LMFDB - Embedded newform 770.2.i.m.221.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(221,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, 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("770.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 12x^{8} - 6x^{7} + 113x^{6} - 43x^{5} + 381x^{4} - 75x^{3} + 982x^{2} - 217x + 49 $ x^10 + 12x^8 - 6x^7 + 113x^6 - 43x^5 + 381x^4 - 75x^3 + 982x^2 - 217x + 49
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			221.3
Root			$0.112651 + 0.195118i$ of defining polynomial
Character	$\chi$	$=$	770.221
Dual form			770.2.i.m.331.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.112651 + 0.195118i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.225302 q^{6} +(-2.14481 - 1.54913i) q^{7} +1.00000 q^{8} +(1.47462 + 2.55412i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.112651 + 0.195118i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.225302 q^{6} +(-2.14481 - 1.54913i) q^{7} +1.00000 q^{8} +(1.47462 + 2.55412i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.112651 - 0.195118i) q^{12} -0.878738 q^{13} +(-0.269180 + 2.63202i) q^{14} +0.225302 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.25746 + 3.91003i) q^{17} +(1.47462 - 2.55412i) q^{18} +(1.86197 + 3.22502i) q^{19} +1.00000 q^{20} +(0.543877 - 0.243979i) q^{21} +1.00000 q^{22} +(-1.15653 - 2.00317i) q^{23} +(-0.112651 + 0.195118i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.439369 + 0.761009i) q^{26} -1.34038 q^{27} +(2.41399 - 1.08289i) q^{28} +7.36634 q^{29} +(-0.112651 - 0.195118i) q^{30} +(-2.86197 + 4.95707i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.112651 - 0.195118i) q^{33} +4.51492 q^{34} +(-0.269180 + 2.63202i) q^{35} -2.94924 q^{36} +(1.79582 + 3.11045i) q^{37} +(1.86197 - 3.22502i) q^{38} +(0.0989909 - 0.171457i) q^{39} +(-0.500000 - 0.866025i) q^{40} +2.52114 q^{41} +(-0.483231 - 0.349022i) q^{42} +1.68694 q^{43} +(-0.500000 - 0.866025i) q^{44} +(1.47462 - 2.55412i) q^{45} +(-1.15653 + 2.00317i) q^{46} +(3.72394 + 6.45005i) q^{47} +0.225302 q^{48} +(2.20041 + 6.64516i) q^{49} +1.00000 q^{50} +(-0.508611 - 0.880940i) q^{51} +(0.439369 - 0.761009i) q^{52} +(-4.24069 + 7.34509i) q^{53} +(0.670189 + 1.16080i) q^{54} +1.00000 q^{55} +(-2.14481 - 1.54913i) q^{56} -0.839012 q^{57} +(-3.68317 - 6.37943i) q^{58} +(-4.85025 + 8.40088i) q^{59} +(-0.112651 + 0.195118i) q^{60} +(2.62805 + 4.55192i) q^{61} +5.72394 q^{62} +(0.793876 - 7.76246i) q^{63} +1.00000 q^{64} +(0.439369 + 0.761009i) q^{65} +(-0.112651 + 0.195118i) q^{66} +(-0.725302 + 1.25626i) q^{67} +(-2.25746 - 3.91003i) q^{68} +0.521137 q^{69} +(2.41399 - 1.08289i) q^{70} +2.90218 q^{71} +(1.47462 + 2.55412i) q^{72} +(0.661578 - 1.14589i) q^{73} +(1.79582 - 3.11045i) q^{74} +(-0.112651 - 0.195118i) q^{75} -3.72394 q^{76} +(2.41399 - 1.08289i) q^{77} -0.197982 q^{78} +(-6.93800 - 12.0170i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.27286 + 7.40082i) q^{81} +(-1.26057 - 2.18337i) q^{82} +4.89229 q^{83} +(-0.0606469 + 0.593001i) q^{84} +4.51492 q^{85} +(-0.843471 - 1.46094i) q^{86} +(-0.829827 + 1.43730i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(4.73760 + 8.20576i) q^{89} -2.94924 q^{90} +(1.88472 + 1.36128i) q^{91} +2.31306 q^{92} +(-0.644808 - 1.11684i) q^{93} +(3.72394 - 6.45005i) q^{94} +(1.86197 - 3.22502i) q^{95} +(-0.112651 - 0.195118i) q^{96} -13.6784 q^{97} +(4.65468 - 5.22819i) q^{98} -2.94924 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 5 q^{4} - 5 q^{5} + 10 q^{8} - 9 q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 - 5 * q^4 - 5 * q^5 + 10 * q^8 - 9 * q^9	$ 10 q - 5 q^{2} - 5 q^{4} - 5 q^{5} + 10 q^{8} - 9 q^{9} - 5 q^{10} - 5 q^{11} - 2 q^{13} + 3 q^{14} - 5 q^{16} - 9 q^{18} - 4 q^{19} + 10 q^{20} + 2 q^{21} + 10 q^{22} - 7 q^{23} - 5 q^{25} + q^{26} - 18 q^{27} - 3 q^{28} + 8 q^{29} - 6 q^{31} - 5 q^{32} + 3 q^{35} + 18 q^{36} - 16 q^{37} - 4 q^{38} - 7 q^{39} - 5 q^{40} - 2 q^{41} + 11 q^{42} + 26 q^{43} - 5 q^{44} - 9 q^{45} - 7 q^{46} - 8 q^{47} + 14 q^{49} + 10 q^{50} - 13 q^{51} + q^{52} - 4 q^{53} + 9 q^{54} + 10 q^{55} + 30 q^{57} - 4 q^{58} - 9 q^{59} - 2 q^{61} + 12 q^{62} + 25 q^{63} + 10 q^{64} + q^{65} - 5 q^{67} - 22 q^{69} - 3 q^{70} + 56 q^{71} - 9 q^{72} + q^{73} - 16 q^{74} + 8 q^{76} - 3 q^{77} + 14 q^{78} - 23 q^{79} - 5 q^{80} + 7 q^{81} + q^{82} - 46 q^{83} - 13 q^{84} - 13 q^{86} - 15 q^{87} - 5 q^{88} + 9 q^{89} + 18 q^{90} + 29 q^{91} + 14 q^{92} + 15 q^{93} - 8 q^{94} - 4 q^{95} - 26 q^{97} - 19 q^{98} + 18 q^{99}+O(q^{100}) $ 10 * q - 5 * q^2 - 5 * q^4 - 5 * q^5 + 10 * q^8 - 9 * q^9 - 5 * q^10 - 5 * q^11 - 2 * q^13 + 3 * q^14 - 5 * q^16 - 9 * q^18 - 4 * q^19 + 10 * q^20 + 2 * q^21 + 10 * q^22 - 7 * q^23 - 5 * q^25 + q^26 - 18 * q^27 - 3 * q^28 + 8 * q^29 - 6 * q^31 - 5 * q^32 + 3 * q^35 + 18 * q^36 - 16 * q^37 - 4 * q^38 - 7 * q^39 - 5 * q^40 - 2 * q^41 + 11 * q^42 + 26 * q^43 - 5 * q^44 - 9 * q^45 - 7 * q^46 - 8 * q^47 + 14 * q^49 + 10 * q^50 - 13 * q^51 + q^52 - 4 * q^53 + 9 * q^54 + 10 * q^55 + 30 * q^57 - 4 * q^58 - 9 * q^59 - 2 * q^61 + 12 * q^62 + 25 * q^63 + 10 * q^64 + q^65 - 5 * q^67 - 22 * q^69 - 3 * q^70 + 56 * q^71 - 9 * q^72 + q^73 - 16 * q^74 + 8 * q^76 - 3 * q^77 + 14 * q^78 - 23 * q^79 - 5 * q^80 + 7 * q^81 + q^82 - 46 * q^83 - 13 * q^84 - 13 * q^86 - 15 * q^87 - 5 * q^88 + 9 * q^89 + 18 * q^90 + 29 * q^91 + 14 * q^92 + 15 * q^93 - 8 * q^94 - 4 * q^95 - 26 * q^97 - 19 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$617$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.112651	+	0.195118i	−0.0650392	+	0.112651i	−0.896711	−	0.442616i	$-0.854051\pi$
$3$	−0.112651	+	0.195118i	−0.0650392	+	0.112651i	0.831672	+	0.555267i	$0.187384\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.225302			0.0919793
$7$	−2.14481	−	1.54913i	−0.810661	−	0.585515i
$7$	−2.14481	−	1.54913i	−0.810661	−	0.585515i
$8$	1.00000			0.353553
$9$	1.47462	+	2.55412i	0.491540	+	0.851372i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−0.112651	−	0.195118i	−0.0325196	−	0.0563256i
$13$	−0.878738			−0.243718			−0.121859	−	0.992547i	$-0.538886\pi$
$13$	−0.878738			−0.243718			−0.121859	+	0.992547i	$0.538886\pi$
$14$	−0.269180	+	2.63202i	−0.0719413	+	0.703438i
$15$	0.225302			0.0581728
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.25746	+	3.91003i	−0.547514	+	0.948323i	0.450930	+	0.892559i	$0.351093\pi$
$17$	−2.25746	+	3.91003i	−0.547514	+	0.948323i	−0.998444	+	0.0557632i	$0.982241\pi$
$18$	1.47462	−	2.55412i	0.347571	−	0.602011i
$19$	1.86197	+	3.22502i	0.427165	+	0.739871i	0.996620	−	0.0821513i	$-0.0261791\pi$
$19$	1.86197	+	3.22502i	0.427165	+	0.739871i	−0.569455	+	0.822022i	$0.692846\pi$
$20$	1.00000			0.223607
$21$	0.543877	−	0.243979i	0.118684	−	0.0532405i
$22$	1.00000			0.213201
$23$	−1.15653	−	2.00317i	−0.241153	−	0.417689i	0.719890	−	0.694088i	$-0.244192\pi$
$23$	−1.15653	−	2.00317i	−0.241153	−	0.417689i	−0.961043	+	0.276399i	$0.910859\pi$
$24$	−0.112651	+	0.195118i	−0.0229948	+	0.0398282i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.439369	+	0.761009i	0.0861673	+	0.149246i
$27$	−1.34038			−0.257956
$28$	2.41399	−	1.08289i	0.456201	−	0.204648i
$29$	7.36634			1.36789			0.683947	−	0.729532i	$-0.260262\pi$
$29$	7.36634			1.36789			0.683947	+	0.729532i	$0.260262\pi$
$30$	−0.112651	−	0.195118i	−0.0205672	−	0.0356234i
$31$	−2.86197	+	4.95707i	−0.514025	+	0.890317i	0.485843	+	0.874046i	$0.338513\pi$
$31$	−2.86197	+	4.95707i	−0.514025	+	0.890317i	−0.999868	+	0.0162707i	$0.994821\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.112651	−	0.195118i	−0.0196101	−	0.0339656i
$34$	4.51492			0.774302
$35$	−0.269180	+	2.63202i	−0.0454997	+	0.444893i
$36$	−2.94924			−0.491540
$37$	1.79582	+	3.11045i	0.295231	+	0.511355i	0.975039	−	0.222036i	$-0.0712701\pi$
$37$	1.79582	+	3.11045i	0.295231	+	0.511355i	−0.679808	+	0.733390i	$0.737937\pi$
$38$	1.86197	−	3.22502i	0.302051	−	0.523168i
$39$	0.0989909	−	0.171457i	0.0158512	−	0.0274551i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	2.52114			0.393736			0.196868	−	0.980430i	$-0.436923\pi$
$41$	2.52114			0.393736			0.196868	+	0.980430i	$0.436923\pi$
$42$	−0.483231	−	0.349022i	−0.0745641	−	0.0538553i
$43$	1.68694			0.257256			0.128628	−	0.991693i	$-0.458943\pi$
$43$	1.68694			0.257256			0.128628	+	0.991693i	$0.458943\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$	1.47462	−	2.55412i	0.219823	−	0.380745i
$46$	−1.15653	+	2.00317i	−0.170521	+	0.295351i
$47$	3.72394	+	6.45005i	0.543192	+	0.940836i	0.998718	+	0.0506138i	$0.0161177\pi$
$47$	3.72394	+	6.45005i	0.543192	+	0.940836i	−0.455526	+	0.890222i	$0.650549\pi$
$48$	0.225302			0.0325196
$49$	2.20041	+	6.64516i	0.314344	+	0.949309i
$50$	1.00000			0.141421
$51$	−0.508611	−	0.880940i	−0.0712198	−	0.123356i
$52$	0.439369	−	0.761009i	0.0609295	−	0.105533i
$53$	−4.24069	+	7.34509i	−0.582504	+	1.00893i	0.412678	+	0.910877i	$0.364593\pi$
$53$	−4.24069	+	7.34509i	−0.582504	+	1.00893i	−0.995182	+	0.0980488i	$0.968740\pi$
$54$	0.670189	+	1.16080i	0.0912012	+	0.157965i
$55$	1.00000			0.134840
$56$	−2.14481	−	1.54913i	−0.286612	−	0.207011i
$57$	−0.839012			−0.111130
$58$	−3.68317	−	6.37943i	−0.483624	−	0.837661i
$59$	−4.85025	+	8.40088i	−0.631448	+	1.09370i	0.355807	+	0.934559i	$0.384206\pi$
$59$	−4.85025	+	8.40088i	−0.631448	+	1.09370i	−0.987256	+	0.159142i	$0.949127\pi$
$60$	−0.112651	+	0.195118i	−0.0145432	+	0.0251896i
$61$	2.62805	+	4.55192i	0.336488	+	0.582814i	0.983770	−	0.179437i	$-0.0574275\pi$
$61$	2.62805	+	4.55192i	0.336488	+	0.582814i	−0.647282	+	0.762251i	$0.724094\pi$
$62$	5.72394			0.726941
$63$	0.793876	−	7.76246i	0.100019	−	0.977978i
$64$	1.00000			0.125000
$65$	0.439369	+	0.761009i	0.0544970	+	0.0943916i
$66$	−0.112651	+	0.195118i	−0.0138664	+	0.0240173i
$67$	−0.725302	+	1.25626i	−0.0886098	+	0.153477i	−0.906924	−	0.421295i	$-0.861576\pi$
$67$	−0.725302	+	1.25626i	−0.0886098	+	0.153477i	0.818314	+	0.574772i	$0.194909\pi$
$68$	−2.25746	−	3.91003i	−0.273757	−	0.474161i
$69$	0.521137			0.0627376
$70$	2.41399	−	1.08289i	0.288527	−	0.129431i
$71$	2.90218			0.344425			0.172213	−	0.985060i	$-0.444908\pi$
$71$	2.90218			0.344425			0.172213	+	0.985060i	$0.444908\pi$
$72$	1.47462	+	2.55412i	0.173786	+	0.301005i
$73$	0.661578	−	1.14589i	0.0774318	−	0.134116i	−0.824709	−	0.565557i	$-0.808661\pi$
$73$	0.661578	−	1.14589i	0.0774318	−	0.134116i	0.902141	+	0.431441i	$0.141995\pi$
$74$	1.79582	−	3.11045i	0.208760	−	0.361582i
$75$	−0.112651	−	0.195118i	−0.0130078	−	0.0225302i
$76$	−3.72394			−0.427165
$77$	2.41399	−	1.08289i	0.275099	−	0.123407i
$78$	−0.197982			−0.0224170
$79$	−6.93800	−	12.0170i	−0.780586	−	1.35202i	−0.931601	−	0.363484i	$-0.881587\pi$
$79$	−6.93800	−	12.0170i	−0.780586	−	1.35202i	0.151014	−	0.988532i	$-0.451746\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−4.27286	+	7.40082i	−0.474763	+	0.822313i
$82$	−1.26057	−	2.18337i	−0.139207	−	0.241113i
$83$	4.89229			0.536999			0.268499	−	0.963280i	$-0.413472\pi$
$83$	4.89229			0.536999			0.268499	+	0.963280i	$0.413472\pi$
$84$	−0.0606469	+	0.593001i	−0.00661712	+	0.0647017i
$85$	4.51492			0.489712
$86$	−0.843471	−	1.46094i	−0.0909539	−	0.157537i
$87$	−0.829827	+	1.43730i	−0.0889668	+	0.154095i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	4.73760	+	8.20576i	0.502184	+	0.869809i	0.999997	+	0.00252399i	$0.000803413\pi$
$89$	4.73760	+	8.20576i	0.502184	+	0.869809i	−0.497813	+	0.867285i	$0.665863\pi$
$90$	−2.94924			−0.310877
$91$	1.88472	+	1.36128i	0.197573	+	0.142701i
$92$	2.31306			0.241153
$93$	−0.644808	−	1.11684i	−0.0668635	−	0.115811i
$94$	3.72394	−	6.45005i	0.384095	−	0.665272i
$95$	1.86197	−	3.22502i	0.191034	−	0.330880i
$96$	−0.112651	−	0.195118i	−0.0114974	−	0.0199141i
$97$	−13.6784			−1.38883			−0.694417	−	0.719573i	$-0.744338\pi$
$97$	−13.6784			−1.38883			−0.694417	+	0.719573i	$0.744338\pi$
$98$	4.65468	−	5.22819i	0.470194	−	0.528127i
$99$	−2.94924			−0.296410
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−2.15344	+	3.72986i	−0.214275	+	0.371135i	−0.953048	−	0.302819i	$-0.902072\pi$
$101$	−2.15344	+	3.72986i	−0.214275	+	0.371135i	0.738773	+	0.673954i	$0.235405\pi$
$102$	−0.508611	+	0.880940i	−0.0503600	+	0.0872261i
$103$	−8.39538	−	14.5412i	−0.827222	−	1.43279i	−0.900209	−	0.435457i	$-0.856587\pi$
$103$	−8.39538	−	14.5412i	−0.827222	−	1.43279i	0.0729876	−	0.997333i	$-0.476747\pi$
$104$	−0.878738			−0.0861673
$105$	−0.483231	−	0.349022i	−0.0471585	−	0.0340611i
$106$	8.48138			0.823784
$107$	−1.80996	−	3.13495i	−0.174976	−	0.303067i	0.765177	−	0.643820i	$-0.222651\pi$
$107$	−1.80996	−	3.13495i	−0.174976	−	0.303067i	−0.940153	+	0.340753i	$0.889318\pi$
$108$	0.670189	−	1.16080i	0.0644890	−	0.111698i
$109$	1.69681	−	2.93897i	0.162525	−	0.281502i	−0.773248	−	0.634103i	$-0.781369\pi$
$109$	1.69681	−	2.93897i	0.162525	−	0.281502i	0.935774	+	0.352601i	$0.114703\pi$
$110$	−0.500000	−	0.866025i	−0.0476731	−	0.0825723i
$111$	−0.809205			−0.0768063
$112$	−0.269180	+	2.63202i	−0.0254351	+	0.248703i
$113$	21.1263			1.98739			0.993697	−	0.112095i	$-0.0357562\pi$
$113$	21.1263			1.98739			0.993697	+	0.112095i	$0.0357562\pi$
$114$	0.419506	+	0.726606i	0.0392903	+	0.0680529i
$115$	−1.15653	+	2.00317i	−0.107847	+	0.186796i
$116$	−3.68317	+	6.37943i	−0.341974	+	0.592316i
$117$	−1.29580	−	2.24440i	−0.119797	−	0.207495i
$118$	9.70050			0.893003
$119$	10.8990	−	4.88918i	0.999106	−	0.448191i
$120$	0.225302			0.0205672
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	2.62805	−	4.55192i	0.237933	−	0.412112i
$123$	−0.284009	+	0.491918i	−0.0256082	+	0.0443548i
$124$	−2.86197	−	4.95707i	−0.257012	−	0.445158i
$125$	1.00000			0.0894427
$126$	−7.11943	+	3.19371i	−0.634249	+	0.284519i
$127$	11.2785			1.00081			0.500405	−	0.865792i	$-0.333185\pi$
$127$	11.2785			1.00081			0.500405	+	0.865792i	$0.333185\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−0.190036	+	0.329152i	−0.0167317	+	0.0289802i
$130$	0.439369	−	0.761009i	0.0385352	−	0.0667449i
$131$	−2.80685	−	4.86162i	−0.245236	−	0.424761i	0.716962	−	0.697112i	$-0.245532\pi$
$131$	−2.80685	−	4.86162i	−0.245236	−	0.424761i	−0.962198	+	0.272351i	$0.912199\pi$
$132$	0.225302			0.0196101
$133$	1.00241	−	9.80148i	0.0869199	−	0.849896i
$134$	1.45060			0.125313
$135$	0.670189	+	1.16080i	0.0576807	+	0.0999059i
$136$	−2.25746	+	3.91003i	−0.193576	+	0.335283i
$137$	−8.33785	+	14.4416i	−0.712350	+	1.23383i	0.251622	+	0.967825i	$0.419036\pi$
$137$	−8.33785	+	14.4416i	−0.712350	+	1.23383i	−0.963973	+	0.266001i	$0.914297\pi$
$138$	−0.260569	−	0.451318i	−0.0221811	−	0.0384188i
$139$	−17.5707			−1.49033			−0.745164	−	0.666881i	$-0.767629\pi$
$139$	−17.5707			−1.49033			−0.745164	+	0.666881i	$0.767629\pi$
$140$	−2.14481	−	1.54913i	−0.181269	−	0.130925i
$141$	−1.67802			−0.141315
$142$	−1.45109	−	2.51336i	−0.121773	−	0.210916i
$143$	0.439369	−	0.761009i	0.0367419	−	0.0636388i
$144$	1.47462	−	2.55412i	0.122885	−	0.212843i
$145$	−3.68317	−	6.37943i	−0.305870	−	0.529783i
$146$	−1.32316			−0.109505
$147$	−1.54447	−	0.319248i	−0.127386	−	0.0263311i
$148$	−3.59164			−0.295231
$149$	−0.986340	−	1.70839i	−0.0808041	−	0.139957i	0.822791	−	0.568343i	$-0.192415\pi$
$149$	−0.986340	−	1.70839i	−0.0808041	−	0.139957i	−0.903596	+	0.428387i	$0.859082\pi$
$150$	−0.112651	+	0.195118i	−0.00919793	+	0.0159313i
$151$	6.92078	−	11.9871i	0.563205	−	0.975500i	−0.434009	−	0.900909i	$-0.642901\pi$
$151$	6.92078	−	11.9871i	0.563205	−	0.975500i	0.997214	−	0.0745914i	$-0.0237652\pi$
$152$	1.86197	+	3.22502i	0.151026	+	0.261584i
$153$	−13.3156			−1.07650
$154$	−2.14481	−	1.54913i	−0.172834	−	0.124832i
$155$	5.72394			0.459758
$156$	0.0989909	+	0.171457i	0.00792561	+	0.0137276i
$157$	5.52159	−	9.56367i	0.440671	−	0.763264i	−0.557069	−	0.830467i	$-0.688074\pi$
$157$	5.52159	−	9.56367i	0.440671	−	0.763264i	0.997739	+	0.0672022i	$0.0214073\pi$
$158$	−6.93800	+	12.0170i	−0.551958	+	0.956019i
$159$	−0.955438	−	1.65487i	−0.0757711	−	0.131239i
$160$	1.00000			0.0790569
$161$	−0.622628	+	6.08802i	−0.0490700	+	0.479803i
$162$	8.54573			0.671416
$163$	−5.12448	−	8.87585i	−0.401380	−	0.695211i	0.592513	−	0.805561i	$-0.298136\pi$
$163$	−5.12448	−	8.87585i	−0.401380	−	0.695211i	−0.993893	+	0.110351i	$0.964803\pi$
$164$	−1.26057	+	2.18337i	−0.0984339	+	0.170492i
$165$	−0.112651	+	0.195118i	−0.00876989	+	0.0151899i
$166$	−2.44615	−	4.23685i	−0.189858	−	0.328843i
$167$	−22.3319			−1.72809			−0.864046	−	0.503414i	$-0.832077\pi$
$167$	−22.3319			−1.72809			−0.864046	+	0.503414i	$0.832077\pi$
$168$	0.543877	−	0.243979i	0.0419611	−	0.0188234i
$169$	−12.2278			−0.940602
$170$	−2.25746	−	3.91003i	−0.173139	−	0.299886i
$171$	−5.49139	+	9.51136i	−0.419937	+	0.727352i
$172$	−0.843471	+	1.46094i	−0.0643141	+	0.111395i
$173$	−5.92697	−	10.2658i	−0.450619	−	0.780495i	0.547806	−	0.836606i	$-0.315463\pi$
$173$	−5.92697	−	10.2658i	−0.450619	−	0.780495i	−0.998425	+	0.0561107i	$0.982130\pi$
$174$	1.65965			0.125818
$175$	2.41399	−	1.08289i	0.182480	−	0.0818591i
$176$	1.00000			0.0753778
$177$	−1.09277	−	1.89274i	−0.0821378	−	0.142267i
$178$	4.73760	−	8.20576i	0.355098	−	0.615048i
$179$	−6.71270	+	11.6267i	−0.501731	+	0.869023i	0.498267	+	0.867024i	$0.333970\pi$
$179$	−6.71270	+	11.6267i	−0.501731	+	0.869023i	−0.999998	+	0.00199969i	$0.999363\pi$
$180$	1.47462	+	2.55412i	0.109912	+	0.190373i
$181$	−13.8279			−1.02782			−0.513912	−	0.857843i	$-0.671804\pi$
$181$	−13.8279			−1.02782			−0.513912	+	0.857843i	$0.671804\pi$
$182$	0.236538	−	2.31286i	0.0175334	−	0.171440i
$183$	−1.18421			−0.0875396
$184$	−1.15653	−	2.00317i	−0.0852604	−	0.147675i
$185$	1.79582	−	3.11045i	0.132031	−	0.228685i
$186$	−0.644808	+	1.11684i	−0.0472796	+	0.0818907i
$187$	−2.25746	−	3.91003i	−0.165082	−	0.285930i
$188$	−7.44787			−0.543192
$189$	2.87485	+	2.07642i	0.209115	+	0.151037i
$190$	−3.72394			−0.270163
$191$	7.66503	+	13.2762i	0.554622	+	0.960634i	0.997933	+	0.0642659i	$0.0204706\pi$
$191$	7.66503	+	13.2762i	0.554622	+	0.960634i	−0.443311	+	0.896368i	$0.646196\pi$
$192$	−0.112651	+	0.195118i	−0.00812990	+	0.0140814i
$193$	0.812589	−	1.40745i	0.0584914	−	0.101310i	−0.835297	−	0.549799i	$-0.814704\pi$
$193$	0.812589	−	1.40745i	0.0584914	−	0.101310i	0.893788	+	0.448489i	$0.148038\pi$
$194$	6.83921	+	11.8459i	0.491027	+	0.850483i
$195$	−0.197982			−0.0141778
$196$	−6.85508	−	1.41697i	−0.489649	−	0.101212i
$197$	−13.5320			−0.964112			−0.482056	−	0.876140i	$-0.660110\pi$
$197$	−13.5320			−0.964112			−0.482056	+	0.876140i	$0.660110\pi$
$198$	1.47462	+	2.55412i	0.104797	+	0.181513i
$199$	1.68511	−	2.91869i	0.119454	−	0.206901i	−0.800097	−	0.599870i	$-0.795219\pi$
$199$	1.68511	−	2.91869i	0.119454	−	0.206901i	0.919551	+	0.392970i	$0.128552\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−0.163412	−	0.283039i	−0.0115262	−	0.0199640i
$202$	4.30687			0.303030
$203$	−15.7994	−	11.4114i	−1.10890	−	0.800923i
$204$	1.01722			0.0712198
$205$	−1.26057	−	2.18337i	−0.0880419	−	0.152493i
$206$	−8.39538	+	14.5412i	−0.584934	+	1.01314i
$207$	3.41088	−	5.90782i	0.237072	−	0.410622i
$208$	0.439369	+	0.761009i	0.0304647	+	0.0527665i
$209$	−3.72394			−0.257590
$210$	−0.0606469	+	0.593001i	−0.00418503	+	0.0409210i
$211$	4.99126			0.343613			0.171806	−	0.985131i	$-0.445040\pi$
$211$	4.99126			0.343613			0.171806	+	0.985131i	$0.445040\pi$
$212$	−4.24069	−	7.34509i	−0.291252	−	0.504463i
$213$	−0.326934	+	0.566266i	−0.0224011	+	0.0387999i
$214$	−1.80996	+	3.13495i	−0.123727	+	0.214301i
$215$	−0.843471	−	1.46094i	−0.0575243	−	0.0996350i
$216$	−1.34038			−0.0912012
$217$	13.8175	−	6.19842i	0.937994	−	0.420776i
$218$	−3.39363			−0.229845
$219$	0.149055	+	0.258171i	0.0100722	+	0.0174456i
$220$	−0.500000	+	0.866025i	−0.0337100	+	0.0583874i
$221$	1.98371	−	3.43589i	0.133439	−	0.231123i
$222$	0.404602	+	0.700792i	0.0271551	+	0.0470341i
$223$	14.0271			0.939325			0.469662	−	0.882846i	$-0.344376\pi$
$223$	14.0271			0.939325			0.469662	+	0.882846i	$0.344376\pi$
$224$	2.41399	−	1.08289i	0.161291	−	0.0723539i
$225$	−2.94924			−0.196616
$226$	−10.5631	−	18.2959i	−0.702650	−	1.21703i
$227$	−10.9973	+	19.0478i	−0.729914	+	1.26425i	0.227005	+	0.973894i	$0.427107\pi$
$227$	−10.9973	+	19.0478i	−0.729914	+	1.26425i	−0.956919	+	0.290355i	$0.906227\pi$
$228$	0.419506	−	0.726606i	0.0277825	−	0.0481206i
$229$	3.11023	+	5.38707i	0.205530	+	0.355988i	0.950301	−	0.311332i	$-0.100775\pi$
$229$	3.11023	+	5.38707i	0.205530	+	0.355988i	−0.744772	+	0.667319i	$0.767442\pi$
$230$	2.31306			0.152518
$231$	−0.0606469	+	0.593001i	−0.00399027	+	0.0390166i
$232$	7.36634			0.483624
$233$	1.05511	+	1.82751i	0.0691228	+	0.119724i	0.898515	−	0.438942i	$-0.144647\pi$
$233$	1.05511	+	1.82751i	0.0691228	+	0.119724i	−0.829393	+	0.558666i	$0.811313\pi$
$234$	−1.29580	+	2.24440i	−0.0847093	+	0.146721i
$235$	3.72394	−	6.45005i	0.242923	−	0.420755i
$236$	−4.85025	−	8.40088i	−0.315724	−	0.546850i
$237$	3.12630			0.203075
$238$	−9.68364	−	6.99419i	−0.627697	−	0.453366i
$239$	10.3487			0.669401			0.334700	−	0.942325i	$-0.391365\pi$
$239$	10.3487			0.669401			0.334700	+	0.942325i	$0.391365\pi$
$240$	−0.112651	−	0.195118i	−0.00727160	−	0.0125948i
$241$	1.20808	−	2.09246i	0.0778193	−	0.134787i	−0.824490	−	0.565877i	$-0.808538\pi$
$241$	1.20808	−	2.09246i	0.0778193	−	0.134787i	0.902309	+	0.431090i	$0.141871\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$	−2.97325	−	5.14983i	−0.190734	−	0.330361i
$244$	−5.25611			−0.336488
$245$	4.65468	−	5.22819i	0.297376	−	0.334017i
$246$	0.568018			0.0362155
$247$	−1.63618	−	2.83395i	−0.104108	−	0.180320i
$248$	−2.86197	+	4.95707i	−0.181735	+	0.314775i
$249$	−0.551123	+	0.954572i	−0.0349260	+	0.0604936i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−7.79005			−0.491703			−0.245852	−	0.969307i	$-0.579068\pi$
$251$	−7.79005			−0.491703			−0.245852	+	0.969307i	$0.579068\pi$
$252$	6.32555	+	4.56875i	0.398472	+	0.287804i
$253$	2.31306			0.145421
$254$	−5.63927	−	9.76751i	−0.353840	−	0.612868i
$255$	−0.508611	+	0.880940i	−0.0318505	+	0.0551666i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.63735	+	8.03213i	0.289270	+	0.501030i	0.973636	−	0.228109i	$-0.0732541\pi$
$257$	4.63735	+	8.03213i	0.289270	+	0.501030i	−0.684366	+	0.729139i	$0.739921\pi$
$258$	0.380072			0.0236623
$259$	0.966797	−	9.45327i	0.0600738	−	0.587398i
$260$	−0.878738			−0.0544970
$261$	10.8625	+	18.8145i	0.672374	+	1.16459i
$262$	−2.80685	+	4.86162i	−0.173408	+	0.300352i
$263$	13.2672	−	22.9795i	0.818093	−	1.41698i	−0.0889926	−	0.996032i	$-0.528365\pi$
$263$	13.2672	−	22.9795i	0.818093	−	1.41698i	0.907086	−	0.420946i	$-0.138302\pi$
$264$	−0.112651	−	0.195118i	−0.00693320	−	0.0120087i
$265$	8.48138			0.521007
$266$	−8.98954	+	4.03263i	−0.551184	+	0.247256i
$267$	−2.13478			−0.130647
$268$	−0.725302	−	1.25626i	−0.0443049	−	0.0767383i
$269$	−10.6379	+	18.4255i	−0.648607	+	1.12342i	0.334849	+	0.942272i	$0.391315\pi$
$269$	−10.6379	+	18.4255i	−0.648607	+	1.12342i	−0.983456	+	0.181148i	$0.942019\pi$
$270$	0.670189	−	1.16080i	0.0407864	−	0.0706441i
$271$	5.93703	+	10.2832i	0.360649	+	0.624663i	0.988068	−	0.154019i	$-0.0492218\pi$
$271$	5.93703	+	10.2832i	0.360649	+	0.624663i	−0.627419	+	0.778682i	$0.715889\pi$
$272$	4.51492			0.273757
$273$	−0.477926	+	0.214393i	−0.0289254	+	0.0129757i
$274$	16.6757			1.00742
$275$	−0.500000	−	0.866025i	−0.0301511	−	0.0522233i
$276$	−0.260569	+	0.451318i	−0.0156844	+	0.0271662i
$277$	−4.45565	+	7.71742i	−0.267714	+	0.463695i	−0.968271	−	0.249902i	$-0.919602\pi$
$277$	−4.45565	+	7.71742i	−0.267714	+	0.463695i	0.700557	+	0.713597i	$0.252935\pi$
$278$	8.78536	+	15.2167i	0.526911	+	0.912636i
$279$	−16.8813			−1.01065
$280$	−0.269180	+	2.63202i	−0.0160866	+	0.157293i
$281$	27.6215			1.64776			0.823881	−	0.566764i	$-0.191805\pi$
$281$	27.6215			1.64776			0.823881	+	0.566764i	$0.191805\pi$
$282$	0.839012	+	1.45321i	0.0499624	+	0.0865375i
$283$	11.2921	−	19.5586i	0.671248	−	1.16264i	−0.306303	−	0.951934i	$-0.599092\pi$
$283$	11.2921	−	19.5586i	0.671248	−	1.16264i	0.977551	−	0.210701i	$-0.0675747\pi$
$284$	−1.45109	+	2.51336i	−0.0861063	+	0.149140i
$285$	0.419506	+	0.726606i	0.0248494	+	0.0430404i
$286$	−0.878738			−0.0519608
$287$	−5.40736	−	3.90556i	−0.319186	−	0.230538i
$288$	−2.94924			−0.173786
$289$	−1.69225	−	2.93106i	−0.0995440	−	0.172415i
$290$	−3.68317	+	6.37943i	−0.216283	+	0.374613i
$291$	1.54089	−	2.66890i	0.0903286	−	0.156454i
$292$	0.661578	+	1.14589i	0.0387159	+	0.0670579i
$293$	31.8586			1.86120			0.930599	−	0.366041i	$-0.119287\pi$
$293$	31.8586			1.86120			0.930599	+	0.366041i	$0.119287\pi$
$294$	0.495757	+	1.49717i	0.0289131	+	0.0873168i
$295$	9.70050			0.564785
$296$	1.79582	+	3.11045i	0.104380	+	0.180791i
$297$	0.670189	−	1.16080i	0.0388883	−	0.0673565i
$298$	−0.986340	+	1.70839i	−0.0571371	+	0.0989644i
$299$	1.01629	+	1.76026i	0.0587733	+	0.101798i
$300$	0.225302			0.0130078
$301$	−3.61817	−	2.61329i	−0.208548	−	0.150628i
$302$	−13.8416			−0.796492
$303$	−0.485174	−	0.840346i	−0.0278725	−	0.0482766i
$304$	1.86197	−	3.22502i	0.106791	−	0.184968i
$305$	2.62805	−	4.55192i	0.150482	−	0.260642i
$306$	6.65779	+	11.5316i	0.380600	+	0.659219i
$307$	−20.2441			−1.15539			−0.577696	−	0.816252i	$-0.696048\pi$
$307$	−20.2441			−1.15539			−0.577696	+	0.816252i	$0.696048\pi$
$308$	−0.269180	+	2.63202i	−0.0153379	+	0.149973i
$309$	3.78300			0.215207
$310$	−2.86197	−	4.95707i	−0.162549	−	0.281543i
$311$	4.50253	−	7.79862i	0.255315	−	0.442219i	−0.709666	−	0.704538i	$-0.751154\pi$
$311$	4.50253	−	7.79862i	0.255315	−	0.442219i	0.964981	+	0.262319i	$0.0844874\pi$
$312$	0.0989909	−	0.171457i	0.00560425	−	0.00970685i
$313$	1.86653	+	3.23293i	0.105503	+	0.182736i	0.913943	−	0.405841i	$-0.133022\pi$
$313$	1.86653	+	3.23293i	0.105503	+	0.182736i	−0.808441	+	0.588578i	$0.799688\pi$
$314$	−11.0432			−0.623203
$315$	−7.11943	+	3.19371i	−0.401134	+	0.179945i
$316$	13.8760			0.780586
$317$	−1.94972	−	3.37702i	−0.109507	−	0.189672i	0.806063	−	0.591829i	$-0.201594\pi$
$317$	−1.94972	−	3.37702i	−0.109507	−	0.189672i	−0.915571	+	0.402157i	$0.868261\pi$
$318$	−0.955438	+	1.65487i	−0.0535783	+	0.0928003i
$319$	−3.68317	+	6.37943i	−0.206218	+	0.357180i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	0.815579			0.0455212
$322$	5.58369	−	2.50480i	0.311167	−	0.139587i
$323$	−16.8133			−0.935515
$324$	−4.27286	−	7.40082i	−0.237381	−	0.411156i
$325$	0.439369	−	0.761009i	0.0243718	−	0.0422132i
$326$	−5.12448	+	8.87585i	−0.283819	+	0.491588i
$327$	0.382296	+	0.662156i	0.0211410	+	0.0366173i
$328$	2.52114			0.139207
$329$	2.00482	−	19.6030i	0.110529	−	1.08075i
$330$	0.225302			0.0124025
$331$	−10.3441	−	17.9164i	−0.568561	−	0.984777i	−0.996709	−	0.0810680i	$-0.974167\pi$
$331$	−10.3441	−	17.9164i	−0.568561	−	0.984777i	0.428147	−	0.903709i	$-0.359166\pi$
$332$	−2.44615	+	4.23685i	−0.134250	+	0.232527i
$333$	−5.29630	+	9.17346i	−0.290235	+	0.502703i
$334$	11.1659	+	19.3400i	0.610973	+	1.05824i
$335$	1.45060			0.0792550
$336$	−0.483231	−	0.349022i	−0.0263624	−	0.0190407i
$337$	23.2131			1.26450			0.632250	−	0.774764i	$-0.282131\pi$
$337$	23.2131			1.26450			0.632250	+	0.774764i	$0.282131\pi$
$338$	6.11391	+	10.5896i	0.332553	+	0.575998i
$339$	−2.37990	+	4.12211i	−0.129259	+	0.223882i
$340$	−2.25746	+	3.91003i	−0.122428	+	0.212051i
$341$	−2.86197	−	4.95707i	−0.154984	−	0.268441i
$342$	10.9828			0.593881
$343$	5.57476	−	17.6613i	0.301009	−	0.953621i
$344$	1.68694			0.0909539
$345$	−0.260569	−	0.451318i	−0.0140285	−	0.0242982i
$346$	−5.92697	+	10.2658i	−0.318636	+	0.551893i
$347$	3.01276	−	5.21826i	0.161734	−	0.280131i	−0.773757	−	0.633483i	$-0.781625\pi$
$347$	3.01276	−	5.21826i	0.161734	−	0.280131i	0.935491	+	0.353352i	$0.114958\pi$
$348$	−0.829827	−	1.43730i	−0.0444834	−	0.0770475i
$349$	7.42620			0.397515			0.198758	−	0.980049i	$-0.436309\pi$
$349$	7.42620			0.397515			0.198758	+	0.980049i	$0.436309\pi$
$350$	−2.14481	−	1.54913i	−0.114645	−	0.0828044i
$351$	1.17784			0.0628685
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	−2.55946	+	4.43312i	−0.136226	+	0.235951i	−0.926065	−	0.377363i	$-0.876831\pi$
$353$	−2.55946	+	4.43312i	−0.136226	+	0.235951i	0.789839	+	0.613314i	$0.210164\pi$
$354$	−1.09277	+	1.89274i	−0.0580802	+	0.100598i
$355$	−1.45109	−	2.51336i	−0.0770158	−	0.133395i
$356$	−9.47519			−0.502184
$357$	−0.273816	+	2.67735i	−0.0144919	+	0.141700i
$358$	13.4254			0.709554
$359$	0.256310	+	0.443942i	0.0135275	+	0.0234303i	0.872710	−	0.488239i	$-0.162361\pi$
$359$	0.256310	+	0.443942i	0.0135275	+	0.0234303i	−0.859182	+	0.511669i	$0.829027\pi$
$360$	1.47462	−	2.55412i	0.0777193	−	0.134614i
$361$	2.56615	−	4.44470i	0.135060	−	0.233932i
$362$	6.91397	+	11.9754i	0.363390	+	0.629411i
$363$	0.225302			0.0118253
$364$	−2.12126	+	0.951580i	−0.111184	+	0.0498764i
$365$	−1.32316			−0.0692571
$366$	0.592107	+	1.02556i	0.0309499	+	0.0536069i
$367$	0.651708	−	1.12879i	0.0340189	−	0.0589224i	−0.848515	−	0.529172i	$-0.822503\pi$
$367$	0.651708	−	1.12879i	0.0340189	−	0.0589224i	0.882534	+	0.470249i	$0.155836\pi$
$368$	−1.15653	+	2.00317i	−0.0602882	+	0.104422i
$369$	3.71772	+	6.43928i	0.193537	+	0.335215i
$370$	−3.59164			−0.186720
$371$	20.4740	−	9.18444i	1.06295	−	0.476832i
$372$	1.28962			0.0668635
$373$	16.1759	+	28.0175i	0.837556	+	1.45069i	0.891932	+	0.452169i	$0.149350\pi$
$373$	16.1759	+	28.0175i	0.837556	+	1.45069i	−0.0543766	+	0.998520i	$0.517317\pi$
$374$	−2.25746	+	3.91003i	−0.116730	+	0.202183i
$375$	−0.112651	+	0.195118i	−0.00581728	+	0.0100758i
$376$	3.72394	+	6.45005i	0.192047	+	0.332636i
$377$	−6.47308			−0.333380
$378$	0.360803	−	3.52790i	0.0185577	−	0.181456i
$379$	−33.2875			−1.70986			−0.854932	−	0.518740i	$-0.826401\pi$
$379$	−33.2875			−1.70986			−0.854932	+	0.518740i	$0.826401\pi$
$380$	1.86197	+	3.22502i	0.0955170	+	0.165440i
$381$	−1.27054	+	2.20064i	−0.0650919	+	0.112742i
$382$	7.66503	−	13.2762i	0.392177	−	0.679271i
$383$	8.68773	+	15.0476i	0.443922	+	0.768896i	0.997976	−	0.0635845i	$-0.0202532\pi$
$383$	8.68773	+	15.0476i	0.443922	+	0.768896i	−0.554054	+	0.832481i	$0.686920\pi$
$384$	0.225302			0.0114974
$385$	−2.14481	−	1.54913i	−0.109310	−	0.0789509i
$386$	−1.62518			−0.0827194
$387$	2.48760	+	4.30865i	0.126452	+	0.219021i
$388$	6.83921	−	11.8459i	0.347208	−	0.601383i
$389$	16.4024	−	28.4097i	0.831633	−	1.44043i	−0.0651101	−	0.997878i	$-0.520740\pi$
$389$	16.4024	−	28.4097i	0.831633	−	1.44043i	0.896743	−	0.442552i	$-0.145927\pi$
$390$	0.0989909	+	0.171457i	0.00501260	+	0.00868207i
$391$	10.4433			0.528139
$392$	2.20041	+	6.64516i	0.111137	+	0.335631i
$393$	1.26478			0.0637998
$394$	6.76598	+	11.7190i	0.340865	+	0.590396i
$395$	−6.93800	+	12.0170i	−0.349089	+	0.604640i
$396$	1.47462	−	2.55412i	0.0741024	−	0.128349i
$397$	17.5103	+	30.3287i	0.878815	+	1.52215i	0.852643	+	0.522495i	$0.174999\pi$
$397$	17.5103	+	30.3287i	0.878815	+	1.52215i	0.0261723	+	0.999657i	$0.491668\pi$
$398$	−3.37022			−0.168934
$399$	1.79952	+	1.29974i	0.0900887	+	0.0650682i
$400$	1.00000			0.0500000
$401$	9.97510	+	17.2774i	0.498133	+	0.862791i	0.999998	−	0.00215460i	$-0.000685830\pi$
$401$	9.97510	+	17.2774i	0.498133	+	0.862791i	−0.501865	+	0.864946i	$0.667352\pi$
$402$	−0.163412	+	0.283039i	−0.00815027	+	0.0141167i
$403$	2.51492	−	4.35597i	0.125277	−	0.216986i
$404$	−2.15344	−	3.72986i	−0.107137	−	0.185567i
$405$	8.54573			0.424641
$406$	−1.98287	+	19.3884i	−0.0984081	+	0.962228i
$407$	−3.59164			−0.178031
$408$	−0.508611	−	0.880940i	−0.0251800	−	0.0436130i
$409$	1.82622	−	3.16310i	0.0903007	−	0.156405i	−0.817337	−	0.576160i	$-0.804551\pi$
$409$	1.82622	−	3.16310i	0.0903007	−	0.156405i	0.907638	+	0.419755i	$0.137884\pi$
$410$	−1.26057	+	2.18337i	−0.0622551	+	0.107829i
$411$	−1.87854	−	3.25372i	−0.0926614	−	0.160494i
$412$	16.7908			0.827222
$413$	23.4169	−	10.5046i	1.15227	−	0.516898i
$414$	−6.82176			−0.335271
$415$	−2.44615	−	4.23685i	−0.120077	−	0.207979i
$416$	0.439369	−	0.761009i	0.0215418	−	0.0373115i
$417$	1.97936	−	3.42836i	0.0969298	−	0.167887i
$418$	1.86197	+	3.22502i	0.0910718	+	0.157741i
$419$	31.2898			1.52861			0.764304	−	0.644856i	$-0.223083\pi$
$419$	31.2898			1.52861			0.764304	+	0.644856i	$0.223083\pi$
$420$	0.543877	−	0.243979i	0.0265385	−	0.0119049i
$421$	30.3382			1.47859			0.739297	−	0.673379i	$-0.235158\pi$
$421$	30.3382			1.47859			0.739297	+	0.673379i	$0.235158\pi$
$422$	−2.49563	−	4.32256i	−0.121485	−	0.210419i
$423$	−10.9828	+	19.0227i	−0.534001	+	0.924917i
$424$	−4.24069	+	7.34509i	−0.205946	+	0.356709i
$425$	−2.25746	−	3.91003i	−0.109503	−	0.189665i
$426$	0.653868			0.0316800
$427$	1.41484	−	13.8342i	0.0684688	−	0.669484i
$428$	3.61993			0.174976
$429$	0.0989909	+	0.171457i	0.00477932	+	0.00827803i
$430$	−0.843471	+	1.46094i	−0.0406758	+	0.0704526i
$431$	−3.86653	+	6.69703i	−0.186244	+	0.322585i	−0.943995	−	0.329959i	$-0.892965\pi$
$431$	−3.86653	+	6.69703i	−0.186244	+	0.322585i	0.757751	+	0.652544i	$0.226298\pi$
$432$	0.670189	+	1.16080i	0.0322445	+	0.0558491i
$433$	−19.2104			−0.923192			−0.461596	−	0.887090i	$-0.652723\pi$
$433$	−19.2104			−0.923192			−0.461596	+	0.887090i	$0.652723\pi$
$434$	−12.2767	−	8.86711i	−0.589303	−	0.425635i
$435$	1.65965			0.0795743
$436$	1.69681	+	2.93897i	0.0812626	+	0.140751i
$437$	4.30684	−	7.45966i	0.206024	−	0.356844i
$438$	0.149055	−	0.258171i	0.00712213	−	0.0123359i
$439$	−10.4899	−	18.1691i	−0.500656	−	0.867162i	−1.00000		0.000758062i	$-0.999759\pi$
$439$	−10.4899	−	18.1691i	−0.500656	−	0.867162i	0.499343	−	0.866404i	$-0.333575\pi$
$440$	1.00000			0.0476731
$441$	−13.7278	+	15.4192i	−0.653703	+	0.734247i
$442$	−3.96743			−0.188711
$443$	18.2172	+	31.5531i	0.865524	+	1.49913i	0.866526	+	0.499132i	$0.166348\pi$
$443$	18.2172	+	31.5531i	0.865524	+	1.49913i	−0.00100184	+	0.999999i	$0.500319\pi$
$444$	0.404602	−	0.700792i	0.0192016	−	0.0332581i
$445$	4.73760	−	8.20576i	0.224584	−	0.388990i
$446$	−7.01355	−	12.1478i	−0.332101	−	0.575216i
$447$	0.444449			0.0210217
$448$	−2.14481	−	1.54913i	−0.101333	−	0.0731894i
$449$	11.3537			0.535815			0.267908	−	0.963445i	$-0.413668\pi$
$449$	11.3537			0.535815			0.267908	+	0.963445i	$0.413668\pi$
$450$	1.47462	+	2.55412i	0.0695142	+	0.120402i
$451$	−1.26057	+	2.18337i	−0.0593579	+	0.102811i
$452$	−10.5631	+	18.2959i	−0.496849	+	0.860567i
$453$	1.55927	+	2.70073i	0.0732608	+	0.126891i
$454$	21.9945			1.03225
$455$	0.236538	−	2.31286i	0.0110891	−	0.108428i
$456$	−0.839012			−0.0392903
$457$	9.48186	+	16.4231i	0.443543	+	0.768239i	0.997949	−	0.0640071i	$-0.0203880\pi$
$457$	9.48186	+	16.4231i	0.443543	+	0.768239i	−0.554407	+	0.832246i	$0.687055\pi$
$458$	3.11023	−	5.38707i	0.145331	−	0.251721i
$459$	3.02585	−	5.24092i	0.141235	−	0.244625i
$460$	−1.15653	−	2.00317i	−0.0539234	−	0.0933981i
$461$	−13.8981			−0.647297			−0.323648	−	0.946177i	$-0.604909\pi$
$461$	−13.8981			−0.647297			−0.323648	+	0.946177i	$0.604909\pi$
$462$	0.543877	−	0.243979i	0.0253035	−	0.0113509i
$463$	−3.52381			−0.163765			−0.0818826	−	0.996642i	$-0.526093\pi$
$463$	−3.52381			−0.163765			−0.0818826	+	0.996642i	$0.526093\pi$
$464$	−3.68317	−	6.37943i	−0.170987	−	0.296158i
$465$	−0.644808	+	1.11684i	−0.0299023	+	0.0517923i
$466$	1.05511	−	1.82751i	0.0488772	−	0.0846578i
$467$	4.20109	+	7.27650i	0.194403	+	0.336716i	0.946705	−	0.322103i	$-0.104390\pi$
$467$	4.20109	+	7.27650i	0.194403	+	0.336716i	−0.752301	+	0.658819i	$0.771056\pi$
$468$	2.59161			0.119797
$469$	3.50174	−	1.57085i	0.161695	−	0.0725352i
$470$	−7.44787			−0.343545
$471$	1.24403	+	2.15472i	0.0573218	+	0.0992842i
$472$	−4.85025	+	8.40088i	−0.223251	+	0.386682i
$473$	−0.843471	+	1.46094i	−0.0387829	+	0.0671739i
$474$	−1.56315	−	2.70745i	−0.0717978	−	0.124357i
$475$	−3.72394			−0.170866
$476$	−1.21533	+	11.8834i	−0.0557043	+	0.544673i
$477$	−25.0136			−1.14529
$478$	−5.17434	−	8.96222i	−0.236669	−	0.409922i
$479$	−3.32178	+	5.75348i	−0.151776	+	0.262883i	−0.931880	−	0.362766i	$-0.881833\pi$
$479$	−3.32178	+	5.75348i	−0.151776	+	0.262883i	0.780105	+	0.625649i	$0.215166\pi$
$480$	−0.112651	+	0.195118i	−0.00514180	+	0.00890586i
$481$	−1.57805	−	2.73327i	−0.0719531	−	0.124626i
$482$	−2.41616			−0.110053
$483$	−1.11774	−	0.807308i	−0.0508589	−	0.0367338i
$484$	1.00000			0.0454545
$485$	6.83921	+	11.8459i	0.310553	+	0.537893i
$486$	−2.97325	+	5.14983i	−0.134870	+	0.233601i
$487$	−14.2450	+	24.6731i	−0.645504	+	1.11805i	0.338680	+	0.940902i	$0.390020\pi$
$487$	−14.2450	+	24.6731i	−0.645504	+	1.11805i	−0.984185	+	0.177145i	$0.943314\pi$
$488$	2.62805	+	4.55192i	0.118966	+	0.206056i
$489$	2.30911			0.104422
$490$	−6.85508	−	1.41697i	−0.309681	−	0.0640124i
$491$	29.9072			1.34969			0.674846	−	0.737958i	$-0.264210\pi$
$491$	29.9072			1.34969			0.674846	+	0.737958i	$0.264210\pi$
$492$	−0.284009	−	0.491918i	−0.0128041	−	0.0221774i
$493$	−16.6292	+	28.8026i	−0.748942	+	1.29721i
$494$	−1.63618	+	2.83395i	−0.0736153	+	0.127505i
$495$	1.47462	+	2.55412i	0.0662792	+	0.114799i
$496$	5.72394			0.257012
$497$	−6.22462	−	4.49584i	−0.279212	−	0.201666i
$498$	1.10225			0.0493928
$499$	−12.3654	−	21.4174i	−0.553550	−	0.958777i	−0.998015	−	0.0629803i	$-0.979939\pi$
$499$	−12.3654	−	21.4174i	−0.553550	−	0.958777i	0.444465	−	0.895796i	$-0.353394\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	2.51571	−	4.35734i	0.112394	−	0.194672i
$502$	3.89502	+	6.74638i	0.173843	+	0.301106i
$503$	−12.9620			−0.577945			−0.288973	−	0.957337i	$-0.593314\pi$
$503$	−12.9620			−0.577945			−0.288973	+	0.957337i	$0.593314\pi$
$504$	0.793876	−	7.76246i	0.0353620	−	0.345768i
$505$	4.30687			0.191653
$506$	−1.15653	−	2.00317i	−0.0514140	−	0.0890516i
$507$	1.37748	−	2.38586i	0.0611760	−	0.105960i
$508$	−5.63927	+	9.76751i	−0.250202	+	0.433363i
$509$	−16.0412	−	27.7842i	−0.711015	−	1.23151i	−0.964476	−	0.264169i	$-0.914902\pi$
$509$	−16.0412	−	27.7842i	−0.711015	−	1.23151i	0.253461	−	0.967346i	$-0.418431\pi$
$510$	1.01722			0.0450434
$511$	−3.19408	+	1.43284i	−0.141298	+	0.0633850i
$512$	1.00000			0.0441942
$513$	−2.49574	−	4.32275i	−0.110190	−	0.190854i
$514$	4.63735	−	8.03213i	0.204545	−	0.354282i
$515$	−8.39538	+	14.5412i	−0.369945	+	0.640763i
$516$	−0.190036	−	0.329152i	−0.00836587	−	0.0144901i
$517$	−7.44787			−0.327557
$518$	−8.67017	+	3.88937i	−0.380946	+	0.170889i
$519$	2.67072			0.117232
$520$	0.439369	+	0.761009i	0.0192676	+	0.0333725i
$521$	−3.85956	+	6.68495i	−0.169090	+	0.292873i	−0.938100	−	0.346364i	$-0.887416\pi$
$521$	−3.85956	+	6.68495i	−0.169090	+	0.292873i	0.769010	+	0.639237i	$0.220750\pi$
$522$	10.8625	−	18.8145i	0.475441	−	0.823487i
$523$	−1.01104	−	1.75116i	−0.0442095	−	0.0765731i	0.843074	−	0.537798i	$-0.180744\pi$
$523$	−1.01104	−	1.75116i	−0.0442095	−	0.0765731i	−0.887283	+	0.461225i	$0.847410\pi$
$524$	5.61371			0.245236
$525$	−0.0606469	+	0.593001i	−0.00264685	+	0.0258807i
$526$	−26.5345			−1.15696
$527$	−12.9216	−	22.3808i	−0.562872	−	0.974923i
$528$	−0.112651	+	0.195118i	−0.00490251	+	0.00849140i
$529$	8.82488	−	15.2851i	0.383691	−	0.664572i
$530$	−4.24069	−	7.34509i	−0.184204	−	0.319050i
$531$	−28.6091			−1.24153
$532$	7.98713	+	5.76885i	0.346286	+	0.250112i
$533$	−2.21542			−0.0959604
$534$	1.06739	+	1.84878i	0.0461906	+	0.0800044i
$535$	−1.80996	+	3.13495i	−0.0782516	+	0.135536i
$536$	−0.725302	+	1.25626i	−0.0313283	+	0.0542622i
$537$	−1.51239	−	2.61953i	−0.0652643	−	0.113041i
$538$	21.2759			0.917268
$539$	−6.85508	−	1.41697i	−0.295269	−	0.0610334i
$540$	−1.34038			−0.0576807
$541$	−3.65583	−	6.33208i	−0.157176	−	0.272237i	0.776673	−	0.629904i	$-0.216906\pi$
$541$	−3.65583	−	6.33208i	−0.157176	−	0.272237i	−0.933849	+	0.357667i	$0.883572\pi$
$542$	5.93703	−	10.2832i	0.255017	−	0.441703i
$543$	1.55773	−	2.69808i	0.0668488	−	0.115786i
$544$	−2.25746	−	3.91003i	−0.0967878	−	0.167641i
$545$	−3.39363			−0.145367
$546$	0.424633	+	0.306699i	0.0181726	+	0.0131255i
$547$	−5.10771			−0.218390			−0.109195	−	0.994020i	$-0.534827\pi$
$547$	−5.10771			−0.218390			−0.109195	+	0.994020i	$0.534827\pi$
$548$	−8.33785	−	14.4416i	−0.356175	−	0.616913i
$549$	−7.75076	+	13.4247i	−0.330794	+	0.572953i
$550$	−0.500000	+	0.866025i	−0.0213201	+	0.0369274i
$551$	13.7159	+	23.7566i	0.584316	+	1.01207i
$552$	0.521137			0.0221811
$553$	−3.73514	+	36.5220i	−0.158834	+	1.55307i
$554$	8.91131			0.378605
$555$	0.404602	+	0.700792i	0.0171744	+	0.0297470i
$556$	8.78536	−	15.2167i	0.372582	−	0.645331i
$557$	4.08775	−	7.08020i	0.173204	−	0.299998i	−0.766334	−	0.642442i	$-0.777921\pi$
$557$	4.08775	−	7.08020i	0.173204	−	0.299998i	0.939538	+	0.342444i	$0.111255\pi$
$558$	8.44063	+	14.6196i	0.357320	+	0.618897i
$559$	−1.48238			−0.0626980
$560$	2.41399	−	1.08289i	0.102010	−	0.0457607i
$561$	1.01722			0.0429472
$562$	−13.8108	−	23.9209i	−0.582572	−	1.00904i
$563$	−14.0215	+	24.2859i	−0.590936	+	1.02353i	0.403171	+	0.915125i	$0.367908\pi$
$563$	−14.0215	+	24.2859i	−0.590936	+	1.02353i	−0.994107	+	0.108406i	$0.965425\pi$
$564$	0.839012	−	1.45321i	0.0353288	−	0.0611912i
$565$	−10.5631	−	18.2959i	−0.444395	−	0.769715i
$566$	−22.5843			−0.949288
$567$	20.6293	−	9.25412i	0.866348	−	0.388637i
$568$	2.90218			0.121773
$569$	−3.20629	−	5.55345i	−0.134414	−	0.232813i	0.790959	−	0.611869i	$-0.209582\pi$
$569$	−3.20629	−	5.55345i	−0.134414	−	0.232813i	−0.925374	+	0.379056i	$0.876249\pi$
$570$	0.419506	−	0.726606i	0.0175712	−	0.0304342i
$571$	19.1660	−	33.1965i	0.802074	−	1.38923i	−0.116175	−	0.993229i	$-0.537063\pi$
$571$	19.1660	−	33.1965i	0.802074	−	1.38923i	0.918249	−	0.396004i	$-0.129603\pi$
$572$	0.439369	+	0.761009i	0.0183709	+	0.0318194i
$573$	−3.45390			−0.144289
$574$	−0.678639	+	6.63569i	−0.0283259	+	0.276968i
$575$	2.31306			0.0964612
$576$	1.47462	+	2.55412i	0.0614425	+	0.106421i
$577$	11.6906	−	20.2488i	0.486687	−	0.842967i	−0.513196	−	0.858272i	$-0.671538\pi$
$577$	11.6906	−	20.2488i	0.486687	−	0.842967i	0.999883	+	0.0153046i	$0.00487179\pi$
$578$	−1.69225	+	2.93106i	−0.0703882	+	0.121916i
$579$	0.183078	+	0.317101i	0.00760847	+	0.0131783i
$580$	7.36634			0.305870
$581$	−10.4930	−	7.57878i	−0.435324	−	0.314421i
$582$	−3.08178			−0.127744
$583$	−4.24069	−	7.34509i	−0.175631	−	0.304203i
$584$	0.661578	−	1.14589i	0.0273763	−	0.0474171i
$585$	−1.29580	+	2.24440i	−0.0535749	+	0.0927944i
$586$	−15.9293	−	27.5903i	−0.658033	−	1.13975i
$587$	−17.2902			−0.713643			−0.356821	−	0.934173i	$-0.616140\pi$
$587$	−17.2902			−0.713643			−0.356821	+	0.934173i	$0.616140\pi$
$588$	1.04871	−	1.17792i	0.0432481	−	0.0485768i
$589$	−21.3156			−0.878293
$590$	−4.85025	−	8.40088i	−0.199682	−	0.345859i
$591$	1.52439	−	2.64032i	0.0627051	−	0.108608i
$592$	1.79582	−	3.11045i	0.0738077	−	0.127839i
$593$	10.3103	+	17.8580i	0.423394	+	0.733340i	0.996269	−	0.0863025i	$-0.0275052\pi$
$593$	10.3103	+	17.8580i	0.423394	+	0.733340i	−0.572875	+	0.819643i	$0.694172\pi$
$594$	−1.34038			−0.0549964
$595$	−9.68364	−	6.99419i	−0.396990	−	0.286734i
$596$	1.97268			0.0808041
$597$	0.379659	+	0.657589i	0.0155384	+	0.0269133i
$598$	1.01629	−	1.76026i	0.0415590	−	0.0719823i
$599$	0.740023	−	1.28176i	0.0302365	−	0.0523712i	−0.850511	−	0.525957i	$-0.823707\pi$
$599$	0.740023	−	1.28176i	0.0302365	−	0.0523712i	0.880748	+	0.473586i	$0.157041\pi$
$600$	−0.112651	−	0.195118i	−0.00459897	−	0.00796564i
$601$	41.8461			1.70694			0.853470	−	0.521143i	$-0.174494\pi$
$601$	41.8461			1.70694			0.853470	+	0.521143i	$0.174494\pi$
$602$	−0.454091	+	4.44007i	−0.0185074	+	0.180964i
$603$	−4.27818			−0.174221
$604$	6.92078	+	11.9871i	0.281603	+	0.487750i
$605$	−0.500000	+	0.866025i	−0.0203279	+	0.0352089i
$606$	−0.485174	+	0.840346i	−0.0197089	+	0.0341367i
$607$	10.5890	+	18.3407i	0.429794	+	0.744424i	0.996855	−	0.0792515i	$-0.0252530\pi$
$607$	10.5890	+	18.3407i	0.429794	+	0.744424i	−0.567061	+	0.823676i	$0.691920\pi$
$608$	−3.72394			−0.151026
$609$	4.00638	−	1.79723i	0.162347	−	0.0728274i
$610$	−5.25611			−0.212814
$611$	−3.27236	−	5.66790i	−0.132386	−	0.229299i
$612$	6.65779	−	11.5316i	0.269125	−	0.466138i
$613$	−15.3146	+	26.5257i	−0.618552	+	1.07136i	0.371198	+	0.928554i	$0.378947\pi$
$613$	−15.3146	+	26.5257i	−0.618552	+	1.07136i	−0.989750	+	0.142810i	$0.954386\pi$
$614$	10.1221	+	17.5319i	0.408493	+	0.707530i
$615$	0.568018			0.0229047
$616$	2.41399	−	1.08289i	0.0972624	−	0.0436311i
$617$	−42.1456			−1.69672			−0.848358	−	0.529422i	$-0.822409\pi$
$617$	−42.1456			−1.69672			−0.848358	+	0.529422i	$0.822409\pi$
$618$	−1.89150	−	3.27617i	−0.0760873	−	0.131787i
$619$	−3.50115	+	6.06417i	−0.140723	+	0.243740i	−0.927769	−	0.373155i	$-0.878276\pi$
$619$	−3.50115	+	6.06417i	−0.140723	+	0.243740i	0.787046	+	0.616894i	$0.211609\pi$
$620$	−2.86197	+	4.95707i	−0.114939	+	0.199081i
$621$	1.55019	+	2.68500i	0.0622068	+	0.107745i
$622$	−9.00507			−0.361070
$623$	2.55053	−	24.9389i	0.102185	−	0.999157i
$624$	−0.197982			−0.00792561
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	1.86653	−	3.23293i	0.0746017	−	0.129214i
$627$	0.419506	−	0.726606i	0.0167535	−	0.0290178i
$628$	5.52159	+	9.56367i	0.220335	+	0.381632i
$629$	−16.2160			−0.646573
$630$	6.32555	+	4.56875i	0.252016	+	0.182023i
$631$	15.7079			0.625321			0.312661	−	0.949865i	$-0.398780\pi$
$631$	15.7079			0.625321			0.312661	+	0.949865i	$0.398780\pi$
$632$	−6.93800	−	12.0170i	−0.275979	−	0.478010i
$633$	−0.562272	+	0.973884i	−0.0223483	+	0.0387084i
$634$	−1.94972	+	3.37702i	−0.0774334	+	0.134119i
$635$	−5.63927	−	9.76751i	−0.223788	−	0.387612i
$636$	1.91088			0.0757711
$637$	−1.93358	−	5.83936i	−0.0766112	−	0.231364i
$638$	7.36634			0.291636
$639$	4.27961	+	7.41250i	0.169299	+	0.293234i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	21.2610	−	36.8252i	0.839760	−	1.45451i	−0.0503356	−	0.998732i	$-0.516029\pi$
$641$	21.2610	−	36.8252i	0.839760	−	1.45451i	0.890095	−	0.455774i	$-0.150638\pi$
$642$	−0.407789	−	0.706312i	−0.0160942	−	0.0278759i
$643$	20.4070			0.804775			0.402387	−	0.915470i	$-0.368181\pi$
$643$	20.4070			0.804775			0.402387	+	0.915470i	$0.368181\pi$
$644$	−4.96106	−	3.58322i	−0.195493	−	0.141199i
$645$	0.380072			0.0149653
$646$	8.40664	+	14.5607i	0.330755	+	0.572884i
$647$	11.7185	−	20.2971i	0.460702	−	0.797959i	−0.538294	−	0.842757i	$-0.680931\pi$
$647$	11.7185	−	20.2971i	0.460702	−	0.797959i	0.998996	+	0.0447977i	$0.0142643\pi$
$648$	−4.27286	+	7.40082i	−0.167854	+	0.290732i
$649$	−4.85025	−	8.40088i	−0.190389	−	0.329763i
$650$	−0.878738			−0.0344669
$651$	−0.347139	+	3.39430i	−0.0136054	+	0.133033i
$652$	10.2490			0.401380
$653$	−5.32081	−	9.21591i	−0.208219	−	0.360646i	0.742934	−	0.669364i	$-0.233433\pi$
$653$	−5.32081	−	9.21591i	−0.208219	−	0.360646i	−0.951154	+	0.308718i	$0.900100\pi$
$654$	0.382296	−	0.662156i	0.0149490	−	0.0258924i
$655$	−2.80685	+	4.86162i	−0.109673	+	0.189959i
$656$	−1.26057	−	2.18337i	−0.0492169	−	0.0852462i
$657$	3.90230			0.152243
$658$	−17.9791	+	8.06526i	−0.700897	+	0.314417i
$659$	−15.5572			−0.606022			−0.303011	−	0.952987i	$-0.597992\pi$
$659$	−15.5572			−0.606022			−0.303011	+	0.952987i	$0.597992\pi$
$660$	−0.112651	−	0.195118i	−0.00438494	−	0.00759494i
$661$	5.35314	−	9.27191i	0.208213	−	0.360636i	−0.742939	−	0.669360i	$-0.766569\pi$
$661$	5.35314	−	9.27191i	0.208213	−	0.360636i	0.951152	+	0.308724i	$0.0999019\pi$
$662$	−10.3441	+	17.9164i	−0.402033	+	0.696342i
$663$	0.446936	+	0.774115i	0.0173575	+	0.0300642i
$664$	4.89229			0.189858
$665$	−8.98954	+	4.03263i	−0.348599	+	0.156379i
$666$	10.5926			0.410455
$667$	−8.51938	−	14.7560i	−0.329872	−	0.571354i
$668$	11.1659	−	19.3400i	0.432023	−	0.748285i
$669$	−1.58017	+	2.73694i	−0.0610929	+	0.105816i
$670$	−0.725302	−	1.25626i	−0.0280209	−	0.0485336i
$671$	−5.25611			−0.202910
$672$	−0.0606469	+	0.593001i	−0.00233950	+	0.0228755i
$673$	−41.0868			−1.58378			−0.791890	−	0.610664i	$-0.790903\pi$
$673$	−41.0868			−1.58378			−0.791890	+	0.610664i	$0.790903\pi$
$674$	−11.6066	−	20.1032i	−0.447069	−	0.774345i
$675$	0.670189	−	1.16080i	0.0257956	−	0.0446793i
$676$	6.11391	−	10.5896i	0.235150	−	0.407292i
$677$	−5.37255	−	9.30554i	−0.206484	−	0.357641i	0.744121	−	0.668045i	$-0.232869\pi$
$677$	−5.37255	−	9.30554i	−0.206484	−	0.357641i	−0.950605	+	0.310405i	$0.899535\pi$
$678$	4.75981			0.182799
$679$	29.3376	+	21.1896i	1.12587	+	0.813183i
$680$	4.51492			0.173139
$681$	−2.47771	−	4.29152i	−0.0949461	−	0.164451i
$682$	−2.86197	+	4.95707i	−0.109590	+	0.189816i
$683$	−6.79638	+	11.7717i	−0.260056	+	0.450430i	−0.966257	−	0.257582i	$-0.917074\pi$
$683$	−6.79638	+	11.7717i	−0.260056	+	0.450430i	0.706200	+	0.708012i	$0.250408\pi$
$684$	−5.49139	−	9.51136i	−0.209969	−	0.363676i
$685$	16.6757			0.637145
$686$	−18.0825	+	4.00277i	−0.690394	+	0.152827i
$687$	−1.40148			−0.0534699
$688$	−0.843471	−	1.46094i	−0.0321570	−	0.0556976i
$689$	3.72645	−	6.45441i	0.141967	−	0.245893i
$690$	−0.260569	+	0.451318i	−0.00991968	+	0.0171814i
$691$	−18.8438	−	32.6385i	−0.716854	−	1.24163i	−0.962240	−	0.272202i	$-0.912248\pi$
$691$	−18.8438	−	32.6385i	−0.716854	−	1.24163i	0.245386	−	0.969425i	$-0.421085\pi$
$692$	11.8539			0.450619
$693$	6.32555	+	4.56875i	0.240288	+	0.173552i
$694$	−6.02553			−0.228726
$695$	8.78536	+	15.2167i	0.333248	+	0.577202i
$696$	−0.829827	+	1.43730i	−0.0314545	+	0.0544808i
$697$	−5.69137	+	9.85773i	−0.215576	+	0.373388i
$698$	−3.71310	−	6.43127i	−0.140543	−	0.243427i
$699$	−0.475439			−0.0179828
$700$	−0.269180	+	2.63202i	−0.0101740	+	0.0994811i
$701$	−19.7357			−0.745407			−0.372703	−	0.927951i	$-0.621569\pi$
$701$	−19.7357			−0.745407			−0.372703	+	0.927951i	$0.621569\pi$
$702$	−0.588920	−	1.02004i	−0.0222274	−	0.0384989i
$703$	−6.68752	+	11.5831i	−0.252224	+	0.436866i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$	0.839012	+	1.45321i	0.0315990	+	0.0547311i
$706$	5.11892			0.192653
$707$	10.3967	−	4.66389i	0.391009	−	0.175404i
$708$	2.18555			0.0821378
$709$	1.10850	+	1.91998i	0.0416306	+	0.0721063i	0.886090	−	0.463513i	$-0.153411\pi$
$709$	1.10850	+	1.91998i	0.0416306	+	0.0721063i	−0.844459	+	0.535620i	$0.820078\pi$
$710$	−1.45109	+	2.51336i	−0.0544584	+	0.0943247i
$711$	20.4618	−	35.4409i	0.767378	−	1.32914i
$712$	4.73760	+	8.20576i	0.177549	+	0.307524i
$713$	13.2398			0.495834
$714$	2.45556	−	1.10154i	0.0918971	−	0.0412243i
$715$	−0.878738			−0.0328629
$716$	−6.71270	−	11.6267i	−0.250865	−	0.434512i
$717$	−1.16579	+	2.01921i	−0.0435373	+	0.0754088i
$718$	0.256310	−	0.443942i	0.00956540	−	0.0165678i
$719$	22.3794	+	38.7623i	0.834611	+	1.44559i	0.894347	+	0.447374i	$0.147641\pi$
$719$	22.3794	+	38.7623i	0.834611	+	1.44559i	−0.0597358	+	0.998214i	$0.519026\pi$
$720$	−2.94924			−0.109912
$721$	−4.51974	+	44.1937i	−0.168324	+	1.64586i
$722$	−5.13230			−0.191004
$723$	0.272183	+	0.471435i	0.0101226	+	0.0175329i
$724$	6.91397	−	11.9754i	0.256956	−	0.445060i
$725$	−3.68317	+	6.37943i	−0.136789	+	0.236926i
$726$	−0.112651	−	0.195118i	−0.00418088	−	0.00724149i
$727$	21.8606			0.810764			0.405382	−	0.914147i	$-0.367139\pi$
$727$	21.8606			0.810764			0.405382	+	0.914147i	$0.367139\pi$
$728$	1.88472	+	1.36128i	0.0698525	+	0.0504523i
$729$	−24.2974			−0.899904
$730$	0.661578	+	1.14589i	0.0244861	+	0.0424112i
$731$	−3.80821	+	6.59600i	−0.140852	+	0.243962i
$732$	0.592107	−	1.02556i	0.0218849	−	0.0379058i
$733$	−9.68444	−	16.7739i	−0.357703	−	0.619560i	0.629874	−	0.776698i	$-0.283107\pi$
$733$	−9.68444	−	16.7739i	−0.357703	−	0.619560i	−0.987577	+	0.157138i	$0.949773\pi$
$734$	−1.30342			−0.0481100
$735$	0.495757	+	1.49717i	0.0182863	+	0.0552240i
$736$	2.31306			0.0852604
$737$	−0.725302	−	1.25626i	−0.0267169	−	0.0462750i
$738$	3.71772	−	6.43928i	0.136851	−	0.237033i
$739$	−22.6641	+	39.2554i	−0.833712	+	1.44403i	0.0613624	+	0.998116i	$0.480455\pi$
$739$	−22.6641	+	39.2554i	−0.833712	+	1.44403i	−0.895075	+	0.445916i	$0.852878\pi$
$740$	1.79582	+	3.11045i	0.0660156	+	0.114342i
$741$	0.737271			0.0270843
$742$	−18.1909	−	13.1387i	−0.667810	−	0.482338i
$743$	8.26985			0.303391			0.151696	−	0.988427i	$-0.451527\pi$
$743$	8.26985			0.303391			0.151696	+	0.988427i	$0.451527\pi$
$744$	−0.644808	−	1.11684i	−0.0236398	−	0.0409454i
$745$	−0.986340	+	1.70839i	−0.0361367	+	0.0625906i
$746$	16.1759	−	28.0175i	0.592241	−	1.02579i
$747$	7.21427	+	12.4955i	0.263956	+	0.457186i
$748$	4.51492			0.165082
$749$	−0.974412	+	9.52773i	−0.0356042	+	0.348136i
$750$	0.225302			0.00822688
$751$	−18.9729	−	32.8620i	−0.692331	−	1.19915i	−0.971072	−	0.238787i	$-0.923250\pi$
$751$	−18.9729	−	32.8620i	−0.692331	−	1.19915i	0.278741	−	0.960366i	$-0.410083\pi$
$752$	3.72394	−	6.45005i	0.135798	−	0.235209i
$753$	0.877558	−	1.51998i	0.0319800	−	0.0553910i
$754$	3.23654	+	5.60585i	0.117868	+	0.204153i
$755$	−13.8416			−0.503746
$756$	−3.23566	+	1.45149i	−0.117680	+	0.0527901i
$757$	−27.7118			−1.00720			−0.503601	−	0.863936i	$-0.667992\pi$
$757$	−27.7118			−1.00720			−0.503601	+	0.863936i	$0.667992\pi$
$758$	16.6437	+	28.8278i	0.604528	+	1.04707i
$759$	−0.260569	+	0.451318i	−0.00945804	+	0.0163818i
$760$	1.86197	−	3.22502i	0.0675407	−	0.116984i
$761$	−11.4506	−	19.8330i	−0.415084	−	0.718947i	0.580353	−	0.814365i	$-0.302915\pi$
$761$	−11.4506	−	19.8330i	−0.415084	−	0.718947i	−0.995437	+	0.0954181i	$0.969581\pi$
$762$	2.54108			0.0920538
$763$	−8.19217	+	3.67494i	−0.296577	+	0.133042i
$764$	−15.3301			−0.554622
$765$	6.65779	+	11.5316i	0.240713	+	0.416927i
$766$	8.68773	−	15.0476i	0.313901	−	0.543692i
$767$	4.26210	−	7.38217i	0.153895	−	0.266555i
$768$	−0.112651	−	0.195118i	−0.00406495	−	0.00704070i
$769$	4.59161			0.165578			0.0827888	−	0.996567i	$-0.473617\pi$
$769$	4.59161			0.165578			0.0827888	+	0.996567i	$0.473617\pi$
$770$	−0.269180	+	2.63202i	−0.00970057	+	0.0948515i
$771$	−2.08961			−0.0752556
$772$	0.812589	+	1.40745i	0.0292457	+	0.0506551i
$773$	5.47266	−	9.47893i	0.196838	−	0.340933i	−0.750663	−	0.660685i	$-0.770266\pi$
$773$	5.47266	−	9.47893i	0.196838	−	0.340933i	0.947502	+	0.319751i	$0.103599\pi$
$774$	2.48760	−	4.30865i	0.0894149	−	0.154871i
$775$	−2.86197	−	4.95707i	−0.102805	−	0.178063i
$776$	−13.6784			−0.491027
$777$	1.73559	+	1.25356i	0.0622639	+	0.0449713i
$778$	−32.8047			−1.17611
$779$	4.69428	+	8.13073i	0.168190	+	0.291314i
$780$	0.0989909	−	0.171457i	0.00354444	−	0.00613915i
$781$	−1.45109	+	2.51336i	−0.0519240	+	0.0899351i
$782$	−5.22163	−	9.04413i	−0.186725	−	0.323418i
$783$	−9.87367			−0.352856
$784$	4.65468	−	5.22819i	0.166239	−	0.186721i
$785$	−11.0432			−0.394148
$786$	−0.632391	−	1.09533i	−0.0225566	−	0.0390693i
$787$	7.74910	−	13.4218i	0.276226	−	0.478437i	−0.694218	−	0.719765i	$-0.744250\pi$
$787$	7.74910	−	13.4218i	0.276226	−	0.478437i	0.970444	+	0.241328i	$0.0775829\pi$
$788$	6.76598	−	11.7190i	0.241028	−	0.417473i
$789$	2.98914	+	5.17734i	0.106416	+	0.184318i
$790$	13.8760			0.493686
$791$	−45.3119	−	32.7273i	−1.61110	−	1.16365i
$792$	−2.94924			−0.104797
$793$	−2.30937	−	3.99995i	−0.0820082	−	0.142042i
$794$	17.5103	−	30.3287i	0.621416	−	1.07632i
$795$	−0.955438	+	1.65487i	−0.0338859	+	0.0586921i
$796$	1.68511	+	2.91869i	0.0597271	+	0.103450i
$797$	−33.6792			−1.19298			−0.596489	−	0.802621i	$-0.703438\pi$
$797$	−33.6792			−1.19298			−0.596489	+	0.802621i	$0.703438\pi$
$798$	0.225845	−	2.20830i	0.00799483	−	0.0781729i
$799$	−33.6265			−1.18962
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−13.9723	+	24.2007i	−0.493687	+	0.855091i
$802$	9.97510	−	17.2774i	0.352233	−	0.610086i
$803$	0.661578	+	1.14589i	0.0233466	+	0.0404375i
$804$	0.326825			0.0115262
$805$	5.58369	−	2.50480i	0.196799	−	0.0882825i
$806$	−5.02984			−0.177169
$807$	−2.39675	−	4.15130i	−0.0843697	−	0.146133i
$808$	−2.15344	+	3.72986i	−0.0757576	+	0.131216i
$809$	23.4252	−	40.5737i	0.823587	−	1.42649i	−0.0794075	−	0.996842i	$-0.525303\pi$
$809$	23.4252	−	40.5737i	0.823587	−	1.42649i	0.902994	−	0.429652i	$-0.141364\pi$
$810$	−4.27286	−	7.40082i	−0.150133	−	0.260038i
$811$	3.51765			0.123521			0.0617607	−	0.998091i	$-0.480328\pi$
$811$	3.51765			0.123521			0.0617607	+	0.998091i	$0.480328\pi$
$812$	17.7822	−	7.97697i	0.624035	−	0.279937i
$813$	−2.67526			−0.0938253
$814$	1.79582	+	3.11045i	0.0629434	+	0.109021i
$815$	−5.12448	+	8.87585i	−0.179503	+	0.310908i
$816$	−0.508611	+	0.880940i	−0.0178050	+	0.0308391i
$817$	3.14103	+	5.44043i	0.109891	+	0.190337i
$818$	−3.65244			−0.127704
$819$	−0.697608	+	6.82117i	−0.0243764	+	0.238351i
$820$	2.52114			0.0880419
$821$	8.93277	+	15.4720i	0.311756	+	0.539977i	0.978743	−	0.205093i	$-0.0657496\pi$
$821$	8.93277	+	15.4720i	0.311756	+	0.539977i	−0.666987	+	0.745070i	$0.732416\pi$
$822$	−1.87854	+	3.25372i	−0.0655215	+	0.113487i
$823$	−4.58372	+	7.93924i	−0.159779	+	0.276745i	−0.934789	−	0.355204i	$-0.884411\pi$
$823$	−4.58372	+	7.93924i	−0.159779	+	0.276745i	0.775010	+	0.631949i	$0.217745\pi$
$824$	−8.39538	−	14.5412i	−0.292467	−	0.506568i
$825$	0.225302			0.00784402
$826$	−20.8057	−	15.0273i	−0.723923	−	0.522867i
$827$	15.1146			0.525587			0.262793	−	0.964852i	$-0.415356\pi$
$827$	15.1146			0.525587			0.262793	+	0.964852i	$0.415356\pi$
$828$	3.41088	+	5.90782i	0.118536	+	0.205311i
$829$	20.6362	−	35.7429i	0.716724	−	1.24140i	−0.245567	−	0.969380i	$-0.578974\pi$
$829$	20.6362	−	35.7429i	0.716724	−	1.24140i	0.962291	−	0.272023i	$-0.0876927\pi$
$830$	−2.44615	+	4.23685i	−0.0849069	+	0.147063i
$831$	−1.00387	−	1.73875i	−0.0348239	−	0.0603167i
$832$	−0.878738			−0.0304647
$833$	−30.9502	−	6.39753i	−1.07236	−	0.221661i
$834$	−3.95872			−0.137079
$835$	11.1659	+	19.3400i	0.386413	+	0.669287i
$836$	1.86197	−	3.22502i	0.0643975	−	0.111540i
$837$	3.83612	−	6.64435i	0.132596	−	0.229662i
$838$	−15.6449	−	27.0978i	−0.540445	−	0.936078i
$839$	49.7237			1.71665			0.858327	−	0.513103i	$-0.171504\pi$
$839$	49.7237			1.71665			0.858327	+	0.513103i	$0.171504\pi$
$840$	−0.483231	−	0.349022i	−0.0166730	−	0.0120424i
$841$	25.2629			0.871135
$842$	−15.1691	−	26.2737i	−0.522762	−	0.905451i
$843$	−3.11160	+	5.38944i	−0.107169	+	0.185622i
$844$	−2.49563	+	4.32256i	−0.0859032	+	0.148789i
$845$	6.11391	+	10.5896i	0.210325	+	0.364293i
$846$	21.9656			0.755191
$847$	−0.269180	+	2.63202i	−0.00924913	+	0.0904374i
$848$	8.48138			0.291252
$849$	2.54415	+	4.40659i	0.0873148	+	0.151234i
$850$	−2.25746	+	3.91003i	−0.0774302	+	0.134113i
$851$	4.15383	−	7.19465i	0.142392	−	0.246629i
$852$	−0.326934	−	0.566266i	−0.0112006	−	0.0194000i
$853$	−34.5939			−1.18447			−0.592236	−	0.805764i	$-0.701755\pi$
$853$	−34.5939			−1.18447			−0.592236	+	0.805764i	$0.701755\pi$
$854$	−12.6882	+	5.69181i	−0.434181	+	0.194770i
$855$	10.9828			0.375603
$856$	−1.80996	−	3.13495i	−0.0618633	−	0.107150i
$857$	14.1392	−	24.4898i	0.482985	−	0.836555i	−0.516824	−	0.856092i	$-0.672886\pi$
$857$	14.1392	−	24.4898i	0.482985	−	0.836555i	0.999809	+	0.0195368i	$0.00621916\pi$
$858$	0.0989909	−	0.171457i	0.00337949	−	0.00585345i
$859$	10.0593	+	17.4232i	0.343218	+	0.594470i	0.985028	−	0.172393i	$-0.0551498\pi$
$859$	10.0593	+	17.4232i	0.343218	+	0.594470i	−0.641811	+	0.766863i	$0.721816\pi$
$860$	1.68694			0.0575243
$861$	1.37119	−	0.615104i	0.0467300	−	0.0209627i
$862$	7.73307			0.263389
$863$	7.79268	+	13.4973i	0.265266	+	0.459454i	0.967633	−	0.252361i	$-0.0812069\pi$
$863$	7.79268	+	13.4973i	0.265266	+	0.459454i	−0.702367	+	0.711815i	$0.747874\pi$
$864$	0.670189	−	1.16080i	0.0228003	−	0.0394913i
$865$	−5.92697	+	10.2658i	−0.201523	+	0.349048i
$866$	9.60519	+	16.6367i	0.326398	+	0.565337i
$867$	0.762535			0.0258970
$868$	−1.54077	+	15.0655i	−0.0522971	+	0.511357i
$869$	13.8760			0.470711
$870$	−0.829827	−	1.43730i	−0.0281338	−	0.0487291i
$871$	0.637351	−	1.10392i	0.0215958	−	0.0374050i
$872$	1.69681	−	2.93897i	0.0574613	−	0.0995259i
$873$	−20.1705	−	34.9363i	−0.682667	−	1.18241i
$874$	−8.61368			−0.291362
$875$	−2.14481	−	1.54913i	−0.0725078	−	0.0523701i
$876$	−0.298110			−0.0100722
$877$	17.7368	+	30.7210i	0.598928	+	1.03737i	0.992980	+	0.118285i	$0.0377396\pi$
$877$	17.7368	+	30.7210i	0.598928	+	1.03737i	−0.394052	+	0.919088i	$0.628927\pi$
$878$	−10.4899	+	18.1691i	−0.354018	+	0.613176i
$879$	−3.58891	+	6.21617i	−0.121051	+	0.209666i
$880$	−0.500000	−	0.866025i	−0.0168550	−	0.0291937i
$881$	19.6203			0.661026			0.330513	−	0.943801i	$-0.392778\pi$
$881$	19.6203			0.661026			0.330513	+	0.943801i	$0.392778\pi$
$882$	20.2173	+	4.17900i	0.680751	+	0.140714i
$883$	30.7716			1.03555			0.517774	−	0.855517i	$-0.326761\pi$
$883$	30.7716			1.03555			0.517774	+	0.855517i	$0.326761\pi$
$884$	1.98371	+	3.43589i	0.0667195	+	0.115562i
$885$	−1.09277	+	1.89274i	−0.0367332	+	0.0636237i
$886$	18.2172	−	31.5531i	0.612018	−	1.06005i
$887$	15.5959	+	27.0129i	0.523659	+	0.907004i	0.999621	+	0.0275380i	$0.00876673\pi$
$887$	15.5959	+	27.0129i	0.523659	+	0.907004i	−0.475962	+	0.879466i	$0.657900\pi$
$888$	−0.809205			−0.0271551
$889$	−24.1903	−	17.4719i	−0.811318	−	0.585989i
$890$	−9.47519			−0.317609
$891$	−4.27286	−	7.40082i	−0.143146	−	0.247937i
$892$	−7.01355	+	12.1478i	−0.234831	+	0.406739i
$893$	−13.8677	+	24.0196i	−0.464065	+	0.803784i
$894$	−0.222225	−	0.384905i	−0.00743231	−	0.0128731i
$895$	13.4254			0.448762
$896$	−0.269180	+	2.63202i	−0.00899267	+	0.0879297i
$897$	−0.457943			−0.0152903
$898$	−5.67686	−	9.83261i	−0.189439	−	0.328118i
$899$	−21.0822	+	36.5155i	−0.703131	+	1.21786i
$900$	1.47462	−	2.55412i	0.0491540	−	0.0851372i
$901$	−19.1464	−	33.1625i	−0.637858	−	1.10480i
$902$	2.52114			0.0839447
$903$	0.917490	−	0.411578i	0.0305322	−	0.0136965i
$904$	21.1263			0.702650
$905$	6.91397	+	11.9754i	0.229828	+	0.398074i
$906$	1.55927	−	2.70073i	0.0518032	−	0.0897258i
$907$	−1.89900	+	3.28916i	−0.0630552	+	0.109215i	−0.895830	−	0.444398i	$-0.853418\pi$
$907$	−1.89900	+	3.28916i	−0.0630552	+	0.109215i	0.832774	+	0.553612i	$0.186751\pi$
$908$	−10.9973	−	19.0478i	−0.364957	−	0.632124i
$909$	−12.7020			−0.421298
$910$	−2.12126	+	0.951580i	−0.0703192	+	0.0315446i
$911$	39.5498			1.31034			0.655172	−	0.755480i	$-0.272596\pi$
$911$	39.5498			1.31034			0.655172	+	0.755480i	$0.272596\pi$
$912$	0.419506	+	0.726606i	0.0138912	+	0.0240603i
$913$	−2.44615	+	4.23685i	−0.0809556	+	0.140219i
$914$	9.48186	−	16.4231i	0.313632	−	0.543227i
$915$	0.592107	+	1.02556i	0.0195745	+	0.0339040i
$916$	−6.22045			−0.205530
$917$	−1.51110	+	14.7754i	−0.0499008	+	0.487927i
$918$	−6.05170			−0.199736
$919$	27.5124	+	47.6529i	0.907551	+	1.57192i	0.817457	+	0.575990i	$0.195383\pi$
$919$	27.5124	+	47.6529i	0.907551	+	1.57192i	0.0900940	+	0.995933i	$0.471283\pi$
$920$	−1.15653	+	2.00317i	−0.0381296	+	0.0660424i
$921$	2.28052	−	3.94998i	0.0751458	−	0.130156i
$922$	6.94903	+	12.0361i	0.228854	+	0.396387i
$923$	−2.55025			−0.0839426
$924$	−0.483231	−	0.349022i	−0.0158971	−	0.0114820i
$925$	−3.59164			−0.118092
$926$	1.76190	+	3.05171i	0.0578997	+	0.100285i
$927$	24.7600	−	42.8856i	0.813225	−	1.40855i
$928$	−3.68317	+	6.37943i	−0.120906	+	0.209415i
$929$	3.33039	+	5.76840i	0.109266	+	0.189255i	0.915473	−	0.402379i	$-0.131817\pi$
$929$	3.33039	+	5.76840i	0.109266	+	0.189255i	−0.806207	+	0.591634i	$0.798483\pi$
$930$	1.28962			0.0422882
$931$	−17.3337	+	19.4694i	−0.568090	+	0.638085i
$932$	−2.11023			−0.0691228
$933$	1.01443	+	1.75705i	0.0332110	+	0.0575231i
$934$	4.20109	−	7.27650i	0.137464	−	0.238094i
$935$	−2.25746	+	3.91003i	−0.0738268	+	0.127872i
$936$	−1.29580	−	2.24440i	−0.0423547	−	0.0733604i
$937$	12.1805			0.397921			0.198961	−	0.980008i	$-0.436243\pi$
$937$	12.1805			0.397921			0.198961	+	0.980008i	$0.436243\pi$
$938$	−3.11127	−	2.24717i	−0.101587	−	0.0733728i
$939$	−0.841069			−0.0274472
$940$	3.72394	+	6.45005i	0.121461	+	0.210377i
$941$	−16.7540	+	29.0188i	−0.546165	+	0.945986i	0.452367	+	0.891832i	$0.350580\pi$
$941$	−16.7540	+	29.0188i	−0.546165	+	0.945986i	−0.998533	+	0.0541543i	$0.982754\pi$
$942$	1.24403	−	2.15472i	0.0405326	−	0.0702045i
$943$	−2.91577	−	5.05026i	−0.0949505	−	0.164459i
$944$	9.70050			0.315724
$945$	0.360803	−	3.52790i	0.0117369	−	0.114763i
$946$	1.68694			0.0548472
$947$	9.34649	+	16.1886i	0.303720	+	0.526059i	0.976976	−	0.213351i	$-0.0684379\pi$
$947$	9.34649	+	16.1886i	0.303720	+	0.526059i	−0.673255	+	0.739410i	$0.735105\pi$
$948$	−1.56315	+	2.70745i	−0.0507687	+	0.0879340i
$949$	−0.581353	+	1.00693i	−0.0188715	+	0.0326864i
$950$	1.86197	+	3.22502i	0.0604102	+	0.104634i
$951$	0.878555			0.0284891
$952$	10.8990	−	4.88918i	0.353237	−	0.158459i
$953$	−15.5008			−0.502119			−0.251059	−	0.967972i	$-0.580779\pi$
$953$	−15.5008			−0.502119			−0.251059	+	0.967972i	$0.580779\pi$
$954$	12.5068	+	21.6624i	0.404923	+	0.701347i
$955$	7.66503	−	13.2762i	0.248035	−	0.429609i
$956$	−5.17434	+	8.96222i	−0.167350	+	0.289859i
$957$	−0.829827	−	1.43730i	−0.0268245	−	0.0464614i
$958$	6.64355			0.214643
$959$	40.2549	−	18.0580i	1.29990	−	0.583124i
$960$	0.225302			0.00727160
$961$	−0.881724	−	1.52719i	−0.0284427	−	0.0492642i
$962$	−1.57805	+	2.73327i	−0.0508785	+	0.0881242i
$963$	5.33802	−	9.24571i	0.172015	−	0.297939i
$964$	1.20808	+	2.09246i	0.0389096	+	0.0673935i
$965$	−1.62518			−0.0523163
$966$	−0.140280	+	1.37165i	−0.00451343	+	0.0441320i
$967$	−5.34574			−0.171907			−0.0859537	−	0.996299i	$-0.527394\pi$
$967$	−5.34574			−0.171907			−0.0859537	+	0.996299i	$0.527394\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$	1.89404	−	3.28057i	0.0608452	−	0.105387i
$970$	6.83921	−	11.8459i	0.219594	−	0.380348i
$971$	−21.2637	−	36.8298i	−0.682384	−	1.18192i	−0.974251	−	0.225465i	$-0.927610\pi$
$971$	−21.2637	−	36.8298i	−0.682384	−	1.18192i	0.291867	−	0.956459i	$-0.405723\pi$
$972$	5.94651			0.190734
$973$	37.6858	+	27.2193i	1.20815	+	0.872610i
$974$	28.4901			0.912881
$975$	0.0989909	+	0.171457i	0.00317024	+	0.00549103i
$976$	2.62805	−	4.55192i	0.0841220	−	0.145704i
$977$	26.5500	−	45.9860i	0.849410	−	1.47122i	−0.0323256	−	0.999477i	$-0.510291\pi$
$977$	26.5500	−	45.9860i	0.849410	−	1.47122i	0.881736	−	0.471744i	$-0.156375\pi$
$978$	−1.15456	−	1.99975i	−0.0369187	−	0.0639450i
$979$	−9.47519			−0.302828
$980$	2.20041	+	6.64516i	0.0702894	+	0.212272i
$981$	10.0086			0.319550
$982$	−14.9536	−	25.9004i	−0.477188	−	0.826514i
$983$	13.9363	−	24.1383i	0.444498	−	0.769893i	−0.553519	−	0.832836i	$-0.686716\pi$
$983$	13.9363	−	24.1383i	0.444498	−	0.769893i	0.998017	+	0.0629437i	$0.0200488\pi$
$984$	−0.284009	+	0.491918i	−0.00905388	+	0.0156818i
$985$	6.76598	+	11.7190i	0.215582	+	0.373399i
$986$	33.2584			1.05916
$987$	3.59904	+	2.59947i	0.114559	+	0.0827421i
$988$	3.27236			0.104108
$989$	−1.95100	−	3.37923i	−0.0620381	−	0.107453i
$990$	1.47462	−	2.55412i	0.0468665	−	0.0811751i
$991$	12.7418	−	22.0694i	0.404755	−	0.701056i	−0.589538	−	0.807741i	$-0.700690\pi$
$991$	12.7418	−	22.0694i	0.404755	−	0.701056i	0.994293	+	0.106684i	$0.0340234\pi$
$992$	−2.86197	−	4.95707i	−0.0908676	−	0.157387i
$993$	4.66109			0.147915
$994$	−0.781208	+	7.63860i	−0.0247784	+	0.242282i
$995$	−3.37022			−0.106843
$996$	−0.551123	−	0.954572i	−0.0174630	−	0.0302468i
$997$	23.0197	−	39.8714i	0.729042	−	1.26274i	−0.228246	−	0.973604i	$-0.573299\pi$
$997$	23.0197	−	39.8714i	0.729042	−	1.26274i	0.957288	−	0.289135i	$-0.0933677\pi$
$998$	−12.3654	+	21.4174i	−0.391419	+	0.677957i
$999$	−2.40708	−	4.16918i	−0.0761565	−	0.131907i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.i.m.221.3	✓	10
7.2	even	3	inner	770.2.i.m.331.3	yes	10
7.3	odd	6		5390.2.a.ch.1.3		5
7.4	even	3		5390.2.a.ci.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.i.m.221.3	✓	10	1.1	even	1	trivial
770.2.i.m.331.3	yes	10	7.2	even	3	inner
5390.2.a.ch.1.3		5	7.3	odd	6
5390.2.a.ci.1.3		5	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.112651 + 0.195118i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.225302 q^{6} +(-2.14481 - 1.54913i) q^{7} +1.00000 q^{8} +(1.47462 + 2.55412i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.112651 + 0.195118i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.225302 q^{6} +(-2.14481 - 1.54913i) q^{7} +1.00000 q^{8} +(1.47462 + 2.55412i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.112651 - 0.195118i) q^{12} -0.878738 q^{13} +(-0.269180 + 2.63202i) q^{14} +0.225302 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.25746 + 3.91003i) q^{17} +(1.47462 - 2.55412i) q^{18} +(1.86197 + 3.22502i) q^{19} +1.00000 q^{20} +(0.543877 - 0.243979i) q^{21} +1.00000 q^{22} +(-1.15653 - 2.00317i) q^{23} +(-0.112651 + 0.195118i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.439369 + 0.761009i) q^{26} -1.34038 q^{27} +(2.41399 - 1.08289i) q^{28} +7.36634 q^{29} +(-0.112651 - 0.195118i) q^{30} +(-2.86197 + 4.95707i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.112651 - 0.195118i) q^{33} +4.51492 q^{34} +(-0.269180 + 2.63202i) q^{35} -2.94924 q^{36} +(1.79582 + 3.11045i) q^{37} +(1.86197 - 3.22502i) q^{38} +(0.0989909 - 0.171457i) q^{39} +(-0.500000 - 0.866025i) q^{40} +2.52114 q^{41} +(-0.483231 - 0.349022i) q^{42} +1.68694 q^{43} +(-0.500000 - 0.866025i) q^{44} +(1.47462 - 2.55412i) q^{45} +(-1.15653 + 2.00317i) q^{46} +(3.72394 + 6.45005i) q^{47} +0.225302 q^{48} +(2.20041 + 6.64516i) q^{49} +1.00000 q^{50} +(-0.508611 - 0.880940i) q^{51} +(0.439369 - 0.761009i) q^{52} +(-4.24069 + 7.34509i) q^{53} +(0.670189 + 1.16080i) q^{54} +1.00000 q^{55} +(-2.14481 - 1.54913i) q^{56} -0.839012 q^{57} +(-3.68317 - 6.37943i) q^{58} +(-4.85025 + 8.40088i) q^{59} +(-0.112651 + 0.195118i) q^{60} +(2.62805 + 4.55192i) q^{61} +5.72394 q^{62} +(0.793876 - 7.76246i) q^{63} +1.00000 q^{64} +(0.439369 + 0.761009i) q^{65} +(-0.112651 + 0.195118i) q^{66} +(-0.725302 + 1.25626i) q^{67} +(-2.25746 - 3.91003i) q^{68} +0.521137 q^{69} +(2.41399 - 1.08289i) q^{70} +2.90218 q^{71} +(1.47462 + 2.55412i) q^{72} +(0.661578 - 1.14589i) q^{73} +(1.79582 - 3.11045i) q^{74} +(-0.112651 - 0.195118i) q^{75} -3.72394 q^{76} +(2.41399 - 1.08289i) q^{77} -0.197982 q^{78} +(-6.93800 - 12.0170i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.27286 + 7.40082i) q^{81} +(-1.26057 - 2.18337i) q^{82} +4.89229 q^{83} +(-0.0606469 + 0.593001i) q^{84} +4.51492 q^{85} +(-0.843471 - 1.46094i) q^{86} +(-0.829827 + 1.43730i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(4.73760 + 8.20576i) q^{89} -2.94924 q^{90} +(1.88472 + 1.36128i) q^{91} +2.31306 q^{92} +(-0.644808 - 1.11684i) q^{93} +(3.72394 - 6.45005i) q^{94} +(1.86197 - 3.22502i) q^{95} +(-0.112651 - 0.195118i) q^{96} -13.6784 q^{97} +(4.65468 - 5.22819i) q^{98} -2.94924 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 5 q^{4} - 5 q^{5} + 10 q^{8} - 9 q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 - 5 * q^4 - 5 * q^5 + 10 * q^8 - 9 * q^9	\( 10 q - 5 q^{2} - 5 q^{4} - 5 q^{5} + 10 q^{8} - 9 q^{9} - 5 q^{10} - 5 q^{11} - 2 q^{13} + 3 q^{14} - 5 q^{16} - 9 q^{18} - 4 q^{19} + 10 q^{20} + 2 q^{21} + 10 q^{22} - 7 q^{23} - 5 q^{25} + q^{26} - 18 q^{27} - 3 q^{28} + 8 q^{29} - 6 q^{31} - 5 q^{32} + 3 q^{35} + 18 q^{36} - 16 q^{37} - 4 q^{38} - 7 q^{39} - 5 q^{40} - 2 q^{41} + 11 q^{42} + 26 q^{43} - 5 q^{44} - 9 q^{45} - 7 q^{46} - 8 q^{47} + 14 q^{49} + 10 q^{50} - 13 q^{51} + q^{52} - 4 q^{53} + 9 q^{54} + 10 q^{55} + 30 q^{57} - 4 q^{58} - 9 q^{59} - 2 q^{61} + 12 q^{62} + 25 q^{63} + 10 q^{64} + q^{65} - 5 q^{67} - 22 q^{69} - 3 q^{70} + 56 q^{71} - 9 q^{72} + q^{73} - 16 q^{74} + 8 q^{76} - 3 q^{77} + 14 q^{78} - 23 q^{79} - 5 q^{80} + 7 q^{81} + q^{82} - 46 q^{83} - 13 q^{84} - 13 q^{86} - 15 q^{87} - 5 q^{88} + 9 q^{89} + 18 q^{90} + 29 q^{91} + 14 q^{92} + 15 q^{93} - 8 q^{94} - 4 q^{95} - 26 q^{97} - 19 q^{98} + 18 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 5 * q^4 - 5 * q^5 + 10 * q^8 - 9 * q^9 - 5 * q^10 - 5 * q^11 - 2 * q^13 + 3 * q^14 - 5 * q^16 - 9 * q^18 - 4 * q^19 + 10 * q^20 + 2 * q^21 + 10 * q^22 - 7 * q^23 - 5 * q^25 + q^26 - 18 * q^27 - 3 * q^28 + 8 * q^29 - 6 * q^31 - 5 * q^32 + 3 * q^35 + 18 * q^36 - 16 * q^37 - 4 * q^38 - 7 * q^39 - 5 * q^40 - 2 * q^41 + 11 * q^42 + 26 * q^43 - 5 * q^44 - 9 * q^45 - 7 * q^46 - 8 * q^47 + 14 * q^49 + 10 * q^50 - 13 * q^51 + q^52 - 4 * q^53 + 9 * q^54 + 10 * q^55 + 30 * q^57 - 4 * q^58 - 9 * q^59 - 2 * q^61 + 12 * q^62 + 25 * q^63 + 10 * q^64 + q^65 - 5 * q^67 - 22 * q^69 - 3 * q^70 + 56 * q^71 - 9 * q^72 + q^73 - 16 * q^74 + 8 * q^76 - 3 * q^77 + 14 * q^78 - 23 * q^79 - 5 * q^80 + 7 * q^81 + q^82 - 46 * q^83 - 13 * q^84 - 13 * q^86 - 15 * q^87 - 5 * q^88 + 9 * q^89 + 18 * q^90 + 29 * q^91 + 14 * q^92 + 15 * q^93 - 8 * q^94 - 4 * q^95 - 26 * q^97 - 19 * q^98 + 18 * q^99

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