LMFDB - Embedded newform 210.3.l.a.127.2

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			127.2
Root			$-0.323042 - 0.323042i$ of defining polynomial
Character	$\chi$	$=$	210.127
Dual form			210.3.l.a.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-0.578661 + 4.96640i) q^{5} -2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-0.578661 + 4.96640i) q^{5} -2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-5.54506 + 4.38774i) q^{10} -12.4065 q^{11} +(-2.44949 - 2.44949i) q^{12} +(3.13309 - 3.13309i) q^{13} +3.74166i q^{14} +(-5.37386 - 6.79129i) q^{15} -4.00000 q^{16} +(-5.80341 - 5.80341i) q^{17} +(3.00000 - 3.00000i) q^{18} +26.5813i q^{19} +(-9.93280 - 1.15732i) q^{20} -4.58258 q^{21} +(-12.4065 - 12.4065i) q^{22} +(-10.4235 + 10.4235i) q^{23} -4.89898i q^{24} +(-24.3303 - 5.74773i) q^{25} +6.26617 q^{26} +(3.67423 + 3.67423i) q^{27} +(-3.74166 + 3.74166i) q^{28} +14.5808i q^{29} +(1.41742 - 12.1652i) q^{30} +42.6563 q^{31} +(-4.00000 - 4.00000i) q^{32} +(15.1948 - 15.1948i) q^{33} -11.6068i q^{34} +(-10.3739 + 8.20871i) q^{35} +6.00000 q^{36} +(11.9306 + 11.9306i) q^{37} +(-26.5813 + 26.5813i) q^{38} +7.67446i q^{39} +(-8.77548 - 11.0901i) q^{40} +37.5226 q^{41} +(-4.58258 - 4.58258i) q^{42} +(24.0083 - 24.0083i) q^{43} -24.8131i q^{44} +(14.8992 + 1.73598i) q^{45} -20.8470 q^{46} +(8.83609 + 8.83609i) q^{47} +(4.89898 - 4.89898i) q^{48} +7.00000i q^{49} +(-18.5826 - 30.0780i) q^{50} +14.2154 q^{51} +(6.26617 + 6.26617i) q^{52} +(-1.97883 + 1.97883i) q^{53} +7.34847i q^{54} +(7.17918 - 61.6158i) q^{55} -7.48331 q^{56} +(-32.5553 - 32.5553i) q^{57} +(-14.5808 + 14.5808i) q^{58} +88.2651i q^{59} +(13.5826 - 10.7477i) q^{60} +102.471 q^{61} +(42.6563 + 42.6563i) q^{62} +(5.61249 - 5.61249i) q^{63} -8.00000i q^{64} +(13.7472 + 17.3732i) q^{65} +30.3897 q^{66} +(-22.8107 - 22.8107i) q^{67} +(11.6068 - 11.6068i) q^{68} -25.5322i q^{69} +(-18.5826 - 2.16515i) q^{70} -10.7950 q^{71} +(6.00000 + 6.00000i) q^{72} +(80.4481 - 80.4481i) q^{73} +23.8612i q^{74} +(36.8379 - 22.7589i) q^{75} -53.1625 q^{76} +(-23.2105 - 23.2105i) q^{77} +(-7.67446 + 7.67446i) q^{78} +138.851i q^{79} +(2.31464 - 19.8656i) q^{80} -9.00000 q^{81} +(37.5226 + 37.5226i) q^{82} +(-96.0834 + 96.0834i) q^{83} -9.16515i q^{84} +(32.1803 - 25.4638i) q^{85} +48.0166 q^{86} +(-17.8578 - 17.8578i) q^{87} +(24.8131 - 24.8131i) q^{88} -3.29855i q^{89} +(13.1632 + 16.6352i) q^{90} +11.7229 q^{91} +(-20.8470 - 20.8470i) q^{92} +(-52.2431 + 52.2431i) q^{93} +17.6722i q^{94} +(-132.013 - 15.3815i) q^{95} +9.79796 q^{96} +(-88.5219 - 88.5219i) q^{97} +(-7.00000 + 7.00000i) q^{98} +37.2196i 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
$5$	−0.578661	+	4.96640i	−0.115732	+	0.993280i
$5$	−0.578661	+	4.96640i	−0.115732	+	0.993280i
$6$	−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
$10$	−5.54506	+	4.38774i	−0.554506	+	0.438774i
$11$	−12.4065			−1.12787			−0.563933	−	0.825820i	$-0.690712\pi$
$11$	−12.4065			−1.12787			−0.563933	+	0.825820i	$0.690712\pi$
$12$	−2.44949	−	2.44949i	−0.204124	−	0.204124i
$13$	3.13309	−	3.13309i	0.241007	−	0.241007i	−0.576260	−	0.817267i	$-0.695488\pi$
$13$	3.13309	−	3.13309i	0.241007	−	0.241007i	0.817267	+	0.576260i	$0.195488\pi$
$14$			3.74166i			0.267261i
$15$	−5.37386	−	6.79129i	−0.358258	−	0.452753i
$16$	−4.00000			−0.250000
$17$	−5.80341	−	5.80341i	−0.341377	−	0.341377i	0.515508	−	0.856885i	$-0.327603\pi$
$17$	−5.80341	−	5.80341i	−0.341377	−	0.341377i	−0.856885	+	0.515508i	$0.827603\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$			26.5813i			1.39901i	0.714626	+	0.699507i	$0.246597\pi$
$19$			26.5813i			1.39901i	−0.714626	+	0.699507i	$0.753403\pi$
$20$	−9.93280	−	1.15732i	−0.496640	−	0.0578661i
$21$	−4.58258			−0.218218
$22$	−12.4065	−	12.4065i	−0.563933	−	0.563933i
$23$	−10.4235	+	10.4235i	−0.453195	+	0.453195i	−0.896414	−	0.443218i	$-0.853837\pi$
$23$	−10.4235	+	10.4235i	−0.453195	+	0.453195i	0.443218	+	0.896414i	$0.353837\pi$
$24$		−	4.89898i		−	0.204124i
$25$	−24.3303	−	5.74773i	−0.973212	−	0.229909i
$26$	6.26617			0.241007
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	−3.74166	+	3.74166i	−0.133631	+	0.133631i
$29$			14.5808i			0.502787i	0.967885	+	0.251393i	$0.0808888\pi$
$29$			14.5808i			0.502787i	−0.967885	+	0.251393i	$0.919111\pi$
$30$	1.41742	−	12.1652i	0.0472475	−	0.405505i
$31$	42.6563			1.37601			0.688005	−	0.725706i	$-0.258487\pi$
$31$	42.6563			1.37601			0.688005	+	0.725706i	$0.258487\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	15.1948	−	15.1948i	0.460450	−	0.460450i
$34$		−	11.6068i		−	0.341377i
$35$	−10.3739	+	8.20871i	−0.296396	+	0.234535i
$36$	6.00000			0.166667
$37$	11.9306	+	11.9306i	0.322448	+	0.322448i	0.849706	−	0.527257i	$-0.176780\pi$
$37$	11.9306	+	11.9306i	0.322448	+	0.322448i	−0.527257	+	0.849706i	$0.676780\pi$
$38$	−26.5813	+	26.5813i	−0.699507	+	0.699507i
$39$			7.67446i			0.196781i
$40$	−8.77548	−	11.0901i	−0.219387	−	0.277253i
$41$	37.5226			0.915185			0.457593	−	0.889162i	$-0.348712\pi$
$41$	37.5226			0.915185			0.457593	+	0.889162i	$0.348712\pi$
$42$	−4.58258	−	4.58258i	−0.109109	−	0.109109i
$43$	24.0083	−	24.0083i	0.558332	−	0.558332i	−0.370500	−	0.928832i	$-0.620814\pi$
$43$	24.0083	−	24.0083i	0.558332	−	0.558332i	0.928832	+	0.370500i	$0.120814\pi$
$44$		−	24.8131i		−	0.563933i
$45$	14.8992	+	1.73598i	0.331093	+	0.0385774i
$46$	−20.8470			−0.453195
$47$	8.83609	+	8.83609i	0.188002	+	0.188002i	0.794832	−	0.606830i	$-0.207559\pi$
$47$	8.83609	+	8.83609i	0.188002	+	0.188002i	−0.606830	+	0.794832i	$0.707559\pi$
$48$	4.89898	−	4.89898i	0.102062	−	0.102062i
$49$			7.00000i			0.142857i
$50$	−18.5826	−	30.0780i	−0.371652	−	0.601561i
$51$	14.2154			0.278733
$52$	6.26617	+	6.26617i	0.120503	+	0.120503i
$53$	−1.97883	+	1.97883i	−0.0373364	+	0.0373364i	−0.725529	−	0.688192i	$-0.758405\pi$
$53$	−1.97883	+	1.97883i	−0.0373364	+	0.0373364i	0.688192	+	0.725529i	$0.258405\pi$
$54$			7.34847i			0.136083i
$55$	7.17918	−	61.6158i	0.130530	−	1.12029i
$56$	−7.48331			−0.133631
$57$	−32.5553	−	32.5553i	−0.571145	−	0.571145i
$58$	−14.5808	+	14.5808i	−0.251393	+	0.251393i
$59$			88.2651i			1.49602i	0.663688	+	0.748010i	$0.268990\pi$
$59$			88.2651i			1.49602i	−0.663688	+	0.748010i	$0.731010\pi$
$60$	13.5826	−	10.7477i	0.226376	−	0.179129i
$61$	102.471			1.67985			0.839924	−	0.542704i	$-0.182600\pi$
$61$	102.471			1.67985			0.839924	+	0.542704i	$0.182600\pi$
$62$	42.6563	+	42.6563i	0.688005	+	0.688005i
$63$	5.61249	−	5.61249i	0.0890871	−	0.0890871i
$64$		−	8.00000i		−	0.125000i
$65$	13.7472	+	17.3732i	0.211495	+	0.267279i
$66$	30.3897			0.460450
$67$	−22.8107	−	22.8107i	−0.340458	−	0.340458i	0.516082	−	0.856539i	$-0.327390\pi$
$67$	−22.8107	−	22.8107i	−0.340458	−	0.340458i	−0.856539	+	0.516082i	$0.827390\pi$
$68$	11.6068	−	11.6068i	0.170688	−	0.170688i
$69$		−	25.5322i		−	0.370032i
$70$	−18.5826	−	2.16515i	−0.265465	−	0.0309307i
$71$	−10.7950			−0.152042			−0.0760208	−	0.997106i	$-0.524222\pi$
$71$	−10.7950			−0.152042			−0.0760208	+	0.997106i	$0.524222\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	80.4481	−	80.4481i	1.10203	−	1.10203i	0.107863	−	0.994166i	$-0.465599\pi$
$73$	80.4481	−	80.4481i	1.10203	−	1.10203i	0.994166	−	0.107863i	$-0.0344007\pi$
$74$			23.8612i			0.322448i
$75$	36.8379	−	22.7589i	0.491172	−	0.303452i
$76$	−53.1625			−0.699507
$77$	−23.2105	−	23.2105i	−0.301435	−	0.301435i
$78$	−7.67446	+	7.67446i	−0.0983905	+	0.0983905i
$79$			138.851i			1.75761i	0.477180	+	0.878806i	$0.341659\pi$
$79$			138.851i			1.75761i	−0.477180	+	0.878806i	$0.658341\pi$
$80$	2.31464	−	19.8656i	0.0289331	−	0.248320i
$81$	−9.00000			−0.111111
$82$	37.5226	+	37.5226i	0.457593	+	0.457593i
$83$	−96.0834	+	96.0834i	−1.15763	+	1.15763i	−0.172648	+	0.984984i	$0.555232\pi$
$83$	−96.0834	+	96.0834i	−1.15763	+	1.15763i	−0.984984	+	0.172648i	$0.944768\pi$
$84$		−	9.16515i		−	0.109109i
$85$	32.1803	−	25.4638i	0.378591	−	0.299575i
$86$	48.0166			0.558332
$87$	−17.8578	−	17.8578i	−0.205262	−	0.205262i
$88$	24.8131	−	24.8131i	0.281967	−	0.281967i
$89$		−	3.29855i		−	0.0370623i	−0.999828	−	0.0185312i	$-0.994101\pi$
$89$		−	3.29855i		−	0.0370623i	0.999828	−	0.0185312i	$-0.00589899\pi$
$90$	13.1632	+	16.6352i	0.146258	+	0.184835i
$91$	11.7229			0.128823
$92$	−20.8470	−	20.8470i	−0.226598	−	0.226598i
$93$	−52.2431	+	52.2431i	−0.561754	+	0.561754i
$94$			17.6722i			0.188002i
$95$	−132.013	−	15.3815i	−1.38961	−	0.161911i
$96$	9.79796			0.102062
$97$	−88.5219	−	88.5219i	−0.912597	−	0.912597i	0.0838786	−	0.996476i	$-0.473269\pi$
$97$	−88.5219	−	88.5219i	−0.912597	−	0.912597i	−0.996476	+	0.0838786i	$0.973269\pi$
$98$	−7.00000	+	7.00000i	−0.0714286	+	0.0714286i
$99$			37.2196i			0.375955i
$100$	11.4955	−	48.6606i	0.114955	−	0.486606i
$101$	142.067			1.40661			0.703304	−	0.710889i	$-0.251707\pi$
$101$	142.067			1.40661			0.703304	+	0.710889i	$0.251707\pi$
$102$	14.2154	+	14.2154i	0.139367	+	0.139367i
$103$	60.4386	−	60.4386i	0.586782	−	0.586782i	−0.349976	−	0.936759i	$-0.613810\pi$
$103$	60.4386	−	60.4386i	0.586782	−	0.586782i	0.936759	+	0.349976i	$0.113810\pi$
$104$			12.5323i			0.120503i
$105$	2.65176	−	22.7589i	0.0252548	−	0.216752i
$106$	−3.95766			−0.0373364
$107$	78.7617	+	78.7617i	0.736091	+	0.736091i	0.971819	−	0.235728i	$-0.0757474\pi$
$107$	78.7617	+	78.7617i	0.736091	+	0.736091i	−0.235728	+	0.971819i	$0.575747\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$		−	102.684i		−	0.942053i	−0.882119	−	0.471026i	$-0.843884\pi$
$109$		−	102.684i		−	0.942053i	0.882119	−	0.471026i	$-0.156116\pi$
$110$	68.7950	−	54.4366i	0.625409	−	0.494879i
$111$	−29.2239			−0.263278
$112$	−7.48331	−	7.48331i	−0.0668153	−	0.0668153i
$113$	−34.2131	+	34.2131i	−0.302771	+	0.302771i	−0.842097	−	0.539326i	$-0.818679\pi$
$113$	−34.2131	+	34.2131i	−0.302771	+	0.302771i	0.539326	+	0.842097i	$0.318679\pi$
$114$		−	65.1105i		−	0.571145i
$115$	−45.7356	−	57.7989i	−0.397701	−	0.502599i
$116$	−29.1616			−0.251393
$117$	−9.39926	−	9.39926i	−0.0803355	−	0.0803355i
$118$	−88.2651	+	88.2651i	−0.748010	+	0.748010i
$119$		−	21.7144i		−	0.182474i
$120$	24.3303	+	2.83485i	0.202753	+	0.0236237i
$121$	32.9220			0.272083
$122$	102.471	+	102.471i	0.839924	+	0.839924i
$123$	−45.9556	+	45.9556i	−0.373623	+	0.373623i
$124$			85.3126i			0.688005i
$125$	42.6245	−	117.508i	0.340996	−	0.940065i
$126$	11.2250			0.0890871
$127$	−149.547	−	149.547i	−1.17753	−	1.17753i	−0.980371	−	0.197161i	$-0.936828\pi$
$127$	−149.547	−	149.547i	−1.17753	−	1.17753i	−0.197161	−	0.980371i	$-0.563172\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$			58.8080i			0.455876i
$130$	−3.62599	+	31.1203i	−0.0278922	+	0.239387i
$131$	−93.4871			−0.713642			−0.356821	−	0.934173i	$-0.616139\pi$
$131$	−93.4871			−0.713642			−0.356821	+	0.934173i	$0.616139\pi$
$132$	30.3897	+	30.3897i	0.230225	+	0.230225i
$133$	−49.7290	+	49.7290i	−0.373902	+	0.373902i
$134$		−	45.6213i		−	0.340458i
$135$	−20.3739	+	16.1216i	−0.150918	+	0.119419i
$136$	23.2136			0.170688
$137$	−66.0053	−	66.0053i	−0.481790	−	0.481790i	0.423913	−	0.905703i	$-0.360656\pi$
$137$	−66.0053	−	66.0053i	−0.481790	−	0.481790i	−0.905703	+	0.423913i	$0.860656\pi$
$138$	25.5322	−	25.5322i	0.185016	−	0.185016i
$139$			111.764i			0.804059i	0.915627	+	0.402029i	$0.131695\pi$
$139$			111.764i			0.804059i	−0.915627	+	0.402029i	$0.868305\pi$
$140$	−16.4174	−	20.7477i	−0.117267	−	0.148198i
$141$	−21.6439			−0.153503
$142$	−10.7950	−	10.7950i	−0.0760208	−	0.0760208i
$143$	−38.8707	+	38.8707i	−0.271823	+	0.271823i
$144$			12.0000i			0.0833333i
$145$	−72.4142	−	8.43735i	−0.499408	−	0.0581886i
$146$	160.896			1.10203
$147$	−8.57321	−	8.57321i	−0.0583212	−	0.0583212i
$148$	−23.8612	+	23.8612i	−0.161224	+	0.161224i
$149$		−	214.999i		−	1.44295i	−0.692443	−	0.721473i	$-0.743465\pi$
$149$		−	214.999i		−	1.44295i	0.692443	−	0.721473i	$-0.256535\pi$
$150$	59.5968	+	14.0790i	0.397312	+	0.0938600i
$151$	−62.7527			−0.415581			−0.207790	−	0.978173i	$-0.566627\pi$
$151$	−62.7527			−0.415581			−0.207790	+	0.978173i	$0.566627\pi$
$152$	−53.1625	−	53.1625i	−0.349754	−	0.349754i
$153$	−17.4102	+	17.4102i	−0.113792	+	0.113792i
$154$		−	46.4210i		−	0.301435i
$155$	−24.6835	+	211.848i	−0.159249	+	1.36676i
$156$	−15.3489			−0.0983905
$157$	181.318	+	181.318i	1.15489	+	1.15489i	0.985560	+	0.169329i	$0.0541601\pi$
$157$	181.318	+	181.318i	1.15489	+	1.15489i	0.169329	+	0.985560i	$0.445840\pi$
$158$	−138.851	+	138.851i	−0.878806	+	0.878806i
$159$		−	4.84712i		−	0.0304850i
$160$	22.1803	−	17.5510i	0.138627	−	0.109694i
$161$	−39.0011			−0.242243
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	−52.0026	+	52.0026i	−0.319034	+	0.319034i	−0.848396	−	0.529362i	$-0.822431\pi$
$163$	−52.0026	+	52.0026i	−0.319034	+	0.319034i	0.529362	+	0.848396i	$0.322431\pi$
$164$			75.0452i			0.457593i
$165$	66.6710	+	84.2563i	0.404067	+	0.510644i
$166$	−192.167			−1.15763
$167$	−153.475	−	153.475i	−0.919013	−	0.919013i	0.0779443	−	0.996958i	$-0.475164\pi$
$167$	−153.475	−	153.475i	−0.919013	−	0.919013i	−0.996958	+	0.0779443i	$0.975164\pi$
$168$	9.16515	−	9.16515i	0.0545545	−	0.0545545i
$169$			149.368i			0.883832i
$170$	57.6441	+	6.71641i	0.339083	+	0.0395083i
$171$	79.7438			0.466338
$172$	48.0166	+	48.0166i	0.279166	+	0.279166i
$173$	−86.7956	+	86.7956i	−0.501708	+	0.501708i	−0.911969	−	0.410260i	$-0.865438\pi$
$173$	−86.7956	+	86.7956i	−0.501708	+	0.501708i	0.410260	+	0.911969i	$0.365438\pi$
$174$		−	35.7156i		−	0.205262i
$175$	−34.7648	−	56.2708i	−0.198656	−	0.321548i
$176$	49.6261			0.281967
$177$	−108.102	−	108.102i	−0.610747	−	0.610747i
$178$	3.29855	−	3.29855i	0.0185312	−	0.0185312i
$179$		−	203.414i		−	1.13639i	−0.822893	−	0.568196i	$-0.807641\pi$
$179$		−	203.414i		−	1.13639i	0.822893	−	0.568196i	$-0.192359\pi$
$180$	−3.47197	+	29.7984i	−0.0192887	+	0.165547i
$181$	−251.290			−1.38834			−0.694172	−	0.719810i	$-0.744229\pi$
$181$	−251.290			−1.38834			−0.694172	+	0.719810i	$0.744229\pi$
$182$	11.7229	+	11.7229i	0.0644117	+	0.0644117i
$183$	−125.500	+	125.500i	−0.685795	+	0.685795i
$184$		−	41.6940i		−	0.226598i
$185$	−66.1559	+	52.3483i	−0.357599	+	0.282964i
$186$	−104.486			−0.561754
$187$	72.0001	+	72.0001i	0.385027	+	0.385027i
$188$	−17.6722	+	17.6722i	−0.0940010	+	0.0940010i
$189$			13.7477i			0.0727393i
$190$	−116.632	−	147.395i	−0.613851	−	0.775762i
$191$	367.604			1.92463			0.962315	−	0.271938i	$-0.0876646\pi$
$191$	367.604			1.92463			0.962315	+	0.271938i	$0.0876646\pi$
$192$	9.79796	+	9.79796i	0.0510310	+	0.0510310i
$193$	95.7120	−	95.7120i	0.495917	−	0.495917i	−0.414247	−	0.910164i	$-0.635955\pi$
$193$	95.7120	−	95.7120i	0.495917	−	0.495917i	0.910164	+	0.414247i	$0.135955\pi$
$194$		−	177.044i		−	0.912597i
$195$	−38.1145	−	4.44091i	−0.195459	−	0.0227739i
$196$	−14.0000			−0.0714286
$197$	−194.449	−	194.449i	−0.987048	−	0.987048i	0.0128689	−	0.999917i	$-0.495904\pi$
$197$	−194.449	−	194.449i	−0.987048	−	0.987048i	−0.999917	+	0.0128689i	$0.995904\pi$
$198$	−37.2196	+	37.2196i	−0.187978	+	0.187978i
$199$			91.9043i			0.461831i	0.972974	+	0.230915i	$0.0741720\pi$
$199$			91.9043i			0.461831i	−0.972974	+	0.230915i	$0.925828\pi$
$200$	60.1561	−	37.1652i	0.300780	−	0.185826i
$201$	55.8745			0.277982
$202$	142.067	+	142.067i	0.703304	+	0.703304i
$203$	−27.2782	+	27.2782i	−0.134375	+	0.134375i
$204$			28.4308i			0.139367i
$205$	−21.7129	+	186.352i	−0.105916	+	0.909036i
$206$	120.877			0.586782
$207$	31.2705	+	31.2705i	0.151065	+	0.151065i
$208$	−12.5323	+	12.5323i	−0.0602517	+	0.0602517i
$209$		−	329.781i		−	1.57790i
$210$	25.4107	−	20.1072i	0.121003	−	0.0957484i
$211$	296.539			1.40540			0.702700	−	0.711486i	$-0.251978\pi$
$211$	296.539			1.40540			0.702700	+	0.711486i	$0.251978\pi$
$212$	−3.95766	−	3.95766i	−0.0186682	−	0.0186682i
$213$	13.2211	−	13.2211i	0.0620707	−	0.0620707i
$214$			157.523i			0.736091i
$215$	105.342	+	133.127i	0.489963	+	0.619197i
$216$	−14.6969			−0.0680414
$217$	79.8026	+	79.8026i	0.367754	+	0.367754i
$218$	102.684	−	102.684i	0.471026	−	0.471026i
$219$			197.057i			0.899803i
$220$	123.232	+	14.3584i	0.560144	+	0.0652652i
$221$	−36.3651			−0.164548
$222$	−29.2239	−	29.2239i	−0.131639	−	0.131639i
$223$	99.7016	−	99.7016i	0.447092	−	0.447092i	−0.447295	−	0.894387i	$-0.647612\pi$
$223$	99.7016	−	99.7016i	0.447092	−	0.447092i	0.894387	+	0.447295i	$0.147612\pi$
$224$		−	14.9666i		−	0.0668153i
$225$	−17.2432	+	72.9909i	−0.0766364	+	0.324404i
$226$	−68.4262			−0.302771
$227$	−45.7570	−	45.7570i	−0.201573	−	0.201573i	0.599101	−	0.800674i	$-0.295525\pi$
$227$	−45.7570	−	45.7570i	−0.201573	−	0.201573i	−0.800674	+	0.599101i	$0.795525\pi$
$228$	65.1105	−	65.1105i	0.285573	−	0.285573i
$229$			248.102i			1.08342i	0.840567	+	0.541708i	$0.182222\pi$
$229$			248.102i			1.08342i	−0.840567	+	0.541708i	$0.817778\pi$
$230$	12.0633	−	103.535i	0.0524493	−	0.450150i
$231$	56.8539			0.246121
$232$	−29.1616	−	29.1616i	−0.125697	−	0.125697i
$233$	306.481	−	306.481i	1.31537	−	1.31537i	0.397968	−	0.917399i	$-0.369716\pi$
$233$	306.481	−	306.481i	1.31537	−	1.31537i	0.917399	−	0.397968i	$-0.130284\pi$
$234$		−	18.7985i		−	0.0803355i
$235$	−48.9967	+	38.7705i	−0.208497	+	0.164981i
$236$	−176.530			−0.748010
$237$	−170.057	−	170.057i	−0.717542	−	0.717542i
$238$	21.7144	−	21.7144i	0.0912368	−	0.0912368i
$239$			136.398i			0.570702i	0.958423	+	0.285351i	$0.0921102\pi$
$239$			136.398i			0.570702i	−0.958423	+	0.285351i	$0.907890\pi$
$240$	21.4955	+	27.1652i	0.0895644	+	0.113188i
$241$	332.727			1.38061			0.690305	−	0.723519i	$-0.257477\pi$
$241$	332.727			1.38061			0.690305	+	0.723519i	$0.257477\pi$
$242$	32.9220	+	32.9220i	0.136041	+	0.136041i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$			204.941i			0.839924i
$245$	−34.7648	−	4.05063i	−0.141897	−	0.0165332i
$246$	−91.9112			−0.373623
$247$	83.2814	+	83.2814i	0.337172	+	0.337172i
$248$	−85.3126	+	85.3126i	−0.344002	+	0.344002i
$249$		−	235.355i		−	0.945202i
$250$	160.133	−	74.8836i	0.640530	−	0.299534i
$251$	244.521			0.974186			0.487093	−	0.873350i	$-0.338057\pi$
$251$	244.521			0.974186			0.487093	+	0.873350i	$0.338057\pi$
$252$	11.2250	+	11.2250i	0.0445435	+	0.0445435i
$253$	129.319	−	129.319i	0.511144	−	0.511144i
$254$		−	299.093i		−	1.17753i
$255$	−8.22589	+	70.5993i	−0.0322584	+	0.276860i
$256$	16.0000			0.0625000
$257$	102.592	+	102.592i	0.399191	+	0.399191i	0.877948	−	0.478756i	$-0.158912\pi$
$257$	102.592	+	102.592i	0.399191	+	0.399191i	−0.478756	+	0.877948i	$0.658912\pi$
$258$	−58.8080	+	58.8080i	−0.227938	+	0.227938i
$259$			44.6402i			0.172356i
$260$	−34.7463	+	27.4943i	−0.133640	+	0.105747i
$261$	43.7424			0.167596
$262$	−93.4871	−	93.4871i	−0.356821	−	0.356821i
$263$	253.841	−	253.841i	0.965174	−	0.965174i	−0.0342400	−	0.999414i	$-0.510901\pi$
$263$	253.841	−	253.841i	0.965174	−	0.965174i	0.999414	+	0.0342400i	$0.0109011\pi$
$264$			60.7793i			0.230225i
$265$	−8.68259	−	10.9727i	−0.0327645	−	0.0414065i
$266$	−99.4580			−0.373902
$267$	4.03988	+	4.03988i	0.0151306	+	0.0151306i
$268$	45.6213	−	45.6213i	0.170229	−	0.170229i
$269$		−	207.747i		−	0.772295i	−0.922437	−	0.386147i	$-0.873806\pi$
$269$		−	207.747i		−	0.772295i	0.922437	−	0.386147i	$-0.126194\pi$
$270$	−36.4955	−	4.25227i	−0.135168	−	0.0157492i
$271$	−476.286			−1.75751			−0.878756	−	0.477270i	$-0.841626\pi$
$271$	−476.286			−1.75751			−0.878756	+	0.477270i	$0.841626\pi$
$272$	23.2136	+	23.2136i	0.0853442	+	0.0853442i
$273$	−14.3576	+	14.3576i	−0.0525920	+	0.0525920i
$274$		−	132.011i		−	0.481790i
$275$	301.855	+	71.3094i	1.09765	+	0.259307i
$276$	51.0645			0.185016
$277$	−9.67870	−	9.67870i	−0.0349412	−	0.0349412i	0.689420	−	0.724362i	$-0.257865\pi$
$277$	−9.67870	−	9.67870i	−0.0349412	−	0.0349412i	−0.724362	+	0.689420i	$0.757865\pi$
$278$	−111.764	+	111.764i	−0.402029	+	0.402029i
$279$		−	127.969i		−	0.458670i
$280$	4.33030	−	37.1652i	0.0154654	−	0.132733i
$281$	101.463			0.361079			0.180540	−	0.983568i	$-0.442216\pi$
$281$	101.463			0.361079			0.180540	+	0.983568i	$0.442216\pi$
$282$	−21.6439	−	21.6439i	−0.0767515	−	0.0767515i
$283$	276.026	−	276.026i	0.975358	−	0.975358i	−0.0243452	−	0.999704i	$-0.507750\pi$
$283$	276.026	−	276.026i	0.975358	−	0.975358i	0.999704	+	0.0243452i	$0.00775008\pi$
$284$		−	21.5899i		−	0.0760208i
$285$	180.521	−	142.844i	0.633407	−	0.501207i
$286$	−77.7415			−0.271823
$287$	70.1983	+	70.1983i	0.244594	+	0.244594i
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$		−	221.641i		−	0.766924i
$290$	−63.9768	−	80.8515i	−0.220610	−	0.278798i
$291$	216.834			0.745133
$292$	160.896	+	160.896i	0.551014	+	0.551014i
$293$	104.873	−	104.873i	0.357928	−	0.357928i	−0.505121	−	0.863049i	$-0.668552\pi$
$293$	104.873	−	104.873i	0.357928	−	0.357928i	0.863049	+	0.505121i	$0.168552\pi$
$294$		−	17.1464i		−	0.0583212i
$295$	−438.360	−	51.0756i	−1.48597	−	0.173138i
$296$	−47.7224			−0.161224
$297$	−45.5845	−	45.5845i	−0.153483	−	0.153483i
$298$	214.999	−	214.999i	0.721473	−	0.721473i
$299$			65.3154i			0.218446i
$300$	45.5178	+	73.6758i	0.151726	+	0.245586i
$301$	89.8308			0.298441
$302$	−62.7527	−	62.7527i	−0.207790	−	0.207790i
$303$	−173.996	+	173.996i	−0.574245	+	0.574245i
$304$		−	106.325i		−	0.349754i
$305$	−59.2958	+	508.911i	−0.194412	+	1.66856i
$306$	−34.8204			−0.113792
$307$	158.138	+	158.138i	0.515108	+	0.515108i	0.916087	−	0.400979i	$-0.131330\pi$
$307$	158.138	+	158.138i	0.515108	+	0.515108i	−0.400979	+	0.916087i	$0.631330\pi$
$308$	46.4210	−	46.4210i	0.150717	−	0.150717i
$309$			148.044i			0.479106i
$310$	−236.532	+	187.165i	−0.763006	+	0.603757i
$311$	−519.537			−1.67054			−0.835269	−	0.549842i	$-0.814688\pi$
$311$	−519.537			−1.67054			−0.835269	+	0.549842i	$0.814688\pi$
$312$	−15.3489	−	15.3489i	−0.0491953	−	0.0491953i
$313$	73.0852	−	73.0852i	0.233499	−	0.233499i	−0.580653	−	0.814152i	$-0.697202\pi$
$313$	73.0852	−	73.0852i	0.233499	−	0.233499i	0.814152	+	0.580653i	$0.197202\pi$
$314$			362.635i			1.15489i
$315$	24.6261	+	31.1216i	0.0781782	+	0.0987987i
$316$	−277.703			−0.878806
$317$	279.849	+	279.849i	0.882805	+	0.882805i	0.993819	−	0.111014i	$-0.0354098\pi$
$317$	279.849	+	279.849i	0.882805	+	0.882805i	−0.111014	+	0.993819i	$0.535410\pi$
$318$	4.84712	−	4.84712i	0.0152425	−	0.0152425i
$319$		−	180.897i		−	0.567076i
$320$	39.7312	+	4.62929i	0.124160	+	0.0144665i
$321$	−192.926			−0.601016
$322$	−39.0011	−	39.0011i	−0.121122	−	0.121122i
$323$	154.262	−	154.262i	0.477591	−	0.477591i
$324$		−	18.0000i		−	0.0555556i
$325$	−94.2371	+	58.2208i	−0.289960	+	0.179141i
$326$	−104.005			−0.319034
$327$	125.761	+	125.761i	0.384592	+	0.384592i
$328$	−75.0452	+	75.0452i	−0.228796	+	0.228796i
$329$			33.0616i			0.100491i
$330$	−17.5853	+	150.927i	−0.0532888	+	0.457356i
$331$	−601.834			−1.81823			−0.909115	−	0.416546i	$-0.863241\pi$
$331$	−601.834			−1.81823			−0.909115	+	0.416546i	$0.863241\pi$
$332$	−192.167	−	192.167i	−0.578816	−	0.578816i
$333$	35.7918	−	35.7918i	0.107483	−	0.107483i
$334$		−	306.950i		−	0.919013i
$335$	126.487	−	100.087i	0.377572	−	0.298768i
$336$	18.3303			0.0545545
$337$	17.0969	+	17.0969i	0.0507325	+	0.0507325i	0.732018	−	0.681285i	$-0.238579\pi$
$337$	17.0969	+	17.0969i	0.0507325	+	0.0507325i	−0.681285	+	0.732018i	$0.738579\pi$
$338$	−149.368	+	149.368i	−0.441916	+	0.441916i
$339$		−	83.8046i		−	0.247211i
$340$	50.9277	+	64.3605i	0.149787	+	0.189296i
$341$	−529.217			−1.55195
$342$	79.7438	+	79.7438i	0.233169	+	0.233169i
$343$	−13.0958	+	13.0958i	−0.0381802	+	0.0381802i
$344$			96.0331i			0.279166i
$345$	126.803	+	14.7745i	0.367546	+	0.0428247i
$346$	−173.591			−0.501708
$347$	233.692	+	233.692i	0.673465	+	0.673465i	0.958513	−	0.285048i	$-0.0920095\pi$
$347$	233.692	+	233.692i	0.673465	+	0.673465i	−0.285048	+	0.958513i	$0.592010\pi$
$348$	35.7156	−	35.7156i	0.102631	−	0.102631i
$349$			399.184i			1.14379i	0.820326	+	0.571896i	$0.193792\pi$
$349$			399.184i			1.14379i	−0.820326	+	0.571896i	$0.806208\pi$
$350$	21.5060	−	91.0357i	0.0614458	−	0.260102i
$351$	23.0234			0.0655937
$352$	49.6261	+	49.6261i	0.140983	+	0.140983i
$353$	−137.005	+	137.005i	−0.388117	+	0.388117i	−0.874015	−	0.485898i	$-0.838493\pi$
$353$	−137.005	+	137.005i	−0.388117	+	0.388117i	0.485898	+	0.874015i	$0.338493\pi$
$354$		−	216.205i		−	0.610747i
$355$	6.24662	−	53.6121i	0.0175961	−	0.151020i
$356$	6.59709			0.0185312
$357$	26.5945	+	26.5945i	0.0744945	+	0.0744945i
$358$	203.414	−	203.414i	0.568196	−	0.568196i
$359$			473.333i			1.31848i	0.751934	+	0.659239i	$0.229121\pi$
$359$			473.333i			1.31848i	−0.751934	+	0.659239i	$0.770879\pi$
$360$	−33.2704	+	26.3264i	−0.0924177	+	0.0731290i
$361$	−345.564			−0.957241
$362$	−251.290	−	251.290i	−0.694172	−	0.694172i
$363$	−40.3210	+	40.3210i	−0.111077	+	0.111077i
$364$			23.4459i			0.0644117i
$365$	352.985	+	446.090i	0.967083	+	1.22216i
$366$	−251.001			−0.685795
$367$	−256.657	−	256.657i	−0.699338	−	0.699338i	0.264930	−	0.964268i	$-0.414651\pi$
$367$	−256.657	−	256.657i	−0.699338	−	0.699338i	−0.964268	+	0.264930i	$0.914651\pi$
$368$	41.6940	−	41.6940i	0.113299	−	0.113299i
$369$		−	112.568i		−	0.305062i
$370$	−118.504	−	13.8075i	−0.320282	−	0.0373177i
$371$	−7.40410			−0.0199571
$372$	−104.486	−	104.486i	−0.280877	−	0.280877i
$373$	−278.764	+	278.764i	−0.747355	+	0.747355i	−0.973982	−	0.226627i	$-0.927230\pi$
$373$	−278.764	+	278.764i	−0.747355	+	0.747355i	0.226627	+	0.973982i	$0.427230\pi$
$374$			144.000i			0.385027i
$375$	91.7133	+	196.122i	0.244569	+	0.522991i
$376$	−35.3444			−0.0940010
$377$	45.6830	+	45.6830i	0.121175	+	0.121175i
$378$	−13.7477	+	13.7477i	−0.0363696	+	0.0363696i
$379$			168.579i			0.444800i	0.974955	+	0.222400i	$0.0713891\pi$
$379$			168.579i			0.444800i	−0.974955	+	0.222400i	$0.928611\pi$
$380$	30.7631	−	264.027i	0.0809555	−	0.694807i
$381$	366.313			0.961451
$382$	367.604	+	367.604i	0.962315	+	0.962315i
$383$	−166.588	+	166.588i	−0.434956	+	0.434956i	−0.890310	−	0.455354i	$-0.849513\pi$
$383$	−166.588	+	166.588i	−0.434956	+	0.434956i	0.455354	+	0.890310i	$0.349513\pi$
$384$			19.5959i			0.0510310i
$385$	128.704	−	101.842i	0.334295	−	0.264524i
$386$	191.424			0.495917
$387$	−72.0249	−	72.0249i	−0.186111	−	0.186111i
$388$	177.044	−	177.044i	0.456299	−	0.456299i
$389$			73.9237i			0.190035i	0.995476	+	0.0950176i	$0.0302907\pi$
$389$			73.9237i			0.190035i	−0.995476	+	0.0950176i	$0.969709\pi$
$390$	−33.6736	−	42.5554i	−0.0863424	−	0.109116i
$391$	120.984			0.309421
$392$	−14.0000	−	14.0000i	−0.0357143	−	0.0357143i
$393$	114.498	−	114.498i	0.291343	−	0.291343i
$394$		−	388.897i		−	0.987048i
$395$	−689.591	−	80.3478i	−1.74580	−	0.203412i
$396$	−74.4392			−0.187978
$397$	73.4533	+	73.4533i	0.185021	+	0.185021i	0.793540	−	0.608519i	$-0.208236\pi$
$397$	73.4533	+	73.4533i	0.185021	+	0.185021i	−0.608519	+	0.793540i	$0.708236\pi$
$398$	−91.9043	+	91.9043i	−0.230915	+	0.230915i
$399$		−	121.811i		−	0.305290i
$400$	97.3212	+	22.9909i	0.243303	+	0.0574773i
$401$	−534.615			−1.33321			−0.666603	−	0.745413i	$-0.732252\pi$
$401$	−534.615			−1.33321			−0.666603	+	0.745413i	$0.732252\pi$
$402$	55.8745	+	55.8745i	0.138991	+	0.138991i
$403$	133.646	−	133.646i	0.331627	−	0.331627i
$404$			284.135i			0.703304i
$405$	5.20795	−	44.6976i	0.0128591	−	0.110364i
$406$	−54.5564			−0.134375
$407$	−148.017	−	148.017i	−0.363679	−	0.363679i
$408$	−28.4308	+	28.4308i	−0.0696833	+	0.0696833i
$409$			14.4205i			0.0352578i	0.999845	+	0.0176289i	$0.00561175\pi$
$409$			14.4205i			0.0352578i	−0.999845	+	0.0176289i	$0.994388\pi$
$410$	−208.065	+	164.639i	−0.507476	+	0.401560i
$411$	161.679			0.393380
$412$	120.877	+	120.877i	0.293391	+	0.293391i
$413$	−165.129	+	165.129i	−0.399828	+	0.399828i
$414$			62.5410i			0.151065i
$415$	−421.589	−	532.789i	−1.01588	−	1.28383i
$416$	−25.0647			−0.0602517
$417$	−136.883	−	136.883i	−0.328256	−	0.328256i
$418$	329.781	−	329.781i	0.788951	−	0.788951i
$419$		−	337.860i		−	0.806349i	−0.915123	−	0.403174i	$-0.867907\pi$
$419$		−	337.860i		−	0.806349i	0.915123	−	0.403174i	$-0.132093\pi$
$420$	45.5178	+	5.30352i	0.108376	+	0.0126274i
$421$	372.730			0.885345			0.442672	−	0.896683i	$-0.354031\pi$
$421$	372.730			0.885345			0.442672	+	0.896683i	$0.354031\pi$
$422$	296.539	+	296.539i	0.702700	+	0.702700i
$423$	26.5083	−	26.5083i	0.0626673	−	0.0626673i
$424$		−	7.91531i		−	0.0186682i
$425$	107.842	+	174.555i	0.253746	+	0.410718i
$426$	26.4421			0.0620707
$427$	191.705	+	191.705i	0.448958	+	0.448958i
$428$	−157.523	+	157.523i	−0.368046	+	0.368046i
$429$		−	95.2134i		−	0.221943i
$430$	−27.7853	+	238.470i	−0.0646170	+	0.554580i
$431$	−591.932			−1.37339			−0.686696	−	0.726944i	$-0.740940\pi$
$431$	−591.932			−1.37339			−0.686696	+	0.726944i	$0.740940\pi$
$432$	−14.6969	−	14.6969i	−0.0340207	−	0.0340207i
$433$	−239.916	+	239.916i	−0.554079	+	0.554079i	−0.927615	−	0.373537i	$-0.878145\pi$
$433$	−239.916	+	239.916i	−0.554079	+	0.554079i	0.373537	+	0.927615i	$0.378145\pi$
$434$			159.605i			0.367754i
$435$	99.0225	−	78.3553i	0.227638	−	0.180127i
$436$	205.368			0.471026
$437$	−277.070	−	277.070i	−0.634027	−	0.634027i
$438$	−197.057	+	197.057i	−0.449901	+	0.449901i
$439$		−	243.928i		−	0.555644i	−0.960633	−	0.277822i	$-0.910388\pi$
$439$		−	243.928i		−	0.555644i	0.960633	−	0.277822i	$-0.0896125\pi$
$440$	108.873	+	137.590i	0.247439	+	0.312705i
$441$	21.0000			0.0476190
$442$	−36.3651	−	36.3651i	−0.0822741	−	0.0822741i
$443$	459.426	−	459.426i	1.03708	−	1.03708i	0.0377942	−	0.999286i	$-0.487967\pi$
$443$	459.426	−	459.426i	1.03708	−	1.03708i	0.999286	−	0.0377942i	$-0.0120331\pi$
$444$		−	58.4477i		−	0.131639i
$445$	16.3819	+	1.90874i	0.0368133	+	0.00428931i
$446$	199.403			0.447092
$447$	263.319	+	263.319i	0.589080	+	0.589080i
$448$	14.9666	−	14.9666i	0.0334077	−	0.0334077i
$449$		−	136.444i		−	0.303885i	−0.988389	−	0.151943i	$-0.951447\pi$
$449$		−	136.444i		−	0.303885i	0.988389	−	0.151943i	$-0.0485529\pi$
$450$	−90.2341	+	55.7477i	−0.200520	+	0.123884i
$451$	−465.525			−1.03221
$452$	−68.4262	−	68.4262i	−0.151385	−	0.151385i
$453$	76.8561	−	76.8561i	0.169660	−	0.169660i
$454$		−	91.5140i		−	0.201573i
$455$	−6.78361	+	58.2208i	−0.0149090	+	0.127958i
$456$	130.221			0.285573
$457$	269.807	+	269.807i	0.590388	+	0.590388i	0.937736	−	0.347348i	$-0.112918\pi$
$457$	269.807	+	269.807i	0.590388	+	0.590388i	−0.347348	+	0.937736i	$0.612918\pi$
$458$	−248.102	+	248.102i	−0.541708	+	0.541708i
$459$		−	42.6461i		−	0.0929110i
$460$	115.598	−	91.4712i	0.251300	−	0.198850i
$461$	−238.818			−0.518043			−0.259022	−	0.965872i	$-0.583400\pi$
$461$	−238.818			−0.518043			−0.259022	+	0.965872i	$0.583400\pi$
$462$	56.8539	+	56.8539i	0.123060	+	0.123060i
$463$	308.280	−	308.280i	0.665831	−	0.665831i	−0.290917	−	0.956748i	$-0.593960\pi$
$463$	308.280	−	308.280i	0.665831	−	0.665831i	0.956748	+	0.290917i	$0.0939603\pi$
$464$		−	58.3233i		−	0.125697i
$465$	−229.229	−	289.691i	−0.492966	−	0.622992i
$466$	612.961			1.31537
$467$	228.918	+	228.918i	0.490188	+	0.490188i	0.908365	−	0.418177i	$-0.137331\pi$
$467$	228.918	+	228.918i	0.490188	+	0.490188i	−0.418177	+	0.908365i	$0.637331\pi$
$468$	18.7985	−	18.7985i	0.0401678	−	0.0401678i
$469$		−	85.3497i		−	0.181982i
$470$	−87.7672	−	10.2262i	−0.186739	−	0.0217579i
$471$	−444.135			−0.942963
$472$	−176.530	−	176.530i	−0.374005	−	0.374005i
$473$	−297.860	+	297.860i	−0.629724	+	0.629724i
$474$		−	340.115i		−	0.717542i
$475$	152.782	−	646.730i	0.321646	−	1.36154i
$476$	43.4287			0.0912368
$477$	5.93649	+	5.93649i	0.0124455	+	0.0124455i
$478$	−136.398	+	136.398i	−0.285351	+	0.285351i
$479$			342.177i			0.714357i	0.934036	+	0.357178i	$0.116261\pi$
$479$			342.177i			0.714357i	−0.934036	+	0.357178i	$0.883739\pi$
$480$	−5.66970	+	48.6606i	−0.0118119	+	0.101376i
$481$	74.7591			0.155424
$482$	332.727	+	332.727i	0.690305	+	0.690305i
$483$	47.7665	−	47.7665i	0.0988953	−	0.0988953i
$484$			65.8440i			0.136041i
$485$	490.860	−	388.411i	1.01208	−	0.800848i
$486$	22.0454			0.0453609
$487$	−456.499	−	456.499i	−0.937370	−	0.937370i	0.0607814	−	0.998151i	$-0.480641\pi$
$487$	−456.499	−	456.499i	−0.937370	−	0.937370i	−0.998151	+	0.0607814i	$0.980641\pi$
$488$	−204.941	+	204.941i	−0.419962	+	0.419962i
$489$		−	127.380i		−	0.260491i
$490$	−30.7142	−	38.8154i	−0.0626820	−	0.0792152i
$491$	795.504			1.62017			0.810085	−	0.586312i	$-0.199421\pi$
$491$	795.504			1.62017			0.810085	+	0.586312i	$0.199421\pi$
$492$	−91.9112	−	91.9112i	−0.186811	−	0.186811i
$493$	84.6184	−	84.6184i	0.171640	−	0.171640i
$494$			166.563i			0.337172i
$495$	−184.847	−	21.5375i	−0.373429	−	0.0435102i
$496$	−170.625			−0.344002
$497$	−20.1955	−	20.1955i	−0.0406348	−	0.0406348i
$498$	235.355	−	235.355i	0.472601	−	0.472601i
$499$		−	145.240i		−	0.291062i	−0.989354	−	0.145531i	$-0.953511\pi$
$499$		−	145.240i		−	0.291062i	0.989354	−	0.145531i	$-0.0464890\pi$
$500$	235.016	+	85.2490i	0.470032	+	0.170498i
$501$	375.936			0.750371
$502$	244.521	+	244.521i	0.487093	+	0.487093i
$503$	169.609	−	169.609i	0.337195	−	0.337195i	−0.518115	−	0.855311i	$-0.673366\pi$
$503$	169.609	−	169.609i	0.337195	−	0.337195i	0.855311	+	0.518115i	$0.173366\pi$
$504$			22.4499i			0.0445435i
$505$	−82.2089	+	705.564i	−0.162790	+	1.39716i
$506$	258.639			0.511144
$507$	−182.937	−	182.937i	−0.360823	−	0.360823i
$508$	299.093	−	299.093i	0.588766	−	0.588766i
$509$		−	734.035i		−	1.44211i	−0.692877	−	0.721056i	$-0.743657\pi$
$509$		−	734.035i		−	1.44211i	0.692877	−	0.721056i	$-0.256343\pi$
$510$	−78.8252	+	62.3734i	−0.154559	+	0.122301i
$511$	301.009			0.589059
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−97.6658	+	97.6658i	−0.190382	+	0.190382i
$514$			205.184i			0.399191i
$515$	265.189	+	335.136i	0.514930	+	0.650749i
$516$	−117.616			−0.227938
$517$	−109.625	−	109.625i	−0.212041	−	0.212041i
$518$	−44.6402	+	44.6402i	−0.0861780	+	0.0861780i
$519$		−	212.605i		−	0.409643i
$520$	−62.2407	−	7.25198i	−0.119694	−	0.0139461i
$521$	96.5998			0.185412			0.0927061	−	0.995694i	$-0.470448\pi$
$521$	96.5998			0.185412			0.0927061	+	0.995694i	$0.470448\pi$
$522$	43.7424	+	43.7424i	0.0837978	+	0.0837978i
$523$	256.326	−	256.326i	0.490108	−	0.490108i	−0.418232	−	0.908340i	$-0.637350\pi$
$523$	256.326	−	256.326i	0.490108	−	0.490108i	0.908340	+	0.418232i	$0.137350\pi$
$524$		−	186.974i		−	0.356821i
$525$	111.495	+	26.3394i	0.212372	+	0.0501703i
$526$	507.681			0.965174
$527$	−247.552	−	247.552i	−0.469738	−	0.469738i
$528$	−60.7793	+	60.7793i	−0.115112	+	0.115112i
$529$			311.702i			0.589228i
$530$	2.29014	−	19.6553i	0.00432102	−	0.0370855i
$531$	264.795			0.498673
$532$	−99.4580	−	99.4580i	−0.186951	−	0.186951i
$533$	117.562	−	117.562i	0.220566	−	0.220566i
$534$			8.07976i			0.0151306i
$535$	−436.739	+	345.586i	−0.816334	+	0.645955i
$536$	91.2426			0.170229
$537$	249.131	+	249.131i	0.463930	+	0.463930i
$538$	207.747	−	207.747i	0.386147	−	0.386147i
$539$		−	86.8457i		−	0.161124i
$540$	−32.2432	−	40.7477i	−0.0597096	−	0.0754588i
$541$	−967.814			−1.78894			−0.894468	−	0.447133i	$-0.852445\pi$
$541$	−967.814			−1.78894			−0.894468	+	0.447133i	$0.852445\pi$
$542$	−476.286	−	476.286i	−0.878756	−	0.878756i
$543$	307.766	−	307.766i	0.566789	−	0.566789i
$544$			46.4272i			0.0853442i
$545$	509.969	+	59.4191i	0.935723	+	0.109026i
$546$	−28.7152			−0.0525920
$547$	107.907	+	107.907i	0.197271	+	0.197271i	0.798829	−	0.601558i	$-0.205453\pi$
$547$	107.907	+	107.907i	0.197271	+	0.197271i	−0.601558	+	0.798829i	$0.705453\pi$
$548$	132.011	−	132.011i	0.240895	−	0.240895i
$549$		−	307.412i		−	0.559949i
$550$	230.545	+	373.164i	0.419173	+	0.678480i
$551$	−387.577			−0.703406
$552$	51.0645	+	51.0645i	0.0925081	+	0.0925081i
$553$	−259.767	+	259.767i	−0.469741	+	0.469741i
$554$		−	19.3574i		−	0.0349412i
$555$	16.9107	−	145.137i	0.0304697	−	0.261509i
$556$	−223.528			−0.402029
$557$	106.902	+	106.902i	0.191925	+	0.191925i	0.796527	−	0.604603i	$-0.206668\pi$
$557$	106.902	+	106.902i	0.191925	+	0.191925i	−0.604603	+	0.796527i	$0.706668\pi$
$558$	127.969	−	127.969i	0.229335	−	0.229335i
$559$		−	150.440i		−	0.269123i
$560$	41.4955	−	32.8348i	0.0740990	−	0.0586337i
$561$	−176.364			−0.314374
$562$	101.463	+	101.463i	0.180540	+	0.180540i
$563$	−290.841	+	290.841i	−0.516592	+	0.516592i	−0.916539	−	0.399946i	$-0.869029\pi$
$563$	−290.841	+	290.841i	−0.516592	+	0.516592i	0.399946	+	0.916539i	$0.369029\pi$
$564$		−	43.2878i		−	0.0767515i
$565$	−150.118	−	189.714i	−0.265696	−	0.335777i
$566$	552.053			0.975358
$567$	−16.8375	−	16.8375i	−0.0296957	−	0.0296957i
$568$	21.5899	−	21.5899i	0.0380104	−	0.0380104i
$569$		−	53.2185i		−	0.0935299i	−0.998906	−	0.0467649i	$-0.985109\pi$
$569$		−	53.2185i		−	0.0935299i	0.998906	−	0.0467649i	$-0.0148912\pi$
$570$	323.365	+	37.6769i	0.567307	+	0.0660999i
$571$	437.943			0.766976			0.383488	−	0.923546i	$-0.374723\pi$
$571$	437.943			0.766976			0.383488	+	0.923546i	$0.374723\pi$
$572$	−77.7415	−	77.7415i	−0.135912	−	0.135912i
$573$	−450.221	+	450.221i	−0.785727	+	0.785727i
$574$			140.397i			0.244594i
$575$	313.518	−	193.695i	0.545249	−	0.336862i
$576$	−24.0000			−0.0416667
$577$	−219.701	−	219.701i	−0.380764	−	0.380764i	0.490613	−	0.871377i	$-0.336773\pi$
$577$	−219.701	−	219.701i	−0.380764	−	0.380764i	−0.871377	+	0.490613i	$0.836773\pi$
$578$	221.641	−	221.641i	0.383462	−	0.383462i
$579$			234.446i			0.404915i
$580$	16.8747	−	144.828i	0.0290943	−	0.249704i
$581$	−359.511			−0.618780
$582$	216.834	+	216.834i	0.372566	+	0.372566i
$583$	24.5504	−	24.5504i	0.0421105	−	0.0421105i
$584$			321.792i			0.551014i
$585$	52.1195	−	41.2415i	0.0890931	−	0.0704983i
$586$	209.746			0.357928
$587$	677.250	+	677.250i	1.15375	+	1.15375i	0.985795	+	0.167952i	$0.0537153\pi$
$587$	677.250	+	677.250i	1.15375	+	1.15375i	0.167952	+	0.985795i	$0.446285\pi$
$588$	17.1464	−	17.1464i	0.0291606	−	0.0291606i
$589$			1133.86i			1.92506i
$590$	−387.285	−	489.436i	−0.656415	−	0.829552i
$591$	476.300			0.805922
$592$	−47.7224	−	47.7224i	−0.0806121	−	0.0806121i
$593$	−558.797	+	558.797i	−0.942322	+	0.942322i	−0.998425	−	0.0561035i	$-0.982132\pi$
$593$	−558.797	+	558.797i	−0.942322	+	0.942322i	0.0561035	+	0.998425i	$0.482132\pi$
$594$		−	91.1690i		−	0.153483i
$595$	107.842	+	12.5653i	0.181247	+	0.0211181i
$596$	429.998			0.721473
$597$	−112.559	−	112.559i	−0.188542	−	0.188542i
$598$	−65.3154	+	65.3154i	−0.109223	+	0.109223i
$599$			538.111i			0.898349i	0.893444	+	0.449175i	$0.148282\pi$
$599$			538.111i			0.898349i	−0.893444	+	0.449175i	$0.851718\pi$
$600$	−28.1580	+	119.194i	−0.0469300	+	0.198656i
$601$	573.831			0.954793			0.477397	−	0.878688i	$-0.341580\pi$
$601$	573.831			0.954793			0.477397	+	0.878688i	$0.341580\pi$
$602$	89.8308	+	89.8308i	0.149221	+	0.149221i
$603$	−68.4320	+	68.4320i	−0.113486	+	0.113486i
$604$		−	125.505i		−	0.207790i
$605$	−19.0507	+	163.504i	−0.0314887	+	0.270254i
$606$	−347.993			−0.574245
$607$	409.542	+	409.542i	0.674699	+	0.674699i	0.958796	−	0.284097i	$-0.0916937\pi$
$607$	409.542	+	409.542i	0.674699	+	0.674699i	−0.284097	+	0.958796i	$0.591694\pi$
$608$	106.325	−	106.325i	0.174877	−	0.174877i
$609$		−	66.8177i		−	0.109717i
$610$	−568.207	+	449.615i	−0.931486	+	0.737074i
$611$	55.3685			0.0906195
$612$	−34.8204	−	34.8204i	−0.0568961	−	0.0568961i
$613$	−571.915	+	571.915i	−0.932977	+	0.932977i	−0.997891	−	0.0649138i	$-0.979323\pi$
$613$	−571.915	+	571.915i	−0.932977	+	0.932977i	0.0649138	+	0.997891i	$0.479323\pi$
$614$			316.277i			0.515108i
$615$	−201.641	−	254.827i	−0.327872	−	0.414352i
$616$	92.8420			0.150717
$617$	−479.790	−	479.790i	−0.777617	−	0.777617i	0.201808	−	0.979425i	$-0.435318\pi$
$617$	−479.790	−	479.790i	−0.777617	−	0.777617i	−0.979425	+	0.201808i	$0.935318\pi$
$618$	−148.044	+	148.044i	−0.239553	+	0.239553i
$619$		−	308.772i		−	0.498824i	−0.968398	−	0.249412i	$-0.919763\pi$
$619$		−	308.772i		−	0.498824i	0.968398	−	0.249412i	$-0.0802373\pi$
$620$	−423.697	−	49.3671i	−0.683382	−	0.0796243i
$621$	−76.5967			−0.123344
$622$	−519.537	−	519.537i	−0.835269	−	0.835269i
$623$	6.17102	−	6.17102i	0.00990532	−	0.00990532i
$624$		−	30.6978i		−	0.0491953i
$625$	558.927	+	279.688i	0.894284	+	0.447501i
$626$	146.170			0.233499
$627$	403.898	+	403.898i	0.644175	+	0.644175i
$628$	−362.635	+	362.635i	−0.577444	+	0.577444i
$629$		−	138.476i		−	0.220153i
$630$	−6.49545	+	55.7477i	−0.0103102	+	0.0884885i
$631$	876.945			1.38977			0.694885	−	0.719121i	$-0.255455\pi$
$631$	876.945			1.38977			0.694885	+	0.719121i	$0.255455\pi$
$632$	−277.703	−	277.703i	−0.439403	−	0.439403i
$633$	−363.185	+	363.185i	−0.573752	+	0.573752i
$634$			559.698i			0.882805i
$635$	829.245	−	656.172i	1.30590	−	1.03334i
$636$	9.69424			0.0152425
$637$	21.9316	+	21.9316i	0.0344295	+	0.0344295i
$638$	180.897	−	180.897i	0.283538	−	0.283538i
$639$			32.3849i			0.0506805i
$640$	35.1019	+	44.3605i	0.0548468	+	0.0693133i
$641$	492.966			0.769057			0.384529	−	0.923113i	$-0.374364\pi$
$641$	492.966			0.769057			0.384529	+	0.923113i	$0.374364\pi$
$642$	−192.926	−	192.926i	−0.300508	−	0.300508i
$643$	−30.0997	+	30.0997i	−0.0468114	+	0.0468114i	−0.730125	−	0.683314i	$-0.760538\pi$
$643$	−30.0997	+	30.0997i	−0.0468114	+	0.0468114i	0.683314	+	0.730125i	$0.260538\pi$
$644$		−	78.0023i		−	0.121122i
$645$	−292.064	−	34.0299i	−0.452813	−	0.0527596i
$646$	308.524			0.477591
$647$	−484.636	−	484.636i	−0.749051	−	0.749051i	0.225250	−	0.974301i	$-0.427680\pi$
$647$	−484.636	−	484.636i	−0.749051	−	0.749051i	−0.974301	+	0.225250i	$0.927680\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$		−	1095.06i		−	1.68731i
$650$	−152.458	−	36.0162i	−0.234551	−	0.0554096i
$651$	−195.476			−0.300270
$652$	−104.005	−	104.005i	−0.159517	−	0.159517i
$653$	−113.485	+	113.485i	−0.173791	+	0.173791i	−0.788643	−	0.614852i	$-0.789216\pi$
$653$	−113.485	+	113.485i	−0.173791	+	0.173791i	0.614852	+	0.788643i	$0.289216\pi$
$654$			251.523i			0.384592i
$655$	54.0973	−	464.295i	0.0825914	−	0.708847i
$656$	−150.090			−0.228796
$657$	−241.344	−	241.344i	−0.367343	−	0.367343i
$658$	−33.0616	+	33.0616i	−0.0502456	+	0.0502456i
$659$			625.067i			0.948509i	0.880388	+	0.474254i	$0.157282\pi$
$659$			625.067i			0.948509i	−0.880388	+	0.474254i	$0.842718\pi$
$660$	−168.513	+	133.342i	−0.255322	+	0.202033i
$661$	608.913			0.921200			0.460600	−	0.887608i	$-0.347634\pi$
$661$	608.913			0.921200			0.460600	+	0.887608i	$0.347634\pi$
$662$	−601.834	−	601.834i	−0.909115	−	0.909115i
$663$	44.5380	−	44.5380i	0.0671765	−	0.0671765i
$664$		−	384.334i		−	0.578816i
$665$	−218.198	−	275.750i	−0.328117	−	0.414662i
$666$	71.5835			0.107483
$667$	−151.983	−	151.983i	−0.227861	−	0.227861i
$668$	306.950	−	306.950i	0.459507	−	0.459507i
$669$			244.218i			0.365049i
$670$	226.574	+	26.3993i	0.338170	+	0.0394019i
$671$	−1271.31			−1.89464
$672$	18.3303	+	18.3303i	0.0272772	+	0.0272772i
$673$	−884.941	+	884.941i	−1.31492	+	1.31492i	−0.397179	+	0.917741i	$0.630011\pi$
$673$	−884.941	+	884.941i	−1.31492	+	1.31492i	−0.917741	+	0.397179i	$0.869989\pi$
$674$			34.1937i			0.0507325i
$675$	−68.2767	−	110.514i	−0.101151	−	0.163724i
$676$	−298.735			−0.441916
$677$	−390.548	−	390.548i	−0.576881	−	0.576881i	0.357162	−	0.934043i	$-0.383745\pi$
$677$	−390.548	−	390.548i	−0.576881	−	0.576881i	−0.934043	+	0.357162i	$0.883745\pi$
$678$	83.8046	−	83.8046i	0.123606	−	0.123606i
$679$		−	331.219i		−	0.487804i
$680$	−13.4328	+	115.288i	−0.0197541	+	0.169541i
$681$	112.081			0.164583
$682$	−529.217	−	529.217i	−0.775977	−	0.775977i
$683$	869.027	−	869.027i	1.27237	−	1.27237i	0.327526	−	0.944842i	$-0.393785\pi$
$683$	869.027	−	869.027i	1.27237	−	1.27237i	0.944842	−	0.327526i	$-0.106215\pi$
$684$			159.488i			0.233169i
$685$	366.003	−	289.614i	0.534311	−	0.422794i
$686$	−26.1916			−0.0381802
$687$	−303.862	−	303.862i	−0.442303	−	0.442303i
$688$	−96.0331	+	96.0331i	−0.139583	+	0.139583i
$689$			12.3997i			0.0179966i
$690$	112.029	+	141.578i	0.162361	+	0.205185i
$691$	−148.448			−0.214831			−0.107415	−	0.994214i	$-0.534257\pi$
$691$	−148.448			−0.214831			−0.107415	+	0.994214i	$0.534257\pi$
$692$	−173.591	−	173.591i	−0.250854	−	0.250854i
$693$	−69.6315	+	69.6315i	−0.100478	+	0.100478i
$694$			467.385i			0.673465i
$695$	−555.066	−	64.6736i	−0.798656	−	0.0930555i
$696$	71.4311			0.102631
$697$	−217.759	−	217.759i	−0.312423	−	0.312423i
$698$	−399.184	+	399.184i	−0.571896	+	0.571896i
$699$			750.721i			1.07399i
$700$	112.542	−	69.5296i	0.160774	−	0.0993280i
$701$	65.2652			0.0931029			0.0465515	−	0.998916i	$-0.485177\pi$
$701$	65.2652			0.0931029			0.0465515	+	0.998916i	$0.485177\pi$
$702$	23.0234	+	23.0234i	0.0327968	+	0.0327968i
$703$	−317.130	+	317.130i	−0.451110	+	0.451110i
$704$			99.2522i			0.140983i
$705$	12.5245	−	107.492i	0.0177652	−	0.152472i
$706$	−274.011			−0.388117
$707$	265.784	+	265.784i	0.375932	+	0.375932i
$708$	216.205	−	216.205i	0.305374	−	0.305374i
$709$			817.389i			1.15288i	0.817141	+	0.576438i	$0.195558\pi$
$709$			817.389i			1.15288i	−0.817141	+	0.576438i	$0.804442\pi$
$710$	59.8587	−	47.3655i	0.0843080	−	0.0667119i
$711$	416.554			0.585870
$712$	6.59709	+	6.59709i	0.00926558	+	0.00926558i
$713$	−444.628	+	444.628i	−0.623601	+	0.623601i
$714$			53.1891i			0.0744945i
$715$	−170.555	−	215.541i	−0.238538	−	0.301455i
$716$	406.828			0.568196
$717$	−167.052	−	167.052i	−0.232988	−	0.232988i
$718$	−473.333	+	473.333i	−0.659239	+	0.659239i
$719$		−	1151.64i		−	1.60173i	−0.598846	−	0.800864i	$-0.704374\pi$
$719$		−	1151.64i		−	1.60173i	0.598846	−	0.800864i	$-0.295626\pi$
$720$	−59.5968	−	6.94393i	−0.0827734	−	0.00964435i
$721$	226.141			0.313648
$722$	−345.564	−	345.564i	−0.478620	−	0.478620i
$723$	−407.505	+	407.505i	−0.563631	+	0.563631i
$724$		−	502.580i		−	0.694172i
$725$	83.8066	−	354.756i	0.115595	−	0.489318i
$726$	−80.6421			−0.111077
$727$	−82.3587	−	82.3587i	−0.113286	−	0.113286i	0.648192	−	0.761477i	$-0.275526\pi$
$727$	−82.3587	−	82.3587i	−0.113286	−	0.113286i	−0.761477	+	0.648192i	$0.775526\pi$
$728$	−23.4459	+	23.4459i	−0.0322059	+	0.0322059i
$729$			27.0000i			0.0370370i
$730$	−93.1043	+	799.075i	−0.127540	+	1.09462i
$731$	−278.660			−0.381203
$732$	−251.001	−	251.001i	−0.342897	−	0.342897i
$733$	−482.749	+	482.749i	−0.658593	+	0.658593i	−0.955047	−	0.296454i	$-0.904196\pi$
$733$	−482.749	+	482.749i	−0.658593	+	0.658593i	0.296454	+	0.955047i	$0.404196\pi$
$734$		−	513.314i		−	0.699338i
$735$	47.5390	−	37.6170i	0.0646789	−	0.0511797i
$736$	83.3880			0.113299
$737$	283.001	+	283.001i	0.383991	+	0.383991i
$738$	112.568	−	112.568i	0.152531	−	0.152531i
$739$		−	430.657i		−	0.582757i	−0.956608	−	0.291379i	$-0.905886\pi$
$739$		−	430.657i		−	0.582757i	0.956608	−	0.291379i	$-0.0941139\pi$
$740$	−104.697	−	132.312i	−0.141482	−	0.178800i
$741$	−203.997			−0.275300
$742$	−7.40410	−	7.40410i	−0.00997857	−	0.00997857i
$743$	902.316	−	902.316i	1.21442	−	1.21442i	0.244866	−	0.969557i	$-0.421256\pi$
$743$	902.316	−	902.316i	1.21442	−	1.21442i	0.969557	−	0.244866i	$-0.0787438\pi$
$744$		−	208.972i		−	0.280877i
$745$	1067.77	+	124.411i	1.43325	+	0.166995i
$746$	−557.527			−0.747355
$747$	288.250	+	288.250i	0.385877	+	0.385877i
$748$	−144.000	+	144.000i	−0.192514	+	0.192514i
$749$			294.699i			0.393457i
$750$	−104.408	+	287.835i	−0.139211	+	0.383780i
$751$	−262.783			−0.349910			−0.174955	−	0.984576i	$-0.555978\pi$
$751$	−262.783			−0.349910			−0.174955	+	0.984576i	$0.555978\pi$
$752$	−35.3444	−	35.3444i	−0.0470005	−	0.0470005i
$753$	−299.475	+	299.475i	−0.397710	+	0.397710i
$754$			91.3659i			0.121175i
$755$	36.3126	−	311.655i	0.0480961	−	0.412788i
$756$	−27.4955			−0.0363696
$757$	−786.569	−	786.569i	−1.03906	−	1.03906i	−0.999205	−	0.0398555i	$-0.987310\pi$
$757$	−786.569	−	786.569i	−1.03906	−	1.03906i	−0.0398555	−	0.999205i	$-0.512690\pi$
$758$	−168.579	+	168.579i	−0.222400	+	0.222400i
$759$			316.767i			0.417347i
$760$	294.790	−	233.263i	0.387881	−	0.306926i
$761$	1469.36			1.93082			0.965412	−	0.260728i	$-0.0839627\pi$
$761$	1469.36			1.93082			0.965412	+	0.260728i	$0.0839627\pi$
$762$	366.313	+	366.313i	0.480725	+	0.480725i
$763$	192.104	−	192.104i	0.251774	−	0.251774i
$764$			735.208i			0.962315i
$765$	−76.3915	−	96.5408i	−0.0998582	−	0.126197i
$766$	−333.177			−0.434956
$767$	276.542	+	276.542i	0.360551	+	0.360551i
$768$	−19.5959	+	19.5959i	−0.0255155	+	0.0255155i
$769$			1018.45i			1.32439i	0.749333	+	0.662193i	$0.230374\pi$
$769$			1018.45i			1.32439i	−0.749333	+	0.662193i	$0.769626\pi$
$770$	230.545	+	26.8620i	0.299409	+	0.0348857i
$771$	−251.299			−0.325938
$772$	191.424	+	191.424i	0.247958	+	0.247958i
$773$	570.658	−	570.658i	0.738238	−	0.738238i	−0.233999	−	0.972237i	$-0.575181\pi$
$773$	570.658	−	570.658i	0.738238	−	0.738238i	0.972237	+	0.233999i	$0.0751813\pi$
$774$		−	144.050i		−	0.186111i
$775$	−1037.84	−	245.177i	−1.33915	−	0.316357i
$776$	354.088			0.456299
$777$	−54.6728	−	54.6728i	−0.0703640	−	0.0703640i
$778$	−73.9237	+	73.9237i	−0.0950176	+	0.0950176i
$779$			997.398i			1.28036i
$780$	8.88182	−	76.2289i	0.0113870	−	0.0977294i
$781$	133.928			0.171483
$782$	120.984	+	120.984i	0.154710	+	0.154710i
$783$	−53.5733	+	53.5733i	−0.0684206	+	0.0684206i
$784$		−	28.0000i		−	0.0357143i
$785$	−1005.42	+	795.574i	−1.28079	+	1.01347i
$786$	228.996			0.291343
$787$	1053.50	+	1053.50i	1.33862	+	1.33862i	0.897395	+	0.441227i	$0.145457\pi$
$787$	1053.50	+	1053.50i	1.33862	+	1.33862i	0.441227	+	0.897395i	$0.354543\pi$
$788$	388.897	−	388.897i	0.493524	−	0.493524i
$789$			621.780i			0.788061i
$790$	−609.244	−	769.939i	−0.771194	−	0.974607i
$791$	−128.014			−0.161838
$792$	−74.4392	−	74.4392i	−0.0939889	−	0.0939889i
$793$	321.050	−	321.050i	0.404854	−	0.404854i
$794$			146.907i			0.185021i
$795$	24.0727	+	2.80484i	0.0302802	+	0.00352810i
$796$	−183.809			−0.230915
$797$	874.260	+	874.260i	1.09694	+	1.09694i	0.994767	+	0.102172i	$0.0325791\pi$
$797$	874.260	+	874.260i	1.09694	+	1.09694i	0.102172	+	0.994767i	$0.467421\pi$
$798$	121.811	−	121.811i	0.152645	−	0.152645i
$799$		−	102.559i		−	0.128359i
$800$	74.3303	+	120.312i	0.0929129	+	0.150390i
$801$	−9.89564			−0.0123541
$802$	−534.615	−	534.615i	−0.666603	−	0.666603i
$803$	−998.082	+	998.082i	−1.24294	+	1.24294i
$804$			111.749i			0.138991i
$805$	22.5684	−	193.695i	0.0280353	−	0.240615i
$806$	267.292			0.331627
$807$	254.437	+	254.437i	0.315288	+	0.315288i
$808$	−284.135	+	284.135i	−0.351652	+	0.351652i
$809$		−	938.860i		−	1.16052i	−0.814432	−	0.580260i	$-0.802951\pi$
$809$		−	938.860i		−	1.16052i	0.814432	−	0.580260i	$-0.197049\pi$
$810$	49.9056	−	39.4897i	0.0616118	−	0.0487527i
$811$	422.265			0.520672			0.260336	−	0.965518i	$-0.416167\pi$
$811$	422.265			0.520672			0.260336	+	0.965518i	$0.416167\pi$
$812$	−54.5564	−	54.5564i	−0.0671877	−	0.0671877i
$813$	583.329	−	583.329i	0.717502	−	0.717502i
$814$		−	296.034i		−	0.363679i
$815$	−228.174	−	288.358i	−0.279968	−	0.353813i
$816$	−56.8615			−0.0696833
$817$	638.171	+	638.171i	0.781115	+	0.781115i
$818$	−14.4205	+	14.4205i	−0.0176289	+	0.0176289i
$819$		−	35.1688i		−	0.0429412i
$820$	−372.705	−	43.4257i	−0.454518	−	0.0529582i
$821$	750.531			0.914167			0.457083	−	0.889424i	$-0.348894\pi$
$821$	750.531			0.914167			0.457083	+	0.889424i	$0.348894\pi$
$822$	161.679	+	161.679i	0.196690	+	0.196690i
$823$	−755.539	+	755.539i	−0.918031	+	0.918031i	−0.996886	−	0.0788552i	$-0.974874\pi$
$823$	−755.539	+	755.539i	−0.918031	+	0.918031i	0.0788552	+	0.996886i	$0.474874\pi$
$824$			241.754i			0.293391i
$825$	−457.031	+	282.359i	−0.553977	+	0.342254i
$826$	−330.258			−0.399828
$827$	−578.780	−	578.780i	−0.699854	−	0.699854i	0.264525	−	0.964379i	$-0.414785\pi$
$827$	−578.780	−	578.780i	−0.699854	−	0.699854i	−0.964379	+	0.264525i	$0.914785\pi$
$828$	−62.5410	+	62.5410i	−0.0755326	+	0.0755326i
$829$		−	318.623i		−	0.384346i	−0.981361	−	0.192173i	$-0.938447\pi$
$829$		−	318.623i		−	0.384346i	0.981361	−	0.192173i	$-0.0615534\pi$
$830$	111.199	−	954.378i	0.133975	−	1.14985i
$831$	23.7079			0.0285293
$832$	−25.0647	−	25.0647i	−0.0301258	−	0.0301258i
$833$	40.6238	−	40.6238i	0.0487681	−	0.0487681i
$834$		−	273.765i		−	0.328256i
$835$	851.030	−	673.410i	1.01920	−	0.806479i
$836$	659.563			0.788951
$837$	156.729	+	156.729i	0.187251	+	0.187251i
$838$	337.860	−	337.860i	0.403174	−	0.403174i
$839$			264.028i			0.314694i	0.987543	+	0.157347i	$0.0502940\pi$
$839$			264.028i			0.314694i	−0.987543	+	0.157347i	$0.949706\pi$
$840$	40.2143	+	50.8213i	0.0478742	+	0.0605016i
$841$	628.400			0.747205
$842$	372.730	+	372.730i	0.442672	+	0.442672i
$843$	−124.267	+	124.267i	−0.147410	+	0.147410i
$844$			593.079i			0.702700i
$845$	−741.819	−	86.4332i	−0.877893	−	0.102288i
$846$	53.0166			0.0626673
$847$	61.5914	+	61.5914i	0.0727171	+	0.0727171i
$848$	7.91531	−	7.91531i	0.00933410	−	0.00933410i
$849$			676.124i			0.796377i
$850$	−66.7128	+	282.397i	−0.0784856	+	0.332232i
$851$	−248.717			−0.292264
$852$	26.4421	+	26.4421i	0.0310354	+	0.0310354i
$853$	−426.618	+	426.618i	−0.500138	+	0.500138i	−0.911481	−	0.411343i	$-0.865060\pi$
$853$	−426.618	+	426.618i	−0.500138	+	0.500138i	0.411343	+	0.911481i	$0.365060\pi$
$854$			383.410i			0.448958i
$855$	−46.1446	+	396.040i	−0.0539703	+	0.463205i
$856$	−315.047			−0.368046
$857$	670.381	+	670.381i	0.782242	+	0.782242i	0.980209	−	0.197967i	$-0.0634339\pi$
$857$	670.381	+	670.381i	0.782242	+	0.782242i	−0.197967	+	0.980209i	$0.563434\pi$
$858$	95.2134	−	95.2134i	0.110971	−	0.110971i
$859$		−	383.866i		−	0.446875i	−0.974718	−	0.223437i	$-0.928272\pi$
$859$		−	383.866i		−	0.446875i	0.974718	−	0.223437i	$-0.0717278\pi$
$860$	−266.255	+	210.684i	−0.309599	+	0.244982i
$861$	−171.950			−0.199710
$862$	−591.932	−	591.932i	−0.686696	−	0.686696i
$863$	563.290	−	563.290i	0.652711	−	0.652711i	−0.300934	−	0.953645i	$-0.597298\pi$
$863$	563.290	−	563.290i	0.652711	−	0.652711i	0.953645	+	0.300934i	$0.0972983\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	−380.836	−	481.287i	−0.440273	−	0.556401i
$866$	−479.832			−0.554079
$867$	271.454	+	271.454i	0.313095	+	0.313095i
$868$	−159.605	+	159.605i	−0.183877	+	0.183877i
$869$		−	1722.66i		−	1.98235i
$870$	177.378	+	20.6672i	0.203883	+	0.0237554i
$871$	−142.935			−0.164105
$872$	205.368	+	205.368i	0.235513	+	0.235513i
$873$	−265.566	+	265.566i	−0.304199	+	0.304199i
$874$		−	554.139i		−	0.634027i
$875$	299.581	−	140.094i	0.342378	−	0.160108i
$876$	−394.114			−0.449901
$877$	−617.434	−	617.434i	−0.704029	−	0.704029i	0.261244	−	0.965273i	$-0.415867\pi$
$877$	−617.434	−	617.434i	−0.704029	−	0.704029i	−0.965273	+	0.261244i	$0.915867\pi$
$878$	243.928	−	243.928i	0.277822	−	0.277822i
$879$			256.885i			0.292247i
$880$	−28.7167	+	246.463i	−0.0326326	+	0.280072i
$881$	−456.278			−0.517910			−0.258955	−	0.965889i	$-0.583378\pi$
$881$	−456.278			−0.517910			−0.258955	+	0.965889i	$0.583378\pi$
$882$	21.0000	+	21.0000i	0.0238095	+	0.0238095i
$883$	−161.141	+	161.141i	−0.182493	+	0.182493i	−0.792441	−	0.609948i	$-0.791190\pi$
$883$	−161.141	+	161.141i	−0.182493	+	0.182493i	0.609948	+	0.792441i	$0.291190\pi$
$884$		−	72.7303i		−	0.0822741i
$885$	599.434	−	474.325i	0.677327	−	0.535960i
$886$	918.853			1.03708
$887$	701.018	+	701.018i	0.790324	+	0.790324i	0.981547	−	0.191222i	$-0.0612452\pi$
$887$	701.018	+	701.018i	0.790324	+	0.790324i	−0.191222	+	0.981547i	$0.561245\pi$
$888$	58.4477	−	58.4477i	0.0658195	−	0.0658195i
$889$		−	559.552i		−	0.629417i
$890$	14.4732	+	18.2907i	0.0162620	+	0.0205513i
$891$	111.659			0.125318
$892$	199.403	+	199.403i	0.223546	+	0.223546i
$893$	−234.875	+	234.875i	−0.263017	+	0.263017i
$894$			526.638i			0.589080i
$895$	1010.24	+	117.708i	1.12876	+	0.131517i
$896$	29.9333			0.0334077
$897$	−79.9947	−	79.9947i	−0.0891803	−	0.0891803i
$898$	136.444	−	136.444i	0.151943	−	0.151943i
$899$			621.964i			0.691839i
$900$	−145.982	−	34.4864i	−0.162202	−	0.0383182i
$901$	22.9679			0.0254916
$902$	−465.525	−	465.525i	−0.516103	−	0.516103i
$903$	−110.020	+	110.020i	−0.121838	+	0.121838i
$904$		−	136.852i		−	0.151385i
$905$	145.412	−	1248.01i	0.160676	−	1.37901i
$906$	153.712			0.169660
$907$	−126.915	−	126.915i	−0.139928	−	0.139928i	0.633673	−	0.773601i	$-0.281546\pi$
$907$	−126.915	−	126.915i	−0.139928	−	0.139928i	−0.773601	+	0.633673i	$0.781546\pi$
$908$	91.5140	−	91.5140i	0.100786	−	0.100786i
$909$		−	426.202i		−	0.468869i
$910$	−65.0044	+	51.4372i	−0.0714334	+	0.0565244i
$911$	−508.167			−0.557813			−0.278906	−	0.960318i	$-0.589972\pi$
$911$	−508.167			−0.557813			−0.278906	+	0.960318i	$0.589972\pi$
$912$	130.221	+	130.221i	0.142786	+	0.142786i
$913$	1192.06	−	1192.06i	1.30565	−	1.30565i
$914$			539.614i			0.590388i
$915$	−550.664	−	695.908i	−0.601818	−	0.760555i
$916$	−496.205			−0.541708
$917$	−174.898	−	174.898i	−0.190729	−	0.190729i
$918$	42.6461	−	42.6461i	0.0464555	−	0.0464555i
$919$		−	671.030i		−	0.730174i	−0.930973	−	0.365087i	$-0.881039\pi$
$919$		−	671.030i		−	0.730174i	0.930973	−	0.365087i	$-0.118961\pi$
$920$	207.069	+	24.1267i	0.225075	+	0.0262247i
$921$	−387.358			−0.420584
$922$	−238.818	−	238.818i	−0.259022	−	0.259022i
$923$	−33.8215	+	33.8215i	−0.0366430	+	0.0366430i
$924$			113.708i			0.123060i
$925$	−221.701	−	358.849i	−0.239677	−	0.387944i
$926$	616.560			0.665831
$927$	−181.316	−	181.316i	−0.195594	−	0.195594i
$928$	58.3233	−	58.3233i	0.0628483	−	0.0628483i
$929$			198.819i			0.214014i	0.994258	+	0.107007i	$0.0341267\pi$
$929$			198.819i			0.214014i	−0.994258	+	0.107007i	$0.965873\pi$
$930$	60.4621	−	518.920i	0.0650130	−	0.557979i
$931$	−186.069			−0.199859
$932$	612.961	+	612.961i	0.657684	+	0.657684i
$933$	636.300	−	636.300i	0.681994	−	0.681994i
$934$			457.836i			0.490188i
$935$	−399.245	+	315.918i	−0.427000	+	0.337880i
$936$	37.5970			0.0401678
$937$	691.159	+	691.159i	0.737630	+	0.737630i	0.972119	−	0.234489i	$-0.0753417\pi$
$937$	691.159	+	691.159i	0.737630	+	0.737630i	−0.234489	+	0.972119i	$0.575342\pi$
$938$	85.3497	−	85.3497i	0.0909911	−	0.0909911i
$939$			179.021i			0.190651i
$940$	−77.5410	−	97.9934i	−0.0824904	−	0.104248i
$941$	1460.09			1.55164			0.775819	−	0.630956i	$-0.217337\pi$
$941$	1460.09			1.55164			0.775819	+	0.630956i	$0.217337\pi$
$942$	−444.135	−	444.135i	−0.471481	−	0.471481i
$943$	−391.117	+	391.117i	−0.414758	+	0.414758i
$944$		−	353.061i		−	0.374005i
$945$	−68.2767	−	7.95527i	−0.0722505	−	0.00841828i
$946$	−595.719			−0.629724
$947$	−332.380	−	332.380i	−0.350982	−	0.350982i	0.509493	−	0.860475i	$-0.329833\pi$
$947$	−332.380	−	332.380i	−0.350982	−	0.350982i	−0.860475	+	0.509493i	$0.829833\pi$
$948$	340.115	−	340.115i	0.358771	−	0.358771i
$949$		−	504.102i		−	0.531192i
$950$	799.512	−	493.948i	0.841592	−	0.519946i
$951$	−685.488			−0.720807
$952$	43.4287	+	43.4287i	0.0456184	+	0.0456184i
$953$	−473.427	+	473.427i	−0.496776	+	0.496776i	−0.910433	−	0.413657i	$-0.864251\pi$
$953$	−473.427	+	473.427i	−0.496776	+	0.496776i	0.413657	+	0.910433i	$0.364251\pi$
$954$			11.8730i			0.0124455i
$955$	−212.718	+	1825.67i	−0.222742	+	1.91170i
$956$	−272.796			−0.285351
$957$	221.553	+	221.553i	0.231508	+	0.231508i
$958$	−342.177	+	342.177i	−0.357178	+	0.357178i
$959$		−	246.969i		−	0.257528i
$960$	−54.3303	+	42.9909i	−0.0565941	+	0.0447822i
$961$	858.560			0.893402
$962$	74.7591	+	74.7591i	0.0777122	+	0.0777122i
$963$	236.285	−	236.285i	0.245364	−	0.245364i
$964$			665.454i			0.690305i
$965$	419.959	+	530.729i	0.435191	+	0.549978i
$966$	95.5329			0.0988953
$967$	−696.942	−	696.942i	−0.720726	−	0.720726i	0.248027	−	0.968753i	$-0.420218\pi$
$967$	−696.942	−	696.942i	−0.720726	−	0.720726i	−0.968753	+	0.248027i	$0.920218\pi$
$968$	−65.8440	+	65.8440i	−0.0680207	+	0.0680207i
$969$			377.863i			0.389951i
$970$	879.271	+	102.448i	0.906465	+	0.105617i
$971$	−262.031			−0.269857			−0.134929	−	0.990855i	$-0.543081\pi$
$971$	−262.031			−0.269857			−0.134929	+	0.990855i	$0.543081\pi$
$972$	22.0454	+	22.0454i	0.0226805	+	0.0226805i
$973$	−209.092	+	209.092i	−0.214894	+	0.214894i
$974$		−	912.998i		−	0.937370i
$975$	44.1107	−	186.722i	0.0452418	−	0.191510i
$976$	−409.883			−0.419962
$977$	363.414	+	363.414i	0.371969	+	0.371969i	0.868194	−	0.496225i	$-0.165281\pi$
$977$	363.414	+	363.414i	0.371969	+	0.371969i	−0.496225	+	0.868194i	$0.665281\pi$
$978$	127.380	−	127.380i	0.130245	−	0.130245i
$979$			40.9235i			0.0418014i
$980$	8.10125	−	69.5296i	0.00826659	−	0.0709486i
$981$	−308.051			−0.314018
$982$	795.504	+	795.504i	0.810085	+	0.810085i
$983$	589.265	−	589.265i	0.599456	−	0.599456i	−0.340712	−	0.940168i	$-0.610668\pi$
$983$	589.265	−	589.265i	0.599456	−	0.599456i	0.940168	+	0.340712i	$0.110668\pi$
$984$		−	183.822i		−	0.186811i
$985$	1078.23	−	853.190i	1.09465	−	0.866182i
$986$	169.237			0.171640
$987$	−40.4921	−	40.4921i	−0.0410254	−	0.0410254i
$988$	−166.563	+	166.563i	−0.168586	+	0.168586i
$989$			500.500i			0.506067i
$990$	−163.310	−	206.385i	−0.164960	−	0.208470i
$991$	1470.51			1.48386			0.741931	−	0.670476i	$-0.233910\pi$
$991$	1470.51			1.48386			0.741931	+	0.670476i	$0.233910\pi$
$992$	−170.625	−	170.625i	−0.172001	−	0.172001i
$993$	737.093	−	737.093i	0.742289	−	0.742289i
$994$		−	40.3910i		−	0.0406348i
$995$	−456.434	−	53.1814i	−0.458727	−	0.0534487i
$996$	470.711			0.472601
$997$	639.149	+	639.149i	0.641073	+	0.641073i	0.950819	−	0.309747i	$-0.100244\pi$
$997$	639.149	+	639.149i	0.641073	+	0.641073i	−0.309747	+	0.950819i	$0.600244\pi$
$998$	145.240	−	145.240i	0.145531	−	0.145531i
$999$			87.6716i			0.0877593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.l.a.127.2	yes	8
3.2	odd	2		630.3.o.b.127.3		8
5.2	odd	4		1050.3.l.b.43.3		8
5.3	odd	4	inner	210.3.l.a.43.2	✓	8
5.4	even	2		1050.3.l.b.757.3		8
15.8	even	4		630.3.o.b.253.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.a.43.2	✓	8	5.3	odd	4	inner
210.3.l.a.127.2	yes	8	1.1	even	1	trivial
630.3.o.b.127.3		8	3.2	odd	2
630.3.o.b.253.3		8	15.8	even	4
1050.3.l.b.43.3		8	5.2	odd	4
1050.3.l.b.757.3		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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-0.578661 + 4.96640i) q^{5} -2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-0.578661 + 4.96640i) q^{5} -2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-5.54506 + 4.38774i) q^{10} -12.4065 q^{11} +(-2.44949 - 2.44949i) q^{12} +(3.13309 - 3.13309i) q^{13} +3.74166i q^{14} +(-5.37386 - 6.79129i) q^{15} -4.00000 q^{16} +(-5.80341 - 5.80341i) q^{17} +(3.00000 - 3.00000i) q^{18} +26.5813i q^{19} +(-9.93280 - 1.15732i) q^{20} -4.58258 q^{21} +(-12.4065 - 12.4065i) q^{22} +(-10.4235 + 10.4235i) q^{23} -4.89898i q^{24} +(-24.3303 - 5.74773i) q^{25} +6.26617 q^{26} +(3.67423 + 3.67423i) q^{27} +(-3.74166 + 3.74166i) q^{28} +14.5808i q^{29} +(1.41742 - 12.1652i) q^{30} +42.6563 q^{31} +(-4.00000 - 4.00000i) q^{32} +(15.1948 - 15.1948i) q^{33} -11.6068i q^{34} +(-10.3739 + 8.20871i) q^{35} +6.00000 q^{36} +(11.9306 + 11.9306i) q^{37} +(-26.5813 + 26.5813i) q^{38} +7.67446i q^{39} +(-8.77548 - 11.0901i) q^{40} +37.5226 q^{41} +(-4.58258 - 4.58258i) q^{42} +(24.0083 - 24.0083i) q^{43} -24.8131i q^{44} +(14.8992 + 1.73598i) q^{45} -20.8470 q^{46} +(8.83609 + 8.83609i) q^{47} +(4.89898 - 4.89898i) q^{48} +7.00000i q^{49} +(-18.5826 - 30.0780i) q^{50} +14.2154 q^{51} +(6.26617 + 6.26617i) q^{52} +(-1.97883 + 1.97883i) q^{53} +7.34847i q^{54} +(7.17918 - 61.6158i) q^{55} -7.48331 q^{56} +(-32.5553 - 32.5553i) q^{57} +(-14.5808 + 14.5808i) q^{58} +88.2651i q^{59} +(13.5826 - 10.7477i) q^{60} +102.471 q^{61} +(42.6563 + 42.6563i) q^{62} +(5.61249 - 5.61249i) q^{63} -8.00000i q^{64} +(13.7472 + 17.3732i) q^{65} +30.3897 q^{66} +(-22.8107 - 22.8107i) q^{67} +(11.6068 - 11.6068i) q^{68} -25.5322i q^{69} +(-18.5826 - 2.16515i) q^{70} -10.7950 q^{71} +(6.00000 + 6.00000i) q^{72} +(80.4481 - 80.4481i) q^{73} +23.8612i q^{74} +(36.8379 - 22.7589i) q^{75} -53.1625 q^{76} +(-23.2105 - 23.2105i) q^{77} +(-7.67446 + 7.67446i) q^{78} +138.851i q^{79} +(2.31464 - 19.8656i) q^{80} -9.00000 q^{81} +(37.5226 + 37.5226i) q^{82} +(-96.0834 + 96.0834i) q^{83} -9.16515i q^{84} +(32.1803 - 25.4638i) q^{85} +48.0166 q^{86} +(-17.8578 - 17.8578i) q^{87} +(24.8131 - 24.8131i) q^{88} -3.29855i q^{89} +(13.1632 + 16.6352i) q^{90} +11.7229 q^{91} +(-20.8470 - 20.8470i) q^{92} +(-52.2431 + 52.2431i) q^{93} +17.6722i q^{94} +(-132.013 - 15.3815i) q^{95} +9.79796 q^{96} +(-88.5219 - 88.5219i) q^{97} +(-7.00000 + 7.00000i) q^{98} +37.2196i 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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