LMFDB - Embedded newform 230.3.f.b.47.12

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:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.12
Character	$\chi$	$=$	230.47
Dual form			230.3.f.b.93.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(4.03568 - 4.03568i) q^{3} +2.00000i q^{4} +(-1.56820 - 4.74771i) q^{5} +8.07136 q^{6} +(6.17013 + 6.17013i) q^{7} +(-2.00000 + 2.00000i) q^{8} -23.5735i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(4.03568 - 4.03568i) q^{3} +2.00000i q^{4} +(-1.56820 - 4.74771i) q^{5} +8.07136 q^{6} +(6.17013 + 6.17013i) q^{7} +(-2.00000 + 2.00000i) q^{8} -23.5735i q^{9} +(3.17952 - 6.31591i) q^{10} -0.724813 q^{11} +(8.07136 + 8.07136i) q^{12} +(-8.24673 + 8.24673i) q^{13} +12.3403i q^{14} +(-25.4890 - 12.8315i) q^{15} -4.00000 q^{16} +(12.1461 + 12.1461i) q^{17} +(23.5735 - 23.5735i) q^{18} -25.7326i q^{19} +(9.49542 - 3.13639i) q^{20} +49.8013 q^{21} +(-0.724813 - 0.724813i) q^{22} +(3.39116 - 3.39116i) q^{23} +16.1427i q^{24} +(-20.0815 + 14.8907i) q^{25} -16.4935 q^{26} +(-58.8138 - 58.8138i) q^{27} +(-12.3403 + 12.3403i) q^{28} +44.6652i q^{29} +(-12.6575 - 38.3205i) q^{30} -21.4180 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-2.92511 + 2.92511i) q^{33} +24.2922i q^{34} +(19.6180 - 38.9699i) q^{35} +47.1469 q^{36} +(-6.02016 - 6.02016i) q^{37} +(25.7326 - 25.7326i) q^{38} +66.5623i q^{39} +(12.6318 + 6.35903i) q^{40} +62.9812 q^{41} +(49.8013 + 49.8013i) q^{42} +(-22.3539 + 22.3539i) q^{43} -1.44963i q^{44} +(-111.920 + 36.9678i) q^{45} +6.78233 q^{46} +(59.0982 + 59.0982i) q^{47} +(-16.1427 + 16.1427i) q^{48} +27.1409i q^{49} +(-34.9722 - 5.19084i) q^{50} +98.0355 q^{51} +(-16.4935 - 16.4935i) q^{52} +(-23.4423 + 23.4423i) q^{53} -117.628i q^{54} +(1.13665 + 3.44120i) q^{55} -24.6805 q^{56} +(-103.849 - 103.849i) q^{57} +(-44.6652 + 44.6652i) q^{58} +65.3535i q^{59} +(25.6630 - 50.9780i) q^{60} +4.47673 q^{61} +(-21.4180 - 21.4180i) q^{62} +(145.451 - 145.451i) q^{63} -8.00000i q^{64} +(52.0856 + 26.2206i) q^{65} -5.85023 q^{66} +(3.14266 + 3.14266i) q^{67} +(-24.2922 + 24.2922i) q^{68} -27.3713i q^{69} +(58.5879 - 19.3519i) q^{70} -116.389 q^{71} +(47.1469 + 47.1469i) q^{72} +(-23.6714 + 23.6714i) q^{73} -12.0403i q^{74} +(-20.9486 + 141.137i) q^{75} +51.4652 q^{76} +(-4.47218 - 4.47218i) q^{77} +(-66.5623 + 66.5623i) q^{78} -35.5924i q^{79} +(6.27278 + 18.9908i) q^{80} -262.547 q^{81} +(62.9812 + 62.9812i) q^{82} +(24.3664 - 24.3664i) q^{83} +99.6026i q^{84} +(38.6187 - 76.7136i) q^{85} -44.7078 q^{86} +(180.254 + 180.254i) q^{87} +(1.44963 - 1.44963i) q^{88} -95.7824i q^{89} +(-148.888 - 74.9522i) q^{90} -101.767 q^{91} +(6.78233 + 6.78233i) q^{92} +(-86.4361 + 86.4361i) q^{93} +118.196i q^{94} +(-122.171 + 40.3537i) q^{95} -32.2855 q^{96} +(-33.7217 - 33.7217i) q^{97} +(-27.1409 + 27.1409i) q^{98} +17.0863i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8}+O(q^{10}) $ 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8	$ 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8} + 16 q^{10} - 8 q^{11} - 24 q^{13} - 24 q^{15} - 96 q^{16} - 12 q^{17} + 88 q^{18} + 24 q^{20} - 24 q^{21} - 8 q^{22} - 48 q^{25} - 48 q^{26} + 60 q^{27} - 16 q^{28} + 12 q^{30} + 12 q^{31} - 96 q^{32} + 92 q^{33} + 48 q^{35} + 176 q^{36} - 100 q^{37} + 56 q^{38} + 16 q^{40} + 116 q^{41} - 24 q^{42} - 120 q^{43} - 204 q^{45} + 56 q^{47} - 104 q^{50} + 176 q^{51} - 48 q^{52} - 192 q^{53} + 180 q^{55} - 32 q^{56} + 28 q^{58} + 72 q^{60} - 152 q^{61} + 12 q^{62} + 364 q^{63} + 40 q^{65} + 184 q^{66} + 72 q^{67} + 24 q^{68} - 100 q^{70} - 28 q^{71} + 176 q^{72} - 364 q^{73} + 276 q^{75} + 112 q^{76} - 92 q^{77} - 32 q^{78} - 16 q^{80} - 440 q^{81} + 116 q^{82} + 360 q^{83} + 232 q^{85} - 240 q^{86} + 176 q^{87} + 16 q^{88} - 84 q^{90} - 432 q^{91} + 192 q^{93} + 144 q^{95} - 432 q^{97} - 484 q^{98}+O(q^{100}) $ 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8 + 16 * q^10 - 8 * q^11 - 24 * q^13 - 24 * q^15 - 96 * q^16 - 12 * q^17 + 88 * q^18 + 24 * q^20 - 24 * q^21 - 8 * q^22 - 48 * q^25 - 48 * q^26 + 60 * q^27 - 16 * q^28 + 12 * q^30 + 12 * q^31 - 96 * q^32 + 92 * q^33 + 48 * q^35 + 176 * q^36 - 100 * q^37 + 56 * q^38 + 16 * q^40 + 116 * q^41 - 24 * q^42 - 120 * q^43 - 204 * q^45 + 56 * q^47 - 104 * q^50 + 176 * q^51 - 48 * q^52 - 192 * q^53 + 180 * q^55 - 32 * q^56 + 28 * q^58 + 72 * q^60 - 152 * q^61 + 12 * q^62 + 364 * q^63 + 40 * q^65 + 184 * q^66 + 72 * q^67 + 24 * q^68 - 100 * q^70 - 28 * q^71 + 176 * q^72 - 364 * q^73 + 276 * q^75 + 112 * q^76 - 92 * q^77 - 32 * q^78 - 16 * q^80 - 440 * q^81 + 116 * q^82 + 360 * q^83 + 232 * q^85 - 240 * q^86 + 176 * q^87 + 16 * q^88 - 84 * q^90 - 432 * q^91 + 192 * q^93 + 144 * q^95 - 432 * q^97 - 484 * 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
$3$	4.03568	−	4.03568i	1.34523	−	1.34523i	0.454460	−	0.890767i	$-0.349832\pi$
$3$	4.03568	−	4.03568i	1.34523	−	1.34523i	0.890767	−	0.454460i	$-0.150168\pi$
$4$			2.00000i			0.500000i
$5$	−1.56820	−	4.74771i	−0.313639	−	0.949542i
$5$	−1.56820	−	4.74771i	−0.313639	−	0.949542i
$6$	8.07136			1.34523
$7$	6.17013	+	6.17013i	0.881447	+	0.881447i	0.993682	−	0.112235i	$-0.0358010\pi$
$7$	6.17013	+	6.17013i	0.881447	+	0.881447i	−0.112235	+	0.993682i	$0.535801\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	23.5735i		−	2.61927i
$10$	3.17952	−	6.31591i	0.317952	−	0.631591i
$11$	−0.724813			−0.0658920			−0.0329460	−	0.999457i	$-0.510489\pi$
$11$	−0.724813			−0.0658920			−0.0329460	+	0.999457i	$0.510489\pi$
$12$	8.07136	+	8.07136i	0.672614	+	0.672614i
$13$	−8.24673	+	8.24673i	−0.634364	+	0.634364i	−0.949159	−	0.314796i	$-0.898064\pi$
$13$	−8.24673	+	8.24673i	−0.634364	+	0.634364i	0.314796	+	0.949159i	$0.398064\pi$
$14$			12.3403i			0.881447i
$15$	−25.4890	−	12.8315i	−1.69927	−	0.855434i
$16$	−4.00000			−0.250000
$17$	12.1461	+	12.1461i	0.714476	+	0.714476i	0.967468	−	0.252993i	$-0.0814148\pi$
$17$	12.1461	+	12.1461i	0.714476	+	0.714476i	−0.252993	+	0.967468i	$0.581415\pi$
$18$	23.5735	−	23.5735i	1.30964	−	1.30964i
$19$		−	25.7326i		−	1.35435i	−0.735824	−	0.677173i	$-0.763205\pi$
$19$		−	25.7326i		−	1.35435i	0.735824	−	0.677173i	$-0.236795\pi$
$20$	9.49542	−	3.13639i	0.474771	−	0.156820i
$21$	49.8013			2.37149
$22$	−0.724813	−	0.724813i	−0.0329460	−	0.0329460i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$24$			16.1427i			0.672614i
$25$	−20.0815	+	14.8907i	−0.803261	+	0.595627i
$26$	−16.4935			−0.634364
$27$	−58.8138	−	58.8138i	−2.17829	−	2.17829i
$28$	−12.3403	+	12.3403i	−0.440723	+	0.440723i
$29$			44.6652i			1.54018i	0.637936	+	0.770089i	$0.279788\pi$
$29$			44.6652i			1.54018i	−0.637936	+	0.770089i	$0.720212\pi$
$30$	−12.6575	−	38.3205i	−0.421916	−	1.27735i
$31$	−21.4180			−0.690902			−0.345451	−	0.938437i	$-0.612274\pi$
$31$	−21.4180			−0.690902			−0.345451	+	0.938437i	$0.612274\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−2.92511	+	2.92511i	−0.0886398	+	0.0886398i
$34$			24.2922i			0.714476i
$35$	19.6180	−	38.9699i	0.560515	−	1.11343i
$36$	47.1469			1.30964
$37$	−6.02016	−	6.02016i	−0.162707	−	0.162707i	0.621058	−	0.783765i	$-0.286703\pi$
$37$	−6.02016	−	6.02016i	−0.162707	−	0.162707i	−0.783765	+	0.621058i	$0.786703\pi$
$38$	25.7326	−	25.7326i	0.677173	−	0.677173i
$39$			66.5623i			1.70673i
$40$	12.6318	+	6.35903i	0.315795	+	0.158976i
$41$	62.9812			1.53613			0.768064	−	0.640374i	$-0.221220\pi$
$41$	62.9812			1.53613			0.768064	+	0.640374i	$0.221220\pi$
$42$	49.8013	+	49.8013i	1.18575	+	1.18575i
$43$	−22.3539	+	22.3539i	−0.519859	+	0.519859i	−0.917529	−	0.397670i	$-0.869819\pi$
$43$	−22.3539	+	22.3539i	−0.519859	+	0.519859i	0.397670	+	0.917529i	$0.369819\pi$
$44$		−	1.44963i		−	0.0329460i
$45$	−111.920	+	36.9678i	−2.48711	+	0.821506i
$46$	6.78233			0.147442
$47$	59.0982	+	59.0982i	1.25741	+	1.25741i	0.952326	+	0.305084i	$0.0986844\pi$
$47$	59.0982	+	59.0982i	1.25741	+	1.25741i	0.305084	+	0.952326i	$0.401316\pi$
$48$	−16.1427	+	16.1427i	−0.336307	+	0.336307i
$49$			27.1409i			0.553896i
$50$	−34.9722	−	5.19084i	−0.699444	−	0.103817i
$51$	98.0355			1.92226
$52$	−16.4935	−	16.4935i	−0.317182	−	0.317182i
$53$	−23.4423	+	23.4423i	−0.442307	+	0.442307i	−0.892787	−	0.450480i	$-0.851253\pi$
$53$	−23.4423	+	23.4423i	−0.442307	+	0.442307i	0.450480	+	0.892787i	$0.351253\pi$
$54$		−	117.628i		−	2.17829i
$55$	1.13665	+	3.44120i	0.0206663	+	0.0625673i
$56$	−24.6805			−0.440723
$57$	−103.849	−	103.849i	−1.82190	−	1.82190i
$58$	−44.6652	+	44.6652i	−0.770089	+	0.770089i
$59$			65.3535i			1.10769i	0.832621	+	0.553843i	$0.186839\pi$
$59$			65.3535i			1.10769i	−0.832621	+	0.553843i	$0.813161\pi$
$60$	25.6630	−	50.9780i	0.427717	−	0.849633i
$61$	4.47673			0.0733890			0.0366945	−	0.999327i	$-0.488317\pi$
$61$	4.47673			0.0733890			0.0366945	+	0.999327i	$0.488317\pi$
$62$	−21.4180	−	21.4180i	−0.345451	−	0.345451i
$63$	145.451	−	145.451i	2.30875	−	2.30875i
$64$		−	8.00000i		−	0.125000i
$65$	52.0856	+	26.2206i	0.801316	+	0.403394i
$66$	−5.85023			−0.0886398
$67$	3.14266	+	3.14266i	0.0469053	+	0.0469053i	0.730170	−	0.683265i	$-0.239441\pi$
$67$	3.14266	+	3.14266i	0.0469053	+	0.0469053i	−0.683265	+	0.730170i	$0.739441\pi$
$68$	−24.2922	+	24.2922i	−0.357238	+	0.357238i
$69$		−	27.3713i		−	0.396686i
$70$	58.5879	−	19.3519i	0.836971	−	0.276456i
$71$	−116.389			−1.63928			−0.819641	−	0.572878i	$-0.805827\pi$
$71$	−116.389			−1.63928			−0.819641	+	0.572878i	$0.805827\pi$
$72$	47.1469	+	47.1469i	0.654818	+	0.654818i
$73$	−23.6714	+	23.6714i	−0.324266	+	0.324266i	−0.850401	−	0.526135i	$-0.823641\pi$
$73$	−23.6714	+	23.6714i	−0.324266	+	0.324266i	0.526135	+	0.850401i	$0.323641\pi$
$74$		−	12.0403i		−	0.162707i
$75$	−20.9486	+	141.137i	−0.279315	+	1.88182i
$76$	51.4652			0.677173
$77$	−4.47218	−	4.47218i	−0.0580803	−	0.0580803i
$78$	−66.5623	+	66.5623i	−0.853363	+	0.853363i
$79$		−	35.5924i		−	0.450536i	−0.974297	−	0.225268i	$-0.927674\pi$
$79$		−	35.5924i		−	0.450536i	0.974297	−	0.225268i	$-0.0723258\pi$
$80$	6.27278	+	18.9908i	0.0784098	+	0.237386i
$81$	−262.547			−3.24132
$82$	62.9812	+	62.9812i	0.768064	+	0.768064i
$83$	24.3664	−	24.3664i	0.293572	−	0.293572i	−0.544918	−	0.838489i	$-0.683439\pi$
$83$	24.3664	−	24.3664i	0.293572	−	0.293572i	0.838489	+	0.544918i	$0.183439\pi$
$84$			99.6026i			1.18575i
$85$	38.6187	−	76.7136i	0.454337	−	0.902512i
$86$	−44.7078			−0.519859
$87$	180.254	+	180.254i	2.07189	+	2.07189i
$88$	1.44963	−	1.44963i	0.0164730	−	0.0164730i
$89$		−	95.7824i		−	1.07621i	−0.842879	−	0.538103i	$-0.819141\pi$
$89$		−	95.7824i		−	1.07621i	0.842879	−	0.538103i	$-0.180859\pi$
$90$	−148.888	−	74.9522i	−1.65431	−	0.832802i
$91$	−101.767			−1.11832
$92$	6.78233	+	6.78233i	0.0737210	+	0.0737210i
$93$	−86.4361	+	86.4361i	−0.929420	+	0.929420i
$94$			118.196i			1.25741i
$95$	−122.171	+	40.3537i	−1.28601	+	0.424776i
$96$	−32.2855			−0.336307
$97$	−33.7217	−	33.7217i	−0.347647	−	0.347647i	0.511586	−	0.859232i	$-0.329058\pi$
$97$	−33.7217	−	33.7217i	−0.347647	−	0.347647i	−0.859232	+	0.511586i	$0.829058\pi$
$98$	−27.1409	+	27.1409i	−0.276948	+	0.276948i
$99$			17.0863i			0.172589i
$100$	−29.7814	−	40.1630i	−0.297814	−	0.401630i
$101$	−42.9802			−0.425546			−0.212773	−	0.977102i	$-0.568250\pi$
$101$	−42.9802			−0.425546			−0.212773	+	0.977102i	$0.568250\pi$
$102$	98.0355	+	98.0355i	0.961132	+	0.961132i
$103$	98.6987	−	98.6987i	0.958240	−	0.958240i	−0.0409228	−	0.999162i	$-0.513030\pi$
$103$	98.6987	−	98.6987i	0.958240	−	0.958240i	0.999162	+	0.0409228i	$0.0130298\pi$
$104$		−	32.9869i		−	0.317182i
$105$	−78.0982	−	236.442i	−0.743793	−	2.25183i
$106$	−46.8845			−0.442307
$107$	−120.750	−	120.750i	−1.12851	−	1.12851i	−0.990420	−	0.138086i	$-0.955905\pi$
$107$	−120.750	−	120.750i	−1.12851	−	1.12851i	−0.138086	−	0.990420i	$-0.544095\pi$
$108$	117.628	−	117.628i	1.08914	−	1.08914i
$109$		−	131.422i		−	1.20571i	−0.797851	−	0.602854i	$-0.794030\pi$
$109$		−	131.422i		−	1.20571i	0.797851	−	0.602854i	$-0.205970\pi$
$110$	−2.30455	+	4.57785i	−0.0209505	+	0.0416168i
$111$	−48.5909			−0.437756
$112$	−24.6805	−	24.6805i	−0.220362	−	0.220362i
$113$	−31.8364	+	31.8364i	−0.281738	+	0.281738i	−0.833802	−	0.552064i	$-0.813840\pi$
$113$	−31.8364	+	31.8364i	−0.281738	+	0.281738i	0.552064	+	0.833802i	$0.313840\pi$
$114$		−	207.697i		−	1.82190i
$115$	−21.4183	−	10.7823i	−0.186246	−	0.0937588i
$116$	−89.3304			−0.770089
$117$	194.404	+	194.404i	1.66157	+	1.66157i
$118$	−65.3535	+	65.3535i	−0.553843	+	0.553843i
$119$			149.886i			1.25954i
$120$	76.6410	−	25.3150i	0.638675	−	0.210958i
$121$	−120.475			−0.995658
$122$	4.47673	+	4.47673i	0.0366945	+	0.0366945i
$123$	254.172	−	254.172i	2.06644	−	2.06644i
$124$		−	42.8359i		−	0.345451i
$125$	102.188	+	71.9898i	0.817507	+	0.575918i
$126$	290.902			2.30875
$127$	105.932	+	105.932i	0.834113	+	0.834113i	0.988077	−	0.153964i	$-0.0492038\pi$
$127$	105.932	+	105.932i	0.834113	+	0.834113i	−0.153964	+	0.988077i	$0.549204\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$			180.427i			1.39866i
$130$	25.8650	+	78.3062i	0.198961	+	0.602355i
$131$	−28.6777			−0.218913			−0.109457	−	0.993992i	$-0.534911\pi$
$131$	−28.6777			−0.218913			−0.109457	+	0.993992i	$0.534911\pi$
$132$	−5.85023	−	5.85023i	−0.0443199	−	0.0443199i
$133$	158.773	−	158.773i	1.19378	−	1.19378i
$134$			6.28531i			0.0469053i
$135$	−186.999	+	371.463i	−1.38518	+	2.75157i
$136$	−48.5843			−0.357238
$137$	51.4865	+	51.4865i	0.375814	+	0.375814i	0.869589	−	0.493775i	$-0.164384\pi$
$137$	51.4865	+	51.4865i	0.375814	+	0.375814i	−0.493775	+	0.869589i	$0.664384\pi$
$138$	27.3713	−	27.3713i	0.198343	−	0.198343i
$139$		−	19.6365i		−	0.141270i	−0.997502	−	0.0706348i	$-0.977498\pi$
$139$		−	19.6365i		−	0.141270i	0.997502	−	0.0706348i	$-0.0225025\pi$
$140$	77.9399	+	39.2360i	0.556713	+	0.280257i
$141$	477.003			3.38300
$142$	−116.389	−	116.389i	−0.819641	−	0.819641i
$143$	5.97733	−	5.97733i	0.0417995	−	0.0417995i
$144$			94.2938i			0.654818i
$145$	212.057	−	70.0437i	1.46246	−	0.483060i
$146$	−47.3429			−0.324266
$147$	109.532	+	109.532i	0.745116	+	0.745116i
$148$	12.0403	−	12.0403i	0.0813536	−	0.0813536i
$149$			1.97762i			0.0132726i	0.999978	+	0.00663632i	$0.00211242\pi$
$149$			1.97762i			0.0132726i	−0.999978	+	0.00663632i	$0.997888\pi$
$150$	−162.085	+	120.188i	−1.08057	+	0.801254i
$151$	−2.68828			−0.0178032			−0.00890160	−	0.999960i	$-0.502834\pi$
$151$	−2.68828			−0.0178032			−0.00890160	+	0.999960i	$0.502834\pi$
$152$	51.4652	+	51.4652i	0.338587	+	0.338587i
$153$	286.325	−	286.325i	1.87141	−	1.87141i
$154$		−	8.94437i		−	0.0580803i
$155$	33.5876	+	101.686i	0.216694	+	0.656041i
$156$	−133.125			−0.853363
$157$	−168.859	−	168.859i	−1.07554	−	1.07554i	−0.996904	−	0.0786313i	$-0.974945\pi$
$157$	−168.859	−	168.859i	−1.07554	−	1.07554i	−0.0786313	−	0.996904i	$-0.525055\pi$
$158$	35.5924	−	35.5924i	0.225268	−	0.225268i
$159$			189.211i			1.19001i
$160$	−12.7181	+	25.2636i	−0.0794879	+	0.157898i
$161$	41.8478			0.259924
$162$	−262.547	−	262.547i	−1.62066	−	1.62066i
$163$	162.141	−	162.141i	0.994728	−	0.994728i	−0.00525769	−	0.999986i	$-0.501674\pi$
$163$	162.141	−	162.141i	0.994728	−	0.994728i	0.999986	+	0.00525769i	$0.00167358\pi$
$164$			125.962i			0.768064i
$165$	18.4747	+	9.30044i	0.111968	+	0.0563663i
$166$	48.7329			0.293572
$167$	−32.6312	−	32.6312i	−0.195397	−	0.195397i	0.602627	−	0.798023i	$-0.294121\pi$
$167$	−32.6312	−	32.6312i	−0.195397	−	0.195397i	−0.798023	+	0.602627i	$0.794121\pi$
$168$	−99.6026	+	99.6026i	−0.592873	+	0.592873i
$169$			32.9829i			0.195165i
$170$	115.332	−	38.0949i	0.678425	−	0.224088i
$171$	−606.606			−3.54740
$172$	−44.7078	−	44.7078i	−0.259929	−	0.259929i
$173$	92.0321	−	92.0321i	0.531977	−	0.531977i	−0.389183	−	0.921160i	$-0.627243\pi$
$173$	92.0321	−	92.0321i	0.531977	−	0.531977i	0.921160	+	0.389183i	$0.127243\pi$
$174$			360.509i			2.07189i
$175$	−215.783	−	32.0282i	−1.23305	−	0.183018i
$176$	2.89925			0.0164730
$177$	263.746	+	263.746i	1.49009	+	1.49009i
$178$	95.7824	−	95.7824i	0.538103	−	0.538103i
$179$		−	253.117i		−	1.41406i	−0.707184	−	0.707030i	$-0.750035\pi$
$179$		−	253.117i		−	1.41406i	0.707184	−	0.707030i	$-0.249965\pi$
$180$	−73.9356	−	223.840i	−0.410753	−	1.24355i
$181$	17.8508			0.0986230			0.0493115	−	0.998783i	$-0.484297\pi$
$181$	17.8508			0.0986230			0.0493115	+	0.998783i	$0.484297\pi$
$182$	−101.767	−	101.767i	−0.559158	−	0.559158i
$183$	18.0667	−	18.0667i	0.0987249	−	0.0987249i
$184$			13.5647i			0.0737210i
$185$	−19.1412	+	38.0228i	−0.103466	+	0.205529i
$186$	−172.872			−0.929420
$187$	−8.80364	−	8.80364i	−0.0470783	−	0.0470783i
$188$	−118.196	+	118.196i	−0.628705	+	0.628705i
$189$		−	725.777i		−	3.84009i
$190$	−162.525	−	81.8172i	−0.855393	−	0.430617i
$191$	284.021			1.48702			0.743510	−	0.668725i	$-0.233160\pi$
$191$	284.021			1.48702			0.743510	+	0.668725i	$0.233160\pi$
$192$	−32.2855	−	32.2855i	−0.168153	−	0.168153i
$193$	86.3395	−	86.3395i	0.447355	−	0.447355i	−0.447119	−	0.894474i	$-0.647550\pi$
$193$	86.3395	−	86.3395i	0.447355	−	0.447355i	0.894474	+	0.447119i	$0.147550\pi$
$194$		−	67.4435i		−	0.347647i
$195$	316.019	−	104.383i	1.62061	−	0.535296i
$196$	−54.2818			−0.276948
$197$	−26.9977	−	26.9977i	−0.137044	−	0.137044i	0.635257	−	0.772301i	$-0.280894\pi$
$197$	−26.9977	−	26.9977i	−0.137044	−	0.137044i	−0.772301	+	0.635257i	$0.780894\pi$
$198$	−17.0863	+	17.0863i	−0.0862946	+	0.0862946i
$199$			294.774i			1.48127i	0.671905	+	0.740637i	$0.265476\pi$
$199$			294.774i			1.48127i	−0.671905	+	0.740637i	$0.734524\pi$
$200$	10.3817	−	69.9444i	0.0519084	−	0.349722i
$201$	25.3655			0.126197
$202$	−42.9802	−	42.9802i	−0.212773	−	0.212773i
$203$	−275.590	+	275.590i	−1.35759	+	1.35759i
$204$			196.071i			0.961132i
$205$	−98.7669	−	299.017i	−0.481790	−	1.45862i
$206$	197.397			0.958240
$207$	−79.9415	−	79.9415i	−0.386191	−	0.386191i
$208$	32.9869	−	32.9869i	0.158591	−	0.158591i
$209$			18.6513i			0.0892407i
$210$	158.344	−	314.541i	0.754019	−	1.49781i
$211$	9.20580			0.0436294			0.0218147	−	0.999762i	$-0.493056\pi$
$211$	9.20580			0.0436294			0.0218147	+	0.999762i	$0.493056\pi$
$212$	−46.8845	−	46.8845i	−0.221153	−	0.221153i
$213$	−469.709	+	469.709i	−2.20521	+	2.20521i
$214$		−	241.500i		−	1.12851i
$215$	141.185	+	71.0746i	0.656676	+	0.330580i
$216$	235.255			1.08914
$217$	−132.152	−	132.152i	−0.608993	−	0.608993i
$218$	131.422	−	131.422i	0.602854	−	0.602854i
$219$			191.061i			0.872424i
$220$	−6.88240	+	2.27330i	−0.0312836	+	0.0103332i
$221$	−200.331			−0.906475
$222$	−48.5909	−	48.5909i	−0.218878	−	0.218878i
$223$	−198.904	+	198.904i	−0.891948	+	0.891948i	−0.994706	−	0.102758i	$-0.967233\pi$
$223$	−198.904	+	198.904i	−0.891948	+	0.891948i	0.102758	+	0.994706i	$0.467233\pi$
$224$		−	49.3610i		−	0.220362i
$225$	351.025	+	473.391i	1.56011	+	2.10396i
$226$	−63.6728			−0.281738
$227$	176.347	+	176.347i	0.776860	+	0.776860i	0.979296	−	0.202436i	$-0.0648858\pi$
$227$	176.347	+	176.347i	0.776860	+	0.776860i	−0.202436	+	0.979296i	$0.564886\pi$
$228$	207.697	−	207.697i	0.910952	−	0.910952i
$229$		−	139.620i		−	0.609695i	−0.952401	−	0.304848i	$-0.901394\pi$
$229$		−	139.620i		−	0.609695i	0.952401	−	0.304848i	$-0.0986055\pi$
$230$	−10.6360	−	32.2005i	−0.0462436	−	0.140002i
$231$	−36.0966			−0.156262
$232$	−89.3304	−	89.3304i	−0.385045	−	0.385045i
$233$	−46.2369	+	46.2369i	−0.198441	+	0.198441i	−0.799332	−	0.600890i	$-0.794813\pi$
$233$	−46.2369	+	46.2369i	−0.198441	+	0.198441i	0.600890	+	0.799332i	$0.294813\pi$
$234$			388.808i			1.66157i
$235$	187.904	−	373.259i	0.799590	−	1.58834i
$236$	−130.707			−0.553843
$237$	−143.639	−	143.639i	−0.606074	−	0.606074i
$238$	−149.886	+	149.886i	−0.629772	+	0.629772i
$239$			298.604i			1.24939i	0.780870	+	0.624694i	$0.214776\pi$
$239$			298.604i			1.24939i	−0.780870	+	0.624694i	$0.785224\pi$
$240$	101.956	+	51.3261i	0.424816	+	0.213859i
$241$	−402.475			−1.67002			−0.835011	−	0.550233i	$-0.814539\pi$
$241$	−402.475			−1.67002			−0.835011	+	0.550233i	$0.814539\pi$
$242$	−120.475	−	120.475i	−0.497829	−	0.497829i
$243$	−530.230	+	530.230i	−2.18202	+	2.18202i
$244$			8.95346i			0.0366945i
$245$	128.857	−	42.5622i	0.525948	−	0.173723i
$246$	508.344			2.06644
$247$	212.210	+	212.210i	0.859148	+	0.859148i
$248$	42.8359	−	42.8359i	0.172726	−	0.172726i
$249$		−	196.670i		−	0.789841i
$250$	30.1986	+	174.178i	0.120795	+	0.696713i
$251$	−13.3235			−0.0530816			−0.0265408	−	0.999648i	$-0.508449\pi$
$251$	−13.3235			−0.0530816			−0.0265408	+	0.999648i	$0.508449\pi$
$252$	290.902	+	290.902i	1.15437	+	1.15437i
$253$	−2.45796	+	2.45796i	−0.00971525	+	0.00971525i
$254$			211.865i			0.834113i
$255$	−153.739	−	465.444i	−0.602897	−	1.82527i
$256$	16.0000			0.0625000
$257$	−228.386	−	228.386i	−0.888661	−	0.888661i	0.105734	−	0.994394i	$-0.466281\pi$
$257$	−228.386	−	228.386i	−0.888661	−	0.888661i	−0.994394	+	0.105734i	$0.966281\pi$
$258$	−180.427	+	180.427i	−0.699328	+	0.699328i
$259$		−	74.2903i		−	0.286835i
$260$	−52.4412	+	104.171i	−0.201697	+	0.400658i
$261$	1052.91			4.03415
$262$	−28.6777	−	28.6777i	−0.109457	−	0.109457i
$263$	315.031	−	315.031i	1.19784	−	1.19784i	0.223022	−	0.974814i	$-0.428408\pi$
$263$	315.031	−	315.031i	1.19784	−	1.19784i	0.974814	−	0.223022i	$-0.0715920\pi$
$264$		−	11.7005i		−	0.0443199i
$265$	148.059	+	74.5350i	0.558714	+	0.281264i
$266$	317.547			1.19378
$267$	−386.547	−	386.547i	−1.44774	−	1.44774i
$268$	−6.28531	+	6.28531i	−0.0234527	+	0.0234527i
$269$		−	220.576i		−	0.819986i	−0.912089	−	0.409993i	$-0.865531\pi$
$269$		−	220.576i		−	0.819986i	0.912089	−	0.409993i	$-0.134469\pi$
$270$	−558.462	+	184.463i	−2.06838	+	0.683197i
$271$	−345.263			−1.27403			−0.637017	−	0.770850i	$-0.719832\pi$
$271$	−345.263			−1.27403			−0.637017	+	0.770850i	$0.719832\pi$
$272$	−48.5843	−	48.5843i	−0.178619	−	0.178619i
$273$	−410.698	+	410.698i	−1.50439	+	1.50439i
$274$			102.973i			0.375814i
$275$	14.5553	−	10.7930i	0.0529285	−	0.0392471i
$276$	54.7426			0.198343
$277$	16.6105	+	16.6105i	0.0599656	+	0.0599656i	0.736454	−	0.676488i	$-0.236499\pi$
$277$	16.6105	+	16.6105i	0.0599656	+	0.0599656i	−0.676488	+	0.736454i	$0.736499\pi$
$278$	19.6365	−	19.6365i	0.0706348	−	0.0706348i
$279$			504.895i			1.80966i
$280$	38.7039	+	117.176i	0.138228	+	0.418485i
$281$	−40.9492			−0.145727			−0.0728633	−	0.997342i	$-0.523214\pi$
$281$	−40.9492			−0.145727			−0.0728633	+	0.997342i	$0.523214\pi$
$282$	477.003	+	477.003i	1.69150	+	1.69150i
$283$	−42.6150	+	42.6150i	−0.150583	+	0.150583i	−0.778378	−	0.627795i	$-0.783957\pi$
$283$	−42.6150	+	42.6150i	−0.150583	+	0.150583i	0.627795	+	0.778378i	$0.283957\pi$
$284$		−	232.778i		−	0.819641i
$285$	−330.188	+	655.898i	−1.15855	+	2.30140i
$286$	11.9547			0.0417995
$287$	388.602	+	388.602i	1.35401	+	1.35401i
$288$	−94.2938	+	94.2938i	−0.327409	+	0.327409i
$289$			6.05488i			0.0209512i
$290$	282.101	+	142.014i	0.972762	+	0.489702i
$291$	−272.180			−0.935328
$292$	−47.3429	−	47.3429i	−0.162133	−	0.162133i
$293$	337.952	−	337.952i	1.15342	−	1.15342i	0.167558	−	0.985862i	$-0.446412\pi$
$293$	337.952	−	337.952i	1.15342	−	1.15342i	0.985862	−	0.167558i	$-0.0535880\pi$
$294$			219.064i			0.745116i
$295$	310.280	−	102.487i	1.05180	−	0.347414i
$296$	24.0807			0.0813536
$297$	42.6290	+	42.6290i	0.143532	+	0.143532i
$298$	−1.97762	+	1.97762i	−0.00663632	+	0.00663632i
$299$			55.9320i			0.187064i
$300$	−282.273	−	41.8972i	−0.940911	−	0.139657i
$301$	−275.853			−0.916455
$302$	−2.68828	−	2.68828i	−0.00890160	−	0.00890160i
$303$	−173.454	+	173.454i	−0.572457	+	0.572457i
$304$			102.930i			0.338587i
$305$	−7.02039	−	21.2542i	−0.0230177	−	0.0696860i
$306$	572.650			1.87141
$307$	−177.271	−	177.271i	−0.577430	−	0.577430i	0.356764	−	0.934194i	$-0.383880\pi$
$307$	−177.271	−	177.271i	−0.577430	−	0.577430i	−0.934194	+	0.356764i	$0.883880\pi$
$308$	8.94437	−	8.94437i	0.0290402	−	0.0290402i
$309$		−	796.633i		−	2.57810i
$310$	−68.0988	+	135.274i	−0.219673	+	0.436367i
$311$	327.598			1.05337			0.526686	−	0.850060i	$-0.323435\pi$
$311$	327.598			1.05337			0.526686	+	0.850060i	$0.323435\pi$
$312$	−133.125	−	133.125i	−0.426682	−	0.426682i
$313$	−52.4677	+	52.4677i	−0.167628	+	0.167628i	−0.785936	−	0.618308i	$-0.787819\pi$
$313$	−52.4677	+	52.4677i	−0.167628	+	0.167628i	0.618308	+	0.785936i	$0.287819\pi$
$314$		−	337.718i		−	1.07554i
$315$	−918.656	−	462.464i	−2.91637	−	1.46814i
$316$	71.1847			0.225268
$317$	−188.054	−	188.054i	−0.593230	−	0.593230i	0.345272	−	0.938503i	$-0.387787\pi$
$317$	−188.054	−	188.054i	−0.593230	−	0.593230i	−0.938503	+	0.345272i	$0.887787\pi$
$318$	−189.211	+	189.211i	−0.595003	+	0.595003i
$319$		−	32.3739i		−	0.101486i
$320$	−37.9817	+	12.5456i	−0.118693	+	0.0392049i
$321$	−974.619			−3.03620
$322$	41.8478	+	41.8478i	0.129962	+	0.129962i
$323$	312.550	−	312.550i	0.967648	−	0.967648i
$324$		−	525.093i		−	1.62066i
$325$	42.8075	−	288.406i	0.131715	−	0.887404i
$326$	324.281			0.994728
$327$	−530.378	−	530.378i	−1.62195	−	1.62195i
$328$	−125.962	+	125.962i	−0.384032	+	0.384032i
$329$			729.287i			2.21668i
$330$	9.17430	+	27.7752i	0.0278009	+	0.0841672i
$331$	−411.903			−1.24442			−0.622211	−	0.782850i	$-0.713765\pi$
$331$	−411.903			−1.24442			−0.622211	+	0.782850i	$0.713765\pi$
$332$	48.7329	+	48.7329i	0.146786	+	0.146786i
$333$	−141.916	+	141.916i	−0.426174	+	0.426174i
$334$		−	65.2625i		−	0.195397i
$335$	9.99212	−	19.8487i	0.0298272	−	0.0592499i
$336$	−199.205			−0.592873
$337$	227.170	+	227.170i	0.674096	+	0.674096i	0.958658	−	0.284562i	$-0.0918480\pi$
$337$	227.170	+	227.170i	0.674096	+	0.674096i	−0.284562	+	0.958658i	$0.591848\pi$
$338$	−32.9829	+	32.9829i	−0.0975826	+	0.0975826i
$339$			256.963i			0.758003i
$340$	153.427	+	77.2374i	0.451256	+	0.227169i
$341$	15.5240			0.0455250
$342$	−606.606	−	606.606i	−1.77370	−	1.77370i
$343$	134.873	−	134.873i	0.393217	−	0.393217i
$344$		−	89.4157i		−	0.259929i
$345$	−129.951	+	42.9236i	−0.376670	+	0.124416i
$346$	184.064			0.531977
$347$	30.5267	+	30.5267i	0.0879731	+	0.0879731i	0.749724	−	0.661751i	$-0.230186\pi$
$347$	30.5267	+	30.5267i	0.0879731	+	0.0879731i	−0.661751	+	0.749724i	$0.730186\pi$
$348$	−360.509	+	360.509i	−1.03595	+	1.03595i
$349$			54.8757i			0.157237i	0.996905	+	0.0786185i	$0.0250509\pi$
$349$			54.8757i			0.157237i	−0.996905	+	0.0786185i	$0.974949\pi$
$350$	−183.755	−	247.811i	−0.525014	−	0.708032i
$351$	970.043			2.76366
$352$	2.89925	+	2.89925i	0.00823651	+	0.00823651i
$353$	−286.119	+	286.119i	−0.810536	+	0.810536i	−0.984714	−	0.174178i	$-0.944273\pi$
$353$	−286.119	+	286.119i	−0.810536	+	0.810536i	0.174178	+	0.984714i	$0.444273\pi$
$354$			527.492i			1.49009i
$355$	182.521	+	552.581i	0.514143	+	1.55657i
$356$	191.565			0.538103
$357$	604.891	+	604.891i	1.69437	+	1.69437i
$358$	253.117	−	253.117i	0.707030	−	0.707030i
$359$			545.919i			1.52067i	0.649533	+	0.760333i	$0.274964\pi$
$359$			545.919i			1.52067i	−0.649533	+	0.760333i	$0.725036\pi$
$360$	149.904	−	297.775i	0.416401	−	0.827154i
$361$	−301.166			−0.834255
$362$	17.8508	+	17.8508i	0.0493115	+	0.0493115i
$363$	−486.197	+	486.197i	−1.33939	+	1.33939i
$364$		−	203.533i		−	0.559158i
$365$	149.507	+	75.2637i	0.409607	+	0.206202i
$366$	36.1333			0.0987249
$367$	−99.6848	−	99.6848i	−0.271621	−	0.271621i	0.558132	−	0.829752i	$-0.311518\pi$
$367$	−99.6848	−	99.6848i	−0.271621	−	0.271621i	−0.829752	+	0.558132i	$0.811518\pi$
$368$	−13.5647	+	13.5647i	−0.0368605	+	0.0368605i
$369$		−	1484.68i		−	4.02354i
$370$	−57.1640	+	18.8816i	−0.154497	+	0.0510313i
$371$	−289.283			−0.779740
$372$	−172.872	−	172.872i	−0.464710	−	0.464710i
$373$	184.070	−	184.070i	0.493485	−	0.493485i	−0.415917	−	0.909402i	$-0.636539\pi$
$373$	184.070	−	184.070i	0.493485	−	0.493485i	0.909402	+	0.415917i	$0.136539\pi$
$374$		−	17.6073i		−	0.0470783i
$375$	702.928	−	121.872i	1.87447	−	0.324992i
$376$	−236.393			−0.628705
$377$	−368.342	−	368.342i	−0.977034	−	0.977034i
$378$	725.777	−	725.777i	1.92005	−	1.92005i
$379$		−	425.333i		−	1.12225i	−0.827731	−	0.561125i	$-0.810369\pi$
$379$		−	425.333i		−	1.12225i	0.827731	−	0.561125i	$-0.189631\pi$
$380$	−80.7075	−	244.342i	−0.212388	−	0.643005i
$381$	855.018			2.24414
$382$	284.021	+	284.021i	0.743510	+	0.743510i
$383$	−322.962	+	322.962i	−0.843244	+	0.843244i	−0.989279	−	0.146035i	$-0.953349\pi$
$383$	−322.962	+	322.962i	−0.843244	+	0.843244i	0.146035	+	0.989279i	$0.453349\pi$
$384$		−	64.5709i		−	0.168153i
$385$	−14.2194	+	28.2459i	−0.0369335	+	0.0733660i
$386$	172.679			0.447355
$387$	526.959	+	526.959i	1.36165	+	1.36165i
$388$	67.4435	−	67.4435i	0.173823	−	0.173823i
$389$			38.7279i			0.0995577i	0.998760	+	0.0497788i	$0.0158516\pi$
$389$			38.7279i			0.0995577i	−0.998760	+	0.0497788i	$0.984148\pi$
$390$	420.402	+	211.636i	1.07795	+	0.542656i
$391$	82.3788			0.210687
$392$	−54.2818	−	54.2818i	−0.138474	−	0.138474i
$393$	−115.734	+	115.734i	−0.294488	+	0.294488i
$394$		−	53.9953i		−	0.137044i
$395$	−168.982	+	55.8158i	−0.427803	+	0.141306i
$396$	−34.1727			−0.0862946
$397$	310.122	+	310.122i	0.781165	+	0.781165i	0.980027	−	0.198863i	$-0.0637248\pi$
$397$	310.122	+	310.122i	0.781165	+	0.781165i	−0.198863	+	0.980027i	$0.563725\pi$
$398$	−294.774	+	294.774i	−0.740637	+	0.740637i
$399$		−	1281.52i		−	3.21182i
$400$	80.3261	−	59.5627i	0.200815	−	0.148907i
$401$	154.599			0.385534			0.192767	−	0.981245i	$-0.438254\pi$
$401$	154.599			0.385534			0.192767	+	0.981245i	$0.438254\pi$
$402$	25.3655	+	25.3655i	0.0630983	+	0.0630983i
$403$	176.628	−	176.628i	0.438283	−	0.438283i
$404$		−	85.9604i		−	0.212773i
$405$	411.724	+	1246.50i	1.01660	+	3.07777i
$406$	−551.180			−1.35759
$407$	4.36349	+	4.36349i	0.0107211	+	0.0107211i
$408$	−196.071	+	196.071i	−0.480566	+	0.480566i
$409$			199.354i			0.487419i	0.969848	+	0.243709i	$0.0783643\pi$
$409$			199.354i			0.487419i	−0.969848	+	0.243709i	$0.921636\pi$
$410$	200.250	−	397.784i	0.488414	−	0.970204i
$411$	415.566			1.01111
$412$	197.397	+	197.397i	0.479120	+	0.479120i
$413$	−403.239	+	403.239i	−0.976366	+	0.976366i
$414$		−	159.883i		−	0.386191i
$415$	−153.896	−	77.4735i	−0.370834	−	0.186683i
$416$	65.9738			0.158591
$417$	−79.2465	−	79.2465i	−0.190040	−	0.190040i
$418$	−18.6513	+	18.6513i	−0.0446203	+	0.0446203i
$419$			508.909i			1.21458i	0.794480	+	0.607290i	$0.207743\pi$
$419$			508.909i			1.21458i	−0.794480	+	0.607290i	$0.792257\pi$
$420$	472.885	−	156.196i	1.12592	−	0.371896i
$421$	−402.703			−0.956538			−0.478269	−	0.878213i	$-0.658736\pi$
$421$	−402.703			−0.956538			−0.478269	+	0.878213i	$0.658736\pi$
$422$	9.20580	+	9.20580i	0.0218147	+	0.0218147i
$423$	1393.15	−	1393.15i	3.29350	−	3.29350i
$424$		−	93.7690i		−	0.221153i
$425$	−424.775	−	63.0485i	−0.999472	−	0.148349i
$426$	−939.418			−2.20521
$427$	27.6220	+	27.6220i	0.0646885	+	0.0646885i
$428$	241.500	−	241.500i	0.564253	−	0.564253i
$429$		−	48.2452i		−	0.112460i
$430$	70.1106	+	212.260i	0.163048	+	0.493628i
$431$	168.573			0.391120			0.195560	−	0.980692i	$-0.437348\pi$
$431$	168.573			0.391120			0.195560	+	0.980692i	$0.437348\pi$
$432$	235.255	+	235.255i	0.544572	+	0.544572i
$433$	491.359	−	491.359i	1.13478	−	1.13478i	0.145405	−	0.989372i	$-0.453551\pi$
$433$	491.359	−	491.359i	1.13478	−	1.13478i	0.989372	−	0.145405i	$-0.0464485\pi$
$434$		−	264.303i		−	0.608993i
$435$	573.122	−	1138.47i	1.31752	−	2.61717i
$436$	262.845			0.602854
$437$	−87.2634	−	87.2634i	−0.199688	−	0.199688i
$438$	−191.061	+	191.061i	−0.436212	+	0.436212i
$439$		−	112.222i		−	0.255631i	−0.991798	−	0.127816i	$-0.959203\pi$
$439$		−	112.222i		−	0.255631i	0.991798	−	0.127816i	$-0.0407966\pi$
$440$	−9.15570	−	4.60911i	−0.0208084	−	0.0104752i
$441$	639.805			1.45080
$442$	−200.331	−	200.331i	−0.453238	−	0.453238i
$443$	463.871	−	463.871i	1.04711	−	1.04711i	0.0482799	−	0.998834i	$-0.484626\pi$
$443$	463.871	−	463.871i	1.04711	−	1.04711i	0.998834	−	0.0482799i	$-0.0153739\pi$
$444$		−	97.1818i		−	0.218878i
$445$	−454.747	+	150.206i	−1.02190	+	0.337541i
$446$	−397.809			−0.891948
$447$	7.98105	+	7.98105i	0.0178547	+	0.0178547i
$448$	49.3610	−	49.3610i	0.110181	−	0.110181i
$449$			342.770i			0.763408i	0.924285	+	0.381704i	$0.124663\pi$
$449$			342.770i			0.763408i	−0.924285	+	0.381704i	$0.875337\pi$
$450$	−122.366	+	824.416i	−0.271925	+	1.83203i
$451$	−45.6496			−0.101219
$452$	−63.6728	−	63.6728i	−0.140869	−	0.140869i
$453$	−10.8491	+	10.8491i	−0.0239494	+	0.0239494i
$454$			352.694i			0.776860i
$455$	159.590	+	483.159i	0.350747	+	1.06189i
$456$	415.394			0.910952
$457$	−249.571	−	249.571i	−0.546107	−	0.546107i	0.379206	−	0.925312i	$-0.376197\pi$
$457$	−249.571	−	249.571i	−0.546107	−	0.546107i	−0.925312	+	0.379206i	$0.876197\pi$
$458$	139.620	−	139.620i	0.304848	−	0.304848i
$459$		−	1428.72i		−	3.11267i
$460$	21.5645	−	42.8366i	0.0468794	−	0.0931230i
$461$	73.6640			0.159792			0.0798959	−	0.996803i	$-0.474541\pi$
$461$	73.6640			0.159792			0.0798959	+	0.996803i	$0.474541\pi$
$462$	−36.0966	−	36.0966i	−0.0781312	−	0.0781312i
$463$	−179.579	+	179.579i	−0.387859	+	0.387859i	−0.873923	−	0.486064i	$-0.838432\pi$
$463$	−179.579	+	179.579i	−0.387859	+	0.387859i	0.486064	+	0.873923i	$0.338432\pi$
$464$		−	178.661i		−	0.385045i
$465$	545.922	+	274.825i	1.17403	+	0.591021i
$466$	−92.4737			−0.198441
$467$	13.8984	+	13.8984i	0.0297609	+	0.0297609i	0.721831	−	0.692070i	$-0.243301\pi$
$467$	13.8984	+	13.8984i	0.0297609	+	0.0297609i	−0.692070	+	0.721831i	$0.743301\pi$
$468$	−388.808	+	388.808i	−0.830786	+	0.830786i
$469$			38.7812i			0.0826891i
$470$	561.163	−	185.355i	1.19396	−	0.394373i
$471$	−1362.92			−2.89368
$472$	−130.707	−	130.707i	−0.276922	−	0.276922i
$473$	16.2024	−	16.2024i	0.0342546	−	0.0342546i
$474$		−	287.279i		−	0.606074i
$475$	383.176	+	516.750i	0.806686	+	1.08789i
$476$	−299.772			−0.629772
$477$	552.615	+	552.615i	1.15852	+	1.15852i
$478$	−298.604	+	298.604i	−0.624694	+	0.624694i
$479$			707.716i			1.47749i	0.673987	+	0.738743i	$0.264580\pi$
$479$			707.716i			1.47749i	−0.673987	+	0.738743i	$0.735420\pi$
$480$	50.6299	+	153.282i	0.105479	+	0.319338i
$481$	99.2933			0.206431
$482$	−402.475	−	402.475i	−0.835011	−	0.835011i
$483$	168.885	−	168.885i	0.349657	−	0.349657i
$484$		−	240.949i		−	0.497829i
$485$	−107.219	+	212.983i	−0.221070	+	0.439141i
$486$	−1060.46			−2.18202
$487$	128.922	+	128.922i	0.264727	+	0.264727i	0.826971	−	0.562244i	$-0.190062\pi$
$487$	128.922	+	128.922i	0.264727	+	0.264727i	−0.562244	+	0.826971i	$0.690062\pi$
$488$	−8.95346	+	8.95346i	−0.0183473	+	0.0183473i
$489$		−	1308.70i		−	2.67627i
$490$	171.419	+	86.2949i	0.349835	+	0.176112i
$491$	−195.979			−0.399142			−0.199571	−	0.979883i	$-0.563955\pi$
$491$	−195.979			−0.399142			−0.199571	+	0.979883i	$0.563955\pi$
$492$	508.344	+	508.344i	1.03322	+	1.03322i
$493$	−542.507	+	542.507i	−1.10042	+	1.10042i
$494$			424.419i			0.859148i
$495$	81.1210	−	26.7947i	0.163881	−	0.0541307i
$496$	85.6719			0.172726
$497$	−718.135	−	718.135i	−1.44494	−	1.44494i
$498$	196.670	−	196.670i	0.394921	−	0.394921i
$499$			842.473i			1.68832i	0.536089	+	0.844161i	$0.319901\pi$
$499$			842.473i			1.68832i	−0.536089	+	0.844161i	$0.680099\pi$
$500$	−143.980	+	204.377i	−0.287959	+	0.408754i
$501$	−263.379			−0.525706
$502$	−13.3235	−	13.3235i	−0.0265408	−	0.0265408i
$503$	72.0448	−	72.0448i	0.143230	−	0.143230i	−0.631856	−	0.775086i	$-0.717707\pi$
$503$	72.0448	−	72.0448i	0.143230	−	0.143230i	0.775086	+	0.631856i	$0.217707\pi$
$504$			581.805i			1.15437i
$505$	67.4013	+	204.057i	0.133468	+	0.404074i
$506$	−4.91592			−0.00971525
$507$	133.109	+	133.109i	0.262542	+	0.262542i
$508$	−211.865	+	211.865i	−0.417056	+	0.417056i
$509$			737.964i			1.44983i	0.688837	+	0.724916i	$0.258121\pi$
$509$			737.964i			1.44983i	−0.688837	+	0.724916i	$0.741879\pi$
$510$	311.705	−	619.183i	0.611187	−	1.21408i
$511$	−292.112			−0.571647
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−1513.43	+	1513.43i	−2.95016	+	2.95016i
$514$		−	456.772i		−	0.888661i
$515$	−623.372	−	313.814i	−1.21043	−	0.609348i
$516$	−360.853			−0.699328
$517$	−42.8351	−	42.8351i	−0.0828533	−	0.0828533i
$518$	74.2903	−	74.2903i	0.143418	−	0.143418i
$519$		−	742.825i		−	1.43126i
$520$	−156.612	+	51.7299i	−0.301178	+	0.0994806i
$521$	892.279			1.71263			0.856314	−	0.516456i	$-0.172749\pi$
$521$	892.279			1.71263			0.856314	+	0.516456i	$0.172749\pi$
$522$	1052.91	+	1052.91i	2.01707	+	2.01707i
$523$	−332.739	+	332.739i	−0.636213	+	0.636213i	−0.949619	−	0.313406i	$-0.898530\pi$
$523$	−332.739	+	332.739i	−0.636213	+	0.636213i	0.313406	+	0.949619i	$0.398530\pi$
$524$		−	57.3553i		−	0.109457i
$525$	−1000.09	+	741.576i	−1.90493	+	1.41252i
$526$	630.061			1.19784
$527$	−260.144	−	260.144i	−0.493633	−	0.493633i
$528$	11.7005	−	11.7005i	0.0221599	−	0.0221599i
$529$		−	23.0000i		−	0.0434783i
$530$	73.5241	+	222.594i	0.138725	+	0.419989i
$531$	1540.61			2.90133
$532$	317.547	+	317.547i	0.596892	+	0.596892i
$533$	−519.389	+	519.389i	−0.974463	+	0.974463i
$534$		−	773.094i		−	1.44774i
$535$	−383.927	+	762.647i	−0.717621	+	1.42551i
$536$	−12.5706			−0.0234527
$537$	−1021.50	−	1021.50i	−1.90223	−	1.90223i
$538$	220.576	−	220.576i	0.409993	−	0.409993i
$539$		−	19.6721i		−	0.0364973i
$540$	−742.925	−	373.999i	−1.37579	−	0.692590i
$541$	−167.411			−0.309447			−0.154724	−	0.987958i	$-0.549449\pi$
$541$	−167.411			−0.309447			−0.154724	+	0.987958i	$0.549449\pi$
$542$	−345.263	−	345.263i	−0.637017	−	0.637017i
$543$	72.0400	−	72.0400i	0.132670	−	0.132670i
$544$		−	97.1687i		−	0.178619i
$545$	−623.955	+	206.096i	−1.14487	+	0.378158i
$546$	−821.396			−1.50439
$547$	−30.6410	−	30.6410i	−0.0560165	−	0.0560165i	0.678544	−	0.734560i	$-0.262611\pi$
$547$	−30.6410	−	30.6410i	−0.0560165	−	0.0560165i	−0.734560	+	0.678544i	$0.762611\pi$
$548$	−102.973	+	102.973i	−0.187907	+	0.187907i
$549$		−	105.532i		−	0.192226i
$550$	25.3483	+	3.76239i	0.0460878	+	0.00684071i
$551$	1149.35			2.08594
$552$	54.7426	+	54.7426i	0.0991715	+	0.0991715i
$553$	219.609	−	219.609i	0.397124	−	0.397124i
$554$			33.2209i			0.0599656i
$555$	76.2001	+	230.696i	0.137297	+	0.415668i
$556$	39.2729			0.0706348
$557$	−74.7071	−	74.7071i	−0.134124	−	0.134124i	0.636857	−	0.770982i	$-0.280234\pi$
$557$	−74.7071	−	74.7071i	−0.134124	−	0.134124i	−0.770982	+	0.636857i	$0.780234\pi$
$558$	−504.895	+	504.895i	−0.904830	+	0.904830i
$559$		−	368.693i		−	0.659559i
$560$	−78.4720	+	155.880i	−0.140129	+	0.278357i
$561$	−71.0573			−0.126662
$562$	−40.9492	−	40.9492i	−0.0728633	−	0.0728633i
$563$	475.349	−	475.349i	0.844315	−	0.844315i	−0.145102	−	0.989417i	$-0.546351\pi$
$563$	475.349	−	475.349i	0.844315	−	0.844315i	0.989417	+	0.145102i	$0.0463510\pi$
$564$			954.007i			1.69150i
$565$	201.076	+	101.224i	0.355886	+	0.179158i
$566$	−85.2299			−0.150583
$567$	−1619.95	−	1619.95i	−2.85705	−	2.85705i
$568$	232.778	−	232.778i	0.409820	−	0.409820i
$569$			470.572i			0.827016i	0.910501	+	0.413508i	$0.135697\pi$
$569$			470.572i			0.827016i	−0.910501	+	0.413508i	$0.864303\pi$
$570$	−986.086	+	325.710i	−1.72997	+	0.571420i
$571$	695.175			1.21747			0.608735	−	0.793374i	$-0.291677\pi$
$571$	695.175			1.21747			0.608735	+	0.793374i	$0.291677\pi$
$572$	11.9547	+	11.9547i	0.0208998	+	0.0208998i
$573$	1146.22	−	1146.22i	2.00038	−	2.00038i
$574$			777.204i			1.35401i
$575$	−17.6030	+	118.597i	−0.0306139	+	0.206255i
$576$	−188.588			−0.327409
$577$	136.810	+	136.810i	0.237106	+	0.237106i	0.815651	−	0.578545i	$-0.196379\pi$
$577$	136.810	+	136.810i	0.237106	+	0.237106i	−0.578545	+	0.815651i	$0.696379\pi$
$578$	−6.05488	+	6.05488i	−0.0104756	+	0.0104756i
$579$		−	696.878i		−	1.20359i
$580$	140.087	+	424.115i	0.241530	+	0.731232i
$581$	300.688			0.517535
$582$	−272.180	−	272.180i	−0.467664	−	0.467664i
$583$	16.9912	−	16.9912i	0.0291445	−	0.0291445i
$584$		−	94.6858i		−	0.162133i
$585$	618.110	−	1227.84i	1.05660	−	2.09887i
$586$	675.904			1.15342
$587$	636.514	+	636.514i	1.08435	+	1.08435i	0.996098	+	0.0882531i	$0.0281284\pi$
$587$	636.514	+	636.514i	1.08435	+	1.08435i	0.0882531	+	0.996098i	$0.471872\pi$
$588$	−219.064	+	219.064i	−0.372558	+	0.372558i
$589$			551.140i			0.935721i
$590$	412.767	+	207.792i	0.699604	+	0.352191i
$591$	−217.908			−0.368710
$592$	24.0807	+	24.0807i	0.0406768	+	0.0406768i
$593$	−541.335	+	541.335i	−0.912876	+	0.912876i	−0.996498	−	0.0836220i	$-0.973351\pi$
$593$	−541.335	+	541.335i	−0.912876	+	0.912876i	0.0836220	+	0.996498i	$0.473351\pi$
$594$			85.2580i			0.143532i
$595$	711.614	−	235.050i	1.19599	−	0.395042i
$596$	−3.95524			−0.00663632
$597$	1189.61	+	1189.61i	1.99265	+	1.99265i
$598$	−55.9320	+	55.9320i	−0.0935318	+	0.0935318i
$599$			75.3917i			0.125863i	0.998018	+	0.0629313i	$0.0200449\pi$
$599$			75.3917i			0.125863i	−0.998018	+	0.0629313i	$0.979955\pi$
$600$	−240.376	−	324.171i	−0.400627	−	0.540284i
$601$	579.293			0.963881			0.481941	−	0.876204i	$-0.339932\pi$
$601$	579.293			0.963881			0.481941	+	0.876204i	$0.339932\pi$
$602$	−275.853	−	275.853i	−0.458228	−	0.458228i
$603$	74.0833	−	74.0833i	0.122858	−	0.122858i
$604$		−	5.37657i		−	0.00890160i
$605$	188.928	+	571.979i	0.312277	+	0.945420i
$606$	−346.909			−0.572457
$607$	277.236	+	277.236i	0.456731	+	0.456731i	0.897581	−	0.440850i	$-0.145323\pi$
$607$	277.236	+	277.236i	0.456731	+	0.456731i	−0.440850	+	0.897581i	$0.645323\pi$
$608$	−102.930	+	102.930i	−0.169293	+	0.169293i
$609$			2224.39i			3.65252i
$610$	14.2338	−	28.2746i	0.0233342	−	0.0463518i
$611$	−974.734			−1.59531
$612$	572.650	+	572.650i	0.935703	+	0.935703i
$613$	686.889	−	686.889i	1.12054	−	1.12054i	0.128876	−	0.991661i	$-0.458863\pi$
$613$	686.889	−	686.889i	1.12054	−	1.12054i	0.991661	−	0.128876i	$-0.0411368\pi$
$614$		−	354.542i		−	0.577430i
$615$	−1605.33	−	808.144i	−2.61029	−	1.31406i
$616$	17.8887			0.0290402
$617$	−588.091	−	588.091i	−0.953145	−	0.953145i	0.0458050	−	0.998950i	$-0.485415\pi$
$617$	−588.091	−	588.091i	−0.953145	−	0.953145i	−0.998950	+	0.0458050i	$0.985415\pi$
$618$	796.633	−	796.633i	1.28905	−	1.28905i
$619$			510.860i			0.825298i	0.910890	+	0.412649i	$0.135396\pi$
$619$			510.860i			0.825298i	−0.910890	+	0.412649i	$0.864604\pi$
$620$	−203.373	+	67.1751i	−0.328020	+	0.108347i
$621$	−398.895			−0.642342
$622$	327.598	+	327.598i	0.526686	+	0.526686i
$623$	590.989	−	590.989i	0.948619	−	0.948619i
$624$		−	266.249i		−	0.426682i
$625$	181.535	−	598.055i	0.290456	−	0.956888i
$626$	−104.935			−0.167628
$627$	75.2707	+	75.2707i	0.120049	+	0.120049i
$628$	337.718	−	337.718i	0.537768	−	0.537768i
$629$		−	146.243i		−	0.232501i
$630$	−456.192	−	1381.12i	−0.724114	−	2.19225i
$631$	−1013.58			−1.60631			−0.803157	−	0.595768i	$-0.796848\pi$
$631$	−1013.58			−1.60631			−0.803157	+	0.595768i	$0.796848\pi$
$632$	71.1847	+	71.1847i	0.112634	+	0.112634i
$633$	37.1517	−	37.1517i	0.0586915	−	0.0586915i
$634$		−	376.108i		−	0.593230i
$635$	336.814	−	669.059i	0.530415	−	1.05364i
$636$	−378.422			−0.595003
$637$	−223.824	−	223.824i	−0.351371	−	0.351371i
$638$	32.3739	−	32.3739i	0.0507428	−	0.0507428i
$639$			2743.69i			4.29373i
$640$	−50.5273	−	25.4361i	−0.0789488	−	0.0397439i
$641$	741.895			1.15740			0.578701	−	0.815540i	$-0.303560\pi$
$641$	741.895			1.15740			0.578701	+	0.815540i	$0.303560\pi$
$642$	−974.619	−	974.619i	−1.51810	−	1.51810i
$643$	−649.933	+	649.933i	−1.01078	+	1.01078i	−0.0108409	+	0.999941i	$0.503451\pi$
$643$	−649.933	+	649.933i	−1.01078	+	1.01078i	−0.999941	+	0.0108409i	$0.996549\pi$
$644$			83.6957i			0.129962i
$645$	856.614	−	282.944i	1.32808	−	0.438673i
$646$	625.101			0.967648
$647$	−186.236	−	186.236i	−0.287846	−	0.287846i	0.548382	−	0.836228i	$-0.315244\pi$
$647$	−186.236	−	186.236i	−0.287846	−	0.287846i	−0.836228	+	0.548382i	$0.815244\pi$
$648$	525.093	−	525.093i	0.810329	−	0.810329i
$649$		−	47.3690i		−	0.0729877i
$650$	331.214	−	245.599i	0.509560	−	0.377844i
$651$	−1066.64			−1.63847
$652$	324.281	+	324.281i	0.497364	+	0.497364i
$653$	572.840	−	572.840i	0.877243	−	0.877243i	−0.116005	−	0.993249i	$-0.537009\pi$
$653$	572.840	−	572.840i	0.877243	−	0.877243i	0.993249	+	0.116005i	$0.0370090\pi$
$654$		−	1060.76i		−	1.62195i
$655$	44.9722	+	136.153i	0.0686598	+	0.207867i
$656$	−251.925			−0.384032
$657$	558.018	+	558.018i	0.849342	+	0.849342i
$658$	−729.287	+	729.287i	−1.10834	+	1.10834i
$659$			186.044i			0.282312i	0.989987	+	0.141156i	$0.0450820\pi$
$659$			186.044i			0.282312i	−0.989987	+	0.141156i	$0.954918\pi$
$660$	−18.6009	+	36.9495i	−0.0281832	+	0.0559841i
$661$	−269.862			−0.408263			−0.204131	−	0.978944i	$-0.565437\pi$
$661$	−269.862			−0.408263			−0.204131	+	0.978944i	$0.565437\pi$
$662$	−411.903	−	411.903i	−0.622211	−	0.622211i
$663$	−808.472	+	808.472i	−1.21941	+	1.21941i
$664$			97.4658i			0.146786i
$665$	−1002.80	−	504.822i	−1.50797	−	0.759131i
$666$	−283.832			−0.426174
$667$	151.467	+	151.467i	0.227087	+	0.227087i
$668$	65.2625	−	65.2625i	0.0976983	−	0.0976983i
$669$			1605.43i			2.39975i
$670$	29.8408	−	9.85660i	0.0445386	−	0.0147113i
$671$	−3.24479			−0.00483575
$672$	−199.205	−	199.205i	−0.296436	−	0.296436i
$673$	801.955	−	801.955i	1.19161	−	1.19161i	0.214997	−	0.976615i	$-0.431026\pi$
$673$	801.955	−	801.955i	1.19161	−	1.19161i	0.976615	−	0.214997i	$-0.0689741\pi$
$674$			454.341i			0.674096i
$675$	2056.85	+	305.293i	3.04718	+	0.452286i
$676$	−65.9659			−0.0975826
$677$	−563.323	−	563.323i	−0.832088	−	0.832088i	0.155714	−	0.987802i	$-0.450232\pi$
$677$	−563.323	−	563.323i	−0.832088	−	0.832088i	−0.987802	+	0.155714i	$0.950232\pi$
$678$	−256.963	+	256.963i	−0.379002	+	0.379002i
$679$		−	416.135i		−	0.612864i
$680$	76.1898	+	230.664i	0.112044	+	0.339212i
$681$	1423.36			2.09011
$682$	15.5240	+	15.5240i	0.0227625	+	0.0227625i
$683$	−22.0385	+	22.0385i	−0.0322672	+	0.0322672i	−0.723056	−	0.690789i	$-0.757263\pi$
$683$	−22.0385	+	22.0385i	−0.0322672	+	0.0322672i	0.690789	+	0.723056i	$0.257263\pi$
$684$		−	1213.21i		−	1.77370i
$685$	163.702	−	325.184i	0.238981	−	0.474721i
$686$	269.747			0.393217
$687$	−563.463	−	563.463i	−0.820178	−	0.820178i
$688$	89.4157	−	89.4157i	0.129965	−	0.129965i
$689$		−	386.644i		−	0.561167i
$690$	−172.875	−	87.0276i	−0.250543	−	0.126127i
$691$	−66.4937			−0.0962283			−0.0481141	−	0.998842i	$-0.515321\pi$
$691$	−66.4937			−0.0962283			−0.0481141	+	0.998842i	$0.515321\pi$
$692$	184.064	+	184.064i	0.265989	+	0.265989i
$693$	−105.425	+	105.425i	−0.152128	+	0.152128i
$694$			61.0534i			0.0879731i
$695$	−93.2283	+	30.7938i	−0.134141	+	0.0443077i
$696$	−721.018			−1.03595
$697$	764.975	+	764.975i	1.09753	+	1.09753i
$698$	−54.8757	+	54.8757i	−0.0786185	+	0.0786185i
$699$			373.195i			0.533898i
$700$	64.0563	−	431.566i	0.0915090	−	0.616523i
$701$	112.563			0.160576			0.0802878	−	0.996772i	$-0.474416\pi$
$701$	112.563			0.160576			0.0802878	+	0.996772i	$0.474416\pi$
$702$	970.043	+	970.043i	1.38183	+	1.38183i
$703$	−154.914	+	154.914i	−0.220362	+	0.220362i
$704$			5.79850i			0.00823651i
$705$	−748.034	−	2264.67i	−1.06104	−	3.21230i
$706$	−572.238			−0.810536
$707$	−265.193	−	265.193i	−0.375096	−	0.375096i
$708$	−527.492	+	527.492i	−0.745045	+	0.745045i
$709$		−	566.340i		−	0.798787i	−0.916780	−	0.399394i	$-0.869221\pi$
$709$		−	566.340i		−	0.798787i	0.916780	−	0.399394i	$-0.130779\pi$
$710$	−370.061	+	735.102i	−0.521212	+	1.03536i
$711$	−839.035			−1.18008
$712$	191.565	+	191.565i	0.269052	+	0.269052i
$713$	−72.6319	+	72.6319i	−0.101868	+	0.101868i
$714$			1209.78i			1.69437i
$715$	−37.7523	−	19.0050i	−0.0528004	−	0.0265804i
$716$	506.233			0.707030
$717$	1205.07	+	1205.07i	1.68071	+	1.68071i
$718$	−545.919	+	545.919i	−0.760333	+	0.760333i
$719$			828.194i			1.15187i	0.817496	+	0.575934i	$0.195362\pi$
$719$			828.194i			1.15187i	−0.817496	+	0.575934i	$0.804638\pi$
$720$	447.680	−	147.871i	0.621777	−	0.205377i
$721$	1217.97			1.68927
$722$	−301.166	−	301.166i	−0.417127	−	0.417127i
$723$	−1624.26	+	1624.26i	−2.24656	+	2.24656i
$724$			35.7015i			0.0493115i
$725$	−665.095	−	896.945i	−0.917372	−	1.23717i
$726$	−972.395			−1.33939
$727$	−137.468	−	137.468i	−0.189090	−	0.189090i	0.606213	−	0.795303i	$-0.292688\pi$
$727$	−137.468	−	137.468i	−0.189090	−	0.189090i	−0.795303	+	0.606213i	$0.792688\pi$
$728$	203.533	−	203.533i	0.279579	−	0.279579i
$729$			1916.76i			2.62930i
$730$	74.2429	+	224.770i	0.101703	+	0.307905i
$731$	−543.025			−0.742853
$732$	36.1333	+	36.1333i	0.0493625	+	0.0493625i
$733$	−690.713	+	690.713i	−0.942310	+	0.942310i	−0.998424	−	0.0561147i	$-0.982129\pi$
$733$	−690.713	+	690.713i	−0.942310	+	0.942310i	0.0561147	+	0.998424i	$0.482129\pi$
$734$		−	199.370i		−	0.271621i
$735$	348.259	−	691.794i	0.473821	−	0.941216i
$736$	−27.1293			−0.0368605
$737$	−2.27784	−	2.27784i	−0.00309069	−	0.00309069i
$738$	1484.68	−	1484.68i	2.01177	−	2.01177i
$739$			77.5070i			0.104881i	0.998624	+	0.0524405i	$0.0167000\pi$
$739$			77.5070i			0.104881i	−0.998624	+	0.0524405i	$0.983300\pi$
$740$	−76.0456	−	38.2824i	−0.102764	−	0.0517330i
$741$	1712.82			2.31150
$742$	−289.283	−	289.283i	−0.389870	−	0.389870i
$743$	−154.641	+	154.641i	−0.208131	+	0.208131i	−0.803473	−	0.595342i	$-0.797017\pi$
$743$	−154.641	+	154.641i	−0.208131	+	0.208131i	0.595342	+	0.803473i	$0.297017\pi$
$744$		−	345.744i		−	0.464710i
$745$	9.38918	−	3.10130i	0.0126029	−	0.00416282i
$746$	368.140			0.493485
$747$	−574.401	−	574.401i	−0.768944	−	0.768944i
$748$	17.6073	−	17.6073i	0.0235391	−	0.0235391i
$749$		−	1490.09i		−	1.98944i
$750$	824.800	+	581.056i	1.09973	+	0.774741i
$751$	691.108			0.920250			0.460125	−	0.887854i	$-0.347805\pi$
$751$	691.108			0.920250			0.460125	+	0.887854i	$0.347805\pi$
$752$	−236.393	−	236.393i	−0.314352	−	0.314352i
$753$	−53.7693	+	53.7693i	−0.0714068	+	0.0714068i
$754$		−	736.683i		−	0.977034i
$755$	4.21576	+	12.7632i	0.00558378	+	0.0169049i
$756$	1451.55			1.92005
$757$	198.386	+	198.386i	0.262068	+	0.262068i	0.825894	−	0.563826i	$-0.190671\pi$
$757$	198.386	+	198.386i	0.262068	+	0.262068i	−0.563826	+	0.825894i	$0.690671\pi$
$758$	425.333	−	425.333i	0.561125	−	0.561125i
$759$			19.8391i			0.0261384i
$760$	163.634	−	325.049i	0.215308	−	0.427696i
$761$	−506.006			−0.664923			−0.332461	−	0.943117i	$-0.607879\pi$
$761$	−506.006			−0.664923			−0.332461	+	0.943117i	$0.607879\pi$
$762$	855.018	+	855.018i	1.12207	+	1.12207i
$763$	810.892	−	810.892i	1.06277	−	1.06277i
$764$			568.042i			0.743510i
$765$	−1808.40	−	910.375i	−2.36393	−	1.19003i
$766$	−645.925			−0.843244
$767$	−538.953	−	538.953i	−0.702676	−	0.702676i
$768$	64.5709	−	64.5709i	0.0840767	−	0.0840767i
$769$		−	293.494i		−	0.381657i	−0.981623	−	0.190828i	$-0.938883\pi$
$769$		−	293.494i		−	0.381657i	0.981623	−	0.190828i	$-0.0611174\pi$
$770$	−42.4653	+	14.0265i	−0.0551497	+	0.0182163i
$771$	−1843.39			−2.39090
$772$	172.679	+	172.679i	0.223678	+	0.223678i
$773$	−101.751	+	101.751i	−0.131631	+	0.131631i	−0.769853	−	0.638222i	$-0.779670\pi$
$773$	−101.751	+	101.751i	−0.131631	+	0.131631i	0.638222	+	0.769853i	$0.279670\pi$
$774$			1053.92i			1.36165i
$775$	430.105	−	318.928i	0.554975	−	0.411520i
$776$	134.887			0.173823
$777$	−299.812	−	299.812i	−0.385859	−	0.385859i
$778$	−38.7279	+	38.7279i	−0.0497788	+	0.0497788i
$779$		−	1620.67i		−	2.08045i
$780$	208.766	+	632.038i	0.267648	+	0.810305i
$781$	84.3602			0.108016
$782$	82.3788	+	82.3788i	0.105344	+	0.105344i
$783$	2626.93	−	2626.93i	3.35495	−	3.35495i
$784$		−	108.564i		−	0.138474i
$785$	−536.890	+	1066.50i	−0.683936	+	1.35860i
$786$	−231.468			−0.294488
$787$	79.3248	+	79.3248i	0.100794	+	0.100794i	0.755706	−	0.654912i	$-0.227294\pi$
$787$	79.3248	+	79.3248i	0.100794	+	0.100794i	−0.654912	+	0.755706i	$0.727294\pi$
$788$	53.9953	−	53.9953i	0.0685220	−	0.0685220i
$789$		−	2542.73i		−	3.22272i
$790$	−224.798	−	113.167i	−0.284555	−	0.143249i
$791$	−392.869			−0.496674
$792$	−34.1727	−	34.1727i	−0.0431473	−	0.0431473i
$793$	−36.9184	+	36.9184i	−0.0465553	+	0.0465553i
$794$			620.245i			0.781165i
$795$	898.319	−	296.720i	1.12996	−	0.373232i
$796$	−589.547			−0.740637
$797$	458.121	+	458.121i	0.574806	+	0.574806i	0.933468	−	0.358661i	$-0.116767\pi$
$797$	458.121	+	458.121i	0.574806	+	0.574806i	−0.358661	+	0.933468i	$0.616767\pi$
$798$	1281.52	−	1281.52i	1.60591	−	1.60591i
$799$			1435.62i			1.79678i
$800$	139.889	+	20.7634i	0.174861	+	0.0259542i
$801$	−2257.92			−2.81888
$802$	154.599	+	154.599i	0.192767	+	0.192767i
$803$	17.1574	−	17.1574i	0.0213666	−	0.0213666i
$804$			50.7310i			0.0630983i
$805$	−65.6256	−	198.681i	−0.0815225	−	0.246809i
$806$	353.256			0.438283
$807$	−890.175	−	890.175i	−1.10307	−	1.10307i
$808$	85.9604	−	85.9604i	0.106387	−	0.106387i
$809$		−	21.2907i		−	0.0263173i	−0.999913	−	0.0131586i	$-0.995811\pi$
$809$		−	21.2907i		−	0.0263173i	0.999913	−	0.0131586i	$-0.00418864\pi$
$810$	−834.771	+	1658.22i	−1.03058	+	2.04718i
$811$	1197.72			1.47685			0.738425	−	0.674336i	$-0.235570\pi$
$811$	1197.72			1.47685			0.738425	+	0.674336i	$0.235570\pi$
$812$	−551.180	−	551.180i	−0.678793	−	0.678793i
$813$	−1393.37	+	1393.37i	−1.71387	+	1.71387i
$814$			8.72698i			0.0107211i
$815$	−1024.07	−	515.529i	−1.25652	−	0.632551i
$816$	−392.142			−0.480566
$817$	575.224	+	575.224i	0.704069	+	0.704069i
$818$	−199.354	+	199.354i	−0.243709	+	0.243709i
$819$			2398.99i			2.92917i
$820$	598.033	−	197.534i	0.729309	−	0.240895i
$821$	828.574			1.00923			0.504613	−	0.863346i	$-0.331635\pi$
$821$	828.574			1.00923			0.504613	+	0.863346i	$0.331635\pi$
$822$	415.566	+	415.566i	0.505555	+	0.505555i
$823$	363.645	−	363.645i	0.441853	−	0.441853i	−0.450781	−	0.892634i	$-0.648855\pi$
$823$	363.645	−	363.645i	0.441853	−	0.441853i	0.892634	+	0.450781i	$0.148855\pi$
$824$			394.795i			0.479120i
$825$	15.1838	−	102.298i	0.0184046	−	0.123997i
$826$	−806.479			−0.976366
$827$	34.3037	+	34.3037i	0.0414797	+	0.0414797i	0.727542	−	0.686063i	$-0.240662\pi$
$827$	34.3037	+	34.3037i	0.0414797	+	0.0414797i	−0.686063	+	0.727542i	$0.740662\pi$
$828$	159.883	−	159.883i	0.193095	−	0.193095i
$829$			472.535i			0.570007i	0.958527	+	0.285003i	$0.0919947\pi$
$829$			472.535i			0.570007i	−0.958527	+	0.285003i	$0.908005\pi$
$830$	−76.4227	−	231.370i	−0.0920756	−	0.278759i
$831$	134.069			0.161335
$832$	65.9738	+	65.9738i	0.0792955	+	0.0792955i
$833$	−329.656	+	329.656i	−0.395745	+	0.395745i
$834$		−	158.493i		−	0.190040i
$835$	−103.752	+	206.096i	−0.124253	+	0.246821i
$836$	−37.3026			−0.0446203
$837$	1259.67	+	1259.67i	1.50498	+	1.50498i
$838$	−508.909	+	508.909i	−0.607290	+	0.607290i
$839$		−	470.622i		−	0.560932i	−0.959864	−	0.280466i	$-0.909511\pi$
$839$		−	470.622i		−	0.560932i	0.959864	−	0.280466i	$-0.0904890\pi$
$840$	629.081	+	316.688i	0.748906	+	0.377010i
$841$	−1153.98			−1.37215
$842$	−402.703	−	402.703i	−0.478269	−	0.478269i
$843$	−165.258	+	165.258i	−0.196035	+	0.196035i
$844$			18.4116i			0.0218147i
$845$	156.593	−	51.7237i	0.185318	−	0.0612115i
$846$	2786.30			3.29350
$847$	−743.344	−	743.344i	−0.877619	−	0.877619i
$848$	93.7690	−	93.7690i	0.110577	−	0.110577i
$849$			343.961i			0.405136i
$850$	−361.727	−	487.824i	−0.425561	−	0.573910i
$851$	−40.8307			−0.0479797
$852$	−939.418	−	939.418i	−1.10260	−	1.10260i
$853$	417.094	−	417.094i	0.488973	−	0.488973i	−0.419009	−	0.907982i	$-0.637622\pi$
$853$	417.094	−	417.094i	0.488973	−	0.488973i	0.907982	+	0.419009i	$0.137622\pi$
$854$			55.2440i			0.0646885i
$855$	951.277	+	2879.99i	1.11260	+	3.36841i
$856$	483.001			0.564253
$857$	−332.777	−	332.777i	−0.388305	−	0.388305i	0.485778	−	0.874082i	$-0.338537\pi$
$857$	−332.777	−	332.777i	−0.388305	−	0.388305i	−0.874082	+	0.485778i	$0.838537\pi$
$858$	48.2452	−	48.2452i	0.0562299	−	0.0562299i
$859$		−	1401.82i		−	1.63192i	−0.578109	−	0.815960i	$-0.696209\pi$
$859$		−	1401.82i		−	1.63192i	0.578109	−	0.815960i	$-0.303791\pi$
$860$	−142.149	+	282.371i	−0.165290	+	0.328338i
$861$	3136.55			3.64291
$862$	168.573	+	168.573i	0.195560	+	0.195560i
$863$	173.054	−	173.054i	0.200526	−	0.200526i	−0.599699	−	0.800225i	$-0.704713\pi$
$863$	173.054	−	173.054i	0.200526	−	0.200526i	0.800225	+	0.599699i	$0.204713\pi$
$864$			470.510i			0.544572i
$865$	−581.266	−	292.618i	−0.671984	−	0.338286i
$866$	982.717			1.13478
$867$	24.4356	+	24.4356i	0.0281841	+	0.0281841i
$868$	264.303	−	264.303i	0.304497	−	0.304497i
$869$			25.7978i			0.0296868i
$870$	1711.59	−	565.348i	1.96735	−	0.649826i
$871$	−51.8333			−0.0595101
$872$	262.845	+	262.845i	0.301427	+	0.301427i
$873$	−794.938	+	794.938i	−0.910582	+	0.910582i
$874$		−	174.527i		−	0.199688i
$875$	186.329	+	1074.70i	0.212948	+	1.22823i
$876$	−382.122			−0.436212
$877$	581.006	+	581.006i	0.662492	+	0.662492i	0.955967	−	0.293475i	$-0.0948117\pi$
$877$	581.006	+	581.006i	0.662492	+	0.662492i	−0.293475	+	0.955967i	$0.594812\pi$
$878$	112.222	−	112.222i	0.127816	−	0.127816i
$879$		−	2727.73i		−	3.10322i
$880$	−4.54659	−	13.7648i	−0.00516658	−	0.0156418i
$881$	−1354.55			−1.53752			−0.768759	−	0.639539i	$-0.779125\pi$
$881$	−1354.55			−1.53752			−0.768759	+	0.639539i	$0.779125\pi$
$882$	639.805	+	639.805i	0.725402	+	0.725402i
$883$	280.247	−	280.247i	0.317380	−	0.317380i	−0.530380	−	0.847760i	$-0.677951\pi$
$883$	280.247	−	280.247i	0.317380	−	0.317380i	0.847760	+	0.530380i	$0.177951\pi$
$884$		−	400.662i		−	0.453238i
$885$	838.584	−	1665.79i	0.947553	−	1.88225i
$886$	927.743			1.04711
$887$	1036.77	+	1036.77i	1.16885	+	1.16885i	0.982480	+	0.186369i	$0.0596721\pi$
$887$	1036.77	+	1036.77i	1.16885	+	1.16885i	0.186369	+	0.982480i	$0.440328\pi$
$888$	97.1818	−	97.1818i	0.109439	−	0.109439i
$889$			1307.23i			1.47045i
$890$	−604.953	−	304.542i	−0.679722	−	0.342182i
$891$	190.297			0.213577
$892$	−397.809	−	397.809i	−0.445974	−	0.445974i
$893$	1520.75	−	1520.75i	1.70297	−	1.70297i
$894$			15.9621i			0.0178547i
$895$	−1201.73	+	396.937i	−1.34271	+	0.443504i
$896$	98.7220			0.110181
$897$	225.724	+	225.724i	0.251643	+	0.251643i
$898$	−342.770	+	342.770i	−0.381704	+	0.381704i
$899$		−	956.637i		−	1.06411i
$900$	−946.782	+	702.049i	−1.05198	+	0.780055i
$901$	−569.463			−0.632035
$902$	−45.6496	−	45.6496i	−0.0506093	−	0.0506093i
$903$	−1113.25	+	1113.25i	−1.23284	+	1.23284i
$904$		−	127.346i		−	0.140869i
$905$	−27.9935	−	84.7503i	−0.0309320	−	0.0936467i
$906$	−21.6981			−0.0239494
$907$	763.418	+	763.418i	0.841696	+	0.841696i	0.989079	−	0.147383i	$-0.0470851\pi$
$907$	763.418	+	763.418i	0.841696	+	0.841696i	−0.147383	+	0.989079i	$0.547085\pi$
$908$	−352.694	+	352.694i	−0.388430	+	0.388430i
$909$			1013.19i			1.11462i
$910$	−323.569	+	642.749i	−0.355570	+	0.706318i
$911$	1645.97			1.80678			0.903388	−	0.428824i	$-0.141072\pi$
$911$	1645.97			1.80678			0.903388	+	0.428824i	$0.141072\pi$
$912$	415.394	+	415.394i	0.455476	+	0.455476i
$913$	−17.6611	+	17.6611i	−0.0193440	+	0.0193440i
$914$		−	499.141i		−	0.546107i
$915$	−114.107	−	57.4432i	−0.124707	−	0.0627795i
$916$	279.240			0.304848
$917$	−176.945	−	176.945i	−0.192960	−	0.192960i
$918$	1428.72	−	1428.72i	1.55633	−	1.55633i
$919$			202.442i			0.220285i	0.993916	+	0.110142i	$0.0351307\pi$
$919$			202.442i			0.220285i	−0.993916	+	0.110142i	$0.964869\pi$
$920$	64.4011	−	21.2720i	0.0700012	−	0.0231218i
$921$	−1430.82			−1.55355
$922$	73.6640	+	73.6640i	0.0798959	+	0.0798959i
$923$	959.829	−	959.829i	1.03990	−	1.03990i
$924$		−	72.1932i		−	0.0781312i
$925$	210.538	+	31.2497i	0.227609	+	0.0337835i
$926$	−359.157			−0.387859
$927$	−2326.67	−	2326.67i	−2.50989	−	2.50989i
$928$	178.661	−	178.661i	0.192522	−	0.192522i
$929$		−	1432.71i		−	1.54220i	−0.636713	−	0.771101i	$-0.719706\pi$
$929$		−	1432.71i		−	1.54220i	0.636713	−	0.771101i	$-0.280294\pi$
$930$	271.097	+	820.747i	0.291503	+	0.882524i
$931$	698.406			0.750167
$932$	−92.4737	−	92.4737i	−0.0992207	−	0.0992207i
$933$	1322.08	−	1322.08i	1.41702	−	1.41702i
$934$			27.7967i			0.0297609i
$935$	−27.9913	+	55.6029i	−0.0299372	+	0.0594684i
$936$	−777.615			−0.830786
$937$	438.901	+	438.901i	0.468411	+	0.468411i	0.901400	−	0.432988i	$-0.142541\pi$
$937$	438.901	+	438.901i	0.468411	+	0.468411i	−0.432988	+	0.901400i	$0.642541\pi$
$938$	−38.7812	+	38.7812i	−0.0413445	+	0.0413445i
$939$			423.486i			0.450997i
$940$	746.518	+	375.808i	0.794168	+	0.399795i
$941$	−1707.58			−1.81465			−0.907324	−	0.420432i	$-0.861879\pi$
$941$	−1707.58			−1.81465			−0.907324	+	0.420432i	$0.861879\pi$
$942$	−1362.92	−	1362.92i	−1.44684	−	1.44684i
$943$	213.580	−	213.580i	0.226490	−	0.226490i
$944$		−	261.414i		−	0.276922i
$945$	−3445.78	+	1138.16i	−3.64633	+	1.20440i
$946$	32.4048			0.0342546
$947$	557.571	+	557.571i	0.588776	+	0.588776i	0.937300	−	0.348524i	$-0.113317\pi$
$947$	557.571	+	557.571i	0.588776	+	0.588776i	−0.348524	+	0.937300i	$0.613317\pi$
$948$	287.279	−	287.279i	0.303037	−	0.303037i
$949$		−	390.424i		−	0.411406i
$950$	−133.574	+	899.925i	−0.140604	+	0.947290i
$951$	−1517.85			−1.59606
$952$	−299.772	−	299.772i	−0.314886	−	0.314886i
$953$	689.721	−	689.721i	0.723737	−	0.723737i	−0.245628	−	0.969364i	$-0.578994\pi$
$953$	689.721	−	689.721i	0.723737	−	0.723737i	0.969364	+	0.245628i	$0.0789941\pi$
$954$			1105.23i			1.15852i
$955$	−445.400	−	1348.45i	−0.466388	−	1.41199i
$956$	−597.207			−0.624694
$957$	−130.651	−	130.651i	−0.136521	−	0.136521i
$958$	−707.716	+	707.716i	−0.738743	+	0.738743i
$959$			635.356i			0.662520i
$960$	−102.652	+	203.912i	−0.106929	+	0.212408i
$961$	−502.271			−0.522654
$962$	99.2933	+	99.2933i	0.103215	+	0.103215i
$963$	−2846.50	+	2846.50i	−2.95587	+	2.95587i
$964$		−	804.951i		−	0.835011i
$965$	−545.312	−	274.518i	−0.565091	−	0.284474i
$966$	337.769			0.349657
$967$	−605.949	−	605.949i	−0.626627	−	0.626627i	0.320591	−	0.947218i	$-0.396119\pi$
$967$	−605.949	−	605.949i	−0.626627	−	0.626627i	−0.947218	+	0.320591i	$0.896119\pi$
$968$	240.949	−	240.949i	0.248915	−	0.248915i
$969$		−	2522.71i		−	2.60341i
$970$	−320.202	+	105.765i	−0.330105	+	0.109036i
$971$	1405.04			1.44700			0.723501	−	0.690323i	$-0.242532\pi$
$971$	1405.04			1.44700			0.723501	+	0.690323i	$0.242532\pi$
$972$	−1060.46	−	1060.46i	−1.09101	−	1.09101i
$973$	121.159	−	121.159i	0.124522	−	0.124522i
$974$			257.845i			0.264727i
$975$	−991.159	−	1336.67i	−1.01657	−	1.37095i
$976$	−17.9069			−0.0183473
$977$	490.862	+	490.862i	0.502418	+	0.502418i	0.912189	−	0.409771i	$-0.134391\pi$
$977$	490.862	+	490.862i	0.502418	+	0.502418i	−0.409771	+	0.912189i	$0.634391\pi$
$978$	1308.70	−	1308.70i	1.33814	−	1.33814i
$979$			69.4243i			0.0709135i
$980$	85.1245	+	257.714i	0.0868617	+	0.262974i
$981$	−3098.08			−3.15808
$982$	−195.979	−	195.979i	−0.199571	−	0.199571i
$983$	107.794	−	107.794i	0.109658	−	0.109658i	−0.650149	−	0.759807i	$-0.725293\pi$
$983$	107.794	−	107.794i	0.109658	−	0.109658i	0.759807	+	0.650149i	$0.225293\pi$
$984$			1016.69i			1.03322i
$985$	−85.8395	+	170.515i	−0.0871467	+	0.173111i
$986$	−1085.01			−1.10042
$987$	2943.17	+	2943.17i	2.98194	+	2.98194i
$988$	−424.419	+	424.419i	−0.429574	+	0.429574i
$989$			151.612i			0.153298i
$990$	107.916	+	54.3263i	0.109006	+	0.0548750i
$991$	−786.700			−0.793845			−0.396922	−	0.917852i	$-0.629922\pi$
$991$	−786.700			−0.793845			−0.396922	+	0.917852i	$0.629922\pi$
$992$	85.6719	+	85.6719i	0.0863628	+	0.0863628i
$993$	−1662.31	+	1662.31i	−1.67403	+	1.67403i
$994$		−	1436.27i		−	1.44494i
$995$	1399.50	−	462.263i	1.40653	−	0.464586i
$996$	393.341			0.394921
$997$	−468.640	−	468.640i	−0.470050	−	0.470050i	0.431881	−	0.901931i	$-0.357850\pi$
$997$	−468.640	−	468.640i	−0.470050	−	0.470050i	−0.901931	+	0.431881i	$0.857850\pi$
$998$	−842.473	+	842.473i	−0.844161	+	0.844161i
$999$			708.137i			0.708846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.f.b.47.12	✓	24
5.3	odd	4	inner	230.3.f.b.93.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.b.47.12	✓	24	1.1	even	1	trivial
230.3.f.b.93.12	yes	24	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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(4.03568 - 4.03568i) q^{3} +2.00000i q^{4} +(-1.56820 - 4.74771i) q^{5} +8.07136 q^{6} +(6.17013 + 6.17013i) q^{7} +(-2.00000 + 2.00000i) q^{8} -23.5735i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(4.03568 - 4.03568i) q^{3} +2.00000i q^{4} +(-1.56820 - 4.74771i) q^{5} +8.07136 q^{6} +(6.17013 + 6.17013i) q^{7} +(-2.00000 + 2.00000i) q^{8} -23.5735i q^{9} +(3.17952 - 6.31591i) q^{10} -0.724813 q^{11} +(8.07136 + 8.07136i) q^{12} +(-8.24673 + 8.24673i) q^{13} +12.3403i q^{14} +(-25.4890 - 12.8315i) q^{15} -4.00000 q^{16} +(12.1461 + 12.1461i) q^{17} +(23.5735 - 23.5735i) q^{18} -25.7326i q^{19} +(9.49542 - 3.13639i) q^{20} +49.8013 q^{21} +(-0.724813 - 0.724813i) q^{22} +(3.39116 - 3.39116i) q^{23} +16.1427i q^{24} +(-20.0815 + 14.8907i) q^{25} -16.4935 q^{26} +(-58.8138 - 58.8138i) q^{27} +(-12.3403 + 12.3403i) q^{28} +44.6652i q^{29} +(-12.6575 - 38.3205i) q^{30} -21.4180 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-2.92511 + 2.92511i) q^{33} +24.2922i q^{34} +(19.6180 - 38.9699i) q^{35} +47.1469 q^{36} +(-6.02016 - 6.02016i) q^{37} +(25.7326 - 25.7326i) q^{38} +66.5623i q^{39} +(12.6318 + 6.35903i) q^{40} +62.9812 q^{41} +(49.8013 + 49.8013i) q^{42} +(-22.3539 + 22.3539i) q^{43} -1.44963i q^{44} +(-111.920 + 36.9678i) q^{45} +6.78233 q^{46} +(59.0982 + 59.0982i) q^{47} +(-16.1427 + 16.1427i) q^{48} +27.1409i q^{49} +(-34.9722 - 5.19084i) q^{50} +98.0355 q^{51} +(-16.4935 - 16.4935i) q^{52} +(-23.4423 + 23.4423i) q^{53} -117.628i q^{54} +(1.13665 + 3.44120i) q^{55} -24.6805 q^{56} +(-103.849 - 103.849i) q^{57} +(-44.6652 + 44.6652i) q^{58} +65.3535i q^{59} +(25.6630 - 50.9780i) q^{60} +4.47673 q^{61} +(-21.4180 - 21.4180i) q^{62} +(145.451 - 145.451i) q^{63} -8.00000i q^{64} +(52.0856 + 26.2206i) q^{65} -5.85023 q^{66} +(3.14266 + 3.14266i) q^{67} +(-24.2922 + 24.2922i) q^{68} -27.3713i q^{69} +(58.5879 - 19.3519i) q^{70} -116.389 q^{71} +(47.1469 + 47.1469i) q^{72} +(-23.6714 + 23.6714i) q^{73} -12.0403i q^{74} +(-20.9486 + 141.137i) q^{75} +51.4652 q^{76} +(-4.47218 - 4.47218i) q^{77} +(-66.5623 + 66.5623i) q^{78} -35.5924i q^{79} +(6.27278 + 18.9908i) q^{80} -262.547 q^{81} +(62.9812 + 62.9812i) q^{82} +(24.3664 - 24.3664i) q^{83} +99.6026i q^{84} +(38.6187 - 76.7136i) q^{85} -44.7078 q^{86} +(180.254 + 180.254i) q^{87} +(1.44963 - 1.44963i) q^{88} -95.7824i q^{89} +(-148.888 - 74.9522i) q^{90} -101.767 q^{91} +(6.78233 + 6.78233i) q^{92} +(-86.4361 + 86.4361i) q^{93} +118.196i q^{94} +(-122.171 + 40.3537i) q^{95} -32.2855 q^{96} +(-33.7217 - 33.7217i) q^{97} +(-27.1409 + 27.1409i) q^{98} +17.0863i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8}+O(q^{10}) \) 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8	\( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8} + 16 q^{10} - 8 q^{11} - 24 q^{13} - 24 q^{15} - 96 q^{16} - 12 q^{17} + 88 q^{18} + 24 q^{20} - 24 q^{21} - 8 q^{22} - 48 q^{25} - 48 q^{26} + 60 q^{27} - 16 q^{28} + 12 q^{30} + 12 q^{31} - 96 q^{32} + 92 q^{33} + 48 q^{35} + 176 q^{36} - 100 q^{37} + 56 q^{38} + 16 q^{40} + 116 q^{41} - 24 q^{42} - 120 q^{43} - 204 q^{45} + 56 q^{47} - 104 q^{50} + 176 q^{51} - 48 q^{52} - 192 q^{53} + 180 q^{55} - 32 q^{56} + 28 q^{58} + 72 q^{60} - 152 q^{61} + 12 q^{62} + 364 q^{63} + 40 q^{65} + 184 q^{66} + 72 q^{67} + 24 q^{68} - 100 q^{70} - 28 q^{71} + 176 q^{72} - 364 q^{73} + 276 q^{75} + 112 q^{76} - 92 q^{77} - 32 q^{78} - 16 q^{80} - 440 q^{81} + 116 q^{82} + 360 q^{83} + 232 q^{85} - 240 q^{86} + 176 q^{87} + 16 q^{88} - 84 q^{90} - 432 q^{91} + 192 q^{93} + 144 q^{95} - 432 q^{97} - 484 q^{98}+O(q^{100}) \) 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8 + 16 * q^10 - 8 * q^11 - 24 * q^13 - 24 * q^15 - 96 * q^16 - 12 * q^17 + 88 * q^18 + 24 * q^20 - 24 * q^21 - 8 * q^22 - 48 * q^25 - 48 * q^26 + 60 * q^27 - 16 * q^28 + 12 * q^30 + 12 * q^31 - 96 * q^32 + 92 * q^33 + 48 * q^35 + 176 * q^36 - 100 * q^37 + 56 * q^38 + 16 * q^40 + 116 * q^41 - 24 * q^42 - 120 * q^43 - 204 * q^45 + 56 * q^47 - 104 * q^50 + 176 * q^51 - 48 * q^52 - 192 * q^53 + 180 * q^55 - 32 * q^56 + 28 * q^58 + 72 * q^60 - 152 * q^61 + 12 * q^62 + 364 * q^63 + 40 * q^65 + 184 * q^66 + 72 * q^67 + 24 * q^68 - 100 * q^70 - 28 * q^71 + 176 * q^72 - 364 * q^73 + 276 * q^75 + 112 * q^76 - 92 * q^77 - 32 * q^78 - 16 * q^80 - 440 * q^81 + 116 * q^82 + 360 * q^83 + 232 * q^85 - 240 * q^86 + 176 * q^87 + 16 * q^88 - 84 * q^90 - 432 * q^91 + 192 * q^93 + 144 * q^95 - 432 * q^97 - 484 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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