LMFDB - Embedded newform 385.2.i.c.221.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(221,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("385.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 17 x^{14} - 28 x^{13} + 127 x^{12} - 178 x^{11} + 612 x^{10} - 527 x^{9} + 1556 x^{8} + \cdots + 81 $ x^16 - 3x^15 + 17x^14 - 28x^13 + 127x^12 - 178x^11 + 612x^10 - 527x^9 + 1556x^8 - 1065x^7 + 2812x^6 - 1224x^5 + 2359x^4 - 1154x^3 + 1351x^2 - 333*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			221.5
Root			$0.139605 + 0.241804i$ of defining polynomial
Character	$\chi$	$=$	385.221
Dual form			385.2.i.c.331.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.139605 - 0.241804i) q^{2} +(-0.137980 + 0.238988i) q^{3} +(0.961021 - 1.66454i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.0770509 q^{6} +(1.16250 + 2.37668i) q^{7} -1.09508 q^{8} +(1.46192 + 2.53213i) q^{9} +O(q^{10})$	\(q+(-0.139605 - 0.241804i) q^{2} +(-0.137980 + 0.238988i) q^{3} +(0.961021 - 1.66454i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.0770509 q^{6} +(1.16250 + 2.37668i) q^{7} -1.09508 q^{8} +(1.46192 + 2.53213i) q^{9} +(-0.139605 + 0.241804i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.265203 + 0.459345i) q^{12} +6.03636 q^{13} +(0.412399 - 0.612893i) q^{14} +0.275960 q^{15} +(-1.76916 - 3.06428i) q^{16} +(2.24113 - 3.88176i) q^{17} +(0.408185 - 0.706997i) q^{18} +(-3.08895 - 5.35022i) q^{19} -1.92204 q^{20} +(-0.728399 - 0.0501106i) q^{21} -0.279211 q^{22} +(0.0705230 + 0.122149i) q^{23} +(0.151098 - 0.261710i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.842708 - 1.45961i) q^{26} -1.63474 q^{27} +(5.07325 + 0.349018i) q^{28} -5.06132 q^{29} +(-0.0385254 - 0.0667280i) q^{30} +(1.67673 - 2.90419i) q^{31} +(-1.58905 + 2.75231i) q^{32} +(0.137980 + 0.238988i) q^{33} -1.25150 q^{34} +(1.47702 - 2.19509i) q^{35} +5.61975 q^{36} +(4.74619 + 8.22065i) q^{37} +(-0.862469 + 1.49384i) q^{38} +(-0.832895 + 1.44262i) q^{39} +(0.547538 + 0.948364i) q^{40} +1.23914 q^{41} +(0.0895715 + 0.183125i) q^{42} +5.53959 q^{43} +(-0.961021 - 1.66454i) q^{44} +(1.46192 - 2.53213i) q^{45} +(0.0196908 - 0.0341054i) q^{46} +(-3.46456 - 6.00079i) q^{47} +0.976435 q^{48} +(-4.29720 + 5.52576i) q^{49} +0.279211 q^{50} +(0.618462 + 1.07121i) q^{51} +(5.80106 - 10.0477i) q^{52} +(-5.40363 + 9.35936i) q^{53} +(0.228219 + 0.395287i) q^{54} -1.00000 q^{55} +(-1.27302 - 2.60264i) q^{56} +1.70485 q^{57} +(0.706588 + 1.22385i) q^{58} +(-5.01669 + 8.68916i) q^{59} +(0.265203 - 0.459345i) q^{60} +(4.58717 + 7.94521i) q^{61} -0.936325 q^{62} +(-4.31857 + 6.41811i) q^{63} -6.18929 q^{64} +(-3.01818 - 5.22764i) q^{65} +(0.0385254 - 0.0667280i) q^{66} +(-5.24073 + 9.07721i) q^{67} +(-4.30755 - 7.46090i) q^{68} -0.0389230 q^{69} +(-0.736980 - 0.0507010i) q^{70} +9.66631 q^{71} +(-1.60092 - 2.77287i) q^{72} +(2.03241 - 3.52025i) q^{73} +(1.32519 - 2.29529i) q^{74} +(-0.137980 - 0.238988i) q^{75} -11.8742 q^{76} +(2.63951 + 0.181587i) q^{77} +0.465107 q^{78} +(-7.24243 - 12.5443i) q^{79} +(-1.76916 + 3.06428i) q^{80} +(-4.16021 + 7.20569i) q^{81} +(-0.172991 - 0.299628i) q^{82} +2.71493 q^{83} +(-0.783417 + 1.16429i) q^{84} -4.48227 q^{85} +(-0.773356 - 1.33949i) q^{86} +(0.698360 - 1.20960i) q^{87} +(-0.547538 + 0.948364i) q^{88} +(-8.92468 - 15.4580i) q^{89} -0.816369 q^{90} +(7.01725 + 14.3465i) q^{91} +0.271096 q^{92} +(0.462711 + 0.801439i) q^{93} +(-0.967342 + 1.67549i) q^{94} +(-3.08895 + 5.35022i) q^{95} +(-0.438512 - 0.759526i) q^{96} -0.310934 q^{97} +(1.93606 + 0.267652i) q^{98} +2.92385 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9	\( 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9} - 3 q^{10} + 8 q^{11} - 9 q^{12} + 28 q^{13} - 9 q^{14} + 2 q^{15} - 7 q^{16} - 5 q^{17} - 27 q^{18} - q^{19} + 18 q^{20} - 18 q^{21} - 6 q^{22} + 2 q^{23} + 24 q^{24} - 8 q^{25} - 21 q^{26} - 10 q^{27} + 32 q^{28} + 52 q^{29} + 3 q^{30} - 2 q^{31} - 16 q^{32} + q^{33} - 52 q^{34} + 5 q^{35} + 108 q^{36} + q^{37} + 31 q^{38} - 19 q^{39} - 9 q^{40} - 6 q^{41} + 44 q^{42} + 8 q^{43} + 9 q^{44} - 19 q^{45} - 10 q^{46} - q^{47} - 42 q^{48} + 17 q^{49} + 6 q^{50} - 3 q^{51} - 37 q^{52} - 26 q^{53} + 5 q^{54} - 16 q^{55} + 40 q^{57} + q^{58} + 19 q^{59} - 9 q^{60} - 52 q^{62} - 21 q^{63} + 2 q^{64} - 14 q^{65} - 3 q^{66} + 13 q^{67} - 15 q^{68} - 28 q^{69} + 15 q^{70} - 18 q^{71} - 32 q^{72} - 11 q^{73} - 24 q^{74} - q^{75} - 36 q^{76} + 4 q^{77} - 66 q^{78} + 8 q^{79} - 7 q^{80} - 52 q^{81} - 41 q^{82} + 64 q^{83} + 138 q^{84} + 10 q^{85} - 28 q^{86} + 16 q^{87} + 9 q^{88} - 5 q^{89} + 54 q^{90} + 13 q^{91} + 60 q^{92} + 14 q^{93} + 5 q^{94} - q^{95} - q^{96} + 18 q^{97} + 22 q^{98} - 38 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9 - 3 * q^10 + 8 * q^11 - 9 * q^12 + 28 * q^13 - 9 * q^14 + 2 * q^15 - 7 * q^16 - 5 * q^17 - 27 * q^18 - q^19 + 18 * q^20 - 18 * q^21 - 6 * q^22 + 2 * q^23 + 24 * q^24 - 8 * q^25 - 21 * q^26 - 10 * q^27 + 32 * q^28 + 52 * q^29 + 3 * q^30 - 2 * q^31 - 16 * q^32 + q^33 - 52 * q^34 + 5 * q^35 + 108 * q^36 + q^37 + 31 * q^38 - 19 * q^39 - 9 * q^40 - 6 * q^41 + 44 * q^42 + 8 * q^43 + 9 * q^44 - 19 * q^45 - 10 * q^46 - q^47 - 42 * q^48 + 17 * q^49 + 6 * q^50 - 3 * q^51 - 37 * q^52 - 26 * q^53 + 5 * q^54 - 16 * q^55 + 40 * q^57 + q^58 + 19 * q^59 - 9 * q^60 - 52 * q^62 - 21 * q^63 + 2 * q^64 - 14 * q^65 - 3 * q^66 + 13 * q^67 - 15 * q^68 - 28 * q^69 + 15 * q^70 - 18 * q^71 - 32 * q^72 - 11 * q^73 - 24 * q^74 - q^75 - 36 * q^76 + 4 * q^77 - 66 * q^78 + 8 * q^79 - 7 * q^80 - 52 * q^81 - 41 * q^82 + 64 * q^83 + 138 * q^84 + 10 * q^85 - 28 * q^86 + 16 * q^87 + 9 * q^88 - 5 * q^89 + 54 * q^90 + 13 * q^91 + 60 * q^92 + 14 * q^93 + 5 * q^94 - q^95 - q^96 + 18 * q^97 + 22 * q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.139605	−	0.241804i	−0.0987159	−	0.170981i	0.812437	−	0.583048i	$-0.198140\pi$
$2$	−0.139605	−	0.241804i	−0.0987159	−	0.170981i	−0.911153	+	0.412067i	$0.864807\pi$
$3$	−0.137980	+	0.238988i	−0.0796627	+	0.137980i	−0.903104	−	0.429421i	$-0.858718\pi$
$3$	−0.137980	+	0.238988i	−0.0796627	+	0.137980i	0.823442	+	0.567401i	$0.192051\pi$
$4$	0.961021	−	1.66454i	0.480510	−	0.832268i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.0770509			0.0314559
$7$	1.16250	+	2.37668i	0.439383	+	0.898300i
$7$	1.16250	+	2.37668i	0.439383	+	0.898300i
$8$	−1.09508			−0.387168
$9$	1.46192	+	2.53213i	0.487308	+	0.844042i
$10$	−0.139605	+	0.241804i	−0.0441471	+	0.0764650i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	0.265203	+	0.459345i	0.0765575	+	0.132601i
$13$	6.03636			1.67418			0.837092	−	0.547062i	$-0.184254\pi$
$13$	6.03636			1.67418			0.837092	+	0.547062i	$0.184254\pi$
$14$	0.412399	−	0.612893i	0.110218	−	0.163803i
$15$	0.275960			0.0712525
$16$	−1.76916	−	3.06428i	−0.442291	−	0.766070i
$17$	2.24113	−	3.88176i	0.543555	−	0.941465i	−0.455142	−	0.890419i	$-0.650411\pi$
$17$	2.24113	−	3.88176i	0.543555	−	0.941465i	0.998696	−	0.0510454i	$-0.0162553\pi$
$18$	0.408185	−	0.706997i	0.0962100	−	0.166641i
$19$	−3.08895	−	5.35022i	−0.708654	−	1.22743i	−0.965356	−	0.260935i	$-0.915969\pi$
$19$	−3.08895	−	5.35022i	−0.708654	−	1.22743i	0.256702	−	0.966491i	$-0.417364\pi$
$20$	−1.92204			−0.429782
$21$	−0.728399	−	0.0501106i	−0.158950	−	0.0109350i
$22$	−0.279211			−0.0595279
$23$	0.0705230	+	0.122149i	0.0147051	+	0.0254699i	0.873284	−	0.487211i	$-0.161986\pi$
$23$	0.0705230	+	0.122149i	0.0147051	+	0.0254699i	−0.858579	+	0.512681i	$0.828652\pi$
$24$	0.151098	−	0.261710i	0.0308428	−	0.0534213i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.842708	−	1.45961i	−0.165269	−	0.286254i
$27$	−1.63474			−0.314606
$28$	5.07325	+	0.349018i	0.958755	+	0.0659581i
$29$	−5.06132			−0.939864			−0.469932	−	0.882703i	$-0.655722\pi$
$29$	−5.06132			−0.939864			−0.469932	+	0.882703i	$0.655722\pi$
$30$	−0.0385254	−	0.0667280i	−0.00703375	−	0.0121828i
$31$	1.67673	−	2.90419i	0.301150	−	0.521608i	−0.675246	−	0.737592i	$-0.735963\pi$
$31$	1.67673	−	2.90419i	0.301150	−	0.521608i	0.976397	+	0.215984i	$0.0692960\pi$
$32$	−1.58905	+	2.75231i	−0.280906	+	0.486544i
$33$	0.137980	+	0.238988i	0.0240192	+	0.0416025i
$34$	−1.25150			−0.214630
$35$	1.47702	−	2.19509i	0.249661	−	0.371038i
$36$	5.61975			0.936626
$37$	4.74619	+	8.22065i	0.780269	+	1.35147i	0.931785	+	0.363011i	$0.118251\pi$
$37$	4.74619	+	8.22065i	0.780269	+	1.35147i	−0.151515	+	0.988455i	$0.548415\pi$
$38$	−0.862469	+	1.49384i	−0.139911	+	0.242333i
$39$	−0.832895	+	1.44262i	−0.133370	+	0.231004i
$40$	0.547538	+	0.948364i	0.0865734	+	0.149949i
$41$	1.23914			0.193521			0.0967605	−	0.995308i	$-0.469152\pi$
$41$	1.23914			0.193521			0.0967605	+	0.995308i	$0.469152\pi$
$42$	0.0895715	+	0.183125i	0.0138212	+	0.0282568i
$43$	5.53959			0.844779			0.422389	−	0.906414i	$-0.361191\pi$
$43$	5.53959			0.844779			0.422389	+	0.906414i	$0.361191\pi$
$44$	−0.961021	−	1.66454i	−0.144879	−	0.250938i
$45$	1.46192	−	2.53213i	0.217931	−	0.377467i
$46$	0.0196908	−	0.0341054i	0.00290325	−	0.00502857i
$47$	−3.46456	−	6.00079i	−0.505358	−	0.875306i	−0.999981	−	0.00619803i	$-0.998027\pi$
$47$	−3.46456	−	6.00079i	−0.505358	−	0.875306i	0.494623	−	0.869108i	$-0.335306\pi$
$48$	0.976435			0.140936
$49$	−4.29720	+	5.52576i	−0.613886	+	0.789395i
$50$	0.279211			0.0394864
$51$	0.618462	+	1.07121i	0.0866021	+	0.149999i
$52$	5.80106	−	10.0477i	0.804463	−	1.39337i
$53$	−5.40363	+	9.35936i	−0.742246	+	1.28561i	0.209225	+	0.977868i	$0.432906\pi$
$53$	−5.40363	+	9.35936i	−0.742246	+	1.28561i	−0.951471	+	0.307740i	$0.900427\pi$
$54$	0.228219	+	0.395287i	0.0310566	+	0.0537917i
$55$	−1.00000			−0.134840
$56$	−1.27302	−	2.60264i	−0.170115	−	0.347793i
$57$	1.70485			0.225813
$58$	0.706588	+	1.22385i	0.0927795	+	0.160699i
$59$	−5.01669	+	8.68916i	−0.653117	+	1.13123i	0.329245	+	0.944245i	$0.393206\pi$
$59$	−5.01669	+	8.68916i	−0.653117	+	1.13123i	−0.982362	+	0.186988i	$0.940128\pi$
$60$	0.265203	−	0.459345i	0.0342375	−	0.0593012i
$61$	4.58717	+	7.94521i	0.587327	+	1.01728i	0.994581	+	0.103965i	$0.0331529\pi$
$61$	4.58717	+	7.94521i	0.587327	+	1.01728i	−0.407254	+	0.913315i	$0.633514\pi$
$62$	−0.936325			−0.118913
$63$	−4.31857	+	6.41811i	−0.544088	+	0.808606i
$64$	−6.18929			−0.773662
$65$	−3.01818	−	5.22764i	−0.374359	−	0.648409i
$66$	0.0385254	−	0.0667280i	0.00474215	−	0.00821365i
$67$	−5.24073	+	9.07721i	−0.640257	+	1.10896i	0.345118	+	0.938559i	$0.387839\pi$
$67$	−5.24073	+	9.07721i	−0.640257	+	1.10896i	−0.985375	+	0.170398i	$0.945495\pi$
$68$	−4.30755	−	7.46090i	−0.522367	−	0.904767i
$69$	−0.0389230			−0.00468578
$70$	−0.736980	−	0.0507010i	−0.0880860	−	0.00605993i
$71$	9.66631			1.14718			0.573590	−	0.819143i	$-0.305550\pi$
$71$	9.66631			1.14718			0.573590	+	0.819143i	$0.305550\pi$
$72$	−1.60092	−	2.77287i	−0.188670	−	0.326786i
$73$	2.03241	−	3.52025i	0.237876	−	0.412014i	−0.722228	−	0.691655i	$-0.756882\pi$
$73$	2.03241	−	3.52025i	0.237876	−	0.412014i	0.960105	+	0.279641i	$0.0902154\pi$
$74$	1.32519	−	2.29529i	0.154050	−	0.266822i
$75$	−0.137980	−	0.238988i	−0.0159325	−	0.0275960i
$76$	−11.8742			−1.36206
$77$	2.63951	+	0.181587i	0.300800	+	0.0206937i
$78$	0.465107			0.0526629
$79$	−7.24243	−	12.5443i	−0.814838	−	1.41134i	−0.909445	−	0.415825i	$-0.863493\pi$
$79$	−7.24243	−	12.5443i	−0.814838	−	1.41134i	0.0946070	−	0.995515i	$-0.469841\pi$
$80$	−1.76916	+	3.06428i	−0.197798	+	0.342597i
$81$	−4.16021	+	7.20569i	−0.462245	+	0.800632i
$82$	−0.172991	−	0.299628i	−0.0191036	−	0.0330884i
$83$	2.71493			0.298002			0.149001	−	0.988837i	$-0.452394\pi$
$83$	2.71493			0.298002			0.149001	+	0.988837i	$0.452394\pi$
$84$	−0.783417	+	1.16429i	−0.0854778	+	0.127034i
$85$	−4.48227			−0.486170
$86$	−0.773356	−	1.33949i	−0.0833931	−	0.144441i
$87$	0.698360	−	1.20960i	0.0748721	−	0.129682i
$88$	−0.547538	+	0.948364i	−0.0583678	+	0.101096i
$89$	−8.92468	−	15.4580i	−0.946014	−	1.63854i	−0.753708	−	0.657209i	$-0.771737\pi$
$89$	−8.92468	−	15.4580i	−0.946014	−	1.63854i	−0.192306	−	0.981335i	$-0.561597\pi$
$90$	−0.816369			−0.0860529
$91$	7.01725	+	14.3465i	0.735607	+	1.50392i
$92$	0.271096			0.0282637
$93$	0.462711	+	0.801439i	0.0479809	+	0.0831054i
$94$	−0.967342	+	1.67549i	−0.0997738	+	0.172813i
$95$	−3.08895	+	5.35022i	−0.316920	+	0.548921i
$96$	−0.438512	−	0.759526i	−0.0447555	−	0.0775188i
$97$	−0.310934			−0.0315705			−0.0157853	−	0.999875i	$-0.505025\pi$
$97$	−0.310934			−0.0315705			−0.0157853	+	0.999875i	$0.505025\pi$
$98$	1.93606	+	0.267652i	0.195572	+	0.0270369i
$99$	2.92385			0.293858
$100$	0.961021	+	1.66454i	0.0961021	+	0.166454i
$101$	−4.32356	+	7.48862i	−0.430210	+	0.745146i	−0.996891	−	0.0787915i	$-0.974894\pi$
$101$	−4.32356	+	7.48862i	−0.430210	+	0.745146i	0.566681	+	0.823937i	$0.308227\pi$
$102$	0.172681	−	0.299093i	0.0170980	−	0.0296146i
$103$	3.61474	+	6.26092i	0.356171	+	0.616906i	0.987318	−	0.158757i	$-0.0507487\pi$
$103$	3.61474	+	6.26092i	0.356171	+	0.616906i	−0.631147	+	0.775664i	$0.717415\pi$
$104$	−6.61027			−0.648190
$105$	0.320802	+	0.655867i	0.0313071	+	0.0640061i
$106$	3.01750			0.293086
$107$	−4.21112	−	7.29387i	−0.407104	−	0.705125i	0.587460	−	0.809254i	$-0.300128\pi$
$107$	−4.21112	−	7.29387i	−0.407104	−	0.705125i	−0.994564	+	0.104128i	$0.966795\pi$
$108$	−1.57102	+	2.72109i	−0.151172	+	0.261837i
$109$	−6.06327	+	10.5019i	−0.580756	+	1.00590i	0.414634	+	0.909988i	$0.363910\pi$
$109$	−6.06327	+	10.5019i	−0.580756	+	1.00590i	−0.995390	+	0.0959108i	$0.969424\pi$
$110$	0.139605	+	0.241804i	0.0133109	+	0.0230551i
$111$	−2.61952			−0.248633
$112$	5.22616	−	7.76695i	0.493826	−	0.733908i
$113$	1.38668			0.130448			0.0652239	−	0.997871i	$-0.479224\pi$
$113$	1.38668			0.130448			0.0652239	+	0.997871i	$0.479224\pi$
$114$	−0.238007	−	0.412239i	−0.0222914	−	0.0386098i
$115$	0.0705230	−	0.122149i	0.00657630	−	0.0113905i
$116$	−4.86403	+	8.42475i	−0.451614	+	0.782219i
$117$	8.82469	+	15.2848i	0.815843	+	1.41308i
$118$	2.80143			0.257892
$119$	11.8310	+	0.813921i	1.08455	+	0.0746120i
$120$	−0.302197			−0.0275867
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	1.28079	−	2.21839i	0.115957	−	0.200843i
$123$	−0.170976	+	0.296140i	−0.0154164	+	0.0267020i
$124$	−3.22275	−	5.58197i	−0.289412	−	0.501276i
$125$	1.00000			0.0894427
$126$	2.15482	+	0.148242i	0.191966	+	0.0132064i
$127$	−14.2544			−1.26487			−0.632437	−	0.774612i	$-0.717945\pi$
$127$	−14.2544			−1.26487			−0.632437	+	0.774612i	$0.717945\pi$
$128$	4.04215	+	7.00121i	0.357279	+	0.618825i
$129$	−0.764351	+	1.32389i	−0.0672974	+	0.116562i
$130$	−0.842708	+	1.45961i	−0.0739104	+	0.128016i
$131$	−2.81952	−	4.88355i	−0.246343	−	0.426678i	0.716166	−	0.697930i	$-0.245896\pi$
$131$	−2.81952	−	4.88355i	−0.246343	−	0.426678i	−0.962508	+	0.271252i	$0.912562\pi$
$132$	0.530406			0.0461659
$133$	9.12486	−	13.5611i	0.791226	−	1.17589i
$134$	2.92654			0.252814
$135$	0.817371	+	1.41573i	0.0703481	+	0.121846i
$136$	−2.45421	+	4.25082i	−0.210447	+	0.364505i
$137$	−1.49084	+	2.58220i	−0.127371	+	0.220612i	−0.922657	−	0.385621i	$-0.873987\pi$
$137$	−1.49084	+	2.58220i	−0.127371	+	0.220612i	0.795286	+	0.606234i	$0.207320\pi$
$138$	0.00543386	+	0.00941172i	0.000462561	+	0.000801179i
$139$	−7.74208			−0.656675			−0.328337	−	0.944561i	$-0.606488\pi$
$139$	−7.74208			−0.656675			−0.328337	+	0.944561i	$0.606488\pi$
$140$	−2.23437	−	4.56807i	−0.188839	−	0.386073i
$141$	1.91216			0.161033
$142$	−1.34947	−	2.33735i	−0.113245	−	0.196146i
$143$	3.01818	−	5.22764i	0.252393	−	0.437157i
$144$	5.17276	−	8.95948i	0.431063	−	0.746624i
$145$	2.53066	+	4.38323i	0.210160	+	0.364008i
$146$	−1.13494			−0.0939286
$147$	−0.727665	−	1.78942i	−0.0600168	−	0.147589i
$148$	18.2448			1.49971
$149$	−2.70587	−	4.68670i	−0.221673	−	0.383949i	0.733643	−	0.679535i	$-0.237818\pi$
$149$	−2.70587	−	4.68670i	−0.221673	−	0.383949i	−0.955316	+	0.295586i	$0.904485\pi$
$150$	−0.0385254	+	0.0667280i	−0.00314559	+	0.00544832i
$151$	8.89472	−	15.4061i	0.723842	−	1.25373i	−0.235607	−	0.971848i	$-0.575708\pi$
$151$	8.89472	−	15.4061i	0.723842	−	1.25373i	0.959449	−	0.281883i	$-0.0909589\pi$
$152$	3.38264	+	5.85890i	0.274368	+	0.475220i
$153$	13.1055			1.05951
$154$	−0.324582	−	0.663594i	−0.0261555	−	0.0534739i
$155$	−3.35347			−0.269357
$156$	1.60086	+	2.77277i	0.128171	+	0.221999i
$157$	−3.82218	+	6.62021i	−0.305043	+	0.528350i	−0.977271	−	0.211994i	$-0.932004\pi$
$157$	−3.82218	+	6.62021i	−0.305043	+	0.528350i	0.672228	+	0.740344i	$0.265338\pi$
$158$	−2.02217	+	3.50249i	−0.160875	+	0.278643i
$159$	−1.49118	−	2.58281i	−0.118259	−	0.204830i
$160$	3.17809			0.251250
$161$	−0.208327	+	0.309609i	−0.0164185	+	0.0244006i
$162$	2.32315			0.182524
$163$	3.85871	+	6.68349i	0.302238	+	0.523491i	0.976643	−	0.214871i	$-0.0689330\pi$
$163$	3.85871	+	6.68349i	0.302238	+	0.523491i	−0.674405	+	0.738362i	$0.735600\pi$
$164$	1.19084	−	2.06259i	0.0929889	−	0.161061i
$165$	0.137980	−	0.238988i	0.0107417	−	0.0186052i
$166$	−0.379019	−	0.656480i	−0.0294176	−	0.0509527i
$167$	−23.7258			−1.83596			−0.917978	−	0.396630i	$-0.870179\pi$
$167$	−23.7258			−1.83596			−0.917978	+	0.396630i	$0.870179\pi$
$168$	0.797652	+	0.0548750i	0.0615402	+	0.00423370i
$169$	23.4376			1.80289
$170$	0.625749	+	1.08383i	0.0479927	+	0.0831259i
$171$	9.03162	−	15.6432i	0.690665	−	1.19627i
$172$	5.32366	−	9.22084i	0.405925	−	0.703083i
$173$	−5.88023	−	10.1849i	−0.447066	−	0.774341i	0.551128	−	0.834421i	$-0.314198\pi$
$173$	−5.88023	−	10.1849i	−0.447066	−	0.774341i	−0.998194	+	0.0600801i	$0.980864\pi$
$174$	−0.389979			−0.0295643
$175$	−2.63951	−	0.181587i	−0.199528	−	0.0137267i
$176$	−3.53833			−0.266711
$177$	−1.38440	−	2.39786i	−0.104058	−	0.180234i
$178$	−2.49187	+	4.31604i	−0.186773	+	0.323501i
$179$	−7.09093	+	12.2819i	−0.530001	+	0.917989i	0.469386	+	0.882993i	$0.344475\pi$
$179$	−7.09093	+	12.2819i	−0.530001	+	0.917989i	−0.999387	+	0.0349959i	$0.988858\pi$
$180$	−2.80988	−	4.86685i	−0.209436	−	0.362754i
$181$	8.64623			0.642669			0.321335	−	0.946966i	$-0.395869\pi$
$181$	8.64623			0.642669			0.321335	+	0.946966i	$0.395869\pi$
$182$	2.48938	−	3.69964i	0.184525	−	0.274236i
$183$	−2.53175			−0.187152
$184$	−0.0772280	−	0.133763i	−0.00569332	−	0.00986113i
$185$	4.74619	−	8.22065i	0.348947	−	0.604394i
$186$	0.129194	−	0.223770i	0.00947296	−	0.0164076i
$187$	−2.24113	−	3.88176i	−0.163888	−	0.283862i
$188$	−13.3181			−0.971319
$189$	−1.90038	−	3.88526i	−0.138233	−	0.282611i
$190$	1.72494			0.125140
$191$	−1.56088	−	2.70353i	−0.112942	−	0.195621i	0.804013	−	0.594611i	$-0.202694\pi$
$191$	−1.56088	−	2.70353i	−0.112942	−	0.195621i	−0.916955	+	0.398990i	$0.869361\pi$
$192$	0.853998	−	1.47917i	0.0616320	−	0.106750i
$193$	−4.59240	+	7.95428i	−0.330568	+	0.572561i	−0.982623	−	0.185610i	$-0.940574\pi$
$193$	−4.59240	+	7.95428i	−0.330568	+	0.572561i	0.652055	+	0.758172i	$0.273907\pi$
$194$	0.0434080	+	0.0751849i	0.00311651	+	0.00539796i
$195$	1.66579			0.119290
$196$	5.06814	+	12.4632i	0.362010	+	0.890230i
$197$	14.7284			1.04935			0.524677	−	0.851301i	$-0.324186\pi$
$197$	14.7284			1.04935			0.524677	+	0.851301i	$0.324186\pi$
$198$	−0.408185	−	0.706997i	−0.0290084	−	0.0502441i
$199$	4.66322	−	8.07693i	0.330567	−	0.572559i	−0.652056	−	0.758171i	$-0.726093\pi$
$199$	4.66322	−	8.07693i	0.330567	−	0.572559i	0.982623	+	0.185612i	$0.0594268\pi$
$200$	0.547538	−	0.948364i	0.0387168	−	0.0670594i
$201$	−1.44623	−	2.50494i	−0.102009	−	0.176685i
$202$	2.41437			0.169874
$203$	−5.88377	−	12.0291i	−0.412960	−	0.844280i
$204$	2.37742			0.166453
$205$	−0.619570	−	1.07313i	−0.0432726	−	0.0749504i
$206$	1.00927	−	1.74812i	0.0703195	−	0.121797i
$207$	−0.206198	+	0.357146i	−0.0143318	+	0.0248234i
$208$	−10.6793	−	18.4971i	−0.740476	−	1.28254i
$209$	−6.17791			−0.427335
$210$	0.113805	−	0.169134i	0.00785331	−	0.0116713i
$211$	−2.60436			−0.179291			−0.0896457	−	0.995974i	$-0.528573\pi$
$211$	−2.60436			−0.179291			−0.0896457	+	0.995974i	$0.528573\pi$
$212$	10.3860	+	17.9891i	0.713314	+	1.23550i
$213$	−1.33375	+	2.31013i	−0.0913874	+	0.158288i
$214$	−1.17579	+	2.03653i	−0.0803753	+	0.139214i
$215$	−2.76979	−	4.79742i	−0.188898	−	0.327181i
$216$	1.79017			0.121805
$217$	8.85152	+	0.608946i	0.600881	+	0.0413379i
$218$	3.38586			0.229319
$219$	0.560864	+	0.971446i	0.0378997	+	0.0656442i
$220$	−0.961021	+	1.66454i	−0.0647920	+	0.112223i
$221$	13.5283	−	23.4317i	0.910011	−	1.57618i
$222$	0.365698	+	0.633408i	0.0245441	+	0.0425116i
$223$	−4.65166			−0.311498			−0.155749	−	0.987797i	$-0.549779\pi$
$223$	−4.65166			−0.311498			−0.155749	+	0.987797i	$0.549779\pi$
$224$	−8.38861	−	0.577100i	−0.560488	−	0.0385591i
$225$	−2.92385			−0.194923
$226$	−0.193588	−	0.335304i	−0.0128773	−	0.0223041i
$227$	−6.90185	+	11.9544i	−0.458092	+	0.793438i	−0.998860	−	0.0477333i	$-0.984800\pi$
$227$	−6.90185	+	11.9544i	−0.458092	+	0.793438i	0.540768	+	0.841172i	$0.318134\pi$
$228$	1.63840	−	2.83779i	0.108506	−	0.187937i
$229$	2.85641	+	4.94745i	0.188757	+	0.326936i	0.944836	−	0.327544i	$-0.106221\pi$
$229$	2.85641	+	4.94745i	0.188757	+	0.326936i	−0.756079	+	0.654480i	$0.772888\pi$
$230$	−0.0393815			−0.00259674
$231$	−0.407597	+	0.605757i	−0.0268179	+	0.0398559i
$232$	5.54253			0.363885
$233$	2.08780	+	3.61618i	0.136776	+	0.236904i	0.926275	−	0.376849i	$-0.122993\pi$
$233$	2.08780	+	3.61618i	0.136776	+	0.236904i	−0.789498	+	0.613753i	$0.789659\pi$
$234$	2.46395	−	4.26768i	0.161073	−	0.278987i
$235$	−3.46456	+	6.00079i	−0.226003	+	0.391449i
$236$	9.64228	+	16.7009i	0.627659	+	1.08714i
$237$	3.99724			0.259649
$238$	−1.45486	−	2.97441i	−0.0943047	−	0.192802i
$239$	13.1008			0.847419			0.423710	−	0.905798i	$-0.360728\pi$
$239$	13.1008			0.847419			0.423710	+	0.905798i	$0.360728\pi$
$240$	−0.488217	−	0.845617i	−0.0315143	−	0.0545844i
$241$	8.64107	−	14.9668i	0.556620	−	0.964094i	−0.441155	−	0.897431i	$-0.645431\pi$
$241$	8.64107	−	14.9668i	0.556620	−	0.964094i	0.997776	−	0.0666635i	$-0.0212354\pi$
$242$	−0.139605	+	0.241804i	−0.00897417	+	0.0155437i
$243$	−3.60016	−	6.23566i	−0.230951	−	0.400018i
$244$	17.6334			1.12887
$245$	6.93405	+	0.958602i	0.443000	+	0.0612428i
$246$	0.0954768			0.00608738
$247$	−18.6460	−	32.2958i	−1.18642	−	2.05494i
$248$	−1.83615	+	3.18031i	−0.116596	+	0.201950i
$249$	−0.374606	+	0.648836i	−0.0237397	+	0.0411183i
$250$	−0.139605	−	0.241804i	−0.00882942	−	0.0152930i
$251$	−20.1119			−1.26945			−0.634725	−	0.772738i	$-0.718887\pi$
$251$	−20.1119			−1.26945			−0.634725	+	0.772738i	$0.718887\pi$
$252$	6.53295	+	13.3563i	0.411537	+	0.841371i
$253$	0.141046			0.00886748
$254$	1.98999	+	3.44677i	0.124863	+	0.216269i
$255$	0.618462	−	1.07121i	0.0387296	−	0.0670817i
$256$	−5.06068	+	8.76536i	−0.316293	+	0.547835i
$257$	15.3668	+	26.6161i	0.958557	+	1.66027i	0.726010	+	0.687684i	$0.241372\pi$
$257$	15.3668	+	26.6161i	0.958557	+	1.66027i	0.232547	+	0.972585i	$0.425294\pi$
$258$	0.426830			0.0265733
$259$	−14.0204	+	20.8367i	−0.871185	+	1.29473i
$260$	−11.6021			−0.719533
$261$	−7.39926	−	12.8159i	−0.458003	−	0.793284i
$262$	−0.787241	+	1.36354i	−0.0486359	+	0.0842398i
$263$	−5.62318	+	9.73964i	−0.346740	+	0.600572i	−0.985668	−	0.168695i	$-0.946045\pi$
$263$	−5.62318	+	9.73964i	−0.346740	+	0.600572i	0.638928	+	0.769266i	$0.279378\pi$
$264$	−0.151098	−	0.261710i	−0.00929946	−	0.0161071i
$265$	10.8073			0.663885
$266$	−4.55299	−	0.313226i	−0.279162	−	0.0192051i
$267$	4.92570			0.301448
$268$	10.0729	+	17.4468i	0.615300	+	1.06573i
$269$	−4.47238	+	7.74638i	−0.272686	+	0.472305i	−0.969549	−	0.244899i	$-0.921245\pi$
$269$	−4.47238	+	7.74638i	−0.272686	+	0.472305i	0.696863	+	0.717204i	$0.254579\pi$
$270$	0.228219	−	0.395287i	0.0138890	−	0.0240564i
$271$	−6.55354	−	11.3511i	−0.398099	−	0.689528i	0.595392	−	0.803435i	$-0.296997\pi$
$271$	−6.55354	−	11.3511i	−0.398099	−	0.689528i	−0.993491	+	0.113907i	$0.963663\pi$
$272$	−15.8597			−0.961637
$273$	−4.39687	−	0.302486i	−0.266111	−	0.0183073i
$274$	0.832514			0.0502940
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$	−0.0374058	+	0.0647887i	−0.00225156	+	0.00389982i
$277$	4.33201	−	7.50327i	0.260285	−	0.450828i	−0.706032	−	0.708180i	$-0.749517\pi$
$277$	4.33201	−	7.50327i	0.260285	−	0.450828i	0.966318	+	0.257352i	$0.0828500\pi$
$278$	1.08084	+	1.87206i	0.0648242	+	0.112279i
$279$	9.80503			0.587012
$280$	−1.61744	+	2.40379i	−0.0966608	+	0.143654i
$281$	7.01062			0.418218			0.209109	−	0.977892i	$-0.432944\pi$
$281$	7.01062			0.418218			0.209109	+	0.977892i	$0.432944\pi$
$282$	−0.266947	−	0.462367i	−0.0158965	−	0.0275335i
$283$	5.65483	−	9.79445i	0.336145	−	0.582219i	−0.647559	−	0.762015i	$-0.724210\pi$
$283$	5.65483	−	9.79445i	0.336145	−	0.582219i	0.983704	+	0.179796i	$0.0575436\pi$
$284$	9.28952	−	16.0899i	0.551232	−	0.954761i
$285$	−0.852426	−	1.47645i	−0.0504934	−	0.0874571i
$286$	−1.68542			−0.0996607
$287$	1.44050	+	2.94504i	0.0850298	+	0.173840i
$288$	−9.29225			−0.547551
$289$	−1.54536	−	2.67665i	−0.0909037	−	0.157450i
$290$	0.706588	−	1.22385i	0.0414923	−	0.0718667i
$291$	0.0429026	−	0.0743094i	0.00251499	−	0.00435609i
$292$	−3.90639	−	6.76606i	−0.228604	−	0.395954i
$293$	29.3418			1.71416			0.857082	−	0.515180i	$-0.172275\pi$
$293$	29.3418			1.71416			0.857082	+	0.515180i	$0.172275\pi$
$294$	−0.331103	+	0.425765i	−0.0193103	+	0.0248311i
$295$	10.0334			0.584166
$296$	−5.19744	−	9.00224i	−0.302095	−	0.523244i
$297$	−0.817371	+	1.41573i	−0.0474287	+	0.0821489i
$298$	−0.755507	+	1.30858i	−0.0437653	+	0.0758038i
$299$	0.425702	+	0.737337i	0.0246190	+	0.0426413i
$300$	−0.530406			−0.0306230
$301$	6.43975	+	13.1658i	0.371181	+	0.758865i
$302$	−4.96700			−0.285819
$303$	−1.19313	−	2.06656i	−0.0685434	−	0.118721i
$304$	−10.9297	+	18.9308i	−0.626862	+	1.08576i
$305$	4.58717	−	7.94521i	0.262660	−	0.454941i
$306$	−1.82959	−	3.16895i	−0.104591	−	0.181157i
$307$	19.8056			1.13036			0.565182	−	0.824967i	$-0.308806\pi$
$307$	19.8056			1.13036			0.565182	+	0.824967i	$0.308806\pi$
$308$	2.83888	−	4.21906i	0.161760	−	0.240403i
$309$	−1.99505			−0.113494
$310$	0.468162	+	0.810881i	0.0265898	+	0.0460549i
$311$	2.21269	−	3.83249i	0.125470	−	0.217321i	−0.796446	−	0.604709i	$-0.793289\pi$
$311$	2.21269	−	3.83249i	0.125470	−	0.217321i	0.921917	+	0.387388i	$0.126623\pi$
$312$	0.912084	−	1.57978i	0.0516366	−	0.0894372i
$313$	−2.68424	−	4.64925i	−0.151722	−	0.262791i	0.780138	−	0.625607i	$-0.215149\pi$
$313$	−2.68424	−	4.64925i	−0.151722	−	0.262791i	−0.931861	+	0.362816i	$0.881815\pi$
$314$	2.13439			0.120450
$315$	7.71753	+	0.530932i	0.434833	+	0.0299146i
$316$	−27.8405			−1.56615
$317$	−7.49114	−	12.9750i	−0.420744	−	0.728750i	0.575268	−	0.817965i	$-0.304898\pi$
$317$	−7.49114	−	12.9750i	−0.420744	−	0.728750i	−0.996012	+	0.0892144i	$0.971564\pi$
$318$	−0.416355	+	0.721147i	−0.0233480	+	0.0404399i
$319$	−2.53066	+	4.38323i	−0.141690	+	0.245414i
$320$	3.09465	+	5.36009i	0.172996	+	0.299638i
$321$	2.32420			0.129724
$322$	0.103948	+	0.00715117i	0.00579280	+	0.000398519i
$323$	−27.6910			−1.54077
$324$	7.99609	+	13.8496i	0.444227	+	0.769424i
$325$	−3.01818	+	5.22764i	−0.167418	+	0.289977i
$326$	1.07739	−	1.86610i	0.0596714	−	0.103354i
$327$	−1.67322	−	2.89810i	−0.0925292	−	0.160265i
$328$	−1.35695			−0.0749251
$329$	10.2344	−	15.2101i	0.564242	−	0.838557i
$330$	−0.0770509			−0.00424151
$331$	9.58890	+	16.6085i	0.527054	+	0.912883i	0.999503	+	0.0315257i	$0.0100366\pi$
$331$	9.58890	+	16.6085i	0.527054	+	0.912883i	−0.472449	+	0.881358i	$0.656630\pi$
$332$	2.60911	−	4.51910i	0.143193	−	0.248018i
$333$	−13.8771	+	24.0359i	−0.760463	+	1.31716i
$334$	3.31225	+	5.73698i	0.181238	+	0.313914i
$335$	10.4815			0.572663
$336$	1.13510	+	2.32067i	0.0619250	+	0.126603i
$337$	−20.9041			−1.13872			−0.569359	−	0.822089i	$-0.692809\pi$
$337$	−20.9041			−1.13872			−0.569359	+	0.822089i	$0.692809\pi$
$338$	−3.27201	−	5.66729i	−0.177974	−	0.308260i
$339$	−0.191334	+	0.331400i	−0.0103918	+	0.0179992i
$340$	−4.30755	+	7.46090i	−0.233610	+	0.404624i
$341$	−1.67673	−	2.90419i	−0.0908003	−	0.157271i
$342$	−5.04345			−0.272719
$343$	−18.1284	−	3.78937i	−0.978844	−	0.204607i
$344$	−6.06627			−0.327071
$345$	0.0194615	+	0.0337083i	0.00104777	+	0.00181479i
$346$	−1.64182	+	2.84372i	−0.0882650	+	0.152880i
$347$	−5.98578	+	10.3677i	−0.321334	+	0.556566i	−0.980763	−	0.195200i	$-0.937464\pi$
$347$	−5.98578	+	10.3677i	−0.321334	+	0.556566i	0.659430	+	0.751766i	$0.270798\pi$
$348$	−1.34228	−	2.32489i	−0.0719536	−	0.124627i
$349$	2.81828			0.150859			0.0754297	−	0.997151i	$-0.475967\pi$
$349$	2.81828			0.150859			0.0754297	+	0.997151i	$0.475967\pi$
$350$	0.324582	+	0.663594i	0.0173496	+	0.0354706i
$351$	−9.86789			−0.526709
$352$	1.58905	+	2.75231i	0.0846964	+	0.146698i
$353$	−9.14242	+	15.8351i	−0.486602	+	0.842819i	−0.999881	−	0.0154022i	$-0.995097\pi$
$353$	−9.14242	+	15.8351i	−0.486602	+	0.842819i	0.513279	+	0.858222i	$0.328430\pi$
$354$	−0.386540	+	0.669507i	−0.0205444	+	0.0355839i
$355$	−4.83315	−	8.37127i	−0.256517	−	0.444301i
$356$	−34.3072			−1.81828
$357$	−1.82696	+	2.71516i	−0.0966928	+	0.143702i
$358$	3.95973			0.209278
$359$	15.6345	+	27.0798i	0.825159	+	1.42922i	0.901798	+	0.432159i	$0.142248\pi$
$359$	15.6345	+	27.0798i	0.825159	+	1.42922i	−0.0766383	+	0.997059i	$0.524419\pi$
$360$	−1.60092	+	2.77287i	−0.0843757	+	0.146143i
$361$	−9.58326	+	16.5987i	−0.504382	+	0.873615i
$362$	−1.20706	−	2.09069i	−0.0634417	−	0.109884i
$363$	0.275960			0.0144841
$364$	30.6240	+	2.10679i	1.60513	+	0.110426i
$365$	−4.06483			−0.212763
$366$	0.353445	+	0.612185i	0.0184749	+	0.0319994i
$367$	0.506132	−	0.876646i	0.0264199	−	0.0457606i	−0.852513	−	0.522706i	$-0.824923\pi$
$367$	0.506132	−	0.876646i	0.0264199	−	0.0457606i	0.878933	+	0.476945i	$0.158256\pi$
$368$	0.249533	−	0.432204i	0.0130078	−	0.0225302i
$369$	1.81153	+	3.13766i	0.0943043	+	0.163340i
$370$	−2.65038			−0.137787
$371$	−28.5259	−	1.96246i	−1.48099	−	0.101886i
$372$	1.77870			0.0922213
$373$	2.40253	+	4.16130i	0.124398	+	0.215464i	0.921498	−	0.388384i	$-0.126967\pi$
$373$	2.40253	+	4.16130i	0.124398	+	0.215464i	−0.797099	+	0.603848i	$0.793633\pi$
$374$	−0.625749	+	1.08383i	−0.0323567	+	0.0560434i
$375$	−0.137980	+	0.238988i	−0.00712525	+	0.0123413i
$376$	3.79396	+	6.57133i	0.195658	+	0.338890i
$377$	−30.5519			−1.57350
$378$	−0.674165	+	1.00192i	−0.0346753	+	0.0515333i
$379$	−28.9344			−1.48626			−0.743130	−	0.669147i	$-0.766660\pi$
$379$	−28.9344			−1.48626			−0.743130	+	0.669147i	$0.766660\pi$
$380$	5.93709	+	10.2833i	0.304567	+	0.527525i
$381$	1.96682	−	3.40663i	0.100763	−	0.174527i
$382$	−0.435816	+	0.754855i	−0.0222983	+	0.0386217i
$383$	−2.09649	−	3.63122i	−0.107125	−	0.185547i	0.807479	−	0.589896i	$-0.200831\pi$
$383$	−2.09649	−	3.63122i	−0.107125	−	0.185547i	−0.914605	+	0.404349i	$0.867498\pi$
$384$	−2.23094			−0.113847
$385$	−1.16250	−	2.37668i	−0.0592464	−	0.121127i
$386$	2.56450			0.130529
$387$	8.09845	+	14.0269i	0.411667	+	0.713029i
$388$	−0.298814	+	0.517560i	−0.0151700	+	0.0262751i
$389$	19.4724	−	33.7272i	0.987290	−	1.71004i	0.356008	−	0.934483i	$-0.384138\pi$
$389$	19.4724	−	33.7272i	0.987290	−	1.71004i	0.631282	−	0.775554i	$-0.282529\pi$
$390$	−0.232553	−	0.402794i	−0.0117758	−	0.0203963i
$391$	0.632206			0.0319720
$392$	4.70576	−	6.05113i	0.237677	−	0.305628i
$393$	1.55615			0.0784973
$394$	−2.05616	−	3.56138i	−0.103588	−	0.179420i
$395$	−7.24243	+	12.5443i	−0.364406	+	0.631170i
$396$	2.80988	−	4.86685i	0.141202	−	0.244568i
$397$	−18.5749	−	32.1726i	−0.932245	−	1.61470i	−0.779474	−	0.626434i	$-0.784514\pi$
$397$	−18.5749	−	32.1726i	−0.932245	−	1.61470i	−0.152771	−	0.988262i	$-0.548820\pi$
$398$	−2.60404			−0.130529
$399$	1.98189	+	4.05189i	0.0992184	+	0.202848i
$400$	3.53833			0.176916
$401$	−4.38915	−	7.60223i	−0.219184	−	0.379637i	0.735375	−	0.677660i	$-0.237006\pi$
$401$	−4.38915	−	7.60223i	−0.219184	−	0.379637i	−0.954559	+	0.298023i	$0.903673\pi$
$402$	−0.403803	+	0.699407i	−0.0201399	+	0.0348833i
$403$	10.1214	−	17.5307i	0.504181	−	0.873267i
$404$	8.31006	+	14.3934i	0.413441	+	0.716101i
$405$	8.32042			0.413445
$406$	−2.08728	+	3.10205i	−0.103590	+	0.153952i
$407$	9.49239			0.470520
$408$	−0.677263	−	1.17305i	−0.0335295	−	0.0580749i
$409$	11.1518	−	19.3154i	0.551419	−	0.955085i	−0.446754	−	0.894657i	$-0.647420\pi$
$409$	11.1518	−	19.3154i	0.551419	−	0.955085i	0.998173	−	0.0604284i	$-0.0192467\pi$
$410$	−0.172991	+	0.299628i	−0.00854339	+	0.0147976i
$411$	−0.411410	−	0.712583i	−0.0202934	−	0.0351491i
$412$	13.8954			0.684576
$413$	−26.4832	−	1.82193i	−1.30315	−	0.0896513i
$414$	0.115146			0.00565910
$415$	−1.35747	−	2.35120i	−0.0666354	−	0.115416i
$416$	−9.59204	+	16.6139i	−0.470289	+	0.814564i
$417$	1.06825	−	1.85026i	0.0523125	−	0.0906078i
$418$	0.862469	+	1.49384i	0.0421847	+	0.0730661i
$419$	−19.0544			−0.930869			−0.465434	−	0.885082i	$-0.654102\pi$
$419$	−19.0544			−0.930869			−0.465434	+	0.885082i	$0.654102\pi$
$420$	1.40001	+	0.0963147i	0.0683136	+	0.00469968i
$421$	18.7130			0.912016			0.456008	−	0.889976i	$-0.349279\pi$
$421$	18.7130			0.912016			0.456008	+	0.889976i	$0.349279\pi$
$422$	0.363582	+	0.629743i	0.0176989	+	0.0306554i
$423$	10.1298	−	17.5454i	0.492530	−	0.853087i
$424$	5.91739	−	10.2492i	0.287374	−	0.497746i
$425$	2.24113	+	3.88176i	0.108711	+	0.188293i
$426$	0.744797			0.0360856
$427$	−13.5506	+	20.1385i	−0.655761	+	0.974570i
$428$	−16.1879			−0.782471
$429$	0.832895	+	1.44262i	0.0402126	+	0.0696502i
$430$	−0.773356	+	1.33949i	−0.0372945	+	0.0645960i
$431$	17.0466	−	29.5257i	0.821108	−	1.42220i	−0.0837498	−	0.996487i	$-0.526690\pi$
$431$	17.0466	−	29.5257i	0.821108	−	1.42220i	0.904858	−	0.425714i	$-0.139977\pi$
$432$	2.89213	+	5.00931i	0.139147	+	0.241010i
$433$	−11.2439			−0.540347			−0.270174	−	0.962812i	$-0.587081\pi$
$433$	−11.2439			−0.540347			−0.270174	+	0.962812i	$0.587081\pi$
$434$	−1.08847	−	2.22534i	−0.0522485	−	0.106820i
$435$	−1.39672			−0.0669676
$436$	11.6539	+	20.1851i	0.558119	+	0.966690i
$437$	0.435684	−	0.754627i	0.0208416	−	0.0360987i
$438$	0.156599	−	0.271238i	0.00748261	−	0.0129603i
$439$	7.54026	+	13.0601i	0.359877	+	0.623326i	0.987940	−	0.154837i	$-0.0494853\pi$
$439$	7.54026	+	13.0601i	0.359877	+	0.623326i	−0.628063	+	0.778163i	$0.716152\pi$
$440$	1.09508			0.0522057
$441$	−20.2741	−	2.80280i	−0.965433	−	0.133467i
$442$	−7.55448			−0.359330
$443$	−11.8924	−	20.5983i	−0.565026	−	0.978653i	−0.997047	−	0.0767899i	$-0.975533\pi$
$443$	−11.8924	−	20.5983i	−0.565026	−	0.978653i	0.432022	−	0.901863i	$-0.357800\pi$
$444$	−2.51741	+	4.36028i	−0.119471	+	0.206930i
$445$	−8.92468	+	15.4580i	−0.423070	+	0.732779i
$446$	0.649397	+	1.12479i	0.0307498	+	0.0532603i
$447$	1.49342			0.0706363
$448$	−7.19504	−	14.7100i	−0.339934	−	0.694980i
$449$	26.2117			1.23701			0.618504	−	0.785781i	$-0.287739\pi$
$449$	26.2117			1.23701			0.618504	+	0.785781i	$0.287739\pi$
$450$	0.408185	+	0.706997i	0.0192420	+	0.0333281i
$451$	0.619570	−	1.07313i	0.0291744	−	0.0505315i
$452$	1.33263	−	2.30818i	0.0626815	−	0.108568i
$453$	2.45458	+	4.25146i	0.115326	+	0.199751i
$454$	3.85414			0.180884
$455$	8.91579	−	13.2504i	0.417979	−	0.621186i
$456$	−1.86694			−0.0874276
$457$	6.80660	+	11.7894i	0.318399	+	0.551484i	0.980154	−	0.198236i	$-0.0635214\pi$
$457$	6.80660	+	11.7894i	0.318399	+	0.551484i	−0.661755	+	0.749720i	$0.730188\pi$
$458$	0.797540	−	1.38138i	0.0372666	−	0.0645477i
$459$	−3.66368	+	6.34567i	−0.171006	+	0.296191i
$460$	−0.135548	−	0.234776i	−0.00631996	−	0.0109465i
$461$	22.8464			1.06406			0.532032	−	0.846724i	$-0.321429\pi$
$461$	22.8464			1.06406			0.532032	+	0.846724i	$0.321429\pi$
$462$	0.203377	+	0.0139914i	0.00946194	+	0.000650940i
$463$	−42.7331			−1.98598			−0.992989	−	0.118207i	$-0.962285\pi$
$463$	−42.7331			−1.98598			−0.992989	+	0.118207i	$0.962285\pi$
$464$	8.95430	+	15.5093i	0.415693	+	0.720001i
$465$	0.462711	−	0.801439i	0.0214577	−	0.0371658i
$466$	0.582936	−	1.00968i	0.0270040	−	0.0467723i
$467$	5.78661	+	10.0227i	0.267772	+	0.463795i	0.968286	−	0.249844i	$-0.0803792\pi$
$467$	5.78661	+	10.0227i	0.267772	+	0.463795i	−0.700514	+	0.713639i	$0.747046\pi$
$468$	33.9228			1.56808
$469$	−27.6659	−	1.90330i	−1.27749	−	0.0878860i
$470$	1.93468			0.0892404
$471$	−1.05477	−	1.82691i	−0.0486011	−	0.0841796i
$472$	5.49366	−	9.51529i	0.252866	−	0.437977i
$473$	2.76979	−	4.79742i	0.127355	−	0.220586i
$474$	−0.558036	−	0.966547i	−0.0256314	−	0.0443950i
$475$	6.17791			0.283462
$476$	12.7246	−	18.9109i	0.583233	−	0.866782i
$477$	−31.5988			−1.44681
$478$	−1.82894	−	3.16782i	−0.0836538	−	0.144893i
$479$	15.6260	−	27.0650i	0.713969	−	1.23663i	−0.249386	−	0.968404i	$-0.580229\pi$
$479$	15.6260	−	27.0650i	0.713969	−	1.23663i	0.963356	−	0.268227i	$-0.0864377\pi$
$480$	−0.438512	+	0.759526i	−0.0200153	+	0.0346674i
$481$	28.6497	+	49.6228i	1.30631	+	2.26260i
$482$	−4.82536			−0.219789
$483$	−0.0452479	−	0.0925074i	−0.00205885	−	0.00420923i
$484$	−1.92204			−0.0873655
$485$	0.155467	+	0.269276i	0.00705938	+	0.0122272i
$486$	−1.00520	+	1.74106i	−0.0455970	+	0.0789763i
$487$	17.8975	−	30.9993i	0.811012	−	1.40471i	−0.101145	−	0.994872i	$-0.532251\pi$
$487$	17.8975	−	30.9993i	0.811012	−	1.40471i	0.912157	−	0.409842i	$-0.134416\pi$
$488$	−5.02330	−	8.70061i	−0.227394	−	0.393858i
$489$	−2.12970			−0.0963083
$490$	−0.736238	−	1.81050i	−0.0332598	−	0.0817903i
$491$	23.3469			1.05363			0.526815	−	0.849980i	$-0.323386\pi$
$491$	23.3469			1.05363			0.526815	+	0.849980i	$0.323386\pi$
$492$	0.328623	+	0.569192i	0.0148155	+	0.0256612i
$493$	−11.3431	+	19.6468i	−0.510867	+	0.884848i
$494$	−5.20617	+	9.01735i	−0.234237	+	0.405710i
$495$	−1.46192	−	2.53213i	−0.0657086	−	0.113811i
$496$	−11.8657			−0.532784
$497$	11.2371	+	22.9737i	0.504051	+	1.03051i
$498$	0.209188			0.00937393
$499$	3.98962	+	6.91023i	0.178600	+	0.309344i	0.941401	−	0.337289i	$-0.109510\pi$
$499$	3.98962	+	6.91023i	0.178600	+	0.309344i	−0.762801	+	0.646633i	$0.776177\pi$
$500$	0.961021	−	1.66454i	0.0429782	−	0.0744403i
$501$	3.27368	−	5.67018i	0.146257	−	0.253325i
$502$	2.80773	+	4.86312i	0.125315	+	0.217052i
$503$	24.0054			1.07035			0.535173	−	0.844742i	$-0.320246\pi$
$503$	24.0054			1.07035			0.535173	+	0.844742i	$0.320246\pi$
$504$	4.72916	−	7.02832i	0.210653	−	0.313066i
$505$	8.64712			0.384792
$506$	−0.0196908	−	0.0341054i	−0.000875361	−	0.00151617i
$507$	−3.23391	+	5.60130i	−0.143623	+	0.248763i
$508$	−13.6988	+	23.7270i	−0.607785	+	1.05271i
$509$	18.0056	+	31.1867i	0.798086	+	1.38233i	0.920861	+	0.389891i	$0.127487\pi$
$509$	18.0056	+	31.1867i	0.798086	+	1.38233i	−0.122775	+	0.992434i	$0.539179\pi$
$510$	−0.345363			−0.0152929
$511$	10.7292	+	0.738120i	0.474630	+	0.0326525i
$512$	18.9946			0.839450
$513$	5.04964	+	8.74624i	0.222947	+	0.386156i
$514$	4.29059	−	7.43151i	0.189250	−	0.327790i
$515$	3.61474	−	6.26092i	0.159285	−	0.275889i
$516$	1.46911	+	2.54458i	0.0646741	+	0.112019i
$517$	−6.92912			−0.304742
$518$	6.99570	+	0.481274i	0.307374	+	0.0211460i
$519$	3.24541			0.142458
$520$	3.30513	+	5.72466i	0.144940	+	0.251043i
$521$	6.84850	−	11.8619i	0.300038	−	0.519681i	−0.676106	−	0.736804i	$-0.736334\pi$
$521$	6.84850	−	11.8619i	0.300038	−	0.519681i	0.976144	+	0.217123i	$0.0696673\pi$
$522$	−2.06595	+	3.57834i	−0.0904243	+	0.156620i
$523$	−11.4412	−	19.8167i	−0.500289	−	0.866525i	−1.00000		0.000333229i	$-0.999894\pi$
$523$	−11.4412	−	19.8167i	−0.500289	−	0.866525i	0.499711	−	0.866192i	$-0.333439\pi$
$524$	−10.8385			−0.473481
$525$	0.407597	−	0.605757i	0.0177890	−	0.0264374i
$526$	3.14011			0.136915
$527$	−7.51557	−	13.0174i	−0.327384	−	0.567045i
$528$	0.488217	−	0.845617i	0.0212469	−	0.0368008i
$529$	11.4901	−	19.9014i	0.499568	−	0.865276i
$530$	−1.50875	−	2.61324i	−0.0655360	−	0.113512i
$531$	−29.3361			−1.27308
$532$	−13.8037	−	28.2211i	−0.598467	−	1.22354i
$533$	7.47989			0.323990
$534$	−0.687654	−	1.19105i	−0.0297577	−	0.0515419i
$535$	−4.21112	+	7.29387i	−0.182063	+	0.315342i
$536$	5.73900	−	9.94023i	0.247887	−	0.429353i
$537$	−1.95681	−	3.38930i	−0.0844426	−	0.146259i
$538$	2.49747			0.107674
$539$	2.63685	+	6.48437i	0.113577	+	0.279301i
$540$	3.14204			0.135212
$541$	−17.9416	−	31.0758i	−0.771372	−	1.33605i	−0.936811	−	0.349835i	$-0.886238\pi$
$541$	−17.9416	−	31.0758i	−0.771372	−	1.33605i	0.165440	−	0.986220i	$-0.447096\pi$
$542$	−1.82982	+	3.16934i	−0.0785974	+	0.136135i
$543$	−1.19301	+	2.06635i	−0.0511968	+	0.0886754i
$544$	7.12253	+	12.3366i	0.305376	+	0.528926i
$545$	12.1265			0.519444
$546$	0.540685	+	1.10541i	0.0231392	+	0.0473071i
$547$	12.2566			0.524056			0.262028	−	0.965060i	$-0.415609\pi$
$547$	12.2566			0.524056			0.262028	+	0.965060i	$0.415609\pi$
$548$	2.86545	+	4.96310i	0.122406	+	0.212013i
$549$	−13.4122	+	23.2306i	−0.572418	+	0.991456i
$550$	0.139605	−	0.241804i	0.00595279	−	0.0103105i
$551$	15.6342	+	27.0792i	0.666039	+	1.15361i
$552$	0.0426236			0.00181418
$553$	21.3944	−	31.7956i	0.909781	−	1.35209i
$554$	−2.41909			−0.102777
$555$	1.30976	+	2.26857i	0.0555961	+	0.0962953i
$556$	−7.44030	+	12.8870i	−0.315539	+	0.546529i
$557$	21.0158	−	36.4004i	0.890466	−	1.54233i	0.0511489	−	0.998691i	$-0.483712\pi$
$557$	21.0158	−	36.4004i	0.890466	−	1.54233i	0.839317	−	0.543642i	$-0.182955\pi$
$558$	−1.36883	−	2.37089i	−0.0579474	−	0.100368i
$559$	33.4389			1.41432
$560$	−9.33945	−	0.642514i	−0.394664	−	0.0271512i
$561$	1.23692			0.0522230
$562$	−0.978720	−	1.69519i	−0.0412848	−	0.0715074i
$563$	−3.18838	+	5.52243i	−0.134374	+	0.232743i	−0.925358	−	0.379094i	$-0.876236\pi$
$563$	−3.18838	+	5.52243i	−0.134374	+	0.232743i	0.790984	+	0.611837i	$0.209569\pi$
$564$	1.83762	−	3.18286i	0.0773779	−	0.134022i
$565$	−0.693340	−	1.20090i	−0.0291690	−	0.0505222i
$566$	−3.15778			−0.132731
$567$	−21.9618	−	1.51088i	−0.922311	−	0.0634509i
$568$	−10.5853			−0.444151
$569$	−14.0331	−	24.3061i	−0.588299	−	1.01896i	−0.994455	−	0.105161i	$-0.966464\pi$
$569$	−14.0331	−	24.3061i	−0.588299	−	1.01896i	0.406156	−	0.913804i	$-0.366869\pi$
$570$	−0.238007	+	0.412239i	−0.00996900	+	0.0172668i
$571$	−9.32205	+	16.1463i	−0.390116	+	0.675700i	−0.992464	−	0.122533i	$-0.960898\pi$
$571$	−9.32205	+	16.1463i	−0.390116	+	0.675700i	0.602349	+	0.798233i	$0.294232\pi$
$572$	−5.80106	−	10.0477i	−0.242555	−	0.420117i
$573$	0.861482			0.0359889
$574$	0.511019	−	0.759460i	0.0213295	−	0.0316993i
$575$	−0.141046			−0.00588202
$576$	−9.04827	−	15.6721i	−0.377011	−	0.653003i
$577$	−3.72168	+	6.44614i	−0.154936	+	0.268356i	−0.933036	−	0.359784i	$-0.882850\pi$
$577$	−3.72168	+	6.44614i	−0.154936	+	0.268356i	0.778100	+	0.628141i	$0.216184\pi$
$578$	−0.431482	+	0.747348i	−0.0179473	+	0.0310856i
$579$	−1.26732	−	2.19506i	−0.0526679	−	0.0912235i
$580$	9.72807			0.403936
$581$	3.15610	+	6.45252i	0.130937	+	0.267696i
$582$	−0.0239577			−0.000993079
$583$	5.40363	+	9.35936i	0.223796	+	0.387625i
$584$	−2.22565	+	3.85494i	−0.0920980	+	0.159518i
$585$	8.82469	−	15.2848i	0.364856	−	0.631949i
$586$	−4.09627	−	7.09494i	−0.169215	−	0.293089i
$587$	43.9273			1.81307			0.906536	−	0.422128i	$-0.138717\pi$
$587$	43.9273			1.81307			0.906536	+	0.422128i	$0.138717\pi$
$588$	−3.67786	−	0.508448i	−0.151672	−	0.0209680i
$589$	−20.7174			−0.853646
$590$	−1.40071	−	2.42611i	−0.0576665	−	0.0998812i
$591$	−2.03222	+	3.51991i	−0.0835944	+	0.144790i
$592$	16.7936	−	29.0873i	0.690212	−	1.19548i
$593$	3.52287	+	6.10179i	0.144667	+	0.250570i	0.929249	−	0.369455i	$-0.120456\pi$
$593$	3.52287	+	6.10179i	0.144667	+	0.250570i	−0.784582	+	0.620025i	$0.787122\pi$
$594$	0.456438			0.0187279
$595$	−5.21062	−	10.6529i	−0.213615	−	0.436727i
$596$	−10.4016			−0.426065
$597$	1.28686	+	2.22891i	0.0526677	+	0.0912231i
$598$	0.118860	−	0.205872i	0.00486057	−	0.00841875i
$599$	−12.6379	+	21.8895i	−0.516371	+	0.894382i	0.483448	+	0.875373i	$0.339384\pi$
$599$	−12.6379	+	21.8895i	−0.516371	+	0.894382i	−0.999819	+	0.0190085i	$0.993949\pi$
$600$	0.151098	+	0.261710i	0.00616857	+	0.0106843i
$601$	−35.8144			−1.46090			−0.730450	−	0.682967i	$-0.760689\pi$
$601$	−35.8144			−1.46090			−0.730450	+	0.682967i	$0.760689\pi$
$602$	2.28452	−	3.39517i	0.0931100	−	0.138377i
$603$	−30.6462			−1.24801
$604$	−17.0960	−	29.6112i	−0.695627	−	1.20486i
$605$	−0.500000	+	0.866025i	−0.0203279	+	0.0352089i
$606$	−0.333134	+	0.577005i	−0.0135326	+	0.0234392i
$607$	7.73847	+	13.4034i	0.314095	+	0.544028i	0.979245	−	0.202682i	$-0.0649657\pi$
$607$	7.73847	+	13.4034i	0.314095	+	0.544028i	−0.665150	+	0.746710i	$0.731632\pi$
$608$	19.6339			0.796262
$609$	3.68666	+	0.253626i	0.149391	+	0.0102774i
$610$	−2.56157			−0.103715
$611$	−20.9133	−	36.2229i	−0.846062	−	1.46542i
$612$	12.5946	−	21.8145i	0.509107	−	0.881800i
$613$	−10.3347	+	17.9002i	−0.417415	+	0.722984i	−0.995679	−	0.0928659i	$-0.970397\pi$
$613$	−10.3347	+	17.9002i	−0.417415	+	0.722984i	0.578264	+	0.815850i	$0.303731\pi$
$614$	−2.76496	−	4.78906i	−0.111585	−	0.193271i
$615$	0.341952			0.0137889
$616$	−2.89047	−	0.198851i	−0.116460	−	0.00801195i
$617$	8.80214			0.354361			0.177180	−	0.984178i	$-0.443302\pi$
$617$	8.80214			0.354361			0.177180	+	0.984178i	$0.443302\pi$
$618$	0.278519	+	0.482409i	0.0112037	+	0.0194053i
$619$	12.7775	−	22.1313i	0.513571	−	0.889532i	−0.486305	−	0.873789i	$-0.661656\pi$
$619$	12.7775	−	22.1313i	0.513571	−	0.889532i	0.999876	−	0.0157424i	$-0.00501116\pi$
$620$	−3.22275	+	5.58197i	−0.129429	+	0.224177i
$621$	−0.115287	−	0.199683i	−0.00462630	−	0.00801299i
$622$	−1.23561			−0.0495436
$623$	26.3638	−	39.1810i	1.05624	−	1.56975i
$624$	5.89411			0.235953
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−0.749470	+	1.29812i	−0.0299548	+	0.0518833i
$627$	0.852426	−	1.47645i	0.0340426	−	0.0589635i
$628$	7.34638	+	12.7243i	0.293153	+	0.507755i
$629$	42.5474			1.69648
$630$	−0.949027	−	1.94025i	−0.0378101	−	0.0773013i
$631$	8.18725			0.325929			0.162965	−	0.986632i	$-0.447894\pi$
$631$	8.18725			0.325929			0.162965	+	0.986632i	$0.447894\pi$
$632$	7.93102	+	13.7369i	0.315479	+	0.546426i
$633$	0.359349	−	0.622410i	0.0142828	−	0.0247386i
$634$	−2.09161	+	3.62277i	−0.0830683	+	0.143879i
$635$	7.12720	+	12.3447i	0.282834	+	0.489884i
$636$	−5.73223			−0.227298
$637$	−25.9394	+	33.3555i	−1.02776	+	1.32159i
$638$	1.41318			0.0559481
$639$	14.1314	+	24.4763i	0.559029	+	0.968267i
$640$	4.04215	−	7.00121i	0.159780	−	0.276747i
$641$	−0.394542	+	0.683367i	−0.0155835	+	0.0269914i	−0.873712	−	0.486444i	$-0.838294\pi$
$641$	−0.394542	+	0.683367i	−0.0155835	+	0.0269914i	0.858129	+	0.513435i	$0.171627\pi$
$642$	−0.324471	−	0.561999i	−0.0128058	−	0.0221803i
$643$	9.03854			0.356445			0.178223	−	0.983990i	$-0.442965\pi$
$643$	9.03854			0.356445			0.178223	+	0.983990i	$0.442965\pi$
$644$	0.315149	+	0.644308i	0.0124186	+	0.0253893i
$645$	1.52870			0.0601926
$646$	3.86582	+	6.69579i	0.152098	+	0.263442i
$647$	2.24104	−	3.88159i	0.0881042	−	0.152601i	−0.818606	−	0.574356i	$-0.805252\pi$
$647$	2.24104	−	3.88159i	0.0881042	−	0.152601i	0.906710	+	0.421755i	$0.138586\pi$
$648$	4.55574	−	7.89078i	0.178967	−	0.309979i
$649$	5.01669	+	8.68916i	0.196922	+	0.341079i
$650$	1.68542			0.0661074
$651$	−1.36686	+	2.03139i	−0.0535716	+	0.0796163i
$652$	14.8332			0.580914
$653$	−0.625386	−	1.08320i	−0.0244732	−	0.0423889i	0.853529	−	0.521045i	$-0.174458\pi$
$653$	−0.625386	−	1.08320i	−0.0244732	−	0.0423889i	−0.878003	+	0.478656i	$0.841124\pi$
$654$	−0.467181	+	0.809180i	−0.0182682	+	0.0316415i
$655$	−2.81952	+	4.88355i	−0.110168	+	0.190816i
$656$	−2.19224	−	3.79707i	−0.0855926	−	0.148251i
$657$	11.8849			0.463676
$658$	−5.10663	−	0.351313i	−0.199077	−	0.0136956i
$659$	−1.74776			−0.0680831			−0.0340416	−	0.999420i	$-0.510838\pi$
$659$	−1.74776			−0.0680831			−0.0340416	+	0.999420i	$0.510838\pi$
$660$	−0.265203	−	0.459345i	−0.0103230	−	0.0178800i
$661$	−18.9456	+	32.8148i	−0.736900	+	1.27635i	0.216984	+	0.976175i	$0.430378\pi$
$661$	−18.9456	+	32.8148i	−0.736900	+	1.27635i	−0.953885	+	0.300173i	$0.902955\pi$
$662$	2.67732	−	4.63726i	0.104057	−	0.180232i
$663$	3.73326	+	6.46619i	0.144988	+	0.251126i
$664$	−2.97306			−0.115377
$665$	−16.3067	−	1.12183i	−0.632345	−	0.0435026i
$666$	7.74929			0.300279
$667$	−0.356939	−	0.618237i	−0.0138207	−	0.0239382i
$668$	−22.8010	+	39.4924i	−0.882196	+	1.52801i
$669$	0.641835	−	1.11169i	0.0248148	−	0.0429805i
$670$	−1.46327	−	2.53445i	−0.0565310	−	0.0979145i
$671$	9.17433			0.354171
$672$	1.29538	−	1.92515i	0.0499703	−	0.0742643i
$673$	5.14338			0.198263			0.0991313	−	0.995074i	$-0.468394\pi$
$673$	5.14338			0.198263			0.0991313	+	0.995074i	$0.468394\pi$
$674$	2.91832	+	5.05469i	0.112410	+	0.194699i
$675$	0.817371	−	1.41573i	0.0314606	−	0.0544914i
$676$	22.5240	−	39.0127i	0.866308	−	1.50049i
$677$	11.0192	+	19.0858i	0.423502	+	0.733527i	0.996279	−	0.0861839i	$-0.0274673\pi$
$677$	11.0192	+	19.0858i	0.423502	+	0.733527i	−0.572777	+	0.819711i	$0.694134\pi$
$678$	0.106845			0.00410335
$679$	−0.361459	−	0.738989i	−0.0138715	−	0.0283598i
$680$	4.90842			0.188229
$681$	−1.90463	−	3.29892i	−0.0729856	−	0.126415i
$682$	−0.468162	+	0.810881i	−0.0179269	+	0.0310502i
$683$	−11.7850	+	20.4122i	−0.450940	+	0.781051i	−0.998445	−	0.0557514i	$-0.982245\pi$
$683$	−11.7850	+	20.4122i	−0.450940	+	0.781051i	0.547504	+	0.836803i	$0.315578\pi$
$684$	−17.3592	−	30.0669i	−0.663744	−	1.14964i
$685$	2.98167			0.113924
$686$	1.61454	+	4.91254i	0.0616436	+	0.187562i
$687$	−1.57651			−0.0601475
$688$	−9.80043	−	16.9748i	−0.373638	−	0.647160i
$689$	−32.6182	+	56.4964i	−1.24266	+	2.15234i
$690$	0.00543386	−	0.00941172i	0.000206863	−	0.000358298i
$691$	−3.76358	−	6.51871i	−0.143173	−	0.247983i	0.785517	−	0.618841i	$-0.212397\pi$
$691$	−3.76358	−	6.51871i	−0.143173	−	0.247983i	−0.928690	+	0.370857i	$0.879064\pi$
$692$	−22.6041			−0.859279
$693$	3.39896	+	6.94904i	0.129116	+	0.263972i
$694$	3.34259			0.126883
$695$	3.87104	+	6.70484i	0.146837	+	0.254329i
$696$	−0.764758	+	1.32460i	−0.0289881	+	0.0502088i
$697$	2.77708	−	4.81004i	0.105189	−	0.182193i
$698$	−0.393448	−	0.681471i	−0.0148922	−	0.0257941i
$699$	−1.15230			−0.0435839
$700$	−2.83888	+	4.21906i	−0.107300	+	0.159465i
$701$	26.0178			0.982678			0.491339	−	0.870968i	$-0.336508\pi$
$701$	26.0178			0.982678			0.491339	+	0.870968i	$0.336508\pi$
$702$	1.37761	+	2.38609i	0.0519945	+	0.0900572i
$703$	29.3215	−	50.7864i	1.10588	−	1.91545i
$704$	−3.09465	+	5.36009i	−0.116634	+	0.202016i
$705$	−0.956079	−	1.65598i	−0.0360080	−	0.0623677i
$706$	5.10532			0.192141
$707$	−22.8242	−	1.57020i	−0.858391	−	0.0590536i
$708$	−5.32176			−0.200004
$709$	−20.4751	−	35.4639i	−0.768959	−	1.33188i	−0.938128	−	0.346289i	$-0.887442\pi$
$709$	−20.4751	−	35.4639i	−0.768959	−	1.33188i	0.169169	−	0.985587i	$-0.445892\pi$
$710$	−1.34947	+	2.33735i	−0.0506446	+	0.0877191i
$711$	21.1758	−	36.6775i	0.794153	−	1.37551i
$712$	9.77320	+	16.9277i	0.366266	+	0.634392i
$713$	0.472993			0.0177137
$714$	0.911589	+	0.0627133i	0.0341154	+	0.00234699i
$715$	−6.03636			−0.225747
$716$	13.6291	+	23.6062i	0.509342	+	0.882206i
$717$	−1.80764	+	3.13093i	−0.0675077	+	0.116927i
$718$	4.36533	−	7.56097i	0.162913	−	0.282173i
$719$	9.77381	+	16.9287i	0.364502	+	0.631335i	0.988696	−	0.149934i	$-0.0479060\pi$
$719$	9.77381	+	16.9287i	0.364502	+	0.631335i	−0.624194	+	0.781269i	$0.714573\pi$
$720$	−10.3455			−0.385555
$721$	−10.6781	+	15.8694i	−0.397672	+	0.591007i
$722$	5.35150			0.199162
$723$	2.38459	+	4.13022i	0.0886837	+	0.153605i
$724$	8.30921	−	14.3920i	0.308809	−	0.534873i
$725$	2.53066	−	4.38323i	0.0939864	−	0.162789i
$726$	−0.0385254	−	0.0667280i	−0.00142981	−	0.00247651i
$727$	−9.16431			−0.339885			−0.169943	−	0.985454i	$-0.554358\pi$
$727$	−9.16431			−0.339885			−0.169943	+	0.985454i	$0.554358\pi$
$728$	−7.68442	−	15.7105i	−0.284804	−	0.582269i
$729$	−22.9742			−0.850898
$730$	0.567472	+	0.982890i	0.0210031	+	0.0363784i
$731$	12.4150	−	21.5033i	0.459184	−	0.795329i
$732$	−2.43306	+	4.21418i	−0.0899285	+	0.155761i
$733$	−3.47537	−	6.01951i	−0.128366	−	0.222336i	0.794678	−	0.607031i	$-0.207640\pi$
$733$	−3.47537	−	6.01951i	−0.128366	−	0.222336i	−0.923043	+	0.384696i	$0.874306\pi$
$734$	−0.282635			−0.0104322
$735$	−1.18585	+	1.52489i	−0.0437409	+	0.0562463i
$736$	−0.448257			−0.0165230
$737$	5.24073	+	9.07721i	0.193045	+	0.334363i
$738$	0.505798	−	0.876067i	0.0186187	−	0.0322485i
$739$	−0.650367	+	1.12647i	−0.0239242	+	0.0414378i	−0.877740	−	0.479138i	$-0.840949\pi$
$739$	−0.650367	+	1.12647i	−0.0239242	+	0.0414378i	0.853815	+	0.520576i	$0.174283\pi$
$740$	−9.12238	−	15.8004i	−0.335345	−	0.580835i
$741$	10.2911			0.378053
$742$	3.50784	+	7.17164i	0.128777	+	0.263279i
$743$	31.0258			1.13823			0.569113	−	0.822260i	$-0.307287\pi$
$743$	31.0258			1.13823			0.569113	+	0.822260i	$0.307287\pi$
$744$	−0.506704	−	0.877637i	−0.0185767	−	0.0321757i
$745$	−2.70587	+	4.68670i	−0.0991352	+	0.171707i
$746$	0.670811	−	1.16188i	0.0245601	−	0.0425394i
$747$	3.96902	+	6.87455i	0.145219	+	0.251526i
$748$	−8.61510			−0.314999
$749$	12.4398	−	18.4876i	0.454539	−	0.675522i
$750$	0.0770509			0.00281350
$751$	0.660561	+	1.14413i	0.0241042	+	0.0417497i	0.877826	−	0.478980i	$-0.158993\pi$
$751$	0.660561	+	1.14413i	0.0241042	+	0.0417497i	−0.853722	+	0.520730i	$0.825660\pi$
$752$	−12.2587	+	21.2328i	−0.447030	+	0.774279i
$753$	2.77503	−	4.80650i	0.101128	−	0.175158i
$754$	4.26521	+	7.38757i	0.155330	+	0.269039i
$755$	−17.7894			−0.647424
$756$	−8.29346	−	0.570554i	−0.301630	−	0.0207508i
$757$	6.28325			0.228368			0.114184	−	0.993460i	$-0.463575\pi$
$757$	6.28325			0.228368			0.114184	+	0.993460i	$0.463575\pi$
$758$	4.03940	+	6.99644i	0.146718	+	0.254122i
$759$	−0.0194615	+	0.0337083i	−0.000706407	+	0.00122353i
$760$	3.38264	−	5.85890i	0.122701	−	0.212525i
$761$	8.94753	+	15.4976i	0.324348	+	0.561787i	0.981380	−	0.192076i	$-0.0615219\pi$
$761$	8.94753	+	15.4976i	0.324348	+	0.561787i	−0.657032	+	0.753862i	$0.728189\pi$
$762$	−1.09831			−0.0397877
$763$	−32.0082	−	2.20202i	−1.15877	−	0.0797185i
$764$	−6.00017			−0.217079
$765$	−6.55273	−	11.3497i	−0.236914	−	0.410348i
$766$	−0.585361	+	1.01388i	−0.0211500	+	0.0366328i
$767$	−30.2825	+	52.4509i	−1.09344	+	1.89389i
$768$	−1.39654	−	2.41889i	−0.0503934	−	0.0872840i
$769$	−17.3712			−0.626421			−0.313210	−	0.949684i	$-0.601404\pi$
$769$	−17.3712			−0.626421			−0.313210	+	0.949684i	$0.601404\pi$
$770$	−0.412399	+	0.612893i	−0.0148618	+	0.0220871i
$771$	−8.48125			−0.305445
$772$	8.82679	+	15.2884i	0.317683	+	0.550243i
$773$	−8.71257	+	15.0906i	−0.313369	+	0.542772i	−0.979090	−	0.203430i	$-0.934791\pi$
$773$	−8.71257	+	15.0906i	−0.313369	+	0.542772i	0.665720	+	0.746202i	$0.268124\pi$
$774$	2.26117	−	3.91647i	0.0812762	−	0.140775i
$775$	1.67673	+	2.90419i	0.0602301	+	0.104322i
$776$	0.340496			0.0122231
$777$	−3.04518	−	6.22575i	−0.109245	−	0.223347i
$778$	−10.8738			−0.389845
$779$	−3.82764	−	6.62967i	−0.137140	−	0.237533i
$780$	1.60086	−	2.77277i	0.0573199	−	0.0992811i
$781$	4.83315	−	8.37127i	0.172944	−	0.299547i
$782$	−0.0882593	−	0.152870i	−0.00315615	−	0.00546661i
$783$	8.27396			0.295687
$784$	24.5349	+	3.39185i	0.876248	+	0.121137i
$785$	7.64436			0.272839
$786$	−0.217247	−	0.376282i	−0.00774893	−	0.0134215i
$787$	−6.11697	+	10.5949i	−0.218047	+	0.377668i	−0.954211	−	0.299135i	$-0.903302\pi$
$787$	−6.11697	+	10.5949i	−0.218047	+	0.377668i	0.736164	+	0.676803i	$0.236635\pi$
$788$	14.1543	−	24.5159i	0.504226	−	0.873344i
$789$	−1.55177	−	2.68775i	−0.0552445	−	0.0956863i
$790$	4.04433			0.143891
$791$	1.61201	+	3.29569i	0.0573165	+	0.117181i
$792$	−3.20183			−0.113772
$793$	27.6898	+	47.9601i	0.983293	+	1.70311i
$794$	−5.18630	+	8.98293i	−0.184055	+	0.318792i
$795$	−1.49118	+	2.58281i	−0.0528868	+	0.0916027i
$796$	−8.96290	−	15.5242i	−0.317682	−	0.550241i
$797$	10.3230			0.365658			0.182829	−	0.983145i	$-0.441475\pi$
$797$	10.3230			0.365658			0.182829	+	0.983145i	$0.441475\pi$
$798$	0.703079	−	1.04489i	0.0248887	−	0.0369888i
$799$	−31.0582			−1.09876
$800$	−1.58905	−	2.75231i	−0.0561812	−	0.0973088i
$801$	26.0944	−	45.1968i	0.922000	−	1.59695i
$802$	−1.22550	+	2.12262i	−0.0432738	+	0.0749525i
$803$	−2.03241	−	3.52025i	−0.0717224	−	0.124227i
$804$	−5.55943			−0.196066
$805$	0.372292	+	0.0256121i	0.0131216	+	0.000902708i
$806$	−5.65199			−0.199083
$807$	−1.23420	−	2.13769i	−0.0434457	−	0.0752502i
$808$	4.73463	−	8.20061i	0.166564	−	0.288497i
$809$	−7.94749	+	13.7655i	−0.279419	+	0.483968i	−0.971240	−	0.238101i	$-0.923475\pi$
$809$	−7.94749	+	13.7655i	−0.279419	+	0.483968i	0.691821	+	0.722069i	$0.256809\pi$
$810$	−1.16157	−	2.01191i	−0.0408136	−	0.0706912i
$811$	−1.63833			−0.0575295			−0.0287648	−	0.999586i	$-0.509157\pi$
$811$	−1.63833			−0.0575295			−0.0287648	+	0.999586i	$0.509157\pi$
$812$	−25.6774	−	1.76649i	−0.901099	−	0.0619916i
$813$	3.61702			0.126855
$814$	−1.32519	−	2.29529i	−0.0464478	−	0.0804500i
$815$	3.85871	−	6.68349i	0.135165	−	0.234112i
$816$	2.18832	−	3.79028i	0.0766066	−	0.132686i
$817$	−17.1115	−	29.6380i	−0.598656	−	1.03690i
$818$	−6.22738			−0.217735
$819$	−26.0684	+	38.7420i	−0.910903	+	1.35375i
$820$	−2.38168			−0.0831718
$821$	−7.96844	−	13.8017i	−0.278100	−	0.481684i	0.692812	−	0.721118i	$-0.256371\pi$
$821$	−7.96844	−	13.8017i	−0.278100	−	0.481684i	−0.970913	+	0.239434i	$0.923038\pi$
$822$	−0.114870	+	0.198961i	−0.00400656	+	0.00693956i
$823$	−25.2324	+	43.7038i	−0.879546	+	1.52342i	−0.0277071	+	0.999616i	$0.508821\pi$
$823$	−25.2324	+	43.7038i	−0.879546	+	1.52342i	−0.851839	+	0.523803i	$0.824513\pi$
$824$	−3.95842	−	6.85618i	−0.137898	−	0.238846i
$825$	−0.275960			−0.00960768
$826$	3.25665	+	6.65809i	0.113313	+	0.231665i
$827$	0.696629			0.0242242			0.0121121	−	0.999927i	$-0.496145\pi$
$827$	0.696629			0.0242242			0.0121121	+	0.999927i	$0.496145\pi$
$828$	0.396322	+	0.686449i	0.0137731	+	0.0238558i
$829$	24.9632	−	43.2375i	0.867008	−	1.50170i	0.00196843	−	0.999998i	$-0.499373\pi$
$829$	24.9632	−	43.2375i	0.867008	−	1.50170i	0.865040	−	0.501704i	$-0.167293\pi$
$830$	−0.379019	+	0.656480i	−0.0131559	+	0.0227868i
$831$	1.19546	+	2.07060i	0.0414701	+	0.0718283i
$832$	−37.3608			−1.29525
$833$	11.8191	+	29.0647i	0.409507	+	1.00703i
$834$	−0.596534			−0.0206563
$835$	11.8629	+	20.5471i	0.410532	+	0.711063i
$836$	−5.93709	+	10.2833i	−0.205339	+	0.355657i
$837$	−2.74103	+	4.74760i	−0.0947438	+	0.164101i
$838$	2.66010	+	4.60742i	0.0918915	+	0.159161i
$839$	−19.0422			−0.657409			−0.328704	−	0.944433i	$-0.606612\pi$
$839$	−19.0422			−0.657409			−0.328704	+	0.944433i	$0.606612\pi$
$840$	−0.351303	−	0.718225i	−0.0121211	−	0.0247811i
$841$	−3.38303			−0.116656
$842$	−2.61244	−	4.52487i	−0.0900305	−	0.155937i
$843$	−0.967323	+	1.67545i	−0.0333164	+	0.0577057i
$844$	−2.50284	+	4.33505i	−0.0861513	+	0.149218i
$845$	−11.7188	−	20.2975i	−0.403139	−	0.698257i
$846$	−5.65672			−0.194482
$847$	1.47702	−	2.19509i	0.0507508	−	0.0754242i
$848$	38.2396			1.31315
$849$	1.56050	+	2.70287i	0.0535563	+	0.0927623i
$850$	0.625749	−	1.08383i	0.0214630	−	0.0371750i
$851$	−0.669431	+	1.15949i	−0.0229478	+	0.0397468i
$852$	2.56353	+	4.44017i	0.0878252	+	0.152118i
$853$	3.57347			0.122353			0.0611767	−	0.998127i	$-0.480515\pi$
$853$	3.57347			0.122353			0.0611767	+	0.998127i	$0.480515\pi$
$854$	6.76130	+	0.465148i	0.231367	+	0.0159170i
$855$	−18.0632			−0.617750
$856$	4.61150	+	7.98735i	0.157618	+	0.273002i
$857$	−14.5668	+	25.2304i	−0.497592	+	0.861855i	−0.999996	−	0.00277806i	$-0.999116\pi$
$857$	−14.5668	+	25.2304i	−0.497592	+	0.861855i	0.502404	+	0.864633i	$0.332449\pi$
$858$	0.232553	−	0.402794i	0.00793924	−	0.0137512i
$859$	16.5751	+	28.7090i	0.565537	+	0.979538i	0.997000	+	0.0774075i	$0.0246642\pi$
$859$	16.5751	+	28.7090i	0.565537	+	0.979538i	−0.431463	+	0.902131i	$0.642002\pi$
$860$	−10.6473			−0.363070
$861$	−0.902588	−	0.0620941i	−0.0307601	−	0.00211616i
$862$	−9.51921			−0.324226
$863$	11.0563	+	19.1501i	0.376361	+	0.651877i	0.990530	−	0.137298i	$-0.0438417\pi$
$863$	11.0563	+	19.1501i	0.376361	+	0.651877i	−0.614168	+	0.789175i	$0.710508\pi$
$864$	2.59768	−	4.49931i	0.0883749	−	0.153070i
$865$	−5.88023	+	10.1849i	−0.199934	+	0.346296i
$866$	1.56971	+	2.71882i	0.0533409	+	0.0923891i
$867$	0.852915			0.0289665
$868$	9.52011	−	14.1485i	0.323134	−	0.480231i
$869$	−14.4849			−0.491366
$870$	0.194990	+	0.337732i	0.00661077	+	0.0114502i
$871$	−31.6349	+	54.7933i	−1.07191	+	1.85660i
$872$	6.63974	−	11.5004i	0.224850	−	0.389452i
$873$	−0.454561	−	0.787323i	−0.0153846	−	0.0266468i
$874$	−0.243295			−0.00822959
$875$	1.16250	+	2.37668i	0.0392996	+	0.0803464i
$876$	2.15601			0.0728448
$877$	−9.13710	−	15.8259i	−0.308538	−	0.534403i	0.669505	−	0.742808i	$-0.266506\pi$
$877$	−9.13710	−	15.8259i	−0.308538	−	0.534403i	−0.978043	+	0.208404i	$0.933173\pi$
$878$	2.10532	−	3.64653i	0.0710512	−	0.123064i
$879$	−4.04857	+	7.01233i	−0.136555	+	0.236520i
$880$	1.76916	+	3.06428i	0.0596385	+	0.103297i
$881$	−40.8714			−1.37699			−0.688495	−	0.725241i	$-0.741728\pi$
$881$	−40.8714			−1.37699			−0.688495	+	0.725241i	$0.741728\pi$
$882$	2.15265	+	5.29364i	0.0724834	+	0.178246i
$883$	−23.8690			−0.803256			−0.401628	−	0.915803i	$-0.631555\pi$
$883$	−23.8690			−0.803256			−0.401628	+	0.915803i	$0.631555\pi$
$884$	−26.0019	−	45.0366i	−0.874539	−	1.51475i
$885$	−1.38440	+	2.39786i	−0.0465362	+	0.0806031i
$886$	−3.32049	+	5.75126i	−0.111554	+	0.193217i
$887$	5.29482	+	9.17089i	0.177783	+	0.307928i	0.941121	−	0.338071i	$-0.109774\pi$
$887$	5.29482	+	9.17089i	0.177783	+	0.307928i	−0.763338	+	0.645999i	$0.776441\pi$
$888$	2.86857			0.0962629
$889$	−16.5707	−	33.8781i	−0.555764	−	1.13624i
$890$	4.98373			0.167055
$891$	4.16021	+	7.20569i	0.139372	+	0.241400i
$892$	−4.47034	+	7.74286i	−0.149678	+	0.259250i
$893$	−21.4037	+	37.0723i	−0.716248	+	1.24058i
$894$	−0.208489	−	0.361114i	−0.00697293	−	0.0120775i
$895$	14.1819			0.474047
$896$	−11.9406	+	17.7458i	−0.398909	+	0.592845i
$897$	−0.234953			−0.00784485
$898$	−3.65930	−	6.33809i	−0.122112	−	0.211505i
$899$	−8.48649	+	14.6990i	−0.283040	+	0.490240i
$900$	−2.80988	+	4.86685i	−0.0936626	+	0.162228i
$901$	24.2205	+	41.9512i	0.806903	+	1.39760i
$902$	−0.345981			−0.0115199
$903$	−4.03503	−	0.277592i	−0.134277	−	0.00923769i
$904$	−1.51852			−0.0505052
$905$	−4.32312	−	7.48786i	−0.143705	−	0.248905i
$906$	0.685346	−	1.18705i	0.0227691	−	0.0394372i
$907$	16.7930	−	29.0863i	0.557602	−	0.965794i	−0.440094	−	0.897951i	$-0.645055\pi$
$907$	16.7930	−	29.0863i	0.557602	−	0.965794i	0.997696	−	0.0678428i	$-0.0216116\pi$
$908$	13.2656	+	22.9768i	0.440236	+	0.762511i
$909$	−25.2828			−0.838579
$910$	−4.44867	−	0.306049i	−0.147472	−	0.0101454i
$911$	−35.5767			−1.17871			−0.589355	−	0.807874i	$-0.700618\pi$
$911$	−35.5767			−1.17871			−0.589355	+	0.807874i	$0.700618\pi$
$912$	−3.01616	−	5.22414i	−0.0998751	−	0.172989i
$913$	1.35747	−	2.35120i	0.0449256	−	0.0778133i
$914$	1.90048	−	3.29172i	0.0628622	−	0.108880i
$915$	1.26587	+	2.19256i	0.0418485	+	0.0724837i
$916$	10.9803			0.362798
$917$	8.32895	−	12.3782i	0.275046	−	0.408765i
$918$	2.04588			0.0675240
$919$	−17.6426	−	30.5578i	−0.581974	−	1.00801i	−0.995245	−	0.0974009i	$-0.968947\pi$
$919$	−17.6426	−	30.5578i	−0.581974	−	1.00801i	0.413271	−	0.910608i	$-0.364386\pi$
$920$	−0.0772280	+	0.133763i	−0.00254613	+	0.00441003i
$921$	−2.73277	+	4.73329i	−0.0900478	+	0.155967i
$922$	−3.18948	−	5.52435i	−0.105040	−	0.181935i
$923$	58.3493			1.92059
$924$	0.616595	+	1.26060i	0.0202845	+	0.0414708i
$925$	−9.49239			−0.312108
$926$	5.96578	+	10.3330i	0.196048	+	0.339564i
$927$	−10.5690	+	18.3060i	−0.347130	+	0.601247i
$928$	8.04267	−	13.9303i	0.264014	−	0.457285i
$929$	−1.26331	−	2.18811i	−0.0414477	−	0.0717896i	0.844557	−	0.535465i	$-0.179864\pi$
$929$	−1.26331	−	2.18811i	−0.0414477	−	0.0717896i	−0.886005	+	0.463676i	$0.846530\pi$
$930$	−0.258388			−0.00847287
$931$	42.8379	+	5.92215i	1.40396	+	0.194091i
$932$	8.02568			0.262890
$933$	0.610613	+	1.05761i	0.0199906	+	0.0346247i
$934$	1.61568	−	2.79844i	0.0528668	−	0.0915679i
$935$	−2.24113	+	3.88176i	−0.0732929	+	0.126947i
$936$	−9.66370	−	16.7380i	−0.315868	−	0.547100i
$937$	−37.6599			−1.23030			−0.615148	−	0.788411i	$-0.710904\pi$
$937$	−37.6599			−1.23030			−0.615148	+	0.788411i	$0.710904\pi$
$938$	3.40209	+	6.95543i	0.111082	+	0.227103i
$939$	1.48149			0.0483465
$940$	6.65903	+	11.5338i	0.217194	+	0.376190i
$941$	13.1756	−	22.8208i	0.429512	−	0.743937i	−0.567318	−	0.823499i	$-0.692019\pi$
$941$	13.1756	−	22.8208i	0.429512	−	0.743937i	0.996830	+	0.0795620i	$0.0253522\pi$
$942$	−0.294502	+	0.510093i	−0.00959540	+	0.0166197i
$943$	0.0873878	+	0.151360i	0.00284574	+	0.00492896i
$944$	35.5014			1.15547
$945$	−2.41454	+	3.58841i	−0.0785450	+	0.116731i
$946$	−1.54671			−0.0502879
$947$	15.7892	+	27.3478i	0.513081	+	0.888683i	0.999885	+	0.0151714i	$0.00482938\pi$
$947$	15.7892	+	27.3478i	0.513081	+	0.888683i	−0.486804	+	0.873511i	$0.661837\pi$
$948$	3.84143	−	6.65355i	0.124764	−	0.216097i
$949$	12.2684	−	21.2495i	0.398248	−	0.689786i
$950$	−0.862469	−	1.49384i	−0.0279822	−	0.0484666i
$951$	4.13450			0.134070
$952$	−12.9558	−	0.891306i	−0.419901	−	0.0288874i
$953$	28.4947			0.923035			0.461518	−	0.887131i	$-0.347305\pi$
$953$	28.4947			0.923035			0.461518	+	0.887131i	$0.347305\pi$
$954$	4.41136	+	7.64070i	0.142823	+	0.247377i
$955$	−1.56088	+	2.70353i	−0.0505090	+	0.0874842i
$956$	12.5901	−	21.8067i	0.407194	−	0.705280i
$957$	−0.698360	−	1.20960i	−0.0225748	−	0.0391007i
$958$	−8.72588			−0.281921
$959$	−7.87016	−	0.541432i	−0.254141	−	0.0174838i
$960$	−1.70800			−0.0551253
$961$	9.87712	+	17.1077i	0.318617	+	0.551861i
$962$	7.99931	−	13.8552i	0.257908	−	0.446710i
$963$	12.3127	−	21.3262i	0.396770	−	0.687226i
$964$	−16.6085	−	28.7667i	−0.534923	−	0.926514i
$965$	9.18481			0.295669
$966$	−0.0160518	+	0.0238556i	−0.000516458	+	0.000767542i
$967$	32.5955			1.04820			0.524100	−	0.851657i	$-0.324402\pi$
$967$	32.5955			1.04820			0.524100	+	0.851657i	$0.324402\pi$
$968$	0.547538	+	0.948364i	0.0175985	+	0.0304816i
$969$	3.82080	−	6.61782i	0.122742	−	0.212595i
$970$	0.0434080	−	0.0751849i	0.00139375	−	0.00241404i
$971$	−2.74840	−	4.76036i	−0.0882002	−	0.152767i	0.818550	−	0.574435i	$-0.194778\pi$
$971$	−2.74840	−	4.76036i	−0.0882002	−	0.152767i	−0.906750	+	0.421668i	$0.861445\pi$
$972$	−13.8393			−0.443897
$973$	−9.00015	−	18.4004i	−0.288531	−	0.589891i
$974$	−9.99433			−0.320239
$975$	−0.832895	−	1.44262i	−0.0266740	−	0.0462007i
$976$	16.2309	−	28.1127i	0.519538	−	0.899867i
$977$	4.73456	−	8.20049i	0.151472	−	0.262357i	−0.780297	−	0.625409i	$-0.784932\pi$
$977$	4.73456	−	8.20049i	0.151472	−	0.262357i	0.931769	+	0.363052i	$0.118265\pi$
$978$	0.297317	+	0.514969i	0.00950716	+	0.0164669i
$979$	−17.8494			−0.570468
$980$	8.25940	−	10.6207i	0.263837	−	0.339267i
$981$	−35.4562			−1.13203
$982$	−3.25935	−	5.64536i	−0.104010	−	0.180151i
$983$	−1.17866	+	2.04150i	−0.0375935	+	0.0651139i	−0.884210	−	0.467090i	$-0.845303\pi$
$983$	−1.17866	+	2.04150i	−0.0375935	+	0.0651139i	0.846616	+	0.532203i	$0.178636\pi$
$984$	0.187232	−	0.324295i	0.00596874	−	0.0103382i
$985$	−7.36420	−	12.7552i	−0.234643	−	0.406413i
$986$	6.33423			0.201723
$987$	2.22288	+	4.54458i	0.0707550	+	0.144656i
$988$	−71.6768			−2.28034
$989$	0.390668	+	0.676657i	0.0124225	+	0.0215164i
$990$	−0.408185	+	0.706997i	−0.0129730	+	0.0224698i
$991$	16.1880	−	28.0384i	0.514227	−	0.890668i	−0.485636	−	0.874161i	$-0.661412\pi$
$991$	16.1880	−	28.0384i	0.514227	−	0.890668i	0.999864	−	0.0165071i	$-0.00525460\pi$
$992$	5.32881	+	9.22978i	0.169190	+	0.293046i
$993$	−5.29230			−0.167946
$994$	3.98637	−	5.92441i	0.126440	−	0.187911i
$995$	−9.32644			−0.295668
$996$	0.720008	+	1.24709i	0.0228143	+	0.0395156i
$997$	13.3043	−	23.0438i	0.421353	−	0.729804i	−0.574720	−	0.818350i	$-0.694889\pi$
$997$	13.3043	−	23.0438i	0.421353	−	0.729804i	0.996072	+	0.0885465i	$0.0282222\pi$
$998$	1.11395	−	1.92941i	0.0352613	−	0.0610744i
$999$	−7.75880	−	13.4386i	−0.245478	−	0.425180i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.i.c.221.5	✓	16
7.2	even	3	inner	385.2.i.c.331.5	yes	16
7.3	odd	6		2695.2.a.s.1.4		8
7.4	even	3		2695.2.a.t.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.c.221.5	✓	16	1.1	even	1	trivial
385.2.i.c.331.5	yes	16	7.2	even	3	inner
2695.2.a.s.1.4		8	7.3	odd	6
2695.2.a.t.1.4		8	7.4	even	3

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:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.139605 - 0.241804i) q^{2} +(-0.137980 + 0.238988i) q^{3} +(0.961021 - 1.66454i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.0770509 q^{6} +(1.16250 + 2.37668i) q^{7} -1.09508 q^{8} +(1.46192 + 2.53213i) q^{9} +O(q^{10})\)	\(q+(-0.139605 - 0.241804i) q^{2} +(-0.137980 + 0.238988i) q^{3} +(0.961021 - 1.66454i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.0770509 q^{6} +(1.16250 + 2.37668i) q^{7} -1.09508 q^{8} +(1.46192 + 2.53213i) q^{9} +(-0.139605 + 0.241804i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.265203 + 0.459345i) q^{12} +6.03636 q^{13} +(0.412399 - 0.612893i) q^{14} +0.275960 q^{15} +(-1.76916 - 3.06428i) q^{16} +(2.24113 - 3.88176i) q^{17} +(0.408185 - 0.706997i) q^{18} +(-3.08895 - 5.35022i) q^{19} -1.92204 q^{20} +(-0.728399 - 0.0501106i) q^{21} -0.279211 q^{22} +(0.0705230 + 0.122149i) q^{23} +(0.151098 - 0.261710i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.842708 - 1.45961i) q^{26} -1.63474 q^{27} +(5.07325 + 0.349018i) q^{28} -5.06132 q^{29} +(-0.0385254 - 0.0667280i) q^{30} +(1.67673 - 2.90419i) q^{31} +(-1.58905 + 2.75231i) q^{32} +(0.137980 + 0.238988i) q^{33} -1.25150 q^{34} +(1.47702 - 2.19509i) q^{35} +5.61975 q^{36} +(4.74619 + 8.22065i) q^{37} +(-0.862469 + 1.49384i) q^{38} +(-0.832895 + 1.44262i) q^{39} +(0.547538 + 0.948364i) q^{40} +1.23914 q^{41} +(0.0895715 + 0.183125i) q^{42} +5.53959 q^{43} +(-0.961021 - 1.66454i) q^{44} +(1.46192 - 2.53213i) q^{45} +(0.0196908 - 0.0341054i) q^{46} +(-3.46456 - 6.00079i) q^{47} +0.976435 q^{48} +(-4.29720 + 5.52576i) q^{49} +0.279211 q^{50} +(0.618462 + 1.07121i) q^{51} +(5.80106 - 10.0477i) q^{52} +(-5.40363 + 9.35936i) q^{53} +(0.228219 + 0.395287i) q^{54} -1.00000 q^{55} +(-1.27302 - 2.60264i) q^{56} +1.70485 q^{57} +(0.706588 + 1.22385i) q^{58} +(-5.01669 + 8.68916i) q^{59} +(0.265203 - 0.459345i) q^{60} +(4.58717 + 7.94521i) q^{61} -0.936325 q^{62} +(-4.31857 + 6.41811i) q^{63} -6.18929 q^{64} +(-3.01818 - 5.22764i) q^{65} +(0.0385254 - 0.0667280i) q^{66} +(-5.24073 + 9.07721i) q^{67} +(-4.30755 - 7.46090i) q^{68} -0.0389230 q^{69} +(-0.736980 - 0.0507010i) q^{70} +9.66631 q^{71} +(-1.60092 - 2.77287i) q^{72} +(2.03241 - 3.52025i) q^{73} +(1.32519 - 2.29529i) q^{74} +(-0.137980 - 0.238988i) q^{75} -11.8742 q^{76} +(2.63951 + 0.181587i) q^{77} +0.465107 q^{78} +(-7.24243 - 12.5443i) q^{79} +(-1.76916 + 3.06428i) q^{80} +(-4.16021 + 7.20569i) q^{81} +(-0.172991 - 0.299628i) q^{82} +2.71493 q^{83} +(-0.783417 + 1.16429i) q^{84} -4.48227 q^{85} +(-0.773356 - 1.33949i) q^{86} +(0.698360 - 1.20960i) q^{87} +(-0.547538 + 0.948364i) q^{88} +(-8.92468 - 15.4580i) q^{89} -0.816369 q^{90} +(7.01725 + 14.3465i) q^{91} +0.271096 q^{92} +(0.462711 + 0.801439i) q^{93} +(-0.967342 + 1.67549i) q^{94} +(-3.08895 + 5.35022i) q^{95} +(-0.438512 - 0.759526i) q^{96} -0.310934 q^{97} +(1.93606 + 0.267652i) q^{98} +2.92385 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9	\( 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9} - 3 q^{10} + 8 q^{11} - 9 q^{12} + 28 q^{13} - 9 q^{14} + 2 q^{15} - 7 q^{16} - 5 q^{17} - 27 q^{18} - q^{19} + 18 q^{20} - 18 q^{21} - 6 q^{22} + 2 q^{23} + 24 q^{24} - 8 q^{25} - 21 q^{26} - 10 q^{27} + 32 q^{28} + 52 q^{29} + 3 q^{30} - 2 q^{31} - 16 q^{32} + q^{33} - 52 q^{34} + 5 q^{35} + 108 q^{36} + q^{37} + 31 q^{38} - 19 q^{39} - 9 q^{40} - 6 q^{41} + 44 q^{42} + 8 q^{43} + 9 q^{44} - 19 q^{45} - 10 q^{46} - q^{47} - 42 q^{48} + 17 q^{49} + 6 q^{50} - 3 q^{51} - 37 q^{52} - 26 q^{53} + 5 q^{54} - 16 q^{55} + 40 q^{57} + q^{58} + 19 q^{59} - 9 q^{60} - 52 q^{62} - 21 q^{63} + 2 q^{64} - 14 q^{65} - 3 q^{66} + 13 q^{67} - 15 q^{68} - 28 q^{69} + 15 q^{70} - 18 q^{71} - 32 q^{72} - 11 q^{73} - 24 q^{74} - q^{75} - 36 q^{76} + 4 q^{77} - 66 q^{78} + 8 q^{79} - 7 q^{80} - 52 q^{81} - 41 q^{82} + 64 q^{83} + 138 q^{84} + 10 q^{85} - 28 q^{86} + 16 q^{87} + 9 q^{88} - 5 q^{89} + 54 q^{90} + 13 q^{91} + 60 q^{92} + 14 q^{93} + 5 q^{94} - q^{95} - q^{96} + 18 q^{97} + 22 q^{98} - 38 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9 - 3 * q^10 + 8 * q^11 - 9 * q^12 + 28 * q^13 - 9 * q^14 + 2 * q^15 - 7 * q^16 - 5 * q^17 - 27 * q^18 - q^19 + 18 * q^20 - 18 * q^21 - 6 * q^22 + 2 * q^23 + 24 * q^24 - 8 * q^25 - 21 * q^26 - 10 * q^27 + 32 * q^28 + 52 * q^29 + 3 * q^30 - 2 * q^31 - 16 * q^32 + q^33 - 52 * q^34 + 5 * q^35 + 108 * q^36 + q^37 + 31 * q^38 - 19 * q^39 - 9 * q^40 - 6 * q^41 + 44 * q^42 + 8 * q^43 + 9 * q^44 - 19 * q^45 - 10 * q^46 - q^47 - 42 * q^48 + 17 * q^49 + 6 * q^50 - 3 * q^51 - 37 * q^52 - 26 * q^53 + 5 * q^54 - 16 * q^55 + 40 * q^57 + q^58 + 19 * q^59 - 9 * q^60 - 52 * q^62 - 21 * q^63 + 2 * q^64 - 14 * q^65 - 3 * q^66 + 13 * q^67 - 15 * q^68 - 28 * q^69 + 15 * q^70 - 18 * q^71 - 32 * q^72 - 11 * q^73 - 24 * q^74 - q^75 - 36 * q^76 + 4 * q^77 - 66 * q^78 + 8 * q^79 - 7 * q^80 - 52 * q^81 - 41 * q^82 + 64 * q^83 + 138 * q^84 + 10 * q^85 - 28 * q^86 + 16 * q^87 + 9 * q^88 - 5 * q^89 + 54 * q^90 + 13 * q^91 + 60 * q^92 + 14 * q^93 + 5 * q^94 - q^95 - q^96 + 18 * q^97 + 22 * q^98 - 38 * q^99

Introduction

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