LMFDB - Embedded newform 930.2.be.a.37.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(37,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("930.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.be (of order $12$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.12
Character	$\chi$	$=$	930.37
Dual form			930.2.be.a.553.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(0.247692 + 2.22231i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.08066 + 4.03306i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(0.247692 + 2.22231i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.08066 + 4.03306i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.39626 + 1.74655i) q^{10} +(-0.754170 - 0.435420i) q^{11} +(0.965926 + 0.258819i) q^{12} +(3.83136 - 1.02661i) q^{13} +(-3.61595 + 2.08767i) q^{14} +(2.21069 + 0.335923i) q^{15} -1.00000 q^{16} +(-5.56460 - 1.49103i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-5.57986 + 3.22153i) q^{19} +(-2.22231 + 0.247692i) q^{20} +(3.61595 + 2.08767i) q^{21} +(-0.225390 - 0.841167i) q^{22} +(0.693877 + 0.693877i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.87730 + 1.10090i) q^{25} +(3.43511 + 1.98326i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-4.03306 - 1.08066i) q^{28} +1.10860 q^{29} +(1.32566 + 1.80073i) q^{30} +(4.99147 - 2.46682i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.615777 + 0.615777i) q^{33} +(-2.88045 - 4.98908i) q^{34} +(-9.23038 - 1.40259i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.24712 - 0.602113i) q^{37} +(-6.22353 - 1.66759i) q^{38} -3.96652i q^{39} +(-1.74655 - 1.39626i) q^{40} +(1.16860 - 2.02407i) q^{41} +(1.08066 + 4.03306i) q^{42} +(-2.43636 + 9.09264i) q^{43} +(0.435420 - 0.754170i) q^{44} +(0.896646 - 2.04842i) q^{45} +0.981290i q^{46} +(8.44460 + 8.44460i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(-9.03561 - 5.21671i) q^{49} +(-4.22722 - 2.67032i) q^{50} +(-2.88045 + 4.98908i) q^{51} +(1.02661 + 3.83136i) q^{52} +(7.58508 - 2.03242i) q^{53} -1.00000 q^{54} +(0.780835 - 1.78385i) q^{55} +(-2.08767 - 3.61595i) q^{56} +(1.66759 + 6.22353i) q^{57} +(0.783899 + 0.783899i) q^{58} +(-1.24572 + 0.719216i) q^{59} +(-0.335923 + 2.21069i) q^{60} +9.69276i q^{61} +(5.27381 + 1.78520i) q^{62} +(2.95241 - 2.95241i) q^{63} -1.00000i q^{64} +(3.23044 + 8.26018i) q^{65} -0.870840 q^{66} +(7.33025 - 1.96413i) q^{67} +(1.49103 - 5.56460i) q^{68} +(0.849822 - 0.490645i) q^{69} +(-5.53508 - 7.51864i) q^{70} +(2.39411 - 4.14672i) q^{71} +(0.965926 - 0.258819i) q^{72} +(1.64227 - 0.440045i) q^{73} +(-1.16319 - 2.01471i) q^{74} +(-0.198954 + 4.99604i) q^{75} +(-3.22153 - 5.57986i) q^{76} +(2.57108 - 2.57108i) q^{77} +(2.80475 - 2.80475i) q^{78} +(6.22318 + 10.7789i) q^{79} +(-0.247692 - 2.22231i) q^{80} +(0.500000 + 0.866025i) q^{81} +(2.25755 - 0.604910i) q^{82} +(4.45332 - 1.19326i) q^{83} +(-2.08767 + 3.61595i) q^{84} +(1.93522 - 12.7356i) q^{85} +(-8.15223 + 4.70669i) q^{86} +(0.286927 - 1.07083i) q^{87} +(0.841167 - 0.225390i) q^{88} -0.0539934 q^{89} +(2.08248 - 0.814428i) q^{90} +16.5615i q^{91} +(-0.693877 + 0.693877i) q^{92} +(-1.09088 - 5.45985i) q^{93} +11.9425i q^{94} +(-8.54132 - 11.6022i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-1.75845 - 1.75845i) q^{97} +(-2.70037 - 10.0779i) q^{98} +(0.435420 + 0.754170i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7}+O(q^{10}) $ 64 * q - 8 * q^7	$ 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) $ 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$			1.00000i			0.500000i
$5$	0.247692	+	2.22231i	0.110771	+	0.993846i
$5$	0.247692	+	2.22231i	0.110771	+	0.993846i
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	−1.08066	+	4.03306i	−0.408450	+	1.52436i	0.389154	+	0.921173i	$0.372767\pi$
$7$	−1.08066	+	4.03306i	−0.408450	+	1.52436i	−0.797603	+	0.603182i	$0.793899\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−1.39626	+	1.74655i	−0.441537	+	0.552309i
$11$	−0.754170	−	0.435420i	−0.227391	−	0.131284i	0.381977	−	0.924172i	$-0.375243\pi$
$11$	−0.754170	−	0.435420i	−0.227391	−	0.131284i	−0.609368	+	0.792888i	$0.708577\pi$
$12$	0.965926	+	0.258819i	0.278839	+	0.0747146i
$13$	3.83136	−	1.02661i	1.06263	−	0.284731i	0.315168	−	0.949036i	$-0.397939\pi$
$13$	3.83136	−	1.02661i	1.06263	−	0.284731i	0.747461	+	0.664305i	$0.231273\pi$
$14$	−3.61595	+	2.08767i	−0.966402	+	0.557953i
$15$	2.21069	+	0.335923i	0.570798	+	0.0867350i
$16$	−1.00000			−0.250000
$17$	−5.56460	−	1.49103i	−1.34961	−	0.361628i	−0.489621	−	0.871935i	$-0.662865\pi$
$17$	−5.56460	−	1.49103i	−1.34961	−	0.361628i	−0.859992	+	0.510307i	$0.829532\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	−5.57986	+	3.22153i	−1.28011	+	0.739071i	−0.976868	−	0.213844i	$-0.931402\pi$
$19$	−5.57986	+	3.22153i	−1.28011	+	0.739071i	−0.303240	+	0.952914i	$0.598068\pi$
$20$	−2.22231	+	0.247692i	−0.496923	+	0.0553856i
$21$	3.61595	+	2.08767i	0.789064	+	0.455566i
$22$	−0.225390	−	0.841167i	−0.0480533	−	0.179337i
$23$	0.693877	+	0.693877i	0.144683	+	0.144683i	0.775738	−	0.631055i	$-0.217378\pi$
$23$	0.693877	+	0.693877i	0.144683	+	0.144683i	−0.631055	+	0.775738i	$0.717378\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−4.87730	+	1.10090i	−0.975459	+	0.220179i
$26$	3.43511	+	1.98326i	0.673680	+	0.388949i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−4.03306	−	1.08066i	−0.762178	−	0.204225i
$29$	1.10860			0.205862			0.102931	−	0.994689i	$-0.467178\pi$
$29$	1.10860			0.205862			0.102931	+	0.994689i	$0.467178\pi$
$30$	1.32566	+	1.80073i	0.242032	+	0.328767i
$31$	4.99147	−	2.46682i	0.896495	−	0.443054i
$31$	4.99147	−	2.46682i	0.896495	−	0.443054i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−0.615777	+	0.615777i	−0.107193	+	0.107193i
$34$	−2.88045	−	4.98908i	−0.493993	−	0.855621i
$35$	−9.23038	−	1.40259i	−1.56022	−	0.237081i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−2.24712	−	0.602113i	−0.369423	−	0.0989867i	0.0693310	−	0.997594i	$-0.477914\pi$
$37$	−2.24712	−	0.602113i	−0.369423	−	0.0989867i	−0.438754	+	0.898607i	$0.644580\pi$
$38$	−6.22353	−	1.66759i	−1.00959	−	0.270519i
$39$		−	3.96652i		−	0.635151i
$40$	−1.74655	−	1.39626i	−0.276154	−	0.220769i
$41$	1.16860	−	2.02407i	0.182504	−	0.316106i	−0.760229	−	0.649656i	$-0.774913\pi$
$41$	1.16860	−	2.02407i	0.182504	−	0.316106i	0.942733	+	0.333549i	$0.108246\pi$
$42$	1.08066	+	4.03306i	0.166749	+	0.622315i
$43$	−2.43636	+	9.09264i	−0.371542	+	1.38661i	0.486790	+	0.873519i	$0.338168\pi$
$43$	−2.43636	+	9.09264i	−0.371542	+	1.38661i	−0.858332	+	0.513095i	$0.828499\pi$
$44$	0.435420	−	0.754170i	0.0656420	−	0.113695i
$45$	0.896646	−	2.04842i	0.133664	−	0.305360i
$46$			0.981290i			0.144683i
$47$	8.44460	+	8.44460i	1.23177	+	1.23177i	0.963283	+	0.268488i	$0.0865239\pi$
$47$	8.44460	+	8.44460i	1.23177	+	1.23177i	0.268488	+	0.963283i	$0.413476\pi$
$48$	−0.258819	+	0.965926i	−0.0373573	+	0.139419i
$49$	−9.03561	−	5.21671i	−1.29080	−	0.745245i
$50$	−4.22722	−	2.67032i	−0.597819	−	0.377640i
$51$	−2.88045	+	4.98908i	−0.403343	+	0.698611i
$52$	1.02661	+	3.83136i	0.142365	+	0.531314i
$53$	7.58508	−	2.03242i	1.04189	−	0.279174i	0.302994	−	0.952992i	$-0.402014\pi$
$53$	7.58508	−	2.03242i	1.04189	−	0.279174i	0.738897	+	0.673819i	$0.235347\pi$
$54$	−1.00000			−0.136083
$55$	0.780835	−	1.78385i	0.105288	−	0.240534i
$56$	−2.08767	−	3.61595i	−0.278976	−	0.483201i
$57$	1.66759	+	6.22353i	0.220878	+	0.824326i
$58$	0.783899	+	0.783899i	0.102931	+	0.102931i
$59$	−1.24572	+	0.719216i	−0.162179	+	0.0936340i	−0.578893	−	0.815404i	$-0.696515\pi$
$59$	−1.24572	+	0.719216i	−0.162179	+	0.0936340i	0.416714	+	0.909038i	$0.363182\pi$
$60$	−0.335923	+	2.21069i	−0.0433675	+	0.285399i
$61$			9.69276i			1.24103i	0.784194	+	0.620515i	$0.213077\pi$
$61$			9.69276i			1.24103i	−0.784194	+	0.620515i	$0.786923\pi$
$62$	5.27381	+	1.78520i	0.669775	+	0.226720i
$63$	2.95241	−	2.95241i	0.371968	−	0.371968i
$64$		−	1.00000i		−	0.125000i
$65$	3.23044	+	8.26018i	0.400687	+	1.02455i
$66$	−0.870840			−0.107193
$67$	7.33025	−	1.96413i	0.895532	−	0.239957i	0.218436	−	0.975851i	$-0.429905\pi$
$67$	7.33025	−	1.96413i	0.895532	−	0.239957i	0.677096	+	0.735894i	$0.263238\pi$
$68$	1.49103	−	5.56460i	0.180814	−	0.674807i
$69$	0.849822	−	0.490645i	0.102307	−	0.0590667i
$70$	−5.53508	−	7.51864i	−0.661569	−	0.898650i
$71$	2.39411	−	4.14672i	0.284129	−	0.492125i	−0.688269	−	0.725456i	$-0.741629\pi$
$71$	2.39411	−	4.14672i	0.284129	−	0.492125i	0.972397	+	0.233331i	$0.0749624\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	1.64227	−	0.440045i	0.192213	−	0.0515033i	−0.161428	−	0.986884i	$-0.551610\pi$
$73$	1.64227	−	0.440045i	0.192213	−	0.0515033i	0.353641	+	0.935381i	$0.384943\pi$
$74$	−1.16319	−	2.01471i	−0.135218	−	0.234205i
$75$	−0.198954	+	4.99604i	−0.0229732	+	0.576893i
$76$	−3.22153	−	5.57986i	−0.369535	−	0.640054i
$77$	2.57108	−	2.57108i	0.293001	−	0.293001i
$78$	2.80475	−	2.80475i	0.317576	−	0.317576i
$79$	6.22318	+	10.7789i	0.700163	+	1.21272i	0.968409	+	0.249367i	$0.0802225\pi$
$79$	6.22318	+	10.7789i	0.700163	+	1.21272i	−0.268246	+	0.963350i	$0.586444\pi$
$80$	−0.247692	−	2.22231i	−0.0276928	−	0.248461i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	2.25755	−	0.604910i	0.249305	−	0.0668011i
$83$	4.45332	−	1.19326i	0.488815	−	0.130978i	−0.00598927	−	0.999982i	$-0.501906\pi$
$83$	4.45332	−	1.19326i	0.488815	−	0.130978i	0.494804	+	0.869005i	$0.335240\pi$
$84$	−2.08767	+	3.61595i	−0.227783	+	0.394532i
$85$	1.93522	−	12.7356i	0.209904	−	1.38137i
$86$	−8.15223	+	4.70669i	−0.879078	+	0.507536i
$87$	0.286927	−	1.07083i	0.0307618	−	0.114805i
$88$	0.841167	−	0.225390i	0.0896687	−	0.0240267i
$89$	−0.0539934			−0.00572329			−0.00286164	−	0.999996i	$-0.500911\pi$
$89$	−0.0539934			−0.00572329			−0.00286164	+	0.999996i	$0.500911\pi$
$90$	2.08248	−	0.814428i	0.219512	−	0.0858482i
$91$			16.5615i			1.73612i
$92$	−0.693877	+	0.693877i	−0.0723417	+	0.0723417i
$93$	−1.09088	−	5.45985i	−0.113119	−	0.566160i
$94$			11.9425i			1.23177i
$95$	−8.54132	−	11.6022i	−0.876321	−	1.19036i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−1.75845	−	1.75845i	−0.178544	−	0.178544i	0.612177	−	0.790721i	$-0.290294\pi$
$97$	−1.75845	−	1.75845i	−0.178544	−	0.178544i	−0.790721	+	0.612177i	$0.790294\pi$
$98$	−2.70037	−	10.0779i	−0.272779	−	1.01802i
$99$	0.435420	+	0.754170i	0.0437614	+	0.0757969i
$100$	−1.10090	−	4.87730i	−0.110090	−	0.487730i
$101$	−1.02596			−0.102087			−0.0510433	−	0.998696i	$-0.516255\pi$
$101$	−1.02596			−0.102087			−0.0510433	+	0.998696i	$0.516255\pi$
$102$	−5.56460	+	1.49103i	−0.550977	+	0.147634i
$103$	4.27638	+	15.9597i	0.421364	+	1.57255i	0.771737	+	0.635942i	$0.219388\pi$
$103$	4.27638	+	15.9597i	0.421364	+	1.57255i	−0.350372	+	0.936610i	$0.613945\pi$
$104$	−1.98326	+	3.43511i	−0.194475	+	0.336840i
$105$	−3.74380	+	8.55284i	−0.365357	+	0.834672i
$106$	6.80060	+	3.92633i	0.660532	+	0.381358i
$107$	2.15494	−	8.04236i	0.208326	−	0.777484i	−0.780084	−	0.625675i	$-0.784823\pi$
$107$	2.15494	−	8.04236i	0.208326	−	0.777484i	0.988410	−	0.151809i	$-0.0485098\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$			8.00977i			0.767196i	0.923500	+	0.383598i	$0.125315\pi$
$109$			8.00977i			0.767196i	−0.923500	+	0.383598i	$0.874685\pi$
$110$	1.81350	−	0.709236i	0.172911	−	0.0676230i
$111$	−1.16319	+	2.01471i	−0.110405	+	0.191228i
$112$	1.08066	−	4.03306i	0.102112	−	0.381089i
$113$	1.63043	+	6.08484i	0.153378	+	0.572413i	0.999239	+	0.0390102i	$0.0124205\pi$
$113$	1.63043	+	6.08484i	0.153378	+	0.572413i	−0.845861	+	0.533403i	$0.820913\pi$
$114$	−3.22153	+	5.57986i	−0.301724	+	0.522602i
$115$	−1.37014	+	1.71388i	−0.127766	+	0.159820i
$116$			1.10860i			0.102931i
$117$	−3.83136	−	1.02661i	−0.354210	−	0.0949102i
$118$	−1.38942	−	0.372294i	−0.127906	−	0.0342724i
$119$	12.0268	−	20.8311i	1.10250	−	1.90958i
$120$	−1.80073	+	1.32566i	−0.164383	+	0.121016i
$121$	−5.12082	−	8.86952i	−0.465529	−	0.806320i
$122$	−6.85382	+	6.85382i	−0.620515	+	0.620515i
$123$	−1.65264	−	1.65264i	−0.149014	−	0.149014i
$124$	2.46682	+	4.99147i	0.221527	+	0.448247i
$125$	−3.65460	−	10.5662i	−0.326877	−	0.945067i
$126$	4.17534			0.371968
$127$	3.58628	+	0.960940i	0.318231	+	0.0852697i	0.414399	−	0.910095i	$-0.363992\pi$
$127$	3.58628	+	0.960940i	0.318231	+	0.0852697i	−0.0961680	+	0.995365i	$0.530659\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	8.15223	+	4.70669i	0.717764	+	0.414401i
$130$	−3.55656	+	8.12510i	−0.311931	+	0.712618i
$131$	−10.8140	−	18.7304i	−0.944822	−	1.63648i	−0.756107	−	0.654448i	$-0.772901\pi$
$131$	−10.8140	−	18.7304i	−0.944822	−	1.63648i	−0.188716	−	0.982032i	$-0.560432\pi$
$132$	−0.615777	−	0.615777i	−0.0535965	−	0.0535965i
$133$	−6.96274	−	25.9853i	−0.603746	−	2.25321i
$134$	6.57212	+	3.79441i	0.567745	+	0.327787i
$135$	−1.74655	−	1.39626i	−0.150319	−	0.120171i
$136$	4.98908	−	2.88045i	0.427810	−	0.246996i
$137$	−3.45174	−	12.8821i	−0.294902	−	1.10059i	−0.941295	−	0.337585i	$-0.890390\pi$
$137$	−3.45174	−	12.8821i	−0.294902	−	1.10059i	0.646393	−	0.763005i	$-0.276277\pi$
$138$	0.947853	+	0.253977i	0.0806866	+	0.0216199i
$139$	11.5875			0.982841			0.491420	−	0.870922i	$-0.336478\pi$
$139$	11.5875			0.982841			0.491420	+	0.870922i	$0.336478\pi$
$140$	1.40259	−	9.23038i	0.118541	−	0.780109i
$141$	10.3425	−	5.97123i	0.870994	−	0.502868i
$142$	4.62507	−	1.23928i	0.388127	−	0.103998i
$143$	−3.33650	−	0.894014i	−0.279012	−	0.0747612i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	0.274592	+	2.46365i	0.0228036	+	0.204595i
$146$	1.47242	+	0.850101i	0.121858	+	0.0703548i
$147$	−7.37755	+	7.37755i	−0.608490	+	0.608490i
$148$	0.602113	−	2.24712i	0.0494934	−	0.184712i
$149$	−4.13570	+	2.38775i	−0.338810	+	0.195612i	−0.659746	−	0.751489i	$-0.729336\pi$
$149$	−4.13570	+	2.38775i	−0.338810	+	0.195612i	0.320936	+	0.947101i	$0.396003\pi$
$150$	−3.67342	+	3.39205i	−0.299933	+	0.276960i
$151$			3.26695i			0.265860i	0.991125	+	0.132930i	$0.0424386\pi$
$151$			3.26695i			0.265860i	−0.991125	+	0.132930i	$0.957561\pi$
$152$	1.66759	−	6.22353i	0.135259	−	0.504795i
$153$	4.07357	+	4.07357i	0.329328	+	0.329328i
$154$	3.63605			0.293001
$155$	6.71839	+	10.4816i	0.539634	+	0.841900i
$156$	3.96652			0.317576
$157$	−11.0292	−	11.0292i	−0.880223	−	0.880223i	0.113334	−	0.993557i	$-0.463847\pi$
$157$	−11.0292	−	11.0292i	−0.880223	−	0.880223i	−0.993557	+	0.113334i	$0.963847\pi$
$158$	−3.22136	+	12.0223i	−0.256277	+	0.956440i
$159$		−	7.85265i		−	0.622756i
$160$	1.39626	−	1.74655i	0.110384	−	0.138077i
$161$	−3.54829	+	2.04861i	−0.279645	+	0.161453i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	14.9053	−	14.9053i	1.16748	−	1.16748i	0.184677	−	0.982799i	$-0.440876\pi$
$163$	14.9053	−	14.9053i	1.16748	−	1.16748i	0.982799	−	0.184677i	$-0.0591240\pi$
$164$	2.02407	+	1.16860i	0.158053	+	0.0912520i
$165$	−1.52097	−	1.21592i	−0.118407	−	0.0946594i
$166$	3.99273	+	2.30521i	0.309896	+	0.178919i
$167$	23.8543	+	6.39173i	1.84590	+	0.494607i	0.999292	−	0.0376136i	$-0.0119756\pi$
$167$	23.8543	+	6.39173i	1.84590	+	0.494607i	0.846606	+	0.532221i	$0.178642\pi$
$168$	−4.03306	+	1.08066i	−0.311158	+	0.0833744i
$169$	2.36708	−	1.36664i	0.182083	−	0.105126i
$170$	10.3738	−	7.63700i	0.795635	−	0.585731i
$171$	6.44307			0.492714
$172$	−9.09264	−	2.43636i	−0.693307	−	0.185771i
$173$	−2.44020	−	9.10694i	−0.185525	−	0.692387i	−0.994518	−	0.104569i	$-0.966654\pi$
$173$	−2.44020	−	9.10694i	−0.185525	−	0.692387i	0.808993	−	0.587818i	$-0.200013\pi$
$174$	0.960076	−	0.554300i	0.0727832	−	0.0420214i
$175$	0.830699	−	20.8601i	0.0627949	−	1.57688i
$176$	0.754170	+	0.435420i	0.0568477	+	0.0328210i
$177$	0.372294	+	1.38942i	0.0279833	+	0.104435i
$178$	−0.0381791	−	0.0381791i	−0.00286164	−	0.00286164i
$179$	−4.13795	−	7.16714i	−0.309285	−	0.535697i	0.668921	−	0.743333i	$-0.266756\pi$
$179$	−4.13795	−	7.16714i	−0.309285	−	0.535697i	−0.978206	+	0.207636i	$0.933423\pi$
$180$	2.04842	+	0.896646i	0.152680	+	0.0668320i
$181$	−20.1771	−	11.6492i	−1.49975	−	0.865880i	−0.499748	−	0.866171i	$-0.666574\pi$
$181$	−20.1771	−	11.6492i	−1.49975	−	0.865880i	−1.00000		0.000290528i	$0.999908\pi$
$182$	−11.7108	+	11.7108i	−0.868061	+	0.868061i
$183$	9.36249	+	2.50867i	0.692095	+	0.185446i
$184$	−0.981290			−0.0723417
$185$	0.781487	−	5.14292i	0.0574560	−	0.378115i
$186$	3.08933	−	4.63207i	0.226521	−	0.339640i
$187$	3.54743	+	3.54743i	0.259414	+	0.259414i
$188$	−8.44460	+	8.44460i	−0.615885	+	0.615885i
$189$	−2.08767	−	3.61595i	−0.151855	−	0.263021i
$190$	2.16438	−	14.2436i	0.157020	−	1.03334i
$191$	−2.10098	+	3.63900i	−0.152022	+	0.263309i	−0.931971	−	0.362534i	$-0.881912\pi$
$191$	−2.10098	+	3.63900i	−0.152022	+	0.263309i	0.779949	+	0.625843i	$0.215245\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	19.3796	+	5.19274i	1.39497	+	0.373782i	0.876537	−	0.481335i	$-0.159848\pi$
$193$	19.3796	+	5.19274i	1.39497	+	0.373782i	0.518436	+	0.855117i	$0.326515\pi$
$194$		−	2.48683i		−	0.178544i
$195$	8.81482	−	0.982475i	0.631243	−	0.0703565i
$196$	5.21671	−	9.03561i	0.372622	−	0.645401i
$197$	2.01754	+	7.52956i	0.143744	+	0.536459i	0.999808	+	0.0195895i	$0.00623594\pi$
$197$	2.01754	+	7.52956i	0.143744	+	0.536459i	−0.856064	+	0.516869i	$0.827097\pi$
$198$	−0.225390	+	0.841167i	−0.0160178	+	0.0597791i
$199$	−12.1075	+	20.9708i	−0.858278	+	1.48658i	0.0152925	+	0.999883i	$0.495132\pi$
$199$	−12.1075	+	20.9708i	−0.858278	+	1.48658i	−0.873570	+	0.486698i	$0.838201\pi$
$200$	2.67032	−	4.22722i	0.188820	−	0.298910i
$201$		−	7.58883i		−	0.535275i
$202$	−0.725462	−	0.725462i	−0.0510433	−	0.0510433i
$203$	−1.19802	+	4.47106i	−0.0840842	+	0.313807i
$204$	−4.98908	−	2.88045i	−0.349306	−	0.201672i
$205$	4.78755	+	2.09563i	0.334377	+	0.146365i
$206$	−8.26133	+	14.3090i	−0.575594	+	0.996958i
$207$	−0.253977	−	0.947853i	−0.0176526	−	0.0658804i
$208$	−3.83136	+	1.02661i	−0.265657	+	0.0711826i
$209$	5.61088			0.388113
$210$	−8.69504	+	3.40051i	−0.600015	+	0.234657i
$211$	12.8549	+	22.2653i	0.884965	+	1.53280i	0.845754	+	0.533573i	$0.179151\pi$
$211$	12.8549	+	22.2653i	0.884965	+	1.53280i	0.0392102	+	0.999231i	$0.487516\pi$
$212$	2.03242	+	7.58508i	0.139587	+	0.520945i
$213$	−3.38578	−	3.38578i	−0.231990	−	0.231990i
$214$	7.21058	−	4.16303i	0.492905	−	0.284579i
$215$	−20.8101	−	3.16218i	−1.41924	−	0.215659i
$216$		−	1.00000i		−	0.0680414i
$217$	4.55479	+	22.7967i	0.309199	+	1.54754i
$218$	−5.66376	+	5.66376i	−0.383598	+	0.383598i
$219$		−	1.70020i		−	0.114889i
$220$	1.78385	+	0.780835i	0.120267	+	0.0526439i
$221$	−22.8507			−1.53710
$222$	−2.24712	+	0.602113i	−0.150816	+	0.0404112i
$223$	5.47960	−	20.4501i	0.366941	−	1.36944i	−0.497829	−	0.867275i	$-0.665869\pi$
$223$	5.47960	−	20.4501i	0.366941	−	1.36944i	0.864770	−	0.502168i	$-0.167464\pi$
$224$	3.61595	−	2.08767i	0.241601	−	0.139488i
$225$	4.77431	+	1.48525i	0.318287	+	0.0990163i
$226$	−3.14974	+	5.45552i	−0.209518	+	0.362896i
$227$	10.4878	−	2.81019i	0.696098	−	0.186519i	0.106616	−	0.994300i	$-0.465998\pi$
$227$	10.4878	−	2.81019i	0.696098	−	0.186519i	0.589482	+	0.807781i	$0.299332\pi$
$228$	−6.22353	+	1.66759i	−0.412163	+	0.110439i
$229$	11.5120	+	19.9394i	0.760734	+	1.31763i	0.942473	+	0.334283i	$0.108494\pi$
$229$	11.5120	+	19.9394i	0.760734	+	1.31763i	−0.181739	+	0.983347i	$0.558173\pi$
$230$	−2.18073	+	0.243058i	−0.143793	+	0.0160268i
$231$	−1.81802	−	3.14891i	−0.119617	−	0.207183i
$232$	−0.783899	+	0.783899i	−0.0514655	+	0.0514655i
$233$	−0.731249	+	0.731249i	−0.0479057	+	0.0479057i	−0.730654	−	0.682748i	$-0.760785\pi$
$233$	−0.731249	+	0.731249i	−0.0479057	+	0.0479057i	0.682748	+	0.730654i	$0.260785\pi$
$234$	−1.98326	−	3.43511i	−0.129650	−	0.224560i
$235$	−16.6748	+	20.8581i	−1.08775	+	1.36064i
$236$	−0.719216	−	1.24572i	−0.0468170	−	0.0810894i
$237$	12.0223	−	3.22136i	0.780930	−	0.209250i
$238$	23.2341	−	6.22555i	1.50604	−	0.403542i
$239$	−0.269420	+	0.466649i	−0.0174273	+	0.0301850i	−0.874608	−	0.484832i	$-0.838881\pi$
$239$	−0.269420	+	0.466649i	−0.0174273	+	0.0301850i	0.857180	+	0.515017i	$0.172214\pi$
$240$	−2.21069	−	0.335923i	−0.142700	−	0.0216838i
$241$	8.03294	−	4.63782i	0.517447	−	0.298748i	−0.218442	−	0.975850i	$-0.570098\pi$
$241$	8.03294	−	4.63782i	0.517447	−	0.298748i	0.735890	+	0.677102i	$0.236764\pi$
$242$	2.65073	−	9.89266i	0.170395	−	0.635924i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	−9.69276			−0.620515
$245$	9.35509	−	21.3720i	0.597675	−	1.36541i
$246$		−	2.33719i		−	0.149014i
$247$	−18.0712	+	18.0712i	−1.14984	+	1.14984i
$248$	−1.78520	+	5.27381i	−0.113360	+	0.334887i
$249$		−	4.61041i		−	0.292173i
$250$	4.88722	−	10.0556i	0.309095	−	0.635972i
$251$	−3.59307	+	2.07446i	−0.226793	+	0.130939i	−0.609092	−	0.793100i	$-0.708466\pi$
$251$	−3.59307	+	2.07446i	−0.226793	+	0.130939i	0.382299	+	0.924039i	$0.375132\pi$
$252$	2.95241	+	2.95241i	0.185984	+	0.185984i
$253$	−0.221173	−	0.825429i	−0.0139050	−	0.0518943i
$254$	1.85639	+	3.21537i	0.116481	+	0.201750i
$255$	−11.8007	−	5.16548i	−0.738991	−	0.323475i
$256$	1.00000			0.0625000
$257$	19.1058	−	5.11938i	1.19179	−	0.319338i	0.392195	−	0.919882i	$-0.371716\pi$
$257$	19.1058	−	5.11938i	1.19179	−	0.319338i	0.799592	+	0.600544i	$0.205049\pi$
$258$	2.43636	+	9.09264i	0.151681	+	0.566083i
$259$	4.85672	−	8.41208i	0.301782	−	0.522701i
$260$	−8.26018	+	3.23044i	−0.512275	+	0.200344i
$261$	−0.960076	−	0.554300i	−0.0594272	−	0.0343103i
$262$	5.59773	−	20.8910i	0.345829	−	1.29065i
$263$	−8.29311	−	8.29311i	−0.511375	−	0.511375i	0.403572	−	0.914948i	$-0.367768\pi$
$263$	−8.29311	−	8.29311i	−0.511375	−	0.511375i	−0.914948	+	0.403572i	$0.867768\pi$
$264$		−	0.870840i		−	0.0535965i
$265$	6.39542	+	16.3530i	0.392867	+	1.00455i
$266$	13.4510	−	23.2978i	0.824733	−	1.42848i
$267$	−0.0139745	+	0.0521536i	−0.000855226	+	0.00319175i
$268$	1.96413	+	7.33025i	0.119979	+	0.447766i
$269$	10.5909	−	18.3439i	0.645736	−	1.11845i	−0.338395	−	0.941004i	$-0.609884\pi$
$269$	10.5909	−	18.3439i	0.645736	−	1.11845i	0.984131	−	0.177443i	$-0.0567825\pi$
$270$	−0.247692	−	2.22231i	−0.0150741	−	0.135245i
$271$			20.4681i			1.24335i	0.783277	+	0.621673i	$0.213547\pi$
$271$			20.4681i			1.24335i	−0.783277	+	0.621673i	$0.786453\pi$
$272$	5.56460	+	1.49103i	0.337403	+	0.0904069i
$273$	15.9972	+	4.28644i	0.968196	+	0.259427i
$274$	6.66825	−	11.5498i	0.402844	−	0.697746i
$275$	4.15766	+	1.29341i	0.250716	+	0.0779956i
$276$	0.490645	+	0.849822i	0.0295334	+	0.0511533i
$277$	11.5436	−	11.5436i	0.693590	−	0.693590i	−0.269430	−	0.963020i	$-0.586835\pi$
$277$	11.5436	−	11.5436i	0.693590	−	0.693590i	0.963020	+	0.269430i	$0.0868353\pi$
$278$	8.19362	+	8.19362i	0.491420	+	0.491420i
$279$	−5.55615	−	0.359404i	−0.332638	−	0.0215170i
$280$	7.51864	−	5.53508i	0.449325	−	0.330784i
$281$	−18.9118			−1.12818			−0.564092	−	0.825712i	$-0.690773\pi$
$281$	−18.9118			−1.12818			−0.564092	+	0.825712i	$0.690773\pi$
$282$	11.5355	+	3.09094i	0.686931	+	0.184063i
$283$	−17.0473	+	17.0473i	−1.01336	+	1.01336i	−0.0134486	+	0.999910i	$0.504281\pi$
$283$	−17.0473	+	17.0473i	−1.01336	+	1.01336i	−0.999910	+	0.0134486i	$0.995719\pi$
$284$	4.14672	+	2.39411i	0.246063	+	0.142064i
$285$	−13.4175	+	5.24741i	−0.794786	+	0.310830i
$286$	−1.72710	−	2.99143i	−0.102126	−	0.176887i
$287$	6.90034	+	6.90034i	0.407314	+	0.407314i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	14.0191	+	8.09396i	0.824656	+	0.476115i
$290$	−1.54790	+	1.93623i	−0.0908957	+	0.113699i
$291$	−2.15366	+	1.24341i	−0.126250	+	0.0728903i
$292$	0.440045	+	1.64227i	0.0257517	+	0.0961065i
$293$	17.2490	+	4.62185i	1.00770	+	0.270011i	0.724666	−	0.689100i	$-0.241994\pi$
$293$	17.2490	+	4.62185i	1.00770	+	0.270011i	0.283030	+	0.959111i	$0.408661\pi$
$294$	−10.4334			−0.608490
$295$	−1.90687	−	2.59023i	−0.111022	−	0.150809i
$296$	2.01471	−	1.16319i	0.117103	−	0.0676092i
$297$	0.841167	−	0.225390i	0.0488095	−	0.0130785i
$298$	−4.61278	−	1.23599i	−0.267211	−	0.0715990i
$299$	3.37084	+	1.94615i	0.194940	+	0.112549i
$300$	−4.99604	−	0.198954i	−0.288447	−	0.0114866i
$301$	−34.0383	−	19.6520i	−1.96194	−	1.13272i
$302$	−2.31008	+	2.31008i	−0.132930	+	0.132930i
$303$	−0.265537	+	0.990999i	−0.0152547	+	0.0569314i
$304$	5.57986	−	3.22153i	0.320027	−	0.184768i
$305$	−21.5403	+	2.40082i	−1.23339	+	0.137471i
$306$			5.76090i			0.329328i
$307$	−2.53190	+	9.44917i	−0.144503	+	0.539292i	0.855274	+	0.518176i	$0.173389\pi$
$307$	−2.53190	+	9.44917i	−0.144503	+	0.539292i	−0.999777	+	0.0211165i	$0.993278\pi$
$308$	2.57108	+	2.57108i	0.146501	+	0.146501i
$309$	16.5227			0.939941
$310$	−2.66097	+	12.1622i	−0.151133	+	0.690767i
$311$	−17.5075			−0.992758			−0.496379	−	0.868106i	$-0.665337\pi$
$311$	−17.5075			−0.992758			−0.496379	+	0.868106i	$0.665337\pi$
$312$	2.80475	+	2.80475i	0.158788	+	0.158788i
$313$	1.91610	−	7.15099i	0.108304	−	0.404198i	−0.890395	−	0.455189i	$-0.849572\pi$
$313$	1.91610	−	7.15099i	0.108304	−	0.404198i	0.998699	+	0.0509918i	$0.0162382\pi$
$314$		−	15.5976i		−	0.880223i
$315$	7.29245	+	5.82987i	0.410883	+	0.328476i
$316$	−10.7789	+	6.22318i	−0.606359	+	0.350081i
$317$	−4.60398	+	17.1823i	−0.258585	+	0.965054i	0.707475	+	0.706738i	$0.249834\pi$
$317$	−4.60398	+	17.1823i	−0.258585	+	0.965054i	−0.966061	+	0.258316i	$0.916832\pi$
$318$	5.55266	−	5.55266i	0.311378	−	0.311378i
$319$	−0.836073	−	0.482707i	−0.0468111	−	0.0270264i
$320$	2.22231	−	0.247692i	0.124231	−	0.0138464i
$321$	−7.21058	−	4.16303i	−0.402455	−	0.232358i
$322$	−3.95761	−	1.06044i	−0.220549	−	0.0590959i
$323$	35.8531	−	9.60680i	1.99492	−	0.534537i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	−17.5565	+	9.22502i	−0.973860	+	0.511712i
$326$	21.0793			1.16748
$327$	7.73684	+	2.07308i	0.427848	+	0.114642i
$328$	0.604910	+	2.25755i	0.0334006	+	0.124653i
$329$	−43.1833	+	24.9319i	−2.38077	+	1.37454i
$330$	−0.215700	−	1.93527i	−0.0118739	−	0.106533i
$331$	−4.50150	−	2.59894i	−0.247425	−	0.142851i	0.371160	−	0.928569i	$-0.378960\pi$
$331$	−4.50150	−	2.59894i	−0.247425	−	0.142851i	−0.618585	+	0.785718i	$0.712294\pi$
$332$	1.19326	+	4.45332i	0.0654888	+	0.244407i
$333$	1.64500	+	1.64500i	0.0901456	+	0.0901456i
$334$	12.3479	+	21.3871i	0.675646	+	1.17025i
$335$	6.18055	+	15.8036i	0.337680	+	0.863441i
$336$	−3.61595	−	2.08767i	−0.197266	−	0.113892i
$337$	−10.2307	+	10.2307i	−0.557303	+	0.557303i	−0.928539	−	0.371236i	$-0.878934\pi$
$337$	−10.2307	+	10.2307i	−0.557303	+	0.557303i	0.371236	+	0.928539i	$0.378934\pi$
$338$	2.64014	+	0.707423i	0.143605	+	0.0384787i
$339$	6.29949			0.342141
$340$	12.7356	+	1.93522i	0.690683	+	0.104952i
$341$	−4.83852	−	0.312984i	−0.262021	−	0.0169490i
$342$	4.55594	+	4.55594i	0.246357	+	0.246357i
$343$	10.1369	−	10.1369i	0.547340	−	0.547340i
$344$	−4.70669	−	8.15223i	−0.253768	−	0.439539i
$345$	1.30086	+	1.76704i	0.0700358	+	0.0951341i
$346$	4.71410	−	8.16505i	0.253431	−	0.438956i
$347$	21.1304	+	5.66187i	1.13434	+	0.303945i	0.776672	−	0.629905i	$-0.216906\pi$
$347$	21.1304	+	5.66187i	1.13434	+	0.303945i	0.357666	+	0.933850i	$0.383573\pi$
$348$	1.07083	+	0.286927i	0.0574023	+	0.0153809i
$349$		−	2.50062i		−	0.133855i	−0.997758	−	0.0669275i	$-0.978680\pi$
$349$		−	2.50062i		−	0.133855i	0.997758	−	0.0669275i	$-0.0213196\pi$
$350$	15.3377	−	14.1630i	0.819837	−	0.757042i
$351$	−1.98326	+	3.43511i	−0.105859	+	0.183352i
$352$	0.225390	+	0.841167i	0.0120133	+	0.0448343i
$353$	3.71582	−	13.8676i	0.197773	−	0.738100i	−0.793758	−	0.608233i	$-0.791878\pi$
$353$	3.71582	−	13.8676i	0.197773	−	0.738100i	0.991531	−	0.129867i	$-0.0414549\pi$
$354$	−0.719216	+	1.24572i	−0.0382259	+	0.0662092i
$355$	9.80829	+	4.29334i	0.520570	+	0.227867i
$356$		−	0.0539934i		−	0.00286164i
$357$	−17.0085	−	17.0085i	−0.900186	−	0.900186i
$358$	2.14196	−	7.99391i	0.113206	−	0.422491i
$359$	−32.4084	−	18.7110i	−1.71045	−	0.987527i	−0.933947	−	0.357410i	$-0.883660\pi$
$359$	−32.4084	−	18.7110i	−1.71045	−	0.987527i	−0.776500	−	0.630117i	$-0.783007\pi$
$360$	0.814428	+	2.08248i	0.0429241	+	0.109756i
$361$	11.2566	−	19.4969i	0.592451	−	1.02615i
$362$	−6.03008	−	22.5046i	−0.316934	−	1.18281i
$363$	−9.89266	+	2.65073i	−0.519230	+	0.139127i
$364$	−16.5615			−0.868061
$365$	1.38469	+	3.54063i	0.0724780	+	0.185325i
$366$	4.84638	+	8.39418i	0.253324	+	0.438771i
$367$	6.04493	+	22.5600i	0.315543	+	1.17762i	0.923483	+	0.383640i	$0.125329\pi$
$367$	6.04493	+	22.5600i	0.315543	+	1.17762i	−0.607940	+	0.793983i	$0.708004\pi$
$368$	−0.693877	−	0.693877i	−0.0361708	−	0.0361708i
$369$	−2.02407	+	1.16860i	−0.105369	+	0.0608347i
$370$	4.18919	−	3.08400i	0.217785	−	0.160329i
$371$			32.7875i			1.70224i
$372$	5.45985	−	1.09088i	0.283080	−	0.0565595i
$373$	13.0011	−	13.0011i	0.673174	−	0.673174i	−0.285273	−	0.958446i	$-0.592084\pi$
$373$	13.0011	−	13.0011i	0.673174	−	0.673174i	0.958446	+	0.285273i	$0.0920841\pi$
$374$			5.01682i			0.259414i
$375$	−11.1520	+	0.795343i	−0.575888	+	0.0410713i
$376$	−11.9425			−0.615885
$377$	4.24745	−	1.13810i	0.218755	−	0.0586152i
$378$	1.08066	−	4.03306i	0.0555830	−	0.207438i
$379$	−0.699603	+	0.403916i	−0.0359362	+	0.0207478i	−0.517860	−	0.855465i	$-0.673271\pi$
$379$	−0.699603	+	0.403916i	−0.0359362	+	0.0207478i	0.481924	+	0.876213i	$0.339938\pi$
$380$	11.6022	−	8.54132i	0.595181	−	0.438161i
$381$	1.85639	−	3.21537i	0.0951059	−	0.164728i
$382$	−4.05878	+	1.08755i	−0.207665	+	0.0556437i
$383$	0.531882	−	0.142517i	0.0271779	−	0.00728229i	−0.245204	−	0.969471i	$-0.578855\pi$
$383$	0.531882	−	0.142517i	0.0271779	−	0.00728229i	0.272382	+	0.962189i	$0.412188\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	6.35055	+	5.07688i	0.323654	+	0.258742i
$386$	10.0316	+	17.3753i	0.510595	+	0.884377i
$387$	6.65627	−	6.65627i	0.338357	−	0.338357i
$388$	1.75845	−	1.75845i	0.0892720	−	0.0892720i
$389$	5.41465	+	9.37846i	0.274534	+	0.475507i	0.970017	−	0.243035i	$-0.0781431\pi$
$389$	5.41465	+	9.37846i	0.274534	+	0.475507i	−0.695484	+	0.718542i	$0.744810\pi$
$390$	6.92774	+	5.53831i	0.350800	+	0.280443i
$391$	−2.82655	−	4.89574i	−0.142945	−	0.247588i
$392$	10.0779	−	2.70037i	0.509012	−	0.136389i
$393$	−20.8910	+	5.59773i	−1.05381	+	0.282368i
$394$	−3.89758	+	6.75081i	−0.196357	+	0.340101i
$395$	−22.4125	+	16.4997i	−1.12770	+	0.830188i
$396$	−0.754170	+	0.435420i	−0.0378984	+	0.0218807i
$397$	−0.332757	+	1.24187i	−0.0167006	+	0.0623275i	−0.973773	−	0.227521i	$-0.926938\pi$
$397$	−0.332757	+	1.24187i	−0.0167006	+	0.0623275i	0.957073	+	0.289848i	$0.0936048\pi$
$398$	−23.3899	+	6.26730i	−1.17243	+	0.314152i
$399$	−26.9020			−1.34678
$400$	4.87730	−	1.10090i	0.243865	−	0.0550448i
$401$		−	35.5501i		−	1.77529i	−0.460531	−	0.887644i	$-0.652341\pi$
$401$		−	35.5501i		−	1.77529i	0.460531	−	0.887644i	$-0.347659\pi$
$402$	5.36611	−	5.36611i	0.267637	−	0.267637i
$403$	16.5917	−	14.5756i	0.826490	−	0.726062i
$404$		−	1.02596i		−	0.0510433i
$405$	−1.80073	+	1.32566i	−0.0894789	+	0.0658726i
$406$	−4.00864	+	2.31439i	−0.198945	+	0.114861i
$407$	1.43253	+	1.43253i	0.0710081	+	0.0710081i
$408$	−1.49103	−	5.56460i	−0.0738170	−	0.275489i
$409$	9.82547	+	17.0182i	0.485838	+	0.841497i	0.999868	−	0.0162760i	$-0.00518103\pi$
$409$	9.82547	+	17.0182i	0.485838	+	0.841497i	−0.514029	+	0.857773i	$0.671848\pi$
$410$	1.90347	+	4.86715i	0.0940059	+	0.240371i
$411$	−13.3365			−0.657841
$412$	−15.9597	+	4.27638i	−0.786276	+	0.210682i
$413$	−1.55445	−	5.80129i	−0.0764895	−	0.285463i
$414$	0.490645	−	0.849822i	0.0241139	−	0.0417665i
$415$	3.75485	+	9.60107i	0.184318	+	0.471298i
$416$	−3.43511	−	1.98326i	−0.168420	−	0.0972373i
$417$	2.99907	−	11.1927i	0.146865	−	0.548108i
$418$	3.96749	+	3.96749i	0.194056	+	0.194056i
$419$			0.647286i			0.0316220i	0.999875	+	0.0158110i	$0.00503301\pi$
$419$			0.647286i			0.0316220i	−0.999875	+	0.0158110i	$0.994967\pi$
$420$	−8.55284	−	3.74380i	−0.417336	−	0.182679i
$421$	18.0654	−	31.2902i	0.880455	−	1.52499i	0.0296198	−	0.999561i	$-0.490570\pi$
$421$	18.0654	−	31.2902i	0.880455	−	1.52499i	0.850836	−	0.525432i	$-0.176096\pi$
$422$	−6.65416	+	24.8337i	−0.323919	+	1.20888i
$423$	−3.09094	−	11.5355i	−0.150286	−	0.560877i
$424$	−3.92633	+	6.80060i	−0.190679	+	0.330266i
$425$	28.7817	+	1.14615i	1.39612	+	0.0555966i
$426$		−	4.78822i		−	0.231990i
$427$	−39.0915	−	10.4745i	−1.89177	−	0.506899i
$428$	8.04236	+	2.15494i	0.388742	+	0.104163i
$429$	−1.72710	+	2.99143i	−0.0833853	+	0.144427i
$430$	−12.4790	−	16.9510i	−0.601789	−	0.817448i
$431$	−13.7281	−	23.7777i	−0.661257	−	1.14533i	−0.980285	−	0.197586i	$-0.936690\pi$
$431$	−13.7281	−	23.7777i	−0.661257	−	1.14533i	0.319028	−	0.947745i	$-0.396644\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−1.36845	−	1.36845i	−0.0657635	−	0.0657635i	0.673460	−	0.739224i	$-0.264807\pi$
$433$	−1.36845	−	1.36845i	−0.0657635	−	0.0657635i	−0.739224	+	0.673460i	$0.764807\pi$
$434$	−12.8990	+	19.3404i	−0.619171	+	0.928371i
$435$	2.45077	+	0.372405i	0.117506	+	0.0178554i
$436$	−8.00977			−0.383598
$437$	−6.10708	−	1.63639i	−0.292141	−	0.0782791i
$438$	1.20222	−	1.20222i	0.0574445	−	0.0574445i
$439$	−22.3625	−	12.9110i	−1.06730	−	0.616208i	−0.139860	−	0.990171i	$-0.544665\pi$
$439$	−22.3625	−	12.9110i	−1.06730	−	0.616208i	−0.927444	+	0.373963i	$0.877999\pi$
$440$	0.709236	+	1.81350i	0.0338115	+	0.0864554i
$441$	5.21671	+	9.03561i	0.248415	+	0.430267i
$442$	−16.1579	−	16.1579i	−0.768552	−	0.768552i
$443$	4.18478	+	15.6178i	0.198825	+	0.742025i	0.991243	+	0.132047i	$0.0421549\pi$
$443$	4.18478	+	15.6178i	0.198825	+	0.742025i	−0.792419	+	0.609978i	$0.791178\pi$
$444$	−2.01471	−	1.16319i	−0.0956138	−	0.0552027i
$445$	−0.0133737	−	0.119990i	−0.000633976	−	0.00568807i
$446$	18.3351	−	10.5858i	0.868192	−	0.501251i
$447$	1.23599	+	4.61278i	0.0584603	+	0.218177i
$448$	4.03306	+	1.08066i	0.190544	+	0.0510562i
$449$	−8.33811			−0.393500			−0.196750	−	0.980454i	$-0.563039\pi$
$449$	−8.33811			−0.393500			−0.196750	+	0.980454i	$0.563039\pi$
$450$	2.32572	+	4.42617i	0.109636	+	0.208652i
$451$	−1.76264	+	1.01766i	−0.0829994	+	0.0479197i
$452$	−6.08484	+	1.63043i	−0.286207	+	0.0766888i
$453$	3.15563	+	0.845548i	0.148264	+	0.0397273i
$454$	9.40308	+	5.42887i	0.441309	+	0.254790i
$455$	−36.8048	+	4.10216i	−1.72544	+	0.192312i
$456$	−5.57986	−	3.22153i	−0.261301	−	0.150862i
$457$	−4.66903	+	4.66903i	−0.218408	+	0.218408i	−0.807827	−	0.589419i	$-0.799357\pi$
$457$	−4.66903	+	4.66903i	−0.218408	+	0.218408i	0.589419	+	0.807827i	$0.299357\pi$
$458$	−5.95905	+	22.2395i	−0.278448	+	1.03918i
$459$	4.98908	−	2.88045i	0.232870	−	0.134448i
$460$	−1.71388	−	1.37014i	−0.0799098	−	0.0638831i
$461$			7.05026i			0.328363i	0.986430	+	0.164182i	$0.0524983\pi$
$461$			7.05026i			0.328363i	−0.986430	+	0.164182i	$0.947502\pi$
$462$	0.941079	−	3.51215i	0.0437829	−	0.163400i
$463$	−14.1668	−	14.1668i	−0.658385	−	0.658385i	0.296613	−	0.954998i	$-0.404143\pi$
$463$	−14.1668	−	14.1668i	−0.658385	−	0.658385i	−0.954998	+	0.296613i	$0.904143\pi$
$464$	−1.10860			−0.0514655
$465$	11.8633	−	3.77663i	0.550146	−	0.175137i
$466$	−1.03414			−0.0479057
$467$	2.77237	+	2.77237i	0.128290	+	0.128290i	0.768336	−	0.640046i	$-0.221085\pi$
$467$	2.77237	+	2.77237i	0.128290	+	0.128290i	−0.640046	+	0.768336i	$0.721085\pi$
$468$	1.02661	−	3.83136i	0.0474551	−	0.177105i
$469$			31.6859i			1.46312i
$470$	−26.5398	+	2.95805i	−1.22419	+	0.136445i
$471$	−13.5079	+	7.79880i	−0.622412	+	0.359350i
$472$	0.372294	−	1.38942i	0.0171362	−	0.0639532i
$473$	5.79655	−	5.79655i	0.266526	−	0.266526i
$474$	10.7789	+	6.22318i	0.495090	+	0.285840i
$475$	23.6681	−	21.8552i	1.08597	−	1.00279i
$476$	20.8311	+	12.0268i	0.954792	+	0.551249i
$477$	−7.58508	−	2.03242i	−0.347297	−	0.0930579i
$478$	−0.520479	+	0.139462i	−0.0238062	+	0.00637884i
$479$	−8.72858	+	5.03945i	−0.398819	+	0.230258i	−0.685974	−	0.727626i	$-0.740624\pi$
$479$	−8.72858	+	5.03945i	−0.398819	+	0.230258i	0.287155	+	0.957884i	$0.407290\pi$
$480$	−1.32566	−	1.80073i	−0.0605079	−	0.0821916i
$481$	−9.22765			−0.420745
$482$	8.95958	+	2.40071i	0.408098	+	0.109349i
$483$	1.06044	+	3.95761i	0.0482516	+	0.180077i
$484$	8.86952	−	5.12082i	0.403160	−	0.232764i
$485$	3.47227	−	4.34338i	0.157668	−	0.197223i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	−0.816027	−	3.04545i	−0.0369777	−	0.138003i	0.944969	−	0.327159i	$-0.106091\pi$
$487$	−0.816027	−	3.04545i	−0.0369777	−	0.138003i	−0.981947	+	0.189156i	$0.939425\pi$
$488$	−6.85382	−	6.85382i	−0.310258	−	0.310258i
$489$	−10.5397	−	18.2552i	−0.476620	−	0.825531i
$490$	21.7274	−	8.49727i	0.981542	−	0.383868i
$491$	16.9215	+	9.76963i	0.763656	+	0.440897i	0.830607	−	0.556859i	$-0.187994\pi$
$491$	16.9215	+	9.76963i	0.763656	+	0.440897i	−0.0669507	+	0.997756i	$0.521327\pi$
$492$	1.65264	−	1.65264i	0.0745070	−	0.0745070i
$493$	−6.16891	−	1.65296i	−0.277834	−	0.0744454i
$494$	−25.5565			−1.14984
$495$	−1.56815	+	1.15444i	−0.0704829	+	0.0518882i
$496$	−4.99147	+	2.46682i	−0.224124	+	0.110764i
$497$	14.1368	+	14.1368i	0.634121	+	0.634121i
$498$	3.26005	−	3.26005i	0.146086	−	0.146086i
$499$	−9.15954	−	15.8648i	−0.410037	−	0.710206i	0.584856	−	0.811137i	$-0.301151\pi$
$499$	−9.15954	−	15.8648i	−0.410037	−	0.710206i	−0.994893	+	0.100931i	$0.967818\pi$
$500$	10.5662	−	3.65460i	0.472533	−	0.163439i
$501$	12.3479	−	21.3871i	0.551662	−	0.955507i
$502$	−4.00755	−	1.07382i	−0.178866	−	0.0479269i
$503$	−30.3754	−	8.13907i	−1.35437	−	0.362903i	−0.492626	−	0.870241i	$-0.663963\pi$
$503$	−30.3754	−	8.13907i	−1.35437	−	0.362903i	−0.861747	+	0.507338i	$0.830630\pi$
$504$			4.17534i			0.185984i
$505$	−0.254122	−	2.27999i	−0.0113083	−	0.101458i
$506$	0.427273	−	0.740059i	0.0189946	−	0.0328996i
$507$	−0.707423	−	2.64014i	−0.0314178	−	0.117253i
$508$	−0.960940	+	3.58628i	−0.0426348	+	0.159115i
$509$	−15.5407	+	26.9172i	−0.688828	+	1.19308i	0.283389	+	0.959005i	$0.408541\pi$
$509$	−15.5407	+	26.9172i	−0.688828	+	1.19308i	−0.972217	+	0.234080i	$0.924792\pi$
$510$	−4.69183	−	11.9969i	−0.207758	−	0.531233i
$511$			7.09891i			0.314037i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	1.66759	−	6.22353i	0.0736258	−	0.274775i
$514$	17.1298	+	9.88989i	0.755563	+	0.436224i
$515$	−34.4081	+	13.4565i	−1.51620	+	0.592965i
$516$	−4.70669	+	8.15223i	−0.207201	+	0.358882i
$517$	−2.69171	−	10.0456i	−0.118381	−	0.441805i
$518$	9.38246	−	2.51402i	0.412242	−	0.110460i
$519$	−9.42819			−0.413852
$520$	−8.12510	−	3.55656i	−0.356309	−	0.155966i
$521$	12.8799	+	22.3087i	0.564279	+	0.977360i	0.997116	+	0.0758879i	$0.0241791\pi$
$521$	12.8799	+	22.3087i	0.564279	+	0.977360i	−0.432837	+	0.901472i	$0.642488\pi$
$522$	−0.286927	−	1.07083i	−0.0125584	−	0.0468688i
$523$	−4.90085	−	4.90085i	−0.214299	−	0.214299i	0.591792	−	0.806091i	$-0.298421\pi$
$523$	−4.90085	−	4.90085i	−0.214299	−	0.214299i	−0.806091	+	0.591792i	$0.798421\pi$
$524$	18.7304	−	10.8140i	0.818240	−	0.472411i
$525$	−19.9344	−	6.20140i	−0.870006	−	0.270651i
$526$		−	11.7282i		−	0.511375i
$527$	−31.4536	+	6.28445i	−1.37014	+	0.273755i
$528$	0.615777	−	0.615777i	0.0267982	−	0.0267982i
$529$		−	22.0371i		−	0.958133i
$530$	−7.04105	+	16.0855i	−0.305844	+	0.698711i
$531$	1.43843			0.0624226
$532$	25.9853	−	6.96274i	1.12661	−	0.301873i
$533$	2.39939	−	8.95463i	0.103929	−	0.387868i
$534$	−0.0467596	+	0.0269967i	−0.00202349	+	0.00116826i
$535$	18.4064	+	2.79692i	0.795776	+	0.120921i
$536$	−3.79441	+	6.57212i	−0.163894	+	0.283872i
$537$	−7.99391	+	2.14196i	−0.344963	+	0.0924324i
$538$	20.4600	−	5.48223i	0.882091	−	0.236356i
$539$	4.54292	+	7.86857i	0.195678	+	0.338923i
$540$	1.39626	−	1.74655i	0.0600856	−	0.0751597i
$541$	−8.84320	−	15.3169i	−0.380199	−	0.658523i	0.610892	−	0.791714i	$-0.290811\pi$
$541$	−8.84320	−	15.3169i	−0.380199	−	0.658523i	−0.991090	+	0.133191i	$0.957478\pi$
$542$	−14.4731	+	14.4731i	−0.621673	+	0.621673i
$543$	−16.4745	+	16.4745i	−0.706988	+	0.706988i
$544$	2.88045	+	4.98908i	0.123498	+	0.213905i
$545$	−17.8002	+	1.98396i	−0.762475	+	0.0849833i
$546$	8.28077	+	14.3427i	0.354384	+	0.613812i
$547$	−34.0454	+	9.12243i	−1.45568	+	0.390047i	−0.897994	−	0.440008i	$-0.854976\pi$
$547$	−34.0454	+	9.12243i	−1.45568	+	0.390047i	−0.557682	+	0.830055i	$0.688309\pi$
$548$	12.8821	−	3.45174i	0.550295	−	0.147451i
$549$	4.84638	−	8.39418i	0.206838	−	0.358255i
$550$	2.02533	+	3.85449i	0.0863604	+	0.164356i
$551$	−6.18583	+	3.57139i	−0.263525	+	0.152146i
$552$	−0.253977	+	0.947853i	−0.0108100	+	0.0403433i
$553$	−50.1970	+	13.4502i	−2.13459	+	0.571962i
$554$	16.3252			0.693590
$555$	−4.76541	−	2.08594i	−0.202281	−	0.0885434i
$556$			11.5875i			0.491420i
$557$	30.0497	−	30.0497i	1.27324	−	1.27324i	0.328869	−	0.944375i	$-0.393332\pi$
$557$	30.0497	−	30.0497i	1.27324	−	1.27324i	0.944375	−	0.328869i	$-0.106668\pi$
$558$	−3.67466	−	4.18293i	−0.155561	−	0.177078i
$559$			37.3384i			1.57925i
$560$	9.23038	+	1.40259i	0.390055	+	0.0592703i
$561$	4.34469	−	2.50841i	0.183433	−	0.105905i
$562$	−13.3727	−	13.3727i	−0.564092	−	0.564092i
$563$	4.67892	+	17.4620i	0.197193	+	0.735934i	0.991688	+	0.128664i	$0.0410688\pi$
$563$	4.67892	+	17.4620i	0.197193	+	0.735934i	−0.794495	+	0.607270i	$0.792265\pi$
$564$	5.97123	+	10.3425i	0.251434	+	0.435497i
$565$	−13.1185	+	5.13048i	−0.551901	+	0.215841i
$566$	−24.1086			−1.01336
$567$	−4.03306	+	1.08066i	−0.169373	+	0.0453833i
$568$	1.23928	+	4.62507i	0.0519991	+	0.194063i
$569$	18.7961	−	32.5558i	0.787974	−	1.36481i	−0.139232	−	0.990260i	$-0.544463\pi$
$569$	18.7961	−	32.5558i	0.787974	−	1.36481i	0.927206	−	0.374551i	$-0.122203\pi$
$570$	−13.1981	−	5.77715i	−0.552808	−	0.241978i
$571$	−25.6173	−	14.7902i	−1.07205	−	0.618950i	−0.143311	−	0.989678i	$-0.545775\pi$
$571$	−25.6173	−	14.7902i	−1.07205	−	0.618950i	−0.928741	+	0.370728i	$0.879108\pi$
$572$	0.894014	−	3.33650i	0.0373806	−	0.139506i
$573$	2.97123	+	2.97123i	0.124125	+	0.124125i
$574$			9.75856i			0.407314i
$575$	−4.14813	−	2.62036i	−0.172989	−	0.109276i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	4.29413	−	16.0259i	0.178767	−	0.667167i	−0.817113	−	0.576478i	$-0.804427\pi$
$577$	4.29413	−	16.0259i	0.178767	−	0.667167i	0.995879	−	0.0906886i	$-0.0289068\pi$
$578$	4.18974	+	15.6363i	0.174270	+	0.650386i
$579$	10.0316	−	17.3753i	0.416899	−	0.722091i
$580$	−2.46365	+	0.274592i	−0.102298	+	0.0114018i
$581$			19.2500i			0.798625i
$582$	−2.40209	−	0.643639i	−0.0995700	−	0.0266797i
$583$	−6.60539	−	1.76991i	−0.273567	−	0.0733021i
$584$	−0.850101	+	1.47242i	−0.0351774	+	0.0609291i
$585$	1.33245	−	8.76875i	0.0550899	−	0.362543i
$586$	8.92873	+	15.4650i	0.368842	+	0.638854i
$587$	12.2086	−	12.2086i	0.503901	−	0.503901i	−0.408746	−	0.912648i	$-0.634034\pi$
$587$	12.2086	−	12.2086i	0.503901	−	0.503901i	0.912648	+	0.408746i	$0.134034\pi$
$588$	−7.37755	−	7.37755i	−0.304245	−	0.304245i
$589$	−19.9048	+	29.8447i	−0.820161	+	1.22973i
$590$	0.483203	−	3.17993i	0.0198931	−	0.130916i
$591$	7.79517			0.320650
$592$	2.24712	+	0.602113i	0.0923559	+	0.0247467i
$593$	−1.11525	+	1.11525i	−0.0457978	+	0.0457978i	−0.729635	−	0.683837i	$-0.760310\pi$
$593$	−1.11525	+	1.11525i	−0.0457978	+	0.0457978i	0.683837	+	0.729635i	$0.260310\pi$
$594$	0.754170	+	0.435420i	0.0309440	+	0.0178655i
$595$	49.2720	+	21.5676i	2.01996	+	0.884186i
$596$	−2.38775	−	4.13570i	−0.0978061	−	0.169405i
$597$	17.1226	+	17.1226i	0.700781	+	0.700781i
$598$	1.00740	+	3.75968i	0.0411958	+	0.153745i
$599$	35.9287	+	20.7435i	1.46801	+	0.847554i	0.999358	−	0.0358297i	$-0.0114074\pi$
$599$	35.9287	+	20.7435i	1.46801	+	0.847554i	0.468650	+	0.883384i	$0.344741\pi$
$600$	−3.39205	−	3.67342i	−0.138480	−	0.149967i
$601$	−11.1838	+	6.45696i	−0.456196	+	0.263385i	−0.710443	−	0.703754i	$-0.751506\pi$
$601$	−11.1838	+	6.45696i	−0.456196	+	0.263385i	0.254248	+	0.967139i	$0.418172\pi$
$602$	−10.1726	−	37.9648i	−0.414606	−	1.54733i
$603$	−7.33025	−	1.96413i	−0.298511	−	0.0799857i
$604$	−3.26695			−0.132930
$605$	18.4424	−	13.5769i	0.749790	−	0.551981i
$606$	−0.888505	+	0.512979i	−0.0360931	+	0.0208383i
$607$	7.23289	−	1.93805i	0.293574	−	0.0786629i	−0.109026	−	0.994039i	$-0.534773\pi$
$607$	7.23289	−	1.93805i	0.293574	−	0.0786629i	0.402600	+	0.915376i	$0.368107\pi$
$608$	6.22353	+	1.66759i	0.252397	+	0.0676296i
$609$	4.00864	+	2.31439i	0.162438	+	0.0937838i
$610$	−16.9289	−	13.5336i	−0.685432	−	0.547961i
$611$	41.0236	+	23.6850i	1.65964	+	0.958193i
$612$	−4.07357	+	4.07357i	−0.164664	+	0.164664i
$613$	−3.22799	+	12.0470i	−0.130377	+	0.486575i	−0.999974	−	0.00718759i	$-0.997712\pi$
$613$	−3.22799	+	12.0470i	−0.130377	+	0.486575i	0.869597	+	0.493762i	$0.164379\pi$
$614$	−8.47189	+	4.89125i	−0.341898	+	0.197395i
$615$	3.26334	−	4.08203i	0.131590	−	0.164603i
$616$			3.63605i			0.146501i
$617$	−12.6474	+	47.2008i	−0.509166	+	1.90023i	−0.0805366	+	0.996752i	$0.525663\pi$
$617$	−12.6474	+	47.2008i	−0.509166	+	1.90023i	−0.428629	+	0.903481i	$0.641003\pi$
$618$	11.6833	+	11.6833i	0.469971	+	0.469971i
$619$	20.9307			0.841276			0.420638	−	0.907229i	$-0.361806\pi$
$619$	20.9307			0.841276			0.420638	+	0.907229i	$0.361806\pi$
$620$	−10.4816	+	6.71839i	−0.420950	+	0.269817i
$621$	−0.981290			−0.0393778
$622$	−12.3797	−	12.3797i	−0.496379	−	0.496379i
$623$	0.0583483	−	0.217759i	0.00233768	−	0.00872432i
$624$			3.96652i			0.158788i
$625$	22.5761	−	10.7388i	0.903042	−	0.429552i
$626$	6.41140	−	3.70162i	0.256251	−	0.147947i
$627$	1.45220	−	5.41969i	0.0579954	−	0.216442i
$628$	11.0292	−	11.0292i	0.440112	−	0.440112i
$629$	11.6065	+	6.70103i	0.462782	+	0.267188i
$630$	1.03420	+	9.27888i	0.0412034	+	0.369679i
$631$	−1.84815	−	1.06703i	−0.0735739	−	0.0424779i	0.462762	−	0.886483i	$-0.346859\pi$
$631$	−1.84815	−	1.06703i	−0.0735739	−	0.0424779i	−0.536336	+	0.844005i	$0.680192\pi$
$632$	−12.0223	−	3.22136i	−0.478220	−	0.128139i
$633$	24.8337	−	6.65416i	0.987050	−	0.264479i
$634$	−15.4052	+	8.89421i	−0.611820	+	0.353234i
$635$	−1.24721	+	8.20783i	−0.0494941	+	0.325718i
$636$	7.85265			0.311378
$637$	−39.9742	−	10.7111i	−1.58384	−	0.424388i
$638$	−0.249867	−	0.932518i	−0.00989235	−	0.0369187i
$639$	−4.14672	+	2.39411i	−0.164042	+	0.0947095i
$640$	1.74655	+	1.39626i	0.0690386	+	0.0551922i
$641$	9.82275	+	5.67117i	0.387975	+	0.223998i	0.681282	−	0.732021i	$-0.261423\pi$
$641$	9.82275	+	5.67117i	0.387975	+	0.223998i	−0.293307	+	0.956018i	$0.594756\pi$
$642$	−2.15494	−	8.04236i	−0.0850489	−	0.317407i
$643$	11.4718	+	11.4718i	0.452403	+	0.452403i	0.896151	−	0.443748i	$-0.146352\pi$
$643$	11.4718	+	11.4718i	0.452403	+	0.452403i	−0.443748	+	0.896151i	$0.646352\pi$
$644$	−2.04861	−	3.54829i	−0.0807264	−	0.139822i
$645$	−8.44048	+	19.2826i	−0.332343	+	0.759251i
$646$	32.1450	+	18.5589i	1.26473	+	0.730191i
$647$	−33.2601	+	33.2601i	−1.30759	+	1.30759i	−0.384436	+	0.923151i	$0.625604\pi$
$647$	−33.2601	+	33.2601i	−1.30759	+	1.30759i	−0.923151	+	0.384436i	$0.874396\pi$
$648$	−0.965926	−	0.258819i	−0.0379452	−	0.0101674i
$649$	1.25264			0.0491706
$650$	−18.9374	−	5.89125i	−0.742786	−	0.231074i
$651$	23.1988	+	1.50063i	0.909233	+	0.0588144i
$652$	14.9053	+	14.9053i	0.583738	+	0.583738i
$653$	31.3569	−	31.3569i	1.22709	−	1.22709i	0.262032	−	0.965059i	$-0.415607\pi$
$653$	31.3569	−	31.3569i	1.22709	−	1.22709i	0.965059	−	0.262032i	$-0.0843927\pi$
$654$	4.00488	+	6.93666i	0.156603	+	0.271245i
$655$	38.9461	−	28.6714i	1.52175	−	1.12028i
$656$	−1.16860	+	2.02407i	−0.0456260	+	0.0790266i
$657$	−1.64227	−	0.440045i	−0.0640710	−	0.0171678i
$658$	−48.1647	−	12.9057i	−1.87766	−	0.503116i
$659$		−	7.26049i		−	0.282828i	−0.989951	−	0.141414i	$-0.954835\pi$
$659$		−	7.26049i		−	0.282828i	0.989951	−	0.141414i	$-0.0451649\pi$
$660$	1.21592	−	1.52097i	0.0473297	−	0.0592036i
$661$	−7.68366	+	13.3085i	−0.298860	+	0.517640i	−0.975875	−	0.218328i	$-0.929940\pi$
$661$	−7.68366	+	13.3085i	−0.298860	+	0.517640i	0.677016	+	0.735969i	$0.263273\pi$
$662$	−1.34531	−	5.02078i	−0.0522871	−	0.195138i
$663$	−5.91420	+	22.0721i	−0.229688	+	0.857209i
$664$	−2.30521	+	3.99273i	−0.0894593	+	0.154948i
$665$	56.0227	−	21.9097i	2.17247	−	0.849622i
$666$			2.32638i			0.0901456i
$667$	0.769232	+	0.769232i	0.0297848	+	0.0297848i
$668$	−6.39173	+	23.8543i	−0.247303	+	0.922949i
$669$	−18.3351	−	10.5858i	−0.708876	−	0.409270i
$670$	−6.80449	+	15.5451i	−0.262880	+	0.600560i
$671$	4.22042	−	7.30998i	0.162928	−	0.282199i
$672$	−1.08066	−	4.03306i	−0.0416872	−	0.155579i
$673$	12.5538	−	3.36378i	0.483914	−	0.129664i	−0.00861079	−	0.999963i	$-0.502741\pi$
$673$	12.5538	−	3.36378i	0.483914	−	0.129664i	0.492524	+	0.870299i	$0.336074\pi$
$674$	−14.4684			−0.557303
$675$	2.67032	−	4.22722i	0.102781	−	0.162706i
$676$	1.36664	+	2.36708i	0.0525629	+	0.0910417i
$677$	8.94242	+	33.3736i	0.343685	+	1.28265i	0.894141	+	0.447786i	$0.147787\pi$
$677$	8.94242	+	33.3736i	0.343685	+	1.28265i	−0.550455	+	0.834865i	$0.685546\pi$
$678$	4.45441	+	4.45441i	0.171071	+	0.171071i
$679$	8.99224	−	5.19167i	0.345091	−	0.199238i
$680$	7.63700	+	10.3738i	0.292865	+	0.397817i
$681$		−	10.8577i		−	0.416070i
$682$	−3.20004	−	3.64266i	−0.122536	−	0.139485i
$683$	−35.3674	+	35.3674i	−1.35329	+	1.35329i	−0.471346	+	0.881948i	$0.656232\pi$
$683$	−35.3674	+	35.3674i	−1.35329	+	1.35329i	−0.881948	+	0.471346i	$0.843768\pi$
$684$			6.44307i			0.246357i
$685$	27.7730	−	10.8616i	1.06115	−	0.415001i
$686$	14.3357			0.547340
$687$	22.2395	−	5.95905i	0.848488	−	0.227352i
$688$	2.43636	−	9.09264i	0.0928855	−	0.346653i
$689$	26.9747	−	15.5738i	1.02765	−	0.593316i
$690$	−0.329638	+	2.16933i	−0.0125491	+	0.0825849i
$691$	−20.3718	+	35.2850i	−0.774980	+	1.34230i	0.159826	+	0.987145i	$0.448907\pi$
$691$	−20.3718	+	35.2850i	−0.774980	+	1.34230i	−0.934806	+	0.355159i	$0.884427\pi$
$692$	9.10694	−	2.44020i	0.346194	−	0.0927623i
$693$	−3.51215	+	0.941079i	−0.133416	+	0.0357486i
$694$	10.9379	+	18.9450i	0.415196	+	0.719141i
$695$	2.87014	+	25.7510i	0.108871	+	0.976793i
$696$	0.554300	+	0.960076i	0.0210107	+	0.0363916i
$697$	−9.52071	+	9.52071i	−0.360623	+	0.360623i
$698$	1.76820	−	1.76820i	0.0669275	−	0.0669275i
$699$	0.517071	+	0.895594i	0.0195574	+	0.0338745i
$700$	20.8601	+	0.830699i	0.788439	+	0.0313975i
$701$	13.1724	+	22.8153i	0.497515	+	0.861721i	0.999996	−	0.00286732i	$-0.000912697\pi$
$701$	13.1724	+	22.8153i	0.497515	+	0.861721i	−0.502481	+	0.864588i	$0.667579\pi$
$702$	−3.83136	+	1.02661i	−0.144605	+	0.0387469i
$703$	14.4783	−	3.87945i	0.546060	−	0.146316i
$704$	−0.435420	+	0.754170i	−0.0164105	+	0.0284238i
$705$	15.8317	+	21.5051i	0.596255	+	0.809930i
$706$	12.4334	−	7.17842i	0.467937	−	0.270163i
$707$	1.10871	−	4.13775i	0.0416972	−	0.155616i
$708$	−1.38942	+	0.372294i	−0.0522176	+	0.0139917i
$709$	21.0997			0.792414			0.396207	−	0.918161i	$-0.370326\pi$
$709$	21.0997			0.792414			0.396207	+	0.918161i	$0.370326\pi$
$710$	3.89966	+	9.97135i	0.146352	+	0.374218i
$711$		−	12.4464i		−	0.466775i
$712$	0.0381791	−	0.0381791i	0.00143082	−	0.00143082i
$713$	5.17514	+	1.75179i	0.193810	+	0.0656052i
$714$		−	24.0537i		−	0.900186i
$715$	1.16035	−	7.63618i	0.0433945	−	0.285577i
$716$	7.16714	−	4.13795i	0.267849	−	0.154642i
$717$	0.381017	+	0.381017i	0.0142293	+	0.0142293i
$718$	−9.68551	−	36.1468i	−0.361460	−	1.34899i
$719$	−17.0520	−	29.5349i	−0.635931	−	1.10146i	−0.986317	−	0.164859i	$-0.947283\pi$
$719$	−17.0520	−	29.5349i	−0.635931	−	1.10146i	0.350386	−	0.936605i	$-0.386050\pi$
$720$	−0.896646	+	2.04842i	−0.0334160	+	0.0763401i
$721$	−68.9877			−2.56923
$722$	21.7460	−	5.82682i	0.809302	−	0.216852i
$723$	−2.40071	−	8.95958i	−0.0892835	−	0.333210i
$724$	11.6492	−	20.1771i	0.432940	−	0.749874i
$725$	−5.40697	+	1.22045i	−0.200810	+	0.0453265i
$726$	−8.86952	−	5.12082i	−0.329179	−	0.190051i
$727$	10.3605	−	38.6660i	0.384251	−	1.43404i	−0.455093	−	0.890444i	$-0.650394\pi$
$727$	10.3605	−	38.6660i	0.384251	−	1.43404i	0.839344	−	0.543600i	$-0.182939\pi$
$728$	−11.7108	−	11.7108i	−0.434030	−	0.434030i
$729$		−	1.00000i		−	0.0370370i
$730$	−1.52448	+	3.48273i	−0.0564235	+	0.128902i
$731$	27.1148	−	46.9642i	1.00288	−	1.73703i
$732$	−2.50867	+	9.36249i	−0.0927231	+	0.346047i
$733$	−9.26180	−	34.5655i	−0.342093	−	1.27671i	−0.895972	−	0.444110i	$-0.853520\pi$
$733$	−9.26180	−	34.5655i	−0.342093	−	1.27671i	0.553880	−	0.832597i	$-0.313147\pi$
$734$	−11.6779	+	20.2267i	−0.431040	+	0.746583i
$735$	−18.2225	−	14.5678i	−0.672148	−	0.537342i
$736$		−	0.981290i		−	0.0361708i
$737$	−6.38347	−	1.71045i	−0.235138	−	0.0630051i
$738$	−2.25755	−	0.604910i	−0.0831017	−	0.0222670i
$739$	14.5011	−	25.1166i	0.533430	−	0.923928i	−0.465807	−	0.884886i	$-0.654236\pi$
$739$	14.5011	−	25.1166i	0.533430	−	0.923928i	0.999238	−	0.0390422i	$-0.0124307\pi$
$740$	5.14292	+	0.781487i	0.189057	+	0.0287280i
$741$	12.7783	+	22.1326i	0.469422	+	0.813062i
$742$	−23.1842	+	23.1842i	−0.851120	+	0.851120i
$743$	2.96070	+	2.96070i	0.108618	+	0.108618i	0.759327	−	0.650709i	$-0.225528\pi$
$743$	2.96070	+	2.96070i	0.108618	+	0.108618i	−0.650709	+	0.759327i	$0.725528\pi$
$744$	4.63207	+	3.08933i	0.169820	+	0.113260i
$745$	−6.33070	−	8.59938i	−0.231939	−	0.315057i
$746$	18.3864			0.673174
$747$	−4.45332	−	1.19326i	−0.162938	−	0.0436592i
$748$	−3.54743	+	3.54743i	−0.129707	+	0.129707i
$749$	30.1066	+	17.3821i	1.10007	+	0.635126i
$750$	−8.44806	−	7.32327i	−0.308479	−	0.267408i
$751$	14.4220	+	24.9796i	0.526265	+	0.911519i	0.999532	+	0.0305991i	$0.00974152\pi$
$751$	14.4220	+	24.9796i	0.526265	+	0.911519i	−0.473266	+	0.880919i	$0.656925\pi$
$752$	−8.44460	−	8.44460i	−0.307943	−	0.307943i
$753$	1.07382	+	4.00755i	0.0391322	+	0.146043i
$754$	3.80816	+	2.19864i	0.138685	+	0.0800698i
$755$	−7.26016	+	0.809197i	−0.264224	+	0.0294497i
$756$	3.61595	−	2.08767i	0.131511	−	0.0759277i
$757$	−13.9889	−	52.2072i	−0.508434	−	1.89750i	−0.435556	−	0.900162i	$-0.643448\pi$
$757$	−13.9889	−	52.2072i	−0.508434	−	1.89750i	−0.0728780	−	0.997341i	$-0.523218\pi$
$758$	−0.780306	−	0.209082i	−0.0283420	−	0.00759421i
$759$	−0.854547			−0.0310181
$760$	14.2436	+	2.16438i	0.516671	+	0.0785102i
$761$	−35.3011	+	20.3811i	−1.27967	+	0.738815i	−0.976787	−	0.214214i	$-0.931281\pi$
$761$	−35.3011	+	20.3811i	−1.27967	+	0.738815i	−0.302879	+	0.953029i	$0.597948\pi$
$762$	3.58628	−	0.960940i	0.129917	−	0.0348112i
$763$	−32.3039	−	8.65580i	−1.16948	−	0.313361i
$764$	−3.63900	−	2.10098i	−0.131655	−	0.0760108i
$765$	−8.04373	+	10.0617i	−0.290822	+	0.363782i
$766$	0.476872	+	0.275322i	0.0172301	+	0.00994779i
$767$	−4.03445	+	4.03445i	−0.145675	+	0.145675i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	−36.5031	+	21.0750i	−1.31633	+	0.759986i	−0.983137	−	0.182872i	$-0.941461\pi$
$769$	−36.5031	+	21.0750i	−1.31633	+	0.759986i	−0.333197	+	0.942857i	$0.608127\pi$
$770$	0.900621	+	8.08042i	0.0324561	+	0.291198i
$771$		−	19.7798i		−	0.712352i
$772$	−5.19274	+	19.3796i	−0.186891	+	0.697486i
$773$	−4.21777	−	4.21777i	−0.151703	−	0.151703i	0.627175	−	0.778878i	$-0.284211\pi$
$773$	−4.21777	−	4.21777i	−0.151703	−	0.151703i	−0.778878	+	0.627175i	$0.784211\pi$
$774$	9.41339			0.338357
$775$	−21.6292	+	17.5265i	−0.776943	+	0.629571i
$776$	2.48683			0.0892720
$777$	−6.86844	−	6.86844i	−0.246404	−	0.246404i
$778$	−2.80283	+	10.4603i	−0.100486	+	0.375020i
$779$			15.0587i			0.539533i
$780$	0.982475	+	8.81482i	0.0351783	+	0.315621i
$781$	−3.61113	+	2.08489i	−0.129216	+	0.0746031i
$782$	1.46313	−	5.46048i	0.0523215	−	0.195267i
$783$	−0.783899	+	0.783899i	−0.0280143	+	0.0280143i
$784$	9.03561	+	5.21671i	0.322700	+	0.186311i
$785$	21.7784	−	27.2420i	0.777303	−	0.972310i
$786$	−18.7304	−	10.8140i	−0.668090	−	0.385722i
$787$	−4.94080	−	1.32388i	−0.176121	−	0.0471914i	0.169681	−	0.985499i	$-0.445726\pi$
$787$	−4.94080	−	1.32388i	−0.176121	−	0.0471914i	−0.345802	+	0.938308i	$0.612393\pi$
$788$	−7.52956	+	2.01754i	−0.268229	+	0.0718718i
$789$	−10.1569	+	5.86412i	−0.361597	+	0.208768i
$790$	−27.5151	−	4.18102i	−0.978942	−	0.148754i
$791$	−26.3025			−0.935208
$792$	−0.841167	−	0.225390i	−0.0298896	−	0.00800888i
$793$	9.95069	+	37.1365i	0.353359	+	1.31875i
$794$	−1.11343	+	0.642837i	−0.0395141	+	0.0228134i
$795$	17.4510	−	1.94504i	0.618923	−	0.0689834i
$796$	−20.9708	−	12.1075i	−0.743290	−	0.429139i
$797$	10.8572	+	40.5196i	0.384581	+	1.43528i	0.838826	+	0.544399i	$0.183242\pi$
$797$	10.8572	+	40.5196i	0.384581	+	1.43528i	−0.454245	+	0.890877i	$0.650091\pi$
$798$	−19.0226	−	19.0226i	−0.673391	−	0.673391i
$799$	−34.3996	−	59.5819i	−1.21697	−	2.10786i
$800$	4.22722	+	2.67032i	0.149455	+	0.0944100i
$801$	0.0467596	+	0.0269967i	0.00165217	+	0.000953881i
$802$	25.1377	−	25.1377i	0.887644	−	0.887644i
$803$	−1.43015	−	0.383208i	−0.0504690	−	0.0135231i
$804$	7.58883			0.267637
$805$	−5.43152	−	7.37797i	−0.191436	−	0.260039i
$806$	22.0386	+	1.42558i	0.776276	+	0.0502140i
$807$	−14.9777	−	14.9777i	−0.527241	−	0.527241i
$808$	0.725462	−	0.725462i	0.0255216	−	0.0255216i
$809$	−21.9495	−	38.0177i	−0.771704	−	1.33663i	−0.936629	−	0.350324i	$-0.886072\pi$
$809$	−21.9495	−	38.0177i	−0.771704	−	1.33663i	0.164925	−	0.986306i	$-0.447262\pi$
$810$	−2.21069	−	0.335923i	−0.0776758	−	0.0118031i
$811$	0.173454	−	0.300431i	0.00609078	−	0.0105495i	−0.862964	−	0.505265i	$-0.831395\pi$
$811$	0.173454	−	0.300431i	0.00609078	−	0.0105495i	0.869055	+	0.494716i	$0.164728\pi$
$812$	−4.47106	−	1.19802i	−0.156903	−	0.0420421i
$813$	19.7706	+	5.29753i	0.693387	+	0.185792i
$814$			2.02591i			0.0710081i
$815$	36.8162	+	29.4323i	1.28961	+	1.03097i
$816$	2.88045	−	4.98908i	0.100836	−	0.174653i
$817$	−15.6977	−	58.5845i	−0.549192	−	2.04961i
$818$	−5.08604	+	18.9814i	−0.177829	+	0.663668i
$819$	8.28077	−	14.3427i	0.289354	−	0.501175i
$820$	−2.09563	+	4.78755i	−0.0731827	+	0.167189i
$821$			20.9130i			0.729868i	0.931033	+	0.364934i	$0.118909\pi$
$821$			20.9130i			0.729868i	−0.931033	+	0.364934i	$0.881091\pi$
$822$	−9.43033	−	9.43033i	−0.328921	−	0.328921i
$823$	−2.87126	+	10.7157i	−0.100086	+	0.373525i	−0.997741	−	0.0671723i	$-0.978602\pi$
$823$	−2.87126	+	10.7157i	−0.100086	+	0.373525i	0.897656	+	0.440698i	$0.145269\pi$
$824$	−14.3090	−	8.26133i	−0.498479	−	0.287797i
$825$	2.32542	−	3.68123i	0.0809608	−	0.128164i
$826$	3.00297	−	5.20129i	0.104487	−	0.180976i
$827$	−8.48065	−	31.6502i	−0.294901	−	1.10059i	−0.941296	−	0.337583i	$-0.890391\pi$
$827$	−8.48065	−	31.6502i	−0.294901	−	1.10059i	0.646395	−	0.763003i	$-0.276276\pi$
$828$	0.947853	−	0.253977i	0.0329402	−	0.00882629i
$829$	4.94110			0.171612			0.0858058	−	0.996312i	$-0.472654\pi$
$829$	4.94110			0.171612			0.0858058	+	0.996312i	$0.472654\pi$
$830$	−4.13391	+	9.44406i	−0.143490	+	0.327808i
$831$	−8.16258	−	14.1380i	−0.283157	−	0.490442i
$832$	−1.02661	−	3.83136i	−0.0355913	−	0.132829i
$833$	42.5013	+	42.5013i	1.47258	+	1.47258i
$834$	10.0351	−	5.79376i	0.347487	−	0.200622i
$835$	−8.29588	+	54.5947i	−0.287091	+	1.88933i
$836$			5.61088i			0.194056i
$837$	−1.78520	+	5.27381i	−0.0617054	+	0.182290i
$838$	−0.457700	+	0.457700i	−0.0158110	+	0.0158110i
$839$		−	5.44839i		−	0.188099i	−0.995568	−	0.0940497i	$-0.970019\pi$
$839$		−	5.44839i		−	0.188099i	0.995568	−	0.0940497i	$-0.0299813\pi$
$840$	−3.40051	−	8.69504i	−0.117329	−	0.300007i
$841$	−27.7710			−0.957621
$842$	34.8997	−	9.35136i	1.20272	−	0.322269i
$843$	−4.89473	+	18.2674i	−0.168584	+	0.629162i
$844$	−22.2653	+	12.8549i	−0.766402	+	0.442482i
$845$	3.62339	+	4.92188i	0.124648	+	0.169318i
$846$	5.97123	−	10.3425i	0.205295	−	0.355582i
$847$	41.3052	−	11.0677i	1.41926	−	0.380290i
$848$	−7.58508	+	2.03242i	−0.260473	+	0.0697934i
$849$	12.0543	+	20.8786i	0.413702	+	0.716552i
$850$	19.5413	+	21.1622i	0.670260	+	0.725856i
$851$	−1.14143	−	1.97701i	−0.0391277	−	0.0677711i
$852$	3.38578	−	3.38578i	0.115995	−	0.115995i
$853$	4.12249	−	4.12249i	0.141151	−	0.141151i	−0.633000	−	0.774152i	$-0.718177\pi$
$853$	4.12249	−	4.12249i	0.141151	−	0.141151i	0.774152	+	0.633000i	$0.218177\pi$
$854$	−20.2353	−	35.0485i	−0.692436	−	1.19933i
$855$	1.59590	+	14.3185i	0.0545785	+	0.489681i
$856$	4.16303	+	7.21058i	0.142290	+	0.246453i
$857$	−0.836263	+	0.224076i	−0.0285662	+	0.00765429i	−0.273074	−	0.961993i	$-0.588040\pi$
$857$	−0.836263	+	0.224076i	−0.0285662	+	0.00765429i	0.244508	+	0.969647i	$0.421374\pi$
$858$	−3.33650	+	0.894014i	−0.113906	+	0.0305211i
$859$	17.4305	−	30.1904i	0.594720	−	1.03008i	−0.398867	−	0.917009i	$-0.630596\pi$
$859$	17.4305	−	30.1904i	0.594720	−	1.03008i	0.993586	−	0.113076i	$-0.0360703\pi$
$860$	3.16218	−	20.8101i	0.107829	−	0.709618i
$861$	8.45116	−	4.87928i	0.288015	−	0.166285i
$862$	7.10617	−	26.5206i	0.242037	−	0.903295i
$863$	52.2505	−	14.0005i	1.77863	−	0.476582i	0.788294	−	0.615298i	$-0.210964\pi$
$863$	52.2505	−	14.0005i	1.77863	−	0.476582i	0.990332	+	0.138717i	$0.0442977\pi$
$864$	1.00000			0.0340207
$865$	19.6340	−	7.67858i	0.667576	−	0.261080i
$866$		−	1.93528i		−	0.0657635i
$867$	11.4466	−	11.4466i	0.388746	−	0.388746i
$868$	−22.7967	+	4.55479i	−0.773771	+	0.154600i
$869$		−	10.8388i		−	0.367681i
$870$	1.46963	+	1.99629i	0.0498251	+	0.0676805i
$871$	26.0684	−	15.0506i	0.883295	−	0.509971i
$872$	−5.66376	−	5.66376i	−0.191799	−	0.191799i
$873$	0.643639	+	2.40209i	0.0217839	+	0.0812985i
$874$	−3.16126	−	5.47546i	−0.106931	−	0.185210i
$875$	46.5634	−	3.32082i	1.57413	−	0.112264i
$876$	1.70020			0.0574445
$877$	2.18516	−	0.585511i	0.0737875	−	0.0197713i	−0.221736	−	0.975107i	$-0.571172\pi$
$877$	2.18516	−	0.585511i	0.0737875	−	0.0197713i	0.295524	+	0.955335i	$0.404506\pi$
$878$	−6.68322	−	24.9421i	−0.225548	−	0.841756i
$879$	8.92873	−	15.4650i	0.301159	−	0.521622i
$880$	−0.780835	+	1.78385i	−0.0263219	+	0.0601335i
$881$	−10.0757	−	5.81719i	−0.339458	−	0.195986i	0.320574	−	0.947223i	$-0.396124\pi$
$881$	−10.0757	−	5.81719i	−0.339458	−	0.195986i	−0.660032	+	0.751237i	$0.729457\pi$
$882$	−2.70037	+	10.0779i	−0.0909262	+	0.339341i
$883$	35.7593	+	35.7593i	1.20340	+	1.20340i	0.973127	+	0.230271i	$0.0739612\pi$
$883$	35.7593	+	35.7593i	1.20340	+	1.20340i	0.230271	+	0.973127i	$0.426039\pi$
$884$		−	22.8507i		−	0.768552i
$885$	−2.99550	+	1.17150i	−0.100693	+	0.0393795i
$886$	−8.08437	+	14.0025i	−0.271600	+	0.470425i
$887$	−7.21287	+	26.9188i	−0.242185	+	0.903845i	0.732593	+	0.680667i	$0.238310\pi$
$887$	−7.21287	+	26.9188i	−0.242185	+	0.903845i	−0.974778	+	0.223178i	$0.928357\pi$
$888$	−0.602113	−	2.24712i	−0.0202056	−	0.0754082i
$889$	−7.75107	+	13.4252i	−0.259962	+	0.450268i
$890$	0.0753890	−	0.0943023i	0.00252704	−	0.00316102i
$891$		−	0.870840i		−	0.0291742i
$892$	20.4501	+	5.47960i	0.684721	+	0.183471i
$893$	−74.3242	−	19.9151i	−2.48716	−	0.666434i
$894$	−2.38775	+	4.13570i	−0.0798583	+	0.138319i
$895$	14.9027	−	10.9710i	0.498141	−	0.366721i
$896$	2.08767	+	3.61595i	0.0697441	+	0.120800i
$897$	2.75228	−	2.75228i	0.0918958	−	0.0918958i
$898$	−5.89594	−	5.89594i	−0.196750	−	0.196750i
$899$	5.53355	−	2.73472i	0.184554	−	0.0912080i
$900$	−1.48525	+	4.77431i	−0.0495082	+	0.159144i
$901$	−45.2383			−1.50711
$902$	−1.96597	−	0.526780i	−0.0654596	−	0.0175398i
$903$	−27.7922	+	27.7922i	−0.924865	+	0.924865i
$904$	−5.45552	−	3.14974i	−0.181448	−	0.104759i
$905$	20.8905	−	47.7250i	0.694422	−	1.58643i
$906$	1.63347	+	2.82926i	0.0542685	+	0.0939958i
$907$	−42.0792	−	42.0792i	−1.39722	−	1.39722i	−0.807911	−	0.589305i	$-0.799402\pi$
$907$	−42.0792	−	42.0792i	−1.39722	−	1.39722i	−0.589305	−	0.807911i	$-0.700598\pi$
$908$	2.81019	+	10.4878i	0.0932595	+	0.348049i
$909$	0.888505	+	0.512979i	0.0294699	+	0.0170144i
$910$	−28.9256	−	23.1243i	−0.958875	−	0.766563i
$911$	32.2883	−	18.6417i	1.06976	−	0.617627i	0.141645	−	0.989918i	$-0.454761\pi$
$911$	32.2883	−	18.6417i	1.06976	−	0.617627i	0.928116	+	0.372291i	$0.121428\pi$
$912$	−1.66759	−	6.22353i	−0.0552194	−	0.206082i
$913$	−3.87813	−	1.03914i	−0.128347	−	0.0343905i
$914$	−6.60301			−0.218408
$915$	−3.25602	+	21.4277i	−0.107641	+	0.708378i
$916$	−19.9394	+	11.5120i	−0.658815	+	0.380367i
$917$	87.2270	−	23.3724i	2.88049	−	0.771825i
$918$	5.56460	+	1.49103i	0.183659	+	0.0492113i
$919$	43.5042	+	25.1172i	1.43507	+	0.828539i	0.997501	−	0.0706461i	$-0.0225061\pi$
$919$	43.5042	+	25.1172i	1.43507	+	0.828539i	0.437569	+	0.899185i	$0.355839\pi$
$920$	−0.243058	−	2.18073i	−0.00801338	−	0.0718965i
$921$	8.47189	+	4.89125i	0.279158	+	0.161172i
$922$	−4.98528	+	4.98528i	−0.164182	+	0.164182i
$923$	4.91564	−	18.3454i	0.161800	−	0.603846i
$924$	3.14891	−	1.81802i	0.103592	−	0.0598086i
$925$	11.6227	+	0.462843i	0.382152	+	0.0152182i
$926$		−	20.0348i		−	0.658385i
$927$	4.27638	−	15.9597i	0.140455	−	0.524184i
$928$	−0.783899	−	0.783899i	−0.0257327	−	0.0257327i
$929$	−7.21422			−0.236691			−0.118346	−	0.992972i	$-0.537759\pi$
$929$	−7.21422			−0.236691			−0.118346	+	0.992972i	$0.537759\pi$
$930$	11.0591	+	5.71811i	0.362641	+	0.187504i
$931$	67.2233			2.20315
$932$	−0.731249	−	0.731249i	−0.0239529	−	0.0239529i
$933$	−4.53127	+	16.9109i	−0.148347	+	0.553639i
$934$			3.92073i			0.128290i
$935$	−7.00480	+	8.76214i	−0.229081	+	0.286553i
$936$	3.43511	−	1.98326i	0.112280	−	0.0648249i
$937$	0.734470	−	2.74108i	0.0239941	−	0.0895472i	−0.952891	−	0.303314i	$-0.901907\pi$
$937$	0.734470	−	2.74108i	0.0239941	−	0.0895472i	0.976885	+	0.213767i	$0.0685734\pi$
$938$	−22.4053	+	22.4053i	−0.731560	+	0.731560i
$939$	−6.41140	−	3.70162i	−0.209228	−	0.120798i
$940$	−20.8581	−	16.6748i	−0.680318	−	0.543873i
$941$	6.35585	+	3.66955i	0.207195	+	0.119624i	0.600007	−	0.799995i	$-0.295164\pi$
$941$	6.35585	+	3.66955i	0.207195	+	0.119624i	−0.392812	+	0.919619i	$0.628498\pi$
$942$	−15.0661	−	4.03695i	−0.490881	−	0.131531i
$943$	2.21531	−	0.593592i	0.0721406	−	0.0193300i
$944$	1.24572	−	0.719216i	0.0405447	−	0.0234085i
$945$	7.51864	−	5.53508i	0.244582	−	0.180056i
$946$	8.19756			0.266526
$947$	10.0686	+	2.69786i	0.327184	+	0.0876688i	0.418672	−	0.908137i	$-0.362496\pi$
$947$	10.0686	+	2.69786i	0.327184	+	0.0876688i	−0.0914880	+	0.995806i	$0.529162\pi$
$948$	3.22136	+	12.0223i	0.104625	+	0.390465i
$949$	5.84037	−	3.37194i	0.189587	−	0.109458i
$950$	32.1898	+	1.28187i	1.04438	+	0.0415895i
$951$	15.4052	+	8.89421i	0.499549	+	0.288415i
$952$	6.22555	+	23.2341i	0.201771	+	0.753020i
$953$	−30.5291	−	30.5291i	−0.988934	−	0.988934i	0.0110050	−	0.999939i	$-0.496497\pi$
$953$	−30.5291	−	30.5291i	−0.988934	−	0.988934i	−0.999939	+	0.0110050i	$0.996497\pi$
$954$	−3.92633	−	6.80060i	−0.127119	−	0.220177i
$955$	−8.60738	−	3.76767i	−0.278528	−	0.121919i
$956$	−0.466649	−	0.269420i	−0.0150925	−	0.00871366i
$957$	−0.682650	+	0.682650i	−0.0220670	+	0.0220670i
$958$	−9.73547	−	2.60861i	−0.314539	−	0.0842804i
$959$	55.6844			1.79814
$960$	0.335923	−	2.21069i	0.0108419	−	0.0713498i
$961$	18.8296	−	24.6262i	0.607405	−	0.794392i
$962$	−6.52493	−	6.52493i	−0.210372	−	0.210372i
$963$	−5.88742	+	5.88742i	−0.189719	+	0.189719i
$964$	4.63782	+	8.03294i	0.149374	+	0.258724i
$965$	−6.73970	+	44.3536i	−0.216959	+	1.42779i
$966$	−2.04861	+	3.54829i	−0.0659129	+	0.114164i
$967$	48.7804	+	13.0707i	1.56867	+	0.420325i	0.935397	−	0.353600i	$-0.115043\pi$
$967$	48.7804	+	13.0707i	1.56867	+	0.420325i	0.633277	+	0.773925i	$0.281709\pi$
$968$	9.89266	+	2.65073i	0.317962	+	0.0851977i
$969$		−	37.1178i		−	1.19240i
$970$	5.52650	−	0.615968i	0.177445	−	0.0197775i
$971$	9.01898	−	15.6213i	0.289433	−	0.501312i	−0.684242	−	0.729255i	$-0.739867\pi$
$971$	9.01898	−	15.6213i	0.289433	−	0.501312i	0.973674	+	0.227943i	$0.0732000\pi$
$972$	0.258819	+	0.965926i	0.00830162	+	0.0309821i
$973$	−12.5221	+	46.7332i	−0.401441	+	1.49820i
$974$	1.57644	−	2.73048i	0.0505125	−	0.0874902i
$975$	4.36672	+	19.3459i	0.139847	+	0.619564i
$976$		−	9.69276i		−	0.310258i
$977$	−34.3100	−	34.3100i	−1.09767	−	1.09767i	−0.994682	−	0.102991i	$-0.967159\pi$
$977$	−34.3100	−	34.3100i	−1.09767	−	1.09767i	−0.102991	−	0.994682i	$-0.532841\pi$
$978$	5.45573	−	20.3611i	0.174455	−	0.651075i
$979$	0.0407202	+	0.0235098i	0.00130142	+	0.000751376i
$980$	21.3720	+	9.35509i	0.682705	+	0.298837i
$981$	4.00488	−	6.93666i	0.127866	−	0.221471i
$982$	5.05713	+	18.8735i	0.161380	+	0.602277i
$983$	−50.6613	+	13.5747i	−1.61585	+	0.432965i	−0.949777	−	0.312926i	$-0.898691\pi$
$983$	−50.6613	+	13.5747i	−1.61585	+	0.432965i	−0.666068	+	0.745891i	$0.732024\pi$
$984$	2.33719			0.0745070
$985$	−16.2333	+	6.34860i	−0.517235	+	0.202283i
$986$	−3.19327	−	5.53090i	−0.101694	−	0.176140i
$987$	12.9057	+	48.1647i	0.410793	+	1.53310i
$988$	−18.0712	−	18.0712i	−0.574922	−	0.574922i
$989$	−7.99970	+	4.61863i	−0.254376	+	0.146864i
$990$	−1.92516	−	0.292535i	−0.0611855	−	0.00929738i
$991$		−	41.6226i		−	1.32218i	−0.750305	−	0.661092i	$-0.770093\pi$
$991$		−	41.6226i		−	1.32218i	0.750305	−	0.661092i	$-0.229907\pi$
$992$	−5.27381	−	1.78520i	−0.167444	−	0.0566800i
$993$	−3.67546	+	3.67546i	−0.116637	+	0.116637i
$994$			19.9924i			0.634121i
$995$	−49.6025	−	21.7123i	−1.57250	−	0.688326i
$996$	4.61041			0.146086
$997$	38.6345	−	10.3521i	1.22357	−	0.327854i	0.411495	−	0.911412i	$-0.365007\pi$
$997$	38.6345	−	10.3521i	1.22357	−	0.327854i	0.812071	+	0.583559i	$0.198340\pi$
$998$	4.74133	−	17.6949i	0.150084	−	0.560122i
$999$	2.01471	−	1.16319i	0.0637425	−	0.0368018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.a.37.12	✓	64
5.3	odd	4		930.2.be.b.223.11	yes	64
31.26	odd	6		930.2.be.b.367.11	yes	64
155.88	even	12	inner	930.2.be.a.553.12	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.37.12	✓	64	1.1	even	1	trivial
930.2.be.a.553.12	yes	64	155.88	even	12	inner
930.2.be.b.223.11	yes	64	5.3	odd	4
930.2.be.b.367.11	yes	64	31.26	odd	6

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(0.247692 + 2.22231i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.08066 + 4.03306i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(0.247692 + 2.22231i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.08066 + 4.03306i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.39626 + 1.74655i) q^{10} +(-0.754170 - 0.435420i) q^{11} +(0.965926 + 0.258819i) q^{12} +(3.83136 - 1.02661i) q^{13} +(-3.61595 + 2.08767i) q^{14} +(2.21069 + 0.335923i) q^{15} -1.00000 q^{16} +(-5.56460 - 1.49103i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-5.57986 + 3.22153i) q^{19} +(-2.22231 + 0.247692i) q^{20} +(3.61595 + 2.08767i) q^{21} +(-0.225390 - 0.841167i) q^{22} +(0.693877 + 0.693877i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.87730 + 1.10090i) q^{25} +(3.43511 + 1.98326i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-4.03306 - 1.08066i) q^{28} +1.10860 q^{29} +(1.32566 + 1.80073i) q^{30} +(4.99147 - 2.46682i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.615777 + 0.615777i) q^{33} +(-2.88045 - 4.98908i) q^{34} +(-9.23038 - 1.40259i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.24712 - 0.602113i) q^{37} +(-6.22353 - 1.66759i) q^{38} -3.96652i q^{39} +(-1.74655 - 1.39626i) q^{40} +(1.16860 - 2.02407i) q^{41} +(1.08066 + 4.03306i) q^{42} +(-2.43636 + 9.09264i) q^{43} +(0.435420 - 0.754170i) q^{44} +(0.896646 - 2.04842i) q^{45} +0.981290i q^{46} +(8.44460 + 8.44460i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(-9.03561 - 5.21671i) q^{49} +(-4.22722 - 2.67032i) q^{50} +(-2.88045 + 4.98908i) q^{51} +(1.02661 + 3.83136i) q^{52} +(7.58508 - 2.03242i) q^{53} -1.00000 q^{54} +(0.780835 - 1.78385i) q^{55} +(-2.08767 - 3.61595i) q^{56} +(1.66759 + 6.22353i) q^{57} +(0.783899 + 0.783899i) q^{58} +(-1.24572 + 0.719216i) q^{59} +(-0.335923 + 2.21069i) q^{60} +9.69276i q^{61} +(5.27381 + 1.78520i) q^{62} +(2.95241 - 2.95241i) q^{63} -1.00000i q^{64} +(3.23044 + 8.26018i) q^{65} -0.870840 q^{66} +(7.33025 - 1.96413i) q^{67} +(1.49103 - 5.56460i) q^{68} +(0.849822 - 0.490645i) q^{69} +(-5.53508 - 7.51864i) q^{70} +(2.39411 - 4.14672i) q^{71} +(0.965926 - 0.258819i) q^{72} +(1.64227 - 0.440045i) q^{73} +(-1.16319 - 2.01471i) q^{74} +(-0.198954 + 4.99604i) q^{75} +(-3.22153 - 5.57986i) q^{76} +(2.57108 - 2.57108i) q^{77} +(2.80475 - 2.80475i) q^{78} +(6.22318 + 10.7789i) q^{79} +(-0.247692 - 2.22231i) q^{80} +(0.500000 + 0.866025i) q^{81} +(2.25755 - 0.604910i) q^{82} +(4.45332 - 1.19326i) q^{83} +(-2.08767 + 3.61595i) q^{84} +(1.93522 - 12.7356i) q^{85} +(-8.15223 + 4.70669i) q^{86} +(0.286927 - 1.07083i) q^{87} +(0.841167 - 0.225390i) q^{88} -0.0539934 q^{89} +(2.08248 - 0.814428i) q^{90} +16.5615i q^{91} +(-0.693877 + 0.693877i) q^{92} +(-1.09088 - 5.45985i) q^{93} +11.9425i q^{94} +(-8.54132 - 11.6022i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-1.75845 - 1.75845i) q^{97} +(-2.70037 - 10.0779i) q^{98} +(0.435420 + 0.754170i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7}+O(q^{10}) \) 64 * q - 8 * q^7	\( 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * q^98 - 4 * q^99

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