LMFDB - Embedded newform 210.3.l.a.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(43,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("210.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.l (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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.12745506816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 23x^{4} + 1 $ x^8 + 23*x^4 + 1
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			127.1
Root			$1.54779 + 1.54779i$ of defining polynomial
Character	$\chi$	$=$	210.127
Dual form			210.3.l.a.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.32032 - 2.51691i) q^{5} -2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.32032 - 2.51691i) q^{5} -2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-1.80341 - 6.83723i) q^{10} -14.0884 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-6.03207 + 6.03207i) q^{13} -3.74166i q^{14} +(8.37386 - 2.20871i) q^{15} -4.00000 q^{16} +(-9.54506 - 9.54506i) q^{17} +(3.00000 - 3.00000i) q^{18} -21.6823i q^{19} +(5.03383 - 8.64064i) q^{20} +4.58258 q^{21} +(-14.0884 - 14.0884i) q^{22} +(0.423494 - 0.423494i) q^{23} -4.89898i q^{24} +(12.3303 + 21.7477i) q^{25} -12.0641 q^{26} +(3.67423 + 3.67423i) q^{27} +(3.74166 - 3.74166i) q^{28} +11.2171i q^{29} +(10.5826 + 6.16515i) q^{30} -16.4543 q^{31} +(-4.00000 - 4.00000i) q^{32} +(17.2547 - 17.2547i) q^{33} -19.0901i q^{34} +(3.37386 + 12.7913i) q^{35} +6.00000 q^{36} +(47.6653 + 47.6653i) q^{37} +(21.6823 - 21.6823i) q^{38} -14.7755i q^{39} +(13.6745 - 3.60681i) q^{40} -44.0379 q^{41} +(4.58258 + 4.58258i) q^{42} +(-46.7052 + 46.7052i) q^{43} -28.1767i q^{44} +(-7.55074 + 12.9610i) q^{45} +0.846988 q^{46} +(-20.3412 - 20.3412i) q^{47} +(4.89898 - 4.89898i) q^{48} +7.00000i q^{49} +(-9.41742 + 34.0780i) q^{50} +23.3805 q^{51} +(-12.0641 - 12.0641i) q^{52} +(-18.6273 + 18.6273i) q^{53} +7.34847i q^{54} +(60.8662 + 35.4592i) q^{55} +7.48331 q^{56} +(26.5553 + 26.5553i) q^{57} +(-11.2171 + 11.2171i) q^{58} -13.4774i q^{59} +(4.41742 + 16.7477i) q^{60} -10.8748 q^{61} +(-16.4543 - 16.4543i) q^{62} +(-5.61249 + 5.61249i) q^{63} -8.00000i q^{64} +(41.2426 - 10.8783i) q^{65} +34.5093 q^{66} +(72.2045 + 72.2045i) q^{67} +(19.0901 - 19.0901i) q^{68} +1.03734i q^{69} +(-9.41742 + 16.1652i) q^{70} -64.1040 q^{71} +(6.00000 + 6.00000i) q^{72} +(51.4407 - 51.4407i) q^{73} +95.3307i q^{74} +(-41.7369 - 11.5339i) q^{75} +43.3646 q^{76} +(26.3569 + 26.3569i) q^{77} +(14.7755 - 14.7755i) q^{78} -157.457i q^{79} +(17.2813 + 10.0677i) q^{80} -9.00000 q^{81} +(-44.0379 - 44.0379i) q^{82} +(-76.9972 + 76.9972i) q^{83} +9.16515i q^{84} +(17.2136 + 65.2618i) q^{85} -93.4104 q^{86} +(-13.7381 - 13.7381i) q^{87} +(28.1767 - 28.1767i) q^{88} -37.6912i q^{89} +(-20.5117 + 5.41022i) q^{90} +22.5699 q^{91} +(0.846988 + 0.846988i) q^{92} +(20.1523 - 20.1523i) q^{93} -40.6824i q^{94} +(-54.5724 + 93.6744i) q^{95} +9.79796 q^{96} +(97.2189 + 97.2189i) q^{97} +(-7.00000 + 7.00000i) q^{98} +42.2651i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 16 q^{8}+O(q^{10}) $ 8 * q + 8 * q^2 - 16 * q^8	$ 8 q + 8 q^{2} - 16 q^{8} - 8 q^{11} + 8 q^{13} + 12 q^{15} - 32 q^{16} - 32 q^{17} + 24 q^{18} - 8 q^{22} - 40 q^{23} - 48 q^{25} + 16 q^{26} + 48 q^{30} + 144 q^{31} - 32 q^{32} + 120 q^{33} - 28 q^{35} + 48 q^{36} + 160 q^{37} - 320 q^{41} - 32 q^{43} - 80 q^{46} - 144 q^{47} - 112 q^{50} + 72 q^{51} + 16 q^{52} - 200 q^{53} + 184 q^{55} - 24 q^{57} - 64 q^{58} + 72 q^{60} + 288 q^{61} + 144 q^{62} + 24 q^{65} + 240 q^{66} + 80 q^{67} + 64 q^{68} - 112 q^{70} - 280 q^{71} + 48 q^{72} + 312 q^{73} - 56 q^{77} + 48 q^{78} - 72 q^{81} - 320 q^{82} - 320 q^{83} + 80 q^{85} - 64 q^{86} - 48 q^{87} + 16 q^{88} - 80 q^{92} + 48 q^{93} - 472 q^{95} - 24 q^{97} - 56 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 - 16 * q^8 - 8 * q^11 + 8 * q^13 + 12 * q^15 - 32 * q^16 - 32 * q^17 + 24 * q^18 - 8 * q^22 - 40 * q^23 - 48 * q^25 + 16 * q^26 + 48 * q^30 + 144 * q^31 - 32 * q^32 + 120 * q^33 - 28 * q^35 + 48 * q^36 + 160 * q^37 - 320 * q^41 - 32 * q^43 - 80 * q^46 - 144 * q^47 - 112 * q^50 + 72 * q^51 + 16 * q^52 - 200 * q^53 + 184 * q^55 - 24 * q^57 - 64 * q^58 + 72 * q^60 + 288 * q^61 + 144 * q^62 + 24 * q^65 + 240 * q^66 + 80 * q^67 + 64 * q^68 - 112 * q^70 - 280 * q^71 + 48 * q^72 + 312 * q^73 - 56 * q^77 + 48 * q^78 - 72 * q^81 - 320 * q^82 - 320 * q^83 + 80 * q^85 - 64 * q^86 - 48 * q^87 + 16 * q^88 - 80 * q^92 + 48 * q^93 - 472 * q^95 - 24 * q^97 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$			2.00000i			0.500000i
$5$	−4.32032	−	2.51691i	−0.864064	−	0.503383i
$5$	−4.32032	−	2.51691i	−0.864064	−	0.503383i
$6$	−2.44949			−0.408248
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	−1.80341	−	6.83723i	−0.180341	−	0.683723i
$11$	−14.0884			−1.28076			−0.640380	−	0.768058i	$-0.721223\pi$
$11$	−14.0884			−1.28076			−0.640380	+	0.768058i	$0.721223\pi$
$12$	−2.44949	−	2.44949i	−0.204124	−	0.204124i
$13$	−6.03207	+	6.03207i	−0.464005	+	0.464005i	−0.899966	−	0.435961i	$-0.856409\pi$
$13$	−6.03207	+	6.03207i	−0.464005	+	0.464005i	0.435961	+	0.899966i	$0.356409\pi$
$14$		−	3.74166i		−	0.267261i
$15$	8.37386	−	2.20871i	0.558258	−	0.147247i
$16$	−4.00000			−0.250000
$17$	−9.54506	−	9.54506i	−0.561474	−	0.561474i	0.368252	−	0.929726i	$-0.379956\pi$
$17$	−9.54506	−	9.54506i	−0.561474	−	0.561474i	−0.929726	+	0.368252i	$0.879956\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$		−	21.6823i		−	1.14117i	−0.821237	−	0.570587i	$-0.806716\pi$
$19$		−	21.6823i		−	1.14117i	0.821237	−	0.570587i	$-0.193284\pi$
$20$	5.03383	−	8.64064i	0.251691	−	0.432032i
$21$	4.58258			0.218218
$22$	−14.0884	−	14.0884i	−0.640380	−	0.640380i
$23$	0.423494	−	0.423494i	0.0184128	−	0.0184128i	−0.697840	−	0.716253i	$-0.745856\pi$
$23$	0.423494	−	0.423494i	0.0184128	−	0.0184128i	0.716253	+	0.697840i	$0.245856\pi$
$24$		−	4.89898i		−	0.204124i
$25$	12.3303	+	21.7477i	0.493212	+	0.869909i
$26$	−12.0641			−0.464005
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	3.74166	−	3.74166i	0.133631	−	0.133631i
$29$			11.2171i			0.386798i	0.981120	+	0.193399i	$0.0619512\pi$
$29$			11.2171i			0.386798i	−0.981120	+	0.193399i	$0.938049\pi$
$30$	10.5826	+	6.16515i	0.352753	+	0.205505i
$31$	−16.4543			−0.530782			−0.265391	−	0.964141i	$-0.585501\pi$
$31$	−16.4543			−0.530782			−0.265391	+	0.964141i	$0.585501\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	17.2547	−	17.2547i	0.522868	−	0.522868i
$34$		−	19.0901i		−	0.561474i
$35$	3.37386	+	12.7913i	0.0963961	+	0.365465i
$36$	6.00000			0.166667
$37$	47.6653	+	47.6653i	1.28825	+	1.28825i	0.935848	+	0.352404i	$0.114636\pi$
$37$	47.6653	+	47.6653i	1.28825	+	1.28825i	0.352404	+	0.935848i	$0.385364\pi$
$38$	21.6823	−	21.6823i	0.570587	−	0.570587i
$39$		−	14.7755i		−	0.378859i
$40$	13.6745	−	3.60681i	0.341862	−	0.0901703i
$41$	−44.0379			−1.07410			−0.537048	−	0.843552i	$-0.680460\pi$
$41$	−44.0379			−1.07410			−0.537048	+	0.843552i	$0.680460\pi$
$42$	4.58258	+	4.58258i	0.109109	+	0.109109i
$43$	−46.7052	+	46.7052i	−1.08617	+	1.08617i	−0.0902487	+	0.995919i	$0.528766\pi$
$43$	−46.7052	+	46.7052i	−1.08617	+	1.08617i	−0.995919	+	0.0902487i	$0.971234\pi$
$44$		−	28.1767i		−	0.640380i
$45$	−7.55074	+	12.9610i	−0.167794	+	0.288021i
$46$	0.846988			0.0184128
$47$	−20.3412	−	20.3412i	−0.432791	−	0.432791i	0.456785	−	0.889577i	$-0.349001\pi$
$47$	−20.3412	−	20.3412i	−0.432791	−	0.432791i	−0.889577	+	0.456785i	$0.849001\pi$
$48$	4.89898	−	4.89898i	0.102062	−	0.102062i
$49$			7.00000i			0.142857i
$50$	−9.41742	+	34.0780i	−0.188348	+	0.681561i
$51$	23.3805			0.458442
$52$	−12.0641	−	12.0641i	−0.232003	−	0.232003i
$53$	−18.6273	+	18.6273i	−0.351458	+	0.351458i	−0.860652	−	0.509194i	$-0.829944\pi$
$53$	−18.6273	+	18.6273i	−0.351458	+	0.351458i	0.509194	+	0.860652i	$0.329944\pi$
$54$			7.34847i			0.136083i
$55$	60.8662	+	35.4592i	1.10666	+	0.644712i
$56$	7.48331			0.133631
$57$	26.5553	+	26.5553i	0.465882	+	0.465882i
$58$	−11.2171	+	11.2171i	−0.193399	+	0.193399i
$59$		−	13.4774i		−	0.228430i	−0.993456	−	0.114215i	$-0.963565\pi$
$59$		−	13.4774i		−	0.228430i	0.993456	−	0.114215i	$-0.0364353\pi$
$60$	4.41742	+	16.7477i	0.0736237	+	0.279129i
$61$	−10.8748			−0.178275			−0.0891376	−	0.996019i	$-0.528411\pi$
$61$	−10.8748			−0.178275			−0.0891376	+	0.996019i	$0.528411\pi$
$62$	−16.4543	−	16.4543i	−0.265391	−	0.265391i
$63$	−5.61249	+	5.61249i	−0.0890871	+	0.0890871i
$64$		−	8.00000i		−	0.125000i
$65$	41.2426	−	10.8783i	0.634502	−	0.167358i
$66$	34.5093			0.522868
$67$	72.2045	+	72.2045i	1.07768	+	1.07768i	0.996717	+	0.0809624i	$0.0257994\pi$
$67$	72.2045	+	72.2045i	1.07768	+	1.07768i	0.0809624	+	0.996717i	$0.474201\pi$
$68$	19.0901	−	19.0901i	0.280737	−	0.280737i
$69$			1.03734i			0.0150340i
$70$	−9.41742	+	16.1652i	−0.134535	+	0.230931i
$71$	−64.1040			−0.902874			−0.451437	−	0.892303i	$-0.649088\pi$
$71$	−64.1040			−0.902874			−0.451437	+	0.892303i	$0.649088\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	51.4407	−	51.4407i	0.704667	−	0.704667i	−0.260742	−	0.965409i	$-0.583967\pi$
$73$	51.4407	−	51.4407i	0.704667	−	0.704667i	0.965409	+	0.260742i	$0.0839671\pi$
$74$			95.3307i			1.28825i
$75$	−41.7369	−	11.5339i	−0.556492	−	0.153786i
$76$	43.3646			0.570587
$77$	26.3569	+	26.3569i	0.342298	+	0.342298i
$78$	14.7755	−	14.7755i	0.189429	−	0.189429i
$79$		−	157.457i		−	1.99313i	−0.0828028	−	0.996566i	$-0.526387\pi$
$79$		−	157.457i		−	1.99313i	0.0828028	−	0.996566i	$-0.473613\pi$
$80$	17.2813	+	10.0677i	0.216016	+	0.125846i
$81$	−9.00000			−0.111111
$82$	−44.0379	−	44.0379i	−0.537048	−	0.537048i
$83$	−76.9972	+	76.9972i	−0.927677	+	0.927677i	−0.997555	−	0.0698788i	$-0.977739\pi$
$83$	−76.9972	+	76.9972i	−0.927677	+	0.927677i	0.0698788	+	0.997555i	$0.477739\pi$
$84$			9.16515i			0.109109i
$85$	17.2136	+	65.2618i	0.202513	+	0.767786i
$86$	−93.4104			−1.08617
$87$	−13.7381	−	13.7381i	−0.157910	−	0.157910i
$88$	28.1767	−	28.1767i	0.320190	−	0.320190i
$89$		−	37.6912i		−	0.423497i	−0.977324	−	0.211749i	$-0.932084\pi$
$89$		−	37.6912i		−	0.423497i	0.977324	−	0.211749i	$-0.0679158\pi$
$90$	−20.5117	+	5.41022i	−0.227908	+	0.0601135i
$91$	22.5699			0.248021
$92$	0.846988	+	0.846988i	0.00920639	+	0.00920639i
$93$	20.1523	−	20.1523i	0.216691	−	0.216691i
$94$		−	40.6824i		−	0.432791i
$95$	−54.5724	+	93.6744i	−0.574447	+	0.986046i
$96$	9.79796			0.102062
$97$	97.2189	+	97.2189i	1.00226	+	1.00226i	0.999997	+	0.00225910i	$0.000719096\pi$
$97$	97.2189	+	97.2189i	1.00226	+	1.00226i	0.00225910	+	0.999997i	$0.499281\pi$
$98$	−7.00000	+	7.00000i	−0.0714286	+	0.0714286i
$99$			42.2651i			0.426920i
$100$	−43.4955	+	24.6606i	−0.434955	+	0.246606i
$101$	26.1142			0.258557			0.129278	−	0.991608i	$-0.458734\pi$
$101$	26.1142			0.258557			0.129278	+	0.991608i	$0.458734\pi$
$102$	23.3805	+	23.3805i	0.229221	+	0.229221i
$103$	52.9553	−	52.9553i	0.514129	−	0.514129i	−0.401660	−	0.915789i	$-0.631567\pi$
$103$	52.9553	−	52.9553i	0.514129	−	0.514129i	0.915789	+	0.401660i	$0.131567\pi$
$104$		−	24.1283i		−	0.232003i
$105$	−19.7982	−	11.5339i	−0.188554	−	0.109847i
$106$	−37.2546			−0.351458
$107$	−81.7515	−	81.7515i	−0.764033	−	0.764033i	0.213016	−	0.977049i	$-0.431671\pi$
$107$	−81.7515	−	81.7515i	−0.764033	−	0.764033i	−0.977049	+	0.213016i	$0.931671\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$		−	59.2958i		−	0.543998i	−0.962297	−	0.271999i	$-0.912315\pi$
$109$		−	59.2958i		−	0.543998i	0.962297	−	0.271999i	$-0.0876848\pi$
$110$	25.4070	+	96.3254i	0.230973	+	0.875686i
$111$	−116.756			−1.05185
$112$	7.48331	+	7.48331i	0.0668153	+	0.0668153i
$113$	142.193	−	142.193i	1.25834	−	1.25834i	0.306458	−	0.951884i	$-0.400856\pi$
$113$	142.193	−	142.193i	1.25834	−	1.25834i	0.951884	−	0.306458i	$-0.0991440\pi$
$114$			53.1105i			0.465882i
$115$	−2.89553	+	0.763732i	−0.0251785	+	0.00664114i
$116$	−22.4343			−0.193399
$117$	18.0962	+	18.0962i	0.154668	+	0.154668i
$118$	13.4774	−	13.4774i	0.114215	−	0.114215i
$119$			35.7144i			0.300121i
$120$	−12.3303	+	21.1652i	−0.102753	+	0.176376i
$121$	77.4821			0.640348
$122$	−10.8748	−	10.8748i	−0.0891376	−	0.0891376i
$123$	53.9352	−	53.9352i	0.438498	−	0.438498i
$124$		−	32.9085i		−	0.265391i
$125$	1.46629	−	124.991i	0.0117303	−	0.999931i
$126$	−11.2250			−0.0890871
$127$	−95.3116	−	95.3116i	−0.750485	−	0.750485i	0.224085	−	0.974570i	$-0.428061\pi$
$127$	−95.3116	−	95.3116i	−0.750485	−	0.750485i	−0.974570	+	0.224085i	$0.928061\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$		−	114.404i		−	0.886852i
$130$	52.1209	+	30.3644i	0.400930	+	0.233572i
$131$	−191.866			−1.46463			−0.732313	−	0.680968i	$-0.761559\pi$
$131$	−191.866			−1.46463			−0.732313	+	0.680968i	$0.761559\pi$
$132$	34.5093	+	34.5093i	0.261434	+	0.261434i
$133$	−40.5639	+	40.5639i	−0.304991	+	0.304991i
$134$			144.409i			1.07768i
$135$	−6.62614	−	25.1216i	−0.0490825	−	0.186086i
$136$	38.1803			0.280737
$137$	134.702	+	134.702i	0.983228	+	0.983228i	0.999862	−	0.0166339i	$-0.00529498\pi$
$137$	134.702	+	134.702i	0.983228	+	0.983228i	−0.0166339	+	0.999862i	$0.505295\pi$
$138$	−1.03734	+	1.03734i	−0.00751699	+	0.00751699i
$139$			49.6297i			0.357048i	0.983936	+	0.178524i	$0.0571323\pi$
$139$			49.6297i			0.357048i	−0.983936	+	0.178524i	$0.942868\pi$
$140$	−25.5826	+	6.74773i	−0.182733	+	0.0481981i
$141$	49.8256			0.353373
$142$	−64.1040	−	64.1040i	−0.451437	−	0.451437i
$143$	84.9820	−	84.9820i	0.594279	−	0.594279i
$144$			12.0000i			0.0833333i
$145$	28.2326	−	48.4616i	0.194707	−	0.334218i
$146$	102.881			0.704667
$147$	−8.57321	−	8.57321i	−0.0583212	−	0.0583212i
$148$	−95.3307	+	95.3307i	−0.644126	+	0.644126i
$149$		−	137.142i		−	0.920415i	−0.887811	−	0.460208i	$-0.847775\pi$
$149$		−	137.142i		−	0.920415i	0.887811	−	0.460208i	$-0.152225\pi$
$150$	−30.2030	−	53.2708i	−0.201353	−	0.355139i
$151$	−197.792			−1.30988			−0.654941	−	0.755680i	$-0.727307\pi$
$151$	−197.792			−1.30988			−0.654941	+	0.755680i	$0.727307\pi$
$152$	43.3646	+	43.3646i	0.285293	+	0.285293i
$153$	−28.6352	+	28.6352i	−0.187158	+	0.187158i
$154$			52.7138i			0.342298i
$155$	71.0876	+	41.4139i	0.458630	+	0.267187i
$156$	29.5510			0.189429
$157$	−179.903	−	179.903i	−1.14588	−	1.14588i	−0.987355	−	0.158526i	$-0.949326\pi$
$157$	−179.903	−	179.903i	−1.14588	−	1.14588i	−0.158526	−	0.987355i	$-0.550674\pi$
$158$	157.457	−	157.457i	0.996566	−	0.996566i
$159$		−	45.6274i		−	0.286965i
$160$	7.21362	+	27.3489i	0.0450851	+	0.170931i
$161$	−1.58457			−0.00984205
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	−19.4617	+	19.4617i	−0.119397	+	0.119397i	−0.764281	−	0.644884i	$-0.776906\pi$
$163$	−19.4617	+	19.4617i	−0.119397	+	0.119397i	0.644884	+	0.764281i	$0.276906\pi$
$164$		−	88.0758i		−	0.537048i
$165$	−117.974	+	31.1171i	−0.714994	+	0.188589i
$166$	−153.994			−0.927677
$167$	−78.3023	−	78.3023i	−0.468876	−	0.468876i	0.432674	−	0.901550i	$-0.357570\pi$
$167$	−78.3023	−	78.3023i	−0.468876	−	0.468876i	−0.901550	+	0.432674i	$0.857570\pi$
$168$	−9.16515	+	9.16515i	−0.0545545	+	0.0545545i
$169$			96.2284i			0.569399i
$170$	−48.0482	+	82.4754i	−0.282636	+	0.485150i
$171$	−65.0469			−0.380391
$172$	−93.4104	−	93.4104i	−0.543084	−	0.543084i
$173$	66.9522	−	66.9522i	0.387007	−	0.387007i	−0.486612	−	0.873618i	$-0.661767\pi$
$173$	66.9522	−	66.9522i	0.387007	−	0.387007i	0.873618	+	0.486612i	$0.161767\pi$
$174$		−	27.4763i		−	0.157910i
$175$	17.6184	−	63.7542i	0.100677	−	0.364309i
$176$	56.3535			0.320190
$177$	16.5064	+	16.5064i	0.0932563	+	0.0932563i
$178$	37.6912	−	37.6912i	0.211749	−	0.211749i
$179$			66.4948i			0.371479i	0.982599	+	0.185740i	$0.0594681\pi$
$179$			66.4948i			0.371479i	−0.982599	+	0.185740i	$0.940532\pi$
$180$	−25.9219	−	15.1015i	−0.144011	−	0.0838971i
$181$	−33.5180			−0.185183			−0.0925913	−	0.995704i	$-0.529515\pi$
$181$	−33.5180			−0.185183			−0.0925913	+	0.995704i	$0.529515\pi$
$182$	22.5699	+	22.5699i	0.124011	+	0.124011i
$183$	13.3188	−	13.3188i	0.0727805	−	0.0727805i
$184$			1.69398i			0.00920639i
$185$	−85.9599	−	325.899i	−0.464648	−	1.76162i
$186$	40.3045			0.216691
$187$	134.474	+	134.474i	0.719114	+	0.719114i
$188$	40.6824	−	40.6824i	0.216396	−	0.216396i
$189$		−	13.7477i		−	0.0727393i
$190$	−148.247	+	39.1020i	−0.780246	+	0.205800i
$191$	−209.877			−1.09883			−0.549415	−	0.835549i	$-0.685150\pi$
$191$	−209.877			−1.09883			−0.549415	+	0.835549i	$0.685150\pi$
$192$	9.79796	+	9.79796i	0.0510310	+	0.0510310i
$193$	−247.934	+	247.934i	−1.28463	+	1.28463i	−0.346634	+	0.938001i	$0.612675\pi$
$193$	−247.934	+	247.934i	−1.28463	+	1.28463i	−0.938001	+	0.346634i	$0.887325\pi$
$194$			194.438i			1.00226i
$195$	−37.1886	+	63.8348i	−0.190711	+	0.327358i
$196$	−14.0000			−0.0714286
$197$	−14.3392	−	14.3392i	−0.0727881	−	0.0727881i	0.669776	−	0.742564i	$-0.266390\pi$
$197$	−14.3392	−	14.3392i	−0.0727881	−	0.0727881i	−0.742564	+	0.669776i	$0.766390\pi$
$198$	−42.2651	+	42.2651i	−0.213460	+	0.213460i
$199$		−	282.601i		−	1.42011i	−0.704148	−	0.710053i	$-0.748671\pi$
$199$		−	282.601i		−	1.42011i	0.704148	−	0.710053i	$-0.251329\pi$
$200$	−68.1561	−	18.8348i	−0.340780	−	0.0941742i
$201$	−176.864			−0.879922
$202$	26.1142	+	26.1142i	0.129278	+	0.129278i
$203$	20.9854	−	20.9854i	0.103376	−	0.103376i
$204$			46.7611i			0.229221i
$205$	190.258	+	110.840i	0.928087	+	0.540681i
$206$	105.911			0.514129
$207$	−1.27048	−	1.27048i	−0.00613759	−	0.00613759i
$208$	24.1283	−	24.1283i	0.116001	−	0.116001i
$209$			305.468i			1.46157i
$210$	−8.26424	−	31.3321i	−0.0393535	−	0.149201i
$211$	208.591			0.988584			0.494292	−	0.869296i	$-0.335427\pi$
$211$	208.591			0.988584			0.494292	+	0.869296i	$0.335427\pi$
$212$	−37.2546	−	37.2546i	−0.175729	−	0.175729i
$213$	78.5111	−	78.5111i	0.368597	−	0.368597i
$214$		−	163.503i		−	0.764033i
$215$	319.334	−	84.2285i	1.48528	−	0.391760i
$216$	−14.6969			−0.0680414
$217$	30.7831	+	30.7831i	0.141858	+	0.141858i
$218$	59.2958	−	59.2958i	0.271999	−	0.271999i
$219$			126.003i			0.575358i
$220$	−70.9184	+	121.732i	−0.322356	+	0.553329i
$221$	115.153			0.521054
$222$	−116.756	−	116.756i	−0.525927	−	0.525927i
$223$	−205.186	+	205.186i	−0.920118	+	0.920118i	−0.997037	−	0.0769196i	$-0.975492\pi$
$223$	−205.186	+	205.186i	−0.920118	+	0.920118i	0.0769196	+	0.997037i	$0.475492\pi$
$224$			14.9666i			0.0668153i
$225$	65.2432	−	36.9909i	0.289970	−	0.164404i
$226$	284.385			1.25834
$227$	316.050	+	316.050i	1.39229	+	1.39229i	0.820170	+	0.572120i	$0.193879\pi$
$227$	316.050	+	316.050i	1.39229	+	1.39229i	0.572120	+	0.820170i	$0.306121\pi$
$228$	−53.1105	+	53.1105i	−0.232941	+	0.232941i
$229$			123.494i			0.539274i	0.962962	+	0.269637i	$0.0869036\pi$
$229$			123.494i			0.539274i	−0.962962	+	0.269637i	$0.913096\pi$
$230$	−3.65926	−	2.13179i	−0.0159098	−	0.00926867i
$231$	−64.5610			−0.279485
$232$	−22.4343	−	22.4343i	−0.0966995	−	0.0966995i
$233$	209.367	−	209.367i	0.898572	−	0.898572i	−0.0967375	−	0.995310i	$-0.530841\pi$
$233$	209.367	−	209.367i	0.898572	−	0.898572i	0.995310	+	0.0967375i	$0.0308407\pi$
$234$			36.1924i			0.154668i
$235$	36.6834	+	139.077i	0.156100	+	0.591819i
$236$	26.9548			0.114215
$237$	192.845	+	192.845i	0.813693	+	0.813693i
$238$	−35.7144	+	35.7144i	−0.150060	+	0.150060i
$239$			147.491i			0.617117i	0.951205	+	0.308559i	$0.0998466\pi$
$239$			147.491i			0.617117i	−0.951205	+	0.308559i	$0.900153\pi$
$240$	−33.4955	+	8.83485i	−0.139564	+	0.0368119i
$241$	−180.182			−0.747643			−0.373821	−	0.927501i	$-0.621953\pi$
$241$	−180.182			−0.747643			−0.373821	+	0.927501i	$0.621953\pi$
$242$	77.4821	+	77.4821i	0.320174	+	0.320174i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$		−	21.7496i		−	0.0891376i
$245$	17.6184	−	30.2422i	0.0719118	−	0.123438i
$246$	107.870			0.438498
$247$	130.789	+	130.789i	0.529510	+	0.529510i
$248$	32.9085	−	32.9085i	0.132696	−	0.132696i
$249$		−	188.604i		−	0.757445i
$250$	126.458	−	123.525i	0.505831	−	0.494100i
$251$	25.2366			0.100544			0.0502720	−	0.998736i	$-0.483991\pi$
$251$	25.2366			0.100544			0.0502720	+	0.998736i	$0.483991\pi$
$252$	−11.2250	−	11.2250i	−0.0445435	−	0.0445435i
$253$	−5.96634	+	5.96634i	−0.0235824	+	0.0235824i
$254$		−	190.623i		−	0.750485i
$255$	−101.011	−	58.8468i	−0.396123	−	0.230772i
$256$	16.0000			0.0625000
$257$	228.675	+	228.675i	0.889784	+	0.889784i	0.994502	−	0.104718i	$-0.0333938\pi$
$257$	228.675	+	228.675i	0.889784	+	0.889784i	−0.104718	+	0.994502i	$0.533394\pi$
$258$	114.404	−	114.404i	0.443426	−	0.443426i
$259$		−	178.347i		−	0.688600i
$260$	21.7565	+	82.4852i	0.0836789	+	0.317251i
$261$	33.6514			0.128933
$262$	−191.866	−	191.866i	−0.732313	−	0.732313i
$263$	−17.1641	+	17.1641i	−0.0652629	+	0.0652629i	−0.738985	−	0.673722i	$-0.764695\pi$
$263$	−17.1641	+	17.1641i	−0.0652629	+	0.0652629i	0.673722	+	0.738985i	$0.264695\pi$
$264$			69.0186i			0.261434i
$265$	127.359	−	33.5926i	0.480600	−	0.126764i
$266$	−81.1277			−0.304991
$267$	46.1622	+	46.1622i	0.172892	+	0.172892i
$268$	−144.409	+	144.409i	−0.538840	+	0.538840i
$269$			503.847i			1.87304i	0.350617	+	0.936519i	$0.385972\pi$
$269$			503.847i			1.87304i	−0.350617	+	0.936519i	$0.614028\pi$
$270$	18.4955	−	31.7477i	0.0685017	−	0.117584i
$271$	147.700			0.545019			0.272510	−	0.962153i	$-0.412146\pi$
$271$	147.700			0.545019			0.272510	+	0.962153i	$0.412146\pi$
$272$	38.1803	+	38.1803i	0.140369	+	0.140369i
$273$	−27.6424	+	27.6424i	−0.101254	+	0.101254i
$274$			269.404i			0.983228i
$275$	−173.714	−	306.390i	−0.631687	−	1.11415i
$276$	−2.07469			−0.00751699
$277$	2.85013	+	2.85013i	0.0102893	+	0.0102893i	0.712233	−	0.701943i	$-0.247684\pi$
$277$	2.85013	+	2.85013i	0.0102893	+	0.0102893i	−0.701943	+	0.712233i	$0.747684\pi$
$278$	−49.6297	+	49.6297i	−0.178524	+	0.178524i
$279$			49.3628i			0.176927i
$280$	−32.3303	−	18.8348i	−0.115465	−	0.0672673i
$281$	384.657			1.36889			0.684443	−	0.729066i	$-0.260045\pi$
$281$	384.657			1.36889			0.684443	+	0.729066i	$0.260045\pi$
$282$	49.8256	+	49.8256i	0.176686	+	0.176686i
$283$	−201.734	+	201.734i	−0.712839	+	0.712839i	−0.967128	−	0.254289i	$-0.918159\pi$
$283$	−201.734	+	201.734i	−0.712839	+	0.712839i	0.254289	+	0.967128i	$0.418159\pi$
$284$		−	128.208i		−	0.451437i
$285$	−47.8899	−	181.565i	−0.168035	−	0.637069i
$286$	169.964			0.594279
$287$	82.3874	+	82.3874i	0.287064	+	0.287064i
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$		−	106.784i		−	0.369493i
$290$	76.6942	−	20.2291i	0.264463	−	0.0697554i
$291$	−238.137			−0.818339
$292$	102.881	+	102.881i	0.352334	+	0.352334i
$293$	−366.878	+	366.878i	−1.25214	+	1.25214i	−0.297384	+	0.954758i	$0.596114\pi$
$293$	−366.878	+	366.878i	−1.25214	+	1.25214i	−0.954758	+	0.297384i	$0.903886\pi$
$294$		−	17.1464i		−	0.0583212i
$295$	−33.9214	+	58.2266i	−0.114988	+	0.197378i
$296$	−190.661			−0.644126
$297$	−51.7640	−	51.7640i	−0.174289	−	0.174289i
$298$	137.142	−	137.142i	0.460208	−	0.460208i
$299$			5.10909i			0.0170872i
$300$	23.0679	−	83.4738i	0.0768929	−	0.278246i
$301$	174.755			0.580581
$302$	−197.792	−	197.792i	−0.654941	−	0.654941i
$303$	−31.9833	+	31.9833i	−0.105555	+	0.105555i
$304$			86.7292i			0.285293i
$305$	46.9825	+	27.3709i	0.154041	+	0.0897406i
$306$	−57.2704			−0.187158
$307$	−412.785	−	412.785i	−1.34458	−	1.34458i	−0.891442	−	0.453136i	$-0.850305\pi$
$307$	−412.785	−	412.785i	−1.34458	−	1.34458i	−0.453136	−	0.891442i	$-0.649695\pi$
$308$	−52.7138	+	52.7138i	−0.171149	+	0.171149i
$309$			129.713i			0.419785i
$310$	29.6737	+	112.502i	0.0957216	+	0.362908i
$311$	512.668			1.64845			0.824225	−	0.566263i	$-0.191611\pi$
$311$	512.668			1.64845			0.824225	+	0.566263i	$0.191611\pi$
$312$	29.5510	+	29.5510i	0.0947146	+	0.0947146i
$313$	−101.469	+	101.469i	−0.324182	+	0.324182i	−0.850369	−	0.526187i	$-0.823621\pi$
$313$	−101.469	+	101.469i	−0.324182	+	0.324182i	0.526187	+	0.850369i	$0.323621\pi$
$314$		−	359.806i		−	1.14588i
$315$	38.3739	−	10.1216i	0.121822	−	0.0321320i
$316$	314.915			0.996566
$317$	−202.617	−	202.617i	−0.639169	−	0.639169i	0.311182	−	0.950350i	$-0.399275\pi$
$317$	−202.617	−	202.617i	−0.639169	−	0.639169i	−0.950350	+	0.311182i	$0.899275\pi$
$318$	45.6274	−	45.6274i	0.143482	−	0.143482i
$319$		−	158.031i		−	0.495396i
$320$	−20.1353	+	34.5625i	−0.0629228	+	0.108008i
$321$	200.250			0.623830
$322$	−1.58457	−	1.58457i	−0.00492102	−	0.00492102i
$323$	−206.959	+	206.959i	−0.640739	+	0.640739i
$324$		−	18.0000i		−	0.0555556i
$325$	−205.561	−	56.8065i	−0.632495	−	0.174789i
$326$	−38.9233			−0.119397
$327$	72.6223	+	72.6223i	0.222086	+	0.222086i
$328$	88.0758	−	88.0758i	0.268524	−	0.268524i
$329$			76.1098i			0.231337i
$330$	−149.091	−	86.8569i	−0.451792	−	0.263203i
$331$	65.9564			0.199264			0.0996321	−	0.995024i	$-0.468233\pi$
$331$	65.9564			0.199264			0.0996321	+	0.995024i	$0.468233\pi$
$332$	−153.994	−	153.994i	−0.463838	−	0.463838i
$333$	142.996	−	142.996i	0.429417	−	0.429417i
$334$		−	156.605i		−	0.468876i
$335$	−130.214	−	493.679i	−0.388699	−	1.47367i
$336$	−18.3303			−0.0545545
$337$	−360.772	−	360.772i	−1.07054	−	1.07054i	−0.997315	−	0.0732257i	$-0.976671\pi$
$337$	−360.772	−	360.772i	−1.07054	−	1.07054i	−0.0732257	−	0.997315i	$-0.523329\pi$
$338$	−96.2284	+	96.2284i	−0.284699	+	0.284699i
$339$			348.300i			1.02743i
$340$	−130.524	+	34.4272i	−0.383893	+	0.101257i
$341$	231.814			0.679805
$342$	−65.0469	−	65.0469i	−0.190196	−	0.190196i
$343$	13.0958	−	13.0958i	0.0381802	−	0.0381802i
$344$		−	186.821i		−	0.543084i
$345$	2.61090	−	4.48166i	0.00756784	−	0.0129903i
$346$	133.904			0.387007
$347$	−195.218	−	195.218i	−0.562588	−	0.562588i	0.367454	−	0.930042i	$-0.380230\pi$
$347$	−195.218	−	195.218i	−0.562588	−	0.562588i	−0.930042	+	0.367454i	$0.880230\pi$
$348$	27.4763	−	27.4763i	0.0789548	−	0.0789548i
$349$			204.957i			0.587270i	0.955918	+	0.293635i	$0.0948650\pi$
$349$			204.957i			0.587270i	−0.955918	+	0.293635i	$0.905135\pi$
$350$	81.3725	−	46.1358i	0.232493	−	0.131816i
$351$	−44.3264			−0.126286
$352$	56.3535	+	56.3535i	0.160095	+	0.160095i
$353$	−233.494	+	233.494i	−0.661457	+	0.661457i	−0.955723	−	0.294267i	$-0.904925\pi$
$353$	−233.494	+	233.494i	−0.661457	+	0.661457i	0.294267	+	0.955723i	$0.404925\pi$
$354$			33.0127i			0.0932563i
$355$	276.950	+	161.344i	0.780140	+	0.454491i
$356$	75.3825			0.211749
$357$	−43.7410	−	43.7410i	−0.122524	−	0.122524i
$358$	−66.4948	+	66.4948i	−0.185740	+	0.185740i
$359$		−	263.565i		−	0.734164i	−0.930189	−	0.367082i	$-0.880357\pi$
$359$		−	263.565i		−	0.734164i	0.930189	−	0.367082i	$-0.119643\pi$
$360$	−10.8204	−	41.0234i	−0.0300568	−	0.113954i
$361$	−109.122			−0.302276
$362$	−33.5180	−	33.5180i	−0.0925913	−	0.0925913i
$363$	−94.8958	+	94.8958i	−0.261421	+	0.261421i
$364$			45.1398i			0.124011i
$365$	−351.712	+	92.7684i	−0.963594	+	0.254160i
$366$	26.6377			0.0727805
$367$	22.0009	+	22.0009i	0.0599481	+	0.0599481i	0.736445	−	0.676497i	$-0.236503\pi$
$367$	22.0009	+	22.0009i	0.0599481	+	0.0599481i	−0.676497	+	0.736445i	$0.736503\pi$
$368$	−1.69398	+	1.69398i	−0.00460320	+	0.00460320i
$369$			132.114i			0.358032i
$370$	239.939	−	411.859i	0.648484	−	1.11313i
$371$	69.6970			0.187862
$372$	40.3045	+	40.3045i	0.108346	+	0.108346i
$373$	−170.973	+	170.973i	−0.458373	+	0.458373i	−0.898121	−	0.439748i	$-0.855068\pi$
$373$	−170.973	+	170.973i	−0.458373	+	0.458373i	0.439748	+	0.898121i	$0.355068\pi$
$374$			268.949i			0.719114i
$375$	151.287	+	154.878i	0.403431	+	0.413009i
$376$	81.3648			0.216396
$377$	−67.6625	−	67.6625i	−0.179476	−	0.179476i
$378$	13.7477	−	13.7477i	0.0363696	−	0.0363696i
$379$		−	272.520i		−	0.719050i	−0.933135	−	0.359525i	$-0.882939\pi$
$379$		−	272.520i		−	0.719050i	0.933135	−	0.359525i	$-0.117061\pi$
$380$	−187.349	−	109.145i	−0.493023	−	0.287223i
$381$	233.465			0.612769
$382$	−209.877	−	209.877i	−0.549415	−	0.549415i
$383$	−283.977	+	283.977i	−0.741454	+	0.741454i	−0.972858	−	0.231403i	$-0.925668\pi$
$383$	−283.977	+	283.977i	−0.741454	+	0.741454i	0.231403	+	0.972858i	$0.425668\pi$
$384$			19.5959i			0.0510310i
$385$	−47.5322	−	180.208i	−0.123460	−	0.468074i
$386$	−495.869			−1.28463
$387$	140.116	+	140.116i	0.362056	+	0.362056i
$388$	−194.438	+	194.438i	−0.501128	+	0.501128i
$389$		−	12.8522i		−	0.0330392i	−0.999864	−	0.0165196i	$-0.994741\pi$
$389$		−	12.8522i		−	0.0330392i	0.999864	−	0.0165196i	$-0.00525859\pi$
$390$	−101.023	+	26.6462i	−0.259034	+	0.0683236i
$391$	−8.08455			−0.0206766
$392$	−14.0000	−	14.0000i	−0.0357143	−	0.0357143i
$393$	234.987	−	234.987i	0.597931	−	0.597931i
$394$		−	28.6785i		−	0.0727881i
$395$	−396.307	+	680.266i	−1.00331	+	1.72219i
$396$	−84.5302			−0.213460
$397$	−242.868	−	242.868i	−0.611757	−	0.611757i	0.331647	−	0.943404i	$-0.392396\pi$
$397$	−242.868	−	242.868i	−0.611757	−	0.611757i	−0.943404	+	0.331647i	$0.892396\pi$
$398$	282.601	−	282.601i	0.710053	−	0.710053i
$399$		−	99.3607i		−	0.249024i
$400$	−49.3212	−	86.9909i	−0.123303	−	0.217477i
$401$	−523.505			−1.30550			−0.652749	−	0.757574i	$-0.726385\pi$
$401$	−523.505			−1.30550			−0.652749	+	0.757574i	$0.726385\pi$
$402$	−176.864	−	176.864i	−0.439961	−	0.439961i
$403$	99.2531	−	99.2531i	0.246286	−	0.246286i
$404$			52.2284i			0.129278i
$405$	38.8829	+	22.6522i	0.0960071	+	0.0559314i
$406$	41.9707			0.103376
$407$	−671.527	−	671.527i	−1.64994	−	1.64994i
$408$	−46.7611	+	46.7611i	−0.114610	+	0.114610i
$409$		−	39.5511i		−	0.0967019i	−0.998830	−	0.0483509i	$-0.984603\pi$
$409$		−	39.5511i		−	0.0967019i	0.998830	−	0.0483509i	$-0.0153966\pi$
$410$	79.4182	+	301.097i	0.193703	+	0.734384i
$411$	−329.952			−0.802802
$412$	105.911	+	105.911i	0.257064	+	0.257064i
$413$	−25.2139	+	25.2139i	−0.0610506	+	0.0610506i
$414$		−	2.54096i		−	0.00613759i
$415$	526.447	−	138.857i	1.26855	−	0.334596i
$416$	48.2565			0.116001
$417$	−60.7838	−	60.7838i	−0.145764	−	0.145764i
$418$	−305.468	+	305.468i	−0.730785	+	0.730785i
$419$		−	171.715i		−	0.409822i	−0.978781	−	0.204911i	$-0.934310\pi$
$419$		−	171.715i		−	0.409822i	0.978781	−	0.204911i	$-0.0656905\pi$
$420$	23.0679	−	39.5964i	0.0549235	−	0.0942771i
$421$	361.127			0.857784			0.428892	−	0.903356i	$-0.358904\pi$
$421$	361.127			0.857784			0.428892	+	0.903356i	$0.358904\pi$
$422$	208.591	+	208.591i	0.494292	+	0.494292i
$423$	−61.0236	+	61.0236i	−0.144264	+	0.144264i
$424$		−	74.5092i		−	0.175729i
$425$	89.8899	−	325.277i	0.211506	−	0.765358i
$426$	157.022			0.368597
$427$	20.3449	+	20.3449i	0.0476460	+	0.0476460i
$428$	163.503	−	163.503i	0.382017	−	0.382017i
$429$			208.162i			0.485227i
$430$	403.563	+	235.106i	0.938518	+	0.546758i
$431$	323.054			0.749545			0.374772	−	0.927117i	$-0.377721\pi$
$431$	323.054			0.749545			0.374772	+	0.927117i	$0.377721\pi$
$432$	−14.6969	−	14.6969i	−0.0340207	−	0.0340207i
$433$	76.7446	−	76.7446i	0.177239	−	0.177239i	−0.612912	−	0.790151i	$-0.710002\pi$
$433$	76.7446	−	76.7446i	0.177239	−	0.177239i	0.790151	+	0.612912i	$0.210002\pi$
$434$			61.5662i			0.141858i
$435$	24.7754	+	93.9308i	0.0569550	+	0.215933i
$436$	118.592			0.271999
$437$	−9.18232	−	9.18232i	−0.0210122	−	0.0210122i
$438$	−126.003	+	126.003i	−0.287679	+	0.287679i
$439$		−	864.627i		−	1.96954i	−0.173872	−	0.984768i	$-0.555628\pi$
$439$		−	864.627i		−	1.96954i	0.173872	−	0.984768i	$-0.444372\pi$
$440$	−192.651	+	50.8141i	−0.437843	+	0.115487i
$441$	21.0000			0.0476190
$442$	115.153	+	115.153i	0.260527	+	0.260527i
$443$	−326.831	+	326.831i	−0.737768	+	0.737768i	−0.972146	−	0.234377i	$-0.924695\pi$
$443$	−326.831	+	326.831i	−0.737768	+	0.737768i	0.234377	+	0.972146i	$0.424695\pi$
$444$		−	233.511i		−	0.525927i
$445$	−94.8656	+	162.838i	−0.213181	+	0.365929i
$446$	−410.372			−0.920118
$447$	167.964	+	167.964i	0.375758	+	0.375758i
$448$	−14.9666	+	14.9666i	−0.0334077	+	0.0334077i
$449$		−	331.011i		−	0.737217i	−0.929585	−	0.368609i	$-0.879834\pi$
$449$		−	331.011i		−	0.737217i	0.929585	−	0.368609i	$-0.120166\pi$
$450$	102.234	+	28.2523i	0.227187	+	0.0627828i
$451$	620.422			1.37566
$452$	284.385	+	284.385i	0.629171	+	0.629171i
$453$	242.245	−	242.245i	0.534757	−	0.534757i
$454$			632.100i			1.39229i
$455$	−97.5093	−	56.8065i	−0.214306	−	0.124849i
$456$	−106.221			−0.232941
$457$	485.728	+	485.728i	1.06286	+	1.06286i	0.997887	+	0.0649742i	$0.0206965\pi$
$457$	485.728	+	485.728i	1.06286	+	1.06286i	0.0649742	+	0.997887i	$0.479304\pi$
$458$	−123.494	+	123.494i	−0.269637	+	0.269637i
$459$		−	70.1416i		−	0.152814i
$460$	−1.52746	−	5.79105i	−0.00332057	−	0.0125892i
$461$	−560.524			−1.21589			−0.607944	−	0.793980i	$-0.708005\pi$
$461$	−560.524			−1.21589			−0.607944	+	0.793980i	$0.708005\pi$
$462$	−64.5610	−	64.5610i	−0.139742	−	0.139742i
$463$	279.103	−	279.103i	0.602814	−	0.602814i	−0.338245	−	0.941058i	$-0.609833\pi$
$463$	279.103	−	279.103i	0.602814	−	0.602814i	0.941058	+	0.338245i	$0.109833\pi$
$464$		−	44.8686i		−	0.0966995i
$465$	−137.786	+	36.3427i	−0.296313	+	0.0781564i
$466$	418.735			0.898572
$467$	201.253	+	201.253i	0.430948	+	0.430948i	0.888951	−	0.458003i	$-0.151435\pi$
$467$	201.253	+	201.253i	0.430948	+	0.430948i	−0.458003	+	0.888951i	$0.651435\pi$
$468$	−36.1924	+	36.1924i	−0.0773342	+	0.0773342i
$469$		−	270.165i		−	0.576044i
$470$	−102.394	+	175.761i	−0.217860	+	0.373959i
$471$	440.671			0.935607
$472$	26.9548	+	26.9548i	0.0571076	+	0.0571076i
$473$	658.000	−	658.000i	1.39112	−	1.39112i
$474$			385.690i			0.813693i
$475$	471.541	−	267.349i	0.992717	−	0.562840i
$476$	−71.4287			−0.150060
$477$	55.8819	+	55.8819i	0.117153	+	0.117153i
$478$	−147.491	+	147.491i	−0.308559	+	0.308559i
$479$			705.419i			1.47269i	0.676606	+	0.736346i	$0.263450\pi$
$479$			705.419i			1.47269i	−0.676606	+	0.736346i	$0.736550\pi$
$480$	−42.3303	−	24.6606i	−0.0881881	−	0.0513763i
$481$	−575.041			−1.19551
$482$	−180.182	−	180.182i	−0.373821	−	0.373821i
$483$	1.94069	−	1.94069i	0.00401800	−	0.00401800i
$484$			154.964i			0.320174i
$485$	−175.325	−	664.708i	−0.361495	−	1.37053i
$486$	22.0454			0.0453609
$487$	−457.935	−	457.935i	−0.940317	−	0.940317i	0.0579991	−	0.998317i	$-0.481528\pi$
$487$	−457.935	−	457.935i	−0.940317	−	0.940317i	−0.998317	+	0.0579991i	$0.981528\pi$
$488$	21.7496	−	21.7496i	0.0445688	−	0.0445688i
$489$		−	47.6711i		−	0.0974870i
$490$	47.8606	−	12.6238i	0.0976747	−	0.0257629i
$491$	714.606			1.45541			0.727704	−	0.685891i	$-0.240587\pi$
$491$	714.606			1.45541			0.727704	+	0.685891i	$0.240587\pi$
$492$	107.870	+	107.870i	0.219249	+	0.219249i
$493$	107.068	−	107.068i	0.217177	−	0.217177i
$494$			261.578i			0.529510i
$495$	106.378	−	182.599i	0.214904	−	0.368886i
$496$	65.8170			0.132696
$497$	119.928	+	119.928i	0.241303	+	0.241303i
$498$	188.604	−	188.604i	0.378722	−	0.378722i
$499$			746.370i			1.49573i	0.663850	+	0.747866i	$0.268922\pi$
$499$			746.370i			1.49573i	−0.663850	+	0.747866i	$0.731078\pi$
$500$	249.983	+	2.93258i	0.499966	+	0.00586517i
$501$	191.801			0.382836
$502$	25.2366	+	25.2366i	0.0502720	+	0.0502720i
$503$	10.5315	−	10.5315i	0.0209375	−	0.0209375i	−0.696561	−	0.717498i	$-0.745287\pi$
$503$	10.5315	−	10.5315i	0.0209375	−	0.0209375i	0.717498	+	0.696561i	$0.245287\pi$
$504$		−	22.4499i		−	0.0445435i
$505$	−112.822	−	65.7272i	−0.223409	−	0.130153i
$506$	−11.9327			−0.0235824
$507$	−117.855	−	117.855i	−0.232456	−	0.232456i
$508$	190.623	−	190.623i	0.375243	−	0.375243i
$509$			137.581i			0.270296i	0.990825	+	0.135148i	$0.0431510\pi$
$509$			137.581i			0.270296i	−0.990825	+	0.135148i	$0.956849\pi$
$510$	−42.1646	−	159.858i	−0.0826757	−	0.313447i
$511$	−192.473			−0.376660
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	79.6658	−	79.6658i	0.155294	−	0.155294i
$514$			457.349i			0.889784i
$515$	−362.067	+	95.4999i	−0.703044	+	0.185437i
$516$	228.808			0.443426
$517$	286.574	+	286.574i	0.554302	+	0.554302i
$518$	178.347	−	178.347i	0.344300	−	0.344300i
$519$			163.999i			0.315990i
$520$	−60.7287	+	104.242i	−0.116786	+	0.200465i
$521$	397.521			0.762995			0.381498	−	0.924370i	$-0.375408\pi$
$521$	397.521			0.762995			0.381498	+	0.924370i	$0.375408\pi$
$522$	33.6514	+	33.6514i	0.0644663	+	0.0644663i
$523$	59.4921	−	59.4921i	0.113752	−	0.113752i	−0.647940	−	0.761692i	$-0.724369\pi$
$523$	59.4921	−	59.4921i	0.113752	−	0.113752i	0.761692	+	0.647940i	$0.224369\pi$
$524$		−	383.732i		−	0.732313i
$525$	56.5045	+	99.6606i	0.107628	+	0.189830i
$526$	−34.3283			−0.0652629
$527$	157.057	+	157.057i	0.298021	+	0.298021i
$528$	−69.0186	+	69.0186i	−0.130717	+	0.130717i
$529$			528.641i			0.999322i
$530$	160.952	+	93.7665i	0.303682	+	0.176918i
$531$	−40.4322			−0.0761434
$532$	−81.1277	−	81.1277i	−0.152496	−	0.152496i
$533$	265.640	−	265.640i	0.498386	−	0.498386i
$534$			92.3243i			0.172892i
$535$	147.431	+	558.954i	0.275572	+	1.04477i
$536$	−288.818			−0.538840
$537$	−81.4392	−	81.4392i	−0.151656	−	0.151656i
$538$	−503.847	+	503.847i	−0.936519	+	0.936519i
$539$		−	98.6186i		−	0.182966i
$540$	50.2432	−	13.2523i	0.0930429	−	0.0245412i
$541$	−964.790			−1.78335			−0.891673	−	0.452680i	$-0.850468\pi$
$541$	−964.790			−1.78335			−0.891673	+	0.452680i	$0.850468\pi$
$542$	147.700	+	147.700i	0.272510	+	0.272510i
$543$	41.0510	−	41.0510i	0.0756004	−	0.0756004i
$544$			76.3605i			0.140369i
$545$	−149.242	+	256.177i	−0.273839	+	0.470049i
$546$	−55.2848			−0.101254
$547$	−397.442	−	397.442i	−0.726585	−	0.726585i	0.243353	−	0.969938i	$-0.421753\pi$
$547$	−397.442	−	397.442i	−0.726585	−	0.726585i	−0.969938	+	0.243353i	$0.921753\pi$
$548$	−269.404	+	269.404i	−0.491614	+	0.491614i
$549$			32.6244i			0.0594251i
$550$	132.676	−	480.104i	0.241229	−	0.872916i
$551$	243.213			0.441404
$552$	−2.07469	−	2.07469i	−0.00375849	−	0.00375849i
$553$	−294.576	+	294.576i	−0.532687	+	0.532687i
$554$			5.70025i			0.0102893i
$555$	504.422	+	293.864i	0.908868	+	0.529485i
$556$	−99.2595			−0.178524
$557$	236.896	+	236.896i	0.425307	+	0.425307i	0.887026	−	0.461719i	$-0.152767\pi$
$557$	236.896	+	236.896i	0.425307	+	0.425307i	−0.461719	+	0.887026i	$0.652767\pi$
$558$	−49.3628	+	49.3628i	−0.0884637	+	0.0884637i
$559$		−	563.458i		−	1.00797i
$560$	−13.4955	−	51.1652i	−0.0240990	−	0.0913663i
$561$	−329.394			−0.587154
$562$	384.657	+	384.657i	0.684443	+	0.684443i
$563$	−113.926	+	113.926i	−0.202355	+	0.202355i	−0.801008	−	0.598653i	$-0.795703\pi$
$563$	−113.926	+	113.926i	−0.202355	+	0.202355i	0.598653	+	0.801008i	$0.295703\pi$
$564$			99.6511i			0.176686i
$565$	−972.204	+	256.431i	−1.72072	+	0.453860i
$566$	−403.467			−0.712839
$567$	16.8375	+	16.8375i	0.0296957	+	0.0296957i
$568$	128.208	−	128.208i	0.225718	−	0.225718i
$569$			932.914i			1.63957i	0.572673	+	0.819784i	$0.305907\pi$
$569$			932.914i			1.63957i	−0.572673	+	0.819784i	$0.694093\pi$
$570$	133.675	−	229.454i	0.234517	−	0.402552i
$571$	384.804			0.673912			0.336956	−	0.941520i	$-0.390603\pi$
$571$	384.804			0.673912			0.336956	+	0.941520i	$0.390603\pi$
$572$	169.964	+	169.964i	0.297140	+	0.297140i
$573$	257.045	−	257.045i	0.448596	−	0.448596i
$574$			164.775i			0.287064i
$575$	14.4318	+	3.98822i	0.0250989	+	0.00693604i
$576$	−24.0000			−0.0416667
$577$	−207.248	−	207.248i	−0.359182	−	0.359182i	0.504329	−	0.863512i	$-0.331740\pi$
$577$	−207.248	−	207.248i	−0.359182	−	0.359182i	−0.863512	+	0.504329i	$0.831740\pi$
$578$	106.784	−	106.784i	0.184747	−	0.184747i
$579$		−	607.313i		−	1.04890i
$580$	96.9233	+	56.4651i	0.167109	+	0.0973537i
$581$	288.097			0.495864
$582$	−238.137	−	238.137i	−0.409170	−	0.409170i
$583$	262.428	−	262.428i	0.450134	−	0.450134i
$584$			205.763i			0.352334i
$585$	−32.6348	−	123.728i	−0.0557860	−	0.211501i
$586$	−733.755			−1.25214
$587$	517.152	+	517.152i	0.881009	+	0.881009i	0.993637	−	0.112628i	$-0.0359268\pi$
$587$	517.152	+	517.152i	0.881009	+	0.881009i	−0.112628	+	0.993637i	$0.535927\pi$
$588$	17.1464	−	17.1464i	0.0291606	−	0.0291606i
$589$			356.766i			0.605715i
$590$	−92.1480	+	24.3052i	−0.156183	+	0.0411953i
$591$	35.1238			0.0594312
$592$	−190.661	−	190.661i	−0.322063	−	0.322063i
$593$	−455.580	+	455.580i	−0.768264	+	0.768264i	−0.977801	−	0.209537i	$-0.932804\pi$
$593$	−455.580	+	455.580i	−0.768264	+	0.768264i	0.209537	+	0.977801i	$0.432804\pi$
$594$		−	103.528i		−	0.174289i
$595$	89.8899	−	154.297i	0.151075	−	0.259323i
$596$	274.284			0.460208
$597$	346.114	+	346.114i	0.579756	+	0.579756i
$598$	−5.10909	+	5.10909i	−0.00854362	+	0.00854362i
$599$		−	812.606i		−	1.35660i	−0.734783	−	0.678302i	$-0.762716\pi$
$599$		−	812.606i		−	1.35660i	0.734783	−	0.678302i	$-0.237284\pi$
$600$	106.542	−	60.4059i	0.177569	−	0.100677i
$601$	−315.588			−0.525105			−0.262552	−	0.964918i	$-0.584564\pi$
$601$	−315.588			−0.525105			−0.262552	+	0.964918i	$0.584564\pi$
$602$	174.755	+	174.755i	0.290291	+	0.290291i
$603$	216.614	−	216.614i	0.359227	−	0.359227i
$604$		−	395.584i		−	0.654941i
$605$	−334.747	−	195.016i	−0.553301	−	0.322340i
$606$	−63.9665			−0.105555
$607$	523.720	+	523.720i	0.862801	+	0.862801i	0.991663	−	0.128862i	$-0.0411324\pi$
$607$	523.720	+	523.720i	0.862801	+	0.862801i	−0.128862	+	0.991663i	$0.541132\pi$
$608$	−86.7292	+	86.7292i	−0.142647	+	0.142647i
$609$			51.4034i			0.0844063i
$610$	19.6117	+	74.3534i	0.0321503	+	0.121891i
$611$	245.399			0.401635
$612$	−57.2704	−	57.2704i	−0.0935791	−	0.0935791i
$613$	−239.438	+	239.438i	−0.390601	+	0.390601i	−0.874901	−	0.484301i	$-0.839074\pi$
$613$	−239.438	+	239.438i	−0.390601	+	0.390601i	0.484301	+	0.874901i	$0.339074\pi$
$614$		−	825.570i		−	1.34458i
$615$	−368.767	+	97.2670i	−0.599622	+	0.158158i
$616$	−105.428			−0.171149
$617$	−508.117	−	508.117i	−0.823529	−	0.823529i	0.163083	−	0.986612i	$-0.447856\pi$
$617$	−508.117	−	508.117i	−0.823529	−	0.823529i	−0.986612	+	0.163083i	$0.947856\pi$
$618$	−129.713	+	129.713i	−0.209892	+	0.209892i
$619$			237.357i			0.383453i	0.981448	+	0.191727i	$0.0614087\pi$
$619$			237.357i			0.383453i	−0.981448	+	0.191727i	$0.938591\pi$
$620$	−82.8278	+	142.175i	−0.133593	+	0.229315i
$621$	3.11203			0.00501132
$622$	512.668	+	512.668i	0.824225	+	0.824225i
$623$	−70.5139	+	70.5139i	−0.113184	+	0.113184i
$624$			59.1019i			0.0947146i
$625$	−320.927	+	536.312i	−0.513484	+	0.858099i
$626$	−202.938			−0.324182
$627$	−374.120	−	374.120i	−0.596683	−	0.596683i
$628$	359.806	−	359.806i	0.572940	−	0.572940i
$629$		−	909.937i		−	1.44664i
$630$	48.4955	+	28.2523i	0.0769769	+	0.0448449i
$631$	717.680			1.13737			0.568685	−	0.822556i	$-0.307453\pi$
$631$	717.680			1.13737			0.568685	+	0.822556i	$0.307453\pi$
$632$	314.915	+	314.915i	0.498283	+	0.498283i
$633$	−255.471	+	255.471i	−0.403588	+	0.403588i
$634$		−	405.233i		−	0.639169i
$635$	171.886	+	651.667i	0.270686	+	1.02625i
$636$	91.2547			0.143482
$637$	−42.2245	−	42.2245i	−0.0662864	−	0.0662864i
$638$	158.031	−	158.031i	0.247698	−	0.247698i
$639$			192.312i			0.300958i
$640$	−54.6978	+	14.4272i	−0.0854654	+	0.0225426i
$641$	−894.582			−1.39560			−0.697802	−	0.716291i	$-0.745838\pi$
$641$	−894.582			−1.39560			−0.697802	+	0.716291i	$0.745838\pi$
$642$	200.250	+	200.250i	0.311915	+	0.311915i
$643$	27.5752	−	27.5752i	0.0428853	−	0.0428853i	−0.685339	−	0.728224i	$-0.740346\pi$
$643$	27.5752	−	27.5752i	0.0428853	−	0.0428853i	0.728224	+	0.685339i	$0.240346\pi$
$644$		−	3.16914i		−	0.00492102i
$645$	−287.945	+	494.262i	−0.446426	+	0.766297i
$646$	−413.918			−0.640739
$647$	76.5361	+	76.5361i	0.118294	+	0.118294i	0.763776	−	0.645482i	$-0.223343\pi$
$647$	76.5361	+	76.5361i	0.118294	+	0.118294i	−0.645482	+	0.763776i	$0.723343\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$			189.874i			0.292565i
$650$	−148.754	−	262.367i	−0.228853	−	0.403642i
$651$	−75.4029			−0.115826
$652$	−38.9233	−	38.9233i	−0.0596983	−	0.0596983i
$653$	873.233	−	873.233i	1.33726	−	1.33726i	0.438564	−	0.898700i	$-0.355487\pi$
$653$	873.233	−	873.233i	1.33726	−	1.33726i	0.898700	−	0.438564i	$-0.144513\pi$
$654$			145.245i			0.222086i
$655$	828.922	+	482.910i	1.26553	+	0.737267i
$656$	176.152			0.268524
$657$	−154.322	−	154.322i	−0.234889	−	0.234889i
$658$	−76.1098	+	76.1098i	−0.115668	+	0.115668i
$659$			62.2133i			0.0944055i	0.998885	+	0.0472028i	$0.0150307\pi$
$659$			62.2133i			0.0944055i	−0.998885	+	0.0472028i	$0.984969\pi$
$660$	−62.2343	−	235.948i	−0.0942944	−	0.357497i
$661$	−1086.21			−1.64328			−0.821639	−	0.570008i	$-0.806940\pi$
$661$	−1086.21			−1.64328			−0.821639	+	0.570008i	$0.806940\pi$
$662$	65.9564	+	65.9564i	0.0996321	+	0.0996321i
$663$	−141.033	+	141.033i	−0.212719	+	0.212719i
$664$		−	307.989i		−	0.463838i
$665$	277.344	−	73.1531i	0.417059	−	0.110005i
$666$	285.992			0.429417
$667$	4.75039	+	4.75039i	0.00712203	+	0.00712203i
$668$	156.605	−	156.605i	0.234438	−	0.234438i
$669$		−	502.602i		−	0.751273i
$670$	363.465	−	623.893i	0.542485	−	0.931184i
$671$	153.208			0.228328
$672$	−18.3303	−	18.3303i	−0.0272772	−	0.0272772i
$673$	663.103	−	663.103i	0.985294	−	0.985294i	−0.0145998	−	0.999893i	$-0.504647\pi$
$673$	663.103	−	663.103i	0.985294	−	0.985294i	0.999893	+	0.0145998i	$0.00464744\pi$
$674$		−	721.545i		−	1.07054i
$675$	−34.6018	+	125.211i	−0.0512620	+	0.185497i
$676$	−192.457			−0.284699
$677$	363.300	+	363.300i	0.536632	+	0.536632i	0.922538	−	0.385906i	$-0.126111\pi$
$677$	363.300	+	363.300i	0.536632	+	0.536632i	−0.385906	+	0.922538i	$0.626111\pi$
$678$	−348.300	+	348.300i	−0.513716	+	0.513716i
$679$		−	363.760i		−	0.535729i
$680$	−164.951	−	96.0964i	−0.242575	−	0.141318i
$681$	−774.161			−1.13680
$682$	231.814	+	231.814i	0.339903	+	0.339903i
$683$	133.225	−	133.225i	0.195058	−	0.195058i	−0.602819	−	0.797878i	$-0.705956\pi$
$683$	133.225	−	133.225i	0.195058	−	0.195058i	0.797878	+	0.602819i	$0.205956\pi$
$684$		−	130.094i		−	0.190196i
$685$	−242.923	−	920.990i	−0.354632	−	1.34451i
$686$	26.1916			0.0381802
$687$	−151.248	−	151.248i	−0.220157	−	0.220157i
$688$	186.821	−	186.821i	0.271542	−	0.271542i
$689$		−	224.722i		−	0.326157i
$690$	7.09256	−	1.87075i	0.0102791	−	0.00271124i
$691$	−1151.29			−1.66612			−0.833060	−	0.553183i	$-0.813413\pi$
$691$	−1151.29			−1.66612			−0.833060	+	0.553183i	$0.813413\pi$
$692$	133.904	+	133.904i	0.193503	+	0.193503i
$693$	79.0708	−	79.0708i	0.114099	−	0.114099i
$694$		−	390.436i		−	0.562588i
$695$	124.914	−	214.416i	0.179732	−	0.308513i
$696$	54.9526			0.0789548
$697$	420.345	+	420.345i	0.603077	+	0.603077i
$698$	−204.957	+	204.957i	−0.293635	+	0.293635i
$699$			512.843i			0.733681i
$700$	127.508	+	35.2368i	0.182155	+	0.0503383i
$701$	181.482			0.258890			0.129445	−	0.991587i	$-0.458680\pi$
$701$	181.482			0.258890			0.129445	+	0.991587i	$0.458680\pi$
$702$	−44.3264	−	44.3264i	−0.0631431	−	0.0631431i
$703$	1033.49	−	1033.49i	1.47012	−	1.47012i
$704$			112.707i			0.160095i
$705$	−215.262	−	125.407i	−0.305337	−	0.177882i
$706$	−466.988			−0.661457
$707$	−48.8552	−	48.8552i	−0.0691022	−	0.0691022i
$708$	−33.0127	+	33.0127i	−0.0466281	+	0.0466281i
$709$		−	436.784i		−	0.616057i	−0.951377	−	0.308029i	$-0.900331\pi$
$709$		−	436.784i		−	0.616057i	0.951377	−	0.308029i	$-0.0996692\pi$
$710$	115.606	+	438.294i	0.162825	+	0.617316i
$711$	−472.372			−0.664377
$712$	75.3825	+	75.3825i	0.105874	+	0.105874i
$713$	−6.96828	+	6.96828i	−0.00977318	+	0.00977318i
$714$		−	87.4820i		−	0.122524i
$715$	−581.041	+	153.257i	−0.812645	+	0.214345i
$716$	−132.990			−0.185740
$717$	−180.639	−	180.639i	−0.251937	−	0.251937i
$718$	263.565	−	263.565i	0.367082	−	0.367082i
$719$		−	553.810i		−	0.770250i	−0.922864	−	0.385125i	$-0.874158\pi$
$719$		−	553.810i		−	0.770250i	0.922864	−	0.385125i	$-0.125842\pi$
$720$	30.2030	−	51.8438i	0.0419485	−	0.0720053i
$721$	−198.141			−0.274813
$722$	−109.122	−	109.122i	−0.151138	−	0.151138i
$723$	220.677	−	220.677i	0.305224	−	0.305224i
$724$		−	67.0361i		−	0.0925913i
$725$	−243.947	+	138.311i	−0.336479	+	0.190773i
$726$	−189.792			−0.261421
$727$	−377.156	−	377.156i	−0.518783	−	0.518783i	0.398420	−	0.917203i	$-0.369559\pi$
$727$	−377.156	−	377.156i	−0.518783	−	0.518783i	−0.917203	+	0.398420i	$0.869559\pi$
$728$	−45.1398	+	45.1398i	−0.0620053	+	0.0620053i
$729$			27.0000i			0.0370370i
$730$	−444.480	−	258.943i	−0.608877	−	0.354717i
$731$	891.609			1.21971
$732$	26.6377	+	26.6377i	0.0363903	+	0.0363903i
$733$	−100.250	+	100.250i	−0.136767	+	0.136767i	−0.772176	−	0.635409i	$-0.780832\pi$
$733$	−100.250	+	100.250i	−0.136767	+	0.136767i	0.635409	+	0.772176i	$0.280832\pi$
$734$			44.0019i			0.0599481i
$735$	15.4610	+	58.6170i	0.0210354	+	0.0797511i
$736$	−3.38795			−0.00460320
$737$	−1017.24	−	1017.24i	−1.38025	−	1.38025i
$738$	−132.114	+	132.114i	−0.179016	+	0.179016i
$739$			606.576i			0.820806i	0.911904	+	0.410403i	$0.134612\pi$
$739$			606.576i			0.820806i	−0.911904	+	0.410403i	$0.865388\pi$
$740$	651.798	−	171.920i	0.880808	−	0.232324i
$741$	−320.366			−0.432343
$742$	69.6970	+	69.6970i	0.0939312	+	0.0939312i
$743$	−345.903	+	345.903i	−0.465549	+	0.465549i	−0.900469	−	0.434920i	$-0.856777\pi$
$743$	−345.903	+	345.903i	−0.465549	+	0.465549i	0.434920	+	0.900469i	$0.356777\pi$
$744$			80.6091i			0.108346i
$745$	−345.174	+	592.497i	−0.463321	+	0.795298i
$746$	−341.946			−0.458373
$747$	230.992	+	230.992i	0.309226	+	0.309226i
$748$	−268.949	+	268.949i	−0.359557	+	0.359557i
$749$			305.886i			0.408393i
$750$	−3.59167	+	306.165i	−0.00478889	+	0.408220i
$751$	−203.256			−0.270647			−0.135324	−	0.990801i	$-0.543207\pi$
$751$	−203.256			−0.270647			−0.135324	+	0.990801i	$0.543207\pi$
$752$	81.3648	+	81.3648i	0.108198	+	0.108198i
$753$	−30.9083	+	30.9083i	−0.0410469	+	0.0410469i
$754$		−	135.325i		−	0.179476i
$755$	854.525	+	497.826i	1.13182	+	0.659372i
$756$	27.4955			0.0363696
$757$	−6.94517	−	6.94517i	−0.00917460	−	0.00917460i	0.702505	−	0.711679i	$-0.252065\pi$
$757$	−6.94517	−	6.94517i	−0.00917460	−	0.00917460i	−0.711679	+	0.702505i	$0.752065\pi$
$758$	272.520	−	272.520i	0.359525	−	0.359525i
$759$		−	14.6145i		−	0.0192549i
$760$	−78.2039	−	296.494i	−0.102900	−	0.390123i
$761$	977.803			1.28489			0.642446	−	0.766331i	$-0.277920\pi$
$761$	977.803			1.28489			0.642446	+	0.766331i	$0.277920\pi$
$762$	233.465	+	233.465i	0.306384	+	0.306384i
$763$	−110.932	+	110.932i	−0.145390	+	0.145390i
$764$		−	419.753i		−	0.549415i
$765$	195.785	−	51.6409i	0.255929	−	0.0675044i
$766$	−567.954			−0.741454
$767$	81.2965	+	81.2965i	0.105993	+	0.105993i
$768$	−19.5959	+	19.5959i	−0.0255155	+	0.0255155i
$769$			821.202i			1.06788i	0.845521	+	0.533942i	$0.179290\pi$
$769$			821.202i			1.06788i	−0.845521	+	0.533942i	$0.820710\pi$
$770$	132.676	−	227.741i	0.172307	−	0.295767i
$771$	−560.136			−0.726506
$772$	−495.869	−	495.869i	−0.642317	−	0.642317i
$773$	433.236	−	433.236i	0.560460	−	0.560460i	−0.368978	−	0.929438i	$-0.620292\pi$
$773$	433.236	−	433.236i	0.560460	−	0.560460i	0.929438	+	0.368978i	$0.120292\pi$
$774$			280.231i			0.362056i
$775$	−202.886	−	357.843i	−0.261788	−	0.461732i
$776$	−388.876			−0.501128
$777$	218.430	+	218.430i	0.281120	+	0.281120i
$778$	12.8522	−	12.8522i	0.0165196	−	0.0165196i
$779$			954.843i			1.22573i
$780$	−127.670	−	74.3772i	−0.163679	−	0.0953554i
$781$	903.121			1.15636
$782$	−8.08455	−	8.08455i	−0.0103383	−	0.0103383i
$783$	−41.2144	+	41.2144i	−0.0526365	+	0.0526365i
$784$		−	28.0000i		−	0.0357143i
$785$	324.439	+	1230.04i	0.413298	+	1.56693i
$786$	469.974			0.597931
$787$	427.998	+	427.998i	0.543835	+	0.543835i	0.924651	−	0.380816i	$-0.124357\pi$
$787$	427.998	+	427.998i	0.543835	+	0.543835i	−0.380816	+	0.924651i	$0.624357\pi$
$788$	28.6785	−	28.6785i	0.0363940	−	0.0363940i
$789$		−	42.0434i		−	0.0532869i
$790$	−1076.57	+	283.960i	−1.36275	+	0.359443i
$791$	−532.036			−0.672612
$792$	−84.5302	−	84.5302i	−0.106730	−	0.106730i
$793$	65.5974	−	65.5974i	0.0827206	−	0.0827206i
$794$		−	485.735i		−	0.611757i
$795$	−114.840	+	197.125i	−0.144453	+	0.247956i
$796$	565.202			0.710053
$797$	156.240	+	156.240i	0.196035	+	0.196035i	0.798298	−	0.602263i	$-0.205734\pi$
$797$	156.240	+	156.240i	0.196035	+	0.196035i	−0.602263	+	0.798298i	$0.705734\pi$
$798$	99.3607	−	99.3607i	0.124512	−	0.124512i
$799$			388.316i			0.486003i
$800$	37.6697	−	136.312i	0.0470871	−	0.170390i
$801$	−113.074			−0.141166
$802$	−523.505	−	523.505i	−0.652749	−	0.652749i
$803$	−724.715	+	724.715i	−0.902510	+	0.902510i
$804$		−	353.729i		−	0.439961i
$805$	6.84584	+	3.98822i	0.00850415	+	0.00495431i
$806$	198.506			0.246286
$807$	−617.084	−	617.084i	−0.764665	−	0.764665i
$808$	−52.2284	+	52.2284i	−0.0646392	+	0.0646392i
$809$			475.750i			0.588072i	0.955794	+	0.294036i	$0.0949985\pi$
$809$			475.750i			0.588072i	−0.955794	+	0.294036i	$0.905002\pi$
$810$	16.2307	+	61.5351i	0.0200378	+	0.0759692i
$811$	321.958			0.396989			0.198494	−	0.980102i	$-0.436395\pi$
$811$	321.958			0.396989			0.198494	+	0.980102i	$0.436395\pi$
$812$	41.9707	+	41.9707i	0.0516881	+	0.0516881i
$813$	−180.895	+	180.895i	−0.222503	+	0.222503i
$814$		−	1343.05i		−	1.64994i
$815$	133.064	−	35.0973i	0.163269	−	0.0430641i
$816$	−93.5221			−0.114610
$817$	1012.68	+	1012.68i	1.23951	+	1.23951i
$818$	39.5511	−	39.5511i	0.0483509	−	0.0483509i
$819$		−	67.7098i		−	0.0826737i
$820$	−221.679	+	380.516i	−0.270340	+	0.464043i
$821$	−372.833			−0.454121			−0.227060	−	0.973881i	$-0.572911\pi$
$821$	−372.833			−0.454121			−0.227060	+	0.973881i	$0.572911\pi$
$822$	−329.952	−	329.952i	−0.401401	−	0.401401i
$823$	−514.145	+	514.145i	−0.624721	+	0.624721i	−0.946735	−	0.322014i	$-0.895640\pi$
$823$	−514.145	+	514.145i	−0.624721	+	0.624721i	0.322014	+	0.946735i	$0.395640\pi$
$824$			211.821i			0.257064i
$825$	588.005	+	162.494i	0.712733	+	0.196963i
$826$	−50.4278			−0.0610506
$827$	−389.845	−	389.845i	−0.471397	−	0.471397i	0.430970	−	0.902366i	$-0.358172\pi$
$827$	−389.845	−	389.845i	−0.471397	−	0.471397i	−0.902366	+	0.430970i	$0.858172\pi$
$828$	2.54096	−	2.54096i	0.00306880	−	0.00306880i
$829$		−	1442.33i		−	1.73984i	−0.493194	−	0.869919i	$-0.664171\pi$
$829$		−	1442.33i		−	1.73984i	0.493194	−	0.869919i	$-0.335829\pi$
$830$	665.305	+	387.590i	0.801572	+	0.466976i
$831$	−6.98135			−0.00840115
$832$	48.2565	+	48.2565i	0.0580006	+	0.0580006i
$833$	66.8154	−	66.8154i	0.0802106	−	0.0802106i
$834$		−	121.568i		−	0.145764i
$835$	141.211	+	535.371i	0.169115	+	0.641163i
$836$	−610.936			−0.730785
$837$	−60.4568	−	60.4568i	−0.0722303	−	0.0722303i
$838$	171.715	−	171.715i	0.204911	−	0.204911i
$839$		−	1101.83i		−	1.31326i	−0.754212	−	0.656630i	$-0.771981\pi$
$839$		−	1101.83i		−	1.31326i	0.754212	−	0.656630i	$-0.228019\pi$
$840$	62.6643	−	16.5285i	0.0746003	−	0.0196768i
$841$	715.176			0.850387
$842$	361.127	+	361.127i	0.428892	+	0.428892i
$843$	−471.107	+	471.107i	−0.558846	+	0.558846i
$844$			417.183i			0.494292i
$845$	242.198	−	415.737i	0.286625	−	0.491997i
$846$	−122.047			−0.144264
$847$	−144.956	−	144.956i	−0.171140	−	0.171140i
$848$	74.5092	−	74.5092i	0.0878646	−	0.0878646i
$849$		−	494.144i		−	0.582031i
$850$	415.167	−	235.387i	0.488432	−	0.276926i
$851$	40.3720			0.0474406
$852$	157.022	+	157.022i	0.184298	+	0.184298i
$853$	842.879	−	842.879i	0.988135	−	0.988135i	−0.0117957	−	0.999930i	$-0.503755\pi$
$853$	842.879	−	842.879i	0.988135	−	0.988135i	0.999930	+	0.0117957i	$0.00375478\pi$
$854$			40.6897i			0.0476460i
$855$	281.023	+	163.717i	0.328682	+	0.191482i
$856$	327.006			0.382017
$857$	−655.750	−	655.750i	−0.765169	−	0.765169i	0.212083	−	0.977252i	$-0.431975\pi$
$857$	−655.750	−	655.750i	−0.765169	−	0.765169i	−0.977252	+	0.212083i	$0.931975\pi$
$858$	−208.162	+	208.162i	−0.242614	+	0.242614i
$859$			800.197i			0.931545i	0.884904	+	0.465773i	$0.154223\pi$
$859$			800.197i			0.931545i	−0.884904	+	0.465773i	$0.845777\pi$
$860$	168.457	+	638.669i	0.195880	+	0.742638i
$861$	−201.807			−0.234387
$862$	323.054	+	323.054i	0.374772	+	0.374772i
$863$	−112.663	+	112.663i	−0.130549	+	0.130549i	−0.769362	−	0.638813i	$-0.779426\pi$
$863$	−112.663	+	112.663i	−0.130549	+	0.130549i	0.638813	+	0.769362i	$0.279426\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	−457.768	+	120.742i	−0.529211	+	0.139586i
$866$	153.489			0.177239
$867$	130.783	+	130.783i	0.150845	+	0.150845i
$868$	−61.5662	+	61.5662i	−0.0709288	+	0.0709288i
$869$			2218.32i			2.55272i
$870$	−69.1554	+	118.706i	−0.0794889	+	0.136444i
$871$	−871.085			−1.00010
$872$	118.592	+	118.592i	0.136000	+	0.136000i
$873$	291.657	−	291.657i	0.334086	−	0.334086i
$874$		−	18.3646i		−	0.0210122i
$875$	−236.581	+	231.094i	−0.270378	+	0.264108i
$876$	−252.007			−0.287679
$877$	9.31315	+	9.31315i	0.0106193	+	0.0106193i	0.712397	−	0.701777i	$-0.247610\pi$
$877$	9.31315	+	9.31315i	0.0106193	+	0.0106193i	−0.701777	+	0.712397i	$0.747610\pi$
$878$	864.627	−	864.627i	0.984768	−	0.984768i
$879$		−	898.663i		−	1.02237i
$880$	−243.465	−	141.837i	−0.276665	−	0.161178i
$881$	−59.1359			−0.0671236			−0.0335618	−	0.999437i	$-0.510685\pi$
$881$	−59.1359			−0.0671236			−0.0335618	+	0.999437i	$0.510685\pi$
$882$	21.0000	+	21.0000i	0.0238095	+	0.0238095i
$883$	77.6453	−	77.6453i	0.0879335	−	0.0879335i	−0.661772	−	0.749705i	$-0.730195\pi$
$883$	77.6453	−	77.6453i	0.0879335	−	0.0879335i	0.749705	+	0.661772i	$0.230195\pi$
$884$			230.306i			0.260527i
$885$	−29.7677	−	112.858i	−0.0336358	−	0.127523i
$886$	−653.663			−0.737768
$887$	−176.382	−	176.382i	−0.198852	−	0.198852i	0.600656	−	0.799508i	$-0.294906\pi$
$887$	−176.382	−	176.382i	−0.198852	−	0.198852i	−0.799508	+	0.600656i	$0.794906\pi$
$888$	233.511	−	233.511i	0.262963	−	0.262963i
$889$			356.623i			0.401151i
$890$	−257.704	+	67.9726i	−0.289555	+	0.0763737i
$891$	126.795			0.142307
$892$	−410.372	−	410.372i	−0.460059	−	0.460059i
$893$	−441.044	+	441.044i	−0.493890	+	0.493890i
$894$			335.928i			0.375758i
$895$	167.362	−	287.279i	0.186996	−	0.320982i
$896$	−29.9333			−0.0334077
$897$	−6.25733	−	6.25733i	−0.00697584	−	0.00697584i
$898$	331.011	−	331.011i	0.368609	−	0.368609i
$899$		−	184.570i		−	0.205306i
$900$	73.9818	+	130.486i	0.0822020	+	0.144985i
$901$	355.597			0.394670
$902$	620.422	+	620.422i	0.687829	+	0.687829i
$903$	−214.030	+	214.030i	−0.237021	+	0.237021i
$904$			568.771i			0.629171i
$905$	144.809	+	84.3620i	0.160009	+	0.0932176i
$906$	484.490			0.534757
$907$	−626.216	−	626.216i	−0.690425	−	0.690425i	0.271900	−	0.962326i	$-0.412348\pi$
$907$	−626.216	−	626.216i	−0.690425	−	0.690425i	−0.962326	+	0.271900i	$0.912348\pi$
$908$	−632.100	+	632.100i	−0.696145	+	0.696145i
$909$		−	78.3427i		−	0.0861855i
$910$	−40.7027	−	154.316i	−0.0447283	−	0.169578i
$911$	−969.279			−1.06397			−0.531986	−	0.846753i	$-0.678554\pi$
$911$	−969.279			−1.06397			−0.531986	+	0.846753i	$0.678554\pi$
$912$	−106.221	−	106.221i	−0.116471	−	0.116471i
$913$	1084.76	−	1084.76i	1.18813	−	1.18813i
$914$			971.455i			1.06286i
$915$	−91.0640	+	24.0193i	−0.0995235	+	0.0262506i
$916$	−246.987			−0.269637
$917$	358.948	+	358.948i	0.391438	+	0.391438i
$918$	70.1416	−	70.1416i	0.0764070	−	0.0764070i
$919$			581.291i			0.632526i	0.948672	+	0.316263i	$0.102428\pi$
$919$			581.291i			0.632526i	−0.948672	+	0.316263i	$0.897572\pi$
$920$	4.26359	−	7.31852i	0.00463434	−	0.00795491i
$921$	1011.11			1.09784
$922$	−560.524	−	560.524i	−0.607944	−	0.607944i
$923$	386.680	−	386.680i	0.418938	−	0.418938i
$924$		−	129.122i		−	0.139742i
$925$	−448.885	+	1624.34i	−0.485281	+	1.75604i
$926$	558.205			0.602814
$927$	−158.866	−	158.866i	−0.171376	−	0.171376i
$928$	44.8686	−	44.8686i	0.0483498	−	0.0483498i
$929$		−	1578.20i		−	1.69882i	−0.527736	−	0.849409i	$-0.676959\pi$
$929$		−	1578.20i		−	1.69882i	0.527736	−	0.849409i	$-0.323041\pi$
$930$	−174.128	−	101.443i	−0.187235	−	0.109078i
$931$	151.776			0.163025
$932$	418.735	+	418.735i	0.449286	+	0.449286i
$933$	−627.887	+	627.887i	−0.672977	+	0.672977i
$934$			402.505i			0.430948i
$935$	−242.512	−	919.432i	−0.259371	−	0.983350i
$936$	−72.3848			−0.0773342
$937$	448.839	+	448.839i	0.479017	+	0.479017i	0.904817	−	0.425800i	$-0.140007\pi$
$937$	448.839	+	448.839i	0.479017	+	0.479017i	−0.425800	+	0.904817i	$0.640007\pi$
$938$	270.165	−	270.165i	0.288022	−	0.288022i
$939$		−	248.547i		−	0.264693i
$940$	−278.155	+	73.3669i	−0.295909	+	0.0780499i
$941$	−10.8693			−0.0115508			−0.00577540	−	0.999983i	$-0.501838\pi$
$941$	−10.8693			−0.0115508			−0.00577540	+	0.999983i	$0.501838\pi$
$942$	440.671	+	440.671i	0.467804	+	0.467804i
$943$	−18.6498	+	18.6498i	−0.0197771	+	0.0197771i
$944$			53.9096i			0.0571076i
$945$	−34.6018	+	59.3946i	−0.0366157	+	0.0628514i
$946$	1316.00			1.39112
$947$	−223.851	−	223.851i	−0.236379	−	0.236379i	0.578970	−	0.815349i	$-0.303455\pi$
$947$	−223.851	−	223.851i	−0.236379	−	0.236379i	−0.815349	+	0.578970i	$0.803455\pi$
$948$	−385.690	+	385.690i	−0.406846	+	0.406846i
$949$			620.587i			0.653938i
$950$	738.890	+	204.191i	0.777779	+	0.214938i
$951$	496.307			0.521879
$952$	−71.4287	−	71.4287i	−0.0750302	−	0.0750302i
$953$	732.839	−	732.839i	0.768981	−	0.768981i	−0.208946	−	0.977927i	$-0.567003\pi$
$953$	732.839	−	732.839i	0.768981	−	0.768981i	0.977927	+	0.208946i	$0.0670032\pi$
$954$			111.764i			0.117153i
$955$	906.734	+	528.241i	0.949460	+	0.553132i
$956$	−294.982			−0.308559
$957$	193.548	+	193.548i	0.202244	+	0.202244i
$958$	−705.419	+	705.419i	−0.736346	+	0.736346i
$959$		−	504.009i		−	0.525557i
$960$	−17.6697	−	66.9909i	−0.0184059	−	0.0697822i
$961$	−690.258			−0.718270
$962$	−575.041	−	575.041i	−0.597755	−	0.597755i
$963$	−245.255	+	245.255i	−0.254678	+	0.254678i
$964$		−	360.364i		−	0.373821i
$965$	1695.18	−	447.126i	1.75667	−	0.463343i
$966$	3.88139			0.00401800
$967$	−334.532	−	334.532i	−0.345948	−	0.345948i	0.512650	−	0.858598i	$-0.328664\pi$
$967$	−334.532	−	334.532i	−0.345948	−	0.345948i	−0.858598	+	0.512650i	$0.828664\pi$
$968$	−154.964	+	154.964i	−0.160087	+	0.160087i
$969$		−	506.944i		−	0.523162i
$970$	489.383	−	840.033i	0.504518	−	0.866013i
$971$	922.031			0.949569			0.474784	−	0.880102i	$-0.342526\pi$
$971$	922.031			0.949569			0.474784	+	0.880102i	$0.342526\pi$
$972$	22.0454	+	22.0454i	0.0226805	+	0.0226805i
$973$	92.8487	−	92.8487i	0.0954252	−	0.0954252i
$974$		−	915.869i		−	0.940317i
$975$	321.333	−	182.186i	0.329572	−	0.186858i
$976$	43.4991			0.0445688
$977$	0.111963	+	0.111963i	0.000114599	+	0.000114599i	0.707164	−	0.707049i	$-0.249974\pi$
$977$	0.111963	+	0.111963i	0.000114599	+	0.000114599i	−0.707049	+	0.707164i	$0.749974\pi$
$978$	47.6711	−	47.6711i	0.0487435	−	0.0487435i
$979$			531.008i			0.542399i
$980$	60.4845	+	35.2368i	0.0617188	+	0.0359559i
$981$	−177.887			−0.181333
$982$	714.606	+	714.606i	0.727704	+	0.727704i
$983$	−631.195	+	631.195i	−0.642111	+	0.642111i	−0.951074	−	0.308963i	$-0.900018\pi$
$983$	−631.195	+	631.195i	−0.642111	+	0.642111i	0.308963	+	0.951074i	$0.400018\pi$
$984$			215.741i			0.219249i
$985$	25.8595	+	98.0408i	0.0262533	+	0.0995338i
$986$	214.137			0.217177
$987$	−93.2151	−	93.2151i	−0.0944428	−	0.0944428i
$988$	−261.578	+	261.578i	−0.264755	+	0.264755i
$989$			39.5588i			0.0399987i
$990$	288.976	−	76.2211i	0.291895	−	0.0769910i
$991$	784.199			0.791321			0.395661	−	0.918397i	$-0.370516\pi$
$991$	784.199			0.791321			0.395661	+	0.918397i	$0.370516\pi$
$992$	65.8170	+	65.8170i	0.0663478	+	0.0663478i
$993$	−80.7798	+	80.7798i	−0.0813492	+	0.0813492i
$994$			239.855i			0.241303i
$995$	−711.283	+	1220.93i	−0.714857	+	1.22706i
$996$	377.208			0.378722
$997$	−365.331	−	365.331i	−0.366430	−	0.366430i	0.499743	−	0.866174i	$-0.333428\pi$
$997$	−365.331	−	365.331i	−0.366430	−	0.366430i	−0.866174	+	0.499743i	$0.833428\pi$
$998$	−746.370	+	746.370i	−0.747866	+	0.747866i
$999$			350.267i			0.350618i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.l.a.127.1	yes	8
3.2	odd	2		630.3.o.b.127.4		8
5.2	odd	4		1050.3.l.b.43.4		8
5.3	odd	4	inner	210.3.l.a.43.1	✓	8
5.4	even	2		1050.3.l.b.757.4		8
15.8	even	4		630.3.o.b.253.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.a.43.1	✓	8	5.3	odd	4	inner
210.3.l.a.127.1	yes	8	1.1	even	1	trivial
630.3.o.b.127.4		8	3.2	odd	2
630.3.o.b.253.4		8	15.8	even	4
1050.3.l.b.43.4		8	5.2	odd	4
1050.3.l.b.757.4		8	5.4	even	2

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.32032 - 2.51691i) q^{5} -2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.32032 - 2.51691i) q^{5} -2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-1.80341 - 6.83723i) q^{10} -14.0884 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-6.03207 + 6.03207i) q^{13} -3.74166i q^{14} +(8.37386 - 2.20871i) q^{15} -4.00000 q^{16} +(-9.54506 - 9.54506i) q^{17} +(3.00000 - 3.00000i) q^{18} -21.6823i q^{19} +(5.03383 - 8.64064i) q^{20} +4.58258 q^{21} +(-14.0884 - 14.0884i) q^{22} +(0.423494 - 0.423494i) q^{23} -4.89898i q^{24} +(12.3303 + 21.7477i) q^{25} -12.0641 q^{26} +(3.67423 + 3.67423i) q^{27} +(3.74166 - 3.74166i) q^{28} +11.2171i q^{29} +(10.5826 + 6.16515i) q^{30} -16.4543 q^{31} +(-4.00000 - 4.00000i) q^{32} +(17.2547 - 17.2547i) q^{33} -19.0901i q^{34} +(3.37386 + 12.7913i) q^{35} +6.00000 q^{36} +(47.6653 + 47.6653i) q^{37} +(21.6823 - 21.6823i) q^{38} -14.7755i q^{39} +(13.6745 - 3.60681i) q^{40} -44.0379 q^{41} +(4.58258 + 4.58258i) q^{42} +(-46.7052 + 46.7052i) q^{43} -28.1767i q^{44} +(-7.55074 + 12.9610i) q^{45} +0.846988 q^{46} +(-20.3412 - 20.3412i) q^{47} +(4.89898 - 4.89898i) q^{48} +7.00000i q^{49} +(-9.41742 + 34.0780i) q^{50} +23.3805 q^{51} +(-12.0641 - 12.0641i) q^{52} +(-18.6273 + 18.6273i) q^{53} +7.34847i q^{54} +(60.8662 + 35.4592i) q^{55} +7.48331 q^{56} +(26.5553 + 26.5553i) q^{57} +(-11.2171 + 11.2171i) q^{58} -13.4774i q^{59} +(4.41742 + 16.7477i) q^{60} -10.8748 q^{61} +(-16.4543 - 16.4543i) q^{62} +(-5.61249 + 5.61249i) q^{63} -8.00000i q^{64} +(41.2426 - 10.8783i) q^{65} +34.5093 q^{66} +(72.2045 + 72.2045i) q^{67} +(19.0901 - 19.0901i) q^{68} +1.03734i q^{69} +(-9.41742 + 16.1652i) q^{70} -64.1040 q^{71} +(6.00000 + 6.00000i) q^{72} +(51.4407 - 51.4407i) q^{73} +95.3307i q^{74} +(-41.7369 - 11.5339i) q^{75} +43.3646 q^{76} +(26.3569 + 26.3569i) q^{77} +(14.7755 - 14.7755i) q^{78} -157.457i q^{79} +(17.2813 + 10.0677i) q^{80} -9.00000 q^{81} +(-44.0379 - 44.0379i) q^{82} +(-76.9972 + 76.9972i) q^{83} +9.16515i q^{84} +(17.2136 + 65.2618i) q^{85} -93.4104 q^{86} +(-13.7381 - 13.7381i) q^{87} +(28.1767 - 28.1767i) q^{88} -37.6912i q^{89} +(-20.5117 + 5.41022i) q^{90} +22.5699 q^{91} +(0.846988 + 0.846988i) q^{92} +(20.1523 - 20.1523i) q^{93} -40.6824i q^{94} +(-54.5724 + 93.6744i) q^{95} +9.79796 q^{96} +(97.2189 + 97.2189i) q^{97} +(-7.00000 + 7.00000i) q^{98} +42.2651i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 16 q^{8}+O(q^{10}) \) 8 * q + 8 * q^2 - 16 * q^8	\( 8 q + 8 q^{2} - 16 q^{8} - 8 q^{11} + 8 q^{13} + 12 q^{15} - 32 q^{16} - 32 q^{17} + 24 q^{18} - 8 q^{22} - 40 q^{23} - 48 q^{25} + 16 q^{26} + 48 q^{30} + 144 q^{31} - 32 q^{32} + 120 q^{33} - 28 q^{35} + 48 q^{36} + 160 q^{37} - 320 q^{41} - 32 q^{43} - 80 q^{46} - 144 q^{47} - 112 q^{50} + 72 q^{51} + 16 q^{52} - 200 q^{53} + 184 q^{55} - 24 q^{57} - 64 q^{58} + 72 q^{60} + 288 q^{61} + 144 q^{62} + 24 q^{65} + 240 q^{66} + 80 q^{67} + 64 q^{68} - 112 q^{70} - 280 q^{71} + 48 q^{72} + 312 q^{73} - 56 q^{77} + 48 q^{78} - 72 q^{81} - 320 q^{82} - 320 q^{83} + 80 q^{85} - 64 q^{86} - 48 q^{87} + 16 q^{88} - 80 q^{92} + 48 q^{93} - 472 q^{95} - 24 q^{97} - 56 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 - 16 * q^8 - 8 * q^11 + 8 * q^13 + 12 * q^15 - 32 * q^16 - 32 * q^17 + 24 * q^18 - 8 * q^22 - 40 * q^23 - 48 * q^25 + 16 * q^26 + 48 * q^30 + 144 * q^31 - 32 * q^32 + 120 * q^33 - 28 * q^35 + 48 * q^36 + 160 * q^37 - 320 * q^41 - 32 * q^43 - 80 * q^46 - 144 * q^47 - 112 * q^50 + 72 * q^51 + 16 * q^52 - 200 * q^53 + 184 * q^55 - 24 * q^57 - 64 * q^58 + 72 * q^60 + 288 * q^61 + 144 * q^62 + 24 * q^65 + 240 * q^66 + 80 * q^67 + 64 * q^68 - 112 * q^70 - 280 * q^71 + 48 * q^72 + 312 * q^73 - 56 * q^77 + 48 * q^78 - 72 * q^81 - 320 * q^82 - 320 * q^83 + 80 * q^85 - 64 * q^86 - 48 * q^87 + 16 * q^88 - 80 * q^92 + 48 * q^93 - 472 * q^95 - 24 * q^97 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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