LMFDB - Embedded newform 429.2.n.c.196.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 0]))

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.n (of order $5$, degree $4$, 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:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			196.2
Character	$\chi$	$=$	429.196
Dual form			429.2.n.c.313.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.488036 + 1.50202i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.399850 - 0.290508i) q^{4} +(1.09306 + 3.36409i) q^{5} +(0.488036 + 1.50202i) q^{6} +(3.87810 + 2.81760i) q^{7} +(-1.92390 + 1.39779i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.488036 + 1.50202i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.399850 - 0.290508i) q^{4} +(1.09306 + 3.36409i) q^{5} +(0.488036 + 1.50202i) q^{6} +(3.87810 + 2.81760i) q^{7} +(-1.92390 + 1.39779i) q^{8} +(0.309017 - 0.951057i) q^{9} -5.58638 q^{10} +(-0.697635 - 3.24242i) q^{11} -0.494242 q^{12} +(0.309017 - 0.951057i) q^{13} +(-6.12474 + 4.44988i) q^{14} +(2.86167 + 2.07912i) q^{15} +(-1.46604 - 4.51201i) q^{16} +(-1.69021 - 5.20194i) q^{17} +(1.27769 + 0.928299i) q^{18} +(4.58871 - 3.33389i) q^{19} +(0.540235 - 1.66267i) q^{20} +4.79359 q^{21} +(5.21065 + 0.534556i) q^{22} -6.72817 q^{23} +(-0.734864 + 2.26168i) q^{24} +(-6.07724 + 4.41537i) q^{25} +(1.27769 + 0.928299i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.732120 - 2.25324i) q^{28} +(3.06929 + 2.22997i) q^{29} +(-4.51948 + 3.28359i) q^{30} +(-1.31193 + 4.03770i) q^{31} +2.73647 q^{32} +(-2.47025 - 2.21312i) q^{33} +8.63830 q^{34} +(-5.23968 + 16.1261i) q^{35} +(-0.399850 + 0.290508i) q^{36} +(-6.25384 - 4.54368i) q^{37} +(2.76812 + 8.51939i) q^{38} +(-0.309017 - 0.951057i) q^{39} +(-6.80524 - 4.94430i) q^{40} +(1.48582 - 1.07951i) q^{41} +(-2.33944 + 7.20006i) q^{42} +5.88277 q^{43} +(-0.663000 + 1.49915i) q^{44} +3.53721 q^{45} +(3.28359 - 10.1058i) q^{46} +(4.66999 - 3.39295i) q^{47} +(-3.83815 - 2.78858i) q^{48} +(4.93763 + 15.1965i) q^{49} +(-3.66607 - 11.2830i) q^{50} +(-4.42503 - 3.21498i) q^{51} +(-0.399850 + 0.290508i) q^{52} +(0.787948 - 2.42505i) q^{53} +1.57932 q^{54} +(10.1452 - 5.89107i) q^{55} -11.3995 q^{56} +(1.75273 - 5.39435i) q^{57} +(-4.84739 + 3.52183i) q^{58} +(0.226494 + 0.164557i) q^{59} +(-0.540235 - 1.66267i) q^{60} +(-1.50584 - 4.63449i) q^{61} +(-5.42444 - 3.94108i) q^{62} +(3.87810 - 2.81760i) q^{63} +(1.59659 - 4.91379i) q^{64} +3.53721 q^{65} +(4.52971 - 2.63028i) q^{66} -15.5816 q^{67} +(-0.835374 + 2.57102i) q^{68} +(-5.44320 + 3.95472i) q^{69} +(-21.6645 - 15.7402i) q^{70} +(3.92652 + 12.0846i) q^{71} +(0.734864 + 2.26168i) q^{72} +(-6.42964 - 4.67141i) q^{73} +(9.87680 - 7.17592i) q^{74} +(-2.32130 + 7.14423i) q^{75} -2.80332 q^{76} +(6.43036 - 14.5401i) q^{77} +1.57932 q^{78} +(0.194080 - 0.597317i) q^{79} +(13.5763 - 9.86379i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.896315 + 2.75857i) q^{82} +(1.20284 + 3.70197i) q^{83} +(-1.91672 - 1.39258i) q^{84} +(15.6523 - 11.3721i) q^{85} +(-2.87100 + 8.83603i) q^{86} +3.79385 q^{87} +(5.87442 + 5.26294i) q^{88} +6.59318 q^{89} +(-1.72629 + 5.31296i) q^{90} +(3.87810 - 2.81760i) q^{91} +(2.69026 + 1.95459i) q^{92} +(1.31193 + 4.03770i) q^{93} +(2.81715 + 8.67030i) q^{94} +(16.2312 + 11.7927i) q^{95} +(2.21385 - 1.60846i) q^{96} +(-1.39868 + 4.30469i) q^{97} -25.2351 q^{98} +(-3.29931 - 0.338473i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9}+O(q^{10}) $ 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9} - 2 q^{10} + 14 q^{11} - 30 q^{12} - 7 q^{13} - 9 q^{14} + 4 q^{15} + q^{16} - 12 q^{17} - 4 q^{18} + 10 q^{19} - 41 q^{20} - 6 q^{21} + 5 q^{22} + 30 q^{23} + 2 q^{24} + 3 q^{25} - 4 q^{26} + 7 q^{27} - 12 q^{28} - 4 q^{29} + 7 q^{30} - 4 q^{31} + 22 q^{32} + q^{33} - 24 q^{34} - 6 q^{35} - 5 q^{36} - 8 q^{37} + 73 q^{38} + 7 q^{39} - 28 q^{40} + 10 q^{41} + 9 q^{42} - 12 q^{43} - 22 q^{44} + 16 q^{45} + 35 q^{46} + 12 q^{47} + 14 q^{48} + 16 q^{49} - 57 q^{50} - 13 q^{51} - 5 q^{52} + q^{53} - 6 q^{54} - 28 q^{55} + 48 q^{56} - 30 q^{58} - 15 q^{59} + 41 q^{60} - 22 q^{61} - 40 q^{62} + q^{63} - 19 q^{64} + 16 q^{65} + 20 q^{66} - 88 q^{67} + 39 q^{68} + 14 q^{70} + 34 q^{71} - 2 q^{72} - 59 q^{73} + 79 q^{74} + 27 q^{75} - 124 q^{76} - 42 q^{77} - 6 q^{78} - 3 q^{79} + 37 q^{80} - 7 q^{81} + 82 q^{82} - 8 q^{83} - 8 q^{84} + 70 q^{85} - 35 q^{86} - 36 q^{87} + 59 q^{88} + 126 q^{89} + 8 q^{90} + q^{91} - 82 q^{92} + 4 q^{93} + 23 q^{94} - 77 q^{95} + 73 q^{96} - 18 q^{97} - 66 q^{98} - 6 q^{99}+O(q^{100}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9 - 2 * q^10 + 14 * q^11 - 30 * q^12 - 7 * q^13 - 9 * q^14 + 4 * q^15 + q^16 - 12 * q^17 - 4 * q^18 + 10 * q^19 - 41 * q^20 - 6 * q^21 + 5 * q^22 + 30 * q^23 + 2 * q^24 + 3 * q^25 - 4 * q^26 + 7 * q^27 - 12 * q^28 - 4 * q^29 + 7 * q^30 - 4 * q^31 + 22 * q^32 + q^33 - 24 * q^34 - 6 * q^35 - 5 * q^36 - 8 * q^37 + 73 * q^38 + 7 * q^39 - 28 * q^40 + 10 * q^41 + 9 * q^42 - 12 * q^43 - 22 * q^44 + 16 * q^45 + 35 * q^46 + 12 * q^47 + 14 * q^48 + 16 * q^49 - 57 * q^50 - 13 * q^51 - 5 * q^52 + q^53 - 6 * q^54 - 28 * q^55 + 48 * q^56 - 30 * q^58 - 15 * q^59 + 41 * q^60 - 22 * q^61 - 40 * q^62 + q^63 - 19 * q^64 + 16 * q^65 + 20 * q^66 - 88 * q^67 + 39 * q^68 + 14 * q^70 + 34 * q^71 - 2 * q^72 - 59 * q^73 + 79 * q^74 + 27 * q^75 - 124 * q^76 - 42 * q^77 - 6 * q^78 - 3 * q^79 + 37 * q^80 - 7 * q^81 + 82 * q^82 - 8 * q^83 - 8 * q^84 + 70 * q^85 - 35 * q^86 - 36 * q^87 + 59 * q^88 + 126 * q^89 + 8 * q^90 + q^91 - 82 * q^92 + 4 * q^93 + 23 * q^94 - 77 * q^95 + 73 * q^96 - 18 * q^97 - 66 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	−0.488036	+	1.50202i	−0.345093	+	1.06209i	0.616440	+	0.787402i	$0.288574\pi$
$2$	−0.488036	+	1.50202i	−0.345093	+	1.06209i	−0.961534	+	0.274687i	$0.911426\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	−0.399850	−	0.290508i	−0.199925	−	0.145254i
$5$	1.09306	+	3.36409i	0.488831	+	1.50447i	0.826355	+	0.563150i	$0.190411\pi$
$5$	1.09306	+	3.36409i	0.488831	+	1.50447i	−0.337524	+	0.941317i	$0.609589\pi$
$6$	0.488036	+	1.50202i	0.199240	+	0.613197i
$7$	3.87810	+	2.81760i	1.46578	+	1.06495i	0.981809	+	0.189870i	$0.0608067\pi$
$7$	3.87810	+	2.81760i	1.46578	+	1.06495i	0.483973	+	0.875083i	$0.339193\pi$
$8$	−1.92390	+	1.39779i	−0.680201	+	0.494195i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−5.58638			−1.76657
$11$	−0.697635	−	3.24242i	−0.210345	−	0.977627i
$11$	−0.697635	−	3.24242i	−0.210345	−	0.977627i
$12$	−0.494242			−0.142675
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$14$	−6.12474	+	4.44988i	−1.63691	+	1.18928i
$15$	2.86167	+	2.07912i	0.738879	+	0.536827i
$16$	−1.46604	−	4.51201i	−0.366510	−	1.12800i
$17$	−1.69021	−	5.20194i	−0.409937	−	1.26166i	−0.916702	−	0.399572i	$-0.869159\pi$
$17$	−1.69021	−	5.20194i	−0.409937	−	1.26166i	0.506765	−	0.862084i	$-0.330841\pi$
$18$	1.27769	+	0.928299i	0.301155	+	0.218802i
$19$	4.58871	−	3.33389i	1.05272	−	0.764847i	0.0799937	−	0.996795i	$-0.474510\pi$
$19$	4.58871	−	3.33389i	1.05272	−	0.764847i	0.972728	+	0.231948i	$0.0745100\pi$
$20$	0.540235	−	1.66267i	0.120800	−	0.371785i
$21$	4.79359			1.04605
$22$	5.21065	+	0.534556i	1.11092	+	0.113968i
$23$	−6.72817			−1.40292			−0.701460	−	0.712709i	$-0.747468\pi$
$23$	−6.72817			−1.40292			−0.701460	+	0.712709i	$0.747468\pi$
$24$	−0.734864	+	2.26168i	−0.150003	+	0.461663i
$25$	−6.07724	+	4.41537i	−1.21545	+	0.883075i
$26$	1.27769	+	0.928299i	0.250576	+	0.182054i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−0.732120	−	2.25324i	−0.138358	−	0.425821i
$29$	3.06929	+	2.22997i	0.569953	+	0.414095i	0.835088	−	0.550116i	$-0.185416\pi$
$29$	3.06929	+	2.22997i	0.569953	+	0.414095i	−0.265135	+	0.964211i	$0.585416\pi$
$30$	−4.51948	+	3.28359i	−0.825140	+	0.599499i
$31$	−1.31193	+	4.03770i	−0.235629	+	0.725192i	0.761408	+	0.648273i	$0.224508\pi$
$31$	−1.31193	+	4.03770i	−0.235629	+	0.725192i	−0.997037	+	0.0769193i	$0.975492\pi$
$32$	2.73647			0.483744
$33$	−2.47025	−	2.21312i	−0.430015	−	0.385254i
$34$	8.63830			1.48146
$35$	−5.23968	+	16.1261i	−0.885667	+	2.72580i
$36$	−0.399850	+	0.290508i	−0.0666417	+	0.0484180i
$37$	−6.25384	−	4.54368i	−1.02813	−	0.746977i	−0.0601930	−	0.998187i	$-0.519172\pi$
$37$	−6.25384	−	4.54368i	−1.02813	−	0.746977i	−0.967933	+	0.251210i	$0.919172\pi$
$38$	2.76812	+	8.51939i	0.449048	+	1.38203i
$39$	−0.309017	−	0.951057i	−0.0494823	−	0.152291i
$40$	−6.80524	−	4.94430i	−1.07600	−	0.781762i
$41$	1.48582	−	1.07951i	0.232046	−	0.168591i	−0.465686	−	0.884950i	$-0.654192\pi$
$41$	1.48582	−	1.07951i	0.232046	−	0.168591i	0.697732	+	0.716358i	$0.254192\pi$
$42$	−2.33944	+	7.20006i	−0.360984	+	1.11099i
$43$	5.88277			0.897114			0.448557	−	0.893754i	$-0.351938\pi$
$43$	5.88277			0.897114			0.448557	+	0.893754i	$0.351938\pi$
$44$	−0.663000	+	1.49915i	−0.0999510	+	0.226006i
$45$	3.53721			0.527297
$46$	3.28359	−	10.1058i	0.484139	−	1.49003i
$47$	4.66999	−	3.39295i	0.681188	−	0.494912i	−0.192563	−	0.981285i	$-0.561680\pi$
$47$	4.66999	−	3.39295i	0.681188	−	0.494912i	0.873752	+	0.486372i	$0.161680\pi$
$48$	−3.83815	−	2.78858i	−0.553989	−	0.402496i
$49$	4.93763	+	15.1965i	0.705375	+	2.17092i
$50$	−3.66607	−	11.2830i	−0.518460	−	1.59566i
$51$	−4.42503	−	3.21498i	−0.619629	−	0.450187i
$52$	−0.399850	+	0.290508i	−0.0554492	+	0.0402862i
$53$	0.787948	−	2.42505i	0.108233	−	0.333107i	−0.882243	−	0.470795i	$-0.843967\pi$
$53$	0.787948	−	2.42505i	0.108233	−	0.333107i	0.990476	+	0.137688i	$0.0439672\pi$
$54$	1.57932			0.214918
$55$	10.1452	−	5.89107i	1.36798	−	0.794352i
$56$	−11.3995			−1.52332
$57$	1.75273	−	5.39435i	0.232155	−	0.714499i
$58$	−4.84739	+	3.52183i	−0.636493	+	0.462439i
$59$	0.226494	+	0.164557i	0.0294870	+	0.0214235i	0.602431	−	0.798171i	$-0.294199\pi$
$59$	0.226494	+	0.164557i	0.0294870	+	0.0214235i	−0.572944	+	0.819594i	$0.694199\pi$
$60$	−0.540235	−	1.66267i	−0.0697441	−	0.214650i
$61$	−1.50584	−	4.63449i	−0.192803	−	0.593386i	−0.999995	−	0.00309733i	$-0.999014\pi$
$61$	−1.50584	−	4.63449i	−0.192803	−	0.593386i	0.807193	−	0.590288i	$-0.200986\pi$
$62$	−5.42444	−	3.94108i	−0.688904	−	0.500518i
$63$	3.87810	−	2.81760i	0.488594	−	0.354984i
$64$	1.59659	−	4.91379i	0.199573	−	0.614224i
$65$	3.53721			0.438737
$66$	4.52971	−	2.63028i	0.557569	−	0.323765i
$67$	−15.5816			−1.90359			−0.951797	−	0.306729i	$-0.900766\pi$
$67$	−15.5816			−1.90359			−0.951797	+	0.306729i	$0.900766\pi$
$68$	−0.835374	+	2.57102i	−0.101304	+	0.311781i
$69$	−5.44320	+	3.95472i	−0.655285	+	0.476092i
$70$	−21.6645	−	15.7402i	−2.58941	−	1.88131i
$71$	3.92652	+	12.0846i	0.465992	+	1.43418i	0.857730	+	0.514100i	$0.171874\pi$
$71$	3.92652	+	12.0846i	0.465992	+	1.43418i	−0.391738	+	0.920077i	$0.628126\pi$
$72$	0.734864	+	2.26168i	0.0866045	+	0.266541i
$73$	−6.42964	−	4.67141i	−0.752532	−	0.546747i	0.144078	−	0.989566i	$-0.453978\pi$
$73$	−6.42964	−	4.67141i	−0.752532	−	0.546747i	−0.896611	+	0.442819i	$0.853978\pi$
$74$	9.87680	−	7.17592i	1.14815	−	0.834183i
$75$	−2.32130	+	7.14423i	−0.268041	+	0.824944i
$76$	−2.80332			−0.321562
$77$	6.43036	−	14.5401i	0.732807	−	1.65700i
$78$	1.57932			0.178822
$79$	0.194080	−	0.597317i	0.0218357	−	0.0672035i	−0.939545	−	0.342426i	$-0.888751\pi$
$79$	0.194080	−	0.597317i	0.0218357	−	0.0672035i	0.961381	+	0.275222i	$0.0887515\pi$
$80$	13.5763	−	9.86379i	1.51788	−	1.10281i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	0.896315	+	2.75857i	0.0989814	+	0.304633i
$83$	1.20284	+	3.70197i	0.132029	+	0.406344i	0.995116	−	0.0987117i	$-0.0314721\pi$
$83$	1.20284	+	3.70197i	0.132029	+	0.406344i	−0.863087	+	0.505055i	$0.831472\pi$
$84$	−1.91672	−	1.39258i	−0.209131	−	0.151942i
$85$	15.6523	−	11.3721i	1.69773	−	1.23347i
$86$	−2.87100	+	8.83603i	−0.309588	+	0.952814i
$87$	3.79385			0.406744
$88$	5.87442	+	5.26294i	0.626215	+	0.561031i
$89$	6.59318			0.698875			0.349438	−	0.936960i	$-0.386373\pi$
$89$	6.59318			0.698875			0.349438	+	0.936960i	$0.386373\pi$
$90$	−1.72629	+	5.31296i	−0.181967	+	0.560036i
$91$	3.87810	−	2.81760i	0.406535	−	0.295365i
$92$	2.69026	+	1.95459i	0.280479	+	0.203780i
$93$	1.31193	+	4.03770i	0.136041	+	0.418690i
$94$	2.81715	+	8.67030i	0.290567	+	0.894273i
$95$	16.2312	+	11.7927i	1.66529	+	1.20990i
$96$	2.21385	−	1.60846i	0.225950	−	0.164162i
$97$	−1.39868	+	4.30469i	−0.142014	+	0.437075i	−0.996615	−	0.0822109i	$-0.973802\pi$
$97$	−1.39868	+	4.30469i	−0.142014	+	0.437075i	0.854601	+	0.519286i	$0.173802\pi$
$98$	−25.2351			−2.54913
$99$	−3.29931	−	0.338473i	−0.331593	−	0.0340178i
$100$	3.71269			0.371269
$101$	0.299802	−	0.922696i	0.0298314	−	0.0918116i	−0.935032	−	0.354563i	$-0.884630\pi$
$101$	0.299802	−	0.922696i	0.0298314	−	0.0918116i	0.964864	+	0.262751i	$0.0846298\pi$
$102$	6.98853	−	5.07747i	0.691968	−	0.502744i
$103$	−7.44397	−	5.40836i	−0.733476	−	0.532902i	0.157185	−	0.987569i	$-0.449758\pi$
$103$	−7.44397	−	5.40836i	−0.733476	−	0.532902i	−0.890661	+	0.454668i	$0.849758\pi$
$104$	0.734864	+	2.26168i	0.0720593	+	0.221776i
$105$	5.23968	+	16.1261i	0.511340	+	1.57374i
$106$	3.25793	+	2.36703i	0.316438	+	0.229906i
$107$	−7.02145	+	5.10138i	−0.678789	+	0.493169i	−0.872956	−	0.487799i	$-0.837800\pi$
$107$	−7.02145	+	5.10138i	−0.678789	+	0.493169i	0.194167	+	0.980969i	$0.437800\pi$
$108$	−0.152729	+	0.470052i	−0.0146964	+	0.0452308i
$109$	14.3632			1.37574			0.687871	−	0.725833i	$-0.258546\pi$
$109$	14.3632			1.37574			0.687871	+	0.725833i	$0.258546\pi$
$110$	3.89726	+	18.1134i	0.371589	+	1.72705i
$111$	−7.73018			−0.733716
$112$	7.02760	−	21.6287i	0.664046	−	2.04372i
$113$	1.13656	−	0.825762i	0.106919	−	0.0776812i	−0.533041	−	0.846089i	$-0.678951\pi$
$113$	1.13656	−	0.825762i	0.106919	−	0.0776812i	0.639960	+	0.768408i	$0.278951\pi$
$114$	7.24702	+	5.26527i	0.678746	+	0.493138i
$115$	−7.35429	−	22.6342i	−0.685791	−	2.11065i
$116$	−0.579432	−	1.78331i	−0.0537989	−	0.165576i
$117$	−0.809017	−	0.587785i	−0.0747936	−	0.0543408i
$118$	−0.357705	+	0.259888i	−0.0329294	+	0.0239246i
$119$	8.10219	−	24.9360i	0.742726	−	2.28588i
$120$	−8.41174			−0.767883
$121$	−10.0266	+	4.52406i	−0.911510	+	0.411278i
$122$	7.69600			0.696763
$123$	0.567533	−	1.74669i	0.0511727	−	0.157494i
$124$	1.69756	−	1.23335i	0.152445	−	0.110758i
$125$	−7.18817	−	5.22251i	−0.642929	−	0.467116i
$126$	2.33944	+	7.20006i	0.208414	+	0.641433i
$127$	1.67676	+	5.16055i	0.148789	+	0.457925i	0.997479	−	0.0709660i	$-0.0226082\pi$
$127$	1.67676	+	5.16055i	0.148789	+	0.457925i	−0.848690	+	0.528891i	$0.822608\pi$
$128$	11.0291	+	8.01312i	0.974846	+	0.708267i
$129$	4.75926	−	3.45780i	0.419029	−	0.304443i
$130$	−1.72629	+	5.31296i	−0.151405	+	0.465978i
$131$	−1.65849			−0.144903			−0.0724515	−	0.997372i	$-0.523082\pi$
$131$	−1.65849			−0.144903			−0.0724515	+	0.997372i	$0.523082\pi$
$132$	0.344800	+	1.60254i	0.0300110	+	0.139483i
$133$	27.1890			2.35759
$134$	7.60437	−	23.4039i	0.656918	−	2.02178i
$135$	2.86167	−	2.07912i	0.246293	−	0.178942i
$136$	10.5230	+	7.64544i	0.902343	+	0.655591i
$137$	−1.82861	−	5.62789i	−0.156229	−	0.480823i	0.842054	−	0.539392i	$-0.181346\pi$
$137$	−1.82861	−	5.62789i	−0.156229	−	0.480823i	−0.998283	+	0.0585695i	$0.981346\pi$
$138$	−3.28359	−	10.1058i	−0.279517	−	0.860266i
$139$	−1.83471	−	1.33299i	−0.155618	−	0.113063i	0.507252	−	0.861798i	$-0.330661\pi$
$139$	−1.83471	−	1.33299i	−0.155618	−	0.113063i	−0.662869	+	0.748735i	$0.730661\pi$
$140$	6.77984	−	4.92584i	0.573001	−	0.416309i
$141$	1.78378	−	5.48991i	0.150221	−	0.462333i
$142$	−20.0676			−1.68403
$143$	−3.29931	−	0.338473i	−0.275902	−	0.0283045i
$144$	−4.74421			−0.395351
$145$	−4.14691	+	12.7629i	−0.344382	+	1.05990i
$146$	10.1544	−	7.37763i	0.840387	−	0.610577i
$147$	12.9269	+	9.39192i	1.06619	+	0.774633i
$148$	1.18062	+	3.63358i	0.0970466	+	0.298679i
$149$	2.64564	+	8.14246i	0.216740	+	0.667056i	0.999026	+	0.0441364i	$0.0140536\pi$
$149$	2.64564	+	8.14246i	0.216740	+	0.667056i	−0.782286	+	0.622920i	$0.785946\pi$
$150$	−9.59789	−	6.97327i	−0.783664	−	0.569365i
$151$	7.58910	−	5.51380i	0.617592	−	0.448707i	−0.234488	−	0.972119i	$-0.575341\pi$
$151$	7.58910	−	5.51380i	0.617592	−	0.448707i	0.852080	+	0.523412i	$0.175341\pi$
$152$	−4.16812	+	12.8281i	−0.338079	+	1.04050i
$153$	−5.46964			−0.442194
$154$	18.7012	+	16.7546i	1.50699	+	1.35012i
$155$	−15.0172			−1.20621
$156$	−0.152729	+	0.470052i	−0.0122281	+	0.0376343i
$157$	3.18355	−	2.31299i	0.254075	−	0.184596i	−0.453456	−	0.891279i	$-0.649809\pi$
$157$	3.18355	−	2.31299i	0.254075	−	0.184596i	0.707531	+	0.706682i	$0.249809\pi$
$158$	0.802464	+	0.583025i	0.0638406	+	0.0463829i
$159$	−0.787948	−	2.42505i	−0.0624883	−	0.192319i
$160$	2.99112	+	9.20573i	0.236469	+	0.727777i
$161$	−26.0925	−	18.9573i	−2.05638	−	1.49404i
$162$	1.27769	−	0.928299i	0.100385	−	0.0729341i
$163$	−4.29704	+	13.2249i	−0.336570	+	1.03586i	0.629373	+	0.777103i	$0.283312\pi$
$163$	−4.29704	+	13.2249i	−0.336570	+	1.03586i	−0.965943	+	0.258753i	$0.916688\pi$
$164$	−0.907712			−0.0708804
$165$	4.74499	−	10.7292i	0.369397	−	0.835267i
$166$	−6.14745			−0.477135
$167$	1.57248	−	4.83960i	0.121682	−	0.374500i	−0.871600	−	0.490218i	$-0.836917\pi$
$167$	1.57248	−	4.83960i	0.121682	−	0.374500i	0.993282	+	0.115719i	$0.0369171\pi$
$168$	−9.22238	+	6.70045i	−0.711522	+	0.516951i
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	9.44217	+	29.0600i	0.724182	+	2.22880i
$171$	−1.75273	−	5.39435i	−0.134035	−	0.412516i
$172$	−2.35222	−	1.70899i	−0.179355	−	0.130309i
$173$	16.5290	−	12.0090i	1.25667	−	0.913028i	0.258085	−	0.966122i	$-0.416908\pi$
$173$	16.5290	−	12.0090i	1.25667	−	0.913028i	0.998589	+	0.0530945i	$0.0169085\pi$
$174$	−1.85154	+	5.69844i	−0.140365	+	0.431998i
$175$	−36.0089			−2.72202
$176$	−13.6071	+	7.90126i	−1.02567	+	0.595580i
$177$	0.279962			0.0210432
$178$	−3.21771	+	9.90308i	−0.241177	+	0.742267i
$179$	−8.07143	+	5.86424i	−0.603287	+	0.438314i	−0.847044	−	0.531523i	$-0.821620\pi$
$179$	−8.07143	+	5.86424i	−0.603287	+	0.438314i	0.243757	+	0.969836i	$0.421620\pi$
$180$	−1.41435	−	1.02759i	−0.105420	−	0.0765920i
$181$	1.42297	+	4.37947i	0.105769	+	0.325523i	0.989910	−	0.141697i	$-0.0452557\pi$
$181$	1.42297	+	4.37947i	0.105769	+	0.325523i	−0.884141	+	0.467220i	$0.845256\pi$
$182$	2.33944	+	7.20006i	0.173411	+	0.533704i
$183$	−3.94233	−	2.86427i	−0.291426	−	0.211733i
$184$	12.9443	−	9.40460i	0.954268	−	0.693316i
$185$	8.44954	−	26.0050i	0.621223	−	1.91193i
$186$	−6.70497			−0.491632
$187$	−15.6877	+	9.10944i	−1.14720	+	0.666148i
$188$	−2.85297			−0.208075
$189$	1.48130	−	4.55897i	0.107749	−	0.331617i
$190$	−25.6343	+	18.6244i	−1.85971	+	1.35116i
$191$	−19.6227	−	14.2567i	−1.41985	−	1.03158i	−0.991796	−	0.127828i	$-0.959200\pi$
$191$	−19.6227	−	14.2567i	−1.41985	−	1.03158i	−0.428053	−	0.903753i	$-0.640800\pi$
$192$	−1.59659	−	4.91379i	−0.115224	−	0.354622i
$193$	1.03291	+	3.17896i	0.0743503	+	0.228827i	0.981325	−	0.192359i	$-0.0616139\pi$
$193$	1.03291	+	3.17896i	0.0743503	+	0.228827i	−0.906974	+	0.421186i	$0.861614\pi$
$194$	−5.78312	−	4.20168i	−0.415204	−	0.301663i
$195$	2.86167	−	2.07912i	0.204928	−	0.148889i
$196$	2.44038	−	7.51072i	0.174313	−	0.536480i
$197$	−0.929088			−0.0661948			−0.0330974	−	0.999452i	$-0.510537\pi$
$197$	−0.929088			−0.0661948			−0.0330974	+	0.999452i	$0.510537\pi$
$198$	2.11857	−	4.79044i	0.150560	−	0.340442i
$199$	5.98713			0.424416			0.212208	−	0.977225i	$-0.431935\pi$
$199$	5.98713			0.424416			0.212208	+	0.977225i	$0.431935\pi$
$200$	5.52021	−	16.9895i	0.390338	−	1.20134i
$201$	−12.6058	+	9.15863i	−0.889142	+	0.646000i
$202$	1.23959	+	0.900617i	0.0872174	+	0.0633672i
$203$	5.61984	+	17.2961i	0.394435	+	1.21395i
$204$	0.835374	+	2.57102i	0.0584878	+	0.180007i
$205$	5.25567	+	3.81847i	0.367072	+	0.266693i
$206$	11.7564	−	8.54151i	0.819106	−	0.595116i
$207$	−2.07912	+	6.39887i	−0.144509	+	0.444752i
$208$	−4.74421			−0.328952
$209$	−14.0111	−	12.5527i	−0.969170	−	0.868288i
$210$	−26.7788			−1.84791
$211$	−5.38007	+	16.5581i	−0.370379	+	1.13991i	0.576164	+	0.817334i	$0.304549\pi$
$211$	−5.38007	+	16.5581i	−0.370379	+	1.13991i	−0.946544	+	0.322576i	$0.895451\pi$
$212$	−1.01956	+	0.740753i	−0.0700236	+	0.0508751i
$213$	10.2798	+	7.46869i	0.704358	+	0.511746i
$214$	−4.23566	−	13.0360i	−0.289544	−	0.891124i
$215$	6.43021	+	19.7902i	0.438537	+	1.34968i
$216$	1.92390	+	1.39779i	0.130905	+	0.0951078i
$217$	−16.4644	+	11.9621i	−1.11768	+	0.812040i
$218$	−7.00974	+	21.5738i	−0.474759	+	1.46116i
$219$	−7.94747			−0.537040
$220$	−5.76798	−	0.591732i	−0.388877	−	0.0398945i
$221$	−5.46964			−0.367928
$222$	3.77260	−	11.6109i	0.253201	−	0.779271i
$223$	−2.51905	+	1.83019i	−0.168688	+	0.122559i	−0.668926	−	0.743329i	$-0.733246\pi$
$223$	−2.51905	+	1.83019i	−0.168688	+	0.122559i	0.500238	+	0.865888i	$0.333246\pi$
$224$	10.6123	+	7.71028i	0.709063	+	0.515165i
$225$	2.32130	+	7.14423i	0.154753	+	0.476282i
$226$	0.685627	+	2.11014i	0.0456072	+	0.140365i
$227$	−9.66824	−	7.02439i	−0.641704	−	0.466225i	0.218731	−	0.975785i	$-0.429808\pi$
$227$	−9.66824	−	7.02439i	−0.641704	−	0.466225i	−0.860435	+	0.509560i	$0.829808\pi$
$228$	−2.26793	+	1.64775i	−0.150197	+	0.109125i
$229$	−1.85605	+	5.71235i	−0.122652	+	0.377483i	−0.993466	−	0.114129i	$-0.963592\pi$
$229$	−1.85605	+	5.71235i	−0.122652	+	0.377483i	0.870814	+	0.491612i	$0.163592\pi$
$230$	37.5861			2.47836
$231$	−3.34418	−	15.5428i	−0.220031	−	1.02264i
$232$	−9.02205			−0.592327
$233$	2.45098	−	7.54333i	0.160569	−	0.494180i	−0.838114	−	0.545496i	$-0.816341\pi$
$233$	2.45098	−	7.54333i	0.160569	−	0.494180i	0.998682	+	0.0513157i	$0.0163415\pi$
$234$	1.27769	−	0.928299i	0.0835255	−	0.0606848i
$235$	16.5188	+	12.0016i	1.07757	+	0.782897i
$236$	−0.0427583	−	0.131596i	−0.00278333	−	0.00856620i
$237$	−0.194080	−	0.597317i	−0.0126069	−	0.0387999i
$238$	33.5001	+	24.3393i	2.17149	+	1.57768i
$239$	13.6476	−	9.91556i	0.882790	−	0.641384i	−0.0511983	−	0.998689i	$-0.516304\pi$
$239$	13.6476	−	9.91556i	0.882790	−	0.641384i	0.933988	+	0.357304i	$0.116304\pi$
$240$	5.18570	−	15.9599i	0.334736	−	1.03021i
$241$	−8.82831			−0.568681			−0.284341	−	0.958723i	$-0.591775\pi$
$241$	−8.82831			−0.568681			−0.284341	+	0.958723i	$0.591775\pi$
$242$	−1.90188	−	17.2681i	−0.122257	−	1.11003i
$243$	−1.00000			−0.0641500
$244$	−0.744247	+	2.29056i	−0.0476456	+	0.146638i
$245$	−45.7251	+	33.2212i	−2.92127	+	2.12243i
$246$	2.34658	+	1.70489i	0.149613	+	0.108700i
$247$	−1.75273	−	5.39435i	−0.111524	−	0.343234i
$248$	−3.11986	−	9.60193i	−0.198111	−	0.609723i
$249$	3.14908	+	2.28794i	0.199565	+	0.144992i
$250$	11.3524	−	8.24800i	0.717989	−	0.521649i
$251$	2.87320	−	8.84281i	0.181355	−	0.558153i	−0.818512	−	0.574490i	$-0.805200\pi$
$251$	2.87320	−	8.84281i	0.181355	−	0.558153i	0.999867	+	0.0163370i	$0.00520046\pi$
$252$	−2.36919			−0.149245
$253$	4.69381	+	21.8156i	0.295097	+	1.37153i
$254$	−8.56956			−0.537702
$255$	5.97864	−	18.4004i	0.374397	−	1.15228i
$256$	−9.05863	+	6.58148i	−0.566165	+	0.411343i
$257$	18.4423	+	13.3991i	1.15040	+	0.835813i	0.988534	−	0.151000i	$-0.0482493\pi$
$257$	18.4423	+	13.3991i	1.15040	+	0.835813i	0.161864	+	0.986813i	$0.448249\pi$
$258$	2.87100	+	8.83603i	0.178741	+	0.550107i
$259$	−11.4507	−	35.2417i	−0.711513	−	2.18981i
$260$	−1.41435	−	1.02759i	−0.0877146	−	0.0637284i
$261$	3.06929	−	2.22997i	0.189984	−	0.138032i
$262$	0.809403	−	2.49109i	0.0500051	−	0.153900i
$263$	−25.6969			−1.58454			−0.792268	−	0.610173i	$-0.791100\pi$
$263$	−25.6969			−1.58454			−0.792268	+	0.610173i	$0.791100\pi$
$264$	7.84598	+	0.804912i	0.482887	+	0.0495389i
$265$	9.01938			0.554056
$266$	−13.2692	+	40.8384i	−0.813588	+	2.50397i
$267$	5.33399	−	3.87537i	0.326435	−	0.237169i
$268$	6.23030	+	4.52658i	0.380576	+	0.276505i
$269$	7.69974	+	23.6974i	0.469461	+	1.44485i	0.853284	+	0.521447i	$0.174608\pi$
$269$	7.69974	+	23.6974i	0.469461	+	1.44485i	−0.383822	+	0.923407i	$0.625392\pi$
$270$	1.72629	+	5.31296i	0.105058	+	0.323337i
$271$	−16.7388	−	12.1615i	−1.01681	−	0.738756i	−0.0511837	−	0.998689i	$-0.516299\pi$
$271$	−16.7388	−	12.1615i	−1.01681	−	0.738756i	−0.965627	+	0.259933i	$0.916299\pi$
$272$	−20.9933	+	15.2525i	−1.27290	+	0.924820i
$273$	1.48130	−	4.55897i	0.0896524	−	0.275922i
$274$	9.34563			0.564590
$275$	18.5562	+	16.6247i	1.11898	+	1.00250i
$276$	3.32534			0.200162
$277$	1.54576	−	4.75735i	0.0928755	−	0.285841i	−0.893819	−	0.448429i	$-0.851984\pi$
$277$	1.54576	−	4.75735i	0.0928755	−	0.285841i	0.986694	+	0.162587i	$0.0519838\pi$
$278$	2.89758	−	2.10522i	0.173785	−	0.126262i
$279$	3.43467	+	2.49544i	0.205628	+	0.149398i
$280$	−12.4603	−	38.3489i	−0.744646	−	2.29179i
$281$	−0.158623	−	0.488192i	−0.00946267	−	0.0291231i	0.946214	−	0.323542i	$-0.104874\pi$
$281$	−0.158623	−	0.488192i	−0.00946267	−	0.0291231i	−0.955676	+	0.294419i	$0.904874\pi$
$282$	7.37540	+	5.35854i	0.439199	+	0.319096i
$283$	−12.5863	+	9.14451i	−0.748180	+	0.543585i	−0.895262	−	0.445540i	$-0.853012\pi$
$283$	−12.5863	+	9.14451i	−0.748180	+	0.543585i	0.147082	+	0.989124i	$0.453012\pi$
$284$	1.94065	−	5.97271i	0.115156	−	0.354415i
$285$	20.0629			1.18842
$286$	2.11857	−	4.79044i	0.125274	−	0.283265i
$287$	8.80379			0.519671
$288$	0.845616	−	2.60254i	0.0498284	−	0.153356i
$289$	−10.4501	+	7.59242i	−0.614710	+	0.446613i
$290$	−17.1462	−	12.4575i	−1.00686	−	0.731528i
$291$	1.39868	+	4.30469i	0.0819919	+	0.252345i
$292$	1.21381	+	3.73572i	0.0710329	+	0.218617i
$293$	4.44262	+	3.22775i	0.259541	+	0.188567i	0.709945	−	0.704258i	$-0.248720\pi$
$293$	4.44262	+	3.22775i	0.259541	+	0.188567i	−0.450404	+	0.892825i	$0.648720\pi$
$294$	−20.4156	+	14.8328i	−1.19066	+	0.865068i
$295$	−0.306015	+	0.941816i	−0.0178169	+	0.0548347i
$296$	18.3829			1.06848
$297$	−2.86815	+	1.66545i	−0.166427	+	0.0966395i
$298$	−13.5213			−0.783268
$299$	−2.07912	+	6.39887i	−0.120239	+	0.370056i
$300$	3.00363	−	2.18226i	0.173414	−	0.125993i
$301$	22.8139	+	16.5753i	1.31497	+	0.955384i
$302$	4.57809	+	14.0899i	0.263439	+	0.810783i
$303$	−0.299802	−	0.922696i	−0.0172232	−	0.0530075i
$304$	−21.7698	−	15.8167i	−1.24858	−	0.907149i
$305$	13.9449	−	10.1315i	0.798481	−	0.580130i
$306$	2.66938	−	8.21551i	0.152598	−	0.469650i
$307$	27.4189			1.56488			0.782441	−	0.622725i	$-0.213974\pi$
$307$	27.4189			1.56488			0.782441	+	0.622725i	$0.213974\pi$
$308$	−6.79519	+	3.94578i	−0.387192	+	0.224832i
$309$	−9.20125			−0.523441
$310$	7.32893	−	22.5561i	0.416255	−	1.28110i
$311$	15.7459	−	11.4400i	0.892867	−	0.648706i	−0.0437573	−	0.999042i	$-0.513933\pi$
$311$	15.7459	−	11.4400i	0.892867	−	0.648706i	0.936624	+	0.350337i	$0.113933\pi$
$312$	1.92390	+	1.39779i	0.108919	+	0.0791345i
$313$	3.69801	+	11.3813i	0.209024	+	0.643310i	0.999524	+	0.0308478i	$0.00982073\pi$
$313$	3.69801	+	11.3813i	0.209024	+	0.643310i	−0.790500	+	0.612462i	$0.790179\pi$
$314$	1.92046	+	5.91058i	0.108378	+	0.333553i
$315$	13.7177	+	9.96646i	0.772902	+	0.561546i
$316$	−0.251128	+	0.182455i	−0.0141271	+	0.0102639i
$317$	−0.769091	+	2.36702i	−0.0431964	+	0.132945i	−0.970329	−	0.241789i	$-0.922266\pi$
$317$	−0.769091	+	2.36702i	−0.0431964	+	0.132945i	0.927132	+	0.374734i	$0.122266\pi$
$318$	4.02703			0.225824
$319$	5.08926	−	11.5077i	0.284944	−	0.644305i
$320$	18.2756			1.02164
$321$	−2.68196	+	8.25421i	−0.149692	+	0.460705i
$322$	41.2083	−	29.9396i	2.29645	−	1.66847i
$323$	−25.0986	−	18.2352i	−1.39652	−	1.01463i
$324$	0.152729	+	0.470052i	0.00848495	+	0.0261140i
$325$	2.32130	+	7.14423i	0.128763	+	0.396290i
$326$	−17.7670	−	12.9085i	−0.984023	−	0.714934i
$327$	11.6200	−	8.44246i	0.642590	−	0.466869i
$328$	−1.34963	+	4.15374i	−0.0745210	+	0.229352i
$329$	27.6707			1.52553
$330$	13.7997	+	12.3633i	0.759651	+	0.680578i
$331$	30.9126			1.69911			0.849555	−	0.527500i	$-0.176870\pi$
$331$	30.9126			1.69911			0.849555	+	0.527500i	$0.176870\pi$
$332$	0.594494	−	1.82967i	0.0326271	−	0.100416i
$333$	−6.25384	+	4.54368i	−0.342709	+	0.248992i
$334$	6.50175	+	4.72380i	0.355760	+	0.258475i
$335$	−17.0316	−	52.4179i	−0.930536	−	2.86389i
$336$	−7.02760	−	21.6287i	−0.383387	−	1.17994i
$337$	14.5973	+	10.6056i	0.795168	+	0.577723i	0.909493	−	0.415720i	$-0.136470\pi$
$337$	14.5973	+	10.6056i	0.795168	+	0.577723i	−0.114325	+	0.993443i	$0.536470\pi$
$338$	1.27769	−	0.928299i	0.0694974	−	0.0504928i
$339$	0.434129	−	1.33611i	0.0235786	−	0.0725676i
$340$	−9.56224			−0.518585
$341$	14.0072	+	1.43698i	0.758531	+	0.0778170i
$342$	8.95781			0.484383
$343$	−13.2999	+	40.9327i	−0.718124	+	2.21016i
$344$	−11.3178	+	8.22290i	−0.610217	+	0.443349i
$345$	−19.2538	−	13.9887i	−1.03659	−	0.753126i
$346$	9.97103	+	30.6877i	0.536046	+	1.64978i
$347$	3.94319	+	12.1359i	0.211681	+	0.651488i	0.999373	+	0.0354179i	$0.0112762\pi$
$347$	3.94319	+	12.1359i	0.211681	+	0.651488i	−0.787691	+	0.616070i	$0.788724\pi$
$348$	−1.51697	−	1.10215i	−0.0813183	−	0.0590812i
$349$	−15.5381	+	11.2891i	−0.831736	+	0.604291i	−0.920050	−	0.391801i	$-0.871852\pi$
$349$	−15.5381	+	11.2891i	−0.831736	+	0.604291i	0.0883142	+	0.996093i	$0.471852\pi$
$350$	17.5736	−	54.0860i	0.939350	−	2.89102i
$351$	−1.00000			−0.0533761
$352$	−1.90906	−	8.87279i	−0.101753	−	0.472921i
$353$	−26.4204			−1.40622			−0.703109	−	0.711082i	$-0.748205\pi$
$353$	−26.4204			−1.40622			−0.703109	+	0.711082i	$0.748205\pi$
$354$	−0.136631	+	0.420508i	−0.00726187	+	0.0223497i
$355$	−36.3617	+	26.4184i	−1.92988	+	1.40214i
$356$	−2.63628	−	1.91537i	−0.139723	−	0.101514i
$357$	−8.10219	−	24.9360i	−0.428813	−	1.31975i
$358$	−4.86905	−	14.9854i	−0.257337	−	0.792003i
$359$	−18.8429	−	13.6902i	−0.994493	−	0.722541i	−0.0335923	−	0.999436i	$-0.510695\pi$
$359$	−18.8429	−	13.6902i	−0.994493	−	0.722541i	−0.960900	+	0.276894i	$0.910695\pi$
$360$	−6.80524	+	4.94430i	−0.358668	+	0.260587i
$361$	4.07009	−	12.5264i	0.214215	−	0.659286i
$362$	−7.27251			−0.382234
$363$	−5.45252	+	9.55353i	−0.286183	+	0.501430i
$364$	−2.36919			−0.124179
$365$	8.68706	−	26.7360i	0.454701	−	1.39943i
$366$	6.22619	−	4.52359i	0.325448	−	0.236452i
$367$	−29.1430	−	21.1736i	−1.52125	−	1.10525i	−0.960863	−	0.277023i	$-0.910652\pi$
$367$	−29.1430	−	21.1736i	−1.52125	−	1.10525i	−0.560387	−	0.828231i	$-0.689348\pi$
$368$	9.86377	+	30.3576i	0.514185	+	1.58250i
$369$	−0.567533	−	1.74669i	−0.0295446	−	0.0909289i
$370$	34.9364	+	25.3828i	1.81626	+	1.31959i
$371$	9.88857	−	7.18447i	0.513389	−	0.372999i
$372$	0.648410	−	1.99560i	0.0336185	−	0.103467i
$373$	−25.0376			−1.29640			−0.648200	−	0.761470i	$-0.724478\pi$
$373$	−25.0376			−1.29640			−0.648200	+	0.761470i	$0.724478\pi$
$374$	−6.02638	−	28.0090i	−0.311617	−	1.44831i
$375$	−8.88507			−0.458823
$376$	−4.24195	+	13.0554i	−0.218762	+	0.673280i
$377$	3.06929	−	2.22997i	0.158077	−	0.114849i
$378$	6.12474	+	4.44988i	0.315023	+	0.228877i
$379$	−2.15060	−	6.61886i	−0.110469	−	0.339988i	0.880506	−	0.474035i	$-0.157203\pi$
$379$	−2.15060	−	6.61886i	−0.110469	−	0.339988i	−0.990975	+	0.134047i	$0.957203\pi$
$380$	−3.06419	−	9.43061i	−0.157190	−	0.483780i
$381$	4.38982	+	3.18939i	0.224898	+	0.163398i
$382$	30.9905	−	22.5159i	1.58561	−	1.15201i
$383$	−7.59228	+	23.3666i	−0.387947	+	1.19398i	0.546372	+	0.837543i	$0.316009\pi$
$383$	−7.59228	+	23.3666i	−0.387947	+	1.19398i	−0.934319	+	0.356437i	$0.883991\pi$
$384$	13.6327			0.695693
$385$	55.9429	+	5.73913i	2.85111	+	0.292493i
$386$	−5.27896			−0.268692
$387$	1.81788	−	5.59484i	0.0924078	−	0.284402i
$388$	1.80981	−	1.31490i	0.0918790	−	0.0667540i
$389$	3.02193	+	2.19556i	0.153218	+	0.111319i	0.661753	−	0.749722i	$-0.269813\pi$
$389$	3.02193	+	2.19556i	0.153218	+	0.111319i	−0.508535	+	0.861041i	$0.669813\pi$
$390$	1.72629	+	5.31296i	0.0874139	+	0.269032i
$391$	11.3720	+	34.9995i	0.575109	+	1.77000i
$392$	−30.7410	−	22.3346i	−1.55266	−	1.12807i
$393$	−1.34175	+	0.974837i	−0.0676822	+	0.0491740i
$394$	0.453428	−	1.39551i	0.0228434	−	0.0703047i
$395$	2.22157			0.111779
$396$	1.22090	+	1.09381i	0.0613525	+	0.0549662i
$397$	1.57434			0.0790139			0.0395070	−	0.999219i	$-0.487421\pi$
$397$	1.57434			0.0790139			0.0395070	+	0.999219i	$0.487421\pi$
$398$	−2.92193	+	8.99278i	−0.146463	+	0.450767i
$399$	21.9964	−	15.9813i	1.10120	−	0.800066i
$400$	28.8317	+	20.9475i	1.44158	+	1.04737i
$401$	0.381071	+	1.17282i	0.0190298	+	0.0585677i	0.960120	−	0.279587i	$-0.0901974\pi$
$401$	0.381071	+	1.17282i	0.0190298	+	0.0585677i	−0.941091	+	0.338154i	$0.890197\pi$
$402$	−7.60437	−	23.4039i	−0.379272	−	1.16728i
$403$	3.43467	+	2.49544i	0.171093	+	0.124306i
$404$	−0.387926	+	0.281845i	−0.0193000	+	0.0140223i
$405$	1.09306	−	3.36409i	0.0543146	−	0.167163i
$406$	−28.7217			−1.42544
$407$	−10.3696	+	23.4474i	−0.514004	+	1.16225i
$408$	13.0072			0.643952
$409$	4.73169	−	14.5626i	0.233967	−	0.720076i	−0.763290	−	0.646056i	$-0.776417\pi$
$409$	4.73169	−	14.5626i	0.233967	−	0.720076i	0.997257	−	0.0740201i	$-0.0235829\pi$
$410$	−8.30036	+	6.03057i	−0.409926	+	0.297829i
$411$	−4.78737	−	3.47823i	−0.236143	−	0.171568i
$412$	1.40530	+	4.32506i	0.0692341	+	0.213081i
$413$	0.414707	+	1.27634i	0.0204064	+	0.0628045i
$414$	−8.59654	−	6.24575i	−0.422497	−	0.306962i
$415$	−11.1390	+	8.09294i	−0.546791	+	0.397267i
$416$	0.845616	−	2.60254i	0.0414597	−	0.127600i
$417$	−2.26782			−0.111056
$418$	25.6923	−	14.9188i	1.25665	−	0.729704i
$419$	13.3165			0.650552			0.325276	−	0.945619i	$-0.394543\pi$
$419$	13.3165			0.650552			0.325276	+	0.945619i	$0.394543\pi$
$420$	2.58967	−	7.97017i	0.126363	−	0.388905i
$421$	8.51610	−	6.18731i	0.415049	−	0.301551i	−0.360594	−	0.932723i	$-0.617426\pi$
$421$	8.51610	−	6.18731i	0.415049	−	0.301551i	0.775643	+	0.631172i	$0.217426\pi$
$422$	−22.2450	−	16.1619i	−1.08287	−	0.786751i
$423$	−1.78378	−	5.48991i	−0.0867303	−	0.266928i
$424$	1.87380	+	5.76695i	0.0909995	+	0.280068i
$425$	33.2403	+	24.1505i	1.61239	+	1.17147i
$426$	−16.2350	+	11.7954i	−0.786589	+	0.571490i
$427$	7.21836	−	22.2158i	0.349321	−	1.07510i
$428$	4.28952			0.207342
$429$	−2.86815	+	1.66545i	−0.138475	+	0.0804089i
$430$	−32.8634			−1.58481
$431$	2.69707	−	8.30074i	0.129913	−	0.399833i	−0.864851	−	0.502029i	$-0.832587\pi$
$431$	2.69707	−	8.30074i	0.129913	−	0.399833i	0.994764	+	0.102197i	$0.0325871\pi$
$432$	−3.83815	+	2.78858i	−0.184663	+	0.134165i
$433$	8.38025	+	6.08861i	0.402729	+	0.292600i	0.770652	−	0.637257i	$-0.219931\pi$
$433$	8.38025	+	6.08861i	0.402729	+	0.292600i	−0.367923	+	0.929856i	$0.619931\pi$
$434$	−9.93208	−	30.5678i	−0.476755	−	1.46730i
$435$	4.14691	+	12.7629i	0.198829	+	0.611933i
$436$	−5.74311	−	4.17261i	−0.275045	−	0.199832i
$437$	−30.8736	+	22.4310i	−1.47688	+	1.07302i
$438$	3.87865	−	11.9373i	0.185329	−	0.570384i
$439$	−12.2585			−0.585067			−0.292533	−	0.956255i	$-0.594498\pi$
$439$	−12.2585			−0.585067			−0.292533	+	0.956255i	$0.594498\pi$
$440$	−11.2839	+	25.5148i	−0.537940	+	1.21637i
$441$	15.9785			0.760881
$442$	2.66938	−	8.21551i	0.126970	−	0.390772i
$443$	−16.7479	+	12.1680i	−0.795716	+	0.578121i	−0.909654	−	0.415367i	$-0.863653\pi$
$443$	−16.7479	+	12.1680i	−0.795716	+	0.578121i	0.113939	+	0.993488i	$0.463653\pi$
$444$	3.09091	+	2.24568i	0.146688	+	0.106575i
$445$	7.20673	+	22.1800i	0.341632	+	1.05143i
$446$	−1.51960	−	4.67686i	−0.0719553	−	0.221456i
$447$	6.92639	+	5.03231i	0.327607	+	0.238020i
$448$	20.0368	−	14.5576i	0.946651	−	0.687782i
$449$	5.73644	−	17.6550i	0.270719	−	0.833189i	−0.719601	−	0.694388i	$-0.755675\pi$
$449$	5.73644	−	17.6550i	0.270719	−	0.833189i	0.990320	−	0.138801i	$-0.0443248\pi$
$450$	−11.8636			−0.559257
$451$	−4.53680	−	4.06455i	−0.213629	−	0.191392i
$452$	−0.694346			−0.0326593
$453$	2.89878	−	8.92152i	0.136196	−	0.419169i
$454$	15.2692	−	11.0937i	0.716620	−	0.520655i
$455$	13.7177	+	9.96646i	0.643093	+	0.467235i
$456$	4.16812	+	12.8281i	0.195190	+	0.600733i
$457$	−2.60112	−	8.00544i	−0.121675	−	0.374478i	0.871605	−	0.490208i	$-0.163079\pi$
$457$	−2.60112	−	8.00544i	−0.121675	−	0.374478i	−0.993281	+	0.115730i	$0.963079\pi$
$458$	−7.67424	−	5.57566i	−0.358594	−	0.260533i
$459$	−4.42503	+	3.21498i	−0.206543	+	0.150062i
$460$	−3.63480	+	11.1867i	−0.169473	+	0.521585i
$461$	37.0527			1.72572			0.862858	−	0.505446i	$-0.168672\pi$
$461$	37.0527			1.72572			0.862858	+	0.505446i	$0.168672\pi$
$462$	24.9777	+	2.56244i	1.16207	+	0.119216i
$463$	−6.74736			−0.313576			−0.156788	−	0.987632i	$-0.550114\pi$
$463$	−6.74736			−0.313576			−0.156788	+	0.987632i	$0.550114\pi$
$464$	5.56195	−	17.1179i	0.258207	−	0.794679i
$465$	−12.1492	+	8.82689i	−0.563404	+	0.409337i
$466$	10.1341	+	7.36283i	0.469451	+	0.341076i
$467$	−3.00621	−	9.25217i	−0.139111	−	0.428139i	0.857096	−	0.515157i	$-0.172266\pi$
$467$	−3.00621	−	9.25217i	−0.139111	−	0.428139i	−0.996207	+	0.0870177i	$0.972266\pi$
$468$	0.152729	+	0.470052i	0.00705990	+	0.0217282i
$469$	−60.4269	−	43.9027i	−2.79025	−	2.02724i
$470$	−26.0884	+	18.9543i	−1.20337	+	0.874297i
$471$	1.21601	−	3.74249i	0.0560307	−	0.172445i
$472$	−0.665768			−0.0306445
$473$	−4.10403	−	19.0744i	−0.188703	−	0.877043i
$474$	0.991901			0.0455595
$475$	−13.1663	+	40.5217i	−0.604112	+	1.85926i
$476$	−10.4838	+	7.61689i	−0.480522	+	0.349120i
$477$	−2.06287	−	1.49877i	−0.0944526	−	0.0686238i
$478$	8.23285	+	25.3381i	0.376562	+	1.15894i
$479$	8.48960	+	26.1283i	0.387900	+	1.19383i	0.934355	+	0.356344i	$0.115977\pi$
$479$	8.48960	+	26.1283i	0.387900	+	1.19383i	−0.546455	+	0.837488i	$0.684023\pi$
$480$	7.83086	+	5.68945i	0.357428	+	0.259687i
$481$	−6.25384	+	4.54368i	−0.285151	+	0.207174i
$482$	4.30853	−	13.2603i	0.196248	−	0.603990i
$483$	−32.2521			−1.46752
$484$	5.32341	+	1.10387i	0.241973	+	0.0501757i
$485$	−16.0102			−0.726985
$486$	0.488036	−	1.50202i	0.0221378	−	0.0681330i
$487$	17.4370	−	12.6687i	0.790146	−	0.574075i	−0.117860	−	0.993030i	$-0.537604\pi$
$487$	17.4370	−	12.6687i	0.790146	−	0.574075i	0.908007	+	0.418955i	$0.137604\pi$
$488$	9.37514	+	6.81144i	0.424393	+	0.308339i
$489$	4.29704	+	13.2249i	0.194319	+	0.598052i
$490$	−27.5835	−	84.8932i	−1.24609	−	3.83508i
$491$	−31.6279	−	22.9790i	−1.42735	−	1.03703i	−0.990503	−	0.137490i	$-0.956097\pi$
$491$	−31.6279	−	22.9790i	−1.42735	−	1.03703i	−0.436843	−	0.899538i	$-0.643903\pi$
$492$	−0.734355	+	0.533540i	−0.0331073	+	0.0240538i
$493$	6.41242	−	19.7354i	0.288801	−	0.888838i
$494$	8.95781			0.403031
$495$	−2.46769	−	11.4691i	−0.110914	−	0.515500i
$496$	20.1415			0.904379
$497$	−18.8221	+	57.9286i	−0.844288	+	2.59845i
$498$	−4.97339	+	3.61338i	−0.222863	+	0.161920i
$499$	−11.9311	−	8.66847i	−0.534111	−	0.388054i	0.287783	−	0.957696i	$-0.407082\pi$
$499$	−11.9311	−	8.66847i	−0.534111	−	0.388054i	−0.821893	+	0.569642i	$0.807082\pi$
$500$	1.35701	+	4.17644i	0.0606872	+	0.186776i
$501$	−1.57248	−	4.83960i	−0.0702533	−	0.216217i
$502$	11.8798	+	8.63121i	0.530223	+	0.385230i
$503$	−35.2373	+	25.6014i	−1.57116	+	1.14151i	−0.645116	+	0.764085i	$0.723191\pi$
$503$	−35.2373	+	25.6014i	−1.57116	+	1.14151i	−0.926040	+	0.377427i	$0.876809\pi$
$504$	−3.52264	+	10.8416i	−0.156911	+	0.482921i
$505$	3.43173			0.152710
$506$	−35.0582	−	3.59658i	−1.55853	−	0.159888i
$507$	−1.00000			−0.0444116
$508$	0.828726	−	2.55056i	0.0367688	−	0.113163i
$509$	−20.0649	+	14.5780i	−0.889360	+	0.646158i	−0.935711	−	0.352767i	$-0.885241\pi$
$509$	−20.0649	+	14.5780i	−0.889360	+	0.646158i	0.0463512	+	0.998925i	$0.485241\pi$
$510$	24.7199	+	17.9601i	1.09462	+	0.795286i
$511$	−11.7726	−	36.2323i	−0.520789	−	1.60282i
$512$	2.96092	+	9.11277i	0.130855	+	0.402731i
$513$	−4.58871	−	3.33389i	−0.202596	−	0.147195i
$514$	−29.1262	+	21.1614i	−1.28470	+	0.933391i
$515$	10.0575	−	30.9538i	0.443187	−	1.36399i
$516$	−2.90751			−0.127996
$517$	−14.2593	−	12.7750i	−0.627124	−	0.561846i
$518$	58.5220			2.57131
$519$	6.31351	−	19.4310i	0.277132	−	0.852925i
$520$	−6.80524	+	4.94430i	−0.298430	+	0.216822i
$521$	−8.09807	−	5.88359i	−0.354783	−	0.257765i	0.396090	−	0.918212i	$-0.370367\pi$
$521$	−8.09807	−	5.88359i	−0.354783	−	0.257765i	−0.750873	+	0.660447i	$0.770367\pi$
$522$	1.85154	+	5.69844i	0.0810396	+	0.249414i
$523$	10.1392	+	31.2053i	0.443357	+	1.36451i	0.884276	+	0.466965i	$0.154653\pi$
$523$	10.1392	+	31.2053i	0.443357	+	1.36451i	−0.440919	+	0.897547i	$0.645347\pi$
$524$	0.663148	+	0.481805i	0.0289697	+	0.0210477i
$525$	−29.1318	+	21.1655i	−1.27142	+	0.923738i
$526$	12.5410	−	38.5972i	0.546813	−	1.68292i
$527$	23.2213			1.01154
$528$	−6.36412	+	14.3903i	−0.276963	+	0.626257i
$529$	22.2683			0.968185
$530$	−4.40178	+	13.5473i	−0.191201	+	0.588456i
$531$	0.226494	−	0.164557i	0.00982899	−	0.00714118i
$532$	−10.8715	−	7.89863i	−0.471341	−	0.342449i
$533$	−0.567533	−	1.74669i	−0.0245826	−	0.0756574i
$534$	3.21771	+	9.90308i	0.139244	+	0.428548i
$535$	−24.8364	−	18.0447i	−1.07377	−	0.780140i
$536$	29.9774	−	21.7799i	1.29483	−	0.940746i
$537$	−3.08301	+	9.48854i	−0.133042	+	0.409461i
$538$	−39.3517			−1.69657
$539$	45.8287	−	26.6115i	1.97398	−	1.14624i
$540$	−1.74824			−0.0752322
$541$	10.5018	−	32.3213i	0.451509	−	1.38960i	−0.423676	−	0.905814i	$-0.639260\pi$
$541$	10.5018	−	32.3213i	0.451509	−	1.38960i	0.875185	−	0.483789i	$-0.160740\pi$
$542$	26.4359	−	19.2068i	1.13552	−	0.825002i
$543$	3.72540	+	2.70666i	0.159872	+	0.116154i
$544$	−4.62522	−	14.2349i	−0.198304	−	0.610318i
$545$	15.6998	+	48.3190i	0.672505	+	2.06976i
$546$	6.12474	+	4.44988i	0.262115	+	0.190437i
$547$	−3.84009	+	2.78999i	−0.164190	+	0.119291i	−0.666846	−	0.745195i	$-0.732356\pi$
$547$	−3.84009	+	2.78999i	−0.164190	+	0.119291i	0.502656	+	0.864487i	$0.332356\pi$
$548$	−0.903776	+	2.78154i	−0.0386074	+	0.118821i
$549$	−4.87299			−0.207974
$550$	−34.0267	+	19.7584i	−1.45090	+	0.842499i
$551$	21.5186			0.916722
$552$	4.94429	−	15.2170i	0.210443	−	0.647677i
$553$	2.43566	−	1.76961i	0.103575	−	0.0752516i
$554$	6.39125	+	4.64351i	0.271538	+	0.197284i
$555$	−8.44954	−	26.0050i	−0.358663	−	1.10385i
$556$	0.346362	+	1.06599i	0.0146890	+	0.0452082i
$557$	30.3420	+	22.0448i	1.28563	+	0.934066i	0.999707	−	0.0241857i	$-0.00769929\pi$
$557$	30.3420	+	22.0448i	1.28563	+	0.934066i	0.285925	+	0.958252i	$0.407699\pi$
$558$	−5.42444	+	3.94108i	−0.229635	+	0.166839i
$559$	1.81788	−	5.59484i	0.0768879	−	0.236637i
$560$	80.4426			3.39932
$561$	−7.33725	+	16.5907i	−0.309779	+	0.700460i
$562$	0.810688			0.0341968
$563$	8.99296	−	27.6775i	0.379008	−	1.16647i	−0.561727	−	0.827323i	$-0.689863\pi$
$563$	8.99296	−	27.6775i	0.379008	−	1.16647i	0.940735	−	0.339144i	$-0.110137\pi$
$564$	−2.30810	+	1.67694i	−0.0971888	+	0.0706118i
$565$	4.02027	+	2.92090i	0.169134	+	0.122883i
$566$	−7.59265	−	23.3678i	−0.319143	−	0.982221i
$567$	−1.48130	−	4.55897i	−0.0622088	−	0.191459i
$568$	−24.4460	−	17.7611i	−1.02573	−	0.745238i
$569$	−1.20820	+	0.877806i	−0.0506502	+	0.0367995i	−0.612822	−	0.790221i	$-0.709966\pi$
$569$	−1.20820	+	0.877806i	−0.0506502	+	0.0367995i	0.562172	+	0.827020i	$0.309966\pi$
$570$	−9.79142	+	30.1349i	−0.410118	+	1.26221i
$571$	−34.8920			−1.46019			−0.730093	−	0.683348i	$-0.760523\pi$
$571$	−34.8920			−1.46019			−0.730093	+	0.683348i	$0.760523\pi$
$572$	1.22090	+	1.09381i	0.0510484	+	0.0457347i
$573$	−24.2550			−1.01327
$574$	−4.29656	+	13.2235i	−0.179335	+	0.551937i
$575$	40.8887	−	29.7074i	1.70518	−	1.23888i
$576$	−4.17992	−	3.03689i	−0.174163	−	0.126537i
$577$	−9.23651	−	28.4270i	−0.384521	−	1.18343i	−0.936827	−	0.349792i	$-0.886252\pi$
$577$	−9.23651	−	28.4270i	−0.384521	−	1.18343i	0.552306	−	0.833641i	$-0.313748\pi$
$578$	−6.30396	−	19.4016i	−0.262210	−	0.806999i
$579$	2.70419	+	1.96471i	0.112382	+	0.0816505i
$580$	5.36586	−	3.89852i	0.222805	−	0.161877i
$581$	−5.76593	+	17.7457i	−0.239211	+	0.736216i
$582$	−7.14833			−0.296308
$583$	−8.41275	−	0.863057i	−0.348421	−	0.0357442i
$584$	18.8996			0.782073
$585$	1.09306	−	3.36409i	0.0451924	−	0.139088i
$586$	−7.01631	+	5.09765i	−0.289841	+	0.210582i
$587$	7.42738	+	5.39631i	0.306561	+	0.222730i	0.730419	−	0.682999i	$-0.239325\pi$
$587$	7.42738	+	5.39631i	0.306561	+	0.222730i	−0.423859	+	0.905728i	$0.639325\pi$
$588$	−2.44038	−	7.51072i	−0.100640	−	0.309737i
$589$	7.44120	+	22.9017i	0.306609	+	0.943646i
$590$	−1.26528	−	0.919280i	−0.0520908	−	0.0378462i
$591$	−0.751648	+	0.546104i	−0.0309187	+	0.0224637i
$592$	−11.3328	+	34.8786i	−0.465773	+	1.43350i
$593$	15.7540			0.646938			0.323469	−	0.946239i	$-0.395151\pi$
$593$	15.7540			0.646938			0.323469	+	0.946239i	$0.395151\pi$
$594$	−1.10179	−	5.12081i	−0.0452069	−	0.210109i
$595$	92.7430			3.80209
$596$	1.30759	−	4.02434i	0.0535609	−	0.164843i
$597$	4.84369	−	3.51914i	0.198239	−	0.144029i
$598$	−8.59654	−	6.24575i	−0.351539	−	0.255408i
$599$	4.88208	+	15.0255i	0.199476	+	0.613925i	0.999895	+	0.0144836i	$0.00461042\pi$
$599$	4.88208	+	15.0255i	0.199476	+	0.613925i	−0.800419	+	0.599441i	$0.795390\pi$
$600$	−5.52021	−	16.9895i	−0.225362	−	0.693592i
$601$	−36.0846	−	26.2170i	−1.47192	−	1.06942i	−0.980051	−	0.198748i	$-0.936312\pi$
$601$	−36.0846	−	26.2170i	−1.47192	−	1.06942i	−0.491873	−	0.870667i	$-0.663688\pi$
$602$	−36.0304	+	26.1776i	−1.46849	+	1.06692i
$603$	−4.81498	+	14.8190i	−0.196081	+	0.603475i
$604$	−4.63630			−0.188648
$605$	−26.1790	−	28.7854i	−1.06433	−	1.17029i
$606$	1.53222			0.0622422
$607$	−4.62259	+	14.2269i	−0.187625	+	0.577451i	−0.999984	−	0.00570758i	$-0.998183\pi$
$607$	−4.62259	+	14.2269i	−0.187625	+	0.577451i	0.812359	+	0.583158i	$0.198183\pi$
$608$	12.5569	−	9.12309i	0.509248	−	0.369990i
$609$	14.7129	+	10.6896i	0.596198	+	0.433163i
$610$	8.41218	+	25.8900i	0.340599	+	1.04826i
$611$	−1.78378	−	5.48991i	−0.0721640	−	0.222098i
$612$	2.18704	+	1.58897i	0.0884057	+	0.0642305i
$613$	13.0922	−	9.51204i	0.528789	−	0.384188i	−0.291116	−	0.956688i	$-0.594026\pi$
$613$	13.0922	−	9.51204i	0.528789	−	0.384188i	0.819905	+	0.572500i	$0.194026\pi$
$614$	−13.3814	+	41.1838i	−0.540030	+	1.66204i
$615$	6.49636			0.261959
$616$	7.95269	+	36.9620i	0.320423	+	1.48924i
$617$	−3.26745			−0.131542			−0.0657712	−	0.997835i	$-0.520951\pi$
$617$	−3.26745			−0.131542			−0.0657712	+	0.997835i	$0.520951\pi$
$618$	4.49054	−	13.8205i	0.180636	−	0.555940i
$619$	−18.8838	+	13.7199i	−0.759003	+	0.551448i	−0.898604	−	0.438760i	$-0.855418\pi$
$619$	−18.8838	+	13.7199i	−0.759003	+	0.551448i	0.139601	+	0.990208i	$0.455418\pi$
$620$	6.00463	+	4.36262i	0.241152	+	0.175207i
$621$	2.07912	+	6.39887i	0.0834322	+	0.256778i
$622$	9.49863	+	29.2338i	0.380860	+	1.17217i
$623$	25.5690	+	18.5769i	1.02440	+	0.744269i
$624$	−3.83815	+	2.78858i	−0.153649	+	0.111632i
$625$	−1.89459	+	5.83096i	−0.0757837	+	0.233238i
$626$	−18.8997			−0.755385
$627$	−18.7135	−	1.91980i	−0.747346	−	0.0766696i
$628$	−1.94488			−0.0776093
$629$	−13.0656	+	40.2119i	−0.520961	+	1.60335i
$630$	−21.6645	+	15.7402i	−0.863135	+	0.627104i
$631$	7.07439	+	5.13984i	0.281627	+	0.204614i	0.719627	−	0.694361i	$-0.244313\pi$
$631$	7.07439	+	5.13984i	0.281627	+	0.204614i	−0.438000	+	0.898975i	$0.644313\pi$
$632$	0.461536	+	1.42046i	0.0183589	+	0.0565030i
$633$	5.38007	+	16.5581i	0.213838	+	0.658127i
$634$	−3.17996	−	2.31038i	−0.126292	−	0.0917568i
$635$	−15.5277	+	11.2816i	−0.616200	+	0.447695i
$636$	−0.389437	+	1.19856i	−0.0154422	+	0.0475261i
$637$	15.9785			0.633091
$638$	14.8010	+	13.2603i	0.585976	+	0.524981i
$639$	12.7065			0.502661
$640$	−14.9014	+	45.8618i	−0.589029	+	1.81285i
$641$	23.7436	−	17.2507i	0.937815	−	0.681362i	−0.0100788	−	0.999949i	$-0.503208\pi$
$641$	23.7436	−	17.2507i	0.937815	−	0.681362i	0.947894	+	0.318587i	$0.103208\pi$
$642$	−11.0891	−	8.05670i	−0.437652	−	0.317973i
$643$	1.23221	+	3.79236i	0.0485937	+	0.149556i	0.972409	−	0.233282i	$-0.0749466\pi$
$643$	1.23221	+	3.79236i	0.0485937	+	0.149556i	−0.923815	+	0.382838i	$0.874947\pi$
$644$	4.92583	+	15.1601i	0.194105	+	0.597393i
$645$	16.8345	+	12.2310i	0.662858	+	0.481595i
$646$	39.6386	−	28.7992i	1.55956	−	1.13309i
$647$	6.68981	−	20.5891i	0.263004	−	0.809442i	−0.729143	−	0.684361i	$-0.760081\pi$
$647$	6.68981	−	20.5891i	0.263004	−	0.809442i	0.992147	−	0.125080i	$-0.0399189\pi$
$648$	2.37807			0.0934194
$649$	0.375554	−	0.849189i	0.0147418	−	0.0333336i
$650$	−11.8636			−0.465330
$651$	−6.28884	+	19.3551i	−0.246479	+	0.758585i
$652$	5.56012	−	4.03966i	0.217751	−	0.158205i
$653$	−23.2022	−	16.8574i	−0.907973	−	0.659681i	0.0325287	−	0.999471i	$-0.489644\pi$
$653$	−23.2022	−	16.8574i	−0.907973	−	0.659681i	−0.940501	+	0.339790i	$0.889644\pi$
$654$	7.00974	+	21.5738i	0.274102	+	0.843601i
$655$	−1.81283	−	5.57931i	−0.0708331	−	0.218002i
$656$	−7.04905	−	5.12143i	−0.275219	−	0.199958i
$657$	−6.42964	+	4.67141i	−0.250844	+	0.182249i
$658$	−13.5043	+	41.5619i	−0.526451	+	1.62025i
$659$	31.9199			1.24342			0.621712	−	0.783246i	$-0.286437\pi$
$659$	31.9199			1.24342			0.621712	+	0.783246i	$0.286437\pi$
$660$	−5.01420	+	2.91161i	−0.195178	+	0.113334i
$661$	12.1689			0.473316			0.236658	−	0.971593i	$-0.423948\pi$
$661$	12.1689			0.473316			0.236658	+	0.971593i	$0.423948\pi$
$662$	−15.0865	+	46.4313i	−0.586352	+	1.80461i
$663$	−4.42503	+	3.21498i	−0.171854	+	0.124859i
$664$	−7.48873	−	5.44088i	−0.290619	−	0.211147i
$665$	29.7192	+	91.4663i	1.15246	+	3.54691i
$666$	−3.77260	−	11.6109i	−0.146185	−	0.449912i
$667$	−20.6507	−	15.0036i	−0.799599	−	0.580943i
$668$	−2.03470	+	1.47830i	−0.0787249	+	0.0571970i
$669$	−0.962190	+	2.96132i	−0.0372004	+	0.114491i
$670$	87.0447			3.36283
$671$	−13.9764	+	8.11574i	−0.539555	+	0.313305i
$672$	13.1175			0.506019
$673$	1.78788	−	5.50252i	0.0689176	−	0.212107i	−0.910666	−	0.413143i	$-0.864431\pi$
$673$	1.78788	−	5.50252i	0.0689176	−	0.212107i	0.979584	+	0.201036i	$0.0644309\pi$
$674$	−23.0538	+	16.7496i	−0.888000	+	0.645170i
$675$	6.07724	+	4.41537i	0.233913	+	0.169948i
$676$	0.152729	+	0.470052i	0.00587420	+	0.0180789i
$677$	−2.12690	−	6.54594i	−0.0817435	−	0.251581i	0.901829	−	0.432093i	$-0.142225\pi$
$677$	−2.12690	−	6.54594i	−0.0817435	−	0.251581i	−0.983573	+	0.180512i	$0.942225\pi$
$678$	1.79500	+	1.30414i	0.0689364	+	0.0500852i
$679$	−17.5531	+	12.7531i	−0.673626	+	0.489418i
$680$	−14.2176	+	43.7574i	−0.545221	+	1.67802i
$681$	−11.9506			−0.457948
$682$	−8.99438	+	20.3378i	−0.344413	+	0.778773i
$683$	−8.99262			−0.344093			−0.172047	−	0.985089i	$-0.555038\pi$
$683$	−8.99262			−0.344093			−0.172047	+	0.985089i	$0.555038\pi$
$684$	−0.866272	+	2.66611i	−0.0331228	+	0.101941i
$685$	16.9339	−	12.3032i	0.647013	−	0.470082i
$686$	−54.9910	−	39.9533i	−2.09956	−	1.52542i
$687$	1.85605	+	5.71235i	0.0708129	+	0.217940i
$688$	−8.62438	−	26.5431i	−0.328801	−	1.01195i
$689$	−2.06287	−	1.49877i	−0.0785893	−	0.0570984i
$690$	30.4078	−	22.0926i	1.15761	−	0.841050i
$691$	−8.89686	+	27.3817i	−0.338452	+	1.04165i	0.626544	+	0.779386i	$0.284469\pi$
$691$	−8.89686	+	27.3817i	−0.338452	+	1.04165i	−0.964996	+	0.262263i	$0.915531\pi$
$692$	−10.0978			−0.383862
$693$	−11.8413	−	10.6088i	−0.449816	−	0.402994i
$694$	−20.1527			−0.764988
$695$	2.47886	−	7.62915i	0.0940286	−	0.289390i
$696$	−7.29899	+	5.30303i	−0.276668	+	0.201011i
$697$	−8.12691	−	5.90455i	−0.307829	−	0.223651i
$698$	−9.37329	−	28.8480i	−0.354784	−	1.09191i
$699$	−2.45098	−	7.54333i	−0.0927044	−	0.285315i
$700$	14.3981	+	10.4609i	0.544199	+	0.395384i
$701$	34.4195	−	25.0072i	1.30001	−	0.944510i	0.300050	−	0.953923i	$-0.402997\pi$
$701$	34.4195	−	25.0072i	1.30001	−	0.944510i	0.999956	+	0.00941373i	$0.00299653\pi$
$702$	0.488036	−	1.50202i	0.0184197	−	0.0566901i
$703$	−43.8452			−1.65365
$704$	−17.0464	−	1.74878i	−0.642461	−	0.0659095i
$705$	20.4183			0.768998
$706$	12.8941	−	39.6840i	0.485276	−	1.49353i
$707$	3.76245	−	2.73358i	0.141501	−	0.102807i
$708$	−0.111943	−	0.0813311i	−0.00420706	−	0.00305661i
$709$	−5.88578	−	18.1146i	−0.221045	−	0.680306i	−0.998669	−	0.0515769i	$-0.983575\pi$
$709$	−5.88578	−	18.1146i	−0.221045	−	0.680306i	0.777624	−	0.628730i	$-0.216425\pi$
$710$	−21.9351	−	67.5091i	−0.823208	−	2.53357i
$711$	−0.508109	−	0.369162i	−0.0190556	−	0.0138447i
$712$	−12.6846	+	9.21590i	−0.475376	+	0.345381i
$713$	8.82687	−	27.1663i	0.330569	−	1.01739i
$714$	41.4085			1.54967
$715$	−2.46769	−	11.4691i	−0.0922862	−	0.428922i
$716$	4.93097			0.184279
$717$	5.21292	−	16.0437i	0.194680	−	0.599163i
$718$	29.7590	−	21.6212i	1.11060	−	0.806895i
$719$	−19.2866	−	14.0125i	−0.719268	−	0.522579i	0.166882	−	0.985977i	$-0.446630\pi$
$719$	−19.2866	−	14.0125i	−0.719268	−	0.522579i	−0.886150	+	0.463398i	$0.846630\pi$
$720$	−5.18570	−	15.9599i	−0.193260	−	0.594792i
$721$	−13.6298	−	41.9483i	−0.507601	−	1.56224i
$722$	16.8286	+	12.2267i	0.626296	+	0.455031i
$723$	−7.14225	+	5.18915i	−0.265623	+	0.192987i
$724$	0.703293	−	2.16451i	0.0261377	−	0.0804435i
$725$	−28.4990			−1.05843
$726$	−11.6886	−	12.8523i	−0.433803	−	0.476992i
$727$	−48.5392			−1.80022			−0.900109	−	0.435665i	$-0.856513\pi$
$727$	−48.5392			−1.80022			−0.900109	+	0.435665i	$0.856513\pi$
$728$	−3.52264	+	10.8416i	−0.130558	+	0.401815i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	35.9184	+	26.0963i	1.32940	+	0.965866i
$731$	−9.94313	−	30.6018i	−0.367760	−	1.13185i
$732$	0.744247	+	2.29056i	0.0275082	+	0.0846615i
$733$	2.54834	+	1.85147i	0.0941249	+	0.0683858i	0.633852	−	0.773454i	$-0.281473\pi$
$733$	2.54834	+	1.85147i	0.0941249	+	0.0683858i	−0.539727	+	0.841840i	$0.681473\pi$
$734$	46.0260	−	33.4398i	1.69885	−	1.23429i
$735$	−17.4654	+	53.7531i	−0.644223	+	1.98271i
$736$	−18.4114			−0.678654
$737$	10.8703	+	50.5221i	0.400411	+	1.86101i
$738$	2.90054			0.106770
$739$	−13.0665	+	40.2145i	−0.480658	+	1.47931i	0.357514	+	0.933908i	$0.383624\pi$
$739$	−13.0665	+	40.2145i	−0.480658	+	1.47931i	−0.838172	+	0.545405i	$0.816376\pi$
$740$	−10.9332	+	7.94344i	−0.401913	+	0.292007i
$741$	−4.58871	−	3.33389i	−0.168570	−	0.122474i
$742$	5.96524	+	18.3591i	0.218991	+	0.673984i
$743$	4.98709	+	15.3487i	0.182959	+	0.563089i	0.999907	−	0.0136218i	$-0.00433608\pi$
$743$	4.98709	+	15.3487i	0.182959	+	0.563089i	−0.816949	+	0.576710i	$0.804336\pi$
$744$	−8.16789	−	5.93432i	−0.299449	−	0.217563i
$745$	−24.5001	+	17.8004i	−0.897615	+	0.652155i
$746$	12.2193	−	37.6070i	0.447379	−	1.37689i
$747$	3.89248			0.142418
$748$	8.91910	+	0.915003i	0.326115	+	0.0334558i
$749$	−41.6035			−1.52016
$750$	4.33623	−	13.3455i	0.158337	−	0.487310i
$751$	39.4208	−	28.6409i	1.43849	−	1.04512i	0.450129	−	0.892964i	$-0.351378\pi$
$751$	39.4208	−	28.6409i	1.43849	−	1.04512i	0.988356	−	0.152157i	$-0.0486220\pi$
$752$	−22.1554	−	16.0969i	−0.807925	−	0.586992i
$753$	−2.87320	−	8.84281i	−0.104705	−	0.322250i
$754$	1.85154	+	5.69844i	0.0674290	+	0.207525i
$755$	26.8443	+	19.5035i	0.976962	+	0.709805i
$756$	−1.91672	+	1.39258i	−0.0697103	+	0.0506475i
$757$	11.9330	−	36.7261i	0.433713	−	1.33483i	−0.460687	−	0.887563i	$-0.652397\pi$
$757$	11.9330	−	36.7261i	0.433713	−	1.33483i	0.894400	−	0.447269i	$-0.147603\pi$
$758$	10.9912			0.399219
$759$	16.6202	+	14.8902i	0.603277	+	0.540481i
$760$	−47.7110			−1.73066
$761$	6.57317	−	20.2301i	0.238277	−	0.733342i	−0.758393	−	0.651798i	$-0.774015\pi$
$761$	6.57317	−	20.2301i	0.238277	−	0.733342i	0.996670	−	0.0815437i	$-0.0259850\pi$
$762$	−6.93292	+	5.03706i	−0.251153	+	0.182474i
$763$	55.7017	+	40.4697i	2.01654	+	1.46510i
$764$	3.70445	+	11.4011i	0.134022	+	0.412478i
$765$	−5.97864	−	18.4004i	−0.216158	−	0.665267i
$766$	−31.3918	−	22.8075i	−1.13423	−	0.824069i
$767$	0.226494	−	0.164557i	0.00817821	−	0.00594182i
$768$	−3.46009	+	10.6491i	−0.124855	+	0.384265i
$769$	22.0036			0.793469			0.396734	−	0.917933i	$-0.370143\pi$
$769$	22.0036			0.793469			0.396734	+	0.917933i	$0.370143\pi$
$770$	−35.9224	+	81.2264i	−1.29455	+	2.92720i
$771$	22.7959			0.820975
$772$	0.510506	−	1.57118i	0.0183735	−	0.0565479i
$773$	−34.5043	+	25.0688i	−1.24103	+	0.901664i	−0.997667	−	0.0682708i	$-0.978252\pi$
$773$	−34.5043	+	25.0688i	−1.24103	+	0.901664i	−0.243367	+	0.969934i	$0.578252\pi$
$774$	7.51638	+	5.46097i	0.270171	+	0.196290i
$775$	−9.85505	−	30.3307i	−0.354004	−	1.08951i
$776$	−3.32615	−	10.2368i	−0.119402	−	0.367481i
$777$	−29.9784	−	21.7806i	−1.07547	−	0.781373i
$778$	−4.77259	+	3.46749i	−0.171106	+	0.124316i
$779$	3.21902	−	9.90713i	0.115333	−	0.354960i
$780$	−1.74824			−0.0625970
$781$	36.4441	−	21.1621i	1.30407	−	0.757239i
$782$	−58.1199			−2.07836
$783$	1.17237	−	3.60817i	0.0418969	−	0.128945i
$784$	61.3278	−	44.5572i	2.19028	−	1.59133i
$785$	11.2609	+	8.18153i	0.401919	+	0.292011i
$786$	−0.809403	−	2.49109i	−0.0288704	−	0.0888541i
$787$	−2.01272	−	6.19452i	−0.0717458	−	0.220811i	0.908754	−	0.417333i	$-0.137035\pi$
$787$	−2.01272	−	6.19452i	−0.0717458	−	0.220811i	−0.980499	+	0.196522i	$0.937035\pi$
$788$	0.371496	+	0.269907i	0.0132340	+	0.00961506i
$789$	−20.7892	+	15.1042i	−0.740115	+	0.537725i
$790$	−1.08421	+	3.33684i	−0.0385743	+	0.118720i
$791$	6.73437			0.239447
$792$	6.82065	−	3.96057i	0.242361	−	0.140733i
$793$	−4.87299			−0.173045
$794$	−0.768335	+	2.36469i	−0.0272672	+	0.0839198i
$795$	7.29683	−	5.30146i	0.258792	−	0.188023i
$796$	−2.39395	−	1.73931i	−0.0848514	−	0.0616481i
$797$	−9.67301	−	29.7705i	−0.342636	−	1.05452i	−0.962837	−	0.270082i	$-0.912949\pi$
$797$	−9.67301	−	29.7705i	−0.342636	−	1.05452i	0.620202	−	0.784442i	$-0.287051\pi$
$798$	13.2692	+	40.8384i	0.469725	+	1.44567i
$799$	−25.5432	−	18.5582i	−0.903653	−	0.656543i
$800$	−16.6302	+	12.0825i	−0.587966	+	0.427182i
$801$	2.03740	−	6.27048i	0.0719881	−	0.221557i
$802$	−1.94757			−0.0687711
$803$	−10.6611	+	24.1065i	−0.376223	+	0.850702i
$804$	7.70107			0.271596
$805$	35.2534	−	108.499i	1.24252	−	3.82408i
$806$	−5.42444	+	3.94108i	−0.191068	+	0.138819i
$807$	20.1582	+	14.6458i	0.709602	+	0.515556i
$808$	0.712950	+	2.19423i	0.0250815	+	0.0771929i
$809$	−10.9441	−	33.6826i	−0.384776	−	1.18422i	−0.936643	−	0.350286i	$-0.886084\pi$
$809$	−10.9441	−	33.6826i	−0.384776	−	1.18422i	0.551867	−	0.833932i	$-0.313916\pi$
$810$	4.51948	+	3.28359i	0.158798	+	0.115374i
$811$	−21.3640	+	15.5219i	−0.750193	+	0.545047i	−0.895887	−	0.444283i	$-0.853459\pi$
$811$	−21.3640	+	15.5219i	−0.750193	+	0.545047i	0.145694	+	0.989330i	$0.453459\pi$
$812$	2.77756	−	8.54845i	0.0974732	−	0.299992i
$813$	−20.6903			−0.725641
$814$	−30.1578	−	27.0186i	−1.05703	−	0.947001i
$815$	−49.1868			−1.72294
$816$	−8.01872	+	24.6791i	−0.280711	+	0.863941i
$817$	26.9943	−	19.6125i	0.944411	−	0.686155i
$818$	19.5641	+	14.2142i	0.684044	+	0.496987i
$819$	−1.48130	−	4.55897i	−0.0517608	−	0.159303i
$820$	−0.992183	−	3.05363i	−0.0346485	−	0.106637i
$821$	19.6024	+	14.2420i	0.684128	+	0.497048i	0.874724	−	0.484621i	$-0.161042\pi$
$821$	19.6024	+	14.2420i	0.684128	+	0.497048i	−0.190597	+	0.981668i	$0.561042\pi$
$822$	7.56077	−	5.49322i	0.263712	−	0.191598i
$823$	−13.4887	+	41.5140i	−0.470187	+	1.44709i	0.382153	+	0.924099i	$0.375183\pi$
$823$	−13.4887	+	41.5140i	−0.470187	+	1.44709i	−0.852340	+	0.522988i	$0.824817\pi$
$824$	21.8812			0.762268
$825$	24.7840	+	2.54257i	0.862869	+	0.0885209i
$826$	−2.11948			−0.0737460
$827$	−4.22693	+	13.0092i	−0.146985	+	0.452373i	−0.997261	−	0.0739640i	$-0.976435\pi$
$827$	−4.22693	+	13.0092i	−0.146985	+	0.452373i	0.850276	+	0.526337i	$0.176435\pi$
$828$	2.69026	−	1.95459i	0.0934929	−	0.0679266i
$829$	39.3137	+	28.5631i	1.36542	+	0.992037i	0.998079	+	0.0619514i	$0.0197324\pi$
$829$	39.3137	+	28.5631i	1.36542	+	0.992037i	0.367343	+	0.930086i	$0.380268\pi$
$830$	−6.71953	−	20.6806i	−0.233238	−	0.717834i
$831$	−1.54576	−	4.75735i	−0.0536217	−	0.165031i
$832$	−4.17992	−	3.03689i	−0.144913	−	0.105285i
$833$	70.7054	−	51.3705i	2.44980	−	1.77988i
$834$	1.10678	−	3.40631i	0.0383246	−	0.117951i
$835$	17.9997			0.622904
$836$	1.95569	+	9.08954i	0.0676390	+	0.314368i
$837$	4.24549			0.146746
$838$	−6.49892	+	20.0016i	−0.224501	+	0.690944i
$839$	−2.27607	+	1.65366i	−0.0785785	+	0.0570906i	−0.626381	−	0.779517i	$-0.715465\pi$
$839$	−2.27607	+	1.65366i	−0.0785785	+	0.0570906i	0.547802	+	0.836608i	$0.315465\pi$
$840$	−32.6215	−	23.7009i	−1.12555	−	0.817760i
$841$	−4.51371	−	13.8918i	−0.155645	−	0.479026i
$842$	5.13730	+	15.8110i	0.177043	+	0.544882i
$843$	−0.415281	−	0.301719i	−0.0143030	−	0.0103918i
$844$	6.96149	−	5.05782i	0.239624	−	0.174097i
$845$	1.09306	−	3.36409i	0.0376024	−	0.115728i
$846$	9.11649			0.313431
$847$	−51.6311	−	10.7063i	−1.77407	−	0.367871i
$848$	−12.0970			−0.415414
$849$	−4.80755	+	14.7961i	−0.164995	+	0.507802i
$850$	−52.4970	+	38.1413i	−1.80063	+	1.30824i
$851$	42.0769	+	30.5707i	1.44238	+	1.04795i
$852$	−1.94065	−	5.97271i	−0.0664856	−	0.204622i
$853$	8.29199	+	25.5201i	0.283912	+	0.873793i	0.986723	+	0.162415i	$0.0519283\pi$
$853$	8.29199	+	25.5201i	0.283912	+	0.873793i	−0.702810	+	0.711377i	$0.748072\pi$
$854$	29.8458	+	21.6842i	1.02130	+	0.742020i
$855$	16.2312	−	11.7927i	0.555097	−	0.403301i
$856$	6.37788	−	19.6291i	0.217991	−	0.670908i
$857$	−38.9270			−1.32972			−0.664860	−	0.746968i	$-0.731509\pi$
$857$	−38.9270			−1.32972			−0.664860	+	0.746968i	$0.731509\pi$
$858$	−1.10179	−	5.12081i	−0.0376144	−	0.174822i
$859$	−48.4078			−1.65165			−0.825826	−	0.563925i	$-0.809291\pi$
$859$	−48.4078			−1.65165			−0.825826	+	0.563925i	$0.809291\pi$
$860$	3.17808	−	9.78112i	0.108372	−	0.333534i
$861$	7.12242	−	5.17474i	0.242731	−	0.176355i
$862$	11.1516	+	8.10211i	0.379825	+	0.275959i
$863$	−12.9915	−	39.9836i	−0.442234	−	1.36106i	−0.885488	−	0.464661i	$-0.846176\pi$
$863$	−12.9915	−	39.9836i	−0.442234	−	1.36106i	0.443254	−	0.896396i	$-0.353824\pi$
$864$	−0.845616	−	2.60254i	−0.0287684	−	0.0885401i
$865$	58.4665	+	42.4784i	1.98792	+	1.44431i
$866$	−13.2351	+	9.61584i	−0.449746	+	0.326760i
$867$	−3.99157	+	12.2848i	−0.135561	+	0.417213i
$868$	10.0584			0.341403
$869$	−2.07215	−	0.212580i	−0.0702930	−	0.00721129i
$870$	−21.1939			−0.718541
$871$	−4.81498	+	14.8190i	−0.163149	+	0.502122i
$872$	−27.6333	+	20.0767i	−0.935781	+	0.679885i
$873$	3.66178	+	2.66044i	0.123933	+	0.0900423i
$874$	−18.6244	−	57.3199i	−0.629978	−	1.93887i
$875$	−13.1615	−	40.5068i	−0.444938	−	1.36938i
$876$	3.17780	+	2.30880i	0.107368	+	0.0780073i
$877$	−17.0251	+	12.3695i	−0.574897	+	0.417687i	−0.836881	−	0.547385i	$-0.815623\pi$
$877$	−17.0251	+	12.3695i	−0.574897	+	0.417687i	0.261984	+	0.965072i	$0.415623\pi$
$878$	5.98259	−	18.4125i	0.201903	−	0.621392i
$879$	5.49138			0.185220
$880$	−41.4539	−	37.1389i	−1.39741	−	1.25195i
$881$	−5.00534			−0.168634			−0.0843172	−	0.996439i	$-0.526871\pi$
$881$	−5.00534			−0.168634			−0.0843172	+	0.996439i	$0.526871\pi$
$882$	−7.79808	+	24.0000i	−0.262575	+	0.808123i
$883$	25.1148	−	18.2470i	0.845181	−	0.614060i	−0.0786323	−	0.996904i	$-0.525055\pi$
$883$	25.1148	−	18.2470i	0.845181	−	0.614060i	0.923813	+	0.382844i	$0.125055\pi$
$884$	2.18704	+	1.58897i	0.0735580	+	0.0534430i
$885$	0.306015	+	0.941816i	0.0102866	+	0.0316588i
$886$	−10.1031	−	31.0941i	−0.339420	−	1.04463i
$887$	6.77744	+	4.92410i	0.227564	+	0.165335i	0.695725	−	0.718308i	$-0.255083\pi$
$887$	6.77744	+	4.92410i	0.227564	+	0.165335i	−0.468161	+	0.883643i	$0.655083\pi$
$888$	14.8721	−	10.8052i	0.499074	−	0.362599i
$889$	−8.03772	+	24.7375i	−0.269576	+	0.829671i
$890$	−36.8320			−1.23461
$891$	−1.34145	+	3.03323i	−0.0449402	+	0.101617i
$892$	1.53893			0.0515271
$893$	10.1175	−	31.1385i	0.338570	−	1.04201i
$894$	−10.9390	+	7.94762i	−0.365853	+	0.265808i
$895$	−28.5504	−	20.7431i	−0.954334	−	0.693364i
$896$	20.1942	+	62.1513i	0.674640	+	2.07633i
$897$	2.07912	+	6.39887i	0.0694198	+	0.213652i
$898$	23.7185	+	17.2325i	0.791496	+	0.575056i
$899$	−13.0306	+	9.46732i	−0.434596	+	0.315753i
$900$	1.14728	−	3.53097i	0.0382428	−	0.117699i
$901$	−13.9468			−0.464635
$902$	8.31916	−	4.83071i	0.276998	−	0.160845i
$903$	28.1996			0.938423
$904$	−1.03239	+	3.17737i	−0.0343367	+	0.105678i
$905$	−13.1775	+	9.57403i	−0.438036	+	0.318252i
$906$	11.9856	+	8.70804i	0.398194	+	0.289305i
$907$	−11.1869	−	34.4296i	−0.371453	−	1.14322i	−0.945840	−	0.324632i	$-0.894760\pi$
$907$	−11.1869	−	34.4296i	−0.371453	−	1.14322i	0.574387	−	0.818584i	$-0.305240\pi$
$908$	1.82520	+	5.61740i	0.0605715	+	0.186420i
$909$	−0.784892	−	0.570257i	−0.0260332	−	0.0189142i
$910$	−21.6645	+	15.7402i	−0.718172	+	0.521782i
$911$	2.56945	−	7.90796i	0.0851297	−	0.262002i	−0.899426	−	0.437073i	$-0.856015\pi$
$911$	2.56945	−	7.90796i	0.0851297	−	0.262002i	0.984556	+	0.175070i	$0.0560153\pi$
$912$	−26.9089			−0.891044
$913$	11.1642	−	6.48274i	0.369481	−	0.214547i
$914$	13.2938			0.439719
$915$	5.32647	−	16.3932i	0.176088	−	0.541942i
$916$	2.40163	−	1.74488i	0.0793519	−	0.0576526i
$917$	−6.43179	−	4.67297i	−0.212396	−	0.154315i
$918$	−2.66938	−	8.21551i	−0.0881027	−	0.271152i
$919$	14.1852	+	43.6575i	0.467926	+	1.44013i	0.855266	+	0.518190i	$0.173394\pi$
$919$	14.1852	+	43.6575i	0.467926	+	1.44013i	−0.387340	+	0.921937i	$0.626606\pi$
$920$	45.7868	+	33.2661i	1.50955	+	1.09675i
$921$	22.1824	−	16.1165i	0.730935	−	0.531055i
$922$	−18.0830	+	55.6539i	−0.595533	+	1.83286i
$923$	12.7065			0.418239
$924$	−3.17815	+	7.18631i	−0.104553	+	0.236412i
$925$	58.0682			1.90927
$926$	3.29295	−	10.1347i	0.108213	−	0.333046i
$927$	−7.44397	+	5.40836i	−0.244492	+	0.177634i
$928$	8.39903	+	6.10225i	0.275712	+	0.200316i
$929$	8.03259	+	24.7218i	0.263541	+	0.811095i	0.992026	+	0.126034i	$0.0402247\pi$
$929$	8.03259	+	24.7218i	0.263541	+	0.811095i	−0.728485	+	0.685062i	$0.759775\pi$
$930$	−7.32893	−	22.5561i	−0.240325	−	0.739645i
$931$	73.3207	+	53.2706i	2.40299	+	1.74587i
$932$	−3.17142	+	2.30417i	−0.103883	+	0.0754756i
$933$	6.01439	−	18.5104i	0.196902	−	0.606003i
$934$	15.3641			0.502728
$935$	−47.7926	−	42.8178i	−1.56299	−	1.40029i
$936$	2.37807			0.0777296
$937$	10.4938	−	32.2966i	0.342818	−	1.05508i	−0.619924	−	0.784662i	$-0.712837\pi$
$937$	10.4938	−	32.2966i	0.342818	−	1.05508i	0.962742	−	0.270422i	$-0.0871634\pi$
$938$	95.4332	−	69.3363i	3.11600	−	2.26391i
$939$	9.68152	+	7.03404i	0.315945	+	0.229547i
$940$	−3.11847	−	9.59766i	−0.101713	−	0.313041i
$941$	11.3149	+	34.8237i	0.368855	+	1.13522i	0.947532	+	0.319662i	$0.103569\pi$
$941$	11.3149	+	34.8237i	0.368855	+	1.13522i	−0.578676	+	0.815557i	$0.696431\pi$
$942$	5.02784	+	3.65294i	0.163816	+	0.119019i
$943$	−9.99686	+	7.26314i	−0.325542	+	0.236520i
$944$	0.410435	−	1.26319i	0.0133585	−	0.0411133i
$945$	16.9560			0.551577
$946$	30.6531	+	3.14467i	0.996617	+	0.102242i
$947$	18.5813			0.603811			0.301905	−	0.953338i	$-0.402377\pi$
$947$	18.5813			0.603811			0.301905	+	0.953338i	$0.402377\pi$
$948$	−0.0959225	+	0.295219i	−0.00311542	+	0.00958827i
$949$	−6.42964	+	4.67141i	−0.208715	+	0.151640i
$950$	−54.4388	−	39.5521i	−1.76623	−	1.28324i
$951$	0.769091	+	2.36702i	0.0249395	+	0.0767558i
$952$	19.2676	+	59.2995i	0.624465	+	1.92191i
$953$	−24.9855	−	18.1530i	−0.809361	−	0.588035i	0.104285	−	0.994547i	$-0.466745\pi$
$953$	−24.9855	−	18.1530i	−0.809361	−	0.588035i	−0.913645	+	0.406513i	$0.866745\pi$
$954$	3.25793	−	2.36703i	0.105479	−	0.0766353i
$955$	26.5122	−	81.5960i	0.857913	−	2.64039i
$956$	−8.33754			−0.269655
$957$	−2.64673	−	12.3013i	−0.0855565	−	0.397644i
$958$	−43.3884			−1.40182
$959$	8.76561	−	26.9778i	0.283056	−	0.871158i
$960$	14.7853	−	10.7421i	0.477193	−	0.346701i
$961$	10.4977	+	7.62700i	0.338634	+	0.246032i
$962$	−3.77260	−	11.6109i	−0.121634	−	0.374350i
$963$	2.68196	+	8.25421i	0.0864248	+	0.265988i
$964$	3.53000	+	2.56469i	0.113694	+	0.0826032i
$965$	−9.56529	+	6.94959i	−0.307918	+	0.223715i
$966$	15.7402	−	48.4433i	0.506432	−	1.55864i
$967$	51.0775			1.64254			0.821271	−	0.570539i	$-0.193266\pi$
$967$	51.0775			1.64254			0.821271	+	0.570539i	$0.193266\pi$
$968$	12.9665	−	22.7190i	0.416758	−	0.730215i
$969$	−31.0236			−0.996621
$970$	7.81355	−	24.0476i	0.250878	−	0.772123i
$971$	−20.1653	+	14.6510i	−0.647136	+	0.470172i	−0.862294	−	0.506408i	$-0.830973\pi$
$971$	−20.1653	+	14.6510i	−0.647136	+	0.470172i	0.215159	+	0.976579i	$0.430973\pi$
$972$	0.399850	+	0.290508i	0.0128252	+	0.00931805i
$973$	−3.35932	−	10.3389i	−0.107695	−	0.331451i
$974$	10.5188	+	32.3735i	0.337044	+	1.03731i
$975$	6.07724	+	4.41537i	0.194627	+	0.141405i
$976$	−18.7032	+	13.5887i	−0.598676	+	0.434964i
$977$	1.84773	−	5.68673i	0.0591142	−	0.181935i	−0.917139	−	0.398568i	$-0.869507\pi$
$977$	1.84773	−	5.68673i	0.0591142	−	0.181935i	0.976253	+	0.216633i	$0.0695074\pi$
$978$	−21.9612			−0.702242
$979$	−4.59963	−	21.3779i	−0.147005	−	0.683240i
$980$	27.9342			0.892326
$981$	4.43846	−	13.6602i	0.141709	−	0.436136i
$982$	49.9504	−	36.2911i	1.59398	−	1.15810i
$983$	22.9044	+	16.6410i	0.730538	+	0.530767i	0.889733	−	0.456480i	$-0.150890\pi$
$983$	22.9044	+	16.6410i	0.730538	+	0.530767i	−0.159196	+	0.987247i	$0.550890\pi$
$984$	1.34963	+	4.15374i	0.0430247	+	0.132417i
$985$	−1.01555	−	3.12554i	−0.0323581	−	0.0995879i
$986$	26.5135	+	19.2632i	0.844361	+	0.613464i
$987$	22.3860	−	16.2644i	0.712555	−	0.517702i
$988$	−0.866272	+	2.66611i	−0.0275598	+	0.0848203i
$989$	−39.5803			−1.25858
$990$	18.4312	+	1.89084i	0.585782	+	0.0600948i
$991$	−29.4804			−0.936476			−0.468238	−	0.883603i	$-0.655111\pi$
$991$	−29.4804			−0.936476			−0.468238	+	0.883603i	$0.655111\pi$
$992$	−3.59005	+	11.0490i	−0.113984	+	0.350807i
$993$	25.0088	−	18.1700i	0.793631	−	0.576607i
$994$	−77.8240	−	56.5424i	−2.46843	−	1.79342i
$995$	6.54428	+	20.1412i	0.207468	+	0.638520i
$996$	−0.594494	−	1.82967i	−0.0188373	−	0.0579752i
$997$	18.8278	+	13.6792i	0.596283	+	0.433225i	0.844557	−	0.535465i	$-0.179864\pi$
$997$	18.8278	+	13.6792i	0.596283	+	0.433225i	−0.248275	+	0.968690i	$0.579864\pi$
$998$	18.8430	−	13.6903i	0.596466	−	0.433358i
$999$	−2.38876	+	7.35184i	−0.0755769	+	0.232602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.c.196.2	✓	28
11.4	even	5		4719.2.a.bp.1.3		14
11.5	even	5	inner	429.2.n.c.313.2	yes	28
11.7	odd	10		4719.2.a.bo.1.12		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.c.196.2	✓	28	1.1	even	1	trivial
429.2.n.c.313.2	yes	28	11.5	even	5	inner
4719.2.a.bo.1.12		14	11.7	odd	10
4719.2.a.bp.1.3		14	11.4	even	5

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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.488036 + 1.50202i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.399850 - 0.290508i) q^{4} +(1.09306 + 3.36409i) q^{5} +(0.488036 + 1.50202i) q^{6} +(3.87810 + 2.81760i) q^{7} +(-1.92390 + 1.39779i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.488036 + 1.50202i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.399850 - 0.290508i) q^{4} +(1.09306 + 3.36409i) q^{5} +(0.488036 + 1.50202i) q^{6} +(3.87810 + 2.81760i) q^{7} +(-1.92390 + 1.39779i) q^{8} +(0.309017 - 0.951057i) q^{9} -5.58638 q^{10} +(-0.697635 - 3.24242i) q^{11} -0.494242 q^{12} +(0.309017 - 0.951057i) q^{13} +(-6.12474 + 4.44988i) q^{14} +(2.86167 + 2.07912i) q^{15} +(-1.46604 - 4.51201i) q^{16} +(-1.69021 - 5.20194i) q^{17} +(1.27769 + 0.928299i) q^{18} +(4.58871 - 3.33389i) q^{19} +(0.540235 - 1.66267i) q^{20} +4.79359 q^{21} +(5.21065 + 0.534556i) q^{22} -6.72817 q^{23} +(-0.734864 + 2.26168i) q^{24} +(-6.07724 + 4.41537i) q^{25} +(1.27769 + 0.928299i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.732120 - 2.25324i) q^{28} +(3.06929 + 2.22997i) q^{29} +(-4.51948 + 3.28359i) q^{30} +(-1.31193 + 4.03770i) q^{31} +2.73647 q^{32} +(-2.47025 - 2.21312i) q^{33} +8.63830 q^{34} +(-5.23968 + 16.1261i) q^{35} +(-0.399850 + 0.290508i) q^{36} +(-6.25384 - 4.54368i) q^{37} +(2.76812 + 8.51939i) q^{38} +(-0.309017 - 0.951057i) q^{39} +(-6.80524 - 4.94430i) q^{40} +(1.48582 - 1.07951i) q^{41} +(-2.33944 + 7.20006i) q^{42} +5.88277 q^{43} +(-0.663000 + 1.49915i) q^{44} +3.53721 q^{45} +(3.28359 - 10.1058i) q^{46} +(4.66999 - 3.39295i) q^{47} +(-3.83815 - 2.78858i) q^{48} +(4.93763 + 15.1965i) q^{49} +(-3.66607 - 11.2830i) q^{50} +(-4.42503 - 3.21498i) q^{51} +(-0.399850 + 0.290508i) q^{52} +(0.787948 - 2.42505i) q^{53} +1.57932 q^{54} +(10.1452 - 5.89107i) q^{55} -11.3995 q^{56} +(1.75273 - 5.39435i) q^{57} +(-4.84739 + 3.52183i) q^{58} +(0.226494 + 0.164557i) q^{59} +(-0.540235 - 1.66267i) q^{60} +(-1.50584 - 4.63449i) q^{61} +(-5.42444 - 3.94108i) q^{62} +(3.87810 - 2.81760i) q^{63} +(1.59659 - 4.91379i) q^{64} +3.53721 q^{65} +(4.52971 - 2.63028i) q^{66} -15.5816 q^{67} +(-0.835374 + 2.57102i) q^{68} +(-5.44320 + 3.95472i) q^{69} +(-21.6645 - 15.7402i) q^{70} +(3.92652 + 12.0846i) q^{71} +(0.734864 + 2.26168i) q^{72} +(-6.42964 - 4.67141i) q^{73} +(9.87680 - 7.17592i) q^{74} +(-2.32130 + 7.14423i) q^{75} -2.80332 q^{76} +(6.43036 - 14.5401i) q^{77} +1.57932 q^{78} +(0.194080 - 0.597317i) q^{79} +(13.5763 - 9.86379i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.896315 + 2.75857i) q^{82} +(1.20284 + 3.70197i) q^{83} +(-1.91672 - 1.39258i) q^{84} +(15.6523 - 11.3721i) q^{85} +(-2.87100 + 8.83603i) q^{86} +3.79385 q^{87} +(5.87442 + 5.26294i) q^{88} +6.59318 q^{89} +(-1.72629 + 5.31296i) q^{90} +(3.87810 - 2.81760i) q^{91} +(2.69026 + 1.95459i) q^{92} +(1.31193 + 4.03770i) q^{93} +(2.81715 + 8.67030i) q^{94} +(16.2312 + 11.7927i) q^{95} +(2.21385 - 1.60846i) q^{96} +(-1.39868 + 4.30469i) q^{97} -25.2351 q^{98} +(-3.29931 - 0.338473i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9}+O(q^{10}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9} - 2 q^{10} + 14 q^{11} - 30 q^{12} - 7 q^{13} - 9 q^{14} + 4 q^{15} + q^{16} - 12 q^{17} - 4 q^{18} + 10 q^{19} - 41 q^{20} - 6 q^{21} + 5 q^{22} + 30 q^{23} + 2 q^{24} + 3 q^{25} - 4 q^{26} + 7 q^{27} - 12 q^{28} - 4 q^{29} + 7 q^{30} - 4 q^{31} + 22 q^{32} + q^{33} - 24 q^{34} - 6 q^{35} - 5 q^{36} - 8 q^{37} + 73 q^{38} + 7 q^{39} - 28 q^{40} + 10 q^{41} + 9 q^{42} - 12 q^{43} - 22 q^{44} + 16 q^{45} + 35 q^{46} + 12 q^{47} + 14 q^{48} + 16 q^{49} - 57 q^{50} - 13 q^{51} - 5 q^{52} + q^{53} - 6 q^{54} - 28 q^{55} + 48 q^{56} - 30 q^{58} - 15 q^{59} + 41 q^{60} - 22 q^{61} - 40 q^{62} + q^{63} - 19 q^{64} + 16 q^{65} + 20 q^{66} - 88 q^{67} + 39 q^{68} + 14 q^{70} + 34 q^{71} - 2 q^{72} - 59 q^{73} + 79 q^{74} + 27 q^{75} - 124 q^{76} - 42 q^{77} - 6 q^{78} - 3 q^{79} + 37 q^{80} - 7 q^{81} + 82 q^{82} - 8 q^{83} - 8 q^{84} + 70 q^{85} - 35 q^{86} - 36 q^{87} + 59 q^{88} + 126 q^{89} + 8 q^{90} + q^{91} - 82 q^{92} + 4 q^{93} + 23 q^{94} - 77 q^{95} + 73 q^{96} - 18 q^{97} - 66 q^{98} - 6 q^{99}+O(q^{100}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9 - 2 * q^10 + 14 * q^11 - 30 * q^12 - 7 * q^13 - 9 * q^14 + 4 * q^15 + q^16 - 12 * q^17 - 4 * q^18 + 10 * q^19 - 41 * q^20 - 6 * q^21 + 5 * q^22 + 30 * q^23 + 2 * q^24 + 3 * q^25 - 4 * q^26 + 7 * q^27 - 12 * q^28 - 4 * q^29 + 7 * q^30 - 4 * q^31 + 22 * q^32 + q^33 - 24 * q^34 - 6 * q^35 - 5 * q^36 - 8 * q^37 + 73 * q^38 + 7 * q^39 - 28 * q^40 + 10 * q^41 + 9 * q^42 - 12 * q^43 - 22 * q^44 + 16 * q^45 + 35 * q^46 + 12 * q^47 + 14 * q^48 + 16 * q^49 - 57 * q^50 - 13 * q^51 - 5 * q^52 + q^53 - 6 * q^54 - 28 * q^55 + 48 * q^56 - 30 * q^58 - 15 * q^59 + 41 * q^60 - 22 * q^61 - 40 * q^62 + q^63 - 19 * q^64 + 16 * q^65 + 20 * q^66 - 88 * q^67 + 39 * q^68 + 14 * q^70 + 34 * q^71 - 2 * q^72 - 59 * q^73 + 79 * q^74 + 27 * q^75 - 124 * q^76 - 42 * q^77 - 6 * q^78 - 3 * q^79 + 37 * q^80 - 7 * q^81 + 82 * q^82 - 8 * q^83 - 8 * q^84 + 70 * q^85 - 35 * q^86 - 36 * q^87 + 59 * q^88 + 126 * q^89 + 8 * q^90 + q^91 - 82 * q^92 + 4 * q^93 + 23 * q^94 - 77 * q^95 + 73 * q^96 - 18 * q^97 - 66 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more