LMFDB - Embedded newform 230.3.f.a.47.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,3,Mod(47,230)]

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, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.f (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:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 52 x^{17} + 1020 x^{16} - 1316 x^{15} + 1352 x^{14} - 18724 x^{13} + 250686 x^{12} + \cdots + 88804 $ x^20 - 52x^17 + 1020x^16 - 1316x^15 + 1352x^14 - 18724x^13 + 250686x^12 - 439644x^11 + 460536x^10 - 1833716x^9 + 16970128x^8 - 36894604x^7 + 40544632x^6 - 4380588x^5 + 34721x^4 - 4419956x^3 + 9945800x^2 + 1329080*x + 88804
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.8
Root			$1.94658 - 1.94658i$ of defining polynomial
Character	$\chi$	$=$	230.47
Dual form			230.3.f.a.93.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(1.94658 - 1.94658i) q^{3} +2.00000i q^{4} +(0.283956 - 4.99193i) q^{5} -3.89316 q^{6} +(9.76397 + 9.76397i) q^{7} +(2.00000 - 2.00000i) q^{8} +1.42166i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(1.94658 - 1.94658i) q^{3} +2.00000i q^{4} +(0.283956 - 4.99193i) q^{5} -3.89316 q^{6} +(9.76397 + 9.76397i) q^{7} +(2.00000 - 2.00000i) q^{8} +1.42166i q^{9} +(-5.27589 + 4.70797i) q^{10} +21.6746 q^{11} +(3.89316 + 3.89316i) q^{12} +(-0.532316 + 0.532316i) q^{13} -19.5279i q^{14} +(-9.16444 - 10.2699i) q^{15} -4.00000 q^{16} +(-18.9142 - 18.9142i) q^{17} +(1.42166 - 1.42166i) q^{18} +7.51292i q^{19} +(9.98386 + 0.567911i) q^{20} +38.0127 q^{21} +(-21.6746 - 21.6746i) q^{22} +(-3.39116 + 3.39116i) q^{23} -7.78631i q^{24} +(-24.8387 - 2.83497i) q^{25} +1.06463 q^{26} +(20.2866 + 20.2866i) q^{27} +(-19.5279 + 19.5279i) q^{28} -14.9938i q^{29} +(-1.10548 + 19.4344i) q^{30} -13.8457 q^{31} +(4.00000 + 4.00000i) q^{32} +(42.1913 - 42.1913i) q^{33} +37.8285i q^{34} +(51.5136 - 45.9685i) q^{35} -2.84333 q^{36} +(-34.1988 - 34.1988i) q^{37} +(7.51292 - 7.51292i) q^{38} +2.07239i q^{39} +(-9.41595 - 10.5518i) q^{40} -34.2921 q^{41} +(-38.0127 - 38.0127i) q^{42} +(32.8950 - 32.8950i) q^{43} +43.3491i q^{44} +(7.09685 + 0.403689i) q^{45} +6.78233 q^{46} +(1.95008 + 1.95008i) q^{47} +(-7.78631 + 7.78631i) q^{48} +141.670i q^{49} +(22.0038 + 27.6737i) q^{50} -73.6361 q^{51} +(-1.06463 - 1.06463i) q^{52} +(29.3946 - 29.3946i) q^{53} -40.5732i q^{54} +(6.15462 - 108.198i) q^{55} +39.0559 q^{56} +(14.6245 + 14.6245i) q^{57} +(-14.9938 + 14.9938i) q^{58} +36.8175i q^{59} +(20.5399 - 18.3289i) q^{60} +1.40337 q^{61} +(13.8457 + 13.8457i) q^{62} +(-13.8811 + 13.8811i) q^{63} -8.00000i q^{64} +(2.50613 + 2.80844i) q^{65} -84.3825 q^{66} +(15.7465 + 15.7465i) q^{67} +(37.8285 - 37.8285i) q^{68} +13.2023i q^{69} +(-97.4821 - 5.54507i) q^{70} -56.6402 q^{71} +(2.84333 + 2.84333i) q^{72} +(8.98250 - 8.98250i) q^{73} +68.3976i q^{74} +(-53.8691 + 42.8321i) q^{75} -15.0258 q^{76} +(211.630 + 211.630i) q^{77} +(2.07239 - 2.07239i) q^{78} +78.8377i q^{79} +(-1.13582 + 19.9677i) q^{80} +66.1839 q^{81} +(34.2921 + 34.2921i) q^{82} +(-61.7870 + 61.7870i) q^{83} +76.0253i q^{84} +(-99.7893 + 89.0477i) q^{85} -65.7900 q^{86} +(-29.1865 - 29.1865i) q^{87} +(43.3491 - 43.3491i) q^{88} +36.1338i q^{89} +(-6.69316 - 7.50053i) q^{90} -10.3950 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-26.9517 + 26.9517i) q^{93} -3.90016i q^{94} +(37.5040 + 2.13334i) q^{95} +15.5726 q^{96} +(-89.6141 - 89.6141i) q^{97} +(141.670 - 141.670i) q^{98} +30.8139i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8}+O(q^{10}) $ 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8	$ 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8} + 4 q^{10} + 56 q^{11} - 4 q^{13} - 48 q^{15} - 80 q^{16} - 72 q^{17} - 28 q^{18} - 16 q^{20} + 8 q^{21} - 56 q^{22} + 36 q^{25} + 8 q^{26} + 156 q^{27} - 16 q^{28} + 84 q^{30} - 212 q^{31} + 80 q^{32} - 100 q^{33} + 56 q^{36} + 72 q^{37} + 88 q^{38} + 24 q^{40} - 12 q^{41} - 8 q^{42} + 120 q^{43} - 32 q^{45} + 8 q^{47} - 28 q^{50} + 64 q^{51} - 8 q^{52} - 244 q^{53} + 68 q^{55} + 32 q^{56} - 384 q^{57} - 188 q^{58} - 72 q^{60} + 328 q^{61} + 212 q^{62} + 172 q^{63} + 20 q^{65} + 200 q^{66} + 56 q^{67} + 144 q^{68} - 28 q^{70} - 92 q^{71} - 56 q^{72} + 144 q^{73} - 124 q^{75} - 176 q^{76} + 292 q^{77} - 208 q^{78} - 16 q^{80} - 84 q^{81} + 12 q^{82} - 72 q^{83} - 20 q^{85} - 240 q^{86} - 208 q^{87} + 112 q^{88} - 56 q^{90} - 192 q^{91} + 256 q^{93} - 96 q^{95} - 276 q^{97} + 104 q^{98}+O(q^{100}) $ 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8 + 4 * q^10 + 56 * q^11 - 4 * q^13 - 48 * q^15 - 80 * q^16 - 72 * q^17 - 28 * q^18 - 16 * q^20 + 8 * q^21 - 56 * q^22 + 36 * q^25 + 8 * q^26 + 156 * q^27 - 16 * q^28 + 84 * q^30 - 212 * q^31 + 80 * q^32 - 100 * q^33 + 56 * q^36 + 72 * q^37 + 88 * q^38 + 24 * q^40 - 12 * q^41 - 8 * q^42 + 120 * q^43 - 32 * q^45 + 8 * q^47 - 28 * q^50 + 64 * q^51 - 8 * q^52 - 244 * q^53 + 68 * q^55 + 32 * q^56 - 384 * q^57 - 188 * q^58 - 72 * q^60 + 328 * q^61 + 212 * q^62 + 172 * q^63 + 20 * q^65 + 200 * q^66 + 56 * q^67 + 144 * q^68 - 28 * q^70 - 92 * q^71 - 56 * q^72 + 144 * q^73 - 124 * q^75 - 176 * q^76 + 292 * q^77 - 208 * q^78 - 16 * q^80 - 84 * q^81 + 12 * q^82 - 72 * q^83 - 20 * q^85 - 240 * q^86 - 208 * q^87 + 112 * q^88 - 56 * q^90 - 192 * q^91 + 256 * q^93 - 96 * q^95 - 276 * q^97 + 104 * 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 $

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	1.94658	−	1.94658i	0.648860	−	0.648860i	−0.303858	−	0.952717i	$-0.598275\pi$
$3$	1.94658	−	1.94658i	0.648860	−	0.648860i	0.952717	+	0.303858i	$0.0982748\pi$
$4$			2.00000i			0.500000i
$5$	0.283956	−	4.99193i	0.0567911	−	0.998386i
$5$	0.283956	−	4.99193i	0.0567911	−	0.998386i
$6$	−3.89316			−0.648860
$7$	9.76397	+	9.76397i	1.39485	+	1.39485i	0.814031	+	0.580822i	$0.197269\pi$
$7$	9.76397	+	9.76397i	1.39485	+	1.39485i	0.580822	+	0.814031i	$0.302731\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$			1.42166i			0.157963i
$10$	−5.27589	+	4.70797i	−0.527589	+	0.470797i
$11$	21.6746			1.97042			0.985208	−	0.171364i	$-0.0548173\pi$
$11$	21.6746			1.97042			0.985208	+	0.171364i	$0.0548173\pi$
$12$	3.89316	+	3.89316i	0.324430	+	0.324430i
$13$	−0.532316	+	0.532316i	−0.0409474	+	0.0409474i	−0.727284	−	0.686337i	$-0.759218\pi$
$13$	−0.532316	+	0.532316i	−0.0409474	+	0.0409474i	0.686337	+	0.727284i	$0.259218\pi$
$14$		−	19.5279i		−	1.39485i
$15$	−9.16444	−	10.2699i	−0.610963	−	0.684662i
$16$	−4.00000			−0.250000
$17$	−18.9142	−	18.9142i	−1.11260	−	1.11260i	−0.992798	−	0.119804i	$-0.961773\pi$
$17$	−18.9142	−	18.9142i	−1.11260	−	1.11260i	−0.119804	−	0.992798i	$-0.538227\pi$
$18$	1.42166	−	1.42166i	0.0789813	−	0.0789813i
$19$			7.51292i			0.395417i	0.980261	+	0.197708i	$0.0633499\pi$
$19$			7.51292i			0.395417i	−0.980261	+	0.197708i	$0.936650\pi$
$20$	9.98386	+	0.567911i	0.499193	+	0.0283956i
$21$	38.0127			1.81013
$22$	−21.6746	−	21.6746i	−0.985208	−	0.985208i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$24$		−	7.78631i		−	0.324430i
$25$	−24.8387	−	2.83497i	−0.993550	−	0.113399i
$26$	1.06463			0.0409474
$27$	20.2866	+	20.2866i	0.751355	+	0.751355i
$28$	−19.5279	+	19.5279i	−0.697426	+	0.697426i
$29$		−	14.9938i		−	0.517026i	−0.966008	−	0.258513i	$-0.916767\pi$
$29$		−	14.9938i		−	0.517026i	0.966008	−	0.258513i	$-0.0832326\pi$
$30$	−1.10548	+	19.4344i	−0.0368495	+	0.647812i
$31$	−13.8457			−0.446635			−0.223317	−	0.974746i	$-0.571689\pi$
$31$	−13.8457			−0.446635			−0.223317	+	0.974746i	$0.571689\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	42.1913	−	42.1913i	1.27852	−	1.27852i
$34$			37.8285i			1.11260i
$35$	51.5136	−	45.9685i	1.47182	−	1.31339i
$36$	−2.84333			−0.0789813
$37$	−34.1988	−	34.1988i	−0.924292	−	0.924292i	0.0730376	−	0.997329i	$-0.476731\pi$
$37$	−34.1988	−	34.1988i	−0.924292	−	0.924292i	−0.997329	+	0.0730376i	$0.976731\pi$
$38$	7.51292	−	7.51292i	0.197708	−	0.197708i
$39$			2.07239i			0.0531382i
$40$	−9.41595	−	10.5518i	−0.235399	−	0.263794i
$41$	−34.2921			−0.836394			−0.418197	−	0.908356i	$-0.637338\pi$
$41$	−34.2921			−0.836394			−0.418197	+	0.908356i	$0.637338\pi$
$42$	−38.0127	−	38.0127i	−0.905063	−	0.905063i
$43$	32.8950	−	32.8950i	0.765000	−	0.765000i	−0.212222	−	0.977222i	$-0.568070\pi$
$43$	32.8950	−	32.8950i	0.765000	−	0.765000i	0.977222	+	0.212222i	$0.0680699\pi$
$44$			43.3491i			0.985208i
$45$	7.09685	+	0.403689i	0.157708	+	0.00897088i
$46$	6.78233			0.147442
$47$	1.95008	+	1.95008i	0.0414911	+	0.0414911i	0.727548	−	0.686057i	$-0.240660\pi$
$47$	1.95008	+	1.95008i	0.0414911	+	0.0414911i	−0.686057	+	0.727548i	$0.740660\pi$
$48$	−7.78631	+	7.78631i	−0.162215	+	0.162215i
$49$			141.670i			2.89123i
$50$	22.0038	+	27.6737i	0.440075	+	0.553474i
$51$	−73.6361			−1.44384
$52$	−1.06463	−	1.06463i	−0.0204737	−	0.0204737i
$53$	29.3946	−	29.3946i	0.554616	−	0.554616i	−0.373154	−	0.927769i	$-0.621724\pi$
$53$	29.3946	−	29.3946i	0.554616	−	0.554616i	0.927769	+	0.373154i	$0.121724\pi$
$54$		−	40.5732i		−	0.751355i
$55$	6.15462	−	108.198i	0.111902	−	1.96724i
$56$	39.0559			0.697426
$57$	14.6245	+	14.6245i	0.256570	+	0.256570i
$58$	−14.9938	+	14.9938i	−0.258513	+	0.258513i
$59$			36.8175i			0.624025i	0.950078	+	0.312012i	$0.101003\pi$
$59$			36.8175i			0.624025i	−0.950078	+	0.312012i	$0.898997\pi$
$60$	20.5399	−	18.3289i	0.342331	−	0.305481i
$61$	1.40337			0.0230061			0.0115030	−	0.999934i	$-0.496338\pi$
$61$	1.40337			0.0230061			0.0115030	+	0.999934i	$0.496338\pi$
$62$	13.8457	+	13.8457i	0.223317	+	0.223317i
$63$	−13.8811	+	13.8811i	−0.220335	+	0.220335i
$64$		−	8.00000i		−	0.125000i
$65$	2.50613	+	2.80844i	0.0385558	+	0.0432067i
$66$	−84.3825			−1.27852
$67$	15.7465	+	15.7465i	0.235022	+	0.235022i	0.814785	−	0.579763i	$-0.196855\pi$
$67$	15.7465	+	15.7465i	0.235022	+	0.235022i	−0.579763	+	0.814785i	$0.696855\pi$
$68$	37.8285	−	37.8285i	0.556301	−	0.556301i
$69$			13.2023i			0.191338i
$70$	−97.4821	−	5.54507i	−1.39260	−	0.0792153i
$71$	−56.6402			−0.797749			−0.398874	−	0.917006i	$-0.630599\pi$
$71$	−56.6402			−0.797749			−0.398874	+	0.917006i	$0.630599\pi$
$72$	2.84333	+	2.84333i	0.0394907	+	0.0394907i
$73$	8.98250	−	8.98250i	0.123048	−	0.123048i	−0.642901	−	0.765949i	$-0.722269\pi$
$73$	8.98250	−	8.98250i	0.123048	−	0.123048i	0.765949	+	0.642901i	$0.222269\pi$
$74$			68.3976i			0.924292i
$75$	−53.8691	+	42.8321i	−0.718254	+	0.571094i
$76$	−15.0258			−0.197708
$77$	211.630	+	211.630i	2.74844	+	2.74844i
$78$	2.07239	−	2.07239i	0.0265691	−	0.0265691i
$79$			78.8377i			0.997946i	0.866618	+	0.498973i	$0.166289\pi$
$79$			78.8377i			0.997946i	−0.866618	+	0.498973i	$0.833711\pi$
$80$	−1.13582	+	19.9677i	−0.0141978	+	0.249597i
$81$	66.1839			0.817085
$82$	34.2921	+	34.2921i	0.418197	+	0.418197i
$83$	−61.7870	+	61.7870i	−0.744422	+	0.744422i	−0.973426	−	0.229004i	$-0.926453\pi$
$83$	−61.7870	+	61.7870i	−0.744422	+	0.744422i	0.229004	+	0.973426i	$0.426453\pi$
$84$			76.0253i			0.905063i
$85$	−99.7893	+	89.0477i	−1.17399	+	1.04762i
$86$	−65.7900			−0.765000
$87$	−29.1865	−	29.1865i	−0.335478	−	0.335478i
$88$	43.3491	−	43.3491i	0.492604	−	0.492604i
$89$			36.1338i			0.405998i	0.979179	+	0.202999i	$0.0650688\pi$
$89$			36.1338i			0.405998i	−0.979179	+	0.202999i	$0.934931\pi$
$90$	−6.69316	−	7.50053i	−0.0743684	−	0.0833393i
$91$	−10.3950			−0.114231
$92$	−6.78233	−	6.78233i	−0.0737210	−	0.0737210i
$93$	−26.9517	+	26.9517i	−0.289803	+	0.289803i
$94$		−	3.90016i		−	0.0414911i
$95$	37.5040	+	2.13334i	0.394779	+	0.0224562i
$96$	15.5726			0.162215
$97$	−89.6141	−	89.6141i	−0.923857	−	0.923857i	0.0734423	−	0.997299i	$-0.476602\pi$
$97$	−89.6141	−	89.6141i	−0.923857	−	0.923857i	−0.997299	+	0.0734423i	$0.976602\pi$
$98$	141.670	−	141.670i	1.44561	−	1.44561i
$99$			30.8139i			0.311252i
$100$	5.66995	−	49.6775i	0.0566995	−	0.496775i
$101$	−92.9192			−0.919992			−0.459996	−	0.887921i	$-0.652149\pi$
$101$	−92.9192			−0.919992			−0.459996	+	0.887921i	$0.652149\pi$
$102$	73.6361	+	73.6361i	0.721922	+	0.721922i
$103$	−16.8396	+	16.8396i	−0.163491	+	0.163491i	−0.784111	−	0.620620i	$-0.786881\pi$
$103$	−16.8396	+	16.8396i	−0.163491	+	0.163491i	0.620620	+	0.784111i	$0.286881\pi$
$104$			2.12926i			0.0204737i
$105$	10.7939	−	189.757i	0.102799	−	1.80721i
$106$	−58.7893			−0.554616
$107$	−55.1257	−	55.1257i	−0.515194	−	0.515194i	0.400919	−	0.916113i	$-0.368691\pi$
$107$	−55.1257	−	55.1257i	−0.515194	−	0.515194i	−0.916113	+	0.400919i	$0.868691\pi$
$108$	−40.5732	+	40.5732i	−0.375678	+	0.375678i
$109$		−	3.66113i		−	0.0335883i	−0.999859	−	0.0167942i	$-0.994654\pi$
$109$		−	3.66113i		−	0.0335883i	0.999859	−	0.0167942i	$-0.00534600\pi$
$110$	−114.353	+	102.043i	−1.03957	+	0.927667i
$111$	−133.141			−1.19947
$112$	−39.0559	−	39.0559i	−0.348713	−	0.348713i
$113$	55.5662	−	55.5662i	0.491736	−	0.491736i	−0.417117	−	0.908853i	$-0.636959\pi$
$113$	55.5662	−	55.5662i	0.491736	−	0.491736i	0.908853	+	0.417117i	$0.136959\pi$
$114$		−	29.2490i		−	0.256570i
$115$	15.9655	+	17.8914i	0.138831	+	0.155577i
$116$	29.9875			0.258513
$117$	−0.756774	−	0.756774i	−0.00646815	−	0.00646815i
$118$	36.8175	−	36.8175i	0.312012	−	0.312012i
$119$		−	369.356i		−	3.10383i
$120$	−38.8687	−	2.21097i	−0.323906	−	0.0184247i
$121$	348.787			2.88254
$122$	−1.40337	−	1.40337i	−0.0115030	−	0.0115030i
$123$	−66.7524	+	66.7524i	−0.542702	+	0.542702i
$124$		−	27.6914i		−	0.223317i
$125$	−21.2051	+	123.188i	−0.169641	+	0.985506i
$126$	27.7622			0.220335
$127$	−81.4452	−	81.4452i	−0.641301	−	0.641301i	0.309574	−	0.950875i	$-0.399813\pi$
$127$	−81.4452	−	81.4452i	−0.641301	−	0.641301i	−0.950875	+	0.309574i	$0.899813\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		−	128.065i		−	0.992755i
$130$	0.302308	−	5.31457i	0.00232545	−	0.0408813i
$131$	−36.7271			−0.280360			−0.140180	−	0.990126i	$-0.544768\pi$
$131$	−36.7271			−0.280360			−0.140180	+	0.990126i	$0.544768\pi$
$132$	84.3825	+	84.3825i	0.639262	+	0.639262i
$133$	−73.3559	+	73.3559i	−0.551548	+	0.551548i
$134$		−	31.4930i		−	0.235022i
$135$	107.030	−	95.5087i	0.792813	−	0.707472i
$136$	−75.6569			−0.556301
$137$	26.0189	+	26.0189i	0.189919	+	0.189919i	0.795661	−	0.605742i	$-0.207124\pi$
$137$	26.0189	+	26.0189i	0.189919	+	0.189919i	−0.605742	+	0.795661i	$0.707124\pi$
$138$	13.2023	−	13.2023i	0.0956691	−	0.0956691i
$139$			31.2956i			0.225148i	0.993643	+	0.112574i	$0.0359095\pi$
$139$			31.2956i			0.225148i	−0.993643	+	0.112574i	$0.964090\pi$
$140$	91.9370	+	103.027i	0.656693	+	0.735908i
$141$	7.59198			0.0538438
$142$	56.6402	+	56.6402i	0.398874	+	0.398874i
$143$	−11.5377	+	11.5377i	−0.0806833	+	0.0806833i
$144$		−	5.68665i		−	0.0394907i
$145$	−74.8478	−	4.25757i	−0.516192	−	0.0293625i
$146$	−17.9650			−0.123048
$147$	275.772	+	275.772i	1.87600	+	1.87600i
$148$	68.3976	−	68.3976i	0.462146	−	0.462146i
$149$			129.249i			0.867445i	0.901046	+	0.433723i	$0.142800\pi$
$149$			129.249i			0.867445i	−0.901046	+	0.433723i	$0.857200\pi$
$150$	96.7011	+	11.0370i	0.644674	+	0.0735800i
$151$	23.8722			0.158094			0.0790470	−	0.996871i	$-0.474812\pi$
$151$	23.8722			0.158094			0.0790470	+	0.996871i	$0.474812\pi$
$152$	15.0258	+	15.0258i	0.0988542	+	0.0988542i
$153$	26.8897	−	26.8897i	0.175749	−	0.175749i
$154$		−	423.260i		−	2.74844i
$155$	−3.93156	+	69.1167i	−0.0253649	+	0.445914i
$156$	−4.14478			−0.0265691
$157$	18.8241	+	18.8241i	0.119899	+	0.119899i	0.764510	−	0.644612i	$-0.222981\pi$
$157$	18.8241	+	18.8241i	0.119899	+	0.119899i	−0.644612	+	0.764510i	$0.722981\pi$
$158$	78.8377	−	78.8377i	0.498973	−	0.498973i
$159$		−	114.438i		−	0.719735i
$160$	21.1035	−	18.8319i	0.131897	−	0.117699i
$161$	−66.2224			−0.411320
$162$	−66.1839	−	66.1839i	−0.408543	−	0.408543i
$163$	213.024	−	213.024i	1.30689	−	1.30689i	0.383247	−	0.923646i	$-0.374806\pi$
$163$	213.024	−	213.024i	1.30689	−	1.30689i	0.923646	−	0.383247i	$-0.125194\pi$
$164$		−	68.5843i		−	0.418197i
$165$	−198.635	−	222.596i	−1.20385	−	1.34907i
$166$	123.574			0.744422
$167$	−40.3083	−	40.3083i	−0.241367	−	0.241367i	0.576048	−	0.817416i	$-0.304594\pi$
$167$	−40.3083	−	40.3083i	−0.241367	−	0.241367i	−0.817416	+	0.576048i	$0.804594\pi$
$168$	76.0253	−	76.0253i	0.452532	−	0.452532i
$169$			168.433i			0.996647i
$170$	188.837	+	10.7416i	1.11081	+	0.0631859i
$171$	−10.6808			−0.0624611
$172$	65.7900	+	65.7900i	0.382500	+	0.382500i
$173$	108.158	−	108.158i	0.625193	−	0.625193i	−0.321661	−	0.946855i	$-0.604241\pi$
$173$	108.158	−	108.158i	0.625193	−	0.625193i	0.946855	+	0.321661i	$0.104241\pi$
$174$			58.3731i			0.335478i
$175$	−214.844	−	270.205i	−1.22768	−	1.54403i
$176$	−86.6983			−0.492604
$177$	71.6681	+	71.6681i	0.404904	+	0.404904i
$178$	36.1338	−	36.1338i	0.202999	−	0.202999i
$179$			35.3314i			0.197382i	0.995118	+	0.0986912i	$0.0314656\pi$
$179$			35.3314i			0.197382i	−0.995118	+	0.0986912i	$0.968534\pi$
$180$	−0.807379	+	14.1937i	−0.00448544	+	0.0788538i
$181$	−220.468			−1.21805			−0.609026	−	0.793150i	$-0.708440\pi$
$181$	−220.468			−1.21805			−0.609026	+	0.793150i	$0.708440\pi$
$182$	10.3950	+	10.3950i	0.0571155	+	0.0571155i
$183$	2.73177	−	2.73177i	0.0149277	−	0.0149277i
$184$			13.5647i			0.0737210i
$185$	−180.429	+	161.007i	−0.975291	+	0.870308i
$186$	53.9034			0.289803
$187$	−409.958	−	409.958i	−2.19229	−	2.19229i
$188$	−3.90016	+	3.90016i	−0.0207456	+	0.0207456i
$189$			396.155i			2.09606i
$190$	−35.3706	−	39.6373i	−0.186161	−	0.208617i
$191$	288.600			1.51100			0.755498	−	0.655151i	$-0.227395\pi$
$191$	288.600			1.51100			0.755498	+	0.655151i	$0.227395\pi$
$192$	−15.5726	−	15.5726i	−0.0811074	−	0.0811074i
$193$	−127.290	+	127.290i	−0.659533	+	0.659533i	−0.955270	−	0.295736i	$-0.904435\pi$
$193$	−127.290	+	127.290i	−0.659533	+	0.659533i	0.295736	+	0.955270i	$0.404435\pi$
$194$			179.228i			0.923857i
$195$	10.3452	+	0.588467i	0.0530524	+	0.00301778i
$196$	−283.340			−1.44561
$197$	−134.497	−	134.497i	−0.682726	−	0.682726i	0.277888	−	0.960613i	$-0.410366\pi$
$197$	−134.497	−	134.497i	−0.682726	−	0.682726i	−0.960613	+	0.277888i	$0.910366\pi$
$198$	30.8139	−	30.8139i	0.155626	−	0.155626i
$199$			172.813i			0.868409i	0.900814	+	0.434205i	$0.142971\pi$
$199$			172.813i			0.868409i	−0.900814	+	0.434205i	$0.857029\pi$
$200$	−55.3474	+	44.0075i	−0.276737	+	0.220038i
$201$	61.3035			0.304993
$202$	92.9192	+	92.9192i	0.459996	+	0.459996i
$203$	146.399	−	146.399i	0.721176	−	0.721176i
$204$		−	147.272i		−	0.721922i
$205$	−9.73745	+	171.184i	−0.0474997	+	0.835044i
$206$	33.6792			0.163491
$207$	−4.82110	−	4.82110i	−0.0232903	−	0.0232903i
$208$	2.12926	−	2.12926i	0.0102368	−	0.0102368i
$209$			162.839i			0.779135i
$210$	−200.550	+	178.963i	−0.955002	+	0.852203i
$211$	−264.657			−1.25430			−0.627148	−	0.778900i	$-0.715778\pi$
$211$	−264.657			−1.25430			−0.627148	+	0.778900i	$0.715778\pi$
$212$	58.7893	+	58.7893i	0.277308	+	0.277308i
$213$	−110.255	+	110.255i	−0.517627	+	0.517627i
$214$			110.251i			0.515194i
$215$	−154.869	−	173.550i	−0.720320	−	0.807210i
$216$	81.1463			0.375678
$217$	−135.189	−	135.189i	−0.622990	−	0.622990i
$218$	−3.66113	+	3.66113i	−0.0167942	+	0.0167942i
$219$		−	34.9703i		−	0.159682i
$220$	216.396	+	12.3092i	0.983618	+	0.0559511i
$221$	20.1367			0.0911162
$222$	133.141	+	133.141i	0.599735	+	0.599735i
$223$	−177.977	+	177.977i	−0.798104	+	0.798104i	−0.982796	−	0.184692i	$-0.940871\pi$
$223$	−177.977	+	177.977i	−0.798104	+	0.798104i	0.184692	+	0.982796i	$0.440871\pi$
$224$			78.1117i			0.348713i
$225$	4.03038	−	35.3123i	0.0179128	−	0.156944i
$226$	−111.132			−0.491736
$227$	271.031	+	271.031i	1.19397	+	1.19397i	0.975943	+	0.218027i	$0.0699621\pi$
$227$	271.031	+	271.031i	1.19397	+	1.19397i	0.218027	+	0.975943i	$0.430038\pi$
$228$	−29.2490	+	29.2490i	−0.128285	+	0.128285i
$229$		−	51.6876i		−	0.225710i	−0.993611	−	0.112855i	$-0.964000\pi$
$229$		−	51.6876i		−	0.225710i	0.993611	−	0.112855i	$-0.0359995\pi$
$230$	1.92588	−	33.8569i	0.00837340	−	0.147204i
$231$	823.908			3.56670
$232$	−29.9875	−	29.9875i	−0.129257	−	0.129257i
$233$	251.702	−	251.702i	1.08026	−	1.08026i	0.0837807	−	0.996484i	$-0.473300\pi$
$233$	251.702	−	251.702i	1.08026	−	1.08026i	0.996484	−	0.0837807i	$-0.0266995\pi$
$234$			1.51355i			0.00646815i
$235$	10.2884	−	9.18094i	0.0437805	−	0.0390678i
$236$	−73.6349			−0.312012
$237$	153.464	+	153.464i	0.647526	+	0.647526i
$238$	−369.356	+	369.356i	−1.55191	+	1.55191i
$239$		−	161.182i		−	0.674403i	−0.941433	−	0.337201i	$-0.890520\pi$
$239$		−	161.182i		−	0.674403i	0.941433	−	0.337201i	$-0.109480\pi$
$240$	36.6578	+	41.0797i	0.152741	+	0.171165i
$241$	−348.731			−1.44702			−0.723508	−	0.690316i	$-0.757472\pi$
$241$	−348.731			−1.44702			−0.723508	+	0.690316i	$0.757472\pi$
$242$	−348.787	−	348.787i	−1.44127	−	1.44127i
$243$	−53.7471	+	53.7471i	−0.221182	+	0.221182i
$244$			2.80674i			0.0115030i
$245$	707.207	+	40.2280i	2.88656	+	0.164196i
$246$	133.505			0.542702
$247$	−3.99925	−	3.99925i	−0.0161913	−	0.0161913i
$248$	−27.6914	+	27.6914i	−0.111659	+	0.111659i
$249$			240.547i			0.966051i
$250$	144.393	−	101.983i	0.577573	−	0.407933i
$251$	384.369			1.53135			0.765676	−	0.643227i	$-0.222405\pi$
$251$	384.369			1.53135			0.765676	+	0.643227i	$0.222405\pi$
$252$	−27.7622	−	27.7622i	−0.110167	−	0.110167i
$253$	−73.5021	+	73.5021i	−0.290522	+	0.290522i
$254$			162.890i			0.641301i
$255$	−20.9094	+	367.586i	−0.0819976	+	1.44151i
$256$	16.0000			0.0625000
$257$	−48.2636	−	48.2636i	−0.187796	−	0.187796i	0.606947	−	0.794743i	$-0.292394\pi$
$257$	−48.2636	−	48.2636i	−0.187796	−	0.187796i	−0.794743	+	0.606947i	$0.792394\pi$
$258$	−128.065	+	128.065i	−0.496377	+	0.496377i
$259$		−	667.832i		−	2.57850i
$260$	−5.61688	+	5.01226i	−0.0216034	+	0.0192779i
$261$	21.3161			0.0816709
$262$	36.7271	+	36.7271i	0.140180	+	0.140180i
$263$	−177.216	+	177.216i	−0.673827	+	0.673827i	−0.958596	−	0.284769i	$-0.908083\pi$
$263$	−177.216	+	177.216i	−0.673827	+	0.673827i	0.284769	+	0.958596i	$0.408083\pi$
$264$		−	168.765i		−	0.639262i
$265$	−138.389	−	155.083i	−0.522223	−	0.585218i
$266$	146.712			0.551548
$267$	70.3373	+	70.3373i	0.263436	+	0.263436i
$268$	−31.4930	+	31.4930i	−0.117511	+	0.117511i
$269$			106.990i			0.397733i	0.980027	+	0.198867i	$0.0637261\pi$
$269$			106.990i			0.397733i	−0.980027	+	0.198867i	$0.936274\pi$
$270$	−202.538	−	11.5210i	−0.750142	−	0.0426703i
$271$	83.4806			0.308046			0.154023	−	0.988067i	$-0.450777\pi$
$271$	83.4806			0.308046			0.154023	+	0.988067i	$0.450777\pi$
$272$	75.6569	+	75.6569i	0.278150	+	0.278150i
$273$	−20.2347	+	20.2347i	−0.0741199	+	0.0741199i
$274$		−	52.0378i		−	0.189919i
$275$	−538.369	−	61.4469i	−1.95771	−	0.223443i
$276$	−26.4047			−0.0956691
$277$	−210.157	−	210.157i	−0.758689	−	0.758689i	0.217394	−	0.976084i	$-0.430244\pi$
$277$	−210.157	−	210.157i	−0.758689	−	0.758689i	−0.976084	+	0.217394i	$0.930244\pi$
$278$	31.2956	−	31.2956i	0.112574	−	0.112574i
$279$		−	19.6839i		−	0.0705516i
$280$	11.0901	−	194.964i	0.0396076	−	0.696301i
$281$	63.1340			0.224676			0.112338	−	0.993670i	$-0.464166\pi$
$281$	63.1340			0.224676			0.112338	+	0.993670i	$0.464166\pi$
$282$	−7.59198	−	7.59198i	−0.0269219	−	0.0269219i
$283$	−156.827	+	156.827i	−0.554158	+	0.554158i	−0.927638	−	0.373480i	$-0.878164\pi$
$283$	−156.827	+	156.827i	−0.554158	+	0.554158i	0.373480	+	0.927638i	$0.378164\pi$
$284$		−	113.280i		−	0.398874i
$285$	77.1571	−	68.8517i	0.270727	−	0.241585i
$286$	23.0754			0.0806833
$287$	−334.827	−	334.827i	−1.16665	−	1.16665i
$288$	−5.68665	+	5.68665i	−0.0197453	+	0.0197453i
$289$			426.496i			1.47576i
$290$	70.5903	+	79.1054i	0.243415	+	0.272777i
$291$	−348.882			−1.19891
$292$	17.9650	+	17.9650i	0.0615240	+	0.0615240i
$293$	−374.813	+	374.813i	−1.27923	+	1.27923i	−0.338124	+	0.941102i	$0.609792\pi$
$293$	−374.813	+	374.813i	−1.27923	+	1.27923i	−0.941102	+	0.338124i	$0.890208\pi$
$294$		−	551.544i		−	1.87600i
$295$	183.790	+	10.4545i	0.623017	+	0.0354391i
$296$	−136.795			−0.462146
$297$	439.703	+	439.703i	1.48048	+	1.48048i
$298$	129.249	−	129.249i	0.433723	−	0.433723i
$299$		−	3.61034i		−	0.0120747i
$300$	−85.6641	−	107.738i	−0.285547	−	0.359127i
$301$	642.371			2.13412
$302$	−23.8722	−	23.8722i	−0.0790470	−	0.0790470i
$303$	−180.875	+	180.875i	−0.596946	+	0.596946i
$304$		−	30.0517i		−	0.0988542i
$305$	0.398495	−	7.00553i	0.00130654	−	0.0229690i
$306$	−53.7793			−0.175749
$307$	358.957	+	358.957i	1.16924	+	1.16924i	0.982388	+	0.186851i	$0.0598283\pi$
$307$	358.957	+	358.957i	1.16924	+	1.16924i	0.186851	+	0.982388i	$0.440172\pi$
$308$	−423.260	+	423.260i	−1.37422	+	1.37422i
$309$			65.5592i			0.212166i
$310$	73.0482	−	65.1851i	0.235639	−	0.210275i
$311$	−8.62512			−0.0277335			−0.0138668	−	0.999904i	$-0.504414\pi$
$311$	−8.62512			−0.0277335			−0.0138668	+	0.999904i	$0.504414\pi$
$312$	4.14478	+	4.14478i	0.0132845	+	0.0132845i
$313$	234.501	−	234.501i	0.749204	−	0.749204i	−0.225126	−	0.974330i	$-0.572279\pi$
$313$	234.501	−	234.501i	0.749204	−	0.749204i	0.974330	+	0.225126i	$0.0722793\pi$
$314$		−	37.6482i		−	0.119899i
$315$	65.3518	+	73.2350i	0.207466	+	0.232492i
$316$	−157.675			−0.498973
$317$	−360.256	−	360.256i	−1.13645	−	1.13645i	−0.989081	−	0.147373i	$-0.952918\pi$
$317$	−360.256	−	360.256i	−1.13645	−	1.13645i	−0.147373	−	0.989081i	$-0.547082\pi$
$318$	−114.438	+	114.438i	−0.359868	+	0.359868i
$319$		−	324.984i		−	1.01876i
$320$	−39.9354	−	2.27165i	−0.124798	−	0.00709889i
$321$	−214.613			−0.668577
$322$	66.2224	+	66.2224i	0.205660	+	0.205660i
$323$	142.101	−	142.101i	0.439941	−	0.439941i
$324$			132.368i			0.408543i
$325$	14.7312	−	11.7130i	0.0453266	−	0.0360399i
$326$	−426.047			−1.30689
$327$	−7.12667	−	7.12667i	−0.0217941	−	0.0217941i
$328$	−68.5843	+	68.5843i	−0.209098	+	0.209098i
$329$			38.0811i			0.115748i
$330$	−23.9609	+	421.232i	−0.0726088	+	1.27646i
$331$	547.667			1.65458			0.827291	−	0.561773i	$-0.189881\pi$
$331$	547.667			1.65458			0.827291	+	0.561773i	$0.189881\pi$
$332$	−123.574	−	123.574i	−0.372211	−	0.372211i
$333$	48.6192	−	48.6192i	0.146004	−	0.146004i
$334$			80.6166i			0.241367i
$335$	83.0766	−	74.1340i	0.247990	−	0.221296i
$336$	−152.051			−0.452532
$337$	274.601	+	274.601i	0.814841	+	0.814841i	0.985355	−	0.170514i	$-0.0545430\pi$
$337$	274.601	+	274.601i	0.814841	+	0.814841i	−0.170514	+	0.985355i	$0.554543\pi$
$338$	168.433	−	168.433i	0.498323	−	0.498323i
$339$		−	216.328i		−	0.638135i
$340$	−178.095	−	199.579i	−0.523810	−	0.586996i
$341$	−300.099			−0.880056
$342$	10.6808	+	10.6808i	0.0312305	+	0.0312305i
$343$	−904.828	+	904.828i	−2.63798	+	2.63798i
$344$		−	131.580i		−	0.382500i
$345$	65.9052	+	3.74888i	0.191029	+	0.0108663i
$346$	−216.317			−0.625193
$347$	−257.194	−	257.194i	−0.741192	−	0.741192i	0.231616	−	0.972807i	$-0.425599\pi$
$347$	−257.194	−	257.194i	−0.741192	−	0.741192i	−0.972807	+	0.231616i	$0.925599\pi$
$348$	58.3731	−	58.3731i	0.167739	−	0.167739i
$349$			110.553i			0.316772i	0.987377	+	0.158386i	$0.0506290\pi$
$349$			110.553i			0.316772i	−0.987377	+	0.158386i	$0.949371\pi$
$350$	−55.3612	+	485.049i	−0.158175	+	1.38586i
$351$	−21.5977			−0.0615320
$352$	86.6983	+	86.6983i	0.246302	+	0.246302i
$353$	203.861	−	203.861i	0.577509	−	0.577509i	−0.356707	−	0.934216i	$-0.616101\pi$
$353$	203.861	−	203.861i	0.577509	−	0.577509i	0.934216	+	0.356707i	$0.116101\pi$
$354$		−	143.336i		−	0.404904i
$355$	−16.0833	+	282.744i	−0.0453051	+	0.796461i
$356$	−72.2676			−0.202999
$357$	−718.980	−	718.980i	−2.01395	−	2.01395i
$358$	35.3314	−	35.3314i	0.0986912	−	0.0986912i
$359$		−	358.509i		−	0.998634i	−0.866419	−	0.499317i	$-0.833584\pi$
$359$		−	358.509i		−	0.998634i	0.866419	−	0.499317i	$-0.166416\pi$
$360$	15.0011	−	13.3863i	0.0416696	−	0.0371842i
$361$	304.556			0.843646
$362$	220.468	+	220.468i	0.609026	+	0.609026i
$363$	678.942	−	678.942i	1.87036	−	1.87036i
$364$		−	20.7901i		−	0.0571155i
$365$	−42.2894	−	47.3907i	−0.115861	−	0.129837i
$366$	−5.46354			−0.0149277
$367$	−89.1803	−	89.1803i	−0.242998	−	0.242998i	0.575091	−	0.818089i	$-0.304967\pi$
$367$	−89.1803	−	89.1803i	−0.242998	−	0.242998i	−0.818089	+	0.575091i	$0.804967\pi$
$368$	13.5647	−	13.5647i	0.0368605	−	0.0368605i
$369$		−	48.7519i		−	0.132119i
$370$	341.436	+	19.4219i	0.922800	+	0.0524916i
$371$	574.016			1.54721
$372$	−53.9034	−	53.9034i	−0.144902	−	0.144902i
$373$	311.754	−	311.754i	0.835800	−	0.835800i	−0.152503	−	0.988303i	$-0.548733\pi$
$373$	311.754	−	311.754i	0.835800	−	0.835800i	0.988303	+	0.152503i	$0.0487332\pi$
$374$			819.916i			2.19229i
$375$	198.518	+	281.073i	0.529382	+	0.749528i
$376$	7.80033			0.0207456
$377$	7.98142	+	7.98142i	0.0211709	+	0.0211709i
$378$	396.155	−	396.155i	1.04803	−	1.04803i
$379$			266.437i			0.703001i	0.936188	+	0.351500i	$0.114328\pi$
$379$			266.437i			0.703001i	−0.936188	+	0.351500i	$0.885672\pi$
$380$	−4.26667	+	75.0079i	−0.0112281	+	0.197389i
$381$	−317.079			−0.832228
$382$	−288.600	−	288.600i	−0.755498	−	0.755498i
$383$	−506.226	+	506.226i	−1.32174	+	1.32174i	−0.409369	+	0.912369i	$0.634251\pi$
$383$	−506.226	+	506.226i	−1.32174	+	1.32174i	−0.912369	+	0.409369i	$0.865749\pi$
$384$			31.1453i			0.0811074i
$385$	1116.53	−	996.348i	2.90009	−	2.58792i
$386$	254.580			0.659533
$387$	46.7656	+	46.7656i	0.120841	+	0.120841i
$388$	179.228	−	179.228i	0.461929	−	0.461929i
$389$		−	373.660i		−	0.960566i	−0.877114	−	0.480283i	$-0.840534\pi$
$389$		−	373.660i		−	0.960566i	0.877114	−	0.480283i	$-0.159466\pi$
$390$	−9.75676	−	10.9337i	−0.0250173	−	0.0280351i
$391$	128.283			0.328088
$392$	283.340	+	283.340i	0.722807	+	0.722807i
$393$	−71.4922	+	71.4922i	−0.181914	+	0.181914i
$394$			268.994i			0.682726i
$395$	393.552	+	22.3864i	0.996335	+	0.0566745i
$396$	−61.6279			−0.155626
$397$	109.812	+	109.812i	0.276605	+	0.276605i	0.831752	−	0.555147i	$-0.187338\pi$
$397$	109.812	+	109.812i	0.276605	+	0.276605i	−0.555147	+	0.831752i	$0.687338\pi$
$398$	172.813	−	172.813i	0.434205	−	0.434205i
$399$			285.586i			0.715754i
$400$	99.3550	+	11.3399i	0.248387	+	0.0283497i
$401$	304.662			0.759755			0.379877	−	0.925037i	$-0.375966\pi$
$401$	304.662			0.759755			0.379877	+	0.925037i	$0.375966\pi$
$402$	−61.3035	−	61.3035i	−0.152496	−	0.152496i
$403$	7.37027	−	7.37027i	0.0182885	−	0.0182885i
$404$		−	185.838i		−	0.459996i
$405$	18.7933	−	330.385i	0.0464032	−	0.815766i
$406$	−292.797			−0.721176
$407$	−741.244	−	741.244i	−1.82124	−	1.82124i
$408$	−147.272	+	147.272i	−0.360961	+	0.360961i
$409$		−	228.713i		−	0.559201i	−0.960116	−	0.279600i	$-0.909798\pi$
$409$		−	228.713i		−	0.559201i	0.960116	−	0.279600i	$-0.0902020\pi$
$410$	180.921	−	161.447i	0.441272	−	0.393772i
$411$	101.296			0.246461
$412$	−33.6792	−	33.6792i	−0.0817456	−	0.0817456i
$413$	−359.484	+	359.484i	−0.870422	+	0.870422i
$414$			9.64219i			0.0232903i
$415$	290.892	+	325.981i	0.700944	+	0.785497i
$416$	−4.25853			−0.0102368
$417$	60.9192	+	60.9192i	0.146089	+	0.146089i
$418$	162.839	−	162.839i	0.389568	−	0.389568i
$419$			198.319i			0.473316i	0.971593	+	0.236658i	$0.0760521\pi$
$419$			198.319i			0.473316i	−0.971593	+	0.236658i	$0.923948\pi$
$420$	379.513	+	21.5878i	0.903603	+	0.0513996i
$421$	−571.167			−1.35669			−0.678346	−	0.734743i	$-0.737303\pi$
$421$	−571.167			−1.35669			−0.678346	+	0.734743i	$0.737303\pi$
$422$	264.657	+	264.657i	0.627148	+	0.627148i
$423$	−2.77236	+	2.77236i	−0.00655404	+	0.00655404i
$424$		−	117.579i		−	0.277308i
$425$	416.184	+	523.427i	0.979257	+	1.23159i
$426$	220.509			0.517627
$427$	13.7025	+	13.7025i	0.0320901	+	0.0320901i
$428$	110.251	−	110.251i	0.257597	−	0.257597i
$429$			44.9181i			0.104704i
$430$	−18.6814	+	328.419i	−0.0434452	+	0.763765i
$431$	−575.249			−1.33468			−0.667342	−	0.744751i	$-0.732568\pi$
$431$	−575.249			−1.33468			−0.667342	+	0.744751i	$0.732568\pi$
$432$	−81.1463	−	81.1463i	−0.187839	−	0.187839i
$433$	0.718397	−	0.718397i	0.00165912	−	0.00165912i	−0.706277	−	0.707936i	$-0.749627\pi$
$433$	0.718397	−	0.718397i	0.00165912	−	0.00165912i	0.707936	+	0.706277i	$0.249627\pi$
$434$			270.378i			0.622990i
$435$	−153.985	+	137.410i	−0.353988	+	0.315884i
$436$	7.32226			0.0167942
$437$	−25.4775	−	25.4775i	−0.0583010	−	0.0583010i
$438$	−34.9703	+	34.9703i	−0.0798409	+	0.0798409i
$439$			520.035i			1.18459i	0.805721	+	0.592295i	$0.201778\pi$
$439$			520.035i			1.18459i	−0.805721	+	0.592295i	$0.798222\pi$
$440$	−204.087	−	228.705i	−0.463833	−	0.519784i
$441$	−201.407			−0.456706
$442$	−20.1367	−	20.1367i	−0.0455581	−	0.0455581i
$443$	54.3749	−	54.3749i	0.122742	−	0.122742i	−0.643067	−	0.765810i	$-0.722338\pi$
$443$	54.3749	−	54.3749i	0.122742	−	0.122742i	0.765810	+	0.643067i	$0.222338\pi$
$444$		−	266.283i		−	0.599735i
$445$	180.377	+	10.2604i	0.405343	+	0.0230571i
$446$	355.955			0.798104
$447$	251.594	+	251.594i	0.562850	+	0.562850i
$448$	78.1117	−	78.1117i	0.174357	−	0.174357i
$449$		−	556.320i		−	1.23902i	−0.784989	−	0.619510i	$-0.787331\pi$
$449$		−	556.320i		−	1.23902i	0.784989	−	0.619510i	$-0.212669\pi$
$450$	−39.3427	+	31.2819i	−0.0874282	+	0.0695154i
$451$	−743.268			−1.64804
$452$	111.132	+	111.132i	0.245868	+	0.245868i
$453$	46.4691	−	46.4691i	0.102581	−	0.102581i
$454$		−	542.062i		−	1.19397i
$455$	−2.95173	+	51.8913i	−0.00648731	+	0.114047i
$456$	58.4979			0.128285
$457$	257.657	+	257.657i	0.563801	+	0.563801i	0.930385	−	0.366584i	$-0.119473\pi$
$457$	257.657	+	257.657i	0.563801	+	0.563801i	−0.366584	+	0.930385i	$0.619473\pi$
$458$	−51.6876	+	51.6876i	−0.112855	+	0.112855i
$459$		−	767.410i		−	1.67192i
$460$	−35.7828	+	31.9310i	−0.0777887	+	0.0694153i
$461$	−236.551			−0.513125			−0.256563	−	0.966528i	$-0.582590\pi$
$461$	−236.551			−0.513125			−0.256563	+	0.966528i	$0.582590\pi$
$462$	−823.908	−	823.908i	−1.78335	−	1.78335i
$463$	206.954	−	206.954i	0.446984	−	0.446984i	−0.447366	−	0.894351i	$-0.647638\pi$
$463$	206.954	−	206.954i	0.446984	−	0.446984i	0.894351	+	0.447366i	$0.147638\pi$
$464$			59.9751i			0.129257i
$465$	126.888	+	142.194i	0.272877	+	0.305794i
$466$	−503.403			−1.08026
$467$	−455.160	−	455.160i	−0.974647	−	0.974647i	0.0250398	−	0.999686i	$-0.492029\pi$
$467$	−455.160	−	455.160i	−0.974647	−	0.974647i	−0.999686	+	0.0250398i	$0.992029\pi$
$468$	1.51355	−	1.51355i	0.00323408	−	0.00323408i
$469$			307.496i			0.655642i
$470$	−19.4694	−	1.10747i	−0.0414242	−	0.00235633i
$471$	73.2851			0.155595
$472$	73.6349	+	73.6349i	0.156006	+	0.156006i
$473$	712.985	−	712.985i	1.50737	−	1.50737i
$474$		−	306.928i		−	0.647526i
$475$	21.2989	−	186.611i	0.0448399	−	0.392866i
$476$	738.711			1.55191
$477$	41.7893	+	41.7893i	0.0876085	+	0.0876085i
$478$	−161.182	+	161.182i	−0.337201	+	0.337201i
$479$			15.9362i			0.0332697i	0.999862	+	0.0166349i	$0.00529528\pi$
$479$			15.9362i			0.0332697i	−0.999862	+	0.0166349i	$0.994705\pi$
$480$	4.42194	−	77.7375i	0.00921237	−	0.161953i
$481$	36.4091			0.0756946
$482$	348.731	+	348.731i	0.723508	+	0.723508i
$483$	−128.907	+	128.907i	−0.266889	+	0.266889i
$484$			697.574i			1.44127i
$485$	−472.794	+	421.901i	−0.974833	+	0.869899i
$486$	107.494			0.221182
$487$	373.443	+	373.443i	0.766824	+	0.766824i	0.977546	−	0.210722i	$-0.0675815\pi$
$487$	373.443	+	373.443i	0.766824	+	0.766824i	−0.210722	+	0.977546i	$0.567582\pi$
$488$	2.80674	−	2.80674i	0.00575152	−	0.00575152i
$489$		−	829.334i		−	1.69598i
$490$	−666.979	−	747.435i	−1.36118	−	1.52538i
$491$	253.834			0.516974			0.258487	−	0.966015i	$-0.416776\pi$
$491$	253.834			0.516974			0.258487	+	0.966015i	$0.416776\pi$
$492$	−133.505	−	133.505i	−0.271351	−	0.271351i
$493$	−283.596	+	283.596i	−0.575244	+	0.575244i
$494$			7.99849i			0.0161913i
$495$	153.821	+	8.74980i	0.310750	+	0.0176764i
$496$	55.3827			0.111659
$497$	−553.033	−	553.033i	−1.11274	−	1.11274i
$498$	240.547	−	240.547i	0.483025	−	0.483025i
$499$		−	482.367i		−	0.966668i	−0.875436	−	0.483334i	$-0.839426\pi$
$499$		−	482.367i		−	0.966668i	0.875436	−	0.483334i	$-0.160574\pi$
$500$	−246.376	−	42.4102i	−0.492753	−	0.0848204i
$501$	−156.927			−0.313227
$502$	−384.369	−	384.369i	−0.765676	−	0.765676i
$503$	−426.820	+	426.820i	−0.848549	+	0.848549i	−0.989952	−	0.141403i	$-0.954839\pi$
$503$	−426.820	+	426.820i	−0.848549	+	0.848549i	0.141403	+	0.989952i	$0.454839\pi$
$504$			55.5243i			0.110167i
$505$	−26.3849	+	463.846i	−0.0522474	+	0.918507i
$506$	147.004			0.290522
$507$	327.869	+	327.869i	0.646684	+	0.646684i
$508$	162.890	−	162.890i	0.320650	−	0.320650i
$509$		−	850.581i		−	1.67108i	−0.549427	−	0.835542i	$-0.685154\pi$
$509$		−	850.581i		−	1.67108i	0.549427	−	0.835542i	$-0.314846\pi$
$510$	388.495	−	346.677i	0.761756	−	0.679758i
$511$	175.410			0.343268
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−152.411	+	152.411i	−0.297098	+	0.297098i
$514$			96.5272i			0.187796i
$515$	79.2804	+	88.8438i	0.153943	+	0.172512i
$516$	256.131			0.496377
$517$	42.2672	+	42.2672i	0.0817547	+	0.0817547i
$518$	−667.832	+	667.832i	−1.28925	+	1.28925i
$519$		−	421.078i		−	0.811325i
$520$	10.6291	+	0.604616i	0.0204406	+	0.00116272i
$521$	−98.0266			−0.188151			−0.0940755	−	0.995565i	$-0.529990\pi$
$521$	−98.0266			−0.188151			−0.0940755	+	0.995565i	$0.529990\pi$
$522$	−21.3161	−	21.3161i	−0.0408354	−	0.0408354i
$523$	212.663	−	212.663i	0.406622	−	0.406622i	−0.473937	−	0.880559i	$-0.657167\pi$
$523$	212.663	−	212.663i	0.406622	−	0.406622i	0.880559	+	0.473937i	$0.157167\pi$
$524$		−	73.4542i		−	0.140180i
$525$	−944.187	−	107.765i	−1.79845	−	0.205266i
$526$	354.433			0.673827
$527$	261.880	+	261.880i	0.496927	+	0.496927i
$528$	−168.765	+	168.765i	−0.319631	+	0.319631i
$529$		−	23.0000i		−	0.0434783i
$530$	−16.6935	+	293.472i	−0.0314973	+	0.553721i
$531$	−52.3420			−0.0985726
$532$	−146.712	−	146.712i	−0.275774	−	0.275774i
$533$	18.2542	−	18.2542i	0.0342481	−	0.0342481i
$534$		−	140.675i		−	0.263436i
$535$	−290.837	+	259.531i	−0.543621	+	0.485104i
$536$	62.9859			0.117511
$537$	68.7754	+	68.7754i	0.128073	+	0.128073i
$538$	106.990	−	106.990i	0.198867	−	0.198867i
$539$			3070.64i			5.69692i
$540$	191.017	+	214.059i	0.353736	+	0.396406i
$541$	893.808			1.65214			0.826070	−	0.563568i	$-0.190572\pi$
$541$	893.808			1.65214			0.826070	+	0.563568i	$0.190572\pi$
$542$	−83.4806	−	83.4806i	−0.154023	−	0.154023i
$543$	−429.157	+	429.157i	−0.790345	+	0.790345i
$544$		−	151.314i		−	0.278150i
$545$	−18.2761	−	1.03960i	−0.0335341	−	0.00190752i
$546$	40.4695			0.0741199
$547$	−97.9282	−	97.9282i	−0.179028	−	0.179028i	0.611904	−	0.790932i	$-0.290404\pi$
$547$	−97.9282	−	97.9282i	−0.179028	−	0.179028i	−0.790932	+	0.611904i	$0.790404\pi$
$548$	−52.0378	+	52.0378i	−0.0949595	+	0.0949595i
$549$			1.99512i			0.00363410i
$550$	476.922	+	599.816i	0.867131	+	1.09057i
$551$	112.647			0.204441
$552$	26.4047	+	26.4047i	0.0478346	+	0.0478346i
$553$	−769.769	+	769.769i	−1.39199	+	1.39199i
$554$			420.314i			0.758689i
$555$	−37.8062	+	664.632i	−0.0681193	+	1.19753i
$556$	−62.5911			−0.112574
$557$	196.243	+	196.243i	0.352321	+	0.352321i	0.860972	−	0.508652i	$-0.169856\pi$
$557$	196.243	+	196.243i	0.352321	+	0.352321i	−0.508652	+	0.860972i	$0.669856\pi$
$558$	−19.6839	+	19.6839i	−0.0352758	+	0.0352758i
$559$			35.0210i			0.0626495i
$560$	−206.054	+	183.874i	−0.367954	+	0.328347i
$561$	−1596.03			−2.84497
$562$	−63.1340	−	63.1340i	−0.112338	−	0.112338i
$563$	524.329	−	524.329i	0.931312	−	0.931312i	−0.0664759	−	0.997788i	$-0.521176\pi$
$563$	524.329	−	524.329i	0.931312	−	0.931312i	0.997788	+	0.0664759i	$0.0211755\pi$
$564$			15.1840i			0.0269219i
$565$	−261.604	−	293.161i	−0.463016	−	0.518869i
$566$	313.653			0.554158
$567$	646.217	+	646.217i	1.13971	+	1.13971i
$568$	−113.280	+	113.280i	−0.199437	+	0.199437i
$569$		−	240.822i		−	0.423238i	−0.977352	−	0.211619i	$-0.932126\pi$
$569$		−	240.822i		−	0.423238i	0.977352	−	0.211619i	$-0.0678736\pi$
$570$	−146.009	−	8.30541i	−0.256156	−	0.0145709i
$571$	−145.998			−0.255687			−0.127844	−	0.991794i	$-0.540806\pi$
$571$	−145.998			−0.255687			−0.127844	+	0.991794i	$0.540806\pi$
$572$	−23.0754	−	23.0754i	−0.0403417	−	0.0403417i
$573$	561.783	−	561.783i	0.980424	−	0.980424i
$574$			669.655i			1.16665i
$575$	93.8461	−	74.6184i	0.163211	−	0.129771i
$576$	11.3733			0.0197453
$577$	−45.5478	−	45.5478i	−0.0789390	−	0.0789390i	0.666535	−	0.745474i	$-0.267777\pi$
$577$	−45.5478	−	45.5478i	−0.0789390	−	0.0789390i	−0.745474	+	0.666535i	$0.767777\pi$
$578$	426.496	−	426.496i	0.737882	−	0.737882i
$579$			495.560i			0.855889i
$580$	8.51513	−	149.696i	0.0146813	−	0.258096i
$581$	−1206.57			−2.07672
$582$	348.882	+	348.882i	0.599454	+	0.599454i
$583$	637.116	−	637.116i	1.09282	−	1.09282i
$584$		−	35.9300i		−	0.0615240i
$585$	−3.99265	+	3.56287i	−0.00682505	+	0.00609038i
$586$	749.626			1.27923
$587$	697.050	+	697.050i	1.18748	+	1.18748i	0.977762	+	0.209718i	$0.0672544\pi$
$587$	697.050	+	697.050i	1.18748	+	1.18748i	0.209718	+	0.977762i	$0.432746\pi$
$588$	−551.544	+	551.544i	−0.938000	+	0.938000i
$589$		−	104.021i		−	0.176607i
$590$	−173.336	−	194.245i	−0.293789	−	0.329228i
$591$	−523.618			−0.885986
$592$	136.795	+	136.795i	0.231073	+	0.231073i
$593$	528.700	−	528.700i	0.891568	−	0.891568i	−0.103103	−	0.994671i	$-0.532877\pi$
$593$	528.700	−	528.700i	0.891568	−	0.891568i	0.994671	+	0.103103i	$0.0328771\pi$
$594$		−	879.406i		−	1.48048i
$595$	−1843.80	−	104.881i	−3.09882	−	0.176270i
$596$	−258.499			−0.433723
$597$	336.395	+	336.395i	0.563476	+	0.563476i
$598$	−3.61034	+	3.61034i	−0.00603736	+	0.00603736i
$599$		−	845.156i		−	1.41094i	−0.708738	−	0.705472i	$-0.750735\pi$
$599$		−	845.156i		−	1.41094i	0.708738	−	0.705472i	$-0.249265\pi$
$600$	−22.0740	+	193.402i	−0.0367900	+	0.322337i
$601$	−112.831			−0.187740			−0.0938698	−	0.995584i	$-0.529924\pi$
$601$	−112.831			−0.187740			−0.0938698	+	0.995584i	$0.529924\pi$
$602$	−642.371	−	642.371i	−1.06706	−	1.06706i
$603$	−22.3862	+	22.3862i	−0.0371247	+	0.0371247i
$604$			47.7444i			0.0790470i
$605$	99.0401	−	1741.12i	0.163703	−	2.87789i
$606$	361.749			0.596946
$607$	196.203	+	196.203i	0.323234	+	0.323234i	0.850006	−	0.526773i	$-0.176598\pi$
$607$	196.203	+	196.203i	0.323234	+	0.323234i	−0.526773	+	0.850006i	$0.676598\pi$
$608$	−30.0517	+	30.0517i	−0.0494271	+	0.0494271i
$609$		−	569.953i		−	0.935883i
$610$	−7.40403	+	6.60703i	−0.0121377	+	0.0108312i
$611$	−2.07612			−0.00339790
$612$	53.7793	+	53.7793i	0.0878747	+	0.0878747i
$613$	−371.961	+	371.961i	−0.606788	+	0.606788i	−0.942105	−	0.335318i	$-0.891156\pi$
$613$	−371.961	+	371.961i	−0.606788	+	0.606788i	0.335318	+	0.942105i	$0.391156\pi$
$614$		−	717.913i		−	1.16924i
$615$	314.268	+	352.178i	0.511005	+	0.572647i
$616$	846.519			1.37422
$617$	−201.112	−	201.112i	−0.325951	−	0.325951i	0.525094	−	0.851045i	$-0.324030\pi$
$617$	−201.112	−	201.112i	−0.325951	−	0.325951i	−0.851045	+	0.525094i	$0.824030\pi$
$618$	65.5592	−	65.5592i	0.106083	−	0.106083i
$619$			294.954i			0.476501i	0.971204	+	0.238250i	$0.0765739\pi$
$619$			294.954i			0.476501i	−0.971204	+	0.238250i	$0.923426\pi$
$620$	−138.233	−	7.86312i	−0.222957	−	0.0126825i
$621$	−137.590			−0.221563
$622$	8.62512	+	8.62512i	0.0138668	+	0.0138668i
$623$	−352.809	+	352.809i	−0.566307	+	0.566307i
$624$		−	8.28956i		−	0.0132845i
$625$	608.926	+	140.834i	0.974281	+	0.225335i
$626$	−469.002			−0.749204
$627$	316.980	+	316.980i	0.505549	+	0.505549i
$628$	−37.6482	+	37.6482i	−0.0599493	+	0.0599493i
$629$			1293.69i			2.05674i
$630$	7.88322	−	138.587i	0.0125130	−	0.219979i
$631$	909.467			1.44131			0.720655	−	0.693294i	$-0.243841\pi$
$631$	909.467			1.44131			0.720655	+	0.693294i	$0.243841\pi$
$632$	157.675	+	157.675i	0.249486	+	0.249486i
$633$	−515.175	+	515.175i	−0.813862	+	0.813862i
$634$			720.512i			1.13645i
$635$	−429.696	+	383.442i	−0.676686	+	0.603846i
$636$	228.876			0.359868
$637$	−75.4132	−	75.4132i	−0.118388	−	0.118388i
$638$	−324.984	+	324.984i	−0.509379	+	0.509379i
$639$		−	80.5232i		−	0.126014i
$640$	37.6638	+	42.2071i	0.0588497	+	0.0659486i
$641$	794.199			1.23900			0.619500	−	0.784997i	$-0.287336\pi$
$641$	794.199			1.23900			0.619500	+	0.784997i	$0.287336\pi$
$642$	214.613	+	214.613i	0.334288	+	0.334288i
$643$	444.052	−	444.052i	0.690594	−	0.690594i	−0.271769	−	0.962363i	$-0.587609\pi$
$643$	444.052	−	444.052i	0.690594	−	0.690594i	0.962363	+	0.271769i	$0.0876086\pi$
$644$		−	132.445i		−	0.205660i
$645$	−639.293	−	36.3649i	−0.991153	−	0.0563797i
$646$	−284.202			−0.439941
$647$	−670.308	−	670.308i	−1.03603	−	1.03603i	−0.999326	−	0.0366989i	$-0.988316\pi$
$647$	−670.308	−	670.308i	−1.03603	−	1.03603i	−0.0366989	−	0.999326i	$-0.511684\pi$
$648$	132.368	−	132.368i	0.204271	−	0.204271i
$649$			798.003i			1.22959i
$650$	−26.4441	−	3.01820i	−0.0406832	−	0.00464339i
$651$	−526.311			−0.808466
$652$	426.047	+	426.047i	0.653447	+	0.653447i
$653$	−368.030	+	368.030i	−0.563599	+	0.563599i	−0.930328	−	0.366729i	$-0.880478\pi$
$653$	−368.030	+	368.030i	−0.563599	+	0.563599i	0.366729	+	0.930328i	$0.380478\pi$
$654$			14.2533i			0.0217941i
$655$	−10.4289	+	183.339i	−0.0159219	+	0.279907i
$656$	137.169			0.209098
$657$	12.7701	+	12.7701i	0.0194370	+	0.0194370i
$658$	38.0811	−	38.0811i	0.0578740	−	0.0578740i
$659$		−	505.833i		−	0.767576i	−0.923421	−	0.383788i	$-0.874619\pi$
$659$		−	505.833i		−	0.767576i	0.923421	−	0.383788i	$-0.125381\pi$
$660$	445.193	−	397.271i	0.674534	−	0.601925i
$661$	−208.032			−0.314723			−0.157362	−	0.987541i	$-0.550299\pi$
$661$	−208.032			−0.314723			−0.157362	+	0.987541i	$0.550299\pi$
$662$	−547.667	−	547.667i	−0.827291	−	0.827291i
$663$	39.1976	−	39.1976i	0.0591216	−	0.0591216i
$664$			247.148i			0.372211i
$665$	345.358	+	387.017i	0.519335	+	0.581981i
$666$	−97.2383			−0.146004
$667$	50.8463	+	50.8463i	0.0762314	+	0.0762314i
$668$	80.6166	−	80.6166i	0.120684	−	0.120684i
$669$			692.894i			1.03572i
$670$	−157.211	−	8.94260i	−0.234643	−	0.0133472i
$671$	30.4175			0.0453315
$672$	152.051	+	152.051i	0.226266	+	0.226266i
$673$	215.020	−	215.020i	0.319494	−	0.319494i	−0.529078	−	0.848573i	$-0.677462\pi$
$673$	215.020	−	215.020i	0.319494	−	0.319494i	0.848573	+	0.529078i	$0.177462\pi$
$674$		−	549.203i		−	0.814841i
$675$	−446.381	−	561.405i	−0.661306	−	0.831711i
$676$	−336.867			−0.498323
$677$	500.023	+	500.023i	0.738587	+	0.738587i	0.972305	−	0.233718i	$-0.0750891\pi$
$677$	500.023	+	500.023i	0.738587	+	0.738587i	−0.233718	+	0.972305i	$0.575089\pi$
$678$	−216.328	+	216.328i	−0.319068	+	0.319068i
$679$		−	1749.98i		−	2.57729i
$680$	−21.4832	+	377.674i	−0.0315930	+	0.555403i
$681$	1055.17			1.54944
$682$	300.099	+	300.099i	0.440028	+	0.440028i
$683$	−456.035	+	456.035i	−0.667694	+	0.667694i	−0.957182	−	0.289488i	$-0.906515\pi$
$683$	−456.035	+	456.035i	−0.667694	+	0.667694i	0.289488	+	0.957182i	$0.406515\pi$
$684$		−	21.3617i		−	0.0312305i
$685$	137.273	−	122.496i	0.200398	−	0.178827i
$686$	1809.66			2.63798
$687$	−100.614	−	100.614i	−0.146454	−	0.146454i
$688$	−131.580	+	131.580i	−0.191250	+	0.191250i
$689$			31.2944i			0.0454201i
$690$	−62.1563	−	69.6540i	−0.0900816	−	0.100948i
$691$	470.530			0.680941			0.340470	−	0.940255i	$-0.389414\pi$
$691$	470.530			0.680941			0.340470	+	0.940255i	$0.389414\pi$
$692$	216.317	+	216.317i	0.312597	+	0.312597i
$693$	−300.866	+	300.866i	−0.434151	+	0.434151i
$694$			514.387i			0.741192i
$695$	156.225	+	8.88655i	0.224784	+	0.0127864i
$696$	−116.746			−0.167739
$697$	648.609	+	648.609i	0.930573	+	0.930573i
$698$	110.553	−	110.553i	0.158386	−	0.158386i
$699$		−	979.914i		−	1.40188i
$700$	540.410	−	429.688i	0.772015	−	0.613840i
$701$	98.5546			0.140591			0.0702957	−	0.997526i	$-0.477606\pi$
$701$	98.5546			0.140591			0.0702957	+	0.997526i	$0.477606\pi$
$702$	21.5977	+	21.5977i	0.0307660	+	0.0307660i
$703$	256.933	−	256.933i	0.365480	−	0.365480i
$704$		−	173.397i		−	0.246302i
$705$	2.15579	−	37.8986i	0.00305785	−	0.0537569i
$706$	−407.722			−0.577509
$707$	−907.260	−	907.260i	−1.28325	−	1.28325i
$708$	−143.336	+	143.336i	−0.202452	+	0.202452i
$709$			352.517i			0.497204i	0.968606	+	0.248602i	$0.0799711\pi$
$709$			352.517i			0.497204i	−0.968606	+	0.248602i	$0.920029\pi$
$710$	298.827	−	266.660i	0.420883	−	0.375578i
$711$	−112.081			−0.157638
$712$	72.2676	+	72.2676i	0.101499	+	0.101499i
$713$	46.9530	−	46.9530i	0.0658527	−	0.0658527i
$714$			1437.96i			2.01395i
$715$	54.3193	+	60.8717i	0.0759710	+	0.0851352i
$716$	−70.6629			−0.0986912
$717$	−313.754	−	313.754i	−0.437593	−	0.437593i
$718$	−358.509	+	358.509i	−0.499317	+	0.499317i
$719$			668.139i			0.929261i	0.885505	+	0.464631i	$0.153813\pi$
$719$			668.139i			0.929261i	−0.885505	+	0.464631i	$0.846187\pi$
$720$	−28.3874	−	1.61476i	−0.0394269	−	0.00224272i
$721$	−328.843			−0.456092
$722$	−304.556	−	304.556i	−0.421823	−	0.421823i
$723$	−678.832	+	678.832i	−0.938911	+	0.938911i
$724$		−	440.935i		−	0.609026i
$725$	−42.5069	+	372.426i	−0.0586303	+	0.513691i
$726$	−1357.88			−1.87036
$727$	364.452	+	364.452i	0.501310	+	0.501310i	0.911845	−	0.410535i	$-0.134658\pi$
$727$	364.452	+	364.452i	0.501310	+	0.501310i	−0.410535	+	0.911845i	$0.634658\pi$
$728$	−20.7901	+	20.7901i	−0.0285578	+	0.0285578i
$729$			804.901i			1.10412i
$730$	−5.10127	+	89.6801i	−0.00698803	+	0.122849i
$731$	−1244.37			−1.70228
$732$	5.46354	+	5.46354i	0.00746386	+	0.00746386i
$733$	148.455	−	148.455i	0.202531	−	0.202531i	−0.598553	−	0.801084i	$-0.704257\pi$
$733$	148.455	−	148.455i	0.202531	−	0.202531i	0.801084	+	0.598553i	$0.204257\pi$
$734$			178.361i			0.242998i
$735$	1454.94	−	1298.33i	1.97951	−	1.76643i
$736$	−27.1293			−0.0368605
$737$	341.298	+	341.298i	0.463091	+	0.463091i
$738$	−48.7519	+	48.7519i	−0.0660595	+	0.0660595i
$739$			106.485i			0.144093i	0.997401	+	0.0720467i	$0.0229530\pi$
$739$			106.485i			0.144093i	−0.997401	+	0.0720467i	$0.977047\pi$
$740$	−322.014	−	360.858i	−0.435154	−	0.487646i
$741$	−15.5697			−0.0210117
$742$	−574.016	−	574.016i	−0.773607	−	0.773607i
$743$	760.415	−	760.415i	1.02344	−	1.02344i	0.0237201	−	0.999719i	$-0.492449\pi$
$743$	760.415	−	760.415i	1.02344	−	1.02344i	0.999719	−	0.0237201i	$-0.00755106\pi$
$744$			107.807i			0.144902i
$745$	645.204	+	36.7011i	0.866045	+	0.0492632i
$746$	−623.507			−0.835800
$747$	−87.8404	−	87.8404i	−0.117591	−	0.117591i
$748$	819.916	−	819.916i	1.09614	−	1.09614i
$749$		−	1076.49i		−	1.43724i
$750$	82.5548	−	479.591i	0.110073	−	0.639455i
$751$	665.100			0.885619			0.442810	−	0.896616i	$-0.353982\pi$
$751$	665.100			0.885619			0.442810	+	0.896616i	$0.353982\pi$
$752$	−7.80033	−	7.80033i	−0.0103728	−	0.0103728i
$753$	748.205	−	748.205i	0.993632	−	0.993632i
$754$		−	15.9628i		−	0.0211709i
$755$	6.77865	−	119.168i	0.00897834	−	0.157839i
$756$	−792.310			−1.04803
$757$	−860.269	−	860.269i	−1.13642	−	1.13642i	−0.989087	−	0.147332i	$-0.952932\pi$
$757$	−860.269	−	860.269i	−1.13642	−	1.13642i	−0.147332	−	0.989087i	$-0.547068\pi$
$758$	266.437	−	266.437i	0.351500	−	0.351500i
$759$			286.155i			0.377016i
$760$	79.2746	−	70.7413i	0.104309	−	0.0930806i
$761$	−66.4693			−0.0873447			−0.0436723	−	0.999046i	$-0.513906\pi$
$761$	−66.4693			−0.0873447			−0.0436723	+	0.999046i	$0.513906\pi$
$762$	317.079	+	317.079i	0.416114	+	0.416114i
$763$	35.7471	−	35.7471i	0.0468508	−	0.0468508i
$764$			577.200i			0.755498i
$765$	−126.596	−	141.867i	−0.165485	−	0.185447i
$766$	1012.45			1.32174
$767$	−19.5985	−	19.5985i	−0.0255522	−	0.0255522i
$768$	31.1453	−	31.1453i	0.0405537	−	0.0405537i
$769$		−	894.516i		−	1.16322i	−0.813468	−	0.581610i	$-0.802423\pi$
$769$		−	894.516i		−	1.16322i	0.813468	−	0.581610i	$-0.197577\pi$
$770$	−2112.88	−	120.187i	−2.74400	−	0.156087i
$771$	−187.898			−0.243707
$772$	−254.580	−	254.580i	−0.329767	−	0.329767i
$773$	926.134	−	926.134i	1.19810	−	1.19810i	0.223369	−	0.974734i	$-0.428294\pi$
$773$	926.134	−	926.134i	1.19810	−	1.19810i	0.974734	−	0.223369i	$-0.0717056\pi$
$774$		−	93.5312i		−	0.120841i
$775$	343.909	+	39.2521i	0.443754	+	0.0506479i
$776$	−358.457			−0.461929
$777$	−1299.99	−	1299.99i	−1.67308	−	1.67308i
$778$	−373.660	+	373.660i	−0.480283	+	0.480283i
$779$		−	257.634i		−	0.330724i
$780$	−1.17693	+	20.6904i	−0.00150889	+	0.0265262i
$781$	−1227.65			−1.57190
$782$	−128.283	−	128.283i	−0.164044	−	0.164044i
$783$	304.172	−	304.172i	0.388470	−	0.388470i
$784$		−	566.680i		−	0.722807i
$785$	99.3137	−	88.6233i	0.126514	−	0.112896i
$786$	142.984			0.181914
$787$	271.450	+	271.450i	0.344917	+	0.344917i	0.858212	−	0.513295i	$-0.171575\pi$
$787$	271.450	+	271.450i	0.344917	+	0.344917i	−0.513295	+	0.858212i	$0.671575\pi$
$788$	268.994	−	268.994i	0.341363	−	0.341363i
$789$			689.932i			0.874438i
$790$	−371.166	−	415.939i	−0.469830	−	0.526505i
$791$	1085.09			1.37180
$792$	61.6279	+	61.6279i	0.0778130	+	0.0778130i
$793$	−0.747037	+	0.747037i	−0.000942038	+	0.000942038i
$794$		−	219.624i		−	0.276605i
$795$	−571.266	−	32.4953i	−0.718574	−	0.0408746i
$796$	−345.627			−0.434205
$797$	−89.1775	−	89.1775i	−0.111892	−	0.111892i	0.648944	−	0.760836i	$-0.275211\pi$
$797$	−89.1775	−	89.1775i	−0.111892	−	0.111892i	−0.760836	+	0.648944i	$0.775211\pi$
$798$	285.586	−	285.586i	0.357877	−	0.357877i
$799$		−	73.7686i		−	0.0923261i
$800$	−88.0151	−	110.695i	−0.110019	−	0.138369i
$801$	−51.3701			−0.0641325
$802$	−304.662	−	304.662i	−0.379877	−	0.379877i
$803$	194.692	−	194.692i	0.242456	−	0.242456i
$804$			122.607i			0.152496i
$805$	−18.8042	+	330.578i	−0.0233593	+	0.410656i
$806$	−14.7405			−0.0182885
$807$	208.265	+	208.265i	0.258073	+	0.258073i
$808$	−185.838	+	185.838i	−0.229998	+	0.229998i
$809$			714.152i			0.882759i	0.897321	+	0.441380i	$0.145511\pi$
$809$			714.152i			0.882759i	−0.897321	+	0.441380i	$0.854489\pi$
$810$	−349.179	+	311.592i	−0.431085	+	0.384682i
$811$	938.065			1.15668			0.578339	−	0.815797i	$-0.303701\pi$
$811$	938.065			1.15668			0.578339	+	0.815797i	$0.303701\pi$
$812$	292.797	+	292.797i	0.360588	+	0.360588i
$813$	162.501	−	162.501i	0.199879	−	0.199879i
$814$			1482.49i			1.82124i
$815$	−1002.91	−	1123.89i	−1.23056	−	1.37900i
$816$	294.544			0.360961
$817$	247.137	+	247.137i	0.302494	+	0.302494i
$818$	−228.713	+	228.713i	−0.279600	+	0.279600i
$819$		−	14.7782i		−	0.0180442i
$820$	−342.368	−	19.4749i	−0.417522	−	0.0237499i
$821$	1298.50			1.58160			0.790802	−	0.612073i	$-0.209664\pi$
$821$	1298.50			1.58160			0.790802	+	0.612073i	$0.209664\pi$
$822$	−101.296	−	101.296i	−0.123231	−	0.123231i
$823$	413.358	−	413.358i	0.502258	−	0.502258i	−0.409881	−	0.912139i	$-0.634430\pi$
$823$	413.358	−	413.358i	0.502258	−	0.502258i	0.912139	+	0.409881i	$0.134430\pi$
$824$			67.3584i			0.0817456i
$825$	−1167.59	+	928.367i	−1.41526	+	1.12529i
$826$	718.969			0.870422
$827$	771.519	+	771.519i	0.932913	+	0.932913i	0.997887	−	0.0649739i	$-0.0206964\pi$
$827$	771.519	+	771.519i	0.932913	+	0.932913i	−0.0649739	+	0.997887i	$0.520696\pi$
$828$	9.64219	−	9.64219i	0.0116452	−	0.0116452i
$829$		−	645.980i		−	0.779228i	−0.920978	−	0.389614i	$-0.872608\pi$
$829$		−	645.980i		−	0.779228i	0.920978	−	0.389614i	$-0.127392\pi$
$830$	35.0896	−	616.873i	0.0422766	−	0.743221i
$831$	−818.174			−0.984566
$832$	4.25853	+	4.25853i	0.00511842	+	0.00511842i
$833$	2679.58	−	2679.58i	3.21678	−	3.21678i
$834$		−	121.838i		−	0.146089i
$835$	−212.662	+	189.770i	−0.254685	+	0.227270i
$836$	−325.679			−0.389568
$837$	−280.882	−	280.882i	−0.335581	−	0.335581i
$838$	198.319	−	198.319i	0.236658	−	0.236658i
$839$		−	1586.81i		−	1.89131i	−0.325166	−	0.945657i	$-0.605420\pi$
$839$		−	1586.81i		−	1.89131i	0.325166	−	0.945657i	$-0.394580\pi$
$840$	−357.925	−	401.101i	−0.426102	−	0.477501i
$841$	616.187			0.732684
$842$	571.167	+	571.167i	0.678346	+	0.678346i
$843$	122.895	−	122.895i	0.145783	−	0.145783i
$844$		−	529.313i		−	0.627148i
$845$	840.807	+	47.8276i	0.995038	+	0.0566007i
$846$	5.54472			0.00655404
$847$	3405.55	+	3405.55i	4.02072	+	4.02072i
$848$	−117.579	+	117.579i	−0.138654	+	0.138654i
$849$			610.551i			0.719142i
$850$	107.243	−	939.611i	0.126168	−	1.10542i
$851$	231.947			0.272559
$852$	−220.509	−	220.509i	−0.258813	−	0.258813i
$853$	−633.942	+	633.942i	−0.743192	+	0.743192i	−0.973191	−	0.229999i	$-0.926128\pi$
$853$	−633.942	+	633.942i	−0.743192	+	0.743192i	0.229999	+	0.973191i	$0.426128\pi$
$854$		−	27.4049i		−	0.0320901i
$855$	−3.03289	+	53.3180i	−0.00354723	+	0.0623603i
$856$	−220.503			−0.257597
$857$	−669.720	−	669.720i	−0.781470	−	0.781470i	0.198609	−	0.980079i	$-0.436358\pi$
$857$	−669.720	−	669.720i	−0.781470	−	0.781470i	−0.980079	+	0.198609i	$0.936358\pi$
$858$	44.9181	−	44.9181i	0.0523522	−	0.0523522i
$859$		−	1076.95i		−	1.25372i	−0.779131	−	0.626861i	$-0.784339\pi$
$859$		−	1076.95i		−	1.25372i	0.779131	−	0.626861i	$-0.215661\pi$
$860$	347.100	−	309.738i	0.403605	−	0.360160i
$861$	−1303.54			−1.51398
$862$	575.249	+	575.249i	0.667342	+	0.667342i
$863$	−57.6828	+	57.6828i	−0.0668399	+	0.0668399i	−0.739737	−	0.672897i	$-0.765050\pi$
$863$	−57.6828	+	57.6828i	−0.0668399	+	0.0668399i	0.672897	+	0.739737i	$0.265050\pi$
$864$			162.293i			0.187839i
$865$	−509.207	−	570.632i	−0.588679	−	0.659690i
$866$	−1.43679			−0.00165912
$867$	830.208	+	830.208i	0.957564	+	0.957564i
$868$	270.378	−	270.378i	0.311495	−	0.311495i
$869$			1708.77i			1.96637i
$870$	291.394	+	16.5754i	0.334936	+	0.0190522i
$871$	−16.7642			−0.0192471
$872$	−7.32226	−	7.32226i	−0.00839708	−	0.00839708i
$873$	127.401	−	127.401i	0.145935	−	0.145935i
$874$			50.9551i			0.0583010i
$875$	−1409.85	+	995.760i	−1.61126	+	1.13801i
$876$	69.9406			0.0798409
$877$	−168.052	−	168.052i	−0.191621	−	0.191621i	0.604775	−	0.796396i	$-0.293263\pi$
$877$	−168.052	−	168.052i	−0.191621	−	0.191621i	−0.796396	+	0.604775i	$0.793263\pi$
$878$	520.035	−	520.035i	0.592295	−	0.592295i
$879$			1459.21i			1.66008i
$880$	−24.6185	+	432.792i	−0.0279755	+	0.491809i
$881$	−302.189			−0.343007			−0.171504	−	0.985183i	$-0.554863\pi$
$881$	−302.189			−0.343007			−0.171504	+	0.985183i	$0.554863\pi$
$882$	201.407	+	201.407i	0.228353	+	0.228353i
$883$	−856.409	+	856.409i	−0.969885	+	0.969885i	−0.999560	−	0.0296745i	$-0.990553\pi$
$883$	−856.409	+	856.409i	−0.969885	+	0.969885i	0.0296745	+	0.999560i	$0.490553\pi$
$884$			40.2734i			0.0455581i
$885$	378.113	−	337.411i	0.427246	−	0.381256i
$886$	−108.750			−0.122742
$887$	302.316	+	302.316i	0.340830	+	0.340830i	0.856679	−	0.515849i	$-0.172524\pi$
$887$	302.316	+	302.316i	0.340830	+	0.340830i	−0.515849	+	0.856679i	$0.672524\pi$
$888$	−266.283	+	266.283i	−0.299868	+	0.299868i
$889$		−	1590.46i		−	1.78904i
$890$	−170.117	−	190.638i	−0.191143	−	0.214200i
$891$	1434.51			1.61000
$892$	−355.955	−	355.955i	−0.399052	−	0.399052i
$893$	−14.6508	+	14.6508i	−0.0164063	+	0.0164063i
$894$		−	503.188i		−	0.562850i
$895$	176.372	+	10.0326i	0.197064	+	0.0112096i
$896$	−156.223			−0.174357
$897$	−7.02781	−	7.02781i	−0.00783480	−	0.00783480i
$898$	−556.320	+	556.320i	−0.619510	+	0.619510i
$899$			207.599i			0.230922i
$900$	70.6247	+	8.06076i	0.0784718	+	0.00895640i
$901$	−1111.95			−1.23413
$902$	743.268	+	743.268i	0.824022	+	0.824022i
$903$	1250.43	−	1250.43i	1.38475	−	1.38475i
$904$		−	222.265i		−	0.245868i
$905$	−62.6030	+	1100.56i	−0.0691746	+	1.21609i
$906$	−92.9382			−0.102581
$907$	−522.277	−	522.277i	−0.575829	−	0.575829i	0.357922	−	0.933751i	$-0.383485\pi$
$907$	−522.277	−	522.277i	−0.575829	−	0.575829i	−0.933751	+	0.357922i	$0.883485\pi$
$908$	−542.062	+	542.062i	−0.596985	+	0.596985i
$909$		−	132.100i		−	0.145324i
$910$	54.8430	−	48.9395i	0.0602670	−	0.0537797i
$911$	99.0099			0.108683			0.0543413	−	0.998522i	$-0.482694\pi$
$911$	99.0099			0.108683			0.0543413	+	0.998522i	$0.482694\pi$
$912$	−58.4979	−	58.4979i	−0.0641425	−	0.0641425i
$913$	−1339.21	+	1339.21i	−1.46682	+	1.46682i
$914$		−	515.314i		−	0.563801i
$915$	−12.8611	−	14.4125i	−0.0140559	−	0.0157514i
$916$	103.375			0.112855
$917$	−358.602	−	358.602i	−0.391060	−	0.391060i
$918$	−767.410	+	767.410i	−0.835959	+	0.835959i
$919$			648.385i			0.705534i	0.935711	+	0.352767i	$0.114759\pi$
$919$			648.385i			0.705534i	−0.935711	+	0.352767i	$0.885241\pi$
$920$	67.7138	+	3.85176i	0.0736020	+	0.00418670i
$921$	1397.47			1.51734
$922$	236.551	+	236.551i	0.256563	+	0.256563i
$923$	30.1504	−	30.1504i	0.0326657	−	0.0326657i
$924$			1647.82i			1.78335i
$925$	752.502	+	946.407i	0.813516	+	1.02314i
$926$	−413.908			−0.446984
$927$	−23.9402	−	23.9402i	−0.0258255	−	0.0258255i
$928$	59.9751	−	59.9751i	0.0646283	−	0.0646283i
$929$		−	559.661i		−	0.602434i	−0.953556	−	0.301217i	$-0.902607\pi$
$929$		−	559.661i		−	0.602434i	0.953556	−	0.301217i	$-0.0973929\pi$
$930$	15.3062	−	269.082i	0.0164583	−	0.289336i
$931$	−1064.36			−1.14324
$932$	503.403	+	503.403i	0.540132	+	0.540132i
$933$	−16.7895	+	16.7895i	−0.0179952	+	0.0179952i
$934$			910.320i			0.974647i
$935$	−2162.89	+	1930.07i	−2.31325	+	2.06425i
$936$	−3.02710			−0.00323408
$937$	−490.873	−	490.873i	−0.523878	−	0.523878i	0.394863	−	0.918740i	$-0.370792\pi$
$937$	−490.873	−	490.873i	−0.523878	−	0.523878i	−0.918740	+	0.394863i	$0.870792\pi$
$938$	307.496	−	307.496i	0.327821	−	0.327821i
$939$		−	912.949i		−	0.972256i
$940$	18.3619	+	20.5768i	0.0195339	+	0.0218902i
$941$	−375.476			−0.399018			−0.199509	−	0.979896i	$-0.563935\pi$
$941$	−375.476			−0.399018			−0.199509	+	0.979896i	$0.563935\pi$
$942$	−73.2851	−	73.2851i	−0.0777974	−	0.0777974i
$943$	116.290	−	116.290i	0.123320	−	0.123320i
$944$		−	147.270i		−	0.156006i
$945$	1977.58	+	112.491i	2.09268	+	0.119038i
$946$	−1425.97			−1.50737
$947$	284.861	+	284.861i	0.300804	+	0.300804i	0.841328	−	0.540525i	$-0.181774\pi$
$947$	284.861	+	284.861i	0.300804	+	0.300804i	−0.540525	+	0.841328i	$0.681774\pi$
$948$	−306.928	+	306.928i	−0.323763	+	0.323763i
$949$			9.56306i			0.0100770i
$950$	−207.910	+	165.312i	−0.218853	+	0.174013i
$951$	−1402.53			−1.47480
$952$	−738.711	−	738.711i	−0.775957	−	0.775957i
$953$	930.751	−	930.751i	0.976654	−	0.976654i	−0.0230796	−	0.999734i	$-0.507347\pi$
$953$	930.751	−	930.751i	0.976654	−	0.976654i	0.999734	+	0.0230796i	$0.00734710\pi$
$954$		−	83.5785i		−	0.0876085i
$955$	81.9497	−	1440.67i	0.0858112	−	1.50856i
$956$	322.364			0.337201
$957$	−632.606	−	632.606i	−0.661030	−	0.661030i
$958$	15.9362	−	15.9362i	0.0166349	−	0.0166349i
$959$			508.095i			0.529818i
$960$	−82.1594	+	73.3155i	−0.0855827	+	0.0763704i
$961$	−769.297			−0.800517
$962$	−36.4091	−	36.4091i	−0.0378473	−	0.0378473i
$963$	78.3703	−	78.3703i	0.0813814	−	0.0813814i
$964$		−	697.462i		−	0.723508i
$965$	599.278	+	671.567i	0.621013	+	0.695925i
$966$	257.814			0.266889
$967$	317.651	+	317.651i	0.328491	+	0.328491i	0.852013	−	0.523521i	$-0.175382\pi$
$967$	317.651	+	317.651i	0.328491	+	0.328491i	−0.523521	+	0.852013i	$0.675382\pi$
$968$	697.574	−	697.574i	0.720635	−	0.720635i
$969$		−	553.222i		−	0.570920i
$970$	894.695	+	50.8929i	0.922366	+	0.0524669i
$971$	−1018.91			−1.04934			−0.524672	−	0.851305i	$-0.675812\pi$
$971$	−1018.91			−1.04934			−0.524672	+	0.851305i	$0.675812\pi$
$972$	−107.494	−	107.494i	−0.110591	−	0.110591i
$973$	−305.569	+	305.569i	−0.314048	+	0.314048i
$974$		−	746.886i		−	0.766824i
$975$	5.87517	−	51.4755i	0.00602581	−	0.0527954i
$976$	−5.61348			−0.00575152
$977$	−604.405	−	604.405i	−0.618634	−	0.618634i	0.326547	−	0.945181i	$-0.394115\pi$
$977$	−604.405	−	604.405i	−0.618634	−	0.618634i	−0.945181	+	0.326547i	$0.894115\pi$
$978$	−829.334	+	829.334i	−0.847990	+	0.847990i
$979$			783.185i			0.799984i
$980$	−80.4561	+	1414.41i	−0.0820980	+	1.44328i
$981$	5.20489			0.00530570
$982$	−253.834	−	253.834i	−0.258487	−	0.258487i
$983$	−579.674	+	579.674i	−0.589699	+	0.589699i	−0.937550	−	0.347851i	$-0.886912\pi$
$983$	−579.674	+	579.674i	−0.589699	+	0.589699i	0.347851	+	0.937550i	$0.386912\pi$
$984$			267.009i			0.271351i
$985$	−709.591	+	633.208i	−0.720396	+	0.642851i
$986$	567.191			0.575244
$987$	74.1278	+	74.1278i	0.0751042	+	0.0751042i
$988$	7.99849	−	7.99849i	0.00809564	−	0.00809564i
$989$			223.105i			0.225586i
$990$	−145.071	−	162.571i	−0.146537	−	0.164213i
$991$	−455.864			−0.460004			−0.230002	−	0.973190i	$-0.573873\pi$
$991$	−455.864			−0.460004			−0.230002	+	0.973190i	$0.573873\pi$
$992$	−55.3827	−	55.3827i	−0.0558294	−	0.0558294i
$993$	1066.08	−	1066.08i	1.07359	−	1.07359i
$994$			1106.07i			1.11274i
$995$	862.673	+	49.0714i	0.867008	+	0.0493180i
$996$	−481.093			−0.483025
$997$	71.4972	+	71.4972i	0.0717123	+	0.0717123i	0.742053	−	0.670341i	$-0.233852\pi$
$997$	71.4972	+	71.4972i	0.0717123	+	0.0717123i	−0.670341	+	0.742053i	$0.733852\pi$
$998$	−482.367	+	482.367i	−0.483334	+	0.483334i
$999$		−	1387.55i		−	1.38894i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.f.a.47.8	✓	20
5.3	odd	4	inner	230.3.f.a.93.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.a.47.8	✓	20	1.1	even	1	trivial
230.3.f.a.93.8	yes	20	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.94658 - 1.94658i) q^{3} +2.00000i q^{4} +(0.283956 - 4.99193i) q^{5} -3.89316 q^{6} +(9.76397 + 9.76397i) q^{7} +(2.00000 - 2.00000i) q^{8} +1.42166i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.94658 - 1.94658i) q^{3} +2.00000i q^{4} +(0.283956 - 4.99193i) q^{5} -3.89316 q^{6} +(9.76397 + 9.76397i) q^{7} +(2.00000 - 2.00000i) q^{8} +1.42166i q^{9} +(-5.27589 + 4.70797i) q^{10} +21.6746 q^{11} +(3.89316 + 3.89316i) q^{12} +(-0.532316 + 0.532316i) q^{13} -19.5279i q^{14} +(-9.16444 - 10.2699i) q^{15} -4.00000 q^{16} +(-18.9142 - 18.9142i) q^{17} +(1.42166 - 1.42166i) q^{18} +7.51292i q^{19} +(9.98386 + 0.567911i) q^{20} +38.0127 q^{21} +(-21.6746 - 21.6746i) q^{22} +(-3.39116 + 3.39116i) q^{23} -7.78631i q^{24} +(-24.8387 - 2.83497i) q^{25} +1.06463 q^{26} +(20.2866 + 20.2866i) q^{27} +(-19.5279 + 19.5279i) q^{28} -14.9938i q^{29} +(-1.10548 + 19.4344i) q^{30} -13.8457 q^{31} +(4.00000 + 4.00000i) q^{32} +(42.1913 - 42.1913i) q^{33} +37.8285i q^{34} +(51.5136 - 45.9685i) q^{35} -2.84333 q^{36} +(-34.1988 - 34.1988i) q^{37} +(7.51292 - 7.51292i) q^{38} +2.07239i q^{39} +(-9.41595 - 10.5518i) q^{40} -34.2921 q^{41} +(-38.0127 - 38.0127i) q^{42} +(32.8950 - 32.8950i) q^{43} +43.3491i q^{44} +(7.09685 + 0.403689i) q^{45} +6.78233 q^{46} +(1.95008 + 1.95008i) q^{47} +(-7.78631 + 7.78631i) q^{48} +141.670i q^{49} +(22.0038 + 27.6737i) q^{50} -73.6361 q^{51} +(-1.06463 - 1.06463i) q^{52} +(29.3946 - 29.3946i) q^{53} -40.5732i q^{54} +(6.15462 - 108.198i) q^{55} +39.0559 q^{56} +(14.6245 + 14.6245i) q^{57} +(-14.9938 + 14.9938i) q^{58} +36.8175i q^{59} +(20.5399 - 18.3289i) q^{60} +1.40337 q^{61} +(13.8457 + 13.8457i) q^{62} +(-13.8811 + 13.8811i) q^{63} -8.00000i q^{64} +(2.50613 + 2.80844i) q^{65} -84.3825 q^{66} +(15.7465 + 15.7465i) q^{67} +(37.8285 - 37.8285i) q^{68} +13.2023i q^{69} +(-97.4821 - 5.54507i) q^{70} -56.6402 q^{71} +(2.84333 + 2.84333i) q^{72} +(8.98250 - 8.98250i) q^{73} +68.3976i q^{74} +(-53.8691 + 42.8321i) q^{75} -15.0258 q^{76} +(211.630 + 211.630i) q^{77} +(2.07239 - 2.07239i) q^{78} +78.8377i q^{79} +(-1.13582 + 19.9677i) q^{80} +66.1839 q^{81} +(34.2921 + 34.2921i) q^{82} +(-61.7870 + 61.7870i) q^{83} +76.0253i q^{84} +(-99.7893 + 89.0477i) q^{85} -65.7900 q^{86} +(-29.1865 - 29.1865i) q^{87} +(43.3491 - 43.3491i) q^{88} +36.1338i q^{89} +(-6.69316 - 7.50053i) q^{90} -10.3950 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-26.9517 + 26.9517i) q^{93} -3.90016i q^{94} +(37.5040 + 2.13334i) q^{95} +15.5726 q^{96} +(-89.6141 - 89.6141i) q^{97} +(141.670 - 141.670i) q^{98} +30.8139i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8}+O(q^{10}) \) 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8	\( 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8} + 4 q^{10} + 56 q^{11} - 4 q^{13} - 48 q^{15} - 80 q^{16} - 72 q^{17} - 28 q^{18} - 16 q^{20} + 8 q^{21} - 56 q^{22} + 36 q^{25} + 8 q^{26} + 156 q^{27} - 16 q^{28} + 84 q^{30} - 212 q^{31} + 80 q^{32} - 100 q^{33} + 56 q^{36} + 72 q^{37} + 88 q^{38} + 24 q^{40} - 12 q^{41} - 8 q^{42} + 120 q^{43} - 32 q^{45} + 8 q^{47} - 28 q^{50} + 64 q^{51} - 8 q^{52} - 244 q^{53} + 68 q^{55} + 32 q^{56} - 384 q^{57} - 188 q^{58} - 72 q^{60} + 328 q^{61} + 212 q^{62} + 172 q^{63} + 20 q^{65} + 200 q^{66} + 56 q^{67} + 144 q^{68} - 28 q^{70} - 92 q^{71} - 56 q^{72} + 144 q^{73} - 124 q^{75} - 176 q^{76} + 292 q^{77} - 208 q^{78} - 16 q^{80} - 84 q^{81} + 12 q^{82} - 72 q^{83} - 20 q^{85} - 240 q^{86} - 208 q^{87} + 112 q^{88} - 56 q^{90} - 192 q^{91} + 256 q^{93} - 96 q^{95} - 276 q^{97} + 104 q^{98}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8 + 4 * q^10 + 56 * q^11 - 4 * q^13 - 48 * q^15 - 80 * q^16 - 72 * q^17 - 28 * q^18 - 16 * q^20 + 8 * q^21 - 56 * q^22 + 36 * q^25 + 8 * q^26 + 156 * q^27 - 16 * q^28 + 84 * q^30 - 212 * q^31 + 80 * q^32 - 100 * q^33 + 56 * q^36 + 72 * q^37 + 88 * q^38 + 24 * q^40 - 12 * q^41 - 8 * q^42 + 120 * q^43 - 32 * q^45 + 8 * q^47 - 28 * q^50 + 64 * q^51 - 8 * q^52 - 244 * q^53 + 68 * q^55 + 32 * q^56 - 384 * q^57 - 188 * q^58 - 72 * q^60 + 328 * q^61 + 212 * q^62 + 172 * q^63 + 20 * q^65 + 200 * q^66 + 56 * q^67 + 144 * q^68 - 28 * q^70 - 92 * q^71 - 56 * q^72 + 144 * q^73 - 124 * q^75 - 176 * q^76 + 292 * q^77 - 208 * q^78 - 16 * q^80 - 84 * q^81 + 12 * q^82 - 72 * q^83 - 20 * q^85 - 240 * q^86 - 208 * q^87 + 112 * q^88 - 56 * q^90 - 192 * q^91 + 256 * q^93 - 96 * q^95 - 276 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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