LMFDB - Embedded newform 210.3.l.a.127.4

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			127.4
Root			$-1.54779 - 1.54779i$ of defining polynomial
Character	$\chi$	$=$	210.127
Dual form			210.3.l.a.43.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.32032 + 2.51691i) q^{5} +2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.32032 + 2.51691i) q^{5} +2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(1.80341 + 6.83723i) q^{10} +2.92322 q^{11} +(2.44949 + 2.44949i) q^{12} +(-1.13309 + 1.13309i) q^{13} +3.74166i q^{14} +(8.37386 - 2.20871i) q^{15} -4.00000 q^{16} +(1.54506 + 1.54506i) q^{17} +(3.00000 - 3.00000i) q^{18} +3.35199i q^{19} +(-5.03383 + 8.64064i) q^{20} +4.58258 q^{21} +(2.92322 + 2.92322i) q^{22} +(7.90681 - 7.90681i) q^{23} +4.89898i q^{24} +(12.3303 + 21.7477i) q^{25} -2.26617 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-3.74166 + 3.74166i) q^{28} -13.5474i q^{29} +(10.5826 + 6.16515i) q^{30} +15.7936 q^{31} +(-4.00000 - 4.00000i) q^{32} +(3.58019 - 3.58019i) q^{33} +3.09013i q^{34} +(3.37386 + 12.7913i) q^{35} +6.00000 q^{36} +(-16.8305 - 16.8305i) q^{37} +(-3.35199 + 3.35199i) q^{38} +2.77548i q^{39} +(-13.6745 + 3.60681i) q^{40} -72.6227 q^{41} +(4.58258 + 4.58258i) q^{42} +(20.3749 - 20.3749i) q^{43} +5.84643i q^{44} +(7.55074 - 12.9610i) q^{45} +15.8136 q^{46} +(-52.3194 - 52.3194i) q^{47} +(-4.89898 + 4.89898i) q^{48} +7.00000i q^{49} +(-9.41742 + 34.0780i) q^{50} +3.78462 q^{51} +(-2.26617 - 2.26617i) q^{52} +(-40.5379 + 40.5379i) q^{53} -7.34847i q^{54} +(12.6292 + 7.35748i) q^{55} -7.48331 q^{56} +(4.10533 + 4.10533i) q^{57} +(13.5474 - 13.5474i) q^{58} -117.165i q^{59} +(4.41742 + 16.7477i) q^{60} -45.4373 q^{61} +(15.7936 + 15.7936i) q^{62} +(5.61249 - 5.61249i) q^{63} -8.00000i q^{64} +(-7.74717 + 2.04341i) q^{65} +7.16039 q^{66} +(57.7773 + 57.7773i) q^{67} +(-3.09013 + 3.09013i) q^{68} -19.3676i q^{69} +(-9.41742 + 16.1652i) q^{70} -51.7217 q^{71} +(6.00000 + 6.00000i) q^{72} +(72.3851 - 72.3851i) q^{73} -33.6610i q^{74} +(41.7369 + 11.5339i) q^{75} -6.70398 q^{76} +(5.46884 + 5.46884i) q^{77} +(-2.77548 + 2.77548i) q^{78} -37.1850i q^{79} +(-17.2813 - 10.0677i) q^{80} -9.00000 q^{81} +(-72.6227 - 72.6227i) q^{82} +(-21.3331 + 21.3331i) q^{83} +9.16515i q^{84} +(2.78638 + 10.5640i) q^{85} +40.7498 q^{86} +(-16.5922 - 16.5922i) q^{87} +(-5.84643 + 5.84643i) q^{88} -100.951i q^{89} +(20.5117 - 5.41022i) q^{90} -4.23962 q^{91} +(15.8136 + 15.8136i) q^{92} +(19.3432 - 19.3432i) q^{93} -104.639i q^{94} +(-8.43666 + 14.4817i) q^{95} -9.79796 q^{96} +(52.5887 + 52.5887i) q^{97} +(-7.00000 + 7.00000i) q^{98} -8.76965i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 16 q^{8}+O(q^{10}) $ 8 * q + 8 * q^2 - 16 * q^8	$ 8 q + 8 q^{2} - 16 q^{8} - 8 q^{11} + 8 q^{13} + 12 q^{15} - 32 q^{16} - 32 q^{17} + 24 q^{18} - 8 q^{22} - 40 q^{23} - 48 q^{25} + 16 q^{26} + 48 q^{30} + 144 q^{31} - 32 q^{32} + 120 q^{33} - 28 q^{35} + 48 q^{36} + 160 q^{37} - 320 q^{41} - 32 q^{43} - 80 q^{46} - 144 q^{47} - 112 q^{50} + 72 q^{51} + 16 q^{52} - 200 q^{53} + 184 q^{55} - 24 q^{57} - 64 q^{58} + 72 q^{60} + 288 q^{61} + 144 q^{62} + 24 q^{65} + 240 q^{66} + 80 q^{67} + 64 q^{68} - 112 q^{70} - 280 q^{71} + 48 q^{72} + 312 q^{73} - 56 q^{77} + 48 q^{78} - 72 q^{81} - 320 q^{82} - 320 q^{83} + 80 q^{85} - 64 q^{86} - 48 q^{87} + 16 q^{88} - 80 q^{92} + 48 q^{93} - 472 q^{95} - 24 q^{97} - 56 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 - 16 * q^8 - 8 * q^11 + 8 * q^13 + 12 * q^15 - 32 * q^16 - 32 * q^17 + 24 * q^18 - 8 * q^22 - 40 * q^23 - 48 * q^25 + 16 * q^26 + 48 * q^30 + 144 * q^31 - 32 * q^32 + 120 * q^33 - 28 * q^35 + 48 * q^36 + 160 * q^37 - 320 * q^41 - 32 * q^43 - 80 * q^46 - 144 * q^47 - 112 * q^50 + 72 * q^51 + 16 * q^52 - 200 * q^53 + 184 * q^55 - 24 * q^57 - 64 * q^58 + 72 * q^60 + 288 * q^61 + 144 * q^62 + 24 * q^65 + 240 * q^66 + 80 * q^67 + 64 * q^68 - 112 * q^70 - 280 * q^71 + 48 * q^72 + 312 * q^73 - 56 * q^77 + 48 * q^78 - 72 * q^81 - 320 * q^82 - 320 * q^83 + 80 * q^85 - 64 * q^86 - 48 * q^87 + 16 * q^88 - 80 * q^92 + 48 * q^93 - 472 * q^95 - 24 * q^97 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$4$			2.00000i			0.500000i
$5$	4.32032	+	2.51691i	0.864064	+	0.503383i
$5$	4.32032	+	2.51691i	0.864064	+	0.503383i
$6$	2.44949			0.408248
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	1.80341	+	6.83723i	0.180341	+	0.683723i
$11$	2.92322			0.265747			0.132873	−	0.991133i	$-0.457580\pi$
$11$	2.92322			0.265747			0.132873	+	0.991133i	$0.457580\pi$
$12$	2.44949	+	2.44949i	0.204124	+	0.204124i
$13$	−1.13309	+	1.13309i	−0.0871605	+	0.0871605i	−0.749343	−	0.662182i	$-0.769630\pi$
$13$	−1.13309	+	1.13309i	−0.0871605	+	0.0871605i	0.662182	+	0.749343i	$0.269630\pi$
$14$			3.74166i			0.267261i
$15$	8.37386	−	2.20871i	0.558258	−	0.147247i
$16$	−4.00000			−0.250000
$17$	1.54506	+	1.54506i	0.0908861	+	0.0908861i	0.751088	−	0.660202i	$-0.229529\pi$
$17$	1.54506	+	1.54506i	0.0908861	+	0.0908861i	−0.660202	+	0.751088i	$0.729529\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$			3.35199i			0.176420i	0.996102	+	0.0882102i	$0.0281147\pi$
$19$			3.35199i			0.176420i	−0.996102	+	0.0882102i	$0.971885\pi$
$20$	−5.03383	+	8.64064i	−0.251691	+	0.432032i
$21$	4.58258			0.218218
$22$	2.92322	+	2.92322i	0.132873	+	0.132873i
$23$	7.90681	−	7.90681i	0.343774	−	0.343774i	−0.514010	−	0.857784i	$-0.671841\pi$
$23$	7.90681	−	7.90681i	0.343774	−	0.343774i	0.857784	+	0.514010i	$0.171841\pi$
$24$			4.89898i			0.204124i
$25$	12.3303	+	21.7477i	0.493212	+	0.869909i
$26$	−2.26617			−0.0871605
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	−3.74166	+	3.74166i	−0.133631	+	0.133631i
$29$		−	13.5474i		−	0.467153i	−0.972338	−	0.233577i	$-0.924957\pi$
$29$		−	13.5474i		−	0.467153i	0.972338	−	0.233577i	$-0.0750430\pi$
$30$	10.5826	+	6.16515i	0.352753	+	0.205505i
$31$	15.7936			0.509473			0.254736	−	0.967011i	$-0.418011\pi$
$31$	15.7936			0.509473			0.254736	+	0.967011i	$0.418011\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	3.58019	−	3.58019i	0.108491	−	0.108491i
$34$			3.09013i			0.0908861i
$35$	3.37386	+	12.7913i	0.0963961	+	0.365465i
$36$	6.00000			0.166667
$37$	−16.8305	−	16.8305i	−0.454878	−	0.454878i	0.442092	−	0.896970i	$-0.354236\pi$
$37$	−16.8305	−	16.8305i	−0.454878	−	0.454878i	−0.896970	+	0.442092i	$0.854236\pi$
$38$	−3.35199	+	3.35199i	−0.0882102	+	0.0882102i
$39$			2.77548i			0.0711662i
$40$	−13.6745	+	3.60681i	−0.341862	+	0.0901703i
$41$	−72.6227			−1.77129			−0.885643	−	0.464367i	$-0.846282\pi$
$41$	−72.6227			−1.77129			−0.885643	+	0.464367i	$0.846282\pi$
$42$	4.58258	+	4.58258i	0.109109	+	0.109109i
$43$	20.3749	−	20.3749i	0.473835	−	0.473835i	−0.429318	−	0.903153i	$-0.641246\pi$
$43$	20.3749	−	20.3749i	0.473835	−	0.473835i	0.903153	+	0.429318i	$0.141246\pi$
$44$			5.84643i			0.132873i
$45$	7.55074	−	12.9610i	0.167794	−	0.288021i
$46$	15.8136			0.343774
$47$	−52.3194	−	52.3194i	−1.11318	−	1.11318i	−0.992718	−	0.120461i	$-0.961563\pi$
$47$	−52.3194	−	52.3194i	−1.11318	−	1.11318i	−0.120461	−	0.992718i	$-0.538437\pi$
$48$	−4.89898	+	4.89898i	−0.102062	+	0.102062i
$49$			7.00000i			0.142857i
$50$	−9.41742	+	34.0780i	−0.188348	+	0.681561i
$51$	3.78462			0.0742082
$52$	−2.26617	−	2.26617i	−0.0435802	−	0.0435802i
$53$	−40.5379	+	40.5379i	−0.764865	+	0.764865i	−0.977198	−	0.212332i	$-0.931894\pi$
$53$	−40.5379	+	40.5379i	−0.764865	+	0.764865i	0.212332	+	0.977198i	$0.431894\pi$
$54$		−	7.34847i		−	0.136083i
$55$	12.6292	+	7.35748i	0.229622	+	0.133772i
$56$	−7.48331			−0.133631
$57$	4.10533	+	4.10533i	0.0720233	+	0.0720233i
$58$	13.5474	−	13.5474i	0.233577	−	0.233577i
$59$		−	117.165i		−	1.98585i	−0.118752	−	0.992924i	$-0.537889\pi$
$59$		−	117.165i		−	1.98585i	0.118752	−	0.992924i	$-0.462111\pi$
$60$	4.41742	+	16.7477i	0.0736237	+	0.279129i
$61$	−45.4373			−0.744874			−0.372437	−	0.928057i	$-0.621478\pi$
$61$	−45.4373			−0.744874			−0.372437	+	0.928057i	$0.621478\pi$
$62$	15.7936	+	15.7936i	0.254736	+	0.254736i
$63$	5.61249	−	5.61249i	0.0890871	−	0.0890871i
$64$		−	8.00000i		−	0.125000i
$65$	−7.74717	+	2.04341i	−0.119187	+	0.0314371i
$66$	7.16039			0.108491
$67$	57.7773	+	57.7773i	0.862348	+	0.862348i	0.991610	−	0.129263i	$-0.0412611\pi$
$67$	57.7773	+	57.7773i	0.862348	+	0.862348i	−0.129263	+	0.991610i	$0.541261\pi$
$68$	−3.09013	+	3.09013i	−0.0454430	+	0.0454430i
$69$		−	19.3676i		−	0.280691i
$70$	−9.41742	+	16.1652i	−0.134535	+	0.230931i
$71$	−51.7217			−0.728475			−0.364238	−	0.931306i	$-0.618670\pi$
$71$	−51.7217			−0.728475			−0.364238	+	0.931306i	$0.618670\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	72.3851	−	72.3851i	0.991576	−	0.991576i	−0.00838858	−	0.999965i	$-0.502670\pi$
$73$	72.3851	−	72.3851i	0.991576	−	0.991576i	0.999965	+	0.00838858i	$0.00267020\pi$
$74$		−	33.6610i		−	0.454878i
$75$	41.7369	+	11.5339i	0.556492	+	0.153786i
$76$	−6.70398			−0.0882102
$77$	5.46884	+	5.46884i	0.0710238	+	0.0710238i
$78$	−2.77548	+	2.77548i	−0.0355831	+	0.0355831i
$79$		−	37.1850i		−	0.470696i	−0.971911	−	0.235348i	$-0.924377\pi$
$79$		−	37.1850i		−	0.470696i	0.971911	−	0.235348i	$-0.0756230\pi$
$80$	−17.2813	−	10.0677i	−0.216016	−	0.125846i
$81$	−9.00000			−0.111111
$82$	−72.6227	−	72.6227i	−0.885643	−	0.885643i
$83$	−21.3331	+	21.3331i	−0.257026	+	0.257026i	−0.823843	−	0.566818i	$-0.808174\pi$
$83$	−21.3331	+	21.3331i	−0.257026	+	0.257026i	0.566818	+	0.823843i	$0.308174\pi$
$84$			9.16515i			0.109109i
$85$	2.78638	+	10.5640i	0.0327809	+	0.124282i
$86$	40.7498			0.473835
$87$	−16.5922	−	16.5922i	−0.190715	−	0.190715i
$88$	−5.84643	+	5.84643i	−0.0664367	+	0.0664367i
$89$		−	100.951i		−	1.13428i	−0.823620	−	0.567141i	$-0.808049\pi$
$89$		−	100.951i		−	1.13428i	0.823620	−	0.567141i	$-0.191951\pi$
$90$	20.5117	−	5.41022i	0.227908	−	0.0601135i
$91$	−4.23962			−0.0465892
$92$	15.8136	+	15.8136i	0.171887	+	0.171887i
$93$	19.3432	−	19.3432i	0.207991	−	0.207991i
$94$		−	104.639i		−	1.11318i
$95$	−8.43666	+	14.4817i	−0.0888070	+	0.152438i
$96$	−9.79796			−0.102062
$97$	52.5887	+	52.5887i	0.542151	+	0.542151i	0.924159	−	0.382008i	$-0.124767\pi$
$97$	52.5887	+	52.5887i	0.542151	+	0.542151i	−0.382008	+	0.924159i	$0.624767\pi$
$98$	−7.00000	+	7.00000i	−0.0714286	+	0.0714286i
$99$		−	8.76965i		−	0.0885823i
$100$	−43.4955	+	24.6606i	−0.434955	+	0.246606i
$101$	−129.417			−1.28136			−0.640679	−	0.767808i	$-0.721347\pi$
$101$	−129.417			−1.28136			−0.640679	+	0.767808i	$0.721347\pi$
$102$	3.78462	+	3.78462i	0.0371041	+	0.0371041i
$103$	31.0447	−	31.0447i	0.301405	−	0.301405i	−0.540158	−	0.841563i	$-0.681636\pi$
$103$	31.0447	−	31.0447i	0.301405	−	0.301405i	0.841563	+	0.540158i	$0.181636\pi$
$104$		−	4.53234i		−	0.0435802i
$105$	19.7982	+	11.5339i	0.188554	+	0.109847i
$106$	−81.0757			−0.764865
$107$	109.421	+	109.421i	1.02263	+	1.02263i	0.999738	+	0.0228904i	$0.00728688\pi$
$107$	109.421	+	109.421i	1.02263	+	1.02263i	0.0228904	+	0.999738i	$0.492713\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$			68.6170i			0.629514i	0.949172	+	0.314757i	$0.101923\pi$
$109$			68.6170i			0.629514i	−0.949172	+	0.314757i	$0.898077\pi$
$110$	5.27174	+	19.9867i	0.0479249	+	0.181697i
$111$	−41.2261			−0.371406
$112$	−7.48331	−	7.48331i	−0.0668153	−	0.0668153i
$113$	−68.0366	+	68.0366i	−0.602094	+	0.602094i	−0.940868	−	0.338774i	$-0.889988\pi$
$113$	−68.0366	+	68.0366i	−0.602094	+	0.602094i	0.338774	+	0.940868i	$0.389988\pi$
$114$			8.21066i			0.0720233i
$115$	54.0607	−	14.2592i	0.470093	−	0.123993i
$116$	27.0949			0.233577
$117$	3.39926	+	3.39926i	0.0290535	+	0.0290535i
$118$	117.165	−	117.165i	0.992924	−	0.992924i
$119$			5.78110i			0.0485807i
$120$	−12.3303	+	21.1652i	−0.102753	+	0.176376i
$121$	−112.455			−0.929379
$122$	−45.4373	−	45.4373i	−0.372437	−	0.372437i
$123$	−88.9443	+	88.9443i	−0.723124	+	0.723124i
$124$			31.5873i			0.254736i
$125$	−1.46629	+	124.991i	−0.0117303	+	0.999931i
$126$	11.2250			0.0890871
$127$	142.963	+	142.963i	1.12569	+	1.12569i	0.990870	+	0.134824i	$0.0430470\pi$
$127$	142.963	+	142.963i	1.12569	+	1.12569i	0.134824	+	0.990870i	$0.456953\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$		−	49.9082i		−	0.386885i
$130$	−9.79058	−	5.70376i	−0.0753122	−	0.0438750i
$131$	3.55384			0.0271285			0.0135643	−	0.999908i	$-0.495682\pi$
$131$	3.55384			0.0271285			0.0135643	+	0.999908i	$0.495682\pi$
$132$	7.16039	+	7.16039i	0.0542454	+	0.0542454i
$133$	−6.27100	+	6.27100i	−0.0471503	+	0.0471503i
$134$			115.555i			0.862348i
$135$	−6.62614	−	25.1216i	−0.0490825	−	0.186086i
$136$	−6.18025			−0.0454430
$137$	75.1054	+	75.1054i	0.548214	+	0.548214i	0.925924	−	0.377710i	$-0.123288\pi$
$137$	75.1054	+	75.1054i	0.548214	+	0.548214i	−0.377710	+	0.925924i	$0.623288\pi$
$138$	19.3676	−	19.3676i	0.140345	−	0.140345i
$139$			192.352i			1.38383i	0.721980	+	0.691914i	$0.243232\pi$
$139$			192.352i			1.38383i	−0.721980	+	0.691914i	$0.756768\pi$
$140$	−25.5826	+	6.74773i	−0.182733	+	0.0481981i
$141$	−128.156			−0.908907
$142$	−51.7217	−	51.7217i	−0.364238	−	0.364238i
$143$	−3.31225	+	3.31225i	−0.0231626	+	0.0231626i
$144$			12.0000i			0.0833333i
$145$	34.0977	−	58.5293i	0.235157	−	0.403650i
$146$	144.770			0.991576
$147$	8.57321	+	8.57321i	0.0583212	+	0.0583212i
$148$	33.6610	−	33.6610i	0.227439	−	0.227439i
$149$		−	77.5005i		−	0.520138i	−0.965590	−	0.260069i	$-0.916255\pi$
$149$		−	77.5005i		−	0.520138i	0.965590	−	0.260069i	$-0.0837453\pi$
$150$	30.2030	+	53.2708i	0.201353	+	0.355139i
$151$	36.8195			0.243837			0.121919	−	0.992540i	$-0.461095\pi$
$151$	36.8195			0.243837			0.121919	+	0.992540i	$0.461095\pi$
$152$	−6.70398	−	6.70398i	−0.0441051	−	0.0441051i
$153$	4.63519	−	4.63519i	0.0302954	−	0.0302954i
$154$			10.9377i			0.0710238i
$155$	68.2336	+	39.7512i	0.440217	+	0.256460i
$156$	−5.55096			−0.0355831
$157$	75.7654	+	75.7654i	0.482582	+	0.482582i	0.905955	−	0.423373i	$-0.139154\pi$
$157$	75.7654	+	75.7654i	0.482582	+	0.482582i	−0.423373	+	0.905955i	$0.639154\pi$
$158$	37.1850	−	37.1850i	0.235348	−	0.235348i
$159$			99.2971i			0.624510i
$160$	−7.21362	−	27.3489i	−0.0450851	−	0.170931i
$161$	29.5846			0.183755
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	174.453	−	174.453i	1.07026	−	1.07026i	0.0729236	−	0.997338i	$-0.476767\pi$
$163$	174.453	−	174.453i	1.07026	−	1.07026i	0.997338	−	0.0729236i	$-0.0232329\pi$
$164$		−	145.245i		−	0.885643i
$165$	24.4786	−	6.45654i	0.148355	−	0.0391306i
$166$	−42.6663			−0.257026
$167$	119.275	+	119.275i	0.714222	+	0.714222i	0.967416	−	0.253194i	$-0.0814810\pi$
$167$	119.275	+	119.275i	0.714222	+	0.714222i	−0.253194	+	0.967416i	$0.581481\pi$
$168$	−9.16515	+	9.16515i	−0.0545545	+	0.0545545i
$169$			166.432i			0.984806i
$170$	−7.77758	+	13.3503i	−0.0457505	+	0.0785314i
$171$	10.0560			0.0588068
$172$	40.7498	+	40.7498i	0.236918	+	0.236918i
$173$	110.021	−	110.021i	0.635957	−	0.635957i	−0.313599	−	0.949556i	$-0.601535\pi$
$173$	110.021	−	110.021i	0.635957	−	0.635957i	0.949556	+	0.313599i	$0.101535\pi$
$174$		−	33.1843i		−	0.190715i
$175$	−17.6184	+	63.7542i	−0.100677	+	0.364309i
$176$	−11.6929			−0.0664367
$177$	−143.497	−	143.497i	−0.810719	−	0.810719i
$178$	100.951	−	100.951i	0.567141	−	0.567141i
$179$		−	49.0357i		−	0.273943i	−0.990575	−	0.136971i	$-0.956263\pi$
$179$		−	49.0357i		−	0.273943i	0.990575	−	0.136971i	$-0.0437368\pi$
$180$	25.9219	+	15.1015i	0.144011	+	0.0838971i
$181$	−327.143			−1.80742			−0.903709	−	0.428148i	$-0.859166\pi$
$181$	−327.143			−1.80742			−0.903709	+	0.428148i	$0.859166\pi$
$182$	−4.23962	−	4.23962i	−0.0232946	−	0.0232946i
$183$	−55.6491	+	55.6491i	−0.304094	+	0.304094i
$184$			31.6272i			0.171887i
$185$	−30.3522	−	115.074i	−0.164066	−	0.622021i
$186$	38.6864			0.207991
$187$	4.51655	+	4.51655i	0.0241527	+	0.0241527i
$188$	104.639	−	104.639i	0.556589	−	0.556589i
$189$		−	13.7477i		−	0.0727393i
$190$	−22.9183	+	6.04500i	−0.120623	+	0.0318158i
$191$	289.078			1.51350			0.756749	−	0.653705i	$-0.226786\pi$
$191$	289.078			1.51350			0.756749	+	0.653705i	$0.226786\pi$
$192$	−9.79796	−	9.79796i	−0.0510310	−	0.0510310i
$193$	−131.213	+	131.213i	−0.679858	+	0.679858i	−0.959968	−	0.280110i	$-0.909629\pi$
$193$	−131.213	+	131.213i	−0.679858	+	0.679858i	0.280110	+	0.959968i	$0.409629\pi$
$194$			105.177i			0.542151i
$195$	−6.98565	+	11.9910i	−0.0358238	+	0.0614921i
$196$	−14.0000			−0.0714286
$197$	111.798	+	111.798i	0.567504	+	0.567504i	0.931429	−	0.363924i	$-0.118563\pi$
$197$	111.798	+	111.798i	0.567504	+	0.567504i	−0.363924	+	0.931429i	$0.618563\pi$
$198$	8.76965	−	8.76965i	0.0442911	−	0.0442911i
$199$		−	58.3715i		−	0.293324i	−0.989187	−	0.146662i	$-0.953147\pi$
$199$		−	58.3715i		−	0.293324i	0.989187	−	0.146662i	$-0.0468530\pi$
$200$	−68.1561	−	18.8348i	−0.340780	−	0.0941742i
$201$	141.525			0.704104
$202$	−129.417	−	129.417i	−0.640679	−	0.640679i
$203$	25.3450	−	25.3450i	0.124852	−	0.124852i
$204$			7.56923i			0.0371041i
$205$	−313.753	−	182.785i	−1.53050	−	0.891634i
$206$	62.0894			0.301405
$207$	−23.7204	−	23.7204i	−0.114591	−	0.114591i
$208$	4.53234	−	4.53234i	0.0217901	−	0.0217901i
$209$			9.79858i			0.0468832i
$210$	8.26424	+	31.3321i	0.0393535	+	0.149201i
$211$	55.0602			0.260949			0.130474	−	0.991452i	$-0.458350\pi$
$211$	55.0602			0.260949			0.130474	+	0.991452i	$0.458350\pi$
$212$	−81.0757	−	81.0757i	−0.382433	−	0.382433i
$213$	−63.3459	+	63.3459i	−0.297399	+	0.297399i
$214$			218.842i			1.02263i
$215$	139.308	−	36.7443i	0.647944	−	0.170903i
$216$	14.6969			0.0680414
$217$	29.5472	+	29.5472i	0.136162	+	0.136162i
$218$	−68.6170	+	68.6170i	−0.314757	+	0.314757i
$219$		−	177.306i		−	0.809619i
$220$	−14.7150	+	25.2584i	−0.0668862	+	0.114811i
$221$	−3.50138			−0.0158433
$222$	−41.2261	−	41.2261i	−0.185703	−	0.185703i
$223$	−101.768	+	101.768i	−0.456360	+	0.456360i	−0.897459	−	0.441099i	$-0.854589\pi$
$223$	−101.768	+	101.768i	−0.456360	+	0.456360i	0.441099	+	0.897459i	$0.354589\pi$
$224$		−	14.9666i		−	0.0668153i
$225$	65.2432	−	36.9909i	0.289970	−	0.164404i
$226$	−136.073			−0.602094
$227$	−25.0589	−	25.0589i	−0.110392	−	0.110392i	0.649753	−	0.760145i	$-0.274872\pi$
$227$	−25.0589	−	25.0589i	−0.110392	−	0.110392i	−0.760145	+	0.649753i	$0.774872\pi$
$228$	−8.21066	+	8.21066i	−0.0360117	+	0.0360117i
$229$			283.497i			1.23798i	0.785399	+	0.618990i	$0.212458\pi$
$229$			283.497i			1.23798i	−0.785399	+	0.618990i	$0.787542\pi$
$230$	68.3199	+	39.8015i	0.297043	+	0.173050i
$231$	13.3959			0.0579907
$232$	27.0949	+	27.0949i	0.116788	+	0.116788i
$233$	139.119	−	139.119i	0.597077	−	0.597077i	−0.342457	−	0.939534i	$-0.611259\pi$
$233$	139.119	−	139.119i	0.597077	−	0.597077i	0.939534	+	0.342457i	$0.111259\pi$
$234$			6.79852i			0.0290535i
$235$	−94.3531	−	357.720i	−0.401503	−	1.52221i
$236$	234.330			0.992924
$237$	−45.5421	−	45.5421i	−0.192161	−	0.192161i
$238$	−5.78110	+	5.78110i	−0.0242903	+	0.0242903i
$239$		−	183.280i		−	0.766864i	−0.923569	−	0.383432i	$-0.874742\pi$
$239$		−	183.280i		−	0.766864i	0.923569	−	0.383432i	$-0.125258\pi$
$240$	−33.4955	+	8.83485i	−0.139564	+	0.0368119i
$241$	−280.094			−1.16222			−0.581108	−	0.813827i	$-0.697380\pi$
$241$	−280.094			−1.16222			−0.581108	+	0.813827i	$0.697380\pi$
$242$	−112.455	−	112.455i	−0.464689	−	0.464689i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$		−	90.8747i		−	0.372437i
$245$	−17.6184	+	30.2422i	−0.0719118	+	0.123438i
$246$	−177.889			−0.723124
$247$	−3.79809	−	3.79809i	−0.0153769	−	0.0153769i
$248$	−31.5873	+	31.5873i	−0.127368	+	0.127368i
$249$			52.2553i			0.209861i
$250$	−126.458	+	123.525i	−0.505831	+	0.494100i
$251$	148.745			0.592611			0.296305	−	0.955093i	$-0.404245\pi$
$251$	148.745			0.592611			0.296305	+	0.955093i	$0.404245\pi$
$252$	11.2250	+	11.2250i	0.0445435	+	0.0445435i
$253$	23.1133	−	23.1133i	0.0913569	−	0.0913569i
$254$			285.926i			1.12569i
$255$	16.3507	+	9.52555i	0.0641206	+	0.0373551i
$256$	16.0000			0.0625000
$257$	−241.684	−	241.684i	−0.940404	−	0.940404i	0.0579178	−	0.998321i	$-0.481554\pi$
$257$	−241.684	−	241.684i	−0.940404	−	0.940404i	−0.998321	+	0.0579178i	$0.981554\pi$
$258$	49.9082	−	49.9082i	0.193442	−	0.193442i
$259$		−	62.9739i		−	0.243142i
$260$	−4.08683	−	15.4943i	−0.0157186	−	0.0595936i
$261$	−40.6423			−0.155718
$262$	3.55384	+	3.55384i	0.0135643	+	0.0135643i
$263$	−234.607	+	234.607i	−0.892042	+	0.892042i	−0.994715	−	0.102673i	$-0.967260\pi$
$263$	−234.607	+	234.607i	−0.892042	+	0.892042i	0.102673	+	0.994715i	$0.467260\pi$
$264$			14.3208i			0.0542454i
$265$	−277.167	+	73.1062i	−1.04591	+	0.275872i
$266$	−12.5420			−0.0471503
$267$	−123.639	−	123.639i	−0.463069	−	0.463069i
$268$	−115.555	+	115.555i	−0.431174	+	0.431174i
$269$		−	357.902i		−	1.33049i	−0.746625	−	0.665245i	$-0.768327\pi$
$269$		−	357.902i		−	1.33049i	0.746625	−	0.665245i	$-0.231673\pi$
$270$	18.4955	−	31.7477i	0.0685017	−	0.117584i
$271$	178.869			0.660035			0.330017	−	0.943975i	$-0.392945\pi$
$271$	178.869			0.660035			0.330017	+	0.943975i	$0.392945\pi$
$272$	−6.18025	−	6.18025i	−0.0227215	−	0.0227215i
$273$	−5.19245	+	5.19245i	−0.0190200	+	0.0190200i
$274$			150.211i			0.548214i
$275$	36.0441	+	63.5733i	0.131070	+	0.231176i
$276$	38.7353			0.140345
$277$	−119.355	−	119.355i	−0.430883	−	0.430883i	0.458045	−	0.888929i	$-0.348550\pi$
$277$	−119.355	−	119.355i	−0.430883	−	0.430883i	−0.888929	+	0.458045i	$0.848550\pi$
$278$	−192.352	+	192.352i	−0.691914	+	0.691914i
$279$		−	47.3809i		−	0.169824i
$280$	−32.3303	−	18.8348i	−0.115465	−	0.0672673i
$281$	−42.3632			−0.150759			−0.0753793	−	0.997155i	$-0.524017\pi$
$281$	−42.3632			−0.150759			−0.0753793	+	0.997155i	$0.524017\pi$
$282$	−128.156	−	128.156i	−0.454453	−	0.454453i
$283$	3.43964	−	3.43964i	0.0121542	−	0.0121542i	−0.701004	−	0.713158i	$-0.747264\pi$
$283$	3.43964	−	3.43964i	0.0121542	−	0.0121542i	0.713158	+	0.701004i	$0.247264\pi$
$284$		−	103.443i		−	0.364238i
$285$	7.40358	+	28.0691i	0.0259775	+	0.0984880i
$286$	−6.62451			−0.0231626
$287$	−135.865	−	135.865i	−0.473396	−	0.473396i
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$		−	284.226i		−	0.983479i
$290$	92.6270	−	24.4315i	0.319403	−	0.0842467i
$291$	128.815			0.442665
$292$	144.770	+	144.770i	0.495788	+	0.495788i
$293$	−25.3982	+	25.3982i	−0.0866834	+	0.0866834i	−0.749119	−	0.662436i	$-0.769523\pi$
$293$	−25.3982	+	25.3982i	−0.0866834	+	0.0866834i	0.662436	+	0.749119i	$0.269523\pi$
$294$			17.1464i			0.0583212i
$295$	294.894	−	506.190i	0.999641	−	1.71590i
$296$	67.3219			0.227439
$297$	−10.7406	−	10.7406i	−0.0361636	−	0.0361636i
$298$	77.5005	−	77.5005i	0.260069	−	0.260069i
$299$			17.9182i			0.0599270i
$300$	−23.0679	+	83.4738i	−0.0768929	+	0.278246i
$301$	76.2360			0.253276
$302$	36.8195	+	36.8195i	0.121919	+	0.121919i
$303$	−158.503	+	158.503i	−0.523113	+	0.523113i
$304$		−	13.4080i		−	0.0441051i
$305$	−196.304	−	114.362i	−0.643619	−	0.374957i
$306$	9.27038			0.0302954
$307$	−323.839	−	323.839i	−1.05485	−	1.05485i	−0.998406	−	0.0564445i	$-0.982024\pi$
$307$	−323.839	−	323.839i	−1.05485	−	1.05485i	−0.0564445	−	0.998406i	$-0.517976\pi$
$308$	−10.9377	+	10.9377i	−0.0355119	+	0.0355119i
$309$		−	76.0437i		−	0.246096i
$310$	28.4824	+	107.985i	0.0918786	+	0.348338i
$311$	−284.428			−0.914561			−0.457280	−	0.889323i	$-0.651176\pi$
$311$	−284.428			−0.914561			−0.457280	+	0.889323i	$0.651176\pi$
$312$	−5.55096	−	5.55096i	−0.0177916	−	0.0177916i
$313$	178.964	−	178.964i	0.571771	−	0.571771i	−0.360852	−	0.932623i	$-0.617514\pi$
$313$	178.964	−	178.964i	0.571771	−	0.571771i	0.932623	+	0.360852i	$0.117514\pi$
$314$			151.531i			0.482582i
$315$	38.3739	−	10.1216i	0.121822	−	0.0321320i
$316$	74.3700			0.235348
$317$	335.800	+	335.800i	1.05931	+	1.05931i	0.998127	+	0.0611787i	$0.0194860\pi$
$317$	335.800	+	335.800i	1.05931	+	1.05931i	0.0611787	+	0.998127i	$0.480514\pi$
$318$	−99.2971	+	99.2971i	−0.312255	+	0.312255i
$319$		−	39.6021i		−	0.124145i
$320$	20.1353	−	34.5625i	0.0629228	−	0.108008i
$321$	268.026			0.834973
$322$	29.5846	+	29.5846i	0.0918775	+	0.0918775i
$323$	−5.17903	+	5.17903i	−0.0160342	+	0.0160342i
$324$		−	18.0000i		−	0.0555556i
$325$	−38.6133	−	10.6708i	−0.118810	−	0.0328331i
$326$	348.905			1.07026
$327$	84.0384	+	84.0384i	0.256998	+	0.256998i
$328$	145.245	−	145.245i	0.442821	−	0.442821i
$329$		−	195.761i		−	0.595019i
$330$	30.9352	+	18.0221i	0.0937429	+	0.0546123i
$331$	444.301			1.34230			0.671150	−	0.741322i	$-0.265801\pi$
$331$	444.301			1.34230			0.671150	+	0.741322i	$0.265801\pi$
$332$	−42.6663	−	42.6663i	−0.128513	−	0.128513i
$333$	−50.4914	+	50.4914i	−0.151626	+	0.151626i
$334$			238.550i			0.714222i
$335$	104.196	+	395.037i	0.311033	+	1.17921i
$336$	−18.3303			−0.0545545
$337$	431.469	+	431.469i	1.28032	+	1.28032i	0.940483	+	0.339842i	$0.110374\pi$
$337$	431.469	+	431.469i	1.28032	+	1.28032i	0.339842	+	0.940483i	$0.389626\pi$
$338$	−166.432	+	166.432i	−0.492403	+	0.492403i
$339$			166.655i			0.491608i
$340$	−21.1279	+	5.57275i	−0.0621409	+	0.0163904i
$341$	46.1682			0.135391
$342$	10.0560	+	10.0560i	0.0294034	+	0.0294034i
$343$	−13.0958	+	13.0958i	−0.0381802	+	0.0381802i
$344$			81.4997i			0.236918i
$345$	48.7467	−	83.6744i	0.141295	−	0.242534i
$346$	220.041			0.635957
$347$	−227.893	−	227.893i	−0.656751	−	0.656751i	0.297859	−	0.954610i	$-0.403728\pi$
$347$	−227.893	−	227.893i	−0.656751	−	0.656751i	−0.954610	+	0.297859i	$0.903728\pi$
$348$	33.1843	−	33.1843i	0.0953573	−	0.0953573i
$349$			280.016i			0.802337i	0.916004	+	0.401168i	$0.131396\pi$
$349$			280.016i			0.802337i	−0.916004	+	0.401168i	$0.868604\pi$
$350$	−81.3725	+	46.1358i	−0.232493	+	0.131816i
$351$	8.32645			0.0237221
$352$	−11.6929	−	11.6929i	−0.0332184	−	0.0332184i
$353$	−114.469	+	114.469i	−0.324276	+	0.324276i	−0.850405	−	0.526129i	$-0.823643\pi$
$353$	−114.469	+	114.469i	−0.324276	+	0.324276i	0.526129	+	0.850405i	$0.323643\pi$
$354$		−	286.995i		−	0.810719i
$355$	−223.454	−	130.179i	−0.629449	−	0.366702i
$356$	201.902			0.567141
$357$	7.08037	+	7.08037i	0.0198330	+	0.0198330i
$358$	49.0357	−	49.0357i	0.136971	−	0.136971i
$359$			700.748i			1.95195i	0.217893	+	0.975973i	$0.430082\pi$
$359$			700.748i			1.95195i	−0.217893	+	0.975973i	$0.569918\pi$
$360$	10.8204	+	41.0234i	0.0300568	+	0.113954i
$361$	349.764			0.968876
$362$	−327.143	−	327.143i	−0.903709	−	0.903709i
$363$	−137.728	+	137.728i	−0.379417	+	0.379417i
$364$		−	8.47924i		−	0.0232946i
$365$	494.913	−	130.540i	1.35593	−	0.357643i
$366$	−111.298			−0.304094
$367$	412.257	+	412.257i	1.12332	+	1.12332i	0.991240	+	0.132075i	$0.0421641\pi$
$367$	412.257	+	412.257i	1.12332	+	1.12332i	0.132075	+	0.991240i	$0.457836\pi$
$368$	−31.6272	+	31.6272i	−0.0859436	+	0.0859436i
$369$			217.868i			0.590428i
$370$	84.7217	−	145.426i	0.228978	−	0.393043i
$371$	−151.679			−0.408838
$372$	38.6864	+	38.6864i	0.103996	+	0.103996i
$373$	−121.669	+	121.669i	−0.326191	+	0.326191i	−0.851136	−	0.524945i	$-0.824086\pi$
$373$	−121.669	+	121.669i	−0.326191	+	0.326191i	0.524945	+	0.851136i	$0.324086\pi$
$374$			9.03311i			0.0241527i
$375$	151.287	+	154.878i	0.403431	+	0.413009i
$376$	209.278			0.556589
$377$	15.3504	+	15.3504i	0.0407173	+	0.0407173i
$378$	13.7477	−	13.7477i	0.0363696	−	0.0363696i
$379$		−	709.113i		−	1.87101i	−0.353312	−	0.935506i	$-0.614945\pi$
$379$		−	709.113i		−	1.87101i	0.353312	−	0.935506i	$-0.385055\pi$
$380$	−28.9633	−	16.8733i	−0.0762192	−	0.0444035i
$381$	350.187			0.919125
$382$	289.078	+	289.078i	0.756749	+	0.756749i
$383$	−476.611	+	476.611i	−1.24441	+	1.24441i	−0.286264	+	0.958151i	$0.592413\pi$
$383$	−476.611	+	476.611i	−1.24441	+	1.24441i	−0.958151	+	0.286264i	$0.907587\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	9.86253	+	37.3917i	0.0256170	+	0.0971213i
$386$	−262.425			−0.679858
$387$	−61.1248	−	61.1248i	−0.157945	−	0.157945i
$388$	−105.177	+	105.177i	−0.271076	+	0.271076i
$389$			270.210i			0.694627i	0.937749	+	0.347313i	$0.112906\pi$
$389$			270.210i			0.694627i	−0.937749	+	0.347313i	$0.887094\pi$
$390$	−18.9766	+	5.00532i	−0.0486580	+	0.0128342i
$391$	24.4330			0.0624886
$392$	−14.0000	−	14.0000i	−0.0357143	−	0.0357143i
$393$	4.35255	−	4.35255i	0.0110752	−	0.0110752i
$394$			223.597i			0.567504i
$395$	93.5914	−	160.651i	0.236940	−	0.406712i
$396$	17.5393			0.0442911
$397$	−169.270	−	169.270i	−0.426374	−	0.426374i	0.461017	−	0.887391i	$-0.347485\pi$
$397$	−169.270	−	169.270i	−0.426374	−	0.426374i	−0.887391	+	0.461017i	$0.847485\pi$
$398$	58.3715	−	58.3715i	0.146662	−	0.146662i
$399$			15.3607i			0.0384981i
$400$	−49.3212	−	86.9909i	−0.123303	−	0.217477i
$401$	397.414			0.991058			0.495529	−	0.868592i	$-0.334974\pi$
$401$	397.414			0.991058			0.495529	+	0.868592i	$0.334974\pi$
$402$	141.525	+	141.525i	0.352052	+	0.352052i
$403$	−17.8956	+	17.8956i	−0.0444059	+	0.0444059i
$404$		−	258.834i		−	0.640679i
$405$	−38.8829	−	22.6522i	−0.0960071	−	0.0559314i
$406$	50.6899			0.124852
$407$	−49.1991	−	49.1991i	−0.120882	−	0.120882i
$408$	−7.56923	+	7.56923i	−0.0185520	+	0.0185520i
$409$			787.478i			1.92537i	0.270616	+	0.962687i	$0.412773\pi$
$409$			787.478i			1.92537i	−0.270616	+	0.962687i	$0.587227\pi$
$410$	−130.968	−	496.538i	−0.319435	−	1.21107i
$411$	183.970			0.447615
$412$	62.0894	+	62.0894i	0.150703	+	0.150703i
$413$	219.196	−	219.196i	0.530740	−	0.530740i
$414$		−	47.4409i		−	0.114591i
$415$	−145.860	+	38.4723i	−0.351469	+	0.0927043i
$416$	9.06469			0.0217901
$417$	235.582	+	235.582i	0.564945	+	0.564945i
$418$	−9.79858	+	9.79858i	−0.0234416	+	0.0234416i
$419$		−	293.606i		−	0.700730i	−0.936613	−	0.350365i	$-0.886058\pi$
$419$		−	293.606i		−	0.700730i	0.936613	−	0.350365i	$-0.113942\pi$
$420$	−23.0679	+	39.5964i	−0.0549235	+	0.0942771i
$421$	−294.797			−0.700230			−0.350115	−	0.936707i	$-0.613857\pi$
$421$	−294.797			−0.700230			−0.350115	+	0.936707i	$0.613857\pi$
$422$	55.0602	+	55.0602i	0.130474	+	0.130474i
$423$	−156.958	+	156.958i	−0.371060	+	0.371060i
$424$		−	162.151i		−	0.382433i
$425$	−14.5505	+	52.6527i	−0.0342365	+	0.123889i
$426$	−126.692			−0.297399
$427$	−85.0055	−	85.0055i	−0.199076	−	0.199076i
$428$	−218.842	+	218.842i	−0.511314	+	0.511314i
$429$			8.11333i			0.0189122i
$430$	176.052	+	102.564i	0.409424	+	0.238520i
$431$	−314.916			−0.730663			−0.365332	−	0.930877i	$-0.619044\pi$
$431$	−314.916			−0.730663			−0.365332	+	0.930877i	$0.619044\pi$
$432$	14.6969	+	14.6969i	0.0340207	+	0.0340207i
$433$	236.366	−	236.366i	0.545880	−	0.545880i	−0.379367	−	0.925246i	$-0.623858\pi$
$433$	236.366	−	236.366i	0.545880	−	0.545880i	0.925246	+	0.379367i	$0.123858\pi$
$434$			59.0944i			0.136162i
$435$	−29.9224	−	113.444i	−0.0687871	−	0.260792i
$436$	−137.234			−0.314757
$437$	26.5035	+	26.5035i	0.0606488	+	0.0606488i
$438$	177.306	−	177.306i	0.404809	−	0.404809i
$439$			254.993i			0.580850i	0.956898	+	0.290425i	$0.0937967\pi$
$439$			254.993i			0.580850i	−0.956898	+	0.290425i	$0.906203\pi$
$440$	−39.9734	+	10.5435i	−0.0908486	+	0.0239625i
$441$	21.0000			0.0476190
$442$	−3.50138	−	3.50138i	−0.00792167	−	0.00792167i
$443$	−292.628	+	292.628i	−0.660559	+	0.660559i	−0.955512	−	0.294953i	$-0.904696\pi$
$443$	−292.628	+	292.628i	−0.660559	+	0.660559i	0.294953	+	0.955512i	$0.404696\pi$
$444$		−	82.4522i		−	0.185703i
$445$	254.085	−	436.141i	0.570978	−	0.980093i
$446$	−203.537			−0.456360
$447$	−94.9184	−	94.9184i	−0.212345	−	0.212345i
$448$	14.9666	−	14.9666i	0.0334077	−	0.0334077i
$449$		−	400.989i		−	0.893072i	−0.894766	−	0.446536i	$-0.852657\pi$
$449$		−	400.989i		−	0.893072i	0.894766	−	0.446536i	$-0.147343\pi$
$450$	102.234	+	28.2523i	0.227187	+	0.0627828i
$451$	−212.292			−0.470714
$452$	−136.073	−	136.073i	−0.301047	−	0.301047i
$453$	45.0944	−	45.0944i	0.0995462	−	0.0995462i
$454$		−	50.1179i		−	0.110392i
$455$	−18.3165	−	10.6708i	−0.0402561	−	0.0234522i
$456$	−16.4213			−0.0360117
$457$	−172.040	−	172.040i	−0.376454	−	0.376454i	0.493367	−	0.869821i	$-0.335766\pi$
$457$	−172.040	−	172.040i	−0.376454	−	0.376454i	−0.869821	+	0.493367i	$0.835766\pi$
$458$	−283.497	+	283.497i	−0.618990	+	0.618990i
$459$		−	11.3539i		−	0.0247361i
$460$	28.5184	+	108.121i	0.0619965	+	0.235046i
$461$	153.918			0.333878			0.166939	−	0.985967i	$-0.446612\pi$
$461$	153.918			0.333878			0.166939	+	0.985967i	$0.446612\pi$
$462$	13.3959	+	13.3959i	0.0289954	+	0.0289954i
$463$	−291.763	+	291.763i	−0.630158	+	0.630158i	−0.948108	−	0.317949i	$-0.897006\pi$
$463$	−291.763	+	291.763i	−0.630158	+	0.630158i	0.317949	+	0.948108i	$0.397006\pi$
$464$			54.1898i			0.116788i
$465$	132.254	−	34.8836i	0.284417	−	0.0750185i
$466$	278.238			0.597077
$467$	−503.234	−	503.234i	−1.07759	−	1.07759i	−0.996725	−	0.0808645i	$-0.974232\pi$
$467$	−503.234	−	503.234i	−1.07759	−	1.07759i	−0.0808645	−	0.996725i	$-0.525768\pi$
$468$	−6.79852	+	6.79852i	−0.0145267	+	0.0145267i
$469$			216.183i			0.460944i
$470$	263.367	−	452.073i	0.560355	−	0.961857i
$471$	185.586			0.394026
$472$	234.330	+	234.330i	0.496462	+	0.496462i
$473$	59.5603	−	59.5603i	0.125920	−	0.125920i
$474$		−	91.0843i		−	0.192161i
$475$	−72.8981	+	41.3310i	−0.153470	+	0.0870127i
$476$	−11.5622			−0.0242903
$477$	121.614	+	121.614i	0.254955	+	0.254955i
$478$	183.280	−	183.280i	0.383432	−	0.383432i
$479$			670.857i			1.40054i	0.713880	+	0.700268i	$0.246936\pi$
$479$			670.857i			1.40054i	−0.713880	+	0.700268i	$0.753064\pi$
$480$	−42.3303	−	24.6606i	−0.0881881	−	0.0513763i
$481$	38.1408			0.0792947
$482$	−280.094	−	280.094i	−0.581108	−	0.581108i
$483$	36.2335	−	36.2335i	0.0750177	−	0.0750177i
$484$		−	224.910i		−	0.464689i
$485$	94.8388	+	359.561i	0.195544	+	0.741363i
$486$	−22.0454			−0.0453609
$487$	−431.350	−	431.350i	−0.885729	−	0.885729i	0.108380	−	0.994110i	$-0.465434\pi$
$487$	−431.350	−	431.350i	−0.885729	−	0.885729i	−0.994110	+	0.108380i	$0.965434\pi$
$488$	90.8747	−	90.8747i	0.186219	−	0.186219i
$489$		−	427.320i		−	0.873865i
$490$	−47.8606	+	12.6238i	−0.0976747	+	0.0257629i
$491$	−643.019			−1.30961			−0.654806	−	0.755797i	$-0.727250\pi$
$491$	−643.019			−1.30961			−0.654806	+	0.755797i	$0.727250\pi$
$492$	−177.889	−	177.889i	−0.361562	−	0.361562i
$493$	20.9317	−	20.9317i	0.0424577	−	0.0424577i
$494$		−	7.59618i		−	0.0153769i
$495$	22.0724	−	37.8877i	0.0445908	−	0.0765407i
$496$	−63.1746			−0.127368
$497$	−96.7625	−	96.7625i	−0.194693	−	0.194693i
$498$	−52.2553	+	52.2553i	−0.104930	+	0.104930i
$499$		−	350.058i		−	0.701520i	−0.936465	−	0.350760i	$-0.885923\pi$
$499$		−	350.058i		−	0.701520i	0.936465	−	0.350760i	$-0.114077\pi$
$500$	−249.983	−	2.93258i	−0.499966	−	0.00586517i
$501$	292.163			0.583160
$502$	148.745	+	148.745i	0.296305	+	0.296305i
$503$	160.423	−	160.423i	0.318932	−	0.318932i	−0.529425	−	0.848357i	$-0.677592\pi$
$503$	160.423	−	160.423i	0.318932	−	0.318932i	0.848357	+	0.529425i	$0.177592\pi$
$504$			22.4499i			0.0445435i
$505$	−559.124	−	325.732i	−1.10718	−	0.645014i
$506$	46.2266			0.0913569
$507$	203.837	+	203.837i	0.402045	+	0.402045i
$508$	−285.926	+	285.926i	−0.562847	+	0.562847i
$509$			402.935i			0.791620i	0.918332	+	0.395810i	$0.129536\pi$
$509$			402.935i			0.791620i	−0.918332	+	0.395810i	$0.870464\pi$
$510$	6.82520	+	25.8763i	0.0133827	+	0.0507378i
$511$	270.840			0.530020
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	12.3160	−	12.3160i	0.0240078	−	0.0240078i
$514$		−	483.367i		−	0.940404i
$515$	212.260	−	55.9862i	0.412155	−	0.108711i
$516$	99.8163			0.193442
$517$	−152.941	−	152.941i	−0.295824	−	0.295824i
$518$	62.9739	−	62.9739i	0.121571	−	0.121571i
$519$		−	269.494i		−	0.519257i
$520$	11.4075	−	19.5812i	0.0219375	−	0.0376561i
$521$	−725.448			−1.39241			−0.696207	−	0.717841i	$-0.745131\pi$
$521$	−725.448			−1.39241			−0.696207	+	0.717841i	$0.745131\pi$
$522$	−40.6423	−	40.6423i	−0.0778589	−	0.0778589i
$523$	454.490	−	454.490i	0.869005	−	0.869005i	−0.123357	−	0.992362i	$-0.539366\pi$
$523$	454.490	−	454.490i	0.869005	−	0.869005i	0.992362	+	0.123357i	$0.0393661\pi$
$524$			7.10768i			0.0135643i
$525$	56.5045	+	99.6606i	0.107628	+	0.189830i
$526$	−469.214			−0.892042
$527$	24.4022	+	24.4022i	0.0463040	+	0.0463040i
$528$	−14.3208	+	14.3208i	−0.0271227	+	0.0271227i
$529$			403.965i			0.763638i
$530$	−350.273	−	204.060i	−0.660892	−	0.385020i
$531$	−351.495			−0.661949
$532$	−12.5420	−	12.5420i	−0.0235752	−	0.0235752i
$533$	82.2878	−	82.2878i	0.154386	−	0.154386i
$534$		−	247.279i		−	0.463069i
$535$	197.331	+	748.138i	0.368843	+	1.39839i
$536$	−231.109			−0.431174
$537$	−60.0563	−	60.0563i	−0.111837	−	0.111837i
$538$	357.902	−	357.902i	0.665245	−	0.665245i
$539$			20.4625i			0.0379638i
$540$	50.2432	−	13.2523i	0.0930429	−	0.0245412i
$541$	−173.852			−0.321354			−0.160677	−	0.987007i	$-0.551368\pi$
$541$	−173.852			−0.321354			−0.160677	+	0.987007i	$0.551368\pi$
$542$	178.869	+	178.869i	0.330017	+	0.330017i
$543$	−400.666	+	400.666i	−0.737875	+	0.737875i
$544$		−	12.3605i		−	0.0227215i
$545$	−172.703	+	296.447i	−0.316886	+	0.543940i
$546$	−10.3849			−0.0190200
$547$	−293.440	−	293.440i	−0.536453	−	0.536453i	0.386032	−	0.922485i	$-0.373845\pi$
$547$	−293.440	−	293.440i	−0.536453	−	0.536453i	−0.922485	+	0.386032i	$0.873845\pi$
$548$	−150.211	+	150.211i	−0.274107	+	0.274107i
$549$			136.312i			0.248291i
$550$	−27.5292	+	99.6174i	−0.0500530	+	0.181123i
$551$	45.4109			0.0824154
$552$	38.7353	+	38.7353i	0.0701726	+	0.0701726i
$553$	69.5668	−	69.5668i	0.125799	−	0.125799i
$554$		−	238.709i		−	0.430883i
$555$	−178.110	−	103.762i	−0.320919	−	0.186959i
$556$	−384.704			−0.691914
$557$	234.581	+	234.581i	0.421151	+	0.421151i	0.885600	−	0.464449i	$-0.153747\pi$
$557$	234.581	+	234.581i	0.421151	+	0.421151i	−0.464449	+	0.885600i	$0.653747\pi$
$558$	47.3809	−	47.3809i	0.0849121	−	0.0849121i
$559$			46.1731i			0.0825994i
$560$	−13.4955	−	51.1652i	−0.0240990	−	0.0913663i
$561$	11.0633			0.0197206
$562$	−42.3632	−	42.3632i	−0.0753793	−	0.0753793i
$563$	177.541	−	177.541i	0.315348	−	0.315348i	−0.531629	−	0.846977i	$-0.678420\pi$
$563$	177.541	−	177.541i	0.315348	−	0.315348i	0.846977	+	0.531629i	$0.178420\pi$
$564$		−	256.312i		−	0.454453i
$565$	−465.182	+	122.698i	−0.823331	+	0.217164i
$566$	6.87928			0.0121542
$567$	−16.8375	−	16.8375i	−0.0296957	−	0.0296957i
$568$	103.443	−	103.443i	0.182119	−	0.182119i
$569$			253.619i			0.445727i	0.974850	+	0.222864i	$0.0715405\pi$
$569$			253.619i			0.445727i	−0.974850	+	0.222864i	$0.928460\pi$
$570$	−20.6655	+	35.4727i	−0.0362553	+	0.0622328i
$571$	219.857			0.385038			0.192519	−	0.981293i	$-0.438334\pi$
$571$	219.857			0.385038			0.192519	+	0.981293i	$0.438334\pi$
$572$	−6.62451	−	6.62451i	−0.0115813	−	0.0115813i
$573$	354.047	−	354.047i	0.617883	−	0.617883i
$574$		−	271.729i		−	0.473396i
$575$	269.448	+	74.4618i	0.468606	+	0.129499i
$576$	−24.0000			−0.0416667
$577$	419.350	+	419.350i	0.726776	+	0.726776i	0.969976	−	0.243200i	$-0.0781972\pi$
$577$	419.350	+	419.350i	0.726776	+	0.726776i	−0.243200	+	0.969976i	$0.578197\pi$
$578$	284.226	−	284.226i	0.491740	−	0.491740i
$579$			321.404i			0.555101i
$580$	117.059	+	68.1955i	0.201825	+	0.117578i
$581$	−79.8213			−0.137386
$582$	128.815	+	128.815i	0.221332	+	0.221332i
$583$	−118.501	+	118.501i	−0.203261	+	0.203261i
$584$			289.540i			0.495788i
$585$	6.13024	+	23.2415i	0.0104790	+	0.0397291i
$586$	−50.7965			−0.0866834
$587$	−493.116	−	493.116i	−0.840061	−	0.840061i	0.148805	−	0.988867i	$-0.452457\pi$
$587$	−493.116	−	493.116i	−0.840061	−	0.840061i	−0.988867	+	0.148805i	$0.952457\pi$
$588$	−17.1464	+	17.1464i	−0.0291606	+	0.0291606i
$589$			52.9401i			0.0898814i
$590$	801.084	−	211.296i	1.35777	−	0.358129i
$591$	273.849			0.463365
$592$	67.3219	+	67.3219i	0.113719	+	0.113719i
$593$	528.205	−	528.205i	0.890733	−	0.890733i	−0.103859	−	0.994592i	$-0.533119\pi$
$593$	528.205	−	528.205i	0.890733	−	0.890733i	0.994592	+	0.103859i	$0.0331191\pi$
$594$		−	21.4812i		−	0.0361636i
$595$	−14.5505	+	24.9762i	−0.0244546	+	0.0419768i
$596$	155.001			0.260069
$597$	−71.4902	−	71.4902i	−0.119749	−	0.119749i
$598$	−17.9182	+	17.9182i	−0.0299635	+	0.0299635i
$599$		−	436.395i		−	0.728540i	−0.931293	−	0.364270i	$-0.881319\pi$
$599$		−	436.395i		−	0.728540i	0.931293	−	0.364270i	$-0.118681\pi$
$600$	−106.542	+	60.4059i	−0.177569	+	0.100677i
$601$	907.900			1.51065			0.755324	−	0.655351i	$-0.227479\pi$
$601$	907.900			1.51065			0.755324	+	0.655351i	$0.227479\pi$
$602$	76.2360	+	76.2360i	0.126638	+	0.126638i
$603$	173.332	−	173.332i	0.287449	−	0.287449i
$604$			73.6389i			0.121919i
$605$	−485.841	−	283.039i	−0.803042	−	0.467833i
$606$	−317.006			−0.523113
$607$	−46.6746	−	46.6746i	−0.0768939	−	0.0768939i	0.667614	−	0.744508i	$-0.267316\pi$
$607$	−46.6746	−	46.6746i	−0.0768939	−	0.0768939i	−0.744508	+	0.667614i	$0.767316\pi$
$608$	13.4080	−	13.4080i	0.0220526	−	0.0220526i
$609$		−	62.0822i		−	0.101941i
$610$	−81.9420	−	310.666i	−0.134331	−	0.509288i
$611$	118.565			0.194050
$612$	9.27038	+	9.27038i	0.0151477	+	0.0151477i
$613$	404.981	−	404.981i	0.660653	−	0.660653i	−0.294881	−	0.955534i	$-0.595280\pi$
$613$	404.981	−	404.981i	0.660653	−	0.660653i	0.955534	+	0.294881i	$0.0952799\pi$
$614$		−	647.678i		−	1.05485i
$615$	−608.133	+	160.403i	−0.988834	+	0.260817i
$616$	−21.8753			−0.0355119
$617$	821.889	+	821.889i	1.33207	+	1.33207i	0.903514	+	0.428558i	$0.140978\pi$
$617$	821.889	+	821.889i	1.33207	+	1.33207i	0.428558	+	0.903514i	$0.359022\pi$
$618$	76.0437	−	76.0437i	0.123048	−	0.123048i
$619$			355.855i			0.574886i	0.957798	+	0.287443i	$0.0928052\pi$
$619$			355.855i			0.574886i	−0.957798	+	0.287443i	$0.907195\pi$
$620$	−79.5025	+	136.467i	−0.128230	+	0.220108i
$621$	−58.1029			−0.0935635
$622$	−284.428	−	284.428i	−0.457280	−	0.457280i
$623$	188.862	−	188.862i	0.303150	−	0.303150i
$624$		−	11.1019i		−	0.0177916i
$625$	−320.927	+	536.312i	−0.513484	+	0.858099i
$626$	357.929			0.571771
$627$	12.0008	+	12.0008i	0.0191400	+	0.0191400i
$628$	−151.531	+	151.531i	−0.241291	+	0.241291i
$629$		−	52.0083i		−	0.0826841i
$630$	48.4955	+	28.2523i	0.0769769	+	0.0448449i
$631$	−588.910			−0.933297			−0.466648	−	0.884443i	$-0.654539\pi$
$631$	−588.910			−0.933297			−0.466648	+	0.884443i	$0.654539\pi$
$632$	74.3700	+	74.3700i	0.117674	+	0.117674i
$633$	67.4347	−	67.4347i	0.106532	−	0.106532i
$634$			671.600i			1.05931i
$635$	257.821	+	977.472i	0.406017	+	1.53933i
$636$	−198.594			−0.312255
$637$	−7.93160	−	7.93160i	−0.0124515	−	0.0124515i
$638$	39.6021	−	39.6021i	0.0620723	−	0.0620723i
$639$			155.165i			0.242825i
$640$	54.6978	−	14.4272i	0.0854654	−	0.0225426i
$641$	−703.566			−1.09761			−0.548804	−	0.835951i	$-0.684917\pi$
$641$	−703.566			−1.09761			−0.548804	+	0.835951i	$0.684917\pi$
$642$	268.026	+	268.026i	0.417486	+	0.417486i
$643$	75.8005	−	75.8005i	0.117886	−	0.117886i	−0.645703	−	0.763589i	$-0.723436\pi$
$643$	75.8005	−	75.8005i	0.117886	−	0.117886i	0.763589	+	0.645703i	$0.223436\pi$
$644$			59.1691i			0.0918775i
$645$	125.614	−	215.619i	0.194751	−	0.334293i
$646$	−10.3581			−0.0160342
$647$	362.070	+	362.070i	0.559613	+	0.559613i	0.929197	−	0.369584i	$-0.120500\pi$
$647$	362.070	+	362.070i	0.559613	+	0.559613i	−0.369584	+	0.929197i	$0.620500\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$		−	342.499i		−	0.527733i
$650$	−27.9426	−	49.2841i	−0.0429886	−	0.0758217i
$651$	72.3756			0.111176
$652$	348.905	+	348.905i	0.535131	+	0.535131i
$653$	804.153	−	804.153i	1.23147	−	1.23147i	0.268077	−	0.963397i	$-0.413612\pi$
$653$	804.153	−	804.153i	1.23147	−	1.23147i	0.963397	−	0.268077i	$-0.0863882\pi$
$654$			168.077i			0.256998i
$655$	15.3537	+	8.94470i	0.0234408	+	0.0136560i
$656$	290.491			0.442821
$657$	−217.155	−	217.155i	−0.330525	−	0.330525i
$658$	195.761	−	195.761i	0.297510	−	0.297510i
$659$		−	803.984i		−	1.22001i	−0.792399	−	0.610003i	$-0.791168\pi$
$659$		−	803.984i		−	1.22001i	0.792399	−	0.610003i	$-0.208832\pi$
$660$	12.9131	+	48.9572i	0.0195653	+	0.0741776i
$661$	−923.281			−1.39679			−0.698397	−	0.715710i	$-0.746103\pi$
$661$	−923.281			−1.39679			−0.698397	+	0.715710i	$0.746103\pi$
$662$	444.301	+	444.301i	0.671150	+	0.671150i
$663$	−4.28830	+	4.28830i	−0.00646802	+	0.00646802i
$664$		−	85.3325i		−	0.128513i
$665$	−42.8762	+	11.3092i	−0.0644756	+	0.0170062i
$666$	−100.983			−0.151626
$667$	−107.117	−	107.117i	−0.160595	−	0.160595i
$668$	−238.550	+	238.550i	−0.357111	+	0.357111i
$669$			249.280i			0.372616i
$670$	−290.841	+	499.233i	−0.434091	+	0.745123i
$671$	−132.823			−0.197948
$672$	−18.3303	−	18.3303i	−0.0272772	−	0.0272772i
$673$	−750.322	+	750.322i	−1.11489	+	1.11489i	−0.122413	+	0.992479i	$0.539063\pi$
$673$	−750.322	+	750.322i	−1.11489	+	1.11489i	−0.992479	+	0.122413i	$0.960937\pi$
$674$			862.939i			1.28032i
$675$	34.6018	−	125.211i	0.0512620	−	0.185497i
$676$	−332.864			−0.492403
$677$	−405.042	−	405.042i	−0.598290	−	0.598290i	0.341567	−	0.939857i	$-0.389042\pi$
$677$	−405.042	−	405.042i	−0.598290	−	0.598290i	−0.939857	+	0.341567i	$0.889042\pi$
$678$	−166.655	+	166.655i	−0.245804	+	0.245804i
$679$			196.769i			0.289792i
$680$	−26.7007	−	15.5552i	−0.0392657	−	0.0228752i
$681$	−61.3816			−0.0901345
$682$	46.1682	+	46.1682i	0.0676954	+	0.0676954i
$683$	666.271	−	666.271i	0.975506	−	0.975506i	−0.0242009	−	0.999707i	$-0.507704\pi$
$683$	666.271	−	666.271i	0.975506	−	0.975506i	0.999707	+	0.0242009i	$0.00770413\pi$
$684$			20.1119i			0.0294034i
$685$	135.445	+	513.513i	0.197731	+	0.749654i
$686$	−26.1916			−0.0381802
$687$	347.212	+	347.212i	0.505403	+	0.505403i
$688$	−81.4997	+	81.4997i	−0.118459	+	0.118459i
$689$		−	91.8658i		−	0.133332i
$690$	132.421	−	34.9277i	0.191915	−	0.0506199i
$691$	521.895			0.755275			0.377637	−	0.925954i	$-0.376737\pi$
$691$	521.895			0.755275			0.377637	+	0.925954i	$0.376737\pi$
$692$	220.041	+	220.041i	0.317978	+	0.317978i
$693$	16.4065	−	16.4065i	0.0236746	−	0.0236746i
$694$		−	455.785i		−	0.656751i
$695$	−484.133	+	831.022i	−0.696595	+	1.19572i
$696$	66.3687			0.0953573
$697$	−112.207	−	112.207i	−0.160985	−	0.160985i
$698$	−280.016	+	280.016i	−0.401168	+	0.401168i
$699$		−	340.771i		−	0.487511i
$700$	−127.508	−	35.2368i	−0.182155	−	0.0503383i
$701$	525.400			0.749501			0.374750	−	0.927126i	$-0.377728\pi$
$701$	525.400			0.749501			0.374750	+	0.927126i	$0.377728\pi$
$702$	8.32645	+	8.32645i	0.0118610	+	0.0118610i
$703$	56.4156	−	56.4156i	0.0802497	−	0.0802497i
$704$		−	23.3857i		−	0.0332184i
$705$	−553.674	−	322.557i	−0.785353	−	0.457528i
$706$	−228.939			−0.324276
$707$	−242.117	−	242.117i	−0.342458	−	0.342458i
$708$	286.995	−	286.995i	0.405360	−	0.405360i
$709$		−	269.858i		−	0.380618i	−0.981724	−	0.190309i	$-0.939051\pi$
$709$		−	269.858i		−	0.380618i	0.981724	−	0.190309i	$-0.0609489\pi$
$710$	−93.2753	−	353.633i	−0.131374	−	0.498075i
$711$	−111.555			−0.156899
$712$	201.902	+	201.902i	0.283571	+	0.283571i
$713$	124.877	−	124.877i	0.175144	−	0.175144i
$714$			14.1607i			0.0198330i
$715$	−22.6466	+	5.97334i	−0.0316736	+	0.00835432i
$716$	98.0715			0.136971
$717$	−224.472	−	224.472i	−0.313071	−	0.313071i
$718$	−700.748	+	700.748i	−0.975973	+	0.975973i
$719$		−	42.9232i		−	0.0596985i	−0.999554	−	0.0298493i	$-0.990497\pi$
$719$		−	42.9232i		−	0.0596985i	0.999554	−	0.0298493i	$-0.00950273\pi$
$720$	−30.2030	+	51.8438i	−0.0419485	+	0.0720053i
$721$	116.159			0.161108
$722$	349.764	+	349.764i	0.484438	+	0.484438i
$723$	−343.044	+	343.044i	−0.474472	+	0.474472i
$724$		−	654.285i		−	0.903709i
$725$	294.626	−	167.044i	0.406381	−	0.230406i
$726$	−275.457			−0.379417
$727$	109.192	+	109.192i	0.150195	+	0.150195i	0.778205	−	0.628010i	$-0.216130\pi$
$727$	109.192	+	109.192i	0.150195	+	0.150195i	−0.628010	+	0.778205i	$0.716130\pi$
$728$	8.47924	−	8.47924i	0.0116473	−	0.0116473i
$729$			27.0000i			0.0370370i
$730$	625.453	+	364.374i	0.856785	+	0.499142i
$731$	62.9611			0.0861301
$732$	−111.298	−	111.298i	−0.152047	−	0.152047i
$733$	414.682	−	414.682i	0.565733	−	0.565733i	−0.365197	−	0.930930i	$-0.618999\pi$
$733$	414.682	−	414.682i	0.565733	−	0.565733i	0.930930	+	0.365197i	$0.118999\pi$
$734$			824.513i			1.12332i
$735$	15.4610	+	58.6170i	0.0210354	+	0.0797511i
$736$	−63.2545			−0.0859436
$737$	168.895	+	168.895i	0.229166	+	0.229166i
$738$	−217.868	+	217.868i	−0.295214	+	0.295214i
$739$		−	1042.54i		−	1.41074i	−0.708838	−	0.705372i	$-0.750780\pi$
$739$		−	1042.54i		−	1.41074i	0.708838	−	0.705372i	$-0.249220\pi$
$740$	230.148	−	60.7044i	0.311010	−	0.0820329i
$741$	−9.30338			−0.0125552
$742$	−151.679	−	151.679i	−0.204419	−	0.204419i
$743$	−403.117	+	403.117i	−0.542553	+	0.542553i	−0.924277	−	0.381724i	$-0.875331\pi$
$743$	−403.117	+	403.117i	−0.542553	+	0.542553i	0.381724	+	0.924277i	$0.375331\pi$
$744$			77.3728i			0.103996i
$745$	195.062	−	334.827i	0.261828	−	0.449432i
$746$	−243.338			−0.326191
$747$	63.9994	+	63.9994i	0.0856752	+	0.0856752i
$748$	−9.03311	+	9.03311i	−0.0120763	+	0.0120763i
$749$			409.417i			0.546618i
$750$	−3.59167	+	306.165i	−0.00478889	+	0.408220i
$751$	346.283			0.461096			0.230548	−	0.973061i	$-0.425948\pi$
$751$	346.283			0.461096			0.230548	+	0.973061i	$0.425948\pi$
$752$	209.278	+	209.278i	0.278295	+	0.278295i
$753$	182.175	−	182.175i	0.241932	−	0.241932i
$754$			30.7008i			0.0407173i
$755$	159.072	+	92.6713i	0.210691	+	0.122744i
$756$	27.4955			0.0363696
$757$	284.836	+	284.836i	0.376270	+	0.376270i	0.869754	−	0.493485i	$-0.164277\pi$
$757$	284.836	+	284.836i	0.376270	+	0.376270i	−0.493485	+	0.869754i	$0.664277\pi$
$758$	709.113	−	709.113i	0.935506	−	0.935506i
$759$		−	56.6158i		−	0.0745926i
$760$	−12.0900	−	45.8366i	−0.0159079	−	0.0603114i
$761$	321.609			0.422614			0.211307	−	0.977420i	$-0.432228\pi$
$761$	321.609			0.422614			0.211307	+	0.977420i	$0.432228\pi$
$762$	350.187	+	350.187i	0.459563	+	0.459563i
$763$	−128.371	+	128.371i	−0.168245	+	0.168245i
$764$			578.156i			0.756749i
$765$	31.6919	−	8.35913i	0.0414273	−	0.0109270i
$766$	−953.222			−1.24441
$767$	132.758	+	132.758i	0.173087	+	0.173087i
$768$	19.5959	−	19.5959i	0.0255155	−	0.0255155i
$769$			634.413i			0.824984i	0.910961	+	0.412492i	$0.135342\pi$
$769$			634.413i			0.824984i	−0.910961	+	0.412492i	$0.864658\pi$
$770$	−27.5292	+	47.2542i	−0.0357522	+	0.0613691i
$771$	−592.002			−0.767836
$772$	−262.425	−	262.425i	−0.339929	−	0.339929i
$773$	793.682	−	793.682i	1.02676	−	1.02676i	0.0271240	−	0.999632i	$-0.491365\pi$
$773$	793.682	−	793.682i	1.02676	−	1.02676i	0.999632	−	0.0271240i	$-0.00863490\pi$
$774$		−	122.250i		−	0.157945i
$775$	194.740	+	343.476i	0.251278	+	0.443195i
$776$	−210.355			−0.271076
$777$	−77.1269	−	77.1269i	−0.0992625	−	0.0992625i
$778$	−270.210	+	270.210i	−0.347313	+	0.347313i
$779$		−	243.430i		−	0.312491i
$780$	−23.9819	−	13.9713i	−0.0307461	−	0.0179119i
$781$	−151.194			−0.193590
$782$	24.4330	+	24.4330i	0.0312443	+	0.0312443i
$783$	−49.7765	+	49.7765i	−0.0635715	+	0.0635715i
$784$		−	28.0000i		−	0.0357143i
$785$	136.636	+	518.025i	0.174058	+	0.659905i
$786$	8.70509			0.0110752
$787$	30.7537	+	30.7537i	0.0390771	+	0.0390771i	0.726375	−	0.687298i	$-0.241203\pi$
$787$	30.7537	+	30.7537i	0.0390771	+	0.0390771i	−0.687298	+	0.726375i	$0.741203\pi$
$788$	−223.597	+	223.597i	−0.283752	+	0.283752i
$789$			574.668i			0.728349i
$790$	254.242	−	67.0597i	0.321826	−	0.0848856i
$791$	−254.570			−0.321833
$792$	17.5393	+	17.5393i	0.0221456	+	0.0221456i
$793$	51.4844	−	51.4844i	0.0649236	−	0.0649236i
$794$		−	338.541i		−	0.426374i
$795$	−249.922	+	428.995i	−0.314367	+	0.539616i
$796$	116.743			0.146662
$797$	613.430	+	613.430i	0.769674	+	0.769674i	0.978049	−	0.208375i	$-0.0668175\pi$
$797$	613.430	+	613.430i	0.769674	+	0.769674i	−0.208375	+	0.978049i	$0.566817\pi$
$798$	−15.3607	+	15.3607i	−0.0192490	+	0.0192490i
$799$		−	161.674i		−	0.202345i
$800$	37.6697	−	136.312i	0.0470871	−	0.170390i
$801$	−302.854			−0.378094
$802$	397.414	+	397.414i	0.495529	+	0.495529i
$803$	211.597	−	211.597i	0.263508	−	0.263508i
$804$			283.050i			0.352052i
$805$	127.815	+	74.4618i	0.158776	+	0.0924991i
$806$	−35.7911			−0.0444059
$807$	−438.338	−	438.338i	−0.543170	−	0.543170i
$808$	258.834	−	258.834i	0.320340	−	0.320340i
$809$			23.8289i			0.0294548i	0.999892	+	0.0147274i	$0.00468804\pi$
$809$			23.8289i			0.0294548i	−0.999892	+	0.0147274i	$0.995312\pi$
$810$	−16.2307	−	61.5351i	−0.0200378	−	0.0759692i
$811$	676.685			0.834383			0.417192	−	0.908819i	$-0.363014\pi$
$811$	676.685			0.834383			0.417192	+	0.908819i	$0.363014\pi$
$812$	50.6899	+	50.6899i	0.0624260	+	0.0624260i
$813$	219.069	−	219.069i	0.269458	−	0.269458i
$814$		−	98.3982i		−	0.120882i
$815$	1192.77	−	314.609i	1.46352	−	0.386023i
$816$	−15.1385			−0.0185520
$817$	68.2965	+	68.2965i	0.0835942	+	0.0835942i
$818$	−787.478	+	787.478i	−0.962687	+	0.962687i
$819$			12.7189i			0.0155297i
$820$	365.570	−	627.506i	0.445817	−	0.765252i
$821$	−7.29733			−0.00888834			−0.00444417	−	0.999990i	$-0.501415\pi$
$821$	−7.29733			−0.00888834			−0.00444417	+	0.999990i	$0.501415\pi$
$822$	183.970	+	183.970i	0.223808	+	0.223808i
$823$	3.19071	−	3.19071i	0.00387692	−	0.00387692i	−0.705166	−	0.709043i	$-0.749127\pi$
$823$	3.19071	−	3.19071i	0.00387692	−	0.00387692i	0.709043	+	0.705166i	$0.249127\pi$
$824$			124.179i			0.150703i
$825$	122.006	+	33.7162i	0.147886	+	0.0408681i
$826$	438.391			0.530740
$827$	355.496	+	355.496i	0.429863	+	0.429863i	0.888581	−	0.458719i	$-0.151691\pi$
$827$	355.496	+	355.496i	0.429863	+	0.429863i	−0.458719	+	0.888581i	$0.651691\pi$
$828$	47.4409	−	47.4409i	0.0572957	−	0.0572957i
$829$		−	1466.78i		−	1.76933i	−0.466225	−	0.884666i	$-0.654386\pi$
$829$		−	1466.78i		−	1.76933i	0.466225	−	0.884666i	$-0.345614\pi$
$830$	−184.332	−	107.387i	−0.222087	−	0.129382i
$831$	−292.358			−0.351815
$832$	9.06469	+	9.06469i	0.0108951	+	0.0108951i
$833$	−10.8154	+	10.8154i	−0.0129837	+	0.0129837i
$834$			471.164i			0.564945i
$835$	215.101	+	815.511i	0.257606	+	0.976660i
$836$	−19.5972			−0.0234416
$837$	−58.0296	−	58.0296i	−0.0693304	−	0.0693304i
$838$	293.606	−	293.606i	0.350365	−	0.350365i
$839$		−	807.662i		−	0.962648i	−0.876543	−	0.481324i	$-0.840156\pi$
$839$		−	807.662i		−	0.962648i	0.876543	−	0.481324i	$-0.159844\pi$
$840$	−62.6643	+	16.5285i	−0.0746003	+	0.0196768i
$841$	657.467			0.781768
$842$	−294.797	−	294.797i	−0.350115	−	0.350115i
$843$	−51.8841	+	51.8841i	−0.0615470	+	0.0615470i
$844$			110.120i			0.130474i
$845$	−418.895	+	719.040i	−0.495734	+	0.850935i
$846$	−313.916			−0.371060
$847$	−210.384	−	210.384i	−0.248387	−	0.248387i
$848$	162.151	−	162.151i	0.191216	−	0.191216i
$849$		−	8.42536i		−	0.00992387i
$850$	−67.2032	+	38.1022i	−0.0790626	+	0.0448261i
$851$	−266.151			−0.312751
$852$	−126.692	−	126.692i	−0.148699	−	0.148699i
$853$	34.4347	−	34.4347i	0.0403690	−	0.0403690i	−0.686634	−	0.727003i	$-0.740913\pi$
$853$	34.4347	−	34.4347i	0.0403690	−	0.0403690i	0.727003	+	0.686634i	$0.240913\pi$
$854$		−	170.011i		−	0.199076i
$855$	43.4450	+	25.3100i	0.0508128	+	0.0296023i
$856$	−437.685			−0.511314
$857$	−795.023	−	795.023i	−0.927681	−	0.927681i	0.0698747	−	0.997556i	$-0.477740\pi$
$857$	−795.023	−	795.023i	−0.927681	−	0.927681i	−0.997556	+	0.0698747i	$0.977740\pi$
$858$	−8.11333	+	8.11333i	−0.00945610	+	0.00945610i
$859$		−	367.334i		−	0.427629i	−0.976874	−	0.213815i	$-0.931411\pi$
$859$		−	367.334i		−	0.427629i	0.976874	−	0.213815i	$-0.0685889\pi$
$860$	73.4885	+	278.616i	0.0854517	+	0.323972i
$861$	−332.799			−0.386526
$862$	−314.916	−	314.916i	−0.365332	−	0.365332i
$863$	−97.5396	+	97.5396i	−0.113024	+	0.113024i	−0.761357	−	0.648333i	$-0.775466\pi$
$863$	−97.5396	+	97.5396i	−0.113024	+	0.113024i	0.648333	+	0.761357i	$0.275466\pi$
$864$			29.3939i			0.0340207i
$865$	752.236	−	198.412i	0.869637	−	0.229378i
$866$	472.732			0.545880
$867$	−348.104	−	348.104i	−0.401504	−	0.401504i
$868$	−59.0944	+	59.0944i	−0.0680811	+	0.0680811i
$869$		−	108.700i		−	0.125086i
$870$	83.5221	−	143.367i	0.0960024	−	0.164790i
$871$	−130.933			−0.150325
$872$	−137.234	−	137.234i	−0.157379	−	0.157379i
$873$	157.766	−	157.766i	0.180717	−	0.180717i
$874$			53.0071i			0.0606488i
$875$	−236.581	+	231.094i	−0.270378	+	0.264108i
$876$	354.613			0.404809
$877$	−326.965	−	326.965i	−0.372822	−	0.372822i	0.495682	−	0.868504i	$-0.334918\pi$
$877$	−326.965	−	326.965i	−0.372822	−	0.372822i	−0.868504	+	0.495682i	$0.834918\pi$
$878$	−254.993	+	254.993i	−0.290425	+	0.290425i
$879$			62.2127i			0.0707767i
$880$	−50.5169	−	29.4299i	−0.0574056	−	0.0334431i
$881$	538.293			0.611003			0.305501	−	0.952192i	$-0.401176\pi$
$881$	538.293			0.611003			0.305501	+	0.952192i	$0.401176\pi$
$882$	21.0000	+	21.0000i	0.0238095	+	0.0238095i
$883$	−951.591	+	951.591i	−1.07768	+	1.07768i	−0.0809620	+	0.996717i	$0.525799\pi$
$883$	−951.591	+	951.591i	−1.07768	+	1.07768i	−0.996717	+	0.0809620i	$0.974201\pi$
$884$		−	7.00276i		−	0.00792167i
$885$	−258.784	−	981.124i	−0.292411	−	1.10861i
$886$	−585.255			−0.660559
$887$	300.730	+	300.730i	0.339042	+	0.339042i	0.856007	−	0.516965i	$-0.172938\pi$
$887$	300.730	+	300.730i	0.339042	+	0.339042i	−0.516965	+	0.856007i	$0.672938\pi$
$888$	82.4522	−	82.4522i	0.0928515	−	0.0928515i
$889$			534.919i			0.601709i
$890$	690.226	−	182.056i	0.775535	−	0.204557i
$891$	−26.3089			−0.0295274
$892$	−203.537	−	203.537i	−0.228180	−	0.228180i
$893$	175.374	−	175.374i	0.196388	−	0.196388i
$894$		−	189.837i		−	0.212345i
$895$	123.419	−	211.850i	0.137898	−	0.236704i
$896$	29.9333			0.0334077
$897$	21.9452	+	21.9452i	0.0244651	+	0.0244651i
$898$	400.989	−	400.989i	0.446536	−	0.446536i
$899$		−	213.964i		−	0.238002i
$900$	73.9818	+	130.486i	0.0822020	+	0.144985i
$901$	−125.267			−0.139031
$902$	−212.292	−	212.292i	−0.235357	−	0.235357i
$903$	93.3696	−	93.3696i	0.103399	−	0.103399i
$904$		−	272.147i		−	0.301047i
$905$	−1413.36	−	823.389i	−1.56172	−	0.909822i
$906$	90.1889			0.0995462
$907$	−801.951	−	801.951i	−0.884179	−	0.884179i	0.109777	−	0.993956i	$-0.464986\pi$
$907$	−801.951	−	801.951i	−0.884179	−	0.884179i	−0.993956	+	0.109777i	$0.964986\pi$
$908$	50.1179	−	50.1179i	0.0551959	−	0.0551959i
$909$			388.252i			0.427120i
$910$	−7.64575	−	28.9873i	−0.00840193	−	0.0318541i
$911$	−1437.85			−1.57832			−0.789160	−	0.614187i	$-0.789484\pi$
$911$	−1437.85			−1.57832			−0.789160	+	0.614187i	$0.789484\pi$
$912$	−16.4213	−	16.4213i	−0.0180058	−	0.0180058i
$913$	−62.3613	+	62.3613i	−0.0683038	+	0.0683038i
$914$		−	344.079i		−	0.376454i
$915$	−380.486	+	100.358i	−0.415832	+	0.109681i
$916$	−566.995			−0.618990
$917$	6.64862	+	6.64862i	0.00725041	+	0.00725041i
$918$	11.3539	−	11.3539i	0.0123680	−	0.0123680i
$919$		−	1282.30i		−	1.39532i	−0.716428	−	0.697661i	$-0.754224\pi$
$919$		−	1282.30i		−	1.39532i	0.716428	−	0.697661i	$-0.245776\pi$
$920$	−79.6030	+	136.640i	−0.0865250	+	0.148521i
$921$	−793.240			−0.861282
$922$	153.918	+	153.918i	0.166939	+	0.166939i
$923$	58.6052	−	58.6052i	0.0634942	−	0.0634942i
$924$			26.7917i			0.0289954i
$925$	158.500	−	573.550i	0.171351	−	0.620054i
$926$	−583.527			−0.630158
$927$	−93.1342	−	93.1342i	−0.100468	−	0.100468i
$928$	−54.1898	+	54.1898i	−0.0583942	+	0.0583942i
$929$		−	520.920i		−	0.560732i	−0.959893	−	0.280366i	$-0.909544\pi$
$929$		−	520.920i		−	0.560732i	0.959893	−	0.280366i	$-0.0904558\pi$
$930$	167.137	+	97.3702i	0.179718	+	0.104699i
$931$	−23.4639			−0.0252029
$932$	278.238	+	278.238i	0.298539	+	0.298539i
$933$	−348.352	+	348.352i	−0.373368	+	0.373368i
$934$		−	1006.47i		−	1.07759i
$935$	8.14518	+	30.8807i	0.00871142	+	0.0330275i
$936$	−13.5970			−0.0145267
$937$	−49.7102	−	49.7102i	−0.0530525	−	0.0530525i	0.680083	−	0.733135i	$-0.261944\pi$
$937$	−49.7102	−	49.7102i	−0.0530525	−	0.0530525i	−0.733135	+	0.680083i	$0.761944\pi$
$938$	−216.183	+	216.183i	−0.230472	+	0.230472i
$939$		−	438.371i		−	0.466849i
$940$	715.440	−	188.706i	0.761106	−	0.200751i
$941$	−163.591			−0.173848			−0.0869242	−	0.996215i	$-0.527704\pi$
$941$	−163.591			−0.173848			−0.0869242	+	0.996215i	$0.527704\pi$
$942$	185.586	+	185.586i	0.197013	+	0.197013i
$943$	−574.214	+	574.214i	−0.608922	+	0.608922i
$944$			468.660i			0.496462i
$945$	34.6018	−	59.3946i	0.0366157	−	0.0628514i
$946$	119.121			0.125920
$947$	−1003.15	−	1003.15i	−1.05929	−	1.05929i	−0.998128	−	0.0611651i	$-0.980518\pi$
$947$	−1003.15	−	1003.15i	−1.05929	−	1.05929i	−0.0611651	−	0.998128i	$-0.519482\pi$
$948$	91.0843	−	91.0843i	0.0960805	−	0.0960805i
$949$			164.037i			0.172852i
$950$	−114.229	−	31.5671i	−0.120241	−	0.0332285i
$951$	822.538			0.864919
$952$	−11.5622	−	11.5622i	−0.0121452	−	0.0121452i
$953$	−265.856	+	265.856i	−0.278967	+	0.278967i	−0.832697	−	0.553729i	$-0.813204\pi$
$953$	−265.856	+	265.856i	−0.278967	+	0.278967i	0.553729	+	0.832697i	$0.313204\pi$
$954$			243.227i			0.254955i
$955$	1248.91	+	727.585i	1.30776	+	0.761869i
$956$	366.561			0.383432
$957$	−48.5025	−	48.5025i	−0.0506818	−	0.0506818i
$958$	−670.857	+	670.857i	−0.700268	+	0.700268i
$959$			281.019i			0.293033i
$960$	−17.6697	−	66.9909i	−0.0184059	−	0.0697822i
$961$	−711.561			−0.740438
$962$	38.1408	+	38.1408i	0.0396474	+	0.0396474i
$963$	328.264	−	328.264i	0.340876	−	0.340876i
$964$		−	560.188i		−	0.581108i
$965$	−897.130	+	236.629i	−0.929669	+	0.245212i
$966$	72.4671			0.0750177
$967$	662.074	+	662.074i	0.684668	+	0.684668i	0.961048	−	0.276380i	$-0.0891349\pi$
$967$	662.074	+	662.074i	0.684668	+	0.684668i	−0.276380	+	0.961048i	$0.589135\pi$
$968$	224.910	−	224.910i	0.232345	−	0.232345i
$969$			12.6860i			0.0130918i
$970$	−264.722	+	454.400i	−0.272910	+	0.468453i
$971$	562.832			0.579642			0.289821	−	0.957081i	$-0.406404\pi$
$971$	562.832			0.579642			0.289821	+	0.957081i	$0.406404\pi$
$972$	−22.0454	−	22.0454i	−0.0226805	−	0.0226805i
$973$	−359.858	+	359.858i	−0.369844	+	0.369844i
$974$		−	862.700i		−	0.885729i
$975$	−60.3604	+	34.2225i	−0.0619081	+	0.0351000i
$976$	181.749			0.186219
$977$	1319.92	+	1319.92i	1.35099	+	1.35099i	0.884556	+	0.466433i	$0.154461\pi$
$977$	1319.92	+	1319.92i	1.35099	+	1.35099i	0.466433	+	0.884556i	$0.345539\pi$
$978$	427.320	−	427.320i	0.436932	−	0.436932i
$979$		−	295.102i		−	0.301432i
$980$	−60.4845	−	35.2368i	−0.0617188	−	0.0359559i
$981$	205.851			0.209838
$982$	−643.019	−	643.019i	−0.654806	−	0.654806i
$983$	117.249	−	117.249i	0.119277	−	0.119277i	−0.644949	−	0.764226i	$-0.723121\pi$
$983$	117.249	−	117.249i	0.119277	−	0.119277i	0.764226	+	0.644949i	$0.223121\pi$
$984$		−	355.777i		−	0.361562i
$985$	201.618	+	764.391i	0.204688	+	0.776032i
$986$	41.8633			0.0424577
$987$	−239.758	−	239.758i	−0.242916	−	0.242916i
$988$	7.59618	−	7.59618i	0.00768844	−	0.00768844i
$989$		−	322.201i		−	0.325785i
$990$	59.9601	−	15.8152i	0.0605658	−	0.0159750i
$991$	−354.972			−0.358196			−0.179098	−	0.983831i	$-0.557318\pi$
$991$	−354.972			−0.358196			−0.179098	+	0.983831i	$0.557318\pi$
$992$	−63.1746	−	63.1746i	−0.0636841	−	0.0636841i
$993$	544.156	−	544.156i	0.547991	−	0.547991i
$994$		−	193.525i		−	0.194693i
$995$	146.916	−	252.183i	0.147654	−	0.253451i
$996$	−104.511			−0.104930
$997$	−913.231	−	913.231i	−0.915979	−	0.915979i	0.0807549	−	0.996734i	$-0.474267\pi$
$997$	−913.231	−	913.231i	−0.915979	−	0.915979i	−0.996734	+	0.0807549i	$0.974267\pi$
$998$	350.058	−	350.058i	0.350760	−	0.350760i
$999$			123.678i			0.123802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.l.a.127.4	yes	8
3.2	odd	2		630.3.o.b.127.1		8
5.2	odd	4		1050.3.l.b.43.1		8
5.3	odd	4	inner	210.3.l.a.43.4	✓	8
5.4	even	2		1050.3.l.b.757.1		8
15.8	even	4		630.3.o.b.253.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.a.43.4	✓	8	5.3	odd	4	inner
210.3.l.a.127.4	yes	8	1.1	even	1	trivial
630.3.o.b.127.1		8	3.2	odd	2
630.3.o.b.253.1		8	15.8	even	4
1050.3.l.b.43.1		8	5.2	odd	4
1050.3.l.b.757.1		8	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.32032 + 2.51691i) q^{5} +2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.32032 + 2.51691i) q^{5} +2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(1.80341 + 6.83723i) q^{10} +2.92322 q^{11} +(2.44949 + 2.44949i) q^{12} +(-1.13309 + 1.13309i) q^{13} +3.74166i q^{14} +(8.37386 - 2.20871i) q^{15} -4.00000 q^{16} +(1.54506 + 1.54506i) q^{17} +(3.00000 - 3.00000i) q^{18} +3.35199i q^{19} +(-5.03383 + 8.64064i) q^{20} +4.58258 q^{21} +(2.92322 + 2.92322i) q^{22} +(7.90681 - 7.90681i) q^{23} +4.89898i q^{24} +(12.3303 + 21.7477i) q^{25} -2.26617 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-3.74166 + 3.74166i) q^{28} -13.5474i q^{29} +(10.5826 + 6.16515i) q^{30} +15.7936 q^{31} +(-4.00000 - 4.00000i) q^{32} +(3.58019 - 3.58019i) q^{33} +3.09013i q^{34} +(3.37386 + 12.7913i) q^{35} +6.00000 q^{36} +(-16.8305 - 16.8305i) q^{37} +(-3.35199 + 3.35199i) q^{38} +2.77548i q^{39} +(-13.6745 + 3.60681i) q^{40} -72.6227 q^{41} +(4.58258 + 4.58258i) q^{42} +(20.3749 - 20.3749i) q^{43} +5.84643i q^{44} +(7.55074 - 12.9610i) q^{45} +15.8136 q^{46} +(-52.3194 - 52.3194i) q^{47} +(-4.89898 + 4.89898i) q^{48} +7.00000i q^{49} +(-9.41742 + 34.0780i) q^{50} +3.78462 q^{51} +(-2.26617 - 2.26617i) q^{52} +(-40.5379 + 40.5379i) q^{53} -7.34847i q^{54} +(12.6292 + 7.35748i) q^{55} -7.48331 q^{56} +(4.10533 + 4.10533i) q^{57} +(13.5474 - 13.5474i) q^{58} -117.165i q^{59} +(4.41742 + 16.7477i) q^{60} -45.4373 q^{61} +(15.7936 + 15.7936i) q^{62} +(5.61249 - 5.61249i) q^{63} -8.00000i q^{64} +(-7.74717 + 2.04341i) q^{65} +7.16039 q^{66} +(57.7773 + 57.7773i) q^{67} +(-3.09013 + 3.09013i) q^{68} -19.3676i q^{69} +(-9.41742 + 16.1652i) q^{70} -51.7217 q^{71} +(6.00000 + 6.00000i) q^{72} +(72.3851 - 72.3851i) q^{73} -33.6610i q^{74} +(41.7369 + 11.5339i) q^{75} -6.70398 q^{76} +(5.46884 + 5.46884i) q^{77} +(-2.77548 + 2.77548i) q^{78} -37.1850i q^{79} +(-17.2813 - 10.0677i) q^{80} -9.00000 q^{81} +(-72.6227 - 72.6227i) q^{82} +(-21.3331 + 21.3331i) q^{83} +9.16515i q^{84} +(2.78638 + 10.5640i) q^{85} +40.7498 q^{86} +(-16.5922 - 16.5922i) q^{87} +(-5.84643 + 5.84643i) q^{88} -100.951i q^{89} +(20.5117 - 5.41022i) q^{90} -4.23962 q^{91} +(15.8136 + 15.8136i) q^{92} +(19.3432 - 19.3432i) q^{93} -104.639i q^{94} +(-8.43666 + 14.4817i) q^{95} -9.79796 q^{96} +(52.5887 + 52.5887i) q^{97} +(-7.00000 + 7.00000i) q^{98} -8.76965i 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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