109	+	0.0422105i	$0.986560\pi$
$194$	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	0.814485	−	0.580184i	$-0.197020\pi$
$197$	−315.050	−	576.970i	−0.113941	−	0.208667i	−0.928426	+	0.371517i	$0.878838\pi$
$198$	4485.39	−	1672.96i	1.60991	−	0.600467i
$199$	−301.217	−	193.580i	−0.107300	−	0.0689575i	0.485890	−	0.874020i	$-0.338495\pi$
$199$	−301.217	−	193.580i	−0.107300	−	0.0689575i	−0.593190	+	0.805062i	$0.702132\pi$
$200$	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	0.956431	+	0.291959i	$0.0943071\pi$
$211$	370.849	+	2579.31i	0.120997	+	0.841549i	−0.835434	+	0.549590i	$0.814784\pi$
$212$	−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	−0.526289	−	0.850306i	$-0.676417\pi$
$223$	1577.03	−	2888.11i	0.473567	−	0.867273i	0.999856	−	0.0169674i	$-0.00540114\pi$
$224$	−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	0.607053	+	0.794661i	$0.292351\pi$
$227$	−941.403	+	4327.56i	−0.275256	+	1.26533i	−0.882309	+	0.470670i	$0.844012\pi$
$228$	−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	0.836449	+	0.548045i	$0.184628\pi$
$233$	−540.878	+	2486.38i	−0.152078	+	0.699090i	−0.988527	+	0.151045i	$0.951736\pi$
$234$	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	0.739383	−	0.673285i	$-0.235117\pi$
$239$	2640.86	+	1206.04i	0.714741	+	0.326411i	−0.0246421	+	0.999696i	$0.507845\pi$
$240$	773.086	+	1169.70i	0.207927	+	0.314599i
$241$	1295.89	−	1122.89i	0.346371	−	0.300132i	−0.464249	−	0.885705i	$-0.653676\pi$
$241$	1295.89	−	1122.89i	0.346371	−	0.300132i	0.810620	+	0.585573i	$0.199130\pi$
$242$	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	0.119788	−	0.992800i	$-0.461779\pi$
$251$	−3363.63	−	2914.60i	−0.845859	−	0.732941i	−0.965647	+	0.259859i	$0.916324\pi$
$252$	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	−0.998458	−	0.0555179i	$-0.982319\pi$
$257$	−2735.24	+	3653.86i	−0.663891	+	0.886854i	0.334567	+	0.942372i	$0.391410\pi$
$258$	−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	−0.707767	−	0.706446i	$-0.750297\pi$
$263$	−3921.46	−	7181.61i	−0.919420	−	1.68379i	−0.211653	−	0.977345i	$-0.567885\pi$
$264$	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	−0.903130	−	0.429367i	$-0.858737\pi$
$269$	−1656.69	−	5642.16i	−0.375502	−	1.27884i	0.527628	−	0.849475i	$-0.323081\pi$
$270$	76.2722	−	1300.52i	0.0171918	−	0.293137i
$271$	913.639	+	2000.59i	0.204796	+	0.448440i	0.983962	−	0.178377i	$-0.0570846\pi$
$271$	913.639	+	2000.59i	0.204796	+	0.448440i	−0.779166	+	0.626817i	$0.784357\pi$
$272$	−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	0.998293	−	0.0583969i	$-0.0185989\pi$
$277$	4333.11	+	4333.11i	0.939897	+	0.939897i	−0.0583969	+	0.998293i	$0.518599\pi$
$278$	−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	−0.348371	−	0.937357i	$-0.613265\pi$
$281$	621.310	−	283.743i	0.131901	−	0.0602372i	0.480272	+	0.877119i	$0.340538\pi$
$282$	5294.04	−	3963.07i	1.11793	−	0.836870i
$283$	−1972.12	−	1076.86i	−0.414241	−	0.226193i	0.258592	−	0.965987i	$-0.416741\pi$
$283$	−1972.12	−	1076.86i	−0.414241	−	0.226193i	−0.672834	+	0.739794i	$0.734923\pi$
$284$	−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	−0.857808	−	0.513971i	$-0.828174\pi$
$293$	−3040.95	+	2276.43i	−0.606329	+	0.453892i	0.251479	+	0.967863i	$0.419083\pi$
$294$	−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	−0.996602	−	0.0823638i	$-0.973753\pi$
$307$	−668.491	−	3073.00i	−0.124276	−	0.571288i	0.872326	−	0.488924i	$-0.162611\pi$
$308$	−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	0.991076	+	0.133300i	$0.0425575\pi$
$311$	5385.68	+	6215.41i	0.981974	+	1.13326i	−0.00910136	+	0.999959i	$0.502897\pi$
$312$	316.908	+	580.374i	0.0575045	+	0.105312i
$313$	9001.13	−	3357.25i	1.62548	−	0.606271i	0.638859	−	0.769324i	$-0.279407\pi$
$313$	9001.13	−	3357.25i	1.62548	−	0.606271i	0.986617	+	0.163053i	$0.0521340\pi$
$314$	−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	−0.873098	−	0.487544i	$-0.837893\pi$
$317$	598.374	−	1604.30i	0.106019	−	0.284248i	0.979117	+	0.203296i	$0.0651654\pi$
$318$	−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	0.450763	+	0.892644i	$0.351152\pi$
$331$	−3125.66	+	6844.25i	−0.519039	+	1.13654i	−0.969802	+	0.243894i	$0.921575\pi$
$332$	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	0.218860	−	0.975756i	$-0.429766\pi$
$337$	5093.26	−	1107.97i	0.823286	−	0.179095i	0.604426	+	0.796661i	$0.293403\pi$
$338$	−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	0.688503	−	0.725233i	$-0.258268\pi$
$347$	9522.67	−	681.075i	1.47321	−	0.105366i	0.784707	+	0.619867i	$0.212814\pi$
$348$	−283.750	+	1304.38i	−0.0437086	+	0.200925i
$349$	157.926	−	22.7063i	0.0242223	−	0.00348264i	−0.130193	−	0.991489i	$-0.541560\pi$
$349$	157.926	−	22.7063i	0.0242223	−	0.00348264i	0.154415	+	0.988006i	$0.450651\pi$
$350$	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	−0.949075	−	0.315050i	$-0.897979\pi$
$353$	−11152.2	+	2426.02i	−1.68151	+	0.365790i	−0.732433	+	0.680839i	$0.761615\pi$
$354$	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	−0.900528	−	0.434798i	$-0.856820\pi$
$359$	121.015	−	264.986i	0.0177909	−	0.0389567i	0.918319	+	0.395841i	$0.129547\pi$
$360$	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	−0.713457	−	0.700699i	$-0.752872\pi$
$367$	−89.7047	+	89.7047i	−0.0127590	+	0.0127590i	0.700699	+	0.713457i	$0.252872\pi$
$368$	−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	−0.423445	−	0.905922i	$-0.639179\pi$
$373$	3528.62	−	9460.60i	0.489826	−	1.31327i	0.913271	−	0.407353i	$-0.133548\pi$
$374$	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	0.831892	−	0.554937i	$-0.187258\pi$
$379$	1211.62	+	1398.29i	0.164213	+	0.189512i	−0.667679	+	0.744449i	$0.732712\pi$
$380$	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	0.801154	+	0.598458i	$0.204220\pi$
$383$	2406.09	+	11060.6i	0.321007	+	1.47565i	−0.480147	+	0.877188i	$0.659417\pi$
$384$	−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	−0.899094	−	0.437755i	$-0.855774\pi$
$389$	−2592.01	+	2991.34i	−0.337841	+	0.389889i	0.561254	+	0.827644i	$0.310319\pi$
$390$	−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	−0.0401835	−	0.999192i	$-0.512794\pi$
$397$	7176.21	−	5372.04i	0.907213	−	0.679132i	0.947397	+	0.320061i	$0.103703\pi$
$398$	−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	−0.975636	−	0.219395i	$-0.929592\pi$
$401$	−291.209	+	991.768i	−0.0362651	+	0.123508i	0.939371	+	0.342902i	$0.111410\pi$
$402$	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	0.460199	−	0.887816i	$-0.347778\pi$
$409$	11849.2	−	5411.35i	1.43253	−	0.654215i	0.972333	+	0.233601i	$0.0750509\pi$
$410$	−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	0.814325	−	0.580409i	$-0.197107\pi$
$419$	−1351.59	−	2959.57i	−0.157588	−	0.345070i	−0.971913	+	0.235339i	$0.924380\pi$
$420$	−12027.3	−	705.371i	−1.39732	−	0.0819491i
$421$	−2148.52	−	7317.18i	−0.248723	−	0.847073i	−0.985317	−	0.170737i	$-0.945385\pi$
$421$	−2148.52	−	7317.18i	−0.248723	−	0.847073i	0.736594	−	0.676336i	$-0.236433\pi$
$422$	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	−0.471900	−	0.881652i	$-0.656432\pi$
$431$	−10496.4	−	1509.16i	−1.17307	−	0.168663i	−0.701175	+	0.712989i	$0.747341\pi$
$432$	−325.762	+	873.401i	−0.0362806	+	0.0972721i
$433$	−111.522	+	148.976i	−0.0123774	+	0.0165342i	−0.806687	−	0.590979i	$-0.798742\pi$
$433$	−111.522	+	148.976i	−0.0123774	+	0.0165342i	0.794310	+	0.607513i	$0.207833\pi$
$434$	−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	0.993071	−	0.117516i	$-0.0374931\pi$
$439$	9364.37	+	8114.28i	1.01808	+	0.882171i	0.0250091	+	0.999687i	$0.492039\pi$
$440$	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	0.878007	−	0.478647i	$-0.158873\pi$
$443$	1598.01	+	2134.70i	0.171386	+	0.228945i	−0.706622	+	0.707592i	$0.749782\pi$
$444$	−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	−0.933803	−	0.357787i	$-0.883531\pi$
$449$	−6779.31	+	5874.31i	−0.712551	+	0.617429i	0.221252	+	0.975217i	$0.428986\pi$
$450$	−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	−0.898726	−	0.438510i	$-0.855506\pi$
$457$	986.213	−	4533.55i	0.100948	−	0.464049i	0.999674	−	0.0255386i	$-0.00813009\pi$
$458$	−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	−0.976957	−	0.213437i	$-0.931534\pi$
$463$	3.77954	−	17.3742i	0.000379373	−	0.00174395i	0.977336	+	0.211693i	$0.0678978\pi$
$464$	−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	−0.981296	−	0.192506i	$-0.938339\pi$
$467$	−2914.77	+	5338.00i	−0.288821	+	0.528936i	0.692475	+	0.721442i	$0.256520\pi$
$468$	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	0.988491	+	0.151282i	$0.0483402\pi$
$479$	866.581	+	6027.20i	0.0826620	+	0.574926i	−0.905829	+	0.423644i	$0.860751\pi$
$480$	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	−0.908193	−	0.418552i	$-0.862538\pi$
$487$	−2694.60	+	3599.57i	−0.250727	+	0.334932i	0.657465	+	0.753485i	$0.271629\pi$
$488$	−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	0.982838	+	0.184473i	$0.0590580\pi$
$491$	16960.9	+	10900.1i	1.55893	+	1.00186i	0.576088	+	0.817387i	$0.304578\pi$
$492$	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	0.860897	+	0.508780i	$0.169903\pi$
$499$	4589.49	+	15630.4i	0.411731	+	1.40223i	−0.449165	+	0.893449i	$0.648279\pi$
$500$	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	0.823017	−	0.568016i	$-0.192289\pi$
$503$	15068.2	+	3277.88i	1.33570	+	0.290563i	0.512680	+	0.858580i	$0.328653\pi$
$504$	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	0.561683	−	0.827353i	$-0.310154\pi$
$509$	−4871.73	−	7580.56i	−0.424235	−	0.660123i	−0.985918	+	0.167230i	$0.946518\pi$
$510$	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	−0.976405	−	0.215947i	$-0.930716\pi$
$521$	−4451.90	+	6927.30i	−0.374360	+	0.582515i	0.602045	+	0.798462i	$0.294353\pi$
$522$	2573.51	+	1405.24i	0.215784	+	0.117827i
$523$	2575.11	−	1927.70i	0.215300	−	0.161171i	−0.486185	−	0.873856i	$-0.661612\pi$
$523$	2575.11	−	1927.70i	0.215300	−	0.161171i	0.701485	+	0.712685i	$0.252521\pi$
$524$	−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	0.893025	−	0.450007i	$-0.148579\pi$
$541$	4033.05	+	4654.39i	0.320507	+	0.369885i	−0.572518	+	0.819892i	$0.694033\pi$
$542$	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	−0.00569955	−	0.999984i	$-0.501814\pi$
$547$	8359.85	−	22413.6i	0.653458	−	1.75199i	0.659158	−	0.752005i	$-0.270913\pi$
$548$	−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	−0.212872	−	0.977080i	$-0.568282\pi$
$557$	−13324.5	−	4969.77i	−1.01360	−	0.378054i	−0.800729	+	0.599026i	$0.795554\pi$
$558$	−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	0.959738	+	0.280896i	$0.0906315\pi$
$563$	−403.523	+	5641.99i	−0.0302069	+	0.422347i	−0.989945	+	0.141452i	$0.954823\pi$
$564$	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	−0.778632	−	0.627480i	$-0.784086\pi$
$569$	1971.33	−	13710.9i	0.145242	−	1.01018i	0.923874	−	0.382697i	$-0.125005\pi$
$570$	17172.4	−	9664.64i	1.26188	−	0.710188i
$571$	−22402.1	+	3220.93i	−1.64185	+	0.236063i	−0.900438	−	0.434984i	$-0.856754\pi$
$571$	−22402.1	+	3220.93i	−1.64185	+	0.236063i	−0.741415	+	0.671047i	$0.765845\pi$
$572$	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	0.437360	−	0.899287i	$-0.355914\pi$
$577$	13835.8	−	989.553i	0.998249	−	0.0713962i	0.560890	+	0.827890i	$0.310459\pi$
$578$	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	−0.997285	−	0.0736422i	$-0.976538\pi$
$587$	4.68544	−	65.5110i	0.000329453	−	0.00460635i	0.997614	+	0.0690358i	$0.0219923\pi$
$588$	−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	0.341447	−	0.939901i	$-0.389083\pi$
$593$	−231.169	−	86.2217i	−0.0160084	−	0.00597083i	−0.357456	+	0.933930i	$0.616356\pi$
$594$	−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	$0.0202990\pi$
$599$			1868.53i			0.127456i	−0.997967	+	0.0637281i	$0.979701\pi$
$600$	−6700.16	−	4067.08i	−0.455888	−	0.276730i
$601$	−13961.8	+	8972.72i	−0.947612	+	0.608993i	−0.920543	−	0.390641i	$-0.872254\pi$
$601$	−13961.8	+	8972.72i	−0.947612	+	0.608993i	−0.0270683	+	0.999634i	$0.508617\pi$
$602$	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	−0.595970	−	0.803007i	$-0.703232\pi$
$607$	−7784.25	+	2903.37i	−0.520515	+	0.194142i	0.0754541	+	0.997149i	$0.475959\pi$
$608$	−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	0.989217	+	0.146456i	$0.0467867\pi$
$613$	2280.12	+	10481.6i	0.150234	+	0.690613i	−0.838983	+	0.544157i	$0.816850\pi$
$614$	−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	0.748484	−	0.663153i	$-0.230782\pi$
$617$	4951.29	+	3706.49i	0.323065	+	0.241844i	−0.425418	+	0.904997i	$0.639873\pi$
$618$	3540.74	+	770.241i	0.230469	+	0.0501354i
$619$	−14916.0	+	17213.9i	−0.968535	+	1.11775i	0.0244727	+	0.999700i	$0.492209\pi$
$619$	−14916.0	+	17213.9i	−0.968535	+	1.11775i	−0.993008	+	0.118049i	$0.962336\pi$
$620$	−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	−0.907325	−	0.420431i	$-0.861879\pi$
$631$	1319.83	−	4494.94i	0.0832675	−	0.283583i	0.990592	+	0.136848i	$0.0436971\pi$
$632$	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	−0.999078	−	0.0429205i	$-0.986334\pi$
$641$	−10112.0	−	15734.6i	−0.623088	−	0.969544i	0.375990	−	0.926624i	$-0.377303\pi$
$642$	−2126.76	−	29736.0i	−0.130742	−	1.82802i
$643$	−14668.9	−	14668.9i	−0.899667	−	0.899667i	0.0957393	−	0.995406i	$-0.469478\pi$
$643$	−14668.9	−	14668.9i	−0.899667	−	0.899667i	−0.995406	+	0.0957393i	$0.969478\pi$
$644$	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	−0.362140	−	0.932124i	$-0.617954\pi$
$647$	−17753.6	−	3862.06i	−1.07877	−	0.234673i	−0.716633	+	0.697451i	$0.754318\pi$
$648$	−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	0.947948	+	0.318424i	$0.103154\pi$
$653$	7343.14	+	19687.7i	0.440060	+	1.17985i	−0.507888	+	0.861423i	$0.669574\pi$
$654$	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	0.856460	−	0.516213i	$-0.172659\pi$
$659$	12564.1	+	8074.45i	0.742682	+	0.477293i	−0.113778	+	0.993506i	$0.536295\pi$
$660$	−22292.5	−	9837.25i	−1.31475	−	0.580174i
$661$	−8523.65	−	1225.52i	−0.501560	−	0.0721135i	−0.113109	−	0.993583i	$-0.536081\pi$
$661$	−8523.65	−	1225.52i	−0.501560	−	0.0721135i	−0.388452	+	0.921469i	$0.626990\pi$
$662$	−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	0.428192	−	0.903688i	$-0.359151\pi$
$673$	−9768.83	−	13049.6i	−0.559526	−	0.747439i	−0.987718	+	0.156249i	$0.950060\pi$
$674$	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	−0.149315	−	0.988790i	$-0.547707\pi$
$677$	10600.4	−	5788.26i	0.601782	−	0.328598i	0.751097	+	0.660192i	$0.229525\pi$
$678$	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	−0.674373	−	0.738391i	$-0.735586\pi$
$683$	5558.30	−	10179.3i	0.311394	−	0.570276i	0.985767	+	0.168115i	$0.0537678\pi$
$684$	−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	0.383313	−	0.923619i	$-0.374783\pi$
$701$	25094.6	−	21744.6i	1.35208	−	1.17159i	0.968769	−	0.247967i	$-0.0797624\pi$
$702$	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	0.998469	+	0.0553108i	$0.0176150\pi$
$709$	1057.73	+	7356.65i	0.0560279	+	0.389682i	−0.942441	+	0.334372i	$0.891476\pi$
$710$	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	−0.517689	−	0.855569i	$-0.673208\pi$
$719$	−24204.3	−	3480.05i	−1.25545	−	0.180506i	−0.737761	+	0.675063i	$0.764117\pi$
$720$	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	0.998100	+	0.0616145i	$0.0196249\pi$
$727$	5569.64	+	14932.8i	0.284135	+	0.761796i	−0.713965	+	0.700182i	$0.753102\pi$
$728$	−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	0.928905	−	0.370317i	$-0.120751\pi$
$733$	32149.9	+	6993.78i	1.62003	+	0.352416i	0.691127	+	0.722734i	$0.257115\pi$
$734$	−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	0.522704	−	0.852514i	$-0.324923\pi$
$739$	−9440.18	−	14689.2i	−0.469909	−	0.731193i	−0.992613	+	0.121321i	$0.961287\pi$
$740$	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	0.378240	−	0.925708i	$-0.376530\pi$
$743$	−3970.01	−	2167.79i	−0.196023	−	0.107037i	−0.574263	+	0.818671i	$0.694711\pi$
$744$	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	−0.961684	−	0.274160i	$-0.911600\pi$
$751$	−6437.66	+	10017.2i	−0.312801	+	0.486728i	0.648883	+	0.760888i	$0.275236\pi$
$752$	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	−0.893298	−	0.449466i	$-0.851614\pi$
$757$	−1521.64	−	21275.3i	−0.0730581	−	1.02149i	0.820239	−	0.572020i	$-0.193840\pi$
$758$	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	−0.903287	−	0.429037i	$-0.858853\pi$
$761$	−7348.98	+	8481.18i	−0.350066	+	0.403998i	0.553221	+	0.833035i	$0.313399\pi$
$762$	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	0.101443	−	0.994841i	$-0.467654\pi$
$769$	−7486.56	−	2198.25i	−0.351069	−	0.103083i	−0.452512	+	0.891758i	$0.649472\pi$
$770$	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	−0.486980	−	0.873413i	$-0.661901\pi$
$773$	−6083.20	+	2268.92i	−0.283050	+	0.105572i	0.203930	+	0.978986i	$0.434629\pi$
$774$	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	−0.220966	−	0.975282i	$-0.570921\pi$
$787$	−22666.2	−	8454.04i	−1.02663	−	0.382915i	−0.805668	+	0.592367i	$0.798194\pi$
$788$	−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	−0.781566	−	0.623823i	$-0.785579\pi$
$797$	−27750.9	+	6036.83i	−1.23336	+	0.268300i	−0.451792	+	0.892123i	$0.649215\pi$
$798$	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	−0.320662	−	0.947194i	$-0.603905\pi$
$809$	−8317.76	+	1195.91i	−0.361480	+	0.0519729i	−0.0408176	+	0.999167i	$0.512996\pi$
$810$	10186.6	+	2849.75i	0.441879	+	0.123617i
$811$	180.131	−	1252.84i	0.00779933	−	0.0542455i	−0.985550	−	0.169384i	$-0.945822\pi$
$811$	180.131	−	1252.84i	0.00779933	−	0.0542455i	0.993349	+	0.115139i	$0.0367312\pi$
$812$	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	−0.0763768	−	0.997079i	$-0.524335\pi$
$821$	9372.81	−	2752.10i	0.398433	−	0.116990i	0.474809	+	0.880089i	$0.342517\pi$
$822$	10154.9	+	13565.4i	0.430892	+	0.575604i
$823$	13449.2	+	5016.30i	0.569636	+	0.212463i	0.617744	−	0.786379i	$-0.288047\pi$
$823$	13449.2	+	5016.30i	0.569636	+	0.212463i	−0.0481086	+	0.998842i	$0.515319\pi$
$824$	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	−0.651736	−	0.758446i	$-0.725959\pi$
$827$	2537.83	−	2537.83i	0.106710	−	0.106710i	0.758446	+	0.651736i	$0.225959\pi$
$828$	11934.6	+	9400.91i	0.500913	+	0.394570i
$829$			43329.5i			1.81532i	0.419711	+	0.907658i	$0.362131\pi$
$829$			43329.5i			1.81532i	−0.419711	+	0.907658i	$0.637869\pi$
$830$	−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	0.974888	+	0.222694i	$0.0714852\pi$
$839$	25676.9	+	29632.8i	1.05657	+	1.21935i	0.0816866	+	0.996658i	$0.473969\pi$
$840$	−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	0.997764	−	0.0668282i	$-0.0212879\pi$
$853$	16.0728	+	224.728i	0.000645162	+	0.00902055i	−0.997119	+	0.0758487i	$0.975833\pi$
$854$	−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	−0.228880	−	0.973455i	$-0.573506\pi$
$857$	16073.1	−	12032.1i	0.640659	−	0.479592i	0.869540	+	0.493863i	$0.164416\pi$
$858$	−10086.1	−	5507.45i	−0.401323	−	0.219139i
$859$	−22500.3	+	35011.2i	−0.893714	+	1.39065i	0.0266754	+	0.999644i	$0.491508\pi$
$859$	−22500.3	+	35011.2i	−0.893714	+	1.39065i	−0.920390	+	0.391002i	$0.872128\pi$
$860$	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	0.0143113	−	0.999898i	$-0.495444\pi$
$863$	−2885.68	−	206.388i	−0.113823	−	0.00814081i	−0.128135	+	0.991757i	$0.540899\pi$
$864$	−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	0.460949	−	0.887427i	$-0.347509\pi$
$877$	13286.9	+	2890.39i	0.511593	+	0.111290i	0.0506438	+	0.998717i	$0.483873\pi$
$878$	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	0.804487	+	0.593970i	$0.202440\pi$
$881$	11736.8	+	39971.9i	0.448834	+	1.52859i	−0.355653	+	0.934618i	$0.615741\pi$
$882$	12272.9	+	56417.7i	0.468538	+	2.15384i
$883$	−4304.82	−	11541.7i	−0.164064	−	0.439873i	0.828738	−	0.559636i	$-0.189059\pi$
$883$	−4304.82	−	11541.7i	−0.164064	−	0.439873i	−0.992802	+	0.119763i	$0.961786\pi$
$884$	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	−0.994361	−	0.106044i	$-0.966182\pi$
$887$	−14423.2	−	26414.1i	−0.545979	−	0.999885i	0.448383	−	0.893842i	$-0.352000\pi$
$888$	−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	−0.303685	−	0.952773i	$-0.598217\pi$
$907$	9113.96	−	4976.60i	0.333654	−	0.182189i	0.637339	+	0.770584i	$0.280035\pi$
$908$	−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	0.467399	−	0.884046i	$-0.345191\pi$
$911$	2897.10	+	1323.06i	0.105363	+	0.0481175i	−0.362036	+	0.932164i	$0.617918\pi$
$912$	−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	−0.0221825	−	0.999754i	$-0.507061\pi$
$929$	−22433.6	−	10245.1i	−0.792272	−	0.361819i	−0.770090	+	0.637935i	$0.779789\pi$
$930$	−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	0.998480	+	0.0551096i	$0.0175508\pi$
$937$	22086.7	+	29504.3i	0.770053	+	1.02867i	−0.228427	+	0.973561i	$0.573358\pi$
$938$	−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	0.888044	−	0.459758i	$-0.152064\pi$
$941$	16146.1	+	13990.6i	0.559348	+	0.484678i	−0.328696	+	0.944436i	$0.606609\pi$
$942$	−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	−0.904587	−	0.426290i	$-0.859820\pi$
$947$	−7014.94	+	9370.86i	−0.240713	+	0.321554i	0.663874	+	0.747845i	$0.268911\pi$
$948$	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	0.999922	+	0.0124798i	$0.00397254\pi$
$953$	13822.1	+	25313.2i	0.469822	+	0.860415i	−0.530100	+	0.847935i	$0.677846\pi$
$954$	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	0.687034	−	0.726625i	$-0.258912\pi$
$967$	−1190.51	−	1190.51i	−0.0395908	−	0.0395908i	−0.726625	+	0.687034i	$0.758912\pi$
$968$	−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	0.0907323	−	0.995875i	$-0.471079\pi$
$971$	27315.7	−	12474.6i	0.902782	−	0.412287i	0.812049	+	0.583589i	$0.198352\pi$
$972$	−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	0.296379	−	0.955070i	$-0.404221\pi$
$977$	13858.8	+	991.203i	0.453821	+	0.0324579i	0.157442	+	0.987528i	$0.449675\pi$
$978$	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	−0.981877	−	0.189521i	$-0.939306\pi$
$983$	−33182.5	+	24840.1i	−1.07666	+	0.805977i	−0.0947825	+	0.995498i	$0.530216\pi$
$984$	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	−0.996233	−	0.0867117i	$-0.972364\pi$
$991$	−23978.7	+	27672.9i	−0.768626	+	0.887041i	0.227608	+	0.973753i	$0.426910\pi$
$992$	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	0.988836	+	0.149009i	$0.0476083\pi$
$997$	4761.74	+	21889.4i	0.151260	+	0.695330i	−0.837576	+	0.546321i	$0.816028\pi$
$998$	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.7.34	✓	720
5.3	odd	4	inner	230.4.l.a.53.16	yes	720
23.10	odd	22	inner	230.4.l.a.217.16	yes	720
115.33	even	44	inner	230.4.l.a.33.34	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.l.a.7.34	✓	720	1.1	even	1	trivial
230.4.l.a.33.34	yes	720	115.33	even	44	inner
230.4.l.a.53.16	yes	720	5.3	odd	4	inner
230.4.l.a.217.16	yes	720	23.10	odd	22	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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