LMFDB - Embedded newform 429.2.m.a.307.1

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			307.1
Character	$\chi$	$=$	429.307
Dual form			429.2.m.a.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.92734 + 1.92734i) q^{2} -1.00000 q^{3} -5.42931i q^{4} +(-1.59813 - 1.59813i) q^{5} +(1.92734 - 1.92734i) q^{6} +(-1.66792 - 1.66792i) q^{7} +(6.60946 + 6.60946i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.92734 + 1.92734i) q^{2} -1.00000 q^{3} -5.42931i q^{4} +(-1.59813 - 1.59813i) q^{5} +(1.92734 - 1.92734i) q^{6} +(-1.66792 - 1.66792i) q^{7} +(6.60946 + 6.60946i) q^{8} +1.00000 q^{9} +6.16029 q^{10} +(2.43130 + 2.25584i) q^{11} +5.42931i q^{12} +(1.55693 - 3.25207i) q^{13} +6.42931 q^{14} +(1.59813 + 1.59813i) q^{15} -14.6188 q^{16} -4.73833 q^{17} +(-1.92734 + 1.92734i) q^{18} +(-3.03817 + 3.03817i) q^{19} +(-8.67674 + 8.67674i) q^{20} +(1.66792 + 1.66792i) q^{21} +(-9.03372 + 0.338176i) q^{22} -1.62975i q^{23} +(-6.60946 - 6.60946i) q^{24} +0.108039i q^{25} +(3.26713 + 9.26860i) q^{26} -1.00000 q^{27} +(-9.05565 + 9.05565i) q^{28} +3.51084i q^{29} -6.16029 q^{30} +(4.40334 + 4.40334i) q^{31} +(14.9565 - 14.9565i) q^{32} +(-2.43130 - 2.25584i) q^{33} +(9.13239 - 9.13239i) q^{34} +5.33111i q^{35} -5.42931i q^{36} +(-3.16846 + 3.16846i) q^{37} -11.7112i q^{38} +(-1.55693 + 3.25207i) q^{39} -21.1256i q^{40} +(-4.68212 + 4.68212i) q^{41} -6.42931 q^{42} -4.69039 q^{43} +(12.2476 - 13.2003i) q^{44} +(-1.59813 - 1.59813i) q^{45} +(3.14108 + 3.14108i) q^{46} +(-6.86563 + 6.86563i) q^{47} +14.6188 q^{48} -1.43609i q^{49} +(-0.208228 - 0.208228i) q^{50} +4.73833 q^{51} +(-17.6565 - 8.45304i) q^{52} -0.475204 q^{53} +(1.92734 - 1.92734i) q^{54} +(-0.280412 - 7.49065i) q^{55} -22.0481i q^{56} +(3.03817 - 3.03817i) q^{57} +(-6.76659 - 6.76659i) q^{58} +(8.18948 - 8.18948i) q^{59} +(8.67674 - 8.67674i) q^{60} +9.65019i q^{61} -16.9735 q^{62} +(-1.66792 - 1.66792i) q^{63} +28.4151i q^{64} +(-7.68541 + 2.70906i) q^{65} +(9.03372 - 0.338176i) q^{66} +(5.61068 + 5.61068i) q^{67} +25.7259i q^{68} +1.62975i q^{69} +(-10.2749 - 10.2749i) q^{70} +(5.96802 + 5.96802i) q^{71} +(6.60946 + 6.60946i) q^{72} +(-1.78979 - 1.78979i) q^{73} -12.2134i q^{74} -0.108039i q^{75} +(16.4952 + 16.4952i) q^{76} +(-0.292657 - 7.81776i) q^{77} +(-3.26713 - 9.26860i) q^{78} -1.07811i q^{79} +(23.3627 + 23.3627i) q^{80} +1.00000 q^{81} -18.0481i q^{82} +(-10.3508 + 10.3508i) q^{83} +(9.05565 - 9.05565i) q^{84} +(7.57247 + 7.57247i) q^{85} +(9.03999 - 9.03999i) q^{86} -3.51084i q^{87} +(1.15971 + 30.9794i) q^{88} +(-13.0204 + 13.0204i) q^{89} +6.16029 q^{90} +(-8.02103 + 2.82737i) q^{91} -8.84839 q^{92} +(-4.40334 - 4.40334i) q^{93} -26.4648i q^{94} +9.71077 q^{95} +(-14.9565 + 14.9565i) q^{96} +(8.39275 + 8.39275i) q^{97} +(2.76783 + 2.76783i) q^{98} +(2.43130 + 2.25584i) 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 $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.92734	+	1.92734i	−1.36284	+	1.36284i	−0.492559	+	0.870279i	$0.663938\pi$
$2$	−1.92734	+	1.92734i	−1.36284	+	1.36284i	−0.870279	+	0.492559i	$0.836062\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		−	5.42931i		−	2.71466i
$5$	−1.59813	−	1.59813i	−0.714705	−	0.714705i	0.252810	−	0.967516i	$-0.418645\pi$
$5$	−1.59813	−	1.59813i	−0.714705	−	0.714705i	−0.967516	+	0.252810i	$0.918645\pi$
$6$	1.92734	−	1.92734i	0.786835	−	0.786835i
$7$	−1.66792	−	1.66792i	−0.630414	−	0.630414i	0.317758	−	0.948172i	$-0.397070\pi$
$7$	−1.66792	−	1.66792i	−0.630414	−	0.630414i	−0.948172	+	0.317758i	$0.897070\pi$
$8$	6.60946	+	6.60946i	2.33680	+	2.33680i
$9$	1.00000			0.333333
$10$	6.16029			1.94806
$11$	2.43130	+	2.25584i	0.733064	+	0.680160i
$11$	2.43130	+	2.25584i	0.733064	+	0.680160i
$12$			5.42931i			1.56731i
$13$	1.55693	−	3.25207i	0.431814	−	0.901963i
$13$	1.55693	−	3.25207i	0.431814	−	0.901963i
$14$	6.42931			1.71831
$15$	1.59813	+	1.59813i	0.412635	+	0.412635i
$16$	−14.6188			−3.65470
$17$	−4.73833			−1.14921			−0.574607	−	0.818430i	$-0.694845\pi$
$17$	−4.73833			−1.14921			−0.574607	+	0.818430i	$0.694845\pi$
$18$	−1.92734	+	1.92734i	−0.454279	+	0.454279i
$19$	−3.03817	+	3.03817i	−0.697004	+	0.697004i	−0.963763	−	0.266760i	$-0.914047\pi$
$19$	−3.03817	+	3.03817i	−0.697004	+	0.697004i	0.266760	+	0.963763i	$0.414047\pi$
$20$	−8.67674	+	8.67674i	−1.94018	+	1.94018i
$21$	1.66792	+	1.66792i	0.363970	+	0.363970i
$22$	−9.03372	+	0.338176i	−1.92600	+	0.0720994i
$23$		−	1.62975i		−	0.339825i	−0.985459	−	0.169913i	$-0.945651\pi$
$23$		−	1.62975i		−	0.339825i	0.985459	−	0.169913i	$-0.0543486\pi$
$24$	−6.60946	−	6.60946i	−1.34915	−	1.34915i
$25$			0.108039i			0.0216078i
$26$	3.26713	+	9.26860i	0.640737	+	1.81772i
$27$	−1.00000			−0.192450
$28$	−9.05565	+	9.05565i	−1.71136	+	1.71136i
$29$			3.51084i			0.651946i	0.945379	+	0.325973i	$0.105692\pi$
$29$			3.51084i			0.651946i	−0.945379	+	0.325973i	$0.894308\pi$
$30$	−6.16029			−1.12471
$31$	4.40334	+	4.40334i	0.790863	+	0.790863i	0.981634	−	0.190772i	$-0.0610990\pi$
$31$	4.40334	+	4.40334i	0.790863	+	0.790863i	−0.190772	+	0.981634i	$0.561099\pi$
$32$	14.9565	−	14.9565i	2.64396	−	2.64396i
$33$	−2.43130	−	2.25584i	−0.423235	−	0.392691i
$34$	9.13239	−	9.13239i	1.56619	−	1.56619i
$35$			5.33111i			0.901121i
$36$		−	5.42931i		−	0.904885i
$37$	−3.16846	+	3.16846i	−0.520891	+	0.520891i	−0.917841	−	0.396949i	$-0.870069\pi$
$37$	−3.16846	+	3.16846i	−0.520891	+	0.520891i	0.396949	+	0.917841i	$0.370069\pi$
$38$		−	11.7112i		−	1.89981i
$39$	−1.55693	+	3.25207i	−0.249308	+	0.520748i
$40$		−	21.1256i		−	3.34024i
$41$	−4.68212	+	4.68212i	−0.731224	+	0.731224i	−0.970862	−	0.239638i	$-0.922971\pi$
$41$	−4.68212	+	4.68212i	−0.731224	+	0.731224i	0.239638	+	0.970862i	$0.422971\pi$
$42$	−6.42931			−0.992064
$43$	−4.69039			−0.715278			−0.357639	−	0.933860i	$-0.616418\pi$
$43$	−4.69039			−0.715278			−0.357639	+	0.933860i	$0.616418\pi$
$44$	12.2476	−	13.2003i	1.84640	−	1.99002i
$45$	−1.59813	−	1.59813i	−0.238235	−	0.238235i
$46$	3.14108	+	3.14108i	0.463127	+	0.463127i
$47$	−6.86563	+	6.86563i	−1.00145	+	1.00145i	−0.00145558	+	0.999999i	$0.500463\pi$
$47$	−6.86563	+	6.86563i	−1.00145	+	1.00145i	−0.999999	+	0.00145558i	$0.999537\pi$
$48$	14.6188			2.11004
$49$		−	1.43609i		−	0.205155i
$50$	−0.208228	−	0.208228i	−0.0294479	−	0.0294479i
$51$	4.73833			0.663499
$52$	−17.6565	−	8.45304i	−2.44852	−	1.17223i
$53$	−0.475204			−0.0652743			−0.0326371	−	0.999467i	$-0.510391\pi$
$53$	−0.475204			−0.0652743			−0.0326371	+	0.999467i	$0.510391\pi$
$54$	1.92734	−	1.92734i	0.262278	−	0.262278i
$55$	−0.280412	−	7.49065i	−0.0378107	−	1.01004i
$56$		−	22.0481i		−	2.94630i
$57$	3.03817	−	3.03817i	0.402415	−	0.402415i
$58$	−6.76659	−	6.76659i	−0.888496	−	0.888496i
$59$	8.18948	−	8.18948i	1.06618	−	1.06618i	0.0685310	−	0.997649i	$-0.478169\pi$
$59$	8.18948	−	8.18948i	1.06618	−	1.06618i	0.997649	−	0.0685310i	$-0.0218312\pi$
$60$	8.67674	−	8.67674i	1.12016	−	1.12016i
$61$			9.65019i			1.23558i	0.786343	+	0.617790i	$0.211972\pi$
$61$			9.65019i			1.23558i	−0.786343	+	0.617790i	$0.788028\pi$
$62$	−16.9735			−2.15564
$63$	−1.66792	−	1.66792i	−0.210138	−	0.210138i
$64$			28.4151i			3.55189i
$65$	−7.68541	+	2.70906i	−0.953257	+	0.336018i
$66$	9.03372	−	0.338176i	1.11197	−	0.0416266i
$67$	5.61068	+	5.61068i	0.685454	+	0.685454i	0.961224	−	0.275770i	$-0.0889327\pi$
$67$	5.61068	+	5.61068i	0.685454	+	0.685454i	−0.275770	+	0.961224i	$0.588933\pi$
$68$			25.7259i			3.11972i
$69$			1.62975i			0.196198i
$70$	−10.2749	−	10.2749i	−1.22808	−	1.22808i
$71$	5.96802	+	5.96802i	0.708274	+	0.708274i	0.966172	−	0.257898i	$-0.0830299\pi$
$71$	5.96802	+	5.96802i	0.708274	+	0.708274i	−0.257898	+	0.966172i	$0.583030\pi$
$72$	6.60946	+	6.60946i	0.778933	+	0.778933i
$73$	−1.78979	−	1.78979i	−0.209479	−	0.209479i	0.594567	−	0.804046i	$-0.297323\pi$
$73$	−1.78979	−	1.78979i	−0.209479	−	0.209479i	−0.804046	+	0.594567i	$0.797323\pi$
$74$		−	12.2134i		−	1.41978i
$75$		−	0.108039i		−	0.0124753i
$76$	16.4952	+	16.4952i	1.89212	+	1.89212i
$77$	−0.292657	−	7.81776i	−0.0333514	−	0.890917i
$78$	−3.26713	−	9.26860i	−0.369930	−	1.04946i
$79$		−	1.07811i		−	0.121297i	−0.998159	−	0.0606485i	$-0.980683\pi$
$79$		−	1.07811i		−	0.121297i	0.998159	−	0.0606485i	$-0.0193169\pi$
$80$	23.3627	+	23.3627i	2.61203	+	2.61203i
$81$	1.00000			0.111111
$82$		−	18.0481i		−	1.99308i
$83$	−10.3508	+	10.3508i	−1.13615	+	1.13615i	−0.147012	+	0.989135i	$0.546966\pi$
$83$	−10.3508	+	10.3508i	−1.13615	+	1.13615i	−0.989135	+	0.147012i	$0.953034\pi$
$84$	9.05565	−	9.05565i	0.988053	−	0.988053i
$85$	7.57247	+	7.57247i	0.821349	+	0.821349i
$86$	9.03999	−	9.03999i	0.974808	−	0.974808i
$87$		−	3.51084i		−	0.376401i
$88$	1.15971	+	30.9794i	0.123626	+	3.30242i
$89$	−13.0204	+	13.0204i	−1.38016	+	1.38016i	−0.535851	+	0.844313i	$0.680009\pi$
$89$	−13.0204	+	13.0204i	−1.38016	+	1.38016i	−0.844313	+	0.535851i	$0.819991\pi$
$90$	6.16029			0.649352
$91$	−8.02103	+	2.82737i	−0.840832	+	0.296389i
$92$	−8.84839			−0.922509
$93$	−4.40334	−	4.40334i	−0.456605	−	0.456605i
$94$		−	26.4648i		−	2.72964i
$95$	9.71077			0.996304
$96$	−14.9565	+	14.9565i	−1.52649	+	1.52649i
$97$	8.39275	+	8.39275i	0.852154	+	0.852154i	0.990398	−	0.138244i	$-0.0441457\pi$
$97$	8.39275	+	8.39275i	0.852154	+	0.852154i	−0.138244	+	0.990398i	$0.544146\pi$
$98$	2.76783	+	2.76783i	0.279593	+	0.279593i
$99$	2.43130	+	2.25584i	0.244355	+	0.226720i
$100$	0.586577			0.0586577
$101$	−11.8044			−1.17458			−0.587292	−	0.809375i	$-0.699806\pi$
$101$	−11.8044			−1.17458			−0.587292	+	0.809375i	$0.699806\pi$
$102$	−9.13239	+	9.13239i	−0.904241	+	0.904241i
$103$			12.4745i			1.22915i	0.788860	+	0.614574i	$0.210672\pi$
$103$			12.4745i			1.22915i	−0.788860	+	0.614574i	$0.789328\pi$
$104$	31.7849	−	11.2040i	3.11677	−	1.09864i
$105$		−	5.33111i		−	0.520263i
$106$	0.915882	−	0.915882i	0.0889583	−	0.0889583i
$107$		−	11.8827i		−	1.14875i	−0.818593	−	0.574374i	$-0.805245\pi$
$107$		−	11.8827i		−	1.14875i	0.818593	−	0.574374i	$-0.194755\pi$
$108$			5.42931i			0.522436i
$109$	9.28581	−	9.28581i	0.889420	−	0.889420i	−0.105048	−	0.994467i	$-0.533499\pi$
$109$	9.28581	−	9.28581i	0.889420	−	0.889420i	0.994467	+	0.105048i	$0.0334995\pi$
$110$	14.9775	+	13.8966i	1.42805	+	1.32499i
$111$	3.16846	−	3.16846i	0.300737	−	0.300737i
$112$	24.3830	+	24.3830i	2.30397	+	2.30397i
$113$	−20.3632			−1.91561			−0.957806	−	0.287416i	$-0.907204\pi$
$113$	−20.3632			−1.91561			−0.957806	+	0.287416i	$0.907204\pi$
$114$			11.7112i			1.09685i
$115$	−2.60454	+	2.60454i	−0.242875	+	0.242875i
$116$	19.0614			1.76981
$117$	1.55693	−	3.25207i	0.143938	−	0.300654i
$118$			31.5679i			2.90606i
$119$	7.90315	+	7.90315i	0.724481	+	0.724481i
$120$			21.1256i			1.92849i
$121$	0.822415	+	10.9692i	0.0747650	+	0.997201i
$122$	−18.5992	−	18.5992i	−1.68390	−	1.68390i
$123$	4.68212	−	4.68212i	0.422172	−	0.422172i
$124$	23.9071	−	23.9071i	2.14692	−	2.14692i
$125$	−7.81799	+	7.81799i	−0.699262	+	0.699262i
$126$	6.42931			0.572769
$127$	10.5769			0.938551			0.469275	−	0.883052i	$-0.344515\pi$
$127$	10.5769			0.938551			0.469275	+	0.883052i	$0.344515\pi$
$128$	−24.8527	−	24.8527i	−2.19669	−	2.19669i
$129$	4.69039			0.412966
$130$	9.59113	−	20.0337i	0.841197	−	1.75707i
$131$		−	15.2029i		−	1.32828i	−0.747607	−	0.664142i	$-0.768797\pi$
$131$		−	15.2029i		−	1.32828i	0.747607	−	0.664142i	$-0.231203\pi$
$132$	−12.2476	+	13.2003i	−1.06602	+	1.14894i
$133$	10.1348			0.878802
$134$	−21.6274			−1.86833
$135$	1.59813	+	1.59813i	0.137545	+	0.137545i
$136$	−31.3178	−	31.3178i	−2.68548	−	2.68548i
$137$	9.19698	−	9.19698i	0.785751	−	0.785751i	−0.195043	−	0.980795i	$-0.562485\pi$
$137$	9.19698	−	9.19698i	0.785751	−	0.785751i	0.980795	+	0.195043i	$0.0624847\pi$
$138$	−3.14108	−	3.14108i	−0.267386	−	0.267386i
$139$			3.78076i			0.320680i	0.987062	+	0.160340i	$0.0512591\pi$
$139$			3.78076i			0.320680i	−0.987062	+	0.160340i	$0.948741\pi$
$140$	28.9442			2.44623
$141$	6.86563	−	6.86563i	0.578190	−	0.578190i
$142$	−23.0049			−1.93053
$143$	11.1215	−	4.39459i	0.930026	−	0.367494i
$144$	−14.6188			−1.21823
$145$	5.61077	−	5.61077i	0.465949	−	0.465949i
$146$	6.89907			0.570971
$147$			1.43609i			0.118446i
$148$	17.2025	+	17.2025i	1.41404	+	1.41404i
$149$	−2.98499	+	2.98499i	−0.244540	+	0.244540i	−0.818725	−	0.574185i	$-0.805319\pi$
$149$	−2.98499	+	2.98499i	−0.244540	+	0.244540i	0.574185	+	0.818725i	$0.305319\pi$
$150$	0.208228	+	0.208228i	0.0170018	+	0.0170018i
$151$	3.04820	+	3.04820i	0.248059	+	0.248059i	0.820174	−	0.572115i	$-0.193877\pi$
$151$	3.04820	+	3.04820i	0.248059	+	0.248059i	−0.572115	+	0.820174i	$0.693877\pi$
$152$	−40.1613			−3.25751
$153$	−4.73833			−0.383071
$154$	15.6316	+	14.5035i	1.25963	+	1.16872i
$155$		−	14.0742i		−	1.13047i
$156$	17.6565	+	8.45304i	1.41365	+	0.676785i
$157$	−16.8809			−1.34724			−0.673621	−	0.739077i	$-0.735262\pi$
$157$	−16.8809			−1.34724			−0.673621	+	0.739077i	$0.735262\pi$
$158$	2.07789	+	2.07789i	0.165308	+	0.165308i
$159$	0.475204			0.0376861
$160$	−47.8049			−3.77931
$161$	−2.71828	+	2.71828i	−0.214231	+	0.214231i
$162$	−1.92734	+	1.92734i	−0.151426	+	0.151426i
$163$	1.70753	−	1.70753i	0.133744	−	0.133744i	−0.637065	−	0.770810i	$-0.719852\pi$
$163$	1.70753	−	1.70753i	0.133744	−	0.133744i	0.770810	+	0.637065i	$0.219852\pi$
$164$	25.4207	+	25.4207i	1.98502	+	1.98502i
$165$	0.280412	+	7.49065i	0.0218300	+	0.583146i
$166$		−	39.8991i		−	3.09677i
$167$	−5.98723	−	5.98723i	−0.463306	−	0.463306i	0.436432	−	0.899737i	$-0.356242\pi$
$167$	−5.98723	−	5.98723i	−0.463306	−	0.463306i	−0.899737	+	0.436432i	$0.856242\pi$
$168$			22.0481i			1.70105i
$169$	−8.15196	−	10.1265i	−0.627074	−	0.778960i
$170$	−29.1895			−2.23873
$171$	−3.03817	+	3.03817i	−0.232335	+	0.232335i
$172$			25.4656i			1.94173i
$173$	15.3779			1.16916			0.584579	−	0.811337i	$-0.301260\pi$
$173$	15.3779			1.16916			0.584579	+	0.811337i	$0.301260\pi$
$174$	6.76659	+	6.76659i	0.512974	+	0.512974i
$175$	0.180200	−	0.180200i	0.0136219	−	0.0136219i
$176$	−35.5426	−	32.9776i	−2.67913	−	2.48578i
$177$	−8.18948	+	8.18948i	−0.615559	+	0.615559i
$178$		−	50.1897i		−	3.76188i
$179$		−	2.04934i		−	0.153175i	−0.997063	−	0.0765876i	$-0.975598\pi$
$179$		−	2.04934i		−	0.153175i	0.997063	−	0.0765876i	$-0.0244025\pi$
$180$	−8.67674	+	8.67674i	−0.646726	+	0.646726i
$181$		−	5.12133i		−	0.380665i	−0.981720	−	0.190333i	$-0.939043\pi$
$181$		−	5.12133i		−	0.380665i	0.981720	−	0.190333i	$-0.0609566\pi$
$182$	10.0100	−	20.9086i	0.741988	−	1.54985i
$183$		−	9.65019i		−	0.713363i
$184$	10.7717	−	10.7717i	0.794103	−	0.794103i
$185$	10.1272			0.744568
$186$	16.9735			1.24456
$187$	−11.5203	−	10.6889i	−0.842447	−	0.781649i
$188$	37.2756	+	37.2756i	2.71860	+	2.71860i
$189$	1.66792	+	1.66792i	0.121323	+	0.121323i
$190$	−18.7160	+	18.7160i	−1.35780	+	1.35780i
$191$	22.2094			1.60702			0.803508	−	0.595295i	$-0.202965\pi$
$191$	22.2094			1.60702			0.803508	+	0.595295i	$0.202965\pi$
$192$		−	28.4151i		−	2.05069i
$193$	−8.94328	−	8.94328i	−0.643752	−	0.643752i	0.307724	−	0.951476i	$-0.400433\pi$
$193$	−8.94328	−	8.94328i	−0.643752	−	0.643752i	−0.951476	+	0.307724i	$0.900433\pi$
$194$	−32.3514			−2.32270
$195$	7.68541	−	2.70906i	0.550363	−	0.194000i
$196$	−7.79696			−0.556926
$197$	4.29517	−	4.29517i	0.306018	−	0.306018i	−0.537345	−	0.843363i	$-0.680573\pi$
$197$	4.29517	−	4.29517i	0.306018	−	0.306018i	0.843363	+	0.537345i	$0.180573\pi$
$198$	−9.03372	+	0.338176i	−0.641998	+	0.0240331i
$199$			1.60551i			0.113811i	0.998380	+	0.0569057i	$0.0181234\pi$
$199$			1.60551i			0.113811i	−0.998380	+	0.0569057i	$0.981877\pi$
$200$	−0.714080	+	0.714080i	−0.0504931	+	0.0504931i
$201$	−5.61068	−	5.61068i	−0.395747	−	0.395747i
$202$	22.7512	−	22.7512i	1.60077	−	1.60077i
$203$	5.85579	−	5.85579i	0.410996	−	0.410996i
$204$		−	25.7259i		−	1.80117i
$205$	14.9653			1.04522
$206$	−24.0426	−	24.0426i	−1.67513	−	1.67513i
$207$		−	1.62975i		−	0.113275i
$208$	−22.7604	+	47.5414i	−1.57815	+	3.29640i
$209$	−14.2403	+	0.533084i	−0.985022	+	0.0368742i
$210$	10.2749	+	10.2749i	0.709034	+	0.709034i
$211$			6.93408i			0.477362i	0.971098	+	0.238681i	$0.0767150\pi$
$211$			6.93408i			0.477362i	−0.971098	+	0.238681i	$0.923285\pi$
$212$			2.58003i			0.177197i
$213$	−5.96802	−	5.96802i	−0.408922	−	0.408922i
$214$	22.9021	+	22.9021i	1.56556	+	1.56556i
$215$	7.49585	+	7.49585i	0.511213	+	0.511213i
$216$	−6.60946	−	6.60946i	−0.449717	−	0.449717i
$217$		−	14.6888i		−	0.997143i
$218$			35.7939i			2.42427i
$219$	1.78979	+	1.78979i	0.120943	+	0.120943i
$220$	−40.6691	+	1.52244i	−2.74191	+	0.102643i
$221$	−7.37723	+	15.4094i	−0.496246	+	1.03655i
$222$			12.2134i			0.819711i
$223$	3.50573	+	3.50573i	0.234761	+	0.234761i	0.814677	−	0.579915i	$-0.196914\pi$
$223$	3.50573	+	3.50573i	0.234761	+	0.234761i	−0.579915	+	0.814677i	$0.696914\pi$
$224$	−49.8926			−3.33359
$225$			0.108039i			0.00720260i
$226$	39.2470	−	39.2470i	2.61067	−	2.61067i
$227$	−1.61090	+	1.61090i	−0.106919	+	0.106919i	−0.758543	−	0.651623i	$-0.774088\pi$
$227$	−1.61090	+	1.61090i	−0.106919	+	0.106919i	0.651623	+	0.758543i	$0.274088\pi$
$228$	−16.4952	−	16.4952i	−1.09242	−	1.09242i
$229$	−3.58607	+	3.58607i	−0.236974	+	0.236974i	−0.815596	−	0.578622i	$-0.803591\pi$
$229$	−3.58607	+	3.58607i	−0.236974	+	0.236974i	0.578622	+	0.815596i	$0.303591\pi$
$230$		−	10.0397i		−	0.661999i
$231$	0.292657	+	7.81776i	0.0192554	+	0.514371i
$232$	−23.2047	+	23.2047i	−1.52347	+	1.52347i
$233$	9.90256			0.648738			0.324369	−	0.945931i	$-0.394848\pi$
$233$	9.90256			0.648738			0.324369	+	0.945931i	$0.394848\pi$
$234$	3.26713	+	9.26860i	0.213579	+	0.605907i
$235$	21.9443			1.43149
$236$	−44.4633	−	44.4633i	−2.89431	−	2.89431i
$237$			1.07811i			0.0700308i
$238$	−30.4642			−1.97470
$239$	−9.55134	+	9.55134i	−0.617825	+	0.617825i	−0.944973	−	0.327148i	$-0.893912\pi$
$239$	−9.55134	+	9.55134i	−0.617825	+	0.617825i	0.327148	+	0.944973i	$0.393912\pi$
$240$	−23.3627	−	23.3627i	−1.50806	−	1.50806i
$241$	−11.8064	−	11.8064i	−0.760517	−	0.760517i	0.215898	−	0.976416i	$-0.430732\pi$
$241$	−11.8064	−	11.8064i	−0.760517	−	0.760517i	−0.976416	+	0.215898i	$0.930732\pi$
$242$	−22.7265	−	19.5564i	−1.46092	−	1.25713i
$243$	−1.00000			−0.0641500
$244$	52.3939			3.35417
$245$	−2.29505	+	2.29505i	−0.146626	+	0.146626i
$246$			18.0481i			1.15071i
$247$	5.15014	+	14.6105i	0.327695	+	0.929647i
$248$			58.2074i			3.69617i
$249$	10.3508	−	10.3508i	0.655955	−	0.655955i
$250$		−	30.1359i		−	1.90596i
$251$		−	8.69988i		−	0.549131i	−0.961568	−	0.274566i	$-0.911466\pi$
$251$		−	8.69988i		−	0.549131i	0.961568	−	0.274566i	$-0.0885341\pi$
$252$	−9.05565	+	9.05565i	−0.570453	+	0.570453i
$253$	3.67644	−	3.96240i	0.231136	−	0.249114i
$254$	−20.3854	+	20.3854i	−1.27909	+	1.27909i
$255$	−7.57247	−	7.57247i	−0.474206	−	0.474206i
$256$	38.9692			2.43557
$257$		−	10.7735i		−	0.672030i	−0.941857	−	0.336015i	$-0.890921\pi$
$257$		−	10.7735i		−	0.672030i	0.941857	−	0.336015i	$-0.109079\pi$
$258$	−9.03999	+	9.03999i	−0.562805	+	0.562805i
$259$	10.5695			0.656755
$260$	14.7084	+	41.7265i	0.912173	+	2.58777i
$261$			3.51084i			0.217315i
$262$	29.3012	+	29.3012i	1.81024	+	1.81024i
$263$			27.7455i			1.71086i	0.517919	+	0.855430i	$0.326707\pi$
$263$			27.7455i			1.71086i	−0.517919	+	0.855430i	$0.673293\pi$
$264$	−1.15971	−	30.9794i	−0.0713753	−	1.90665i
$265$	0.759438	+	0.759438i	0.0466519	+	0.0466519i
$266$	−19.5333	+	19.5333i	−1.19767	+	1.19767i
$267$	13.0204	−	13.0204i	0.796838	−	0.796838i
$268$	30.4621	−	30.4621i	1.86077	−	1.86077i
$269$	−5.84397			−0.356313			−0.178157	−	0.984002i	$-0.557013\pi$
$269$	−5.84397			−0.356313			−0.178157	+	0.984002i	$0.557013\pi$
$270$	−6.16029			−0.374903
$271$	4.13754	+	4.13754i	0.251338	+	0.251338i	0.821519	−	0.570181i	$-0.193127\pi$
$271$	4.13754	+	4.13754i	0.251338	+	0.251338i	−0.570181	+	0.821519i	$0.693127\pi$
$272$	69.2687			4.20003
$273$	8.02103	−	2.82737i	0.485455	−	0.171120i
$274$			35.4515i			2.14170i
$275$	−0.243718	+	0.262675i	−0.0146968	+	0.0158399i
$276$	8.84839			0.532611
$277$	6.26647			0.376516			0.188258	−	0.982120i	$-0.439716\pi$
$277$	6.26647			0.376516			0.188258	+	0.982120i	$0.439716\pi$
$278$	−7.28683	−	7.28683i	−0.437035	−	0.437035i
$279$	4.40334	+	4.40334i	0.263621	+	0.263621i
$280$	−35.2357	+	35.2357i	−2.10574	+	2.10574i
$281$	2.23464	+	2.23464i	0.133308	+	0.133308i	0.770612	−	0.637304i	$-0.219951\pi$
$281$	2.23464	+	2.23464i	0.133308	+	0.133308i	−0.637304	+	0.770612i	$0.719951\pi$
$282$			26.4648i			1.57596i
$283$	−11.1658			−0.663735			−0.331868	−	0.943326i	$-0.607679\pi$
$283$	−11.1658			−0.663735			−0.331868	+	0.943326i	$0.607679\pi$
$284$	32.4023	−	32.4023i	1.92272	−	1.92272i
$285$	−9.71077			−0.575217
$286$	−12.9651	+	29.9048i	−0.766640	+	1.76831i
$287$	15.6188			0.921948
$288$	14.9565	−	14.9565i	0.881322	−	0.881322i
$289$	5.45176			0.320692
$290$			21.6278i			1.27003i
$291$	−8.39275	−	8.39275i	−0.491992	−	0.491992i
$292$	−9.71731	+	9.71731i	−0.568663	+	0.568663i
$293$	−10.1968	−	10.1968i	−0.595706	−	0.595706i	0.343461	−	0.939167i	$-0.388401\pi$
$293$	−10.1968	−	10.1968i	−0.595706	−	0.595706i	−0.939167	+	0.343461i	$0.888401\pi$
$294$	−2.76783	−	2.76783i	−0.161423	−	0.161423i
$295$	−26.1757			−1.52401
$296$	−41.8836			−2.43443
$297$	−2.43130	−	2.25584i	−0.141078	−	0.130897i
$298$		−	11.5062i		−	0.666536i
$299$	−5.30005	−	2.53739i	−0.306510	−	0.146741i
$300$	−0.586577			−0.0338661
$301$	7.82319	+	7.82319i	0.450921	+	0.450921i
$302$	−11.7499			−0.676128
$303$	11.8044			0.678146
$304$	44.4144	−	44.4144i	2.54734	−	2.54734i
$305$	15.4223	−	15.4223i	0.883076	−	0.883076i
$306$	9.13239	−	9.13239i	0.522064	−	0.522064i
$307$	−13.6076	−	13.6076i	−0.776629	−	0.776629i	0.202627	−	0.979256i	$-0.435052\pi$
$307$	−13.6076	−	13.6076i	−0.776629	−	0.776629i	−0.979256	+	0.202627i	$0.935052\pi$
$308$	−42.4451	+	1.58893i	−2.41853	+	0.0905375i
$309$		−	12.4745i		−	0.709648i
$310$	27.1258	+	27.1258i	1.54064	+	1.54064i
$311$			1.00832i			0.0571764i	0.999591	+	0.0285882i	$0.00910115\pi$
$311$			1.00832i			0.0571764i	−0.999591	+	0.0285882i	$0.990899\pi$
$312$	−31.7849	+	11.2040i	−1.79947	+	0.634302i
$313$	−5.48997			−0.310311			−0.155156	−	0.987890i	$-0.549588\pi$
$313$	−5.48997			−0.310311			−0.155156	+	0.987890i	$0.549588\pi$
$314$	32.5353	−	32.5353i	1.83607	−	1.83607i
$315$			5.33111i			0.300374i
$316$	−5.85340			−0.329280
$317$	−6.51766	−	6.51766i	−0.366068	−	0.366068i	0.499973	−	0.866041i	$-0.333343\pi$
$317$	−6.51766	−	6.51766i	−0.366068	−	0.366068i	−0.866041	+	0.499973i	$0.833343\pi$
$318$	−0.915882	+	0.915882i	−0.0513601	+	0.0513601i
$319$	−7.91987	+	8.53588i	−0.443427	+	0.477918i
$320$	45.4111	−	45.4111i	2.53856	−	2.53856i
$321$			11.8827i			0.663230i
$322$		−	10.4781i		−	0.583924i
$323$	14.3958	−	14.3958i	0.801006	−	0.801006i
$324$		−	5.42931i		−	0.301628i
$325$	0.351351	+	0.168209i	0.0194894	+	0.00933055i
$326$			6.58200i			0.364543i
$327$	−9.28581	+	9.28581i	−0.513507	+	0.513507i
$328$	−61.8926			−3.41745
$329$	22.9026			1.26266
$330$	−14.9775	−	13.8966i	−0.824485	−	0.764983i
$331$	−13.8564	−	13.8564i	−0.761616	−	0.761616i	0.214998	−	0.976614i	$-0.431025\pi$
$331$	−13.8564	−	13.8564i	−0.761616	−	0.761616i	−0.976614	+	0.214998i	$0.931025\pi$
$332$	56.1976	+	56.1976i	3.08425	+	3.08425i
$333$	−3.16846	+	3.16846i	−0.173630	+	0.173630i
$334$	23.0789			1.26282
$335$		−	17.9332i		−	0.979796i
$336$	−24.3830	−	24.3830i	−1.33020	−	1.33020i
$337$	−6.82312			−0.371679			−0.185840	−	0.982580i	$-0.559500\pi$
$337$	−6.82312			−0.371679			−0.185840	+	0.982580i	$0.559500\pi$
$338$	35.2288	+	3.80558i	1.91620	+	0.206996i
$339$	20.3632			1.10598
$340$	41.1133	−	41.1133i	2.22968	−	2.22968i
$341$	0.772620	+	20.6390i	0.0418397	+	1.11767i
$342$		−	11.7112i		−	0.633269i
$343$	−14.0707	+	14.0707i	−0.759747	+	0.759747i
$344$	−31.0010	−	31.0010i	−1.67146	−	1.67146i
$345$	2.60454	−	2.60454i	0.140224	−	0.140224i
$346$	−29.6384	+	29.6384i	−1.59337	+	1.59337i
$347$		−	8.54732i		−	0.458844i	−0.973327	−	0.229422i	$-0.926316\pi$
$347$		−	8.54732i		−	0.458844i	0.973327	−	0.229422i	$-0.0736836\pi$
$348$	−19.0614			−1.02180
$349$	−20.8993	−	20.8993i	−1.11871	−	1.11871i	−0.991930	−	0.126784i	$-0.959534\pi$
$349$	−20.8993	−	20.8993i	−1.11871	−	1.11871i	−0.126784	−	0.991930i	$-0.540466\pi$
$350$			0.694616i			0.0371288i
$351$	−1.55693	+	3.25207i	−0.0831026	+	0.173583i
$352$	70.1032	−	2.62431i	3.73651	−	0.139876i
$353$	−10.0976	−	10.0976i	−0.537440	−	0.537440i	0.385336	−	0.922776i	$-0.374085\pi$
$353$	−10.0976	−	10.0976i	−0.537440	−	0.537440i	−0.922776	+	0.385336i	$0.874085\pi$
$354$		−	31.5679i		−	1.67782i
$355$		−	19.0754i		−	1.01241i
$356$	70.6920	+	70.6920i	3.74667	+	3.74667i
$357$	−7.90315	−	7.90315i	−0.418279	−	0.418279i
$358$	3.94979	+	3.94979i	0.208753	+	0.208753i
$359$	−8.84497	−	8.84497i	−0.466820	−	0.466820i	0.434063	−	0.900883i	$-0.357080\pi$
$359$	−8.84497	−	8.84497i	−0.466820	−	0.466820i	−0.900883	+	0.434063i	$0.857080\pi$
$360$		−	21.1256i		−	1.11341i
$361$			0.539072i			0.0283722i
$362$	9.87056	+	9.87056i	0.518785	+	0.518785i
$363$	−0.822415	−	10.9692i	−0.0431656	−	0.575734i
$364$	15.3507	+	43.5486i	0.804593	+	2.28257i
$365$			5.72062i			0.299431i
$366$	18.5992	+	18.5992i	0.972198	+	0.972198i
$367$	28.1681			1.47036			0.735181	−	0.677871i	$-0.237097\pi$
$367$	28.1681			1.47036			0.735181	+	0.677871i	$0.237097\pi$
$368$			23.8249i			1.24196i
$369$	−4.68212	+	4.68212i	−0.243741	+	0.243741i
$370$	−19.5186	+	19.5186i	−1.01473	+	1.01473i
$371$	0.792602	+	0.792602i	0.0411498	+	0.0411498i
$372$	−23.9071	+	23.9071i	−1.23952	+	1.23952i
$373$			27.9804i			1.44877i	0.689396	+	0.724385i	$0.257876\pi$
$373$			27.9804i			1.44877i	−0.689396	+	0.724385i	$0.742124\pi$
$374$	42.8047	−	1.60239i	2.21338	−	0.0828576i
$375$	7.81799	−	7.81799i	0.403719	−	0.403719i
$376$	−90.7562			−4.68039
$377$	11.4175	+	5.46611i	0.588031	+	0.281519i
$378$	−6.42931			−0.330688
$379$	10.7680	+	10.7680i	0.553115	+	0.553115i	0.927339	−	0.374223i	$-0.122091\pi$
$379$	10.7680	+	10.7680i	0.553115	+	0.553115i	−0.374223	+	0.927339i	$0.622091\pi$
$380$		−	52.7228i		−	2.70462i
$381$	−10.5769			−0.541872
$382$	−42.8051	+	42.8051i	−2.19010	+	2.19010i
$383$	15.0898	+	15.0898i	0.771054	+	0.771054i	0.978291	−	0.207237i	$-0.0664471\pi$
$383$	15.0898	+	15.0898i	0.771054	+	0.771054i	−0.207237	+	0.978291i	$0.566447\pi$
$384$	24.8527	+	24.8527i	1.26826	+	1.26826i
$385$	−12.0261	+	12.9615i	−0.612907	+	0.660579i
$386$	34.4736			1.75466
$387$	−4.69039			−0.238426
$388$	45.5668	−	45.5668i	2.31331	−	2.31331i
$389$		−	18.0163i		−	0.913463i	−0.889605	−	0.456731i	$-0.849020\pi$
$389$		−	18.0163i		−	0.913463i	0.889605	−	0.456731i	$-0.150980\pi$
$390$	−9.59113	+	20.0337i	−0.485666	+	1.01445i
$391$			7.72227i			0.390532i
$392$	9.49176	−	9.49176i	0.479406	−	0.479406i
$393$			15.2029i			0.766885i
$394$			16.5565i			0.834106i
$395$	−1.72296	+	1.72296i	−0.0866916	+	0.0866916i
$396$	12.2476	−	13.2003i	0.615467	−	0.663339i
$397$	−12.1430	+	12.1430i	−0.609439	+	0.609439i	−0.942799	−	0.333361i	$-0.891817\pi$
$397$	−12.1430	+	12.1430i	−0.609439	+	0.609439i	0.333361	+	0.942799i	$0.391817\pi$
$398$	−3.09437	−	3.09437i	−0.155107	−	0.155107i
$399$	−10.1348			−0.507377
$400$		−	1.57940i		−	0.0789700i
$401$	−26.2981	+	26.2981i	−1.31327	+	1.31327i	−0.394273	+	0.918993i	$0.629004\pi$
$401$	−26.2981	+	26.2981i	−1.31327	+	1.31327i	−0.918993	+	0.394273i	$0.870996\pi$
$402$	21.6274			1.07868
$403$	21.1756	−	7.46430i	1.05483	−	0.371823i
$404$			64.0899i			3.18859i
$405$	−1.59813	−	1.59813i	−0.0794117	−	0.0794117i
$406$			22.5723i			1.12024i
$407$	−14.8510	+	0.555945i	−0.736136	+	0.0275572i
$408$	31.3178	+	31.3178i	1.55046	+	1.55046i
$409$	−21.6669	+	21.6669i	−1.07136	+	1.07136i	−0.0741099	+	0.997250i	$0.523612\pi$
$409$	−21.6669	+	21.6669i	−1.07136	+	1.07136i	−0.997250	+	0.0741099i	$0.976388\pi$
$410$	−28.8432	+	28.8432i	−1.42447	+	1.42447i
$411$	−9.19698	+	9.19698i	−0.453654	+	0.453654i
$412$	67.7278			3.33671
$413$	−27.3188			−1.34427
$414$	3.14108	+	3.14108i	0.154376	+	0.154376i
$415$	33.0838			1.62402
$416$	−25.3535	−	71.9259i	−1.24306	−	3.52646i
$417$		−	3.78076i		−	0.185145i
$418$	26.4185	−	28.4734i	1.29217	−	1.39268i
$419$	−17.7786			−0.868541			−0.434271	−	0.900782i	$-0.642994\pi$
$419$	−17.7786			−0.868541			−0.434271	+	0.900782i	$0.642994\pi$
$420$	−28.9442			−1.41233
$421$	−24.2761	−	24.2761i	−1.18315	−	1.18315i	−0.978925	−	0.204220i	$-0.934534\pi$
$421$	−24.2761	−	24.2761i	−1.18315	−	1.18315i	−0.204220	−	0.978925i	$-0.565466\pi$
$422$	−13.3644	−	13.3644i	−0.650567	−	0.650567i
$423$	−6.86563	+	6.86563i	−0.333818	+	0.333818i
$424$	−3.14084	−	3.14084i	−0.152533	−	0.152533i
$425$		−	0.511924i		−	0.0248320i
$426$	23.0049			1.11459
$427$	16.0957	−	16.0957i	0.778928	−	0.778928i
$428$	−64.5151			−3.11846
$429$	−11.1215	+	4.39459i	−0.536951	+	0.212173i
$430$	−28.8942			−1.39340
$431$	7.49027	−	7.49027i	0.360793	−	0.360793i	−0.503312	−	0.864105i	$-0.667885\pi$
$431$	7.49027	−	7.49027i	0.360793	−	0.360793i	0.864105	+	0.503312i	$0.167885\pi$
$432$	14.6188			0.703347
$433$		−	6.35386i		−	0.305347i	−0.988277	−	0.152674i	$-0.951212\pi$
$433$		−	6.35386i		−	0.305347i	0.988277	−	0.152674i	$-0.0487883\pi$
$434$	28.3104	+	28.3104i	1.35894	+	1.35894i
$435$	−5.61077	+	5.61077i	−0.269016	+	0.269016i
$436$	−50.4156	−	50.4156i	−2.41447	−	2.41447i
$437$	4.95144	+	4.95144i	0.236859	+	0.236859i
$438$	−6.89907			−0.329650
$439$	−17.7800			−0.848592			−0.424296	−	0.905523i	$-0.639478\pi$
$439$	−17.7800			−0.848592			−0.424296	+	0.905523i	$0.639478\pi$
$440$	47.6558	−	51.3625i	2.27190	−	2.44861i
$441$		−	1.43609i		−	0.0683851i
$442$	−15.4807	−	43.9177i	−0.736344	−	2.08895i
$443$	0.526397			0.0250099			0.0125049	−	0.999922i	$-0.496019\pi$
$443$	0.526397			0.0250099			0.0125049	+	0.999922i	$0.496019\pi$
$444$	−17.2025	−	17.2025i	−0.816396	−	0.816396i
$445$	41.6167			1.97282
$446$	−13.5135			−0.639883
$447$	2.98499	−	2.98499i	0.141185	−	0.141185i
$448$	47.3942	−	47.3942i	2.23916	−	2.23916i
$449$	−4.24207	+	4.24207i	−0.200196	+	0.200196i	−0.800084	−	0.599888i	$-0.795212\pi$
$449$	−4.24207	+	4.24207i	−0.200196	+	0.200196i	0.599888	+	0.800084i	$0.295212\pi$
$450$	−0.208228	−	0.208228i	−0.00981598	−	0.00981598i
$451$	−21.9457	+	0.821535i	−1.03338	+	0.0386846i
$452$			110.558i			5.20023i
$453$	−3.04820	−	3.04820i	−0.143217	−	0.143217i
$454$		−	6.20952i		−	0.291427i
$455$	17.3371	+	8.30014i	0.812778	+	0.389117i
$456$	40.1613			1.88073
$457$	−24.7819	+	24.7819i	−1.15925	+	1.15925i	−0.174613	+	0.984637i	$0.555868\pi$
$457$	−24.7819	+	24.7819i	−1.15925	+	1.15925i	−0.984637	+	0.174613i	$0.944132\pi$
$458$		−	13.8232i		−	0.645915i
$459$	4.73833			0.221166
$460$	14.1409	+	14.1409i	0.659322	+	0.659322i
$461$	25.2044	−	25.2044i	1.17388	−	1.17388i	0.192609	−	0.981276i	$-0.438305\pi$
$461$	25.2044	−	25.2044i	1.17388	−	1.17388i	0.981276	−	0.192609i	$-0.0616949\pi$
$462$	−15.6316	−	14.5035i	−0.727246	−	0.674762i
$463$	−6.70936	+	6.70936i	−0.311810	+	0.311810i	−0.845611	−	0.533800i	$-0.820763\pi$
$463$	−6.70936	+	6.70936i	−0.311810	+	0.311810i	0.533800	+	0.845611i	$0.320763\pi$
$464$		−	51.3242i		−	2.38267i
$465$			14.0742i			0.652676i
$466$	−19.0856	+	19.0856i	−0.884125	+	0.884125i
$467$			1.03665i			0.0479702i	0.999712	+	0.0239851i	$0.00763543\pi$
$467$			1.03665i			0.0479702i	−0.999712	+	0.0239851i	$0.992365\pi$
$468$	−17.6565	−	8.45304i	−0.816173	−	0.390742i
$469$		−	18.7163i		−	0.864240i
$470$	−42.2943	+	42.2943i	−1.95089	+	1.95089i
$471$	16.8809			0.777830
$472$	108.256			4.98289
$473$	−11.4037	−	10.5807i	−0.524344	−	0.486503i
$474$	−2.07789	−	2.07789i	−0.0954407	−	0.0954407i
$475$	−0.328241	−	0.328241i	−0.0150607	−	0.0150607i
$476$	42.9087	−	42.9087i	1.96672	−	1.96672i
$477$	−0.475204			−0.0217581
$478$		−	36.8174i		−	1.68399i
$479$	3.32271	+	3.32271i	0.151818	+	0.151818i	0.778930	−	0.627111i	$-0.215763\pi$
$479$	3.32271	+	3.32271i	0.151818	+	0.151818i	−0.627111	+	0.778930i	$0.715763\pi$
$480$	47.8049			2.18199
$481$	5.37100	+	15.2371i	0.244896	+	0.694753i
$482$	45.5100			2.07292
$483$	2.71828	−	2.71828i	0.123686	−	0.123686i
$484$	59.5553	−	4.46515i	2.70706	−	0.202961i
$485$		−	26.8254i		−	1.21808i
$486$	1.92734	−	1.92734i	0.0874261	−	0.0874261i
$487$	−0.234423	−	0.234423i	−0.0106227	−	0.0106227i	0.701775	−	0.712398i	$-0.252391\pi$
$487$	−0.234423	−	0.234423i	−0.0106227	−	0.0106227i	−0.712398	+	0.701775i	$0.752391\pi$
$488$	−63.7826	+	63.7826i	−2.88730	+	2.88730i
$489$	−1.70753	+	1.70753i	−0.0772172	+	0.0772172i
$490$		−	8.84672i		−	0.399654i
$491$	24.9014			1.12378			0.561892	−	0.827210i	$-0.310073\pi$
$491$	24.9014			1.12378			0.561892	+	0.827210i	$0.310073\pi$
$492$	−25.4207	−	25.4207i	−1.14605	−	1.14605i
$493$		−	16.6355i		−	0.749225i
$494$	−38.0856	−	18.2335i	−1.71355	−	0.820362i
$495$	−0.280412	−	7.49065i	−0.0126036	−	0.336680i
$496$	−64.3715	−	64.3715i	−2.89037	−	2.89037i
$497$		−	19.9084i		−	0.893012i
$498$			39.8991i			1.78792i
$499$	−26.1922	−	26.1922i	−1.17252	−	1.17252i	−0.981606	−	0.190917i	$-0.938854\pi$
$499$	−26.1922	−	26.1922i	−1.17252	−	1.17252i	−0.190917	−	0.981606i	$-0.561146\pi$
$500$	42.4463	+	42.4463i	1.89826	+	1.89826i
$501$	5.98723	+	5.98723i	0.267490	+	0.267490i
$502$	16.7677	+	16.7677i	0.748377	+	0.748377i
$503$		−	10.2885i		−	0.458742i	−0.973339	−	0.229371i	$-0.926333\pi$
$503$		−	10.2885i		−	0.458742i	0.973339	−	0.229371i	$-0.0736669\pi$
$504$		−	22.0481i		−	0.982101i
$505$	18.8650	+	18.8650i	0.839482	+	0.839482i
$506$	0.551141	+	14.7227i	0.0245012	+	0.654502i
$507$	8.15196	+	10.1265i	0.362041	+	0.449733i
$508$		−	57.4254i		−	2.54784i
$509$	−17.9247	−	17.9247i	−0.794497	−	0.794497i	0.187724	−	0.982222i	$-0.439889\pi$
$509$	−17.9247	−	17.9247i	−0.794497	−	0.794497i	−0.982222	+	0.187724i	$0.939889\pi$
$510$	29.1895			1.29253
$511$			5.97044i			0.264117i
$512$	−25.4016	+	25.4016i	−1.12260	+	1.12260i
$513$	3.03817	−	3.03817i	0.134138	−	0.134138i
$514$	20.7642	+	20.7642i	0.915868	+	0.915868i
$515$	19.9358	−	19.9358i	0.878478	−	0.878478i
$516$		−	25.4656i		−	1.12106i
$517$	−32.1801	+	1.20466i	−1.41528	+	0.0529808i
$518$	−20.3710	+	20.3710i	−0.895050	+	0.895050i
$519$	−15.3779			−0.675013
$520$	−68.7019	−	32.8910i	−3.01278	−	1.44236i
$521$	−26.3445			−1.15417			−0.577087	−	0.816683i	$-0.695811\pi$
$521$	−26.3445			−1.15417			−0.577087	+	0.816683i	$0.695811\pi$
$522$	−6.76659	−	6.76659i	−0.296165	−	0.296165i
$523$		−	1.80848i		−	0.0790793i	−0.999218	−	0.0395397i	$-0.987411\pi$
$523$		−	1.80848i		−	0.0790793i	0.999218	−	0.0395397i	$-0.0125892\pi$
$524$	−82.5413			−3.60583
$525$	−0.180200	+	0.180200i	−0.00786459	+	0.00786459i
$526$	−53.4751	−	53.4751i	−2.33162	−	2.33162i
$527$	−20.8645	−	20.8645i	−0.908870	−	0.908870i
$528$	35.5426	+	32.9776i	1.54679	+	1.43517i
$529$	20.3439			0.884519
$530$	−2.92740			−0.127158
$531$	8.18948	−	8.18948i	0.355393	−	0.355393i
$532$		−	55.0252i		−	2.38564i
$533$	7.93687	+	22.5163i	0.343784	+	0.975289i
$534$			50.1897i			2.17192i
$535$	−18.9902	+	18.9902i	−0.821017	+	0.821017i
$536$			74.1672i			3.20354i
$537$			2.04934i			0.0884357i
$538$	11.2634	−	11.2634i	0.485598	−	0.485598i
$539$	3.23958	−	3.49156i	0.139538	−	0.150392i
$540$	8.67674	−	8.67674i	0.373388	−	0.373388i
$541$	15.7916	+	15.7916i	0.678933	+	0.678933i	0.959759	−	0.280826i	$-0.0906083\pi$
$541$	15.7916	+	15.7916i	0.678933	+	0.678933i	−0.280826	+	0.959759i	$0.590608\pi$
$542$	−15.9489			−0.685065
$543$			5.12133i			0.219777i
$544$	−70.8689	+	70.8689i	−3.03848	+	3.03848i
$545$	−29.6799			−1.27135
$546$	−10.0100	+	20.9086i	−0.428387	+	0.894805i
$547$		−	22.0217i		−	0.941581i	−0.882245	−	0.470791i	$-0.843969\pi$
$547$		−	22.0217i		−	0.941581i	0.882245	−	0.470791i	$-0.156031\pi$
$548$	−49.9333	−	49.9333i	−2.13304	−	2.13304i
$549$			9.65019i			0.411860i
$550$	−0.0365362	−	0.975994i	−0.00155791	−	0.0416165i
$551$	−10.6665	−	10.6665i	−0.454408	−	0.454408i
$552$	−10.7717	+	10.7717i	−0.458476	+	0.458476i
$553$	−1.79820	+	1.79820i	−0.0764674	+	0.0764674i
$554$	−12.0777	+	12.0777i	−0.513130	+	0.513130i
$555$	−10.1272			−0.429876
$556$	20.5269			0.870535
$557$	−4.89046	−	4.89046i	−0.207215	−	0.207215i	0.595867	−	0.803083i	$-0.296808\pi$
$557$	−4.89046	−	4.89046i	−0.207215	−	0.207215i	−0.803083	+	0.595867i	$0.796808\pi$
$558$	−16.9735			−0.718545
$559$	−7.30259	+	15.2535i	−0.308867	+	0.645154i
$560$		−	77.9343i		−	3.29333i
$561$	11.5203	+	10.6889i	0.486387	+	0.451285i
$562$	−8.61386			−0.363354
$563$	25.3486			1.06831			0.534157	−	0.845385i	$-0.320629\pi$
$563$	25.3486			1.06831			0.534157	+	0.845385i	$0.320629\pi$
$564$	−37.2756	−	37.2756i	−1.56959	−	1.56959i
$565$	32.5431	+	32.5431i	1.36910	+	1.36910i
$566$	21.5203	−	21.5203i	0.904564	−	0.904564i
$567$	−1.66792	−	1.66792i	−0.0700460	−	0.0700460i
$568$			78.8908i			3.31019i
$569$	10.1474			0.425401			0.212701	−	0.977117i	$-0.431774\pi$
$569$	10.1474			0.425401			0.212701	+	0.977117i	$0.431774\pi$
$570$	18.7160	−	18.7160i	0.783927	−	0.783927i
$571$	−4.31092			−0.180407			−0.0902033	−	0.995923i	$-0.528752\pi$
$571$	−4.31092			−0.180407			−0.0902033	+	0.995923i	$0.528752\pi$
$572$	−23.8596	−	60.3820i	−0.997619	−	2.52470i
$573$	−22.2094			−0.927811
$574$	−30.1028	+	30.1028i	−1.25647	+	1.25647i
$575$	0.176076			0.00734288
$576$			28.4151i			1.18396i
$577$	10.8342	+	10.8342i	0.451034	+	0.451034i	0.895698	−	0.444663i	$-0.146677\pi$
$577$	10.8342	+	10.8342i	0.451034	+	0.451034i	−0.444663	+	0.895698i	$0.646677\pi$
$578$	−10.5074	+	10.5074i	−0.437051	+	0.437051i
$579$	8.94328	+	8.94328i	0.371670	+	0.371670i
$580$	−30.4626	−	30.4626i	−1.26489	−	1.26489i
$581$	34.5286			1.43249
$582$	32.3514			1.34101
$583$	−1.15536	−	1.07198i	−0.0478502	−	0.0443970i
$584$		−	23.6591i		−	0.979019i
$585$	−7.68541	+	2.70906i	−0.317752	+	0.112006i
$586$	39.3057			1.62370
$587$	3.07640	+	3.07640i	0.126977	+	0.126977i	0.767739	−	0.640762i	$-0.221382\pi$
$587$	3.07640	+	3.07640i	0.126977	+	0.126977i	−0.640762	+	0.767739i	$0.721382\pi$
$588$	7.79696			0.321541
$589$	−26.7562			−1.10247
$590$	50.4496	−	50.4496i	2.07698	−	2.07698i
$591$	−4.29517	+	4.29517i	−0.176680	+	0.176680i
$592$	46.3190	−	46.3190i	1.90370	−	1.90370i
$593$	7.11007	+	7.11007i	0.291976	+	0.291976i	0.837860	−	0.545885i	$-0.183806\pi$
$593$	7.11007	+	7.11007i	0.291976	+	0.291976i	−0.545885	+	0.837860i	$0.683806\pi$
$594$	9.03372	−	0.338176i	0.370658	−	0.0138755i
$595$		−	25.2605i		−	1.03558i
$596$	16.2064	+	16.2064i	0.663841	+	0.663841i
$597$		−	1.60551i		−	0.0657091i
$598$	15.1055	−	5.32459i	0.617708	−	0.217739i
$599$	−38.4361			−1.57046			−0.785228	−	0.619207i	$-0.787454\pi$
$599$	−38.4361			−1.57046			−0.785228	+	0.619207i	$0.787454\pi$
$600$	0.714080	−	0.714080i	0.0291522	−	0.0291522i
$601$			35.7106i			1.45666i	0.685224	+	0.728332i	$0.259704\pi$
$601$			35.7106i			1.45666i	−0.685224	+	0.728332i	$0.740296\pi$
$602$	−30.1560			−1.22907
$603$	5.61068	+	5.61068i	0.228485	+	0.228485i
$604$	16.5496	−	16.5496i	0.673394	−	0.673394i
$605$	16.2159	−	18.8446i	0.659270	−	0.766140i
$606$	−22.7512	+	22.7512i	−0.924204	+	0.924204i
$607$			10.1914i			0.413655i	0.978377	+	0.206828i	$0.0663139\pi$
$607$			10.1914i			0.413655i	−0.978377	+	0.206828i	$0.933686\pi$
$608$			90.8809i			3.68571i
$609$	−5.85579	+	5.85579i	−0.237289	+	0.237289i
$610$			59.4480i			2.40698i
$611$	11.6382	+	33.0168i	0.470833	+	1.33572i
$612$			25.7259i			1.03991i
$613$	−8.23662	+	8.23662i	−0.332674	+	0.332674i	−0.853601	−	0.520927i	$-0.825586\pi$
$613$	−8.23662	+	8.23662i	−0.332674	+	0.332674i	0.520927	+	0.853601i	$0.325586\pi$
$614$	52.4532			2.11684
$615$	−14.9653			−0.603458
$616$	49.7369	−	53.6055i	2.00396	−	2.15983i
$617$	4.84950	+	4.84950i	0.195234	+	0.195234i	0.797953	−	0.602720i	$-0.205916\pi$
$617$	4.84950	+	4.84950i	0.195234	+	0.195234i	−0.602720	+	0.797953i	$0.705916\pi$
$618$	24.0426	+	24.0426i	0.967136	+	0.967136i
$619$	−29.0193	+	29.0193i	−1.16638	+	1.16638i	−0.183334	+	0.983051i	$0.558689\pi$
$619$	−29.0193	+	29.0193i	−1.16638	+	1.16638i	−0.983051	+	0.183334i	$0.941311\pi$
$620$	−76.4133			−3.06883
$621$			1.62975i			0.0653994i
$622$	−1.94338	−	1.94338i	−0.0779222	−	0.0779222i
$623$	43.4341			1.74015
$624$	22.7604	−	47.5414i	0.911145	−	1.90318i
$625$	25.5285			1.02114
$626$	10.5811	−	10.5811i	0.422904	−	0.422904i
$627$	14.2403	−	0.533084i	0.568703	−	0.0212893i
$628$			91.6516i			3.65730i
$629$	15.0132	−	15.0132i	0.598615	−	0.598615i
$630$	−10.2749	−	10.2749i	−0.409361	−	0.409361i
$631$	−4.08994	+	4.08994i	−0.162818	+	0.162818i	−0.783814	−	0.620996i	$-0.786728\pi$
$631$	−4.08994	+	4.08994i	−0.162818	+	0.162818i	0.620996	+	0.783814i	$0.286728\pi$
$632$	7.12574	−	7.12574i	0.283447	−	0.283447i
$633$		−	6.93408i		−	0.275605i
$634$	25.1235			0.997783
$635$	−16.9033	−	16.9033i	−0.670787	−	0.670787i
$636$		−	2.58003i		−	0.102305i
$637$	−4.67026	−	2.23588i	−0.185042	−	0.0885889i
$638$	−1.18728	−	31.7159i	−0.0470049	−	1.25564i
$639$	5.96802	+	5.96802i	0.236091	+	0.236091i
$640$			79.4358i			3.13997i
$641$		−	18.5318i		−	0.731963i	−0.930622	−	0.365981i	$-0.880733\pi$
$641$		−	18.5318i		−	0.731963i	0.930622	−	0.365981i	$-0.119267\pi$
$642$	−22.9021	−	22.9021i	−0.903875	−	0.903875i
$643$	10.5650	+	10.5650i	0.416644	+	0.416644i	0.884045	−	0.467402i	$-0.154810\pi$
$643$	10.5650	+	10.5650i	0.416644	+	0.416644i	−0.467402	+	0.884045i	$0.654810\pi$
$644$	14.7584	+	14.7584i	0.581563	+	0.581563i
$645$	−7.49585	−	7.49585i	−0.295149	−	0.295149i
$646$			55.4915i			2.18328i
$647$			20.4649i			0.804556i	0.915517	+	0.402278i	$0.131782\pi$
$647$			20.4649i			0.804556i	−0.915517	+	0.402278i	$0.868218\pi$
$648$	6.60946	+	6.60946i	0.259644	+	0.259644i
$649$	38.3852	−	1.43695i	1.50675	−	0.0564050i
$650$	−1.00137	+	0.352977i	−0.0392770	+	0.0138449i
$651$			14.6888i			0.575701i
$652$	−9.27072	−	9.27072i	−0.363069	−	0.363069i
$653$	10.4136			0.407517			0.203758	−	0.979021i	$-0.434684\pi$
$653$	10.4136			0.407517			0.203758	+	0.979021i	$0.434684\pi$
$654$		−	35.7939i		−	1.39965i
$655$	−24.2962	+	24.2962i	−0.949331	+	0.949331i
$656$	68.4469	−	68.4469i	2.67240	−	2.67240i
$657$	−1.78979	−	1.78979i	−0.0698262	−	0.0698262i
$658$	−44.1412	+	44.1412i	−1.72080	+	1.72080i
$659$			1.42637i			0.0555634i	0.999614	+	0.0277817i	$0.00884432\pi$
$659$			1.42637i			0.0555634i	−0.999614	+	0.0277817i	$0.991156\pi$
$660$	40.6691	−	1.52244i	1.58304	−	0.0592610i
$661$	1.24931	−	1.24931i	0.0485926	−	0.0485926i	−0.682393	−	0.730986i	$-0.739061\pi$
$661$	1.24931	−	1.24931i	0.0485926	−	0.0485926i	0.730986	+	0.682393i	$0.239061\pi$
$662$	53.4121			2.07592
$663$	7.37723	−	15.4094i	0.286508	−	0.598451i
$664$	−136.826			−5.30989
$665$	−16.1968	−	16.1968i	−0.628085	−	0.628085i
$666$		−	12.2134i		−	0.473260i
$667$	5.72177			0.221548
$668$	−32.5065	+	32.5065i	−1.25772	+	1.25772i
$669$	−3.50573	−	3.50573i	−0.135540	−	0.135540i
$670$	34.5635	+	34.5635i	1.33530	+	1.33530i
$671$	−21.7692	+	23.4625i	−0.840392	+	0.905759i
$672$	49.8926			1.92465
$673$	−10.8966			−0.420032			−0.210016	−	0.977698i	$-0.567352\pi$
$673$	−10.8966			−0.420032			−0.210016	+	0.977698i	$0.567352\pi$
$674$	13.1505	−	13.1505i	0.506538	−	0.506538i
$675$		−	0.108039i		−	0.00415842i
$676$	−54.9798	+	44.2595i	−2.11461	+	1.70229i
$677$		−	16.2755i		−	0.625517i	−0.949833	−	0.312758i	$-0.898747\pi$
$677$		−	16.2755i		−	0.625517i	0.949833	−	0.312758i	$-0.101253\pi$
$678$	−39.2470	+	39.2470i	−1.50727	+	1.50727i
$679$		−	27.9969i		−	1.07442i
$680$			100.100i			3.83865i
$681$	1.61090	−	1.61090i	0.0617298	−	0.0617298i
$682$	−41.2676	−	38.2894i	−1.58022	−	1.46618i
$683$	−18.4897	+	18.4897i	−0.707490	+	0.707490i	−0.966007	−	0.258517i	$-0.916766\pi$
$683$	−18.4897	+	18.4897i	−0.707490	+	0.707490i	0.258517	+	0.966007i	$0.416766\pi$
$684$	16.4952	+	16.4952i	0.630708	+	0.630708i
$685$	−29.3959			−1.12316
$686$		−	54.2382i		−	2.07083i
$687$	3.58607	−	3.58607i	0.136817	−	0.136817i
$688$	68.5678			2.61412
$689$	−0.739858	+	1.54540i	−0.0281863	+	0.0588750i
$690$			10.0397i			0.382205i
$691$	19.9518	+	19.9518i	0.759002	+	0.759002i	0.976141	−	0.217139i	$-0.0696724\pi$
$691$	19.9518	+	19.9518i	0.759002	+	0.759002i	−0.217139	+	0.976141i	$0.569672\pi$
$692$		−	83.4912i		−	3.17386i
$693$	−0.292657	−	7.81776i	−0.0111171	−	0.296972i
$694$	16.4736	+	16.4736i	0.625330	+	0.625330i
$695$	6.04215	−	6.04215i	0.229192	−	0.229192i
$696$	23.2047	−	23.2047i	0.879573	−	0.879573i
$697$	22.1854	−	22.1854i	0.840332	−	0.840332i
$698$	80.5604			3.04925
$699$	−9.90256			−0.374549
$700$	−0.978364	−	0.978364i	−0.0369787	−	0.0369787i
$701$	−2.24477			−0.0847839			−0.0423920	−	0.999101i	$-0.513498\pi$
$701$	−2.24477			−0.0847839			−0.0423920	+	0.999101i	$0.513498\pi$
$702$	−3.26713	−	9.26860i	−0.123310	−	0.349821i
$703$		−	19.2526i		−	0.726126i
$704$	−64.0999	+	69.0857i	−2.41586	+	2.60376i
$705$	−21.9443			−0.826471
$706$	38.9230			1.46489
$707$	19.6888	+	19.6888i	0.740475	+	0.740475i
$708$	44.4633	+	44.4633i	1.67103	+	1.67103i
$709$	28.7384	−	28.7384i	1.07929	−	1.07929i	0.0827190	−	0.996573i	$-0.473640\pi$
$709$	28.7384	−	28.7384i	1.07929	−	1.07929i	0.996573	−	0.0827190i	$-0.0263604\pi$
$710$	36.7648	+	36.7648i	1.37976	+	1.37976i
$711$		−	1.07811i		−	0.0404323i
$712$	−172.116			−6.45033
$713$	7.17632	−	7.17632i	0.268755	−	0.268755i
$714$	30.4642			1.14009
$715$	−24.7967	−	10.7505i	−0.927344	−	0.402045i
$716$	−11.1265			−0.415818
$717$	9.55134	−	9.55134i	0.356701	−	0.356701i
$718$	34.0946			1.27240
$719$			17.2760i			0.644285i	0.946691	+	0.322143i	$0.104403\pi$
$719$			17.2760i			0.644285i	−0.946691	+	0.322143i	$0.895597\pi$
$720$	23.3627	+	23.3627i	0.870678	+	0.870678i
$721$	20.8064	−	20.8064i	0.774872	−	0.774872i
$722$	−1.03898	−	1.03898i	−0.0386667	−	0.0386667i
$723$	11.8064	+	11.8064i	0.439085	+	0.439085i
$724$	−27.8053			−1.03337
$725$	−0.379307			−0.0140871
$726$	22.7265	+	19.5564i	0.843460	+	0.725805i
$727$			4.09084i			0.151721i	0.997118	+	0.0758603i	$0.0241703\pi$
$727$			4.09084i			0.151721i	−0.997118	+	0.0758603i	$0.975830\pi$
$728$	−71.7020	−	34.3273i	−2.65745	−	1.27225i
$729$	1.00000			0.0370370
$730$	−11.0256	−	11.0256i	−0.408076	−	0.408076i
$731$	22.2246			0.822007
$732$	−52.3939			−1.93653
$733$	10.3819	−	10.3819i	0.383465	−	0.383465i	−0.488884	−	0.872349i	$-0.662596\pi$
$733$	10.3819	−	10.3819i	0.383465	−	0.383465i	0.872349	+	0.488884i	$0.162596\pi$
$734$	−54.2896	+	54.2896i	−2.00387	+	2.00387i
$735$	2.29505	−	2.29505i	0.0846543	−	0.0846543i
$736$	−24.3753	−	24.3753i	−0.898486	−	0.898486i
$737$	0.984463	+	26.2980i	0.0362632	+	0.968700i
$738$		−	18.0481i		−	0.664360i
$739$	−28.9058	−	28.9058i	−1.06332	−	1.06332i	−0.997855	−	0.0654633i	$-0.979147\pi$
$739$	−28.9058	−	28.9058i	−1.06332	−	1.06332i	−0.0654633	−	0.997855i	$-0.520853\pi$
$740$		−	54.9838i		−	2.02124i
$741$	−5.15014	−	14.6105i	−0.189195	−	0.536732i
$742$	−3.05523			−0.112161
$743$	−9.12169	+	9.12169i	−0.334642	+	0.334642i	−0.854346	−	0.519704i	$-0.826042\pi$
$743$	−9.12169	+	9.12169i	−0.334642	+	0.334642i	0.519704	+	0.854346i	$0.326042\pi$
$744$		−	58.2074i		−	2.13399i
$745$	9.54080			0.349548
$746$	−53.9278	−	53.9278i	−1.97444	−	1.97444i
$747$	−10.3508	+	10.3508i	−0.378716	+	0.378716i
$748$	−58.0333	+	62.5472i	−2.12191	+	2.28695i
$749$	−19.8195	+	19.8195i	−0.724188	+	0.724188i
$750$			30.1359i			1.10041i
$751$			42.5746i			1.55357i	0.629766	+	0.776785i	$0.283151\pi$
$751$			42.5746i			1.55357i	−0.629766	+	0.776785i	$0.716849\pi$
$752$	100.367	−	100.367i	3.66001	−	3.66001i
$753$			8.69988i			0.317041i
$754$	−32.5405	+	11.4704i	−1.18506	+	0.417726i
$755$		−	9.74283i		−	0.354578i
$756$	9.05565	−	9.05565i	0.329351	−	0.329351i
$757$	0.612430			0.0222592			0.0111296	−	0.999938i	$-0.496457\pi$
$757$	0.612430			0.0222592			0.0111296	+	0.999938i	$0.496457\pi$
$758$	−41.5073			−1.50761
$759$	−3.67644	+	3.96240i	−0.133446	+	0.143826i
$760$	64.1830	+	64.1830i	2.32816	+	2.32816i
$761$	9.39825	+	9.39825i	0.340686	+	0.340686i	0.856625	−	0.515939i	$-0.172557\pi$
$761$	9.39825	+	9.39825i	0.340686	+	0.340686i	−0.515939	+	0.856625i	$0.672557\pi$
$762$	20.3854	−	20.3854i	0.738484	−	0.738484i
$763$	−30.9760			−1.12141
$764$		−	120.582i		−	4.36249i
$765$	7.57247	+	7.57247i	0.273783	+	0.273783i
$766$	−58.1666			−2.10164
$767$	−13.8824	−	39.3832i	−0.501263	−	1.42205i
$768$	−38.9692			−1.40618
$769$	22.7789	−	22.7789i	0.821428	−	0.821428i	−0.164885	−	0.986313i	$-0.552725\pi$
$769$	22.7789	−	22.7789i	0.821428	−	0.821428i	0.986313	+	0.164885i	$0.0527252\pi$
$770$	−1.80285	−	48.1597i	−0.0649703	−	1.73556i
$771$			10.7735i			0.387997i
$772$	−48.5559	+	48.5559i	−1.74756	+	1.74756i
$773$	24.6264	+	24.6264i	0.885750	+	0.885750i	0.994112	−	0.108361i	$-0.0345604\pi$
$773$	24.6264	+	24.6264i	0.885750	+	0.885750i	−0.108361	+	0.994112i	$0.534560\pi$
$774$	9.03999	−	9.03999i	0.324936	−	0.324936i
$775$	−0.475732	+	0.475732i	−0.0170888	+	0.0170888i
$776$			110.943i			3.98263i
$777$	−10.5695			−0.379177
$778$	34.7236	+	34.7236i	1.24490	+	1.24490i
$779$		−	28.4501i		−	1.01933i
$780$	−14.7084	−	41.7265i	−0.526643	−	1.49405i
$781$	1.04716	+	27.9729i	0.0374704	+	1.00095i
$782$	−14.8835	−	14.8835i	−0.532232	−	0.532232i
$783$		−	3.51084i		−	0.125467i
$784$			20.9939i			0.749781i
$785$	26.9779	+	26.9779i	0.962881	+	0.962881i
$786$	−29.3012	−	29.3012i	−1.04514	−	1.04514i
$787$	13.2325	+	13.2325i	0.471686	+	0.471686i	0.902460	−	0.430774i	$-0.141759\pi$
$787$	13.2325	+	13.2325i	0.471686	+	0.471686i	−0.430774	+	0.902460i	$0.641759\pi$
$788$	−23.3198	−	23.3198i	−0.830733	−	0.830733i
$789$		−	27.7455i		−	0.987765i
$790$		−	6.64148i		−	0.236293i
$791$	33.9642	+	33.9642i	1.20763	+	1.20763i
$792$	1.15971	+	30.9794i	0.0412085	+	1.10081i
$793$	31.3831	+	15.0246i	1.11445	+	0.533541i
$794$		−	46.8074i		−	1.66113i
$795$	−0.759438	−	0.759438i	−0.0269345	−	0.0269345i
$796$	8.71680			0.308959
$797$			18.2094i			0.645010i	0.946568	+	0.322505i	$0.104525\pi$
$797$			18.2094i			0.645010i	−0.946568	+	0.322505i	$0.895475\pi$
$798$	19.5333	−	19.5333i	0.691472	−	0.691472i
$799$	32.5316	−	32.5316i	1.15089	−	1.15089i
$800$	1.61589	+	1.61589i	0.0571303	+	0.0571303i
$801$	−13.0204	+	13.0204i	−0.460054	+	0.460054i
$802$		−	101.371i		−	3.57954i
$803$	−0.314040	−	8.38897i	−0.0110822	−	0.296040i
$804$	−30.4621	+	30.4621i	−1.07432	+	1.07432i
$805$	8.68834			0.306224
$806$	−26.4265	+	55.1990i	−0.930833	+	1.94430i
$807$	5.84397			0.205718
$808$	−78.0209	−	78.0209i	−2.74477	−	2.74477i
$809$		−	30.3076i		−	1.06556i	−0.846254	−	0.532780i	$-0.821147\pi$
$809$		−	30.3076i		−	1.06556i	0.846254	−	0.532780i	$-0.178853\pi$
$810$	6.16029			0.216451
$811$	27.5270	−	27.5270i	0.966604	−	0.966604i	−0.0328557	−	0.999460i	$-0.510460\pi$
$811$	27.5270	−	27.5270i	0.966604	−	0.966604i	0.999460	+	0.0328557i	$0.0104602\pi$
$812$	−31.7929	−	31.7929i	−1.11571	−	1.11571i
$813$	−4.13754	−	4.13754i	−0.145110	−	0.145110i
$814$	27.5515	−	29.6944i	0.965678	−	1.04079i
$815$	−5.45771			−0.191175
$816$	−69.2687			−2.42489
$817$	14.2502	−	14.2502i	0.498551	−	0.498551i
$818$		−	83.5192i		−	2.92018i
$819$	−8.02103	+	2.82737i	−0.280277	+	0.0987962i
$820$		−	81.2511i		−	2.83741i
$821$	12.6657	−	12.6657i	0.442037	−	0.442037i	−0.450659	−	0.892696i	$-0.648811\pi$
$821$	12.6657	−	12.6657i	0.442037	−	0.442037i	0.892696	+	0.450659i	$0.148811\pi$
$822$		−	35.4515i		−	1.23651i
$823$		−	29.5890i		−	1.03141i	−0.856766	−	0.515705i	$-0.827530\pi$
$823$		−	29.5890i		−	1.03141i	0.856766	−	0.515705i	$-0.172470\pi$
$824$	−82.4496	+	82.4496i	−2.87227	+	2.87227i
$825$	0.243718	−	0.262675i	0.00848518	−	0.00914517i
$826$	52.6527	−	52.6527i	1.83202	−	1.83202i
$827$	−11.9438	−	11.9438i	−0.415328	−	0.415328i	0.468262	−	0.883590i	$-0.344880\pi$
$827$	−11.9438	−	11.9438i	−0.415328	−	0.415328i	−0.883590	+	0.468262i	$0.844880\pi$
$828$	−8.84839			−0.307503
$829$			14.9677i			0.519848i	0.965629	+	0.259924i	$0.0836976\pi$
$829$			14.9677i			0.519848i	−0.965629	+	0.259924i	$0.916302\pi$
$830$	−63.7639	+	63.7639i	−2.21328	+	2.21328i
$831$	−6.26647			−0.217382
$832$	92.4081	+	44.2403i	3.20368	+	1.53376i
$833$			6.80465i			0.235767i
$834$	7.28683	+	7.28683i	0.252322	+	0.252322i
$835$			19.1367i			0.662254i
$836$	2.89428	+	77.3150i	0.100101	+	2.67399i
$837$	−4.40334	−	4.40334i	−0.152202	−	0.152202i
$838$	34.2655	−	34.2655i	1.18368	−	1.18368i
$839$	−22.5775	+	22.5775i	−0.779461	+	0.779461i	−0.979739	−	0.200278i	$-0.935816\pi$
$839$	−22.5775	+	22.5775i	−0.779461	+	0.779461i	0.200278	+	0.979739i	$0.435816\pi$
$840$	35.2357	−	35.2357i	1.21575	−	1.21575i
$841$	16.6740			0.574967
$842$	93.5769			3.22487
$843$	−2.23464	−	2.23464i	−0.0769653	−	0.0769653i
$844$	37.6473			1.29587
$845$	−3.15554	+	29.2113i	−0.108554	+	1.00490i
$846$		−	26.4648i		−	0.909880i
$847$	16.9240	−	19.6675i	0.581517	−	0.675783i
$848$	6.94691			0.238558
$849$	11.1658			0.383208
$850$	0.986654	+	0.986654i	0.0338420	+	0.0338420i
$851$	5.16378	+	5.16378i	0.177012	+	0.177012i
$852$	−32.4023	+	32.4023i	−1.11008	+	1.11008i
$853$	−20.4890	−	20.4890i	−0.701532	−	0.701532i	0.263208	−	0.964739i	$-0.415220\pi$
$853$	−20.4890	−	20.4890i	−0.701532	−	0.701532i	−0.964739	+	0.263208i	$0.915220\pi$
$854$			62.0441i			2.12310i
$855$	9.71077			0.332101
$856$	78.5386	−	78.5386i	2.68439	−	2.68439i
$857$	−7.04788			−0.240751			−0.120376	−	0.992728i	$-0.538410\pi$
$857$	−7.04788			−0.240751			−0.120376	+	0.992728i	$0.538410\pi$
$858$	12.9651	−	29.9048i	0.442620	−	1.02093i
$859$	16.3966			0.559446			0.279723	−	0.960081i	$-0.409757\pi$
$859$	16.3966			0.559446			0.279723	+	0.960081i	$0.409757\pi$
$860$	40.6973	−	40.6973i	1.38777	−	1.38777i
$861$	−15.6188			−0.532287
$862$			28.8726i			0.983406i
$863$	−4.28333	−	4.28333i	−0.145806	−	0.145806i	0.630435	−	0.776242i	$-0.282876\pi$
$863$	−4.28333	−	4.28333i	−0.145806	−	0.145806i	−0.776242	+	0.630435i	$0.782876\pi$
$864$	−14.9565	+	14.9565i	−0.508831	+	0.508831i
$865$	−24.5758	−	24.5758i	−0.835603	−	0.835603i
$866$	12.2461	+	12.2461i	0.416139	+	0.416139i
$867$	−5.45176			−0.185151
$868$	−79.7502			−2.70690
$869$	2.43204	−	2.62121i	0.0825013	−	0.0889184i
$870$		−	21.6278i		−	0.733250i
$871$	26.9818	−	9.51093i	0.914243	−	0.322266i
$872$	122.748			4.15679
$873$	8.39275	+	8.39275i	0.284051	+	0.284051i
$874$	−19.0863			−0.645602
$875$	26.0796			0.881650
$876$	9.71731	−	9.71731i	0.328317	−	0.328317i
$877$	27.9050	−	27.9050i	0.942286	−	0.942286i	−0.0561374	−	0.998423i	$-0.517878\pi$
$877$	27.9050	−	27.9050i	0.942286	−	0.942286i	0.998423	+	0.0561374i	$0.0178785\pi$
$878$	34.2681	−	34.2681i	1.15649	−	1.15649i
$879$	10.1968	+	10.1968i	0.343931	+	0.343931i
$880$	4.09928	+	109.504i	0.138187	+	3.69139i
$881$		−	46.5633i		−	1.56876i	−0.620282	−	0.784379i	$-0.712982\pi$
$881$		−	46.5633i		−	1.56876i	0.620282	−	0.784379i	$-0.287018\pi$
$882$	2.76783	+	2.76783i	0.0931978	+	0.0931978i
$883$		−	52.6571i		−	1.77205i	−0.463636	−	0.886026i	$-0.653456\pi$
$883$		−	52.6571i		−	1.77205i	0.463636	−	0.886026i	$-0.346544\pi$
$884$	83.6624	+	40.0533i	2.81387	+	1.34714i
$885$	26.1757			0.879887
$886$	−1.01455	+	1.01455i	−0.0340844	+	0.0340844i
$887$		−	2.54105i		−	0.0853202i	−0.999090	−	0.0426601i	$-0.986417\pi$
$887$		−	2.54105i		−	0.0853202i	0.999090	−	0.0426601i	$-0.0135833\pi$
$888$	41.8836			1.40552
$889$	−17.6415	−	17.6415i	−0.591676	−	0.591676i
$890$	−80.2097	+	80.2097i	−2.68864	+	2.68864i
$891$	2.43130	+	2.25584i	0.0814515	+	0.0755733i
$892$	19.0337	−	19.0337i	0.637296	−	0.637296i
$893$		−	41.7179i		−	1.39603i
$894$			11.5062i			0.384825i
$895$	−3.27512	+	3.27512i	−0.109475	+	0.109475i
$896$			82.9047i			2.76965i
$897$	5.30005	+	2.53739i	0.176964	+	0.0847211i
$898$		−	16.3519i		−	0.545668i
$899$	−15.4594	+	15.4594i	−0.515600	+	0.515600i
$900$	0.586577			0.0195526
$901$	2.25167			0.0750141
$902$	40.7136	−	43.8803i	1.35561	−	1.46105i
$903$	−7.82319	−	7.82319i	−0.260340	−	0.260340i
$904$	−134.590	−	134.590i	−4.47640	−	4.47640i
$905$	−8.18454	+	8.18454i	−0.272063	+	0.272063i
$906$	11.7499			0.390363
$907$		−	13.2041i		−	0.438435i	−0.975676	−	0.219218i	$-0.929650\pi$
$907$		−	13.2041i		−	0.438435i	0.975676	−	0.219218i	$-0.0703504\pi$
$908$	8.74608	+	8.74608i	0.290249	+	0.290249i
$909$	−11.8044			−0.391528
$910$	−49.4119	+	17.4174i	−1.63799	+	0.577382i
$911$	0.600961			0.0199107			0.00995536	−	0.999950i	$-0.496831\pi$
$911$	0.600961			0.0199107			0.00995536	+	0.999950i	$0.496831\pi$
$912$	−44.4144	+	44.4144i	−1.47071	+	1.47071i
$913$	−48.5155	+	1.81617i	−1.60563	+	0.0601066i
$914$		−	95.5267i		−	3.15974i
$915$	−15.4223	+	15.4223i	−0.509844	+	0.509844i
$916$	19.4699	+	19.4699i	0.643304	+	0.643304i
$917$	−25.3572	+	25.3572i	−0.837369	+	0.837369i
$918$	−9.13239	+	9.13239i	−0.301414	+	0.301414i
$919$			14.5639i			0.480420i	0.970721	+	0.240210i	$0.0772163\pi$
$919$			14.5639i			0.480420i	−0.970721	+	0.240210i	$0.922784\pi$
$920$	−34.4293			−1.13510
$921$	13.6076	+	13.6076i	0.448387	+	0.448387i
$922$			97.1550i			3.19963i
$923$	28.7002	−	10.1167i	0.944679	−	0.332994i
$924$	42.4451	−	1.58893i	1.39634	−	0.0522718i
$925$	−0.342317	−	0.342317i	−0.0112553	−	0.0112553i
$926$		−	25.8625i		−	0.849894i
$927$			12.4745i			0.409716i
$928$	52.5099	+	52.5099i	1.72372	+	1.72372i
$929$	0.772534	+	0.772534i	0.0253460	+	0.0253460i	0.719666	−	0.694320i	$-0.244295\pi$
$929$	0.772534	+	0.772534i	0.0253460	+	0.0253460i	−0.694320	+	0.719666i	$0.744295\pi$
$930$	−27.1258	−	27.1258i	−0.889492	−	0.889492i
$931$	4.36307	+	4.36307i	0.142994	+	0.142994i
$932$		−	53.7641i		−	1.76110i
$933$		−	1.00832i		−	0.0330108i
$934$	−1.99797	−	1.99797i	−0.0653756	−	0.0653756i
$935$	1.32868	+	35.4931i	0.0434526	+	1.16075i
$936$	31.7849	−	11.2040i	1.03892	−	0.366214i
$937$			14.1007i			0.460649i	0.973114	+	0.230325i	$0.0739788\pi$
$937$			14.1007i			0.460649i	−0.973114	+	0.230325i	$0.926021\pi$
$938$	36.0728	+	36.0728i	1.17782	+	1.17782i
$939$	5.48997			0.179158
$940$		−	119.143i		−	3.88600i
$941$	16.5248	−	16.5248i	0.538693	−	0.538693i	−0.384452	−	0.923145i	$-0.625610\pi$
$941$	16.5248	−	16.5248i	0.538693	−	0.538693i	0.923145	+	0.384452i	$0.125610\pi$
$942$	−32.5353	+	32.5353i	−1.06006	+	1.06006i
$943$	7.63066	+	7.63066i	0.248488	+	0.248488i
$944$	−119.720	+	119.720i	−3.89657	+	3.89657i
$945$		−	5.33111i		−	0.173421i
$946$	42.3717	−	1.58618i	1.37762	−	0.0515711i
$947$	−26.6532	+	26.6532i	−0.866113	+	0.866113i	−0.992040	−	0.125926i	$-0.959810\pi$
$947$	−26.6532	+	26.6532i	−0.866113	+	0.866113i	0.125926	+	0.992040i	$0.459810\pi$
$948$	5.85340			0.190110
$949$	−8.60709	+	3.03395i	−0.279398	+	0.0984862i
$950$	1.26527			0.0410506
$951$	6.51766	+	6.51766i	0.211350	+	0.211350i
$952$			104.471i			3.38593i
$953$	13.8804			0.449631			0.224815	−	0.974401i	$-0.427822\pi$
$953$	13.8804			0.449631			0.224815	+	0.974401i	$0.427822\pi$
$954$	0.915882	−	0.915882i	0.0296528	−	0.0296528i
$955$	−35.4935	−	35.4935i	−1.14854	−	1.14854i
$956$	51.8572	+	51.8572i	1.67718	+	1.67718i
$957$	7.91987	−	8.53588i	0.256013	−	0.275926i
$958$	−12.8080			−0.413808
$959$	−30.6797			−0.990698
$960$	−45.4111	+	45.4111i	−1.46564	+	1.46564i
$961$			7.77876i			0.250928i
$962$	−39.7189	−	19.0154i	−1.28059	−	0.613081i
$963$		−	11.8827i		−	0.382916i
$964$	−64.1006	+	64.1006i	−2.06454	+	2.06454i
$965$			28.5851i			0.920186i
$966$			10.4781i			0.337129i
$967$	−29.9796	+	29.9796i	−0.964080	+	0.964080i	−0.999377	−	0.0352970i	$-0.988762\pi$
$967$	−29.9796	+	29.9796i	−0.964080	+	0.964080i	0.0352970	+	0.999377i	$0.488762\pi$
$968$	−67.0649	+	77.9363i	−2.15555	+	2.50497i
$969$	−14.3958	+	14.3958i	−0.462461	+	0.462461i
$970$	51.7018	+	51.7018i	1.66004	+	1.66004i
$971$	32.9124			1.05621			0.528104	−	0.849180i	$-0.322903\pi$
$971$	32.9124			1.05621			0.528104	+	0.849180i	$0.322903\pi$
$972$			5.42931i			0.174145i
$973$	6.30601	−	6.30601i	0.202161	−	0.202161i
$974$	0.903629			0.0289541
$975$	−0.351351	−	0.168209i	−0.0112522	−	0.00538699i
$976$		−	141.074i		−	4.51567i
$977$	34.7815	+	34.7815i	1.11276	+	1.11276i	0.992776	+	0.119982i	$0.0382837\pi$
$977$	34.7815	+	34.7815i	1.11276	+	1.11276i	0.119982	+	0.992776i	$0.461716\pi$
$978$		−	6.58200i		−	0.210469i
$979$	−61.0285	+	2.28460i	−1.95048	+	0.0730160i
$980$	12.4606	+	12.4606i	0.398038	+	0.398038i
$981$	9.28581	−	9.28581i	0.296473	−	0.296473i
$982$	−47.9936	+	47.9936i	−1.53154	+	1.53154i
$983$	1.01363	−	1.01363i	0.0323297	−	0.0323297i	−0.690757	−	0.723087i	$-0.742723\pi$
$983$	1.01363	−	1.01363i	0.0323297	−	0.0323297i	0.723087	+	0.690757i	$0.242723\pi$
$984$	61.8926			1.97306
$985$	−13.7285			−0.437425
$986$	32.0623	+	32.0623i	1.02107	+	1.02107i
$987$	−22.9026			−0.728999
$988$	79.3252	−	27.9617i	2.52367	−	0.889580i
$989$			7.64414i			0.243070i
$990$	14.9775	+	13.8966i	0.476016	+	0.441663i
$991$	−0.521268			−0.0165586			−0.00827932	−	0.999966i	$-0.502635\pi$
$991$	−0.521268			−0.0165586			−0.00827932	+	0.999966i	$0.502635\pi$
$992$	131.717			4.18203
$993$	13.8564	+	13.8564i	0.439719	+	0.439719i
$994$	38.3703	+	38.3703i	1.21703	+	1.21703i
$995$	2.56581	−	2.56581i	0.0813417	−	0.0813417i
$996$	−56.1976	−	56.1976i	−1.78069	−	1.78069i
$997$		−	54.0972i		−	1.71327i	−0.515919	−	0.856637i	$-0.672550\pi$
$997$		−	54.0972i		−	1.71327i	0.515919	−	0.856637i	$-0.327450\pi$
$998$	100.963			3.19592
$999$	3.16846	−	3.16846i	0.100246	−	0.100246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.m.a.307.1	yes	28
11.10	odd	2	inner	429.2.m.a.307.14	yes	28
13.5	odd	4	inner	429.2.m.a.109.14	yes	28
143.109	even	4	inner	429.2.m.a.109.1	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.m.a.109.1	✓	28	143.109	even	4	inner
429.2.m.a.109.14	yes	28	13.5	odd	4	inner
429.2.m.a.307.1	yes	28	1.1	even	1	trivial
429.2.m.a.307.14	yes	28	11.10	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-1.92734 + 1.92734i) q^{2} -1.00000 q^{3} -5.42931i q^{4} +(-1.59813 - 1.59813i) q^{5} +(1.92734 - 1.92734i) q^{6} +(-1.66792 - 1.66792i) q^{7} +(6.60946 + 6.60946i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.92734 + 1.92734i) q^{2} -1.00000 q^{3} -5.42931i q^{4} +(-1.59813 - 1.59813i) q^{5} +(1.92734 - 1.92734i) q^{6} +(-1.66792 - 1.66792i) q^{7} +(6.60946 + 6.60946i) q^{8} +1.00000 q^{9} +6.16029 q^{10} +(2.43130 + 2.25584i) q^{11} +5.42931i q^{12} +(1.55693 - 3.25207i) q^{13} +6.42931 q^{14} +(1.59813 + 1.59813i) q^{15} -14.6188 q^{16} -4.73833 q^{17} +(-1.92734 + 1.92734i) q^{18} +(-3.03817 + 3.03817i) q^{19} +(-8.67674 + 8.67674i) q^{20} +(1.66792 + 1.66792i) q^{21} +(-9.03372 + 0.338176i) q^{22} -1.62975i q^{23} +(-6.60946 - 6.60946i) q^{24} +0.108039i q^{25} +(3.26713 + 9.26860i) q^{26} -1.00000 q^{27} +(-9.05565 + 9.05565i) q^{28} +3.51084i q^{29} -6.16029 q^{30} +(4.40334 + 4.40334i) q^{31} +(14.9565 - 14.9565i) q^{32} +(-2.43130 - 2.25584i) q^{33} +(9.13239 - 9.13239i) q^{34} +5.33111i q^{35} -5.42931i q^{36} +(-3.16846 + 3.16846i) q^{37} -11.7112i q^{38} +(-1.55693 + 3.25207i) q^{39} -21.1256i q^{40} +(-4.68212 + 4.68212i) q^{41} -6.42931 q^{42} -4.69039 q^{43} +(12.2476 - 13.2003i) q^{44} +(-1.59813 - 1.59813i) q^{45} +(3.14108 + 3.14108i) q^{46} +(-6.86563 + 6.86563i) q^{47} +14.6188 q^{48} -1.43609i q^{49} +(-0.208228 - 0.208228i) q^{50} +4.73833 q^{51} +(-17.6565 - 8.45304i) q^{52} -0.475204 q^{53} +(1.92734 - 1.92734i) q^{54} +(-0.280412 - 7.49065i) q^{55} -22.0481i q^{56} +(3.03817 - 3.03817i) q^{57} +(-6.76659 - 6.76659i) q^{58} +(8.18948 - 8.18948i) q^{59} +(8.67674 - 8.67674i) q^{60} +9.65019i q^{61} -16.9735 q^{62} +(-1.66792 - 1.66792i) q^{63} +28.4151i q^{64} +(-7.68541 + 2.70906i) q^{65} +(9.03372 - 0.338176i) q^{66} +(5.61068 + 5.61068i) q^{67} +25.7259i q^{68} +1.62975i q^{69} +(-10.2749 - 10.2749i) q^{70} +(5.96802 + 5.96802i) q^{71} +(6.60946 + 6.60946i) q^{72} +(-1.78979 - 1.78979i) q^{73} -12.2134i q^{74} -0.108039i q^{75} +(16.4952 + 16.4952i) q^{76} +(-0.292657 - 7.81776i) q^{77} +(-3.26713 - 9.26860i) q^{78} -1.07811i q^{79} +(23.3627 + 23.3627i) q^{80} +1.00000 q^{81} -18.0481i q^{82} +(-10.3508 + 10.3508i) q^{83} +(9.05565 - 9.05565i) q^{84} +(7.57247 + 7.57247i) q^{85} +(9.03999 - 9.03999i) q^{86} -3.51084i q^{87} +(1.15971 + 30.9794i) q^{88} +(-13.0204 + 13.0204i) q^{89} +6.16029 q^{90} +(-8.02103 + 2.82737i) q^{91} -8.84839 q^{92} +(-4.40334 - 4.40334i) q^{93} -26.4648i q^{94} +9.71077 q^{95} +(-14.9565 + 14.9565i) q^{96} +(8.39275 + 8.39275i) q^{97} +(2.76783 + 2.76783i) q^{98} +(2.43130 + 2.25584i) 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

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