LMFDB - Embedded newform 770.2.w.b.139.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(139,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 7]))

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

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

chi := DirichletCharacter("770.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.w (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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			139.12
Character	$\chi$	$=$	770.139
Dual form			770.2.w.b.349.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.0561872 + 0.172927i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.27672 - 1.83575i) q^{5} +(-0.147100 + 0.106874i) q^{6} +(-2.32414 - 1.26426i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.40030 + 1.74392i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.0561872 + 0.172927i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.27672 - 1.83575i) q^{5} +(-0.147100 + 0.106874i) q^{6} +(-2.32414 - 1.26426i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.40030 + 1.74392i) q^{9} +(0.0461423 - 2.23559i) q^{10} +(1.38526 - 3.01348i) q^{11} -0.181826 q^{12} +(1.69994 - 2.33976i) q^{13} +(-1.13715 - 2.38891i) q^{14} +(0.389186 - 0.117633i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.891897 - 1.22759i) q^{17} +(0.916835 + 2.82173i) q^{18} +(0.292395 - 0.899900i) q^{19} +(1.35138 - 1.78151i) q^{20} +(0.349212 - 0.330870i) q^{21} +(2.89198 - 1.62372i) q^{22} -6.64778i q^{23} +(-0.147100 - 0.106874i) q^{24} +(-1.73998 + 4.68748i) q^{25} +(2.75056 - 0.893710i) q^{26} +(-0.877737 + 0.637714i) q^{27} +(0.484188 - 2.60107i) q^{28} +(6.22359 - 2.02217i) q^{29} +(0.384001 + 0.133591i) q^{30} +(3.86442 - 5.31891i) q^{31} -1.00000 q^{32} +(0.443276 + 0.408868i) q^{33} -1.51739i q^{34} +(0.646396 + 5.88066i) q^{35} +(-0.916835 + 2.82173i) q^{36} +(2.03004 - 0.659601i) q^{37} +(0.765500 - 0.556169i) q^{38} +(0.309092 + 0.425429i) q^{39} +(2.14043 - 0.646952i) q^{40} +(2.81595 - 8.66660i) q^{41} +(0.476999 - 0.0624180i) q^{42} -3.72846 q^{43} +(3.29406 + 0.386249i) q^{44} +(0.136901 - 6.63287i) q^{45} +(3.90747 - 5.37817i) q^{46} +(-1.06924 + 3.29077i) q^{47} +(-0.0561872 - 0.172927i) q^{48} +(3.80327 + 5.87666i) q^{49} +(-4.16291 + 2.76951i) q^{50} +(0.262396 - 0.0852577i) q^{51} +(2.75056 + 0.893710i) q^{52} +(-6.94877 + 9.56417i) q^{53} -1.08494 q^{54} +(-7.30059 + 1.30436i) q^{55} +(1.92059 - 1.81971i) q^{56} +(0.139188 + 0.101126i) q^{57} +(6.22359 + 2.02217i) q^{58} +(6.67433 - 2.16862i) q^{59} +(0.232140 + 0.333787i) q^{60} +(-9.03683 + 6.56564i) q^{61} +(6.25276 - 2.03164i) q^{62} +(-3.37387 - 7.08774i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-6.46557 - 0.133449i) q^{65} +(0.118291 + 0.591332i) q^{66} -3.56425i q^{67} +(0.891897 - 1.22759i) q^{68} +(1.14958 + 0.373521i) q^{69} +(-2.93362 + 5.13750i) q^{70} +(-3.59738 + 2.61365i) q^{71} +(-2.40030 + 1.74392i) q^{72} +(-11.5095 + 3.73965i) q^{73} +(2.03004 + 0.659601i) q^{74} +(-0.712825 - 0.564266i) q^{75} +0.946211 q^{76} +(-7.02938 + 5.25241i) q^{77} +0.525859i q^{78} +(3.00703 - 4.13882i) q^{79} +(2.11192 + 0.734720i) q^{80} +(2.68954 + 8.27757i) q^{81} +(7.37225 - 5.35625i) q^{82} +(7.39042 + 10.1720i) q^{83} +(0.422589 + 0.229876i) q^{84} +(-1.11485 + 3.20459i) q^{85} +(-3.01639 - 2.19153i) q^{86} +1.18984i q^{87} +(2.43792 + 2.24868i) q^{88} +6.90281i q^{89} +(4.00946 - 5.28563i) q^{90} +(-6.90898 + 3.28877i) q^{91} +(6.32242 - 2.05428i) q^{92} +(0.702651 + 0.967116i) q^{93} +(-2.79930 + 2.03381i) q^{94} +(-2.02530 + 0.612153i) q^{95} +(0.0561872 - 0.172927i) q^{96} +(13.6696 + 9.93154i) q^{97} +(-0.377303 + 6.98982i) q^{98} +(8.58033 - 4.81747i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9}+O(q^{10}) $ 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9	$ 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} + 28 q^{18} - 4 q^{22} + 38 q^{25} - 2 q^{28} + 6 q^{30} - 96 q^{32} + 46 q^{35} - 28 q^{36} + 10 q^{39} - 24 q^{43} - 16 q^{44} + 37 q^{49} - 8 q^{50} - 30 q^{51} + 40 q^{53} + 2 q^{56} - 20 q^{57} + 14 q^{60} + 63 q^{63} - 24 q^{64} - 40 q^{65} + 39 q^{70} - 20 q^{71} + 18 q^{72} - 16 q^{77} - 126 q^{81} + 60 q^{85} - 36 q^{86} - 14 q^{88} - 31 q^{91} - 10 q^{92} + 20 q^{93} - 44 q^{95} + 18 q^{98} + 100 q^{99}+O(q^{100}) $ 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 + 28 * q^18 - 4 * q^22 + 38 * q^25 - 2 * q^28 + 6 * q^30 - 96 * q^32 + 46 * q^35 - 28 * q^36 + 10 * q^39 - 24 * q^43 - 16 * q^44 + 37 * q^49 - 8 * q^50 - 30 * q^51 + 40 * q^53 + 2 * q^56 - 20 * q^57 + 14 * q^60 + 63 * q^63 - 24 * q^64 - 40 * q^65 + 39 * q^70 - 20 * q^71 + 18 * q^72 - 16 * q^77 - 126 * q^81 + 60 * q^85 - 36 * q^86 - 14 * q^88 - 31 * q^91 - 10 * q^92 + 20 * q^93 - 44 * q^95 + 18 * q^98 + 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.0561872	+	0.172927i	−0.0324397	+	0.0998392i	−0.965965	−	0.258671i	$-0.916715\pi$
$3$	−0.0561872	+	0.172927i	−0.0324397	+	0.0998392i	0.933526	+	0.358511i	$0.116715\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.27672	−	1.83575i	−0.570966	−	0.820974i
$5$	−1.27672	−	1.83575i	−0.570966	−	0.820974i
$6$	−0.147100	+	0.106874i	−0.0600534	+	0.0436313i
$7$	−2.32414	−	1.26426i	−0.878443	−	0.477847i
$7$	−2.32414	−	1.26426i	−0.878443	−	0.477847i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	2.40030	+	1.74392i	0.800101	+	0.581308i
$10$	0.0461423	−	2.23559i	0.0145915	−	0.706956i
$11$	1.38526	−	3.01348i	0.417673	−	0.908597i
$11$	1.38526	−	3.01348i	0.417673	−	0.908597i
$12$	−0.181826			−0.0524886
$13$	1.69994	−	2.33976i	0.471478	−	0.648934i	−0.505361	−	0.862908i	$-0.668641\pi$
$13$	1.69994	−	2.33976i	0.471478	−	0.648934i	0.976839	+	0.213974i	$0.0686408\pi$
$14$	−1.13715	−	2.38891i	−0.303917	−	0.638462i
$15$	0.389186	−	0.117633i	0.100487	−	0.0303726i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.891897	−	1.22759i	−0.216317	−	0.297735i	0.687044	−	0.726616i	$-0.258908\pi$
$17$	−0.891897	−	1.22759i	−0.216317	−	0.297735i	−0.903361	+	0.428881i	$0.858908\pi$
$18$	0.916835	+	2.82173i	0.216100	+	0.665087i
$19$	0.292395	−	0.899900i	0.0670800	−	0.206451i	−0.911898	−	0.410417i	$-0.865383\pi$
$19$	0.292395	−	0.899900i	0.0670800	−	0.206451i	0.978978	+	0.203966i	$0.0653832\pi$
$20$	1.35138	−	1.78151i	0.302177	−	0.398358i
$21$	0.349212	−	0.330870i	0.0762043	−	0.0722018i
$22$	2.89198	−	1.62372i	0.616572	−	0.346177i
$23$		−	6.64778i		−	1.38616i	−0.720861	−	0.693079i	$-0.756254\pi$
$23$		−	6.64778i		−	1.38616i	0.720861	−	0.693079i	$-0.243746\pi$
$24$	−0.147100	−	0.106874i	−0.0300267	−	0.0218157i
$25$	−1.73998	+	4.68748i	−0.347996	+	0.937496i
$26$	2.75056	−	0.893710i	0.539429	−	0.175271i
$27$	−0.877737	+	0.637714i	−0.168921	+	0.122728i
$28$	0.484188	−	2.60107i	0.0915029	−	0.491556i
$29$	6.22359	−	2.02217i	1.15569	−	0.375507i	0.332407	−	0.943136i	$-0.392139\pi$
$29$	6.22359	−	2.02217i	1.15569	−	0.375507i	0.823285	+	0.567629i	$0.192139\pi$
$30$	0.384001	+	0.133591i	0.0701086	+	0.0243903i
$31$	3.86442	−	5.31891i	0.694070	−	0.955305i	−0.305925	−	0.952056i	$-0.598966\pi$
$31$	3.86442	−	5.31891i	0.694070	−	0.955305i	0.999995	−	0.00324962i	$-0.00103439\pi$
$32$	−1.00000			−0.176777
$33$	0.443276	+	0.408868i	0.0771644	+	0.0711748i
$34$		−	1.51739i		−	0.260230i
$35$	0.646396	+	5.88066i	0.109261	+	0.994013i
$36$	−0.916835	+	2.82173i	−0.152806	+	0.470288i
$37$	2.03004	−	0.659601i	0.333737	−	0.108438i	−0.137355	−	0.990522i	$-0.543860\pi$
$37$	2.03004	−	0.659601i	0.333737	−	0.108438i	0.471092	+	0.882084i	$0.343860\pi$
$38$	0.765500	−	0.556169i	0.124181	−	0.0902225i
$39$	0.309092	+	0.425429i	0.0494944	+	0.0681232i
$40$	2.14043	−	0.646952i	0.338432	−	0.102292i
$41$	2.81595	−	8.66660i	0.439777	−	1.35350i	−0.448334	−	0.893866i	$-0.647982\pi$
$41$	2.81595	−	8.66660i	0.439777	−	1.35350i	0.888111	−	0.459629i	$-0.152018\pi$
$42$	0.476999	−	0.0624180i	0.0736026	−	0.00963131i
$43$	−3.72846			−0.568585			−0.284293	−	0.958738i	$-0.591759\pi$
$43$	−3.72846			−0.568585			−0.284293	+	0.958738i	$0.591759\pi$
$44$	3.29406	+	0.386249i	0.496598	+	0.0582292i
$45$	0.136901	−	6.63287i	0.0204081	−	0.988769i
$46$	3.90747	−	5.37817i	0.576125	−	0.792968i
$47$	−1.06924	+	3.29077i	−0.155964	+	0.480009i	−0.998257	−	0.0590111i	$-0.981205\pi$
$47$	−1.06924	+	3.29077i	−0.155964	+	0.480009i	0.842293	+	0.539020i	$0.181205\pi$
$48$	−0.0561872	−	0.172927i	−0.00810993	−	0.0249598i
$49$	3.80327	+	5.87666i	0.543324	+	0.839523i
$50$	−4.16291	+	2.76951i	−0.588724	+	0.391668i
$51$	0.262396	−	0.0852577i	0.0367428	−	0.0119385i
$52$	2.75056	+	0.893710i	0.381434	+	0.123935i
$53$	−6.94877	+	9.56417i	−0.954488	+	1.31374i	−0.00498257	+	0.999988i	$0.501586\pi$
$53$	−6.94877	+	9.56417i	−0.954488	+	1.31374i	−0.949505	+	0.313752i	$0.898414\pi$
$54$	−1.08494			−0.147642
$55$	−7.30059	+	1.30436i	−0.984412	+	0.175879i
$56$	1.92059	−	1.81971i	0.256649	−	0.243169i
$57$	0.139188	+	0.101126i	0.0184359	+	0.0133944i
$58$	6.22359	+	2.02217i	0.817197	+	0.265524i
$59$	6.67433	−	2.16862i	0.868924	−	0.282331i	0.159573	−	0.987186i	$-0.448988\pi$
$59$	6.67433	−	2.16862i	0.868924	−	0.282331i	0.709351	+	0.704855i	$0.248988\pi$
$60$	0.232140	+	0.333787i	0.0299692	+	0.0430917i
$61$	−9.03683	+	6.56564i	−1.15705	+	0.840644i	−0.989402	−	0.145203i	$-0.953616\pi$
$61$	−9.03683	+	6.56564i	−1.15705	+	0.840644i	−0.167646	+	0.985847i	$0.553616\pi$
$62$	6.25276	−	2.03164i	0.794101	−	0.258019i
$63$	−3.37387	−	7.08774i	−0.425067	−	0.892972i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−6.46557	−	0.133449i	−0.801955	−	0.0165523i
$66$	0.118291	+	0.591332i	0.0145606	+	0.0727880i
$67$		−	3.56425i		−	0.435443i	−0.976011	−	0.217722i	$-0.930138\pi$
$67$		−	3.56425i		−	0.435443i	0.976011	−	0.217722i	$-0.0698625\pi$
$68$	0.891897	−	1.22759i	0.108158	−	0.148867i
$69$	1.14958	+	0.373521i	0.138393	+	0.0449666i
$70$	−2.93362	+	5.13750i	−0.350635	+	0.614048i
$71$	−3.59738	+	2.61365i	−0.426931	+	0.310184i	−0.780421	−	0.625255i	$-0.784995\pi$
$71$	−3.59738	+	2.61365i	−0.426931	+	0.310184i	0.353490	+	0.935438i	$0.384995\pi$
$72$	−2.40030	+	1.74392i	−0.282879	+	0.205523i
$73$	−11.5095	+	3.73965i	−1.34708	+	0.437693i	−0.891710	−	0.452608i	$-0.850494\pi$
$73$	−11.5095	+	3.73965i	−1.34708	+	0.437693i	−0.455372	+	0.890301i	$0.650494\pi$
$74$	2.03004	+	0.659601i	0.235988	+	0.0766771i
$75$	−0.712825	−	0.564266i	−0.0823099	−	0.0651558i
$76$	0.946211			0.108538
$77$	−7.02938	+	5.25241i	−0.801072	+	0.598567i
$78$			0.525859i			0.0595418i
$79$	3.00703	−	4.13882i	0.338317	−	0.465653i	−0.605632	−	0.795745i	$-0.707080\pi$
$79$	3.00703	−	4.13882i	0.338317	−	0.465653i	0.943949	+	0.330092i	$0.107080\pi$
$80$	2.11192	+	0.734720i	0.236119	+	0.0821442i
$81$	2.68954	+	8.27757i	0.298838	+	0.919730i
$82$	7.37225	−	5.35625i	0.814129	−	0.591499i
$83$	7.39042	+	10.1720i	0.811204	+	1.11653i	0.991136	+	0.132848i	$0.0424122\pi$
$83$	7.39042	+	10.1720i	0.811204	+	1.11653i	−0.179932	+	0.983679i	$0.557588\pi$
$84$	0.422589	+	0.229876i	0.0461082	+	0.0250815i
$85$	−1.11485	+	3.20459i	−0.120923	+	0.347587i
$86$	−3.01639	−	2.19153i	−0.325266	−	0.236319i
$87$			1.18984i			0.127565i
$88$	2.43792	+	2.24868i	0.259883	+	0.239710i
$89$			6.90281i			0.731696i	0.930675	+	0.365848i	$0.119221\pi$
$89$			6.90281i			0.731696i	−0.930675	+	0.365848i	$0.880779\pi$
$90$	4.00946	−	5.28563i	0.422634	−	0.557155i
$91$	−6.90898	+	3.28877i	−0.724257	+	0.344757i
$92$	6.32242	−	2.05428i	0.659158	−	0.214173i
$93$	0.702651	+	0.967116i	0.0728615	+	0.100285i
$94$	−2.79930	+	2.03381i	−0.288726	+	0.209772i
$95$	−2.02530	+	0.612153i	−0.207791	+	0.0628055i
$96$	0.0561872	−	0.172927i	0.00573459	−	0.0176492i
$97$	13.6696	+	9.93154i	1.38794	+	1.00840i	0.996088	+	0.0883658i	$0.0281644\pi$
$97$	13.6696	+	9.93154i	1.38794	+	1.00840i	0.391849	+	0.920030i	$0.371836\pi$
$98$	−0.377303	+	6.98982i	−0.0381134	+	0.706079i
$99$	8.58033	−	4.81747i	0.862355	−	0.484174i
$100$	−4.99574	−	0.206311i	−0.499574	−	0.0206311i
$101$	−0.165529	−	0.120264i	−0.0164708	−	0.0119667i	0.579519	−	0.814958i	$-0.303240\pi$
$101$	−0.165529	−	0.120264i	−0.0164708	−	0.0119667i	−0.595990	+	0.802992i	$0.703240\pi$
$102$	0.262396	+	0.0852577i	0.0259811	+	0.00844177i
$103$	−4.32903	−	13.3234i	−0.426552	−	1.31279i	−0.901500	−	0.432778i	$-0.857533\pi$
$103$	−4.32903	−	13.3234i	−0.426552	−	1.31279i	0.474949	−	0.880014i	$-0.342467\pi$
$104$	1.69994	+	2.33976i	0.166693	+	0.229433i
$105$	−1.05324	−	0.218639i	−0.102786	−	0.0213370i
$106$	−11.2434	+	3.65319i	−1.09205	+	0.354829i
$107$	1.80875	−	5.56676i	0.174859	−	0.538159i	−0.824768	−	0.565471i	$-0.808695\pi$
$107$	1.80875	−	5.56676i	0.174859	−	0.538159i	0.999627	+	0.0273113i	$0.00869453\pi$
$108$	−0.877737	−	0.637714i	−0.0844603	−	0.0613640i
$109$		−	10.7302i		−	1.02776i	−0.857861	−	0.513882i	$-0.828207\pi$
$109$		−	10.7302i		−	1.02776i	0.857861	−	0.513882i	$-0.171793\pi$
$110$	−6.67298	−	3.23593i	−0.636244	−	0.308534i
$111$			0.388110i			0.0368377i
$112$	2.62339	−	0.343285i	0.247887	−	0.0324374i
$113$	−8.54385	−	2.77607i	−0.803738	−	0.261150i	−0.121795	−	0.992555i	$-0.538865\pi$
$113$	−8.54385	−	2.77607i	−0.803738	−	0.261150i	−0.681943	+	0.731405i	$0.738865\pi$
$114$	0.0531650	+	0.163625i	0.00497935	+	0.0153249i
$115$	−12.2037	+	8.48734i	−1.13800	+	0.791449i
$116$	3.84639	+	5.29410i	0.357128	+	0.491545i
$117$	8.16073	−	2.65158i	0.754460	−	0.245139i
$118$	6.67433	+	2.16862i	0.614422	+	0.199638i
$119$	0.520896	+	3.98069i	0.0477504	+	0.364909i
$120$	−0.00838986	+	0.406488i	−0.000765886	+	0.0371071i
$121$	−7.16209	−	8.34892i	−0.651099	−	0.758993i
$122$	−11.1701			−1.01130
$123$	1.34046	+	0.973905i	0.120866	+	0.0878140i
$124$	6.25276	+	2.03164i	0.561514	+	0.182447i
$125$	10.8265	−	2.79041i	0.968354	−	0.249582i
$126$	1.43656	−	7.71722i	0.127979	−	0.687504i
$127$	4.70163	−	3.41594i	0.417202	−	0.303115i	−0.359309	−	0.933219i	$-0.616988\pi$
$127$	4.70163	−	3.41594i	0.417202	−	0.303115i	0.776511	+	0.630103i	$0.216988\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	0.209492	−	0.644750i	0.0184447	−	0.0567671i
$130$	−5.15232	−	3.90833i	−0.451888	−	0.342783i
$131$	−4.76825			−0.416604			−0.208302	−	0.978065i	$-0.566794\pi$
$131$	−4.76825			−0.416604			−0.208302	+	0.978065i	$0.566794\pi$
$132$	−0.251877	+	0.547928i	−0.0219231	+	0.0476910i
$133$	−1.81728	+	1.72183i	−0.157578	+	0.149302i
$134$	2.09502	−	2.88354i	0.180982	−	0.249100i
$135$	2.29131	+	0.797129i	0.197204	+	0.0686060i
$136$	1.44312	−	0.468898i	0.123746	−	0.0402077i
$137$	−3.04244	−	4.18756i	−0.259933	−	0.357767i	0.659026	−	0.752120i	$-0.270969\pi$
$137$	−3.04244	−	4.18756i	−0.259933	−	0.357767i	−0.918959	+	0.394353i	$0.870969\pi$
$138$	0.710478	+	0.977890i	0.0604799	+	0.0832435i
$139$	7.09966	+	21.8505i	0.602185	+	1.85334i	0.515091	+	0.857135i	$0.327758\pi$
$139$	7.09966	+	21.8505i	0.602185	+	1.85334i	0.0870939	+	0.996200i	$0.472242\pi$
$140$	−5.39309	+	2.43198i	−0.455800	+	0.205540i
$141$	−0.508985	−	0.369799i	−0.0428643	−	0.0311427i
$142$	−4.44661			−0.373151
$143$	−4.69596	−	8.36391i	−0.392696	−	0.699426i
$144$	−2.96694			−0.247245
$145$	−11.6580	−	8.84324i	−0.968142	−	0.734391i
$146$	−11.5095	−	3.73965i	−0.952531	−	0.309496i
$147$	−1.22993	+	0.327493i	−0.101443	+	0.0270112i
$148$	1.25464	+	1.72686i	0.103130	+	0.141947i
$149$	−3.66274	−	5.04134i	−0.300064	−	0.413002i	0.632187	−	0.774816i	$-0.282158\pi$
$149$	−3.66274	−	5.04134i	−0.300064	−	0.413002i	−0.932250	+	0.361814i	$0.882158\pi$
$150$	−0.245020	−	0.875488i	−0.0200058	−	0.0714833i
$151$	−16.7480	−	5.44176i	−1.36293	−	0.442844i	−0.465912	−	0.884831i	$-0.654274\pi$
$151$	−16.7480	−	5.44176i	−1.36293	−	0.442844i	−0.897021	+	0.441987i	$0.854274\pi$
$152$	0.765500	+	0.556169i	0.0620903	+	0.0451112i
$153$		−	4.50199i		−	0.363964i
$154$	−8.77418	+	0.117519i	−0.707043	+	0.00946998i
$155$	−14.6980	−	0.303365i	−1.18057	−	0.0243668i
$156$	−0.309092	+	0.425429i	−0.0247472	+	0.0340616i
$157$	−2.07604	+	6.38940i	−0.165686	+	0.509930i	−0.999086	−	0.0427404i	$-0.986391\pi$
$157$	−2.07604	+	6.38940i	−0.165686	+	0.509930i	0.833400	+	0.552670i	$0.186391\pi$
$158$	4.86547	−	1.58089i	0.387076	−	0.125769i
$159$	−1.26347	−	1.73901i	−0.100199	−	0.137913i
$160$	1.27672	+	1.83575i	0.100933	+	0.145129i
$161$	−8.40456	+	15.4504i	−0.662372	+	1.21766i
$162$	−2.68954	+	8.27757i	−0.211311	+	0.650347i
$163$	−7.44836	+	10.2518i	−0.583401	+	0.802982i	−0.994063	−	0.108805i	$-0.965297\pi$
$163$	−7.44836	+	10.2518i	−0.583401	+	0.802982i	0.410662	+	0.911787i	$0.365297\pi$
$164$	9.11260			0.711575
$165$	0.184642	−	1.33575i	0.0143744	−	0.103988i
$166$			12.5733i			0.975880i
$167$	13.0064	−	17.9018i	1.00647	−	1.38528i	0.0851964	−	0.996364i	$-0.472848\pi$
$167$	13.0064	−	17.9018i	1.00647	−	1.38528i	0.921272	−	0.388920i	$-0.127152\pi$
$168$	0.206764	+	0.434365i	0.0159522	+	0.0335120i
$169$	1.43252	+	4.40883i	0.110194	+	0.339141i
$170$	−2.78555	+	1.93727i	−0.213642	+	0.148582i
$171$	2.27119	−	1.65012i	0.173682	−	0.126188i
$172$	−1.15216	−	3.54598i	−0.0878512	−	0.270378i
$173$	15.9326	+	5.17681i	1.21133	+	0.393586i	0.843918	−	0.536472i	$-0.180243\pi$
$173$	15.9326	+	5.17681i	1.21133	+	0.393586i	0.367414	+	0.930057i	$0.380243\pi$
$174$	−0.699373	+	0.962604i	−0.0530193	+	0.0729748i
$175$	9.97018	−	8.69457i	0.753675	−	0.657248i
$176$	0.650575	+	3.25219i	0.0490389	+	0.245143i
$177$			1.27602i			0.0959114i
$178$	−4.05737	+	5.58449i	−0.304113	+	0.418575i
$179$	−1.98785	+	6.11798i	−0.148579	+	0.457279i	−0.997454	−	0.0713146i	$-0.977281\pi$
$179$	−1.98785	+	6.11798i	−0.148579	+	0.457279i	0.848875	+	0.528594i	$0.177281\pi$
$180$	6.35053	−	1.91947i	0.473341	−	0.143069i
$181$	6.99333	+	9.62549i	0.519810	+	0.715457i	0.985535	−	0.169472i	$-0.0542063\pi$
$181$	6.99333	+	9.62549i	0.519810	+	0.715457i	−0.465725	+	0.884930i	$0.654206\pi$
$182$	−7.52257	−	1.40032i	−0.557610	−	0.103799i
$183$	−0.627619	−	1.93161i	−0.0463949	−	0.142789i
$184$	6.32242	+	2.05428i	0.466095	+	0.151443i
$185$	−3.80266	−	2.88454i	−0.279577	−	0.212075i
$186$			1.19542i			0.0876525i
$187$	−4.93483	+	0.987173i	−0.360870	+	0.0721892i
$188$	−3.46012			−0.252356
$189$	2.84623	−	0.372445i	0.207032	−	0.0270914i
$190$	−1.99832	−	0.695200i	−0.144973	−	0.0504351i
$191$	4.58213	+	14.1023i	0.331551	+	1.02041i	0.968396	+	0.249418i	$0.0802392\pi$
$191$	4.58213	+	14.1023i	0.331551	+	1.02041i	−0.636845	+	0.770992i	$0.719761\pi$
$192$	0.147100	−	0.106874i	0.0106160	−	0.00771300i
$193$	−0.845270	+	0.614125i	−0.0608439	+	0.0442057i	−0.617791	−	0.786342i	$-0.711972\pi$
$193$	−0.845270	+	0.614125i	−0.0608439	+	0.0442057i	0.556948	+	0.830548i	$0.311972\pi$
$194$	5.22132	+	16.0696i	0.374869	+	1.15373i
$195$	0.386359	−	1.11057i	0.0276678	−	0.0795296i
$196$	−4.41376	+	5.43311i	−0.315269	+	0.388080i
$197$	24.2033			1.72442			0.862208	−	0.506555i	$-0.169081\pi$
$197$	24.2033			1.72442			0.862208	+	0.506555i	$0.169081\pi$
$198$	9.77327	+	1.14598i	0.694556	+	0.0814411i
$199$			14.9107i			1.05699i	0.848935	+	0.528497i	$0.177244\pi$
$199$			14.9107i			1.05699i	−0.848935	+	0.528497i	$0.822756\pi$
$200$	−3.92037	−	3.10333i	−0.277212	−	0.219439i
$201$	0.616354	+	0.200266i	0.0434743	+	0.0141256i
$202$	−0.0632266	−	0.194591i	−0.00444861	−	0.0136914i
$203$	−17.0211	−	3.16846i	−1.19464	−	0.222382i
$204$	0.162170	+	0.223208i	0.0113542	+	0.0156277i
$205$	−19.5049	+	5.89542i	−1.36228	+	0.411754i
$206$	4.32903	−	13.3234i	0.301618	−	0.928284i
$207$	11.5932	−	15.9567i	0.805785	−	1.10907i
$208$			2.89211i			0.200531i
$209$	−2.30678	−	2.12772i	−0.159563	−	0.147178i
$210$	−0.723578	−	0.795963i	−0.0499316	−	0.0549266i
$211$	7.17936	−	9.88154i	0.494247	−	0.680273i	−0.486917	−	0.873448i	$-0.661879\pi$
$211$	7.17936	−	9.88154i	0.494247	−	0.680273i	0.981164	+	0.193175i	$0.0618786\pi$
$212$	−11.2434	−	3.65319i	−0.772197	−	0.250902i
$213$	−0.249843	−	0.768937i	−0.0171190	−	0.0526867i
$214$	4.73537	−	3.44045i	0.323703	−	0.235184i
$215$	4.76019	+	6.84454i	0.324643	+	0.466794i
$216$	−0.335266	−	1.03184i	−0.0228120	−	0.0702080i
$217$	−15.7060	+	7.47627i	−1.06619	+	0.507522i
$218$	6.30704	−	8.68089i	0.427166	−	0.587944i
$219$		−	2.20041i		−	0.148690i
$220$	−3.49652	−	6.54021i	−0.235736	−	0.440941i
$221$	−4.38844			−0.295198
$222$	−0.228125	+	0.313987i	−0.0153108	+	0.0210735i
$223$	9.00900	−	27.7269i	0.603287	−	1.85673i	0.0951272	−	0.995465i	$-0.469674\pi$
$223$	9.00900	−	27.7269i	0.603287	−	1.85673i	0.508160	−	0.861263i	$-0.330326\pi$
$224$	2.32414	+	1.26426i	0.155288	+	0.0844722i
$225$	−12.3511	+	8.21698i	−0.823406	+	0.547799i
$226$	−5.28039	−	7.26783i	−0.351246	−	0.483449i
$227$	−10.1309	+	3.29174i	−0.672414	+	0.218481i	−0.625271	−	0.780408i	$-0.715012\pi$
$227$	−10.1309	+	3.29174i	−0.672414	+	0.218481i	−0.0471429	+	0.998888i	$0.515012\pi$
$228$	−0.0531650	+	0.163625i	−0.00352094	+	0.0108363i
$229$	−10.9147	+	15.0228i	−0.721263	+	0.992733i	0.278218	+	0.960518i	$0.410256\pi$
$229$	−10.9147	+	15.0228i	−0.721263	+	0.992733i	−0.999481	+	0.0322153i	$0.989744\pi$
$230$	−14.8617	−	0.306744i	−0.979953	−	0.0202261i
$231$	−0.513319	−	1.51069i	−0.0337739	−	0.0993958i
$232$			6.54387i			0.429626i
$233$	18.5434	+	13.4726i	1.21482	+	0.882620i	0.995660	−	0.0930690i	$-0.0296677\pi$
$233$	18.5434	+	13.4726i	1.21482	+	0.882620i	0.219162	+	0.975689i	$0.429668\pi$
$234$	8.16073	+	2.65158i	0.533484	+	0.173339i
$235$	7.40617	−	2.23853i	0.483125	−	0.146026i
$236$	4.12497	+	5.67753i	0.268512	+	0.369576i
$237$	0.546755	+	0.752543i	0.0355155	+	0.0488829i
$238$	−1.91838	+	3.52662i	−0.124350	+	0.228597i
$239$	22.7893	+	7.40470i	1.47412	+	0.478971i	0.932350	−	0.361557i	$-0.117755\pi$
$239$	22.7893	+	7.40470i	1.47412	+	0.478971i	0.541770	+	0.840527i	$0.317755\pi$
$240$	−0.245715	+	0.323924i	−0.0158609	+	0.0209092i
$241$	−15.2324			−0.981204			−0.490602	−	0.871384i	$-0.663223\pi$
$241$	−15.2324			−0.981204			−0.490602	+	0.871384i	$0.663223\pi$
$242$	−0.886875	−	10.9642i	−0.0570105	−	0.704805i
$243$	−4.83736			−0.310317
$244$	−9.03683	−	6.56564i	−0.578524	−	0.420322i
$245$	5.93240	−	14.4847i	0.379007	−	0.925394i
$246$	0.512012	+	1.57581i	0.0326447	+	0.100470i
$247$	−1.60850	−	2.21391i	−0.102346	−	0.140868i
$248$	3.86442	+	5.31891i	0.245391	+	0.337751i
$249$	−2.17426	+	0.706461i	−0.137788	+	0.0447702i
$250$	10.3990	+	4.10618i	0.657691	+	0.259698i
$251$	1.82873	−	2.51703i	0.115428	−	0.158873i	−0.747393	−	0.664382i	$-0.768695\pi$
$251$	1.82873	−	2.51703i	0.115428	−	0.158873i	0.862822	+	0.505508i	$0.168695\pi$
$252$	5.69826	−	5.39897i	0.358957	−	0.340103i
$253$	−20.0329	−	9.20894i	−1.25946	−	0.578961i
$254$	5.81154			0.364648
$255$	−0.491518	−	0.372845i	−0.0307801	−	0.0233485i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	4.43854	+	13.6604i	0.276869	+	0.852114i	0.988719	+	0.149783i	$0.0478574\pi$
$257$	4.43854	+	13.6604i	0.276869	+	0.852114i	−0.711850	+	0.702331i	$0.752143\pi$
$258$	0.548457	−	0.398477i	0.0341455	−	0.0248081i
$259$	−5.55202	−	1.03351i	−0.344986	−	0.0642189i
$260$	−1.87105	−	6.19036i	−0.116038	−	0.383910i
$261$	18.4650	+	5.99965i	1.14296	+	0.371369i
$262$	−3.85760	−	2.80271i	−0.238323	−	0.173152i
$263$	−1.12693			−0.0694893			−0.0347446	−	0.999396i	$-0.511062\pi$
$263$	−1.12693			−0.0694893			−0.0347446	+	0.999396i	$0.511062\pi$
$264$	−0.525836	+	0.295233i	−0.0323630	+	0.0181704i
$265$	26.4291	+	0.545493i	1.62353	+	0.0335094i
$266$	−2.48228	+	0.324820i	−0.152198	+	0.0199160i
$267$	−1.19368	−	0.387850i	−0.0730519	−	0.0237360i
$268$	3.38981	−	1.10142i	0.207065	−	0.0672796i
$269$	−1.48775	−	2.04771i	−0.0907096	−	0.124851i	0.761250	−	0.648458i	$-0.224586\pi$
$269$	−1.48775	−	2.04771i	−0.0907096	−	0.124851i	−0.851960	+	0.523607i	$0.824586\pi$
$270$	1.38517	+	1.99169i	0.0842985	+	0.121210i
$271$	−3.84442	−	11.8319i	−0.233532	−	0.718738i	−0.997313	−	0.0732618i	$-0.976659\pi$
$271$	−3.84442	−	11.8319i	−0.233532	−	0.718738i	0.763781	−	0.645476i	$-0.223341\pi$
$272$	1.44312	+	0.468898i	0.0875020	+	0.0284311i
$273$	−0.180520	−	1.37953i	−0.0109255	−	0.0834931i
$274$		−	5.17611i		−	0.312700i
$275$	11.7153	+	11.7368i	0.706458	+	0.707755i
$276$			1.20874i			0.0727575i
$277$	10.5099	+	7.63589i	0.631479	+	0.458796i	0.856912	−	0.515462i	$-0.172380\pi$
$277$	10.5099	+	7.63589i	0.631479	+	0.458796i	−0.225433	+	0.974259i	$0.572380\pi$
$278$	−7.09966	+	21.8505i	−0.425809	+	1.31051i
$279$	18.5516	−	6.02777i	1.11065	−	0.360873i
$280$	−5.79259	−	1.20247i	−0.346173	−	0.0718610i
$281$	−8.13559	−	11.1977i	−0.485328	−	0.667997i	0.494189	−	0.869354i	$-0.335465\pi$
$281$	−8.13559	−	11.1977i	−0.485328	−	0.667997i	−0.979518	+	0.201357i	$0.935465\pi$
$282$	−0.194415	−	0.598347i	−0.0115772	−	0.0356311i
$283$	−16.5588	−	5.38027i	−0.984316	−	0.319824i	−0.227735	−	0.973723i	$-0.573132\pi$
$283$	−16.5588	−	5.38027i	−0.984316	−	0.319824i	−0.756581	+	0.653900i	$0.773132\pi$
$284$	−3.59738	−	2.61365i	−0.213466	−	0.155092i
$285$	0.00793858	−	0.384623i	0.000470241	−	0.0227831i
$286$	1.11707	−	9.52676i	0.0660539	−	0.563329i
$287$	−17.5015	+	16.5823i	−1.03308	+	0.978822i
$288$	−2.40030	−	1.74392i	−0.141439	−	0.102762i
$289$	4.54179	−	13.9782i	0.267164	−	0.822247i
$290$	−4.23357	−	14.0067i	−0.248604	−	0.822503i
$291$	−2.48548	+	1.80581i	−0.145702	+	0.105858i
$292$	−7.11324	−	9.79054i	−0.416271	−	0.572948i
$293$	28.7732	−	9.34899i	1.68095	−	0.546174i	0.695855	−	0.718183i	$-0.255026\pi$
$293$	28.7732	−	9.34899i	1.68095	−	0.546174i	0.985095	+	0.172009i	$0.0550257\pi$
$294$	−1.18753	−	0.457985i	−0.0692580	−	0.0267102i
$295$	−12.5023	−	9.48371i	−0.727912	−	0.552163i
$296$			2.13451i			0.124066i
$297$	0.705837	+	3.52844i	0.0409568	+	0.204741i
$298$		−	6.23143i		−	0.360977i
$299$	−15.5542	−	11.3008i	−0.899525	−	0.653543i
$300$	0.316374	−	0.852304i	0.0182658	−	0.0492078i
$301$	8.66547	+	4.71376i	0.499470	+	0.271697i
$302$	−10.3508	−	14.2467i	−0.595624	−	0.819805i
$303$	0.0300975	−	0.0218671i	0.00172906	−	0.00125623i
$304$	0.292395	+	0.899900i	0.0167700	+	0.0516128i
$305$	23.5904	+	8.20692i	1.35078	+	0.469927i
$306$	2.64620	−	3.64219i	0.151273	−	0.208210i
$307$			6.44463i			0.367815i	0.982944	+	0.183907i	$0.0588746\pi$
$307$			6.44463i			0.367815i	−0.982944	+	0.183907i	$0.941125\pi$
$308$	−7.16753	−	5.06226i	−0.408408	−	0.288449i
$309$	2.54720			0.144905
$310$	−11.7126	−	8.88469i	−0.665232	−	0.504616i
$311$	3.96585	+	1.28858i	0.224883	+	0.0730688i	0.419291	−	0.907852i	$-0.362279\pi$
$311$	3.96585	+	1.28858i	0.224883	+	0.0730688i	−0.194408	+	0.980921i	$0.562279\pi$
$312$	−0.500122	+	0.162499i	−0.0283138	+	0.00919972i
$313$	4.76103	−	3.45909i	0.269110	−	0.195520i	−0.445044	−	0.895509i	$-0.646812\pi$
$313$	4.76103	−	3.45909i	0.269110	−	0.195520i	0.714153	+	0.699989i	$0.246812\pi$
$314$	−5.43515	+	3.94887i	−0.306723	+	0.222848i
$315$	−8.70387	+	15.2426i	−0.490408	+	0.858826i
$316$	4.86547	+	1.58089i	0.273704	+	0.0889319i
$317$	−15.4545	+	21.2712i	−0.868009	+	1.19471i	0.111591	+	0.993754i	$0.464405\pi$
$317$	−15.4545	+	21.2712i	−0.868009	+	1.19471i	−0.979600	+	0.200957i	$0.935595\pi$
$318$		−	2.14954i		−	0.120540i
$319$	2.52756	−	21.5559i	0.141516	−	1.20690i
$320$	−0.0461423	+	2.23559i	−0.00257943	+	0.124973i
$321$	0.861013	+	0.625562i	0.0480570	+	0.0349155i
$322$	−15.8809	+	7.55955i	−0.885010	+	0.421278i
$323$	−1.36549	+	0.443676i	−0.0759782	+	0.0246868i
$324$	−7.04132	+	5.11582i	−0.391184	+	0.284212i
$325$	8.00973	+	12.0396i	0.444300	+	0.667835i
$326$	−12.0517	+	3.91583i	−0.667482	+	0.216878i
$327$	1.85553	+	0.602899i	0.102611	+	0.0333404i
$328$	7.37225	+	5.35625i	0.407064	+	0.295750i
$329$	6.64547	−	6.29643i	0.366377	−	0.347133i
$330$	0.934516	−	0.972118i	0.0514434	−	0.0535133i
$331$	−10.3174			−0.567097			−0.283549	−	0.958958i	$-0.591512\pi$
$331$	−10.3174			−0.567097			−0.283549	+	0.958958i	$0.591512\pi$
$332$	−7.39042	+	10.1720i	−0.405602	+	0.558263i
$333$	6.02302	+	1.95700i	0.330059	+	0.107243i
$334$	21.0448	−	6.83789i	1.15152	−	0.374152i
$335$	−6.54309	+	4.55055i	−0.357487	+	0.248623i
$336$	−0.0880378	+	0.472941i	−0.00480285	+	0.0258011i
$337$	7.48306	+	23.0305i	0.407628	+	1.25455i	0.918681	+	0.395001i	$0.129256\pi$
$337$	7.48306	+	23.0305i	0.407628	+	1.25455i	−0.511052	+	0.859550i	$0.670744\pi$
$338$	−1.43252	+	4.40883i	−0.0779186	+	0.239809i
$339$	0.960111	−	1.32148i	0.0521461	−	0.0717729i
$340$	−3.39226	−	0.0700157i	−0.183971	−	0.00379713i
$341$	−10.6752	−	19.0134i	−0.578094	−	1.02964i
$342$	2.80735			0.151804
$343$	−1.40969	−	18.4665i	−0.0761160	−	0.997099i
$344$	1.15216	−	3.54598i	0.0621202	−	0.191186i
$345$	−0.781995	−	2.58722i	−0.0421012	−	0.139291i
$346$	9.84688	+	13.5531i	0.529372	+	0.728618i
$347$	−10.3736	+	7.53688i	−0.556885	+	0.404601i	−0.830318	−	0.557290i	$-0.811841\pi$
$347$	−10.3736	+	7.53688i	−0.556885	+	0.404601i	0.273432	+	0.961891i	$0.411841\pi$
$348$	−1.13161	+	0.367682i	−0.0606606	+	0.0197098i
$349$	5.86378	−	18.0468i	0.313881	−	0.966026i	−0.662332	−	0.749210i	$-0.730433\pi$
$349$	5.86378	−	18.0468i	0.313881	−	0.966026i	0.976213	−	0.216815i	$-0.0695669\pi$
$350$	13.1766	−	1.17373i	0.704318	−	0.0627385i
$351$			3.13777i			0.167482i
$352$	−1.38526	+	3.01348i	−0.0738348	+	0.160619i
$353$	27.3606			1.45626			0.728129	−	0.685441i	$-0.240390\pi$
$353$	27.3606			1.45626			0.728129	+	0.685441i	$0.240390\pi$
$354$	−0.750025	+	1.03232i	−0.0398634	+	0.0548672i
$355$	9.39087	+	3.26701i	0.498416	+	0.173395i
$356$	−6.56496	+	2.13308i	−0.347942	+	0.113053i
$357$	−0.717635	−	0.133587i	−0.0379812	−	0.00707019i
$358$	−5.20427	+	3.78112i	−0.275054	+	0.199838i
$359$	−0.479141	+	0.155682i	−0.0252881	+	0.00821660i	−0.321634	−	0.946864i	$-0.604232\pi$
$359$	−0.479141	+	0.155682i	−0.0252881	+	0.00821660i	0.296346	+	0.955081i	$0.404232\pi$
$360$	6.26593	+	2.17987i	0.330243	+	0.114889i
$361$	14.6470	+	10.6417i	0.770895	+	0.560088i
$362$			11.8978i			0.625333i
$363$	1.84617	−	0.769412i	0.0968987	−	0.0403836i
$364$	−5.26280	−	5.55454i	−0.275846	−	0.291137i
$365$	21.5594	+	16.3541i	1.12847	+	0.856011i
$366$	0.627619	−	1.93161i	0.0328062	−	0.100967i
$367$	−8.08443	−	24.8813i	−0.422004	−	1.29879i	−0.905834	−	0.423633i	$-0.860755\pi$
$367$	−8.08443	−	24.8813i	−0.422004	−	1.29879i	0.483830	−	0.875162i	$-0.339245\pi$
$368$	3.90747	+	5.37817i	0.203691	+	0.280356i
$369$	21.8730	−	15.8917i	1.13866	−	0.827288i
$370$	−1.38093	−	4.56879i	−0.0717910	−	0.237520i
$371$	28.2416	−	13.4434i	1.46623	−	0.697946i
$372$	−0.702651	+	0.967116i	−0.0364307	+	0.0501426i
$373$	−5.56701			−0.288249			−0.144124	−	0.989560i	$-0.546037\pi$
$373$	−5.56701			−0.288249			−0.144124	+	0.989560i	$0.546037\pi$
$374$	−4.57261	−	2.10198i	−0.236444	−	0.108691i
$375$	−0.125776	+	2.02898i	−0.00649507	+	0.104776i
$376$	−2.79930	−	2.03381i	−0.144363	−	0.104886i
$377$	5.84832	−	17.9993i	0.301204	−	0.927010i
$378$	2.52156	+	1.37166i	0.129695	+	0.0705503i
$379$	−6.16537	+	4.47940i	−0.316694	+	0.230091i	−0.734763	−	0.678324i	$-0.762707\pi$
$379$	−6.16537	+	4.47940i	−0.316694	+	0.230091i	0.418070	+	0.908415i	$0.362707\pi$
$380$	−1.20804	−	1.73701i	−0.0619713	−	0.0891067i
$381$	0.326534	+	1.00497i	0.0167289	+	0.0514861i
$382$	−4.58213	+	14.1023i	−0.234442	+	0.721539i
$383$	8.97093	+	6.51776i	0.458393	+	0.333042i	0.792901	−	0.609351i	$-0.208570\pi$
$383$	8.97093	+	6.51776i	0.458393	+	0.333042i	−0.334507	+	0.942393i	$0.608570\pi$
$384$	0.181826			0.00927876
$385$	18.6167	+	6.19837i	0.948793	+	0.315898i
$386$	−1.04481			−0.0531795
$387$	−8.94944	−	6.50215i	−0.454926	−	0.330523i
$388$	−5.22132	+	16.0696i	−0.265072	+	0.815809i
$389$	6.17604	+	19.0079i	0.313138	+	0.963739i	0.976514	+	0.215453i	$0.0691229\pi$
$389$	6.17604	+	19.0079i	0.313138	+	0.963739i	−0.663376	+	0.748286i	$0.730877\pi$
$390$	0.965348	−	0.671374i	0.0488823	−	0.0339964i
$391$	−8.16076	+	5.92914i	−0.412707	+	0.299849i
$392$	−6.76431	+	1.80114i	−0.341649	+	0.0909712i
$393$	0.267915	−	0.824558i	0.0135145	−	0.0415934i
$394$	19.5809	+	14.2264i	0.986471	+	0.716713i
$395$	−11.4370	−	0.236058i	−0.575457	−	0.0118773i
$396$	7.23315	+	6.67170i	0.363480	+	0.335265i
$397$	−24.2481			−1.21698			−0.608488	−	0.793563i	$-0.708224\pi$
$397$	−24.2481			−1.21698			−0.608488	+	0.793563i	$0.708224\pi$
$398$	−8.76431	+	12.0630i	−0.439315	+	0.604666i
$399$	−0.195642	−	0.411001i	−0.00979436	−	0.0205758i
$400$	−1.34756	−	4.81499i	−0.0673778	−	0.240749i
$401$	4.06370	−	2.95245i	0.202932	−	0.147438i	−0.481678	−	0.876348i	$-0.659973\pi$
$401$	4.06370	−	2.95245i	0.202932	−	0.147438i	0.684610	+	0.728910i	$0.259973\pi$
$402$	0.380928	+	0.524302i	0.0189990	+	0.0261498i
$403$	−5.87573	−	18.0836i	−0.292691	−	0.900811i
$404$	0.0632266	−	0.194591i	0.00314564	−	0.00968129i
$405$	11.7618	−	15.5055i	0.584448	−	0.770472i
$406$	−11.9080	−	12.5681i	−0.590982	−	0.623743i
$407$	0.824454	−	7.03121i	0.0408667	−	0.348524i
$408$			0.275900i			0.0136591i
$409$	−2.20579	−	1.60260i	−0.109069	−	0.0792436i	0.531914	−	0.846799i	$-0.321473\pi$
$409$	−2.20579	−	1.60260i	−0.109069	−	0.0792436i	−0.640983	+	0.767555i	$0.721473\pi$
$410$	−19.2450	−	6.69521i	−0.950445	−	0.330653i
$411$	0.895087	−	0.290831i	0.0441514	−	0.0143457i
$412$	11.3335	−	8.23430i	0.558364	−	0.405675i
$413$	−18.2538	−	3.39794i	−0.898211	−	0.167202i
$414$	18.7582	−	6.09492i	0.921917	−	0.299549i
$415$	9.23788	−	26.5538i	0.453470	−	1.30348i
$416$	−1.69994	+	2.33976i	−0.0833463	+	0.114716i
$417$	−4.17744			−0.204570
$418$	−0.615581	−	3.07726i	−0.0301090	−	0.150514i
$419$			14.4667i			0.706744i	0.935483	+	0.353372i	$0.114965\pi$
$419$			14.4667i			0.706744i	−0.935483	+	0.353372i	$0.885035\pi$
$420$	−0.117531	−	1.06926i	−0.00573494	−	0.0521743i
$421$	1.29615	−	3.98914i	0.0631706	−	0.194419i	−0.914490	−	0.404608i	$-0.867408\pi$
$421$	1.29615	−	3.98914i	0.0631706	−	0.194419i	0.977661	+	0.210189i	$0.0674080\pi$
$422$	11.6164	−	3.77441i	0.565480	−	0.183735i
$423$	−8.30535	+	6.03419i	−0.403820	+	0.293392i
$424$	−6.94877	−	9.56417i	−0.337462	−	0.464477i
$425$	7.30619	−	2.04476i	0.354402	−	0.0991855i
$426$	0.249843	−	0.768937i	0.0121049	−	0.0372551i
$427$	29.3036	−	3.83454i	1.41810	−	0.185566i
$428$	5.85324			0.282927
$429$	1.71020	−	0.342111i	0.0825690	−	0.0165173i
$430$	−0.172040	+	8.33532i	−0.00829650	+	0.401965i
$431$	6.64902	−	9.15159i	0.320272	−	0.440817i	−0.618278	−	0.785959i	$-0.712169\pi$
$431$	6.64902	−	9.15159i	0.320272	−	0.440817i	0.938550	+	0.345143i	$0.112169\pi$
$432$	0.335266	−	1.03184i	0.0161305	−	0.0496445i
$433$	6.48536	+	19.9599i	0.311667	+	0.959211i	0.977105	+	0.212758i	$0.0682447\pi$
$433$	6.48536	+	19.9599i	0.311667	+	0.959211i	−0.665438	+	0.746453i	$0.731755\pi$
$434$	−17.1008	−	3.18331i	−0.820866	−	0.152804i
$435$	2.18426	−	1.51910i	0.104727	−	0.0728350i
$436$	10.2050	−	3.31580i	0.488731	−	0.158798i
$437$	−5.98234	−	1.94378i	−0.286174	−	0.0929836i
$438$	1.29337	−	1.78017i	0.0617997	−	0.0850599i
$439$	−18.8525			−0.899779			−0.449889	−	0.893084i	$-0.648537\pi$
$439$	−18.8525			−0.899779			−0.449889	+	0.893084i	$0.648537\pi$
$440$	1.01549	−	7.34634i	0.0484116	−	0.350223i
$441$	−1.11944	+	20.7384i	−0.0533065	+	0.987542i
$442$	−3.55032	−	2.57946i	−0.168872	−	0.122692i
$443$	27.2151	+	8.84272i	1.29303	+	0.420130i	0.873150	−	0.487451i	$-0.162073\pi$
$443$	27.2151	+	8.84272i	1.29303	+	0.420130i	0.419877	+	0.907581i	$0.362073\pi$
$444$	−0.369114	+	0.119932i	−0.0175174	+	0.00569174i
$445$	12.6719	−	8.81294i	0.600703	−	0.417773i
$446$	23.5859	−	17.1361i	1.11682	−	0.811420i
$447$	1.07758	−	0.350127i	0.0509678	−	0.0165604i
$448$	1.13715	+	2.38891i	0.0537255	+	0.112865i
$449$	25.0840	+	18.2246i	1.18378	+	0.860070i	0.992594	−	0.121483i	$-0.0387649\pi$
$449$	25.0840	+	18.2246i	1.18378	+	0.860070i	0.191191	+	0.981553i	$0.438765\pi$
$450$	−14.8221	−	0.612112i	−0.698719	−	0.0288552i
$451$	−22.2158	−	20.4913i	−1.04610	−	0.964899i
$452$		−	8.98354i		−	0.422550i
$453$	1.88205	−	2.59042i	0.0884263	−	0.121708i
$454$	−10.1309	−	3.29174i	−0.475469	−	0.154489i
$455$	14.8582	+	8.48434i	0.696563	+	0.397752i
$456$	−0.139188	+	0.101126i	−0.00651806	+	0.00473565i
$457$	−0.271535	+	0.197282i	−0.0127019	+	0.00922847i	−0.594118	−	0.804378i	$-0.702499\pi$
$457$	−0.271535	+	0.197282i	−0.0127019	+	0.00922847i	0.581416	+	0.813606i	$0.302499\pi$
$458$	−17.6603	+	5.73819i	−0.825213	+	0.268128i
$459$	1.56570	+	0.508728i	0.0730807	+	0.0237454i
$460$	−11.8431	−	8.98367i	−0.552187	−	0.418866i
$461$	0.305826			0.0142437			0.00712186	−	0.999975i	$-0.497733\pi$
$461$	0.305826			0.0142437			0.00712186	+	0.999975i	$0.497733\pi$
$462$	0.472675	−	1.52389i	0.0219908	−	0.0708978i
$463$			2.02447i			0.0940852i	0.998893	+	0.0470426i	$0.0149797\pi$
$463$			2.02447i			0.0940852i	−0.998893	+	0.0470426i	$0.985020\pi$
$464$	−3.84639	+	5.29410i	−0.178564	+	0.245773i
$465$	0.878299	−	2.52463i	0.0407302	−	0.117077i
$466$	7.08297	+	21.7991i	0.328112	+	1.00983i
$467$	20.0565	−	14.5719i	0.928106	−	0.674309i	−0.0174221	−	0.999848i	$-0.505546\pi$
$467$	20.0565	−	14.5719i	0.928106	−	0.674309i	0.945528	+	0.325540i	$0.105546\pi$
$468$	5.04361	+	6.94194i	0.233141	+	0.320891i
$469$	−4.50616	+	8.28383i	−0.208075	+	0.382512i
$470$	7.30749	+	2.54222i	0.337069	+	0.117264i
$471$	−0.988250	−	0.718006i	−0.0455362	−	0.0330840i
$472$			7.01781i			0.323021i
$473$	−5.16491	+	11.2356i	−0.237483	+	0.516615i
$474$			0.930195i			0.0427253i
$475$	3.70950	+	2.93641i	0.170203	+	0.134732i
$476$	−3.62489	+	1.72550i	−0.166147	+	0.0790882i
$477$	−33.3583	+	10.8388i	−1.52737	+	0.496274i
$478$	14.0846	+	19.3858i	0.644214	+	0.886684i
$479$	8.53693	−	6.20244i	0.390062	−	0.283397i	−0.375419	−	0.926855i	$-0.622501\pi$
$479$	8.53693	−	6.20244i	0.390062	−	0.283397i	0.765481	+	0.643459i	$0.222501\pi$
$480$	−0.389186	+	0.117633i	−0.0177638	+	0.00536916i
$481$	1.90764	−	5.87110i	0.0869808	−	0.267699i
$482$	−12.3233	−	8.95337i	−0.561309	−	0.407815i
$483$	−2.19955	−	2.32149i	−0.100083	−	0.105631i
$484$	5.72709	−	9.39151i	0.260322	−	0.426887i
$485$	0.779646	−	37.7738i	0.0354019	−	1.71522i
$486$	−3.91351	−	2.84333i	−0.177520	−	0.128976i
$487$	18.9043	+	6.14237i	0.856634	+	0.278337i	0.704222	−	0.709980i	$-0.251296\pi$
$487$	18.9043	+	6.14237i	0.856634	+	0.278337i	0.152412	+	0.988317i	$0.451296\pi$
$488$	−3.45176	−	10.6234i	−0.156254	−	0.480900i
$489$	−1.35430	−	1.86404i	−0.0612437	−	0.0842948i
$490$	13.3133	−	8.23140i	0.601434	−	0.371857i
$491$	−30.4746	+	9.90181i	−1.37530	+	0.446863i	−0.901122	−	0.433566i	$-0.857255\pi$
$491$	−30.4746	+	9.90181i	−1.37530	+	0.446863i	−0.474179	+	0.880428i	$0.657255\pi$
$492$	−0.512012	+	1.57581i	−0.0230833	+	0.0710430i
$493$	−8.03320	−	5.83646i	−0.361797	−	0.262861i
$494$		−	2.73654i		−	0.123123i
$495$	−19.7983	−	9.60082i	−0.889869	−	0.431525i
$496$			6.57454i			0.295206i
$497$	11.6652	−	1.52645i	0.523255	−	0.0684708i
$498$	−2.17426	−	0.706461i	−0.0974311	−	0.0316573i
$499$	1.29054	+	3.97187i	0.0577725	+	0.177805i	0.975778	−	0.218761i	$-0.0702016\pi$
$499$	1.29054	+	3.97187i	0.0577725	+	0.177805i	−0.918006	+	0.396567i	$0.870202\pi$
$500$	5.99942	+	9.43435i	0.268302	+	0.421917i
$501$	2.36490	+	3.25501i	0.105656	+	0.145423i
$502$	2.95895	−	0.961420i	0.132064	−	0.0429103i
$503$	−1.91850	−	0.623358i	−0.0855417	−	0.0277942i	0.265933	−	0.963991i	$-0.414320\pi$
$503$	−1.91850	−	0.623358i	−0.0855417	−	0.0277942i	−0.351475	+	0.936197i	$0.614320\pi$
$504$	7.78343	−	1.01851i	0.346701	−	0.0453678i
$505$	−0.00944098	+	0.457415i	−0.000420118	+	0.0203547i
$506$	−10.7941	−	19.2253i	−0.479857	−	0.854667i
$507$	−0.842893			−0.0374342
$508$	4.70163	+	3.41594i	0.208601	+	0.151558i
$509$	−7.29132	−	2.36909i	−0.323182	−	0.105008i	0.142933	−	0.989732i	$-0.454347\pi$
$509$	−7.29132	−	2.36909i	−0.323182	−	0.105008i	−0.466115	+	0.884724i	$0.654347\pi$
$510$	−0.178494	−	0.590545i	−0.00790384	−	0.0261498i
$511$	31.4776	+	5.85953i	1.39249	+	0.259210i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	0.317232	+	0.976340i	0.0140061	+	0.0431065i
$514$	−4.43854	+	13.6604i	−0.195776	+	0.602536i
$515$	−18.9315	+	24.9572i	−0.834221	+	1.09975i
$516$	0.677930			0.0298442
$517$	8.43550	+	7.78071i	0.370993	+	0.342195i
$518$	−3.88420	−	4.09952i	−0.170662	−	0.180123i
$519$	−1.79042	+	2.46430i	−0.0785906	+	0.108171i
$520$	2.12489	−	6.10788i	0.0931825	−	0.267848i
$521$	24.5458	−	7.97541i	1.07537	−	0.349409i	0.282793	−	0.959181i	$-0.408739\pi$
$521$	24.5458	−	7.97541i	1.07537	−	0.349409i	0.792577	+	0.609772i	$0.208739\pi$
$522$	11.4120	+	15.7073i	0.499490	+	0.687489i
$523$	−12.8303	−	17.6594i	−0.561030	−	0.772191i	0.430427	−	0.902625i	$-0.358363\pi$
$523$	−12.8303	−	17.6594i	−0.561030	−	0.772191i	−0.991457	+	0.130434i	$0.958363\pi$
$524$	−1.47347	−	4.53488i	−0.0643689	−	0.198107i
$525$	0.943325	+	2.21263i	0.0411701	+	0.0965672i
$526$	−0.911703	−	0.662391i	−0.0397521	−	0.0288816i
$527$	−9.97611			−0.434566
$528$	−0.598944	−	0.0702300i	−0.0260657	−	0.00305637i
$529$	−21.1930			−0.921436
$530$	21.0609	+	15.9759i	0.914829	+	0.693950i
$531$	19.8023	+	6.43417i	0.859349	+	0.279219i
$532$	−2.19913	−	1.19626i	−0.0953443	−	0.0518645i
$533$	−15.4909	−	21.3213i	−0.670983	−	0.923529i
$534$	−0.737734	−	1.01540i	−0.0319249	−	0.0439408i
$535$	−12.5285	+	3.78677i	−0.541653	+	0.163716i
$536$	3.38981	+	1.10142i	0.146417	+	0.0475739i
$537$	−0.946269	−	0.687505i	−0.0408345	−	0.0296680i
$538$		−	2.53111i		−	0.109124i
$539$	22.9777	−	3.32034i	0.989720	−	0.143017i
$540$	−0.0500618	+	2.42549i	−0.00215432	+	0.104376i
$541$	−6.80734	+	9.36950i	−0.292670	+	0.402826i	−0.929879	−	0.367865i	$-0.880089\pi$
$541$	−6.80734	+	9.36950i	−0.292670	+	0.402826i	0.637209	+	0.770691i	$0.280089\pi$
$542$	3.84442	−	11.8319i	0.165132	−	0.508224i
$543$	−2.05744	+	0.668503i	−0.0882932	+	0.0286882i
$544$	0.891897	+	1.22759i	0.0382398	+	0.0526325i
$545$	−19.6979	+	13.6994i	−0.843767	+	0.586818i
$546$	0.664825	−	1.22217i	0.0284519	−	0.0523041i
$547$	5.51232	−	16.9652i	0.235690	−	0.725378i	−0.761339	−	0.648353i	$-0.775458\pi$
$547$	5.51232	−	16.9652i	0.235690	−	0.725378i	0.997029	−	0.0770249i	$-0.0245421\pi$
$548$	3.04244	−	4.18756i	0.129967	−	0.178884i
$549$	−33.1411			−1.41443
$550$	2.57914	+	16.3813i	0.109975	+	0.698502i
$551$		−	6.19188i		−	0.263783i
$552$	−0.710478	+	0.977890i	−0.0302400	+	0.0416217i
$553$	−12.2213	+	5.81752i	−0.519703	+	0.247386i
$554$	4.01443	+	12.3551i	0.170557	+	0.524919i
$555$	0.712474	−	0.495507i	0.0302428	−	0.0210331i
$556$	−18.5871	+	13.5044i	−0.788271	+	0.572712i
$557$	7.88740	+	24.2749i	0.334200	+	1.02856i	0.967115	+	0.254340i	$0.0818584\pi$
$557$	7.88740	+	24.2749i	0.334200	+	1.02856i	−0.632915	+	0.774222i	$0.718142\pi$
$558$	18.5516	+	6.02777i	0.785350	+	0.255176i
$559$	−6.33815	+	8.72372i	−0.268075	+	0.368974i
$560$	−3.97951	−	4.37761i	−0.168165	−	0.184988i
$561$	0.106566	−	0.908830i	0.00449922	−	0.0383708i
$562$		−	13.8411i		−	0.583851i
$563$	−4.78027	+	6.57948i	−0.201465	+	0.277292i	−0.897780	−	0.440443i	$-0.854821\pi$
$563$	−4.78027	+	6.57948i	−0.201465	+	0.277292i	0.696316	+	0.717735i	$0.254821\pi$
$564$	0.194415	−	0.598347i	0.00818634	−	0.0251950i
$565$	5.81192	+	19.2287i	0.244509	+	0.808956i
$566$	−10.2339	−	14.0857i	−0.430162	−	0.592067i
$567$	4.21415	−	22.6385i	0.176978	−	0.950729i
$568$	−1.37408	−	4.22898i	−0.0576551	−	0.177444i
$569$	4.84318	+	1.57364i	0.203037	+	0.0659706i	0.408770	−	0.912638i	$-0.365958\pi$
$569$	4.84318	+	1.57364i	0.203037	+	0.0659706i	−0.205733	+	0.978608i	$0.565958\pi$
$570$	0.232498	−	0.306501i	0.00973829	−	0.0128379i
$571$		−	41.3329i		−	1.72973i	−0.502005	−	0.864865i	$-0.667404\pi$
$571$		−	41.3329i		−	1.72973i	0.502005	−	0.864865i	$-0.332596\pi$
$572$	6.50342	−	7.05071i	0.271922	−	0.294805i
$573$	−2.69613			−0.112632
$574$	−23.9059	+	3.12822i	−0.997812	+	0.130569i
$575$	31.1613	+	11.5670i	1.29952	+	0.482378i
$576$	−0.916835	−	2.82173i	−0.0382014	−	0.117572i
$577$	−15.1825	+	11.0307i	−0.632055	+	0.459215i	−0.857111	−	0.515131i	$-0.827743\pi$
$577$	−15.1825	+	11.0307i	−0.632055	+	0.459215i	0.225057	+	0.974346i	$0.427743\pi$
$578$	11.8906	−	8.63900i	0.494582	−	0.359335i
$579$	−0.0587051	−	0.180676i	−0.00243970	−	0.00750862i
$580$	4.80791	−	13.8201i	0.199638	−	0.573848i
$581$	−4.31624	−	32.9847i	−0.179068	−	1.36844i
$582$	−3.07223			−0.127348
$583$	19.1955	+	34.1889i	0.794997	+	1.41596i
$584$		−	12.1018i		−	0.500775i
$585$	−15.2866	−	11.5958i	−0.632024	−	0.479426i
$586$	28.7732	+	9.34899i	1.18861	+	0.386203i
$587$	5.80271	+	17.8589i	0.239503	+	0.737116i	0.996492	+	0.0836875i	$0.0266698\pi$
$587$	5.80271	+	17.8589i	0.239503	+	0.737116i	−0.756989	+	0.653428i	$0.773330\pi$
$588$	−0.691533	−	1.06853i	−0.0285183	−	0.0440654i
$589$	−3.65655	−	5.03281i	−0.150666	−	0.207373i
$590$	−4.54019	−	15.0212i	−0.186916	−	0.618411i
$591$	−1.35992	+	4.18540i	−0.0559395	+	0.172164i
$592$	−1.25464	+	1.72686i	−0.0515652	+	0.0709735i
$593$		−	25.7961i		−	1.05932i	−0.848211	−	0.529659i	$-0.822320\pi$
$593$		−	25.7961i		−	1.05932i	0.848211	−	0.529659i	$-0.177680\pi$
$594$	−1.50293	+	3.26945i	−0.0616661	+	0.134147i
$595$	6.64253	−	6.03845i	0.272317	−	0.247552i
$596$	3.66274	−	5.04134i	0.150032	−	0.206501i
$597$	−2.57846	−	0.837793i	−0.105529	−	0.0342886i
$598$	−5.94119	−	18.2851i	−0.242953	−	0.747733i
$599$	−26.4118	+	19.1893i	−1.07916	+	0.784053i	−0.977536	−	0.210770i	$-0.932403\pi$
$599$	−26.4118	+	19.1893i	−1.07916	+	0.784053i	−0.101621	+	0.994823i	$0.532403\pi$
$600$	0.756924	−	0.503569i	0.0309013	−	0.0205581i
$601$	−2.12154	−	6.52944i	−0.0865395	−	0.266341i	0.898417	−	0.439143i	$-0.144718\pi$
$601$	−2.12154	−	6.52944i	−0.0865395	−	0.266341i	−0.984957	+	0.172802i	$0.944718\pi$
$602$	4.23984	+	8.90695i	0.172803	+	0.363020i
$603$	6.21579	−	8.55530i	0.253126	−	0.348399i
$604$		−	17.6099i		−	0.716536i
$605$	−6.18260	+	23.8070i	−0.251359	+	0.967894i
$606$	0.0372026			0.00151125
$607$	5.70852	−	7.85711i	0.231702	−	0.318910i	−0.677296	−	0.735710i	$-0.736849\pi$
$607$	5.70852	−	7.85711i	0.231702	−	0.318910i	0.908998	+	0.416800i	$0.136849\pi$
$608$	−0.292395	+	0.899900i	−0.0118582	+	0.0364958i
$609$	1.50428	−	2.76537i	0.0609564	−	0.112058i
$610$	14.2611	+	20.5056i	0.577416	+	0.830248i
$611$	5.88200	+	8.09587i	0.237960	+	0.327524i
$612$	4.28165	−	1.39119i	0.173075	−	0.0562356i
$613$	6.86550	−	21.1298i	0.277295	−	0.853426i	−0.711308	−	0.702880i	$-0.751897\pi$
$613$	6.86550	−	21.1298i	0.277295	−	0.853426i	0.988603	−	0.150546i	$-0.0481031\pi$
$614$	−3.78806	+	5.21382i	−0.152874	+	0.210413i
$615$	0.0764535	−	3.70416i	0.00308290	−	0.149366i
$616$	−2.82314	−	8.30842i	−0.113747	−	0.334756i
$617$			27.5487i			1.10907i	0.832160	+	0.554535i	$0.187104\pi$
$617$			27.5487i			1.10907i	−0.832160	+	0.554535i	$0.812896\pi$
$618$	2.06073	+	1.49721i	0.0828947	+	0.0602265i
$619$	−18.8510	−	6.12505i	−0.757684	−	0.246187i	−0.0953999	−	0.995439i	$-0.530413\pi$
$619$	−18.8510	−	6.12505i	−0.757684	−	0.246187i	−0.662285	+	0.749252i	$0.730413\pi$
$620$	−4.25341	−	14.0724i	−0.170821	−	0.565160i
$621$	4.23938	+	5.83501i	0.170121	+	0.234151i
$622$	2.45103	+	3.37355i	0.0982774	+	0.135267i
$623$	8.72697	−	16.0431i	0.349639	−	0.642753i
$624$	−0.500122	−	0.162499i	−0.0200209	−	0.00650519i
$625$	−18.9449	−	16.3123i	−0.757797	−	0.652490i
$626$	5.88496			0.235210
$627$	0.497552	−	0.279353i	0.0198703	−	0.0111563i
$628$	−6.71822			−0.268086
$629$	−2.62031	−	1.90377i	−0.104479	−	0.0759082i
$630$	−16.0010	+	7.21555i	−0.637494	+	0.287474i
$631$	2.70733	+	8.33229i	0.107777	+	0.331703i	0.990372	−	0.138430i	$-0.0442057\pi$
$631$	2.70733	+	8.33229i	0.107777	+	0.331703i	−0.882595	+	0.470134i	$0.844206\pi$
$632$	3.00703	+	4.13882i	0.119613	+	0.164633i
$633$	1.30539	+	1.79672i	0.0518847	+	0.0714131i
$634$	−25.0058	+	8.12489i	−0.993109	+	0.322681i
$635$	−12.2735	−	4.26985i	−0.487058	−	0.169444i
$636$	1.26347	−	1.73901i	0.0500997	−	0.0689563i
$637$	20.2153	+	1.09120i	0.800960	+	0.0432350i
$638$	14.7151	−	15.9534i	0.582575	−	0.631602i
$639$	−13.1928			−0.521900
$640$	−1.35138	+	1.78151i	−0.0534179	+	0.0704204i
$641$	11.6391	−	35.8214i	0.459715	−	1.41486i	−0.405793	−	0.913965i	$-0.633005\pi$
$641$	11.6391	−	35.8214i	0.459715	−	1.41486i	0.865509	−	0.500894i	$-0.166995\pi$
$642$	0.328878	+	1.01218i	0.0129798	+	0.0399476i
$643$	−12.7351	+	9.25260i	−0.502224	+	0.364887i	−0.809866	−	0.586615i	$-0.800460\pi$
$643$	−12.7351	+	9.25260i	−0.502224	+	0.364887i	0.307642	+	0.951502i	$0.400460\pi$
$644$	−17.2913	−	3.21877i	−0.681374	−	0.126837i
$645$	−1.45106	+	0.438588i	−0.0571356	+	0.0172694i
$646$	−1.36549	−	0.443676i	−0.0537247	−	0.0174562i
$647$	19.5044	+	14.1708i	0.766799	+	0.557112i	0.900988	−	0.433844i	$-0.142843\pi$
$647$	19.5044	+	14.1708i	0.766799	+	0.557112i	−0.134189	+	0.990956i	$0.542843\pi$
$648$	−8.70355			−0.341908
$649$	2.71062	−	23.1171i	0.106401	−	0.907424i
$650$	−0.596673	+	14.4482i	−0.0234034	+	0.566706i
$651$	−0.410370	−	3.13605i	−0.0160837	−	0.122911i
$652$	−12.0517	−	3.91583i	−0.471981	−	0.153356i
$653$	10.8972	−	3.54072i	0.426441	−	0.138559i	−0.0879303	−	0.996127i	$-0.528025\pi$
$653$	10.8972	−	3.54072i	0.426441	−	0.138559i	0.514371	+	0.857568i	$0.328025\pi$
$654$	1.14678	+	1.57841i	0.0448427	+	0.0617207i
$655$	6.08771	+	8.75334i	0.237867	+	0.342021i
$656$	2.81595	+	8.66660i	0.109944	+	0.338374i
$657$	−34.1479	−	11.0953i	−1.33224	−	0.432870i
$658$	9.07724	−	1.18781i	0.353868	−	0.0463056i
$659$		−	17.3513i		−	0.675912i	−0.941162	−	0.337956i	$-0.890264\pi$
$659$		−	17.3513i		−	0.675912i	0.941162	−	0.337956i	$-0.109736\pi$
$660$	1.32744	−	0.237166i	0.0516704	−	0.00923166i
$661$			32.5079i			1.26441i	0.774801	+	0.632205i	$0.217850\pi$
$661$			32.5079i			1.26441i	−0.774801	+	0.632205i	$0.782150\pi$
$662$	−8.34698	−	6.06444i	−0.324415	−	0.235701i
$663$	0.246574	−	0.758878i	0.00957616	−	0.0294724i
$664$	−11.9580	+	3.88538i	−0.464059	+	0.150782i
$665$	5.48101	+	1.13779i	0.212544	+	0.0441214i
$666$	3.72243	+	5.12349i	0.144241	+	0.198531i
$667$	−13.4429	−	41.3731i	−0.520512	−	1.60197i
$668$	21.0448	+	6.83789i	0.814250	+	0.264566i
$669$	4.28852	+	3.11579i	0.165804	+	0.120463i
$670$	−7.96822	−	0.164463i	−0.307839	−	0.00635376i
$671$	7.26701	+	36.3274i	0.280540	+	1.40240i
$672$	−0.349212	+	0.330870i	−0.0134711	+	0.0127636i
$673$	−22.0671	−	16.0327i	−0.850626	−	0.618016i	0.0746929	−	0.997207i	$-0.476202\pi$
$673$	−22.0671	−	16.0327i	−0.850626	−	0.618016i	−0.925318	+	0.379191i	$0.876202\pi$
$674$	−7.48306	+	23.0305i	−0.288237	+	0.887102i
$675$	−1.46202	−	5.22399i	−0.0562732	−	0.201071i
$676$	−3.75038	+	2.72481i	−0.144245	+	0.104800i
$677$	−12.7840	−	17.5957i	−0.491329	−	0.676256i	0.489303	−	0.872114i	$-0.337251\pi$
$677$	−12.7840	−	17.5957i	−0.491329	−	0.676256i	−0.980632	+	0.195857i	$0.937251\pi$
$678$	1.55349	−	0.504760i	0.0596615	−	0.0193852i
$679$	−19.2140	−	40.3643i	−0.737365	−	1.54904i
$680$	−2.70324	−	2.05056i	−0.103664	−	0.0786354i
$681$		−	1.93686i		−	0.0742207i
$682$	2.53941	−	21.6569i	0.0972390	−	0.829286i
$683$			4.92548i			0.188468i	0.995550	+	0.0942342i	$0.0300403\pi$
$683$			4.92548i			0.188468i	−0.995550	+	0.0942342i	$0.969960\pi$
$684$	2.27119	+	1.65012i	0.0868412	+	0.0630939i
$685$	−3.80299	+	10.9315i	−0.145305	+	0.417671i
$686$	9.71389	−	15.7683i	0.370878	−	0.602038i
$687$	−1.98457	−	2.73153i	−0.0757161	−	0.104214i
$688$	3.01639	−	2.19153i	0.114999	−	0.0835515i
$689$	10.5654	+	32.5170i	0.402510	+	1.23880i
$690$	0.888084	−	2.55275i	0.0338088	−	0.0971816i
$691$	−15.4002	+	21.1965i	−0.585850	+	0.806354i	−0.994322	−	0.106417i	$-0.966062\pi$
$691$	−15.4002	+	21.1965i	−0.585850	+	0.806354i	0.408471	+	0.912771i	$0.366062\pi$
$692$			16.7525i			0.636835i
$693$	−26.0325	+	0.348673i	−0.988891	+	0.0132450i
$694$	−12.8225			−0.486736
$695$	31.0479	−	40.9302i	1.17771	−	1.55257i
$696$	−1.13161	−	0.367682i	−0.0428935	−	0.0139370i
$697$	−13.1506	+	4.27288i	−0.498114	+	0.161847i
$698$	15.3516	−	11.1536i	0.581065	−	0.422169i
$699$	−3.37168	+	2.44967i	−0.127528	+	0.0926549i
$700$	11.3500	+	6.79543i	0.428989	+	0.256843i
$701$	−10.4601	−	3.39871i	−0.395074	−	0.128367i	0.104741	−	0.994500i	$-0.466599\pi$
$701$	−10.4601	−	3.39871i	−0.395074	−	0.128367i	−0.499815	+	0.866132i	$0.666599\pi$
$702$	−1.84434	+	2.53851i	−0.0696100	+	0.0958099i
$703$		−	2.01970i		−	0.0761744i
$704$	−2.89198	+	1.62372i	−0.108996	+	0.0611961i
$705$	−0.0290300	+	1.40650i	−0.00109333	+	0.0529718i
$706$	22.1352	+	16.0822i	0.833069	+	0.605260i
$707$	0.232668	+	0.488784i	0.00875038	+	0.0183826i
$708$	−1.21357	+	0.394311i	−0.0456086	+	0.0148191i
$709$	−15.1027	+	10.9727i	−0.567193	+	0.412090i	−0.834085	−	0.551636i	$-0.814004\pi$
$709$	−15.1027	+	10.9727i	−0.567193	+	0.412090i	0.266891	+	0.963727i	$0.414004\pi$
$710$	5.67707	+	8.16288i	0.213057	+	0.306348i
$711$	14.4356	−	4.69040i	0.541376	−	0.175904i
$712$	−6.56496	−	2.13308i	−0.246032	−	0.0799407i
$713$	−35.3590	−	25.6898i	−1.32420	−	0.962091i
$714$	−0.502058	−	0.529889i	−0.0187890	−	0.0198306i
$715$	−9.35867	+	19.2990i	−0.349994	+	0.721741i
$716$	−6.43283			−0.240406
$717$	−2.56094	+	3.52483i	−0.0956401	+	0.131637i
$718$	−0.479141	−	0.155682i	−0.0178814	−	0.00581001i
$719$	−2.29285	+	0.744993i	−0.0855090	+	0.0277836i	−0.351459	−	0.936203i	$-0.614314\pi$
$719$	−2.29285	+	0.744993i	−0.0855090	+	0.0277836i	0.265950	+	0.963987i	$0.414314\pi$
$720$	3.78794	+	5.44657i	0.141168	+	0.202982i
$721$	−6.78300	+	36.4385i	−0.252612	+	1.35704i
$722$	5.59466	+	17.2186i	0.208212	+	0.640809i
$723$	0.855865	−	2.63408i	0.0318300	−	0.0979626i
$724$	−6.99333	+	9.62549i	−0.259905	+	0.357729i
$725$	−1.35007	+	32.6915i	−0.0501404	+	1.21413i
$726$	1.94583	+	0.462683i	0.0722165	+	0.0171718i
$727$	−6.53792			−0.242478			−0.121239	−	0.992623i	$-0.538687\pi$
$727$	−6.53792			−0.242478			−0.121239	+	0.992623i	$0.538687\pi$
$728$	−0.992816	−	7.58711i	−0.0367962	−	0.281197i
$729$	−7.79683	+	23.9962i	−0.288772	+	0.888748i
$730$	7.82927	+	25.9030i	0.289774	+	0.958714i
$731$	3.32540	+	4.57703i	0.122995	+	0.169287i
$732$	1.64313	−	1.19380i	0.0607318	−	0.0441242i
$733$	1.95032	−	0.633698i	0.0720367	−	0.0234062i	−0.272777	−	0.962077i	$-0.587942\pi$
$733$	1.95032	−	0.633698i	0.0720367	−	0.0234062i	0.344814	+	0.938671i	$0.387942\pi$
$734$	8.08443	−	24.8813i	0.298402	−	0.918387i
$735$	2.17147	+	1.83972i	0.0800957	+	0.0678593i
$736$			6.64778i			0.245041i
$737$	−10.7408	−	4.93743i	−0.395642	−	0.181873i
$738$	27.0365			0.995229
$739$	−24.4085	+	33.5954i	−0.897882	+	1.23583i	0.0732568	+	0.997313i	$0.476661\pi$
$739$	−24.4085	+	33.5954i	−0.897882	+	1.23583i	−0.971139	+	0.238515i	$0.923339\pi$
$740$	1.56827	−	4.50791i	0.0576508	−	0.165714i
$741$	0.473221	−	0.153759i	0.0173842	−	0.00564847i
$742$	30.7497	+	5.72405i	1.12886	+	0.210136i
$743$	0.909631	−	0.660886i	0.0333711	−	0.0242455i	−0.570975	−	0.820968i	$-0.693435\pi$
$743$	0.909631	−	0.660886i	0.0333711	−	0.0242455i	0.604346	+	0.796722i	$0.293435\pi$
$744$	−1.13691	+	0.369405i	−0.0416812	+	0.0135431i
$745$	−4.57836	+	13.1603i	−0.167738	+	0.482155i
$746$	−4.50381	−	3.27221i	−0.164896	−	0.119804i
$747$			37.3043i			1.36489i
$748$	−2.46380	−	4.38825i	−0.0900856	−	0.160450i
$749$	−11.2417	+	10.6512i	−0.410761	+	0.389187i
$750$	−1.29436	+	1.56755i	−0.0472633	+	0.0572388i
$751$	−10.7891	+	33.2055i	−0.393701	+	1.21169i	0.536268	+	0.844048i	$0.319834\pi$
$751$	−10.7891	+	33.2055i	−0.393701	+	1.21169i	−0.929969	+	0.367639i	$0.880166\pi$
$752$	−1.06924	−	3.29077i	−0.0389911	−	0.120002i
$753$	0.332510	+	0.457661i	0.0121173	+	0.0166781i
$754$	15.3111	−	11.1242i	0.557598	−	0.405118i
$755$	11.3928	+	37.6928i	0.414625	+	1.37178i
$756$	1.23375	+	2.59183i	0.0448710	+	0.0942639i
$757$	5.87413	−	8.08505i	0.213499	−	0.293856i	−0.688814	−	0.724939i	$-0.741868\pi$
$757$	5.87413	−	8.08505i	0.213499	−	0.293856i	0.902313	+	0.431082i	$0.141868\pi$
$758$	−7.62082			−0.276800
$759$	2.71807	−	2.94680i	0.0986595	−	0.106962i
$760$	0.0436604	−	2.11534i	0.00158373	−	0.0767315i
$761$	−22.7892	−	16.5573i	−0.826109	−	0.600203i	0.0923470	−	0.995727i	$-0.470563\pi$
$761$	−22.7892	−	16.5573i	−0.826109	−	0.600203i	−0.918456	+	0.395524i	$0.870563\pi$
$762$	−0.326534	+	1.00497i	−0.0118291	+	0.0364062i
$763$	−13.5658	+	24.9384i	−0.491114	+	0.902832i
$764$	−11.9962	+	8.71573i	−0.434006	+	0.315324i
$765$	−8.26455	+	5.74777i	−0.298805	+	0.207811i
$766$	3.42659	+	10.5460i	0.123808	+	0.381041i
$767$	6.27189	−	19.3029i	0.226465	−	0.696987i
$768$	0.147100	+	0.106874i	0.00530802	+	0.00385650i
$769$	31.5794			1.13878			0.569391	−	0.822067i	$-0.307179\pi$
$769$	31.5794			1.13878			0.569391	+	0.822067i	$0.307179\pi$
$770$	11.4179	+	15.9572i	0.411472	+	0.575057i
$771$	−2.61164			−0.0940559
$772$	−0.845270	−	0.614125i	−0.0304219	−	0.0221028i
$773$	8.11197	−	24.9661i	0.291767	−	0.897967i	−0.692521	−	0.721398i	$-0.743500\pi$
$773$	8.11197	−	24.9661i	0.291767	−	0.897967i	0.984288	−	0.176569i	$-0.0565000\pi$
$774$	−3.41838	−	10.5207i	−0.122871	−	0.378159i
$775$	18.2083	+	27.3692i	0.654061	+	0.983131i
$776$	−13.6696	+	9.93154i	−0.490710	+	0.356522i
$777$	0.490673	−	0.902022i	0.0176028	−	0.0323599i
$778$	−6.17604	+	19.0079i	−0.221422	+	0.681467i
$779$	−6.97570	−	5.06814i	−0.249930	−	0.181585i
$780$	1.17561	+	0.0242644i	0.0420935	+	0.000868804i
$781$	2.89285	+	14.4612i	0.103514	+	0.517464i
$782$	−10.0873			−0.360719
$783$	−4.17312	+	5.74380i	−0.149135	+	0.205267i
$784$	−6.53112	−	2.51881i	−0.233254	−	0.0899575i
$785$	14.3799	−	4.34636i	0.513240	−	0.155128i
$786$	0.701411	−	0.509605i	0.0250185	−	0.0181770i
$787$	29.5423	+	40.6614i	1.05307	+	1.44942i	0.886119	+	0.463458i	$0.153392\pi$
$787$	29.5423	+	40.6614i	1.05307	+	1.44942i	0.166949	+	0.985966i	$0.446608\pi$
$788$	7.47924	+	23.0187i	0.266437	+	0.820008i
$789$	0.0633189	−	0.194876i	0.00225421	−	0.00693775i
$790$	−9.11395	−	6.91346i	−0.324260	−	0.245970i
$791$	16.3474	+	17.2537i	0.581248	+	0.613469i
$792$	1.93022	+	9.64906i	0.0685872	+	0.342864i
$793$			32.3052i			1.14719i
$794$	−19.6171	−	14.2527i	−0.696185	−	0.505808i
$795$	−1.57931	+	4.53964i	−0.0560123	+	0.161004i
$796$	−14.1810	+	4.60767i	−0.502631	+	0.163315i
$797$	−23.0191	+	16.7244i	−0.815380	+	0.592408i	−0.915385	−	0.402579i	$-0.868114\pi$
$797$	−23.0191	+	16.7244i	−0.815380	+	0.592408i	0.100006	+	0.994987i	$0.468114\pi$
$798$	0.0833023	−	0.447502i	0.00294887	−	0.0158414i
$799$	4.99337	−	1.62245i	0.176653	−	0.0573980i
$800$	1.73998	−	4.68748i	0.0615177	−	0.165727i
$801$	−12.0380	+	16.5688i	−0.425341	+	0.585431i
$802$	5.02301			0.177369
$803$	−4.67430	+	39.8639i	−0.164952	+	1.40677i
$804$			0.648073i			0.0228558i
$805$	39.0934	−	4.29710i	1.37786	−	0.151453i
$806$	5.87573	−	18.0836i	0.206964	−	0.636969i
$807$	0.437696	−	0.142216i	0.0154076	−	0.00500624i
$808$	0.165529	−	0.120264i	0.00582330	−	0.00423088i
$809$	−28.6390	−	39.4182i	−1.00689	−	1.38587i	−0.920999	−	0.389565i	$-0.872625\pi$
$809$	−28.6390	−	39.4182i	−1.00689	−	1.38587i	−0.0858938	−	0.996304i	$-0.527375\pi$
$810$	18.6294	−	5.63078i	0.654569	−	0.197845i
$811$	−11.6023	+	35.7082i	−0.407412	+	1.25389i	0.511452	+	0.859312i	$0.329108\pi$
$811$	−11.6023	+	35.7082i	−0.407412	+	1.25389i	−0.918864	+	0.394574i	$0.870892\pi$
$812$	−2.24641	−	17.1671i	−0.0788336	−	0.602447i
$813$	2.26206			0.0793339
$814$	4.79984	−	5.20377i	0.168234	−	0.182392i
$815$	28.3292	+	0.584711i	0.992329	+	0.0204815i
$816$	−0.162170	+	0.223208i	−0.00567708	+	0.00781383i
$817$	−1.09018	+	3.35524i	−0.0381407	+	0.117385i
$818$	−0.842538	−	2.59307i	−0.0294587	−	0.0906644i
$819$	−22.3190	−	4.15467i	−0.779889	−	0.145176i
$820$	−11.6342	−	16.7285i	−0.406285	−	0.584184i
$821$	−33.7030	+	10.9508i	−1.17624	+	0.382185i	−0.830970	−	0.556317i	$-0.812214\pi$
$821$	−33.7030	+	10.9508i	−1.17624	+	0.382185i	−0.345274	+	0.938502i	$0.612214\pi$
$822$	0.895087	+	0.290831i	0.0312197	+	0.0101439i
$823$	−20.4403	+	28.1336i	−0.712503	+	0.980676i	0.287237	+	0.957860i	$0.407263\pi$
$823$	−20.4403	+	28.1336i	−0.712503	+	0.980676i	−0.999740	+	0.0228165i	$0.992737\pi$
$824$	14.0090			0.488028
$825$	−2.68785	+	1.36642i	−0.0935790	+	0.0475728i
$826$	−12.7704	−	13.4783i	−0.444339	−	0.468970i
$827$	−17.4625	−	12.6873i	−0.607232	−	0.441180i	0.241206	−	0.970474i	$-0.422457\pi$
$827$	−17.4625	−	12.6873i	−0.607232	−	0.441180i	−0.848439	+	0.529294i	$0.822457\pi$
$828$	18.7582	+	6.09492i	0.651894	+	0.211813i
$829$	−15.3493	+	4.98730i	−0.533105	+	0.173216i	−0.563184	−	0.826331i	$-0.690424\pi$
$829$	−15.3493	+	4.98730i	−0.533105	+	0.173216i	0.0300796	+	0.999548i	$0.490424\pi$
$830$	23.0815	−	16.0526i	0.801172	−	0.557194i
$831$	−1.91097	+	1.38840i	−0.0662909	+	0.0481631i
$832$	−2.75056	+	0.893710i	−0.0953584	+	0.0309838i
$833$	3.82201	−	9.91024i	0.132425	−	0.343369i
$834$	−3.37962	−	2.45544i	−0.117027	−	0.0850249i
$835$	−49.4689	−	1.02103i	−1.71194	−	0.0353342i
$836$	1.31075	−	2.85138i	0.0453333	−	0.0986172i
$837$			7.13300i			0.246553i
$838$	−8.50331	+	11.7038i	−0.293742	+	0.404301i
$839$	−50.8166	−	16.5113i	−1.75438	−	0.570034i	−0.757790	−	0.652498i	$-0.773721\pi$
$839$	−50.8166	−	16.5113i	−1.75438	−	0.570034i	−0.996594	+	0.0824644i	$0.973721\pi$
$840$	0.533408	−	0.934129i	0.0184043	−	0.0322305i
$841$	11.1824	−	8.12451i	0.385601	−	0.280155i
$842$	3.39337	−	2.46543i	0.116943	−	0.0849642i
$843$	2.39349	−	0.777693i	0.0824362	−	0.0267852i
$844$	11.6164	+	3.77441i	0.399854	+	0.129921i
$845$	6.26461	−	8.25858i	0.215509	−	0.284104i
$846$	−10.2660			−0.352952
$847$	6.09046	+	28.4589i	0.209271	+	0.977858i
$848$		−	11.8220i		−	0.405968i
$849$	1.86078	−	2.56115i	0.0638619	−	0.0878983i
$850$	7.11271	+	2.64022i	0.243964	+	0.0905590i
$851$	−4.38489	−	13.4953i	−0.150312	−	0.462613i
$852$	0.654097	−	0.475229i	0.0224090	−	0.0162811i
$853$	−1.01064	−	1.39103i	−0.0346038	−	0.0476281i	0.791365	−	0.611345i	$-0.209371\pi$
$853$	−1.01064	−	1.39103i	−0.0346038	−	0.0476281i	−0.825968	+	0.563717i	$0.809371\pi$
$854$	25.9610	+	14.1220i	0.888367	+	0.483245i
$855$	−5.92888	−	2.06262i	−0.202764	−	0.0705400i
$856$	4.73537	+	3.44045i	0.161852	+	0.117592i
$857$		−	11.6384i		−	0.397559i	−0.980044	−	0.198779i	$-0.936302\pi$
$857$		−	11.6384i		−	0.397559i	0.980044	−	0.198779i	$-0.0636978\pi$
$858$	1.58467	+	0.728454i	0.0540996	+	0.0248690i
$859$			1.51165i			0.0515768i	0.999667	+	0.0257884i	$0.00820961\pi$
$859$			1.51165i			0.0515768i	−0.999667	+	0.0257884i	$0.991790\pi$
$860$	−5.03856	+	6.64229i	−0.171813	+	0.226500i
$861$	−1.88416	−	3.95819i	−0.0642119	−	0.134895i
$862$	10.7583	−	3.49560i	0.366431	−	0.119060i
$863$	31.8152	+	43.7899i	1.08300	+	1.49063i	0.856171	+	0.516692i	$0.172837\pi$
$863$	31.8152	+	43.7899i	1.08300	+	1.49063i	0.226832	+	0.973934i	$0.427163\pi$
$864$	0.877737	−	0.637714i	0.0298612	−	0.0216955i
$865$	−10.8381	−	35.8576i	−0.368506	−	1.21920i
$866$	−6.48536	+	19.9599i	−0.220382	+	0.678265i
$867$	2.16201	+	1.57079i	0.0734257	+	0.0533469i
$868$	−11.9638	−	12.6270i	−0.406077	−	0.428587i
$869$	−8.30670	−	14.7950i	−0.281786	−	0.501885i
$870$	2.66001	+	0.0549022i	0.0901826	+	0.00186136i
$871$	−8.33951	−	6.05901i	−0.282574	−	0.205302i
$872$	10.2050	+	3.31580i	0.345585	+	0.112287i
$873$	15.4913	+	47.6774i	0.524302	+	1.61364i
$874$	−3.69729	−	5.08888i	−0.125063	−	0.172134i
$875$	−28.6902	−	7.20228i	−0.969906	−	0.243481i
$876$	2.09272	−	0.679965i	0.0707064	−	0.0229739i
$877$	0.924811	−	2.84628i	0.0312287	−	0.0961119i	−0.934227	−	0.356678i	$-0.883909\pi$
$877$	0.924811	−	2.84628i	0.0312287	−	0.0961119i	0.965456	+	0.260566i	$0.0839093\pi$
$878$	−15.2520	−	11.0812i	−0.514729	−	0.373972i
$879$			5.50095i			0.185542i
$880$	5.13962	−	5.34643i	0.173257	−	0.180228i
$881$		−	50.0834i		−	1.68735i	−0.536853	−	0.843676i	$-0.680387\pi$
$881$		−	50.0834i		−	1.68735i	0.536853	−	0.843676i	$-0.319613\pi$
$882$	−13.0954	+	16.1197i	−0.440944	+	0.542779i
$883$	−46.5475	−	15.1242i	−1.56645	−	0.508970i	−0.607927	−	0.793993i	$-0.707999\pi$
$883$	−46.5475	−	15.1242i	−1.56645	−	0.508970i	−0.958521	+	0.285023i	$0.907999\pi$
$884$	−1.35610	−	4.17366i	−0.0456107	−	0.140375i
$885$	2.34246	−	1.62912i	0.0787408	−	0.0547621i
$886$	16.8198	+	23.1505i	0.565074	+	0.777757i
$887$	15.3113	−	4.97493i	0.514102	−	0.167042i	−0.0404649	−	0.999181i	$-0.512884\pi$
$887$	15.3113	−	4.97493i	0.514102	−	0.167042i	0.554567	+	0.832139i	$0.312884\pi$
$888$	−0.369114	−	0.119932i	−0.0123867	−	0.00402467i
$889$	−15.2459	+	1.99501i	−0.511331	+	0.0669106i
$890$	15.4319	+	0.318512i	0.517277	+	0.0106765i
$891$	28.6700	+	3.36174i	0.960481	+	0.112622i
$892$	29.1537			0.976140
$893$	2.64873	+	1.92441i	0.0886363	+	0.0643980i
$894$	1.07758	+	0.350127i	0.0360397	+	0.0117100i
$895$	13.7690	−	4.16173i	0.460248	−	0.139111i
$896$	−0.484188	+	2.60107i	−0.0161756	+	0.0868956i
$897$	2.82816	−	2.05478i	0.0944295	−	0.0686071i
$898$	9.58122	+	29.4880i	0.319729	+	0.984026i
$899$	13.2948	−	40.9172i	0.443407	−	1.36467i
$900$	−11.6315	−	9.20740i	−0.387717	−	0.306913i
$901$	17.9385			0.597617
$902$	−5.92843	−	29.6359i	−0.197395	−	0.986769i
$903$	−1.30202	+	1.23364i	−0.0433286	+	0.0410529i
$904$	5.28039	−	7.26783i	0.175623	−	0.241725i
$905$	8.74152	−	25.1271i	0.290578	−	0.835252i
$906$	3.04522	−	0.989451i	0.101171	−	0.0328723i
$907$	−26.6352	−	36.6602i	−0.884408	−	1.21728i	−0.975181	−	0.221411i	$-0.928934\pi$
$907$	−26.6352	−	36.6602i	−0.884408	−	1.21728i	0.0907727	−	0.995872i	$-0.471066\pi$
$908$	−6.26126	−	8.61789i	−0.207787	−	0.285995i
$909$	−0.187589	−	0.577341i	−0.00622195	−	0.0191492i
$910$	7.03355	+	15.5974i	0.233160	+	0.517049i
$911$	−21.2018	−	15.4040i	−0.702445	−	0.510356i	0.178282	−	0.983979i	$-0.442946\pi$
$911$	−21.2018	−	15.4040i	−0.702445	−	0.510356i	−0.880728	+	0.473623i	$0.842946\pi$
$912$	−0.172045			−0.00569699
$913$	40.8909	−	8.17990i	1.35329	−	0.270715i
$914$	−0.335636			−0.0111019
$915$	−2.74467	+	3.61828i	−0.0907361	+	0.119617i
$916$	−17.6603	−	5.73819i	−0.583514	−	0.189595i
$917$	11.0821	+	6.02833i	0.365963	+	0.199073i
$918$	0.967658	+	1.33187i	0.0319375	+	0.0439581i
$919$	7.12593	+	9.80800i	0.235063	+	0.323536i	0.910210	−	0.414147i	$-0.135920\pi$
$919$	7.12593	+	9.80800i	0.235063	+	0.323536i	−0.675147	+	0.737683i	$0.735920\pi$
$920$	−4.30080	−	14.2291i	−0.141793	−	0.469121i
$921$	−1.11445	−	0.362106i	−0.0367223	−	0.0119318i
$922$	0.247418	+	0.179760i	0.00814829	+	0.00592008i
$923$			12.8601i			0.423295i
$924$	1.27812	−	0.955023i	0.0420471	−	0.0314179i
$925$	−0.440373	+	10.6635i	−0.0144794	+	0.350613i
$926$	−1.18996	+	1.63783i	−0.0391044	+	0.0538225i
$927$	12.8440	−	39.5297i	0.421851	−	1.29832i
$928$	−6.22359	+	2.02217i	−0.204299	+	0.0663809i
$929$	−20.5923	−	28.3429i	−0.675612	−	0.929900i	0.324259	−	0.945968i	$-0.394885\pi$
$929$	−20.5923	−	28.3429i	−0.675612	−	0.929900i	−0.999871	+	0.0160682i	$0.994885\pi$
$930$	2.19450	−	1.52622i	0.0719604	−	0.0500466i
$931$	6.40046	−	1.70426i	0.209767	−	0.0558547i
$932$	−7.08297	+	21.7991i	−0.232010	+	0.714054i
$933$	−0.445660	+	0.613399i	−0.0145903	+	0.0200818i
$934$	24.7913			0.811195
$935$	8.11259	+	7.79879i	0.265310	+	0.255048i
$936$			8.58070i			0.280469i
$937$	−27.0839	+	37.2779i	−0.884794	+	1.21781i	0.0902759	+	0.995917i	$0.471225\pi$
$937$	−27.0839	+	37.2779i	−0.884794	+	1.21781i	−0.975070	+	0.221898i	$0.928775\pi$
$938$	−8.51468	+	4.05311i	−0.278014	+	0.132339i
$939$	0.330660	+	1.01767i	0.0107907	+	0.0332103i
$940$	4.41760	+	6.35194i	0.144086	+	0.207177i
$941$	−1.90281	+	1.38247i	−0.0620299	+	0.0450674i	−0.618368	−	0.785889i	$-0.712206\pi$
$941$	−1.90281	+	1.38247i	−0.0620299	+	0.0450674i	0.556338	+	0.830956i	$0.312206\pi$
$942$	−0.377478	−	1.16176i	−0.0122989	−	0.0378521i
$943$	−57.6137	−	18.7198i	−1.87616	−	0.609601i
$944$	−4.12497	+	5.67753i	−0.134256	+	0.184788i
$945$	−4.31754	−	4.74946i	−0.140450	−	0.154500i
$946$	−10.7826	+	6.05396i	−0.350574	+	0.196831i
$947$		−	5.40987i		−	0.175797i	−0.996129	−	0.0878985i	$-0.971985\pi$
$947$		−	5.40987i		−	0.175797i	0.996129	−	0.0878985i	$-0.0280151\pi$
$948$	−0.546755	+	0.752543i	−0.0177578	+	0.0244415i
$949$	−10.8155	+	33.2866i	−0.351085	+	1.08053i
$950$	1.27507	+	4.55599i	0.0413688	+	0.147816i
$951$	−2.81002	−	3.86766i	−0.0911211	−	0.125417i
$952$	−3.94683	−	0.734699i	−0.127917	−	0.0238117i
$953$	−10.2010	−	31.3954i	−0.330442	−	1.01700i	−0.968924	−	0.247360i	$-0.920437\pi$
$953$	−10.2010	−	31.3954i	−0.330442	−	1.01700i	0.638481	−	0.769637i	$-0.279563\pi$
$954$	−33.3583	−	10.8388i	−1.08002	−	0.350919i
$955$	20.0383	−	26.4164i	0.648426	−	0.854814i
$956$			23.9621i			0.774991i
$957$	3.58557	+	1.64825i	0.115905	+	0.0532803i
$958$	10.5522			0.340927
$959$	1.77688	+	13.5789i	0.0573784	+	0.438487i
$960$	−0.384001	−	0.133591i	−0.0123936	−	0.00431163i
$961$	−3.77760	−	11.6263i	−0.121858	−	0.375041i
$962$	4.99426	−	3.62854i	0.161021	−	0.116989i
$963$	14.0496	−	10.2076i	0.452741	−	0.328935i
$964$	−4.70706	−	14.4869i	−0.151604	−	0.466590i
$965$	2.20655	+	0.767644i	0.0710315	+	0.0247113i
$966$	−0.414941	−	3.17099i	−0.0133505	−	0.102025i
$967$	37.4895			1.20558			0.602791	−	0.797899i	$-0.294055\pi$
$967$	37.4895			1.20558			0.602791	+	0.797899i	$0.294055\pi$
$968$	10.1535	−	4.23159i	0.326346	−	0.136008i
$969$		−	0.261059i		−	0.00838643i
$970$	22.8336	−	30.1014i	0.733143	−	0.966497i
$971$	12.5801	+	4.08751i	0.403714	+	0.131174i	0.503833	−	0.863801i	$-0.331923\pi$
$971$	12.5801	+	4.08751i	0.403714	+	0.131174i	−0.100120	+	0.994975i	$0.531923\pi$
$972$	−1.49483	−	4.60060i	−0.0479466	−	0.147564i
$973$	11.1242	−	59.7595i	0.356625	−	1.91580i
$974$	11.6835	+	16.0809i	0.374363	+	0.515266i
$975$	−2.53201	+	0.708625i	−0.0810891	+	0.0226942i
$976$	3.45176	−	10.6234i	0.110488	−	0.340048i
$977$	31.0418	−	42.7254i	0.993117	−	1.36691i	0.0636620	−	0.997972i	$-0.479722\pi$
$977$	31.0418	−	42.7254i	0.993117	−	1.36691i	0.929455	−	0.368936i	$-0.120278\pi$
$978$		−	2.30408i		−	0.0736763i
$979$	20.8014	+	9.56221i	0.664817	+	0.305610i
$980$	15.6090	+	1.16602i	0.498611	+	0.0372472i
$981$	18.7126	−	25.7557i	0.597447	−	0.822315i
$982$	−30.4746	−	9.90181i	−0.972485	−	0.315980i
$983$	0.0544093	+	0.167455i	0.00173539	+	0.00534097i	0.951920	−	0.306345i	$-0.0991062\pi$
$983$	0.0544093	+	0.167455i	0.00173539	+	0.00534097i	−0.950185	+	0.311686i	$0.899106\pi$
$984$	−1.34046	+	0.973905i	−0.0427325	+	0.0310469i
$985$	−30.9008	−	44.4313i	−0.984582	−	1.41570i
$986$	−3.06841	−	9.44359i	−0.0977180	−	0.300745i
$987$	0.715429	+	1.50296i	0.0227724	+	0.0478396i
$988$	1.60850	−	2.21391i	0.0511732	−	0.0704338i
$989$			24.7860i			0.788149i
$990$	−10.3740	−	19.4044i	−0.329707	−	0.616712i
$991$	19.8724			0.631267			0.315634	−	0.948881i	$-0.397783\pi$
$991$	19.8724			0.631267			0.315634	+	0.948881i	$0.397783\pi$
$992$	−3.86442	+	5.31891i	−0.122695	+	0.168876i
$993$	0.579708	−	1.78416i	0.0183965	−	0.0566186i
$994$	10.3346	+	5.62169i	0.327792	+	0.178309i
$995$	27.3724	−	19.0368i	0.867765	−	0.603507i
$996$	−1.34377	−	1.84954i	−0.0425790	−	0.0586049i
$997$	−45.9218	+	14.9209i	−1.45436	+	0.472549i	−0.926341	−	0.376685i	$-0.877064\pi$
$997$	−45.9218	+	14.9209i	−1.45436	+	0.472549i	−0.528016	+	0.849234i	$0.677064\pi$
$998$	−1.29054	+	3.97187i	−0.0408513	+	0.125727i
$999$	−1.36121	+	1.87354i	−0.0430667	+	0.0592763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.w.b.139.12	yes	96
5.4	even	2		770.2.w.a.139.13	yes	96
7.6	odd	2	inner	770.2.w.b.139.13	yes	96
11.8	odd	10		770.2.w.a.349.12	yes	96
35.34	odd	2		770.2.w.a.139.12	✓	96
55.19	odd	10	inner	770.2.w.b.349.13	yes	96
77.41	even	10		770.2.w.a.349.13	yes	96
385.349	even	10	inner	770.2.w.b.349.12	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.w.a.139.12	✓	96	35.34	odd	2
770.2.w.a.139.13	yes	96	5.4	even	2
770.2.w.a.349.12	yes	96	11.8	odd	10
770.2.w.a.349.13	yes	96	77.41	even	10
770.2.w.b.139.12	yes	96	1.1	even	1	trivial
770.2.w.b.139.13	yes	96	7.6	odd	2	inner
770.2.w.b.349.12	yes	96	385.349	even	10	inner
770.2.w.b.349.13	yes	96	55.19	odd	10	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.0561872 + 0.172927i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.27672 - 1.83575i) q^{5} +(-0.147100 + 0.106874i) q^{6} +(-2.32414 - 1.26426i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.40030 + 1.74392i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.0561872 + 0.172927i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.27672 - 1.83575i) q^{5} +(-0.147100 + 0.106874i) q^{6} +(-2.32414 - 1.26426i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.40030 + 1.74392i) q^{9} +(0.0461423 - 2.23559i) q^{10} +(1.38526 - 3.01348i) q^{11} -0.181826 q^{12} +(1.69994 - 2.33976i) q^{13} +(-1.13715 - 2.38891i) q^{14} +(0.389186 - 0.117633i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.891897 - 1.22759i) q^{17} +(0.916835 + 2.82173i) q^{18} +(0.292395 - 0.899900i) q^{19} +(1.35138 - 1.78151i) q^{20} +(0.349212 - 0.330870i) q^{21} +(2.89198 - 1.62372i) q^{22} -6.64778i q^{23} +(-0.147100 - 0.106874i) q^{24} +(-1.73998 + 4.68748i) q^{25} +(2.75056 - 0.893710i) q^{26} +(-0.877737 + 0.637714i) q^{27} +(0.484188 - 2.60107i) q^{28} +(6.22359 - 2.02217i) q^{29} +(0.384001 + 0.133591i) q^{30} +(3.86442 - 5.31891i) q^{31} -1.00000 q^{32} +(0.443276 + 0.408868i) q^{33} -1.51739i q^{34} +(0.646396 + 5.88066i) q^{35} +(-0.916835 + 2.82173i) q^{36} +(2.03004 - 0.659601i) q^{37} +(0.765500 - 0.556169i) q^{38} +(0.309092 + 0.425429i) q^{39} +(2.14043 - 0.646952i) q^{40} +(2.81595 - 8.66660i) q^{41} +(0.476999 - 0.0624180i) q^{42} -3.72846 q^{43} +(3.29406 + 0.386249i) q^{44} +(0.136901 - 6.63287i) q^{45} +(3.90747 - 5.37817i) q^{46} +(-1.06924 + 3.29077i) q^{47} +(-0.0561872 - 0.172927i) q^{48} +(3.80327 + 5.87666i) q^{49} +(-4.16291 + 2.76951i) q^{50} +(0.262396 - 0.0852577i) q^{51} +(2.75056 + 0.893710i) q^{52} +(-6.94877 + 9.56417i) q^{53} -1.08494 q^{54} +(-7.30059 + 1.30436i) q^{55} +(1.92059 - 1.81971i) q^{56} +(0.139188 + 0.101126i) q^{57} +(6.22359 + 2.02217i) q^{58} +(6.67433 - 2.16862i) q^{59} +(0.232140 + 0.333787i) q^{60} +(-9.03683 + 6.56564i) q^{61} +(6.25276 - 2.03164i) q^{62} +(-3.37387 - 7.08774i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-6.46557 - 0.133449i) q^{65} +(0.118291 + 0.591332i) q^{66} -3.56425i q^{67} +(0.891897 - 1.22759i) q^{68} +(1.14958 + 0.373521i) q^{69} +(-2.93362 + 5.13750i) q^{70} +(-3.59738 + 2.61365i) q^{71} +(-2.40030 + 1.74392i) q^{72} +(-11.5095 + 3.73965i) q^{73} +(2.03004 + 0.659601i) q^{74} +(-0.712825 - 0.564266i) q^{75} +0.946211 q^{76} +(-7.02938 + 5.25241i) q^{77} +0.525859i q^{78} +(3.00703 - 4.13882i) q^{79} +(2.11192 + 0.734720i) q^{80} +(2.68954 + 8.27757i) q^{81} +(7.37225 - 5.35625i) q^{82} +(7.39042 + 10.1720i) q^{83} +(0.422589 + 0.229876i) q^{84} +(-1.11485 + 3.20459i) q^{85} +(-3.01639 - 2.19153i) q^{86} +1.18984i q^{87} +(2.43792 + 2.24868i) q^{88} +6.90281i q^{89} +(4.00946 - 5.28563i) q^{90} +(-6.90898 + 3.28877i) q^{91} +(6.32242 - 2.05428i) q^{92} +(0.702651 + 0.967116i) q^{93} +(-2.79930 + 2.03381i) q^{94} +(-2.02530 + 0.612153i) q^{95} +(0.0561872 - 0.172927i) q^{96} +(13.6696 + 9.93154i) q^{97} +(-0.377303 + 6.98982i) q^{98} +(8.58033 - 4.81747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9}+O(q^{10}) \) 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9	\( 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} + 28 q^{18} - 4 q^{22} + 38 q^{25} - 2 q^{28} + 6 q^{30} - 96 q^{32} + 46 q^{35} - 28 q^{36} + 10 q^{39} - 24 q^{43} - 16 q^{44} + 37 q^{49} - 8 q^{50} - 30 q^{51} + 40 q^{53} + 2 q^{56} - 20 q^{57} + 14 q^{60} + 63 q^{63} - 24 q^{64} - 40 q^{65} + 39 q^{70} - 20 q^{71} + 18 q^{72} - 16 q^{77} - 126 q^{81} + 60 q^{85} - 36 q^{86} - 14 q^{88} - 31 q^{91} - 10 q^{92} + 20 q^{93} - 44 q^{95} + 18 q^{98} + 100 q^{99}+O(q^{100}) \) 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 + 28 * q^18 - 4 * q^22 + 38 * q^25 - 2 * q^28 + 6 * q^30 - 96 * q^32 + 46 * q^35 - 28 * q^36 + 10 * q^39 - 24 * q^43 - 16 * q^44 + 37 * q^49 - 8 * q^50 - 30 * q^51 + 40 * q^53 + 2 * q^56 - 20 * q^57 + 14 * q^60 + 63 * q^63 - 24 * q^64 - 40 * q^65 + 39 * q^70 - 20 * q^71 + 18 * q^72 - 16 * q^77 - 126 * q^81 + 60 * q^85 - 36 * q^86 - 14 * q^88 - 31 * q^91 - 10 * q^92 + 20 * q^93 - 44 * q^95 + 18 * q^98 + 100 * q^99

Introduction

L-functions

Modular forms

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