LMFDB - Embedded newform 429.2.bb.b.25.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(25,429)]

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, 5]))

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

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

chi := DirichletCharacter("429.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bb (of order $10$, 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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			25.6
Character	$\chi$	$=$	429.25
Dual form			429.2.bb.b.103.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.386931 - 0.532564i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.484125 - 1.48998i) q^{4} +(-0.663105 + 0.912685i) q^{5} +(-0.386931 + 0.532564i) q^{6} +(-3.82419 - 1.24256i) q^{7} +(-2.23297 + 0.725535i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.386931 - 0.532564i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.484125 - 1.48998i) q^{4} +(-0.663105 + 0.912685i) q^{5} +(-0.386931 + 0.532564i) q^{6} +(-3.82419 - 1.24256i) q^{7} +(-2.23297 + 0.725535i) q^{8} +(-0.809017 + 0.587785i) q^{9} +0.742639 q^{10} +(2.15706 + 2.51935i) q^{11} -1.56666 q^{12} +(-2.97428 + 2.03805i) q^{13} +(0.817956 + 2.51741i) q^{14} +(1.07293 + 0.348615i) q^{15} +(-1.28451 - 0.933253i) q^{16} +(-1.63950 - 1.19117i) q^{17} +(0.626067 + 0.203421i) q^{18} +(-2.02272 + 0.657222i) q^{19} +(1.03886 + 1.42987i) q^{20} +4.02099i q^{21} +(0.507082 - 2.12358i) q^{22} +2.39350 q^{23} +(1.38005 + 1.89948i) q^{24} +(1.15180 + 3.54487i) q^{25} +(2.23623 + 0.795414i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-3.70277 + 5.09643i) q^{28} +(2.23943 - 6.89227i) q^{29} +(-0.229488 - 0.706291i) q^{30} +(-4.11515 - 5.66402i) q^{31} +5.74095i q^{32} +(1.72947 - 2.83000i) q^{33} +1.33404i q^{34} +(3.66990 - 2.66634i) q^{35} +(0.484125 + 1.48998i) q^{36} +(0.801277 + 0.260351i) q^{37} +(1.13267 + 0.822930i) q^{38} +(2.85740 + 2.19892i) q^{39} +(0.818506 - 2.51910i) q^{40} +(-4.60558 + 1.49644i) q^{41} +(2.14144 - 1.55585i) q^{42} -12.2699 q^{43} +(4.79807 - 1.99430i) q^{44} -1.12814i q^{45} +(-0.926117 - 1.27469i) q^{46} +(2.18753 - 0.710772i) q^{47} +(-0.490640 + 1.51003i) q^{48} +(7.41739 + 5.38905i) q^{49} +(1.44221 - 1.98503i) q^{50} +(-0.626235 + 1.92735i) q^{51} +(1.59673 + 5.41830i) q^{52} +(-11.4692 + 8.33286i) q^{53} -0.658286i q^{54} +(-3.72972 + 0.298124i) q^{55} +9.44081 q^{56} +(1.25011 + 1.72063i) q^{57} +(-4.53708 + 1.47419i) q^{58} +(-4.96443 - 1.61304i) q^{59} +(1.03886 - 1.42987i) q^{60} +(-0.578093 - 0.420009i) q^{61} +(-1.42418 + 4.38317i) q^{62} +(3.82419 - 1.24256i) q^{63} +(0.488400 - 0.354843i) q^{64} +(0.112164 - 4.06602i) q^{65} +(-2.17634 + 0.173959i) q^{66} -5.16940i q^{67} +(-2.56855 + 1.86616i) q^{68} +(-0.739632 - 2.27635i) q^{69} +(-2.83999 - 0.922770i) q^{70} +(7.15036 - 9.84163i) q^{71} +(1.38005 - 1.89948i) q^{72} +(-12.8466 - 4.17412i) q^{73} +(-0.171385 - 0.527469i) q^{74} +(3.01545 - 2.19085i) q^{75} +3.33200i q^{76} +(-5.11857 - 12.3147i) q^{77} +(0.0654495 - 2.37258i) q^{78} +(9.87453 - 7.17427i) q^{79} +(1.70353 - 0.553511i) q^{80} +(0.309017 - 0.951057i) q^{81} +(2.57899 + 1.87375i) q^{82} +(6.89236 - 9.48652i) q^{83} +(5.99121 + 1.94666i) q^{84} +(2.17433 - 0.706481i) q^{85} +(4.74761 + 6.53453i) q^{86} -7.24696 q^{87} +(-6.64451 - 4.06060i) q^{88} +10.8606i q^{89} +(-0.600807 + 0.436512i) q^{90} +(13.9066 - 4.09818i) q^{91} +(1.15875 - 3.56627i) q^{92} +(-4.11515 + 5.66402i) q^{93} +(-1.22495 - 0.889981i) q^{94} +(0.741439 - 2.28192i) q^{95} +(5.45997 - 1.77405i) q^{96} +(-5.69825 - 7.84297i) q^{97} -6.03542i q^{98} +(-3.22593 - 0.770308i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9}+O(q^{10}) $ 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9	$ 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9} + 60 q^{12} - 3 q^{13} - 42 q^{14} - 16 q^{16} - 6 q^{17} - 40 q^{22} + 12 q^{23} + 4 q^{25} - 24 q^{26} + 14 q^{27} - 22 q^{29} - 10 q^{30} - 10 q^{35} + 20 q^{36} - 26 q^{38} + 3 q^{39} - 18 q^{42} + 6 q^{48} - 14 q^{49} - 24 q^{51} + 39 q^{52} + 10 q^{53} - 64 q^{55} - 20 q^{56} + 2 q^{61} - 8 q^{62} + 24 q^{64} - 58 q^{65} + 30 q^{66} + 18 q^{68} - 2 q^{69} - 86 q^{74} - 14 q^{75} + 52 q^{77} + 14 q^{78} - 24 q^{79} - 14 q^{81} + 62 q^{82} - 28 q^{87} - 46 q^{88} - 10 q^{90} - 19 q^{91} + 58 q^{92} + 86 q^{94} + 156 q^{95}+O(q^{100}) $ 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9 + 60 * q^12 - 3 * q^13 - 42 * q^14 - 16 * q^16 - 6 * q^17 - 40 * q^22 + 12 * q^23 + 4 * q^25 - 24 * q^26 + 14 * q^27 - 22 * q^29 - 10 * q^30 - 10 * q^35 + 20 * q^36 - 26 * q^38 + 3 * q^39 - 18 * q^42 + 6 * q^48 - 14 * q^49 - 24 * q^51 + 39 * q^52 + 10 * q^53 - 64 * q^55 - 20 * q^56 + 2 * q^61 - 8 * q^62 + 24 * q^64 - 58 * q^65 + 30 * q^66 + 18 * q^68 - 2 * q^69 - 86 * q^74 - 14 * q^75 + 52 * q^77 + 14 * q^78 - 24 * q^79 - 14 * q^81 + 62 * q^82 - 28 * q^87 - 46 * q^88 - 10 * q^90 - 19 * q^91 + 58 * q^92 + 86 * q^94 + 156 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−0.386931	−	0.532564i	−0.273601	−	0.376580i	0.650000	−	0.759934i	$-0.274769\pi$
$2$	−0.386931	−	0.532564i	−0.273601	−	0.376580i	−0.923601	+	0.383354i	$0.874769\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.484125	−	1.48998i	0.242062	−	0.744991i
$5$	−0.663105	+	0.912685i	−0.296549	+	0.408165i	−0.931128	−	0.364693i	$-0.881174\pi$
$5$	−0.663105	+	0.912685i	−0.296549	+	0.408165i	0.634578	+	0.772859i	$0.281174\pi$
$6$	−0.386931	+	0.532564i	−0.157964	+	0.217418i
$7$	−3.82419	−	1.24256i	−1.44541	−	0.469642i	−0.521830	−	0.853050i	$-0.674750\pi$
$7$	−3.82419	−	1.24256i	−1.44541	−	0.469642i	−0.923579	+	0.383408i	$0.874750\pi$
$8$	−2.23297	+	0.725535i	−0.789473	+	0.256515i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	0.742639			0.234843
$11$	2.15706	+	2.51935i	0.650377	+	0.759611i
$11$	2.15706	+	2.51935i	0.650377	+	0.759611i
$12$	−1.56666			−0.452256
$13$	−2.97428	+	2.03805i	−0.824918	+	0.565253i
$13$	−2.97428	+	2.03805i	−0.824918	+	0.565253i
$14$	0.817956	+	2.51741i	0.218608	+	0.672806i
$15$	1.07293	+	0.348615i	0.277028	+	0.0900119i
$16$	−1.28451	−	0.933253i	−0.321128	−	0.233313i
$17$	−1.63950	−	1.19117i	−0.397638	−	0.288901i	0.370940	−	0.928657i	$-0.379036\pi$
$17$	−1.63950	−	1.19117i	−0.397638	−	0.288901i	−0.768578	+	0.639756i	$0.779036\pi$
$18$	0.626067	+	0.203421i	0.147565	+	0.0479469i
$19$	−2.02272	+	0.657222i	−0.464044	+	0.150777i	−0.531702	−	0.846931i	$-0.678447\pi$
$19$	−2.02272	+	0.657222i	−0.464044	+	0.150777i	0.0676578	+	0.997709i	$0.478447\pi$
$20$	1.03886	+	1.42987i	0.232296	+	0.319728i
$21$			4.02099i			0.877453i
$22$	0.507082	−	2.12358i	0.108110	−	0.452749i
$23$	2.39350			0.499079			0.249539	−	0.968365i	$-0.419721\pi$
$23$	2.39350			0.499079			0.249539	+	0.968365i	$0.419721\pi$
$24$	1.38005	+	1.89948i	0.281701	+	0.387729i
$25$	1.15180	+	3.54487i	0.230360	+	0.708974i
$26$	2.23623	+	0.795414i	0.438561	+	0.155993i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−3.70277	+	5.09643i	−0.699758	+	0.963134i
$29$	2.23943	−	6.89227i	0.415852	−	1.27986i	−0.495634	−	0.868532i	$-0.665064\pi$
$29$	2.23943	−	6.89227i	0.415852	−	1.27986i	0.911486	−	0.411331i	$-0.134936\pi$
$30$	−0.229488	−	0.706291i	−0.0418986	−	0.128951i
$31$	−4.11515	−	5.66402i	−0.739104	−	1.01729i	−0.998670	−	0.0515635i	$-0.983580\pi$
$31$	−4.11515	−	5.66402i	−0.739104	−	1.01729i	0.259566	−	0.965725i	$-0.416420\pi$
$32$			5.74095i			1.01487i
$33$	1.72947	−	2.83000i	0.301063	−	0.492640i
$34$			1.33404i			0.228786i
$35$	3.66990	−	2.66634i	0.620327	−	0.450694i
$36$	0.484125	+	1.48998i	0.0806874	+	0.248330i
$37$	0.801277	+	0.260351i	0.131729	+	0.0428014i	0.374140	−	0.927372i	$-0.377938\pi$
$37$	0.801277	+	0.260351i	0.131729	+	0.0428014i	−0.242411	+	0.970174i	$0.577938\pi$
$38$	1.13267	+	0.822930i	0.183743	+	0.133497i
$39$	2.85740	+	2.19892i	0.457551	+	0.352109i
$40$	0.818506	−	2.51910i	0.129417	−	0.398305i
$41$	−4.60558	+	1.49644i	−0.719271	+	0.233705i	−0.645707	−	0.763585i	$-0.723437\pi$
$41$	−4.60558	+	1.49644i	−0.719271	+	0.233705i	−0.0735639	+	0.997291i	$0.523437\pi$
$42$	2.14144	−	1.55585i	0.330431	−	0.240072i
$43$	−12.2699			−1.87115			−0.935574	−	0.353131i	$-0.885117\pi$
$43$	−12.2699			−1.87115			−0.935574	+	0.353131i	$0.885117\pi$
$44$	4.79807	−	1.99430i	0.723336	−	0.300652i
$45$		−	1.12814i		−	0.168173i
$46$	−0.926117	−	1.27469i	−0.136549	−	0.187943i
$47$	2.18753	−	0.710772i	0.319084	−	0.103677i	−0.145096	−	0.989418i	$-0.546349\pi$
$47$	2.18753	−	0.710772i	0.319084	−	0.103677i	0.464180	+	0.885741i	$0.346349\pi$
$48$	−0.490640	+	1.51003i	−0.0708178	+	0.217955i
$49$	7.41739	+	5.38905i	1.05963	+	0.769864i
$50$	1.44221	−	1.98503i	0.203959	−	0.280725i
$51$	−0.626235	+	1.92735i	−0.0876905	+	0.269883i
$52$	1.59673	+	5.41830i	0.221427	+	0.751383i
$53$	−11.4692	+	8.33286i	−1.57542	+	1.14461i	−0.653690	+	0.756762i	$0.726780\pi$
$53$	−11.4692	+	8.33286i	−1.57542	+	1.14461i	−0.921725	+	0.387844i	$0.873220\pi$
$54$		−	0.658286i		−	0.0895813i
$55$	−3.72972	+	0.298124i	−0.502916	+	0.0401990i
$56$	9.44081			1.26158
$57$	1.25011	+	1.72063i	0.165581	+	0.227903i
$58$	−4.53708	+	1.47419i	−0.595748	+	0.193570i
$59$	−4.96443	−	1.61304i	−0.646314	−	0.210000i	−0.0325258	−	0.999471i	$-0.510355\pi$
$59$	−4.96443	−	1.61304i	−0.646314	−	0.210000i	−0.613788	+	0.789471i	$0.710355\pi$
$60$	1.03886	−	1.42987i	0.134116	−	0.184595i
$61$	−0.578093	−	0.420009i	−0.0740172	−	0.0537767i	0.550161	−	0.835058i	$-0.314566\pi$
$61$	−0.578093	−	0.420009i	−0.0740172	−	0.0537767i	−0.624179	+	0.781282i	$0.714566\pi$
$62$	−1.42418	+	4.38317i	−0.180871	+	0.556663i
$63$	3.82419	−	1.24256i	0.481803	−	0.156547i
$64$	0.488400	−	0.354843i	0.0610500	−	0.0443554i
$65$	0.112164	−	4.06602i	0.0139123	−	0.504328i
$66$	−2.17634	+	0.173959i	−0.267890	+	0.0214129i
$67$		−	5.16940i		−	0.631543i	−0.948835	−	0.315772i	$-0.897737\pi$
$67$		−	5.16940i		−	0.631543i	0.948835	−	0.315772i	$-0.102263\pi$
$68$	−2.56855	+	1.86616i	−0.311482	+	0.226305i
$69$	−0.739632	−	2.27635i	−0.0890412	−	0.274041i
$70$	−2.83999	−	0.922770i	−0.339444	−	0.110292i
$71$	7.15036	−	9.84163i	0.848592	−	1.16799i	−0.135579	−	0.990766i	$-0.543290\pi$
$71$	7.15036	−	9.84163i	0.848592	−	1.16799i	0.984171	−	0.177220i	$-0.0567104\pi$
$72$	1.38005	−	1.89948i	0.162640	−	0.223855i
$73$	−12.8466	−	4.17412i	−1.50358	−	0.488544i	−0.562523	−	0.826782i	$-0.690169\pi$
$73$	−12.8466	−	4.17412i	−1.50358	−	0.488544i	−0.941061	+	0.338238i	$0.890169\pi$
$74$	−0.171385	−	0.527469i	−0.0199231	−	0.0613170i
$75$	3.01545	−	2.19085i	0.348194	−	0.252978i
$76$			3.33200i			0.382206i
$77$	−5.11857	−	12.3147i	−0.583316	−	1.40339i
$78$	0.0654495	−	2.37258i	0.00741069	−	0.268642i
$79$	9.87453	−	7.17427i	1.11097	−	0.807168i	0.128155	−	0.991754i	$-0.459094\pi$
$79$	9.87453	−	7.17427i	1.11097	−	0.807168i	0.982816	+	0.184586i	$0.0590943\pi$
$80$	1.70353	−	0.553511i	0.190461	−	0.0618844i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	2.57899	+	1.87375i	0.284802	+	0.206921i
$83$	6.89236	−	9.48652i	0.756534	−	1.04128i	−0.240960	−	0.970535i	$-0.577462\pi$
$83$	6.89236	−	9.48652i	0.756534	−	1.04128i	0.997494	−	0.0707453i	$-0.0225378\pi$
$84$	5.99121	+	1.94666i	0.653695	+	0.212398i
$85$	2.17433	−	0.706481i	0.235839	−	0.0766287i
$86$	4.74761	+	6.53453i	0.511948	+	0.704636i
$87$	−7.24696			−0.776956
$88$	−6.64451	−	4.06060i	−0.708307	−	0.432861i
$89$			10.8606i			1.15122i	0.817725	+	0.575609i	$0.195235\pi$
$89$			10.8606i			1.15122i	−0.817725	+	0.575609i	$0.804765\pi$
$90$	−0.600807	+	0.436512i	−0.0633307	+	0.0460124i
$91$	13.9066	−	4.09818i	1.45781	−	0.429606i
$92$	1.15875	−	3.56627i	0.120808	−	0.371809i
$93$	−4.11515	+	5.66402i	−0.426722	+	0.587332i
$94$	−1.22495	−	0.889981i	−0.126344	−	0.0917946i
$95$	0.741439	−	2.28192i	0.0760701	−	0.234120i
$96$	5.45997	−	1.77405i	0.557256	−	0.181063i
$97$	−5.69825	−	7.84297i	−0.578570	−	0.796333i	0.414968	−	0.909836i	$-0.363793\pi$
$97$	−5.69825	−	7.84297i	−0.578570	−	0.796333i	−0.993538	+	0.113503i	$0.963793\pi$
$98$		−	6.03542i		−	0.609670i
$99$	−3.22593	−	0.770308i	−0.324218	−	0.0774188i
$100$	5.83941			0.583941
$101$	2.98098	−	2.16581i	0.296619	−	0.215506i	−0.429515	−	0.903060i	$-0.641315\pi$
$101$	2.98098	−	2.16581i	0.296619	−	0.215506i	0.726134	+	0.687554i	$0.241315\pi$
$102$	1.26875	−	0.412241i	0.125625	−	0.0408180i
$103$	3.54475	−	10.9096i	0.349274	−	1.07496i	−0.609981	−	0.792416i	$-0.708823\pi$
$103$	3.54475	−	10.9096i	0.349274	−	1.07496i	0.959256	−	0.282540i	$-0.0911770\pi$
$104$	5.16280	−	6.70884i	0.506254	−	0.657856i
$105$	−3.66990	−	2.66634i	−0.358146	−	0.260208i
$106$	8.87556	+	2.88385i	0.862071	+	0.280104i
$107$	2.93213	+	9.02418i	0.283460	+	0.872400i	0.986856	+	0.161602i	$0.0516661\pi$
$107$	2.93213	+	9.02418i	0.283460	+	0.872400i	−0.703396	+	0.710798i	$0.748334\pi$
$108$	1.26745	−	0.920860i	0.121961	−	0.0886098i
$109$		−	14.0974i		−	1.35028i	−0.737688	−	0.675142i	$-0.764082\pi$
$109$		−	14.0974i		−	1.35028i	0.737688	−	0.675142i	$-0.235918\pi$
$110$	1.60191	+	1.87096i	0.152737	+	0.178389i
$111$		−	0.842512i		−	0.0799677i
$112$	3.75260	+	5.16502i	0.354588	+	0.488048i
$113$	4.80092	+	14.7757i	0.451632	+	1.38998i	0.875044	+	0.484044i	$0.160832\pi$
$113$	4.80092	+	14.7757i	0.451632	+	1.38998i	−0.423412	+	0.905937i	$0.639168\pi$
$114$	0.432640	−	1.33153i	0.0405204	−	0.124709i
$115$	−1.58714	+	2.18451i	−0.148002	+	0.203707i
$116$	−9.18519	−	6.67343i	−0.852824	−	0.619613i
$117$	1.20831	−	3.39706i	0.111708	−	0.314058i
$118$	1.06184	+	3.26801i	0.0977505	+	0.300845i
$119$	4.78969	+	6.59244i	0.439070	+	0.604328i
$120$	−2.64874			−0.241796
$121$	−1.69421	+	10.8687i	−0.154019	+	0.988068i
$122$			0.470386i			0.0425867i
$123$	2.84641	+	3.91774i	0.256652	+	0.353251i
$124$	−10.4315	+	3.38941i	−0.936780	+	0.304378i
$125$	−9.36374	−	3.04246i	−0.837519	−	0.272126i
$126$	−2.14144	−	1.55585i	−0.190774	−	0.138606i
$127$	0.0779493	+	0.0566334i	0.00691688	+	0.00502541i	0.591238	−	0.806497i	$-0.298639\pi$
$127$	0.0779493	+	0.0566334i	0.00691688	+	0.00502541i	−0.584321	+	0.811522i	$0.698639\pi$
$128$	10.5420	+	3.42530i	0.931788	+	0.302756i
$129$	3.79162	+	11.6694i	0.333833	+	1.02743i
$130$	−2.20882	+	1.51353i	−0.193726	+	0.132746i
$131$	−13.5704			−1.18565			−0.592824	−	0.805332i	$-0.701987\pi$
$131$	−13.5704			−1.18565			−0.592824	+	0.805332i	$0.701987\pi$
$132$	−3.37938	−	3.94696i	−0.294137	−	0.343539i
$133$	8.55191			0.741545
$134$	−2.75304	+	2.00020i	−0.237826	+	0.172791i
$135$	−1.07293	+	0.348615i	−0.0923427	+	0.0300040i
$136$	4.52520	+	1.47033i	0.388032	+	0.126079i
$137$	5.31065	−	7.30948i	0.453719	−	0.624491i	−0.519472	−	0.854487i	$-0.673871\pi$
$137$	5.31065	−	7.30948i	0.453719	−	0.624491i	0.973192	+	0.229996i	$0.0738714\pi$
$138$	−0.926117	+	1.27469i	−0.0788363	+	0.108509i
$139$	1.04092	−	3.20362i	0.0882897	−	0.271728i	−0.897157	−	0.441711i	$-0.854371\pi$
$139$	1.04092	−	3.20362i	0.0882897	−	0.271728i	0.985447	+	0.169984i	$0.0543715\pi$
$140$	−2.19611	−	6.75893i	−0.185605	−	0.571234i
$141$	−1.35197	−	1.86083i	−0.113856	−	0.156710i
$142$	−8.00799			−0.672016
$143$	−11.5502	−	3.09706i	−0.965880	−	0.258989i
$144$	1.58774			0.132312
$145$	4.80549	+	6.61419i	0.399074	+	0.549279i
$146$	2.74776	+	8.45674i	0.227406	+	0.699885i
$147$	2.83319	−	8.71966i	0.233678	−	0.719186i
$148$	0.775836	−	1.06785i	0.0637733	−	0.0877764i
$149$	−9.88395	+	13.6041i	−0.809725	+	1.11449i	0.181641	+	0.983365i	$0.441859\pi$
$149$	−9.88395	+	13.6041i	−0.809725	+	1.11449i	−0.991366	+	0.131126i	$0.958141\pi$
$150$	−2.33354	−	0.758212i	−0.190533	−	0.0619078i
$151$	14.6385	−	4.75634i	1.19126	−	0.387065i	0.354724	−	0.934971i	$-0.384575\pi$
$151$	14.6385	−	4.75634i	1.19126	−	0.387065i	0.836540	+	0.547906i	$0.184575\pi$
$152$	4.03983	−	2.93511i	0.327674	−	0.238069i
$153$	2.02654			0.163836
$154$	−4.57785	+	7.49091i	−0.368894	+	0.603635i
$155$	7.89825			0.634403
$156$	4.65969	−	3.19293i	0.373074	−	0.255639i
$157$	−2.18396	−	6.72152i	−0.174299	−	0.536436i	0.825302	−	0.564691i	$-0.191005\pi$
$157$	−2.18396	−	6.72152i	−0.174299	−	0.536436i	−0.999601	+	0.0282554i	$0.991005\pi$
$158$	−7.64152	−	2.48288i	−0.607926	−	0.197527i
$159$	11.4692	+	8.33286i	0.909566	+	0.660839i
$160$	−5.23968	−	3.80685i	−0.414233	−	0.300958i
$161$	−9.15320	−	2.97405i	−0.721373	−	0.234388i
$162$	−0.626067	+	0.203421i	−0.0491884	+	0.0159823i
$163$	−1.77287	−	2.44015i	−0.138862	−	0.191127i	0.733922	−	0.679234i	$-0.237688\pi$
$163$	−1.77287	−	2.44015i	−0.138862	−	0.191127i	−0.872784	+	0.488107i	$0.837688\pi$
$164$			7.58670i			0.592422i
$165$	1.43608	+	3.45505i	0.111799	+	0.268976i
$166$	−7.71904			−0.599114
$167$	7.19005	+	9.89626i	0.556383	+	0.765795i	0.990861	−	0.134887i	$-0.0430672\pi$
$167$	7.19005	+	9.89626i	0.556383	+	0.765795i	−0.434478	+	0.900682i	$0.643067\pi$
$168$	−2.91737	−	8.97875i	−0.225080	−	0.692725i
$169$	4.69272	−	12.1235i	0.360978	−	0.932574i
$170$	−1.21756	−	0.884609i	−0.0933826	−	0.0678464i
$171$	1.25011	−	1.72063i	0.0955984	−	0.131580i
$172$	−5.94018	+	18.2820i	−0.452934	+	1.39399i
$173$	−1.23987	−	3.81592i	−0.0942655	−	0.290119i	0.892796	−	0.450461i	$-0.148740\pi$
$173$	−1.23987	−	3.81592i	−0.0942655	−	0.290119i	−0.987062	+	0.160342i	$0.948740\pi$
$174$	2.80407	+	3.85947i	0.212576	+	0.292586i
$175$		−	14.9874i		−	1.13294i
$176$	−0.419579	−	5.24921i	−0.0316270	−	0.395674i
$177$			5.21991i			0.392353i
$178$	5.78395	−	4.20228i	0.433525	−	0.314974i
$179$	1.77240	+	5.45490i	0.132476	+	0.407718i	0.995189	−	0.0979754i	$-0.0312367\pi$
$179$	1.77240	+	5.45490i	0.132476	+	0.407718i	−0.862713	+	0.505694i	$0.831237\pi$
$180$	−1.68091	−	0.546161i	−0.125288	−	0.0407084i
$181$	−0.753102	−	0.547161i	−0.0559777	−	0.0406701i	0.559445	−	0.828868i	$-0.311014\pi$
$181$	−0.753102	−	0.547161i	−0.0559777	−	0.0406701i	−0.615422	+	0.788198i	$0.711014\pi$
$182$	−7.56344	−	5.82046i	−0.560639	−	0.431441i
$183$	−0.220812	+	0.679589i	−0.0163229	+	0.0502367i
$184$	−5.34460	+	1.73657i	−0.394009	+	0.128021i
$185$	−0.768949	+	0.558674i	−0.0565342	+	0.0410745i
$186$	4.60874			0.337929
$187$	−0.535536	−	6.69990i	−0.0391623	−	0.489945i
$188$		−	3.60349i		−	0.262811i
$189$	−2.36348	−	3.25305i	−0.171918	−	0.236625i
$190$	−1.50215	+	0.488079i	−0.108978	+	0.0354090i
$191$	−2.14235	+	6.59348i	−0.155015	+	0.477088i	−0.998162	−	0.0605950i	$-0.980700\pi$
$191$	−2.14235	+	6.59348i	−0.155015	+	0.477088i	0.843147	+	0.537683i	$0.180700\pi$
$192$	−0.488400	−	0.354843i	−0.0352472	−	0.0256086i
$193$	−16.1082	+	22.1710i	−1.15949	+	1.59591i	−0.446410	+	0.894829i	$0.647298\pi$
$193$	−16.1082	+	22.1710i	−1.15949	+	1.59591i	−0.713084	+	0.701078i	$0.752702\pi$
$194$	−1.97206	+	6.06937i	−0.141586	+	0.435756i
$195$	−3.90168	+	1.14980i	−0.279405	+	0.0823386i
$196$	11.6205	−	8.44281i	0.830038	−	0.603058i
$197$		−	2.55033i		−	0.181704i	−0.995864	−	0.0908518i	$-0.971041\pi$
$197$		−	2.55033i		−	0.181704i	0.995864	−	0.0908518i	$-0.0289589\pi$
$198$	0.837973	+	2.01607i	0.0595521	+	0.143276i
$199$	−13.7970			−0.978046			−0.489023	−	0.872271i	$-0.662647\pi$
$199$	−13.7970			−0.978046			−0.489023	+	0.872271i	$0.662647\pi$
$200$	−5.14386	−	7.07991i	−0.363726	−	0.500625i
$201$	−4.91639	+	1.59743i	−0.346776	+	0.112674i
$202$	−2.30686	−	0.749546i	−0.162310	−	0.0527379i
$203$	−17.1281	+	23.5747i	−1.20215	+	1.65462i
$204$	2.56855	+	1.86616i	0.179834	+	0.130657i
$205$	1.68820	−	5.19575i	0.117909	−	0.362887i
$206$	−7.18164	+	2.33346i	−0.500368	+	0.162580i
$207$	−1.93638	+	1.40686i	−0.134588	+	0.0977837i
$208$	5.72252	+	0.157860i	0.396785	+	0.0109456i
$209$	−6.01890	−	3.67827i	−0.416336	−	0.254431i
$210$			2.98615i			0.206064i
$211$	−8.40158	+	6.10411i	−0.578389	+	0.420224i	−0.838143	−	0.545451i	$-0.816358\pi$
$211$	−8.40158	+	6.10411i	−0.578389	+	0.420224i	0.259754	+	0.965675i	$0.416358\pi$
$212$	6.86329	+	21.1230i	0.471373	+	1.45074i
$213$	−11.5695	−	3.75917i	−0.792731	−	0.257574i
$214$	3.67142	−	5.05328i	0.250973	−	0.345435i
$215$	8.13625	−	11.1986i	0.554888	−	0.763737i
$216$	−2.23297	−	0.725535i	−0.151934	−	0.0493664i
$217$	8.69928	+	26.7736i	0.590546	+	1.81751i
$218$	−7.50776	+	5.45470i	−0.508489	+	0.369439i
$219$			13.5077i			0.912768i
$220$	−1.36145	+	5.70155i	−0.0917891	+	0.384399i
$221$	7.30401	+	0.201487i	0.491321	+	0.0135535i
$222$	−0.448692	+	0.325994i	−0.0301142	+	0.0218793i
$223$	9.29582	−	3.02040i	0.622494	−	0.202261i	0.0192469	−	0.999815i	$-0.493873\pi$
$223$	9.29582	−	3.02040i	0.622494	−	0.202261i	0.603247	+	0.797554i	$0.293873\pi$
$224$	7.13345	−	21.9545i	0.476624	−	1.46690i
$225$	−3.01545	−	2.19085i	−0.201030	−	0.146057i
$226$	6.01139	−	8.27397i	0.399872	−	0.550376i
$227$	11.3378	+	3.68387i	0.752516	+	0.244507i	0.660063	−	0.751210i	$-0.270529\pi$
$227$	11.3378	+	3.68387i	0.752516	+	0.244507i	0.0924525	+	0.995717i	$0.470529\pi$
$228$	3.16892	−	1.02964i	0.209867	−	0.0681898i
$229$	17.2787	+	23.7821i	1.14181	+	1.57156i	0.763401	+	0.645925i	$0.223528\pi$
$229$	17.2787	+	23.7821i	1.14181	+	1.57156i	0.378407	+	0.925639i	$0.376472\pi$
$230$	1.77750			0.117205
$231$	−10.1303	+	8.67351i	−0.666523	+	0.570675i
$232$			17.0150i			1.11709i
$233$	3.38877	−	2.46208i	0.222005	−	0.161296i	−0.471224	−	0.882014i	$-0.656187\pi$
$233$	3.38877	−	2.46208i	0.222005	−	0.161296i	0.693229	+	0.720717i	$0.256187\pi$
$234$	−2.27668	+	0.670921i	−0.148831	+	0.0438595i
$235$	−0.801851	+	2.46784i	−0.0523070	+	0.160984i
$236$	−4.80681	+	6.61600i	−0.312896	+	0.430665i
$237$	−9.87453	−	7.17427i	−0.641420	−	0.466019i
$238$	1.65762	−	5.10163i	0.107448	−	0.330690i
$239$	−4.37633	+	1.42196i	−0.283081	+	0.0919787i	−0.447116	−	0.894476i	$-0.647549\pi$
$239$	−4.37633	+	1.42196i	−0.283081	+	0.0919787i	0.164035	+	0.986455i	$0.447549\pi$
$240$	−1.05284	−	1.44911i	−0.0679606	−	0.0935397i
$241$			13.7535i			0.885939i	0.896537	+	0.442969i	$0.146075\pi$
$241$			13.7535i			0.885939i	−0.896537	+	0.442969i	$0.853925\pi$
$242$	6.44385	−	3.30317i	0.414226	−	0.212336i
$243$	−1.00000			−0.0641500
$244$	−0.905675	+	0.658012i	−0.0579799	+	0.0421249i
$245$	−9.83701	+	3.19624i	−0.628463	+	0.204200i
$246$	0.985088	−	3.03179i	0.0628069	−	0.193300i
$247$	4.67670	−	6.07717i	0.297571	−	0.386681i
$248$	13.2985	+	9.66189i	0.844453	+	0.613531i
$249$	−11.1521	−	3.62353i	−0.706734	−	0.229632i
$250$	2.00281	+	6.16402i	0.126669	+	0.389847i
$251$	−3.50995	+	2.55013i	−0.221546	+	0.160963i	−0.693022	−	0.720916i	$-0.743721\pi$
$251$	−3.50995	+	2.55013i	−0.221546	+	0.160963i	0.471476	+	0.881879i	$0.343721\pi$
$252$		−	6.29953i		−	0.396833i
$253$	5.16291	+	6.03005i	0.324589	+	0.379106i
$254$		−	0.0634262i		−	0.00397971i
$255$	−1.34381	−	1.84959i	−0.0841525	−	0.115826i
$256$	−2.62793	−	8.08793i	−0.164246	−	0.505496i
$257$	9.20612	−	28.3335i	0.574262	−	1.76740i	−0.0644179	−	0.997923i	$-0.520519\pi$
$257$	9.20612	−	28.3335i	0.574262	−	1.76740i	0.638680	−	0.769473i	$-0.279481\pi$
$258$	4.74761	−	6.53453i	0.295573	−	0.406822i
$259$	−2.74074	−	1.99126i	−0.170301	−	0.123731i
$260$	−6.00400	−	2.13559i	−0.372352	−	0.132443i
$261$	2.23943	+	6.89227i	0.138617	+	0.426621i
$262$	5.25079	+	7.22709i	0.324395	+	0.446491i
$263$	−8.38343			−0.516944			−0.258472	−	0.966019i	$-0.583219\pi$
$263$	−8.38343			−0.516944			−0.258472	+	0.966019i	$0.583219\pi$
$264$	−1.80859	+	7.57410i	−0.111311	+	0.466154i
$265$		−	15.9933i		−	0.982462i
$266$	−3.30900	−	4.55444i	−0.202888	−	0.279251i
$267$	10.3290	−	3.35610i	0.632125	−	0.205390i
$268$	−7.70232	−	2.50264i	−0.470494	−	0.152873i
$269$	1.26407	+	0.918397i	0.0770714	+	0.0559957i	0.625654	−	0.780101i	$-0.284832\pi$
$269$	1.26407	+	0.918397i	0.0770714	+	0.0559957i	−0.548582	+	0.836097i	$0.684832\pi$
$270$	0.600807	+	0.436512i	0.0365640	+	0.0265653i
$271$	8.23966	+	2.67723i	0.500524	+	0.162630i	0.548388	−	0.836224i	$-0.315242\pi$
$271$	8.23966	+	2.67723i	0.500524	+	0.162630i	−0.0478647	+	0.998854i	$0.515242\pi$
$272$	0.994301	+	3.06014i	0.0602884	+	0.185549i
$273$	−8.19498	−	11.9596i	−0.495983	−	0.723826i
$274$	−5.94762			−0.359309
$275$	−6.44626	+	10.5483i	−0.388724	+	0.636084i
$276$	−3.74980			−0.225711
$277$	19.5158	−	14.1791i	1.17259	−	0.851939i	0.181276	−	0.983432i	$-0.441977\pi$
$277$	19.5158	−	14.1791i	1.17259	−	0.851939i	0.991317	+	0.131494i	$0.0419773\pi$
$278$	−2.10890	+	0.685223i	−0.126483	+	0.0410969i
$279$	6.65846	+	2.16346i	0.398632	+	0.129523i
$280$	−6.26025	+	8.61649i	−0.374121	+	0.514934i
$281$	−2.11948	+	2.91722i	−0.126438	+	0.174027i	−0.867543	−	0.497362i	$-0.834302\pi$
$281$	−2.11948	+	2.91722i	−0.126438	+	0.174027i	0.741105	+	0.671389i	$0.234302\pi$
$282$	−0.467891	+	1.44002i	−0.0278625	+	0.0857519i
$283$	4.25907	+	13.1081i	0.253176	+	0.779194i	0.994184	+	0.107698i	$0.0343480\pi$
$283$	4.25907	+	13.1081i	0.253176	+	0.779194i	−0.741008	+	0.671496i	$0.765652\pi$
$284$	−11.2022	−	15.4185i	−0.664728	−	0.914919i
$285$	−2.39935			−0.142125
$286$	2.81976	+	7.34960i	0.166736	+	0.434591i
$287$	19.4720			1.14940
$288$	−3.37445	−	4.64453i	−0.198841	−	0.273681i
$289$	−3.98420	−	12.2621i	−0.234365	−	0.721300i
$290$	1.66309	−	5.11847i	0.0976600	−	0.300567i
$291$	−5.69825	+	7.84297i	−0.334038	+	0.459763i
$292$	−12.4387	+	17.1204i	−0.727922	+	1.00190i
$293$	−12.1739	−	3.95555i	−0.711208	−	0.231085i	−0.0690008	−	0.997617i	$-0.521981\pi$
$293$	−12.1739	−	3.95555i	−0.711208	−	0.231085i	−0.642207	+	0.766531i	$0.721981\pi$
$294$	−5.74003	+	1.86505i	−0.334765	+	0.108772i
$295$	4.76414	−	3.46135i	0.277379	−	0.201527i
$296$	−1.97812			−0.114976
$297$	0.264261	+	3.30608i	0.0153340	+	0.191838i
$298$	11.0695			0.641236
$299$	−7.11894	+	4.87806i	−0.411699	+	0.282106i
$300$	−1.80448	−	5.55361i	−0.104182	−	0.320638i
$301$	46.9226	+	15.2461i	2.70457	+	0.878769i
$302$	−8.19714	−	5.95557i	−0.471692	−	0.342705i
$303$	−2.98098	−	2.16581i	−0.171253	−	0.124422i
$304$	3.21157	+	1.04350i	0.184196	+	0.0598489i
$305$	0.766672	−	0.249107i	0.0438995	−	0.0142638i
$306$	−0.784130	−	1.07926i	−0.0448257	−	0.0616973i
$307$			20.1735i			1.15137i	0.817673	+	0.575683i	$0.195264\pi$
$307$			20.1735i			1.15137i	−0.817673	+	0.575683i	$0.804736\pi$
$308$	−20.8268	+	1.66472i	−1.18671	+	0.0948563i
$309$	−11.4710			−0.652565
$310$	−3.05607	−	4.20632i	−0.173573	−	0.238903i
$311$	−2.88109	−	8.86707i	−0.163371	−	0.502806i	0.835541	−	0.549428i	$-0.185154\pi$
$311$	−2.88109	−	8.86707i	−0.163371	−	0.502806i	−0.998913	+	0.0466223i	$0.985154\pi$
$312$	−7.97588	−	2.83697i	−0.451545	−	0.160612i
$313$	0.355638	+	0.258386i	0.0201019	+	0.0146049i	0.597791	−	0.801652i	$-0.296045\pi$
$313$	0.355638	+	0.258386i	0.0201019	+	0.0146049i	−0.577689	+	0.816257i	$0.696045\pi$
$314$	−2.73460	+	3.76386i	−0.154323	+	0.212407i
$315$	−1.40178	+	4.31423i	−0.0789812	+	0.243079i
$316$	−5.90903	−	18.1861i	−0.332409	−	1.02305i
$317$	−1.61093	−	2.21725i	−0.0904786	−	0.124533i	0.761378	−	0.648308i	$-0.224523\pi$
$317$	−1.61093	−	2.21725i	−0.0904786	−	0.124533i	−0.851857	+	0.523775i	$0.824523\pi$
$318$		−	9.33232i		−	0.523331i
$319$	22.1946	−	9.22511i	1.24266	−	0.516507i
$320$			0.681054i			0.0380721i
$321$	7.67643	−	5.57725i	0.428456	−	0.311292i
$322$	1.95778	+	6.02542i	0.109103	+	0.335783i
$323$	4.09913	+	1.33189i	0.228081	+	0.0741082i
$324$	−1.26745	−	0.920860i	−0.0704142	−	0.0511589i
$325$	−10.6504	−	8.19603i	−0.590777	−	0.454634i
$326$	−0.613557	+	1.88833i	−0.0339818	+	0.104585i
$327$	−13.4074	+	4.35633i	−0.741431	+	0.240905i
$328$	9.19839	−	6.68302i	0.507896	−	0.369008i
$329$	−9.24871			−0.509898
$330$	1.28437	−	2.10167i	0.0707025	−	0.115693i
$331$			3.04838i			0.167554i	0.996485	+	0.0837770i	$0.0266983\pi$
$331$			3.04838i			0.167554i	−0.996485	+	0.0837770i	$0.973302\pi$
$332$	−10.7980	−	14.8621i	−0.592616	−	0.815666i
$333$	−0.801277	+	0.260351i	−0.0439097	+	0.0142671i
$334$	2.48834	−	7.65833i	0.136156	−	0.419045i
$335$	4.71804	+	3.42786i	0.257774	+	0.187284i
$336$	3.75260	−	5.16502i	0.204721	−	0.281775i
$337$	−4.53967	+	13.9717i	−0.247292	+	0.761086i	0.747959	+	0.663745i	$0.231034\pi$
$337$	−4.53967	+	13.9717i	−0.247292	+	0.761086i	−0.995251	+	0.0973413i	$0.968966\pi$
$338$	−8.27228	+	2.19176i	−0.449953	+	0.119216i
$339$	12.5690	−	9.13189i	0.682652	−	0.495976i
$340$		−	3.58173i		−	0.194247i
$341$	5.39302	−	22.5851i	0.292048	−	1.22305i
$342$	−1.40005			−0.0757061
$343$	−5.12496	−	7.05390i	−0.276722	−	0.380875i
$344$	27.3984	−	8.90227i	1.47722	−	0.479978i
$345$	2.56805	+	0.834409i	0.138259	+	0.0449231i
$346$	−1.55248	+	2.13681i	−0.0834619	+	0.114875i
$347$	−4.42657	−	3.21609i	−0.237631	−	0.172649i	0.462596	−	0.886569i	$-0.346918\pi$
$347$	−4.42657	−	3.21609i	−0.237631	−	0.172649i	−0.700227	+	0.713920i	$0.746918\pi$
$348$	−3.50843	+	10.7978i	−0.188072	+	0.578825i
$349$	−19.8348	+	6.44472i	−1.06173	+	0.344978i	−0.787263	−	0.616618i	$-0.788502\pi$
$349$	−19.8348	+	6.44472i	−1.06173	+	0.344978i	−0.274470	+	0.961596i	$0.588502\pi$
$350$	−7.98178	+	5.79910i	−0.426644	+	0.309975i
$351$	−3.60418	−	0.0994242i	−0.192377	−	0.00530687i
$352$	−14.4634	+	12.3836i	−0.770904	+	0.660046i
$353$		−	15.6505i		−	0.832992i	−0.909138	−	0.416496i	$-0.863258\pi$
$353$		−	15.6505i		−	0.832992i	0.909138	−	0.416496i	$-0.136742\pi$
$354$	2.77994	−	2.01974i	0.147752	−	0.107348i
$355$	4.24087	+	13.0521i	0.225082	+	0.692731i
$356$	16.1820	+	5.25786i	0.857647	+	0.278666i
$357$	4.78969	−	6.59244i	0.253497	−	0.348909i
$358$	2.21929	−	3.05458i	0.117293	−	0.161440i
$359$	4.75791	+	1.54594i	0.251113	+	0.0815914i	0.431869	−	0.901937i	$-0.357854\pi$
$359$	4.75791	+	1.54594i	0.251113	+	0.0815914i	−0.180756	+	0.983528i	$0.557854\pi$
$360$	0.818506	+	2.51910i	0.0431390	+	0.132768i
$361$	−11.7119	+	8.50916i	−0.616414	+	0.447851i
$362$			0.612789i			0.0322074i
$363$	10.8603	−	1.74734i	0.570020	−	0.0917114i
$364$	0.626326	−	22.7046i	0.0328284	−	1.19005i
$365$	12.3283	−	8.95704i	0.645293	−	0.468833i
$366$	0.447364	−	0.145357i	0.0233841	−	0.00759795i
$367$	2.16499	−	6.66316i	0.113012	−	0.347814i	−0.878515	−	0.477714i	$-0.841466\pi$
$367$	2.16499	−	6.66316i	0.113012	−	0.347814i	0.991527	+	0.129900i	$0.0414655\pi$
$368$	−3.07448	−	2.23374i	−0.160268	−	0.116442i
$369$	2.84641	−	3.91774i	0.148178	−	0.203949i
$370$	0.595059	+	0.193346i	0.0309357	+	0.0100516i
$371$	54.2145	−	17.6153i	2.81467	−	0.914543i
$372$	6.44705	+	8.87360i	0.334264	+	0.460075i
$373$	−21.4113			−1.10864			−0.554318	−	0.832305i	$-0.687021\pi$
$373$	−21.4113			−1.10864			−0.554318	+	0.832305i	$0.687021\pi$
$374$	−3.36091	+	2.87760i	−0.173789	+	0.148797i
$375$			9.84562i			0.508426i
$376$	−4.36900	+	3.17426i	−0.225314	+	0.163700i
$377$	7.38607	+	25.0636i	0.380402	+	1.29084i
$378$	−0.817956	+	2.51741i	−0.0420711	+	0.129482i
$379$	14.7779	−	20.3400i	0.759090	−	1.04480i	−0.238199	−	0.971216i	$-0.576557\pi$
$379$	14.7779	−	20.3400i	0.759090	−	1.04480i	0.997289	−	0.0735813i	$-0.0234428\pi$
$380$	−3.04106	−	2.20946i	−0.156003	−	0.113343i
$381$	0.0297740	−	0.0916348i	0.00152537	−	0.00469460i
$382$	4.34039	−	1.41028i	0.222074	−	0.0721562i
$383$	−22.1589	−	30.4991i	−1.13227	−	1.55843i	−0.783690	−	0.621153i	$-0.786665\pi$
$383$	−22.1589	−	30.4991i	−1.13227	−	1.55843i	−0.348578	−	0.937280i	$-0.613335\pi$
$384$		−	11.0845i		−	0.565653i
$385$	14.6336	+	3.49431i	0.745798	+	0.178086i
$386$	18.0403			0.918225
$387$	9.92659	−	7.21209i	0.504597	−	0.366611i
$388$	−14.4446	+	4.69332i	−0.733311	+	0.238267i
$389$	−5.12467	+	15.7721i	−0.259831	+	0.799678i	0.733008	+	0.680220i	$0.238116\pi$
$389$	−5.12467	+	15.7721i	−0.259831	+	0.799678i	−0.992839	+	0.119458i	$0.961884\pi$
$390$	2.12202	+	1.63300i	0.107453	+	0.0826903i
$391$	−3.92415	−	2.85106i	−0.198453	−	0.144184i
$392$	−20.4727	−	6.65199i	−1.03403	−	0.335976i
$393$	4.19347	+	12.9062i	0.211533	+	0.651031i
$394$	−1.35821	+	0.986801i	−0.0684259	+	0.0497143i
$395$			13.7696i			0.692825i
$396$	−2.70950	+	4.43365i	−0.136157	+	0.222800i
$397$		−	0.339439i		−	0.0170360i	−0.999964	−	0.00851799i	$-0.997289\pi$
$397$		−	0.339439i		−	0.0170360i	0.999964	−	0.00851799i	$-0.00271139\pi$
$398$	5.33849	+	7.34781i	0.267595	+	0.368312i
$399$	−2.64269	−	8.13335i	−0.132300	−	0.407177i
$400$	1.82876	−	5.62835i	0.0914381	−	0.281417i
$401$	−14.9459	+	20.5713i	−0.746365	+	1.02728i	0.251862	+	0.967763i	$0.418957\pi$
$401$	−14.9459	+	20.5713i	−0.746365	+	1.02728i	−0.998227	+	0.0595203i	$0.981043\pi$
$402$	2.75304	+	2.00020i	0.137309	+	0.0997609i
$403$	23.7832	+	8.45953i	1.18473	+	0.421399i
$404$	−1.78385	−	5.49013i	−0.0887499	−	0.273144i
$405$	0.663105	+	0.912685i	0.0329499	+	0.0453517i
$406$	19.1824			0.952008
$407$	1.07249	+	2.58028i	0.0531612	+	0.127900i
$408$		−	4.75807i		−	0.235560i
$409$	−12.2047	−	16.7983i	−0.603481	−	0.830621i	0.392540	−	0.919735i	$-0.371596\pi$
$409$	−12.2047	−	16.7983i	−0.603481	−	0.830621i	−0.996021	+	0.0891142i	$0.971596\pi$
$410$	−3.42028	+	1.11132i	−0.168916	+	0.0548841i
$411$	−8.59281	−	2.79197i	−0.423852	−	0.137718i
$412$	−14.5390	−	10.5632i	−0.716287	−	0.520413i
$413$	16.9806	+	12.3372i	0.835563	+	0.607072i
$414$	1.49849	+	0.486889i	0.0736467	+	0.0239293i
$415$	4.08785	+	12.5811i	0.200665	+	0.617582i
$416$	−11.7003	−	17.0752i	−0.573656	−	0.837181i
$417$	−3.36849			−0.164956
$418$	0.369979	+	4.62868i	0.0180963	+	0.226396i
$419$	9.37534			0.458015			0.229008	−	0.973425i	$-0.426452\pi$
$419$	9.37534			0.458015			0.229008	+	0.973425i	$0.426452\pi$
$420$	−5.74949	+	4.17725i	−0.280546	+	0.203829i
$421$	15.0533	−	4.89112i	0.733654	−	0.238379i	0.0817209	−	0.996655i	$-0.473958\pi$
$421$	15.0533	−	4.89112i	0.733654	−	0.238379i	0.651933	+	0.758277i	$0.273958\pi$
$422$	6.50166	+	2.11252i	0.316496	+	0.102836i
$423$	−1.35197	+	1.86083i	−0.0657350	+	0.0904764i
$424$	19.5646	−	26.9283i	0.950139	−	1.30775i
$425$	2.33416	−	7.18382i	0.113224	−	0.348466i
$426$	2.47461	+	7.61605i	0.119895	+	0.368999i
$427$	1.68885	+	2.32451i	0.0817294	+	0.112491i
$428$	14.8654			0.718546
$429$	0.623741	+	11.9420i	0.0301145	+	0.576564i
$430$	−9.11213			−0.439426
$431$	15.8374	+	21.7983i	0.762861	+	1.04999i	0.996971	+	0.0777784i	$0.0247827\pi$
$431$	15.8374	+	21.7983i	0.762861	+	1.04999i	−0.234109	+	0.972210i	$0.575217\pi$
$432$	−0.490640	−	1.51003i	−0.0236059	−	0.0726516i
$433$	5.77784	−	17.7823i	0.277665	−	0.854565i	−0.710837	−	0.703357i	$-0.751684\pi$
$433$	5.77784	−	17.7823i	0.277665	−	0.854565i	0.988502	−	0.151208i	$-0.0483164\pi$
$434$	10.8927	−	14.9925i	0.522864	−	0.719661i
$435$	4.80549	−	6.61419i	0.230406	−	0.317126i
$436$	−21.0048	−	6.82488i	−1.00595	−	0.326853i
$437$	−4.84138	+	1.57306i	−0.231595	+	0.0752497i
$438$	7.19374	−	5.22656i	0.343730	−	0.249734i
$439$	−2.43458			−0.116196			−0.0580981	−	0.998311i	$-0.518504\pi$
$439$	−2.43458			−0.116196			−0.0580981	+	0.998311i	$0.518504\pi$
$440$	8.11205	−	3.37175i	0.386727	−	0.160742i
$441$	−9.16840			−0.436590
$442$	−2.71884	−	3.96782i	−0.129322	−	0.188730i
$443$	2.64704	+	8.14675i	0.125765	+	0.387064i	0.994040	−	0.109020i	$-0.0347711\pi$
$443$	2.64704	+	8.14675i	0.125765	+	0.387064i	−0.868275	+	0.496083i	$0.834771\pi$
$444$	−1.25533	−	0.407881i	−0.0595753	−	0.0193572i
$445$	−9.91227	−	7.20169i	−0.469887	−	0.341393i
$446$	−5.20539	−	3.78194i	−0.246482	−	0.179080i
$447$	15.9926	+	5.19630i	0.756423	+	0.245777i
$448$	−2.30865	+	0.750125i	−0.109073	+	0.0354401i
$449$	17.9020	+	24.6401i	0.844850	+	1.16284i	0.984974	+	0.172702i	$0.0552497\pi$
$449$	17.9020	+	24.6401i	0.844850	+	1.16284i	−0.140124	+	0.990134i	$0.544750\pi$
$450$			2.45363i			0.115665i
$451$	−13.7046	−	8.37514i	−0.645323	−	0.394370i
$452$	24.3398			1.14485
$453$	−9.04709	−	12.4523i	−0.425070	−	0.585058i
$454$	−2.42504	−	7.46351i	−0.113813	−	0.350280i
$455$	−5.48120	+	15.4099i	−0.256963	+	0.722427i
$456$	−4.03983	−	2.93511i	−0.189183	−	0.137449i
$457$	8.36316	−	11.5109i	0.391212	−	0.538457i	−0.567299	−	0.823512i	$-0.692012\pi$
$457$	8.36316	−	11.5109i	0.391212	−	0.538457i	0.958511	+	0.285055i	$0.0920117\pi$
$458$	5.97983	−	18.4040i	0.279419	−	0.859964i
$459$	−0.626235	−	1.92735i	−0.0292302	−	0.0899612i
$460$	2.48651	+	3.42239i	0.115934	+	0.159570i
$461$		−	7.93590i		−	0.369612i	−0.982775	−	0.184806i	$-0.940834\pi$
$461$		−	7.93590i		−	0.369612i	0.982775	−	0.184806i	$-0.0591656\pi$
$462$	8.53892	+	2.03898i	0.397266	+	0.0948617i
$463$		−	19.9380i		−	0.926599i	−0.886202	−	0.463299i	$-0.846665\pi$
$463$		−	19.9380i		−	0.926599i	0.886202	−	0.463299i	$-0.153335\pi$
$464$	−9.30881	+	6.76325i	−0.432151	+	0.313976i
$465$	−2.44069	−	7.51168i	−0.113184	−	0.348346i
$466$	−2.62243	−	0.852080i	−0.121482	−	0.0394719i
$467$	−6.58067	−	4.78114i	−0.304517	−	0.221245i	0.425023	−	0.905182i	$-0.360266\pi$
$467$	−6.58067	−	4.78114i	−0.304517	−	0.221245i	−0.729540	+	0.683938i	$0.760266\pi$
$468$	−4.47658	−	3.44496i	−0.206930	−	0.159243i
$469$	−6.42327	+	19.7688i	−0.296599	+	0.912838i
$470$	1.62455	−	0.527847i	0.0749347	−	0.0243478i
$471$	−5.71767	+	4.15413i	−0.263456	+	0.191412i
$472$	12.2557			0.564116
$473$	−26.4669	−	30.9122i	−1.21695	−	1.42135i
$474$			8.03477i			0.369049i
$475$	−4.65954	−	6.41330i	−0.213794	−	0.294262i
$476$	12.1414	−	3.94499i	0.556501	−	0.180818i
$477$	4.38084	−	13.4828i	0.200585	−	0.617337i
$478$	2.45062	+	1.78048i	0.112089	+	0.0814372i
$479$	3.05847	−	4.20963i	0.139745	−	0.192343i	−0.733408	−	0.679789i	$-0.762071\pi$
$479$	3.05847	−	4.20963i	0.139745	−	0.192343i	0.873153	+	0.487446i	$0.162071\pi$
$480$	−2.00138	+	6.15961i	−0.0913501	+	0.281147i
$481$	−2.91383	+	0.858684i	−0.132859	+	0.0391526i
$482$	7.32461	−	5.32164i	0.333627	−	0.242394i
$483$			9.62424i			0.437918i
$484$	15.3740	+	7.78617i	0.698820	+	0.353917i
$485$	10.9367			0.496610
$486$	0.386931	+	0.532564i	0.0175515	+	0.0241576i
$487$	−0.390286	+	0.126811i	−0.0176855	+	0.00574638i	−0.317846	−	0.948142i	$-0.602960\pi$
$487$	−0.390286	+	0.126811i	−0.0176855	+	0.00574638i	0.300161	+	0.953889i	$0.402960\pi$
$488$	1.59559	+	0.518440i	0.0722292	+	0.0234687i
$489$	−1.77287	+	2.44015i	−0.0801719	+	0.110347i
$490$	5.50844	+	4.00212i	0.248846	+	0.180797i
$491$	6.28993	−	19.3584i	0.283861	−	0.873634i	−0.702877	−	0.711311i	$-0.748102\pi$
$491$	6.28993	−	19.3584i	0.283861	−	0.873634i	0.986738	−	0.162322i	$-0.0518984\pi$
$492$	7.21538	−	2.34442i	0.325295	−	0.105695i
$493$	−11.8814	+	8.63236i	−0.535113	+	0.388782i
$494$	−5.04604	−	0.139199i	−0.227032	−	0.00626286i
$495$	2.84218	−	2.43346i	0.127746	−	0.109376i
$496$			11.1160i			0.499123i
$497$	−39.5731	+	28.7516i	−1.77510	+	1.28968i
$498$	2.38531	+	7.34124i	0.106889	+	0.328969i
$499$	−12.4783	−	4.05444i	−0.558605	−	0.181502i	0.0160883	−	0.999871i	$-0.494879\pi$
$499$	−12.4783	−	4.05444i	−0.558605	−	0.181502i	−0.574693	+	0.818369i	$0.694879\pi$
$500$	−9.06644	+	12.4789i	−0.405463	+	0.558072i
$501$	7.19005	−	9.89626i	0.321228	−	0.442132i
$502$	2.71622	+	0.882553i	0.121231	+	0.0393902i
$503$	−13.7312	−	42.2602i	−0.612242	−	1.88429i	−0.436021	−	0.899936i	$-0.643613\pi$
$503$	−13.7312	−	42.2602i	−0.612242	−	1.88429i	−0.176221	−	0.984351i	$-0.556387\pi$
$504$	−7.63778	+	5.54917i	−0.340214	+	0.247180i
$505$			4.15685i			0.184978i
$506$	1.21370	−	5.08279i	0.0539556	−	0.225958i
$507$	−12.9802	−	0.716685i	−0.576472	−	0.0318291i
$508$	0.122120	−	0.0887254i	0.00541820	−	0.00393655i
$509$	−29.3431	+	9.53417i	−1.30061	+	0.422595i	−0.875794	−	0.482684i	$-0.839662\pi$
$509$	−29.3431	+	9.53417i	−1.30061	+	0.422595i	−0.424818	+	0.905279i	$0.639662\pi$
$510$	−0.465067	+	1.43133i	−0.0205935	+	0.0633802i
$511$	43.9414	+	31.9253i	1.94385	+	1.41229i
$512$	9.74009	−	13.4061i	0.430455	−	0.592471i
$513$	−2.02272	−	0.657222i	−0.0893054	−	0.0290171i
$514$	−18.6515	+	6.06025i	−0.822684	+	0.267306i
$515$	7.60650	+	10.4695i	0.335183	+	0.461339i
$516$	19.2228			0.846237
$517$	6.50931	+	3.97797i	0.286279	+	0.174951i
$518$			2.23010i			0.0979849i
$519$	−3.24602	+	2.35837i	−0.142484	+	0.103521i
$520$	2.69958	+	9.16068i	0.118385	+	0.401722i
$521$	−9.36242	+	28.8146i	−0.410175	+	1.26239i	0.506321	+	0.862345i	$0.331005\pi$
$521$	−9.36242	+	28.8146i	−0.410175	+	1.26239i	−0.916496	+	0.400044i	$0.868995\pi$
$522$	2.80407	−	3.85947i	0.122731	−	0.168924i
$523$	−16.1650	−	11.7446i	−0.706846	−	0.513554i	0.175309	−	0.984514i	$-0.443908\pi$
$523$	−16.1650	−	11.7446i	−0.706846	−	0.513554i	−0.882155	+	0.470960i	$0.843908\pi$
$524$	−6.56975	+	20.2196i	−0.287001	+	0.883298i
$525$	−14.2539	+	4.63137i	−0.622091	+	0.202130i
$526$	3.24380	+	4.46471i	0.141437	+	0.194671i
$527$			14.1880i			0.618041i
$528$	−4.86264	+	2.02114i	−0.211619	+	0.0879588i
$529$	−17.2712			−0.750920
$530$	−8.51747	+	6.18830i	−0.369975	+	0.268803i
$531$	4.96443	−	1.61304i	0.215438	−	0.0700000i
$532$	4.14019	−	12.7422i	0.179500	−	0.552444i
$533$	10.6485	−	13.8372i	0.461237	−	0.599358i
$534$	−5.78395	−	4.20228i	−0.250296	−	0.181851i
$535$	−10.1805	−	3.30786i	−0.440143	−	0.143011i
$536$	3.75058	+	11.5431i	0.162001	+	0.498586i
$537$	4.64021	−	3.37131i	0.200240	−	0.145483i
$538$		−	1.02855i		−	0.0443440i
$539$	2.42285	+	30.3114i	0.104360	+	1.30561i
$540$			1.76741i			0.0760574i
$541$	9.98135	+	13.7382i	0.429132	+	0.590649i	0.967754	−	0.251898i	$-0.0810548\pi$
$541$	9.98135	+	13.7382i	0.429132	+	0.590649i	−0.538622	+	0.842548i	$0.681055\pi$
$542$	−1.76238	−	5.42405i	−0.0757007	−	0.232983i
$543$	−0.287659	+	0.885325i	−0.0123446	+	0.0379929i
$544$	6.83845	−	9.41232i	0.293196	−	0.403550i
$545$	12.8665	+	9.34803i	0.551139	+	0.400426i
$546$	−3.19835	+	8.99188i	−0.136877	+	0.384817i
$547$	−2.83660	−	8.73016i	−0.121284	−	0.373275i	0.871921	−	0.489646i	$-0.162874\pi$
$547$	−2.83660	−	8.73016i	−0.121284	−	0.373275i	−0.993206	+	0.116371i	$0.962874\pi$
$548$	−8.31998	−	11.4515i	−0.355412	−	0.489183i
$549$	0.714562			0.0304968
$550$	8.11189	−	0.648398i	0.345892	−	0.0276478i
$551$			15.4129i			0.656614i
$552$	3.30315	+	4.54639i	0.140591	+	0.193507i
$553$	−46.6766	+	15.1661i	−1.98489	+	0.644929i
$554$	−15.1025	−	4.90711i	−0.641646	−	0.208483i
$555$	0.768949	+	0.558674i	0.0326400	+	0.0237144i
$556$	−4.26941	−	3.10191i	−0.181063	−	0.131550i
$557$	43.0154	+	13.9765i	1.82262	+	0.592205i	0.999711	+	0.0240321i	$0.00765038\pi$
$557$	43.0154	+	13.9765i	1.82262	+	0.592205i	0.822909	+	0.568173i	$0.192350\pi$
$558$	−1.42418	−	4.38317i	−0.0602902	−	0.185554i
$559$	36.4943	−	25.0067i	1.54354	−	1.05767i
$560$	−7.20240			−0.304357
$561$	−6.20650	+	2.57971i	−0.262038	+	0.108915i
$562$	2.37370			0.100129
$563$	−22.6269	+	16.4394i	−0.953612	+	0.692840i	−0.951658	−	0.307158i	$-0.900622\pi$
$563$	−22.6269	+	16.4394i	−0.953612	+	0.692840i	−0.00195373	+	0.999998i	$0.500622\pi$
$564$	−3.42712	+	1.11354i	−0.144308	+	0.0468884i
$565$	−16.6691	−	5.41611i	−0.701273	−	0.227857i
$566$	5.33293	−	7.34014i	0.224160	−	0.308529i
$567$	−2.36348	+	3.25305i	−0.0992569	+	0.136615i
$568$	−8.82608	+	27.1639i	−0.370334	+	1.13977i
$569$	−9.59042	−	29.5163i	−0.402051	−	1.23739i	−0.923332	−	0.384002i	$-0.874546\pi$
$569$	−9.59042	−	29.5163i	−0.402051	−	1.23739i	0.521281	−	0.853385i	$-0.325454\pi$
$570$	0.928381	+	1.27781i	0.0388856	+	0.0535214i
$571$	17.6052			0.736756			0.368378	−	0.929676i	$-0.379913\pi$
$571$	17.6052			0.736756			0.368378	+	0.929676i	$0.379913\pi$
$572$	−10.2063	+	15.7103i	−0.426748	+	0.656881i
$573$	6.93280			0.289622
$574$	−7.53433	−	10.3701i	−0.314477	−	0.432840i
$575$	2.75683	+	8.48464i	0.114968	+	0.353834i
$576$	−0.186552	+	0.574149i	−0.00777301	+	0.0239229i
$577$	−15.8466	+	21.8110i	−0.659704	+	0.908005i	−0.999472	−	0.0325045i	$-0.989652\pi$
$577$	−15.8466	+	21.8110i	−0.659704	+	0.908005i	0.339767	+	0.940510i	$0.389652\pi$
$578$	−4.98875	+	6.86642i	−0.207505	+	0.285606i
$579$	26.0636	+	8.46859i	1.08317	+	0.351942i
$580$	12.1815	−	3.95801i	0.505809	−	0.164347i
$581$	−38.1452	+	27.7141i	−1.58253	+	1.14978i
$582$	6.38172			0.264531
$583$	−45.7331	−	10.9204i	−1.89407	−	0.452278i
$584$	31.7146			1.31236
$585$	2.29921	+	3.35541i	0.0950604	+	0.138729i
$586$	2.60388	+	8.01392i	0.107565	+	0.331052i
$587$	15.8234	+	5.14135i	0.653104	+	0.212206i	0.616782	−	0.787134i	$-0.288436\pi$
$587$	15.8234	+	5.14135i	0.653104	+	0.212206i	0.0363215	+	0.999340i	$0.488436\pi$
$588$	−11.6205	−	8.44281i	−0.479222	−	0.348175i
$589$	12.0463	+	8.75218i	0.496361	+	0.360627i
$590$	−3.68678	−	1.19791i	−0.151782	−	0.0493171i
$591$	−2.42551	+	0.788096i	−0.0997721	+	0.0324179i
$592$	−0.786277	−	1.08222i	−0.0323158	−	0.0444789i
$593$		−	2.17288i		−	0.0892294i	−0.999004	−	0.0446147i	$-0.985794\pi$
$593$		−	2.17288i		−	0.0892294i	0.999004	−	0.0446147i	$-0.0142060\pi$
$594$	1.65845	−	1.41996i	0.0680470	−	0.0582616i
$595$	−9.19289			−0.376872
$596$	15.4848	+	21.3130i	0.634282	+	0.873014i
$597$	4.26352	+	13.1218i	0.174494	+	0.537038i
$598$	5.35242	+	1.90382i	0.218877	+	0.0778530i
$599$	−12.9843	−	9.43364i	−0.530524	−	0.385448i	0.290030	−	0.957018i	$-0.406335\pi$
$599$	−12.9843	−	9.43364i	−0.530524	−	0.385448i	−0.820554	+	0.571570i	$0.806335\pi$
$600$	−5.14386	+	7.07991i	−0.209997	+	0.289036i
$601$	12.1034	−	37.2505i	0.493709	−	1.51948i	−0.325249	−	0.945628i	$-0.605448\pi$
$601$	12.1034	−	37.2505i	0.493709	−	1.51948i	0.818959	−	0.573852i	$-0.194552\pi$
$602$	−10.0363	−	30.8885i	−0.409048	−	1.25892i
$603$	3.03850	+	4.18214i	0.123737	+	0.170310i
$604$		−	24.1138i		−	0.981176i
$605$	−8.79631	−	8.75340i	−0.357621	−	0.355876i
$606$			2.42558i			0.0985325i
$607$	30.6094	−	22.2391i	1.24240	−	0.902656i	0.244643	−	0.969613i	$-0.421329\pi$
$607$	30.6094	−	22.2391i	1.24240	−	0.902656i	0.997756	+	0.0669575i	$0.0213292\pi$
$608$	−3.77308	−	11.6123i	−0.153019	−	0.470943i
$609$	27.7138	+	9.00475i	1.12302	+	0.364891i
$610$	−0.429314	−	0.311915i	−0.0173824	−	0.0126291i
$611$	−5.05775	+	6.57233i	−0.204615	+	0.265888i
$612$	0.981098	−	3.01951i	0.0396585	−	0.122056i
$613$	16.7274	−	5.43506i	0.675612	−	0.219520i	0.0489390	−	0.998802i	$-0.484416\pi$
$613$	16.7274	−	5.43506i	0.675612	−	0.219520i	0.626673	+	0.779282i	$0.284416\pi$
$614$	10.7437	−	7.80576i	0.433581	−	0.315015i
$615$	−5.46313			−0.220295
$616$	20.3644	+	23.7847i	0.820504	+	0.958312i
$617$		−	28.7614i		−	1.15789i	−0.815367	−	0.578945i	$-0.803465\pi$
$617$		−	28.7614i		−	1.15789i	0.815367	−	0.578945i	$-0.196535\pi$
$618$	4.43850	+	6.10907i	0.178543	+	0.245743i
$619$	−23.7054	+	7.70235i	−0.952800	+	0.309584i	−0.743853	−	0.668343i	$-0.767004\pi$
$619$	−23.7054	+	7.70235i	−0.952800	+	0.309584i	−0.208947	+	0.977927i	$0.567004\pi$
$620$	3.82374	−	11.7683i	0.153565	−	0.472624i
$621$	1.93638	+	1.40686i	0.0777043	+	0.0564555i
$622$	−3.60751	+	4.96530i	−0.144648	+	0.199091i
$623$	13.4948	−	41.5329i	0.540660	−	1.66398i
$624$	−1.61822	−	5.49122i	−0.0647807	−	0.219825i
$625$	−6.09128	+	4.42558i	−0.243651	+	0.177023i
$626$		−	0.289378i		−	0.0115659i
$627$	−1.63830	+	6.86096i	−0.0654275	+	0.274000i
$628$	−11.0723			−0.441831
$629$	−1.00358	−	1.38130i	−0.0400152	−	0.0550762i
$630$	2.83999	−	0.922770i	0.113148	−	0.0367640i
$631$	−35.0657	−	11.3935i	−1.39594	−	0.453570i	−0.488067	−	0.872806i	$-0.662298\pi$
$631$	−35.0657	−	11.3935i	−1.39594	−	0.453570i	−0.907877	+	0.419237i	$0.862298\pi$
$632$	−16.8443	+	23.1842i	−0.670031	+	0.922219i
$633$	8.40158	+	6.10411i	0.333933	+	0.242616i
$634$	−0.557511	+	1.71584i	−0.0221416	+	0.0681448i
$635$	−0.103377	+	0.0335892i	−0.00410239	+	0.00133295i
$636$	17.9683	−	13.0548i	0.712491	−	0.517655i
$637$	−33.0445	−	0.911560i	−1.30927	−	0.0361173i
$638$	−13.5007	−	8.25057i	−0.534499	−	0.326643i
$639$			12.1649i			0.481237i
$640$	−10.1167	+	7.35018i	−0.399896	+	0.290541i
$641$	−5.56468	−	17.1263i	−0.219792	−	0.676449i	−0.998779	−	0.0494088i	$-0.984266\pi$
$641$	−5.56468	−	17.1263i	−0.219792	−	0.676449i	0.778987	−	0.627040i	$-0.215734\pi$
$642$	−5.94049	−	1.93018i	−0.234452	−	0.0761782i
$643$	−16.4493	+	22.6405i	−0.648696	+	0.892854i	−0.999042	−	0.0437668i	$-0.986064\pi$
$643$	−16.4493	+	22.6405i	−0.648696	+	0.892854i	0.350346	+	0.936621i	$0.386064\pi$
$644$	−8.86258	+	12.1983i	−0.349234	+	0.480680i
$645$	−13.1647	−	4.27748i	−0.518361	−	0.168426i
$646$	−0.876762	−	2.69839i	−0.0344957	−	0.106167i
$647$	−26.6318	+	19.3491i	−1.04700	+	0.760693i	−0.971640	−	0.236463i	$-0.924012\pi$
$647$	−26.6318	+	19.3491i	−1.04700	+	0.760693i	−0.0753635	+	0.997156i	$0.524012\pi$
$648$			2.34788i			0.0922335i
$649$	−6.64475	−	15.9865i	−0.260829	−	0.627527i
$650$	−0.243950	+	8.84331i	−0.00956850	+	0.346863i
$651$	22.7750	−	16.5470i	0.892623	−	0.648529i
$652$	−4.49406	+	1.46021i	−0.176001	+	0.0571862i
$653$	−10.8922	+	33.5227i	−0.426245	+	1.31185i	0.475553	+	0.879687i	$0.342248\pi$
$653$	−10.8922	+	33.5227i	−0.426245	+	1.31185i	−0.901797	+	0.432159i	$0.857752\pi$
$654$	7.50776	+	5.45470i	0.293576	+	0.213296i
$655$	8.99857	−	12.3855i	0.351603	−	0.483941i
$656$	7.31249	+	2.37597i	0.285505	+	0.0927661i
$657$	12.8466	−	4.17412i	0.501194	−	0.162848i
$658$	3.57861	+	4.92553i	0.139509	+	0.192017i
$659$	16.3220			0.635815			0.317908	−	0.948122i	$-0.397020\pi$
$659$	16.3220			0.635815			0.317908	+	0.948122i	$0.397020\pi$
$660$	5.84321	−	0.467059i	0.227447	−	0.0181802i
$661$			19.2698i			0.749507i	0.927124	+	0.374754i	$0.122273\pi$
$661$			19.2698i			0.749507i	−0.927124	+	0.374754i	$0.877727\pi$
$662$	1.62346	−	1.17951i	0.0630974	−	0.0458430i
$663$	−2.06544	−	7.00879i	−0.0802150	−	0.272199i
$664$	−8.50761	+	26.1837i	−0.330159	+	1.01613i
$665$	−5.67081	+	7.80520i	−0.219905	+	0.302673i
$666$	0.448692	+	0.325994i	0.0173865	+	0.0126320i
$667$	5.36008	−	16.4966i	0.207543	−	0.638752i
$668$	18.2261	−	5.92203i	0.705190	−	0.229130i
$669$	−5.74513	−	7.90750i	−0.222120	−	0.305722i
$670$		−	3.83900i		−	0.148313i
$671$	−0.188831	−	2.36240i	−0.00728974	−	0.0911994i
$672$	−23.0843			−0.890497
$673$	2.35885	−	1.71380i	0.0909269	−	0.0660623i	−0.541393	−	0.840770i	$-0.682103\pi$
$673$	2.35885	−	1.71380i	0.0909269	−	0.0660623i	0.632320	+	0.774707i	$0.282103\pi$
$674$	9.19736	−	2.98840i	0.354269	−	0.115109i
$675$	−1.15180	+	3.54487i	−0.0443327	+	0.136442i
$676$	−15.7919	−	12.8613i	−0.607380	−	0.494667i
$677$	24.9841	+	18.1520i	0.960215	+	0.697637i	0.953201	−	0.302338i	$-0.0977672\pi$
$677$	24.9841	+	18.1520i	0.960215	+	0.697637i	0.00701447	+	0.999975i	$0.497767\pi$
$678$	−9.72663	−	3.16037i	−0.373549	−	0.121373i
$679$	12.0459	+	37.0734i	0.462279	+	1.42275i
$680$	−4.34262	+	3.15510i	−0.166532	+	0.120993i
$681$		−	11.9213i		−	0.456824i
$682$	−14.1147	+	5.86675i	−0.540482	+	0.224649i
$683$			27.3094i			1.04496i	0.852650	+	0.522482i	$0.174994\pi$
$683$			27.3094i			1.04496i	−0.852650	+	0.522482i	$0.825006\pi$
$684$	−1.95850	−	2.69564i	−0.0748851	−	0.103070i
$685$	3.14974	+	9.69390i	0.120345	+	0.370385i
$686$	−1.77365	+	5.45874i	−0.0677184	+	0.208416i
$687$	17.2787	−	23.7821i	0.659223	−	0.907343i
$688$	15.7609	+	11.4510i	0.600878	+	0.436563i
$689$	17.1299	−	48.1591i	0.652596	−	1.83471i
$690$	−0.549279	−	1.69051i	−0.0209107	−	0.0643565i
$691$	1.88200	+	2.59035i	0.0715946	+	0.0985414i	0.843313	−	0.537423i	$-0.180602\pi$
$691$	1.88200	+	2.59035i	0.0715946	+	0.0985414i	−0.771718	+	0.635965i	$0.780602\pi$
$692$	−6.28591			−0.238954
$693$	11.3794	+	6.95420i	0.432269	+	0.264168i
$694$			3.60184i			0.136724i
$695$	2.23366	+	3.07437i	0.0847276	+	0.116618i
$696$	16.1822	−	5.25792i	0.613386	−	0.199301i
$697$	9.33339	+	3.03260i	0.353527	+	0.114868i
$698$	11.1069	+	8.06965i	0.420403	+	0.305441i
$699$	−3.38877	−	2.46208i	−0.128175	−	0.0931245i
$700$	−22.3310	−	7.25579i	−0.844034	−	0.274243i
$701$	5.30992	+	16.3422i	0.200553	+	0.617238i	0.999867	+	0.0163243i	$0.00519641\pi$
$701$	5.30992	+	16.3422i	0.200553	+	0.617238i	−0.799314	+	0.600914i	$0.794804\pi$
$702$	1.34162	+	1.95793i	0.0506361	+	0.0738972i
$703$	−1.79187			−0.0675816
$704$	1.94748	+	0.465031i	0.0733984	+	0.0175265i
$705$	2.59484			0.0977275
$706$	−8.33489	+	6.05565i	−0.313688	+	0.227908i
$707$	−14.0910	+	4.57844i	−0.529946	+	0.172190i
$708$	7.77758	+	2.52709i	0.292299	+	0.0949738i
$709$	−8.13159	+	11.1922i	−0.305388	+	0.420331i	−0.933936	−	0.357440i	$-0.883650\pi$
$709$	−8.13159	+	11.1922i	−0.305388	+	0.420331i	0.628548	+	0.777771i	$0.283650\pi$
$710$	5.31014	−	7.30878i	0.199286	−	0.274293i
$711$	−3.77174	+	11.6082i	−0.141451	+	0.435342i
$712$	−7.87972	−	24.2513i	−0.295305	−	0.908855i
$713$	−9.84962	−	13.5568i	−0.368871	−	0.507707i
$714$	−5.36417			−0.200749
$715$	10.4857	−	8.48806i	0.392142	−	0.317436i
$716$	8.98576			0.335814
$717$	2.70472	+	3.72273i	0.101010	+	0.139028i
$718$	−1.01767	−	3.13206i	−0.0379790	−	0.116887i
$719$	−8.55271	+	26.3225i	−0.318962	+	0.981665i	0.655130	+	0.755516i	$0.272614\pi$
$719$	−8.55271	+	26.3225i	−0.318962	+	0.981665i	−0.974093	+	0.226149i	$0.927386\pi$
$720$	−1.05284	+	1.44911i	−0.0392371	+	0.0540052i
$721$	−27.1116	+	37.3159i	−1.00969	+	1.38972i
$722$	9.06335	+	2.94486i	0.337303	+	0.109596i
$723$	13.0803	−	4.25006i	0.486463	−	0.158061i
$724$	−1.17986	+	0.857215i	−0.0438490	+	0.0318581i
$725$	27.0116			1.00319
$726$	−5.13276	−	5.10773i	−0.190495	−	0.189565i
$727$	−28.7921			−1.06784			−0.533919	−	0.845535i	$-0.679281\pi$
$727$	−28.7921			−1.06784			−0.533919	+	0.845535i	$0.679281\pi$
$728$	−28.0797	+	19.2408i	−1.04070	+	0.713113i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−9.54040	−	3.09986i	−0.353106	−	0.114731i
$731$	20.1166	+	14.6156i	0.744040	+	0.540577i
$732$	0.905675	+	0.658012i	0.0334747	+	0.0243208i
$733$	−23.3976	−	7.60233i	−0.864209	−	0.280798i	−0.156823	−	0.987627i	$-0.550125\pi$
$733$	−23.3976	−	7.60233i	−0.864209	−	0.280798i	−0.707385	+	0.706828i	$0.750125\pi$
$734$	−4.38626	+	1.42518i	−0.161900	+	0.0526045i
$735$	6.07961	+	8.36786i	0.224250	+	0.308653i
$736$			13.7410i			0.506498i
$737$	13.0235	−	11.1507i	0.479727	−	0.410741i
$738$	−3.18781			−0.117345
$739$	−17.9093	−	24.6501i	−0.658805	−	0.906767i	0.340636	−	0.940195i	$-0.389358\pi$
$739$	−17.9093	−	24.6501i	−0.658805	−	0.906767i	−0.999441	+	0.0334282i	$0.989358\pi$
$740$	0.460147	+	1.41619i	0.0169153	+	0.0520601i
$741$	−7.22491	−	2.56985i	−0.265414	−	0.0944060i
$742$	−30.3585	−	22.0568i	−1.11450	−	0.809729i
$743$	4.48167	−	6.16849i	0.164416	−	0.226300i	−0.718857	−	0.695158i	$-0.755334\pi$
$743$	4.48167	−	6.16849i	0.164416	−	0.226300i	0.883274	+	0.468858i	$0.155334\pi$
$744$	5.07956	−	15.6333i	0.186226	−	0.573144i
$745$	−5.86216	−	18.0419i	−0.214773	−	0.661003i
$746$	8.28469	+	11.4029i	0.303324	+	0.417490i
$747$			11.7260i			0.429031i
$748$	−10.2420	−	2.44565i	−0.374485	−	0.0894218i
$749$		−	38.1535i		−	1.39410i
$750$	5.24343	−	3.80957i	0.191463	−	0.139106i
$751$	−9.53925	−	29.3588i	−0.348092	−	1.07132i	−0.959908	−	0.280317i	$-0.909560\pi$
$751$	−9.53925	−	29.3588i	−0.348092	−	1.07132i	0.611815	−	0.791001i	$-0.290440\pi$
$752$	−3.47324	−	1.12852i	−0.126656	−	0.0411530i
$753$	3.50995	+	2.55013i	0.127910	+	0.0929320i
$754$	10.4901	−	13.6314i	0.382027	−	0.496428i
$755$	−5.36582	+	16.5143i	−0.195282	+	0.601017i
$756$	−5.99121	+	1.94666i	−0.217898	+	0.0707994i
$757$	2.94643	−	2.14071i	0.107090	−	0.0778054i	−0.532951	−	0.846146i	$-0.678917\pi$
$757$	2.94643	−	2.14071i	0.107090	−	0.0778054i	0.640041	+	0.768340i	$0.278917\pi$
$758$	−16.5504			−0.601137
$759$	4.13949	−	6.77361i	0.150254	−	0.245866i
$760$			5.63338i			0.204344i
$761$	−6.07366	−	8.35967i	−0.220170	−	0.303038i	0.684617	−	0.728903i	$-0.259970\pi$
$761$	−6.07366	−	8.35967i	−0.220170	−	0.303038i	−0.904786	+	0.425866i	$0.859970\pi$
$762$	−0.0603219	+	0.0195998i	−0.00218523	+	0.000710025i
$763$	−17.5168	+	53.9111i	−0.634150	+	1.95171i
$764$	8.78701	+	6.38414i	0.317903	+	0.230970i
$765$	−1.34381	+	1.84959i	−0.0485855	+	0.0668722i
$766$	−7.66878	+	23.6021i	−0.277084	+	0.852778i
$767$	18.0531	−	5.32011i	0.651859	−	0.192098i
$768$	−6.88001	+	4.99862i	−0.248261	+	0.180372i
$769$		−	31.2861i		−	1.12821i	−0.825704	−	0.564103i	$-0.809222\pi$
$769$		−	31.2861i		−	1.12821i	0.825704	−	0.564103i	$-0.190778\pi$
$770$	−3.80125	−	9.14540i	−0.136988	−	0.329577i
$771$	−29.7916			−1.07292
$772$	25.2361	+	34.7345i	0.908267	+	1.25012i
$773$	−32.1206	+	10.4366i	−1.15530	+	0.375379i	−0.823136	−	0.567844i	$-0.807778\pi$
$773$	−32.1206	+	10.4366i	−1.15530	+	0.375379i	−0.332161	+	0.943223i	$0.607778\pi$
$774$	−7.68180	−	2.49597i	−0.276117	−	0.0897157i
$775$	15.3384	−	21.1115i	0.550972	−	0.758348i
$776$	18.4144	+	13.3788i	0.661037	+	0.480272i
$777$	−1.04687	+	3.22193i	−0.0375562	+	0.115586i
$778$	10.3826	−	3.37350i	0.372233	−	0.120946i
$779$	8.33231	−	6.05378i	0.298536	−	0.216899i
$780$	−0.175724	+	6.37008i	−0.00629191	+	0.228085i
$781$	40.2182	−	3.21472i	1.43912	−	0.115032i
$782$			3.19303i			0.114182i
$783$	5.86291	−	4.25966i	0.209523	−	0.152228i
$784$	−4.49838	−	13.8446i	−0.160656	−	0.494450i
$785$	7.58283	+	2.46381i	0.270643	+	0.0879371i
$786$	5.25079	−	7.22709i	0.187289	−	0.257782i
$787$	−18.7238	+	25.7711i	−0.667432	+	0.918641i	−0.999699	−	0.0245442i	$-0.992187\pi$
$787$	−18.7238	+	25.7711i	−0.667432	+	0.918641i	0.332267	+	0.943185i	$0.392187\pi$
$788$	−3.79995	−	1.23468i	−0.135368	−	0.0439836i
$789$	2.59062	+	7.97311i	0.0922286	+	0.283850i
$790$	7.33321	−	5.32789i	0.260904	−	0.189558i
$791$		−	62.4705i		−	2.22120i
$792$	7.76228	−	0.620454i	0.275821	−	0.0220469i
$793$	2.57541	+	0.0710448i	0.0914555	+	0.00252287i
$794$	−0.180773	+	0.131339i	−0.00641540	+	0.00466106i
$795$	−15.2106	+	4.94221i	−0.539463	+	0.175282i
$796$	−6.67948	+	20.5573i	−0.236748	+	0.728636i
$797$	35.6431	+	25.8962i	1.26254	+	0.917291i	0.998880	−	0.0473232i	$-0.0150691\pi$
$797$	35.6431	+	25.8962i	1.26254	+	0.917291i	0.263664	+	0.964615i	$0.415069\pi$
$798$	−3.30900	+	4.55444i	−0.117137	+	0.161226i
$799$	−4.43312	−	1.44041i	−0.156832	−	0.0509579i
$800$	−20.3509	+	6.61242i	−0.719514	+	0.233784i
$801$	−6.38368	−	8.78638i	−0.225556	−	0.310451i
$802$	16.7386			0.591060
$803$	−17.1948	−	41.3689i	−0.606793	−	1.45988i
$804$			8.09870i			0.285619i
$805$	8.78390	−	6.38188i	0.309592	−	0.224932i
$806$	−4.69720	−	15.9393i	−0.165452	−	0.561439i
$807$	0.482830	−	1.48600i	0.0169964	−	0.0523096i
$808$	−5.08506	+	6.99899i	−0.178892	+	0.246224i
$809$	2.57404	+	1.87015i	0.0904985	+	0.0657510i	0.632114	−	0.774875i	$-0.282187\pi$
$809$	2.57404	+	1.87015i	0.0904985	+	0.0657510i	−0.541616	+	0.840626i	$0.682187\pi$
$810$	0.229488	−	0.706291i	0.00806339	−	0.0248166i
$811$	−15.9175	+	5.17190i	−0.558938	+	0.181610i	−0.574843	−	0.818264i	$-0.694937\pi$
$811$	−15.9175	+	5.17190i	−0.558938	+	0.181610i	0.0159052	+	0.999874i	$0.494937\pi$
$812$	26.8338	+	36.9336i	0.941683	+	1.29612i
$813$		−	8.66369i		−	0.303849i
$814$	0.959190	−	1.56956i	0.0336196	−	0.0550130i
$815$	3.40268			0.119191
$816$	2.60311	−	1.89127i	0.0911272	−	0.0662078i
$817$	24.8187	−	8.06407i	0.868295	−	0.282126i
$818$	−4.22380	+	12.9995i	−0.147682	+	0.454518i
$819$	−8.84184	+	11.4896i	−0.308959	+	0.401479i
$820$	−6.92427	−	5.03078i	−0.241806	−	0.175682i
$821$	10.8649	+	3.53023i	0.379188	+	0.123206i	0.492409	−	0.870364i	$-0.336117\pi$
$821$	10.8649	+	3.53023i	0.379188	+	0.123206i	−0.113220	+	0.993570i	$0.536117\pi$
$822$	1.83792	+	5.65652i	0.0641047	+	0.197294i
$823$	−26.1641	+	19.0093i	−0.912023	+	0.662623i	−0.941526	−	0.336941i	$-0.890608\pi$
$823$	−26.1641	+	19.0093i	−0.912023	+	0.662623i	0.0295027	+	0.999565i	$0.490608\pi$
$824$			26.9326i			0.938243i
$825$	12.0240	+	2.87117i	0.418622	+	0.0999612i
$826$		−	13.8169i		−	0.480752i
$827$	−17.1587	−	23.6170i	−0.596668	−	0.821243i	0.398730	−	0.917068i	$-0.369451\pi$
$827$	−17.1587	−	23.6170i	−0.596668	−	0.821243i	−0.995398	+	0.0958252i	$0.969451\pi$
$828$	1.15875	+	3.56627i	0.0402694	+	0.123936i
$829$	−2.16417	+	6.66064i	−0.0751648	+	0.231334i	−0.981579	−	0.191056i	$-0.938809\pi$
$829$	−2.16417	+	6.66064i	−0.0751648	+	0.231334i	0.906414	+	0.422390i	$0.138809\pi$
$830$	5.11853	−	7.04505i	0.177667	−	0.244537i
$831$	−19.5158	−	14.1791i	−0.676997	−	0.491867i
$832$	−0.729452	+	2.05079i	−0.0252892	+	0.0710982i
$833$	−5.74157	−	17.6707i	−0.198934	−	0.612255i
$834$	1.30337	+	1.79394i	0.0451321	+	0.0621189i
$835$	−13.7999			−0.477566
$836$	−8.39445	+	7.18731i	−0.290328	+	0.248578i
$837$		−	7.00112i		−	0.241994i
$838$	−3.62760	−	4.99297i	−0.125314	−	0.172479i
$839$	38.3309	−	12.4545i	1.32333	−	0.429976i	0.439692	−	0.898148i	$-0.355087\pi$
$839$	38.3309	−	12.4545i	1.32333	−	0.429976i	0.883637	+	0.468173i	$0.155087\pi$
$840$	10.1293	+	3.29121i	0.349494	+	0.113557i
$841$	−19.0268	−	13.8238i	−0.656097	−	0.476683i
$842$	−8.42942	−	6.12433i	−0.290497	−	0.211058i
$843$	3.42940	+	1.11428i	0.118115	+	0.0383778i
$844$	5.02760	+	15.4734i	0.173057	+	0.532615i
$845$	7.95314	+	12.3221i	0.273596	+	0.423893i
$846$	1.51413			0.0520567
$847$	19.9840	−	39.4590i	0.686659	−	1.35583i
$848$	22.5090			0.772962
$849$	11.1504	−	8.10123i	0.382681	−	0.278034i
$850$	−4.72901	+	1.53655i	−0.162204	+	0.0527031i
$851$	1.91785	+	0.623149i	0.0657432	+	0.0213613i
$852$	−11.2022	+	15.4185i	−0.383781	+	0.528229i
$853$	11.4725	−	15.7906i	0.392813	−	0.540660i	−0.566109	−	0.824330i	$-0.691552\pi$
$853$	11.4725	−	15.7906i	0.392813	−	0.540660i	0.958922	+	0.283670i	$0.0915520\pi$
$854$	0.584481	−	1.79885i	0.0200005	−	0.0615553i
$855$	0.741439	+	2.28192i	0.0253567	+	0.0780399i
$856$	−13.0947	−	18.0233i	−0.447568	−	0.616025i
$857$	−3.39761			−0.116060			−0.0580300	−	0.998315i	$-0.518482\pi$
$857$	−3.39761			−0.116060			−0.0580300	+	0.998315i	$0.518482\pi$
$858$	6.11853	−	4.95290i	0.208883	−	0.169089i
$859$	7.52693			0.256816			0.128408	−	0.991721i	$-0.459013\pi$
$859$	7.52693			0.256816			0.128408	+	0.991721i	$0.459013\pi$
$860$	−12.7467	−	17.5444i	−0.434660	−	0.598258i
$861$	−6.01719	−	18.5190i	−0.205065	−	0.631126i
$862$	5.48103	−	16.8689i	0.186685	−	0.574556i
$863$	12.1335	−	16.7003i	0.413029	−	0.568485i	−0.550925	−	0.834555i	$-0.685725\pi$
$863$	12.1335	−	16.7003i	0.413029	−	0.568485i	0.963954	+	0.266069i	$0.0857250\pi$
$864$	−3.37445	+	4.64453i	−0.114801	+	0.158010i
$865$	4.30490	+	1.39875i	0.146371	+	0.0475588i
$866$	−11.7059	+	3.80347i	−0.397781	+	0.129247i
$867$	−10.4308	+	7.57840i	−0.354247	+	0.257376i
$868$	44.1038			1.49698
$869$	39.3744	+	9.40206i	1.33569	+	0.318943i
$870$	−5.38187			−0.182463
$871$	10.5355	+	15.3753i	0.356982	+	0.520971i
$872$	10.2281	+	31.4790i	0.346368	+	1.06601i
$873$	9.21997	+	2.99575i	0.312049	+	0.101391i
$874$	2.71103	+	1.96968i	0.0917021	+	0.0666255i
$875$	32.0283	+	23.2699i	1.08276	+	0.786668i
$876$	20.1263	+	6.53943i	0.680004	+	0.220947i
$877$	6.52474	−	2.12002i	0.220325	−	0.0715879i	−0.196774	−	0.980449i	$-0.563047\pi$
$877$	6.52474	−	2.12002i	0.220325	−	0.0715879i	0.417099	+	0.908861i	$0.363047\pi$
$878$	0.942014	+	1.29657i	0.0317914	+	0.0437571i
$879$			12.8004i			0.431747i
$880$	5.06910	+	3.09783i	0.170879	+	0.104428i
$881$	−52.4884			−1.76838			−0.884189	−	0.467130i	$-0.845288\pi$
$881$	−52.4884			−1.76838			−0.884189	+	0.467130i	$0.845288\pi$
$882$	3.54753	+	4.88276i	0.119452	+	0.164411i
$883$	−4.46924	−	13.7549i	−0.150402	−	0.462889i	0.847264	−	0.531172i	$-0.178248\pi$
$883$	−4.46924	−	13.7549i	−0.150402	−	0.462889i	−0.997666	+	0.0682824i	$0.978248\pi$
$884$	3.83626	−	10.7853i	0.129028	−	0.362749i
$885$	−4.76414	−	3.46135i	−0.160145	−	0.116352i
$886$	3.31444	−	4.56194i	0.111351	−	0.153261i
$887$	−12.8395	+	39.5160i	−0.431109	+	1.32682i	0.465913	+	0.884831i	$0.345726\pi$
$887$	−12.8395	+	39.5160i	−0.431109	+	1.32682i	−0.897022	+	0.441986i	$0.854274\pi$
$888$	0.611272	+	1.88130i	0.0205130	+	0.0631324i
$889$	−0.227723	−	0.313434i	−0.00763758	−	0.0105122i
$890$			8.06547i			0.270355i
$891$	3.06261	−	1.27296i	0.102601	−	0.0426458i
$892$		−	15.3129i		−	0.512712i
$893$	−3.95763	+	2.87539i	−0.132437	+	0.0962212i
$894$	−3.42065	−	10.5277i	−0.114404	−	0.352098i
$895$	−6.15389	−	1.99952i	−0.205702	−	0.0668366i
$896$	−36.0585	−	26.1980i	−1.20463	−	0.875214i
$897$	6.83919	+	5.26311i	0.228354	+	0.175730i
$898$	6.19556	−	19.0680i	0.206749	−	0.636307i
$899$	−48.2536	+	15.6785i	−1.60935	+	0.522909i
$900$	−4.72418	+	3.43232i	−0.157473	+	0.114411i
$901$	28.7297			0.957124
$902$	0.842415	+	10.5392i	0.0280493	+	0.350916i
$903$		−	49.3373i		−	1.64184i
$904$	−21.4406	−	29.5104i	−0.713103	−	0.981502i
$905$	0.998771	−	0.324520i	0.0332003	−	0.0107874i
$906$	−3.13103	+	9.63632i	−0.104021	+	0.320145i
$907$	17.0430	+	12.3825i	0.565905	+	0.411154i	0.833615	−	0.552346i	$-0.186267\pi$
$907$	17.0430	+	12.3825i	0.565905	+	0.411154i	−0.267711	+	0.963499i	$0.586267\pi$
$908$	10.9778	−	15.1097i	0.364312	−	0.501432i
$909$	−1.13863	+	3.50435i	−0.0377661	+	0.116232i
$910$	10.3276	−	3.04347i	0.342356	−	0.100890i
$911$	30.7439	−	22.3367i	1.01859	−	0.740049i	0.0525972	−	0.998616i	$-0.483250\pi$
$911$	30.7439	−	22.3367i	1.01859	−	0.740049i	0.965993	+	0.258566i	$0.0832501\pi$
$912$		−	3.37684i		−	0.111818i
$913$	38.7670	−	3.09872i	1.28300	−	0.102553i
$914$	−9.36625			−0.309808
$915$	−0.473830	−	0.652170i	−0.0156643	−	0.0215601i
$916$	43.7999	−	14.2315i	1.44719	−	0.470221i
$917$	51.8957	+	16.8619i	1.71375	+	0.556830i
$918$	−0.784130	+	1.07926i	−0.0258801	+	0.0356210i
$919$	18.1496	+	13.1865i	0.598700	+	0.434981i	0.845417	−	0.534106i	$-0.179352\pi$
$919$	18.1496	+	13.1865i	0.598700	+	0.434981i	−0.246717	+	0.969088i	$0.579352\pi$
$920$	1.95909	−	6.02947i	0.0645893	−	0.198786i
$921$	19.1862	−	6.23397i	0.632206	−	0.205416i
$922$	−4.22638	+	3.07064i	−0.139188	+	0.101126i
$923$	−1.20949	+	43.8446i	−0.0398108	+	1.44316i
$924$	8.01907	+	19.2930i	0.263808	+	0.634693i
$925$			3.14029i			0.103252i
$926$	−10.6183	+	7.71463i	−0.348938	+	0.253518i
$927$	3.54475	+	10.9096i	0.116425	+	0.358319i
$928$	39.5682	+	12.8565i	1.29889	+	0.422035i
$929$	29.5226	−	40.6344i	0.968605	−	1.33317i	0.0258564	−	0.999666i	$-0.491769\pi$
$929$	29.5226	−	40.6344i	0.968605	−	1.33317i	0.942748	−	0.333505i	$-0.108231\pi$
$930$	−3.05607	+	4.20632i	−0.100213	+	0.137931i
$931$	−18.5451	−	6.02567i	−0.607792	−	0.197483i
$932$	−2.02787	−	6.24116i	−0.0664252	−	0.204436i
$933$	−7.54278	+	5.48015i	−0.246940	+	0.179412i
$934$			5.35460i			0.175208i
$935$	6.47002	+	3.95396i	0.211592	+	0.129308i
$936$	−0.233436	+	8.46219i	−0.00763010	+	0.276595i
$937$	16.1285	−	11.7180i	0.526895	−	0.382812i	−0.292300	−	0.956327i	$-0.594421\pi$
$937$	16.1285	−	11.7180i	0.526895	−	0.382812i	0.819195	+	0.573515i	$0.194421\pi$
$938$	13.0135	−	4.22835i	0.424906	−	0.138060i
$939$	0.135842	−	0.418078i	0.00443303	−	0.0136435i
$940$	3.28885	+	2.38949i	0.107270	+	0.0779365i
$941$	−20.6497	+	28.4219i	−0.673161	+	0.926526i	−0.999827	−	0.0186135i	$-0.994075\pi$
$941$	−20.6497	+	28.4219i	−0.673161	+	0.926526i	0.326666	+	0.945140i	$0.394075\pi$
$942$	4.42468	+	1.43767i	0.144164	+	0.0468417i
$943$	−11.0235	+	3.58174i	−0.358973	+	0.116637i
$944$	4.87150	+	6.70504i	0.158554	+	0.218231i
$945$	4.53625			0.147564
$946$	−6.22187	+	26.0562i	−0.202290	+	0.847161i
$947$		−	20.9549i		−	0.680944i	−0.940255	−	0.340472i	$-0.889413\pi$
$947$		−	20.9549i		−	0.680944i	0.940255	−	0.340472i	$-0.110587\pi$
$948$	−15.4700	+	11.2396i	−0.502444	+	0.365047i
$949$	46.7165	−	13.7670i	1.51648	−	0.446896i
$950$	−1.61258	+	4.96300i	−0.0523189	+	0.161021i
$951$	−1.61093	+	2.21725i	−0.0522378	+	0.0718992i
$952$	−15.4783	−	11.2456i	−0.501653	−	0.364472i
$953$	14.5536	−	44.7913i	0.471436	−	1.45093i	−0.379268	−	0.925287i	$-0.623824\pi$
$953$	14.5536	−	44.7913i	0.471436	−	1.45093i	0.850704	−	0.525645i	$-0.176176\pi$
$954$	−8.87556	+	2.88385i	−0.287357	+	0.0933680i
$955$	−4.59717	−	6.32746i	−0.148761	−	0.204752i
$956$			7.20906i			0.233158i
$957$	−15.6321	−	18.2576i	−0.505314	−	0.590185i
$958$	−3.42531			−0.110667
$959$	−29.3914	+	21.3541i	−0.949097	+	0.689560i
$960$	0.647720	−	0.210457i	0.0209051	−	0.00679247i
$961$	−5.56715	+	17.1339i	−0.179585	+	0.552707i
$962$	1.58475	+	1.21955i	0.0510945	+	0.0393199i
$963$	−7.67643	−	5.57725i	−0.247369	−	0.179724i
$964$	20.4924	+	6.65839i	0.660017	+	0.214452i
$965$	−9.55376	−	29.4034i	−0.307546	−	0.946530i
$966$	5.12553	−	3.72391i	0.164911	−	0.119815i
$967$		−	17.0942i		−	0.549711i	−0.961486	−	0.274856i	$-0.911370\pi$
$967$		−	17.0942i		−	0.549711i	0.961486	−	0.274856i	$-0.0886301\pi$
$968$	−4.10254	−	25.4988i	−0.131861	−	0.819561i
$969$		−	4.31008i		−	0.138460i
$970$	−4.23174	−	5.82450i	−0.135873	−	0.187013i
$971$	−11.0660	−	34.0575i	−0.355124	−	1.09296i	−0.955938	−	0.293569i	$-0.905157\pi$
$971$	−11.0660	−	34.0575i	−0.355124	−	1.09296i	0.600814	−	0.799389i	$-0.294843\pi$
$972$	−0.484125	+	1.48998i	−0.0155283	+	0.0477912i
$973$	−7.96136	+	10.9579i	−0.255230	+	0.351293i
$974$	0.218549	+	0.158785i	0.00700275	+	0.00508780i
$975$	−4.50373	+	12.6618i	−0.144235	+	0.405503i
$976$	0.350593	+	1.07901i	0.0112222	+	0.0345384i
$977$	−12.4711	−	17.1650i	−0.398986	−	0.549157i	0.561503	−	0.827475i	$-0.310223\pi$
$977$	−12.4711	−	17.1650i	−0.398986	−	0.549157i	−0.960489	+	0.278317i	$0.910223\pi$
$978$	1.98551			0.0634896
$979$	−27.3615	+	23.4268i	−0.874478	+	0.748725i
$980$			16.2043i			0.517629i
$981$	8.28623	+	11.4050i	0.264559	+	0.364134i
$982$	−12.7434	+	4.14057i	−0.406657	+	0.132131i
$983$	−57.6906	−	18.7448i	−1.84004	−	0.597867i	−0.998319	−	0.0579603i	$-0.981540\pi$
$983$	−57.6906	−	18.7448i	−1.84004	−	0.597867i	−0.841725	−	0.539906i	$-0.818460\pi$
$984$	−9.19839	−	6.68302i	−0.293234	−	0.213047i
$985$	2.32765	+	1.69114i	0.0741651	+	0.0538841i
$986$	9.19457	+	2.98750i	0.292815	+	0.0951413i
$987$	2.85801	+	8.79605i	0.0909715	+	0.279981i
$988$	−6.79077	−	9.91030i	−0.216043	−	0.315289i
$989$	−29.3681			−0.933850
$990$	−2.39570	−	0.572060i	−0.0761404	−	0.0181813i
$991$	−40.3005			−1.28019			−0.640094	−	0.768297i	$-0.721105\pi$
$991$	−40.3005			−1.28019			−0.640094	+	0.768297i	$0.721105\pi$
$992$	32.5169	−	23.6249i	1.03241	−	0.750091i
$993$	2.89918	−	0.942001i	0.0920027	−	0.0298935i
$994$	30.6241	+	9.95038i	0.971338	+	0.315607i
$995$	9.14888	−	12.5923i	0.290039	−	0.399204i
$996$	−10.7980	+	14.8621i	−0.342147	+	0.470925i
$997$	3.30194	−	10.1623i	0.104574	−	0.321844i	−0.885057	−	0.465483i	$-0.845880\pi$
$997$	3.30194	−	10.1623i	0.104574	−	0.321844i	0.989630	+	0.143639i	$0.0458805\pi$
$998$	2.66898	+	8.21428i	0.0844851	+	0.260018i
$999$	0.495216	+	0.681607i	0.0156680	+	0.0215651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bb.b.25.6	✓	56
11.4	even	5	inner	429.2.bb.b.103.9	yes	56
13.12	even	2	inner	429.2.bb.b.25.9	yes	56
143.103	even	10	inner	429.2.bb.b.103.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bb.b.25.6	✓	56	1.1	even	1	trivial
429.2.bb.b.25.9	yes	56	13.12	even	2	inner
429.2.bb.b.103.6	yes	56	143.103	even	10	inner
429.2.bb.b.103.9	yes	56	11.4	even	5	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.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.386931 - 0.532564i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.484125 - 1.48998i) q^{4} +(-0.663105 + 0.912685i) q^{5} +(-0.386931 + 0.532564i) q^{6} +(-3.82419 - 1.24256i) q^{7} +(-2.23297 + 0.725535i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.386931 - 0.532564i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.484125 - 1.48998i) q^{4} +(-0.663105 + 0.912685i) q^{5} +(-0.386931 + 0.532564i) q^{6} +(-3.82419 - 1.24256i) q^{7} +(-2.23297 + 0.725535i) q^{8} +(-0.809017 + 0.587785i) q^{9} +0.742639 q^{10} +(2.15706 + 2.51935i) q^{11} -1.56666 q^{12} +(-2.97428 + 2.03805i) q^{13} +(0.817956 + 2.51741i) q^{14} +(1.07293 + 0.348615i) q^{15} +(-1.28451 - 0.933253i) q^{16} +(-1.63950 - 1.19117i) q^{17} +(0.626067 + 0.203421i) q^{18} +(-2.02272 + 0.657222i) q^{19} +(1.03886 + 1.42987i) q^{20} +4.02099i q^{21} +(0.507082 - 2.12358i) q^{22} +2.39350 q^{23} +(1.38005 + 1.89948i) q^{24} +(1.15180 + 3.54487i) q^{25} +(2.23623 + 0.795414i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-3.70277 + 5.09643i) q^{28} +(2.23943 - 6.89227i) q^{29} +(-0.229488 - 0.706291i) q^{30} +(-4.11515 - 5.66402i) q^{31} +5.74095i q^{32} +(1.72947 - 2.83000i) q^{33} +1.33404i q^{34} +(3.66990 - 2.66634i) q^{35} +(0.484125 + 1.48998i) q^{36} +(0.801277 + 0.260351i) q^{37} +(1.13267 + 0.822930i) q^{38} +(2.85740 + 2.19892i) q^{39} +(0.818506 - 2.51910i) q^{40} +(-4.60558 + 1.49644i) q^{41} +(2.14144 - 1.55585i) q^{42} -12.2699 q^{43} +(4.79807 - 1.99430i) q^{44} -1.12814i q^{45} +(-0.926117 - 1.27469i) q^{46} +(2.18753 - 0.710772i) q^{47} +(-0.490640 + 1.51003i) q^{48} +(7.41739 + 5.38905i) q^{49} +(1.44221 - 1.98503i) q^{50} +(-0.626235 + 1.92735i) q^{51} +(1.59673 + 5.41830i) q^{52} +(-11.4692 + 8.33286i) q^{53} -0.658286i q^{54} +(-3.72972 + 0.298124i) q^{55} +9.44081 q^{56} +(1.25011 + 1.72063i) q^{57} +(-4.53708 + 1.47419i) q^{58} +(-4.96443 - 1.61304i) q^{59} +(1.03886 - 1.42987i) q^{60} +(-0.578093 - 0.420009i) q^{61} +(-1.42418 + 4.38317i) q^{62} +(3.82419 - 1.24256i) q^{63} +(0.488400 - 0.354843i) q^{64} +(0.112164 - 4.06602i) q^{65} +(-2.17634 + 0.173959i) q^{66} -5.16940i q^{67} +(-2.56855 + 1.86616i) q^{68} +(-0.739632 - 2.27635i) q^{69} +(-2.83999 - 0.922770i) q^{70} +(7.15036 - 9.84163i) q^{71} +(1.38005 - 1.89948i) q^{72} +(-12.8466 - 4.17412i) q^{73} +(-0.171385 - 0.527469i) q^{74} +(3.01545 - 2.19085i) q^{75} +3.33200i q^{76} +(-5.11857 - 12.3147i) q^{77} +(0.0654495 - 2.37258i) q^{78} +(9.87453 - 7.17427i) q^{79} +(1.70353 - 0.553511i) q^{80} +(0.309017 - 0.951057i) q^{81} +(2.57899 + 1.87375i) q^{82} +(6.89236 - 9.48652i) q^{83} +(5.99121 + 1.94666i) q^{84} +(2.17433 - 0.706481i) q^{85} +(4.74761 + 6.53453i) q^{86} -7.24696 q^{87} +(-6.64451 - 4.06060i) q^{88} +10.8606i q^{89} +(-0.600807 + 0.436512i) q^{90} +(13.9066 - 4.09818i) q^{91} +(1.15875 - 3.56627i) q^{92} +(-4.11515 + 5.66402i) q^{93} +(-1.22495 - 0.889981i) q^{94} +(0.741439 - 2.28192i) q^{95} +(5.45997 - 1.77405i) q^{96} +(-5.69825 - 7.84297i) q^{97} -6.03542i q^{98} +(-3.22593 - 0.770308i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9}+O(q^{10}) \) 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9	\( 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9} + 60 q^{12} - 3 q^{13} - 42 q^{14} - 16 q^{16} - 6 q^{17} - 40 q^{22} + 12 q^{23} + 4 q^{25} - 24 q^{26} + 14 q^{27} - 22 q^{29} - 10 q^{30} - 10 q^{35} + 20 q^{36} - 26 q^{38} + 3 q^{39} - 18 q^{42} + 6 q^{48} - 14 q^{49} - 24 q^{51} + 39 q^{52} + 10 q^{53} - 64 q^{55} - 20 q^{56} + 2 q^{61} - 8 q^{62} + 24 q^{64} - 58 q^{65} + 30 q^{66} + 18 q^{68} - 2 q^{69} - 86 q^{74} - 14 q^{75} + 52 q^{77} + 14 q^{78} - 24 q^{79} - 14 q^{81} + 62 q^{82} - 28 q^{87} - 46 q^{88} - 10 q^{90} - 19 q^{91} + 58 q^{92} + 86 q^{94} + 156 q^{95}+O(q^{100}) \) 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9 + 60 * q^12 - 3 * q^13 - 42 * q^14 - 16 * q^16 - 6 * q^17 - 40 * q^22 + 12 * q^23 + 4 * q^25 - 24 * q^26 + 14 * q^27 - 22 * q^29 - 10 * q^30 - 10 * q^35 + 20 * q^36 - 26 * q^38 + 3 * q^39 - 18 * q^42 + 6 * q^48 - 14 * q^49 - 24 * q^51 + 39 * q^52 + 10 * q^53 - 64 * q^55 - 20 * q^56 + 2 * q^61 - 8 * q^62 + 24 * q^64 - 58 * q^65 + 30 * q^66 + 18 * q^68 - 2 * q^69 - 86 * q^74 - 14 * q^75 + 52 * q^77 + 14 * q^78 - 24 * q^79 - 14 * q^81 + 62 * q^82 - 28 * q^87 - 46 * q^88 - 10 * q^90 - 19 * q^91 + 58 * q^92 + 86 * q^94 + 156 * q^95

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