LMFDB - Embedded newform 170.2.k.a.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(111,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("170.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.k (of order $8$, 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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			161.1
Root			$-0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	170.161
Dual form			170.2.k.a.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.548594 - 1.32442i) q^{3} -1.00000i q^{4} +(-0.923880 - 0.382683i) q^{5} +(-0.548594 - 1.32442i) q^{6} +(0.599456 - 0.248303i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.668179 + 0.668179i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.548594 - 1.32442i) q^{3} -1.00000i q^{4} +(-0.923880 - 0.382683i) q^{5} +(-0.548594 - 1.32442i) q^{6} +(0.599456 - 0.248303i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.668179 + 0.668179i) q^{9} +(-0.923880 + 0.382683i) q^{10} +(-1.42788 - 3.44722i) q^{11} +(-1.32442 - 0.548594i) q^{12} +4.08239i q^{13} +(0.248303 - 0.599456i) q^{14} +(-1.01367 + 1.01367i) q^{15} -1.00000 q^{16} +(3.85403 - 1.46508i) q^{17} +0.944947 q^{18} +(-3.03300 + 3.03300i) q^{19} +(-0.382683 + 0.923880i) q^{20} -0.930151i q^{21} +(-3.44722 - 1.42788i) q^{22} +(2.78470 + 6.72286i) q^{23} +(-1.32442 + 0.548594i) q^{24} +(0.707107 + 0.707107i) q^{25} +(2.88669 + 2.88669i) q^{26} +(5.22478 - 2.16417i) q^{27} +(-0.248303 - 0.599456i) q^{28} +(-1.66399 - 0.689246i) q^{29} +1.43355i q^{30} +(1.90342 - 4.59527i) q^{31} +(-0.707107 + 0.707107i) q^{32} -5.34890 q^{33} +(1.68925 - 3.76118i) q^{34} -0.648847 q^{35} +(0.668179 - 0.668179i) q^{36} +(-3.12132 + 7.53553i) q^{37} +4.28931i q^{38} +(5.40682 + 2.23958i) q^{39} +(0.382683 + 0.923880i) q^{40} +(1.78950 - 0.741235i) q^{41} +(-0.657716 - 0.657716i) q^{42} +(0.740108 + 0.740108i) q^{43} +(-3.44722 + 1.42788i) q^{44} +(-0.361616 - 0.873017i) q^{45} +(6.72286 + 2.78470i) q^{46} -4.71031i q^{47} +(-0.548594 + 1.32442i) q^{48} +(-4.65205 + 4.65205i) q^{49} +1.00000 q^{50} +(0.173918 - 5.90810i) q^{51} +4.08239 q^{52} +(-6.16799 + 6.16799i) q^{53} +(2.16417 - 5.22478i) q^{54} +3.73124i q^{55} +(-0.599456 - 0.248303i) q^{56} +(2.35309 + 5.68087i) q^{57} +(-1.66399 + 0.689246i) q^{58} +(-7.34549 - 7.34549i) q^{59} +(1.01367 + 1.01367i) q^{60} +(-3.27209 + 1.35534i) q^{61} +(-1.90342 - 4.59527i) q^{62} +(0.566454 + 0.234633i) q^{63} +1.00000i q^{64} +(1.56226 - 3.77164i) q^{65} +(-3.78224 + 3.78224i) q^{66} -3.48022 q^{67} +(-1.46508 - 3.85403i) q^{68} +10.4316 q^{69} +(-0.458804 + 0.458804i) q^{70} +(5.07933 - 12.2626i) q^{71} -0.944947i q^{72} +(-5.53701 - 2.29350i) q^{73} +(3.12132 + 7.53553i) q^{74} +(1.32442 - 0.548594i) q^{75} +(3.03300 + 3.03300i) q^{76} +(-1.71191 - 1.71191i) q^{77} +(5.40682 - 2.23958i) q^{78} +(-0.112187 - 0.270842i) q^{79} +(0.923880 + 0.382683i) q^{80} -5.27223i q^{81} +(0.741235 - 1.78950i) q^{82} +(1.75650 - 1.75650i) q^{83} -0.930151 q^{84} +(-4.12132 - 0.121320i) q^{85} +1.04667 q^{86} +(-1.82571 + 1.82571i) q^{87} +(-1.42788 + 3.44722i) q^{88} -3.59539i q^{89} +(-0.873017 - 0.361616i) q^{90} +(1.01367 + 2.44722i) q^{91} +(6.72286 - 2.78470i) q^{92} +(-5.04187 - 5.04187i) q^{93} +(-3.33070 - 3.33070i) q^{94} +(3.96281 - 1.64145i) q^{95} +(0.548594 + 1.32442i) q^{96} +(-17.7713 - 7.36110i) q^{97} +6.57900i q^{98} +(1.34927 - 3.25744i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^9	$ 8 q + 8 q^{9} + 16 q^{11} - 8 q^{12} - 8 q^{14} + 8 q^{15} - 8 q^{16} - 16 q^{18} - 16 q^{19} - 8 q^{22} + 24 q^{23} - 8 q^{24} + 8 q^{28} + 8 q^{29} - 16 q^{31} - 16 q^{33} + 8 q^{36} - 8 q^{37} + 32 q^{39} - 8 q^{43} - 8 q^{44} - 16 q^{45} - 8 q^{46} - 8 q^{49} + 8 q^{50} - 40 q^{51} + 24 q^{52} - 8 q^{53} + 40 q^{54} + 16 q^{57} + 8 q^{58} - 40 q^{59} - 8 q^{60} - 24 q^{61} + 16 q^{62} + 8 q^{63} - 8 q^{65} + 16 q^{66} - 16 q^{69} - 8 q^{70} + 24 q^{71} - 16 q^{73} + 8 q^{74} + 8 q^{75} + 16 q^{76} + 8 q^{77} + 32 q^{78} - 8 q^{79} + 8 q^{82} + 8 q^{83} + 16 q^{84} - 16 q^{85} - 16 q^{86} + 32 q^{87} + 16 q^{88} - 8 q^{91} - 8 q^{92} - 32 q^{93} - 8 q^{94} + 16 q^{95} - 32 q^{97} + 72 q^{99}+O(q^{100}) $ 8 * q + 8 * q^9 + 16 * q^11 - 8 * q^12 - 8 * q^14 + 8 * q^15 - 8 * q^16 - 16 * q^18 - 16 * q^19 - 8 * q^22 + 24 * q^23 - 8 * q^24 + 8 * q^28 + 8 * q^29 - 16 * q^31 - 16 * q^33 + 8 * q^36 - 8 * q^37 + 32 * q^39 - 8 * q^43 - 8 * q^44 - 16 * q^45 - 8 * q^46 - 8 * q^49 + 8 * q^50 - 40 * q^51 + 24 * q^52 - 8 * q^53 + 40 * q^54 + 16 * q^57 + 8 * q^58 - 40 * q^59 - 8 * q^60 - 24 * q^61 + 16 * q^62 + 8 * q^63 - 8 * q^65 + 16 * q^66 - 16 * q^69 - 8 * q^70 + 24 * q^71 - 16 * q^73 + 8 * q^74 + 8 * q^75 + 16 * q^76 + 8 * q^77 + 32 * q^78 - 8 * q^79 + 8 * q^82 + 8 * q^83 + 16 * q^84 - 16 * q^85 - 16 * q^86 + 32 * q^87 + 16 * q^88 - 8 * q^91 - 8 * q^92 - 32 * q^93 - 8 * q^94 + 16 * q^95 - 32 * q^97 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	0.548594	−	1.32442i	0.316731	−	0.764656i	−0.682693	−	0.730706i	$-0.739191\pi$
$3$	0.548594	−	1.32442i	0.316731	−	0.764656i	0.999424	−	0.0339504i	$-0.0108088\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−0.923880	−	0.382683i	−0.413171	−	0.171141i
$5$	−0.923880	−	0.382683i	−0.413171	−	0.171141i
$6$	−0.548594	−	1.32442i	−0.223963	−	0.540694i
$7$	0.599456	−	0.248303i	0.226573	−	0.0938497i	−0.266509	−	0.963832i	$-0.585870\pi$
$7$	0.599456	−	0.248303i	0.226573	−	0.0938497i	0.493082	+	0.869983i	$0.335870\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.668179	+	0.668179i	0.222726	+	0.222726i
$10$	−0.923880	+	0.382683i	−0.292156	+	0.121015i
$11$	−1.42788	−	3.44722i	−0.430523	−	1.03937i	−0.979119	−	0.203287i	$-0.934838\pi$
$11$	−1.42788	−	3.44722i	−0.430523	−	1.03937i	0.548596	−	0.836087i	$-0.315162\pi$
$12$	−1.32442	−	0.548594i	−0.382328	−	0.158365i
$13$			4.08239i			1.13225i	0.824319	+	0.566126i	$0.191558\pi$
$13$			4.08239i			1.13225i	−0.824319	+	0.566126i	$0.808442\pi$
$14$	0.248303	−	0.599456i	0.0663617	−	0.160211i
$15$	−1.01367	+	1.01367i	−0.261728	+	0.261728i
$16$	−1.00000			−0.250000
$17$	3.85403	−	1.46508i	0.934740	−	0.355333i
$17$	3.85403	−	1.46508i	0.934740	−	0.355333i
$18$	0.944947			0.222726
$19$	−3.03300	+	3.03300i	−0.695818	+	0.695818i	−0.963506	−	0.267687i	$-0.913741\pi$
$19$	−3.03300	+	3.03300i	−0.695818	+	0.695818i	0.267687	+	0.963506i	$0.413741\pi$
$20$	−0.382683	+	0.923880i	−0.0855706	+	0.206586i
$21$		−	0.930151i		−	0.202976i
$22$	−3.44722	−	1.42788i	−0.734949	−	0.304426i
$23$	2.78470	+	6.72286i	0.580650	+	1.40181i	0.892225	+	0.451591i	$0.149143\pi$
$23$	2.78470	+	6.72286i	0.580650	+	1.40181i	−0.311575	+	0.950222i	$0.600857\pi$
$24$	−1.32442	+	0.548594i	−0.270347	+	0.111981i
$25$	0.707107	+	0.707107i	0.141421	+	0.141421i
$26$	2.88669	+	2.88669i	0.566126	+	0.566126i
$27$	5.22478	−	2.16417i	1.00551	−	0.416496i
$28$	−0.248303	−	0.599456i	−0.0469248	−	0.113287i
$29$	−1.66399	−	0.689246i	−0.308995	−	0.127990i	0.222797	−	0.974865i	$-0.428481\pi$
$29$	−1.66399	−	0.689246i	−0.308995	−	0.127990i	−0.531792	+	0.846875i	$0.678481\pi$
$30$			1.43355i			0.261728i
$31$	1.90342	−	4.59527i	0.341865	−	0.825334i	−0.655663	−	0.755054i	$-0.727611\pi$
$31$	1.90342	−	4.59527i	0.341865	−	0.825334i	0.997527	−	0.0702802i	$-0.0223893\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−5.34890			−0.931124
$34$	1.68925	−	3.76118i	0.289703	−	0.645036i
$35$	−0.648847			−0.109675
$36$	0.668179	−	0.668179i	0.111363	−	0.111363i
$37$	−3.12132	+	7.53553i	−0.513142	+	1.23883i	0.428904	+	0.903350i	$0.358900\pi$
$37$	−3.12132	+	7.53553i	−0.513142	+	1.23883i	−0.942046	+	0.335484i	$0.891100\pi$
$38$			4.28931i			0.695818i
$39$	5.40682	+	2.23958i	0.865783	+	0.358619i
$40$	0.382683	+	0.923880i	0.0605076	+	0.146078i
$41$	1.78950	−	0.741235i	0.279473	−	0.115761i	−0.238544	−	0.971132i	$-0.576670\pi$
$41$	1.78950	−	0.741235i	0.279473	−	0.115761i	0.518017	+	0.855370i	$0.326670\pi$
$42$	−0.657716	−	0.657716i	−0.101488	−	0.101488i
$43$	0.740108	+	0.740108i	0.112865	+	0.112865i	0.761284	−	0.648419i	$-0.224569\pi$
$43$	0.740108	+	0.740108i	0.112865	+	0.112865i	−0.648419	+	0.761284i	$0.724569\pi$
$44$	−3.44722	+	1.42788i	−0.519687	+	0.215262i
$45$	−0.361616	−	0.873017i	−0.0539065	−	0.130142i
$46$	6.72286	+	2.78470i	0.991231	+	0.410581i
$47$		−	4.71031i		−	0.687070i	−0.939140	−	0.343535i	$-0.888376\pi$
$47$		−	4.71031i		−	0.687070i	0.939140	−	0.343535i	$-0.111624\pi$
$48$	−0.548594	+	1.32442i	−0.0791827	+	0.191164i
$49$	−4.65205	+	4.65205i	−0.664579	+	0.664579i
$50$	1.00000			0.141421
$51$	0.173918	−	5.90810i	0.0243534	−	0.827300i
$52$	4.08239			0.566126
$53$	−6.16799	+	6.16799i	−0.847239	+	0.847239i	−0.989788	−	0.142549i	$-0.954470\pi$
$53$	−6.16799	+	6.16799i	−0.847239	+	0.847239i	0.142549	+	0.989788i	$0.454470\pi$
$54$	2.16417	−	5.22478i	0.294507	−	0.711003i
$55$			3.73124i			0.503120i
$56$	−0.599456	−	0.248303i	−0.0801057	−	0.0331809i
$57$	2.35309	+	5.68087i	0.311675	+	0.752449i
$58$	−1.66399	+	0.689246i	−0.218492	+	0.0905025i
$59$	−7.34549	−	7.34549i	−0.956301	−	0.956301i	0.0427829	−	0.999084i	$-0.486378\pi$
$59$	−7.34549	−	7.34549i	−0.956301	−	0.956301i	−0.999084	+	0.0427829i	$0.986378\pi$
$60$	1.01367	+	1.01367i	0.130864	+	0.130864i
$61$	−3.27209	+	1.35534i	−0.418948	+	0.173534i	−0.582191	−	0.813052i	$-0.697805\pi$
$61$	−3.27209	+	1.35534i	−0.418948	+	0.173534i	0.163243	+	0.986586i	$0.447805\pi$
$62$	−1.90342	−	4.59527i	−0.241735	−	0.583599i
$63$	0.566454	+	0.234633i	0.0713666	+	0.0295610i
$64$			1.00000i			0.125000i
$65$	1.56226	−	3.77164i	0.193775	−	0.467814i
$66$	−3.78224	+	3.78224i	−0.465562	+	0.465562i
$67$	−3.48022			−0.425176			−0.212588	−	0.977142i	$-0.568189\pi$
$67$	−3.48022			−0.425176			−0.212588	+	0.977142i	$0.568189\pi$
$68$	−1.46508	−	3.85403i	−0.177667	−	0.467370i
$69$	10.4316			1.25581
$70$	−0.458804	+	0.458804i	−0.0548376	+	0.0548376i
$71$	5.07933	−	12.2626i	0.602805	−	1.45530i	−0.267876	−	0.963453i	$-0.586322\pi$
$71$	5.07933	−	12.2626i	0.602805	−	1.45530i	0.870681	−	0.491847i	$-0.163678\pi$
$72$		−	0.944947i		−	0.111363i
$73$	−5.53701	−	2.29350i	−0.648057	−	0.268434i	0.0343459	−	0.999410i	$-0.489065\pi$
$73$	−5.53701	−	2.29350i	−0.648057	−	0.268434i	−0.682403	+	0.730976i	$0.739065\pi$
$74$	3.12132	+	7.53553i	0.362846	+	0.875988i
$75$	1.32442	−	0.548594i	0.152931	−	0.0633462i
$76$	3.03300	+	3.03300i	0.347909	+	0.347909i
$77$	−1.71191	−	1.71191i	−0.195090	−	0.195090i
$78$	5.40682	−	2.23958i	0.612201	−	0.253582i
$79$	−0.112187	−	0.270842i	−0.0126220	−	0.0304721i	0.917443	−	0.397867i	$-0.130250\pi$
$79$	−0.112187	−	0.270842i	−0.0126220	−	0.0304721i	−0.930065	+	0.367395i	$0.880250\pi$
$80$	0.923880	+	0.382683i	0.103293	+	0.0427853i
$81$		−	5.27223i		−	0.585804i
$82$	0.741235	−	1.78950i	0.0818557	−	0.197617i
$83$	1.75650	−	1.75650i	0.192801	−	0.192801i	−0.604104	−	0.796905i	$-0.706469\pi$
$83$	1.75650	−	1.75650i	0.192801	−	0.192801i	0.796905	+	0.604104i	$0.206469\pi$
$84$	−0.930151			−0.101488
$85$	−4.12132	−	0.121320i	−0.447020	−	0.0131590i
$86$	1.04667			0.112865
$87$	−1.82571	+	1.82571i	−0.195736	+	0.195736i
$88$	−1.42788	+	3.44722i	−0.152213	+	0.367474i
$89$		−	3.59539i		−	0.381110i	−0.981676	−	0.190555i	$-0.938971\pi$
$89$		−	3.59539i		−	0.381110i	0.981676	−	0.190555i	$-0.0610288\pi$
$90$	−0.873017	−	0.361616i	−0.0920241	−	0.0381176i
$91$	1.01367	+	2.44722i	0.106261	+	0.256538i
$92$	6.72286	−	2.78470i	0.700906	−	0.290325i
$93$	−5.04187	−	5.04187i	−0.522818	−	0.522818i
$94$	−3.33070	−	3.33070i	−0.343535	−	0.343535i
$95$	3.96281	−	1.64145i	0.406575	−	0.168409i
$96$	0.548594	+	1.32442i	0.0559907	+	0.135173i
$97$	−17.7713	−	7.36110i	−1.80440	−	0.747406i	−0.984616	−	0.174731i	$-0.944094\pi$
$97$	−17.7713	−	7.36110i	−1.80440	−	0.747406i	−0.819782	−	0.572675i	$-0.805906\pi$
$98$			6.57900i			0.664579i
$99$	1.34927	−	3.25744i	0.135607	−	0.327385i
$100$	0.707107	−	0.707107i	0.0707107	−	0.0707107i
$101$	−9.83938			−0.979055			−0.489527	−	0.871988i	$-0.662831\pi$
$101$	−9.83938			−0.979055			−0.489527	+	0.871988i	$0.662831\pi$
$102$	−4.05468	−	4.30064i	−0.401473	−	0.425826i
$103$	5.96722			0.587968			0.293984	−	0.955810i	$-0.405019\pi$
$103$	5.96722			0.587968			0.293984	+	0.955810i	$0.405019\pi$
$104$	2.88669	−	2.88669i	0.283063	−	0.283063i
$105$	−0.355953	+	0.859348i	−0.0347375	+	0.0838637i
$106$			8.72286i			0.847239i
$107$	5.02349	+	2.08080i	0.485640	+	0.201158i	0.612049	−	0.790820i	$-0.290345\pi$
$107$	5.02349	+	2.08080i	0.485640	+	0.201158i	−0.126410	+	0.991978i	$0.540345\pi$
$108$	−2.16417	−	5.22478i	−0.208248	−	0.502755i
$109$	15.0972	−	6.25345i	1.44605	−	0.598972i	0.484790	−	0.874631i	$-0.338896\pi$
$109$	15.0972	−	6.25345i	1.44605	−	0.598972i	0.961256	+	0.275659i	$0.0888960\pi$
$110$	2.63838	+	2.63838i	0.251560	+	0.251560i
$111$	8.26790	+	8.26790i	0.784754	+	0.784754i
$112$	−0.599456	+	0.248303i	−0.0566433	+	0.0234624i
$113$	−0.953472	−	2.30188i	−0.0896951	−	0.216543i	0.872666	−	0.488318i	$-0.162389\pi$
$113$	−0.953472	−	2.30188i	−0.0896951	−	0.216543i	−0.962361	+	0.271775i	$0.912389\pi$
$114$	5.68087	+	2.35309i	0.532062	+	0.220387i
$115$		−	7.27677i		−	0.678562i
$116$	−0.689246	+	1.66399i	−0.0639949	+	0.154497i
$117$	−2.72777	+	2.72777i	−0.252182	+	0.252182i
$118$	−10.3881			−0.956301
$119$	1.94654	−	1.83522i	0.178439	−	0.168234i
$120$	1.43355			0.130864
$121$	−2.06627	+	2.06627i	−0.187843	+	0.187843i
$122$	−1.35534	+	3.27209i	−0.122707	+	0.296241i
$123$		−	2.77669i		−	0.250366i
$124$	−4.59527	−	1.90342i	−0.412667	−	0.170932i
$125$	−0.382683	−	0.923880i	−0.0342282	−	0.0826343i
$126$	0.566454	−	0.234633i	0.0504638	−	0.0209028i
$127$	6.36642	+	6.36642i	0.564928	+	0.564928i	0.930703	−	0.365775i	$-0.119196\pi$
$127$	6.36642	+	6.36642i	0.564928	+	0.564928i	−0.365775	+	0.930703i	$0.619196\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	1.38624	−	0.574198i	0.122051	−	0.0505553i
$130$	−1.56226	−	3.77164i	−0.137020	−	0.330795i
$131$	−14.6940	−	6.08646i	−1.28382	−	0.531777i	−0.366684	−	0.930346i	$-0.619507\pi$
$131$	−14.6940	−	6.08646i	−1.28382	−	0.531777i	−0.917138	+	0.398569i	$0.869507\pi$
$132$			5.34890i			0.465562i
$133$	−1.06505	+	2.57125i	−0.0923514	+	0.222956i
$134$	−2.46088	+	2.46088i	−0.212588	+	0.212588i
$135$	−5.65526			−0.486727
$136$	−3.76118	−	1.68925i	−0.322518	−	0.144852i
$137$	22.9252			1.95864			0.979318	−	0.202328i	$-0.0648507\pi$
$137$	22.9252			1.95864			0.979318	+	0.202328i	$0.0648507\pi$
$138$	7.37624	−	7.37624i	0.627907	−	0.627907i
$139$	−4.40508	+	10.6348i	−0.373634	+	0.902032i	0.619494	+	0.785001i	$0.287338\pi$
$139$	−4.40508	+	10.6348i	−0.373634	+	0.902032i	−0.993128	+	0.117031i	$0.962662\pi$
$140$			0.648847i			0.0548376i
$141$	−6.23845	−	2.58405i	−0.525372	−	0.217616i
$142$	−5.07933	−	12.2626i	−0.426248	−	1.02905i
$143$	14.0729	−	5.82918i	1.17683	−	0.487460i
$144$	−0.668179	−	0.668179i	−0.0556816	−	0.0556816i
$145$	1.27356	+	1.27356i	0.105764	+	0.105764i
$146$	−5.53701	+	2.29350i	−0.458246	+	0.189812i
$147$	3.60920	+	8.71338i	0.297682	+	0.718667i
$148$	7.53553	+	3.12132i	0.619417	+	0.256571i
$149$			13.8251i			1.13260i	0.824200	+	0.566299i	$0.191625\pi$
$149$			13.8251i			1.13260i	−0.824200	+	0.566299i	$0.808375\pi$
$150$	0.548594	−	1.32442i	0.0447925	−	0.108139i
$151$	−12.9700	+	12.9700i	−1.05549	+	1.05549i	−0.0571190	+	0.998367i	$0.518191\pi$
$151$	−12.9700	+	12.9700i	−1.05549	+	1.05549i	−0.998367	+	0.0571190i	$0.981809\pi$
$152$	4.28931			0.347909
$153$	3.55411	+	1.59625i	0.287333	+	0.129049i
$154$	−2.42100			−0.195090
$155$	−3.51706	+	3.51706i	−0.282497	+	0.282497i
$156$	2.23958	−	5.40682i	0.179310	−	0.432892i
$157$			17.5326i			1.39926i	0.714507	+	0.699629i	$0.246651\pi$
$157$			17.5326i			1.39926i	−0.714507	+	0.699629i	$0.753349\pi$
$158$	−0.270842	−	0.112187i	−0.0215470	−	0.00892508i
$159$	4.78531	+	11.5528i	0.379500	+	0.916193i
$160$	0.923880	−	0.382683i	0.0730391	−	0.0302538i
$161$	3.33861	+	3.33861i	0.263119	+	0.263119i
$162$	−3.72803	−	3.72803i	−0.292902	−	0.292902i
$163$	7.95590	−	3.29544i	0.623154	−	0.258119i	−0.0486872	−	0.998814i	$-0.515504\pi$
$163$	7.95590	−	3.29544i	0.623154	−	0.258119i	0.671841	+	0.740695i	$0.265504\pi$
$164$	−0.741235	−	1.78950i	−0.0578807	−	0.139736i
$165$	4.94174	+	2.04694i	0.384714	+	0.159354i
$166$		−	2.48406i		−	0.192801i
$167$	−4.24877	+	10.2574i	−0.328780	+	0.793744i	0.669904	+	0.742448i	$0.266335\pi$
$167$	−4.24877	+	10.2574i	−0.328780	+	0.793744i	−0.998683	+	0.0512964i	$0.983665\pi$
$168$	−0.657716	+	0.657716i	−0.0507439	+	0.0507439i
$169$	−3.66593			−0.281994
$170$	−3.00000	+	2.82843i	−0.230089	+	0.216930i
$171$	−4.05317			−0.309954
$172$	0.740108	−	0.740108i	0.0564327	−	0.0564327i
$173$	5.86377	−	14.1564i	0.445814	−	1.07629i	−0.528061	−	0.849207i	$-0.677081\pi$
$173$	5.86377	−	14.1564i	0.445814	−	1.07629i	0.973875	−	0.227085i	$-0.0729194\pi$
$174$			2.58194i			0.195736i
$175$	0.599456	+	0.248303i	0.0453146	+	0.0187699i
$176$	1.42788	+	3.44722i	0.107631	+	0.259844i
$177$	−13.7582	+	5.69885i	−1.03413	+	0.428352i
$178$	−2.54232	−	2.54232i	−0.190555	−	0.190555i
$179$	−7.20533	−	7.20533i	−0.538551	−	0.538551i	0.384552	−	0.923103i	$-0.374356\pi$
$179$	−7.20533	−	7.20533i	−0.538551	−	0.538551i	−0.923103	+	0.384552i	$0.874356\pi$
$180$	−0.873017	+	0.361616i	−0.0650709	+	0.0269532i
$181$	5.00086	+	12.0731i	0.371711	+	0.897390i	0.993461	+	0.114174i	$0.0364221\pi$
$181$	5.00086	+	12.0731i	0.371711	+	0.897390i	−0.621750	+	0.783216i	$0.713578\pi$
$182$	2.44722	+	1.01367i	0.181400	+	0.0751382i
$183$			5.07717i			0.375315i
$184$	2.78470	−	6.72286i	0.205291	−	0.495616i
$185$	5.76745	−	5.76745i	0.424031	−	0.424031i
$186$	−7.13028			−0.522818
$187$	−10.5535	−	11.1937i	−0.771751	−	0.818566i
$188$	−4.71031			−0.343535
$189$	2.59466	−	2.59466i	0.188733	−	0.188733i
$190$	1.64145	−	3.96281i	0.119083	−	0.287492i
$191$			19.7531i			1.42929i	0.699489	+	0.714644i	$0.253411\pi$
$191$			19.7531i			1.42929i	−0.699489	+	0.714644i	$0.746589\pi$
$192$	1.32442	+	0.548594i	0.0955820	+	0.0395914i
$193$	3.96501	+	9.57238i	0.285408	+	0.689035i	0.999944	−	0.0105631i	$-0.00336239\pi$
$193$	3.96501	+	9.57238i	0.285408	+	0.689035i	−0.714537	+	0.699598i	$0.753362\pi$
$194$	−17.7713	+	7.36110i	−1.27590	+	0.528496i
$195$	−4.13820	−	4.13820i	−0.296342	−	0.296342i
$196$	4.65205	+	4.65205i	0.332290	+	0.332290i
$197$	15.4145	−	6.38489i	1.09824	−	0.454904i	0.241365	−	0.970434i	$-0.422405\pi$
$197$	15.4145	−	6.38489i	1.09824	−	0.454904i	0.856871	+	0.515530i	$0.172405\pi$
$198$	−1.34927	−	3.25744i	−0.0958888	−	0.231496i
$199$	−8.75167	−	3.62506i	−0.620389	−	0.256974i	0.0502741	−	0.998735i	$-0.483991\pi$
$199$	−8.75167	−	3.62506i	−0.620389	−	0.256974i	−0.670663	+	0.741762i	$0.733991\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−1.90923	+	4.60928i	−0.134666	+	0.325114i
$202$	−6.95749	+	6.95749i	−0.489527	+	0.489527i
$203$	−1.16863			−0.0820217
$204$	−5.90810	−	0.173918i	−0.413650	−	0.0121767i
$205$	−1.93694			−0.135282
$206$	4.21946	−	4.21946i	0.293984	−	0.293984i
$207$	−2.63139	+	6.35275i	−0.182894	+	0.441546i
$208$		−	4.08239i		−	0.283063i
$209$	14.7862	+	6.12464i	1.02278	+	0.423650i
$210$	0.355953	+	0.859348i	0.0245631	+	0.0593006i
$211$	23.2236	−	9.61954i	1.59878	−	0.662236i	0.607538	−	0.794291i	$-0.292157\pi$
$211$	23.2236	−	9.61954i	1.59878	−	0.662236i	0.991242	+	0.132054i	$0.0421573\pi$
$212$	6.16799	+	6.16799i	0.423619	+	0.423619i
$213$	−13.4544	−	13.4544i	−0.921878	−	0.921878i
$214$	5.02349	−	2.08080i	0.343399	−	0.142241i
$215$	−0.400544	−	0.966998i	−0.0273169	−	0.0659487i
$216$	−5.22478	−	2.16417i	−0.355501	−	0.147253i
$217$		−	3.22729i		−	0.219082i
$218$	6.25345	−	15.0972i	0.423537	−	1.02251i
$219$	−6.07514	+	6.07514i	−0.410520	+	0.410520i
$220$	3.73124			0.251560
$221$	5.98101	+	15.7337i	0.402326	+	1.05836i
$222$	11.6926			0.784754
$223$	13.4826	−	13.4826i	0.902859	−	0.902859i	−0.0928234	−	0.995683i	$-0.529589\pi$
$223$	13.4826	−	13.4826i	0.902859	−	0.902859i	0.995683	+	0.0928234i	$0.0295892\pi$
$224$	−0.248303	+	0.599456i	−0.0165904	+	0.0400529i
$225$			0.944947i			0.0629965i
$226$	−2.30188	−	0.953472i	−0.153119	−	0.0634240i
$227$	−1.53539	−	3.70676i	−0.101907	−	0.246026i	0.864700	−	0.502289i	$-0.167509\pi$
$227$	−1.53539	−	3.70676i	−0.101907	−	0.246026i	−0.966607	+	0.256263i	$0.917509\pi$
$228$	5.68087	−	2.35309i	0.376224	−	0.155837i
$229$	−12.1237	−	12.1237i	−0.801154	−	0.801154i	0.182122	−	0.983276i	$-0.441704\pi$
$229$	−12.1237	−	12.1237i	−0.801154	−	0.801154i	−0.983276	+	0.182122i	$0.941704\pi$
$230$	−5.14545	−	5.14545i	−0.339281	−	0.339281i
$231$	−3.20643	+	1.32815i	−0.210968	+	0.0873857i
$232$	0.689246	+	1.66399i	0.0452512	+	0.109246i
$233$	−17.4907	−	7.24486i	−1.14585	−	0.474627i	−0.272710	−	0.962096i	$-0.587920\pi$
$233$	−17.4907	−	7.24486i	−1.14585	−	0.474627i	−0.873140	+	0.487469i	$0.837920\pi$
$234$			3.85765i			0.252182i
$235$	−1.80256	+	4.35176i	−0.117586	+	0.283878i
$236$	−7.34549	+	7.34549i	−0.478151	+	0.478151i
$237$	−0.420255			−0.0272985
$238$	0.0787183	−	2.67411i	0.00510255	−	0.173336i
$239$	−25.1215			−1.62498			−0.812488	−	0.582978i	$-0.801888\pi$
$239$	−25.1215			−1.62498			−0.812488	+	0.582978i	$0.801888\pi$
$240$	1.01367	−	1.01367i	0.0654321	−	0.0654321i
$241$	2.29117	−	5.53137i	0.147587	−	0.356307i	−0.832746	−	0.553655i	$-0.813233\pi$
$241$	2.29117	−	5.53137i	0.147587	−	0.356307i	0.980334	+	0.197348i	$0.0632328\pi$
$242$			2.92214i			0.187843i
$243$	8.69167	+	3.60021i	0.557571	+	0.230953i
$244$	1.35534	+	3.27209i	0.0867670	+	0.209474i
$245$	6.07820	−	2.51767i	0.388322	−	0.160848i
$246$	−1.96342	−	1.96342i	−0.125183	−	0.125183i
$247$	−12.3819	−	12.3819i	−0.787842	−	0.787842i
$248$	−4.59527	+	1.90342i	−0.291800	+	0.120867i
$249$	−1.36274	−	3.28995i	−0.0863603	−	0.208492i
$250$	−0.923880	−	0.382683i	−0.0584313	−	0.0242030i
$251$		−	25.4489i		−	1.60632i	−0.595763	−	0.803160i	$-0.703150\pi$
$251$		−	25.4489i		−	1.60632i	0.595763	−	0.803160i	$-0.296850\pi$
$252$	0.234633	−	0.566454i	0.0147805	−	0.0356833i
$253$	19.1989	−	19.1989i	1.20703	−	1.20703i
$254$	9.00347			0.564928
$255$	−2.42161	+	5.39182i	−0.151647	+	0.337649i
$256$	1.00000			0.0625000
$257$	17.5824	−	17.5824i	1.09676	−	1.09676i	0.101975	−	0.994787i	$-0.467484\pi$
$257$	17.5824	−	17.5824i	1.09676	−	1.09676i	0.994787	−	0.101975i	$-0.0325161\pi$
$258$	0.574198	−	1.38624i	0.0357480	−	0.0863033i
$259$			5.29226i			0.328845i
$260$	−3.77164	−	1.56226i	−0.233907	−	0.0968875i
$261$	−0.651302	−	1.57238i	−0.0403146	−	0.0973279i
$262$	−14.6940	+	6.08646i	−0.907799	+	0.376023i
$263$	3.88755	+	3.88755i	0.239717	+	0.239717i	0.816733	−	0.577016i	$-0.195783\pi$
$263$	3.88755	+	3.88755i	0.239717	+	0.239717i	−0.577016	+	0.816733i	$0.695783\pi$
$264$	3.78224	+	3.78224i	0.232781	+	0.232781i
$265$	8.05887	−	3.33809i	0.495052	−	0.205057i
$266$	1.06505	+	2.57125i	0.0653023	+	0.157654i
$267$	−4.76181	−	1.97241i	−0.291418	−	0.120709i
$268$			3.48022i			0.212588i
$269$	3.47034	−	8.37815i	0.211591	−	0.510825i	−0.782077	−	0.623181i	$-0.785840\pi$
$269$	3.47034	−	8.37815i	0.211591	−	0.510825i	0.993668	+	0.112357i	$0.0358399\pi$
$270$	−3.99887	+	3.99887i	−0.243364	+	0.243364i
$271$	26.0766			1.58404			0.792020	−	0.610496i	$-0.209030\pi$
$271$	26.0766			1.58404			0.792020	+	0.610496i	$0.209030\pi$
$272$	−3.85403	+	1.46508i	−0.233685	+	0.0888333i
$273$	3.79724			0.229820
$274$	16.2106	−	16.2106i	0.979318	−	0.979318i
$275$	1.42788	−	3.44722i	0.0861046	−	0.207875i
$276$		−	10.4316i		−	0.627907i
$277$	−2.31159	−	0.957491i	−0.138890	−	0.0575300i	0.312156	−	0.950031i	$-0.398949\pi$
$277$	−2.31159	−	0.957491i	−0.138890	−	0.0575300i	−0.451046	+	0.892501i	$0.648949\pi$
$278$	4.40508	+	10.6348i	0.264199	+	0.637833i
$279$	4.34228	−	1.79863i	0.259966	−	0.107681i
$280$	0.458804	+	0.458804i	0.0274188	+	0.0274188i
$281$	8.22652	+	8.22652i	0.490753	+	0.490753i	0.908543	−	0.417791i	$-0.137195\pi$
$281$	8.22652	+	8.22652i	0.490753	+	0.490753i	−0.417791	+	0.908543i	$0.637195\pi$
$282$	−6.23845	+	2.58405i	−0.371494	+	0.153878i
$283$	−10.3720	−	25.0401i	−0.616549	−	1.48848i	−0.855686	−	0.517495i	$-0.826865\pi$
$283$	−10.3720	−	25.0401i	−0.616549	−	1.48848i	0.239137	−	0.970986i	$-0.423135\pi$
$284$	−12.2626	−	5.07933i	−0.727650	−	0.301403i
$285$		−	6.14892i		−	0.364231i
$286$	5.82918	−	14.0729i	0.344687	−	0.832147i
$287$	0.888676	−	0.888676i	0.0524569	−	0.0524569i
$288$	−0.944947			−0.0556816
$289$	12.7071	−	11.2929i	0.747477	−	0.664288i
$290$	1.80109			0.105764
$291$	−19.4984	+	19.4984i	−1.14302	+	1.14302i
$292$	−2.29350	+	5.53701i	−0.134217	+	0.324029i
$293$			19.1754i			1.12024i	0.828413	+	0.560118i	$0.189244\pi$
$293$			19.1754i			1.12024i	−0.828413	+	0.560118i	$0.810756\pi$
$294$	8.71338	+	3.60920i	0.508175	+	0.210493i
$295$	3.97535	+	9.59735i	0.231454	+	0.558779i
$296$	7.53553	−	3.12132i	0.437994	−	0.181423i
$297$	−14.9208	−	14.9208i	−0.865790	−	0.865790i
$298$	9.77583	+	9.77583i	0.566299	+	0.566299i
$299$	−27.4453	+	11.3682i	−1.58721	+	0.657442i
$300$	−0.548594	−	1.32442i	−0.0316731	−	0.0764656i
$301$	0.627434	+	0.259892i	0.0361647	+	0.0149799i
$302$			18.3424i			1.05549i
$303$	−5.39782	+	13.0315i	−0.310097	+	0.748640i
$304$	3.03300	−	3.03300i	0.173955	−	0.173955i
$305$	3.54168			0.202796
$306$	3.64186	−	1.38442i	0.208191	−	0.0791420i
$307$	8.72029			0.497693			0.248847	−	0.968543i	$-0.419949\pi$
$307$	8.72029			0.497693			0.248847	+	0.968543i	$0.419949\pi$
$308$	−1.71191	+	1.71191i	−0.0975450	+	0.0975450i
$309$	3.27358	−	7.90313i	0.186228	−	0.449593i
$310$			4.97388i			0.282497i
$311$	−15.5804	−	6.45361i	−0.883483	−	0.365951i	−0.105636	−	0.994405i	$-0.533688\pi$
$311$	−15.5804	−	6.45361i	−0.883483	−	0.365951i	−0.777847	+	0.628454i	$0.783688\pi$
$312$	−2.23958	−	5.40682i	−0.126791	−	0.306101i
$313$	−6.87302	+	2.84690i	−0.388486	+	0.160916i	−0.568373	−	0.822771i	$-0.692427\pi$
$313$	−6.87302	+	2.84690i	−0.388486	+	0.160916i	0.179887	+	0.983687i	$0.442427\pi$
$314$	12.3975	+	12.3975i	0.699629	+	0.699629i
$315$	−0.433546	−	0.433546i	−0.0244275	−	0.0244275i
$316$	−0.270842	+	0.112187i	−0.0152361	+	0.00631098i
$317$	−0.493794	−	1.19212i	−0.0277342	−	0.0669563i	0.909406	−	0.415910i	$-0.136537\pi$
$317$	−0.493794	−	1.19212i	−0.0277342	−	0.0669563i	−0.937140	+	0.348954i	$0.886537\pi$
$318$	11.5528	+	4.78531i	0.647846	+	0.268347i
$319$			6.72029i			0.376264i
$320$	0.382683	−	0.923880i	0.0213927	−	0.0516464i
$321$	5.51172	−	5.51172i	0.307634	−	0.307634i
$322$	4.72151			0.263119
$323$	−7.24571	+	16.1329i	−0.403162	+	0.897656i
$324$	−5.27223			−0.292902
$325$	−2.88669	+	2.88669i	−0.160125	+	0.160125i
$326$	3.29544	−	7.95590i	0.182518	−	0.440636i
$327$		−	23.4256i		−	1.29544i
$328$	−1.78950	−	0.741235i	−0.0988086	−	0.0409278i
$329$	−1.16958	−	2.82363i	−0.0644813	−	0.155672i
$330$	4.94174	−	2.04694i	0.272034	−	0.112680i
$331$	−5.13820	−	5.13820i	−0.282421	−	0.282421i	0.551653	−	0.834074i	$-0.313997\pi$
$331$	−5.13820	−	5.13820i	−0.282421	−	0.282421i	−0.834074	+	0.551653i	$0.813997\pi$
$332$	−1.75650	−	1.75650i	−0.0964003	−	0.0964003i
$333$	−7.12068	+	2.94948i	−0.390211	+	0.161631i
$334$	4.24877	+	10.2574i	0.232482	+	0.561262i
$335$	3.21530	+	1.33182i	0.175671	+	0.0727652i
$336$			0.930151i			0.0507439i
$337$	−6.69206	+	16.1561i	−0.364540	+	0.880077i	0.630085	+	0.776526i	$0.283020\pi$
$337$	−6.69206	+	16.1561i	−0.364540	+	0.880077i	−0.994624	+	0.103550i	$0.966980\pi$
$338$	−2.59220	+	2.59220i	−0.140997	+	0.140997i
$339$	−3.57174			−0.193990
$340$	−0.121320	+	4.12132i	−0.00657952	+	0.223510i
$341$	−18.5587			−1.00501
$342$	−2.86603	+	2.86603i	−0.154977	+	0.154977i
$343$	−3.37170	+	8.14001i	−0.182055	+	0.439519i
$344$		−	1.04667i		−	0.0564327i
$345$	−9.63752	−	3.99199i	−0.518867	−	0.214922i
$346$	−5.86377	−	14.1564i	−0.315238	−	0.761053i
$347$	−20.1394	+	8.34203i	−1.08114	+	0.447824i	−0.850910	−	0.525312i	$-0.823949\pi$
$347$	−20.1394	+	8.34203i	−1.08114	+	0.447824i	−0.230232	+	0.973136i	$0.573949\pi$
$348$	1.82571	+	1.82571i	0.0978682	+	0.0978682i
$349$	9.34399	+	9.34399i	0.500172	+	0.500172i	0.911491	−	0.411319i	$-0.134932\pi$
$349$	9.34399	+	9.34399i	0.500172	+	0.500172i	−0.411319	+	0.911491i	$0.634932\pi$
$350$	0.599456	−	0.248303i	0.0320423	−	0.0132723i
$351$	8.83501	+	21.3296i	0.471578	+	1.13849i
$352$	3.44722	+	1.42788i	0.183737	+	0.0761064i
$353$			29.5181i			1.57109i	0.618803	+	0.785546i	$0.287618\pi$
$353$			29.5181i			1.57109i	−0.618803	+	0.785546i	$0.712382\pi$
$354$	−5.69885	+	13.7582i	−0.302890	+	0.731242i
$355$	−9.38537	+	9.38537i	−0.498124	+	0.498124i
$356$	−3.59539			−0.190555
$357$	−1.36274	−	3.58483i	−0.0721240	−	0.189729i
$358$	−10.1899			−0.538551
$359$	−5.80701	+	5.80701i	−0.306482	+	0.306482i	−0.843543	−	0.537061i	$-0.819535\pi$
$359$	−5.80701	+	5.80701i	−0.306482	+	0.306482i	0.537061	+	0.843543i	$0.319535\pi$
$360$	−0.361616	+	0.873017i	−0.0190588	+	0.0460121i
$361$			0.601802i			0.0316738i
$362$	12.0731	+	5.00086i	0.634551	+	0.262839i
$363$	1.60307	+	3.87016i	0.0841394	+	0.203130i
$364$	2.44722	−	1.01367i	0.128269	−	0.0531307i
$365$	4.23784	+	4.23784i	0.221819	+	0.221819i
$366$	3.59010	+	3.59010i	0.187657	+	0.187657i
$367$	10.0984	−	4.18290i	0.527133	−	0.218345i	−0.103214	−	0.994659i	$-0.532913\pi$
$367$	10.0984	−	4.18290i	0.527133	−	0.218345i	0.630347	+	0.776314i	$0.282913\pi$
$368$	−2.78470	−	6.72286i	−0.145162	−	0.350453i
$369$	1.69098	+	0.700428i	0.0880290	+	0.0364628i
$370$		−	8.15640i		−	0.424031i
$371$	−2.16591	+	5.22897i	−0.112448	+	0.271475i
$372$	−5.04187	+	5.04187i	−0.261409	+	0.261409i
$373$	−4.57353			−0.236808			−0.118404	−	0.992965i	$-0.537778\pi$
$373$	−4.57353			−0.236808			−0.118404	+	0.992965i	$0.537778\pi$
$374$	−15.3776	−	0.452675i	−0.795158	−	0.0234073i
$375$	−1.43355			−0.0740280
$376$	−3.33070	+	3.33070i	−0.171767	+	0.171767i
$377$	2.81377	−	6.79305i	0.144917	−	0.349860i
$378$		−	3.66940i		−	0.188733i
$379$	6.69098	+	2.77150i	0.343693	+	0.142362i	0.547851	−	0.836576i	$-0.315446\pi$
$379$	6.69098	+	2.77150i	0.343693	+	0.142362i	−0.204159	+	0.978938i	$0.565446\pi$
$380$	−1.64145	−	3.96281i	−0.0842045	−	0.203288i
$381$	11.9244	−	4.93925i	0.610906	−	0.253046i
$382$	13.9676	+	13.9676i	0.714644	+	0.714644i
$383$	−25.0497	−	25.0497i	−1.27998	−	1.27998i	−0.940677	−	0.339303i	$-0.889809\pi$
$383$	−25.0497	−	25.0497i	−1.27998	−	1.27998i	−0.339303	−	0.940677i	$-0.610191\pi$
$384$	1.32442	−	0.548594i	0.0675867	−	0.0279953i
$385$	0.926477	+	2.23671i	0.0472177	+	0.113994i
$386$	9.57238	+	3.96501i	0.487221	+	0.201814i
$387$			0.989049i			0.0502762i
$388$	−7.36110	+	17.7713i	−0.373703	+	0.902199i
$389$	23.5600	−	23.5600i	1.19454	−	1.19454i	0.218760	−	0.975779i	$-0.429799\pi$
$389$	23.5600	−	23.5600i	1.19454	−	1.19454i	0.975779	−	0.218760i	$-0.0702011\pi$
$390$	−5.85229			−0.296342
$391$	20.5818	+	21.8303i	1.04087	+	1.10401i
$392$	6.57900			0.332290
$393$	−16.1221	+	16.1221i	−0.813253	+	0.813253i
$394$	6.38489	−	15.4145i	0.321666	−	0.776570i
$395$			0.293157i			0.0147504i
$396$	−3.25744	−	1.34927i	−0.163692	−	0.0678036i
$397$	−5.13254	−	12.3910i	−0.257595	−	0.621888i	0.741184	−	0.671302i	$-0.234265\pi$
$397$	−5.13254	−	12.3910i	−0.257595	−	0.621888i	−0.998778	+	0.0494138i	$0.984265\pi$
$398$	−8.75167	+	3.62506i	−0.438682	+	0.181708i
$399$	2.82115	+	2.82115i	0.141234	+	0.141234i
$400$	−0.707107	−	0.707107i	−0.0353553	−	0.0353553i
$401$	−31.7817	+	13.1644i	−1.58710	+	0.657399i	−0.989518	−	0.144407i	$-0.953873\pi$
$401$	−31.7817	+	13.1644i	−1.58710	+	0.657399i	−0.597584	+	0.801806i	$0.703873\pi$
$402$	1.90923	+	4.60928i	0.0952236	+	0.229890i
$403$	18.7597	+	7.77051i	0.934486	+	0.387077i
$404$			9.83938i			0.489527i
$405$	−2.01760	+	4.87091i	−0.100255	+	0.242037i
$406$	−0.826346	+	0.826346i	−0.0410109	+	0.0410109i
$407$	30.4335			1.50853
$408$	−4.30064	+	4.05468i	−0.212913	+	0.200737i
$409$	37.6365			1.86101			0.930503	−	0.366283i	$-0.119370\pi$
$409$	37.6365			1.86101			0.930503	+	0.366283i	$0.119370\pi$
$410$	−1.36962	+	1.36962i	−0.0676409	+	0.0676409i
$411$	12.5767	−	30.3627i	0.620361	−	1.49768i
$412$		−	5.96722i		−	0.293984i
$413$	−6.22721	−	2.57939i	−0.306421	−	0.126924i
$414$	2.63139	+	6.35275i	0.129326	+	0.312220i
$415$	−2.29497	+	0.950609i	−0.112656	+	0.0466636i
$416$	−2.88669	−	2.88669i	−0.141531	−	0.141531i
$417$	11.6684	+	11.6684i	0.571403	+	0.571403i
$418$	14.7862	−	6.12464i	0.723216	−	0.299566i
$419$	−0.774034	−	1.86868i	−0.0378140	−	0.0912912i	0.903844	−	0.427862i	$-0.140733\pi$
$419$	−0.774034	−	1.86868i	−0.0378140	−	0.0912912i	−0.941658	+	0.336570i	$0.890733\pi$
$420$	0.859348	+	0.355953i	0.0419319	+	0.0173688i
$421$		−	34.7424i		−	1.69324i	−0.532198	−	0.846620i	$-0.678634\pi$
$421$		−	34.7424i		−	1.69324i	0.532198	−	0.846620i	$-0.321366\pi$
$422$	9.61954	−	23.2236i	0.468272	−	1.13051i
$423$	3.14733	−	3.14733i	0.153028	−	0.153028i
$424$	8.72286			0.423619
$425$	3.76118	+	1.68925i	0.182444	+	0.0819405i
$426$	−19.0273			−0.921878
$427$	−1.62494	+	1.62494i	−0.0786363	+	0.0786363i
$428$	2.08080	−	5.02349i	0.100579	−	0.242820i
$429$		−	21.8363i		−	1.05427i
$430$	−0.966998	−	0.400544i	−0.0466328	−	0.0193159i
$431$	9.13585	+	22.0559i	0.440059	+	1.06240i	0.975928	+	0.218094i	$0.0699840\pi$
$431$	9.13585	+	22.0559i	0.440059	+	1.06240i	−0.535869	+	0.844301i	$0.680016\pi$
$432$	−5.22478	+	2.16417i	−0.251377	+	0.104124i
$433$	−0.816086	−	0.816086i	−0.0392186	−	0.0392186i	0.687226	−	0.726444i	$-0.258828\pi$
$433$	−0.816086	−	0.816086i	−0.0392186	−	0.0392186i	−0.726444	+	0.687226i	$0.758828\pi$
$434$	−2.28204	−	2.28204i	−0.109541	−	0.109541i
$435$	2.38540	−	0.988066i	0.114371	−	0.0473741i
$436$	−6.25345	−	15.0972i	−0.299486	−	0.723023i
$437$	−28.8364	−	11.9444i	−1.37943	−	0.571380i
$438$			8.59154i			0.410520i
$439$	−0.151207	+	0.365047i	−0.00721674	+	0.0174227i	−0.927447	−	0.373955i	$-0.878001\pi$
$439$	−0.151207	+	0.365047i	−0.00721674	+	0.0174227i	0.920230	+	0.391378i	$0.128001\pi$
$440$	2.63838	−	2.63838i	0.125780	−	0.125780i
$441$	−6.21681			−0.296038
$442$	15.3546	+	6.89617i	0.730344	+	0.328017i
$443$	−17.8435			−0.847772			−0.423886	−	0.905716i	$-0.639334\pi$
$443$	−17.8435			−0.847772			−0.423886	+	0.905716i	$0.639334\pi$
$444$	8.26790	−	8.26790i	0.392377	−	0.392377i
$445$	−1.37589	+	3.32170i	−0.0652237	+	0.157464i
$446$		−	19.0672i		−	0.902859i
$447$	18.3103	+	7.58437i	0.866047	+	0.358729i
$448$	0.248303	+	0.599456i	0.0117312	+	0.0283216i
$449$	−27.9884	+	11.5932i	−1.32085	+	0.547115i	−0.928032	−	0.372500i	$-0.878500\pi$
$449$	−27.9884	+	11.5932i	−1.32085	+	0.547115i	−0.392820	+	0.919615i	$0.628500\pi$
$450$	0.668179	+	0.668179i	0.0314982	+	0.0314982i
$451$	−5.11039	−	5.11039i	−0.240639	−	0.240639i
$452$	−2.30188	+	0.953472i	−0.108272	+	0.0448475i
$453$	10.0625	+	24.2931i	0.472779	+	1.14139i
$454$	−3.70676	−	1.53539i	−0.173967	−	0.0720595i
$455$		−	2.64885i		−	0.124180i
$456$	2.35309	−	5.68087i	0.110194	−	0.266031i
$457$	24.8070	−	24.8070i	1.16042	−	1.16042i	0.176037	−	0.984384i	$-0.443672\pi$
$457$	24.8070	−	24.8070i	1.16042	−	1.16042i	0.984384	−	0.176037i	$-0.0563278\pi$
$458$	−17.1455			−0.801154
$459$	16.9658	−	15.9955i	0.791895	−	0.746606i
$460$	−7.27677			−0.339281
$461$	28.4656	−	28.4656i	1.32577	−	1.32577i	0.416755	−	0.909019i	$-0.363167\pi$
$461$	28.4656	−	28.4656i	1.32577	−	1.32577i	0.909019	−	0.416755i	$-0.136833\pi$
$462$	−1.32815	+	3.20643i	−0.0617910	+	0.149177i
$463$			1.74763i			0.0812191i	0.999175	+	0.0406096i	$0.0129300\pi$
$463$			1.74763i			0.0812191i	−0.999175	+	0.0406096i	$0.987070\pi$
$464$	1.66399	+	0.689246i	0.0772487	+	0.0319975i
$465$	2.72864	+	6.58752i	0.126538	+	0.305489i
$466$	−17.4907	+	7.24486i	−0.810239	+	0.335612i
$467$	12.0812	+	12.0812i	0.559049	+	0.559049i	0.929037	−	0.369987i	$-0.120638\pi$
$467$	12.0812	+	12.0812i	0.559049	+	0.559049i	−0.369987	+	0.929037i	$0.620638\pi$
$468$	2.72777	+	2.72777i	0.126091	+	0.126091i
$469$	−2.08624	+	0.864148i	−0.0963335	+	0.0399026i
$470$	1.80256	+	4.35176i	0.0831459	+	0.200732i
$471$	23.2206	+	9.61830i	1.06995	+	0.443188i
$472$			10.3881i			0.478151i
$473$	1.49452	−	3.60810i	0.0687183	−	0.165901i
$474$	−0.297165	+	0.297165i	−0.0136492	+	0.0136492i
$475$	−4.28931			−0.196807
$476$	−1.83522	−	1.94654i	−0.0841170	−	0.0892195i
$477$	−8.24264			−0.377405
$478$	−17.7636	+	17.7636i	−0.812488	+	0.812488i
$479$	−8.00249	+	19.3197i	−0.365643	+	0.882740i	0.628810	+	0.777559i	$0.283542\pi$
$479$	−8.00249	+	19.3197i	−0.365643	+	0.882740i	−0.994453	+	0.105181i	$0.966458\pi$
$480$		−	1.43355i		−	0.0654321i
$481$	−30.7630	−	12.7425i	−1.40267	−	0.581006i
$482$	−2.29117	−	5.53137i	−0.104360	−	0.251947i
$483$	6.25327	−	2.59019i	0.284534	−	0.117858i
$484$	2.06627	+	2.06627i	0.0939213	+	0.0939213i
$485$	13.6015	+	13.6015i	0.617614	+	0.617614i
$486$	8.69167	−	3.60021i	0.394262	−	0.163309i
$487$	−6.21937	−	15.0149i	−0.281827	−	0.680390i	0.718052	−	0.695990i	$-0.245034\pi$
$487$	−6.21937	−	15.0149i	−0.281827	−	0.680390i	−0.999878	+	0.0156002i	$0.995034\pi$
$488$	3.27209	+	1.35534i	0.148121	+	0.0613535i
$489$		−	12.3448i		−	0.558253i
$490$	2.51767	−	6.07820i	0.113737	−	0.274585i
$491$	−11.5317	+	11.5317i	−0.520420	+	0.520420i	−0.917698	−	0.397278i	$-0.869955\pi$
$491$	−11.5317	+	11.5317i	−0.520420	+	0.520420i	0.397278	+	0.917698i	$0.369955\pi$
$492$	−2.77669			−0.125183
$493$	−7.42286	−	0.218509i	−0.334309	−	0.00984113i
$494$	−17.5107			−0.787842
$495$	−2.49313	+	2.49313i	−0.112058	+	0.112058i
$496$	−1.90342	+	4.59527i	−0.0854661	+	0.206334i
$497$		−	8.61209i		−	0.386305i
$498$	−3.28995	−	1.36274i	−0.147426	−	0.0610659i
$499$	−12.5137	−	30.2109i	−0.560192	−	1.35242i	−0.909613	−	0.415458i	$-0.863621\pi$
$499$	−12.5137	−	30.2109i	−0.560192	−	1.35242i	0.349420	−	0.936966i	$-0.386379\pi$
$500$	−0.923880	+	0.382683i	−0.0413171	+	0.0171141i
$501$	11.2543	+	11.2543i	0.502807	+	0.502807i
$502$	−17.9951	−	17.9951i	−0.803160	−	0.803160i
$503$	−16.2893	+	6.74725i	−0.726305	+	0.300845i	−0.715032	−	0.699091i	$-0.753588\pi$
$503$	−16.2893	+	6.74725i	−0.726305	+	0.300845i	−0.0112721	+	0.999936i	$0.503588\pi$
$504$	−0.234633	−	0.566454i	−0.0104514	−	0.0252319i
$505$	9.09040	+	3.76537i	0.404517	+	0.167557i
$506$		−	27.1514i		−	1.20703i
$507$	−2.01111	+	4.85524i	−0.0893163	+	0.215629i
$508$	6.36642	−	6.36642i	0.282464	−	0.282464i
$509$	18.7525			0.831189			0.415595	−	0.909550i	$-0.363574\pi$
$509$	18.7525			0.831189			0.415595	+	0.909550i	$0.363574\pi$
$510$	2.10025	+	5.52493i	0.0930007	+	0.244648i
$511$	−3.88868			−0.172025
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−9.28282	+	22.4107i	−0.409847	+	0.989457i
$514$		−	24.8653i		−	1.09676i
$515$	−5.51299	−	2.28356i	−0.242932	−	0.100626i
$516$	−0.574198	−	1.38624i	−0.0252776	−	0.0610256i
$517$	−16.2375	+	6.72578i	−0.714123	+	0.295799i
$518$	3.74219	+	3.74219i	0.164422	+	0.164422i
$519$	−15.5322	−	15.5322i	−0.681790	−	0.681790i
$520$	−3.77164	+	1.56226i	−0.165397	+	0.0685098i
$521$	7.60180	+	18.3524i	0.333041	+	0.804032i	0.998348	+	0.0574619i	$0.0183008\pi$
$521$	7.60180	+	18.3524i	0.333041	+	0.804032i	−0.665307	+	0.746570i	$0.731699\pi$
$522$	−1.57238	−	0.651302i	−0.0688212	−	0.0285067i
$523$		−	16.9141i		−	0.739601i	−0.929111	−	0.369801i	$-0.879426\pi$
$523$		−	16.9141i		−	0.739601i	0.929111	−	0.369801i	$-0.120574\pi$
$524$	−6.08646	+	14.6940i	−0.265888	+	0.641911i
$525$	0.657716	−	0.657716i	0.0287051	−	0.0287051i
$526$	5.49782			0.239717
$527$	0.603433	−	20.4990i	0.0262859	−	0.892948i
$528$	5.34890			0.232781
$529$	−21.1788	+	21.1788i	−0.920818	+	0.920818i
$530$	3.33809	−	8.05887i	0.144997	−	0.350055i
$531$		−	9.81620i		−	0.425987i
$532$	2.57125	+	1.06505i	0.111478	+	0.0461757i
$533$	3.02601	+	7.30544i	0.131071	+	0.316434i
$534$	−4.76181	+	1.97241i	−0.206064	+	0.0853544i
$535$	−3.84482	−	3.84482i	−0.166226	−	0.166226i
$536$	2.46088	+	2.46088i	0.106294	+	0.106294i
$537$	−13.4957	+	5.59010i	−0.582383	+	0.241231i
$538$	−3.47034	−	8.37815i	−0.149617	−	0.361208i
$539$	22.6792	+	9.39404i	0.976863	+	0.404630i
$540$			5.65526i			0.243364i
$541$	8.46190	−	20.4288i	0.363806	−	0.878304i	−0.630931	−	0.775839i	$-0.717327\pi$
$541$	8.46190	−	20.4288i	0.363806	−	0.878304i	0.994737	−	0.102465i	$-0.0326731\pi$
$542$	18.4389	−	18.4389i	0.792020	−	0.792020i
$543$	18.7334			0.803927
$544$	−1.68925	+	3.76118i	−0.0724258	+	0.161259i
$545$	−16.3410			−0.699974
$546$	2.68506	−	2.68506i	0.114910	−	0.114910i
$547$	−13.5956	+	32.8227i	−0.581307	+	1.40340i	0.310322	+	0.950632i	$0.399563\pi$
$547$	−13.5956	+	32.8227i	−0.581307	+	1.40340i	−0.891629	+	0.452767i	$0.850437\pi$
$548$		−	22.9252i		−	0.979318i
$549$	−3.09195	−	1.28073i	−0.131961	−	0.0546602i
$550$	−1.42788	−	3.44722i	−0.0608851	−	0.146990i
$551$	7.13736	−	2.95639i	0.304062	−	0.125947i
$552$	−7.37624	−	7.37624i	−0.313954	−	0.313954i
$553$	−0.134502	−	0.134502i	−0.00571960	−	0.00571960i
$554$	−2.31159	+	0.957491i	−0.0982099	+	0.0406799i
$555$	−4.47455	−	10.8025i	−0.189934	−	0.458542i
$556$	10.6348	+	4.40508i	0.451016	+	0.186817i
$557$			5.78242i			0.245009i	0.992468	+	0.122504i	$0.0390926\pi$
$557$			5.78242i			0.245009i	−0.992468	+	0.122504i	$0.960907\pi$
$558$	1.79863	−	4.34228i	0.0761422	−	0.183824i
$559$	−3.02141	+	3.02141i	−0.127792	+	0.127792i
$560$	0.648847			0.0274188
$561$	−20.6148	+	7.83654i	−0.870359	+	0.330859i
$562$	11.6341			0.490753
$563$	0.624450	−	0.624450i	0.0263174	−	0.0263174i	−0.693826	−	0.720143i	$-0.744076\pi$
$563$	0.624450	−	0.624450i	0.0263174	−	0.0263174i	0.720143	+	0.693826i	$0.244076\pi$
$564$	−2.58405	+	6.23845i	−0.108808	+	0.262686i
$565$			2.49154i			0.104820i
$566$	−25.0401	−	10.3720i	−1.05251	−	0.435966i
$567$	−1.30911	−	3.16047i	−0.0549775	−	0.132727i
$568$	−12.2626	+	5.07933i	−0.514527	+	0.213124i
$569$	−4.28648	−	4.28648i	−0.179699	−	0.179699i	0.611526	−	0.791224i	$-0.290556\pi$
$569$	−4.28648	−	4.28648i	−0.179699	−	0.179699i	−0.791224	+	0.611526i	$0.790556\pi$
$570$	−4.34795	−	4.34795i	−0.182115	−	0.182115i
$571$	20.4305	−	8.46257i	0.854988	−	0.354148i	0.0882426	−	0.996099i	$-0.471875\pi$
$571$	20.4305	−	8.46257i	0.854988	−	0.354148i	0.766745	+	0.641951i	$0.221875\pi$
$572$	−5.82918	−	14.0729i	−0.243730	−	0.588417i
$573$	26.1615	+	10.8365i	1.09291	+	0.452699i
$574$		−	1.25678i		−	0.0524569i
$575$	−2.78470	+	6.72286i	−0.116130	+	0.280363i
$576$	−0.668179	+	0.668179i	−0.0278408	+	0.0278408i
$577$	11.1949			0.466051			0.233026	−	0.972471i	$-0.425137\pi$
$577$	11.1949			0.466051			0.233026	+	0.972471i	$0.425137\pi$
$578$	1.00000	−	16.9706i	0.0415945	−	0.705882i
$579$	14.8531			0.617272
$580$	1.27356	−	1.27356i	0.0528818	−	0.0528818i
$581$	0.616800	−	1.48909i	0.0255892	−	0.0617777i
$582$			27.5749i			1.14302i
$583$	30.0696	+	12.4552i	1.24535	+	0.515843i
$584$	2.29350	+	5.53701i	0.0949058	+	0.229123i
$585$	3.56400	−	1.47626i	0.147353	−	0.0610357i
$586$	13.5590	+	13.5590i	0.560118	+	0.560118i
$587$	9.94683	+	9.94683i	0.410549	+	0.410549i	0.881930	−	0.471380i	$-0.156244\pi$
$587$	9.94683	+	9.94683i	0.410549	+	0.410549i	−0.471380	+	0.881930i	$0.656244\pi$
$588$	8.71338	−	3.60920i	0.359334	−	0.148841i
$589$	8.16437	+	19.7105i	0.336407	+	0.812158i
$590$	9.59735	+	3.97535i	0.395117	+	0.163663i
$591$		−	23.9180i		−	0.983855i
$592$	3.12132	−	7.53553i	0.128285	−	0.309709i
$593$	7.06788	−	7.06788i	0.290243	−	0.290243i	−0.546933	−	0.837176i	$-0.684205\pi$
$593$	7.06788	−	7.06788i	0.290243	−	0.290243i	0.837176	+	0.546933i	$0.184205\pi$
$594$	−21.1011			−0.865790
$595$	−2.50068	+	0.950609i	−0.102518	+	0.0389712i
$596$	13.8251			0.566299
$597$	−9.60223	+	9.60223i	−0.392993	+	0.392993i
$598$	−11.3682	+	27.4453i	−0.464882	+	1.12232i
$599$		−	17.8658i		−	0.729976i	−0.931012	−	0.364988i	$-0.881073\pi$
$599$		−	17.8658i		−	0.729976i	0.931012	−	0.364988i	$-0.118927\pi$
$600$	−1.32442	−	0.548594i	−0.0540694	−	0.0223963i
$601$	−8.37878	−	20.2282i	−0.341778	−	0.825124i	−0.997536	−	0.0701534i	$-0.977651\pi$
$601$	−8.37878	−	20.2282i	−0.341778	−	0.825124i	0.655759	−	0.754971i	$-0.272349\pi$
$602$	0.627434	−	0.259892i	0.0255723	−	0.0105924i
$603$	−2.32541	−	2.32541i	−0.0946979	−	0.0946979i
$604$	12.9700	+	12.9700i	0.527743	+	0.527743i
$605$	2.69971	−	1.11826i	0.109759	−	0.0454636i
$606$	5.39782	+	13.0315i	0.219272	+	0.529369i
$607$	−15.5502	−	6.44109i	−0.631161	−	0.261436i	0.0440850	−	0.999028i	$-0.485963\pi$
$607$	−15.5502	−	6.44109i	−0.631161	−	0.261436i	−0.675246	+	0.737592i	$0.735963\pi$
$608$		−	4.28931i		−	0.173955i
$609$	−0.641103	+	1.54776i	−0.0259788	+	0.0627184i
$610$	2.50435	−	2.50435i	0.101398	−	0.101398i
$611$	19.2293			0.777936
$612$	1.59625	−	3.55411i	0.0645245	−	0.143667i
$613$	−16.8709			−0.681408			−0.340704	−	0.940171i	$-0.610665\pi$
$613$	−16.8709			−0.681408			−0.340704	+	0.940171i	$0.610665\pi$
$614$	6.16617	−	6.16617i	0.248847	−	0.248847i
$615$	−1.06259	+	2.56533i	−0.0428479	+	0.103444i
$616$			2.42100i			0.0975450i
$617$	28.6140	+	11.8523i	1.15196	+	0.477156i	0.875189	−	0.483781i	$-0.160737\pi$
$617$	28.6140	+	11.8523i	1.15196	+	0.477156i	0.276767	+	0.960937i	$0.410737\pi$
$618$	−3.27358	−	7.90313i	−0.131683	−	0.317910i
$619$	−8.34821	+	3.45794i	−0.335543	+	0.138986i	−0.544092	−	0.839025i	$-0.683126\pi$
$619$	−8.34821	+	3.45794i	−0.335543	+	0.138986i	0.208549	+	0.978012i	$0.433126\pi$
$620$	3.51706	+	3.51706i	0.141249	+	0.141249i
$621$	29.0989	+	29.0989i	1.16770	+	1.16770i
$622$	−15.5804	+	6.45361i	−0.624717	+	0.258766i
$623$	−0.892745	−	2.15528i	−0.0357671	−	0.0863493i
$624$	−5.40682	−	2.23958i	−0.216446	−	0.0896548i
$625$			1.00000i			0.0400000i
$626$	−2.84690	+	6.87302i	−0.113785	+	0.274701i
$627$	16.2232	−	16.2232i	0.647893	−	0.647893i
$628$	17.5326			0.699629
$629$	−0.989538	+	33.6152i	−0.0394554	+	1.34032i
$630$	−0.613126			−0.0244275
$631$	−17.5159	+	17.5159i	−0.697298	+	0.697298i	−0.963827	−	0.266529i	$-0.914123\pi$
$631$	−17.5159	+	17.5159i	−0.697298	+	0.697298i	0.266529	+	0.963827i	$0.414123\pi$
$632$	−0.112187	+	0.270842i	−0.00446254	+	0.0107735i
$633$		−	36.0351i		−	1.43227i
$634$	−1.19212	−	0.493794i	−0.0473453	−	0.0196111i
$635$	−3.44548	−	8.31812i	−0.136730	−	0.330095i
$636$	11.5528	−	4.78531i	0.458097	−	0.189750i
$637$	−18.9915	−	18.9915i	−0.752471	−	0.752471i
$638$	4.75196	+	4.75196i	0.188132	+	0.188132i
$639$	11.5875	−	4.79970i	0.458394	−	0.189873i
$640$	−0.382683	−	0.923880i	−0.0151269	−	0.0365195i
$641$	28.3008	+	11.7226i	1.11781	+	0.463014i	0.863622	−	0.504140i	$-0.168190\pi$
$641$	28.3008	+	11.7226i	1.11781	+	0.463014i	0.254192	+	0.967154i	$0.418190\pi$
$642$		−	7.79475i		−	0.307634i
$643$	−0.913274	+	2.20484i	−0.0360160	+	0.0869504i	−0.940864	−	0.338784i	$-0.889984\pi$
$643$	−0.913274	+	2.20484i	−0.0360160	+	0.0869504i	0.904848	+	0.425735i	$0.139984\pi$
$644$	3.33861	−	3.33861i	0.131560	−	0.131560i
$645$	−1.50045			−0.0590802
$646$	6.28417	+	16.5311i	0.247247	+	0.650409i
$647$	−25.0527			−0.984924			−0.492462	−	0.870334i	$-0.663903\pi$
$647$	−25.0527			−0.984924			−0.492462	+	0.870334i	$0.663903\pi$
$648$	−3.72803	+	3.72803i	−0.146451	+	0.146451i
$649$	−14.8330	+	35.8100i	−0.582246	+	1.40567i
$650$			4.08239i			0.160125i
$651$	−4.27429	−	1.77047i	−0.167523	−	0.0693902i
$652$	−3.29544	−	7.95590i	−0.129059	−	0.311577i
$653$	−14.3005	+	5.92347i	−0.559623	+	0.231803i	−0.644521	−	0.764586i	$-0.722943\pi$
$653$	−14.3005	+	5.92347i	−0.559623	+	0.231803i	0.0848986	+	0.996390i	$0.472943\pi$
$654$	−16.5644	−	16.5644i	−0.647720	−	0.647720i
$655$	11.2463	+	11.2463i	0.439430	+	0.439430i
$656$	−1.78950	+	0.741235i	−0.0698682	+	0.0289404i
$657$	−2.16724	−	5.23218i	−0.0845521	−	0.204127i
$658$	−2.82363	−	1.16958i	−0.110076	−	0.0455952i
$659$			8.19841i			0.319365i	0.987168	+	0.159682i	$0.0510470\pi$
$659$			8.19841i			0.319365i	−0.987168	+	0.159682i	$0.948953\pi$
$660$	2.04694	−	4.94174i	0.0796769	−	0.192357i
$661$	−31.9638	+	31.9638i	−1.24325	+	1.24325i	−0.284601	+	0.958646i	$0.591861\pi$
$661$	−31.9638	+	31.9638i	−1.24325	+	1.24325i	−0.958646	+	0.284601i	$0.908139\pi$
$662$	−7.26651			−0.282421
$663$	24.1192	+	0.710002i	0.936711	+	0.0275742i
$664$	−2.48406			−0.0964003
$665$	1.96795	−	1.96795i	0.0763139	−	0.0763139i
$666$	−2.94948	+	7.12068i	−0.114290	+	0.275921i
$667$		−	13.1061i		−	0.507470i
$668$	10.2574	+	4.24877i	0.396872	+	0.164390i
$669$	−10.4602	−	25.2531i	−0.404413	−	0.976340i
$670$	3.21530	−	1.33182i	0.124218	−	0.0514527i
$671$	9.34432	+	9.34432i	0.360734	+	0.360734i
$672$	0.657716	+	0.657716i	0.0253720	+	0.0253720i
$673$	16.2917	−	6.74826i	0.628000	−	0.260126i	−0.0459028	−	0.998946i	$-0.514616\pi$
$673$	16.2917	−	6.74826i	0.628000	−	0.260126i	0.673903	+	0.738820i	$0.264616\pi$
$674$	6.69206	+	16.1561i	0.257768	+	0.622308i
$675$	5.22478	+	2.16417i	0.201102	+	0.0832991i
$676$			3.66593i			0.140997i
$677$	−16.1407	+	38.9670i	−0.620336	+	1.49762i	0.230974	+	0.972960i	$0.425809\pi$
$677$	−16.1407	+	38.9670i	−0.620336	+	1.49762i	−0.851310	+	0.524663i	$0.824191\pi$
$678$	−2.52560	+	2.52560i	−0.0969951	+	0.0969951i
$679$	−12.4809			−0.478972
$680$	2.82843	+	3.00000i	0.108465	+	0.115045i
$681$	−5.75163			−0.220403
$682$	−13.1230	+	13.1230i	−0.502506	+	0.502506i
$683$	4.61287	−	11.1365i	0.176507	−	0.426125i	−0.810723	−	0.585430i	$-0.800926\pi$
$683$	4.61287	−	11.1365i	0.176507	−	0.426125i	0.987229	+	0.159306i	$0.0509255\pi$
$684$			4.05317i			0.154977i
$685$	−21.1802	−	8.77311i	−0.809252	−	0.335203i
$686$	3.37170	+	8.14001i	0.128732	+	0.310787i
$687$	−22.7078	+	9.40589i	−0.866358	+	0.358857i
$688$	−0.740108	−	0.740108i	−0.0282164	−	0.0282164i
$689$	−25.1802	−	25.1802i	−0.959288	−	0.959288i
$690$	−9.63752	+	3.99199i	−0.366894	+	0.151973i
$691$	−12.0484	−	29.0873i	−0.458341	−	1.10653i	−0.969069	−	0.246791i	$-0.920624\pi$
$691$	−12.0484	−	29.0873i	−0.458341	−	1.10653i	0.510728	−	0.859743i	$-0.329376\pi$
$692$	−14.1564	−	5.86377i	−0.538146	−	0.222907i
$693$		−	2.28772i		−	0.0869033i
$694$	−8.34203	+	20.1394i	−0.316659	+	0.764483i
$695$	8.13953	−	8.13953i	0.308750	−	0.308750i
$696$	2.58194			0.0978682
$697$	5.81082	−	5.47849i	0.220100	−	0.207513i
$698$	13.2144			0.500172
$699$	−19.1905	+	19.1905i	−0.725853	+	0.725853i
$700$	0.248303	−	0.599456i	0.00938497	−	0.0226573i
$701$		−	7.86897i		−	0.297207i	−0.988897	−	0.148603i	$-0.952522\pi$
$701$		−	7.86897i		−	0.297207i	0.988897	−	0.148603i	$-0.0474778\pi$
$702$	21.3296	+	8.83501i	0.805034	+	0.333456i
$703$	−13.3883	−	32.3223i	−0.504950	−	1.21906i
$704$	3.44722	−	1.42788i	0.129922	−	0.0538154i
$705$	4.77470	+	4.77470i	0.179826	+	0.179826i
$706$	20.8725	+	20.8725i	0.785546	+	0.785546i
$707$	−5.89828	+	2.44315i	−0.221827	+	0.0918840i
$708$	5.69885	+	13.7582i	0.214176	+	0.517066i
$709$	−14.8176	−	6.13766i	−0.556487	−	0.230505i	0.0866721	−	0.996237i	$-0.472377\pi$
$709$	−14.8176	−	6.13766i	−0.556487	−	0.230505i	−0.643159	+	0.765732i	$0.722377\pi$
$710$			13.2729i			0.498124i
$711$	0.106010	−	0.255932i	0.00397570	−	0.00959818i
$712$	−2.54232	+	2.54232i	−0.0952776	+	0.0952776i
$713$	36.1938			1.35547
$714$	−3.49846	−	1.57125i	−0.130927	−	0.0588027i
$715$	−15.2324			−0.569659
$716$	−7.20533	+	7.20533i	−0.269276	+	0.269276i
$717$	−13.7815	+	33.2715i	−0.514680	+	1.24255i
$718$			8.21236i			0.306482i
$719$	−1.04991	−	0.434886i	−0.0391549	−	0.0162185i	0.363020	−	0.931781i	$-0.381746\pi$
$719$	−1.04991	−	0.434886i	−0.0391549	−	0.0162185i	−0.402175	+	0.915563i	$0.631746\pi$
$720$	0.361616	+	0.873017i	0.0134766	+	0.0325354i
$721$	3.57709	−	1.48168i	0.133218	−	0.0551806i
$722$	0.425538	+	0.425538i	0.0158369	+	0.0158369i
$723$	−6.06896	−	6.06896i	−0.225707	−	0.225707i
$724$	12.0731	−	5.00086i	0.448695	−	0.185856i
$725$	−0.689246	−	1.66399i	−0.0255980	−	0.0617990i
$726$	3.87016	+	1.60307i	0.143635	+	0.0594955i
$727$			16.5261i			0.612918i	0.951884	+	0.306459i	$0.0991442\pi$
$727$			16.5261i			0.612918i	−0.951884	+	0.306459i	$0.900856\pi$
$728$	1.01367	−	2.44722i	0.0375691	−	0.0906998i
$729$	20.7205	−	20.7205i	0.767426	−	0.767426i
$730$	5.99321			0.221819
$731$	3.93672	+	1.76809i	0.145605	+	0.0653950i
$732$	5.07717			0.187657
$733$	3.39332	−	3.39332i	0.125335	−	0.125335i	−0.641657	−	0.766992i	$-0.721753\pi$
$733$	3.39332	−	3.39332i	0.125335	−	0.125335i	0.766992	+	0.641657i	$0.221753\pi$
$734$	4.18290	−	10.0984i	0.154394	−	0.372739i
$735$		−	9.43129i		−	0.347878i
$736$	−6.72286	−	2.78470i	−0.247808	−	0.102645i
$737$	4.96934	+	11.9971i	0.183048	+	0.441917i
$738$	1.69098	−	0.700428i	0.0622459	−	0.0257831i
$739$	34.0696	+	34.0696i	1.25327	+	1.25327i	0.954246	+	0.299024i	$0.0966609\pi$
$739$	34.0696	+	34.0696i	1.25327	+	1.25327i	0.299024	+	0.954246i	$0.403339\pi$
$740$	−5.76745	−	5.76745i	−0.212016	−	0.212016i
$741$	−23.1915	+	9.60624i	−0.851962	+	0.352894i
$742$	2.16591	+	5.22897i	0.0795131	+	0.191962i
$743$	−18.2530	−	7.56064i	−0.669637	−	0.277373i	0.0218502	−	0.999761i	$-0.493044\pi$
$743$	−18.2530	−	7.56064i	−0.669637	−	0.277373i	−0.691488	+	0.722388i	$0.743044\pi$
$744$			7.13028i			0.261409i
$745$	5.29064	−	12.7727i	0.193834	−	0.467957i
$746$	−3.23397	+	3.23397i	−0.118404	+	0.118404i
$747$	2.34731			0.0858835
$748$	−11.1937	+	10.5535i	−0.409283	+	0.385876i
$749$	3.52803			0.128912
$750$	−1.01367	+	1.01367i	−0.0370140	+	0.0370140i
$751$	−6.23471	+	15.0519i	−0.227508	+	0.549253i	−0.995873	−	0.0907592i	$-0.971071\pi$
$751$	−6.23471	+	15.0519i	−0.227508	+	0.549253i	0.768365	+	0.640012i	$0.221071\pi$
$752$			4.71031i			0.171767i
$753$	−33.7051	−	13.9611i	−1.22828	−	0.508771i
$754$	−2.81377	−	6.79305i	−0.102472	−	0.247388i
$755$	16.9462	−	7.01933i	0.616734	−	0.255460i
$756$	−2.59466	−	2.59466i	−0.0943667	−	0.0943667i
$757$	11.3255	+	11.3255i	0.411631	+	0.411631i	0.882306	−	0.470676i	$-0.155990\pi$
$757$	11.3255	+	11.3255i	0.411631	+	0.411631i	−0.470676	+	0.882306i	$0.655990\pi$
$758$	6.69098	−	2.77150i	0.243027	−	0.100665i
$759$	−14.8951	−	35.9599i	−0.540657	−	1.30526i
$760$	−3.96281	−	1.64145i	−0.143746	−	0.0595416i
$761$			14.4363i			0.523314i	0.965161	+	0.261657i	$0.0842690\pi$
$761$			14.4363i			0.523314i	−0.965161	+	0.261657i	$0.915731\pi$
$762$	4.93925	−	11.9244i	0.178930	−	0.431976i
$763$	7.49734	−	7.49734i	0.271422	−	0.271422i
$764$	19.7531			0.714644
$765$	−2.67271	−	2.83484i	−0.0966322	−	0.102494i
$766$	−35.4256			−1.27998
$767$	29.9872	−	29.9872i	1.08277	−	1.08277i
$768$	0.548594	−	1.32442i	0.0197957	−	0.0477910i
$769$			55.2022i			1.99064i	0.0966274	+	0.995321i	$0.469194\pi$
$769$			55.2022i			1.99064i	−0.0966274	+	0.995321i	$0.530806\pi$
$770$	2.23671	+	0.926477i	0.0806056	+	0.0333879i
$771$	−13.6410	−	32.9322i	−0.491267	−	1.18602i
$772$	9.57238	−	3.96501i	0.344518	−	0.142704i
$773$	0.0691582	+	0.0691582i	0.00248745	+	0.00248745i	0.708349	−	0.705862i	$-0.249440\pi$
$773$	0.0691582	+	0.0691582i	0.00248745	+	0.00248745i	−0.705862	+	0.708349i	$0.749440\pi$
$774$	0.699363	+	0.699363i	0.0251381	+	0.0251381i
$775$	4.59527	−	1.90342i	0.165067	−	0.0683729i
$776$	7.36110	+	17.7713i	0.264248	+	0.637951i
$777$	7.00919	+	2.90330i	0.251453	+	0.104155i
$778$		−	33.3188i		−	1.19454i
$779$	−3.17939	+	7.67572i	−0.113913	+	0.275011i
$780$	−4.13820	+	4.13820i	−0.148171	+	0.148171i
$781$	−49.5244			−1.77212
$782$	29.9899	+	0.882820i	1.07244	+	0.0315696i
$783$	−10.1856			−0.364004
$784$	4.65205	−	4.65205i	0.166145	−	0.166145i
$785$	6.70945	−	16.1981i	0.239471	−	0.578133i
$786$			22.8001i			0.813253i
$787$	34.6262	+	14.3427i	1.23429	+	0.511260i	0.901926	−	0.431890i	$-0.142153\pi$
$787$	34.6262	+	14.3427i	1.23429	+	0.511260i	0.332365	+	0.943151i	$0.392153\pi$
$788$	−6.38489	−	15.4145i	−0.227452	−	0.549118i
$789$	7.28145	−	3.01607i	0.259226	−	0.107375i
$790$	0.207294	+	0.207294i	0.00737518	+	0.00737518i
$791$	−1.14313	−	1.14313i	−0.0406450	−	0.0406450i
$792$	−3.25744	+	1.34927i	−0.115748	+	0.0479444i
$793$	−5.53305	−	13.3580i	−0.196484	−	0.474355i
$794$	−12.3910	−	5.13254i	−0.439741	−	0.182147i
$795$		−	12.5046i		−	0.443493i
$796$	−3.62506	+	8.75167i	−0.128487	+	0.310195i
$797$	18.9951	−	18.9951i	0.672841	−	0.672841i	−0.285529	−	0.958370i	$-0.592169\pi$
$797$	18.9951	−	18.9951i	0.672841	−	0.672841i	0.958370	+	0.285529i	$0.0921694\pi$
$798$	3.98971			0.141234
$799$	−6.90097	−	18.1537i	−0.244139	−	0.642232i
$800$	−1.00000			−0.0353553
$801$	2.40236	−	2.40236i	0.0848832	−	0.0848832i
$802$	−13.1644	+	31.7817i	−0.464852	+	1.12225i
$803$			22.3621i			0.789142i
$804$	4.60928	+	1.90923i	0.162557	+	0.0673332i
$805$	−1.80684	−	4.36210i	−0.0636828	−	0.153744i
$806$	18.7597	−	7.77051i	0.660781	−	0.273705i
$807$	−9.19240	−	9.19240i	−0.323588	−	0.323588i
$808$	6.95749	+	6.95749i	0.244764	+	0.244764i
$809$	29.5789	−	12.2520i	1.03994	−	0.430757i	0.203648	−	0.979044i	$-0.434720\pi$
$809$	29.5789	−	12.2520i	1.03994	−	0.430757i	0.836290	+	0.548288i	$0.184720\pi$
$810$	2.01760	+	4.87091i	0.0708911	+	0.171146i
$811$	29.5923	+	12.2575i	1.03913	+	0.430420i	0.835998	−	0.548732i	$-0.184889\pi$
$811$	29.5923	+	12.2575i	1.03913	+	0.430420i	0.203128	+	0.979152i	$0.434889\pi$
$812$			1.16863i			0.0410109i
$813$	14.3055	−	34.5364i	0.501714	−	1.21125i
$814$	21.5197	−	21.5197i	0.754266	−	0.754266i
$815$	−8.61140			−0.301644
$816$	−0.173918	+	5.90810i	−0.00608836	+	0.206825i
$817$	−4.48950			−0.157068
$818$	26.6130	−	26.6130i	0.930503	−	0.930503i
$819$	−0.957864	+	2.31249i	−0.0334705	+	0.0808049i
$820$			1.93694i			0.0676409i
$821$	−3.57138	−	1.47931i	−0.124642	−	0.0516284i	0.319491	−	0.947589i	$-0.396488\pi$
$821$	−3.57138	−	1.47931i	−0.124642	−	0.0516284i	−0.444133	+	0.895961i	$0.646488\pi$
$822$	−12.5767	−	30.3627i	−0.438661	−	1.05902i
$823$	3.90191	−	1.61622i	0.136012	−	0.0563380i	−0.313639	−	0.949542i	$-0.601548\pi$
$823$	3.90191	−	1.61622i	0.136012	−	0.0563380i	0.449651	+	0.893204i	$0.351548\pi$
$824$	−4.21946	−	4.21946i	−0.146992	−	0.146992i
$825$	−3.78224	−	3.78224i	−0.131681	−	0.131681i
$826$	−6.22721	+	2.57939i	−0.216672	+	0.0897486i
$827$	16.2655	+	39.2683i	0.565606	+	1.36549i	0.905226	+	0.424931i	$0.139702\pi$
$827$	16.2655	+	39.2683i	0.565606	+	1.36549i	−0.339620	+	0.940563i	$0.610298\pi$
$828$	6.35275	+	2.63139i	0.220773	+	0.0914472i
$829$			10.9929i			0.381798i	0.981610	+	0.190899i	$0.0611403\pi$
$829$			10.9929i			0.381798i	−0.981610	+	0.190899i	$0.938860\pi$
$830$	−0.950609	+	2.29497i	−0.0329961	+	0.0796597i
$831$	−2.53625	+	2.53625i	−0.0879814	+	0.0879814i
$832$	−4.08239			−0.141531
$833$	−11.1135	+	24.7448i	−0.385062	+	0.857355i
$834$	16.5016			0.571403
$835$	7.85070	−	7.85070i	0.271685	−	0.271685i
$836$	6.12464	−	14.7862i	0.211825	−	0.511391i
$837$		−	28.1286i		−	0.972266i
$838$	−1.86868	−	0.774034i	−0.0645526	−	0.0267386i
$839$	−12.8714	−	31.0742i	−0.444369	−	1.07280i	−0.974400	−	0.224823i	$-0.927819\pi$
$839$	−12.8714	−	31.0742i	−0.444369	−	1.07280i	0.530030	−	0.847979i	$-0.322181\pi$
$840$	0.859348	−	0.355953i	0.0296503	−	0.0122816i
$841$	−18.2123	−	18.2123i	−0.628010	−	0.628010i
$842$	−24.5666	−	24.5666i	−0.846620	−	0.846620i
$843$	15.4084	−	6.38237i	0.530694	−	0.219821i
$844$	−9.61954	−	23.2236i	−0.331118	−	0.799390i
$845$	3.38687	+	1.40289i	0.116512	+	0.0482609i
$846$		−	4.45100i		−	0.153028i
$847$	−0.725577	+	1.75170i	−0.0249311	+	0.0601890i
$848$	6.16799	−	6.16799i	0.211810	−	0.211810i
$849$	−38.8537			−1.33346
$850$	3.85403	−	1.46508i	0.132192	−	0.0502517i
$851$	−59.3523			−2.03457
$852$	−13.4544	+	13.4544i	−0.460939	+	0.460939i
$853$	4.07881	−	9.84712i	0.139656	−	0.337159i	−0.838541	−	0.544838i	$-0.816591\pi$
$853$	4.07881	−	9.84712i	0.139656	−	0.337159i	0.978197	+	0.207679i	$0.0665910\pi$
$854$			2.29801i			0.0786363i
$855$	3.74464	+	1.55108i	0.128064	+	0.0530459i
$856$	−2.08080	−	5.02349i	−0.0711203	−	0.171699i
$857$	−22.3523	+	9.25864i	−0.763542	+	0.316269i	−0.730253	−	0.683177i	$-0.760598\pi$
$857$	−22.3523	+	9.25864i	−0.763542	+	0.316269i	−0.0332883	+	0.999446i	$0.510598\pi$
$858$	−15.4406	−	15.4406i	−0.527134	−	0.527134i
$859$	13.6445	+	13.6445i	0.465546	+	0.465546i	0.900468	−	0.434922i	$-0.143224\pi$
$859$	13.6445	+	13.6445i	0.465546	+	0.465546i	−0.434922	+	0.900468i	$0.643224\pi$
$860$	−0.966998	+	0.400544i	−0.0329744	+	0.0136584i
$861$	−0.689460	−	1.66450i	−0.0234967	−	0.0567262i
$862$	22.0559	+	9.13585i	0.751227	+	0.311168i
$863$		−	31.7534i		−	1.08090i	−0.841377	−	0.540449i	$-0.818254\pi$
$863$		−	31.7534i		−	1.08090i	0.841377	−	0.540449i	$-0.181746\pi$
$864$	−2.16417	+	5.22478i	−0.0736267	+	0.177751i
$865$	−10.8348	+	10.8348i	−0.368396	+	0.368396i
$866$	−1.15412			−0.0392186
$867$	−7.98553	−	23.0248i	−0.271203	−	0.781963i
$868$	−3.22729			−0.109541
$869$	−0.773462	+	0.773462i	−0.0262379	+	0.0262379i
$870$	0.988066	−	2.38540i	0.0334986	−	0.0808727i
$871$		−	14.2076i		−	0.481407i
$872$	−15.0972	−	6.25345i	−0.511254	−	0.211768i
$873$	−6.95585	−	16.7929i	−0.235420	−	0.568354i
$874$	−28.8364	+	11.9444i	−0.975407	+	0.404027i
$875$	−0.458804	−	0.458804i	−0.0155104	−	0.0155104i
$876$	6.07514	+	6.07514i	0.205260	+	0.205260i
$877$	34.2435	−	14.1841i	1.15632	−	0.478964i	0.279673	−	0.960095i	$-0.409774\pi$
$877$	34.2435	−	14.1841i	1.15632	−	0.478964i	0.876649	+	0.481131i	$0.159774\pi$
$878$	0.151207	+	0.365047i	0.00510300	+	0.0123197i
$879$	25.3963	+	10.5195i	0.856596	+	0.354814i
$880$		−	3.73124i		−	0.125780i
$881$	12.6307	−	30.4933i	0.425540	−	1.02735i	−0.555145	−	0.831753i	$-0.687337\pi$
$881$	12.6307	−	30.4933i	0.425540	−	1.02735i	0.980685	−	0.195592i	$-0.0626627\pi$
$882$	−4.39595	+	4.39595i	−0.148019	+	0.148019i
$883$	−25.4716			−0.857188			−0.428594	−	0.903497i	$-0.640991\pi$
$883$	−25.4716			−0.857188			−0.428594	+	0.903497i	$0.640991\pi$
$884$	15.7337	−	5.98101i	0.529180	−	0.201163i
$885$	14.8918			0.500583
$886$	−12.6173	+	12.6173i	−0.423886	+	0.423886i
$887$	11.1926	−	27.0213i	0.375810	−	0.907287i	−0.616931	−	0.787017i	$-0.711624\pi$
$887$	11.1926	−	27.0213i	0.375810	−	0.907287i	0.992741	−	0.120269i	$-0.0383758\pi$
$888$		−	11.6926i		−	0.392377i
$889$	5.39719	+	2.23559i	0.181016	+	0.0749792i
$890$	1.37589	+	3.32170i	0.0461201	+	0.111344i
$891$	−18.1745	+	7.52813i	−0.608869	+	0.252202i
$892$	−13.4826	−	13.4826i	−0.451430	−	0.451430i
$893$	14.2864	+	14.2864i	0.478076	+	0.478076i
$894$	18.3103	−	7.58437i	0.612388	−	0.253659i
$895$	3.89949	+	9.41421i	0.130346	+	0.314682i
$896$	0.599456	+	0.248303i	0.0200264	+	0.00829522i
$897$			42.5858i			1.42190i
$898$	−11.5932	+	27.9884i	−0.386869	+	0.933983i
$899$	−6.33454	+	6.33454i	−0.211269	+	0.211269i
$900$	0.944947			0.0314982
$901$	−14.7351	+	32.8082i	−0.490896	+	1.09300i
$902$	−7.22718			−0.240639
$903$	0.688413	−	0.688413i	0.0229089	−	0.0229089i
$904$	−0.953472	+	2.30188i	−0.0317120	+	0.0765595i
$905$		−	13.0679i		−	0.434391i
$906$	24.2931	+	10.0625i	0.807084	+	0.334305i
$907$	15.9140	+	38.4199i	0.528417	+	1.27571i	0.932560	+	0.361016i	$0.117570\pi$
$907$	15.9140	+	38.4199i	0.528417	+	1.27571i	−0.404143	+	0.914696i	$0.632430\pi$
$908$	−3.70676	+	1.53539i	−0.123013	+	0.0509537i
$909$	−6.57446	−	6.57446i	−0.218061	−	0.218061i
$910$	−1.87302	−	1.87302i	−0.0620899	−	0.0620899i
$911$	0.0576221	−	0.0238679i	0.00190911	−	0.000790777i	−0.381729	−	0.924274i	$-0.624671\pi$
$911$	0.0576221	−	0.0238679i	0.00190911	−	0.000790777i	0.383638	+	0.923484i	$0.374671\pi$
$912$	−2.35309	−	5.68087i	−0.0779186	−	0.188112i
$913$	−8.56310	−	3.54695i	−0.283397	−	0.117387i
$914$		−	35.0823i		−	1.16042i
$915$	1.94295	−	4.69069i	0.0642319	−	0.155069i
$916$	−12.1237	+	12.1237i	−0.400577	+	0.400577i
$917$	−10.3197			−0.340787
$918$	0.686098	−	23.3071i	0.0226446	−	0.769250i
$919$	17.0376			0.562019			0.281009	−	0.959705i	$-0.409331\pi$
$919$	17.0376			0.562019			0.281009	+	0.959705i	$0.409331\pi$
$920$	−5.14545	+	5.14545i	−0.169641	+	0.169641i
$921$	4.78390	−	11.5494i	0.157635	−	0.380564i
$922$		−	40.2564i		−	1.32577i
$923$	50.0607	+	20.7358i	1.64777	+	0.682527i
$924$	1.32815	+	3.20643i	0.0436928	+	0.105484i
$925$	−7.53553	+	3.12132i	−0.247767	+	0.102628i
$926$	1.23576	+	1.23576i	0.0406096	+	0.0406096i
$927$	3.98717	+	3.98717i	0.130956	+	0.130956i
$928$	1.66399	−	0.689246i	0.0546231	−	0.0226256i
$929$	2.63169	+	6.35346i	0.0863429	+	0.208450i	0.961153	−	0.276015i	$-0.0890141\pi$
$929$	2.63169	+	6.35346i	0.0863429	+	0.208450i	−0.874810	+	0.484466i	$0.839014\pi$
$930$	6.58752	+	2.72864i	0.216013	+	0.0894757i
$931$		−	28.2194i		−	0.924853i
$932$	−7.24486	+	17.4907i	−0.237313	+	0.572925i
$933$	−17.0946	+	17.0946i	−0.559653	+	0.559653i
$934$	17.0853			0.559049
$935$	5.46655	+	14.3803i	0.178775	+	0.470286i
$936$	3.85765			0.126091
$937$	13.4652	−	13.4652i	0.439890	−	0.439890i	−0.452085	−	0.891975i	$-0.649320\pi$
$937$	13.4652	−	13.4652i	0.439890	−	0.439890i	0.891975	+	0.452085i	$0.149320\pi$
$938$	−0.864148	+	2.08624i	−0.0282154	+	0.0681181i
$939$			10.6646i			0.348025i
$940$	4.35176	+	1.80256i	0.141939	+	0.0587930i
$941$	0.996369	+	2.40545i	0.0324807	+	0.0784153i	0.939288	−	0.343131i	$-0.111487\pi$
$941$	0.996369	+	2.40545i	0.0324807	+	0.0784153i	−0.906807	+	0.421546i	$0.861487\pi$
$942$	23.2206	−	9.61830i	0.756569	−	0.313381i
$943$	9.96643	+	9.96643i	0.324552	+	0.324552i
$944$	7.34549	+	7.34549i	0.239075	+	0.239075i
$945$	−3.39008	+	1.40422i	−0.110279	+	0.0456792i
$946$	−1.49452	−	3.60810i	−0.0485912	−	0.117310i
$947$	6.85990	+	2.84147i	0.222917	+	0.0923352i	0.491347	−	0.870964i	$-0.336505\pi$
$947$	6.85990	+	2.84147i	0.222917	+	0.0923352i	−0.268430	+	0.963299i	$0.586505\pi$
$948$			0.420255i			0.0136492i
$949$	9.36298	−	22.6042i	0.303935	−	0.733764i
$950$	−3.03300	+	3.03300i	−0.0984036	+	0.0984036i
$951$	−1.84977			−0.0599829
$952$	−2.67411	−	0.0787183i	−0.0866682	−	0.00255127i
$953$	37.5558			1.21655			0.608277	−	0.793725i	$-0.291861\pi$
$953$	37.5558			1.21655			0.608277	+	0.793725i	$0.291861\pi$
$954$	−5.82843	+	5.82843i	−0.188702	+	0.188702i
$955$	7.55920	−	18.2495i	0.244610	−	0.590541i
$956$			25.1215i			0.812488i
$957$	8.90051	+	3.68671i	0.287713	+	0.119174i
$958$	8.00249	+	19.3197i	0.258549	+	0.624192i
$959$	13.7427	−	5.69240i	0.443774	−	0.183817i
$960$	−1.01367	−	1.01367i	−0.0327161	−	0.0327161i
$961$	4.42686	+	4.42686i	0.142802	+	0.142802i
$962$	−30.7630	+	12.7425i	−0.991839	+	0.410833i
$963$	1.96625	+	4.74694i	0.0633614	+	0.152968i
$964$	−5.53137	−	2.29117i	−0.178153	−	0.0737936i
$965$		−	10.3611i		−	0.333535i
$966$	2.59019	−	6.25327i	0.0833380	−	0.201196i
$967$	−34.7364	+	34.7364i	−1.11705	+	1.11705i	−0.124874	+	0.992173i	$0.539853\pi$
$967$	−34.7364	+	34.7364i	−1.11705	+	1.11705i	−0.992173	+	0.124874i	$0.960147\pi$
$968$	2.92214			0.0939213
$969$	17.3918	+	18.4468i	0.558705	+	0.592596i
$970$	19.2355			0.617614
$971$	−14.1996	+	14.1996i	−0.455688	+	0.455688i	−0.897237	−	0.441549i	$-0.854429\pi$
$971$	−14.1996	+	14.1996i	−0.455688	+	0.455688i	0.441549	+	0.897237i	$0.354429\pi$
$972$	3.60021	−	8.69167i	0.115477	−	0.278786i
$973$			7.46889i			0.239442i
$974$	−15.0149	−	6.21937i	−0.481108	−	0.199281i
$975$	2.23958	+	5.40682i	0.0717238	+	0.173157i
$976$	3.27209	−	1.35534i	0.104737	−	0.0433835i
$977$	−27.5071	−	27.5071i	−0.880029	−	0.880029i	0.113508	−	0.993537i	$-0.463791\pi$
$977$	−27.5071	−	27.5071i	−0.880029	−	0.880029i	−0.993537	+	0.113508i	$0.963791\pi$
$978$	−8.72912	−	8.72912i	−0.279126	−	0.279126i
$979$	−12.3941	+	5.13379i	−0.396116	+	0.164077i
$980$	−2.51767	−	6.07820i	−0.0804241	−	0.194161i
$981$	14.2660	+	5.90918i	0.455479	+	0.188666i
$982$			16.3083i			0.520420i
$983$	1.69233	−	4.08564i	0.0539769	−	0.130312i	−0.894591	−	0.446886i	$-0.852533\pi$
$983$	1.69233	−	4.08564i	0.0539769	−	0.130312i	0.948568	+	0.316575i	$0.102533\pi$
$984$	−1.96342	+	1.96342i	−0.0625915	+	0.0625915i
$985$	−16.6845			−0.531613
$986$	−5.40326	+	5.09425i	−0.172075	+	0.162234i
$987$	−4.38130			−0.139458
$988$	−12.3819	+	12.3819i	−0.393921	+	0.393921i
$989$	−2.91466	+	7.03662i	−0.0926809	+	0.223752i
$990$			3.52582i			0.112058i
$991$	−15.2551	−	6.31887i	−0.484594	−	0.200726i	0.126991	−	0.991904i	$-0.459468\pi$
$991$	−15.2551	−	6.31887i	−0.484594	−	0.200726i	−0.611586	+	0.791178i	$0.709468\pi$
$992$	1.90342	+	4.59527i	0.0604337	+	0.145900i
$993$	−9.62393	+	3.98636i	−0.305406	+	0.126503i
$994$	−6.08967	−	6.08967i	−0.193153	−	0.193153i
$995$	6.69824	+	6.69824i	0.212348	+	0.212348i
$996$	−3.28995	+	1.36274i	−0.104246	+	0.0431801i
$997$	21.5733	+	52.0826i	0.683234	+	1.64947i	0.757986	+	0.652270i	$0.226183\pi$
$997$	21.5733	+	52.0826i	0.683234	+	1.64947i	−0.0747525	+	0.997202i	$0.523817\pi$
$998$	−30.2109	−	12.5137i	−0.956308	−	0.396116i
$999$			46.1266i			1.45938i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.k.a.161.1	yes	8
5.2	odd	4		850.2.o.c.399.2		8
5.3	odd	4		850.2.o.f.399.1		8
5.4	even	2		850.2.l.d.501.2		8
17.6	odd	16		2890.2.b.p.2311.4		8
17.7	odd	16		2890.2.a.bc.1.3		4
17.10	odd	16		2890.2.a.bf.1.2		4
17.11	odd	16		2890.2.b.p.2311.5		8
17.15	even	8	inner	170.2.k.a.151.1	✓	8
85.32	odd	8		850.2.o.f.49.1		8
85.49	even	8		850.2.l.d.151.2		8
85.83	odd	8		850.2.o.c.49.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.k.a.151.1	✓	8	17.15	even	8	inner
170.2.k.a.161.1	yes	8	1.1	even	1	trivial
850.2.l.d.151.2		8	85.49	even	8
850.2.l.d.501.2		8	5.4	even	2
850.2.o.c.49.2		8	85.83	odd	8
850.2.o.c.399.2		8	5.2	odd	4
850.2.o.f.49.1		8	85.32	odd	8
850.2.o.f.399.1		8	5.3	odd	4
2890.2.a.bc.1.3		4	17.7	odd	16
2890.2.a.bf.1.2		4	17.10	odd	16
2890.2.b.p.2311.4		8	17.6	odd	16
2890.2.b.p.2311.5		8	17.11	odd	16

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.k (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.548594 - 1.32442i) q^{3} -1.00000i q^{4} +(-0.923880 - 0.382683i) q^{5} +(-0.548594 - 1.32442i) q^{6} +(0.599456 - 0.248303i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.668179 + 0.668179i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.548594 - 1.32442i) q^{3} -1.00000i q^{4} +(-0.923880 - 0.382683i) q^{5} +(-0.548594 - 1.32442i) q^{6} +(0.599456 - 0.248303i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.668179 + 0.668179i) q^{9} +(-0.923880 + 0.382683i) q^{10} +(-1.42788 - 3.44722i) q^{11} +(-1.32442 - 0.548594i) q^{12} +4.08239i q^{13} +(0.248303 - 0.599456i) q^{14} +(-1.01367 + 1.01367i) q^{15} -1.00000 q^{16} +(3.85403 - 1.46508i) q^{17} +0.944947 q^{18} +(-3.03300 + 3.03300i) q^{19} +(-0.382683 + 0.923880i) q^{20} -0.930151i q^{21} +(-3.44722 - 1.42788i) q^{22} +(2.78470 + 6.72286i) q^{23} +(-1.32442 + 0.548594i) q^{24} +(0.707107 + 0.707107i) q^{25} +(2.88669 + 2.88669i) q^{26} +(5.22478 - 2.16417i) q^{27} +(-0.248303 - 0.599456i) q^{28} +(-1.66399 - 0.689246i) q^{29} +1.43355i q^{30} +(1.90342 - 4.59527i) q^{31} +(-0.707107 + 0.707107i) q^{32} -5.34890 q^{33} +(1.68925 - 3.76118i) q^{34} -0.648847 q^{35} +(0.668179 - 0.668179i) q^{36} +(-3.12132 + 7.53553i) q^{37} +4.28931i q^{38} +(5.40682 + 2.23958i) q^{39} +(0.382683 + 0.923880i) q^{40} +(1.78950 - 0.741235i) q^{41} +(-0.657716 - 0.657716i) q^{42} +(0.740108 + 0.740108i) q^{43} +(-3.44722 + 1.42788i) q^{44} +(-0.361616 - 0.873017i) q^{45} +(6.72286 + 2.78470i) q^{46} -4.71031i q^{47} +(-0.548594 + 1.32442i) q^{48} +(-4.65205 + 4.65205i) q^{49} +1.00000 q^{50} +(0.173918 - 5.90810i) q^{51} +4.08239 q^{52} +(-6.16799 + 6.16799i) q^{53} +(2.16417 - 5.22478i) q^{54} +3.73124i q^{55} +(-0.599456 - 0.248303i) q^{56} +(2.35309 + 5.68087i) q^{57} +(-1.66399 + 0.689246i) q^{58} +(-7.34549 - 7.34549i) q^{59} +(1.01367 + 1.01367i) q^{60} +(-3.27209 + 1.35534i) q^{61} +(-1.90342 - 4.59527i) q^{62} +(0.566454 + 0.234633i) q^{63} +1.00000i q^{64} +(1.56226 - 3.77164i) q^{65} +(-3.78224 + 3.78224i) q^{66} -3.48022 q^{67} +(-1.46508 - 3.85403i) q^{68} +10.4316 q^{69} +(-0.458804 + 0.458804i) q^{70} +(5.07933 - 12.2626i) q^{71} -0.944947i q^{72} +(-5.53701 - 2.29350i) q^{73} +(3.12132 + 7.53553i) q^{74} +(1.32442 - 0.548594i) q^{75} +(3.03300 + 3.03300i) q^{76} +(-1.71191 - 1.71191i) q^{77} +(5.40682 - 2.23958i) q^{78} +(-0.112187 - 0.270842i) q^{79} +(0.923880 + 0.382683i) q^{80} -5.27223i q^{81} +(0.741235 - 1.78950i) q^{82} +(1.75650 - 1.75650i) q^{83} -0.930151 q^{84} +(-4.12132 - 0.121320i) q^{85} +1.04667 q^{86} +(-1.82571 + 1.82571i) q^{87} +(-1.42788 + 3.44722i) q^{88} -3.59539i q^{89} +(-0.873017 - 0.361616i) q^{90} +(1.01367 + 2.44722i) q^{91} +(6.72286 - 2.78470i) q^{92} +(-5.04187 - 5.04187i) q^{93} +(-3.33070 - 3.33070i) q^{94} +(3.96281 - 1.64145i) q^{95} +(0.548594 + 1.32442i) q^{96} +(-17.7713 - 7.36110i) q^{97} +6.57900i q^{98} +(1.34927 - 3.25744i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^9	\( 8 q + 8 q^{9} + 16 q^{11} - 8 q^{12} - 8 q^{14} + 8 q^{15} - 8 q^{16} - 16 q^{18} - 16 q^{19} - 8 q^{22} + 24 q^{23} - 8 q^{24} + 8 q^{28} + 8 q^{29} - 16 q^{31} - 16 q^{33} + 8 q^{36} - 8 q^{37} + 32 q^{39} - 8 q^{43} - 8 q^{44} - 16 q^{45} - 8 q^{46} - 8 q^{49} + 8 q^{50} - 40 q^{51} + 24 q^{52} - 8 q^{53} + 40 q^{54} + 16 q^{57} + 8 q^{58} - 40 q^{59} - 8 q^{60} - 24 q^{61} + 16 q^{62} + 8 q^{63} - 8 q^{65} + 16 q^{66} - 16 q^{69} - 8 q^{70} + 24 q^{71} - 16 q^{73} + 8 q^{74} + 8 q^{75} + 16 q^{76} + 8 q^{77} + 32 q^{78} - 8 q^{79} + 8 q^{82} + 8 q^{83} + 16 q^{84} - 16 q^{85} - 16 q^{86} + 32 q^{87} + 16 q^{88} - 8 q^{91} - 8 q^{92} - 32 q^{93} - 8 q^{94} + 16 q^{95} - 32 q^{97} + 72 q^{99}+O(q^{100}) \) 8 * q + 8 * q^9 + 16 * q^11 - 8 * q^12 - 8 * q^14 + 8 * q^15 - 8 * q^16 - 16 * q^18 - 16 * q^19 - 8 * q^22 + 24 * q^23 - 8 * q^24 + 8 * q^28 + 8 * q^29 - 16 * q^31 - 16 * q^33 + 8 * q^36 - 8 * q^37 + 32 * q^39 - 8 * q^43 - 8 * q^44 - 16 * q^45 - 8 * q^46 - 8 * q^49 + 8 * q^50 - 40 * q^51 + 24 * q^52 - 8 * q^53 + 40 * q^54 + 16 * q^57 + 8 * q^58 - 40 * q^59 - 8 * q^60 - 24 * q^61 + 16 * q^62 + 8 * q^63 - 8 * q^65 + 16 * q^66 - 16 * q^69 - 8 * q^70 + 24 * q^71 - 16 * q^73 + 8 * q^74 + 8 * q^75 + 16 * q^76 + 8 * q^77 + 32 * q^78 - 8 * q^79 + 8 * q^82 + 8 * q^83 + 16 * q^84 - 16 * q^85 - 16 * q^86 + 32 * q^87 + 16 * q^88 - 8 * q^91 - 8 * q^92 - 32 * q^93 - 8 * q^94 + 16 * q^95 - 32 * q^97 + 72 * q^99

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