LMFDB - Embedded newform 230.4.e.a.137.17

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			137.17
Character	$\chi$	$=$	230.137
Dual form			230.4.e.a.183.17

$q$-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} +(-40.3765 + 102.649i) 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} +(-410.594 - 161.506i) 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	−0.946073	−	0.323955i	$-0.894987\pi$
$7$	−11.5218	+	11.5218i	−0.622118	+	0.622118i	0.323955	+	0.946073i	$0.394987\pi$
$8$	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	$0.000163317\pi$
$11$			0.0374369i			0.00102615i	−1.00000		0.000513075i	$0.999837\pi$
$12$	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	−0.873391	−	0.487019i	$-0.838084\pi$
$17$	−27.0819	+	27.0819i	−0.386373	+	0.386373i	0.487019	+	0.873391i	$0.338084\pi$
$18$	−72.9919	+	72.9919i	−0.955797	+	0.955797i
$19$	−144.357			−1.74304			−0.871520	−	0.490361i	$-0.836865\pi$
$19$	−144.357			−1.74304			−0.871520	+	0.490361i	$0.836865\pi$
$20$	−27.4691	−	35.2909i	−0.307114	−	0.394564i
$21$			144.471i			1.50125i
$22$	0.0529438	−	0.0529438i	0.000513075	−	0.000513075i
$23$	−40.3765	+	102.649i	−0.366047	+	0.930596i
$23$	−40.3765	+	102.649i	−0.366047	+	0.930596i
$24$		−	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	$-0.457383\pi$
$37$	253.090	−	253.090i	1.12454	−	1.12454i	0.991051	−	0.133484i	$-0.0426165\pi$
$38$	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	0.522978	−	0.852346i	$-0.324821\pi$
$43$	−92.8721	−	92.8721i	−0.329369	−	0.329369i	−0.852346	+	0.522978i	$0.824821\pi$
$44$	−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	0.687427	−	0.726254i	$-0.258740\pi$
$53$	−14.9812	−	14.9812i	−0.0388269	−	0.0388269i	−0.726254	+	0.687427i	$0.758740\pi$
$54$			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	$0.283519\pi$
$61$			740.854i			1.55503i	−0.628866	+	0.777514i	$0.716481\pi$
$62$	−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	$-0.427854\pi$
$67$	657.632	−	657.632i	1.19914	−	1.19914i	0.974424	−	0.224718i	$-0.0721462\pi$
$68$	−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	$-0.568253\pi$
$79$	−298.820			−0.425569			−0.212784	+	0.977099i	$0.568253\pi$
$80$	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	0.512482	−	0.858698i	$-0.328726\pi$
$83$	−261.796	−	261.796i	−0.346215	−	0.346215i	−0.858698	+	0.512482i	$0.828726\pi$
$84$	−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	$-0.783167\pi$
$89$	−1304.47			−1.55363			−0.776817	+	0.629727i	$0.783167\pi$
$90$	142.732	−	1145.24i	0.167170	−	1.34132i
$91$		−	886.764i		−	1.02152i
$92$	−410.594	−	161.506i	−0.465298	−	0.183024i
$93$	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	−0.828384	−	0.560160i	$-0.810740\pi$
$97$	−256.245	+	256.245i	−0.268224	+	0.268224i	0.560160	+	0.828384i	$0.310740\pi$
$98$	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	$-0.793556\pi$
$103$	−1464.51	−	1464.51i	−1.40099	−	1.40099i	−0.604041	−	0.796954i	$-0.706444\pi$
$104$			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	−0.954146	−	0.299343i	$-0.903233\pi$
$107$	−724.747	+	724.747i	−0.654803	+	0.654803i	0.299343	+	0.954146i	$0.403233\pi$
$108$	617.245	−	617.245i	0.549948	−	0.549948i
$109$	580.039			0.509703			0.254852	−	0.966980i	$-0.417973\pi$
$109$	580.039			0.509703			0.254852	+	0.966980i	$0.417973\pi$
$110$	−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	0.818406	−	0.574641i	$-0.194858\pi$
$113$	292.812	+	292.812i	0.243765	+	0.243765i	−0.574641	+	0.818406i	$0.694858\pi$
$114$	2559.85			2.10309
$115$	−348.685	−	1182.92i	−0.282740	−	0.959197i
$116$	−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	−0.931812	−	0.362941i	$-0.881773\pi$
$137$	−912.209	+	912.209i	−0.568871	+	0.568871i	0.362941	+	0.931812i	$0.381773\pi$
$138$	715.989	−	1820.25i	0.441660	−	1.12282i
$139$			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	$-0.689955\pi$
$149$	−2044.19			−1.12394			−0.561968	+	0.827159i	$0.689955\pi$
$150$	−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	−0.679403	−	0.733765i	$-0.737761\pi$
$157$	106.942	−	106.942i	0.0543626	−	0.0543626i	0.733765	+	0.679403i	$0.237761\pi$
$158$	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	$-0.843923\pi$
$181$		−	2293.46i		−	0.941832i	0.882178	−	0.470916i	$-0.156077\pi$
$182$	−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	$0.412392\pi$
$191$			5080.65i			1.92473i	−0.271767	+	0.962363i	$0.587608\pi$
$192$	−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	$-0.169591\pi$
$199$	4836.29			1.72279			0.861396	+	0.507935i	$0.169591\pi$
$200$	−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
$207$	5298.01	+	2083.96i	1.77892	+	0.699734i
$208$	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	−0.241813	−	0.970323i	$-0.577742\pi$
$227$	2491.58	−	2491.58i	0.728510	−	0.728510i	0.970323	+	0.241813i	$0.0777421\pi$
$228$	−3620.18	−	3620.18i	−1.05154	−	1.05154i
$229$	−319.396			−0.0921671			−0.0460835	−	0.998938i	$-0.514674\pi$
$229$	−319.396			−0.0921671			−0.0460835	+	0.998938i	$0.514674\pi$
$230$	−1179.78	+	2166.01i	−0.338229	+	0.620968i
$231$	−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	$-0.866058\pi$
$241$		−	3056.54i		−	0.816967i	0.912766	−	0.408484i	$-0.133942\pi$
$242$	−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	$0.0391808\pi$
$251$			976.488i			0.245559i	−0.992434	+	0.122780i	$0.960819\pi$
$252$	−2378.70	+	2378.70i	−0.594618	+	0.594618i
$253$	−3.84284	−	1.51157i	−0.000954931	−	0.000375619i
$254$		−	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	0.866798	−	0.498659i	$-0.166174\pi$
$263$	1570.17	+	1570.17i	0.368139	+	0.368139i	−0.498659	+	0.866798i	$0.666174\pi$
$264$	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	$0.221021\pi$
$281$			6028.31i			1.27978i	−0.768465	+	0.639891i	$0.778979\pi$
$282$	6151.02	+	6151.02i	1.29889	+	1.29889i
$283$	3959.02	+	3959.02i	0.831587	+	0.831587i	0.987734	−	0.156146i	$-0.0499072\pi$
$283$	3959.02	+	3959.02i	0.831587	+	0.831587i	−0.156146	+	0.987734i	$0.549907\pi$
$284$			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	0.397813	−	0.917467i	$-0.369769\pi$
$293$	−2606.25	−	2606.25i	−0.519654	−	0.519654i	−0.917467	+	0.397813i	$0.869769\pi$
$294$		−	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	0.804558	−	0.593874i	$-0.202402\pi$
$313$	1166.67	+	1166.67i	0.210684	+	0.210684i	−0.593874	+	0.804558i	$0.702402\pi$
$314$	−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
$322$	−1315.81	+	3345.17i	−0.227725	+	0.578940i
$323$	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	−0.341014	−	0.940058i	$-0.610770\pi$
$337$	3705.99	−	3705.99i	0.599045	−	0.599045i	0.940058	+	0.341014i	$0.110770\pi$
$338$	−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
$345$	−9602.37	−	5230.21i	−1.49848	−	0.816189i
$346$	−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	$-0.303421\pi$
$359$	7877.56			1.15811			0.579055	+	0.815288i	$0.303421\pi$
$360$	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	−0.409159	−	0.912463i	$-0.634178\pi$
$367$	3538.58	−	3538.58i	0.503304	−	0.503304i	0.912463	+	0.409159i	$0.134178\pi$
$368$	646.025	−	1642.38i	0.0915118	−	0.232649i
$369$			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	$0.0465390\pi$
$373$	8176.47	+	8176.47i	1.13502	+	1.13502i	0.145686	+	0.989331i	$0.453461\pi$
$374$			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	$-0.446352\pi$
$379$	2475.34			0.335487			0.167744	+	0.985831i	$0.446352\pi$
$380$	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	0.995189	−	0.0979695i	$-0.0312347\pi$
$383$	6725.07	+	6725.07i	0.897220	+	0.897220i	−0.0979695	+	0.995189i	$0.531235\pi$
$384$			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	$-0.790335\pi$
$389$	−12134.5			−1.58160			−0.790800	+	0.612074i	$0.790335\pi$
$390$	−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	$0.0614729\pi$
$401$			3082.32i			0.383849i	−0.981410	+	0.191925i	$0.938527\pi$
$402$	−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	$-0.625731\pi$
$419$	−6600.70			−0.769607			−0.384803	+	0.922999i	$0.625731\pi$
$420$	5098.53	−	3968.50i	0.592340	−	0.461055i
$421$		−	5739.52i		−	0.664434i	−0.943203	−	0.332217i	$-0.892203\pi$
$421$		−	5739.52i		−	0.664434i	0.943203	−	0.332217i	$-0.107797\pi$
$422$	−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	$0.0429346\pi$
$431$			2406.50i			0.268949i	−0.990917	+	0.134474i	$0.957065\pi$
$432$	2468.98	+	2468.98i	0.274974	+	0.274974i
$433$	−76.5756	−	76.5756i	−0.00849882	−	0.00849882i	0.702845	−	0.711343i	$-0.251913\pi$
$433$	−76.5756	−	76.5756i	−0.00849882	−	0.00849882i	−0.711343	+	0.702845i	$0.751913\pi$
$434$	4660.31			0.515443
$435$	−16529.2	−	2060.04i	−1.82187	−	0.227060i
$436$			2320.16i			0.254852i
$437$	5828.63	−	14818.0i	0.638035	−	1.62207i
$438$	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	−0.987617	−	0.156883i	$-0.949855\pi$
$457$	−8115.89	+	8115.89i	−0.830734	+	0.830734i	0.156883	+	0.987617i	$0.449855\pi$
$458$	451.694	+	451.694i	0.0460835	+	0.0460835i
$459$	8358.09			0.849940
$460$	4731.67	−	1394.74i	0.479598	−	0.141370i
$461$	−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	$-0.461658\pi$
$467$	11231.5	−	11231.5i	1.11292	−	1.11292i	0.992754	−	0.120164i	$-0.0383419\pi$
$468$	−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	$-0.439831\pi$
$479$	3939.70			0.375803			0.187901	+	0.982188i	$0.439831\pi$
$480$	−2503.23	+	1948.42i	−0.238034	+	0.185276i
$481$			19478.9i			1.84649i
$482$	−4322.60	+	4322.60i	−0.408484	+	0.408484i
$483$	−14829.8	−	5833.26i	−1.39706	−	0.549529i
$484$			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	0.992037	−	0.125943i	$-0.0401958\pi$
$503$	9770.50	+	9770.50i	0.866094	+	0.866094i	−0.125943	+	0.992037i	$0.540196\pi$
$504$	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	$0.0857346\pi$
$521$			6328.91i			0.532196i	−0.963946	+	0.266098i	$0.914265\pi$
$522$	−12265.1	−	12265.1i	−1.02841	−	1.02841i
$523$	−9799.89	−	9799.89i	−0.819348	−	0.819348i	0.166665	−	0.986014i	$-0.446700\pi$
$523$	−9799.89	−	9799.89i	−0.819348	−	0.819348i	−0.986014	+	0.166665i	$0.946700\pi$
$524$			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
$552$	7280.99	+	2863.96i	0.561412	+	0.220830i
$553$	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	−0.957315	−	0.289046i	$-0.906662\pi$
$557$	−8784.85	+	8784.85i	−0.668269	+	0.668269i	0.289046	+	0.957315i	$0.406662\pi$
$558$	−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	0.998446	−	0.0557244i	$-0.0177468\pi$
$563$	12593.5	+	12593.5i	0.942722	+	0.942722i	−0.0557244	+	0.998446i	$0.517747\pi$
$564$		−	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	$-0.522389\pi$
$569$	−1907.80			−0.140561			−0.0702806	+	0.997527i	$0.522389\pi$
$570$	−22584.9	+	17579.2i	−1.65961	+	1.29178i
$571$		−	18929.9i		−	1.38738i	−0.720274	−	0.693690i	$-0.755984\pi$
$571$		−	18929.9i		−	1.38738i	0.720274	−	0.693690i	$-0.244016\pi$
$572$	5.76259	−	5.76259i	0.000421234	−	0.000421234i
$573$	31853.1	+	31853.1i	2.32231	+	2.32231i
$574$	−6910.91			−0.502537
$575$	11199.8	+	8042.04i	0.812283	+	0.583263i
$576$	−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
$598$	−4394.73	+	11172.7i	−0.300525	+	0.764020i
$599$			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	$-0.916824\pi$
$613$	−18582.9	−	18582.9i	−1.22440	−	1.22440i	−0.258342	−	0.966054i	$-0.583176\pi$
$614$			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	−0.916306	−	0.400480i	$-0.868843\pi$
$617$	−7905.52	+	7905.52i	−0.515826	+	0.515826i	0.400480	+	0.916306i	$0.368843\pi$
$618$	25969.9	+	25969.9i	1.69039	+	1.69039i
$619$	−13356.3			−0.867262			−0.433631	−	0.901090i	$-0.642768\pi$
$619$	−13356.3			−0.867262			−0.433631	+	0.901090i	$0.642768\pi$
$620$	−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	$-0.908026\pi$
$631$		−	9032.92i		−	0.569881i	0.958545	−	0.284941i	$-0.0919739\pi$
$632$	−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	$-0.992862\pi$
$641$		−	727.808i		−	0.0448467i	0.999749	−	0.0224233i	$-0.00713817\pi$
$642$	12851.8	−	12851.8i	0.790062	−	0.790062i
$643$	−2870.41	−	2870.41i	−0.176046	−	0.176046i	0.613584	−	0.789630i	$-0.289727\pi$
$643$	−2870.41	−	2870.41i	−0.176046	−	0.176046i	−0.789630	+	0.613584i	$0.789727\pi$
$644$	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	$-0.291905\pi$
$659$	20576.9			1.21633			0.608167	+	0.793809i	$0.291905\pi$
$660$	1.83586	−	14.7304i	0.000108274	−	0.000868759i
$661$			22824.8i			1.34309i	0.740963	+	0.671545i	$0.234369\pi$
$661$			22824.8i			1.34309i	−0.740963	+	0.671545i	$0.765631\pi$
$662$	−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
$667$	−17248.4	−	6784.61i	−1.00129	−	0.393855i
$668$	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	−0.314838	−	0.949146i	$-0.601950\pi$
$677$	11173.3	−	11173.3i	0.634308	−	0.634308i	0.949146	+	0.314838i	$0.101950\pi$
$678$	−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
$690$	6183.16	+	20976.4i	0.341143	+	1.15733i
$691$	−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	$-0.921242\pi$
$701$		−	9091.02i		−	0.489819i	0.969546	−	0.244909i	$-0.0787582\pi$
$702$	−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	$-0.316288\pi$
$709$	20601.7			1.09127			0.545637	+	0.838021i	$0.316288\pi$
$710$	9797.96	+	1221.12i	0.517903	+	0.0645464i
$711$			15423.0i			0.813515i
$712$	−7379.19	+	7379.19i	−0.388408	+	0.388408i
$713$	−5774.04	+	14679.2i	−0.303281	+	0.771026i
$714$			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	−0.723228	−	0.690610i	$-0.757342\pi$
$727$	−639.386	+	639.386i	−0.0326183	+	0.0326183i	0.690610	+	0.723228i	$0.257342\pi$
$728$	−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	0.999984	−	0.00561325i	$-0.00178676\pi$
$733$	19733.5	+	19733.5i	0.994371	+	0.994371i	−0.00561325	+	0.999984i	$0.501787\pi$
$734$	−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	0.711681	−	0.702502i	$-0.247934\pi$
$743$	185.896	+	185.896i	0.00917882	+	0.00917882i	−0.702502	+	0.711681i	$0.747934\pi$
$744$		−	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	$-0.974413\pi$
$751$		−	3305.10i		−	0.160592i	0.996771	−	0.0802962i	$-0.0255866\pi$
$752$	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	$0.553023\pi$
$757$	−23992.9	+	23992.9i	−1.15196	+	1.15196i	−0.986158	+	0.165806i	$0.946977\pi$
$758$	−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	$-0.513693\pi$
$769$	−1834.19			−0.0860113			−0.0430057	+	0.999075i	$0.513693\pi$
$770$	−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	$-0.959192\pi$
$773$	−24063.0	−	24063.0i	−1.11964	−	1.11964i	−0.127851	−	0.991793i	$-0.540808\pi$
$774$	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
$782$	−3092.81	+	7862.81i	−0.141431	+	0.359557i
$783$	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	−0.696132	−	0.717914i	$-0.745097\pi$
$787$	480.919	−	480.919i	0.0217826	−	0.0217826i	0.717914	+	0.696132i	$0.245097\pi$
$788$	−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	−0.134565	−	0.990905i	$-0.542964\pi$
$797$	19267.9	−	19267.9i	0.856340	−	0.856340i	0.990905	+	0.134565i	$0.0429636\pi$
$798$	−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
$805$	17646.8	+	9611.84i	0.772631	+	0.420836i
$806$	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	−0.645227	−	0.763991i	$-0.723237\pi$
$827$	2824.49	−	2824.49i	0.118763	−	0.118763i	0.763991	+	0.645227i	$0.223237\pi$
$828$	−8335.82	+	21192.0i	−0.349867	+	0.889461i
$829$			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	$-0.452922\pi$
$839$	7162.39			0.294723			0.147362	+	0.989083i	$0.452922\pi$
$840$	−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	$0.190592\pi$
$881$			29476.8i			1.12724i	−0.826034	+	0.563620i	$0.809408\pi$
$882$	−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
$897$	−49530.6	−	19482.7i	−1.84368	−	0.725205i
$898$	−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	−0.836391	−	0.548134i	$-0.815339\pi$
$907$	−7873.92	+	7873.92i	−0.288257	+	0.288257i	0.548134	+	0.836391i	$0.315339\pi$
$908$	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	$0.148134\pi$
$911$			24678.6i			0.897516i	−0.893653	+	0.448758i	$0.851866\pi$
$912$	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	$-0.909075\pi$
$919$	−53461.2			−1.91896			−0.959479	+	0.281780i	$0.909075\pi$
$920$	−8664.05	−	4719.13i	−0.310484	−	0.169114i
$921$	−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	−0.802272	−	0.596959i	$-0.796375\pi$
$937$	−5888.78	+	5888.78i	−0.205313	+	0.205313i	0.596959	+	0.802272i	$0.296375\pi$
$938$	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	$0.121858\pi$
$941$			21565.4i			0.747089i	−0.927612	+	0.373545i	$0.878142\pi$
$942$	−1896.39	+	1896.39i	−0.0655920	+	0.0655920i
$943$	8562.49	−	21768.3i	0.295687	−	0.751720i
$944$		−	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	0.503447	−	0.864026i	$-0.332065\pi$
$953$	−10608.1	−	10608.1i	−0.360579	−	0.360579i	−0.864026	+	0.503447i	$0.832065\pi$
$954$	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	$-0.767250\pi$
$971$		−	40409.5i		−	1.33553i	0.744370	−	0.667767i	$-0.232750\pi$
$972$	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	−0.998250	−	0.0591324i	$-0.981167\pi$
$977$	−28678.9	+	28678.9i	−0.939118	+	0.939118i	0.0591324	+	0.998250i	$0.481167\pi$
$978$	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	0.986670	−	0.162734i	$-0.0520312\pi$
$983$	25393.6	+	25393.6i	0.823936	+	0.823936i	−0.162734	+	0.986670i	$0.552031\pi$
$984$			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.137.17	✓	72
5.3	odd	4	inner	230.4.e.a.183.18	yes	72
23.22	odd	2	inner	230.4.e.a.137.18	yes	72
115.68	even	4	inner	230.4.e.a.183.17	yes	72

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

\(f(q)\)	\(=\)	\(q+(-1.41421 - 1.41421i) q^{2} +(6.26949 - 6.26949i) q^{3} +4.00000i q^{4} +(-8.82273 + 6.86728i) q^{5} -17.7328 q^{6} +(-11.5218 + 11.5218i) q^{7} +(5.65685 - 5.65685i) q^{8} -51.6130i q^{9} +O(q^{10})\)	\(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} +(-40.3765 + 102.649i) 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} +(-410.594 - 161.506i) 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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