LMFDB - Embedded newform 230.4.e.a.137.18

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			137.18
Character	$\chi$	$=$	230.137
Dual form			230.4.e.a.183.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 - 1.41421i) q^{2} +(6.26949 - 6.26949i) q^{3} +4.00000i q^{4} +(8.82273 - 6.86728i) q^{5} -17.7328 q^{6} +(11.5218 - 11.5218i) q^{7} +(5.65685 - 5.65685i) q^{8} -51.6130i q^{9} +O(q^{10})$	\(q+(-1.41421 - 1.41421i) q^{2} +(6.26949 - 6.26949i) q^{3} +4.00000i q^{4} +(8.82273 - 6.86728i) q^{5} -17.7328 q^{6} +(11.5218 - 11.5218i) q^{7} +(5.65685 - 5.65685i) q^{8} -51.6130i q^{9} +(-22.1890 - 2.76543i) q^{10} -0.0374369i q^{11} +(25.0780 + 25.0780i) q^{12} +(-38.4820 + 38.4820i) q^{13} -32.5885 q^{14} +(12.2597 - 98.3683i) q^{15} -16.0000 q^{16} +(27.0819 - 27.0819i) q^{17} +(-72.9919 + 72.9919i) q^{18} +144.357 q^{19} +(27.4691 + 35.2909i) q^{20} -144.471i q^{21} +(-0.0529438 + 0.0529438i) q^{22} +(-102.649 + 40.3765i) q^{23} -70.9312i q^{24} +(30.6810 - 121.176i) q^{25} +108.844 q^{26} +(-154.311 - 154.311i) q^{27} +(46.0871 + 46.0871i) q^{28} +168.034i q^{29} +(-156.452 + 121.776i) q^{30} +143.005 q^{31} +(22.6274 + 22.6274i) q^{32} +(-0.234710 - 0.234710i) q^{33} -76.5993 q^{34} +(22.5303 - 180.777i) q^{35} +206.452 q^{36} +(-253.090 + 253.090i) q^{37} +(-204.152 - 204.152i) q^{38} +482.526i q^{39} +(11.0617 - 88.7561i) q^{40} -212.066 q^{41} +(-204.313 + 204.313i) q^{42} +(92.8721 + 92.8721i) q^{43} +0.149748 q^{44} +(-354.441 - 455.368i) q^{45} +(202.268 + 88.0660i) q^{46} +(-346.873 - 346.873i) q^{47} +(-100.312 + 100.312i) q^{48} +77.4971i q^{49} +(-214.759 + 127.980i) q^{50} -339.580i q^{51} +(-153.928 - 153.928i) q^{52} +(14.9812 + 14.9812i) q^{53} +436.458i q^{54} +(-0.257089 - 0.330295i) q^{55} -130.354i q^{56} +(905.044 - 905.044i) q^{57} +(237.635 - 237.635i) q^{58} +86.5373i q^{59} +(393.473 + 49.0387i) q^{60} -740.854i q^{61} +(-202.239 - 202.239i) q^{62} +(-594.674 - 594.674i) q^{63} -64.0000i q^{64} +(-75.2498 + 603.783i) q^{65} +0.663861i q^{66} +(-657.632 + 657.632i) q^{67} +(108.328 + 108.328i) q^{68} +(-390.414 + 896.695i) q^{69} +(-287.520 + 223.794i) q^{70} +441.568 q^{71} +(-291.967 - 291.967i) q^{72} +(-129.327 + 129.327i) q^{73} +715.848 q^{74} +(-567.359 - 952.068i) q^{75} +577.428i q^{76} +(-0.431340 - 0.431340i) q^{77} +(682.394 - 682.394i) q^{78} +298.820 q^{79} +(-141.164 + 109.876i) q^{80} -541.354 q^{81} +(299.906 + 299.906i) q^{82} +(261.796 + 261.796i) q^{83} +577.886 q^{84} +(52.9574 - 424.916i) q^{85} -262.682i q^{86} +(1053.48 + 1053.48i) q^{87} +(-0.211775 - 0.211775i) q^{88} +1304.47 q^{89} +(-142.732 + 1145.24i) q^{90} +886.764i q^{91} +(-161.506 - 410.594i) q^{92} +(896.567 - 896.567i) q^{93} +981.104i q^{94} +(1273.62 - 991.339i) q^{95} +283.725 q^{96} +(256.245 - 256.245i) q^{97} +(109.597 - 109.597i) q^{98} -1.93223 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
$3$	6.26949	−	6.26949i	1.20656	−	1.20656i	0.234431	−	0.972133i	$-0.424677\pi$
$3$	6.26949	−	6.26949i	1.20656	−	1.20656i	0.972133	−	0.234431i	$-0.0753228\pi$
$4$			4.00000i			0.500000i
$5$	8.82273	−	6.86728i	0.789129	−	0.614228i
$5$	8.82273	−	6.86728i	0.789129	−	0.614228i
$6$	−17.7328			−1.20656
$7$	11.5218	−	11.5218i	0.622118	−	0.622118i	−0.323955	−	0.946073i	$-0.605013\pi$
$7$	11.5218	−	11.5218i	0.622118	−	0.622118i	0.946073	+	0.323955i	$0.105013\pi$
$8$	5.65685	−	5.65685i	0.250000	−	0.250000i
$9$		−	51.6130i		−	1.91159i
$10$	−22.1890	−	2.76543i	−0.701678	−	0.0874504i
$11$		−	0.0374369i		−	0.00102615i	−1.00000		0.000513075i	$-0.999837\pi$
$11$		−	0.0374369i		−	0.00102615i	1.00000		0.000513075i	$-0.000163317\pi$
$12$	25.0780	+	25.0780i	0.603282	+	0.603282i
$13$	−38.4820	+	38.4820i	−0.821000	+	0.821000i	−0.986251	−	0.165251i	$-0.947156\pi$
$13$	−38.4820	+	38.4820i	−0.821000	+	0.821000i	0.165251	+	0.986251i	$0.447156\pi$
$14$	−32.5885			−0.622118
$15$	12.2597	−	98.3683i	0.211029	−	1.69324i
$16$	−16.0000			−0.250000
$17$	27.0819	−	27.0819i	0.386373	−	0.386373i	−0.487019	−	0.873391i	$-0.661916\pi$
$17$	27.0819	−	27.0819i	0.386373	−	0.386373i	0.873391	+	0.487019i	$0.161916\pi$
$18$	−72.9919	+	72.9919i	−0.955797	+	0.955797i
$19$	144.357			1.74304			0.871520	−	0.490361i	$-0.163135\pi$
$19$	144.357			1.74304			0.871520	+	0.490361i	$0.163135\pi$
$20$	27.4691	+	35.2909i	0.307114	+	0.394564i
$21$		−	144.471i		−	1.50125i
$22$	−0.0529438	+	0.0529438i	−0.000513075	+	0.000513075i
$23$	−102.649	+	40.3765i	−0.930596	+	0.366047i
$23$	−102.649	+	40.3765i	−0.930596	+	0.366047i
$24$		−	70.9312i		−	0.603282i
$25$	30.6810	−	121.176i	0.245448	−	0.969410i
$26$	108.844			0.821000
$27$	−154.311	−	154.311i	−1.09990	−	1.09990i
$28$	46.0871	+	46.0871i	0.311059	+	0.311059i
$29$			168.034i			1.07597i	0.842955	+	0.537983i	$0.180814\pi$
$29$			168.034i			1.07597i	−0.842955	+	0.537983i	$0.819186\pi$
$30$	−156.452	+	121.776i	−0.952134	+	0.741105i
$31$	143.005			0.828530			0.414265	−	0.910156i	$-0.364039\pi$
$31$	143.005			0.828530			0.414265	+	0.910156i	$0.364039\pi$
$32$	22.6274	+	22.6274i	0.125000	+	0.125000i
$33$	−0.234710	−	0.234710i	−0.00123812	−	0.00123812i
$34$	−76.5993			−0.386373
$35$	22.5303	−	180.777i	0.108809	−	0.873053i
$36$	206.452			0.955797
$37$	−253.090	+	253.090i	−1.12454	+	1.12454i	−0.133484	+	0.991051i	$0.542617\pi$
$37$	−253.090	+	253.090i	−1.12454	+	1.12454i	−0.991051	+	0.133484i	$0.957383\pi$
$38$	−204.152	−	204.152i	−0.871520	−	0.871520i
$39$			482.526i			1.98118i
$40$	11.0617	−	88.7561i	0.0437252	−	0.350839i
$41$	−212.066			−0.807784			−0.403892	−	0.914807i	$-0.632343\pi$
$41$	−212.066			−0.807784			−0.403892	+	0.914807i	$0.632343\pi$
$42$	−204.313	+	204.313i	−0.750625	+	0.750625i
$43$	92.8721	+	92.8721i	0.329369	+	0.329369i	0.852346	−	0.522978i	$-0.175179\pi$
$43$	92.8721	+	92.8721i	0.329369	+	0.329369i	−0.522978	+	0.852346i	$0.675179\pi$
$44$	0.149748			0.000513075
$45$	−354.441	−	455.368i	−1.17415	−	1.50849i
$46$	202.268	+	88.0660i	0.648322	+	0.282274i
$47$	−346.873	−	346.873i	−1.07652	−	1.07652i	−0.996819	−	0.0797040i	$-0.974602\pi$
$47$	−346.873	−	346.873i	−1.07652	−	1.07652i	−0.0797040	−	0.996819i	$-0.525398\pi$
$48$	−100.312	+	100.312i	−0.301641	+	0.301641i
$49$			77.4971i			0.225939i
$50$	−214.759	+	127.980i	−0.607429	+	0.361981i
$51$		−	339.580i		−	0.932367i
$52$	−153.928	−	153.928i	−0.410500	−	0.410500i
$53$	14.9812	+	14.9812i	0.0388269	+	0.0388269i	0.726254	−	0.687427i	$-0.241260\pi$
$53$	14.9812	+	14.9812i	0.0388269	+	0.0388269i	−0.687427	+	0.726254i	$0.741260\pi$
$54$			436.458i			1.09990i
$55$	−0.257089	−	0.330295i	−0.000630290	−	0.000809764i
$56$		−	130.354i		−	0.311059i
$57$	905.044	−	905.044i	2.10309	−	2.10309i
$58$	237.635	−	237.635i	0.537983	−	0.537983i
$59$			86.5373i			0.190952i	0.995432	+	0.0954762i	$0.0304374\pi$
$59$			86.5373i			0.190952i	−0.995432	+	0.0954762i	$0.969563\pi$
$60$	393.473	+	49.0387i	0.846620	+	0.105515i
$61$		−	740.854i		−	1.55503i	−0.628866	−	0.777514i	$-0.716481\pi$
$61$		−	740.854i		−	1.55503i	0.628866	−	0.777514i	$-0.283519\pi$
$62$	−202.239	−	202.239i	−0.414265	−	0.414265i
$63$	−594.674	−	594.674i	−1.18924	−	1.18924i
$64$		−	64.0000i		−	0.125000i
$65$	−75.2498	+	603.783i	−0.143594	+	1.15216i
$66$			0.663861i			0.00123812i
$67$	−657.632	+	657.632i	−1.19914	+	1.19914i	−0.224718	+	0.974424i	$0.572146\pi$
$67$	−657.632	+	657.632i	−1.19914	+	1.19914i	−0.974424	+	0.224718i	$0.927854\pi$
$68$	108.328	+	108.328i	0.193186	+	0.193186i
$69$	−390.414	+	896.695i	−0.681164	+	1.56448i
$70$	−287.520	+	223.794i	−0.490931	+	0.382122i
$71$	441.568			0.738092			0.369046	−	0.929411i	$-0.379685\pi$
$71$	441.568			0.738092			0.369046	+	0.929411i	$0.379685\pi$
$72$	−291.967	−	291.967i	−0.477898	−	0.477898i
$73$	−129.327	+	129.327i	−0.207350	+	0.207350i	−0.803140	−	0.595790i	$-0.796839\pi$
$73$	−129.327	+	129.327i	−0.207350	+	0.207350i	0.595790	+	0.803140i	$0.296839\pi$
$74$	715.848			1.12454
$75$	−567.359	−	952.068i	−0.873506	−	1.46580i
$76$			577.428i			0.871520i
$77$	−0.431340	−	0.431340i	−0.000638386	−	0.000638386i
$78$	682.394	−	682.394i	0.990589	−	0.990589i
$79$	298.820			0.425569			0.212784	−	0.977099i	$-0.431747\pi$
$79$	298.820			0.425569			0.212784	+	0.977099i	$0.431747\pi$
$80$	−141.164	+	109.876i	−0.197282	+	0.153557i
$81$	−541.354			−0.742597
$82$	299.906	+	299.906i	0.403892	+	0.403892i
$83$	261.796	+	261.796i	0.346215	+	0.346215i	0.858698	−	0.512482i	$-0.171274\pi$
$83$	261.796	+	261.796i	0.346215	+	0.346215i	−0.512482	+	0.858698i	$0.671274\pi$
$84$	577.886			0.750625
$85$	52.9574	−	424.916i	0.0675769	−	0.542219i
$86$		−	262.682i		−	0.329369i
$87$	1053.48	+	1053.48i	1.29822	+	1.29822i
$88$	−0.211775	−	0.211775i	−0.000256537	−	0.000256537i
$89$	1304.47			1.55363			0.776817	−	0.629727i	$-0.216833\pi$
$89$	1304.47			1.55363			0.776817	+	0.629727i	$0.216833\pi$
$90$	−142.732	+	1145.24i	−0.167170	+	1.34132i
$91$			886.764i			1.02152i
$92$	−161.506	−	410.594i	−0.183024	−	0.465298i
$93$	896.567	−	896.567i	0.999674	−	0.999674i
$94$			981.104i			1.07652i
$95$	1273.62	−	991.339i	1.37548	−	1.07062i
$96$	283.725			0.301641
$97$	256.245	−	256.245i	0.268224	−	0.268224i	−0.560160	−	0.828384i	$-0.689260\pi$
$97$	256.245	−	256.245i	0.268224	−	0.268224i	0.828384	+	0.560160i	$0.189260\pi$
$98$	109.597	−	109.597i	0.112969	−	0.112969i
$99$	−1.93223			−0.00196158
$100$	484.705	+	122.724i	0.484705	+	0.122724i
$101$	−1474.22			−1.45238			−0.726191	−	0.687493i	$-0.758711\pi$
$101$	−1474.22			−1.45238			−0.726191	+	0.687493i	$0.758711\pi$
$102$	−480.238	+	480.238i	−0.466183	+	0.466183i
$103$	1464.51	+	1464.51i	1.40099	+	1.40099i	0.796954	+	0.604041i	$0.206444\pi$
$103$	1464.51	+	1464.51i	1.40099	+	1.40099i	0.604041	+	0.796954i	$0.293556\pi$
$104$			435.375i			0.410500i
$105$	−992.125	−	1274.63i	−0.922110	−	1.18468i
$106$		−	42.3733i		−	0.0388269i
$107$	724.747	−	724.747i	0.654803	−	0.654803i	−0.299343	−	0.954146i	$-0.596767\pi$
$107$	724.747	−	724.747i	0.654803	−	0.654803i	0.954146	+	0.299343i	$0.0967674\pi$
$108$	617.245	−	617.245i	0.549948	−	0.549948i
$109$	−580.039			−0.509703			−0.254852	−	0.966980i	$-0.582027\pi$
$109$	−580.039			−0.509703			−0.254852	+	0.966980i	$0.582027\pi$
$110$	−0.103529	+	0.830688i	−8.97372e−5	+	0.000720027i
$111$			3173.50i			2.71365i
$112$	−184.349	+	184.349i	−0.155529	+	0.155529i
$113$	−292.812	−	292.812i	−0.243765	−	0.243765i	0.574641	−	0.818406i	$-0.305142\pi$
$113$	−292.812	−	292.812i	−0.243765	−	0.243765i	−0.818406	+	0.574641i	$0.805142\pi$
$114$	−2559.85			−2.10309
$115$	−628.364	+	1061.15i	−0.509524	+	0.860457i
$116$	−672.134			−0.537983
$117$	1986.18	+	1986.18i	1.56942	+	1.56942i
$118$	122.382	−	122.382i	0.0954762	−	0.0954762i
$119$		−	624.064i		−	0.480738i
$120$	−487.104	−	625.807i	−0.370553	−	0.476067i
$121$	1331.00			0.999999
$122$	−1047.73	+	1047.73i	−0.777514	+	0.777514i
$123$	−1329.55	+	1329.55i	−0.974643	+	0.974643i
$124$			572.019i			0.414265i
$125$	−561.460	−	1279.80i	−0.401748	−	0.915750i
$126$			1681.99i			1.18924i
$127$	597.943	+	597.943i	0.417787	+	0.417787i	0.884440	−	0.466654i	$-0.154541\pi$
$127$	597.943	+	597.943i	0.417787	+	0.417787i	−0.466654	+	0.884440i	$0.654541\pi$
$128$	−90.5097	+	90.5097i	−0.0625000	+	0.0625000i
$129$	1164.52			0.794809
$130$	960.298	−	747.460i	0.647875	−	0.504281i
$131$	510.224			0.340294			0.170147	−	0.985419i	$-0.445576\pi$
$131$	510.224			0.340294			0.170147	+	0.985419i	$0.445576\pi$
$132$	0.938841	−	0.938841i	0.000619058	−	0.000619058i
$133$	1663.25	−	1663.25i	1.08438	−	1.08438i
$134$	1860.06			1.19914
$135$	−2421.14	−	301.748i	−1.54355	−	0.192373i
$136$		−	306.397i		−	0.193186i
$137$	912.209	−	912.209i	0.568871	−	0.568871i	−0.362941	−	0.931812i	$-0.618227\pi$
$137$	912.209	−	912.209i	0.568871	−	0.568871i	0.931812	+	0.362941i	$0.118227\pi$
$138$	1820.25	−	715.989i	1.12282	−	0.441660i
$139$			160.994i			0.0982395i	0.998793	+	0.0491198i	$0.0156416\pi$
$139$			160.994i			0.0982395i	−0.998793	+	0.0491198i	$0.984358\pi$
$140$	723.107	+	90.1211i	0.436527	+	0.0544045i
$141$	−4349.43			−2.59779
$142$	−624.472	−	624.472i	−0.369046	−	0.369046i
$143$	1.44065	+	1.44065i	0.000842469	+	0.000842469i
$144$			825.809i			0.477898i
$145$	1153.93	+	1482.51i	0.660889	+	0.849076i
$146$	365.791			0.207350
$147$	485.867	+	485.867i	0.272610	+	0.272610i
$148$	−1012.36	−	1012.36i	−0.562268	−	0.562268i
$149$	2044.19			1.12394			0.561968	−	0.827159i	$-0.310045\pi$
$149$	2044.19			1.12394			0.561968	+	0.827159i	$0.310045\pi$
$150$	−544.061	+	2148.79i	−0.296149	+	1.16965i
$151$	109.052			0.0587717			0.0293859	−	0.999568i	$-0.490645\pi$
$151$	109.052			0.0587717			0.0293859	+	0.999568i	$0.490645\pi$
$152$	816.606	−	816.606i	0.435760	−	0.435760i
$153$	−1397.78	−	1397.78i	−0.738587	−	0.738587i
$154$			1.22001i			0.000638386i
$155$	1261.69	−	982.053i	0.653816	−	0.508906i
$156$	−1930.10			−0.990589
$157$	−106.942	+	106.942i	−0.0543626	+	0.0543626i	−0.733765	−	0.679403i	$-0.762239\pi$
$157$	−106.942	+	106.942i	−0.0543626	+	0.0543626i	0.679403	+	0.733765i	$0.262239\pi$
$158$	−422.596	−	422.596i	−0.212784	−	0.212784i
$159$	187.849			0.0936944
$160$	355.024	+	44.2468i	0.175420	+	0.0218626i
$161$	−717.485	+	1647.90i	−0.351216	+	0.806665i
$162$	765.590	+	765.590i	0.371299	+	0.371299i
$163$	−932.983	+	932.983i	−0.448325	+	0.448325i	−0.894797	−	0.446473i	$-0.852680\pi$
$163$	−932.983	+	932.983i	−0.448325	+	0.448325i	0.446473	+	0.894797i	$0.352680\pi$
$164$		−	848.264i		−	0.403892i
$165$	−3.68260	−	0.458964i	−0.00173752	−	0.000216547i
$166$		−	740.472i		−	0.346215i
$167$	−2427.90	−	2427.90i	−1.12501	−	1.12501i	−0.990977	−	0.134030i	$-0.957208\pi$
$167$	−2427.90	−	2427.90i	−1.12501	−	1.12501i	−0.134030	−	0.990977i	$-0.542792\pi$
$168$	−817.254	−	817.254i	−0.375312	−	0.375312i
$169$		−	764.736i		−	0.348082i
$170$	−675.815	+	526.028i	−0.304898	+	0.237321i
$171$		−	7450.70i		−	3.33198i
$172$	−371.488	+	371.488i	−0.164684	+	0.164684i
$173$	1515.22	−	1515.22i	0.665894	−	0.665894i	−0.290869	−	0.956763i	$-0.593944\pi$
$173$	1515.22	−	1515.22i	0.665894	−	0.665894i	0.956763	+	0.290869i	$0.0939443\pi$
$174$		−	2979.70i		−	1.29822i
$175$	−1042.67	−	1749.67i	−0.450389	−	0.755785i
$176$			0.598990i			0.000256537i
$177$	542.545	+	542.545i	0.230396	+	0.230396i
$178$	−1844.80	−	1844.80i	−0.776817	−	0.776817i
$179$			548.193i			0.228904i	0.993429	+	0.114452i	$0.0365113\pi$
$179$			548.193i			0.228904i	−0.993429	+	0.114452i	$0.963489\pi$
$180$	1821.47	−	1417.76i	0.754247	−	0.587077i
$181$			2293.46i			0.941832i	0.882178	+	0.470916i	$0.156077\pi$
$181$			2293.46i			0.941832i	−0.882178	+	0.470916i	$0.843923\pi$
$182$	1254.07	−	1254.07i	0.510759	−	0.510759i
$183$	−4644.78	−	4644.78i	−1.87624	−	1.87624i
$184$	−352.264	+	809.072i	−0.141137	+	0.324161i
$185$	−494.906	+	3970.99i	−0.196682	+	1.57812i
$186$	−2535.87			−0.999674
$187$	−1.01386	−	1.01386i	−0.000396476	−	0.000396476i
$188$	1387.49	−	1387.49i	0.538261	−	0.538261i
$189$	−3555.88			−1.36853
$190$	−3203.14	−	399.208i	−1.22305	−	0.152430i
$191$		−	5080.65i		−	1.92473i	−0.271767	−	0.962363i	$-0.587608\pi$
$191$		−	5080.65i		−	1.92473i	0.271767	−	0.962363i	$-0.412392\pi$
$192$	−401.247	−	401.247i	−0.150821	−	0.150821i
$193$	1232.92	−	1232.92i	0.459830	−	0.459830i	−0.438770	−	0.898600i	$-0.644586\pi$
$193$	1232.92	−	1232.92i	0.459830	−	0.459830i	0.898600	+	0.438770i	$0.144586\pi$
$194$	−724.771			−0.268224
$195$	3313.64	+	4257.19i	1.21689	+	1.56340i
$196$	−309.988			−0.112969
$197$	227.507	+	227.507i	0.0822801	+	0.0822801i	0.747049	−	0.664769i	$-0.231470\pi$
$197$	227.507	+	227.507i	0.0822801	+	0.0822801i	−0.664769	+	0.747049i	$0.731470\pi$
$198$	2.73259	+	2.73259i	0.000980791	+	0.000980791i
$199$	−4836.29			−1.72279			−0.861396	−	0.507935i	$-0.830409\pi$
$199$	−4836.29			−1.72279			−0.861396	+	0.507935i	$0.830409\pi$
$200$	−511.918	−	859.034i	−0.180990	−	0.303714i
$201$			8246.03i			2.89368i
$202$	2084.87	+	2084.87i	0.726191	+	0.726191i
$203$	1936.05	+	1936.05i	0.669378	+	0.669378i
$204$	1358.32			0.466183
$205$	−1871.00	+	1456.32i	−0.637445	+	0.496163i
$206$		−	4142.26i		−	1.40099i
$207$	2083.96	+	5298.01i	0.699734	+	1.77892i
$208$	615.713	−	615.713i	0.205250	−	0.205250i
$209$		−	5.40427i		−	0.00178862i
$210$	−399.525	+	3205.68i	−0.131285	+	1.05339i
$211$	111.466			0.0363678			0.0181839	−	0.999835i	$-0.494212\pi$
$211$	111.466			0.0363678			0.0181839	+	0.999835i	$0.494212\pi$
$212$	−59.9248	+	59.9248i	−0.0194135	+	0.0194135i
$213$	2768.41	−	2768.41i	0.890555	−	0.890555i
$214$	−2049.89			−0.654803
$215$	1457.16	+	181.607i	0.462222	+	0.0576069i
$216$	−1745.83			−0.549948
$217$	1647.67	−	1647.67i	0.515443	−	0.515443i
$218$	820.299	+	820.299i	0.254852	+	0.254852i
$219$			1621.62i			0.500362i
$220$	1.32118	−	1.02836i	0.000404882	−	0.000315145i
$221$			2084.34i			0.634424i
$222$	4488.00	−	4488.00i	1.35682	−	1.35682i
$223$	−2738.36	+	2738.36i	−0.822306	+	0.822306i	−0.986438	−	0.164132i	$-0.947518\pi$
$223$	−2738.36	+	2738.36i	−0.822306	+	0.822306i	0.164132	+	0.986438i	$0.447518\pi$
$224$	521.416			0.155529
$225$	−6254.27	−	1583.54i	−1.85312	−	0.469197i
$226$			828.198i			0.243765i
$227$	−2491.58	+	2491.58i	−0.728510	+	0.728510i	−0.970323	−	0.241813i	$-0.922258\pi$
$227$	−2491.58	+	2491.58i	−0.728510	+	0.728510i	0.241813	+	0.970323i	$0.422258\pi$
$228$	3620.18	+	3620.18i	1.05154	+	1.05154i
$229$	319.396			0.0921671			0.0460835	−	0.998938i	$-0.485326\pi$
$229$	319.396			0.0921671			0.0460835	+	0.998938i	$0.485326\pi$
$230$	2389.33	−	612.049i	0.684990	−	0.175466i
$231$	−5.40856			−0.00154051
$232$	950.541	+	950.541i	0.268992	+	0.268992i
$233$	2728.98	−	2728.98i	0.767304	−	0.767304i	−0.210327	−	0.977631i	$-0.567453\pi$
$233$	2728.98	−	2728.98i	0.767304	−	0.767304i	0.977631	+	0.210327i	$0.0674530\pi$
$234$		−	5617.75i		−	1.56942i
$235$	−5442.43	−	678.292i	−1.51075	−	0.188285i
$236$	−346.149			−0.0954762
$237$	1873.45	−	1873.45i	0.513476	−	0.513476i
$238$	−882.560	+	882.560i	−0.240369	+	0.240369i
$239$			6380.85i			1.72696i	0.504386	+	0.863479i	$0.331719\pi$
$239$			6380.85i			1.72696i	−0.504386	+	0.863479i	$0.668281\pi$
$240$	−196.155	+	1573.89i	−0.0527573	+	0.423310i
$241$			3056.54i			0.816967i	0.912766	+	0.408484i	$0.133942\pi$
$241$			3056.54i			0.816967i	−0.912766	+	0.408484i	$0.866058\pi$
$242$	−1882.32	−	1882.32i	−0.499999	−	0.499999i
$243$	772.391	−	772.391i	0.203905	−	0.203905i
$244$	2963.42			0.777514
$245$	532.194	+	683.736i	0.138778	+	0.178295i
$246$	3760.52			0.974643
$247$	−5555.15	+	5555.15i	−1.43104	+	1.43104i
$248$	808.957	−	808.957i	0.207132	−	0.207132i
$249$	3282.66			0.835462
$250$	−1015.89	+	2603.93i	−0.257001	+	0.658749i
$251$		−	976.488i		−	0.245559i	−0.992434	−	0.122780i	$-0.960819\pi$
$251$		−	976.488i		−	0.245559i	0.992434	−	0.122780i	$-0.0391808\pi$
$252$	2378.70	−	2378.70i	0.594618	−	0.594618i
$253$	1.51157	+	3.84284i	0.000375619	+	0.000954931i
$254$		−	1691.24i		−	0.417787i
$255$	−2331.99	−	2996.02i	−0.572686	−	0.735757i
$256$	256.000			0.0625000
$257$	616.915	+	616.915i	0.149736	+	0.149736i	0.778000	−	0.628264i	$-0.216234\pi$
$257$	616.915	+	616.915i	0.149736	+	0.149736i	−0.628264	+	0.778000i	$0.716234\pi$
$258$	−1646.88	−	1646.88i	−0.397405	−	0.397405i
$259$			5832.10i			1.39919i
$260$	−2415.13	−	300.999i	−0.576078	−	0.0717968i
$261$	8672.72			2.05681
$262$	−721.565	−	721.565i	−0.170147	−	0.170147i
$263$	−1570.17	−	1570.17i	−0.368139	−	0.368139i	0.498659	−	0.866798i	$-0.333826\pi$
$263$	−1570.17	−	1570.17i	−0.368139	−	0.368139i	−0.866798	+	0.498659i	$0.833826\pi$
$264$	−2.65544			−0.000619058
$265$	235.055	+	29.2950i	0.0544880	+	0.00679086i
$266$	−4704.38			−1.08438
$267$	8178.35	−	8178.35i	1.87456	−	1.87456i
$268$	−2630.53	−	2630.53i	−0.599571	−	0.599571i
$269$			4092.80i			0.927668i	0.885922	+	0.463834i	$0.153527\pi$
$269$			4092.80i			0.927668i	−0.885922	+	0.463834i	$0.846473\pi$
$270$	2997.28	+	3850.75i	0.675587	+	0.867960i
$271$	−4164.25			−0.933432			−0.466716	−	0.884407i	$-0.654563\pi$
$271$	−4164.25			−0.933432			−0.466716	+	0.884407i	$0.654563\pi$
$272$	−433.311	+	433.311i	−0.0965931	+	0.0965931i
$273$	5559.56	+	5559.56i	1.23253	+	1.23253i
$274$	−2580.12			−0.568871
$275$	−4.53646	−	1.14860i	−0.000994759	−	0.000251867i
$276$	−3586.78	−	1561.66i	−0.782242	−	0.340582i
$277$	−1875.07	−	1875.07i	−0.406721	−	0.406721i	0.473872	−	0.880594i	$-0.342856\pi$
$277$	−1875.07	−	1875.07i	−0.406721	−	0.406721i	−0.880594	+	0.473872i	$0.842856\pi$
$278$	227.679	−	227.679i	0.0491198	−	0.0491198i
$279$		−	7380.91i		−	1.58381i
$280$	−895.178	−	1150.08i	−0.191061	−	0.245465i
$281$		−	6028.31i		−	1.27978i	−0.768465	−	0.639891i	$-0.778979\pi$
$281$		−	6028.31i		−	1.27978i	0.768465	−	0.639891i	$-0.221021\pi$
$282$	6151.02	+	6151.02i	1.29889	+	1.29889i
$283$	−3959.02	−	3959.02i	−0.831587	−	0.831587i	0.156146	−	0.987734i	$-0.450093\pi$
$283$	−3959.02	−	3959.02i	−0.831587	−	0.831587i	−0.987734	+	0.156146i	$0.950093\pi$
$284$			1766.27i			0.369046i
$285$	1769.77	−	14200.1i	0.367832	−	2.95138i
$286$		−	4.07477i		−	0.000842469i
$287$	−2443.38	+	2443.38i	−0.502537	+	0.502537i
$288$	1167.87	−	1167.87i	0.238949	−	0.238949i
$289$			3446.14i			0.701432i
$290$	464.684	−	3728.50i	0.0940938	−	0.754983i
$291$		−	3213.06i		−	0.647260i
$292$	−517.306	−	517.306i	−0.103675	−	0.103675i
$293$	2606.25	+	2606.25i	0.519654	+	0.519654i	0.917467	−	0.397813i	$-0.130231\pi$
$293$	2606.25	+	2606.25i	0.519654	+	0.519654i	−0.397813	+	0.917467i	$0.630231\pi$
$294$		−	1374.24i		−	0.272610i
$295$	594.276	+	763.495i	0.117288	+	0.150686i
$296$			2863.39i			0.562268i
$297$	−5.77693	+	5.77693i	−0.00112866	+	0.00112866i
$298$	−2890.92	−	2890.92i	−0.561968	−	0.561968i
$299$	2396.36	−	5503.90i	0.463495	−	1.06454i
$300$	3808.27	−	2269.43i	0.732902	−	0.436753i
$301$	2140.10			0.409812
$302$	−154.223	−	154.223i	−0.0293859	−	0.0293859i
$303$	−9242.63	+	9242.63i	−1.75239	+	1.75239i
$304$	−2309.71			−0.435760
$305$	−5087.65	−	6536.35i	−0.955141	−	1.22712i
$306$			3953.52i			0.738587i
$307$	−3498.34	−	3498.34i	−0.650361	−	0.650361i	0.302719	−	0.953080i	$-0.402106\pi$
$307$	−3498.34	−	3498.34i	−0.650361	−	0.650361i	−0.953080	+	0.302719i	$0.902106\pi$
$308$	1.72536	−	1.72536i	0.000319193	−	0.000319193i
$309$	18363.5			3.38078
$310$	−3173.14	−	395.469i	−0.581361	−	0.0724553i
$311$	7304.43			1.33182			0.665911	−	0.746032i	$-0.268043\pi$
$311$	7304.43			1.33182			0.665911	+	0.746032i	$0.268043\pi$
$312$	2729.58	+	2729.58i	0.495295	+	0.495295i
$313$	−1166.67	−	1166.67i	−0.210684	−	0.210684i	0.593874	−	0.804558i	$-0.297598\pi$
$313$	−1166.67	−	1166.67i	−0.210684	−	0.210684i	−0.804558	+	0.593874i	$0.797598\pi$
$314$	302.479			0.0543626
$315$	−9330.44	−	1162.86i	−1.66892	−	0.207998i
$316$			1195.28i			0.212784i
$317$	3710.49	+	3710.49i	0.657419	+	0.657419i	0.954769	−	0.297349i	$-0.0961026\pi$
$317$	3710.49	+	3710.49i	0.657419	+	0.657419i	−0.297349	+	0.954769i	$0.596103\pi$
$318$	−265.659	−	265.659i	−0.0468472	−	0.0468472i
$319$	6.29065			0.00110410
$320$	−439.506	−	564.655i	−0.0767785	−	0.0986411i
$321$		−	9087.59i		−	1.58012i
$322$	3345.17	−	1315.81i	0.578940	−	0.227725i
$323$	3909.46	−	3909.46i	0.673463	−	0.673463i
$324$		−	2165.41i		−	0.371299i
$325$	3482.44	+	5843.78i	0.594372	+	0.997398i
$326$	2638.88			0.448325
$327$	−3636.55	+	3636.55i	−0.614990	+	0.614990i
$328$	−1199.63	+	1199.63i	−0.201946	+	0.201946i
$329$	−7993.18			−1.33945
$330$	4.55892	+	5.85706i	0.000760485	+	0.000977032i
$331$	7561.94			1.25572			0.627858	−	0.778328i	$-0.283932\pi$
$331$	7561.94			1.25572			0.627858	+	0.778328i	$0.283932\pi$
$332$	−1047.18	+	1047.18i	−0.173108	+	0.173108i
$333$	13062.8	+	13062.8i	2.14965	+	2.14965i
$334$			6867.13i			1.12501i
$335$	−1285.97	+	10318.2i	−0.209731	+	1.68282i
$336$			2311.54i			0.375312i
$337$	−3705.99	+	3705.99i	−0.599045	+	0.599045i	−0.940058	−	0.341014i	$-0.889230\pi$
$337$	−3705.99	+	3705.99i	−0.599045	+	0.599045i	0.341014	+	0.940058i	$0.389230\pi$
$338$	−1081.50	+	1081.50i	−0.174041	+	0.174041i
$339$	−3671.57			−0.588237
$340$	1699.66	+	211.830i	0.271109	+	0.0337884i
$341$		−	5.35365i		−	0.000850195i
$342$	−10536.9	+	10536.9i	−1.66599	+	1.66599i
$343$	4844.88	+	4844.88i	0.762678	+	0.762678i
$344$	1050.73			0.164684
$345$	2713.33	+	10592.4i	0.423423	+	1.65297i
$346$	−4285.68			−0.665894
$347$	−8153.61	−	8153.61i	−1.26141	−	1.26141i	−0.950411	−	0.310997i	$-0.899337\pi$
$347$	−8153.61	−	8153.61i	−1.26141	−	1.26141i	−0.310997	−	0.950411i	$-0.600663\pi$
$348$	−4213.94	+	4213.94i	−0.649112	+	0.649112i
$349$			4655.66i			0.714073i	0.934090	+	0.357037i	$0.116213\pi$
$349$			4655.66i			0.714073i	−0.934090	+	0.357037i	$0.883787\pi$
$350$	−999.850	+	3948.95i	−0.152698	+	0.603087i
$351$	11876.4			1.80603
$352$	0.847100	−	0.847100i	0.000128269	−	0.000128269i
$353$	−8762.14	+	8762.14i	−1.32114	+	1.32114i	−0.408281	+	0.912856i	$0.633872\pi$
$353$	−8762.14	+	8762.14i	−1.32114	+	1.32114i	−0.912856	+	0.408281i	$0.866128\pi$
$354$		−	1534.55i		−	0.230396i
$355$	3895.84	−	3032.37i	0.582449	−	0.453356i
$356$			5217.87i			0.776817i
$357$	−3912.57	−	3912.57i	−0.580042	−	0.580042i
$358$	775.262	−	775.262i	0.114452	−	0.114452i
$359$	−7877.56			−1.15811			−0.579055	−	0.815288i	$-0.696579\pi$
$359$	−7877.56			−1.15811			−0.579055	+	0.815288i	$0.696579\pi$
$360$	−4580.97	−	570.928i	−0.670662	−	0.0835849i
$361$	13979.9			2.03819
$362$	3243.44	−	3243.44i	0.470916	−	0.470916i
$363$	8344.68	−	8344.68i	1.20656	−	1.20656i
$364$	−3547.05			−0.510759
$365$	−252.892	+	2029.13i	−0.0362657	+	0.290986i
$366$			13137.4i			1.87624i
$367$	−3538.58	+	3538.58i	−0.503304	+	0.503304i	−0.912463	−	0.409159i	$-0.865822\pi$
$367$	−3538.58	+	3538.58i	−0.503304	+	0.503304i	0.409159	+	0.912463i	$0.365822\pi$
$368$	1642.38	−	646.025i	0.232649	−	0.0915118i
$369$			10945.4i			1.54415i
$370$	6315.73	−	4915.92i	0.887403	−	0.690721i
$371$	345.221			0.0483099
$372$	3586.27	+	3586.27i	0.499837	+	0.499837i
$373$	−8176.47	−	8176.47i	−1.13502	−	1.13502i	−0.989331	−	0.145686i	$-0.953461\pi$
$373$	−8176.47	−	8176.47i	−1.13502	−	1.13502i	−0.145686	−	0.989331i	$-0.546539\pi$
$374$			2.86764i			0.000396476i
$375$	−11543.8	−	4503.62i	−1.58965	−	0.620176i
$376$	−3924.41			−0.538261
$377$	−6466.27	−	6466.27i	−0.883369	−	0.883369i
$378$	5028.77	+	5028.77i	0.684265	+	0.684265i
$379$	−2475.34			−0.335487			−0.167744	−	0.985831i	$-0.553648\pi$
$379$	−2475.34			−0.335487			−0.167744	+	0.985831i	$0.553648\pi$
$380$	3965.36	+	5094.49i	0.535312	+	0.687741i
$381$	7497.60			1.00817
$382$	−7185.12	+	7185.12i	−0.962363	+	0.962363i
$383$	−6725.07	−	6725.07i	−0.897220	−	0.897220i	0.0979695	−	0.995189i	$-0.468765\pi$
$383$	−6725.07	−	6725.07i	−0.897220	−	0.897220i	−0.995189	+	0.0979695i	$0.968765\pi$
$384$			1134.90i			0.150821i
$385$	−6.76772	−	0.843464i	−0.000895883	−	0.000111654i
$386$	−3487.21			−0.459830
$387$	4793.41	−	4793.41i	0.629619	−	0.629619i
$388$	1024.98	+	1024.98i	0.134112	+	0.134112i
$389$	12134.5			1.58160			0.790800	−	0.612074i	$-0.209665\pi$
$389$	12134.5			1.58160			0.790800	+	0.612074i	$0.209665\pi$
$390$	1334.39	−	10706.8i	0.173255	−	1.39015i
$391$	−1686.45	+	3873.40i	−0.218126	+	0.500988i
$392$	438.390	+	438.390i	0.0564847	+	0.0564847i
$393$	3198.84	−	3198.84i	0.410586	−	0.410586i
$394$		−	643.486i		−	0.0822801i
$395$	2636.41	−	2052.08i	0.335829	−	0.261396i
$396$		−	7.72893i		−	0.000980791i
$397$	−1509.13	−	1509.13i	−0.190783	−	0.190783i	0.605251	−	0.796035i	$-0.293073\pi$
$397$	−1509.13	−	1509.13i	−0.190783	−	0.190783i	−0.796035	+	0.605251i	$0.793073\pi$
$398$	6839.55	+	6839.55i	0.861396	+	0.861396i
$399$		−	20855.4i		−	2.61674i
$400$	−490.897	+	1938.82i	−0.0613621	+	0.242352i
$401$		−	3082.32i		−	0.383849i	−0.981410	−	0.191925i	$-0.938527\pi$
$401$		−	3082.32i		−	0.383849i	0.981410	−	0.191925i	$-0.0614729\pi$
$402$	11661.7	−	11661.7i	1.44684	−	1.44684i
$403$	−5503.12	+	5503.12i	−0.680223	+	0.680223i
$404$		−	5896.89i		−	0.726191i
$405$	−4776.21	+	3717.62i	−0.586005	+	0.456124i
$406$		−	5475.96i		−	0.669378i
$407$	9.47491	+	9.47491i	0.00115394	+	0.00115394i
$408$	−1920.95	−	1920.95i	−0.233092	−	0.233092i
$409$		−	2760.91i		−	0.333786i	−0.985975	−	0.166893i	$-0.946627\pi$
$409$		−	2760.91i		−	0.333786i	0.985975	−	0.166893i	$-0.0533734\pi$
$410$	4705.53	+	586.452i	0.566804	+	0.0706410i
$411$		−	11438.2i		−	1.37276i
$412$	−5858.04	+	5858.04i	−0.700497	+	0.700497i
$413$	997.064	+	997.064i	0.118795	+	0.118795i
$414$	4545.35	−	10439.7i	0.539594	−	1.23933i
$415$	4107.58	+	511.930i	0.485864	+	0.0605534i
$416$	−1741.50			−0.205250
$417$	1009.35	+	1009.35i	0.118532	+	0.118532i
$418$	−7.64280	+	7.64280i	−0.000894310	+	0.000894310i
$419$	6600.70			0.769607			0.384803	−	0.922999i	$-0.374269\pi$
$419$	6600.70			0.769607			0.384803	+	0.922999i	$0.374269\pi$
$420$	5098.53	−	3968.50i	0.592340	−	0.461055i
$421$			5739.52i			0.664434i	0.943203	+	0.332217i	$0.107797\pi$
$421$			5739.52i			0.664434i	−0.943203	+	0.332217i	$0.892203\pi$
$422$	−157.636	−	157.636i	−0.0181839	−	0.0181839i
$423$	−17903.1	+	17903.1i	−2.05787	+	2.05787i
$424$	169.493			0.0194135
$425$	−2450.78	−	4112.59i	−0.279719	−	0.469388i
$426$	−7830.24			−0.890555
$427$	−8535.96	−	8535.96i	−0.967410	−	0.967410i
$428$	2898.99	+	2898.99i	0.327402	+	0.327402i
$429$	18.0643			0.00203299
$430$	−1803.91	−	2317.57i	−0.202307	−	0.259914i
$431$		−	2406.50i		−	0.268949i	−0.990917	−	0.134474i	$-0.957065\pi$
$431$		−	2406.50i		−	0.268949i	0.990917	−	0.134474i	$-0.0429346\pi$
$432$	2468.98	+	2468.98i	0.274974	+	0.274974i
$433$	76.5756	+	76.5756i	0.00849882	+	0.00849882i	0.711343	−	0.702845i	$-0.248087\pi$
$433$	76.5756	+	76.5756i	0.00849882	+	0.00849882i	−0.702845	+	0.711343i	$0.748087\pi$
$434$	−4660.31			−0.515443
$435$	16529.2	+	2060.04i	1.82187	+	0.227060i
$436$		−	2320.16i		−	0.254852i
$437$	−14818.0	+	5828.63i	−1.62207	+	0.638035i
$438$	2293.32	−	2293.32i	0.250181	−	0.250181i
$439$			15784.8i			1.71610i	0.513563	+	0.858052i	$0.328325\pi$
$439$			15784.8i			1.71610i	−0.513563	+	0.858052i	$0.671675\pi$
$440$	−3.32275	−	0.414116i	−0.000360013	−	4.48686e-5i
$441$	3999.86			0.431904
$442$	2947.70	−	2947.70i	0.317212	−	0.317212i
$443$	−9121.94	+	9121.94i	−0.978322	+	0.978322i	−0.999770	−	0.0214480i	$-0.993172\pi$
$443$	−9121.94	+	9121.94i	−0.978322	+	0.978322i	0.0214480	+	0.999770i	$0.493172\pi$
$444$	−12694.0			−1.35682
$445$	11509.0	−	8958.15i	1.22602	−	0.954285i
$446$	7745.26			0.822306
$447$	12816.0	−	12816.0i	1.35610	−	1.35610i
$448$	−737.394	−	737.394i	−0.0777647	−	0.0777647i
$449$		−	14490.9i		−	1.52309i	−0.648110	−	0.761547i	$-0.724440\pi$
$449$		−	14490.9i		−	1.52309i	0.648110	−	0.761547i	$-0.275560\pi$
$450$	6605.41	+	11084.3i	0.691960	+	1.16116i
$451$			7.93909i			0.000828907i
$452$	1171.25	−	1171.25i	0.121883	−	0.121883i
$453$	683.701	−	683.701i	0.0709118	−	0.0709118i
$454$	7047.24			0.728510
$455$	6089.65	+	7823.67i	0.627444	+	0.806109i
$456$		−	10239.4i		−	1.05154i
$457$	8115.89	−	8115.89i	0.830734	−	0.830734i	−0.156883	−	0.987617i	$-0.550145\pi$
$457$	8115.89	−	8115.89i	0.830734	−	0.830734i	0.987617	+	0.156883i	$0.0501446\pi$
$458$	−451.694	−	451.694i	−0.0460835	−	0.0460835i
$459$	−8358.09			−0.849940
$460$	−4244.59	−	2513.46i	−0.430228	−	0.254762i
$461$	−13486.4			−1.36253			−0.681265	−	0.732037i	$-0.738570\pi$
$461$	−13486.4			−1.36253			−0.681265	+	0.732037i	$0.738570\pi$
$462$	7.64886	+	7.64886i	0.000770254	+	0.000770254i
$463$	1198.33	−	1198.33i	0.120283	−	0.120283i	−0.644403	−	0.764686i	$-0.722894\pi$
$463$	1198.33	−	1198.33i	0.120283	−	0.120283i	0.764686	+	0.644403i	$0.222894\pi$
$464$		−	2688.54i		−	0.268992i
$465$	1753.19	−	14067.1i	0.174844	−	1.40290i
$466$	−7718.73			−0.767304
$467$	−11231.5	+	11231.5i	−1.11292	+	1.11292i	−0.120164	+	0.992754i	$0.538342\pi$
$467$	−11231.5	+	11231.5i	−1.11292	+	1.11292i	−0.992754	+	0.120164i	$0.961658\pi$
$468$	−7944.70	+	7944.70i	−0.784709	+	0.784709i
$469$			15154.2i			1.49202i
$470$	6737.51	+	8656.01i	0.661230	+	0.849515i
$471$			1340.95i			0.131184i
$472$	489.529	+	489.529i	0.0477381	+	0.0477381i
$473$	3.47684	−	3.47684i	0.000337982	−	0.000337982i
$474$	−5298.92			−0.513476
$475$	4429.02	−	17492.6i	0.427826	−	1.68972i
$476$	2496.26			0.240369
$477$	773.226	−	773.226i	0.0742213	−	0.0742213i
$478$	9023.88	−	9023.88i	0.863479	−	0.863479i
$479$	−3939.70			−0.375803			−0.187901	−	0.982188i	$-0.560169\pi$
$479$	−3939.70			−0.375803			−0.187901	+	0.982188i	$0.560169\pi$
$480$	2503.23	−	1948.42i	0.238034	−	0.185276i
$481$		−	19478.9i		−	1.84649i
$482$	4322.60	−	4322.60i	0.408484	−	0.408484i
$483$	5833.26	+	14829.8i	0.549529	+	1.39706i
$484$			5323.99i			0.499999i
$485$	501.075	−	4020.49i	0.0469127	−	0.376415i
$486$	−2184.65			−0.203905
$487$	3503.66	+	3503.66i	0.326008	+	0.326008i	0.851066	−	0.525058i	$-0.175956\pi$
$487$	3503.66	+	3503.66i	0.326008	+	0.326008i	−0.525058	+	0.851066i	$0.675956\pi$
$488$	−4190.90	−	4190.90i	−0.388757	−	0.388757i
$489$			11698.7i			1.08186i
$490$	214.312	−	1719.58i	0.0197585	−	0.158536i
$491$	−12055.7			−1.10808			−0.554040	−	0.832490i	$-0.686915\pi$
$491$	−12055.7			−1.10808			−0.554040	+	0.832490i	$0.686915\pi$
$492$	−5318.18	−	5318.18i	−0.487321	−	0.487321i
$493$	4550.67	+	4550.67i	0.415724	+	0.415724i
$494$	15712.3			1.43104
$495$	−17.0476	+	13.2692i	−0.00154794	+	0.00120486i
$496$	−2288.08			−0.207132
$497$	5087.65	−	5087.65i	0.459180	−	0.459180i
$498$	−4642.38	−	4642.38i	−0.417731	−	0.417731i
$499$		−	9971.46i		−	0.894557i	−0.894395	−	0.447278i	$-0.852393\pi$
$499$		−	9971.46i		−	0.894557i	0.894395	−	0.447278i	$-0.147607\pi$
$500$	5119.20	−	2245.84i	0.457875	−	0.200874i
$501$	−30443.4			−2.71479
$502$	−1380.96	+	1380.96i	−0.122780	+	0.122780i
$503$	−9770.50	−	9770.50i	−0.866094	−	0.866094i	0.125943	−	0.992037i	$-0.459804\pi$
$503$	−9770.50	−	9770.50i	−0.866094	−	0.866094i	−0.992037	+	0.125943i	$0.959804\pi$
$504$	−6727.97			−0.594618
$505$	−13006.7	+	10123.9i	−1.14612	+	0.892094i
$506$	3.29692	−	7.57229i	0.000289656	−	0.000665275i
$507$	−4794.51	−	4794.51i	−0.419983	−	0.419983i
$508$	−2391.77	+	2391.77i	−0.208893	+	0.208893i
$509$			8798.93i			0.766219i	0.923703	+	0.383110i	$0.125147\pi$
$509$			8798.93i			0.766219i	−0.923703	+	0.383110i	$0.874853\pi$
$510$	−939.083	+	7534.94i	−0.0815359	+	0.654221i
$511$			2980.15i			0.257992i
$512$	−362.039	−	362.039i	−0.0312500	−	0.0312500i
$513$	−22275.9	−	22275.9i	−1.91716	−	1.91716i
$514$		−	1744.90i		−	0.149736i
$515$	22978.2	+	2863.78i	1.96609	+	0.245035i
$516$			4658.09i			0.397405i
$517$	−12.9858	+	12.9858i	−0.00110467	+	0.00110467i
$518$	8247.84	−	8247.84i	0.699593	−	0.699593i
$519$		−	18999.3i		−	1.60689i
$520$	2989.84	+	3841.19i	0.252141	+	0.323937i
$521$		−	6328.91i		−	0.532196i	−0.963946	−	0.266098i	$-0.914265\pi$
$521$		−	6328.91i		−	0.532196i	0.963946	−	0.266098i	$-0.0857346\pi$
$522$	−12265.1	−	12265.1i	−1.02841	−	1.02841i
$523$	9799.89	+	9799.89i	0.819348	+	0.819348i	0.986014	−	0.166665i	$-0.0533000\pi$
$523$	9799.89	+	9799.89i	0.819348	+	0.819348i	−0.166665	+	0.986014i	$0.553300\pi$
$524$			2040.90i			0.170147i
$525$	−17506.5	−	4432.53i	−1.45533	−	0.368479i
$526$			4441.10i			0.368139i
$527$	3872.85	−	3872.85i	0.320121	−	0.320121i
$528$	3.75536	+	3.75536i	0.000309529	+	0.000309529i
$529$	8906.47	−	8289.19i	0.732019	−	0.681285i
$530$	−290.989	−	373.848i	−0.0238486	−	0.0306395i
$531$	4466.45			0.365024
$532$	6653.00	+	6653.00i	0.542188	+	0.542188i
$533$	8160.73	−	8160.73i	0.663190	−	0.663190i
$534$	−23131.9			−1.87456
$535$	1417.21	−	11371.3i	0.114526	−	0.918922i
$536$			7440.26i			0.599571i
$537$	3436.89	+	3436.89i	0.276188	+	0.276188i
$538$	5788.10	−	5788.10i	0.463834	−	0.463834i
$539$	2.90125			0.000231847
$540$	1206.99	−	9684.57i	0.0961864	−	0.771774i
$541$	−12189.1			−0.968671			−0.484336	−	0.874882i	$-0.660939\pi$
$541$	−12189.1			−0.968671			−0.484336	+	0.874882i	$0.660939\pi$
$542$	5889.13	+	5889.13i	0.466716	+	0.466716i
$543$	14378.8	+	14378.8i	1.13638	+	1.13638i
$544$	1225.59			0.0965931
$545$	−5117.53	+	3983.29i	−0.402222	+	0.313074i
$546$		−	15724.8i		−	1.23253i
$547$	17050.3	+	17050.3i	1.33276	+	1.33276i	0.902891	+	0.429870i	$0.141441\pi$
$547$	17050.3	+	17050.3i	1.33276	+	1.33276i	0.429870	+	0.902891i	$0.358559\pi$
$548$	3648.84	+	3648.84i	0.284435	+	0.284435i
$549$	−38237.7			−2.97258
$550$	4.79115	+	8.03989i	0.000371446	+	0.000623313i
$551$			24256.8i			1.87545i
$552$	2863.96	+	7280.99i	0.220830	+	0.561412i
$553$	3442.94	−	3442.94i	0.264754	−	0.264754i
$554$			5303.49i			0.406721i
$555$	21793.3	+	27998.9i	1.66680	+	2.14142i
$556$	−643.974			−0.0491198
$557$	8784.85	−	8784.85i	0.668269	−	0.668269i	−0.289046	−	0.957315i	$-0.593338\pi$
$557$	8784.85	−	8784.85i	0.668269	−	0.668269i	0.957315	+	0.289046i	$0.0933381\pi$
$558$	−10438.2	+	10438.2i	−0.791906	+	0.791906i
$559$	−7147.82			−0.540824
$560$	−360.484	+	2892.43i	−0.0272022	+	0.218263i
$561$	−12.7128			−0.000956748
$562$	−8525.32	+	8525.32i	−0.639891	+	0.639891i
$563$	−12593.5	−	12593.5i	−0.942722	−	0.942722i	0.0557244	−	0.998446i	$-0.482253\pi$
$563$	−12593.5	−	12593.5i	−0.942722	−	0.942722i	−0.998446	+	0.0557244i	$0.982253\pi$
$564$		−	17397.7i		−	1.29889i
$565$	−4594.23	−	572.580i	−0.342090	−	0.0426347i
$566$			11197.8i			0.831587i
$567$	−6237.36	+	6237.36i	−0.461983	+	0.461983i
$568$	2497.89	−	2497.89i	0.184523	−	0.184523i
$569$	1907.80			0.140561			0.0702806	−	0.997527i	$-0.477611\pi$
$569$	1907.80			0.140561			0.0702806	+	0.997527i	$0.477611\pi$
$570$	−22584.9	+	17579.2i	−1.65961	+	1.29178i
$571$			18929.9i			1.38738i	0.720274	+	0.693690i	$0.244016\pi$
$571$			18929.9i			1.38738i	−0.720274	+	0.693690i	$0.755984\pi$
$572$	−5.76259	+	5.76259i	−0.000421234	+	0.000421234i
$573$	−31853.1	−	31853.1i	−2.32231	−	2.32231i
$574$	6910.91			0.502537
$575$	1743.31	+	13677.4i	0.126437	+	0.991975i
$576$	−3303.23			−0.238949
$577$	−13330.2	−	13330.2i	−0.961777	−	0.961777i	0.0375186	−	0.999296i	$-0.488055\pi$
$577$	−13330.2	−	13330.2i	−0.961777	−	0.961777i	−0.999296	+	0.0375186i	$0.988055\pi$
$578$	4873.57	−	4873.57i	0.350716	−	0.350716i
$579$		−	15459.5i		−	1.10963i
$580$	−5930.06	+	4615.73i	−0.424538	+	0.330444i
$581$	6032.72			0.430773
$582$	−4543.95	+	4543.95i	−0.323630	+	0.323630i
$583$	0.560850	−	0.560850i	3.98423e−5	−	3.98423e-5i
$584$			1463.16i			0.103675i
$585$	31163.1	+	3883.87i	2.20245	+	0.274493i
$586$		−	7371.58i		−	0.519654i
$587$	−5071.12	−	5071.12i	−0.356572	−	0.356572i	0.505976	−	0.862548i	$-0.331132\pi$
$587$	−5071.12	−	5071.12i	−0.356572	−	0.356572i	−0.862548	+	0.505976i	$0.831132\pi$
$588$	−1943.47	+	1943.47i	−0.136305	+	0.136305i
$589$	20643.7			1.44416
$590$	239.312	−	1920.18i	0.0166989	−	0.133987i
$591$	2852.70			0.198552
$592$	4049.45	−	4049.45i	0.281134	−	0.281134i
$593$	10320.8	−	10320.8i	0.714711	−	0.714711i	−0.252806	−	0.967517i	$-0.581354\pi$
$593$	10320.8	−	10320.8i	0.714711	−	0.714711i	0.967517	+	0.252806i	$0.0813536\pi$
$594$	16.3396			0.00112866
$595$	−4285.62	−	5505.95i	−0.295283	−	0.379365i
$596$			8176.75i			0.561968i
$597$	−30321.1	+	30321.1i	−2.07866	+	2.07866i
$598$	−11172.7	+	4394.73i	−0.764020	+	0.300525i
$599$			14247.6i			0.971856i	0.873999	+	0.485928i	$0.161518\pi$
$599$			14247.6i			0.971856i	−0.873999	+	0.485928i	$0.838482\pi$
$600$	−8595.17	−	2176.24i	−0.584827	−	0.148075i
$601$	−25471.1			−1.72876			−0.864382	−	0.502835i	$-0.832290\pi$
$601$	−25471.1			−1.72876			−0.864382	+	0.502835i	$0.832290\pi$
$602$	−3026.56	−	3026.56i	−0.204906	−	0.204906i
$603$	33942.4	+	33942.4i	2.29227	+	2.29227i
$604$			436.208i			0.0293859i
$605$	11743.0	−	9140.34i	0.789128	−	0.614227i
$606$	26142.1			1.75239
$607$	3213.59	+	3213.59i	0.214886	+	0.214886i	0.806339	−	0.591453i	$-0.201446\pi$
$607$	3213.59	+	3213.59i	0.214886	+	0.214886i	−0.591453	+	0.806339i	$0.701446\pi$
$608$	3266.42	+	3266.42i	0.217880	+	0.217880i
$609$	24276.0			1.61530
$610$	−2048.78	+	16438.8i	−0.135988	+	1.09113i
$611$	26696.7			1.76765
$612$	5591.12	−	5591.12i	0.369294	−	0.369294i
$613$	18582.9	+	18582.9i	1.22440	+	1.22440i	0.966054	+	0.258342i	$0.0831760\pi$
$613$	18582.9	+	18582.9i	1.22440	+	1.22440i	0.258342	+	0.966054i	$0.416824\pi$
$614$			9894.80i			0.650361i
$615$	−2599.86	+	20860.6i	−0.170466	+	1.36777i
$616$	−4.88005			−0.000319193
$617$	7905.52	−	7905.52i	0.515826	−	0.515826i	−0.400480	−	0.916306i	$-0.631157\pi$
$617$	7905.52	−	7905.52i	0.515826	−	0.515826i	0.916306	+	0.400480i	$0.131157\pi$
$618$	−25969.9	−	25969.9i	−1.69039	−	1.69039i
$619$	13356.3			0.867262			0.433631	−	0.901090i	$-0.357232\pi$
$619$	13356.3			0.867262			0.433631	+	0.901090i	$0.357232\pi$
$620$	3928.21	+	5046.77i	0.254453	+	0.326908i
$621$	22070.4	+	9609.28i	1.42617	+	0.620945i
$622$	−10330.0	−	10330.0i	−0.665911	−	0.665911i
$623$	15029.8	−	15029.8i	0.966543	−	0.966543i
$624$		−	7720.41i		−	0.495295i
$625$	−13742.3	−	7435.62i	−0.879510	−	0.475880i
$626$			3299.85i			0.210684i
$627$	−33.8820	−	33.8820i	−0.00215808	−	0.00215808i
$628$	−427.769	−	427.769i	−0.0271813	−	0.0271813i
$629$			13708.4i			0.868979i
$630$	11550.7	+	14839.8i	0.730462	+	0.938461i
$631$			9032.92i			0.569881i	0.958545	+	0.284941i	$0.0919739\pi$
$631$			9032.92i			0.569881i	−0.958545	+	0.284941i	$0.908026\pi$
$632$	1690.38	−	1690.38i	0.106392	−	0.106392i
$633$	698.832	−	698.832i	0.0438801	−	0.0438801i
$634$		−	10494.9i		−	0.657419i
$635$	9381.73	+	1169.25i	0.586304	+	0.0730712i
$636$			751.397i			0.0468472i
$637$	−2982.25	−	2982.25i	−0.185496	−	0.185496i
$638$	−8.89633	−	8.89633i	−0.000552052	−	0.000552052i
$639$		−	22790.7i		−	1.41093i
$640$	−176.987	+	1420.10i	−0.0109313	+	0.0877098i
$641$			727.808i			0.0448467i	0.999749	+	0.0224233i	$0.00713817\pi$
$641$			727.808i			0.0448467i	−0.999749	+	0.0224233i	$0.992862\pi$
$642$	−12851.8	+	12851.8i	−0.790062	+	0.790062i
$643$	2870.41	+	2870.41i	0.176046	+	0.176046i	0.789630	−	0.613584i	$-0.210273\pi$
$643$	2870.41	+	2870.41i	0.176046	+	0.176046i	−0.613584	+	0.789630i	$0.710273\pi$
$644$	−6591.62	−	2869.94i	−0.403333	−	0.175608i
$645$	10274.3	−	7997.09i	0.627207	−	0.488194i
$646$	−11057.6			−0.673463
$647$	−6143.11	−	6143.11i	−0.373278	−	0.373278i	0.495392	−	0.868670i	$-0.335024\pi$
$647$	−6143.11	−	6143.11i	−0.373278	−	0.373278i	−0.868670	+	0.495392i	$0.835024\pi$
$648$	−3062.36	+	3062.36i	−0.185649	+	0.185649i
$649$	3.23969			0.000195946
$650$	3339.44	−	13189.3i	0.201513	−	0.795885i
$651$		−	20660.1i		−	1.24383i
$652$	−3731.93	−	3731.93i	−0.224162	−	0.224162i
$653$	−19977.6	+	19977.6i	−1.19722	+	1.19722i	−0.222223	+	0.974996i	$0.571331\pi$
$653$	−19977.6	+	19977.6i	−1.19722	+	1.19722i	−0.974996	+	0.222223i	$0.928669\pi$
$654$	10285.7			0.614990
$655$	4501.57	−	3503.85i	0.268535	−	0.209018i
$656$	3393.05			0.201946
$657$	6674.94	+	6674.94i	0.396369	+	0.396369i
$658$	11304.1	+	11304.1i	0.669724	+	0.669724i
$659$	−20576.9			−1.21633			−0.608167	−	0.793809i	$-0.708095\pi$
$659$	−20576.9			−1.21633			−0.608167	+	0.793809i	$0.708095\pi$
$660$	1.83586	−	14.7304i	0.000108274	−	0.000868759i
$661$		−	22824.8i		−	1.34309i	−0.740963	−	0.671545i	$-0.765631\pi$
$661$		−	22824.8i		−	1.34309i	0.740963	−	0.671545i	$-0.234369\pi$
$662$	−10694.2	−	10694.2i	−0.627858	−	0.627858i
$663$	13067.7	+	13067.7i	0.765473	+	0.765473i
$664$	2961.89			0.173108
$665$	3252.40	−	26096.4i	0.189658	−	1.52177i
$666$		−	36947.1i		−	2.14965i
$667$	−6784.61	−	17248.4i	−0.393855	−	1.00129i
$668$	9711.59	−	9711.59i	0.562504	−	0.562504i
$669$			34336.3i			1.98433i
$670$	16410.8	−	12773.6i	0.946277	−	0.736547i
$671$	−27.7353			−0.00159569
$672$	3269.02	−	3269.02i	0.187656	−	0.187656i
$673$	7016.81	−	7016.81i	0.401899	−	0.401899i	−0.477003	−	0.878902i	$-0.658277\pi$
$673$	7016.81	−	7016.81i	0.401899	−	0.401899i	0.878902	+	0.477003i	$0.158277\pi$
$674$	10482.1			0.599045
$675$	−23433.3	+	13964.4i	−1.33622	+	0.796283i
$676$	3058.95			0.174041
$677$	−11173.3	+	11173.3i	−0.634308	+	0.634308i	−0.949146	−	0.314838i	$-0.898050\pi$
$677$	−11173.3	+	11173.3i	−0.634308	+	0.634308i	0.314838	+	0.949146i	$0.398050\pi$
$678$	5192.38	+	5192.38i	0.294118	+	0.294118i
$679$		−	5904.81i		−	0.333734i
$680$	−2104.11	−	2703.26i	−0.118660	−	0.152449i
$681$			31241.8i			1.75799i
$682$	−7.57121	+	7.57121i	−0.000425098	+	0.000425098i
$683$	−3285.32	+	3285.32i	−0.184054	+	0.184054i	−0.793120	−	0.609065i	$-0.791545\pi$
$683$	−3285.32	+	3285.32i	−0.184054	+	0.184054i	0.609065	+	0.793120i	$0.291545\pi$
$684$	29802.8			1.66599
$685$	1783.78	−	14312.6i	0.0994960	−	0.798328i
$686$		−	13703.4i		−	0.762678i
$687$	2002.45	−	2002.45i	0.111205	−	0.111205i
$688$	−1485.95	−	1485.95i	−0.0823422	−	0.0823422i
$689$	−1153.02			−0.0637538
$690$	11142.6	−	18817.1i	0.614773	−	1.03820i
$691$	−5855.87			−0.322385			−0.161192	−	0.986923i	$-0.551534\pi$
$691$	−5855.87			−0.322385			−0.161192	+	0.986923i	$0.551534\pi$
$692$	6060.86	+	6060.86i	0.332947	+	0.332947i
$693$	−22.2628	+	22.2628i	−0.00122033	+	0.00122033i
$694$			23061.9i			1.26141i
$695$	1105.59	+	1420.40i	0.0603415	+	0.0775236i
$696$	11918.8			0.649112
$697$	−5743.15	+	5743.15i	−0.312105	+	0.312105i
$698$	6584.09	−	6584.09i	0.357037	−	0.357037i
$699$		−	34218.7i		−	1.85160i
$700$	6998.66	−	4170.66i	0.377892	−	0.225195i
$701$			9091.02i			0.489819i	0.969546	+	0.244909i	$0.0787582\pi$
$701$			9091.02i			0.489819i	−0.969546	+	0.244909i	$0.921242\pi$
$702$	−16795.8	−	16795.8i	−0.903015	−	0.903015i
$703$	−36535.3	+	36535.3i	−1.96011	+	1.96011i
$704$	−2.39596			−0.000128269
$705$	−38373.8	+	29868.7i	−2.04999	+	1.59563i
$706$	24783.1			1.32114
$707$	−16985.7	+	16985.7i	−0.903553	+	0.903553i
$708$	−2170.18	+	2170.18i	−0.115198	+	0.115198i
$709$	−20601.7			−1.09127			−0.545637	−	0.838021i	$-0.683712\pi$
$709$	−20601.7			−1.09127			−0.545637	+	0.838021i	$0.683712\pi$
$710$	−9797.96	−	1221.12i	−0.517903	−	0.0645464i
$711$		−	15423.0i		−	0.813515i
$712$	7379.19	−	7379.19i	0.388408	−	0.388408i
$713$	−14679.2	+	5774.04i	−0.771026	+	0.303281i
$714$			11066.4i			0.580042i
$715$	22.6038	+	2.81712i	0.00118228	+	0.000147349i
$716$	−2192.77			−0.114452
$717$	40004.7	+	40004.7i	2.08368	+	2.08368i
$718$	11140.6	+	11140.6i	0.579055	+	0.579055i
$719$			9304.86i			0.482632i	0.970447	+	0.241316i	$0.0775791\pi$
$719$			9304.86i			0.482632i	−0.970447	+	0.241316i	$0.922421\pi$
$720$	5671.06	+	7285.88i	0.293539	+	0.377123i
$721$	33747.5			1.74317
$722$	−19770.6	−	19770.6i	−1.01909	−	1.01909i
$723$	19163.0	+	19163.0i	0.985723	+	0.985723i
$724$	−9173.84			−0.470916
$725$	20361.7	+	5155.44i	1.04305	+	0.264094i
$726$	−23602.3			−1.20656
$727$	639.386	−	639.386i	0.0326183	−	0.0326183i	−0.690610	−	0.723228i	$-0.742658\pi$
$727$	639.386	−	639.386i	0.0326183	−	0.0326183i	0.723228	+	0.690610i	$0.242658\pi$
$728$	5016.29	+	5016.29i	0.255379	+	0.255379i
$729$		−	24301.5i		−	1.23465i
$730$	3227.27	−	2511.99i	0.163626	−	0.127360i
$731$	5030.31			0.254518
$732$	18579.1	−	18579.1i	0.938120	−	0.938120i
$733$	−19733.5	−	19733.5i	−0.994371	−	0.994371i	0.00561325	−	0.999984i	$-0.498213\pi$
$733$	−19733.5	−	19733.5i	−0.994371	−	0.994371i	−0.999984	+	0.00561325i	$0.998213\pi$
$734$	10008.6			0.503304
$735$	7623.26	+	950.090i	0.382569	+	0.0476797i
$736$	−3236.29	−	1409.06i	−0.162080	−	0.0705686i
$737$	24.6197	+	24.6197i	0.00123050	+	0.00123050i
$738$	15479.1	−	15479.1i	0.772077	−	0.772077i
$739$		−	34122.0i		−	1.69851i	−0.527985	−	0.849254i	$-0.677052\pi$
$739$		−	34122.0i		−	1.69851i	0.527985	−	0.849254i	$-0.322948\pi$
$740$	−15884.0	−	1979.62i	−0.789062	−	0.0983411i
$741$			69655.9i			3.45327i
$742$	−488.216	−	488.216i	−0.0241549	−	0.0241549i
$743$	−185.896	−	185.896i	−0.00917882	−	0.00917882i	0.702502	−	0.711681i	$-0.252066\pi$
$743$	−185.896	−	185.896i	−0.00917882	−	0.00917882i	−0.711681	+	0.702502i	$0.752066\pi$
$744$		−	10143.5i		−	0.499837i
$745$	18035.3	−	14038.0i	0.886930	−	0.690352i
$746$			23126.5i			1.13502i
$747$	13512.1	−	13512.1i	0.661823	−	0.661823i
$748$	4.05545	−	4.05545i	0.000198238	−	0.000198238i
$749$		−	16700.8i		−	0.814729i
$750$	9956.26	+	22694.4i	0.484735	+	1.10491i
$751$			3305.10i			0.160592i	0.996771	+	0.0802962i	$0.0255866\pi$
$751$			3305.10i			0.160592i	−0.996771	+	0.0802962i	$0.974413\pi$
$752$	5549.96	+	5549.96i	0.269131	+	0.269131i
$753$	−6122.08	−	6122.08i	−0.296283	−	0.296283i
$754$			18289.4i			0.883369i
$755$	962.136	−	748.890i	0.0463784	−	0.0360992i
$756$		−	14223.5i		−	0.684265i
$757$	23992.9	−	23992.9i	1.15196	−	1.15196i	0.165806	−	0.986158i	$-0.446977\pi$
$757$	23992.9	−	23992.9i	1.15196	−	1.15196i	0.986158	−	0.165806i	$-0.0530225\pi$
$758$	3500.66	+	3500.66i	0.167744	+	0.167744i
$759$	33.5695	+	14.6159i	0.00160539	+	0.000698977i
$760$	1596.83	−	12812.6i	0.0762148	−	0.611526i
$761$	−17864.8			−0.850986			−0.425493	−	0.904962i	$-0.639899\pi$
$761$	−17864.8			−0.850986			−0.425493	+	0.904962i	$0.639899\pi$
$762$	−10603.2	−	10603.2i	−0.504086	−	0.504086i
$763$	−6683.08	+	6683.08i	−0.317095	+	0.317095i
$764$	20322.6			0.962363
$765$	−21931.2	−	2733.29i	−1.03650	−	0.129180i
$766$			19021.4i			0.897220i
$767$	−3330.13	−	3330.13i	−0.156772	−	0.156772i
$768$	1604.99	−	1604.99i	0.0754103	−	0.0754103i
$769$	1834.19			0.0860113			0.0430057	−	0.999075i	$-0.486307\pi$
$769$	1834.19			0.0860113			0.0430057	+	0.999075i	$0.486307\pi$
$770$	8.37817	+	10.7638i	0.000392114	+	0.000503769i
$771$	7735.49			0.361332
$772$	4931.66	+	4931.66i	0.229915	+	0.229915i
$773$	24063.0	+	24063.0i	1.11964	+	1.11964i	0.991793	+	0.127851i	$0.0408079\pi$
$773$	24063.0	+	24063.0i	1.11964	+	1.11964i	0.127851	+	0.991793i	$0.459192\pi$
$774$	−13557.8			−0.629619
$775$	4387.53	−	17328.8i	0.203361	−	0.803185i
$776$		−	2899.09i		−	0.134112i
$777$	36564.3	+	36564.3i	1.68821	+	1.68821i
$778$	−17160.8	−	17160.8i	−0.790800	−	0.790800i
$779$	−30613.2			−1.40800
$780$	−17028.8	+	13254.5i	−0.781702	+	0.608447i
$781$		−	16.5309i		−	0.000757392i
$782$	7862.81	−	3092.81i	0.359557	−	0.141431i
$783$	25929.5	−	25929.5i	1.18345	−	1.18345i
$784$		−	1239.95i		−	0.0564847i
$785$	−209.121	+	1677.93i	−0.00950807	+	0.0762901i
$786$	−9047.70			−0.410586
$787$	−480.919	+	480.919i	−0.0217826	+	0.0217826i	−0.717914	−	0.696132i	$-0.754903\pi$
$787$	−480.919	+	480.919i	−0.0217826	+	0.0217826i	0.696132	+	0.717914i	$0.254903\pi$
$788$	−910.026	+	910.026i	−0.0411400	+	0.0411400i
$789$	−19688.3			−0.888368
$790$	−6630.53	−	826.366i	−0.298612	−	0.0372162i
$791$	−6747.44			−0.303301
$792$	−10.9304	+	10.9304i	−0.000490395	+	0.000490395i
$793$	28509.6	+	28509.6i	1.27668	+	1.27668i
$794$			4268.46i			0.190783i
$795$	1657.34	−	1290.01i	0.0739369	−	0.0575497i
$796$		−	19345.2i		−	0.861396i
$797$	−19267.9	+	19267.9i	−0.856340	+	0.856340i	−0.990905	−	0.134565i	$-0.957036\pi$
$797$	−19267.9	+	19267.9i	−0.856340	+	0.856340i	0.134565	+	0.990905i	$0.457036\pi$
$798$	−29494.1	+	29494.1i	−1.30837	+	1.30837i
$799$	−18788.0			−0.831878
$800$	3436.14	−	2047.67i	0.151857	−	0.0904952i
$801$		−	67327.6i		−	2.96992i
$802$	−4359.05	+	4359.05i	−0.191925	+	0.191925i
$803$	4.84159	+	4.84159i	0.000212772	+	0.000212772i
$804$	−32984.1			−1.44684
$805$	4986.44	+	19466.2i	0.218322	+	0.852289i
$806$	15565.2			0.680223
$807$	25659.8	+	25659.8i	1.11929	+	1.11929i
$808$	−8339.46	+	8339.46i	−0.363096	+	0.363096i
$809$			15062.1i			0.654579i	0.944924	+	0.327289i	$0.106135\pi$
$809$			15062.1i			0.654579i	−0.944924	+	0.327289i	$0.893865\pi$
$810$	12012.1	+	1497.07i	0.521065	+	0.0649405i
$811$	35275.9			1.52738			0.763690	−	0.645583i	$-0.223386\pi$
$811$	35275.9			1.52738			0.763690	+	0.645583i	$0.223386\pi$
$812$	−7744.18	+	7744.18i	−0.334689	+	0.334689i
$813$	−26107.7	+	26107.7i	−1.12624	+	1.12624i
$814$		−	26.7991i		−	0.00115394i
$815$	−1824.40	+	14638.5i	−0.0784124	+	0.629159i
$816$			5433.28i			0.233092i
$817$	13406.7	+	13406.7i	0.574103	+	0.574103i
$818$	−3904.52	+	3904.52i	−0.166893	+	0.166893i
$819$	45768.6			1.95273
$820$	−5825.26	−	7484.00i	−0.248082	−	0.318723i
$821$	−39635.4			−1.68488			−0.842439	−	0.538792i	$-0.818881\pi$
$821$	−39635.4			−1.68488			−0.842439	+	0.538792i	$0.818881\pi$
$822$	−16176.0	+	16176.0i	−0.686379	+	0.686379i
$823$	−18998.9	+	18998.9i	−0.804692	+	0.804692i	−0.983825	−	0.179133i	$-0.942671\pi$
$823$	−18998.9	+	18998.9i	−0.804692	+	0.804692i	0.179133	+	0.983825i	$0.442671\pi$
$824$	16569.0			0.700497
$825$	−35.6425	+	21.2401i	−0.00150413	+	0.000896348i
$826$		−	2820.12i		−	0.118795i
$827$	−2824.49	+	2824.49i	−0.118763	+	0.118763i	−0.763991	−	0.645227i	$-0.776763\pi$
$827$	−2824.49	+	2824.49i	−0.118763	+	0.118763i	0.645227	+	0.763991i	$0.276763\pi$
$828$	−21192.0	+	8335.82i	−0.889461	+	0.349867i
$829$			5398.90i			0.226190i	0.993584	+	0.113095i	$0.0360764\pi$
$829$			5398.90i			0.226190i	−0.993584	+	0.113095i	$0.963924\pi$
$830$	−5085.02	−	6532.98i	−0.212655	−	0.273208i
$831$	−23511.4			−0.981471
$832$	2462.85	+	2462.85i	0.102625	+	0.102625i
$833$	2098.77	+	2098.77i	0.0872966	+	0.0872966i
$834$		−	2854.87i		−	0.118532i
$835$	−38093.7	−	4747.63i	−1.57879	−	0.196765i
$836$	21.6171			0.000894310
$837$	−22067.2	−	22067.2i	−0.911297	−	0.911297i
$838$	−9334.80	−	9334.80i	−0.384803	−	0.384803i
$839$	−7162.39			−0.294723			−0.147362	−	0.989083i	$-0.547078\pi$
$839$	−7162.39			−0.294723			−0.147362	+	0.989083i	$0.547078\pi$
$840$	−12822.7	−	1598.10i	−0.526697	−	0.0656425i
$841$	−3846.26			−0.157705
$842$	8116.90	−	8116.90i	0.332217	−	0.332217i
$843$	−37794.4	−	37794.4i	−1.54414	−	1.54414i
$844$			445.862i			0.0181839i
$845$	−5251.66	−	6747.06i	−0.213802	−	0.274682i
$846$	50637.7			2.05787
$847$	15335.5	−	15335.5i	0.622117	−	0.622117i
$848$	−239.699	−	239.699i	−0.00970673	−	0.00970673i
$849$	−49642.1			−2.00673
$850$	−2350.15	+	9282.01i	−0.0948345	+	0.374553i
$851$	15760.5	−	36198.3i	0.634855	−	1.45812i
$852$	11073.6	+	11073.6i	0.445277	+	0.445277i
$853$	25986.3	−	25986.3i	1.04309	−	1.04309i	0.0440588	−	0.999029i	$-0.485971\pi$
$853$	25986.3	−	25986.3i	1.04309	−	1.04309i	0.999029	−	0.0440588i	$-0.0140289\pi$
$854$			24143.3i			0.967410i
$855$	−51166.0	−	65735.5i	−2.04660	−	2.62936i
$856$		−	8199.57i		−	0.327402i
$857$	−5376.72	−	5376.72i	−0.214312	−	0.214312i	0.591784	−	0.806096i	$-0.298424\pi$
$857$	−5376.72	−	5376.72i	−0.214312	−	0.214312i	−0.806096	+	0.591784i	$0.798424\pi$
$858$	−25.5467	−	25.5467i	−0.00101649	−	0.00101649i
$859$			20202.7i			0.802455i	0.915979	+	0.401227i	$0.131416\pi$
$859$			20202.7i			0.802455i	−0.915979	+	0.401227i	$0.868584\pi$
$860$	−726.427	+	5828.65i	−0.0288034	+	0.231111i
$861$			30637.5i			1.21269i
$862$	−3403.30	+	3403.30i	−0.134474	+	0.134474i
$863$	−5519.92	+	5519.92i	−0.217729	+	0.217729i	−0.807541	−	0.589812i	$-0.799202\pi$
$863$	−5519.92	+	5519.92i	−0.217729	+	0.217729i	0.589812	+	0.807541i	$0.299202\pi$
$864$		−	6983.33i		−	0.274974i
$865$	2962.93	−	23773.7i	0.116465	−	0.934487i
$866$		−	216.589i		−	0.00849882i
$867$	21605.5	+	21605.5i	0.846323	+	0.846323i
$868$	6590.68	+	6590.68i	0.257721	+	0.257721i
$869$		−	11.1869i		−	0.000436697i
$870$	−20462.5	−	26289.1i	−0.797405	−	1.02447i
$871$		−	50614.0i		−	1.96899i
$872$	−3281.20	+	3281.20i	−0.127426	+	0.127426i
$873$	−13225.6	−	13225.6i	−0.512736	−	0.512736i
$874$	29198.8	+	12712.9i	1.13005	+	0.492015i
$875$	−21214.6	−	8276.55i	−0.819639	−	0.319770i
$876$	−6486.50			−0.250181
$877$	−3787.34	−	3787.34i	−0.145826	−	0.145826i	0.630425	−	0.776251i	$-0.282881\pi$
$877$	−3787.34	−	3787.34i	−0.145826	−	0.145826i	−0.776251	+	0.630425i	$0.782881\pi$
$878$	22323.1	−	22323.1i	0.858052	−	0.858052i
$879$	32679.7			1.25399
$880$	4.11343	+	5.28473i	0.000157572	+	0.000202441i
$881$		−	29476.8i		−	1.12724i	−0.826034	−	0.563620i	$-0.809408\pi$
$881$		−	29476.8i		−	1.12724i	0.826034	−	0.563620i	$-0.190592\pi$
$882$	−5656.66	−	5656.66i	−0.215952	−	0.215952i
$883$	−4289.15	+	4289.15i	−0.163467	+	0.163467i	−0.784101	−	0.620634i	$-0.786875\pi$
$883$	−4289.15	+	4289.15i	−0.163467	+	0.163467i	0.620634	+	0.784101i	$0.286875\pi$
$884$	−8337.35			−0.317212
$885$	8512.53	+	1060.92i	0.323328	+	0.0402965i
$886$	25800.8			0.978322
$887$	−16280.6	−	16280.6i	−0.616291	−	0.616291i	0.328287	−	0.944578i	$-0.393529\pi$
$887$	−16280.6	−	16280.6i	−0.616291	−	0.616291i	−0.944578	+	0.328287i	$0.893529\pi$
$888$	17952.0	+	17952.0i	0.678412	+	0.678412i
$889$	13778.7			0.519825
$890$	−28944.9	−	3607.41i	−1.09015	−	0.135866i
$891$			20.2666i			0.000762016i
$892$	−10953.5	−	10953.5i	−0.411153	−	0.411153i
$893$	−50073.5	−	50073.5i	−1.87642	−	1.87642i
$894$	−36249.2			−1.35610
$895$	3764.59	+	4836.56i	0.140599	+	0.180635i
$896$			2085.67i			0.0777647i
$897$	−19482.7	−	49530.6i	−0.725205	−	1.84368i
$898$	−20493.3	+	20493.3i	−0.761547	+	0.761547i
$899$			24029.6i			0.891470i
$900$	6334.17	−	25017.1i	0.234599	−	0.926559i
$901$	811.440			0.0300033
$902$	11.2276	−	11.2276i	0.000414453	−	0.000414453i
$903$	13417.4	−	13417.4i	0.494465	−	0.494465i
$904$	−3312.79			−0.121883
$905$	15749.8	+	20234.6i	0.578499	+	0.743227i
$906$	−1933.80			−0.0709118
$907$	7873.92	−	7873.92i	0.288257	−	0.288257i	−0.548134	−	0.836391i	$-0.684661\pi$
$907$	7873.92	−	7873.92i	0.288257	−	0.288257i	0.836391	+	0.548134i	$0.184661\pi$
$908$	−9966.30	−	9966.30i	−0.364255	−	0.364255i
$909$			76089.1i			2.77637i
$910$	2452.28	−	19676.4i	0.0893321	−	0.716777i
$911$		−	24678.6i		−	0.897516i	−0.893653	−	0.448758i	$-0.851866\pi$
$911$		−	24678.6i		−	0.897516i	0.893653	−	0.448758i	$-0.148134\pi$
$912$	−14480.7	+	14480.7i	−0.525772	+	0.525772i
$913$	9.80084	−	9.80084i	0.000355269	−	0.000355269i
$914$	−22955.2			−0.830734
$915$	−72876.6	−	9082.64i	−2.63303	−	0.328156i
$916$			1277.58i			0.0460835i
$917$	5878.69	−	5878.69i	0.211703	−	0.211703i
$918$	11820.1	+	11820.1i	0.424970	+	0.424970i
$919$	53461.2			1.91896			0.959479	−	0.281780i	$-0.0909249\pi$
$919$	53461.2			1.91896			0.959479	+	0.281780i	$0.0909249\pi$
$920$	2448.19	+	9557.32i	0.0877332	+	0.342495i
$921$	−43865.6			−1.56940
$922$	19072.7	+	19072.7i	0.681265	+	0.681265i
$923$	−16992.4	+	16992.4i	−0.605973	+	0.605973i
$924$		−	21.6342i		−	0.000770254i
$925$	22903.5	+	38433.6i	0.814120	+	1.36615i
$926$	−3389.39			−0.120283
$927$	75587.8	−	75587.8i	2.67813	−	2.67813i
$928$	−3802.16	+	3802.16i	−0.134496	+	0.134496i
$929$			15330.1i			0.541406i	0.962663	+	0.270703i	$0.0872561\pi$
$929$			15330.1i			0.541406i	−0.962663	+	0.270703i	$0.912744\pi$
$930$	−22373.3	+	17414.6i	−0.788872	+	0.614028i
$931$			11187.2i			0.393821i
$932$	10915.9	+	10915.9i	0.383652	+	0.383652i
$933$	45795.1	−	45795.1i	1.60693	−	1.60693i
$934$	31767.5			1.11292
$935$	−15.9075	−	1.98256i	−0.000556397	−	6.93440e-5i
$936$	22471.0			0.784709
$937$	5888.78	−	5888.78i	0.205313	−	0.205313i	−0.596959	−	0.802272i	$-0.703625\pi$
$937$	5888.78	−	5888.78i	0.205313	−	0.205313i	0.802272	+	0.596959i	$0.203625\pi$
$938$	21431.3	−	21431.3i	0.746008	−	0.746008i
$939$	−14628.9			−0.508408
$940$	2713.17	−	21769.7i	0.0941424	−	0.755373i
$941$		−	21565.4i		−	0.747089i	−0.927612	−	0.373545i	$-0.878142\pi$
$941$		−	21565.4i		−	0.747089i	0.927612	−	0.373545i	$-0.121858\pi$
$942$	1896.39	−	1896.39i	0.0655920	−	0.0655920i
$943$	21768.3	−	8562.49i	0.751720	−	0.295687i
$944$		−	1384.60i		−	0.0477381i
$945$	−31372.6	+	24419.2i	−1.07995	+	0.840589i
$946$	−9.83399			−0.000337982
$947$	2452.07	+	2452.07i	0.0841411	+	0.0841411i	0.747925	−	0.663784i	$-0.231050\pi$
$947$	2452.07	+	2452.07i	0.0841411	+	0.0841411i	−0.663784	+	0.747925i	$0.731050\pi$
$948$	7493.81	+	7493.81i	0.256738	+	0.256738i
$949$		−	9953.50i		−	0.340468i
$950$	−31001.9	+	18474.7i	−1.05877	+	0.630947i
$951$	46525.8			1.58644
$952$	−3530.24	−	3530.24i	−0.120185	−	0.120185i
$953$	10608.1	+	10608.1i	0.360579	+	0.360579i	0.864026	−	0.503447i	$-0.167935\pi$
$953$	10608.1	+	10608.1i	0.360579	+	0.360579i	−0.503447	+	0.864026i	$0.667935\pi$
$954$	−2187.01			−0.0742213
$955$	−34890.2	−	44825.2i	−1.18222	−	1.51886i
$956$	−25523.4			−0.863479
$957$	39.4392	−	39.4392i	0.00133217	−	0.00133217i
$958$	5571.58	+	5571.58i	0.187901	+	0.187901i
$959$		−	21020.5i		−	0.707809i
$960$	−6295.57	−	784.620i	−0.211655	−	0.0263786i
$961$	−9340.63			−0.313539
$962$	−27547.3	+	27547.3i	−0.923243	+	0.923243i
$963$	−37406.4	−	37406.4i	−1.25172	−	1.25172i
$964$	−12226.2			−0.408484
$965$	2410.91	−	19344.5i	0.0804247	−	0.645306i
$966$	12723.0	−	29222.0i	0.423764	−	0.973293i
$967$	12213.2	+	12213.2i	0.406153	+	0.406153i	0.880395	−	0.474242i	$-0.157278\pi$
$967$	12213.2	+	12213.2i	0.406153	+	0.406153i	−0.474242	+	0.880395i	$0.657278\pi$
$968$	7529.27	−	7529.27i	0.250000	−	0.250000i
$969$		−	49020.7i		−	1.62515i
$970$	−6394.46	+	4977.21i	−0.211664	+	0.164751i
$971$			40409.5i			1.33553i	0.744370	+	0.667767i	$0.232750\pi$
$971$			40409.5i			1.33553i	−0.744370	+	0.667767i	$0.767250\pi$
$972$	3089.57	+	3089.57i	0.101953	+	0.101953i
$973$	1854.93	+	1854.93i	0.0611166	+	0.0611166i
$974$		−	9909.85i		−	0.326008i
$975$	58470.6	+	14804.4i	1.92057	+	0.486277i
$976$			11853.7i			0.388757i
$977$	28678.9	−	28678.9i	0.939118	−	0.939118i	−0.0591324	−	0.998250i	$-0.518833\pi$
$977$	28678.9	−	28678.9i	0.939118	−	0.939118i	0.998250	+	0.0591324i	$0.0188334\pi$
$978$	16544.4	−	16544.4i	0.540932	−	0.540932i
$979$		−	48.8352i		−	0.00159426i
$980$	−2734.94	+	2128.78i	−0.0891475	+	0.0693890i
$981$			29937.6i			0.974346i
$982$	17049.4	+	17049.4i	0.554040	+	0.554040i
$983$	−25393.6	−	25393.6i	−0.823936	−	0.823936i	0.162734	−	0.986670i	$-0.447969\pi$
$983$	−25393.6	−	25393.6i	−0.823936	−	0.823936i	−0.986670	+	0.162734i	$0.947969\pi$
$984$			15042.1i			0.487321i
$985$	3569.58	+	444.878i	0.115468	+	0.0143909i
$986$		−	12871.2i		−	0.415724i
$987$	−50113.2	+	50113.2i	−1.61613	+	1.61613i
$988$	−22220.6	−	22220.6i	−0.715518	−	0.715518i
$989$	−13283.0	−	5783.34i	−0.427074	−	0.185945i
$990$	42.8743	+	5.34344i	0.00137640	+	0.000171541i
$991$	−53664.8			−1.72020			−0.860101	−	0.510124i	$-0.829599\pi$
$991$	−53664.8			−1.72020			−0.860101	+	0.510124i	$0.829599\pi$
$992$	3235.83	+	3235.83i	0.103566	+	0.103566i
$993$	47409.5	−	47409.5i	1.51510	−	1.51510i
$994$	−14390.1			−0.459180
$995$	−42669.3	+	33212.1i	−1.35950	+	1.05819i
$996$			13130.6i			0.417731i
$997$	−41708.4	−	41708.4i	−1.32489	−	1.32489i	−0.909761	−	0.415133i	$-0.863735\pi$
$997$	−41708.4	−	41708.4i	−1.32489	−	1.32489i	−0.415133	−	0.909761i	$-0.636265\pi$
$998$	−14101.8	+	14101.8i	−0.447278	+	0.447278i
$999$	78109.4			2.47374

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.e.a.137.18	yes	72
5.3	odd	4	inner	230.4.e.a.183.17	yes	72
23.22	odd	2	inner	230.4.e.a.137.17	✓	72
115.68	even	4	inner	230.4.e.a.183.18	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.e.a.137.17	✓	72	23.22	odd	2	inner
230.4.e.a.137.18	yes	72	1.1	even	1	trivial
230.4.e.a.183.17	yes	72	5.3	odd	4	inner
230.4.e.a.183.18	yes	72	115.68	even	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)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 1.41421i) q^{2} +(6.26949 - 6.26949i) q^{3} +4.00000i q^{4} +(8.82273 - 6.86728i) q^{5} -17.7328 q^{6} +(11.5218 - 11.5218i) q^{7} +(5.65685 - 5.65685i) q^{8} -51.6130i q^{9} +O(q^{10})\)	\(q+(-1.41421 - 1.41421i) q^{2} +(6.26949 - 6.26949i) q^{3} +4.00000i q^{4} +(8.82273 - 6.86728i) q^{5} -17.7328 q^{6} +(11.5218 - 11.5218i) q^{7} +(5.65685 - 5.65685i) q^{8} -51.6130i q^{9} +(-22.1890 - 2.76543i) q^{10} -0.0374369i q^{11} +(25.0780 + 25.0780i) q^{12} +(-38.4820 + 38.4820i) q^{13} -32.5885 q^{14} +(12.2597 - 98.3683i) q^{15} -16.0000 q^{16} +(27.0819 - 27.0819i) q^{17} +(-72.9919 + 72.9919i) q^{18} +144.357 q^{19} +(27.4691 + 35.2909i) q^{20} -144.471i q^{21} +(-0.0529438 + 0.0529438i) q^{22} +(-102.649 + 40.3765i) q^{23} -70.9312i q^{24} +(30.6810 - 121.176i) q^{25} +108.844 q^{26} +(-154.311 - 154.311i) q^{27} +(46.0871 + 46.0871i) q^{28} +168.034i q^{29} +(-156.452 + 121.776i) q^{30} +143.005 q^{31} +(22.6274 + 22.6274i) q^{32} +(-0.234710 - 0.234710i) q^{33} -76.5993 q^{34} +(22.5303 - 180.777i) q^{35} +206.452 q^{36} +(-253.090 + 253.090i) q^{37} +(-204.152 - 204.152i) q^{38} +482.526i q^{39} +(11.0617 - 88.7561i) q^{40} -212.066 q^{41} +(-204.313 + 204.313i) q^{42} +(92.8721 + 92.8721i) q^{43} +0.149748 q^{44} +(-354.441 - 455.368i) q^{45} +(202.268 + 88.0660i) q^{46} +(-346.873 - 346.873i) q^{47} +(-100.312 + 100.312i) q^{48} +77.4971i q^{49} +(-214.759 + 127.980i) q^{50} -339.580i q^{51} +(-153.928 - 153.928i) q^{52} +(14.9812 + 14.9812i) q^{53} +436.458i q^{54} +(-0.257089 - 0.330295i) q^{55} -130.354i q^{56} +(905.044 - 905.044i) q^{57} +(237.635 - 237.635i) q^{58} +86.5373i q^{59} +(393.473 + 49.0387i) q^{60} -740.854i q^{61} +(-202.239 - 202.239i) q^{62} +(-594.674 - 594.674i) q^{63} -64.0000i q^{64} +(-75.2498 + 603.783i) q^{65} +0.663861i q^{66} +(-657.632 + 657.632i) q^{67} +(108.328 + 108.328i) q^{68} +(-390.414 + 896.695i) q^{69} +(-287.520 + 223.794i) q^{70} +441.568 q^{71} +(-291.967 - 291.967i) q^{72} +(-129.327 + 129.327i) q^{73} +715.848 q^{74} +(-567.359 - 952.068i) q^{75} +577.428i q^{76} +(-0.431340 - 0.431340i) q^{77} +(682.394 - 682.394i) q^{78} +298.820 q^{79} +(-141.164 + 109.876i) q^{80} -541.354 q^{81} +(299.906 + 299.906i) q^{82} +(261.796 + 261.796i) q^{83} +577.886 q^{84} +(52.9574 - 424.916i) q^{85} -262.682i q^{86} +(1053.48 + 1053.48i) q^{87} +(-0.211775 - 0.211775i) q^{88} +1304.47 q^{89} +(-142.732 + 1145.24i) q^{90} +886.764i q^{91} +(-161.506 - 410.594i) q^{92} +(896.567 - 896.567i) q^{93} +981.104i q^{94} +(1273.62 - 991.339i) q^{95} +283.725 q^{96} +(256.245 - 256.245i) q^{97} +(109.597 - 109.597i) q^{98} -1.93223 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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