LMFDB - Embedded newform 230.4.e.a.137.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,4,Mod(137,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("230.137");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			137.13
Character	$\chi$	$=$	230.137
Dual form			230.4.e.a.183.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 - 1.41421i) q^{2} +(3.25915 - 3.25915i) q^{3} +4.00000i q^{4} +(-7.62223 + 8.17934i) q^{5} -9.21827 q^{6} +(22.5290 - 22.5290i) q^{7} +(5.65685 - 5.65685i) q^{8} +5.75586i q^{9} +O(q^{10})$	\(q+(-1.41421 - 1.41421i) q^{2} +(3.25915 - 3.25915i) q^{3} +4.00000i q^{4} +(-7.62223 + 8.17934i) q^{5} -9.21827 q^{6} +(22.5290 - 22.5290i) q^{7} +(5.65685 - 5.65685i) q^{8} +5.75586i q^{9} +(22.3468 - 0.787870i) q^{10} -20.5286i q^{11} +(13.0366 + 13.0366i) q^{12} +(-37.5226 + 37.5226i) q^{13} -63.7217 q^{14} +(1.81570 + 51.4997i) q^{15} -16.0000 q^{16} +(96.6448 - 96.6448i) q^{17} +(8.14001 - 8.14001i) q^{18} +51.6811 q^{19} +(-32.7174 - 30.4889i) q^{20} -146.851i q^{21} +(-29.0318 + 29.0318i) q^{22} +(78.1401 - 77.8532i) q^{23} -36.8731i q^{24} +(-8.80319 - 124.690i) q^{25} +106.130 q^{26} +(106.756 + 106.756i) q^{27} +(90.1161 + 90.1161i) q^{28} -204.476i q^{29} +(70.2638 - 75.3994i) q^{30} -328.130 q^{31} +(22.6274 + 22.6274i) q^{32} +(-66.9057 - 66.9057i) q^{33} -273.353 q^{34} +(12.5511 + 355.994i) q^{35} -23.0234 q^{36} +(86.2739 - 86.2739i) q^{37} +(-73.0881 - 73.0881i) q^{38} +244.584i q^{39} +(3.15148 + 89.3872i) q^{40} +97.1639 q^{41} +(-207.679 + 207.679i) q^{42} +(-268.734 - 268.734i) q^{43} +82.1143 q^{44} +(-47.0791 - 43.8725i) q^{45} +(-220.608 - 0.405832i) q^{46} +(191.459 + 191.459i) q^{47} +(-52.1464 + 52.1464i) q^{48} -672.114i q^{49} +(-163.888 + 188.787i) q^{50} -629.960i q^{51} +(-150.090 - 150.090i) q^{52} +(-256.695 - 256.695i) q^{53} -301.952i q^{54} +(167.910 + 156.473i) q^{55} -254.887i q^{56} +(168.437 - 168.437i) q^{57} +(-289.172 + 289.172i) q^{58} +20.3230i q^{59} +(-205.999 + 7.26280i) q^{60} +350.137i q^{61} +(464.045 + 464.045i) q^{62} +(129.674 + 129.674i) q^{63} -64.0000i q^{64} +(-20.9042 - 592.916i) q^{65} +189.238i q^{66} +(80.2897 - 80.2897i) q^{67} +(386.579 + 386.579i) q^{68} +(0.935268 - 508.406i) q^{69} +(485.701 - 521.201i) q^{70} +711.743 q^{71} +(32.5601 + 32.5601i) q^{72} +(-159.541 + 159.541i) q^{73} -244.020 q^{74} +(-435.073 - 377.692i) q^{75} +206.724i q^{76} +(-462.489 - 462.489i) q^{77} +(345.894 - 345.894i) q^{78} +31.7719 q^{79} +(121.956 - 130.869i) q^{80} +540.462 q^{81} +(-137.410 - 137.410i) q^{82} +(421.261 + 421.261i) q^{83} +587.404 q^{84} +(53.8416 + 1527.14i) q^{85} +760.094i q^{86} +(-666.417 - 666.417i) q^{87} +(-116.127 - 116.127i) q^{88} +1522.01 q^{89} +(4.53487 + 128.625i) q^{90} +1690.70i q^{91} +(311.413 + 312.561i) q^{92} +(-1069.42 + 1069.42i) q^{93} -541.527i q^{94} +(-393.925 + 422.717i) q^{95} +147.492 q^{96} +(-601.487 + 601.487i) q^{97} +(-950.512 + 950.512i) q^{98} +118.160 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 16 q^{3} - 16 q^{6}+O(q^{10}) $ 72 * q - 16 * q^3 - 16 * q^6	$ 72 q - 16 q^{3} - 16 q^{6} - 64 q^{12} + 192 q^{13} - 1152 q^{16} + 32 q^{18} + 276 q^{23} + 880 q^{25} + 304 q^{26} + 728 q^{27} + 608 q^{31} + 688 q^{35} + 2816 q^{36} - 2208 q^{41} - 256 q^{46} + 144 q^{47} + 256 q^{48} + 272 q^{50} + 768 q^{52} - 2360 q^{55} - 1376 q^{62} - 1104 q^{70} + 4528 q^{71} + 128 q^{72} - 1296 q^{73} - 2568 q^{75} - 752 q^{77} + 6000 q^{78} - 11560 q^{81} + 80 q^{82} - 904 q^{85} + 6760 q^{87} + 1104 q^{92} - 5288 q^{93} + 9264 q^{95} + 256 q^{96} - 448 q^{98}+O(q^{100}) $ 72 * q - 16 * q^3 - 16 * q^6 - 64 * q^12 + 192 * q^13 - 1152 * q^16 + 32 * q^18 + 276 * q^23 + 880 * q^25 + 304 * q^26 + 728 * q^27 + 608 * q^31 + 688 * q^35 + 2816 * q^36 - 2208 * q^41 - 256 * q^46 + 144 * q^47 + 256 * q^48 + 272 * q^50 + 768 * q^52 - 2360 * q^55 - 1376 * q^62 - 1104 * q^70 + 4528 * q^71 + 128 * q^72 - 1296 * q^73 - 2568 * q^75 - 752 * q^77 + 6000 * q^78 - 11560 * q^81 + 80 * q^82 - 904 * q^85 + 6760 * q^87 + 1104 * q^92 - 5288 * q^93 + 9264 * q^95 + 256 * q^96 - 448 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.41421	−	1.41421i	−0.500000	−	0.500000i
$2$	−1.41421	−	1.41421i	−0.500000	−	0.500000i
$3$	3.25915	−	3.25915i	0.627224	−	0.627224i	−0.320145	−	0.947369i	$-0.603732\pi$
$3$	3.25915	−	3.25915i	0.627224	−	0.627224i	0.947369	+	0.320145i	$0.103732\pi$
$4$			4.00000i			0.500000i
$5$	−7.62223	+	8.17934i	−0.681753	+	0.731582i
$5$	−7.62223	+	8.17934i	−0.681753	+	0.731582i
$6$	−9.21827			−0.627224
$7$	22.5290	−	22.5290i	1.21645	−	1.21645i	0.247587	−	0.968866i	$-0.420362\pi$
$7$	22.5290	−	22.5290i	1.21645	−	1.21645i	0.968866	−	0.247587i	$-0.0796377\pi$
$8$	5.65685	−	5.65685i	0.250000	−	0.250000i
$9$			5.75586i			0.213180i
$10$	22.3468	−	0.787870i	0.706668	−	0.0249146i
$11$		−	20.5286i		−	0.562691i	−0.959607	−	0.281345i	$-0.909219\pi$
$11$		−	20.5286i		−	0.562691i	0.959607	−	0.281345i	$-0.0907806\pi$
$12$	13.0366	+	13.0366i	0.313612	+	0.313612i
$13$	−37.5226	+	37.5226i	−0.800531	+	0.800531i	−0.983178	−	0.182648i	$-0.941533\pi$
$13$	−37.5226	+	37.5226i	−0.800531	+	0.800531i	0.182648	+	0.983178i	$0.441533\pi$
$14$	−63.7217			−1.21645
$15$	1.81570	+	51.4997i	0.0312541	+	0.886478i
$16$	−16.0000			−0.250000
$17$	96.6448	−	96.6448i	1.37881	−	1.37881i	0.532182	−	0.846630i	$-0.321372\pi$
$17$	96.6448	−	96.6448i	1.37881	−	1.37881i	0.846630	−	0.532182i	$-0.178628\pi$
$18$	8.14001	−	8.14001i	0.106590	−	0.106590i
$19$	51.6811			0.624024			0.312012	−	0.950078i	$-0.398997\pi$
$19$	51.6811			0.624024			0.312012	+	0.950078i	$0.398997\pi$
$20$	−32.7174	−	30.4889i	−0.365791	−	0.340877i
$21$		−	146.851i		−	1.52598i
$22$	−29.0318	+	29.0318i	−0.281345	+	0.281345i
$23$	78.1401	−	77.8532i	0.708406	−	0.705805i
$23$	78.1401	−	77.8532i	0.708406	−	0.705805i
$24$		−	36.8731i		−	0.313612i
$25$	−8.80319	−	124.690i	−0.0704255	−	0.997517i
$26$	106.130			0.800531
$27$	106.756	+	106.756i	0.760936	+	0.760936i
$28$	90.1161	+	90.1161i	0.608226	+	0.608226i
$29$		−	204.476i		−	1.30932i	−0.755925	−	0.654658i	$-0.772813\pi$
$29$		−	204.476i		−	1.30932i	0.755925	−	0.654658i	$-0.227187\pi$
$30$	70.2638	−	75.3994i	0.427612	−	0.458866i
$31$	−328.130			−1.90109			−0.950546	−	0.310585i	$-0.899475\pi$
$31$	−328.130			−1.90109			−0.950546	+	0.310585i	$0.899475\pi$
$32$	22.6274	+	22.6274i	0.125000	+	0.125000i
$33$	−66.9057	−	66.9057i	−0.352933	−	0.352933i
$34$	−273.353			−1.37881
$35$	12.5511	+	355.994i	0.0606150	+	1.71926i
$36$	−23.0234			−0.106590
$37$	86.2739	−	86.2739i	0.383334	−	0.383334i	−0.488968	−	0.872302i	$-0.662627\pi$
$37$	86.2739	−	86.2739i	0.383334	−	0.383334i	0.872302	+	0.488968i	$0.162627\pi$
$38$	−73.0881	−	73.0881i	−0.312012	−	0.312012i
$39$			244.584i			1.00422i
$40$	3.15148	+	89.3872i	0.0124573	+	0.353334i
$41$	97.1639			0.370108			0.185054	−	0.982728i	$-0.440754\pi$
$41$	97.1639			0.370108			0.185054	+	0.982728i	$0.440754\pi$
$42$	−207.679	+	207.679i	−0.762988	+	0.762988i
$43$	−268.734	−	268.734i	−0.953058	−	0.953058i	0.0458884	−	0.998947i	$-0.485388\pi$
$43$	−268.734	−	268.734i	−0.953058	−	0.953058i	−0.998947	+	0.0458884i	$0.985388\pi$
$44$	82.1143			0.281345
$45$	−47.0791	−	43.8725i	−0.155959	−	0.145336i
$46$	−220.608	−	0.405832i	−0.707106	−	0.00130080i
$47$	191.459	+	191.459i	0.594194	+	0.594194i	0.938762	−	0.344567i	$-0.111974\pi$
$47$	191.459	+	191.459i	0.594194	+	0.594194i	−0.344567	+	0.938762i	$0.611974\pi$
$48$	−52.1464	+	52.1464i	−0.156806	+	0.156806i
$49$		−	672.114i		−	1.95951i
$50$	−163.888	+	188.787i	−0.463546	+	0.533971i
$51$		−	629.960i		−	1.72965i
$52$	−150.090	−	150.090i	−0.400265	−	0.400265i
$53$	−256.695	−	256.695i	−0.665278	−	0.665278i	0.291341	−	0.956619i	$-0.405898\pi$
$53$	−256.695	−	256.695i	−0.665278	−	0.665278i	−0.956619	+	0.291341i	$0.905898\pi$
$54$		−	301.952i		−	0.760936i
$55$	167.910	+	156.473i	0.411654	+	0.383616i
$56$		−	254.887i		−	0.608226i
$57$	168.437	−	168.437i	0.391403	−	0.391403i
$58$	−289.172	+	289.172i	−0.654658	+	0.654658i
$59$			20.3230i			0.0448446i	0.999749	+	0.0224223i	$0.00713785\pi$
$59$			20.3230i			0.0448446i	−0.999749	+	0.0224223i	$0.992862\pi$
$60$	−205.999	+	7.26280i	−0.443239	+	0.0156271i
$61$			350.137i			0.734926i	0.930038	+	0.367463i	$0.119774\pi$
$61$			350.137i			0.734926i	−0.930038	+	0.367463i	$0.880226\pi$
$62$	464.045	+	464.045i	0.950546	+	0.950546i
$63$	129.674	+	129.674i	0.259323	+	0.259323i
$64$		−	64.0000i		−	0.125000i
$65$	−20.9042	−	592.916i	−0.0398899	−	1.13142i
$66$			189.238i			0.352933i
$67$	80.2897	−	80.2897i	0.146402	−	0.146402i	−0.630107	−	0.776509i	$-0.716989\pi$
$67$	80.2897	−	80.2897i	0.146402	−	0.146402i	0.776509	+	0.630107i	$0.216989\pi$
$68$	386.579	+	386.579i	0.689406	+	0.689406i
$69$	0.935268	−	508.406i	0.00163178	−	0.887027i
$70$	485.701	−	521.201i	0.829320	−	0.889935i
$71$	711.743			1.18970			0.594848	−	0.803838i	$-0.297212\pi$
$71$	711.743			1.18970			0.594848	+	0.803838i	$0.297212\pi$
$72$	32.5601	+	32.5601i	0.0532950	+	0.0532950i
$73$	−159.541	+	159.541i	−0.255793	+	0.255793i	−0.823341	−	0.567548i	$-0.807892\pi$
$73$	−159.541	+	159.541i	−0.255793	+	0.255793i	0.567548	+	0.823341i	$0.307892\pi$
$74$	−244.020			−0.383334
$75$	−435.073	−	377.692i	−0.669839	−	0.581494i
$76$			206.724i			0.312012i
$77$	−462.489	−	462.489i	−0.684486	−	0.684486i
$78$	345.894	−	345.894i	0.502112	−	0.502112i
$79$	31.7719			0.0452483			0.0226241	−	0.999744i	$-0.492798\pi$
$79$	31.7719			0.0452483			0.0226241	+	0.999744i	$0.492798\pi$
$80$	121.956	−	130.869i	0.170438	−	0.182896i
$81$	540.462			0.741374
$82$	−137.410	−	137.410i	−0.185054	−	0.185054i
$83$	421.261	+	421.261i	0.557101	+	0.557101i	0.928481	−	0.371380i	$-0.121115\pi$
$83$	421.261	+	421.261i	0.557101	+	0.557101i	−0.371380	+	0.928481i	$0.621115\pi$
$84$	587.404			0.762988
$85$	53.8416	+	1527.14i	0.0687052	+	1.94872i
$86$			760.094i			0.953058i
$87$	−666.417	−	666.417i	−0.821235	−	0.821235i
$88$	−116.127	−	116.127i	−0.140673	−	0.140673i
$89$	1522.01			1.81273			0.906364	−	0.422498i	$-0.138846\pi$
$89$	1522.01			1.81273			0.906364	+	0.422498i	$0.138846\pi$
$90$	4.53487	+	128.625i	0.00531130	+	0.150647i
$91$			1690.70i			1.94762i
$92$	311.413	+	312.561i	0.352902	+	0.354203i
$93$	−1069.42	+	1069.42i	−1.19241	+	1.19241i
$94$		−	541.527i		−	0.594194i
$95$	−393.925	+	422.717i	−0.425430	+	0.456525i
$96$	147.492			0.156806
$97$	−601.487	+	601.487i	−0.629606	+	0.629606i	−0.947969	−	0.318363i	$-0.896867\pi$
$97$	−601.487	+	601.487i	−0.629606	+	0.629606i	0.318363	+	0.947969i	$0.396867\pi$
$98$	−950.512	+	950.512i	−0.979757	+	0.979757i
$99$	118.160			0.119954
$100$	498.759	−	35.2128i	0.498759	−	0.0352128i
$101$	−850.040			−0.837447			−0.418724	−	0.908114i	$-0.637522\pi$
$101$	−850.040			−0.837447			−0.418724	+	0.908114i	$0.637522\pi$
$102$	−890.898	+	890.898i	−0.864824	+	0.864824i
$103$	−247.327	−	247.327i	−0.236601	−	0.236601i	0.578840	−	0.815441i	$-0.303505\pi$
$103$	−247.327	−	247.327i	−0.236601	−	0.236601i	−0.815441	+	0.578840i	$0.803505\pi$
$104$			424.520i			0.400265i
$105$	1201.14	+	1119.33i	1.11638	+	1.04034i
$106$			726.042i			0.665278i
$107$	−238.103	+	238.103i	−0.215124	+	0.215124i	−0.806440	−	0.591316i	$-0.798609\pi$
$107$	−238.103	+	238.103i	−0.215124	+	0.215124i	0.591316	+	0.806440i	$0.298609\pi$
$108$	−427.025	+	427.025i	−0.380468	+	0.380468i
$109$	556.477			0.488999			0.244499	−	0.969649i	$-0.421376\pi$
$109$	556.477			0.488999			0.244499	+	0.969649i	$0.421376\pi$
$110$	−16.1738	−	458.748i	−0.0140192	−	0.397635i
$111$		−	562.360i		−	0.480872i
$112$	−360.464	+	360.464i	−0.304113	+	0.304113i
$113$	776.038	+	776.038i	0.646048	+	0.646048i	0.952036	−	0.305987i	$-0.0989865\pi$
$113$	776.038	+	776.038i	0.646048	+	0.646048i	−0.305987	+	0.952036i	$0.598986\pi$
$114$	−476.411			−0.391403
$115$	41.1853	+	1232.55i	0.0333961	+	0.999442i
$116$	817.903			0.654658
$117$	−215.975	−	215.975i	−0.170657	−	0.170657i
$118$	28.7411	−	28.7411i	0.0224223	−	0.0224223i
$119$		−	4354.63i		−	3.35452i
$120$	301.598	+	281.055i	0.229433	+	0.213806i
$121$	909.578			0.683379
$122$	495.169	−	495.169i	0.367463	−	0.367463i
$123$	316.672	−	316.672i	0.232141	−	0.232141i
$124$		−	1312.52i		−	0.950546i
$125$	1086.98	+	878.409i	0.777779	+	0.628538i
$126$		−	366.773i		−	0.259323i
$127$	1091.07	+	1091.07i	0.762340	+	0.762340i	0.976745	−	0.214405i	$-0.0687811\pi$
$127$	1091.07	+	1091.07i	0.762340	+	0.762340i	−0.214405	+	0.976745i	$0.568781\pi$
$128$	−90.5097	+	90.5097i	−0.0625000	+	0.0625000i
$129$	−1751.69			−1.19556
$130$	−808.947	+	868.073i	−0.545764	+	0.585654i
$131$	182.635			0.121808			0.0609042	−	0.998144i	$-0.480602\pi$
$131$	182.635			0.121808			0.0609042	+	0.998144i	$0.480602\pi$
$132$	267.623	−	267.623i	0.176467	−	0.176467i
$133$	1164.33	−	1164.33i	0.759096	−	0.759096i
$134$	−227.094			−0.146402
$135$	−1686.92	+	59.4748i	−1.07546	+	0.0379169i
$136$		−	1093.41i		−	0.689406i
$137$	1203.97	−	1203.97i	0.750816	−	0.750816i	−0.223815	−	0.974632i	$-0.571851\pi$
$137$	1203.97	−	1203.97i	0.750816	−	0.750816i	0.974632	+	0.223815i	$0.0718512\pi$
$138$	−720.317	+	717.672i	−0.444330	+	0.442698i
$139$			2917.08i			1.78003i	0.455936	+	0.890013i	$0.349305\pi$
$139$			2917.08i			1.78003i	−0.455936	+	0.890013i	$0.650695\pi$
$140$	−1423.98	+	50.2044i	−0.859628	+	0.0303075i
$141$	1247.99			0.745386
$142$	−1006.56	−	1006.56i	−0.594848	−	0.594848i
$143$	770.285	+	770.285i	0.450451	+	0.450451i
$144$		−	92.0937i		−	0.0532950i
$145$	1672.48	+	1558.56i	0.957873	+	0.892630i
$146$	451.251			0.255793
$147$	−2190.52	−	2190.52i	−1.22905	−	1.22905i
$148$	345.096	+	345.096i	0.191667	+	0.191667i
$149$	−3027.43			−1.66454			−0.832271	−	0.554370i	$-0.812959\pi$
$149$	−3027.43			−1.66454			−0.832271	+	0.554370i	$0.812959\pi$
$150$	81.1502	+	1149.42i	0.0441726	+	0.625667i
$151$	1546.80			0.833621			0.416811	−	0.908993i	$-0.363148\pi$
$151$	1546.80			0.833621			0.416811	+	0.908993i	$0.363148\pi$
$152$	292.353	−	292.353i	0.156006	−	0.156006i
$153$	556.274	+	556.274i	0.293935	+	0.293935i
$154$			1308.12i			0.684486i
$155$	2501.08	−	2683.88i	1.29607	−	1.39081i
$156$	−978.335			−0.502112
$157$	−142.522	+	142.522i	−0.0724490	+	0.0724490i	−0.742403	−	0.669954i	$-0.766314\pi$
$157$	−142.522	+	142.522i	−0.0724490	+	0.0724490i	0.669954	+	0.742403i	$0.266314\pi$
$158$	−44.9322	−	44.9322i	−0.0226241	−	0.0226241i
$159$	−1673.21			−0.834556
$160$	−357.549	+	12.6059i	−0.176667	+	0.00622866i
$161$	6.46508	−	3514.38i	0.00316472	−	1.72032i
$162$	−764.329	−	764.329i	−0.370687	−	0.370687i
$163$	−2348.77	+	2348.77i	−1.12865	+	1.12865i	−0.138251	+	0.990397i	$0.544148\pi$
$163$	−2348.77	+	2348.77i	−1.12865	+	1.12865i	−0.990397	+	0.138251i	$0.955852\pi$
$164$			388.656i			0.185054i
$165$	1057.22	−	37.2737i	0.498813	−	0.0175864i
$166$		−	1191.51i		−	0.557101i
$167$	1065.23	+	1065.23i	0.493595	+	0.493595i	0.909437	−	0.415842i	$-0.136513\pi$
$167$	1065.23	+	1065.23i	0.493595	+	0.493595i	−0.415842	+	0.909437i	$0.636513\pi$
$168$	−830.715	−	830.715i	−0.381494	−	0.381494i
$169$		−	618.893i		−	0.281699i
$170$	2083.56	−	2235.85i	0.940009	−	1.00871i
$171$			297.469i			0.133029i
$172$	1074.93	−	1074.93i	0.476529	−	0.476529i
$173$	−2913.87	+	2913.87i	−1.28056	+	1.28056i	−0.340218	+	0.940347i	$0.610501\pi$
$173$	−2913.87	+	2913.87i	−1.28056	+	1.28056i	−0.940347	+	0.340218i	$0.889499\pi$
$174$			1884.91i			0.821235i
$175$	−3007.46	−	2610.81i	−1.29910	−	1.12776i
$176$			328.457i			0.140673i
$177$	66.2359	+	66.2359i	0.0281276	+	0.0281276i
$178$	−2152.45	−	2152.45i	−0.906364	−	0.906364i
$179$		−	1242.29i		−	0.518731i	−0.965779	−	0.259365i	$-0.916487\pi$
$179$		−	1242.29i		−	0.518731i	0.965779	−	0.259365i	$-0.0835134\pi$
$180$	175.490	−	188.316i	0.0726680	−	0.0779793i
$181$		−	1126.55i		−	0.462628i	−0.972879	−	0.231314i	$-0.925698\pi$
$181$		−	1126.55i		−	0.462628i	0.972879	−	0.231314i	$-0.0743024\pi$
$182$	2391.00	−	2391.00i	0.973808	−	0.973808i
$183$	1141.15	+	1141.15i	0.460964	+	0.460964i
$184$	1.62333	−	882.432i	0.000650399	−	0.353553i
$185$	48.0639	+	1363.26i	0.0191012	+	0.541779i
$186$	3024.79			1.19241
$187$	−1983.98	−	1983.98i	−0.775844	−	0.775844i
$188$	−765.835	+	765.835i	−0.297097	+	0.297097i
$189$	4810.23			1.85128
$190$	1154.91	−	40.7180i	0.440978	−	0.0155473i
$191$			1159.40i			0.439223i	0.975587	+	0.219611i	$0.0704789\pi$
$191$			1159.40i			0.439223i	−0.975587	+	0.219611i	$0.929521\pi$
$192$	−208.586	−	208.586i	−0.0784030	−	0.0784030i
$193$	−1346.48	+	1346.48i	−0.502184	+	0.502184i	−0.912116	−	0.409932i	$-0.865552\pi$
$193$	−1346.48	+	1346.48i	−0.502184	+	0.502184i	0.409932	+	0.912116i	$0.365552\pi$
$194$	1701.26			0.629606
$195$	−2000.53	−	1864.27i	−0.734673	−	0.684633i
$196$	2688.45			0.979757
$197$	−3039.52	−	3039.52i	−1.09927	−	1.09927i	−0.994496	−	0.104776i	$-0.966587\pi$
$197$	−3039.52	−	3039.52i	−1.09927	−	1.09927i	−0.104776	−	0.994496i	$-0.533413\pi$
$198$	−167.103	−	167.103i	−0.0599772	−	0.0599772i
$199$	−4989.80			−1.77748			−0.888738	−	0.458416i	$-0.848417\pi$
$199$	−4989.80			−1.77748			−0.888738	+	0.458416i	$0.848417\pi$
$200$	−755.149	−	655.553i	−0.266986	−	0.231773i
$201$		−	523.353i		−	0.183654i
$202$	1202.14	+	1202.14i	0.418724	+	0.418724i
$203$	−4606.64	−	4606.64i	−1.59272	−	1.59272i
$204$	2519.84			0.864824
$205$	−740.606	+	794.736i	−0.252323	+	0.270765i
$206$			699.547i			0.236601i
$207$	448.112	+	449.764i	0.150463	+	0.151018i
$208$	600.362	−	600.362i	0.200133	−	0.200133i
$209$		−	1060.94i		−	0.351133i
$210$	−115.700	−	3281.65i	−0.0380192	−	1.07836i
$211$	−1659.27			−0.541369			−0.270685	−	0.962668i	$-0.587250\pi$
$211$	−1659.27			−0.541369			−0.270685	+	0.962668i	$0.587250\pi$
$212$	1026.78	−	1026.78i	0.332639	−	0.332639i
$213$	2319.68	−	2319.68i	0.746206	−	0.746206i
$214$	673.457			0.215124
$215$	4246.41	−	149.714i	1.34699	−	0.0474902i
$216$	1207.81			0.380468
$217$	−7392.44	+	7392.44i	−2.31259	+	2.31259i
$218$	−786.978	−	786.978i	−0.244499	−	0.244499i
$219$			1039.94i			0.320879i
$220$	−625.894	+	671.640i	−0.191808	+	0.205827i
$221$			7252.73i			2.20756i
$222$	−795.297	+	795.297i	−0.240436	+	0.240436i
$223$	3392.94	−	3392.94i	1.01887	−	1.01887i	0.0190518	−	0.999818i	$-0.493935\pi$
$223$	3392.94	−	3392.94i	1.01887	−	1.01887i	0.999818	−	0.0190518i	$-0.00606473\pi$
$224$	1019.55			0.304113
$225$	717.696	−	50.6699i	0.212651	−	0.0150133i
$226$		−	2194.97i		−	0.646048i
$227$	1815.07	−	1815.07i	0.530706	−	0.530706i	−0.390077	−	0.920782i	$-0.627551\pi$
$227$	1815.07	−	1815.07i	0.530706	−	0.530706i	0.920782	+	0.390077i	$0.127551\pi$
$228$	673.746	+	673.746i	0.195702	+	0.195702i
$229$	3762.84			1.08583			0.542916	−	0.839787i	$-0.317320\pi$
$229$	3762.84			1.08583			0.542916	+	0.839787i	$0.317320\pi$
$230$	1684.84	−	1801.33i	0.483023	−	0.516419i
$231$	−3014.64			−0.858653
$232$	−1156.69	−	1156.69i	−0.327329	−	0.327329i
$233$	−1313.67	+	1313.67i	−0.369361	+	0.369361i	−0.867244	−	0.497883i	$-0.834111\pi$
$233$	−1313.67	+	1313.67i	−0.369361	+	0.369361i	0.497883	+	0.867244i	$0.334111\pi$
$234$			610.869i			0.170657i
$235$	−3025.35	+	106.663i	−0.839796	+	0.0296083i
$236$	−81.2922			−0.0224223
$237$	103.549	−	103.549i	0.0283808	−	0.0283808i
$238$	−6158.37	+	6158.37i	−1.67726	+	1.67726i
$239$			4234.59i			1.14608i	0.819528	+	0.573040i	$0.194236\pi$
$239$			4234.59i			1.14608i	−0.819528	+	0.573040i	$0.805764\pi$
$240$	−29.0512	−	823.995i	−0.00781353	−	0.221620i
$241$		−	4301.10i		−	1.14962i	−0.818288	−	0.574809i	$-0.805076\pi$
$241$		−	4301.10i		−	1.14962i	0.818288	−	0.574809i	$-0.194924\pi$
$242$	−1286.34	−	1286.34i	−0.341690	−	0.341690i
$243$	−1120.97	+	1120.97i	−0.295928	+	0.295928i
$244$	−1400.55			−0.367463
$245$	5497.45	+	5123.01i	1.43355	+	1.33591i
$246$	−895.683			−0.232141
$247$	−1939.21	+	1939.21i	−0.499551	+	0.499551i
$248$	−1856.18	+	1856.18i	−0.475273	+	0.475273i
$249$	2745.91			0.698854
$250$	−294.962	−	2779.48i	−0.0746202	−	0.703158i
$251$		−	757.418i		−	0.190469i	−0.995455	−	0.0952346i	$-0.969640\pi$
$251$		−	757.418i		−	0.190469i	0.995455	−	0.0952346i	$-0.0303601\pi$
$252$	−518.695	+	518.695i	−0.129662	+	0.129662i
$253$	−1598.21	−	1604.11i	−0.397150	−	0.398614i
$254$		−	3086.03i		−	0.762340i
$255$	5152.66	+	4801.70i	1.26538	+	1.17919i
$256$	256.000			0.0625000
$257$	2009.49	+	2009.49i	0.487737	+	0.487737i	0.907591	−	0.419855i	$-0.137919\pi$
$257$	2009.49	+	2009.49i	0.487737	+	0.487737i	−0.419855	+	0.907591i	$0.637919\pi$
$258$	2477.26	+	2477.26i	0.597781	+	0.597781i
$259$		−	3887.33i		−	0.932615i
$260$	2371.66	−	83.6167i	0.565709	−	0.0199449i
$261$	1176.93			0.279120
$262$	−258.285	−	258.285i	−0.0609042	−	0.0609042i
$263$	−2340.92	−	2340.92i	−0.548850	−	0.548850i	0.377258	−	0.926108i	$-0.376867\pi$
$263$	−2340.92	−	2340.92i	−0.548850	−	0.548850i	−0.926108	+	0.377258i	$0.876867\pi$
$264$	−756.952			−0.176467
$265$	4056.18	−	143.007i	0.940261	−	0.0331503i
$266$	−3293.21			−0.759096
$267$	4960.46	−	4960.46i	1.13699	−	1.13699i
$268$	321.159	+	321.159i	0.0732011	+	0.0732011i
$269$		−	1336.25i		−	0.302872i	−0.988467	−	0.151436i	$-0.951610\pi$
$269$		−	1336.25i		−	0.302872i	0.988467	−	0.151436i	$-0.0483897\pi$
$270$	2469.77	+	2301.55i	0.556687	+	0.518770i
$271$	−2700.99			−0.605436			−0.302718	−	0.953080i	$-0.597894\pi$
$271$	−2700.99			−0.605436			−0.302718	+	0.953080i	$0.597894\pi$
$272$	−1546.32	+	1546.32i	−0.344703	+	0.344703i
$273$	5510.23	+	5510.23i	1.22159	+	1.22159i
$274$	−3405.33			−0.750816
$275$	−2559.70	+	180.717i	−0.561293	+	0.0396278i
$276$	2033.62	+	3.74107i	0.443514	+	0.000815892i
$277$	−200.656	−	200.656i	−0.0435244	−	0.0435244i	0.685010	−	0.728534i	$-0.259798\pi$
$277$	−200.656	−	200.656i	−0.0435244	−	0.0435244i	−0.728534	+	0.685010i	$0.759798\pi$
$278$	4125.37	−	4125.37i	0.890013	−	0.890013i
$279$		−	1888.67i		−	0.405275i
$280$	2084.81	+	1942.81i	0.444968	+	0.414660i
$281$			2868.76i			0.609024i	0.952508	+	0.304512i	$0.0984934\pi$
$281$			2868.76i			0.609024i	−0.952508	+	0.304512i	$0.901507\pi$
$282$	−1764.92	−	1764.92i	−0.372693	−	0.372693i
$283$	2610.93	+	2610.93i	0.548422	+	0.548422i	0.925984	−	0.377562i	$-0.123237\pi$
$283$	2610.93	+	2610.93i	0.548422	+	0.548422i	−0.377562	+	0.925984i	$0.623237\pi$
$284$			2846.97i			0.594848i
$285$	93.8375	+	2661.56i	0.0195033	+	0.553184i
$286$		−	2178.70i		−	0.450451i
$287$	2189.01	−	2189.01i	0.450220	−	0.450220i
$288$	−130.240	+	130.240i	−0.0266475	+	0.0266475i
$289$		−	13767.4i		−	2.80225i
$290$	−161.100	−	4569.38i	−0.0326212	−	0.925252i
$291$			3920.68i			0.789808i
$292$	−638.165	−	638.165i	−0.127896	−	0.127896i
$293$	−4181.70	−	4181.70i	−0.833779	−	0.833779i	0.154252	−	0.988032i	$-0.450703\pi$
$293$	−4181.70	−	4181.70i	−0.833779	−	0.833779i	−0.988032	+	0.154252i	$0.950703\pi$
$294$			6195.73i			1.22905i
$295$	−166.229	−	154.907i	−0.0328076	−	0.0305730i
$296$		−	976.078i		−	0.191667i
$297$	2191.55	−	2191.55i	0.428171	−	0.428171i
$298$	4281.43	+	4281.43i	0.832271	+	0.832271i
$299$	−10.7677	+	5853.28i	−0.00208266	+	1.13212i
$300$	1510.77	−	1740.29i	0.290747	−	0.334920i
$301$	−12108.6			−2.31870
$302$	−2187.51	−	2187.51i	−0.416811	−	0.416811i
$303$	−2770.41	+	2770.41i	−0.525267	+	0.525267i
$304$	−826.898			−0.156006
$305$	−2863.89	−	2668.83i	−0.537659	−	0.501038i
$306$		−	1573.38i		−	0.293935i
$307$	1232.37	+	1232.37i	0.229104	+	0.229104i	0.812318	−	0.583214i	$-0.198205\pi$
$307$	1232.37	+	1232.37i	0.229104	+	0.229104i	−0.583214	+	0.812318i	$0.698205\pi$
$308$	1849.95	−	1849.95i	0.342243	−	0.342243i
$309$	−1612.15			−0.296803
$310$	−7332.65	+	258.524i	−1.34344	+	0.0473650i
$311$	−254.489			−0.0464011			−0.0232006	−	0.999731i	$-0.507386\pi$
$311$	−254.489			−0.0464011			−0.0232006	+	0.999731i	$0.507386\pi$
$312$	1383.57	+	1383.57i	0.251056	+	0.251056i
$313$	1752.28	+	1752.28i	0.316438	+	0.316438i	0.847397	−	0.530960i	$-0.178168\pi$
$313$	1752.28	+	1752.28i	0.316438	+	0.316438i	−0.530960	+	0.847397i	$0.678168\pi$
$314$	403.113			0.0724490
$315$	−2049.05	+	72.2424i	−0.366511	+	0.0129219i
$316$			127.087i			0.0226241i
$317$	5914.40	+	5914.40i	1.04790	+	1.04790i	0.998793	+	0.0491114i	$0.0156390\pi$
$317$	5914.40	+	5914.40i	1.04790	+	1.04790i	0.0491114	+	0.998793i	$0.484361\pi$
$318$	2366.28	+	2366.28i	0.417278	+	0.417278i
$319$	−4197.59			−0.736740
$320$	523.478	+	487.823i	0.0914478	+	0.0852191i
$321$			1552.03i			0.269862i
$322$	−4979.22	+	4960.94i	−0.861743	+	0.858578i
$323$	4994.71	−	4994.71i	0.860412	−	0.860412i
$324$			2161.85i			0.370687i
$325$	5009.00	+	4348.36i	0.854921	+	0.742165i
$326$	6643.32			1.12865
$327$	1813.64	−	1813.64i	0.306712	−	0.306712i
$328$	549.642	−	549.642i	0.0925271	−	0.0925271i
$329$	8626.76			1.44562
$330$	−1547.84	−	1442.42i	−0.258200	−	0.240613i
$331$	313.323			0.0520297			0.0260148	−	0.999662i	$-0.491718\pi$
$331$	313.323			0.0520297			0.0260148	+	0.999662i	$0.491718\pi$
$332$	−1685.04	+	1685.04i	−0.278550	+	0.278550i
$333$	496.580	+	496.580i	0.0817190	+	0.0817190i
$334$		−	3012.94i		−	0.493595i
$335$	44.7301	+	1268.70i	0.00729512	+	0.206915i
$336$			2349.62i			0.381494i
$337$	−1329.52	+	1329.52i	−0.214907	+	0.214907i	−0.806348	−	0.591441i	$-0.798559\pi$
$337$	−1329.52	+	1329.52i	−0.214907	+	0.214907i	0.591441	+	0.806348i	$0.298559\pi$
$338$	−875.246	+	875.246i	−0.140849	+	0.140849i
$339$	5058.45			0.810434
$340$	−6108.56	+	215.367i	−0.974362	+	0.0343526i
$341$			6736.03i			1.06973i
$342$	420.685	−	420.685i	0.0665147	−	0.0665147i
$343$	−7414.61	−	7414.61i	−1.16720	−	1.16720i
$344$	−3040.37			−0.476529
$345$	4151.30	+	3882.84i	0.647821	+	0.605927i
$346$	8241.68			1.28056
$347$	5016.54	+	5016.54i	0.776086	+	0.776086i	0.979163	−	0.203077i	$-0.0650941\pi$
$347$	5016.54	+	5016.54i	0.776086	+	0.776086i	−0.203077	+	0.979163i	$0.565094\pi$
$348$	2665.67	−	2665.67i	0.410617	−	0.410617i
$349$			4573.03i			0.701400i	0.936488	+	0.350700i	$0.114056\pi$
$349$			4573.03i			0.701400i	−0.936488	+	0.350700i	$0.885944\pi$
$350$	560.954	+	7945.43i	0.0856693	+	1.21343i
$351$	−8011.55			−1.21830
$352$	464.508	−	464.508i	0.0703363	−	0.0703363i
$353$	2066.27	−	2066.27i	0.311548	−	0.311548i	−0.533961	−	0.845509i	$-0.679297\pi$
$353$	2066.27	−	2066.27i	0.311548	−	0.311548i	0.845509	+	0.533961i	$0.179297\pi$
$354$		−	187.343i		−	0.0281276i
$355$	−5425.07	+	5821.59i	−0.811079	+	0.870360i
$356$			6088.04i			0.906364i
$357$	−14192.4	−	14192.4i	−2.10404	−	2.10404i
$358$	−1756.86	+	1756.86i	−0.259365	+	0.259365i
$359$	−11279.7			−1.65828			−0.829139	−	0.559043i	$-0.811169\pi$
$359$	−11279.7			−1.65828			−0.829139	+	0.559043i	$0.811169\pi$
$360$	−514.500	+	18.1395i	−0.0753237	+	0.00265565i
$361$	−4188.06			−0.610594
$362$	−1593.18	+	1593.18i	−0.231314	+	0.231314i
$363$	2964.45	−	2964.45i	0.428632	−	0.428632i
$364$	−6762.78			−0.973808
$365$	−88.8818	−	2521.00i	−0.0127460	−	0.361521i
$366$		−	3227.66i		−	0.460964i
$367$	−2785.59	+	2785.59i	−0.396203	+	0.396203i	−0.876891	−	0.480689i	$-0.840387\pi$
$367$	−2785.59	+	2785.59i	−0.396203	+	0.396203i	0.480689	+	0.876891i	$0.340387\pi$
$368$	−1250.24	+	1245.65i	−0.177102	+	0.176451i
$369$			559.261i			0.0788997i
$370$	1859.97	−	1995.92i	0.261339	−	0.280440i
$371$	−11566.2			−1.61856
$372$	−4277.70	−	4277.70i	−0.596205	−	0.596205i
$373$	6934.40	+	6934.40i	0.962599	+	0.962599i	0.999325	−	0.0367259i	$-0.0116928\pi$
$373$	6934.40	+	6934.40i	0.962599	+	0.962599i	−0.0367259	+	0.999325i	$0.511693\pi$
$374$			5611.54i			0.775844i
$375$	6405.50	−	679.761i	0.882076	−	0.0936072i
$376$	2166.11			0.297097
$377$	7672.46	+	7672.46i	1.04815	+	1.04815i
$378$	−6802.69	−	6802.69i	−0.925642	−	0.925642i
$379$	−3434.70			−0.465511			−0.232756	−	0.972535i	$-0.574774\pi$
$379$	−3434.70			−0.465511			−0.232756	+	0.972535i	$0.574774\pi$
$380$	−1690.87	−	1575.70i	−0.228263	−	0.212715i
$381$	7111.96			0.956316
$382$	1639.64	−	1639.64i	0.219611	−	0.219611i
$383$	6029.73	+	6029.73i	0.804451	+	0.804451i	0.983788	−	0.179337i	$-0.0573953\pi$
$383$	6029.73	+	6029.73i	0.804451	+	0.804451i	−0.179337	+	0.983788i	$0.557395\pi$
$384$			589.970i			0.0784030i
$385$	7308.04	−	257.656i	0.967409	−	0.0341075i
$386$	3808.41			0.502184
$387$	1546.79	−	1546.79i	0.203173	−	0.203173i
$388$	−2405.95	−	2405.95i	−0.314803	−	0.314803i
$389$	−1748.35			−0.227879			−0.113940	−	0.993488i	$-0.536347\pi$
$389$	−1748.35			−0.227879			−0.113940	+	0.993488i	$0.536347\pi$
$390$	192.700	+	5465.66i	0.0250199	+	0.709653i
$391$	27.7338	−	15075.9i	0.00358711	−	1.94993i
$392$	−3802.05	−	3802.05i	−0.489879	−	0.489879i
$393$	595.236	−	595.236i	0.0764012	−	0.0764012i
$394$			8597.05i			1.09927i
$395$	−242.172	+	259.873i	−0.0308482	+	0.0331028i
$396$			472.638i			0.0599772i
$397$	4880.55	+	4880.55i	0.616997	+	0.616997i	0.944760	−	0.327763i	$-0.106295\pi$
$397$	4880.55	+	4880.55i	0.616997	+	0.616997i	−0.327763	+	0.944760i	$0.606295\pi$
$398$	7056.65	+	7056.65i	0.888738	+	0.888738i
$399$		−	7589.42i		−	0.952247i
$400$	140.851	+	1995.03i	0.0176064	+	0.249379i
$401$		−	9670.61i		−	1.20431i	−0.798380	−	0.602154i	$-0.794309\pi$
$401$		−	9670.61i		−	1.20431i	0.798380	−	0.602154i	$-0.205691\pi$
$402$	−740.132	+	740.132i	−0.0918270	+	0.0918270i
$403$	12312.3	−	12312.3i	1.52188	−	1.52188i
$404$		−	3400.16i		−	0.418724i
$405$	−4119.53	+	4420.62i	−0.505434	+	0.542376i
$406$			13029.5i			1.59272i
$407$	−1771.08	−	1771.08i	−0.215698	−	0.215698i
$408$	−3563.59	−	3563.59i	−0.432412	−	0.432412i
$409$			1809.43i			0.218754i	0.994000	+	0.109377i	$0.0348856\pi$
$409$			1809.43i			0.218754i	−0.994000	+	0.109377i	$0.965114\pi$
$410$	2171.30	−	76.5525i	0.261544	−	0.00922112i
$411$		−	7847.82i		−	0.941860i
$412$	989.309	−	989.309i	0.118300	−	0.118300i
$413$	457.858	+	457.858i	0.0545514	+	0.0545514i
$414$	2.33591	−	1269.79i	0.000277304	−	0.150741i
$415$	−6656.58	+	234.688i	−0.787370	+	0.0277599i
$416$	−1698.08			−0.200133
$417$	9507.21	+	9507.21i	1.11647	+	1.11647i
$418$	−1500.39	+	1500.39i	−0.175566	+	0.175566i
$419$	156.834			0.0182860			0.00914299	−	0.999958i	$-0.497090\pi$
$419$	156.834			0.0182860			0.00914299	+	0.999958i	$0.497090\pi$
$420$	−4477.33	+	4804.58i	−0.520170	+	0.558189i
$421$			9783.93i			1.13264i	0.824187	+	0.566318i	$0.191633\pi$
$421$			9783.93i			1.13264i	−0.824187	+	0.566318i	$0.808367\pi$
$422$	2346.56	+	2346.56i	0.270685	+	0.270685i
$423$	−1102.01	+	1102.01i	−0.126670	+	0.126670i
$424$	−2904.17			−0.332639
$425$	−12901.4	−	11199.8i	−1.47249	−	1.27829i
$426$	−6561.04			−0.746206
$427$	7888.25	+	7888.25i	0.894003	+	0.894003i
$428$	−952.411	−	952.411i	−0.107562	−	0.107562i
$429$	5020.95			0.565068
$430$	−6217.06	−	5793.61i	−0.697241	−	0.649750i
$431$		−	7652.24i		−	0.855210i	−0.903966	−	0.427605i	$-0.859357\pi$
$431$		−	7652.24i		−	0.855210i	0.903966	−	0.427605i	$-0.140643\pi$
$432$	−1708.10	−	1708.10i	−0.190234	−	0.190234i
$433$	2595.71	+	2595.71i	0.288087	+	0.288087i	0.836323	−	0.548236i	$-0.184701\pi$
$433$	2595.71	+	2595.71i	0.288087	+	0.288087i	−0.548236	+	0.836323i	$0.684701\pi$
$434$	20909.0			2.31259
$435$	10530.4	−	371.267i	1.16068	−	0.0409215i
$436$			2225.91i			0.244499i
$437$	4038.37	−	4023.54i	0.442063	−	0.440439i
$438$	1470.69	−	1470.69i	0.160439	−	0.160439i
$439$			9437.95i			1.02608i	0.858365	+	0.513040i	$0.171481\pi$
$439$			9437.95i			1.02608i	−0.858365	+	0.513040i	$0.828519\pi$
$440$	1834.99	−	64.6954i	0.198818	−	0.00700962i
$441$	3868.59			0.417729
$442$	10256.9	−	10256.9i	1.10378	−	1.10378i
$443$	2818.47	−	2818.47i	0.302279	−	0.302279i	−0.539626	−	0.841905i	$-0.681434\pi$
$443$	2818.47	−	2818.47i	0.302279	−	0.302279i	0.841905	+	0.539626i	$0.181434\pi$
$444$	2249.44			0.240436
$445$	−11601.1	+	12449.0i	−1.23583	+	1.32616i
$446$	−9596.68			−1.01887
$447$	−9866.85	+	9866.85i	−1.04404	+	1.04404i
$448$	−1441.86	−	1441.86i	−0.152057	−	0.152057i
$449$		−	6865.58i		−	0.721618i	−0.932640	−	0.360809i	$-0.882501\pi$
$449$		−	6865.58i		−	0.721618i	0.932640	−	0.360809i	$-0.117499\pi$
$450$	−1086.63	−	943.317i	−0.113832	−	0.0988187i
$451$		−	1994.64i		−	0.208257i
$452$	−3104.15	+	3104.15i	−0.323024	+	0.323024i
$453$	5041.26	−	5041.26i	0.522867	−	0.522867i
$454$	−5133.79			−0.530706
$455$	−13828.8	−	12886.9i	−1.42484	−	1.32779i
$456$		−	1905.64i		−	0.195702i
$457$	1259.54	−	1259.54i	0.128925	−	0.128925i	−0.639700	−	0.768625i	$-0.720941\pi$
$457$	1259.54	−	1259.54i	0.128925	−	0.128925i	0.768625	+	0.639700i	$0.220941\pi$
$458$	−5321.46	−	5321.46i	−0.542916	−	0.542916i
$459$	20634.9			2.09837
$460$	−4930.20	+	164.741i	−0.499721	+	0.0166981i
$461$	−11546.8			−1.16657			−0.583286	−	0.812267i	$-0.698233\pi$
$461$	−11546.8			−1.16657			−0.583286	+	0.812267i	$0.698233\pi$
$462$	4263.35	+	4263.35i	0.429326	+	0.429326i
$463$	4028.74	−	4028.74i	0.404387	−	0.404387i	−0.475389	−	0.879776i	$-0.657693\pi$
$463$	4028.74	−	4028.74i	0.404387	−	0.404387i	0.879776	+	0.475389i	$0.157693\pi$
$464$			3271.61i			0.327329i
$465$	−595.785	−	16898.6i	−0.0594170	−	1.68528i
$466$	3715.61			0.369361
$467$	4820.75	−	4820.75i	0.477682	−	0.477682i	−0.426708	−	0.904390i	$-0.640327\pi$
$467$	4820.75	−	4820.75i	0.477682	−	0.477682i	0.904390	+	0.426708i	$0.140327\pi$
$468$	863.899	−	863.899i	0.0853285	−	0.0853285i
$469$		−	3617.70i		−	0.356183i
$470$	4429.33	+	4127.65i	0.434702	+	0.405094i
$471$			929.002i			0.0908836i
$472$	114.964	+	114.964i	0.0112112	+	0.0112112i
$473$	−5516.72	+	5516.72i	−0.536277	+	0.536277i
$474$	−292.882			−0.0283808
$475$	−454.959	−	6444.10i	−0.0439472	−	0.622475i
$476$	17418.5			1.67726
$477$	1477.50	−	1477.50i	0.141824	−	0.141824i
$478$	5988.62	−	5988.62i	0.573040	−	0.573040i
$479$	−9374.84			−0.894254			−0.447127	−	0.894471i	$-0.647553\pi$
$479$	−9374.84			−0.894254			−0.447127	+	0.894471i	$0.647553\pi$
$480$	−1124.22	+	1206.39i	−0.106903	+	0.114717i
$481$			6474.45i			0.613741i
$482$	−6082.67	+	6082.67i	−0.574809	+	0.574809i
$483$	−11432.8	−	11475.0i	−1.07704	−	1.08101i
$484$			3638.31i			0.341690i
$485$	−335.094	−	9504.45i	−0.0313728	−	0.889845i
$486$	3170.59			0.295928
$487$	−810.400	−	810.400i	−0.0754060	−	0.0754060i	0.668398	−	0.743804i	$-0.266980\pi$
$487$	−810.400	−	810.400i	−0.0754060	−	0.0754060i	−0.743804	+	0.668398i	$0.766980\pi$
$488$	1980.68	+	1980.68i	0.183732	+	0.183732i
$489$			15310.0i			1.41583i
$490$	−529.538	−	15019.6i	−0.0488206	−	1.38473i
$491$	6178.20			0.567858			0.283929	−	0.958845i	$-0.408362\pi$
$491$	6178.20			0.567858			0.283929	+	0.958845i	$0.408362\pi$
$492$	1266.69	+	1266.69i	0.116070	+	0.116070i
$493$	−19761.5	−	19761.5i	−1.80530	−	1.80530i
$494$	5484.92			0.499551
$495$	−900.639	+	966.467i	−0.0817792	+	0.0877565i
$496$	5250.08			0.475273
$497$	16034.9	−	16034.9i	1.44721	−	1.44721i
$498$	−3883.30	−	3883.30i	−0.349427	−	0.349427i
$499$		−	11349.0i		−	1.01814i	−0.860726	−	0.509068i	$-0.829990\pi$
$499$		−	11349.0i		−	1.01814i	0.860726	−	0.509068i	$-0.170010\pi$
$500$	−3513.64	+	4347.92i	−0.314269	+	0.388889i
$501$	6943.52			0.619189
$502$	−1071.15	+	1071.15i	−0.0952346	+	0.0952346i
$503$	10784.1	+	10784.1i	0.955940	+	0.955940i	0.999070	−	0.0431291i	$-0.0137327\pi$
$503$	10784.1	+	10784.1i	0.955940	+	0.955940i	−0.0431291	+	0.999070i	$0.513733\pi$
$504$	1467.09			0.129662
$505$	6479.20	−	6952.77i	0.570932	−	0.612662i
$506$	−8.33115	+	4528.76i	−0.000731946	+	0.397882i
$507$	−2017.07	−	2017.07i	−0.176688	−	0.176688i
$508$	−4364.30	+	4364.30i	−0.381170	+	0.381170i
$509$		−	5494.54i		−	0.478470i	−0.970962	−	0.239235i	$-0.923103\pi$
$509$		−	5494.54i		−	0.478470i	0.970962	−	0.239235i	$-0.0768966\pi$
$510$	−496.327	−	14077.6i	−0.0430936	−	1.22229i
$511$			7188.61i			0.622320i
$512$	−362.039	−	362.039i	−0.0312500	−	0.0312500i
$513$	5517.29	+	5517.29i	0.474842	+	0.474842i
$514$		−	5683.69i		−	0.487737i
$515$	3908.16	−	137.788i	0.334396	−	0.0117896i
$516$		−	7006.75i		−	0.597781i
$517$	3930.37	−	3930.37i	0.334348	−	0.334348i
$518$	−5497.52	+	5497.52i	−0.466307	+	0.466307i
$519$			18993.5i			1.60640i
$520$	−3472.29	−	3235.79i	−0.292827	−	0.272882i
$521$		−	7580.92i		−	0.637478i	−0.947843	−	0.318739i	$-0.896741\pi$
$521$		−	7580.92i		−	0.637478i	0.947843	−	0.318739i	$-0.103259\pi$
$522$	−1664.43	−	1664.43i	−0.139560	−	0.139560i
$523$	−1702.78	−	1702.78i	−0.142366	−	0.142366i	0.632332	−	0.774698i	$-0.282098\pi$
$523$	−1702.78	−	1702.78i	−0.142366	−	0.142366i	−0.774698	+	0.632332i	$0.782098\pi$
$524$			730.540i			0.0609042i
$525$	−18310.8	+	1292.76i	−1.52219	+	0.107468i
$526$			6621.13i			0.548850i
$527$	−31712.0	+	31712.0i	−2.62125	+	2.62125i
$528$	1070.49	+	1070.49i	0.0882333	+	0.0882333i
$529$	44.7649	−	12166.9i	0.00367921	−	0.999993i
$530$	−5938.54	−	5534.06i	−0.486705	−	0.453555i
$531$	−116.977			−0.00955998
$532$	4657.30	+	4657.30i	0.379548	+	0.379548i
$533$	−3645.84	+	3645.84i	−0.296283	+	0.296283i
$534$	−14030.3			−1.13699
$535$	−132.649	−	3762.40i	−0.0107195	−	0.304042i
$536$		−	908.374i		−	0.0732011i
$537$	−4048.80	−	4048.80i	−0.325360	−	0.325360i
$538$	−1889.74	+	1889.74i	−0.151436	+	0.151436i
$539$	−13797.5			−1.10260
$540$	−237.899	−	6747.67i	−0.0189584	−	0.537729i
$541$	11688.6			0.928896			0.464448	−	0.885600i	$-0.346253\pi$
$541$	11688.6			0.928896			0.464448	+	0.885600i	$0.346253\pi$
$542$	3819.77	+	3819.77i	0.302718	+	0.302718i
$543$	−3671.59	−	3671.59i	−0.290171	−	0.290171i
$544$	4373.64			0.344703
$545$	−4241.60	+	4551.62i	−0.333376	+	0.357743i
$546$		−	15585.3i		−	1.22159i
$547$	12271.9	+	12271.9i	0.959247	+	0.959247i	0.999201	−	0.0399546i	$-0.0127213\pi$
$547$	12271.9	+	12271.9i	0.959247	+	0.959247i	−0.0399546	+	0.999201i	$0.512721\pi$
$548$	4815.87	+	4815.87i	0.375408	+	0.375408i
$549$	−2015.34			−0.156672
$550$	3875.53	+	3364.39i	0.300461	+	0.260833i
$551$		−	10567.5i		−	0.817045i
$552$	−2870.69	−	2881.27i	−0.221349	−	0.222165i
$553$	715.789	−	715.789i	0.0550424	−	0.0550424i
$554$			567.541i			0.0435244i
$555$	4599.73	+	4286.44i	0.351798	+	0.327836i
$556$	−11668.3			−0.890013
$557$	−149.728	+	149.728i	−0.0113899	+	0.0113899i	−0.712779	−	0.701389i	$-0.752564\pi$
$557$	−149.728	+	149.728i	−0.0113899	+	0.0113899i	0.701389	+	0.712779i	$0.252564\pi$
$558$	−2670.98	+	2670.98i	−0.202637	+	0.202637i
$559$	20167.2			1.52590
$560$	−200.818	−	5695.90i	−0.0151537	−	0.429814i
$561$	−12932.2			−0.973257
$562$	4057.04	−	4057.04i	0.304512	−	0.304512i
$563$	−2136.83	−	2136.83i	−0.159959	−	0.159959i	0.622590	−	0.782548i	$-0.286081\pi$
$563$	−2136.83	−	2136.83i	−0.159959	−	0.159959i	−0.782548	+	0.622590i	$0.786081\pi$
$564$			4991.95i			0.372693i
$565$	−12262.6	+	432.337i	−0.913083	+	0.0321921i
$566$		−	7384.82i		−	0.548422i
$567$	12176.1	−	12176.1i	0.901847	−	0.901847i
$568$	4026.23	−	4026.23i	0.297424	−	0.297424i
$569$	−9280.51			−0.683760			−0.341880	−	0.939744i	$-0.611064\pi$
$569$	−9280.51			−0.683760			−0.341880	+	0.939744i	$0.611064\pi$
$570$	3631.31	−	3896.72i	0.266840	−	0.286344i
$571$			6771.92i			0.496316i	0.968720	+	0.248158i	$0.0798252\pi$
$571$			6771.92i			0.496316i	−0.968720	+	0.248158i	$0.920175\pi$
$572$	−3081.14	+	3081.14i	−0.225226	+	0.225226i
$573$	3778.67	+	3778.67i	0.275491	+	0.275491i
$574$	−6191.45			−0.450220
$575$	−10395.4	−	9057.91i	−0.753942	−	0.656941i
$576$	368.375			0.0266475
$577$	−12124.0	−	12124.0i	−0.874744	−	0.874744i	0.118241	−	0.992985i	$-0.462275\pi$
$577$	−12124.0	−	12124.0i	−0.874744	−	0.874744i	−0.992985	+	0.118241i	$0.962275\pi$
$578$	−19470.1	+	19470.1i	−1.40112	+	1.40112i
$579$			8776.75i			0.629964i
$580$	−6234.24	+	6689.90i	−0.446315	+	0.478936i
$581$	18981.2			1.35537
$582$	5544.68	−	5544.68i	0.394904	−	0.394904i
$583$	−5269.57	+	5269.57i	−0.374345	+	0.374345i
$584$			1805.00i			0.127896i
$585$	3412.74	−	120.321i	0.241196	−	0.00850372i
$586$			11827.6i			0.833779i
$587$	13909.3	+	13909.3i	0.978019	+	0.978019i	0.999764	−	0.0217444i	$-0.00692201\pi$
$587$	13909.3	+	13909.3i	0.978019	+	0.978019i	−0.0217444	+	0.999764i	$0.506922\pi$
$588$	8762.08	−	8762.08i	0.614527	−	0.614527i
$589$	−16958.1			−1.18633
$590$	16.0119	+	454.155i	0.00111729	+	0.0316903i
$591$	−19812.5			−1.37898
$592$	−1380.38	+	1380.38i	−0.0958334	+	0.0958334i
$593$	3711.43	−	3711.43i	0.257015	−	0.257015i	−0.566824	−	0.823839i	$-0.691828\pi$
$593$	3711.43	−	3711.43i	0.257015	−	0.257015i	0.823839	+	0.566824i	$0.191828\pi$
$594$	−6198.65			−0.428171
$595$	35618.0	+	33192.0i	2.45411	+	2.28695i
$596$		−	12109.7i		−	0.832271i
$597$	−16262.5	+	16262.5i	−1.11488	+	1.11488i
$598$	8293.01	−	8262.56i	0.567101	−	0.565018i
$599$			24037.0i			1.63961i	0.572643	+	0.819805i	$0.305918\pi$
$599$			24037.0i			1.63961i	−0.572643	+	0.819805i	$0.694082\pi$
$600$	−4597.69	+	324.601i	−0.312833	+	0.0220863i
$601$	396.101			0.0268840			0.0134420	−	0.999910i	$-0.495721\pi$
$601$	396.101			0.0268840			0.0134420	+	0.999910i	$0.495721\pi$
$602$	17124.2	+	17124.2i	1.15935	+	1.15935i
$603$	462.136	+	462.136i	0.0312100	+	0.0312100i
$604$			6187.20i			0.416811i
$605$	−6933.01	+	7439.75i	−0.465896	+	0.499948i
$606$	7835.91			0.525267
$607$	−9885.65	−	9885.65i	−0.661032	−	0.661032i	0.294591	−	0.955623i	$-0.404816\pi$
$607$	−9885.65	−	9885.65i	−0.661032	−	0.661032i	−0.955623	+	0.294591i	$0.904816\pi$
$608$	1169.41	+	1169.41i	0.0780030	+	0.0780030i
$609$	−30027.5			−1.99799
$610$	275.863	+	7824.45i	0.0183104	+	0.519349i
$611$	−14368.1			−0.951342
$612$	−2225.09	+	2225.09i	−0.146968	+	0.146968i
$613$	17592.7	+	17592.7i	1.15916	+	1.15916i	0.984657	+	0.174501i	$0.0558312\pi$
$613$	17592.7	+	17592.7i	1.15916	+	1.15916i	0.174501	+	0.984657i	$0.444169\pi$
$614$		−	3485.66i		−	0.229104i
$615$	176.421	+	5003.91i	0.0115674	+	0.328093i
$616$	−5232.46			−0.342243
$617$	18163.9	−	18163.9i	1.18517	−	1.18517i	0.206788	−	0.978386i	$-0.433699\pi$
$617$	18163.9	−	18163.9i	1.18517	−	1.18517i	0.978386	−	0.206788i	$-0.0663009\pi$
$618$	2279.93	+	2279.93i	0.148402	+	0.148402i
$619$	15708.4			1.01999			0.509997	−	0.860176i	$-0.329647\pi$
$619$	15708.4			1.01999			0.509997	+	0.860176i	$0.329647\pi$
$620$	10735.5	+	10004.3i	0.695403	+	0.648037i
$621$	16653.3	+	30.6355i	1.07612	+	0.00197965i
$622$	359.902	+	359.902i	0.0232006	+	0.0232006i
$623$	34289.4	−	34289.4i	2.20510	−	2.20510i
$624$		−	3913.34i		−	0.251056i
$625$	−15470.0	+	2195.33i	−0.990080	+	0.140501i
$626$		−	4956.21i		−	0.316438i
$627$	−3457.76	−	3457.76i	−0.220239	−	0.220239i
$628$	−570.088	−	570.088i	−0.0362245	−	0.0362245i
$629$		−	16675.9i		−	1.05709i
$630$	2999.96	+	2795.63i	0.189716	+	0.176794i
$631$		−	663.267i		−	0.0418450i	−0.999781	−	0.0209225i	$-0.993340\pi$
$631$		−	663.267i		−	0.0418450i	0.999781	−	0.0209225i	$-0.00666033\pi$
$632$	179.729	−	179.729i	0.0113121	−	0.0113121i
$633$	−5407.82	+	5407.82i	−0.339560	+	0.339560i
$634$		−	16728.4i		−	1.04790i
$635$	−17240.7	+	607.847i	−1.07744	+	0.0379869i
$636$		−	6692.85i		−	0.417278i
$637$	25219.5	+	25219.5i	1.56865	+	1.56865i
$638$	5936.29	+	5936.29i	0.368370	+	0.368370i
$639$			4096.69i			0.253619i
$640$	−50.4237	−	1430.19i	−0.00311433	−	0.0883335i
$641$			7629.00i			0.470090i	0.971985	+	0.235045i	$0.0755237\pi$
$641$			7629.00i			0.470090i	−0.971985	+	0.235045i	$0.924476\pi$
$642$	2194.90	−	2194.90i	0.134931	−	0.134931i
$643$	−13517.2	−	13517.2i	−0.829028	−	0.829028i	0.158354	−	0.987382i	$-0.449381\pi$
$643$	−13517.2	−	13517.2i	−0.829028	−	0.829028i	−0.987382	+	0.158354i	$0.949381\pi$
$644$	14057.5	+	25.8603i	0.860161	+	0.00158236i
$645$	13351.8	−	14327.6i	0.815078	−	0.874652i
$646$	−14127.2			−0.860412
$647$	−3628.74	−	3628.74i	−0.220496	−	0.220496i	0.588212	−	0.808707i	$-0.299832\pi$
$647$	−3628.74	−	3628.74i	−0.220496	−	0.220496i	−0.808707	+	0.588212i	$0.799832\pi$
$648$	3057.31	−	3057.31i	0.185344	−	0.185344i
$649$	417.203			0.0252337
$650$	−934.282	−	13233.3i	−0.0563778	−	0.798543i
$651$			48186.2i			2.90102i
$652$	−9395.07	−	9395.07i	−0.564324	−	0.564324i
$653$	5218.75	−	5218.75i	0.312750	−	0.312750i	−0.533224	−	0.845974i	$-0.679020\pi$
$653$	5218.75	−	5218.75i	0.312750	−	0.312750i	0.845974	+	0.533224i	$0.179020\pi$
$654$	−5129.76			−0.306712
$655$	−1392.09	+	1493.83i	−0.0830433	+	0.0891129i
$656$	−1554.62			−0.0925271
$657$	−918.297	−	918.297i	−0.0545299	−	0.0545299i
$658$	−12200.1	−	12200.1i	−0.722809	−	0.722809i
$659$	18113.6			1.07072			0.535362	−	0.844623i	$-0.320175\pi$
$659$	18113.6			1.07072			0.535362	+	0.844623i	$0.320175\pi$
$660$	149.095	+	4228.86i	0.00879320	+	0.249406i
$661$		−	12099.8i		−	0.711991i	−0.934488	−	0.355996i	$-0.884142\pi$
$661$		−	12099.8i		−	0.711991i	0.934488	−	0.355996i	$-0.115858\pi$
$662$	−443.106	−	443.106i	−0.0260148	−	0.0260148i
$663$	23637.7	+	23637.7i	1.38464	+	1.38464i
$664$	4766.02			0.278550
$665$	648.655	+	18398.2i	0.0378252	+	1.07286i
$666$		−	1404.54i		−	0.0817190i
$667$	−15919.1	−	15977.8i	−0.924122	−	0.927528i
$668$	−4260.94	+	4260.94i	−0.246797	+	0.246797i
$669$		−	22116.2i		−	1.27812i
$670$	1730.96	−	1857.48i	0.0998101	−	0.107105i
$671$	7187.82			0.413536
$672$	3322.86	−	3322.86i	0.190747	−	0.190747i
$673$	−3061.53	+	3061.53i	−0.175354	+	0.175354i	−0.789327	−	0.613973i	$-0.789570\pi$
$673$	−3061.53	+	3061.53i	−0.175354	+	0.175354i	0.613973	+	0.789327i	$0.289570\pi$
$674$	3760.45			0.214907
$675$	12371.6	−	14251.2i	0.705457	−	0.812636i
$676$	2475.57			0.140849
$677$	−10300.3	+	10300.3i	−0.584747	+	0.584747i	−0.936204	−	0.351457i	$-0.885686\pi$
$677$	−10300.3	+	10300.3i	−0.584747	+	0.584747i	0.351457	+	0.936204i	$0.385686\pi$
$678$	−7153.73	−	7153.73i	−0.405217	−	0.405217i
$679$			27101.8i			1.53177i
$680$	8943.38	+	8334.23i	0.504357	+	0.470005i
$681$		−	11831.2i		−	0.665743i
$682$	9526.19	−	9526.19i	0.534863	−	0.534863i
$683$	−9533.37	+	9533.37i	−0.534091	+	0.534091i	−0.921787	−	0.387696i	$-0.873271\pi$
$683$	−9533.37	+	9533.37i	−0.534091	+	0.534091i	0.387696	+	0.921787i	$0.373271\pi$
$684$	−1189.88			−0.0665147
$685$	670.740	+	19024.6i	0.0374127	+	1.06116i
$686$			20971.7i			1.16720i
$687$	12263.7	−	12263.7i	0.681060	−	0.681060i
$688$	4299.74	+	4299.74i	0.238265	+	0.238265i
$689$	19263.7			1.06515
$690$	−379.658	−	11362.0i	−0.0209468	−	0.626874i
$691$	18750.0			1.03225			0.516124	−	0.856514i	$-0.327375\pi$
$691$	18750.0			1.03225			0.516124	+	0.856514i	$0.327375\pi$
$692$	−11655.5	−	11655.5i	−0.640282	−	0.640282i
$693$	2662.02	−	2662.02i	0.145919	−	0.145919i
$694$		−	14188.9i		−	0.776086i
$695$	−23859.8	−	22234.7i	−1.30224	−	1.21354i
$696$	−7539.65			−0.410617
$697$	9390.38	−	9390.38i	0.510310	−	0.510310i
$698$	6467.24	−	6467.24i	0.350700	−	0.350700i
$699$			8562.88i			0.463345i
$700$	10443.2	−	12029.9i	0.563882	−	0.649551i
$701$			14575.8i			0.785337i	0.919680	+	0.392668i	$0.128448\pi$
$701$			14575.8i			0.785337i	−0.919680	+	0.392668i	$0.871552\pi$
$702$	11330.0	+	11330.0i	0.609152	+	0.609152i
$703$	4458.73	−	4458.73i	0.239210	−	0.239210i
$704$	−1313.83			−0.0703363
$705$	−9512.44	+	10207.7i	−0.508169	+	0.545311i
$706$	−5844.30			−0.311548
$707$	−19150.6	+	19150.6i	−1.01872	+	1.01872i
$708$	−264.943	+	264.943i	−0.0140638	+	0.0140638i
$709$	−5030.30			−0.266455			−0.133228	−	0.991085i	$-0.542534\pi$
$709$	−5030.30			−0.266455			−0.133228	+	0.991085i	$0.542534\pi$
$710$	15905.2	−	560.761i	0.840719	−	0.0296408i
$711$			182.874i			0.00964602i
$712$	8609.79	−	8609.79i	0.453182	−	0.453182i
$713$	−25640.1	+	25545.9i	−1.34675	+	1.34180i
$714$			40142.1i			2.10404i
$715$	−12171.7	+	429.133i	−0.636638	+	0.0224457i
$716$	4969.14			0.259365
$717$	13801.2	+	13801.2i	0.718849	+	0.718849i
$718$	15952.0	+	15952.0i	0.829139	+	0.829139i
$719$		−	11459.1i		−	0.594370i	−0.954820	−	0.297185i	$-0.903952\pi$
$719$		−	11459.1i		−	0.594370i	0.954820	−	0.297185i	$-0.0960479\pi$
$720$	753.266	+	701.960i	0.0389897	+	0.0363340i
$721$	−11144.1			−0.575627
$722$	5922.81	+	5922.81i	0.305297	+	0.305297i
$723$	−14017.9	−	14017.9i	−0.721068	−	0.721068i
$724$	4506.19			0.231314
$725$	−25496.0	+	1800.04i	−1.30607	+	0.0922093i
$726$	−8384.74			−0.428632
$727$	−20764.6	+	20764.6i	−1.05931	+	1.05931i	−0.0611811	+	0.998127i	$0.519487\pi$
$727$	−20764.6	+	20764.6i	−1.05931	+	1.05931i	−0.998127	+	0.0611811i	$0.980513\pi$
$728$	9564.02	+	9564.02i	0.486904	+	0.486904i
$729$			21899.3i			1.11260i
$730$	−3439.54	+	3690.93i	−0.174388	+	0.187134i
$731$	−51943.4			−2.62818
$732$	−4564.60	+	4564.60i	−0.230482	+	0.230482i
$733$	7383.80	+	7383.80i	0.372069	+	0.372069i	0.868230	−	0.496161i	$-0.165257\pi$
$733$	7383.80	+	7383.80i	0.372069	+	0.372069i	−0.496161	+	0.868230i	$0.665257\pi$
$734$	7878.83			0.396203
$735$	34613.7	−	1220.36i	1.73707	−	0.0612429i
$736$	3529.73	+	6.49332i	0.176776	+	0.000325199i
$737$	−1648.23	−	1648.23i	−0.0823791	−	0.0823791i
$738$	790.915	−	790.915i	0.0394499	−	0.0394499i
$739$		−	8684.56i		−	0.432296i	−0.976361	−	0.216148i	$-0.930651\pi$
$739$		−	8684.56i		−	0.432296i	0.976361	−	0.216148i	$-0.0693494\pi$
$740$	−5453.05	+	192.256i	−0.270890	+	0.00955062i
$741$			12640.4i			0.626660i
$742$	16357.0	+	16357.0i	0.809279	+	0.809279i
$743$	17571.8	+	17571.8i	0.867627	+	0.867627i	0.992209	−	0.124582i	$-0.0397591\pi$
$743$	17571.8	+	17571.8i	0.867627	+	0.867627i	−0.124582	+	0.992209i	$0.539759\pi$
$744$			12099.2i			0.596205i
$745$	23075.8	−	24762.4i	1.13481	−	1.21775i
$746$		−	19613.4i		−	0.962599i
$747$	−2424.72	+	2424.72i	−0.118763	+	0.118763i
$748$	7935.92	−	7935.92i	0.387922	−	0.387922i
$749$			10728.4i			0.523376i
$750$	−10020.1	−	8097.41i	−0.487842	−	0.394234i
$751$			15654.3i			0.760632i	0.924857	+	0.380316i	$0.124185\pi$
$751$			15654.3i			0.760632i	−0.924857	+	0.380316i	$0.875815\pi$
$752$	−3063.34	−	3063.34i	−0.148549	−	0.148549i
$753$	−2468.54	−	2468.54i	−0.119467	−	0.119467i
$754$		−	21701.0i		−	1.04815i
$755$	−11790.1	+	12651.8i	−0.568324	+	0.609863i
$756$			19240.9i			0.925642i
$757$	−19990.6	+	19990.6i	−0.959803	+	0.959803i	−0.999223	−	0.0394201i	$-0.987449\pi$
$757$	−19990.6	+	19990.6i	−0.959803	+	0.959803i	0.0394201	+	0.999223i	$0.487449\pi$
$758$	4857.40	+	4857.40i	0.232756	+	0.232756i
$759$	−10436.8	−	19.1997i	−0.499122	−	0.000918189i
$760$	162.872	+	4619.63i	0.00777367	+	0.220489i
$761$	5549.93			0.264369			0.132184	−	0.991225i	$-0.457801\pi$
$761$	5549.93			0.264369			0.132184	+	0.991225i	$0.457801\pi$
$762$	−10057.8	−	10057.8i	−0.478158	−	0.478158i
$763$	12536.9	−	12536.9i	0.594844	−	0.594844i
$764$	−4637.62			−0.219611
$765$	−8790.00	+	309.905i	−0.415429	+	0.0146466i
$766$		−	17054.6i		−	0.804451i
$767$	−762.573	−	762.573i	−0.0358995	−	0.0358995i
$768$	834.343	−	834.343i	0.0392015	−	0.0392015i
$769$	−9242.72			−0.433422			−0.216711	−	0.976236i	$-0.569533\pi$
$769$	−9242.72			−0.433422			−0.216711	+	0.976236i	$0.569533\pi$
$770$	−10699.5	−	9970.76i	−0.500758	−	0.466651i
$771$	13098.4			0.611840
$772$	−5385.91	−	5385.91i	−0.251092	−	0.251092i
$773$	−8307.19	−	8307.19i	−0.386531	−	0.386531i	0.486917	−	0.873448i	$-0.338121\pi$
$773$	−8307.19	−	8307.19i	−0.386531	−	0.386531i	−0.873448	+	0.486917i	$0.838121\pi$
$774$	−4374.99			−0.203173
$775$	2888.59	+	40914.4i	0.133885	+	1.89637i
$776$			6805.05i			0.314803i
$777$	−12669.4	−	12669.4i	−0.584958	−	0.584958i
$778$	2472.55	+	2472.55i	0.113940	+	0.113940i
$779$	5021.54			0.230957
$780$	7457.10	−	8002.13i	0.342317	−	0.367336i
$781$		−	14611.1i		−	0.669430i
$782$	−21359.8	+	21281.4i	−0.976759	+	0.973172i
$783$	21829.1	−	21829.1i	0.996306	−	0.996306i
$784$			10753.8i			0.489879i
$785$	−79.4002	−	2252.07i	−0.00361008	−	0.102395i
$786$	−1683.58			−0.0764012
$787$	29714.8	−	29714.8i	1.34589	−	1.34589i	0.455822	−	0.890071i	$-0.349345\pi$
$787$	29714.8	−	29714.8i	1.34589	−	1.34589i	0.890071	−	0.455822i	$-0.150655\pi$
$788$	12158.1	−	12158.1i	0.549636	−	0.549636i
$789$	−15258.8			−0.688504
$790$	709.999	−	25.0321i	0.0319755	−	0.00112734i
$791$	34966.7			1.57177
$792$	668.411	−	668.411i	0.0299886	−	0.0299886i
$793$	−13138.1	−	13138.1i	−0.588331	−	0.588331i
$794$		−	13804.3i		−	0.616997i
$795$	12753.6	−	13685.8i	0.568961	−	0.610547i
$796$		−	19959.2i		−	0.888738i
$797$	−5933.76	+	5933.76i	−0.263719	+	0.263719i	−0.826563	−	0.562844i	$-0.809707\pi$
$797$	−5933.76	+	5933.76i	−0.263719	+	0.263719i	0.562844	+	0.826563i	$0.309707\pi$
$798$	−10733.1	+	10733.1i	−0.476123	+	0.476123i
$799$	37007.0			1.63856
$800$	2622.21	−	3020.60i	0.115886	−	0.133493i
$801$			8760.48i			0.386437i
$802$	−13676.3	+	13676.3i	−0.602154	+	0.602154i
$803$	3275.15	+	3275.15i	0.143932	+	0.143932i
$804$	2093.41			0.0918270
$805$	28696.0	+	26840.3i	1.25640	+	1.17515i
$806$	−34824.4			−1.52188
$807$	−4355.04	−	4355.04i	−0.189969	−	0.189969i
$808$	−4808.55	+	4808.55i	−0.209362	+	0.209362i
$809$		−	20609.3i		−	0.895655i	−0.894120	−	0.447828i	$-0.852198\pi$
$809$		−	20609.3i		−	0.895655i	0.894120	−	0.447828i	$-0.147802\pi$
$810$	12077.6	−	425.814i	0.523905	−	0.0184711i
$811$	−18567.7			−0.803947			−0.401973	−	0.915651i	$-0.631676\pi$
$811$	−18567.7			−0.803947			−0.401973	+	0.915651i	$0.631676\pi$
$812$	18426.5	−	18426.5i	0.796361	−	0.796361i
$813$	−8802.92	+	8802.92i	−0.379744	+	0.379744i
$814$			5009.37i			0.215698i
$815$	−1308.52	−	37114.2i	−0.0562398	−	1.59516i
$816$			10079.4i			0.432412i
$817$	−13888.5	−	13888.5i	−0.594731	−	0.594731i
$818$	2558.91	−	2558.91i	0.109377	−	0.109377i
$819$	−9731.40			−0.415193
$820$	−3178.95	−	2962.42i	−0.135382	−	0.126161i
$821$	35252.4			1.49856			0.749281	−	0.662253i	$-0.230399\pi$
$821$	35252.4			1.49856			0.749281	+	0.662253i	$0.230399\pi$
$822$	−11098.5	+	11098.5i	−0.470930	+	0.470930i
$823$	18459.9	−	18459.9i	0.781861	−	0.781861i	−0.198283	−	0.980145i	$-0.563537\pi$
$823$	18459.9	−	18459.9i	0.781861	−	0.781861i	0.980145	+	0.198283i	$0.0635366\pi$
$824$	−2798.19			−0.118300
$825$	−7753.47	+	8931.43i	−0.327201	+	0.376912i
$826$		−	1295.02i		−	0.0545514i
$827$	37.7194	−	37.7194i	0.00158601	−	0.00158601i	−0.706313	−	0.707899i	$-0.749643\pi$
$827$	37.7194	−	37.7194i	0.00158601	−	0.00158601i	0.707899	+	0.706313i	$0.249643\pi$
$828$	−1799.05	+	1792.45i	−0.0755090	+	0.0752317i
$829$			4140.87i			0.173484i	0.996231	+	0.0867420i	$0.0276456\pi$
$829$			4140.87i			0.173484i	−0.996231	+	0.0867420i	$0.972354\pi$
$830$	9745.73	+	9081.93i	0.407565	+	0.379805i
$831$	−1307.94			−0.0545991
$832$	2401.45	+	2401.45i	0.100066	+	0.100066i
$833$	−64956.3	−	64956.3i	−2.70180	−	2.70180i
$834$		−	26890.4i		−	1.11647i
$835$	−16832.4	+	593.451i	−0.697615	+	0.0245955i
$836$	4243.76			0.175566
$837$	−35029.9	−	35029.9i	−1.44661	−	1.44661i
$838$	−221.796	−	221.796i	−0.00914299	−	0.00914299i
$839$	−16194.9			−0.666402			−0.333201	−	0.942856i	$-0.608129\pi$
$839$	−16194.9			−0.666402			−0.333201	+	0.942856i	$0.608129\pi$
$840$	13126.6	−	462.798i	0.539179	−	0.0190096i
$841$	−17421.3			−0.714309
$842$	13836.6	−	13836.6i	0.566318	−	0.566318i
$843$	9349.72	+	9349.72i	0.381995	+	0.381995i
$844$		−	6637.09i		−	0.270685i
$845$	5062.13	+	4717.34i	0.206086	+	0.192049i
$846$	3116.95			0.126670
$847$	20491.9	−	20491.9i	0.831299	−	0.831299i
$848$	4107.11	+	4107.11i	0.166319	+	0.166319i
$849$	17018.8			0.687968
$850$	2406.38	+	34084.3i	0.0971035	+	1.37539i
$851$	24.7577	−	13458.2i	0.000997279	−	0.542115i
$852$	9278.72	+	9278.72i	0.373103	+	0.373103i
$853$	11043.6	−	11043.6i	0.443290	−	0.443290i	−0.449826	−	0.893116i	$-0.648514\pi$
$853$	11043.6	−	11043.6i	0.443290	−	0.443290i	0.893116	+	0.449826i	$0.148514\pi$
$854$		−	22311.4i		−	0.894003i
$855$	−2433.10	−	2267.38i	−0.0973220	−	0.0906932i
$856$			2693.83i			0.107562i
$857$	16917.5	+	16917.5i	0.674319	+	0.674319i	0.958709	−	0.284389i	$-0.0917909\pi$
$857$	16917.5	+	16917.5i	0.674319	+	0.674319i	−0.284389	+	0.958709i	$0.591791\pi$
$858$	−7100.70	−	7100.70i	−0.282534	−	0.282534i
$859$			19623.9i			0.779464i	0.920928	+	0.389732i	$0.127432\pi$
$859$			19623.9i			0.779464i	−0.920928	+	0.389732i	$0.872568\pi$
$860$	598.855	+	16985.7i	0.0237451	+	0.673495i
$861$		−	14268.6i		−	0.564777i
$862$	−10821.9	+	10821.9i	−0.427605	+	0.427605i
$863$	−22879.4	+	22879.4i	−0.902461	+	0.902461i	−0.995649	−	0.0931879i	$-0.970294\pi$
$863$	−22879.4	+	22879.4i	−0.902461	+	0.902461i	0.0931879	+	0.995649i	$0.470294\pi$
$864$			4831.24i			0.190234i
$865$	−1623.34	−	46043.8i	−0.0638096	−	1.80987i
$866$		−	7341.77i		−	0.288087i
$867$	−44870.2	−	44870.2i	−1.75764	−	1.75764i
$868$	−29569.8	−	29569.8i	−1.15629	−	1.15629i
$869$		−	652.231i		−	0.0254608i
$870$	−15417.3	−	14367.2i	−0.600801	−	0.559879i
$871$			6025.36i			0.234399i
$872$	3147.91	−	3147.91i	0.122250	−	0.122250i
$873$	−3462.08	−	3462.08i	−0.134219	−	0.134219i
$874$	−11401.3	−	20.9739i	−0.441251	−	0.000811729i
$875$	44278.3	−	4698.87i	1.71072	−	0.181544i
$876$	−4159.75			−0.160439
$877$	−11175.2	−	11175.2i	−0.430287	−	0.430287i	0.458439	−	0.888726i	$-0.348409\pi$
$877$	−11175.2	−	11175.2i	−0.430287	−	0.430287i	−0.888726	+	0.458439i	$0.848409\pi$
$878$	13347.3	−	13347.3i	0.513040	−	0.513040i
$879$	−27257.6			−1.04593
$880$	−2686.56	−	2503.58i	−0.102914	−	0.0959040i
$881$		−	28496.0i		−	1.08973i	−0.838523	−	0.544865i	$-0.816581\pi$
$881$		−	28496.0i		−	1.08973i	0.838523	−	0.544865i	$-0.183419\pi$
$882$	−5471.01	−	5471.01i	−0.208865	−	0.208865i
$883$	−13355.2	+	13355.2i	−0.508989	+	0.508989i	−0.914216	−	0.405227i	$-0.867193\pi$
$883$	−13355.2	+	13355.2i	−0.508989	+	0.508989i	0.405227	+	0.914216i	$0.367193\pi$
$884$	−29010.9			−1.10378
$885$	−1046.63	+	36.9006i	−0.0397538	+	0.00140158i
$886$	−7971.83			−0.302279
$887$	14325.3	+	14325.3i	0.542274	+	0.542274i	0.924195	−	0.381921i	$-0.124737\pi$
$887$	14325.3	+	14325.3i	0.542274	+	0.542274i	−0.381921	+	0.924195i	$0.624737\pi$
$888$	−3181.19	−	3181.19i	−0.120218	−	0.120218i
$889$	49161.7			1.85470
$890$	34012.1	−	1199.15i	1.28100	−	0.0451635i
$891$		−	11094.9i		−	0.417164i
$892$	13571.8	+	13571.8i	0.509435	+	0.509435i
$893$	9894.80	+	9894.80i	0.370792	+	0.370792i
$894$	27907.7			1.04404
$895$	10161.1	+	9468.99i	0.379494	+	0.353646i
$896$			4078.19i			0.152057i
$897$	19041.6	+	19111.8i	0.708786	+	0.711399i
$898$	−9709.39	+	9709.39i	−0.360809	+	0.360809i
$899$			67094.5i			2.48913i
$900$	202.680	+	2870.78i	0.00750665	+	0.106325i
$901$	−49616.4			−1.83459
$902$	−2820.84	+	2820.84i	−0.104128	+	0.104128i
$903$	−39463.8	+	39463.8i	−1.45434	+	1.45434i
$904$	8779.86			0.323024
$905$	9214.42	+	8586.81i	0.338450	+	0.315398i
$906$	−14258.8			−0.522867
$907$	17477.1	−	17477.1i	0.639819	−	0.639819i	−0.310692	−	0.950511i	$-0.600561\pi$
$907$	17477.1	−	17477.1i	0.639819	−	0.639819i	0.950511	+	0.310692i	$0.100561\pi$
$908$	7260.27	+	7260.27i	0.265353	+	0.265353i
$909$		−	4892.71i		−	0.178527i
$910$	1332.05	+	37781.6i	0.0485242	+	1.37632i
$911$		−	40680.6i		−	1.47948i	−0.672891	−	0.739741i	$-0.734948\pi$
$911$		−	40680.6i		−	1.47948i	0.672891	−	0.739741i	$-0.265052\pi$
$912$	−2694.99	+	2694.99i	−0.0978508	+	0.0978508i
$913$	8647.88	−	8647.88i	0.313475	−	0.313475i
$914$	−3562.51			−0.128925
$915$	−18032.0	+	635.745i	−0.651496	+	0.0229695i
$916$			15051.4i			0.542916i
$917$	4114.59	−	4114.59i	0.148174	−	0.148174i
$918$	−29182.1	−	29182.1i	−1.04919	−	1.04919i
$919$	−2774.59			−0.0995921			−0.0497961	−	0.998759i	$-0.515857\pi$
$919$	−2774.59			−0.0995921			−0.0497961	+	0.998759i	$0.515857\pi$
$920$	7205.33	+	6739.37i	0.258210	+	0.241512i
$921$	8032.95			0.287399
$922$	16329.7	+	16329.7i	0.583286	+	0.583286i
$923$	−26706.5	+	26706.5i	−0.952388	+	0.952388i
$924$		−	12058.6i		−	0.429326i
$925$	−11516.9	−	9997.98i	−0.409378	−	0.355385i
$926$	−11395.0			−0.404387
$927$	1423.58	−	1423.58i	0.0504385	−	0.0504385i
$928$	4626.76	−	4626.76i	0.163665	−	0.163665i
$929$		−	21566.5i		−	0.761651i	−0.924647	−	0.380825i	$-0.875640\pi$
$929$		−	21566.5i		−	0.761651i	0.924647	−	0.380825i	$-0.124360\pi$
$930$	−23055.6	+	24740.8i	−0.812929	+	0.872346i
$931$		−	34735.6i		−	1.22278i
$932$	−5254.67	−	5254.67i	−0.184681	−	0.184681i
$933$	−829.418	+	829.418i	−0.0291039	+	0.0291039i
$934$	−13635.1			−0.477682
$935$	31350.0	−	1105.29i	1.09653	−	0.0386598i
$936$	−2443.48			−0.0853285
$937$	−16233.9	+	16233.9i	−0.565997	+	0.565997i	−0.931005	−	0.365008i	$-0.881066\pi$
$937$	−16233.9	+	16233.9i	−0.565997	+	0.565997i	0.365008	+	0.931005i	$0.381066\pi$
$938$	−5116.20	+	5116.20i	−0.178091	+	0.178091i
$939$	11421.9			0.396954
$940$	−426.653	−	12101.4i	−0.0148041	−	0.419898i
$941$		−	20940.1i		−	0.725429i	−0.931900	−	0.362714i	$-0.881850\pi$
$941$		−	20940.1i		−	0.725429i	0.931900	−	0.362714i	$-0.118150\pi$
$942$	1313.81	−	1313.81i	0.0454418	−	0.0454418i
$943$	7592.40	−	7564.52i	0.262187	−	0.261224i
$944$		−	325.169i		−	0.0112112i
$945$	−36664.7	+	39344.5i	−1.26212	+	1.35437i
$946$	15603.6			0.536277
$947$	−258.525	−	258.525i	−0.00887109	−	0.00887109i	0.702657	−	0.711528i	$-0.251997\pi$
$947$	−258.525	−	258.525i	−0.00887109	−	0.00887109i	−0.711528	+	0.702657i	$0.751997\pi$
$948$	414.197	+	414.197i	0.0141904	+	0.0141904i
$949$		−	11972.8i		−	0.409540i
$950$	−8469.92	+	9756.74i	−0.289264	+	0.333211i
$951$	38551.9			1.31454
$952$	−24633.5	−	24633.5i	−0.838630	−	0.838630i
$953$	−22053.4	−	22053.4i	−0.749613	−	0.749613i	0.224793	−	0.974406i	$-0.427829\pi$
$953$	−22053.4	−	22053.4i	−0.749613	−	0.749613i	−0.974406	+	0.224793i	$0.927829\pi$
$954$	−4178.99			−0.141824
$955$	−9483.16	−	8837.25i	−0.321328	−	0.299441i
$956$	−16938.4			−0.573040
$957$	−13680.6	+	13680.6i	−0.462101	+	0.462101i
$958$	13258.0	+	13258.0i	0.447127	+	0.447127i
$959$		−	54248.4i		−	1.82667i
$960$	3295.98	−	116.205i	0.110810	−	0.00390677i
$961$	77878.1			2.61415
$962$	9156.25	−	9156.25i	0.306870	−	0.306870i
$963$	−1370.49	−	1370.49i	−0.0458601	−	0.0458601i
$964$	17204.4			0.574809
$965$	−750.134	−	21276.4i	−0.0250235	−	0.709755i
$966$	−59.5969	+	32396.5i	−0.00198499	+	1.07903i
$967$	−28788.8	−	28788.8i	−0.957380	−	0.957380i	0.0417485	−	0.999128i	$-0.486707\pi$
$967$	−28788.8	−	28788.8i	−0.957380	−	0.957380i	−0.999128	+	0.0417485i	$0.986707\pi$
$968$	5145.35	−	5145.35i	0.170845	−	0.170845i
$969$		−	32557.0i		−	1.07934i
$970$	−12967.4	+	13915.2i	−0.429236	+	0.460609i
$971$			11518.7i			0.380692i	0.981717	+	0.190346i	$0.0609610\pi$
$971$			11518.7i			0.380692i	−0.981717	+	0.190346i	$0.939039\pi$
$972$	−4483.89	−	4483.89i	−0.147964	−	0.147964i
$973$	65719.0	+	65719.0i	2.16532	+	2.16532i
$974$			2292.16i			0.0754060i
$975$	30497.1	−	2153.12i	1.00173	−	0.0707230i
$976$		−	5602.20i		−	0.183732i
$977$	27549.1	−	27549.1i	0.902122	−	0.902122i	−0.0934975	−	0.995620i	$-0.529805\pi$
$977$	27549.1	−	27549.1i	0.902122	−	0.902122i	0.995620	+	0.0934975i	$0.0298047\pi$
$978$	21651.6	−	21651.6i	0.707915	−	0.707915i
$979$		−	31244.7i		−	1.02000i
$980$	−20492.0	+	21989.8i	−0.667953	+	0.716773i
$981$			3203.00i			0.104245i
$982$	−8737.29	−	8737.29i	−0.283929	−	0.283929i
$983$	19609.7	+	19609.7i	0.636270	+	0.636270i	0.949633	−	0.313364i	$-0.101456\pi$
$983$	19609.7	+	19609.7i	0.636270	+	0.636270i	−0.313364	+	0.949633i	$0.601456\pi$
$984$		−	3582.73i		−	0.116070i
$985$	48029.1	−	1693.34i	1.55364	−	0.0547759i
$986$			55894.0i			1.80530i
$987$	28115.9	−	28115.9i	0.906727	−	0.906727i
$988$	−7756.84	−	7756.84i	−0.249775	−	0.249775i
$989$	−41920.7	−	77.1176i	−1.34783	−	0.00247947i
$990$	2640.49	−	93.0944i	0.0847678	−	0.00298862i
$991$	6175.70			0.197959			0.0989796	−	0.995089i	$-0.468442\pi$
$991$	6175.70			0.197959			0.0989796	+	0.995089i	$0.468442\pi$
$992$	−7424.73	−	7424.73i	−0.237636	−	0.237636i
$993$	1021.17	−	1021.17i	0.0326343	−	0.0326343i
$994$	−45353.5			−1.44721
$995$	38033.4	−	40813.3i	1.21180	−	1.30037i
$996$			10983.6i			0.349427i
$997$	−9426.32	−	9426.32i	−0.299433	−	0.299433i	0.541359	−	0.840792i	$-0.317910\pi$
$997$	−9426.32	−	9426.32i	−0.299433	−	0.299433i	−0.840792	+	0.541359i	$0.817910\pi$
$998$	−16049.9	+	16049.9i	−0.509068	+	0.509068i
$999$	18420.6			0.583385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.e.a.137.13	✓	72
5.3	odd	4	inner	230.4.e.a.183.14	yes	72
23.22	odd	2	inner	230.4.e.a.137.14	yes	72
115.68	even	4	inner	230.4.e.a.183.13	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.e.a.137.13	✓	72	1.1	even	1	trivial
230.4.e.a.137.14	yes	72	23.22	odd	2	inner
230.4.e.a.183.13	yes	72	115.68	even	4	inner
230.4.e.a.183.14	yes	72	5.3	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.41421 - 1.41421i) q^{2} +(3.25915 - 3.25915i) q^{3} +4.00000i q^{4} +(-7.62223 + 8.17934i) q^{5} -9.21827 q^{6} +(22.5290 - 22.5290i) q^{7} +(5.65685 - 5.65685i) q^{8} +5.75586i q^{9} +O(q^{10})\)	\(q+(-1.41421 - 1.41421i) q^{2} +(3.25915 - 3.25915i) q^{3} +4.00000i q^{4} +(-7.62223 + 8.17934i) q^{5} -9.21827 q^{6} +(22.5290 - 22.5290i) q^{7} +(5.65685 - 5.65685i) q^{8} +5.75586i q^{9} +(22.3468 - 0.787870i) q^{10} -20.5286i q^{11} +(13.0366 + 13.0366i) q^{12} +(-37.5226 + 37.5226i) q^{13} -63.7217 q^{14} +(1.81570 + 51.4997i) q^{15} -16.0000 q^{16} +(96.6448 - 96.6448i) q^{17} +(8.14001 - 8.14001i) q^{18} +51.6811 q^{19} +(-32.7174 - 30.4889i) q^{20} -146.851i q^{21} +(-29.0318 + 29.0318i) q^{22} +(78.1401 - 77.8532i) q^{23} -36.8731i q^{24} +(-8.80319 - 124.690i) q^{25} +106.130 q^{26} +(106.756 + 106.756i) q^{27} +(90.1161 + 90.1161i) q^{28} -204.476i q^{29} +(70.2638 - 75.3994i) q^{30} -328.130 q^{31} +(22.6274 + 22.6274i) q^{32} +(-66.9057 - 66.9057i) q^{33} -273.353 q^{34} +(12.5511 + 355.994i) q^{35} -23.0234 q^{36} +(86.2739 - 86.2739i) q^{37} +(-73.0881 - 73.0881i) q^{38} +244.584i q^{39} +(3.15148 + 89.3872i) q^{40} +97.1639 q^{41} +(-207.679 + 207.679i) q^{42} +(-268.734 - 268.734i) q^{43} +82.1143 q^{44} +(-47.0791 - 43.8725i) q^{45} +(-220.608 - 0.405832i) q^{46} +(191.459 + 191.459i) q^{47} +(-52.1464 + 52.1464i) q^{48} -672.114i q^{49} +(-163.888 + 188.787i) q^{50} -629.960i q^{51} +(-150.090 - 150.090i) q^{52} +(-256.695 - 256.695i) q^{53} -301.952i q^{54} +(167.910 + 156.473i) q^{55} -254.887i q^{56} +(168.437 - 168.437i) q^{57} +(-289.172 + 289.172i) q^{58} +20.3230i q^{59} +(-205.999 + 7.26280i) q^{60} +350.137i q^{61} +(464.045 + 464.045i) q^{62} +(129.674 + 129.674i) q^{63} -64.0000i q^{64} +(-20.9042 - 592.916i) q^{65} +189.238i q^{66} +(80.2897 - 80.2897i) q^{67} +(386.579 + 386.579i) q^{68} +(0.935268 - 508.406i) q^{69} +(485.701 - 521.201i) q^{70} +711.743 q^{71} +(32.5601 + 32.5601i) q^{72} +(-159.541 + 159.541i) q^{73} -244.020 q^{74} +(-435.073 - 377.692i) q^{75} +206.724i q^{76} +(-462.489 - 462.489i) q^{77} +(345.894 - 345.894i) q^{78} +31.7719 q^{79} +(121.956 - 130.869i) q^{80} +540.462 q^{81} +(-137.410 - 137.410i) q^{82} +(421.261 + 421.261i) q^{83} +587.404 q^{84} +(53.8416 + 1527.14i) q^{85} +760.094i q^{86} +(-666.417 - 666.417i) q^{87} +(-116.127 - 116.127i) q^{88} +1522.01 q^{89} +(4.53487 + 128.625i) q^{90} +1690.70i q^{91} +(311.413 + 312.561i) q^{92} +(-1069.42 + 1069.42i) q^{93} -541.527i q^{94} +(-393.925 + 422.717i) q^{95} +147.492 q^{96} +(-601.487 + 601.487i) q^{97} +(-950.512 + 950.512i) q^{98} +118.160 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 16 q^{3} - 16 q^{6}+O(q^{10}) \) 72 * q - 16 * q^3 - 16 * q^6	\( 72 q - 16 q^{3} - 16 q^{6} - 64 q^{12} + 192 q^{13} - 1152 q^{16} + 32 q^{18} + 276 q^{23} + 880 q^{25} + 304 q^{26} + 728 q^{27} + 608 q^{31} + 688 q^{35} + 2816 q^{36} - 2208 q^{41} - 256 q^{46} + 144 q^{47} + 256 q^{48} + 272 q^{50} + 768 q^{52} - 2360 q^{55} - 1376 q^{62} - 1104 q^{70} + 4528 q^{71} + 128 q^{72} - 1296 q^{73} - 2568 q^{75} - 752 q^{77} + 6000 q^{78} - 11560 q^{81} + 80 q^{82} - 904 q^{85} + 6760 q^{87} + 1104 q^{92} - 5288 q^{93} + 9264 q^{95} + 256 q^{96} - 448 q^{98}+O(q^{100}) \) 72 * q - 16 * q^3 - 16 * q^6 - 64 * q^12 + 192 * q^13 - 1152 * q^16 + 32 * q^18 + 276 * q^23 + 880 * q^25 + 304 * q^26 + 728 * q^27 + 608 * q^31 + 688 * q^35 + 2816 * q^36 - 2208 * q^41 - 256 * q^46 + 144 * q^47 + 256 * q^48 + 272 * q^50 + 768 * q^52 - 2360 * q^55 - 1376 * q^62 - 1104 * q^70 + 4528 * q^71 + 128 * q^72 - 1296 * q^73 - 2568 * q^75 - 752 * q^77 + 6000 * q^78 - 11560 * q^81 + 80 * q^82 - 904 * q^85 + 6760 * q^87 + 1104 * q^92 - 5288 * q^93 + 9264 * q^95 + 256 * q^96 - 448 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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