LMFDB - Embedded newform 429.2.m.a.109.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(109,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("429.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.m (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.9
Character	$\chi$	$=$	429.109
Dual form			429.2.m.a.307.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.200229 + 0.200229i) q^{2} -1.00000 q^{3} -1.91982i q^{4} +(-0.906673 + 0.906673i) q^{5} +(-0.200229 - 0.200229i) q^{6} +(-2.29691 + 2.29691i) q^{7} +(0.784861 - 0.784861i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.200229 + 0.200229i) q^{2} -1.00000 q^{3} -1.91982i q^{4} +(-0.906673 + 0.906673i) q^{5} +(-0.200229 - 0.200229i) q^{6} +(-2.29691 + 2.29691i) q^{7} +(0.784861 - 0.784861i) q^{8} +1.00000 q^{9} -0.363084 q^{10} +(2.54486 + 2.12689i) q^{11} +1.91982i q^{12} +(0.213548 + 3.59922i) q^{13} -0.919817 q^{14} +(0.906673 - 0.906673i) q^{15} -3.52533 q^{16} +2.75112 q^{17} +(0.200229 + 0.200229i) q^{18} +(5.56967 + 5.56967i) q^{19} +(1.74065 + 1.74065i) q^{20} +(2.29691 - 2.29691i) q^{21} +(0.0836901 + 0.935421i) q^{22} -7.57062i q^{23} +(-0.784861 + 0.784861i) q^{24} +3.35589i q^{25} +(-0.677910 + 0.763427i) q^{26} -1.00000 q^{27} +(4.40965 + 4.40965i) q^{28} +7.96199i q^{29} +0.363084 q^{30} +(-0.992189 + 0.992189i) q^{31} +(-2.27559 - 2.27559i) q^{32} +(-2.54486 - 2.12689i) q^{33} +(0.550853 + 0.550853i) q^{34} -4.16510i q^{35} -1.91982i q^{36} +(1.31245 + 1.31245i) q^{37} +2.23042i q^{38} +(-0.213548 - 3.59922i) q^{39} +1.42322i q^{40} +(-0.985090 - 0.985090i) q^{41} +0.919817 q^{42} -5.76458 q^{43} +(4.08324 - 4.88567i) q^{44} +(-0.906673 + 0.906673i) q^{45} +(1.51586 - 1.51586i) q^{46} +(-1.14457 - 1.14457i) q^{47} +3.52533 q^{48} -3.55162i q^{49} +(-0.671946 + 0.671946i) q^{50} -2.75112 q^{51} +(6.90985 - 0.409972i) q^{52} -9.13461 q^{53} +(-0.200229 - 0.200229i) q^{54} +(-4.23575 + 0.378964i) q^{55} +3.60551i q^{56} +(-5.56967 - 5.56967i) q^{57} +(-1.59422 + 1.59422i) q^{58} +(4.44515 + 4.44515i) q^{59} +(-1.74065 - 1.74065i) q^{60} +3.40717i q^{61} -0.397330 q^{62} +(-2.29691 + 2.29691i) q^{63} +6.13938i q^{64} +(-3.45693 - 3.06970i) q^{65} +(-0.0836901 - 0.935421i) q^{66} +(2.76558 - 2.76558i) q^{67} -5.28164i q^{68} +7.57062i q^{69} +(0.833973 - 0.833973i) q^{70} +(3.33835 - 3.33835i) q^{71} +(0.784861 - 0.784861i) q^{72} +(-5.69171 + 5.69171i) q^{73} +0.525582i q^{74} -3.35589i q^{75} +(10.6928 - 10.6928i) q^{76} +(-10.7306 + 0.960046i) q^{77} +(0.677910 - 0.763427i) q^{78} -5.17350i q^{79} +(3.19632 - 3.19632i) q^{80} +1.00000 q^{81} -0.394487i q^{82} +(-6.70505 - 6.70505i) q^{83} +(-4.40965 - 4.40965i) q^{84} +(-2.49436 + 2.49436i) q^{85} +(-1.15424 - 1.15424i) q^{86} -7.96199i q^{87} +(3.66668 - 0.328050i) q^{88} +(3.99735 + 3.99735i) q^{89} -0.363084 q^{90} +(-8.75760 - 7.77660i) q^{91} -14.5342 q^{92} +(0.992189 - 0.992189i) q^{93} -0.458354i q^{94} -10.0997 q^{95} +(2.27559 + 2.27559i) q^{96} +(12.2427 - 12.2427i) q^{97} +(0.711137 - 0.711137i) q^{98} +(2.54486 + 2.12689i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{3} + 4 q^{5} + 28 q^{9}+O(q^{10}) $ 28 * q - 28 * q^3 + 4 * q^5 + 28 * q^9	$ 28 q - 28 q^{3} + 4 q^{5} + 28 q^{9} + 4 q^{11} + 48 q^{14} - 4 q^{15} - 52 q^{16} - 8 q^{20} - 32 q^{22} - 4 q^{26} - 28 q^{27} + 24 q^{31} - 4 q^{33} + 16 q^{34} - 12 q^{37} - 48 q^{42} - 24 q^{44} + 4 q^{45} - 8 q^{47} + 52 q^{48} - 8 q^{53} + 48 q^{55} - 64 q^{58} + 4 q^{59} + 8 q^{60} + 32 q^{66} + 28 q^{67} - 4 q^{70} + 12 q^{71} + 4 q^{78} + 56 q^{80} + 28 q^{81} - 8 q^{86} - 104 q^{89} - 76 q^{91} - 24 q^{93} - 8 q^{97} + 4 q^{99}+O(q^{100}) $ 28 * q - 28 * q^3 + 4 * q^5 + 28 * q^9 + 4 * q^11 + 48 * q^14 - 4 * q^15 - 52 * q^16 - 8 * q^20 - 32 * q^22 - 4 * q^26 - 28 * q^27 + 24 * q^31 - 4 * q^33 + 16 * q^34 - 12 * q^37 - 48 * q^42 - 24 * q^44 + 4 * q^45 - 8 * q^47 + 52 * q^48 - 8 * q^53 + 48 * q^55 - 64 * q^58 + 4 * q^59 + 8 * q^60 + 32 * q^66 + 28 * q^67 - 4 * q^70 + 12 * q^71 + 4 * q^78 + 56 * q^80 + 28 * q^81 - 8 * q^86 - 104 * q^89 - 76 * q^91 - 24 * q^93 - 8 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.200229	+	0.200229i	0.141583	+	0.141583i	0.774346	−	0.632763i	$-0.218079\pi$
$2$	0.200229	+	0.200229i	0.141583	+	0.141583i	−0.632763	+	0.774346i	$0.718079\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		−	1.91982i		−	0.959908i
$5$	−0.906673	+	0.906673i	−0.405476	+	0.405476i	−0.880158	−	0.474681i	$-0.842563\pi$
$5$	−0.906673	+	0.906673i	−0.405476	+	0.405476i	0.474681	+	0.880158i	$0.342563\pi$
$6$	−0.200229	−	0.200229i	−0.0817431	−	0.0817431i
$7$	−2.29691	+	2.29691i	−0.868151	+	0.868151i	−0.992268	−	0.124116i	$-0.960390\pi$
$7$	−2.29691	+	2.29691i	−0.868151	+	0.868151i	0.124116	+	0.992268i	$0.460390\pi$
$8$	0.784861	−	0.784861i	0.277490	−	0.277490i
$9$	1.00000			0.333333
$10$	−0.363084			−0.114817
$11$	2.54486	+	2.12689i	0.767305	+	0.641282i
$11$	2.54486	+	2.12689i	0.767305	+	0.641282i
$12$			1.91982i			0.554203i
$13$	0.213548	+	3.59922i	0.0592275	+	0.998245i
$13$	0.213548	+	3.59922i	0.0592275	+	0.998245i
$14$	−0.919817			−0.245831
$15$	0.906673	−	0.906673i	0.234102	−	0.234102i
$16$	−3.52533			−0.881332
$17$	2.75112			0.667244			0.333622	−	0.942707i	$-0.391729\pi$
$17$	2.75112			0.667244			0.333622	+	0.942707i	$0.391729\pi$
$18$	0.200229	+	0.200229i	0.0471944	+	0.0471944i
$19$	5.56967	+	5.56967i	1.27777	+	1.27777i	0.941913	+	0.335858i	$0.109026\pi$
$19$	5.56967	+	5.56967i	1.27777	+	1.27777i	0.335858	+	0.941913i	$0.390974\pi$
$20$	1.74065	+	1.74065i	0.389220	+	0.389220i
$21$	2.29691	−	2.29691i	0.501228	−	0.501228i
$22$	0.0836901	+	0.935421i	0.0178428	+	0.199432i
$23$		−	7.57062i		−	1.57858i	−0.614019	−	0.789291i	$-0.710448\pi$
$23$		−	7.57062i		−	1.57858i	0.614019	−	0.789291i	$-0.289552\pi$
$24$	−0.784861	+	0.784861i	−0.160209	+	0.160209i
$25$			3.35589i			0.671178i
$26$	−0.677910	+	0.763427i	−0.132949	+	0.149720i
$27$	−1.00000			−0.192450
$28$	4.40965	+	4.40965i	0.833346	+	0.833346i
$29$			7.96199i			1.47850i	0.673429	+	0.739252i	$0.264821\pi$
$29$			7.96199i			1.47850i	−0.673429	+	0.739252i	$0.735179\pi$
$30$	0.363084			0.0662898
$31$	−0.992189	+	0.992189i	−0.178202	+	0.178202i	−0.790572	−	0.612369i	$-0.790217\pi$
$31$	−0.992189	+	0.992189i	−0.178202	+	0.178202i	0.612369	+	0.790572i	$0.290217\pi$
$32$	−2.27559	−	2.27559i	−0.402272	−	0.402272i
$33$	−2.54486	−	2.12689i	−0.443004	−	0.370244i
$34$	0.550853	+	0.550853i	0.0944705	+	0.0944705i
$35$		−	4.16510i		−	0.704030i
$36$		−	1.91982i		−	0.319969i
$37$	1.31245	+	1.31245i	0.215766	+	0.215766i	0.806711	−	0.590946i	$-0.201245\pi$
$37$	1.31245	+	1.31245i	0.215766	+	0.215766i	−0.590946	+	0.806711i	$0.701245\pi$
$38$			2.23042i			0.361822i
$39$	−0.213548	−	3.59922i	−0.0341950	−	0.576337i
$40$			1.42322i			0.225031i
$41$	−0.985090	−	0.985090i	−0.153845	−	0.153845i	0.625988	−	0.779833i	$-0.284696\pi$
$41$	−0.985090	−	0.985090i	−0.153845	−	0.153845i	−0.779833	+	0.625988i	$0.784696\pi$
$42$	0.919817			0.141931
$43$	−5.76458			−0.879091			−0.439545	−	0.898220i	$-0.644860\pi$
$43$	−5.76458			−0.879091			−0.439545	+	0.898220i	$0.644860\pi$
$44$	4.08324	−	4.88567i	0.615572	−	0.736543i
$45$	−0.906673	+	0.906673i	−0.135159	+	0.135159i
$46$	1.51586	−	1.51586i	0.223501	−	0.223501i
$47$	−1.14457	−	1.14457i	−0.166953	−	0.166953i	0.618685	−	0.785639i	$-0.287666\pi$
$47$	−1.14457	−	1.14457i	−0.166953	−	0.166953i	−0.785639	+	0.618685i	$0.787666\pi$
$48$	3.52533			0.508838
$49$		−	3.55162i		−	0.507374i
$50$	−0.671946	+	0.671946i	−0.0950275	+	0.0950275i
$51$	−2.75112			−0.385233
$52$	6.90985	−	0.409972i	0.958223	−	0.0568529i
$53$	−9.13461			−1.25474			−0.627368	−	0.778723i	$-0.715868\pi$
$53$	−9.13461			−1.25474			−0.627368	+	0.778723i	$0.715868\pi$
$54$	−0.200229	−	0.200229i	−0.0272477	−	0.0272477i
$55$	−4.23575	+	0.378964i	−0.571149	+	0.0510995i
$56$			3.60551i			0.481807i
$57$	−5.56967	−	5.56967i	−0.737721	−	0.737721i
$58$	−1.59422	+	1.59422i	−0.209331	+	0.209331i
$59$	4.44515	+	4.44515i	0.578709	+	0.578709i	0.934547	−	0.355839i	$-0.115805\pi$
$59$	4.44515	+	4.44515i	0.578709	+	0.578709i	−0.355839	+	0.934547i	$0.615805\pi$
$60$	−1.74065	−	1.74065i	−0.224716	−	0.224716i
$61$			3.40717i			0.436243i	0.975922	+	0.218122i	$0.0699929\pi$
$61$			3.40717i			0.436243i	−0.975922	+	0.218122i	$0.930007\pi$
$62$	−0.397330			−0.0504610
$63$	−2.29691	+	2.29691i	−0.289384	+	0.289384i
$64$			6.13938i			0.767423i
$65$	−3.45693	−	3.06970i	−0.428780	−	0.380749i
$66$	−0.0836901	−	0.935421i	−0.0103015	−	0.115142i
$67$	2.76558	−	2.76558i	0.337869	−	0.337869i	−0.517695	−	0.855565i	$-0.673210\pi$
$67$	2.76558	−	2.76558i	0.337869	−	0.337869i	0.855565	+	0.517695i	$0.173210\pi$
$68$		−	5.28164i		−	0.640493i
$69$			7.57062i			0.911395i
$70$	0.833973	−	0.833973i	0.0996788	−	0.0996788i
$71$	3.33835	−	3.33835i	0.396189	−	0.396189i	−0.480697	−	0.876886i	$-0.659616\pi$
$71$	3.33835	−	3.33835i	0.396189	−	0.396189i	0.876886	+	0.480697i	$0.159616\pi$
$72$	0.784861	−	0.784861i	0.0924967	−	0.0924967i
$73$	−5.69171	+	5.69171i	−0.666164	+	0.666164i	−0.956826	−	0.290662i	$-0.906125\pi$
$73$	−5.69171	+	5.69171i	−0.666164	+	0.666164i	0.290662	+	0.956826i	$0.406125\pi$
$74$			0.525582i			0.0610977i
$75$		−	3.35589i		−	0.387505i
$76$	10.6928	−	10.6928i	1.22654	−	1.22654i
$77$	−10.7306	+	0.960046i	−1.22287	+	0.109407i
$78$	0.677910	−	0.763427i	0.0767582	−	0.0864410i
$79$		−	5.17350i		−	0.582064i	−0.956713	−	0.291032i	$-0.906001\pi$
$79$		−	5.17350i		−	0.582064i	0.956713	−	0.291032i	$-0.0939986\pi$
$80$	3.19632	−	3.19632i	0.357359	−	0.357359i
$81$	1.00000			0.111111
$82$		−	0.394487i		−	0.0435638i
$83$	−6.70505	−	6.70505i	−0.735975	−	0.735975i	0.235822	−	0.971796i	$-0.424222\pi$
$83$	−6.70505	−	6.70505i	−0.735975	−	0.735975i	−0.971796	+	0.235822i	$0.924222\pi$
$84$	−4.40965	−	4.40965i	−0.481132	−	0.481132i
$85$	−2.49436	+	2.49436i	−0.270551	+	0.270551i
$86$	−1.15424	−	1.15424i	−0.124464	−	0.124464i
$87$		−	7.96199i		−	0.853614i
$88$	3.66668	−	0.328050i	0.390869	−	0.0349703i
$89$	3.99735	+	3.99735i	0.423719	+	0.423719i	0.886482	−	0.462763i	$-0.153142\pi$
$89$	3.99735	+	3.99735i	0.423719	+	0.423719i	−0.462763	+	0.886482i	$0.653142\pi$
$90$	−0.363084			−0.0382724
$91$	−8.75760	−	7.77660i	−0.918046	−	0.815209i
$92$	−14.5342			−1.51529
$93$	0.992189	−	0.992189i	0.102885	−	0.102885i
$94$		−	0.458354i		−	0.0472756i
$95$	−10.0997			−1.03621
$96$	2.27559	+	2.27559i	0.232252	+	0.232252i
$97$	12.2427	−	12.2427i	1.24306	−	1.24306i	0.284332	−	0.958726i	$-0.408228\pi$
$97$	12.2427	−	12.2427i	1.24306	−	1.24306i	0.958726	−	0.284332i	$-0.0917718\pi$
$98$	0.711137	−	0.711137i	0.0718357	−	0.0718357i
$99$	2.54486	+	2.12689i	0.255768	+	0.213761i
$100$	6.44269			0.644269
$101$	15.3633			1.52871			0.764354	−	0.644797i	$-0.223058\pi$
$101$	15.3633			1.52871			0.764354	+	0.644797i	$0.223058\pi$
$102$	−0.550853	−	0.550853i	−0.0545426	−	0.0545426i
$103$			1.14327i			0.112650i	0.998412	+	0.0563249i	$0.0179383\pi$
$103$			1.14327i			0.112650i	−0.998412	+	0.0563249i	$0.982062\pi$
$104$	2.99249	+	2.65728i	0.293438	+	0.260568i
$105$			4.16510i			0.406472i
$106$	−1.82901	−	1.82901i	−0.177650	−	0.177650i
$107$		−	17.9297i		−	1.73333i	−0.498889	−	0.866666i	$-0.666258\pi$
$107$		−	17.9297i		−	1.73333i	0.498889	−	0.866666i	$-0.333742\pi$
$108$			1.91982i			0.184734i
$109$	4.05051	+	4.05051i	0.387968	+	0.387968i	0.873962	−	0.485994i	$-0.161542\pi$
$109$	4.05051	+	4.05051i	0.387968	+	0.387968i	−0.485994	+	0.873962i	$0.661542\pi$
$110$	−0.924000	−	0.772241i	−0.0880999	−	0.0736302i
$111$	−1.31245	−	1.31245i	−0.124573	−	0.124573i
$112$	8.09738	−	8.09738i	0.765130	−	0.765130i
$113$	15.1029			1.42076			0.710380	−	0.703818i	$-0.248523\pi$
$113$	15.1029			1.42076			0.710380	+	0.703818i	$0.248523\pi$
$114$		−	2.23042i		−	0.208898i
$115$	6.86407	+	6.86407i	0.640078	+	0.640078i
$116$	15.2856			1.41923
$117$	0.213548	+	3.59922i	0.0197425	+	0.332748i
$118$			1.78009i			0.163871i
$119$	−6.31907	+	6.31907i	−0.579268	+	0.579268i
$120$		−	1.42322i		−	0.129922i
$121$	1.95266	+	10.8253i	0.177515	+	0.984118i
$122$	−0.682214	+	0.682214i	−0.0617647	+	0.0617647i
$123$	0.985090	+	0.985090i	0.0888225	+	0.0888225i
$124$	1.90482	+	1.90482i	0.171058	+	0.171058i
$125$	−7.57606	−	7.57606i	−0.677623	−	0.677623i
$126$	−0.919817			−0.0819438
$127$	−20.5742			−1.82567			−0.912833	−	0.408334i	$-0.866110\pi$
$127$	−20.5742			−1.82567			−0.912833	+	0.408334i	$0.866110\pi$
$128$	−5.78047	+	5.78047i	−0.510926	+	0.510926i
$129$	5.76458			0.507543
$130$	−0.0775358	−	1.30682i	−0.00680034	−	0.114616i
$131$		−	14.6387i		−	1.27899i	−0.768797	−	0.639493i	$-0.779144\pi$
$131$		−	14.6387i		−	1.27899i	0.768797	−	0.639493i	$-0.220856\pi$
$132$	−4.08324	+	4.88567i	−0.355401	+	0.425243i
$133$	−25.5861			−2.21860
$134$	1.10750			0.0956733
$135$	0.906673	−	0.906673i	0.0780340	−	0.0780340i
$136$	2.15924	−	2.15924i	0.185154	−	0.185154i
$137$	−0.869856	−	0.869856i	−0.0743168	−	0.0743168i	0.668971	−	0.743288i	$-0.266735\pi$
$137$	−0.869856	−	0.869856i	−0.0743168	−	0.0743168i	−0.743288	+	0.668971i	$0.766735\pi$
$138$	−1.51586	+	1.51586i	−0.129038	+	0.129038i
$139$			12.3110i			1.04420i	0.852884	+	0.522101i	$0.174851\pi$
$139$			12.3110i			1.04420i	−0.852884	+	0.522101i	$0.825149\pi$
$140$	−7.99622			−0.675804
$141$	1.14457	+	1.14457i	0.0963906	+	0.0963906i
$142$	1.33687			0.112187
$143$	−7.11170	+	9.61372i	−0.594711	+	0.803940i
$144$	−3.52533			−0.293777
$145$	−7.21891	−	7.21891i	−0.599498	−	0.599498i
$146$	−2.27929			−0.188635
$147$			3.55162i			0.292933i
$148$	2.51967	−	2.51967i	0.207116	−	0.207116i
$149$	1.17341	+	1.17341i	0.0961299	+	0.0961299i	0.753536	−	0.657406i	$-0.228346\pi$
$149$	1.17341	+	1.17341i	0.0961299	+	0.0961299i	−0.657406	+	0.753536i	$0.728346\pi$
$150$	0.671946	−	0.671946i	0.0548642	−	0.0548642i
$151$	−6.70391	+	6.70391i	−0.545556	+	0.545556i	−0.925152	−	0.379596i	$-0.876063\pi$
$151$	−6.70391	+	6.70391i	−0.545556	+	0.545556i	0.379596	+	0.925152i	$0.376063\pi$
$152$	8.74283			0.709137
$153$	2.75112			0.222415
$154$	−2.34081	−	1.95635i	−0.188628	−	0.157647i
$155$		−	1.79918i		−	0.144514i
$156$	−6.90985	+	0.409972i	−0.553230	+	0.0328241i
$157$	9.78356			0.780813			0.390407	−	0.920643i	$-0.372334\pi$
$157$	9.78356			0.780813			0.390407	+	0.920643i	$0.372334\pi$
$158$	1.03588	−	1.03588i	0.0824105	−	0.0824105i
$159$	9.13461			0.724422
$160$	4.12644			0.326224
$161$	17.3890	+	17.3890i	1.37045	+	1.37045i
$162$	0.200229	+	0.200229i	0.0157315	+	0.0157315i
$163$	13.0847	+	13.0847i	1.02487	+	1.02487i	0.999683	+	0.0251864i	$0.00801793\pi$
$163$	13.0847	+	13.0847i	1.02487	+	1.02487i	0.0251864	+	0.999683i	$0.491982\pi$
$164$	−1.89119	+	1.89119i	−0.147677	+	0.147677i
$165$	4.23575	−	0.378964i	0.329753	−	0.0295023i
$166$		−	2.68509i		−	0.208403i
$167$	0.588793	−	0.588793i	0.0455622	−	0.0455622i	−0.683959	−	0.729521i	$-0.739743\pi$
$167$	0.588793	−	0.588793i	0.0455622	−	0.0455622i	0.729521	+	0.683959i	$0.239743\pi$
$168$		−	3.60551i		−	0.278171i
$169$	−12.9088	+	1.53721i	−0.992984	+	0.118247i
$170$	−0.998886			−0.0766111
$171$	5.56967	+	5.56967i	0.425924	+	0.425924i
$172$			11.0669i			0.843846i
$173$	4.89018			0.371794			0.185897	−	0.982569i	$-0.440481\pi$
$173$	4.89018			0.371794			0.185897	+	0.982569i	$0.440481\pi$
$174$	1.59422	−	1.59422i	0.120857	−	0.120857i
$175$	−7.70819	−	7.70819i	−0.582684	−	0.582684i
$176$	−8.97148	−	7.49799i	−0.676251	−	0.565183i
$177$	−4.44515	−	4.44515i	−0.334118	−	0.334118i
$178$			1.60077i			0.119983i
$179$		−	4.68760i		−	0.350368i	−0.984536	−	0.175184i	$-0.943948\pi$
$179$		−	4.68760i		−	0.350368i	0.984536	−	0.175184i	$-0.0560520\pi$
$180$	1.74065	+	1.74065i	0.129740	+	0.129740i
$181$		−	2.66536i		−	0.198114i	−0.995082	−	0.0990572i	$-0.968417\pi$
$181$		−	2.66536i		−	0.198114i	0.995082	−	0.0990572i	$-0.0315827\pi$
$182$	−0.196425	−	3.31062i	−0.0145600	−	0.245400i
$183$		−	3.40717i		−	0.251865i
$184$	−5.94188	−	5.94188i	−0.438041	−	0.438041i
$185$	−2.37993			−0.174976
$186$	0.397330			0.0291337
$187$	7.00121	+	5.85132i	0.511980	+	0.427891i
$188$	−2.19737	+	2.19737i	−0.160260	+	0.160260i
$189$	2.29691	−	2.29691i	0.167076	−	0.167076i
$190$	−2.02226	−	2.02226i	−0.146710	−	0.146710i
$191$	7.25273			0.524789			0.262395	−	0.964961i	$-0.415488\pi$
$191$	7.25273			0.524789			0.262395	+	0.964961i	$0.415488\pi$
$192$		−	6.13938i		−	0.443072i
$193$	−14.6171	+	14.6171i	−1.05216	+	1.05216i	−0.0536001	+	0.998562i	$0.517070\pi$
$193$	−14.6171	+	14.6171i	−1.05216	+	1.05216i	−0.998562	+	0.0536001i	$0.982930\pi$
$194$	4.90269			0.351992
$195$	3.45693	+	3.06970i	0.247556	+	0.219826i
$196$	−6.81846			−0.487033
$197$	8.23994	+	8.23994i	0.587071	+	0.587071i	0.936837	−	0.349766i	$-0.113739\pi$
$197$	8.23994	+	8.23994i	0.587071	+	0.587071i	−0.349766	+	0.936837i	$0.613739\pi$
$198$	0.0836901	+	0.935421i	0.00594760	+	0.0664774i
$199$			5.16520i			0.366151i	0.983099	+	0.183076i	$0.0586054\pi$
$199$			5.16520i			0.366151i	−0.983099	+	0.183076i	$0.941395\pi$
$200$	2.63391	+	2.63391i	0.186245	+	0.186245i
$201$	−2.76558	+	2.76558i	−0.195069	+	0.195069i
$202$	3.07618	+	3.07618i	0.216439	+	0.216439i
$203$	−18.2880	−	18.2880i	−1.28357	−	1.28357i
$204$			5.28164i			0.369789i
$205$	1.78631			0.124761
$206$	−0.228916	+	0.228916i	−0.0159493	+	0.0159493i
$207$		−	7.57062i		−	0.526194i
$208$	−0.752826	−	12.6884i	−0.0521991	−	0.879785i
$209$	2.32797	+	26.0201i	0.161029	+	1.79985i
$210$	−0.833973	+	0.833973i	−0.0575496	+	0.0575496i
$211$		−	18.1695i		−	1.25084i	−0.780290	−	0.625418i	$-0.784928\pi$
$211$		−	18.1695i		−	1.25084i	0.780290	−	0.625418i	$-0.215072\pi$
$212$			17.5368i			1.20443i
$213$	−3.33835	+	3.33835i	−0.228740	+	0.228740i
$214$	3.59005	−	3.59005i	0.245411	−	0.245411i
$215$	5.22659	−	5.22659i	0.356450	−	0.356450i
$216$	−0.784861	+	0.784861i	−0.0534030	+	0.0534030i
$217$		−	4.55795i		−	0.309413i
$218$			1.62206i			0.109860i
$219$	5.69171	−	5.69171i	0.384610	−	0.384610i
$220$	0.727542	+	8.13187i	0.0490508	+	0.548250i
$221$	0.587494	+	9.90188i	0.0395191	+	0.666072i
$222$		−	0.525582i		−	0.0352748i
$223$	1.20158	−	1.20158i	0.0804640	−	0.0804640i	−0.665729	−	0.746193i	$-0.731879\pi$
$223$	1.20158	−	1.20158i	0.0804640	−	0.0804640i	0.746193	+	0.665729i	$0.231879\pi$
$224$	10.4537			0.698466
$225$			3.35589i			0.223726i
$226$	3.02404	+	3.02404i	0.201156	+	0.201156i
$227$	13.2914	+	13.2914i	0.882181	+	0.882181i	0.993756	−	0.111575i	$-0.0355896\pi$
$227$	13.2914	+	13.2914i	0.882181	+	0.882181i	−0.111575	+	0.993756i	$0.535590\pi$
$228$	−10.6928	+	10.6928i	−0.708145	+	0.708145i
$229$	−18.2271	−	18.2271i	−1.20448	−	1.20448i	−0.972790	−	0.231689i	$-0.925575\pi$
$229$	−18.2271	−	18.2271i	−1.20448	−	1.20448i	−0.231689	−	0.972790i	$-0.574425\pi$
$230$			2.74877i			0.181249i
$231$	10.7306	−	0.960046i	0.706023	−	0.0631664i
$232$	6.24905	+	6.24905i	0.410270	+	0.410270i
$233$	6.70887			0.439513			0.219756	−	0.975555i	$-0.429474\pi$
$233$	6.70887			0.439513			0.219756	+	0.975555i	$0.429474\pi$
$234$	−0.677910	+	0.763427i	−0.0443164	+	0.0499068i
$235$	2.07551			0.135391
$236$	8.53387	−	8.53387i	0.555507	−	0.555507i
$237$			5.17350i			0.336055i
$238$	−2.53052			−0.164029
$239$	−14.1784	−	14.1784i	−0.917126	−	0.917126i	0.0796933	−	0.996819i	$-0.474606\pi$
$239$	−14.1784	−	14.1784i	−0.917126	−	0.917126i	−0.996819	+	0.0796933i	$0.974606\pi$
$240$	−3.19632	+	3.19632i	−0.206322	+	0.206322i
$241$	16.5905	−	16.5905i	1.06869	−	1.06869i	0.0712280	−	0.997460i	$-0.477308\pi$
$241$	16.5905	−	16.5905i	1.06869	−	1.06869i	0.997460	−	0.0712280i	$-0.0226918\pi$
$242$	−1.77656	+	2.55852i	−0.114201	+	0.164468i
$243$	−1.00000			−0.0641500
$244$	6.54114			0.418753
$245$	3.22015	+	3.22015i	0.205728	+	0.205728i
$246$			0.394487i			0.0251516i
$247$	−18.8571	+	21.2359i	−1.19985	+	1.35121i
$248$			1.55746i			0.0988989i
$249$	6.70505	+	6.70505i	0.424915	+	0.424915i
$250$		−	3.03389i		−	0.191880i
$251$			17.1485i			1.08240i	0.840893	+	0.541202i	$0.182031\pi$
$251$			17.1485i			1.08240i	−0.840893	+	0.541202i	$0.817969\pi$
$252$	4.40965	+	4.40965i	0.277782	+	0.277782i
$253$	16.1019	−	19.2662i	1.01232	−	1.21126i
$254$	−4.11955	−	4.11955i	−0.258484	−	0.258484i
$255$	2.49436	−	2.49436i	0.156203	−	0.156203i
$256$	9.96393			0.622745
$257$			10.0555i			0.627245i	0.949548	+	0.313622i	$0.101543\pi$
$257$			10.0555i			0.627245i	−0.949548	+	0.313622i	$0.898457\pi$
$258$	1.15424	+	1.15424i	0.0718596	+	0.0718596i
$259$	−6.02918			−0.374635
$260$	−5.89326	+	6.63668i	−0.365484	+	0.411589i
$261$			7.96199i			0.492835i
$262$	2.93108	−	2.93108i	0.181083	−	0.181083i
$263$			11.1981i			0.690504i	0.938510	+	0.345252i	$0.112207\pi$
$263$			11.1981i			0.690504i	−0.938510	+	0.345252i	$0.887793\pi$
$264$	−3.66668	+	0.328050i	−0.225668	+	0.0201901i
$265$	8.28210	−	8.28210i	0.508766	−	0.508766i
$266$	−5.12308	−	5.12308i	−0.314116	−	0.314116i
$267$	−3.99735	−	3.99735i	−0.244634	−	0.244634i
$268$	−5.30941	−	5.30941i	−0.324324	−	0.324324i
$269$	−8.41449			−0.513040			−0.256520	−	0.966539i	$-0.582576\pi$
$269$	−8.41449			−0.513040			−0.256520	+	0.966539i	$0.582576\pi$
$270$	0.363084			0.0220966
$271$	16.1509	−	16.1509i	0.981100	−	0.981100i	−0.0187243	−	0.999825i	$-0.505960\pi$
$271$	16.1509	−	16.1509i	0.981100	−	0.981100i	0.999825	+	0.0187243i	$0.00596049\pi$
$272$	−9.69859			−0.588063
$273$	8.75760	+	7.77660i	0.530034	+	0.470661i
$274$		−	0.348341i		−	0.0210440i
$275$	−7.13761	+	8.54028i	−0.430414	+	0.514998i
$276$	14.5342			0.874856
$277$	1.72895			0.103883			0.0519414	−	0.998650i	$-0.483459\pi$
$277$	1.72895			0.103883			0.0519414	+	0.998650i	$0.483459\pi$
$278$	−2.46501	+	2.46501i	−0.147841	+	0.147841i
$279$	−0.992189	+	0.992189i	−0.0594008	+	0.0594008i
$280$	−3.26902	−	3.26902i	−0.195361	−	0.195361i
$281$	−12.4273	+	12.4273i	−0.741352	+	0.741352i	−0.972838	−	0.231486i	$-0.925641\pi$
$281$	−12.4273	+	12.4273i	−0.741352	+	0.741352i	0.231486	+	0.972838i	$0.425641\pi$
$282$			0.458354i			0.0272946i
$283$	10.9404			0.650341			0.325170	−	0.945655i	$-0.394578\pi$
$283$	10.9404			0.650341			0.325170	+	0.945655i	$0.394578\pi$
$284$	−6.40902	−	6.40902i	−0.380305	−	0.380305i
$285$	10.0997			0.598257
$286$	−3.34891	+	0.500976i	−0.198025	+	0.0296233i
$287$	4.52533			0.267122
$288$	−2.27559	−	2.27559i	−0.134091	−	0.134091i
$289$	−9.43136			−0.554786
$290$		−	2.89087i		−	0.169758i
$291$	−12.2427	+	12.2427i	−0.717680	+	0.717680i
$292$	10.9270	+	10.9270i	0.639457	+	0.639457i
$293$	−7.32526	+	7.32526i	−0.427947	+	0.427947i	−0.887928	−	0.459982i	$-0.847856\pi$
$293$	−7.32526	+	7.32526i	−0.427947	+	0.427947i	0.459982	+	0.887928i	$0.347856\pi$
$294$	−0.711137	+	0.711137i	−0.0414743	+	0.0414743i
$295$	−8.06059			−0.469305
$296$	2.06019			0.119746
$297$	−2.54486	−	2.12689i	−0.147668	−	0.123415i
$298$			0.469903i			0.0272208i
$299$	27.2483	−	1.61669i	1.57581	−	0.0934955i
$300$	−6.44269			−0.371969
$301$	13.2407	−	13.2407i	0.763184	−	0.763184i
$302$	−2.68463			−0.154483
$303$	−15.3633			−0.882600
$304$	−19.6349	−	19.6349i	−1.12614	−	1.12614i
$305$	−3.08919	−	3.08919i	−0.176886	−	0.176886i
$306$	0.550853	+	0.550853i	0.0314902	+	0.0314902i
$307$	11.5989	−	11.5989i	0.661981	−	0.661981i	−0.293865	−	0.955847i	$-0.594942\pi$
$307$	11.5989	−	11.5989i	0.661981	−	0.661981i	0.955847	+	0.293865i	$0.0949417\pi$
$308$	1.84311	+	20.6008i	0.105021	+	1.17384i
$309$		−	1.14327i		−	0.0650384i
$310$	0.360248	−	0.360248i	0.0204607	−	0.0204607i
$311$		−	19.0560i		−	1.08056i	−0.841484	−	0.540282i	$-0.818318\pi$
$311$		−	19.0560i		−	1.08056i	0.841484	−	0.540282i	$-0.181682\pi$
$312$	−2.99249	−	2.65728i	−0.169417	−	0.150439i
$313$	26.5255			1.49931			0.749655	−	0.661829i	$-0.230219\pi$
$313$	26.5255			1.49931			0.749655	+	0.661829i	$0.230219\pi$
$314$	1.95895	+	1.95895i	0.110550	+	0.110550i
$315$		−	4.16510i		−	0.234677i
$316$	−9.93216			−0.558728
$317$	15.6418	−	15.6418i	0.878528	−	0.878528i	−0.114854	−	0.993382i	$-0.536640\pi$
$317$	15.6418	−	15.6418i	0.878528	−	0.878528i	0.993382	+	0.114854i	$0.0366400\pi$
$318$	1.82901	+	1.82901i	0.102566	+	0.102566i
$319$	−16.9343	+	20.2622i	−0.948138	+	1.13446i
$320$	−5.56641	−	5.56641i	−0.311172	−	0.311172i
$321$			17.9297i			1.00074i
$322$			6.96358i			0.388065i
$323$	15.3228	+	15.3228i	0.852584	+	0.852584i
$324$		−	1.91982i		−	0.106656i
$325$	−12.0786	+	0.716642i	−0.670000	+	0.0397522i
$326$			5.23985i			0.290209i
$327$	−4.05051	−	4.05051i	−0.223993	−	0.223993i
$328$	−1.54632			−0.0853810
$329$	5.25798			0.289882
$330$	0.924000	+	0.772241i	0.0508645	+	0.0425104i
$331$	18.7281	−	18.7281i	1.02939	−	1.02939i	0.0298324	−	0.999555i	$-0.490503\pi$
$331$	18.7281	−	18.7281i	1.02939	−	1.02939i	0.999555	−	0.0298324i	$-0.00949736\pi$
$332$	−12.8725	+	12.8725i	−0.706468	+	0.706468i
$333$	1.31245	+	1.31245i	0.0719220	+	0.0719220i
$334$	0.235787			0.0129017
$335$			5.01495i			0.273996i
$336$	−8.09738	+	8.09738i	−0.441748	+	0.441748i
$337$	−10.9910			−0.598717			−0.299359	−	0.954141i	$-0.596773\pi$
$337$	−10.9910			−0.598717			−0.299359	+	0.954141i	$0.596773\pi$
$338$	−2.89251	−	2.27692i	−0.157332	−	0.123848i
$339$	−15.1029			−0.820276
$340$	4.78872	+	4.78872i	0.259705	+	0.259705i
$341$	−4.63527	+	0.414708i	−0.251014	+	0.0224577i
$342$			2.23042i			0.120607i
$343$	−7.92063	−	7.92063i	−0.427674	−	0.427674i
$344$	−4.52439	+	4.52439i	−0.243939	+	0.243939i
$345$	−6.86407	−	6.86407i	−0.369549	−	0.369549i
$346$	0.979156	+	0.979156i	0.0526398	+	0.0526398i
$347$		−	35.0449i		−	1.88131i	−0.339367	−	0.940654i	$-0.610213\pi$
$347$		−	35.0449i		−	1.88131i	0.339367	−	0.940654i	$-0.389787\pi$
$348$	−15.2856			−0.819392
$349$	−5.59377	+	5.59377i	−0.299428	+	0.299428i	−0.840790	−	0.541362i	$-0.817909\pi$
$349$	−5.59377	+	5.59377i	−0.299428	+	0.299428i	0.541362	+	0.840790i	$0.317909\pi$
$350$		−	3.08680i		−	0.164997i
$351$	−0.213548	−	3.59922i	−0.0113983	−	0.192112i
$352$	−0.951135	−	10.6310i	−0.0506957	−	0.566635i
$353$	10.5592	−	10.5592i	0.562007	−	0.562007i	−0.367870	−	0.929877i	$-0.619913\pi$
$353$	10.5592	−	10.5592i	0.562007	−	0.562007i	0.929877	+	0.367870i	$0.119913\pi$
$354$		−	1.78009i		−	0.0946109i
$355$			6.05358i			0.321290i
$356$	7.67418	−	7.67418i	0.406731	−	0.406731i
$357$	6.31907	−	6.31907i	0.334441	−	0.334441i
$358$	0.938593	−	0.938593i	0.0496062	−	0.0496062i
$359$	3.13684	−	3.13684i	0.165556	−	0.165556i	−0.619467	−	0.785023i	$-0.712651\pi$
$359$	3.13684	−	3.13684i	0.165556	−	0.165556i	0.785023	+	0.619467i	$0.212651\pi$
$360$			1.42322i			0.0750105i
$361$			43.0425i			2.26539i
$362$	0.533682	−	0.533682i	0.0280497	−	0.0280497i
$363$	−1.95266	−	10.8253i	−0.102488	−	0.568181i
$364$	−14.9296	+	16.8130i	−0.782526	+	0.881240i
$365$		−	10.3210i		−	0.540228i
$366$	0.682214	−	0.682214i	0.0356599	−	0.0356599i
$367$	−18.3746			−0.959148			−0.479574	−	0.877501i	$-0.659209\pi$
$367$	−18.3746			−0.959148			−0.479574	+	0.877501i	$0.659209\pi$
$368$			26.6889i			1.39126i
$369$	−0.985090	−	0.985090i	−0.0512817	−	0.0512817i
$370$	−0.476531	−	0.476531i	−0.0247737	−	0.0247737i
$371$	20.9814	−	20.9814i	1.08930	−	1.08930i
$372$	−1.90482	−	1.90482i	−0.0987604	−	0.0987604i
$373$		−	36.4916i		−	1.88947i	−0.327841	−	0.944733i	$-0.606321\pi$
$373$		−	36.4916i		−	1.88947i	0.327841	−	0.944733i	$-0.393679\pi$
$374$	0.230241	+	2.57345i	0.0119055	+	0.133070i
$375$	7.57606	+	7.57606i	0.391226	+	0.391226i
$376$	−1.79666			−0.0926558
$377$	−28.6570	+	1.70026i	−1.47591	+	0.0875680i
$378$	0.919817			0.0473103
$379$	−6.95342	+	6.95342i	−0.357173	+	0.357173i	−0.862770	−	0.505597i	$-0.831272\pi$
$379$	−6.95342	+	6.95342i	−0.357173	+	0.357173i	0.505597	+	0.862770i	$0.331272\pi$
$380$			19.3896i			0.994668i
$381$	20.5742			1.05405
$382$	1.45221	+	1.45221i	0.0743013	+	0.0743013i
$383$	13.1241	−	13.1241i	0.670610	−	0.670610i	−0.287247	−	0.957857i	$-0.592740\pi$
$383$	13.1241	−	13.1241i	0.670610	−	0.670610i	0.957857	+	0.287247i	$0.0927400\pi$
$384$	5.78047	−	5.78047i	0.294983	−	0.294983i
$385$	8.85871	−	10.5996i	0.451482	−	0.540206i
$386$	−5.85354			−0.297937
$387$	−5.76458			−0.293030
$388$	−23.5037	−	23.5037i	−1.19322	−	1.19322i
$389$			1.41409i			0.0716971i	0.999357	+	0.0358486i	$0.0114134\pi$
$389$			1.41409i			0.0716971i	−0.999357	+	0.0358486i	$0.988587\pi$
$390$	0.0775358	+	1.30682i	0.00392618	+	0.0661734i
$391$		−	20.8276i		−	1.05330i
$392$	−2.78753	−	2.78753i	−0.140791	−	0.140791i
$393$			14.6387i			0.738422i
$394$			3.29975i			0.166239i
$395$	4.69067	+	4.69067i	0.236013	+	0.236013i
$396$	4.08324	−	4.88567i	0.205191	−	0.245514i
$397$	5.68404	+	5.68404i	0.285274	+	0.285274i	0.835208	−	0.549934i	$-0.185347\pi$
$397$	5.68404	+	5.68404i	0.285274	+	0.285274i	−0.549934	+	0.835208i	$0.685347\pi$
$398$	−1.03422	+	1.03422i	−0.0518409	+	0.0518409i
$399$	25.5861			1.28091
$400$		−	11.8306i		−	0.591531i
$401$	20.8615	+	20.8615i	1.04177	+	1.04177i	0.999089	+	0.0426848i	$0.0135911\pi$
$401$	20.8615	+	20.8615i	1.04177	+	1.04177i	0.0426848	+	0.999089i	$0.486409\pi$
$402$	−1.10750			−0.0552370
$403$	−3.78299	−	3.35923i	−0.188444	−	0.167335i
$404$		−	29.4948i		−	1.46742i
$405$	−0.906673	+	0.906673i	−0.0450529	+	0.0450529i
$406$		−	7.32357i		−	0.363463i
$407$	0.548569	+	6.13146i	0.0271916	+	0.303925i
$408$	−2.15924	+	2.15924i	−0.106898	+	0.106898i
$409$	−6.82197	−	6.82197i	−0.337324	−	0.337324i	0.518035	−	0.855359i	$-0.326664\pi$
$409$	−6.82197	−	6.82197i	−0.337324	−	0.337324i	−0.855359	+	0.518035i	$0.826664\pi$
$410$	0.357670	+	0.357670i	0.0176641	+	0.0176641i
$411$	0.869856	+	0.869856i	0.0429068	+	0.0429068i
$412$	2.19487			0.108133
$413$	−20.4202			−1.00481
$414$	1.51586	−	1.51586i	0.0745003	−	0.0745003i
$415$	12.1586			0.596841
$416$	7.70442	−	8.67632i	0.377740	−	0.425391i
$417$		−	12.3110i		−	0.602870i
$418$	−4.74386	+	5.67611i	−0.232030	+	0.277628i
$419$	9.18831			0.448878			0.224439	−	0.974488i	$-0.427945\pi$
$419$	9.18831			0.448878			0.224439	+	0.974488i	$0.427945\pi$
$420$	7.99622			0.390176
$421$	−0.464501	+	0.464501i	−0.0226384	+	0.0226384i	−0.718335	−	0.695697i	$-0.755096\pi$
$421$	−0.464501	+	0.464501i	−0.0226384	+	0.0226384i	0.695697	+	0.718335i	$0.255096\pi$
$422$	3.63805	−	3.63805i	0.177098	−	0.177098i
$423$	−1.14457	−	1.14457i	−0.0556511	−	0.0556511i
$424$	−7.16940	+	7.16940i	−0.348177	+	0.348177i
$425$			9.23244i			0.447839i
$426$	−1.33687			−0.0647714
$427$	−7.82597	−	7.82597i	−0.378725	−	0.378725i
$428$	−34.4218			−1.66384
$429$	7.11170	−	9.61372i	0.343356	−	0.464155i
$430$	2.09303			0.100935
$431$	−19.1843	−	19.1843i	−0.924078	−	0.924078i	0.0732370	−	0.997315i	$-0.476667\pi$
$431$	−19.1843	−	19.1843i	−0.924078	−	0.924078i	−0.997315	+	0.0732370i	$0.976667\pi$
$432$	3.52533			0.169613
$433$			3.17248i			0.152460i	0.997090	+	0.0762298i	$0.0242882\pi$
$433$			3.17248i			0.152460i	−0.997090	+	0.0762298i	$0.975712\pi$
$434$	0.912632	−	0.912632i	0.0438078	−	0.0438078i
$435$	7.21891	+	7.21891i	0.346120	+	0.346120i
$436$	7.77623	−	7.77623i	0.372414	−	0.372414i
$437$	42.1659	−	42.1659i	2.01707	−	2.01707i
$438$	2.27929			0.108909
$439$	−18.4845			−0.882218			−0.441109	−	0.897453i	$-0.645415\pi$
$439$	−18.4845			−0.882218			−0.441109	+	0.897453i	$0.645415\pi$
$440$	−3.02704	+	3.62191i	−0.144309	+	0.172668i
$441$		−	3.55162i		−	0.169125i
$442$	−1.86501	+	2.10028i	−0.0887094	+	0.0998999i
$443$	−16.2499			−0.772055			−0.386027	−	0.922487i	$-0.626153\pi$
$443$	−16.2499			−0.772055			−0.386027	+	0.922487i	$0.626153\pi$
$444$	−2.51967	+	2.51967i	−0.119578	+	0.119578i
$445$	−7.24858			−0.343616
$446$	0.481184			0.0227847
$447$	−1.17341	−	1.17341i	−0.0555006	−	0.0555006i
$448$	−14.1016	−	14.1016i	−0.666239	−	0.666239i
$449$	−20.8070	−	20.8070i	−0.981941	−	0.981941i	0.0178985	−	0.999840i	$-0.494302\pi$
$449$	−20.8070	−	20.8070i	−0.981941	−	0.981941i	−0.999840	+	0.0178985i	$0.994302\pi$
$450$	−0.671946	+	0.671946i	−0.0316758	+	0.0316758i
$451$	−0.411740	−	4.60210i	−0.0193881	−	0.216704i
$452$		−	28.9948i		−	1.36380i
$453$	6.70391	−	6.70391i	0.314977	−	0.314977i
$454$			5.32264i			0.249804i
$455$	14.9911	−	0.889447i	0.702794	−	0.0416979i
$456$	−8.74283			−0.409421
$457$	13.3026	+	13.3026i	0.622270	+	0.622270i	0.946111	−	0.323841i	$-0.104974\pi$
$457$	13.3026	+	13.3026i	0.622270	+	0.622270i	−0.323841	+	0.946111i	$0.604974\pi$
$458$		−	7.29918i		−	0.341068i
$459$	−2.75112			−0.128411
$460$	13.1778	−	13.1778i	0.614416	−	0.614416i
$461$	18.8391	+	18.8391i	0.877424	+	0.877424i	0.993267	−	0.115844i	$-0.0369572\pi$
$461$	18.8391	+	18.8391i	0.877424	+	0.877424i	−0.115844	+	0.993267i	$0.536957\pi$
$462$	2.34081	+	1.95635i	0.108904	+	0.0910177i
$463$	7.82301	+	7.82301i	0.363566	+	0.363566i	0.865124	−	0.501558i	$-0.167240\pi$
$463$	7.82301	+	7.82301i	0.363566	+	0.363566i	−0.501558	+	0.865124i	$0.667240\pi$
$464$		−	28.0686i		−	1.30305i
$465$			1.79918i			0.0834351i
$466$	1.34331	+	1.34331i	0.0622276	+	0.0622276i
$467$		−	24.6783i		−	1.14197i	−0.820959	−	0.570987i	$-0.806561\pi$
$467$		−	24.6783i		−	1.14197i	0.820959	−	0.570987i	$-0.193439\pi$
$468$	6.90985	−	0.409972i	0.319408	−	0.0189510i
$469$			12.7046i			0.586644i
$470$	0.415577	+	0.415577i	0.0191691	+	0.0191691i
$471$	−9.78356			−0.450803
$472$	6.97764			0.321172
$473$	−14.6701	−	12.2606i	−0.674531	−	0.563745i
$474$	−1.03588	+	1.03588i	−0.0475797	+	0.0475797i
$475$	−18.6912	+	18.6912i	−0.857611	+	0.857611i
$476$	12.1315	+	12.1315i	0.556045	+	0.556045i
$477$	−9.13461			−0.418245
$478$		−	5.67786i		−	0.259699i
$479$	15.2582	−	15.2582i	0.697165	−	0.697165i	−0.266633	−	0.963798i	$-0.585911\pi$
$479$	15.2582	−	15.2582i	0.697165	−	0.697165i	0.963798	+	0.266633i	$0.0859111\pi$
$480$	−4.12644			−0.188345
$481$	−4.44354	+	5.00408i	−0.202608	+	0.228166i
$482$	6.64380			0.302617
$483$	−17.3890	−	17.3890i	−0.791229	−	0.791229i
$484$	20.7826	−	3.74876i	0.944663	−	0.170398i
$485$			22.2002i			1.00806i
$486$	−0.200229	−	0.200229i	−0.00908257	−	0.00908257i
$487$	13.9118	−	13.9118i	0.630402	−	0.630402i	−0.317767	−	0.948169i	$-0.602933\pi$
$487$	13.9118	−	13.9118i	0.630402	−	0.630402i	0.948169	+	0.317767i	$0.102933\pi$
$488$	2.67415	+	2.67415i	0.121053	+	0.121053i
$489$	−13.0847	−	13.0847i	−0.591709	−	0.591709i
$490$			1.28954i			0.0582553i
$491$	−6.99821			−0.315825			−0.157912	−	0.987453i	$-0.550476\pi$
$491$	−6.99821			−0.315825			−0.157912	+	0.987453i	$0.550476\pi$
$492$	1.89119	−	1.89119i	0.0852615	−	0.0852615i
$493$			21.9043i			0.986522i
$494$	−8.02777	+	0.476301i	−0.361187	+	0.0214298i
$495$	−4.23575	+	0.378964i	−0.190383	+	0.0170332i
$496$	3.49780	−	3.49780i	0.157056	−	0.157056i
$497$			15.3358i			0.687904i
$498$			2.68509i			0.120322i
$499$	27.3030	−	27.3030i	1.22225	−	1.22225i	0.255419	−	0.966830i	$-0.417787\pi$
$499$	27.3030	−	27.3030i	1.22225	−	1.22225i	0.966830	−	0.255419i	$-0.0822134\pi$
$500$	−14.5446	+	14.5446i	−0.650456	+	0.650456i
$501$	−0.588793	+	0.588793i	−0.0263053	+	0.0263053i
$502$	−3.43363	+	3.43363i	−0.153250	+	0.153250i
$503$			35.1457i			1.56707i	0.621348	+	0.783534i	$0.286585\pi$
$503$			35.1457i			1.56707i	−0.621348	+	0.783534i	$0.713415\pi$
$504$			3.60551i			0.160602i
$505$	−13.9295	+	13.9295i	−0.619855	+	0.619855i
$506$	7.08171	−	0.633586i	0.314820	−	0.0281663i
$507$	12.9088	−	1.53721i	0.573300	−	0.0682699i
$508$			39.4987i			1.75247i
$509$	−17.6178	+	17.6178i	−0.780897	+	0.780897i	−0.979982	−	0.199085i	$-0.936203\pi$
$509$	−17.6178	+	17.6178i	−0.780897	+	0.780897i	0.199085	+	0.979982i	$0.436203\pi$
$510$	0.998886			0.0442314
$511$		−	26.1467i		−	1.15666i
$512$	13.5560	+	13.5560i	0.599096	+	0.599096i
$513$	−5.56967	−	5.56967i	−0.245907	−	0.245907i
$514$	−2.01340	+	2.01340i	−0.0888073	+	0.0888073i
$515$	−1.03657	−	1.03657i	−0.0456768	−	0.0456768i
$516$		−	11.0669i		−	0.487195i
$517$	−0.478401	−	5.34717i	−0.0210400	−	0.235168i
$518$	−1.20722	−	1.20722i	−0.0530420	−	0.0530420i
$519$	−4.89018			−0.214655
$520$	−5.12250	+	0.303926i	−0.224636	+	0.0133280i
$521$	−41.6695			−1.82558			−0.912788	−	0.408434i	$-0.866075\pi$
$521$	−41.6695			−1.82558			−0.912788	+	0.408434i	$0.866075\pi$
$522$	−1.59422	+	1.59422i	−0.0697771	+	0.0697771i
$523$			18.5602i			0.811580i	0.913966	+	0.405790i	$0.133004\pi$
$523$			18.5602i			0.811580i	−0.913966	+	0.405790i	$0.866996\pi$
$524$	−28.1035			−1.22771
$525$	7.70819	+	7.70819i	0.336413	+	0.336413i
$526$	−2.24218	+	2.24218i	−0.0977638	+	0.0977638i
$527$	−2.72963	+	2.72963i	−0.118904	+	0.118904i
$528$	8.97148	+	7.49799i	0.390434	+	0.326308i
$529$	−34.3142			−1.49192
$530$	3.31663			0.144065
$531$	4.44515	+	4.44515i	0.192903	+	0.192903i
$532$			49.1206i			2.12965i
$533$	3.33519	−	3.75592i	0.144463	−	0.162687i
$534$		−	1.60077i		−	0.0692721i
$535$	16.2564	+	16.2564i	0.702825	+	0.702825i
$536$		−	4.34119i		−	0.187511i
$537$			4.68760i			0.202285i
$538$	−1.68482	−	1.68482i	−0.0726379	−	0.0726379i
$539$	7.55391	−	9.03839i	0.325370	−	0.389311i
$540$	−1.74065	−	1.74065i	−0.0749054	−	0.0749054i
$541$	11.4748	−	11.4748i	0.493342	−	0.493342i	−0.416016	−	0.909357i	$-0.636574\pi$
$541$	11.4748	−	11.4748i	0.493342	−	0.493342i	0.909357	+	0.416016i	$0.136574\pi$
$542$	6.46777			0.277815
$543$			2.66536i			0.114381i
$544$	−6.26042	−	6.26042i	−0.268413	−	0.268413i
$545$	−7.34497			−0.314624
$546$	0.196425	+	3.31062i	0.00840620	+	0.141682i
$547$			21.5393i			0.920955i	0.887671	+	0.460477i	$0.152322\pi$
$547$			21.5393i			0.920955i	−0.887671	+	0.460477i	$0.847678\pi$
$548$	−1.66996	+	1.66996i	−0.0713373	+	0.0713373i
$549$			3.40717i			0.145414i
$550$	−3.13917	+	0.280855i	−0.133855	+	0.0119757i
$551$	−44.3457	+	44.3457i	−1.88919	+	1.88919i
$552$	5.94188	+	5.94188i	0.252903	+	0.252903i
$553$	11.8831	+	11.8831i	0.505320	+	0.505320i
$554$	0.346187	+	0.346187i	0.0147081	+	0.0147081i
$555$	2.37993			0.101022
$556$	23.6348			1.00234
$557$	−17.0126	+	17.0126i	−0.720846	+	0.720846i	−0.968778	−	0.247931i	$-0.920249\pi$
$557$	−17.0126	+	17.0126i	−0.720846	+	0.720846i	0.247931	+	0.968778i	$0.420249\pi$
$558$	−0.397330			−0.0168203
$559$	−1.23101	−	20.7480i	−0.0520663	−	0.877547i
$560$			14.6833i			0.620484i
$561$	−7.00121	−	5.85132i	−0.295592	−	0.247043i
$562$	−4.97662			−0.209926
$563$	−8.16106			−0.343948			−0.171974	−	0.985102i	$-0.555014\pi$
$563$	−8.16106			−0.343948			−0.171974	+	0.985102i	$0.555014\pi$
$564$	2.19737	−	2.19737i	0.0925261	−	0.0925261i
$565$	−13.6934	+	13.6934i	−0.576085	+	0.576085i
$566$	2.19059	+	2.19059i	0.0920773	+	0.0920773i
$567$	−2.29691	+	2.29691i	−0.0964613	+	0.0964613i
$568$		−	5.24028i		−	0.219877i
$569$	41.5601			1.74229			0.871145	−	0.491025i	$-0.163378\pi$
$569$	41.5601			1.74229			0.871145	+	0.491025i	$0.163378\pi$
$570$	2.02226	+	2.02226i	0.0847031	+	0.0847031i
$571$	22.2058			0.929283			0.464642	−	0.885499i	$-0.346183\pi$
$571$	22.2058			0.929283			0.464642	+	0.885499i	$0.346183\pi$
$572$	18.4566	+	13.6532i	0.771709	+	0.570868i
$573$	−7.25273			−0.302987
$574$	0.906102	+	0.906102i	0.0378200	+	0.0378200i
$575$	25.4062			1.05951
$576$			6.13938i			0.255808i
$577$	15.5097	−	15.5097i	0.645676	−	0.645676i	−0.306269	−	0.951945i	$-0.599081\pi$
$577$	15.5097	−	15.5097i	0.645676	−	0.645676i	0.951945	+	0.306269i	$0.0990808\pi$
$578$	−1.88843	−	1.88843i	−0.0785484	−	0.0785484i
$579$	14.6171	−	14.6171i	0.607466	−	0.607466i
$580$	−13.8590	+	13.8590i	−0.575463	+	0.575463i
$581$	30.8018			1.27788
$582$	−4.90269			−0.203223
$583$	−23.2464	−	19.4283i	−0.962765	−	0.804639i
$584$			8.93440i			0.369708i
$585$	−3.45693	−	3.06970i	−0.142927	−	0.126916i
$586$	−2.93346			−0.121180
$587$	3.39319	−	3.39319i	0.140052	−	0.140052i	−0.633605	−	0.773657i	$-0.718426\pi$
$587$	3.39319	−	3.39319i	0.140052	−	0.140052i	0.773657	+	0.633605i	$0.218426\pi$
$588$	6.81846			0.281188
$589$	−11.0523			−0.455404
$590$	−1.61396	−	1.61396i	−0.0664458	−	0.0664458i
$591$	−8.23994	−	8.23994i	−0.338946	−	0.338946i
$592$	−4.62683	−	4.62683i	−0.190162	−	0.190162i
$593$	−30.6929	+	30.6929i	−1.26041	+	1.26041i	−0.309509	+	0.950896i	$0.600165\pi$
$593$	−30.6929	+	30.6929i	−1.26041	+	1.26041i	−0.950896	+	0.309509i	$0.899835\pi$
$594$	−0.0836901	−	0.935421i	−0.00343385	−	0.0383808i
$595$		−	11.4587i		−	0.469759i
$596$	2.25274	−	2.25274i	0.0922759	−	0.0922759i
$597$		−	5.16520i		−	0.211398i
$598$	5.77961	+	5.13220i	0.236346	+	0.209871i
$599$	28.4738			1.16341			0.581704	−	0.813401i	$-0.302386\pi$
$599$	28.4738			1.16341			0.581704	+	0.813401i	$0.302386\pi$
$600$	−2.63391	−	2.63391i	−0.107529	−	0.107529i
$601$		−	18.5698i		−	0.757478i	−0.925504	−	0.378739i	$-0.876358\pi$
$601$		−	18.5698i		−	0.757478i	0.925504	−	0.378739i	$-0.123642\pi$
$602$	5.30236			0.216108
$603$	2.76558	−	2.76558i	0.112623	−	0.112623i
$604$	12.8703	+	12.8703i	0.523684	+	0.523684i
$605$	−11.5854	−	8.04457i	−0.471015	−	0.327058i
$606$	−3.07618	−	3.07618i	−0.124961	−	0.124961i
$607$			29.1845i			1.18456i	0.805732	+	0.592281i	$0.201772\pi$
$607$			29.1845i			1.18456i	−0.805732	+	0.592281i	$0.798228\pi$
$608$		−	25.3486i		−	1.02802i
$609$	18.2880	+	18.2880i	0.741067	+	0.741067i
$610$		−	1.23709i		−	0.0500883i
$611$	3.87516	−	4.36400i	0.156772	−	0.176549i
$612$		−	5.28164i		−	0.213498i
$613$	12.0502	+	12.0502i	0.486701	+	0.486701i	0.907264	−	0.420562i	$-0.138167\pi$
$613$	12.0502	+	12.0502i	0.486701	+	0.486701i	−0.420562	+	0.907264i	$0.638167\pi$
$614$	4.64485			0.187451
$615$	−1.78631			−0.0720309
$616$	−7.66854	+	9.17554i	−0.308974	+	0.369693i
$617$	17.7182	−	17.7182i	0.713306	−	0.713306i	−0.253919	−	0.967225i	$-0.581720\pi$
$617$	17.7182	−	17.7182i	0.713306	−	0.713306i	0.967225	+	0.253919i	$0.0817198\pi$
$618$	0.228916	−	0.228916i	0.00920834	−	0.00920834i
$619$	23.1102	+	23.1102i	0.928879	+	0.928879i	0.997634	−	0.0687547i	$-0.0219026\pi$
$619$	23.1102	+	23.1102i	0.928879	+	0.928879i	−0.0687547	+	0.997634i	$0.521903\pi$
$620$	−3.45410			−0.138720
$621$			7.57062i			0.303798i
$622$	3.81555	−	3.81555i	0.152990	−	0.152990i
$623$	−18.3631			−0.735704
$624$	0.752826	+	12.6884i	0.0301372	+	0.507944i
$625$	−3.04144			−0.121658
$626$	5.31117	+	5.31117i	0.212277	+	0.212277i
$627$	−2.32797	−	26.0201i	−0.0929701	−	1.03914i
$628$		−	18.7826i		−	0.749509i
$629$	3.61071	+	3.61071i	0.143968	+	0.143968i
$630$	0.833973	−	0.833973i	0.0332263	−	0.0332263i
$631$	−9.67918	−	9.67918i	−0.385322	−	0.385322i	0.487693	−	0.873015i	$-0.337838\pi$
$631$	−9.67918	−	9.67918i	−0.385322	−	0.385322i	−0.873015	+	0.487693i	$0.837838\pi$
$632$	−4.06047	−	4.06047i	−0.161517	−	0.161517i
$633$			18.1695i			0.722171i
$634$	6.26386			0.248770
$635$	18.6541	−	18.6541i	0.740264	−	0.740264i
$636$		−	17.5368i		−	0.695379i
$637$	12.7831	−	0.758440i	0.506483	−	0.0300505i
$638$	−7.44780	+	0.666340i	−0.294861	+	0.0263806i
$639$	3.33835	−	3.33835i	0.132063	−	0.132063i
$640$		−	10.4820i		−	0.414337i
$641$		−	35.8240i		−	1.41496i	−0.706733	−	0.707481i	$-0.749832\pi$
$641$		−	35.8240i		−	1.41496i	0.706733	−	0.707481i	$-0.250168\pi$
$642$	−3.59005	+	3.59005i	−0.141688	+	0.141688i
$643$	−30.1514	+	30.1514i	−1.18905	+	1.18905i	−0.211724	+	0.977329i	$0.567908\pi$
$643$	−30.1514	+	30.1514i	−1.18905	+	1.18905i	−0.977329	+	0.211724i	$0.932092\pi$
$644$	33.3838	−	33.3838i	1.31551	−	1.31551i
$645$	−5.22659	+	5.22659i	−0.205797	+	0.205797i
$646$			6.13614i			0.241423i
$647$			40.6491i			1.59808i	0.601277	+	0.799041i	$0.294659\pi$
$647$			40.6491i			1.59808i	−0.601277	+	0.799041i	$0.705341\pi$
$648$	0.784861	−	0.784861i	0.0308322	−	0.0308322i
$649$	1.85795	+	20.7666i	0.0729309	+	0.815162i
$650$	−2.56198	−	2.27499i	−0.100489	−	0.0892325i
$651$			4.55795i			0.178640i
$652$	25.1201	−	25.1201i	0.983781	−	0.983781i
$653$	−24.5160			−0.959385			−0.479692	−	0.877437i	$-0.659252\pi$
$653$	−24.5160			−0.959385			−0.479692	+	0.877437i	$0.659252\pi$
$654$		−	1.62206i		−	0.0634274i
$655$	13.2725	+	13.2725i	0.518598	+	0.518598i
$656$	3.47277	+	3.47277i	0.135589	+	0.135589i
$657$	−5.69171	+	5.69171i	−0.222055	+	0.222055i
$658$	1.05280	+	1.05280i	0.0410424	+	0.0410424i
$659$			23.4933i			0.915169i	0.889166	+	0.457585i	$0.151285\pi$
$659$			23.4933i			0.915169i	−0.889166	+	0.457585i	$0.848715\pi$
$660$	−0.727542	−	8.13187i	−0.0283195	−	0.316533i
$661$	9.69472	+	9.69472i	0.377081	+	0.377081i	0.870048	−	0.492967i	$-0.164088\pi$
$661$	9.69472	+	9.69472i	0.377081	+	0.377081i	−0.492967	+	0.870048i	$0.664088\pi$
$662$	7.49980			0.291488
$663$	−0.587494	−	9.90188i	−0.0228164	−	0.384557i
$664$	−10.5251			−0.408452
$665$	23.1982	−	23.1982i	0.899588	−	0.899588i
$666$			0.525582i			0.0203659i
$667$	60.2771			2.33394
$668$	−1.13038	−	1.13038i	−0.0437355	−	0.0437355i
$669$	−1.20158	+	1.20158i	−0.0464559	+	0.0464559i
$670$	−1.00414	+	1.00414i	−0.0387933	+	0.0387933i
$671$	−7.24668	+	8.67078i	−0.279755	+	0.334732i
$672$	−10.4537			−0.403260
$673$	18.3362			0.706810			0.353405	−	0.935470i	$-0.385024\pi$
$673$	18.3362			0.706810			0.353405	+	0.935470i	$0.385024\pi$
$674$	−2.20071	−	2.20071i	−0.0847683	−	0.0847683i
$675$		−	3.35589i		−	0.129168i
$676$	2.95116	+	24.7825i	0.113506	+	0.953174i
$677$		−	10.5449i		−	0.405273i	−0.979254	−	0.202637i	$-0.935049\pi$
$677$		−	10.5449i		−	0.405273i	0.979254	−	0.202637i	$-0.0649510\pi$
$678$	−3.02404	−	3.02404i	−0.116137	−	0.116137i
$679$			56.2408i			2.15833i
$680$			3.91545i			0.150151i
$681$	−13.2914	−	13.2914i	−0.509327	−	0.509327i
$682$	−1.01115	−	0.845078i	−0.0387190	−	0.0323597i
$683$	−10.1236	−	10.1236i	−0.387370	−	0.387370i	0.486379	−	0.873748i	$-0.338318\pi$
$683$	−10.1236	−	10.1236i	−0.387370	−	0.387370i	−0.873748	+	0.486379i	$0.838318\pi$
$684$	10.6928	−	10.6928i	0.408848	−	0.408848i
$685$	1.57735			0.0602674
$686$		−	3.17188i		−	0.121103i
$687$	18.2271	+	18.2271i	0.695406	+	0.695406i
$688$	20.3221			0.774771
$689$	−1.95068	−	32.8775i	−0.0743148	−	1.25253i
$690$		−	2.74877i		−	0.104644i
$691$	4.64437	−	4.64437i	0.176680	−	0.176680i	−0.613227	−	0.789907i	$-0.710129\pi$
$691$	4.64437	−	4.64437i	0.176680	−	0.176680i	0.789907	+	0.613227i	$0.210129\pi$
$692$		−	9.38826i		−	0.356888i
$693$	−10.7306	+	0.960046i	−0.407622	+	0.0364691i
$694$	7.01700	−	7.01700i	0.266362	−	0.266362i
$695$	−11.1620	−	11.1620i	−0.423399	−	0.423399i
$696$	−6.24905	−	6.24905i	−0.236870	−	0.236870i
$697$	−2.71010	−	2.71010i	−0.102652	−	0.102652i
$698$	−2.24007			−0.0847879
$699$	−6.70887			−0.253753
$700$	−14.7983	+	14.7983i	−0.559323	+	0.559323i
$701$	13.0755			0.493854			0.246927	−	0.969034i	$-0.420579\pi$
$701$	13.0755			0.493854			0.246927	+	0.969034i	$0.420579\pi$
$702$	0.677910	−	0.763427i	0.0255861	−	0.0288137i
$703$			14.6199i			0.551399i
$704$	−13.0578	+	15.6239i	−0.492134	+	0.588847i
$705$	−2.07551			−0.0781682
$706$	4.22850			0.159142
$707$	−35.2882	+	35.2882i	−1.32715	+	1.32715i
$708$	−8.53387	+	8.53387i	−0.320722	+	0.320722i
$709$	33.1325	+	33.1325i	1.24432	+	1.24432i	0.958192	+	0.286125i	$0.0923671\pi$
$709$	33.1325	+	33.1325i	1.24432	+	1.24432i	0.286125	+	0.958192i	$0.407633\pi$
$710$	−1.21210	+	1.21210i	−0.0454893	+	0.0454893i
$711$		−	5.17350i		−	0.194021i
$712$	6.27473			0.235155
$713$	7.51149	+	7.51149i	0.281307	+	0.281307i
$714$	2.53052			0.0947024
$715$	−2.26851	−	15.1645i	−0.0848375	−	0.567120i
$716$	−8.99933			−0.336321
$717$	14.1784	+	14.1784i	0.529503	+	0.529503i
$718$	1.25617			0.0468799
$719$		−	48.3812i		−	1.80431i	−0.431408	−	0.902157i	$-0.641983\pi$
$719$		−	48.3812i		−	1.80431i	0.431408	−	0.902157i	$-0.358017\pi$
$720$	3.19632	−	3.19632i	0.119120	−	0.119120i
$721$	−2.62599	−	2.62599i	−0.0977970	−	0.0977970i
$722$	−8.61835	+	8.61835i	−0.320742	+	0.320742i
$723$	−16.5905	+	16.5905i	−0.617007	+	0.617007i
$724$	−5.11700			−0.190172
$725$	−26.7195			−0.992339
$726$	1.77656	−	2.55852i	0.0659342	−	0.0949555i
$727$			29.6102i			1.09818i	0.835763	+	0.549090i	$0.185026\pi$
$727$			29.6102i			1.09818i	−0.835763	+	0.549090i	$0.814974\pi$
$728$	−12.9770	+	0.769949i	−0.480961	+	0.0285362i
$729$	1.00000			0.0370370
$730$	2.06657	−	2.06657i	0.0764872	−	0.0764872i
$731$	−15.8590			−0.586568
$732$	−6.54114			−0.241767
$733$	5.18957	+	5.18957i	0.191681	+	0.191681i	0.796422	−	0.604741i	$-0.206723\pi$
$733$	5.18957	+	5.18957i	0.191681	+	0.191681i	−0.604741	+	0.796422i	$0.706723\pi$
$734$	−3.67913	−	3.67913i	−0.135799	−	0.135799i
$735$	−3.22015	−	3.22015i	−0.118777	−	0.118777i
$736$	−17.2277	+	17.2277i	−0.635020	+	0.635020i
$737$	12.9201	−	1.15594i	0.475919	−	0.0425795i
$738$		−	0.394487i		−	0.0145213i
$739$	−11.8728	+	11.8728i	−0.436746	+	0.436746i	−0.890915	−	0.454169i	$-0.849936\pi$
$739$	−11.8728	+	11.8728i	−0.436746	+	0.436746i	0.454169	+	0.890915i	$0.349936\pi$
$740$			4.56903i			0.167961i
$741$	18.8571	−	21.2359i	0.692733	−	0.780119i
$742$	8.40217			0.308453
$743$	−19.4483	−	19.4483i	−0.713490	−	0.713490i	0.253774	−	0.967264i	$-0.418328\pi$
$743$	−19.4483	−	19.4483i	−0.713490	−	0.713490i	−0.967264	+	0.253774i	$0.918328\pi$
$744$		−	1.55746i		−	0.0570993i
$745$	−2.12781			−0.0779568
$746$	7.30668	−	7.30668i	0.267517	−	0.267517i
$747$	−6.70505	−	6.70505i	−0.245325	−	0.245325i
$748$	11.2335	−	13.4410i	0.410736	−	0.491453i
$749$	41.1830	+	41.1830i	1.50479	+	1.50479i
$750$			3.03389i			0.110782i
$751$		−	11.2205i		−	0.409441i	−0.978820	−	0.204720i	$-0.934371\pi$
$751$		−	11.2205i		−	0.409441i	0.978820	−	0.204720i	$-0.0656285\pi$
$752$	4.03500	+	4.03500i	0.147141	+	0.147141i
$753$		−	17.1485i		−	0.624926i
$754$	−6.07839	−	5.39751i	−0.221362	−	0.196566i
$755$		−	12.1565i		−	0.442420i
$756$	−4.40965	−	4.40965i	−0.160377	−	0.160377i
$757$	−32.0218			−1.16385			−0.581925	−	0.813242i	$-0.697700\pi$
$757$	−32.0218			−1.16385			−0.581925	+	0.813242i	$0.697700\pi$
$758$	−2.78455			−0.101139
$759$	−16.1019	+	19.2662i	−0.584461	+	0.699318i
$760$	−7.92689	+	7.92689i	−0.287538	+	0.287538i
$761$	−13.7620	+	13.7620i	−0.498872	+	0.498872i	−0.911087	−	0.412215i	$-0.864755\pi$
$761$	−13.7620	+	13.7620i	−0.498872	+	0.498872i	0.412215	+	0.911087i	$0.364755\pi$
$762$	4.11955	+	4.11955i	0.149236	+	0.149236i
$763$	−18.6073			−0.673630
$764$		−	13.9239i		−	0.503750i
$765$	−2.49436	+	2.49436i	−0.0901838	+	0.0901838i
$766$	5.25564			0.189894
$767$	−15.0498	+	16.9483i	−0.543417	+	0.611968i
$768$	−9.96393			−0.359542
$769$	−7.94411	−	7.94411i	−0.286472	−	0.286472i	0.549212	−	0.835683i	$-0.314928\pi$
$769$	−7.94411	−	7.94411i	−0.286472	−	0.286472i	−0.835683	+	0.549212i	$0.814928\pi$
$770$	3.89612	−	0.348577i	0.140406	−	0.0125619i
$771$		−	10.0555i		−	0.362140i
$772$	28.0622	+	28.0622i	1.00998	+	1.00998i
$773$	14.0695	−	14.0695i	0.506043	−	0.506043i	−0.407266	−	0.913310i	$-0.633518\pi$
$773$	14.0695	−	14.0695i	0.506043	−	0.506043i	0.913310	+	0.407266i	$0.133518\pi$
$774$	−1.15424	−	1.15424i	−0.0414882	−	0.0414882i
$775$	−3.32968	−	3.32968i	−0.119606	−	0.119606i
$776$		−	19.2176i		−	0.689873i
$777$	6.02918			0.216296
$778$	−0.283141	+	0.283141i	−0.0101511	+	0.0101511i
$779$		−	10.9733i		−	0.393158i
$780$	5.89326	−	6.63668i	0.211012	−	0.237631i
$781$	15.5959	−	1.39534i	0.558067	−	0.0499291i
$782$	4.17030	−	4.17030i	0.149130	−	0.149130i
$783$		−	7.96199i		−	0.284538i
$784$			12.5206i			0.447165i
$785$	−8.87049	+	8.87049i	−0.316601	+	0.316601i
$786$	−2.93108	+	2.93108i	−0.104548	+	0.104548i
$787$	10.9674	−	10.9674i	0.390947	−	0.390947i	−0.484078	−	0.875025i	$-0.660845\pi$
$787$	10.9674	−	10.9674i	0.390947	−	0.390947i	0.875025	+	0.484078i	$0.160845\pi$
$788$	15.8192	−	15.8192i	0.563535	−	0.563535i
$789$		−	11.1981i		−	0.398663i
$790$			1.87841i			0.0668310i
$791$	−34.6900	+	34.6900i	−1.23344	+	1.23344i
$792$	3.66668	−	0.328050i	0.130290	−	0.0116568i
$793$	−12.2632	+	0.727593i	−0.435477	+	0.0258376i
$794$			2.27622i			0.0807799i
$795$	−8.28210	+	8.28210i	−0.293736	+	0.293736i
$796$	9.91624			0.351472
$797$		−	3.25273i		−	0.115218i	−0.998339	−	0.0576088i	$-0.981652\pi$
$797$		−	3.25273i		−	0.115218i	0.998339	−	0.0576088i	$-0.0183476\pi$
$798$	5.12308	+	5.12308i	0.181355	+	0.181355i
$799$	−3.14886	−	3.14886i	−0.111399	−	0.111399i
$800$	7.63664	−	7.63664i	0.269996	−	0.269996i
$801$	3.99735	+	3.99735i	0.141240	+	0.141240i
$802$			8.35415i			0.294995i
$803$	−26.5903	+	2.37898i	−0.938351	+	0.0839523i
$804$	5.30941	+	5.30941i	0.187248	+	0.187248i
$805$	−31.5323			−1.11137
$806$	−0.0848489	−	1.43008i	−0.00298868	−	0.0503724i
$807$	8.41449			0.296204
$808$	12.0581	−	12.0581i	0.424202	−	0.424202i
$809$		−	25.8312i		−	0.908175i	−0.890957	−	0.454088i	$-0.849965\pi$
$809$		−	25.8312i		−	0.908175i	0.890957	−	0.454088i	$-0.150035\pi$
$810$	−0.363084			−0.0127575
$811$	6.22270	+	6.22270i	0.218508	+	0.218508i	0.807870	−	0.589361i	$-0.200621\pi$
$811$	6.22270	+	6.22270i	0.218508	+	0.218508i	−0.589361	+	0.807870i	$0.700621\pi$
$812$	−35.1096	+	35.1096i	−1.23210	+	1.23210i
$813$	−16.1509	+	16.1509i	−0.566439	+	0.566439i
$814$	−1.11786	+	1.33753i	−0.0391808	+	0.0468806i
$815$	−23.7270			−0.831120
$816$	9.69859			0.339519
$817$	−32.1068	−	32.1068i	−1.12328	−	1.12328i
$818$		−	2.73191i		−	0.0955190i
$819$	−8.75760	−	7.77660i	−0.306015	−	0.271736i
$820$		−	3.42938i		−	0.119759i
$821$	14.2872	+	14.2872i	0.498628	+	0.498628i	0.911011	−	0.412383i	$-0.135303\pi$
$821$	14.2872	+	14.2872i	0.498628	+	0.498628i	−0.412383	+	0.911011i	$0.635303\pi$
$822$			0.348341i			0.0121498i
$823$		−	27.4363i		−	0.956368i	−0.878260	−	0.478184i	$-0.841295\pi$
$823$		−	27.4363i		−	0.956368i	0.878260	−	0.478184i	$-0.158705\pi$
$824$	0.897308	+	0.897308i	0.0312592	+	0.0312592i
$825$	7.13761	−	8.54028i	0.248500	−	0.297334i
$826$	−4.08872	−	4.08872i	−0.142265	−	0.142265i
$827$	−25.1660	+	25.1660i	−0.875109	+	0.875109i	−0.993024	−	0.117915i	$-0.962379\pi$
$827$	−25.1660	+	25.1660i	−0.875109	+	0.875109i	0.117915	+	0.993024i	$0.462379\pi$
$828$	−14.5342			−0.505098
$829$		−	7.75208i		−	0.269241i	−0.990897	−	0.134620i	$-0.957019\pi$
$829$		−	7.75208i		−	0.269241i	0.990897	−	0.134620i	$-0.0429815\pi$
$830$	2.43450	+	2.43450i	0.0845026	+	0.0845026i
$831$	−1.72895			−0.0599768
$832$	−22.0970	+	1.31105i	−0.766075	+	0.0454525i
$833$		−	9.77091i		−	0.338542i
$834$	2.46501	−	2.46501i	0.0853563	−	0.0853563i
$835$			1.06769i			0.0369488i
$836$	49.9539	−	4.46927i	1.72769	−	0.154573i
$837$	0.992189	−	0.992189i	0.0342951	−	0.0342951i
$838$	1.83976	+	1.83976i	0.0635536	+	0.0635536i
$839$	18.3533	+	18.3533i	0.633625	+	0.633625i	0.948975	−	0.315350i	$-0.102122\pi$
$839$	18.3533	+	18.3533i	0.633625	+	0.633625i	−0.315350	+	0.948975i	$0.602122\pi$
$840$	3.26902	+	3.26902i	0.112792	+	0.112792i
$841$	−34.3932			−1.18597
$842$	−0.186013			−0.00641043
$843$	12.4273	−	12.4273i	0.428020	−	0.428020i
$844$	−34.8820			−1.20069
$845$	10.3103	−	13.0978i	0.354685	−	0.450578i
$846$		−	0.458354i		−	0.0157585i
$847$	−29.3499	−	20.3797i	−1.00847	−	0.700254i
$848$	32.2025			1.10584
$849$	−10.9404			−0.375474
$850$	−1.84860	+	1.84860i	−0.0634065	+	0.0634065i
$851$	9.93608	−	9.93608i	0.340604	−	0.340604i
$852$	6.40902	+	6.40902i	0.219569	+	0.219569i
$853$	16.8689	−	16.8689i	0.577581	−	0.577581i	−0.356655	−	0.934236i	$-0.616083\pi$
$853$	16.8689	−	16.8689i	0.577581	−	0.577581i	0.934236	+	0.356655i	$0.116083\pi$
$854$		−	3.13397i		−	0.107242i
$855$	−10.0997			−0.345404
$856$	−14.0723	−	14.0723i	−0.480982	−	0.480982i
$857$	50.3668			1.72050			0.860249	−	0.509875i	$-0.170308\pi$
$857$	50.3668			1.72050			0.860249	+	0.509875i	$0.170308\pi$
$858$	3.34891	−	0.500976i	0.114330	−	0.0171030i
$859$	36.9656			1.26125			0.630624	−	0.776088i	$-0.282799\pi$
$859$	36.9656			1.26125			0.630624	+	0.776088i	$0.282799\pi$
$860$	−10.0341	−	10.0341i	−0.342160	−	0.342160i
$861$	−4.52533			−0.154223
$862$		−	7.68252i		−	0.261668i
$863$	−22.2597	+	22.2597i	−0.757731	+	0.757731i	−0.975909	−	0.218178i	$-0.929989\pi$
$863$	−22.2597	+	22.2597i	−0.757731	+	0.757731i	0.218178	+	0.975909i	$0.429989\pi$
$864$	2.27559	+	2.27559i	0.0774173	+	0.0774173i
$865$	−4.43380	+	4.43380i	−0.150754	+	0.150754i
$866$	−0.635222	+	0.635222i	−0.0215857	+	0.0215857i
$867$	9.43136			0.320306
$868$	−8.75042			−0.297009
$869$	11.0035	−	13.1658i	0.373267	−	0.446621i
$870$			2.89087i			0.0980097i
$871$	10.5445	+	9.36335i	0.357287	+	0.317265i
$872$	6.35817			0.215315
$873$	12.2427	−	12.2427i	0.414353	−	0.414353i
$874$	16.8856			0.571166
$875$	34.8031			1.17656
$876$	−10.9270	−	10.9270i	−0.369190	−	0.369190i
$877$	−8.08757	−	8.08757i	−0.273098	−	0.273098i	0.557248	−	0.830346i	$-0.311857\pi$
$877$	−8.08757	−	8.08757i	−0.273098	−	0.273098i	−0.830346	+	0.557248i	$0.811857\pi$
$878$	−3.70114	−	3.70114i	−0.124907	−	0.124907i
$879$	7.32526	−	7.32526i	0.247075	−	0.247075i
$880$	14.9324	−	1.33597i	0.503372	−	0.0450357i
$881$		−	32.8537i		−	1.10687i	−0.832892	−	0.553435i	$-0.813317\pi$
$881$		−	32.8537i		−	1.10687i	0.832892	−	0.553435i	$-0.186683\pi$
$882$	0.711137	−	0.711137i	0.0239452	−	0.0239452i
$883$			22.9339i			0.771786i	0.922543	+	0.385893i	$0.126107\pi$
$883$			22.9339i			0.771786i	−0.922543	+	0.385893i	$0.873893\pi$
$884$	19.0098	−	1.12788i	0.639368	−	0.0379348i
$885$	8.06059			0.270954
$886$	−3.25369	−	3.25369i	−0.109310	−	0.109310i
$887$		−	10.2351i		−	0.343660i	−0.985127	−	0.171830i	$-0.945032\pi$
$887$		−	10.2351i		−	0.343660i	0.985127	−	0.171830i	$-0.0549679\pi$
$888$	−2.06019			−0.0691353
$889$	47.2571	−	47.2571i	1.58495	−	1.58495i
$890$	−1.45138	−	1.45138i	−0.0486502	−	0.0486502i
$891$	2.54486	+	2.12689i	0.0852561	+	0.0712535i
$892$	−2.30682	−	2.30682i	−0.0772381	−	0.0772381i
$893$		−	12.7498i		−	0.426656i
$894$		−	0.469903i		−	0.0157159i
$895$	4.25012	+	4.25012i	0.142066	+	0.142066i
$896$		−	26.5545i		−	0.887123i
$897$	−27.2483	+	1.61669i	−0.909795	+	0.0539796i
$898$		−	8.33231i		−	0.278053i
$899$	−7.89980	−	7.89980i	−0.263473	−	0.263473i
$900$	6.44269			0.214756
$901$	−25.1304			−0.837214
$902$	0.839031	−	1.00392i	0.0279367	−	0.0334267i
$903$	−13.2407	+	13.2407i	−0.440624	+	0.440624i
$904$	11.8537	−	11.8537i	0.394247	−	0.394247i
$905$	2.41661	+	2.41661i	0.0803307	+	0.0803307i
$906$	2.68463			0.0891909
$907$		−	2.99021i		−	0.0992883i	−0.998767	−	0.0496442i	$-0.984191\pi$
$907$		−	2.99021i		−	0.0992883i	0.998767	−	0.0496442i	$-0.0158087\pi$
$908$	25.5170	−	25.5170i	0.846813	−	0.846813i
$909$	15.3633			0.509569
$910$	3.17975	+	2.82356i	0.105408	+	0.0936001i
$911$	−34.0228			−1.12722			−0.563612	−	0.826039i	$-0.690589\pi$
$911$	−34.0228			−1.12722			−0.563612	+	0.826039i	$0.690589\pi$
$912$	19.6349	+	19.6349i	0.650178	+	0.650178i
$913$	−2.80253	−	31.3244i	−0.0927501	−	1.03668i
$914$			5.32714i			0.176206i
$915$	3.08919	+	3.08919i	0.102125	+	0.102125i
$916$	−34.9927	+	34.9927i	−1.15619	+	1.15619i
$917$	33.6237	+	33.6237i	1.11035	+	1.11035i
$918$	−0.550853	−	0.550853i	−0.0181809	−	0.0181809i
$919$			19.5678i			0.645481i	0.946488	+	0.322740i	$0.104604\pi$
$919$			19.5678i			0.645481i	−0.946488	+	0.322740i	$0.895396\pi$
$920$	10.7747			0.355231
$921$	−11.5989	+	11.5989i	−0.382195	+	0.382195i
$922$			7.54426i			0.248457i
$923$	12.7284	+	11.3026i	0.418959	+	0.372028i
$924$	−1.84311	−	20.6008i	−0.0606340	−	0.677717i
$925$	−4.40445	+	4.40445i	−0.144817	+	0.144817i
$926$			3.13278i			0.102950i
$927$			1.14327i			0.0375499i
$928$	18.1182	−	18.1182i	0.594761	−	0.594761i
$929$	−31.1746	+	31.1746i	−1.02281	+	1.02281i	−0.0230718	+	0.999734i	$0.507345\pi$
$929$	−31.1746	+	31.1746i	−1.02281	+	1.02281i	−0.999734	+	0.0230718i	$0.992655\pi$
$930$	−0.360248	+	0.360248i	−0.0118130	+	0.0118130i
$931$	19.7814	−	19.7814i	0.648308	−	0.648308i
$932$		−	12.8798i		−	0.421892i
$933$			19.0560i			0.623864i
$934$	4.94130	−	4.94130i	0.161684	−	0.161684i
$935$	−11.6530	+	1.04257i	−0.381095	+	0.0340958i
$936$	2.99249	+	2.65728i	0.0978127	+	0.0868560i
$937$		−	26.3913i		−	0.862165i	−0.902312	−	0.431083i	$-0.858132\pi$
$937$		−	26.3913i		−	0.862165i	0.902312	−	0.431083i	$-0.141868\pi$
$938$	−2.54383	+	2.54383i	−0.0830589	+	0.0830589i
$939$	−26.5255			−0.865627
$940$		−	3.98460i		−	0.129963i
$941$	−24.0908	−	24.0908i	−0.785339	−	0.785339i	0.195387	−	0.980726i	$-0.437404\pi$
$941$	−24.0908	−	24.0908i	−0.785339	−	0.785339i	−0.980726	+	0.195387i	$0.937404\pi$
$942$	−1.95895	−	1.95895i	−0.0638261	−	0.0638261i
$943$	−7.45774	+	7.45774i	−0.242857	+	0.242857i
$944$	−15.6706	−	15.6706i	−0.510035	−	0.510035i
$945$			4.16510i			0.135491i
$946$	−0.482439	−	5.39231i	−0.0156854	−	0.175319i
$947$	−11.7682	−	11.7682i	−0.382414	−	0.382414i	0.489557	−	0.871971i	$-0.337159\pi$
$947$	−11.7682	−	11.7682i	−0.382414	−	0.382414i	−0.871971	+	0.489557i	$0.837159\pi$
$948$	9.93216			0.322582
$949$	−21.7012	−	19.2703i	−0.704450	−	0.625540i
$950$	−7.48504			−0.242847
$951$	−15.6418	+	15.6418i	−0.507219	+	0.507219i
$952$			9.91918i			0.321483i
$953$	−29.2706			−0.948168			−0.474084	−	0.880480i	$-0.657221\pi$
$953$	−29.2706			−0.948168			−0.474084	+	0.880480i	$0.657221\pi$
$954$	−1.82901	−	1.82901i	−0.0592165	−	0.0592165i
$955$	−6.57585	+	6.57585i	−0.212790	+	0.212790i
$956$	−27.2200	+	27.2200i	−0.880357	+	0.880357i
$957$	16.9343	−	20.2622i	0.547408	−	0.654983i
$958$	6.11027			0.197414
$959$	3.99597			0.129037
$960$	5.56641	+	5.56641i	0.179655	+	0.179655i
$961$			29.0311i			0.936488i
$962$	−1.89169	+	0.112237i	−0.0609904	+	0.00361866i
$963$		−	17.9297i		−	0.577777i
$964$	−31.8507	−	31.8507i	−1.02584	−	1.02584i
$965$		−	26.5059i		−	0.853254i
$966$		−	6.96358i		−	0.224050i
$967$	11.7528	+	11.7528i	0.377943	+	0.377943i	0.870360	−	0.492416i	$-0.163886\pi$
$967$	11.7528	+	11.7528i	0.377943	+	0.377943i	−0.492416	+	0.870360i	$0.663886\pi$
$968$	10.0289	+	6.96378i	0.322342	+	0.223824i
$969$	−15.3228	−	15.3228i	−0.492240	−	0.492240i
$970$	−4.44513	+	4.44513i	−0.142725	+	0.142725i
$971$	43.1088			1.38343			0.691714	−	0.722171i	$-0.256856\pi$
$971$	43.1088			1.38343			0.691714	+	0.722171i	$0.256856\pi$
$972$			1.91982i			0.0615782i
$973$	−28.2772	−	28.2772i	−0.906525	−	0.906525i
$974$	5.57107			0.178509
$975$	12.0786	−	0.716642i	0.386825	−	0.0229509i
$976$		−	12.0114i		−	0.384475i
$977$	−31.6473	+	31.6473i	−1.01249	+	1.01249i	−0.0125668	+	0.999921i	$0.504000\pi$
$977$	−31.6473	+	31.6473i	−1.01249	+	1.01249i	−0.999921	+	0.0125668i	$0.996000\pi$
$978$		−	5.23985i		−	0.167552i
$979$	1.67078	+	18.6747i	0.0533985	+	0.596845i
$980$	6.18211	−	6.18211i	0.197480	−	0.197480i
$981$	4.05051	+	4.05051i	0.129323	+	0.129323i
$982$	−1.40124	−	1.40124i	−0.0447155	−	0.0447155i
$983$	31.5798	+	31.5798i	1.00724	+	1.00724i	0.999974	+	0.00726513i	$0.00231258\pi$
$983$	31.5798	+	31.5798i	1.00724	+	1.00724i	0.00726513	+	0.999974i	$0.497687\pi$
$984$	1.54632			0.0492948
$985$	−14.9418			−0.476087
$986$	−4.38588	+	4.38588i	−0.139675	+	0.139675i
$987$	−5.25798			−0.167363
$988$	40.7690	+	36.2022i	1.29703	+	1.15174i
$989$			43.6414i			1.38772i
$990$	−0.924000	−	0.772241i	−0.0293666	−	0.0245434i
$991$	5.41710			0.172080			0.0860399	−	0.996292i	$-0.472579\pi$
$991$	5.41710			0.172080			0.0860399	+	0.996292i	$0.472579\pi$
$992$	4.51564			0.143372
$993$	−18.7281	+	18.7281i	−0.594317	+	0.594317i
$994$	−3.07067	+	3.07067i	−0.0973957	+	0.0973957i
$995$	−4.68315	−	4.68315i	−0.148466	−	0.148466i
$996$	12.8725	−	12.8725i	0.407880	−	0.407880i
$997$		−	45.4825i		−	1.44045i	−0.693743	−	0.720223i	$-0.744040\pi$
$997$		−	45.4825i		−	1.44045i	0.693743	−	0.720223i	$-0.255960\pi$
$998$	10.9337			0.346100
$999$	−1.31245	−	1.31245i	−0.0415242	−	0.0415242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.m.a.109.9	yes	28
11.10	odd	2	inner	429.2.m.a.109.6	✓	28
13.8	odd	4	inner	429.2.m.a.307.6	yes	28
143.21	even	4	inner	429.2.m.a.307.9	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.m.a.109.6	✓	28	11.10	odd	2	inner
429.2.m.a.109.9	yes	28	1.1	even	1	trivial
429.2.m.a.307.6	yes	28	13.8	odd	4	inner
429.2.m.a.307.9	yes	28	143.21	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.200229 + 0.200229i) q^{2} -1.00000 q^{3} -1.91982i q^{4} +(-0.906673 + 0.906673i) q^{5} +(-0.200229 - 0.200229i) q^{6} +(-2.29691 + 2.29691i) q^{7} +(0.784861 - 0.784861i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.200229 + 0.200229i) q^{2} -1.00000 q^{3} -1.91982i q^{4} +(-0.906673 + 0.906673i) q^{5} +(-0.200229 - 0.200229i) q^{6} +(-2.29691 + 2.29691i) q^{7} +(0.784861 - 0.784861i) q^{8} +1.00000 q^{9} -0.363084 q^{10} +(2.54486 + 2.12689i) q^{11} +1.91982i q^{12} +(0.213548 + 3.59922i) q^{13} -0.919817 q^{14} +(0.906673 - 0.906673i) q^{15} -3.52533 q^{16} +2.75112 q^{17} +(0.200229 + 0.200229i) q^{18} +(5.56967 + 5.56967i) q^{19} +(1.74065 + 1.74065i) q^{20} +(2.29691 - 2.29691i) q^{21} +(0.0836901 + 0.935421i) q^{22} -7.57062i q^{23} +(-0.784861 + 0.784861i) q^{24} +3.35589i q^{25} +(-0.677910 + 0.763427i) q^{26} -1.00000 q^{27} +(4.40965 + 4.40965i) q^{28} +7.96199i q^{29} +0.363084 q^{30} +(-0.992189 + 0.992189i) q^{31} +(-2.27559 - 2.27559i) q^{32} +(-2.54486 - 2.12689i) q^{33} +(0.550853 + 0.550853i) q^{34} -4.16510i q^{35} -1.91982i q^{36} +(1.31245 + 1.31245i) q^{37} +2.23042i q^{38} +(-0.213548 - 3.59922i) q^{39} +1.42322i q^{40} +(-0.985090 - 0.985090i) q^{41} +0.919817 q^{42} -5.76458 q^{43} +(4.08324 - 4.88567i) q^{44} +(-0.906673 + 0.906673i) q^{45} +(1.51586 - 1.51586i) q^{46} +(-1.14457 - 1.14457i) q^{47} +3.52533 q^{48} -3.55162i q^{49} +(-0.671946 + 0.671946i) q^{50} -2.75112 q^{51} +(6.90985 - 0.409972i) q^{52} -9.13461 q^{53} +(-0.200229 - 0.200229i) q^{54} +(-4.23575 + 0.378964i) q^{55} +3.60551i q^{56} +(-5.56967 - 5.56967i) q^{57} +(-1.59422 + 1.59422i) q^{58} +(4.44515 + 4.44515i) q^{59} +(-1.74065 - 1.74065i) q^{60} +3.40717i q^{61} -0.397330 q^{62} +(-2.29691 + 2.29691i) q^{63} +6.13938i q^{64} +(-3.45693 - 3.06970i) q^{65} +(-0.0836901 - 0.935421i) q^{66} +(2.76558 - 2.76558i) q^{67} -5.28164i q^{68} +7.57062i q^{69} +(0.833973 - 0.833973i) q^{70} +(3.33835 - 3.33835i) q^{71} +(0.784861 - 0.784861i) q^{72} +(-5.69171 + 5.69171i) q^{73} +0.525582i q^{74} -3.35589i q^{75} +(10.6928 - 10.6928i) q^{76} +(-10.7306 + 0.960046i) q^{77} +(0.677910 - 0.763427i) q^{78} -5.17350i q^{79} +(3.19632 - 3.19632i) q^{80} +1.00000 q^{81} -0.394487i q^{82} +(-6.70505 - 6.70505i) q^{83} +(-4.40965 - 4.40965i) q^{84} +(-2.49436 + 2.49436i) q^{85} +(-1.15424 - 1.15424i) q^{86} -7.96199i q^{87} +(3.66668 - 0.328050i) q^{88} +(3.99735 + 3.99735i) q^{89} -0.363084 q^{90} +(-8.75760 - 7.77660i) q^{91} -14.5342 q^{92} +(0.992189 - 0.992189i) q^{93} -0.458354i q^{94} -10.0997 q^{95} +(2.27559 + 2.27559i) q^{96} +(12.2427 - 12.2427i) q^{97} +(0.711137 - 0.711137i) q^{98} +(2.54486 + 2.12689i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{3} + 4 q^{5} + 28 q^{9}+O(q^{10}) \) 28 * q - 28 * q^3 + 4 * q^5 + 28 * q^9	\( 28 q - 28 q^{3} + 4 q^{5} + 28 q^{9} + 4 q^{11} + 48 q^{14} - 4 q^{15} - 52 q^{16} - 8 q^{20} - 32 q^{22} - 4 q^{26} - 28 q^{27} + 24 q^{31} - 4 q^{33} + 16 q^{34} - 12 q^{37} - 48 q^{42} - 24 q^{44} + 4 q^{45} - 8 q^{47} + 52 q^{48} - 8 q^{53} + 48 q^{55} - 64 q^{58} + 4 q^{59} + 8 q^{60} + 32 q^{66} + 28 q^{67} - 4 q^{70} + 12 q^{71} + 4 q^{78} + 56 q^{80} + 28 q^{81} - 8 q^{86} - 104 q^{89} - 76 q^{91} - 24 q^{93} - 8 q^{97} + 4 q^{99}+O(q^{100}) \) 28 * q - 28 * q^3 + 4 * q^5 + 28 * q^9 + 4 * q^11 + 48 * q^14 - 4 * q^15 - 52 * q^16 - 8 * q^20 - 32 * q^22 - 4 * q^26 - 28 * q^27 + 24 * q^31 - 4 * q^33 + 16 * q^34 - 12 * q^37 - 48 * q^42 - 24 * q^44 + 4 * q^45 - 8 * q^47 + 52 * q^48 - 8 * q^53 + 48 * q^55 - 64 * q^58 + 4 * q^59 + 8 * q^60 + 32 * q^66 + 28 * q^67 - 4 * q^70 + 12 * q^71 + 4 * q^78 + 56 * q^80 + 28 * q^81 - 8 * q^86 - 104 * q^89 - 76 * q^91 - 24 * q^93 - 8 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more