LMFDB - Embedded newform 210.3.l.b.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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + \cdots + 2560000 $ x^16 - 8x^15 + 32x^14 + 152x^13 + 1954x^12 - 12664x^11 + 50336x^10 + 231896x^9 + 1093889x^8 - 4595248x^7 + 18837632x^6 + 86081152x^5 + 178889856x^4 + 70149120x^3 + 10035200x^2 - 7168000*x + 2560000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.2
Root			$-3.99135 - 3.99135i$ of defining polynomial
Character	$\chi$	$=$	210.127
Dual form			210.3.l.b.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.16484 - 2.76660i) q^{5} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.16484 - 2.76660i) q^{5} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(1.39824 + 6.93144i) q^{10} +17.6826 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-12.3956 + 12.3956i) q^{13} +3.74166i q^{14} +(8.48925 - 1.71249i) q^{15} -4.00000 q^{16} +(18.7246 + 18.7246i) q^{17} +(-3.00000 + 3.00000i) q^{18} +25.5476i q^{19} +(5.53321 - 8.32968i) q^{20} +4.58258 q^{21} +(-17.6826 - 17.6826i) q^{22} +(-5.90052 + 5.90052i) q^{23} +4.89898i q^{24} +(9.69181 + 23.0449i) q^{25} +24.7912 q^{26} +(3.67423 + 3.67423i) q^{27} +(3.74166 - 3.74166i) q^{28} -15.3647i q^{29} +(-10.2017 - 6.77677i) q^{30} +11.3491 q^{31} +(4.00000 + 4.00000i) q^{32} +(-21.6567 + 21.6567i) q^{33} -37.4492i q^{34} +(2.61586 + 12.9675i) q^{35} +6.00000 q^{36} +(25.5981 + 25.5981i) q^{37} +(25.5476 - 25.5476i) q^{38} -30.3629i q^{39} +(-13.8629 + 2.79648i) q^{40} +58.8283 q^{41} +(-4.58258 - 4.58258i) q^{42} +(0.282745 - 0.282745i) q^{43} +35.3653i q^{44} +(-8.29981 + 12.4945i) q^{45} +11.8010 q^{46} +(-48.6505 - 48.6505i) q^{47} +(4.89898 - 4.89898i) q^{48} +7.00000i q^{49} +(13.3531 - 32.7367i) q^{50} -45.8657 q^{51} +(-24.7912 - 24.7912i) q^{52} +(3.93909 - 3.93909i) q^{53} -7.34847i q^{54} +(-73.6454 - 48.9209i) q^{55} -7.48331 q^{56} +(-31.2893 - 31.2893i) q^{57} +(-15.3647 + 15.3647i) q^{58} +86.2636i q^{59} +(3.42497 + 16.9785i) q^{60} +29.2079 q^{61} +(-11.3491 - 11.3491i) q^{62} +(-5.61249 + 5.61249i) q^{63} -8.00000i q^{64} +(85.9194 - 17.3320i) q^{65} +43.3135 q^{66} +(-65.7277 - 65.7277i) q^{67} +(-37.4492 + 37.4492i) q^{68} -14.4533i q^{69} +(10.3517 - 15.5834i) q^{70} +1.19194 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-87.0749 + 87.0749i) q^{73} -51.1963i q^{74} +(-40.0942 - 16.3542i) q^{75} -51.0953 q^{76} +(-33.0812 - 33.0812i) q^{77} +(-30.3629 + 30.3629i) q^{78} +55.0959i q^{79} +(16.6594 + 11.0664i) q^{80} -9.00000 q^{81} +(-58.8283 - 58.8283i) q^{82} +(-91.8012 + 91.8012i) q^{83} +9.16515i q^{84} +(-26.1814 - 129.788i) q^{85} -0.565490 q^{86} +(18.8178 + 18.8178i) q^{87} +(35.3653 - 35.3653i) q^{88} -103.966i q^{89} +(20.7943 - 4.19472i) q^{90} +46.3801 q^{91} +(-11.8010 - 11.8010i) q^{92} +(-13.8998 + 13.8998i) q^{93} +97.3010i q^{94} +(70.6802 - 106.402i) q^{95} -9.79796 q^{96} +(87.4734 + 87.4734i) q^{97} +(7.00000 - 7.00000i) q^{98} -53.0479i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} - 16 q^{5} + 32 q^{8}+O(q^{10}) $ 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8	$ 16 q - 16 q^{2} - 16 q^{5} + 32 q^{8} + 24 q^{10} + 8 q^{11} - 32 q^{13} - 12 q^{15} - 64 q^{16} + 56 q^{17} - 48 q^{18} - 16 q^{20} - 8 q^{22} + 24 q^{23} + 40 q^{25} + 64 q^{26} - 112 q^{31} + 64 q^{32} + 24 q^{33} + 28 q^{35} + 96 q^{36} - 152 q^{37} - 16 q^{40} + 24 q^{45} - 48 q^{46} + 80 q^{47} - 72 q^{50} - 72 q^{51} - 64 q^{52} + 48 q^{53} - 24 q^{55} + 24 q^{57} + 96 q^{58} + 24 q^{60} + 96 q^{61} + 112 q^{62} + 16 q^{65} - 48 q^{66} - 80 q^{67} - 112 q^{68} + 536 q^{71} - 96 q^{72} - 288 q^{75} - 168 q^{77} - 48 q^{78} + 64 q^{80} - 144 q^{81} - 256 q^{83} + 40 q^{85} - 144 q^{87} + 16 q^{88} + 24 q^{90} + 48 q^{92} + 192 q^{93} + 360 q^{95} + 688 q^{97} + 112 q^{98}+O(q^{100}) $ 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8 + 24 * q^10 + 8 * q^11 - 32 * q^13 - 12 * q^15 - 64 * q^16 + 56 * q^17 - 48 * q^18 - 16 * q^20 - 8 * q^22 + 24 * q^23 + 40 * q^25 + 64 * q^26 - 112 * q^31 + 64 * q^32 + 24 * q^33 + 28 * q^35 + 96 * q^36 - 152 * q^37 - 16 * q^40 + 24 * q^45 - 48 * q^46 + 80 * q^47 - 72 * q^50 - 72 * q^51 - 64 * q^52 + 48 * q^53 - 24 * q^55 + 24 * q^57 + 96 * q^58 + 24 * q^60 + 96 * q^61 + 112 * q^62 + 16 * q^65 - 48 * q^66 - 80 * q^67 - 112 * q^68 + 536 * q^71 - 96 * q^72 - 288 * q^75 - 168 * q^77 - 48 * q^78 + 64 * q^80 - 144 * q^81 - 256 * q^83 + 40 * q^85 - 144 * q^87 + 16 * q^88 + 24 * q^90 + 48 * q^92 + 192 * q^93 + 360 * q^95 + 688 * q^97 + 112 * 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
$5$	−4.16484	−	2.76660i	−0.832968	−	0.553321i
$5$	−4.16484	−	2.76660i	−0.832968	−	0.553321i
$6$	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
$10$	1.39824	+	6.93144i	0.139824	+	0.693144i
$11$	17.6826			1.60751			0.803757	−	0.594958i	$-0.202831\pi$
$11$	17.6826			1.60751			0.803757	+	0.594958i	$0.202831\pi$
$12$	−2.44949	−	2.44949i	−0.204124	−	0.204124i
$13$	−12.3956	+	12.3956i	−0.953508	+	0.953508i	−0.998966	−	0.0454585i	$-0.985525\pi$
$13$	−12.3956	+	12.3956i	−0.953508	+	0.953508i	0.0454585	+	0.998966i	$0.485525\pi$
$14$			3.74166i			0.267261i
$15$	8.48925	−	1.71249i	0.565950	−	0.114166i
$16$	−4.00000			−0.250000
$17$	18.7246	+	18.7246i	1.10145	+	1.10145i	0.994236	+	0.107210i	$0.0341918\pi$
$17$	18.7246	+	18.7246i	1.10145	+	1.10145i	0.107210	+	0.994236i	$0.465808\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$			25.5476i			1.34461i	0.740273	+	0.672306i	$0.234696\pi$
$19$			25.5476i			1.34461i	−0.740273	+	0.672306i	$0.765304\pi$
$20$	5.53321	−	8.32968i	0.276660	−	0.416484i
$21$	4.58258			0.218218
$22$	−17.6826	−	17.6826i	−0.803757	−	0.803757i
$23$	−5.90052	+	5.90052i	−0.256545	+	0.256545i	−0.823647	−	0.567103i	$-0.808064\pi$
$23$	−5.90052	+	5.90052i	−0.256545	+	0.256545i	0.567103	+	0.823647i	$0.308064\pi$
$24$			4.89898i			0.204124i
$25$	9.69181	+	23.0449i	0.387673	+	0.921797i
$26$	24.7912			0.953508
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	3.74166	−	3.74166i	0.133631	−	0.133631i
$29$		−	15.3647i		−	0.529816i	−0.964274	−	0.264908i	$-0.914658\pi$
$29$		−	15.3647i		−	0.529816i	0.964274	−	0.264908i	$-0.0853416\pi$
$30$	−10.2017	−	6.77677i	−0.340058	−	0.225892i
$31$	11.3491			0.366102			0.183051	−	0.983103i	$-0.441403\pi$
$31$	11.3491			0.366102			0.183051	+	0.983103i	$0.441403\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−21.6567	+	21.6567i	−0.656265	+	0.656265i
$34$		−	37.4492i		−	1.10145i
$35$	2.61586	+	12.9675i	0.0747390	+	0.370501i
$36$	6.00000			0.166667
$37$	25.5981	+	25.5981i	0.691842	+	0.691842i	0.962637	−	0.270795i	$-0.0872866\pi$
$37$	25.5981	+	25.5981i	0.691842	+	0.691842i	−0.270795	+	0.962637i	$0.587287\pi$
$38$	25.5476	−	25.5476i	0.672306	−	0.672306i
$39$		−	30.3629i		−	0.778536i
$40$	−13.8629	+	2.79648i	−0.346572	+	0.0699119i
$41$	58.8283			1.43484			0.717418	−	0.696643i	$-0.245324\pi$
$41$	58.8283			1.43484			0.717418	+	0.696643i	$0.245324\pi$
$42$	−4.58258	−	4.58258i	−0.109109	−	0.109109i
$43$	0.282745	−	0.282745i	0.00657546	−	0.00657546i	−0.703811	−	0.710387i	$-0.748520\pi$
$43$	0.282745	−	0.282745i	0.00657546	−	0.00657546i	0.710387	+	0.703811i	$0.248520\pi$
$44$			35.3653i			0.803757i
$45$	−8.29981	+	12.4945i	−0.184440	+	0.277656i
$46$	11.8010			0.256545
$47$	−48.6505	−	48.6505i	−1.03512	−	1.03512i	−0.999361	−	0.0357569i	$-0.988616\pi$
$47$	−48.6505	−	48.6505i	−1.03512	−	1.03512i	−0.0357569	−	0.999361i	$-0.511384\pi$
$48$	4.89898	−	4.89898i	0.102062	−	0.102062i
$49$			7.00000i			0.142857i
$50$	13.3531	−	32.7367i	0.267062	−	0.654735i
$51$	−45.8657			−0.899327
$52$	−24.7912	−	24.7912i	−0.476754	−	0.476754i
$53$	3.93909	−	3.93909i	0.0743224	−	0.0743224i	−0.668968	−	0.743291i	$-0.733264\pi$
$53$	3.93909	−	3.93909i	0.0743224	−	0.0743224i	0.743291	+	0.668968i	$0.233264\pi$
$54$		−	7.34847i		−	0.136083i
$55$	−73.6454	−	48.9209i	−1.33901	−	0.889470i
$56$	−7.48331			−0.133631
$57$	−31.2893	−	31.2893i	−0.548936	−	0.548936i
$58$	−15.3647	+	15.3647i	−0.264908	+	0.264908i
$59$			86.2636i			1.46210i	0.682326	+	0.731048i	$0.260968\pi$
$59$			86.2636i			1.46210i	−0.682326	+	0.731048i	$0.739032\pi$
$60$	3.42497	+	16.9785i	0.0570828	+	0.282975i
$61$	29.2079			0.478818			0.239409	−	0.970919i	$-0.423046\pi$
$61$	29.2079			0.478818			0.239409	+	0.970919i	$0.423046\pi$
$62$	−11.3491	−	11.3491i	−0.183051	−	0.183051i
$63$	−5.61249	+	5.61249i	−0.0890871	+	0.0890871i
$64$		−	8.00000i		−	0.125000i
$65$	85.9194	−	17.3320i	1.32184	−	0.266646i
$66$	43.3135			0.656265
$67$	−65.7277	−	65.7277i	−0.981010	−	0.981010i	0.0188133	−	0.999823i	$-0.494011\pi$
$67$	−65.7277	−	65.7277i	−0.981010	−	0.981010i	−0.999823	+	0.0188133i	$0.994011\pi$
$68$	−37.4492	+	37.4492i	−0.550723	+	0.550723i
$69$		−	14.4533i		−	0.209468i
$70$	10.3517	−	15.5834i	0.147881	−	0.222620i
$71$	1.19194			0.0167879			0.00839397	−	0.999965i	$-0.497328\pi$
$71$	1.19194			0.0167879			0.00839397	+	0.999965i	$0.497328\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	−87.0749	+	87.0749i	−1.19281	+	1.19281i	−0.216531	+	0.976276i	$0.569474\pi$
$73$	−87.0749	+	87.0749i	−1.19281	+	1.19281i	−0.976276	+	0.216531i	$0.930526\pi$
$74$		−	51.1963i		−	0.691842i
$75$	−40.0942	−	16.3542i	−0.534589	−	0.218055i
$76$	−51.0953			−0.672306
$77$	−33.0812	−	33.0812i	−0.429626	−	0.429626i
$78$	−30.3629	+	30.3629i	−0.389268	+	0.389268i
$79$			55.0959i			0.697417i	0.937231	+	0.348708i	$0.113380\pi$
$79$			55.0959i			0.697417i	−0.937231	+	0.348708i	$0.886620\pi$
$80$	16.6594	+	11.0664i	0.208242	+	0.138330i
$81$	−9.00000			−0.111111
$82$	−58.8283	−	58.8283i	−0.717418	−	0.717418i
$83$	−91.8012	+	91.8012i	−1.10604	+	1.10604i	−0.112372	+	0.993666i	$0.535845\pi$
$83$	−91.8012	+	91.8012i	−1.10604	+	1.10604i	−0.993666	+	0.112372i	$0.964155\pi$
$84$			9.16515i			0.109109i
$85$	−26.1814	−	129.788i	−0.308017	−	1.52692i
$86$	−0.565490			−0.00657546
$87$	18.8178	+	18.8178i	0.216296	+	0.216296i
$88$	35.3653	−	35.3653i	0.401878	−	0.401878i
$89$		−	103.966i		−	1.16815i	−0.811699	−	0.584076i	$-0.801457\pi$
$89$		−	103.966i		−	1.16815i	0.811699	−	0.584076i	$-0.198543\pi$
$90$	20.7943	−	4.19472i	0.231048	−	0.0466079i
$91$	46.3801			0.509671
$92$	−11.8010	−	11.8010i	−0.128272	−	0.128272i
$93$	−13.8998	+	13.8998i	−0.149460	+	0.149460i
$94$			97.3010i			1.03512i
$95$	70.6802	−	106.402i	0.744002	−	1.12002i
$96$	−9.79796			−0.102062
$97$	87.4734	+	87.4734i	0.901788	+	0.901788i	0.995591	−	0.0938032i	$-0.0299024\pi$
$97$	87.4734	+	87.4734i	0.901788	+	0.901788i	−0.0938032	+	0.995591i	$0.529902\pi$
$98$	7.00000	−	7.00000i	0.0714286	−	0.0714286i
$99$		−	53.0479i		−	0.535838i
$100$	−46.0899	+	19.3836i	−0.460899	+	0.193836i
$101$	5.82092			0.0576329			0.0288164	−	0.999585i	$-0.490826\pi$
$101$	5.82092			0.0576329			0.0288164	+	0.999585i	$0.490826\pi$
$102$	45.8657	+	45.8657i	0.449664	+	0.449664i
$103$	60.7804	−	60.7804i	0.590101	−	0.590101i	−0.347558	−	0.937659i	$-0.612989\pi$
$103$	60.7804	−	60.7804i	0.590101	−	0.590101i	0.937659	+	0.347558i	$0.112989\pi$
$104$			49.5824i			0.476754i
$105$	−19.0857	−	12.6782i	−0.181769	−	0.120744i
$106$	−7.87818			−0.0743224
$107$	80.6808	+	80.6808i	0.754026	+	0.754026i	0.975228	−	0.221202i	$-0.0709981\pi$
$107$	80.6808	+	80.6808i	0.754026	+	0.754026i	−0.221202	+	0.975228i	$0.570998\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$			64.4450i			0.591238i	0.955306	+	0.295619i	$0.0955259\pi$
$109$			64.4450i			0.591238i	−0.955306	+	0.295619i	$0.904474\pi$
$110$	24.7246	+	122.566i	0.224769	+	1.11424i
$111$	−62.7024			−0.564887
$112$	7.48331	+	7.48331i	0.0668153	+	0.0668153i
$113$	80.8773	−	80.8773i	0.715729	−	0.715729i	−0.251999	−	0.967728i	$-0.581088\pi$
$113$	80.8773	−	80.8773i	0.715729	−	0.715729i	0.967728	+	0.251999i	$0.0810880\pi$
$114$			62.5787i			0.548936i
$115$	40.8992	−	8.25034i	0.355645	−	0.0717421i
$116$	30.7293			0.264908
$117$	37.1868	+	37.1868i	0.317836	+	0.317836i
$118$	86.2636	−	86.2636i	0.731048	−	0.731048i
$119$		−	70.0610i		−	0.588748i
$120$	13.5535	−	20.4035i	0.112946	−	0.170029i
$121$	191.676			1.58410
$122$	−29.2079	−	29.2079i	−0.239409	−	0.239409i
$123$	−72.0496	+	72.0496i	−0.585769	+	0.585769i
$124$			22.6983i			0.183051i
$125$	23.3913	−	122.792i	0.187130	−	0.982335i
$126$	11.2250			0.0890871
$127$	55.3737	+	55.3737i	0.436014	+	0.436014i	0.890668	−	0.454654i	$-0.150237\pi$
$127$	55.3737	+	55.3737i	0.436014	+	0.436014i	−0.454654	+	0.890668i	$0.650237\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$			0.692581i			0.00536884i
$130$	−103.251	−	68.5874i	−0.794242	−	0.527596i
$131$	−69.2950			−0.528969			−0.264485	−	0.964390i	$-0.585202\pi$
$131$	−69.2950			−0.528969			−0.264485	+	0.964390i	$0.585202\pi$
$132$	−43.3135	−	43.3135i	−0.328132	−	0.328132i
$133$	47.7953	−	47.7953i	0.359363	−	0.359363i
$134$			131.455i			0.981010i
$135$	−5.13746	−	25.4678i	−0.0380552	−	0.188650i
$136$	74.8984			0.550723
$137$	−29.0370	−	29.0370i	−0.211949	−	0.211949i	0.593146	−	0.805095i	$-0.297886\pi$
$137$	−29.0370	−	29.0370i	−0.211949	−	0.211949i	−0.805095	+	0.593146i	$0.797886\pi$
$138$	−14.4533	+	14.4533i	−0.104734	+	0.104734i
$139$		−	80.1068i		−	0.576308i	−0.957584	−	0.288154i	$-0.906958\pi$
$139$		−	80.1068i		−	0.576308i	0.957584	−	0.288154i	$-0.0930415\pi$
$140$	−25.9351	+	5.23173i	−0.185251	+	0.0373695i
$141$	119.169			0.845170
$142$	−1.19194	−	1.19194i	−0.00839397	−	0.00839397i
$143$	−219.187	+	219.187i	−1.53278	+	1.53278i
$144$			12.0000i			0.0833333i
$145$	−42.5079	+	63.9914i	−0.293158	+	0.441320i
$146$	174.150			1.19281
$147$	−8.57321	−	8.57321i	−0.0583212	−	0.0583212i
$148$	−51.1963	+	51.1963i	−0.345921	+	0.345921i
$149$			216.650i			1.45403i	0.686624	+	0.727013i	$0.259092\pi$
$149$			216.650i			1.45403i	−0.686624	+	0.727013i	$0.740908\pi$
$150$	23.7400	+	56.4483i	0.158267	+	0.376322i
$151$	−170.036			−1.12607			−0.563033	−	0.826434i	$-0.690366\pi$
$151$	−170.036			−1.12607			−0.563033	+	0.826434i	$0.690366\pi$
$152$	51.0953	+	51.0953i	0.336153	+	0.336153i
$153$	56.1738	−	56.1738i	0.367149	−	0.367149i
$154$			66.1624i			0.429626i
$155$	−47.2674	−	31.3986i	−0.304951	−	0.202572i
$156$	60.7258			0.389268
$157$	164.649	+	164.649i	1.04872	+	1.04872i	0.998751	+	0.0499682i	$0.0159120\pi$
$157$	164.649	+	164.649i	1.04872	+	1.04872i	0.0499682	+	0.998751i	$0.484088\pi$
$158$	55.0959	−	55.0959i	0.348708	−	0.348708i
$159$			9.64876i			0.0606840i
$160$	−5.59295	−	27.7258i	−0.0349560	−	0.173286i
$161$	22.0777			0.137129
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	104.632	−	104.632i	0.641912	−	0.641912i	−0.309113	−	0.951025i	$-0.600032\pi$
$163$	104.632	−	104.632i	0.641912	−	0.641912i	0.951025	+	0.309113i	$0.100032\pi$
$164$			117.657i			0.717418i
$165$	150.112	−	30.2813i	0.909772	−	0.183523i
$166$	183.602			1.10604
$167$	−215.324	−	215.324i	−1.28937	−	1.28937i	−0.935171	−	0.354196i	$-0.884754\pi$
$167$	−215.324	−	215.324i	−1.28937	−	1.28937i	−0.354196	−	0.935171i	$-0.615246\pi$
$168$	9.16515	−	9.16515i	0.0545545	−	0.0545545i
$169$		−	138.302i		−	0.818354i
$170$	−103.607	+	155.970i	−0.609453	+	0.917470i
$171$	76.6429			0.448204
$172$	0.565490	+	0.565490i	0.00328773	+	0.00328773i
$173$	−50.4009	+	50.4009i	−0.291334	+	0.291334i	−0.837607	−	0.546273i	$-0.816046\pi$
$173$	−50.4009	+	50.4009i	−0.291334	+	0.291334i	0.546273	+	0.837607i	$0.316046\pi$
$174$		−	37.6356i		−	0.216296i
$175$	24.9814	−	61.2448i	0.142751	−	0.349970i
$176$	−70.7306			−0.401878
$177$	−105.651	−	105.651i	−0.596898	−	0.596898i
$178$	−103.966	+	103.966i	−0.584076	+	0.584076i
$179$		−	21.2898i		−	0.118937i	−0.998230	−	0.0594687i	$-0.981059\pi$
$179$		−	21.2898i		−	0.118937i	0.998230	−	0.0594687i	$-0.0189406\pi$
$180$	−24.9891	−	16.5996i	−0.138828	−	0.0922201i
$181$	−22.7581			−0.125736			−0.0628678	−	0.998022i	$-0.520025\pi$
$181$	−22.7581			−0.125736			−0.0628678	+	0.998022i	$0.520025\pi$
$182$	−46.3801	−	46.3801i	−0.254836	−	0.254836i
$183$	−35.7722	+	35.7722i	−0.195476	+	0.195476i
$184$			23.6021i			0.128272i
$185$	−35.7923	−	177.432i	−0.193472	−	0.959093i
$186$	27.7996			0.149460
$187$	331.100	+	331.100i	1.77059	+	1.77059i
$188$	97.3010	−	97.3010i	0.517559	−	0.517559i
$189$		−	13.7477i		−	0.0727393i
$190$	−177.082	+	35.7217i	−0.932011	+	0.188009i
$191$	−113.711			−0.595344			−0.297672	−	0.954668i	$-0.596210\pi$
$191$	−113.711			−0.595344			−0.297672	+	0.954668i	$0.596210\pi$
$192$	9.79796	+	9.79796i	0.0510310	+	0.0510310i
$193$	109.936	−	109.936i	0.569616	−	0.569616i	−0.362405	−	0.932021i	$-0.618044\pi$
$193$	109.936	−	109.936i	0.569616	−	0.569616i	0.932021	+	0.362405i	$0.118044\pi$
$194$		−	174.947i		−	0.901788i
$195$	−84.0021	+	126.457i	−0.430780	+	0.648496i
$196$	−14.0000			−0.0714286
$197$	82.2107	+	82.2107i	0.417313	+	0.417313i	0.884277	−	0.466963i	$-0.154652\pi$
$197$	82.2107	+	82.2107i	0.417313	+	0.417313i	−0.466963	+	0.884277i	$0.654652\pi$
$198$	−53.0479	+	53.0479i	−0.267919	+	0.267919i
$199$			232.689i			1.16929i	0.811289	+	0.584646i	$0.198766\pi$
$199$			232.689i			1.16929i	−0.811289	+	0.584646i	$0.801234\pi$
$200$	65.4735	+	26.7062i	0.327367	+	0.133531i
$201$	160.999			0.800991
$202$	−5.82092	−	5.82092i	−0.0288164	−	0.0288164i
$203$	−28.7447	+	28.7447i	−0.141599	+	0.141599i
$204$		−	91.7314i		−	0.449664i
$205$	−245.011	−	162.755i	−1.19517	−	0.793925i
$206$	−121.561			−0.590101
$207$	17.7016	+	17.7016i	0.0855148	+	0.0855148i
$208$	49.5824	−	49.5824i	0.238377	−	0.238377i
$209$			451.750i			2.16148i
$210$	6.40753	+	31.7639i	0.0305121	+	0.151257i
$211$	−341.021			−1.61621			−0.808107	−	0.589035i	$-0.799508\pi$
$211$	−341.021			−1.61621			−0.808107	+	0.589035i	$0.799508\pi$
$212$	7.87818	+	7.87818i	0.0371612	+	0.0371612i
$213$	−1.45983	+	1.45983i	−0.00685365	+	0.00685365i
$214$		−	161.362i		−	0.754026i
$215$	−1.95983	+	0.395345i	−0.00911549	+	0.00183881i
$216$	14.6969			0.0680414
$217$	−21.2323	−	21.2323i	−0.0978447	−	0.0978447i
$218$	64.4450	−	64.4450i	0.295619	−	0.295619i
$219$		−	213.289i		−	0.973923i
$220$	97.8417	−	147.291i	0.444735	−	0.669504i
$221$	−464.205			−2.10048
$222$	62.7024	+	62.7024i	0.282443	+	0.282443i
$223$	118.521	−	118.521i	0.531482	−	0.531482i	−0.389531	−	0.921013i	$-0.627363\pi$
$223$	118.521	−	118.521i	0.531482	−	0.531482i	0.921013	+	0.389531i	$0.127363\pi$
$224$		−	14.9666i		−	0.0668153i
$225$	69.1348	−	29.0754i	0.307266	−	0.129224i
$226$	−161.755			−0.715729
$227$	−1.59958	−	1.59958i	−0.00704662	−	0.00704662i	0.703575	−	0.710621i	$-0.251586\pi$
$227$	−1.59958	−	1.59958i	−0.00704662	−	0.00704662i	−0.710621	+	0.703575i	$0.751586\pi$
$228$	62.5787	−	62.5787i	0.274468	−	0.274468i
$229$			59.2261i			0.258629i	0.991604	+	0.129315i	$0.0412777\pi$
$229$			59.2261i			0.258629i	−0.991604	+	0.129315i	$0.958722\pi$
$230$	−49.1495	−	32.6488i	−0.213693	−	0.141951i
$231$	81.0321			0.350788
$232$	−30.7293	−	30.7293i	−0.132454	−	0.132454i
$233$	266.052	−	266.052i	1.14185	−	1.14185i	0.153743	−	0.988111i	$-0.450867\pi$
$233$	266.052	−	266.052i	1.14185	−	1.14185i	0.988111	−	0.153743i	$-0.0491327\pi$
$234$		−	74.3736i		−	0.317836i
$235$	68.0250	+	337.218i	0.289468	+	1.43497i
$236$	−172.527			−0.731048
$237$	−67.4784	−	67.4784i	−0.284719	−	0.284719i
$238$	−70.0610	+	70.0610i	−0.294374	+	0.294374i
$239$		−	420.919i		−	1.76117i	−0.473890	−	0.880584i	$-0.657151\pi$
$239$		−	420.919i		−	1.76117i	0.473890	−	0.880584i	$-0.342849\pi$
$240$	−33.9570	+	6.84994i	−0.141488	+	0.0285414i
$241$	−347.574			−1.44222			−0.721108	−	0.692823i	$-0.756367\pi$
$241$	−347.574			−1.44222			−0.721108	+	0.692823i	$0.756367\pi$
$242$	−191.676	−	191.676i	−0.792049	−	0.792049i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$			58.4157i			0.239409i
$245$	19.3662	−	29.1539i	0.0790458	−	0.118995i
$246$	144.099			0.585769
$247$	−316.678	−	316.678i	−1.28210	−	1.28210i
$248$	22.6983	−	22.6983i	0.0915254	−	0.0915254i
$249$		−	224.866i		−	0.903076i
$250$	−146.183	+	99.4006i	−0.584733	+	0.397602i
$251$	175.106			0.697632			0.348816	−	0.937191i	$-0.386584\pi$
$251$	175.106			0.697632			0.348816	+	0.937191i	$0.386584\pi$
$252$	−11.2250	−	11.2250i	−0.0445435	−	0.0445435i
$253$	−104.337	+	104.337i	−0.412399	+	0.412399i
$254$		−	110.747i		−	0.436014i
$255$	191.023	+	126.892i	0.749111	+	0.497616i
$256$	16.0000			0.0625000
$257$	−227.773	−	227.773i	−0.886275	−	0.886275i	0.107888	−	0.994163i	$-0.465591\pi$
$257$	−227.773	−	227.773i	−0.886275	−	0.886275i	−0.994163	+	0.107888i	$0.965591\pi$
$258$	0.692581	−	0.692581i	0.00268442	−	0.00268442i
$259$		−	95.7795i		−	0.369805i
$260$	34.6640	+	171.839i	0.133323	+	0.660919i
$261$	−46.0940			−0.176605
$262$	69.2950	+	69.2950i	0.264485	+	0.264485i
$263$	−37.9825	+	37.9825i	−0.144420	+	0.144420i	−0.775620	−	0.631200i	$-0.782563\pi$
$263$	−37.9825	+	37.9825i	−0.144420	+	0.144420i	0.631200	+	0.775620i	$0.282563\pi$
$264$			86.6269i			0.328132i
$265$	−27.3036	+	5.50778i	−0.103032	+	0.0207841i
$266$	−95.5905			−0.359363
$267$	127.331	+	127.331i	0.476896	+	0.476896i
$268$	131.455	−	131.455i	0.490505	−	0.490505i
$269$		−	236.114i		−	0.877748i	−0.898549	−	0.438874i	$-0.855377\pi$
$269$		−	236.114i		−	0.877748i	0.898549	−	0.438874i	$-0.144623\pi$
$270$	−20.3303	+	30.6052i	−0.0752974	+	0.113353i
$271$	167.587			0.618404			0.309202	−	0.950996i	$-0.399938\pi$
$271$	167.587			0.618404			0.309202	+	0.950996i	$0.399938\pi$
$272$	−74.8984	−	74.8984i	−0.275362	−	0.275362i
$273$	−56.8038	+	56.8038i	−0.208072	+	0.208072i
$274$			58.0741i			0.211949i
$275$	171.377	+	407.495i	0.623189	+	1.48180i
$276$	28.9065			0.104734
$277$	354.986	+	354.986i	1.28154	+	1.28154i	0.939793	+	0.341743i	$0.111017\pi$
$277$	354.986	+	354.986i	1.28154	+	1.28154i	0.341743	+	0.939793i	$0.388983\pi$
$278$	−80.1068	+	80.1068i	−0.288154	+	0.288154i
$279$		−	34.0474i		−	0.122034i
$280$	31.1668	+	20.7034i	0.111310	+	0.0739406i
$281$	396.987			1.41277			0.706383	−	0.707829i	$-0.250326\pi$
$281$	396.987			1.41277			0.706383	+	0.707829i	$0.250326\pi$
$282$	−119.169	−	119.169i	−0.422585	−	0.422585i
$283$	204.927	−	204.927i	0.724124	−	0.724124i	−0.245319	−	0.969442i	$-0.578893\pi$
$283$	204.927	−	204.927i	0.724124	−	0.724124i	0.969442	+	0.245319i	$0.0788926\pi$
$284$			2.38389i			0.00839397i
$285$	43.7500	+	216.880i	0.153509	+	0.760984i
$286$	438.374			1.53278
$287$	−110.058	−	110.058i	−0.383476	−	0.383476i
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$			412.221i			1.42637i
$290$	106.499	−	21.4835i	0.367239	−	0.0740809i
$291$	−214.265			−0.736306
$292$	−174.150	−	174.150i	−0.596404	−	0.596404i
$293$	−320.724	+	320.724i	−1.09462	+	1.09462i	−0.0995946	+	0.995028i	$0.531755\pi$
$293$	−320.724	+	320.724i	−1.09462	+	1.09462i	−0.995028	+	0.0995946i	$0.968245\pi$
$294$			17.1464i			0.0583212i
$295$	238.657	−	359.274i	0.809008	−	1.21788i
$296$	102.393			0.345921
$297$	64.9702	+	64.9702i	0.218755	+	0.218755i
$298$	216.650	−	216.650i	0.727013	−	0.727013i
$299$		−	146.281i		−	0.489234i
$300$	32.7083	−	80.1883i	0.109028	−	0.267294i
$301$	−1.05793			−0.00351473
$302$	170.036	+	170.036i	0.563033	+	0.563033i
$303$	−7.12914	+	7.12914i	−0.0235285	+	0.0235285i
$304$		−	102.191i		−	0.336153i
$305$	−121.646	−	80.8066i	−0.398840	−	0.264940i
$306$	−112.348			−0.367149
$307$	33.1738	+	33.1738i	0.108058	+	0.108058i	0.759069	−	0.651011i	$-0.225655\pi$
$307$	33.1738	+	33.1738i	0.108058	+	0.108058i	−0.651011	+	0.759069i	$0.725655\pi$
$308$	66.1624	−	66.1624i	0.214813	−	0.214813i
$309$			148.881i			0.481815i
$310$	15.8688	+	78.6660i	0.0511897	+	0.253761i
$311$	−31.4965			−0.101275			−0.0506375	−	0.998717i	$-0.516125\pi$
$311$	−31.4965			−0.101275			−0.0506375	+	0.998717i	$0.516125\pi$
$312$	−60.7258	−	60.7258i	−0.194634	−	0.194634i
$313$	117.156	−	117.156i	0.374299	−	0.374299i	−0.494741	−	0.869040i	$-0.664737\pi$
$313$	117.156	−	117.156i	0.374299	−	0.374299i	0.869040	+	0.494741i	$0.164737\pi$
$314$		−	329.298i		−	1.04872i
$315$	38.9026	−	7.84759i	0.123500	−	0.0249130i
$316$	−110.192			−0.348708
$317$	256.649	+	256.649i	0.809619	+	0.809619i	0.984576	−	0.174957i	$-0.0559788\pi$
$317$	256.649	+	256.649i	0.809619	+	0.809619i	−0.174957	+	0.984576i	$0.555979\pi$
$318$	9.64876	−	9.64876i	0.0303420	−	0.0303420i
$319$		−	271.688i		−	0.851686i
$320$	−22.1328	+	33.3187i	−0.0691651	+	0.104121i
$321$	−197.627			−0.615659
$322$	−22.0777	−	22.0777i	−0.0685644	−	0.0685644i
$323$	−478.369	+	478.369i	−1.48102	+	1.48102i
$324$		−	18.0000i		−	0.0555556i
$325$	−405.792	−	165.520i	−1.24859	−	0.509292i
$326$	−209.263			−0.641912
$327$	−78.9287	−	78.9287i	−0.241372	−	0.241372i
$328$	117.657	−	117.657i	0.358709	−	0.358709i
$329$			182.034i			0.553294i
$330$	−180.394	−	119.831i	−0.546648	−	0.363125i
$331$	−536.093			−1.61962			−0.809809	−	0.586694i	$-0.800429\pi$
$331$	−536.093			−1.61962			−0.809809	+	0.586694i	$0.800429\pi$
$332$	−183.602	−	183.602i	−0.553019	−	0.553019i
$333$	76.7944	−	76.7944i	0.230614	−	0.230614i
$334$			430.649i			1.28937i
$335$	91.9029	+	455.588i	0.274337	+	1.35996i
$336$	−18.3303			−0.0545545
$337$	147.571	+	147.571i	0.437896	+	0.437896i	0.891304	−	0.453407i	$-0.149792\pi$
$337$	147.571	+	147.571i	0.437896	+	0.437896i	−0.453407	+	0.891304i	$0.649792\pi$
$338$	−138.302	+	138.302i	−0.409177	+	0.409177i
$339$			198.108i			0.584390i
$340$	259.577	−	52.3629i	0.763462	−	0.154008i
$341$	200.683			0.588513
$342$	−76.6429	−	76.6429i	−0.224102	−	0.224102i
$343$	13.0958	−	13.0958i	0.0381802	−	0.0381802i
$344$		−	1.13098i		−	0.00328773i
$345$	−39.9865	+	60.1956i	−0.115903	+	0.174480i
$346$	100.802			0.291334
$347$	53.7981	+	53.7981i	0.155038	+	0.155038i	0.780364	−	0.625326i	$-0.215034\pi$
$347$	53.7981	+	53.7981i	0.155038	+	0.155038i	−0.625326	+	0.780364i	$0.715034\pi$
$348$	−37.6356	+	37.6356i	−0.108148	+	0.108148i
$349$			71.8031i			0.205740i	0.994695	+	0.102870i	$0.0328025\pi$
$349$			71.8031i			0.205740i	−0.994695	+	0.102870i	$0.967197\pi$
$350$	−86.2262	+	36.2634i	−0.246361	+	0.103610i
$351$	−91.0887			−0.259512
$352$	70.7306	+	70.7306i	0.200939	+	0.200939i
$353$	114.588	−	114.588i	0.324612	−	0.324612i	−0.525921	−	0.850533i	$-0.676279\pi$
$353$	114.588	−	114.588i	0.324612	−	0.324612i	0.850533	+	0.525921i	$0.176279\pi$
$354$			211.302i			0.596898i
$355$	−4.96426	−	3.29764i	−0.0139838	−	0.00928912i
$356$	207.931			0.584076
$357$	85.8069	+	85.8069i	0.240355	+	0.240355i
$358$	−21.2898	+	21.2898i	−0.0594687	+	0.0594687i
$359$			60.5664i			0.168709i	0.996436	+	0.0843543i	$0.0268828\pi$
$359$			60.5664i			0.168709i	−0.996436	+	0.0843543i	$0.973117\pi$
$360$	8.38943	+	41.5887i	0.0233040	+	0.115524i
$361$	−291.682			−0.807983
$362$	22.7581	+	22.7581i	0.0628678	+	0.0628678i
$363$	−234.754	+	234.754i	−0.646706	+	0.646706i
$364$			92.7602i			0.254836i
$365$	603.555	−	121.751i	1.65358	−	0.333566i
$366$	71.5444			0.195476
$367$	−18.4536	−	18.4536i	−0.0502824	−	0.0502824i	0.681519	−	0.731801i	$-0.261320\pi$
$367$	−18.4536	−	18.4536i	−0.0502824	−	0.0502824i	−0.731801	+	0.681519i	$0.761320\pi$
$368$	23.6021	−	23.6021i	0.0641361	−	0.0641361i
$369$		−	176.485i		−	0.478279i
$370$	−141.640	+	213.224i	−0.382810	+	0.576282i
$371$	−14.7387			−0.0397270
$372$	−27.7996	−	27.7996i	−0.0747302	−	0.0747302i
$373$	269.454	−	269.454i	0.722397	−	0.722397i	−0.246696	−	0.969093i	$-0.579345\pi$
$373$	269.454	−	269.454i	0.722397	−	0.722397i	0.969093	+	0.246696i	$0.0793448\pi$
$374$		−	662.201i		−	1.77059i
$375$	121.740	+	179.037i	0.324641	+	0.477432i
$376$	−194.602			−0.517559
$377$	190.454	+	190.454i	0.505184	+	0.505184i
$378$	−13.7477	+	13.7477i	−0.0363696	+	0.0363696i
$379$			10.4860i			0.0276676i	0.999904	+	0.0138338i	$0.00440357\pi$
$379$			10.4860i			0.0276676i	−0.999904	+	0.0138338i	$0.995596\pi$
$380$	212.804	+	141.360i	0.560010	+	0.372001i
$381$	−135.637			−0.356004
$382$	113.711	+	113.711i	0.297672	+	0.297672i
$383$	93.8346	−	93.8346i	0.244999	−	0.244999i	−0.573916	−	0.818915i	$-0.694576\pi$
$383$	93.8346	−	93.8346i	0.244999	−	0.244999i	0.818915	+	0.573916i	$0.194576\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	46.2554	+	229.301i	0.120144	+	0.595586i
$386$	−219.872			−0.569616
$387$	−0.848235	−	0.848235i	−0.00219182	−	0.00219182i
$388$	−174.947	+	174.947i	−0.450894	+	0.450894i
$389$		−	130.485i		−	0.335437i	−0.985835	−	0.167718i	$-0.946360\pi$
$389$		−	130.485i		−	0.335437i	0.985835	−	0.167718i	$-0.0536399\pi$
$390$	210.459	−	42.4546i	0.539638	−	0.108858i
$391$	−220.970			−0.565140
$392$	14.0000	+	14.0000i	0.0357143	+	0.0357143i
$393$	84.8686	−	84.8686i	0.215951	−	0.215951i
$394$		−	164.421i		−	0.417313i
$395$	152.429	−	229.466i	0.385895	−	0.580926i
$396$	106.096			0.267919
$397$	44.8845	+	44.8845i	0.113059	+	0.113059i	0.761373	−	0.648314i	$-0.224526\pi$
$397$	44.8845	+	44.8845i	0.113059	+	0.113059i	−0.648314	+	0.761373i	$0.724526\pi$
$398$	232.689	−	232.689i	0.584646	−	0.584646i
$399$			117.074i			0.293419i
$400$	−38.7673	−	92.1797i	−0.0969181	−	0.230449i
$401$	329.486			0.821660			0.410830	−	0.911712i	$-0.365239\pi$
$401$	329.486			0.821660			0.410830	+	0.911712i	$0.365239\pi$
$402$	−160.999	−	160.999i	−0.400496	−	0.400496i
$403$	−140.679	+	140.679i	−0.349081	+	0.349081i
$404$			11.6418i			0.0288164i
$405$	37.4836	+	24.8994i	0.0925520	+	0.0614801i
$406$	57.4893			0.141599
$407$	452.643	+	452.643i	1.11214	+	1.11214i
$408$	−91.7314	+	91.7314i	−0.224832	+	0.224832i
$409$		−	388.439i		−	0.949730i	−0.880059	−	0.474865i	$-0.842497\pi$
$409$		−	388.439i		−	0.949730i	0.880059	−	0.474865i	$-0.157503\pi$
$410$	82.2560	+	407.765i	0.200624	+	0.994549i
$411$	71.1259			0.173056
$412$	121.561	+	121.561i	0.295051	+	0.295051i
$413$	161.384	−	161.384i	0.390761	−	0.390761i
$414$		−	35.4031i		−	0.0855148i
$415$	636.315	−	128.360i	1.53329	−	0.309301i
$416$	−99.1648			−0.238377
$417$	98.1104	+	98.1104i	0.235277	+	0.235277i
$418$	451.750	−	451.750i	1.08074	−	1.08074i
$419$			268.553i			0.640937i	0.947259	+	0.320469i	$0.103840\pi$
$419$			268.553i			0.640937i	−0.947259	+	0.320469i	$0.896160\pi$
$420$	25.3563	−	38.1714i	0.0603722	−	0.0908843i
$421$	−680.092			−1.61542			−0.807710	−	0.589580i	$-0.799293\pi$
$421$	−680.092			−1.61542			−0.807710	+	0.589580i	$0.799293\pi$
$422$	341.021	+	341.021i	0.808107	+	0.808107i
$423$	−145.952	+	145.952i	−0.345039	+	0.345039i
$424$		−	15.7564i		−	0.0371612i
$425$	−250.032	+	612.982i	−0.588310	+	1.44231i
$426$	2.91965			0.00685365
$427$	−54.6429	−	54.6429i	−0.127969	−	0.127969i
$428$	−161.362	+	161.362i	−0.377013	+	0.377013i
$429$		−	536.896i		−	1.25151i
$430$	2.35518	+	1.56449i	0.00547715	+	0.00363834i
$431$	451.123			1.04669			0.523344	−	0.852121i	$-0.324684\pi$
$431$	451.123			1.04669			0.523344	+	0.852121i	$0.324684\pi$
$432$	−14.6969	−	14.6969i	−0.0340207	−	0.0340207i
$433$	−223.798	+	223.798i	−0.516855	+	0.516855i	−0.916618	−	0.399763i	$-0.869092\pi$
$433$	−223.798	+	223.798i	−0.516855	+	0.516855i	0.399763	+	0.916618i	$0.369092\pi$
$434$			42.4646i			0.0978447i
$435$	−26.3118	−	130.435i	−0.0604868	−	0.299849i
$436$	−128.890			−0.295619
$437$	−150.744	−	150.744i	−0.344953	−	0.344953i
$438$	−213.289	+	213.289i	−0.486961	+	0.486961i
$439$		−	599.647i		−	1.36594i	−0.730447	−	0.682969i	$-0.760688\pi$
$439$		−	599.647i		−	1.36594i	0.730447	−	0.682969i	$-0.239312\pi$
$440$	−245.133	+	49.4491i	−0.557119	+	0.112384i
$441$	21.0000			0.0476190
$442$	464.205	+	464.205i	1.05024	+	1.05024i
$443$	212.227	−	212.227i	0.479068	−	0.479068i	−0.425765	−	0.904834i	$-0.639995\pi$
$443$	212.227	−	212.227i	0.479068	−	0.479068i	0.904834	+	0.425765i	$0.139995\pi$
$444$		−	125.405i		−	0.282443i
$445$	−287.631	+	433.000i	−0.646362	+	0.973033i
$446$	−237.041			−0.531482
$447$	−265.341	−	265.341i	−0.593604	−	0.593604i
$448$	−14.9666	+	14.9666i	−0.0334077	+	0.0334077i
$449$		−	69.3409i		−	0.154434i	−0.997014	−	0.0772170i	$-0.975397\pi$
$449$		−	69.3409i		−	0.154434i	0.997014	−	0.0772170i	$-0.0246034\pi$
$450$	−98.2102	−	40.0594i	−0.218245	−	0.0890208i
$451$	1040.24			2.30652
$452$	161.755	+	161.755i	0.357864	+	0.357864i
$453$	208.251	−	208.251i	0.459715	−	0.459715i
$454$			3.19917i			0.00704662i
$455$	−193.166	−	128.315i	−0.424540	−	0.282012i
$456$	−125.157			−0.274468
$457$	−399.145	−	399.145i	−0.873404	−	0.873404i	0.119438	−	0.992842i	$-0.461891\pi$
$457$	−399.145	−	399.145i	−0.873404	−	0.873404i	−0.992842	+	0.119438i	$0.961891\pi$
$458$	59.2261	−	59.2261i	0.129315	−	0.129315i
$459$			137.597i			0.299776i
$460$	16.5007	+	81.7983i	0.0358710	+	0.177822i
$461$	357.157			0.774743			0.387372	−	0.921924i	$-0.373383\pi$
$461$	357.157			0.774743			0.387372	+	0.921924i	$0.373383\pi$
$462$	−81.0321	−	81.0321i	−0.175394	−	0.175394i
$463$	139.822	−	139.822i	0.301991	−	0.301991i	−0.539801	−	0.841793i	$-0.681501\pi$
$463$	139.822	−	139.822i	0.301991	−	0.301991i	0.841793	+	0.539801i	$0.181501\pi$
$464$			61.4587i			0.132454i
$465$	96.3458	−	19.4352i	0.207195	−	0.0417962i
$466$	−532.104			−1.14185
$467$	−429.131	−	429.131i	−0.918909	−	0.918909i	0.0780407	−	0.996950i	$-0.475134\pi$
$467$	−429.131	−	429.131i	−0.918909	−	0.918909i	−0.996950	+	0.0780407i	$0.975134\pi$
$468$	−74.3736	+	74.3736i	−0.158918	+	0.158918i
$469$			245.930i			0.524372i
$470$	269.193	−	405.243i	0.572752	−	0.862220i
$471$	−403.306			−0.856276
$472$	172.527	+	172.527i	0.365524	+	0.365524i
$473$	4.99968	−	4.99968i	0.0105701	−	0.0105701i
$474$			134.957i			0.284719i
$475$	−588.743	+	247.603i	−1.23946	+	0.521269i
$476$	140.122			0.294374
$477$	−11.8173	−	11.8173i	−0.0247741	−	0.0247741i
$478$	−420.919	+	420.919i	−0.880584	+	0.880584i
$479$		−	524.078i		−	1.09411i	−0.837097	−	0.547054i	$-0.815749\pi$
$479$		−	524.078i		−	1.09411i	0.837097	−	0.547054i	$-0.184251\pi$
$480$	40.8069	+	27.1071i	0.0850145	+	0.0564731i
$481$	−634.609			−1.31935
$482$	347.574	+	347.574i	0.721108	+	0.721108i
$483$	−27.0396	+	27.0396i	−0.0559826	+	0.0559826i
$484$			383.352i			0.792049i
$485$	−122.309	−	606.317i	−0.252183	−	1.25014i
$486$	−22.0454			−0.0453609
$487$	234.249	+	234.249i	0.481005	+	0.481005i	0.905453	−	0.424447i	$-0.139532\pi$
$487$	234.249	+	234.249i	0.481005	+	0.481005i	−0.424447	+	0.905453i	$0.639532\pi$
$488$	58.4157	−	58.4157i	0.119704	−	0.119704i
$489$			256.294i			0.524119i
$490$	−48.5201	+	9.78767i	−0.0990206	+	0.0199748i
$491$	171.731			0.349758			0.174879	−	0.984590i	$-0.444046\pi$
$491$	171.731			0.349758			0.174879	+	0.984590i	$0.444046\pi$
$492$	−144.099	−	144.099i	−0.292885	−	0.292885i
$493$	287.697	−	287.697i	0.583564	−	0.583564i
$494$			633.357i			1.28210i
$495$	−146.763	+	220.936i	−0.296490	+	0.446336i
$496$	−45.3966			−0.0915254
$497$	−2.22992	−	2.22992i	−0.00448677	−	0.00448677i
$498$	−224.866	+	224.866i	−0.451538	+	0.451538i
$499$		−	507.901i		−	1.01784i	−0.860814	−	0.508919i	$-0.830045\pi$
$499$		−	507.901i		−	1.01784i	0.860814	−	0.508919i	$-0.169955\pi$
$500$	245.584	+	46.7826i	0.491168	+	0.0935652i
$501$	527.435			1.05276
$502$	−175.106	−	175.106i	−0.348816	−	0.348816i
$503$	409.302	−	409.302i	0.813722	−	0.813722i	−0.171468	−	0.985190i	$-0.554851\pi$
$503$	409.302	−	409.302i	0.813722	−	0.813722i	0.985190	+	0.171468i	$0.0548510\pi$
$504$			22.4499i			0.0445435i
$505$	−24.2432	−	16.1042i	−0.0480064	−	0.0318895i
$506$	208.674			0.412399
$507$	169.384	+	169.384i	0.334092	+	0.334092i
$508$	−110.747	+	110.747i	−0.218007	+	0.218007i
$509$		−	762.148i		−	1.49734i	−0.662941	−	0.748671i	$-0.730692\pi$
$509$		−	762.148i		−	1.49734i	0.662941	−	0.748671i	$-0.269308\pi$
$510$	−64.1312	−	317.916i	−0.125747	−	0.623364i
$511$	325.805			0.637582
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−93.8680	+	93.8680i	−0.182979	+	0.182979i
$514$			455.545i			0.886275i
$515$	−421.296	+	84.9855i	−0.818051	+	0.165020i
$516$	−1.38516			−0.00268442
$517$	−860.270	−	860.270i	−1.66396	−	1.66396i
$518$	−95.7795	+	95.7795i	−0.184903	+	0.184903i
$519$		−	123.456i		−	0.237874i
$520$	137.175	−	206.503i	0.263798	−	0.397121i
$521$	−870.243			−1.67033			−0.835166	−	0.549999i	$-0.814628\pi$
$521$	−870.243			−1.67033			−0.835166	+	0.549999i	$0.814628\pi$
$522$	46.0940	+	46.0940i	0.0883027	+	0.0883027i
$523$	94.5185	−	94.5185i	0.180724	−	0.180724i	−0.610947	−	0.791671i	$-0.709211\pi$
$523$	94.5185	−	94.5185i	0.180724	−	0.180724i	0.791671	+	0.610947i	$0.209211\pi$
$524$		−	138.590i		−	0.264485i
$525$	44.4135	+	105.605i	0.0845971	+	0.201153i
$526$	75.9650			0.144420
$527$	212.508	+	212.508i	0.403241	+	0.403241i
$528$	86.6269	−	86.6269i	0.164066	−	0.164066i
$529$			459.368i			0.868370i
$530$	32.8114	+	21.7958i	0.0619082	+	0.0411241i
$531$	258.791			0.487365
$532$	95.5905	+	95.5905i	0.179681	+	0.179681i
$533$	−729.212	+	729.212i	−1.36813	+	1.36813i
$534$		−	254.662i		−	0.476896i
$535$	−112.811	−	559.234i	−0.210862	−	1.04530i
$536$	−262.911			−0.490505
$537$	26.0746	+	26.0746i	0.0485560	+	0.0485560i
$538$	−236.114	+	236.114i	−0.438874	+	0.438874i
$539$			123.779i			0.229645i
$540$	50.9355	−	10.2749i	0.0943250	−	0.0190276i
$541$	−211.503			−0.390948			−0.195474	−	0.980709i	$-0.562624\pi$
$541$	−211.503			−0.390948			−0.195474	+	0.980709i	$0.562624\pi$
$542$	−167.587	−	167.587i	−0.309202	−	0.309202i
$543$	27.8729	−	27.8729i	0.0513313	−	0.0513313i
$544$			149.797i			0.275362i
$545$	178.294	−	268.403i	0.327144	−	0.492483i
$546$	113.608			0.208072
$547$	76.5236	+	76.5236i	0.139897	+	0.139897i	0.773587	−	0.633690i	$-0.218461\pi$
$547$	76.5236	+	76.5236i	0.139897	+	0.139897i	−0.633690	+	0.773587i	$0.718461\pi$
$548$	58.0741	−	58.0741i	0.105975	−	0.105975i
$549$		−	87.6236i		−	0.159606i
$550$	236.118	−	578.872i	0.429306	−	1.05249i
$551$	392.531			0.712397
$552$	−28.9065	−	28.9065i	−0.0523669	−	0.0523669i
$553$	103.075	−	103.075i	0.186392	−	0.186392i
$554$		−	709.971i		−	1.28154i
$555$	261.146	+	173.473i	0.470533	+	0.312563i
$556$	160.214			0.288154
$557$	251.466	+	251.466i	0.451465	+	0.451465i	0.895841	−	0.444376i	$-0.146574\pi$
$557$	251.466	+	251.466i	0.451465	+	0.451465i	−0.444376	+	0.895841i	$0.646574\pi$
$558$	−34.0474	+	34.0474i	−0.0610169	+	0.0610169i
$559$			7.00959i			0.0125395i
$560$	−10.4635	−	51.8702i	−0.0186847	−	0.0926253i
$561$	−811.027			−1.44568
$562$	−396.987	−	396.987i	−0.706383	−	0.706383i
$563$	−89.8908	+	89.8908i	−0.159664	+	0.159664i	−0.782418	−	0.622754i	$-0.786014\pi$
$563$	−89.8908	+	89.8908i	−0.159664	+	0.159664i	0.622754	+	0.782418i	$0.286014\pi$
$564$			238.338i			0.422585i
$565$	−560.597	+	113.086i	−0.992207	+	0.200152i
$566$	−409.854			−0.724124
$567$	16.8375	+	16.8375i	0.0296957	+	0.0296957i
$568$	2.38389	−	2.38389i	0.00419699	−	0.00419699i
$569$			404.950i			0.711687i	0.934545	+	0.355844i	$0.115806\pi$
$569$			404.950i			0.711687i	−0.934545	+	0.355844i	$0.884194\pi$
$570$	173.130	−	260.630i	0.303737	−	0.457246i
$571$	186.774			0.327099			0.163550	−	0.986535i	$-0.447706\pi$
$571$	186.774			0.327099			0.163550	+	0.986535i	$0.447706\pi$
$572$	−438.374	−	438.374i	−0.766388	−	0.766388i
$573$	139.267	−	139.267i	0.243048	−	0.243048i
$574$			220.115i			0.383476i
$575$	−193.164	−	78.7904i	−0.335937	−	0.137027i
$576$	−24.0000			−0.0416667
$577$	−428.779	−	428.779i	−0.743117	−	0.743117i	0.230059	−	0.973177i	$-0.426108\pi$
$577$	−428.779	−	428.779i	−0.743117	−	0.743117i	−0.973177	+	0.230059i	$0.926108\pi$
$578$	412.221	−	412.221i	0.713184	−	0.713184i
$579$			269.287i			0.465090i
$580$	−127.983	−	85.0159i	−0.220660	−	0.146579i
$581$	343.489			0.591202
$582$	214.265	+	214.265i	0.368153	+	0.368153i
$583$	69.6535	−	69.6535i	0.119474	−	0.119474i
$584$			348.300i			0.596404i
$585$	−51.9960	−	257.758i	−0.0888821	−	0.440612i
$586$	641.449			1.09462
$587$	−278.861	−	278.861i	−0.475061	−	0.475061i	0.428487	−	0.903548i	$-0.359047\pi$
$587$	−278.861	−	278.861i	−0.475061	−	0.475061i	−0.903548	+	0.428487i	$0.859047\pi$
$588$	17.1464	−	17.1464i	0.0291606	−	0.0291606i
$589$			289.944i			0.492265i
$590$	−597.932	+	120.617i	−1.01344	+	0.204436i
$591$	−201.374			−0.340735
$592$	−102.393	−	102.393i	−0.172960	−	0.172960i
$593$	439.594	−	439.594i	0.741306	−	0.741306i	−0.231523	−	0.972829i	$-0.574371\pi$
$593$	439.594	−	439.594i	0.741306	−	0.741306i	0.972829	+	0.231523i	$0.0743710\pi$
$594$		−	129.940i		−	0.218755i
$595$	−193.831	+	291.793i	−0.325766	+	0.490408i
$596$	−433.300			−0.727013
$597$	−284.985	−	284.985i	−0.477361	−	0.477361i
$598$	−146.281	+	146.281i	−0.244617	+	0.244617i
$599$		−	782.181i		−	1.30581i	−0.757439	−	0.652906i	$-0.773550\pi$
$599$		−	782.181i		−	1.30581i	0.757439	−	0.652906i	$-0.226450\pi$
$600$	−112.897	+	47.4800i	−0.188161	+	0.0791333i
$601$	589.687			0.981177			0.490589	−	0.871391i	$-0.336782\pi$
$601$	589.687			0.981177			0.490589	+	0.871391i	$0.336782\pi$
$602$	1.05793	+	1.05793i	0.00175737	+	0.00175737i
$603$	−197.183	+	197.183i	−0.327003	+	0.327003i
$604$		−	340.072i		−	0.563033i
$605$	−798.300	−	530.291i	−1.31950	−	0.876514i
$606$	14.2583			0.0235285
$607$	−167.200	−	167.200i	−0.275453	−	0.275453i	0.555838	−	0.831291i	$-0.312398\pi$
$607$	−167.200	−	167.200i	−0.275453	−	0.275453i	−0.831291	+	0.555838i	$0.812398\pi$
$608$	−102.191	+	102.191i	−0.168077	+	0.168077i
$609$		−	70.4097i		−	0.115615i
$610$	40.8396	+	202.453i	0.0669501	+	0.331890i
$611$	1206.10			1.97398
$612$	112.348	+	112.348i	0.183574	+	0.183574i
$613$	−334.599	+	334.599i	−0.545838	+	0.545838i	−0.925234	−	0.379396i	$-0.876132\pi$
$613$	−334.599	+	334.599i	−0.545838	+	0.545838i	0.379396	+	0.925234i	$0.376132\pi$
$614$		−	66.3477i		−	0.108058i
$615$	499.408	−	100.743i	0.812046	−	0.163809i
$616$	−132.325			−0.214813
$617$	−79.8866	−	79.8866i	−0.129476	−	0.129476i	0.639399	−	0.768875i	$-0.279183\pi$
$617$	−79.8866	−	79.8866i	−0.129476	−	0.129476i	−0.768875	+	0.639399i	$0.779183\pi$
$618$	148.881	−	148.881i	0.240908	−	0.240908i
$619$			415.380i			0.671050i	0.942031	+	0.335525i	$0.108914\pi$
$619$			415.380i			0.671050i	−0.942031	+	0.335525i	$0.891086\pi$
$620$	62.7972	−	94.5348i	0.101286	−	0.152475i
$621$	−43.3598			−0.0698226
$622$	31.4965	+	31.4965i	0.0506375	+	0.0506375i
$623$	−194.502	+	194.502i	−0.312202	+	0.312202i
$624$			121.452i			0.194634i
$625$	−437.138	+	446.694i	−0.699420	+	0.714711i
$626$	−234.311			−0.374299
$627$	−553.278	−	553.278i	−0.882421	−	0.882421i
$628$	−329.298	+	329.298i	−0.524360	+	0.524360i
$629$			958.630i			1.52405i
$630$	−46.7502	−	31.0550i	−0.0742067	−	0.0492937i
$631$	−452.429			−0.717002			−0.358501	−	0.933529i	$-0.616712\pi$
$631$	−452.429			−0.717002			−0.358501	+	0.933529i	$0.616712\pi$
$632$	110.192	+	110.192i	0.174354	+	0.174354i
$633$	417.664	−	417.664i	0.659817	−	0.659817i
$634$		−	513.298i		−	0.809619i
$635$	−77.4257	−	383.820i	−0.121930	−	0.604441i
$636$	−19.2975			−0.0303420
$637$	−86.7692	−	86.7692i	−0.136215	−	0.136215i
$638$	−271.688	+	271.688i	−0.425843	+	0.425843i
$639$		−	3.57583i		−	0.00559598i
$640$	55.4516	−	11.1859i	0.0866431	−	0.0174780i
$641$	−333.271			−0.519924			−0.259962	−	0.965619i	$-0.583710\pi$
$641$	−333.271			−0.519924			−0.259962	+	0.965619i	$0.583710\pi$
$642$	197.627	+	197.627i	0.307830	+	0.307830i
$643$	614.442	−	614.442i	0.955587	−	0.955587i	−0.0434678	−	0.999055i	$-0.513841\pi$
$643$	614.442	−	614.442i	0.955587	−	0.955587i	0.999055	+	0.0434678i	$0.0138406\pi$
$644$			44.1555i			0.0685644i
$645$	1.91610	−	2.88449i	0.00297069	−	0.00447208i
$646$	956.738			1.48102
$647$	800.292	+	800.292i	1.23693	+	1.23693i	0.961250	+	0.275678i	$0.0889024\pi$
$647$	800.292	+	800.292i	1.23693	+	1.23693i	0.275678	+	0.961250i	$0.411098\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$			1525.37i			2.35034i
$650$	240.272	+	571.311i	0.369649	+	0.878941i
$651$	52.0083			0.0798899
$652$	209.263	+	209.263i	0.320956	+	0.320956i
$653$	−327.250	+	327.250i	−0.501148	+	0.501148i	−0.911795	−	0.410647i	$-0.865303\pi$
$653$	−327.250	+	327.250i	−0.501148	+	0.501148i	0.410647	+	0.911795i	$0.365303\pi$
$654$			157.857i			0.241372i
$655$	288.603	+	191.712i	0.440615	+	0.292690i
$656$	−235.313			−0.358709
$657$	261.225	+	261.225i	0.397602	+	0.397602i
$658$	182.034	−	182.034i	0.276647	−	0.276647i
$659$			1113.68i			1.68995i	0.534802	+	0.844977i	$0.320386\pi$
$659$			1113.68i			1.68995i	−0.534802	+	0.844977i	$0.679614\pi$
$660$	60.5625	+	300.225i	0.0917614	+	0.454886i
$661$	−58.5883			−0.0886359			−0.0443179	−	0.999017i	$-0.514111\pi$
$661$	−58.5883			−0.0886359			−0.0443179	+	0.999017i	$0.514111\pi$
$662$	536.093	+	536.093i	0.809809	+	0.809809i
$663$	568.533	−	568.533i	0.857516	−	0.857516i
$664$			367.205i			0.553019i
$665$	−331.290	+	66.8292i	−0.498181	+	0.100495i
$666$	−153.589			−0.230614
$667$	90.6596	+	90.6596i	0.135921	+	0.135921i
$668$	430.649	−	430.649i	0.644684	−	0.644684i
$669$			290.315i			0.433954i
$670$	363.685	−	547.491i	0.542813	−	0.817150i
$671$	516.472			0.769706
$672$	18.3303	+	18.3303i	0.0272772	+	0.0272772i
$673$	544.810	−	544.810i	0.809524	−	0.809524i	−0.175038	−	0.984562i	$-0.556005\pi$
$673$	544.810	−	544.810i	0.809524	−	0.809524i	0.984562	+	0.175038i	$0.0560048\pi$
$674$		−	295.142i		−	0.437896i
$675$	−49.0625	+	120.282i	−0.0726852	+	0.178196i
$676$	276.604			0.409177
$677$	−654.528	−	654.528i	−0.966807	−	0.966807i	0.0326593	−	0.999467i	$-0.489602\pi$
$677$	−654.528	−	654.528i	−0.966807	−	0.966807i	−0.999467	+	0.0326593i	$0.989602\pi$
$678$	198.108	−	198.108i	0.292195	−	0.292195i
$679$		−	327.295i		−	0.482026i
$680$	−311.940	−	207.214i	−0.458735	−	0.304727i
$681$	3.91816			0.00575354
$682$	−200.683	−	200.683i	−0.294257	−	0.294257i
$683$	−378.585	+	378.585i	−0.554298	+	0.554298i	−0.927678	−	0.373381i	$-0.878199\pi$
$683$	−378.585	+	378.585i	−0.554298	+	0.554298i	0.373381	+	0.927678i	$0.378199\pi$
$684$			153.286i			0.224102i
$685$	40.6007	+	201.269i	0.0592711	+	0.293823i
$686$	−26.1916			−0.0381802
$687$	−72.5369	−	72.5369i	−0.105585	−	0.105585i
$688$	−1.13098	+	1.13098i	−0.00164387	+	0.00164387i
$689$			97.6547i			0.141734i
$690$	100.182	−	20.2091i	0.145191	−	0.0292886i
$691$	612.032			0.885719			0.442859	−	0.896591i	$-0.353964\pi$
$691$	612.032			0.885719			0.442859	+	0.896591i	$0.353964\pi$
$692$	−100.802	−	100.802i	−0.145667	−	0.145667i
$693$	−99.2436	+	99.2436i	−0.143209	+	0.143209i
$694$		−	107.596i		−	0.155038i
$695$	−221.624	+	333.632i	−0.318883	+	0.480046i
$696$	75.2712			0.108148
$697$	1101.54	+	1101.54i	1.58040	+	1.58040i
$698$	71.8031	−	71.8031i	0.102870	−	0.102870i
$699$			651.691i			0.932320i
$700$	122.490	+	49.9628i	0.174985	+	0.0713754i
$701$	351.130			0.500899			0.250450	−	0.968130i	$-0.419422\pi$
$701$	351.130			0.500899			0.250450	+	0.968130i	$0.419422\pi$
$702$	91.0887	+	91.0887i	0.129756	+	0.129756i
$703$	−653.972	+	653.972i	−0.930259	+	0.930259i
$704$		−	141.461i		−	0.200939i
$705$	−496.320	−	329.693i	−0.704000	−	0.467650i
$706$	−229.176			−0.324612
$707$	−10.8899	−	10.8899i	−0.0154030	−	0.0154030i
$708$	211.302	−	211.302i	0.298449	−	0.298449i
$709$			652.326i			0.920065i	0.887902	+	0.460033i	$0.152162\pi$
$709$			652.326i			0.920065i	−0.887902	+	0.460033i	$0.847838\pi$
$710$	1.66662	+	8.26189i	0.00234735	+	0.0116365i
$711$	165.288			0.232472
$712$	−207.931	−	207.931i	−0.292038	−	0.292038i
$713$	−66.9659	+	66.9659i	−0.0939213	+	0.0939213i
$714$		−	171.614i		−	0.240355i
$715$	1519.28	−	306.476i	2.12487	−	0.428637i
$716$	42.5796			0.0594687
$717$	515.519	+	515.519i	0.718994	+	0.718994i
$718$	60.5664	−	60.5664i	0.0843543	−	0.0843543i
$719$			823.559i			1.14542i	0.819757	+	0.572711i	$0.194108\pi$
$719$			823.559i			1.14542i	−0.819757	+	0.572711i	$0.805892\pi$
$720$	33.1992	−	49.9781i	0.0461101	−	0.0694140i
$721$	−227.419			−0.315422
$722$	291.682	+	291.682i	0.403991	+	0.403991i
$723$	425.689	−	425.689i	0.588782	−	0.588782i
$724$		−	45.5163i		−	0.0628678i
$725$	354.078	−	148.911i	0.488383	−	0.205395i
$726$	469.508			0.646706
$727$	−724.914	−	724.914i	−0.997131	−	0.997131i	0.00286477	−	0.999996i	$-0.499088\pi$
$727$	−724.914	−	724.914i	−0.997131	−	0.997131i	−0.999996	+	0.00286477i	$0.999088\pi$
$728$	92.7602	−	92.7602i	0.127418	−	0.127418i
$729$			27.0000i			0.0370370i
$730$	−725.306	−	481.804i	−0.993571	−	0.660005i
$731$	10.5886			0.0144850
$732$	−71.5444	−	71.5444i	−0.0977382	−	0.0977382i
$733$	49.2582	−	49.2582i	0.0672008	−	0.0672008i	−0.672708	−	0.739908i	$-0.734869\pi$
$733$	49.2582	−	49.2582i	0.0672008	−	0.0672008i	0.739908	+	0.672708i	$0.234869\pi$
$734$			36.9073i			0.0502824i
$735$	11.9874	+	59.4248i	0.0163094	+	0.0808500i
$736$	−47.2042			−0.0641361
$737$	−1162.24	−	1162.24i	−1.57699	−	1.57699i
$738$	−176.485	+	176.485i	−0.239139	+	0.239139i
$739$			417.024i			0.564309i	0.959369	+	0.282154i	$0.0910490\pi$
$739$			417.024i			0.564309i	−0.959369	+	0.282154i	$0.908951\pi$
$740$	354.864	−	71.5846i	0.479546	−	0.0967360i
$741$	775.700			1.04683
$742$	14.7387	+	14.7387i	0.0198635	+	0.0198635i
$743$	−736.124	+	736.124i	−0.990746	+	0.990746i	−0.999958	−	0.00921142i	$-0.997068\pi$
$743$	−736.124	+	736.124i	−0.990746	+	0.990746i	0.00921142	+	0.999958i	$0.497068\pi$
$744$			55.5992i			0.0747302i
$745$	599.384	−	902.313i	0.804543	−	1.21116i
$746$	−538.908			−0.722397
$747$	275.404	+	275.404i	0.368679	+	0.368679i
$748$	−662.201	+	662.201i	−0.885295	+	0.885295i
$749$		−	301.880i		−	0.403044i
$750$	57.2968	−	300.777i	0.0763957	−	0.401037i
$751$	1083.70			1.44301			0.721506	−	0.692409i	$-0.243450\pi$
$751$	1083.70			1.44301			0.721506	+	0.692409i	$0.243450\pi$
$752$	194.602	+	194.602i	0.258779	+	0.258779i
$753$	−214.460	+	214.460i	−0.284807	+	0.284807i
$754$		−	380.909i		−	0.505184i
$755$	708.173	+	470.422i	0.937978	+	0.623076i
$756$	27.4955			0.0363696
$757$	1002.25	+	1002.25i	1.32397	+	1.32397i	0.910532	+	0.413439i	$0.135672\pi$
$757$	1002.25	+	1002.25i	1.32397	+	1.32397i	0.413439	+	0.910532i	$0.364328\pi$
$758$	10.4860	−	10.4860i	0.0138338	−	0.0138338i
$759$		−	255.572i		−	0.336722i
$760$	−71.4434	−	354.164i	−0.0940044	−	0.466005i
$761$	1104.17			1.45095			0.725474	−	0.688250i	$-0.241621\pi$
$761$	1104.17			1.45095			0.725474	+	0.688250i	$0.241621\pi$
$762$	135.637	+	135.637i	0.178002	+	0.178002i
$763$	120.566	−	120.566i	0.158015	−	0.158015i
$764$		−	227.421i		−	0.297672i
$765$	−389.365	+	78.5443i	−0.508974	+	0.102672i
$766$	−187.669			−0.244999
$767$	−1069.29	−	1069.29i	−1.39412	−	1.39412i
$768$	−19.5959	+	19.5959i	−0.0255155	+	0.0255155i
$769$		−	198.908i		−	0.258658i	−0.991602	−	0.129329i	$-0.958718\pi$
$769$		−	198.908i		−	0.258658i	0.991602	−	0.129329i	$-0.0412823\pi$
$770$	183.045	−	275.556i	0.237721	−	0.357865i
$771$	557.927			0.723640
$772$	219.872	+	219.872i	0.284808	+	0.284808i
$773$	326.316	−	326.316i	0.422142	−	0.422142i	−0.463798	−	0.885941i	$-0.653514\pi$
$773$	326.316	−	326.316i	0.422142	−	0.422142i	0.885941	+	0.463798i	$0.153514\pi$
$774$			1.69647i			0.00219182i
$775$	109.994	+	261.540i	0.141927	+	0.337471i
$776$	349.894			0.450894
$777$	117.305	+	117.305i	0.150972	+	0.150972i
$778$	−130.485	+	130.485i	−0.167718	+	0.167718i
$779$			1502.92i			1.92930i
$780$	−252.913	−	168.004i	−0.324248	−	0.215390i
$781$	21.0767			0.0269868
$782$	220.970	+	220.970i	0.282570	+	0.282570i
$783$	56.4534	−	56.4534i	0.0720988	−	0.0720988i
$784$		−	28.0000i		−	0.0357143i
$785$	−230.218	−	1141.25i	−0.293272	−	1.45383i
$786$	−169.737			−0.215951
$787$	337.521	+	337.521i	0.428870	+	0.428870i	0.888243	−	0.459373i	$-0.151926\pi$
$787$	337.521	+	337.521i	0.428870	+	0.428870i	−0.459373	+	0.888243i	$0.651926\pi$
$788$	−164.421	+	164.421i	−0.208657	+	0.208657i
$789$		−	93.0378i		−	0.117919i
$790$	−381.894	+	77.0372i	−0.483411	+	0.0975155i
$791$	−302.615			−0.382573
$792$	−106.096	−	106.096i	−0.133959	−	0.133959i
$793$	−362.049	+	362.049i	−0.456556	+	0.456556i
$794$		−	89.7690i		−	0.113059i
$795$	26.6943	−	40.1855i	0.0335777	−	0.0505479i
$796$	−465.378			−0.584646
$797$	111.780	+	111.780i	0.140250	+	0.140250i	0.773746	−	0.633496i	$-0.218381\pi$
$797$	111.780	+	111.780i	0.140250	+	0.140250i	−0.633496	+	0.773746i	$0.718381\pi$
$798$	117.074	−	117.074i	0.146709	−	0.146709i
$799$		−	1821.92i		−	2.28025i
$800$	−53.4125	+	130.947i	−0.0667656	+	0.163684i
$801$	−311.897			−0.389384
$802$	−329.486	−	329.486i	−0.410830	−	0.410830i
$803$	−1539.71	+	1539.71i	−1.91745	+	1.91745i
$804$			321.998i			0.400496i
$805$	−91.9503	−	61.0803i	−0.114224	−	0.0758762i
$806$	281.359			0.349081
$807$	289.180	+	289.180i	0.358339	+	0.358339i
$808$	11.6418	−	11.6418i	0.0144082	−	0.0144082i
$809$			30.4788i			0.0376746i	0.999823	+	0.0188373i	$0.00599646\pi$
$809$			30.4788i			0.0376746i	−0.999823	+	0.0188373i	$0.994004\pi$
$810$	−12.5841	−	62.3830i	−0.0155360	−	0.0770161i
$811$	71.2377			0.0878393			0.0439197	−	0.999035i	$-0.486015\pi$
$811$	71.2377			0.0878393			0.0439197	+	0.999035i	$0.486015\pi$
$812$	−57.4893	−	57.4893i	−0.0707996	−	0.0707996i
$813$	−205.252	+	205.252i	−0.252462	+	0.252462i
$814$		−	905.286i		−	1.11214i
$815$	−725.248	+	146.300i	−0.889875	+	0.179509i
$816$	183.463			0.224832
$817$	7.22346	+	7.22346i	0.00884145	+	0.00884145i
$818$	−388.439	+	388.439i	−0.474865	+	0.474865i
$819$		−	139.140i		−	0.169890i
$820$	325.509	−	490.021i	0.396962	−	0.597587i
$821$	−232.520			−0.283216			−0.141608	−	0.989923i	$-0.545227\pi$
$821$	−232.520			−0.283216			−0.141608	+	0.989923i	$0.545227\pi$
$822$	−71.1259	−	71.1259i	−0.0865279	−	0.0865279i
$823$	−157.877	+	157.877i	−0.191832	+	0.191832i	−0.796487	−	0.604656i	$-0.793311\pi$
$823$	−157.877	+	157.877i	−0.191832	+	0.191832i	0.604656	+	0.796487i	$0.293311\pi$
$824$		−	243.122i		−	0.295051i
$825$	−708.971	−	289.185i	−0.859358	−	0.350527i
$826$	−322.769			−0.390761
$827$	−654.653	−	654.653i	−0.791600	−	0.791600i	0.190154	−	0.981754i	$-0.439101\pi$
$827$	−654.653	−	654.653i	−0.791600	−	0.791600i	−0.981754	+	0.190154i	$0.939101\pi$
$828$	−35.4031	+	35.4031i	−0.0427574	+	0.0427574i
$829$		−	863.280i		−	1.04135i	−0.853755	−	0.520675i	$-0.825680\pi$
$829$		−	863.280i		−	1.04135i	0.853755	−	0.520675i	$-0.174320\pi$
$830$	−764.675	−	507.955i	−0.921295	−	0.611994i
$831$	−869.534			−1.04637
$832$	99.1648	+	99.1648i	0.119188	+	0.119188i
$833$	−131.072	+	131.072i	−0.157349	+	0.157349i
$834$		−	196.221i		−	0.235277i
$835$	301.075	+	1492.51i	0.360569	+	1.78744i
$836$	−903.500			−1.08074
$837$	41.6994	+	41.6994i	0.0498201	+	0.0498201i
$838$	268.553	−	268.553i	0.320469	−	0.320469i
$839$		−	1114.46i		−	1.32832i	−0.747593	−	0.664158i	$-0.768790\pi$
$839$		−	1114.46i		−	1.32832i	0.747593	−	0.664158i	$-0.231210\pi$
$840$	−63.5277	+	12.8151i	−0.0756283	+	0.0152560i
$841$	604.927			0.719295
$842$	680.092	+	680.092i	0.807710	+	0.807710i
$843$	−486.208	+	486.208i	−0.576760	+	0.576760i
$844$		−	682.043i		−	0.808107i
$845$	−382.626	+	576.005i	−0.452812	+	0.681663i
$846$	291.903			0.345039
$847$	−358.593	−	358.593i	−0.423368	−	0.423368i
$848$	−15.7564	+	15.7564i	−0.0185806	+	0.0185806i
$849$			501.967i			0.591245i
$850$	863.014	−	362.950i	1.01531	−	0.427001i
$851$	−302.085			−0.354976
$852$	−2.91965	−	2.91965i	−0.00342682	−	0.00342682i
$853$	981.738	−	981.738i	1.15092	−	1.15092i	0.164556	−	0.986368i	$-0.447381\pi$
$853$	981.738	−	981.738i	1.15092	−	1.15092i	0.986368	−	0.164556i	$-0.0526190\pi$
$854$			109.286i			0.127969i
$855$	−319.206	−	212.041i	−0.373340	−	0.248001i
$856$	322.723			0.377013
$857$	52.3297	+	52.3297i	0.0610615	+	0.0610615i	0.736978	−	0.675917i	$-0.236252\pi$
$857$	52.3297	+	52.3297i	0.0610615	+	0.0610615i	−0.675917	+	0.736978i	$0.736252\pi$
$858$	−536.896	+	536.896i	−0.625753	+	0.625753i
$859$			1321.03i			1.53787i	0.639328	+	0.768934i	$0.279212\pi$
$859$			1321.03i			1.53787i	−0.639328	+	0.768934i	$0.720788\pi$
$860$	−0.790689	−	3.91966i	−0.000919406	−	0.00455775i
$861$	269.585			0.313107
$862$	−451.123	−	451.123i	−0.523344	−	0.523344i
$863$	610.077	−	610.077i	0.706926	−	0.706926i	−0.258962	−	0.965888i	$-0.583380\pi$
$863$	610.077	−	610.077i	0.706926	−	0.706926i	0.965888	+	0.258962i	$0.0833803\pi$
$864$			29.3939i			0.0340207i
$865$	349.351	−	70.4724i	0.403874	−	0.0814710i
$866$	447.596			0.516855
$867$	−504.865	−	504.865i	−0.582313	−	0.582313i
$868$	42.4646	−	42.4646i	0.0489224	−	0.0489224i
$869$			974.242i			1.12111i
$870$	−104.123	+	156.746i	−0.119681	+	0.180168i
$871$	1629.47			1.87080
$872$	128.890	+	128.890i	0.147810	+	0.147810i
$873$	262.420	−	262.420i	0.300596	−	0.300596i
$874$			301.489i			0.344953i
$875$	−273.484	+	185.961i	−0.312553	+	0.212527i
$876$	426.578			0.486961
$877$	−866.286	−	866.286i	−0.987783	−	0.987783i	0.0121430	−	0.999926i	$-0.496135\pi$
$877$	−866.286	−	866.286i	−0.987783	−	0.987783i	−0.999926	+	0.0121430i	$0.996135\pi$
$878$	−599.647	+	599.647i	−0.682969	+	0.682969i
$879$		−	785.611i		−	0.893756i
$880$	294.582	+	195.683i	0.334752	+	0.222368i
$881$	−1215.34			−1.37950			−0.689749	−	0.724049i	$-0.742279\pi$
$881$	−1215.34			−1.37950			−0.689749	+	0.724049i	$0.742279\pi$
$882$	−21.0000	−	21.0000i	−0.0238095	−	0.0238095i
$883$	−590.925	+	590.925i	−0.669224	+	0.669224i	−0.957536	−	0.288312i	$-0.906906\pi$
$883$	−590.925	+	590.925i	−0.669224	+	0.669224i	0.288312	+	0.957536i	$0.406906\pi$
$884$		−	928.410i		−	1.05024i
$885$	147.725	+	732.314i	0.166921	+	0.827473i
$886$	−424.454			−0.479068
$887$	40.6073	+	40.6073i	0.0457805	+	0.0457805i	0.729626	−	0.683846i	$-0.239694\pi$
$887$	40.6073	+	40.6073i	0.0457805	+	0.0457805i	−0.683846	+	0.729626i	$0.739694\pi$
$888$	−125.405	+	125.405i	−0.141222	+	0.141222i
$889$		−	207.189i		−	0.233059i
$890$	720.631	−	145.369i	0.809698	−	0.163335i
$891$	−159.144			−0.178613
$892$	237.041	+	237.041i	0.265741	+	0.265741i
$893$	1242.91	−	1242.91i	1.39183	−	1.39183i
$894$			530.682i			0.593604i
$895$	−58.9004	+	88.6686i	−0.0658105	+	0.0990711i
$896$	29.9333			0.0334077
$897$	179.157	+	179.157i	0.199729	+	0.199729i
$898$	−69.3409	+	69.3409i	−0.0772170	+	0.0772170i
$899$		−	174.376i		−	0.193966i
$900$	58.1509	+	138.270i	0.0646121	+	0.153633i
$901$	147.516			0.163724
$902$	−1040.24	−	1040.24i	−1.15326	−	1.15326i
$903$	1.29570	−	1.29570i	0.00143488	−	0.00143488i
$904$		−	323.509i		−	0.357864i
$905$	94.7841	+	62.9628i	0.104734	+	0.0695721i
$906$	−416.501			−0.459715
$907$	−665.210	−	665.210i	−0.733417	−	0.733417i	0.237878	−	0.971295i	$-0.423548\pi$
$907$	−665.210	−	665.210i	−0.733417	−	0.733417i	−0.971295	+	0.237878i	$0.923548\pi$
$908$	3.19917	−	3.19917i	0.00352331	−	0.00352331i
$909$		−	17.4628i		−	0.0192110i
$910$	64.8504	+	321.481i	0.0712642	+	0.353276i
$911$	−1249.68			−1.37177			−0.685885	−	0.727710i	$-0.740585\pi$
$911$	−1249.68			−1.37177			−0.685885	+	0.727710i	$0.740585\pi$
$912$	125.157	+	125.157i	0.137234	+	0.137234i
$913$	−1623.29	+	1623.29i	−1.77797	+	1.77797i
$914$			798.291i			0.873404i
$915$	247.953	−	50.0181i	0.270987	−	0.0546645i
$916$	−118.452			−0.129315
$917$	129.639	+	129.639i	0.141373	+	0.141373i
$918$	137.597	−	137.597i	0.149888	−	0.149888i
$919$			563.531i			0.613200i	0.951838	+	0.306600i	$0.0991914\pi$
$919$			563.531i			0.613200i	−0.951838	+	0.306600i	$0.900809\pi$
$920$	65.2976	−	98.2990i	0.0709757	−	0.106847i
$921$	−81.2590			−0.0882291
$922$	−357.157	−	357.157i	−0.387372	−	0.387372i
$923$	−14.7749	+	14.7749i	−0.0160074	+	0.0160074i
$924$			162.064i			0.175394i
$925$	−341.815	+	838.000i	−0.369530	+	0.905946i
$926$	−279.644			−0.301991
$927$	−182.341	−	182.341i	−0.196700	−	0.196700i
$928$	61.4587	−	61.4587i	0.0662270	−	0.0662270i
$929$			599.537i			0.645358i	0.946509	+	0.322679i	$0.104583\pi$
$929$			599.537i			0.645358i	−0.946509	+	0.322679i	$0.895417\pi$
$930$	−115.781	−	76.9105i	−0.124496	−	0.0826995i
$931$	−178.833			−0.192087
$932$	532.104	+	532.104i	0.570927	+	0.570927i
$933$	38.5752	−	38.5752i	0.0413453	−	0.0413453i
$934$			858.261i			0.918909i
$935$	−462.957	−	2295.00i	−0.495141	−	2.45455i
$936$	148.747			0.158918
$937$	630.405	+	630.405i	0.672791	+	0.672791i	0.958359	−	0.285568i	$-0.0921821\pi$
$937$	630.405	+	630.405i	0.672791	+	0.672791i	−0.285568	+	0.958359i	$0.592182\pi$
$938$	245.930	−	245.930i	0.262186	−	0.262186i
$939$			286.972i			0.305614i
$940$	−674.437	+	136.050i	−0.717486	+	0.144734i
$941$	−734.091			−0.780118			−0.390059	−	0.920790i	$-0.627545\pi$
$941$	−734.091			−0.780118			−0.390059	+	0.920790i	$0.627545\pi$
$942$	403.306	+	403.306i	0.428138	+	0.428138i
$943$	−347.118	+	347.118i	−0.368099	+	0.368099i
$944$		−	345.055i		−	0.365524i
$945$	−38.0345	+	57.2571i	−0.0402482	+	0.0605895i
$946$	−9.99935			−0.0105701
$947$	−1025.55	−	1025.55i	−1.08294	−	1.08294i	−0.996234	−	0.0867100i	$-0.972365\pi$
$947$	−1025.55	−	1025.55i	−1.08294	−	1.08294i	−0.0867100	−	0.996234i	$-0.527635\pi$
$948$	134.957	−	134.957i	0.142360	−	0.142360i
$949$		−	2158.69i		−	2.27470i
$950$	836.346	+	341.141i	0.880365	+	0.359095i
$951$	−628.659			−0.661051
$952$	−140.122	−	140.122i	−0.147187	−	0.147187i
$953$	1070.88	−	1070.88i	1.12370	−	1.12370i	0.132515	−	0.991181i	$-0.457695\pi$
$953$	1070.88	−	1070.88i	1.12370	−	1.12370i	0.991181	−	0.132515i	$-0.0423052\pi$
$954$			23.6345i			0.0247741i
$955$	473.587	+	314.592i	0.495902	+	0.329416i
$956$	841.838			0.880584
$957$	332.748	+	332.748i	0.347699	+	0.347699i
$958$	−524.078	+	524.078i	−0.547054	+	0.547054i
$959$			108.647i			0.113292i
$960$	−13.6999	−	67.9140i	−0.0142707	−	0.0707438i
$961$	−832.197			−0.865970
$962$	634.609	+	634.609i	0.659677	+	0.659677i
$963$	242.042	−	242.042i	0.251342	−	0.251342i
$964$		−	695.148i		−	0.721108i
$965$	−762.015	+	153.717i	−0.789653	+	0.159292i
$966$	54.0792			0.0559826
$967$	−497.222	−	497.222i	−0.514191	−	0.514191i	0.401617	−	0.915808i	$-0.368448\pi$
$967$	−497.222	−	497.222i	−0.514191	−	0.514191i	−0.915808	+	0.401617i	$0.868448\pi$
$968$	383.352	−	383.352i	0.396025	−	0.396025i
$969$		−	1171.76i		−	1.20925i
$970$	−484.008	+	728.626i	−0.498978	+	0.751161i
$971$	978.176			1.00739			0.503695	−	0.863881i	$-0.331973\pi$
$971$	978.176			1.00739			0.503695	+	0.863881i	$0.331973\pi$
$972$	22.0454	+	22.0454i	0.0226805	+	0.0226805i
$973$	−149.866	+	149.866i	−0.154025	+	0.154025i
$974$		−	468.499i		−	0.481005i
$975$	699.711	−	294.271i	0.717652	−	0.301817i
$976$	−116.831			−0.119704
$977$	964.006	+	964.006i	0.986700	+	0.986700i	0.999913	−	0.0132130i	$-0.00420594\pi$
$977$	964.006	+	964.006i	0.986700	+	0.986700i	−0.0132130	+	0.999913i	$0.504206\pi$
$978$	256.294	−	256.294i	0.262059	−	0.262059i
$979$		−	1838.39i		−	1.87782i
$980$	58.3078	+	38.7324i	0.0594977	+	0.0395229i
$981$	193.335			0.197079
$982$	−171.731	−	171.731i	−0.174879	−	0.174879i
$983$	93.2350	−	93.2350i	0.0948474	−	0.0948474i	−0.658091	−	0.752938i	$-0.728636\pi$
$983$	93.2350	−	93.2350i	0.0948474	−	0.0948474i	0.752938	+	0.658091i	$0.228636\pi$
$984$			288.199i			0.292885i
$985$	−114.950	−	569.839i	−0.116701	−	0.578517i
$986$	−575.394			−0.583564
$987$	−222.945	−	222.945i	−0.225881	−	0.225881i
$988$	633.357	−	633.357i	0.641049	−	0.641049i
$989$			3.33669i			0.00337380i
$990$	367.699	−	74.1737i	0.371413	−	0.0749229i
$991$	684.463			0.690679			0.345340	−	0.938478i	$-0.387764\pi$
$991$	684.463			0.690679			0.345340	+	0.938478i	$0.387764\pi$
$992$	45.3966	+	45.3966i	0.0457627	+	0.0457627i
$993$	656.577	−	656.577i	0.661206	−	0.661206i
$994$			4.45985i			0.00448677i
$995$	643.758	−	969.113i	0.646993	−	0.973982i
$996$	449.732			0.451538
$997$	426.193	+	426.193i	0.427476	+	0.427476i	0.887768	−	0.460292i	$-0.152255\pi$
$997$	426.193	+	426.193i	0.427476	+	0.427476i	−0.460292	+	0.887768i	$0.652255\pi$
$998$	−507.901	+	507.901i	−0.508919	+	0.508919i
$999$			188.107i			0.188296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.l.b.127.2	yes	16
3.2	odd	2		630.3.o.f.127.6		16
5.2	odd	4		1050.3.l.h.43.8		16
5.3	odd	4	inner	210.3.l.b.43.2	✓	16
5.4	even	2		1050.3.l.h.757.8		16
15.8	even	4		630.3.o.f.253.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.b.43.2	✓	16	5.3	odd	4	inner
210.3.l.b.127.2	yes	16	1.1	even	1	trivial
630.3.o.f.127.6		16	3.2	odd	2
630.3.o.f.253.6		16	15.8	even	4
1050.3.l.h.43.8		16	5.2	odd	4
1050.3.l.h.757.8		16	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)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.16484 - 2.76660i) q^{5} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.16484 - 2.76660i) q^{5} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(1.39824 + 6.93144i) q^{10} +17.6826 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-12.3956 + 12.3956i) q^{13} +3.74166i q^{14} +(8.48925 - 1.71249i) q^{15} -4.00000 q^{16} +(18.7246 + 18.7246i) q^{17} +(-3.00000 + 3.00000i) q^{18} +25.5476i q^{19} +(5.53321 - 8.32968i) q^{20} +4.58258 q^{21} +(-17.6826 - 17.6826i) q^{22} +(-5.90052 + 5.90052i) q^{23} +4.89898i q^{24} +(9.69181 + 23.0449i) q^{25} +24.7912 q^{26} +(3.67423 + 3.67423i) q^{27} +(3.74166 - 3.74166i) q^{28} -15.3647i q^{29} +(-10.2017 - 6.77677i) q^{30} +11.3491 q^{31} +(4.00000 + 4.00000i) q^{32} +(-21.6567 + 21.6567i) q^{33} -37.4492i q^{34} +(2.61586 + 12.9675i) q^{35} +6.00000 q^{36} +(25.5981 + 25.5981i) q^{37} +(25.5476 - 25.5476i) q^{38} -30.3629i q^{39} +(-13.8629 + 2.79648i) q^{40} +58.8283 q^{41} +(-4.58258 - 4.58258i) q^{42} +(0.282745 - 0.282745i) q^{43} +35.3653i q^{44} +(-8.29981 + 12.4945i) q^{45} +11.8010 q^{46} +(-48.6505 - 48.6505i) q^{47} +(4.89898 - 4.89898i) q^{48} +7.00000i q^{49} +(13.3531 - 32.7367i) q^{50} -45.8657 q^{51} +(-24.7912 - 24.7912i) q^{52} +(3.93909 - 3.93909i) q^{53} -7.34847i q^{54} +(-73.6454 - 48.9209i) q^{55} -7.48331 q^{56} +(-31.2893 - 31.2893i) q^{57} +(-15.3647 + 15.3647i) q^{58} +86.2636i q^{59} +(3.42497 + 16.9785i) q^{60} +29.2079 q^{61} +(-11.3491 - 11.3491i) q^{62} +(-5.61249 + 5.61249i) q^{63} -8.00000i q^{64} +(85.9194 - 17.3320i) q^{65} +43.3135 q^{66} +(-65.7277 - 65.7277i) q^{67} +(-37.4492 + 37.4492i) q^{68} -14.4533i q^{69} +(10.3517 - 15.5834i) q^{70} +1.19194 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-87.0749 + 87.0749i) q^{73} -51.1963i q^{74} +(-40.0942 - 16.3542i) q^{75} -51.0953 q^{76} +(-33.0812 - 33.0812i) q^{77} +(-30.3629 + 30.3629i) q^{78} +55.0959i q^{79} +(16.6594 + 11.0664i) q^{80} -9.00000 q^{81} +(-58.8283 - 58.8283i) q^{82} +(-91.8012 + 91.8012i) q^{83} +9.16515i q^{84} +(-26.1814 - 129.788i) q^{85} -0.565490 q^{86} +(18.8178 + 18.8178i) q^{87} +(35.3653 - 35.3653i) q^{88} -103.966i q^{89} +(20.7943 - 4.19472i) q^{90} +46.3801 q^{91} +(-11.8010 - 11.8010i) q^{92} +(-13.8998 + 13.8998i) q^{93} +97.3010i q^{94} +(70.6802 - 106.402i) q^{95} -9.79796 q^{96} +(87.4734 + 87.4734i) q^{97} +(7.00000 - 7.00000i) q^{98} -53.0479i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} - 16 q^{5} + 32 q^{8}+O(q^{10}) \) 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8	\( 16 q - 16 q^{2} - 16 q^{5} + 32 q^{8} + 24 q^{10} + 8 q^{11} - 32 q^{13} - 12 q^{15} - 64 q^{16} + 56 q^{17} - 48 q^{18} - 16 q^{20} - 8 q^{22} + 24 q^{23} + 40 q^{25} + 64 q^{26} - 112 q^{31} + 64 q^{32} + 24 q^{33} + 28 q^{35} + 96 q^{36} - 152 q^{37} - 16 q^{40} + 24 q^{45} - 48 q^{46} + 80 q^{47} - 72 q^{50} - 72 q^{51} - 64 q^{52} + 48 q^{53} - 24 q^{55} + 24 q^{57} + 96 q^{58} + 24 q^{60} + 96 q^{61} + 112 q^{62} + 16 q^{65} - 48 q^{66} - 80 q^{67} - 112 q^{68} + 536 q^{71} - 96 q^{72} - 288 q^{75} - 168 q^{77} - 48 q^{78} + 64 q^{80} - 144 q^{81} - 256 q^{83} + 40 q^{85} - 144 q^{87} + 16 q^{88} + 24 q^{90} + 48 q^{92} + 192 q^{93} + 360 q^{95} + 688 q^{97} + 112 q^{98}+O(q^{100}) \) 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8 + 24 * q^10 + 8 * q^11 - 32 * q^13 - 12 * q^15 - 64 * q^16 + 56 * q^17 - 48 * q^18 - 16 * q^20 - 8 * q^22 + 24 * q^23 + 40 * q^25 + 64 * q^26 - 112 * q^31 + 64 * q^32 + 24 * q^33 + 28 * q^35 + 96 * q^36 - 152 * q^37 - 16 * q^40 + 24 * q^45 - 48 * q^46 + 80 * q^47 - 72 * q^50 - 72 * q^51 - 64 * q^52 + 48 * q^53 - 24 * q^55 + 24 * q^57 + 96 * q^58 + 24 * q^60 + 96 * q^61 + 112 * q^62 + 16 * q^65 - 48 * q^66 - 80 * q^67 - 112 * q^68 + 536 * q^71 - 96 * q^72 - 288 * q^75 - 168 * q^77 - 48 * q^78 + 64 * q^80 - 144 * q^81 - 256 * q^83 + 40 * q^85 - 144 * q^87 + 16 * q^88 + 24 * q^90 + 48 * q^92 + 192 * q^93 + 360 * q^95 + 688 * q^97 + 112 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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