LMFDB - Embedded newform 1274.2.o.e.569.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1274,2,Mod(459,1274)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1274, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("1274.459");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.o (of order $6$, degree $2$, not 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:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			569.1
Root			$0.500000 + 1.73154i$ of defining polynomial
Character	$\chi$	$=$	1274.569
Dual form			1274.2.o.e.459.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.432757 + 0.749558i) q^{3} -1.00000 q^{4} +(3.21409 + 1.85566i) q^{5} +(0.749558 + 0.432757i) q^{6} +1.00000i q^{8} +(1.12544 + 1.94932i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.432757 + 0.749558i) q^{3} -1.00000 q^{4} +(3.21409 + 1.85566i) q^{5} +(0.749558 + 0.432757i) q^{6} +1.00000i q^{8} +(1.12544 + 1.94932i) q^{9} +(1.85566 - 3.21409i) q^{10} +(5.00118 + 2.88743i) q^{11} +(0.432757 - 0.749558i) q^{12} +(-2.87757 - 2.17246i) q^{13} +(-2.78184 + 1.60610i) q^{15} +1.00000 q^{16} -0.212197 q^{17} +(1.94932 - 1.12544i) q^{18} +(1.85081 - 1.06857i) q^{19} +(-3.21409 - 1.85566i) q^{20} +(2.88743 - 5.00118i) q^{22} -2.47940 q^{23} +(-0.749558 - 0.432757i) q^{24} +(4.38692 + 7.59837i) q^{25} +(-2.17246 + 2.87757i) q^{26} -4.54472 q^{27} +(0.0492830 + 0.0853606i) q^{29} +(1.60610 + 2.78184i) q^{30} +(2.00118 - 1.15538i) q^{31} -1.00000i q^{32} +(-4.32860 + 2.49912i) q^{33} +0.212197i q^{34} +(-1.12544 - 1.94932i) q^{36} +7.87343i q^{37} +(-1.06857 - 1.85081i) q^{38} +(2.87367 - 1.21676i) q^{39} +(-1.85566 + 3.21409i) q^{40} +(-6.51354 + 3.76060i) q^{41} +(2.28987 - 3.96617i) q^{43} +(-5.00118 - 2.88743i) q^{44} +8.35373i q^{45} +2.47940i q^{46} +(-7.92907 - 4.57785i) q^{47} +(-0.432757 + 0.749558i) q^{48} +(7.59837 - 4.38692i) q^{50} +(0.0918298 - 0.159054i) q^{51} +(2.87757 + 2.17246i) q^{52} +(-6.04740 - 10.4744i) q^{53} +4.54472i q^{54} +(10.7162 + 18.5609i) q^{55} +1.84972i q^{57} +(0.0853606 - 0.0492830i) q^{58} -0.231914i q^{59} +(2.78184 - 1.60610i) q^{60} +(4.01605 + 6.95601i) q^{61} +(-1.15538 - 2.00118i) q^{62} -1.00000 q^{64} +(-5.21745 - 12.3223i) q^{65} +(2.49912 + 4.32860i) q^{66} +(11.2323 + 6.48500i) q^{67} +0.212197 q^{68} +(1.07298 - 1.85845i) q^{69} +(6.37721 + 3.68188i) q^{71} +(-1.94932 + 1.12544i) q^{72} +(4.85333 - 2.80207i) q^{73} +7.87343 q^{74} -7.59389 q^{75} +(-1.85081 + 1.06857i) q^{76} +(-1.21676 - 2.87367i) q^{78} +(4.59875 - 7.96526i) q^{79} +(3.21409 + 1.85566i) q^{80} +(-1.40956 + 2.44144i) q^{81} +(3.76060 + 6.51354i) q^{82} +3.17186i q^{83} +(-0.682021 - 0.393765i) q^{85} +(-3.96617 - 2.28987i) q^{86} -0.0853103 q^{87} +(-2.88743 + 5.00118i) q^{88} +11.8167i q^{89} +8.35373 q^{90} +2.47940 q^{92} +2.00000i q^{93} +(-4.57785 + 7.92907i) q^{94} +7.93158 q^{95} +(0.749558 + 0.432757i) q^{96} +(-12.1952 - 7.04093i) q^{97} +12.9985i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} - 12 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q + 2 * q^3 - 12 * q^4 - 6 * q^6 - 6 * q^9	$ 12 q + 2 q^{3} - 12 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} + 18 q^{11} - 2 q^{12} + 8 q^{13} - 6 q^{15} + 12 q^{16} + 8 q^{17} + 12 q^{19} - 2 q^{22} + 12 q^{23} + 6 q^{24} + 12 q^{25} + 2 q^{26} - 40 q^{27} - 10 q^{29} + 14 q^{30} - 18 q^{31} + 12 q^{33} + 6 q^{36} + 4 q^{38} + 24 q^{39} - 2 q^{40} + 24 q^{41} + 26 q^{43} - 18 q^{44} - 48 q^{47} + 2 q^{48} - 12 q^{50} + 18 q^{51} - 8 q^{52} - 18 q^{53} + 6 q^{55} - 24 q^{58} + 6 q^{60} + 28 q^{61} + 2 q^{62} - 12 q^{64} - 4 q^{65} + 42 q^{67} - 8 q^{68} - 32 q^{69} + 48 q^{71} + 48 q^{73} - 96 q^{75} - 12 q^{76} - 8 q^{78} - 22 q^{79} - 34 q^{81} - 6 q^{82} + 54 q^{85} + 6 q^{86} + 4 q^{87} + 2 q^{88} - 12 q^{90} - 12 q^{92} - 8 q^{94} - 64 q^{95} - 6 q^{96} - 60 q^{97}+O(q^{100}) $ 12 * q + 2 * q^3 - 12 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 + 18 * q^11 - 2 * q^12 + 8 * q^13 - 6 * q^15 + 12 * q^16 + 8 * q^17 + 12 * q^19 - 2 * q^22 + 12 * q^23 + 6 * q^24 + 12 * q^25 + 2 * q^26 - 40 * q^27 - 10 * q^29 + 14 * q^30 - 18 * q^31 + 12 * q^33 + 6 * q^36 + 4 * q^38 + 24 * q^39 - 2 * q^40 + 24 * q^41 + 26 * q^43 - 18 * q^44 - 48 * q^47 + 2 * q^48 - 12 * q^50 + 18 * q^51 - 8 * q^52 - 18 * q^53 + 6 * q^55 - 24 * q^58 + 6 * q^60 + 28 * q^61 + 2 * q^62 - 12 * q^64 - 4 * q^65 + 42 * q^67 - 8 * q^68 - 32 * q^69 + 48 * q^71 + 48 * q^73 - 96 * q^75 - 12 * q^76 - 8 * q^78 - 22 * q^79 - 34 * q^81 - 6 * q^82 + 54 * q^85 + 6 * q^86 + 4 * q^87 + 2 * q^88 - 12 * q^90 - 12 * q^92 - 8 * q^94 - 64 * q^95 - 6 * q^96 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.432757	+	0.749558i	−0.249853	+	0.432757i	−0.963485	−	0.267763i	$-0.913716\pi$
$3$	−0.432757	+	0.749558i	−0.249853	+	0.432757i	0.713632	+	0.700521i	$0.247049\pi$
$4$	−1.00000			−0.500000
$5$	3.21409	+	1.85566i	1.43739	+	0.829875i	0.997667	−	0.0682612i	$-0.0217451\pi$
$5$	3.21409	+	1.85566i	1.43739	+	0.829875i	0.439718	+	0.898136i	$0.355078\pi$
$6$	0.749558	+	0.432757i	0.306006	+	0.176673i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	1.12544	+	1.94932i	0.375147	+	0.649774i
$10$	1.85566	−	3.21409i	0.586810	−	1.01638i
$11$	5.00118	+	2.88743i	1.50791	+	0.870594i	0.999958	+	0.00920984i	$0.00293162\pi$
$11$	5.00118	+	2.88743i	1.50791	+	0.870594i	0.507955	+	0.861384i	$0.330402\pi$
$12$	0.432757	−	0.749558i	0.124926	−	0.216379i
$13$	−2.87757	−	2.17246i	−0.798095	−	0.602531i
$13$	−2.87757	−	2.17246i	−0.798095	−	0.602531i
$14$		0			0
$15$	−2.78184	+	1.60610i	−0.718269	+	0.414693i
$16$	1.00000			0.250000
$17$	−0.212197			−0.0514653			−0.0257327	−	0.999669i	$-0.508192\pi$
$17$	−0.212197			−0.0514653			−0.0257327	+	0.999669i	$0.508192\pi$
$18$	1.94932	−	1.12544i	0.459460	−	0.265269i
$19$	1.85081	−	1.06857i	0.424606	−	0.245146i	−0.272440	−	0.962173i	$-0.587831\pi$
$19$	1.85081	−	1.06857i	0.424606	−	0.245146i	0.697046	+	0.717026i	$0.254497\pi$
$20$	−3.21409	−	1.85566i	−0.718693	−	0.414937i
$21$		0			0
$22$	2.88743	−	5.00118i	0.615603	−	1.06626i
$23$	−2.47940			−0.516990			−0.258495	−	0.966013i	$-0.583227\pi$
$23$	−2.47940			−0.516990			−0.258495	+	0.966013i	$0.583227\pi$
$24$	−0.749558	−	0.432757i	−0.153003	−	0.0883363i
$25$	4.38692	+	7.59837i	0.877384	+	1.51967i
$26$	−2.17246	+	2.87757i	−0.426054	+	0.564339i
$27$	−4.54472			−0.874632
$28$		0			0
$29$	0.0492830	+	0.0853606i	0.00915162	+	0.0158511i	0.870565	−	0.492054i	$-0.163754\pi$
$29$	0.0492830	+	0.0853606i	0.00915162	+	0.0158511i	−0.861413	+	0.507905i	$0.830420\pi$
$30$	1.60610	+	2.78184i	0.293232	+	0.507893i
$31$	2.00118	−	1.15538i	0.359422	−	0.207513i	−0.309405	−	0.950930i	$-0.600130\pi$
$31$	2.00118	−	1.15538i	0.359422	−	0.207513i	0.668827	+	0.743418i	$0.266797\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−4.32860	+	2.49912i	−0.753512	+	0.435040i
$34$			0.212197i			0.0363915i
$35$		0			0
$36$	−1.12544	−	1.94932i	−0.187574	−	0.324887i
$37$			7.87343i			1.29438i	0.762327	+	0.647192i	$0.224057\pi$
$37$			7.87343i			1.29438i	−0.762327	+	0.647192i	$0.775943\pi$
$38$	−1.06857	−	1.85081i	−0.173345	−	0.300242i
$39$	2.87367	−	1.21676i	0.460156	−	0.194838i
$40$	−1.85566	+	3.21409i	−0.293405	+	0.508192i
$41$	−6.51354	+	3.76060i	−1.01724	+	0.587306i	−0.913305	−	0.407277i	$-0.866478\pi$
$41$	−6.51354	+	3.76060i	−1.01724	+	0.587306i	−0.103940	+	0.994584i	$0.533145\pi$
$42$		0			0
$43$	2.28987	−	3.96617i	0.349201	−	0.604835i	−0.636906	−	0.770941i	$-0.719786\pi$
$43$	2.28987	−	3.96617i	0.349201	−	0.604835i	0.986108	+	0.166107i	$0.0531196\pi$
$44$	−5.00118	−	2.88743i	−0.753956	−	0.435297i
$45$			8.35373i			1.24530i
$46$			2.47940i			0.365567i
$47$	−7.92907	−	4.57785i	−1.15657	−	0.667748i	−0.206093	−	0.978532i	$-0.566075\pi$
$47$	−7.92907	−	4.57785i	−1.15657	−	0.667748i	−0.950480	+	0.310785i	$0.899408\pi$
$48$	−0.432757	+	0.749558i	−0.0624632	+	0.108189i
$49$		0			0
$50$	7.59837	−	4.38692i	1.07457	−	0.620404i
$51$	0.0918298	−	0.159054i	0.0128587	−	0.0222720i
$52$	2.87757	+	2.17246i	0.399048	+	0.301266i
$53$	−6.04740	−	10.4744i	−0.830674	−	1.43877i	−0.897504	−	0.441005i	$-0.854622\pi$
$53$	−6.04740	−	10.4744i	−0.830674	−	1.43877i	0.0668303	−	0.997764i	$-0.478711\pi$
$54$			4.54472i			0.618458i
$55$	10.7162	+	18.5609i	1.44497	+	2.50276i
$56$		0			0
$57$			1.84972i			0.245002i
$58$	0.0853606	−	0.0492830i	0.0112084	−	0.00647117i
$59$		−	0.231914i		−	0.0301926i	−0.999886	−	0.0150963i	$-0.995195\pi$
$59$		−	0.231914i		−	0.0301926i	0.999886	−	0.0150963i	$-0.00480549\pi$
$60$	2.78184	−	1.60610i	0.359135	−	0.207346i
$61$	4.01605	+	6.95601i	0.514203	+	0.890626i	0.999864	+	0.0164787i	$0.00524558\pi$
$61$	4.01605	+	6.95601i	0.514203	+	0.890626i	−0.485661	+	0.874147i	$0.661421\pi$
$62$	−1.15538	−	2.00118i	−0.146734	−	0.254150i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−5.21745	−	12.3223i	−0.647145	−	1.52839i
$66$	2.49912	+	4.32860i	0.307620	+	0.532813i
$67$	11.2323	+	6.48500i	1.37225	+	0.792269i	0.991211	−	0.132291i	$-0.0422332\pi$
$67$	11.2323	+	6.48500i	1.37225	+	0.792269i	0.381039	+	0.924559i	$0.375567\pi$
$68$	0.212197			0.0257327
$69$	1.07298	−	1.85845i	0.129171	−	0.223731i
$70$		0			0
$71$	6.37721	+	3.68188i	0.756836	+	0.436959i	0.828158	−	0.560494i	$-0.189389\pi$
$71$	6.37721	+	3.68188i	0.756836	+	0.436959i	−0.0713229	+	0.997453i	$0.522722\pi$
$72$	−1.94932	+	1.12544i	−0.229730	+	0.132635i
$73$	4.85333	−	2.80207i	0.568039	−	0.327958i	−0.188327	−	0.982106i	$-0.560306\pi$
$73$	4.85333	−	2.80207i	0.568039	−	0.327958i	0.756366	+	0.654149i	$0.226973\pi$
$74$	7.87343			0.915268
$75$	−7.59389			−0.876867
$76$	−1.85081	+	1.06857i	−0.212303	+	0.122573i
$77$		0			0
$78$	−1.21676	−	2.87367i	−0.137771	−	0.325380i
$79$	4.59875	−	7.96526i	0.517399	−	0.896162i	−0.482397	−	0.875953i	$-0.660234\pi$
$79$	4.59875	−	7.96526i	0.517399	−	0.896162i	0.999796	−	0.0202088i	$-0.00643311\pi$
$80$	3.21409	+	1.85566i	0.359346	+	0.207469i
$81$	−1.40956	+	2.44144i	−0.156618	+	0.271271i
$82$	3.76060	+	6.51354i	0.415288	+	0.719301i
$83$			3.17186i			0.348157i	0.984732	+	0.174078i	$0.0556946\pi$
$83$			3.17186i			0.348157i	−0.984732	+	0.174078i	$0.944305\pi$
$84$		0			0
$85$	−0.682021	−	0.393765i	−0.0739755	−	0.0427098i
$86$	−3.96617	−	2.28987i	−0.427683	−	0.246923i
$87$	−0.0853103			−0.00914623
$88$	−2.88743	+	5.00118i	−0.307801	+	0.533128i
$89$			11.8167i			1.25256i	0.779597	+	0.626282i	$0.215424\pi$
$89$			11.8167i			1.25256i	−0.779597	+	0.626282i	$0.784576\pi$
$90$	8.35373			0.880561
$91$		0			0
$92$	2.47940			0.258495
$93$			2.00000i			0.207390i
$94$	−4.57785	+	7.92907i	−0.472169	+	0.817821i
$95$	7.93158			0.813763
$96$	0.749558	+	0.432757i	0.0765014	+	0.0441681i
$97$	−12.1952	−	7.04093i	−1.23824	−	0.714898i	−0.269506	−	0.962999i	$-0.586860\pi$
$97$	−12.1952	−	7.04093i	−1.23824	−	0.714898i	−0.968734	+	0.248101i	$0.920194\pi$
$98$		0			0
$99$			12.9985i			1.30640i
$100$	−4.38692	−	7.59837i	−0.438692	−	0.759837i
$101$	3.07622	−	5.32816i	0.306095	−	0.530172i	−0.671410	−	0.741087i	$-0.734311\pi$
$101$	3.07622	−	5.32816i	0.306095	−	0.530172i	0.977505	+	0.210914i	$0.0676441\pi$
$102$	−0.159054	−	0.0918298i	−0.0157487	−	0.00909251i
$103$	9.67453	−	16.7568i	0.953260	−	1.65109i	0.214959	−	0.976623i	$-0.431038\pi$
$103$	9.67453	−	16.7568i	0.953260	−	1.65109i	0.738301	−	0.674471i	$-0.235628\pi$
$104$	2.17246	−	2.87757i	0.213027	−	0.282169i
$105$		0			0
$106$	−10.4744	+	6.04740i	−1.01736	+	0.587375i
$107$	11.6501			1.12626			0.563130	−	0.826368i	$-0.309597\pi$
$107$	11.6501			1.12626			0.563130	+	0.826368i	$0.309597\pi$
$108$	4.54472			0.437316
$109$	4.96499	−	2.86654i	0.475559	−	0.274564i	−0.243005	−	0.970025i	$-0.578133\pi$
$109$	4.96499	−	2.86654i	0.475559	−	0.274564i	0.718564	+	0.695461i	$0.244800\pi$
$110$	18.5609	−	10.7162i	1.76972	−	1.02175i
$111$	−5.90159	−	3.40729i	−0.560154	−	0.323405i
$112$		0			0
$113$	−8.25971	+	14.3062i	−0.777008	+	1.34582i	0.156650	+	0.987654i	$0.449930\pi$
$113$	−8.25971	+	14.3062i	−0.777008	+	1.34582i	−0.933659	+	0.358164i	$0.883403\pi$
$114$	1.84972			0.173243
$115$	−7.96901	−	4.60091i	−0.743114	−	0.429037i
$116$	−0.0492830	−	0.0853606i	−0.00457581	−	0.00792554i
$117$	0.996277	−	8.05429i	0.0921059	−	0.744620i
$118$	−0.231914			−0.0213494
$119$		0			0
$120$	−1.60610	−	2.78184i	−0.146616	−	0.253946i
$121$	11.1745	+	19.3549i	1.01587	+	1.75953i
$122$	6.95601	−	4.01605i	0.629768	−	0.363597i
$123$		−	6.50970i		−	0.586960i
$124$	−2.00118	+	1.15538i	−0.179711	+	0.103756i
$125$			14.0059i			1.25273i
$126$		0			0
$127$	−5.89420	−	10.2090i	−0.523025	−	0.905907i	−0.999641	−	0.0267947i	$-0.991470\pi$
$127$	−5.89420	−	10.2090i	−0.523025	−	0.905907i	0.476616	−	0.879112i	$-0.341863\pi$
$128$			1.00000i			0.0883883i
$129$	1.98191	+	3.43278i	0.174498	+	0.302239i
$130$	−12.3223	+	5.21745i	−1.08073	+	0.457601i
$131$	−2.56429	+	4.44149i	−0.224043	+	0.388055i	−0.956032	−	0.293262i	$-0.905259\pi$
$131$	−2.56429	+	4.44149i	−0.224043	+	0.388055i	0.731989	+	0.681317i	$0.238592\pi$
$132$	4.32860	−	2.49912i	0.376756	−	0.217520i
$133$		0			0
$134$	6.48500	−	11.2323i	0.560219	−	0.970327i
$135$	−14.6071	−	8.43344i	−1.25718	−	0.725835i
$136$		−	0.212197i		−	0.0181957i
$137$			9.39328i			0.802522i	0.915964	+	0.401261i	$0.131428\pi$
$137$			9.39328i			0.802522i	−0.915964	+	0.401261i	$0.868572\pi$
$138$	−1.85845	−	1.07298i	−0.158202	−	0.0913380i
$139$	7.57063	−	13.1127i	0.642133	−	1.11221i	−0.342823	−	0.939400i	$-0.611383\pi$
$139$	7.57063	−	13.1127i	0.642133	−	1.11221i	0.984956	−	0.172806i	$-0.0552835\pi$
$140$		0			0
$141$	6.86273	−	3.96220i	0.577946	−	0.333677i
$142$	3.68188	−	6.37721i	0.308977	−	0.535164i
$143$	−8.11844	−	19.1736i	−0.678898	−	1.60338i
$144$	1.12544	+	1.94932i	0.0937868	+	0.162444i
$145$			0.365809i			0.0303788i
$146$	−2.80207	−	4.85333i	−0.231901	−	0.401664i
$147$		0			0
$148$		−	7.87343i		−	0.647192i
$149$	17.8425	−	10.3013i	1.46171	−	0.843919i	0.462620	−	0.886557i	$-0.346909\pi$
$149$	17.8425	−	10.3013i	1.46171	−	0.843919i	0.999091	+	0.0426374i	$0.0135760\pi$
$150$			7.59389i			0.620039i
$151$	−10.3410	+	5.97036i	−0.841535	+	0.485861i	−0.857786	−	0.514007i	$-0.828160\pi$
$151$	−10.3410	+	5.97036i	−0.841535	+	0.485861i	0.0162505	+	0.999868i	$0.494827\pi$
$152$	1.06857	+	1.85081i	0.0866723	+	0.150121i
$153$	−0.238815	−	0.413640i	−0.0193071	−	0.0334408i
$154$		0			0
$155$	8.57596			0.688838
$156$	−2.87367	+	1.21676i	−0.230078	+	0.0974189i
$157$	4.67011	+	8.08887i	0.372715	+	0.645562i	0.989982	−	0.141192i	$-0.0450934\pi$
$157$	4.67011	+	8.08887i	0.372715	+	0.645562i	−0.617267	+	0.786754i	$0.711760\pi$
$158$	−7.96526	−	4.59875i	−0.633682	−	0.365857i
$159$	10.4682			0.830185
$160$	1.85566	−	3.21409i	0.146703	−	0.254096i
$161$		0			0
$162$	2.44144	+	1.40956i	0.191817	+	0.110746i
$163$	−3.87746	+	2.23865i	−0.303706	+	0.175345i	−0.644106	−	0.764936i	$-0.722771\pi$
$163$	−3.87746	+	2.23865i	−0.303706	+	0.175345i	0.340401	+	0.940280i	$0.389437\pi$
$164$	6.51354	−	3.76060i	0.508622	−	0.293653i
$165$	−18.5500			−1.44412
$166$	3.17186			0.246184
$167$	−12.7365	+	7.35342i	−0.985579	+	0.569025i	−0.903950	−	0.427638i	$-0.859346\pi$
$167$	−12.7365	+	7.35342i	−0.985579	+	0.569025i	−0.0816295	+	0.996663i	$0.526012\pi$
$168$		0			0
$169$	3.56086	+	12.5028i	0.273912	+	0.961755i
$170$	−0.393765	+	0.682021i	−0.0302004	+	0.0523086i
$171$	4.16597	+	2.40522i	0.318580	+	0.183932i
$172$	−2.28987	+	3.96617i	−0.174601	+	0.302417i
$173$	−6.88286	−	11.9215i	−0.523294	−	0.906372i	−0.999632	−	0.0271097i	$-0.991370\pi$
$173$	−6.88286	−	11.9215i	−0.523294	−	0.906372i	0.476339	−	0.879262i	$-0.341964\pi$
$174$			0.0853103i			0.00646736i
$175$		0			0
$176$	5.00118	+	2.88743i	0.376978	+	0.217648i
$177$	0.173833	+	0.100363i	0.0130661	+	0.00754371i
$178$	11.8167			0.885696
$179$	7.63936	−	13.2318i	0.570992	−	0.988988i	−0.425472	−	0.904972i	$-0.639892\pi$
$179$	7.63936	−	13.2318i	0.570992	−	0.988988i	0.996464	−	0.0840164i	$-0.0267748\pi$
$180$		−	8.35373i		−	0.622651i
$181$	1.66748			0.123943			0.0619713	−	0.998078i	$-0.480261\pi$
$181$	1.66748			0.123943			0.0619713	+	0.998078i	$0.480261\pi$
$182$		0			0
$183$	−6.95191			−0.513900
$184$		−	2.47940i		−	0.182784i
$185$	−14.6104	+	25.3059i	−1.07418	+	1.86053i
$186$	2.00000			0.146647
$187$	−1.06124	−	0.612704i	−0.0776052	−	0.0448054i
$188$	7.92907	+	4.57785i	0.578287	+	0.333874i
$189$		0			0
$190$		−	7.93158i		−	0.575418i
$191$	−0.0604880	−	0.104768i	−0.00437676	−	0.00758076i	0.863829	−	0.503786i	$-0.168060\pi$
$191$	−0.0604880	−	0.104768i	−0.00437676	−	0.00758076i	−0.868205	+	0.496205i	$0.834727\pi$
$192$	0.432757	−	0.749558i	0.0312316	−	0.0540947i
$193$	2.38633	+	1.37775i	0.171772	+	0.0991725i	0.583421	−	0.812170i	$-0.301714\pi$
$193$	2.38633	+	1.37775i	0.171772	+	0.0991725i	−0.411649	+	0.911342i	$0.635047\pi$
$194$	−7.04093	+	12.1952i	−0.505509	+	0.875568i
$195$	11.4941	+	1.42177i	0.823113	+	0.101815i
$196$		0			0
$197$	−13.0989	+	7.56267i	−0.933260	+	0.538818i	−0.887841	−	0.460150i	$-0.847796\pi$
$197$	−13.0989	+	7.56267i	−0.933260	+	0.538818i	−0.0454187	+	0.998968i	$0.514462\pi$
$198$	12.9985			0.923767
$199$	5.30640			0.376161			0.188080	−	0.982154i	$-0.439773\pi$
$199$	5.30640			0.376161			0.188080	+	0.982154i	$0.439773\pi$
$200$	−7.59837	+	4.38692i	−0.537286	+	0.310202i
$201$	−9.72176	+	5.61286i	−0.685720	+	0.395901i
$202$	−5.32816	−	3.07622i	−0.374888	−	0.216442i
$203$		0			0
$204$	−0.0918298	+	0.159054i	−0.00642937	+	0.0111360i
$205$	−27.9135			−1.94956
$206$	−16.7568	−	9.67453i	−1.16750	−	0.674056i
$207$	−2.79042	−	4.83315i	−0.193948	−	0.335927i
$208$	−2.87757	−	2.17246i	−0.199524	−	0.150633i
$209$	12.3417			0.853691
$210$		0			0
$211$	−8.94910	−	15.5003i	−0.616081	−	1.06708i	−0.990194	−	0.139701i	$-0.955386\pi$
$211$	−8.94910	−	15.5003i	−0.616081	−	1.06708i	0.374112	−	0.927383i	$-0.377947\pi$
$212$	6.04740	+	10.4744i	0.415337	+	0.719385i
$213$	−5.51957	+	3.18673i	−0.378195	+	0.218351i
$214$		−	11.6501i		−	0.796386i
$215$	14.7197	−	8.49841i	1.00387	−	0.579587i
$216$		−	4.54472i		−	0.309229i
$217$		0			0
$218$	−2.86654	−	4.96499i	−0.194146	−	0.336271i
$219$			4.85047i			0.327764i
$220$	−10.7162	−	18.5609i	−0.722484	−	1.25138i
$221$	0.610613	+	0.460989i	0.0410742	+	0.0310095i
$222$	−3.40729	+	5.90159i	−0.228682	+	0.396089i
$223$	14.2362	−	8.21925i	0.953324	−	0.550402i	0.0592118	−	0.998245i	$-0.481141\pi$
$223$	14.2362	−	8.21925i	0.953324	−	0.550402i	0.894112	+	0.447844i	$0.147808\pi$
$224$		0			0
$225$	−9.87445	+	17.1031i	−0.658297	+	1.14020i
$226$	14.3062	+	8.25971i	0.951637	+	0.549428i
$227$		−	5.63095i		−	0.373739i	−0.982385	−	0.186870i	$-0.940166\pi$
$227$		−	5.63095i		−	0.373739i	0.982385	−	0.186870i	$-0.0598342\pi$
$228$		−	1.84972i		−	0.122501i
$229$	−24.0084	−	13.8613i	−1.58652	−	0.915978i	−0.993874	−	0.110515i	$-0.964750\pi$
$229$	−24.0084	−	13.8613i	−1.58652	−	0.915978i	−0.592646	−	0.805463i	$-0.701917\pi$
$230$	−4.60091	+	7.96901i	−0.303375	+	0.525461i
$231$		0			0
$232$	−0.0853606	+	0.0492830i	−0.00560420	+	0.00323559i
$233$	10.0552	−	17.4161i	0.658737	−	1.14097i	−0.322206	−	0.946669i	$-0.604425\pi$
$233$	10.0552	−	17.4161i	0.658737	−	1.14097i	0.980943	−	0.194296i	$-0.0622422\pi$
$234$	−8.05429	−	0.996277i	−0.526526	−	0.0651287i
$235$	−16.9898	−	29.4272i	−1.10829	−	1.91962i
$236$			0.231914i			0.0150963i
$237$	3.98028	+	6.89405i	0.258547	+	0.447817i
$238$		0			0
$239$		−	6.62968i		−	0.428838i	−0.976742	−	0.214419i	$-0.931214\pi$
$239$		−	6.62968i		−	0.428838i	0.976742	−	0.214419i	$-0.0687858\pi$
$240$	−2.78184	+	1.60610i	−0.179567	+	0.103673i
$241$			1.61687i			0.104151i	0.998643	+	0.0520757i	$0.0165837\pi$
$241$			1.61687i			0.104151i	−0.998643	+	0.0520757i	$0.983416\pi$
$242$	19.3549	−	11.1745i	1.24418	−	0.718326i
$243$	−8.03708	−	13.9206i	−0.515579	−	0.893009i
$244$	−4.01605	−	6.95601i	−0.257102	−	0.445313i
$245$		0			0
$246$	−6.50970			−0.415044
$247$	−7.64727	−	0.945931i	−0.486584	−	0.0601881i
$248$	1.15538	+	2.00118i	0.0733668	+	0.127075i
$249$	−2.37749	−	1.37265i	−0.150667	−	0.0869879i
$250$	14.0059			0.885812
$251$	−0.253506	+	0.439085i	−0.0160011	+	0.0277148i	−0.873915	−	0.486079i	$-0.838427\pi$
$251$	−0.253506	+	0.439085i	−0.0160011	+	0.0277148i	0.857914	+	0.513793i	$0.171760\pi$
$252$		0			0
$253$	−12.3999	−	7.15910i	−0.779576	−	0.450089i
$254$	−10.2090	+	5.89420i	−0.640573	+	0.369835i
$255$	0.590299	−	0.340809i	0.0369660	−	0.0213423i
$256$	1.00000			0.0625000
$257$	−9.64063			−0.601366			−0.300683	−	0.953724i	$-0.597215\pi$
$257$	−9.64063			−0.601366			−0.300683	+	0.953724i	$0.597215\pi$
$258$	3.43278	−	1.98191i	0.213715	−	0.123389i
$259$		0			0
$260$	5.21745	+	12.3223i	0.323573	+	0.764194i
$261$	−0.110930	+	0.192137i	−0.00686641	+	0.0118930i
$262$	4.44149	+	2.56429i	0.274396	+	0.158423i
$263$	3.67309	−	6.36197i	0.226492	−	0.392296i	−0.730274	−	0.683155i	$-0.760608\pi$
$263$	3.67309	−	6.36197i	0.226492	−	0.392296i	0.956766	+	0.290858i	$0.0939409\pi$
$264$	−2.49912	−	4.32860i	−0.153810	−	0.266407i
$265$		−	44.8876i		−	2.75742i
$266$		0			0
$267$	−8.85727	−	5.11375i	−0.542056	−	0.312956i
$268$	−11.2323	−	6.48500i	−0.686125	−	0.396134i
$269$	−22.3541			−1.36295			−0.681476	−	0.731841i	$-0.738662\pi$
$269$	−22.3541			−1.36295			−0.681476	+	0.731841i	$0.738662\pi$
$270$	−8.43344	+	14.6071i	−0.513243	+	0.888962i
$271$			9.61740i			0.584215i	0.956385	+	0.292108i	$0.0943566\pi$
$271$			9.61740i			0.584215i	−0.956385	+	0.292108i	$0.905643\pi$
$272$	−0.212197			−0.0128663
$273$		0			0
$274$	9.39328			0.567469
$275$			50.6678i			3.05538i
$276$	−1.07298	+	1.85845i	−0.0645857	+	0.111866i
$277$	−10.1789			−0.611590			−0.305795	−	0.952097i	$-0.598922\pi$
$277$	−10.1789			−0.611590			−0.305795	+	0.952097i	$0.598922\pi$
$278$	−13.1127	−	7.57063i	−0.786449	−	0.454056i
$279$	4.50442	+	2.60063i	0.269673	+	0.155696i
$280$		0			0
$281$		−	14.1692i		−	0.845265i	−0.906301	−	0.422633i	$-0.861106\pi$
$281$		−	14.1692i		−	0.845265i	0.906301	−	0.422633i	$-0.138894\pi$
$282$	−3.96220	−	6.86273i	−0.235945	−	0.408669i
$283$	−9.46631	+	16.3961i	−0.562714	+	0.974649i	0.434545	+	0.900650i	$0.356909\pi$
$283$	−9.46631	+	16.3961i	−0.562714	+	0.974649i	−0.997258	+	0.0739986i	$0.976424\pi$
$284$	−6.37721	−	3.68188i	−0.378418	−	0.218480i
$285$	−3.43245	+	5.94518i	−0.203321	+	0.352162i
$286$	−19.1736	+	8.11844i	−1.13376	+	0.480053i
$287$		0			0
$288$	1.94932	−	1.12544i	0.114865	−	0.0663173i
$289$	−16.9550			−0.997351
$290$	0.365809			0.0214811
$291$	10.5552	−	6.09403i	0.618755	−	0.357238i
$292$	−4.85333	+	2.80207i	−0.284020	+	0.163979i
$293$	−3.16950	−	1.82991i	−0.185164	−	0.106905i	0.404553	−	0.914515i	$-0.367427\pi$
$293$	−3.16950	−	1.82991i	−0.185164	−	0.106905i	−0.589717	+	0.807610i	$0.700761\pi$
$294$		0			0
$295$	0.430353	−	0.745393i	0.0250561	−	0.0433985i
$296$	−7.87343			−0.457634
$297$	−22.7290	−	13.1226i	−1.31887	−	0.761449i
$298$	−10.3013	−	17.8425i	−0.596741	−	1.03359i
$299$	7.13465	+	5.38639i	0.412608	+	0.311503i
$300$	7.59389			0.438434
$301$		0			0
$302$	5.97036	+	10.3410i	0.343555	+	0.595055i
$303$	2.66251	+	4.61161i	0.152957	+	0.264930i
$304$	1.85081	−	1.06857i	0.106151	−	0.0612866i
$305$			29.8097i			1.70690i
$306$	−0.413640	+	0.238815i	−0.0236462	+	0.0136522i
$307$		−	19.6987i		−	1.12426i	−0.827048	−	0.562132i	$-0.809981\pi$
$307$		−	19.6987i		−	1.12426i	0.827048	−	0.562132i	$-0.190019\pi$
$308$		0			0
$309$	8.37345	+	14.5032i	0.476349	+	0.825061i
$310$		−	8.57596i		−	0.487082i
$311$	8.48425	+	14.6952i	0.481098	+	0.833286i	0.999765	−	0.0216906i	$-0.00690488\pi$
$311$	8.48425	+	14.6952i	0.481098	+	0.833286i	−0.518667	+	0.854976i	$0.673572\pi$
$312$	1.21676	+	2.87367i	0.0688855	+	0.162690i
$313$	−2.26897	+	3.92997i	−0.128250	+	0.222135i	−0.922999	−	0.384803i	$-0.874269\pi$
$313$	−2.26897	+	3.92997i	−0.128250	+	0.222135i	0.794749	+	0.606939i	$0.207603\pi$
$314$	8.08887	−	4.67011i	0.456481	−	0.263550i
$315$		0			0
$316$	−4.59875	+	7.96526i	−0.258700	+	0.448081i
$317$	25.2763	+	14.5933i	1.41966	+	0.819641i	0.996269	−	0.0863056i	$-0.0275061\pi$
$317$	25.2763	+	14.5933i	1.41966	+	0.819641i	0.423392	+	0.905947i	$0.360839\pi$
$318$		−	10.4682i		−	0.587029i
$319$			0.569205i			0.0318694i
$320$	−3.21409	−	1.85566i	−0.179673	−	0.103734i
$321$	−5.04168	+	8.73244i	−0.281399	+	0.487397i
$322$		0			0
$323$	−0.392737	+	0.226747i	−0.0218525	+	0.0126165i
$324$	1.40956	−	2.44144i	0.0783091	−	0.135635i
$325$	3.88344	−	31.3953i	0.215415	−	1.74150i
$326$	2.23865	+	3.87746i	0.123987	+	0.214752i
$327$			4.96206i			0.274403i
$328$	−3.76060	−	6.51354i	−0.207644	−	0.359650i
$329$		0			0
$330$			18.5500i			1.02114i
$331$	−4.16161	+	2.40271i	−0.228743	+	0.132065i	−0.609992	−	0.792408i	$-0.708827\pi$
$331$	−4.16161	+	2.40271i	−0.228743	+	0.132065i	0.381249	+	0.924472i	$0.375494\pi$
$332$		−	3.17186i		−	0.174078i
$333$	−15.3479	+	8.86109i	−0.841057	+	0.485585i
$334$	7.35342	+	12.7365i	0.402361	+	0.696910i
$335$	24.0679	+	41.6868i	1.31497	+	2.27759i
$336$		0			0
$337$	17.7312			0.965883			0.482941	−	0.875653i	$-0.339568\pi$
$337$	17.7312			0.965883			0.482941	+	0.875653i	$0.339568\pi$
$338$	12.5028	−	3.56086i	0.680063	−	0.193685i
$339$	−7.14890	−	12.3823i	−0.388275	−	0.672512i
$340$	0.682021	+	0.393765i	0.0369878	+	0.0213549i
$341$	13.3443			0.722637
$342$	2.40522	−	4.16597i	0.130060	−	0.225270i
$343$		0			0
$344$	3.96617	+	2.28987i	0.213841	+	0.123461i
$345$	6.89730	−	3.98216i	0.371338	−	0.214392i
$346$	−11.9215	+	6.88286i	−0.640902	+	0.370025i
$347$	−16.7048			−0.896760			−0.448380	−	0.893843i	$-0.647999\pi$
$347$	−16.7048			−0.896760			−0.448380	+	0.893843i	$0.647999\pi$
$348$	0.0853103			0.00457311
$349$	−0.0173616	+	0.0100237i	−0.000929347	+	0.000536559i	−0.500465	−	0.865757i	$-0.666837\pi$
$349$	−0.0173616	+	0.0100237i	−0.000929347	+	0.000536559i	0.499535	+	0.866294i	$0.333504\pi$
$350$		0			0
$351$	13.0778	+	9.87321i	0.698039	+	0.526993i
$352$	2.88743	−	5.00118i	0.153901	−	0.266564i
$353$	25.8299	+	14.9129i	1.37479	+	0.793734i	0.991526	−	0.129905i	$-0.0414674\pi$
$353$	25.8299	+	14.9129i	1.37479	+	0.793734i	0.383262	+	0.923640i	$0.374801\pi$
$354$	0.100363	−	0.173833i	0.00533421	−	0.00923912i
$355$	13.6646	+	23.6678i	0.725243	+	1.25616i
$356$		−	11.8167i		−	0.626282i
$357$		0			0
$358$	−13.2318	−	7.63936i	−0.699320	−	0.403753i
$359$	−15.8786	−	9.16753i	−0.838042	−	0.483844i	0.0185563	−	0.999828i	$-0.494093\pi$
$359$	−15.8786	−	9.16753i	−0.838042	−	0.483844i	−0.856598	+	0.515984i	$0.827426\pi$
$360$	−8.35373			−0.440280
$361$	−7.21632	+	12.4990i	−0.379806	+	0.657844i
$362$		−	1.66748i		−	0.0876407i
$363$	−19.3434			−1.01527
$364$		0			0
$365$	20.7987			1.08866
$366$			6.95191i			0.363382i
$367$	0.672426	−	1.16468i	0.0351004	−	0.0607956i	−0.847942	−	0.530090i	$-0.822158\pi$
$367$	0.672426	−	1.16468i	0.0351004	−	0.0607956i	0.883042	+	0.469294i	$0.155492\pi$
$368$	−2.47940			−0.129248
$369$	−14.6612	−	8.46466i	−0.763233	−	0.440653i
$370$	25.3059	+	14.6104i	1.31559	+	0.759558i
$371$		0			0
$372$		−	2.00000i		−	0.103695i
$373$	5.53575	+	9.58821i	0.286630	+	0.496458i	0.973003	−	0.230791i	$-0.0741315\pi$
$373$	5.53575	+	9.58821i	0.286630	+	0.496458i	−0.686373	+	0.727250i	$0.740798\pi$
$374$	−0.612704	+	1.06124i	−0.0316822	+	0.0548752i
$375$	−10.4982	−	6.06116i	−0.542127	−	0.312997i
$376$	4.57785	−	7.92907i	0.236085	−	0.408910i
$377$	0.0436269	−	0.352697i	0.00224690	−	0.0181648i
$378$		0			0
$379$	14.5583	−	8.40523i	0.747808	−	0.431747i	−0.0770930	−	0.997024i	$-0.524564\pi$
$379$	14.5583	−	8.40523i	0.747808	−	0.431747i	0.824902	+	0.565276i	$0.191231\pi$
$380$	−7.93158			−0.406882
$381$	10.2030			0.522717
$382$	−0.104768	+	0.0604880i	−0.00536041	+	0.00309483i
$383$	14.3562	−	8.28855i	0.733567	−	0.423525i	−0.0861585	−	0.996281i	$-0.527459\pi$
$383$	14.3562	−	8.28855i	0.733567	−	0.423525i	0.819726	+	0.572756i	$0.194126\pi$
$384$	−0.749558	−	0.432757i	−0.0382507	−	0.0220841i
$385$		0			0
$386$	1.37775	−	2.38633i	0.0701256	−	0.121461i
$387$	10.3084			0.524008
$388$	12.1952	+	7.04093i	0.619120	+	0.357449i
$389$	0.585065	+	1.01336i	0.0296640	+	0.0513795i	0.880476	−	0.474090i	$-0.157223\pi$
$389$	0.585065	+	1.01336i	0.0296640	+	0.0513795i	−0.850812	+	0.525470i	$0.823890\pi$
$390$	1.42177	−	11.4941i	0.0719941	−	0.582028i
$391$	0.526121			0.0266071
$392$		0			0
$393$	−2.21944	−	3.84418i	−0.111956	−	0.193913i
$394$	7.56267	+	13.0989i	0.381002	+	0.659914i
$395$	29.5616	−	17.0674i	1.48740	−	0.858753i
$396$		−	12.9985i		−	0.653202i
$397$	22.6877	−	13.0987i	1.13866	−	0.657406i	0.192562	−	0.981285i	$-0.438320\pi$
$397$	22.6877	−	13.0987i	1.13866	−	0.657406i	0.946099	+	0.323878i	$0.104987\pi$
$398$		−	5.30640i		−	0.265986i
$399$		0			0
$400$	4.38692	+	7.59837i	0.219346	+	0.379919i
$401$		−	11.3687i		−	0.567726i	−0.958865	−	0.283863i	$-0.908384\pi$
$401$		−	11.3687i		−	0.567726i	0.958865	−	0.283863i	$-0.0916162\pi$
$402$	5.61286	+	9.72176i	0.279944	+	0.484878i
$403$	−8.26856	−	1.02278i	−0.411886	−	0.0509483i
$404$	−3.07622	+	5.32816i	−0.153048	+	0.265086i
$405$	−9.06094	+	5.23134i	−0.450242	+	0.259947i
$406$		0			0
$407$	−22.7340	+	39.3764i	−1.12688	+	1.95182i
$408$	0.159054	+	0.0918298i	0.00787434	+	0.00454625i
$409$		−	23.3314i		−	1.15366i	−0.816863	−	0.576832i	$-0.804289\pi$
$409$		−	23.3314i		−	1.15366i	0.816863	−	0.576832i	$-0.195711\pi$
$410$			27.9135i			1.37855i
$411$	−7.04081	−	4.06501i	−0.347298	−	0.200512i
$412$	−9.67453	+	16.7568i	−0.476630	+	0.825547i
$413$		0			0
$414$	−4.83315	+	2.79042i	−0.237536	+	0.137142i
$415$	−5.88588	+	10.1946i	−0.288926	+	0.500435i
$416$	−2.17246	+	2.87757i	−0.106513	+	0.141085i
$417$	6.55250	+	11.3493i	0.320877	+	0.555775i
$418$		−	12.3417i		−	0.603651i
$419$	−6.33402	−	10.9709i	−0.309437	−	0.535961i	0.668802	−	0.743441i	$-0.266807\pi$
$419$	−6.33402	−	10.9709i	−0.309437	−	0.535961i	−0.978239	+	0.207479i	$0.933474\pi$
$420$		0			0
$421$		−	27.6625i		−	1.34819i	−0.738646	−	0.674094i	$-0.764534\pi$
$421$		−	27.6625i		−	1.34819i	0.738646	−	0.674094i	$-0.235466\pi$
$422$	−15.5003	+	8.94910i	−0.754543	+	0.435635i
$423$		−	20.6084i		−	1.00202i
$424$	10.4744	−	6.04740i	0.508682	−	0.293688i
$425$	−0.930892	−	1.61235i	−0.0451549	−	0.0782105i
$426$	3.18673	+	5.51957i	0.154397	+	0.267424i
$427$		0			0
$428$	−11.6501			−0.563130
$429$	17.8851	+	2.21230i	0.863500	+	0.106811i
$430$	−8.49841	−	14.7197i	−0.409830	−	0.709846i
$431$	−5.55462	−	3.20696i	−0.267557	−	0.154474i	0.360220	−	0.932867i	$-0.382702\pi$
$431$	−5.55462	−	3.20696i	−0.267557	−	0.154474i	−0.627777	+	0.778393i	$0.716035\pi$
$432$	−4.54472			−0.218658
$433$	0.0325135	−	0.0563150i	0.00156250	−	0.00270633i	−0.865243	−	0.501353i	$-0.832836\pi$
$433$	0.0325135	−	0.0563150i	0.00156250	−	0.00270633i	0.866806	+	0.498646i	$0.166169\pi$
$434$		0			0
$435$	−0.274195	−	0.158307i	−0.0131467	−	0.00759022i
$436$	−4.96499	+	2.86654i	−0.237780	+	0.137282i
$437$	−4.58891	+	2.64941i	−0.219517	+	0.126738i
$438$	4.85047			0.231764
$439$	36.7778			1.75531			0.877655	−	0.479294i	$-0.159107\pi$
$439$	36.7778			1.75531			0.877655	+	0.479294i	$0.159107\pi$
$440$	−18.5609	+	10.7162i	−0.884858	+	0.510873i
$441$		0			0
$442$	0.460989	−	0.610613i	0.0219270	−	0.0290439i
$443$	4.23191	−	7.32989i	0.201064	−	0.348254i	−0.747807	−	0.663916i	$-0.768893\pi$
$443$	4.23191	−	7.32989i	0.201064	−	0.348254i	0.948872	+	0.315662i	$0.102227\pi$
$444$	5.90159	+	3.40729i	0.280077	+	0.161703i
$445$	−21.9277	+	37.9798i	−1.03947	+	1.80042i
$446$	−8.21925	−	14.2362i	−0.389193	−	0.674102i
$447$			17.8319i			0.843422i
$448$		0			0
$449$	−19.5984	−	11.3152i	−0.924907	−	0.533995i	−0.0397096	−	0.999211i	$-0.512643\pi$
$449$	−19.5984	−	11.3152i	−0.924907	−	0.533995i	−0.885197	+	0.465216i	$0.845977\pi$
$450$	17.1031	+	9.87445i	0.806246	+	0.465486i
$451$	−43.4339			−2.04522
$452$	8.25971	−	14.3062i	0.388504	−	0.672909i
$453$		−	10.3349i		−	0.485574i
$454$	−5.63095			−0.264274
$455$		0			0
$456$	−1.84972			−0.0866213
$457$		−	16.3170i		−	0.763278i	−0.924311	−	0.381639i	$-0.875360\pi$
$457$		−	16.3170i		−	0.763278i	0.924311	−	0.381639i	$-0.124640\pi$
$458$	−13.8613	+	24.0084i	−0.647694	+	1.12184i
$459$	0.964376			0.0450132
$460$	7.96901	+	4.60091i	0.371557	+	0.214519i
$461$	−16.6951	−	9.63892i	−0.777568	−	0.448929i	0.0579996	−	0.998317i	$-0.481528\pi$
$461$	−16.6951	−	9.63892i	−0.777568	−	0.448929i	−0.835568	+	0.549387i	$0.814861\pi$
$462$		0			0
$463$			2.70218i			0.125581i	0.998027	+	0.0627904i	$0.0200000\pi$
$463$			2.70218i			0.125581i	−0.998027	+	0.0627904i	$0.980000\pi$
$464$	0.0492830	+	0.0853606i	0.00228791	+	0.00396277i
$465$	−3.71131	+	6.42818i	−0.172108	+	0.298100i
$466$	−17.4161	−	10.0552i	−0.806784	−	0.465797i
$467$	−9.19528	+	15.9267i	−0.425507	+	0.736999i	−0.996468	−	0.0839779i	$-0.973237\pi$
$467$	−9.19528	+	15.9267i	−0.425507	+	0.736999i	0.570961	+	0.820977i	$0.306571\pi$
$468$	−0.996277	+	8.05429i	−0.0460529	+	0.372310i
$469$		0			0
$470$	−29.4272	+	16.9898i	−1.35738	+	0.783682i
$471$	−8.08410			−0.372496
$472$	0.231914			0.0106747
$473$	22.9041	−	13.2237i	1.05313	−	0.608025i
$474$	6.89405	−	3.98028i	0.316654	−	0.182820i
$475$	16.2388	+	9.37545i	0.745085	+	0.430175i
$476$		0			0
$477$	13.6120	−	23.5767i	0.623250	−	1.07950i
$478$	−6.62968			−0.303234
$479$	35.3951	+	20.4354i	1.61725	+	0.933717i	0.987629	+	0.156811i	$0.0501213\pi$
$479$	35.3951	+	20.4354i	1.61725	+	0.933717i	0.629617	+	0.776906i	$0.283212\pi$
$480$	1.60610	+	2.78184i	0.0733080	+	0.126973i
$481$	17.1047	−	22.6564i	0.779907	−	1.03304i
$482$	1.61687			0.0736462
$483$		0			0
$484$	−11.1745	−	19.3549i	−0.507933	−	0.879766i
$485$	−26.1311	−	45.2604i	−1.18655	−	2.05517i
$486$	−13.9206	+	8.03708i	−0.631452	+	0.364569i
$487$		−	17.6293i		−	0.798861i	−0.916764	−	0.399430i	$-0.869208\pi$
$487$		−	17.6293i		−	0.798861i	0.916764	−	0.399430i	$-0.130792\pi$
$488$	−6.95601	+	4.01605i	−0.314884	+	0.181798i
$489$		−	3.87517i		−	0.175241i
$490$		0			0
$491$	−9.42997	−	16.3332i	−0.425569	−	0.737106i	0.570905	−	0.821016i	$-0.306593\pi$
$491$	−9.42997	−	16.3332i	−0.425569	−	0.737106i	−0.996473	+	0.0839098i	$0.973259\pi$
$492$			6.50970i			0.293480i
$493$	−0.0104577	−	0.0181133i	−0.000470991	−	0.000815781i
$494$	−0.945931	+	7.64727i	−0.0425594	+	0.344067i
$495$	−24.1208	+	41.7785i	−1.08415	+	1.87780i
$496$	2.00118	−	1.15538i	0.0898556	−	0.0518782i
$497$		0			0
$498$	−1.37265	+	2.37749i	−0.0615097	+	0.106538i
$499$	1.82508	+	1.05371i	0.0817017	+	0.0471705i	0.540294	−	0.841476i	$-0.318313\pi$
$499$	1.82508	+	1.05371i	0.0817017	+	0.0471705i	−0.458593	+	0.888647i	$0.651646\pi$
$500$		−	14.0059i		−	0.626364i
$501$		−	12.7290i		−	0.568689i
$502$	0.439085	+	0.253506i	0.0195973	+	0.0113145i
$503$	10.8942	−	18.8693i	0.485749	−	0.841342i	−0.514117	−	0.857720i	$-0.671880\pi$
$503$	10.8942	−	18.8693i	0.485749	−	0.841342i	0.999866	+	0.0163784i	$0.00521363\pi$
$504$		0			0
$505$	19.7745	−	11.4168i	0.879953	−	0.508041i
$506$	−7.15910	+	12.3999i	−0.318261	+	0.551244i
$507$	−10.9126	−	2.74161i	−0.484644	−	0.121759i
$508$	5.89420	+	10.2090i	0.261513	+	0.452953i
$509$			12.1977i			0.540655i	0.962768	+	0.270328i	$0.0871321\pi$
$509$			12.1977i			0.540655i	−0.962768	+	0.270328i	$0.912868\pi$
$510$	−0.340809	−	0.590299i	−0.0150913	−	0.0261389i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−8.41143	+	4.85634i	−0.371374	+	0.214413i
$514$			9.64063i			0.425230i
$515$	62.1896	−	35.9052i	2.74040	−	1.58217i
$516$	−1.98191	−	3.43278i	−0.0872489	−	0.151120i
$517$	−26.4365	−	45.7893i	−1.16267	−	2.01381i
$518$		0			0
$519$	11.9144			0.522986
$520$	12.3223	−	5.21745i	0.540367	−	0.228800i
$521$	−13.4883	−	23.3624i	−0.590932	−	1.02352i	−0.994107	−	0.108401i	$-0.965427\pi$
$521$	−13.4883	−	23.3624i	−0.590932	−	1.02352i	0.403175	−	0.915123i	$-0.367906\pi$
$522$	0.192137	+	0.110930i	0.00840960	+	0.00485529i
$523$	3.75365			0.164136			0.0820679	−	0.996627i	$-0.473848\pi$
$523$	3.75365			0.164136			0.0820679	+	0.996627i	$0.473848\pi$
$524$	2.56429	−	4.44149i	0.112022	−	0.194027i
$525$		0			0
$526$	−6.36197	−	3.67309i	−0.277395	−	0.160154i
$527$	−0.424644	+	0.245168i	−0.0184978	+	0.0106797i
$528$	−4.32860	+	2.49912i	−0.188378	+	0.108760i
$529$	−16.8526			−0.732721
$530$	−44.8876			−1.94979
$531$	0.452075	−	0.261006i	0.0196184	−	0.0113267i
$532$		0			0
$533$	26.9129	+	3.32900i	1.16573	+	0.144195i
$534$	−5.11375	+	8.85727i	−0.221293	+	0.383292i
$535$	37.4445	+	21.6186i	1.61887	+	0.934654i
$536$	−6.48500	+	11.2323i	−0.280109	+	0.485163i
$537$	6.61198	+	11.4523i	0.285328	+	0.494203i
$538$			22.3541i			0.963752i
$539$		0			0
$540$	14.6071	+	8.43344i	0.628591	+	0.362917i
$541$	−0.0117524	−	0.00678524i	−0.000505274	−	0.000291720i	0.499747	−	0.866171i	$-0.333426\pi$
$541$	−0.0117524	−	0.00678524i	−0.000505274	−	0.000291720i	−0.500253	+	0.865880i	$0.666760\pi$
$542$	9.61740			0.413103
$543$	−0.721614	+	1.24987i	−0.0309674	+	0.0536371i
$544$			0.212197i			0.00909787i
$545$	21.2772			0.911416
$546$		0			0
$547$	−9.66115			−0.413081			−0.206540	−	0.978438i	$-0.566220\pi$
$547$	−9.66115			−0.413081			−0.206540	+	0.978438i	$0.566220\pi$
$548$		−	9.39328i		−	0.401261i
$549$	−9.03967	+	15.6572i	−0.385804	+	0.668232i
$550$	50.6678			2.16048
$551$	0.182427	+	0.105324i	0.00777167	+	0.00448697i
$552$	1.85845	+	1.07298i	0.0791010	+	0.0456690i
$553$		0			0
$554$			10.1789i			0.432460i
$555$	−12.6455	−	21.9027i	−0.536772	−	0.929716i
$556$	−7.57063	+	13.1127i	−0.321066	+	0.556103i
$557$	21.6145	+	12.4791i	0.915834	+	0.528757i	0.882304	−	0.470680i	$-0.155992\pi$
$557$	21.6145	+	12.4791i	0.915834	+	0.528757i	0.0335307	+	0.999438i	$0.489325\pi$
$558$	2.60063	−	4.50442i	0.110093	−	0.190687i
$559$	−15.2056	+	6.43830i	−0.643128	+	0.272311i
$560$		0			0
$561$	0.918515	−	0.530305i	0.0387797	−	0.0223895i
$562$	−14.1692			−0.597693
$563$	15.8994			0.670080			0.335040	−	0.942204i	$-0.391250\pi$
$563$	15.8994			0.670080			0.335040	+	0.942204i	$0.391250\pi$
$564$	−6.86273	+	3.96220i	−0.288973	+	0.166839i
$565$	−53.0949	+	30.6544i	−2.23372	+	1.28964i
$566$	16.3961	+	9.46631i	0.689181	+	0.397899i
$567$		0			0
$568$	−3.68188	+	6.37721i	−0.154488	+	0.267582i
$569$	17.9093			0.750797			0.375398	−	0.926864i	$-0.377506\pi$
$569$	17.9093			0.750797			0.375398	+	0.926864i	$0.377506\pi$
$570$	5.94518	+	3.43245i	0.249016	+	0.143770i
$571$	6.25615	+	10.8360i	0.261812	+	0.453471i	0.966723	−	0.255824i	$-0.0823467\pi$
$571$	6.25615	+	10.8360i	0.261812	+	0.453471i	−0.704912	+	0.709295i	$0.749013\pi$
$572$	8.11844	+	19.1736i	0.339449	+	0.801690i
$573$	0.104707			0.00437418
$574$		0			0
$575$	−10.8769	−	18.8394i	−0.453599	−	0.785657i
$576$	−1.12544	−	1.94932i	−0.0468934	−	0.0812218i
$577$	19.1314	−	11.0455i	0.796450	−	0.459831i	−0.0457781	−	0.998952i	$-0.514577\pi$
$577$	19.1314	−	11.0455i	0.796450	−	0.459831i	0.842228	+	0.539121i	$0.181243\pi$
$578$			16.9550i			0.705234i
$579$	−2.06540	+	1.19246i	−0.0858353	+	0.0495570i
$580$		−	0.365809i		−	0.0151894i
$581$		0			0
$582$	−6.09403	−	10.5552i	−0.252606	−	0.437526i
$583$		−	69.8458i		−	2.89272i
$584$	2.80207	+	4.85333i	0.115951	+	0.200832i
$585$	18.1481	−	24.0385i	0.750333	−	0.993869i
$586$	−1.82991	+	3.16950i	−0.0755929	+	0.130931i
$587$	18.3007	−	10.5659i	0.755352	−	0.436102i	−0.0722727	−	0.997385i	$-0.523025\pi$
$587$	18.3007	−	10.5659i	0.755352	−	0.436102i	0.827624	+	0.561282i	$0.189692\pi$
$588$		0			0
$589$	2.46921	−	4.27679i	0.101742	−	0.176222i
$590$	−0.745393	−	0.430353i	−0.0306873	−	0.0177173i
$591$		−	13.0912i		−	0.538500i
$592$			7.87343i			0.323596i
$593$	7.75520	+	4.47747i	0.318468	+	0.183867i	0.650709	−	0.759327i	$-0.274472\pi$
$593$	7.75520	+	4.47747i	0.318468	+	0.183867i	−0.332242	+	0.943194i	$0.607805\pi$
$594$	−13.1226	+	22.7290i	−0.538425	+	0.932580i
$595$		0			0
$596$	−17.8425	+	10.3013i	−0.730855	+	0.421960i
$597$	−2.29639	+	3.97746i	−0.0939848	+	0.162786i
$598$	5.38639	−	7.13465i	0.220266	−	0.291758i
$599$	−20.8998	−	36.1995i	−0.853942	−	1.47907i	−0.877623	−	0.479351i	$-0.840872\pi$
$599$	−20.8998	−	36.1995i	−0.853942	−	1.47907i	0.0236813	−	0.999720i	$-0.492461\pi$
$600$		−	7.59389i		−	0.310019i
$601$	7.64481	+	13.2412i	0.311838	+	0.540120i	0.978760	−	0.205008i	$-0.0657220\pi$
$601$	7.64481	+	13.2412i	0.311838	+	0.540120i	−0.666922	+	0.745127i	$0.732389\pi$
$602$		0			0
$603$			29.1940i			1.18887i
$604$	10.3410	−	5.97036i	0.420768	−	0.242930i
$605$			82.9444i			3.37217i
$606$	4.61161	−	2.66251i	0.187334	−	0.108157i
$607$	7.30434	+	12.6515i	0.296474	+	0.513508i	0.975327	−	0.220766i	$-0.0708558\pi$
$607$	7.30434	+	12.6515i	0.296474	+	0.513508i	−0.678853	+	0.734275i	$0.737522\pi$
$608$	−1.06857	−	1.85081i	−0.0433362	−	0.0750604i
$609$		0			0
$610$	29.8097			1.20696
$611$	12.8713	+	30.3987i	0.520717	+	1.22980i
$612$	0.238815	+	0.413640i	0.00965354	+	0.0167204i
$613$	33.9623	+	19.6081i	1.37172	+	0.791965i	0.991145	−	0.132783i	$-0.0423914\pi$
$613$	33.9623	+	19.6081i	1.37172	+	0.791965i	0.380579	+	0.924748i	$0.375725\pi$
$614$	−19.6987			−0.794975
$615$	12.0798	−	20.9228i	0.487104	−	0.843688i
$616$		0			0
$617$	8.10486	+	4.67934i	0.326289	+	0.188383i	0.654192	−	0.756328i	$-0.273009\pi$
$617$	8.10486	+	4.67934i	0.326289	+	0.188383i	−0.327903	+	0.944711i	$0.606342\pi$
$618$	14.5032	−	8.37345i	0.583406	−	0.336830i
$619$	37.8518	−	21.8537i	1.52139	−	0.878376i	0.521711	−	0.853122i	$-0.325294\pi$
$619$	37.8518	−	21.8537i	1.52139	−	0.878376i	0.999681	−	0.0252541i	$-0.00803947\pi$
$620$	−8.57596			−0.344419
$621$	11.2682			0.452176
$622$	14.6952	−	8.48425i	0.589222	−	0.340187i
$623$		0			0
$624$	2.87367	−	1.21676i	0.115039	−	0.0487094i
$625$	−4.05556	+	7.02443i	−0.162222	+	0.280977i
$626$	3.92997	+	2.26897i	0.157073	+	0.0906863i
$627$	−5.34095	+	9.25080i	−0.213297	+	0.369441i
$628$	−4.67011	−	8.08887i	−0.186358	−	0.322781i
$629$		−	1.67072i		−	0.0666159i
$630$		0			0
$631$	−18.0096	−	10.3978i	−0.716951	−	0.413932i	0.0966785	−	0.995316i	$-0.469178\pi$
$631$	−18.0096	−	10.3978i	−0.716951	−	0.413932i	−0.813629	+	0.581384i	$0.802511\pi$
$632$	7.96526	+	4.59875i	0.316841	+	0.182928i
$633$	15.4912			0.615718
$634$	14.5933	−	25.2763i	0.579574	−	1.00385i
$635$		−	43.7504i		−	1.73618i
$636$	−10.4682			−0.415092
$637$		0			0
$638$	0.569205			0.0225350
$639$			16.5750i			0.655696i
$640$	−1.85566	+	3.21409i	−0.0733513	+	0.127048i
$641$	7.23795			0.285882			0.142941	−	0.989731i	$-0.454344\pi$
$641$	7.23795			0.285882			0.142941	+	0.989731i	$0.454344\pi$
$642$	8.73244	+	5.04168i	0.344642	+	0.198979i
$643$	−34.7898	−	20.0859i	−1.37198	−	0.792111i	−0.380800	−	0.924658i	$-0.624351\pi$
$643$	−34.7898	−	20.0859i	−1.37198	−	0.792111i	−0.991177	+	0.132547i	$0.957685\pi$
$644$		0			0
$645$			14.7110i			0.579245i
$646$	0.226747	+	0.392737i	0.00892124	+	0.0154520i
$647$	−7.27561	+	12.6017i	−0.286034	+	0.495425i	−0.972859	−	0.231397i	$-0.925670\pi$
$647$	−7.27561	+	12.6017i	−0.286034	+	0.495425i	0.686826	+	0.726822i	$0.259004\pi$
$648$	−2.44144	−	1.40956i	−0.0959087	−	0.0553729i
$649$	0.669636	−	1.15984i	0.0262855	−	0.0455278i
$650$	−31.3953	−	3.88344i	−1.23142	−	0.152321i
$651$		0			0
$652$	3.87746	−	2.23865i	0.151853	−	0.0876723i
$653$	−49.7267			−1.94596			−0.972978	−	0.230896i	$-0.925834\pi$
$653$	−49.7267			−1.94596			−0.972978	+	0.230896i	$0.925834\pi$
$654$	4.96206			0.194032
$655$	−16.4838	+	9.51690i	−0.644074	+	0.371856i
$656$	−6.51354	+	3.76060i	−0.254311	+	0.146827i
$657$	10.9243	+	6.30714i	0.426197	+	0.246065i
$658$		0			0
$659$	15.7988	−	27.3644i	0.615436	−	1.06597i	−0.374872	−	0.927076i	$-0.622313\pi$
$659$	15.7988	−	27.3644i	0.615436	−	1.06597i	0.990308	−	0.138889i	$-0.0443532\pi$
$660$	18.5500			0.722058
$661$	−21.5391	−	12.4356i	−0.837775	−	0.483689i	0.0187325	−	0.999825i	$-0.494037\pi$
$661$	−21.5391	−	12.4356i	−0.837775	−	0.483689i	−0.856507	+	0.516135i	$0.827370\pi$
$662$	2.40271	+	4.16161i	0.0933839	+	0.161746i
$663$	−0.609785	+	0.258193i	−0.0236821	+	0.0100274i
$664$	−3.17186			−0.123092
$665$		0			0
$666$	8.86109	+	15.3479i	0.343360	+	0.594717i
$667$	−0.122192	−	0.211643i	−0.00473130	−	0.00819485i
$668$	12.7365	−	7.35342i	0.492790	−	0.284512i
$669$			14.2278i			0.550077i
$670$	41.6868	−	24.0679i	1.61050	−	0.929822i
$671$			46.3843i			1.79065i
$672$		0			0
$673$	−10.8245	−	18.7486i	−0.417254	−	0.722705i	0.578408	−	0.815748i	$-0.303674\pi$
$673$	−10.8245	−	18.7486i	−0.417254	−	0.722705i	−0.995662	+	0.0930423i	$0.970341\pi$
$674$		−	17.7312i		−	0.682982i
$675$	−19.9373	−	34.5325i	−0.767388	−	1.32916i
$676$	−3.56086	−	12.5028i	−0.136956	−	0.480877i
$677$	7.19675	−	12.4651i	0.276594	−	0.479074i	−0.693942	−	0.720031i	$-0.744128\pi$
$677$	7.19675	−	12.4651i	0.276594	−	0.479074i	0.970536	+	0.240956i	$0.0774611\pi$
$678$	−12.3823	+	7.14890i	−0.475538	+	0.274552i
$679$		0			0
$680$	0.393765	−	0.682021i	0.0151002	−	0.0261543i
$681$	4.22072	+	2.43684i	0.161738	+	0.0933797i
$682$		−	13.3443i		−	0.510981i
$683$			42.3738i			1.62139i	0.585471	+	0.810694i	$0.300910\pi$
$683$			42.3738i			1.62139i	−0.585471	+	0.810694i	$0.699090\pi$
$684$	−4.16597	−	2.40522i	−0.159290	−	0.0919660i
$685$	−17.4307	+	30.1909i	−0.665993	+	1.15353i
$686$		0			0
$687$	20.7796	−	11.9971i	0.792793	−	0.457719i
$688$	2.28987	−	3.96617i	0.0873003	−	0.151209i
$689$	−5.35335	+	43.2786i	−0.203946	+	1.64878i
$690$	−3.98216	−	6.89730i	−0.151598	−	0.262576i
$691$			22.9382i			0.872610i	0.899799	+	0.436305i	$0.143713\pi$
$691$			22.9382i			0.872610i	−0.899799	+	0.436305i	$0.856287\pi$
$692$	6.88286	+	11.9215i	0.261647	+	0.453186i
$693$		0			0
$694$			16.7048i			0.634105i
$695$	48.6654	−	28.0970i	1.84598	−	1.06578i
$696$		−	0.0853103i		−	0.00323368i
$697$	1.38215	−	0.797987i	0.0523528	−	0.0302259i
$698$	0.0100237	+	0.0173616i	0.000379404	+	0.000657147i
$699$	8.70291	+	15.0739i	0.329174	+	0.570146i
$700$		0			0
$701$	1.70699			0.0644723			0.0322361	−	0.999480i	$-0.489737\pi$
$701$	1.70699			0.0644723			0.0322361	+	0.999480i	$0.489737\pi$
$702$	9.87321	−	13.0778i	0.372640	−	0.493588i
$703$	8.41330	+	14.5723i	0.317314	+	0.549603i
$704$	−5.00118	−	2.88743i	−0.188489	−	0.108824i
$705$	29.4099			1.10764
$706$	14.9129	−	25.8299i	0.561255	−	0.972122i
$707$		0			0
$708$	−0.173833	−	0.100363i	−0.00653304	−	0.00377186i
$709$	15.7730	−	9.10657i	0.592369	−	0.342005i	−0.173665	−	0.984805i	$-0.555561\pi$
$709$	15.7730	−	9.10657i	0.592369	−	0.342005i	0.766034	+	0.642800i	$0.222228\pi$
$710$	23.6678	−	13.6646i	0.888237	−	0.512824i
$711$	20.7025			0.776404
$712$	−11.8167			−0.442848
$713$	−4.96172	+	2.86465i	−0.185818	+	0.107282i
$714$		0			0
$715$	9.48629	−	76.6909i	0.354767	−	2.86808i
$716$	−7.63936	+	13.2318i	−0.285496	+	0.494494i
$717$	4.96933	+	2.86904i	0.185583	+	0.107146i
$718$	−9.16753	+	15.8786i	−0.342129	+	0.592585i
$719$	−1.79107	−	3.10222i	−0.0667956	−	0.115693i	0.830694	−	0.556730i	$-0.187944\pi$
$719$	−1.79107	−	3.10222i	−0.0667956	−	0.115693i	−0.897489	+	0.441037i	$0.854611\pi$
$720$			8.35373i			0.311325i
$721$		0			0
$722$	12.4990	+	7.21632i	0.465166	+	0.268564i
$723$	−1.21193	−	0.699710i	−0.0450723	−	0.0260225i
$724$	−1.66748			−0.0619713
$725$	−0.432401	+	0.748941i	−0.0160590	+	0.0278150i
$726$			19.3434i			0.717903i
$727$	−3.21747			−0.119329			−0.0596647	−	0.998218i	$-0.519003\pi$
$727$	−3.21747			−0.119329			−0.0596647	+	0.998218i	$0.519003\pi$
$728$		0			0
$729$	5.45503			0.202038
$730$		−	20.7987i		−	0.769796i
$731$	−0.485903	+	0.841608i	−0.0179718	+	0.0311280i
$732$	6.95191			0.256950
$733$	4.15028	+	2.39616i	0.153294	+	0.0885043i	0.574685	−	0.818375i	$-0.305125\pi$
$733$	4.15028	+	2.39616i	0.153294	+	0.0885043i	−0.421391	+	0.906879i	$0.638458\pi$
$734$	−1.16468	−	0.672426i	−0.0429890	−	0.0248197i
$735$		0			0
$736$			2.47940i			0.0913919i
$737$	37.4500	+	64.8653i	1.37949	+	2.38934i
$738$	−8.46466	+	14.6612i	−0.311589	+	0.539687i
$739$	−9.69853	−	5.59945i	−0.356766	−	0.205979i	0.310895	−	0.950444i	$-0.399371\pi$
$739$	−9.69853	−	5.59945i	−0.356766	−	0.205979i	−0.667661	+	0.744465i	$0.732705\pi$
$740$	14.6104	−	25.3059i	0.537088	−	0.930264i
$741$	4.01845	−	5.32272i	0.147621	−	0.195535i
$742$		0			0
$743$	−33.1315	+	19.1285i	−1.21548	+	0.701757i	−0.963947	−	0.266093i	$-0.914267\pi$
$743$	−33.1315	+	19.1285i	−1.21548	+	0.701757i	−0.251531	+	0.967849i	$0.580934\pi$
$744$	−2.00000			−0.0733236
$745$	76.4630			2.80139
$746$	9.58821	−	5.53575i	0.351049	−	0.202678i
$747$	−6.18297	+	3.56974i	−0.226223	+	0.130610i
$748$	1.06124	+	0.612704i	0.0388026	+	0.0224027i
$749$		0			0
$750$	−6.06116	+	10.4982i	−0.221322	+	0.383342i
$751$	1.84025			0.0671517			0.0335758	−	0.999436i	$-0.489310\pi$
$751$	1.84025			0.0671517			0.0335758	+	0.999436i	$0.489310\pi$
$752$	−7.92907	−	4.57785i	−0.289143	−	0.166937i
$753$	−0.219413	−	0.380034i	−0.00799585	−	0.0138492i
$754$	−0.352697	−	0.0436269i	−0.0128445	−	0.00158880i
$755$	−44.3157			−1.61281
$756$		0			0
$757$	10.5961	+	18.3529i	0.385120	+	0.667048i	0.991786	−	0.127909i	$-0.0408266\pi$
$757$	10.5961	+	18.3529i	0.385120	+	0.667048i	−0.606666	+	0.794957i	$0.707493\pi$
$758$	−8.40523	−	14.5583i	−0.305292	−	0.528780i
$759$	10.7323	−	6.19631i	0.389558	−	0.224912i
$760$			7.93158i			0.287709i
$761$	−12.2381	+	7.06566i	−0.443630	+	0.256130i	−0.705136	−	0.709072i	$-0.749114\pi$
$761$	−12.2381	+	7.06566i	−0.443630	+	0.256130i	0.261506	+	0.965202i	$0.415781\pi$
$762$		−	10.2030i		−	0.369617i
$763$		0			0
$764$	0.0604880	+	0.104768i	0.00218838	+	0.00379038i
$765$		−	1.77264i		−	0.0640898i
$766$	−8.28855	−	14.3562i	−0.299478	−	0.518710i
$767$	−0.503823	+	0.667350i	−0.0181920	+	0.0240966i
$768$	−0.432757	+	0.749558i	−0.0156158	+	0.0270473i
$769$	26.5219	−	15.3124i	0.956405	−	0.552181i	0.0613401	−	0.998117i	$-0.480463\pi$
$769$	26.5219	−	15.3124i	0.956405	−	0.552181i	0.895065	+	0.445936i	$0.147129\pi$
$770$		0			0
$771$	4.17206	−	7.22621i	0.150253	−	0.260246i
$772$	−2.38633	−	1.37775i	−0.0858859	−	0.0495863i
$773$		−	9.79479i		−	0.352294i	−0.984364	−	0.176147i	$-0.943637\pi$
$773$		−	9.79479i		−	0.352294i	0.984364	−	0.176147i	$-0.0563634\pi$
$774$		−	10.3084i		−	0.370529i
$775$	17.5580	+	10.1371i	0.630703	+	0.364137i
$776$	7.04093	−	12.1952i	0.252755	−	0.437784i
$777$		0			0
$778$	1.01336	−	0.585065i	0.0363308	−	0.0209756i
$779$	−8.03691	+	13.9203i	−0.287952	+	0.498748i
$780$	−11.4941	−	1.42177i	−0.411556	−	0.0509075i
$781$	21.2624	+	36.8275i	0.760828	+	1.31779i
$782$		−	0.526121i		−	0.0188140i
$783$	−0.223977	−	0.387940i	−0.00800430	−	0.0138638i
$784$		0			0
$785$			34.6645i			1.23723i
$786$	−3.84418	+	2.21944i	−0.137117	+	0.0791647i
$787$			20.6305i			0.735397i	0.929945	+	0.367699i	$0.119854\pi$
$787$			20.6305i			0.735397i	−0.929945	+	0.367699i	$0.880146\pi$
$788$	13.0989	−	7.56267i	0.466630	−	0.269409i
$789$	3.17911	+	5.50638i	0.113179	+	0.196032i
$790$	−17.0674	−	29.5616i	−0.607230	−	1.05175i
$791$		0			0
$792$	−12.9985			−0.461883
$793$	3.55514	−	28.7411i	0.126247	−	1.02063i
$794$	−13.0987	−	22.6877i	−0.464856	−	0.805155i
$795$	33.6458	+	19.4254i	1.19330	+	0.688949i
$796$	−5.30640			−0.188080
$797$	−3.88584	+	6.73047i	−0.137643	+	0.238405i	−0.926604	−	0.376038i	$-0.877286\pi$
$797$	−3.88584	+	6.73047i	−0.137643	+	0.238405i	0.788961	+	0.614444i	$0.210619\pi$
$798$		0			0
$799$	1.68252	+	0.971406i	0.0595234	+	0.0343659i
$800$	7.59837	−	4.38692i	0.268643	−	0.155101i
$801$	−23.0345	+	13.2990i	−0.813883	+	0.469896i
$802$	−11.3687			−0.401443
$803$	32.3632			1.14207
$804$	9.72176	−	5.61286i	0.342860	−	0.197950i
$805$		0			0
$806$	−1.02278	+	8.26856i	−0.0360259	+	0.291248i
$807$	9.67389	−	16.7557i	0.340537	−	0.589828i
$808$	5.32816	+	3.07622i	0.187444	+	0.108221i
$809$	−21.2715	+	36.8433i	−0.747866	+	1.29534i	0.200977	+	0.979596i	$0.435588\pi$
$809$	−21.2715	+	36.8433i	−0.747866	+	1.29534i	−0.948844	+	0.315746i	$0.897745\pi$
$810$	5.23134	+	9.06094i	0.183810	+	0.318369i
$811$			22.1131i			0.776494i	0.921555	+	0.388247i	$0.126919\pi$
$811$			22.1131i			0.776494i	−0.921555	+	0.388247i	$0.873081\pi$
$812$		0			0
$813$	−7.20880	−	4.16200i	−0.252824	−	0.145968i
$814$	39.3764	+	22.7340i	1.38014	+	0.796826i
$815$	−16.6167			−0.582056
$816$	0.0918298	−	0.159054i	0.00321469	−	0.00556800i
$817$		−	9.78752i		−	0.342422i
$818$	−23.3314			−0.815763
$819$		0			0
$820$	27.9135			0.974782
$821$			24.3549i			0.849992i	0.905195	+	0.424996i	$0.139725\pi$
$821$			24.3549i			0.849992i	−0.905195	+	0.424996i	$0.860275\pi$
$822$	−4.06501	+	7.04081i	−0.141784	+	0.245576i
$823$	4.75914			0.165893			0.0829465	−	0.996554i	$-0.473567\pi$
$823$	4.75914			0.165893			0.0829465	+	0.996554i	$0.473567\pi$
$824$	16.7568	+	9.67453i	0.583750	+	0.337028i
$825$	−37.9784	−	21.9269i	−1.32224	−	0.763395i
$826$		0			0
$827$			7.00333i			0.243530i	0.992559	+	0.121765i	$0.0388554\pi$
$827$			7.00333i			0.243530i	−0.992559	+	0.121765i	$0.961145\pi$
$828$	2.79042	+	4.83315i	0.0969738	+	0.167964i
$829$	2.87619	−	4.98170i	0.0998941	−	0.173022i	−0.811747	−	0.584010i	$-0.801483\pi$
$829$	2.87619	−	4.98170i	0.0998941	−	0.173022i	0.911641	+	0.410988i	$0.134816\pi$
$830$	10.1946	+	5.88588i	0.353861	+	0.204302i
$831$	4.40499	−	7.62967i	0.152807	−	0.264670i
$832$	2.87757	+	2.17246i	0.0997619	+	0.0753164i
$833$		0			0
$834$	11.3493	−	6.55250i	0.392993	−	0.226894i
$835$	−54.5817			−1.88888
$836$	−12.3417			−0.426846
$837$	−9.09480	+	5.25088i	−0.314362	+	0.181497i
$838$	−10.9709	+	6.33402i	−0.378982	+	0.218805i
$839$	35.6863	+	20.6035i	1.23203	+	0.711311i	0.967452	−	0.253054i	$-0.0814350\pi$
$839$	35.6863	+	20.6035i	1.23203	+	0.711311i	0.264575	+	0.964365i	$0.414768\pi$
$840$		0			0
$841$	14.4951	−	25.1063i	0.499832	−	0.865735i
$842$	−27.6625			−0.953312
$843$	10.6207	+	6.13184i	0.365795	+	0.211192i
$844$	8.94910	+	15.5003i	0.308041	+	0.533542i
$845$	−11.7560	+	46.7929i	−0.404418	+	1.60973i
$846$	−20.6084			−0.708532
$847$		0			0
$848$	−6.04740	−	10.4744i	−0.207669	−	0.359692i
$849$	−8.19323	−	14.1911i	−0.281191	−	0.487037i
$850$	−1.61235	+	0.930892i	−0.0553032	+	0.0319293i
$851$		−	19.5214i		−	0.669184i
$852$	5.51957	−	3.18673i	0.189097	−	0.109175i
$853$			2.38939i			0.0818113i	0.999163	+	0.0409056i	$0.0130243\pi$
$853$			2.38939i			0.0818113i	−0.999163	+	0.0409056i	$0.986976\pi$
$854$		0			0
$855$	8.92654	+	15.4612i	0.305281	+	0.528762i
$856$			11.6501i			0.398193i
$857$	−6.90186	−	11.9544i	−0.235763	−	0.408353i	0.723731	−	0.690082i	$-0.242426\pi$
$857$	−6.90186	−	11.9544i	−0.235763	−	0.408353i	−0.959494	+	0.281729i	$0.909092\pi$
$858$	2.21230	−	17.8851i	0.0755266	−	0.610586i
$859$	−18.8638	+	32.6730i	−0.643624	+	1.11479i	0.340994	+	0.940066i	$0.389237\pi$
$859$	−18.8638	+	32.6730i	−0.643624	+	1.11479i	−0.984617	+	0.174724i	$0.944097\pi$
$860$	−14.7197	+	8.49841i	−0.501937	+	0.289793i
$861$		0			0
$862$	−3.20696	+	5.55462i	−0.109230	+	0.189191i
$863$	−22.0992	−	12.7590i	−0.752267	−	0.434322i	0.0742453	−	0.997240i	$-0.476345\pi$
$863$	−22.0992	−	12.7590i	−0.752267	−	0.434322i	−0.826513	+	0.562918i	$0.809679\pi$
$864$			4.54472i			0.154614i
$865$		−	51.0889i		−	1.73707i
$866$	−0.0563150	−	0.0325135i	−0.00191366	−	0.00110485i
$867$	7.33739	−	12.7087i	0.249191	−	0.431611i
$868$		0			0
$869$	45.9983	−	26.5571i	1.56039	−	0.900889i
$870$	−0.158307	+	0.274195i	−0.00536710	+	0.00929609i
$871$	−18.2335	−	43.0628i	−0.617819	−	1.45913i
$872$	2.86654	+	4.96499i	0.0970732	+	0.168136i
$873$		−	31.6966i		−	1.07277i
$874$	2.64941	+	4.58891i	0.0896175	+	0.155222i
$875$		0			0
$876$		−	4.85047i		−	0.163882i
$877$	−10.7726	+	6.21955i	−0.363764	+	0.210019i	−0.670731	−	0.741701i	$-0.734019\pi$
$877$	−10.7726	+	6.21955i	−0.363764	+	0.210019i	0.306966	+	0.951720i	$0.400686\pi$
$878$		−	36.7778i		−	1.24119i
$879$	2.74325	−	1.58382i	0.0925275	−	0.0534208i
$880$	10.7162	+	18.5609i	0.361242	+	0.625689i
$881$	11.2710	+	19.5219i	0.379728	+	0.657709i	0.991023	−	0.133694i	$-0.0426841\pi$
$881$	11.2710	+	19.5219i	0.379728	+	0.657709i	−0.611294	+	0.791404i	$0.709351\pi$
$882$		0			0
$883$	−15.1548			−0.509998			−0.254999	−	0.966941i	$-0.582075\pi$
$883$	−15.1548			−0.509998			−0.254999	+	0.966941i	$0.582075\pi$
$884$	−0.610613	−	0.460989i	−0.0205371	−	0.0155047i
$885$	0.372477	+	0.645149i	0.0125207	+	0.0216864i
$886$	−7.32989	−	4.23191i	−0.246252	−	0.142174i
$887$	−41.7749			−1.40266			−0.701332	−	0.712835i	$-0.747411\pi$
$887$	−41.7749			−1.40266			−0.701332	+	0.712835i	$0.747411\pi$
$888$	3.40729	−	5.90159i	0.114341	−	0.198044i
$889$		0			0
$890$	37.9798	+	21.9277i	1.27309	+	0.735017i
$891$	−14.0990	+	8.14004i	−0.472333	+	0.272702i
$892$	−14.2362	+	8.21925i	−0.476662	+	0.275201i
$893$	−19.5670			−0.654784
$894$	17.8319			0.596389
$895$	49.1072	−	28.3521i	1.64147	−	0.947705i
$896$		0			0
$897$	−7.12498	+	3.01684i	−0.237896	+	0.100729i
$898$	−11.3152	+	19.5984i	−0.377592	+	0.654008i
$899$	0.197248	+	0.113881i	0.00657860	+	0.00379815i
$900$	9.87445	−	17.1031i	0.329148	−	0.570102i
$901$	1.28324	+	2.22264i	0.0427509	+	0.0740468i
$902$			43.4339i			1.44619i
$903$		0			0
$904$	−14.3062	−	8.25971i	−0.475818	−	0.274714i
$905$	5.35943	+	3.09427i	0.178153	+	0.102857i
$906$	−10.3349			−0.343353
$907$	2.14376	−	3.71310i	0.0711823	−	0.123291i	−0.828237	−	0.560377i	$-0.810656\pi$
$907$	2.14376	−	3.71310i	0.0711823	−	0.123291i	0.899420	+	0.437086i	$0.143989\pi$
$908$			5.63095i			0.186870i
$909$	13.8484			0.459323
$910$		0			0
$911$	−3.87618			−0.128423			−0.0642117	−	0.997936i	$-0.520453\pi$
$911$	−3.87618			−0.128423			−0.0642117	+	0.997936i	$0.520453\pi$
$912$			1.84972i			0.0612505i
$913$	−9.15853	+	15.8630i	−0.303103	+	0.524990i
$914$	−16.3170			−0.539719
$915$	−22.3441	−	12.9004i	−0.738672	−	0.426473i
$916$	24.0084	+	13.8613i	0.793260	+	0.457989i
$917$		0			0
$918$		−	0.964376i		−	0.0318291i
$919$	−22.9524	−	39.7547i	−0.757129	−	1.31139i	−0.944309	−	0.329060i	$-0.893268\pi$
$919$	−22.9524	−	39.7547i	−0.757129	−	1.31139i	0.187180	−	0.982326i	$-0.440065\pi$
$920$	4.60091	−	7.96901i	0.151688	−	0.262731i
$921$	14.7653	+	8.52476i	0.486534	+	0.280900i
$922$	−9.63892	+	16.6951i	−0.317441	+	0.549824i
$923$	−10.3522	−	24.4491i	−0.340745	−	0.804752i
$924$		0			0
$925$	−59.8253	+	34.5401i	−1.96704	+	1.13567i
$926$	2.70218			0.0887990
$927$	43.5525			1.43045
$928$	0.0853606	−	0.0492830i	0.00280210	−	0.00161779i
$929$	8.51833	−	4.91806i	0.279477	−	0.161356i	−0.353709	−	0.935355i	$-0.615080\pi$
$929$	8.51833	−	4.91806i	0.279477	−	0.161356i	0.633187	+	0.773999i	$0.281746\pi$
$930$	6.42818	+	3.71131i	0.210788	+	0.121699i
$931$		0			0
$932$	−10.0552	+	17.4161i	−0.329368	+	0.570483i
$933$	−14.6865			−0.480814
$934$	15.9267	+	9.19528i	0.521137	+	0.300879i
$935$	−2.27394	−	3.93858i	−0.0743657	−	0.128805i
$936$	8.05429	+	0.996277i	0.263263	+	0.0325643i
$937$	−21.5135			−0.702815			−0.351407	−	0.936223i	$-0.614297\pi$
$937$	−21.5135			−0.702815			−0.351407	+	0.936223i	$0.614297\pi$
$938$		0			0
$939$	−1.96383	−	3.40145i	−0.0640871	−	0.111002i
$940$	16.9898	+	29.4272i	0.554147	+	0.959811i
$941$	−5.55854	+	3.20923i	−0.181203	+	0.104618i	−0.587858	−	0.808964i	$-0.700029\pi$
$941$	−5.55854	+	3.20923i	−0.181203	+	0.104618i	0.406655	+	0.913582i	$0.366695\pi$
$942$			8.08410i			0.263394i
$943$	16.1497	−	9.32402i	0.525906	−	0.303632i
$944$		−	0.231914i		−	0.00754816i
$945$		0			0
$946$	−13.2237	−	22.9041i	−0.429939	−	0.744675i
$947$			7.57266i			0.246078i	0.992402	+	0.123039i	$0.0392641\pi$
$947$			7.57266i			0.246078i	−0.992402	+	0.123039i	$0.960736\pi$
$948$	−3.98028	−	6.89405i	−0.129274	−	0.223908i
$949$	−20.0532	−	2.48048i	−0.650954	−	0.0805199i
$950$	9.37545	−	16.2388i	0.304180	−	0.526855i
$951$	−21.8770	+	12.6307i	−0.709412	+	0.409579i
$952$		0			0
$953$	−17.9022	+	31.0075i	−0.579909	+	1.00443i	0.415580	+	0.909557i	$0.363579\pi$
$953$	−17.9022	+	31.0075i	−0.579909	+	1.00443i	−0.995489	+	0.0948754i	$0.969755\pi$
$954$	−23.5767	−	13.6120i	−0.763323	−	0.440705i
$955$		−	0.448980i		−	0.0145286i
$956$			6.62968i			0.214419i
$957$	−0.426652	−	0.246328i	−0.0137917	−	0.00796265i
$958$	20.4354	−	35.3951i	0.660238	−	1.14357i
$959$		0			0
$960$	2.78184	−	1.60610i	0.0897836	−	0.0518366i
$961$	−12.8302	+	22.2225i	−0.413877	+	0.716856i
$962$	−22.6564	−	17.1047i	−0.730471	−	0.551477i
$963$	13.1115	+	22.7098i	0.422513	+	0.731814i
$964$		−	1.61687i		−	0.0520757i
$965$	5.11326	+	8.85642i	0.164602	+	0.285098i
$966$		0			0
$967$		−	32.3876i		−	1.04152i	−0.853704	−	0.520758i	$-0.825649\pi$
$967$		−	32.3876i		−	1.04152i	0.853704	−	0.520758i	$-0.174351\pi$
$968$	−19.3549	+	11.1745i	−0.622089	+	0.359163i
$969$		−	0.392506i		−	0.0126091i
$970$	−45.2604	+	26.1311i	−1.45322	+	0.839019i
$971$	17.2033	+	29.7969i	0.552079	+	0.956229i	0.998124	+	0.0612186i	$0.0194987\pi$
$971$	17.2033	+	29.7969i	0.552079	+	0.956229i	−0.446045	+	0.895010i	$0.647168\pi$
$972$	8.03708	+	13.9206i	0.257789	+	0.446504i
$973$		0			0
$974$	−17.6293			−0.564880
$975$	21.8520	+	16.4974i	0.699824	+	0.528340i
$976$	4.01605	+	6.95601i	0.128551	+	0.222656i
$977$	−20.0471	−	11.5742i	−0.641364	−	0.370291i	0.143776	−	0.989610i	$-0.454076\pi$
$977$	−20.0471	−	11.5742i	−0.641364	−	0.370291i	−0.785140	+	0.619319i	$0.787409\pi$
$978$	−3.87517			−0.123914
$979$	−34.1198	+	59.0972i	−1.09047	+	1.88876i
$980$		0			0
$981$	11.1756	+	6.45224i	0.356810	+	0.206004i
$982$	−16.3332	+	9.42997i	−0.521213	+	0.300922i
$983$	−40.7534	+	23.5290i	−1.29983	+	0.750458i	−0.980375	−	0.197143i	$-0.936834\pi$
$983$	−40.7534	+	23.5290i	−1.29983	+	0.750458i	−0.319456	+	0.947601i	$0.603500\pi$
$984$	6.50970			0.207522
$985$	−56.1349			−1.78861
$986$	−0.0181133	+	0.0104577i	−0.000576844	+	0.000333041i
$987$		0			0
$988$	7.64727	+	0.945931i	0.243292	+	0.0300941i
$989$	−5.67749	+	9.83371i	−0.180534	+	0.312694i
$990$	41.7785	+	24.1208i	1.32781	+	0.766611i
$991$	5.95052	−	10.3066i	0.189025	−	0.327400i	−0.755901	−	0.654686i	$-0.772801\pi$
$991$	5.95052	−	10.3066i	0.189025	−	0.327400i	0.944925	+	0.327286i	$0.106134\pi$
$992$	−1.15538	−	2.00118i	−0.0366834	−	0.0635375i
$993$		−	4.15916i		−	0.131987i
$994$		0			0
$995$	17.0553	+	9.84686i	0.540688	+	0.312167i
$996$	2.37749	+	1.37265i	0.0753337	+	0.0434939i
$997$	−13.0143			−0.412166			−0.206083	−	0.978534i	$-0.566072\pi$
$997$	−13.0143			−0.412166			−0.206083	+	0.978534i	$0.566072\pi$
$998$	1.05371	−	1.82508i	0.0333546	−	0.0577718i
$999$		−	35.7825i		−	1.13211i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.o.e.569.1		12
7.2	even	3		1274.2.m.c.491.1		12
7.3	odd	6		1274.2.v.e.361.4		12
7.4	even	3		1274.2.v.d.361.6		12
7.5	odd	6		182.2.m.b.127.3	yes	12
7.6	odd	2		1274.2.o.d.569.3		12
13.4	even	6		1274.2.v.d.667.6		12
21.5	even	6		1638.2.bj.g.127.4		12
28.19	even	6		1456.2.cc.d.673.2		12
91.4	even	6	inner	1274.2.o.e.459.4		12
91.17	odd	6		1274.2.o.d.459.6		12
91.30	even	6		1274.2.m.c.589.1		12
91.54	even	12		2366.2.a.bf.1.2		6
91.68	odd	6		2366.2.d.r.337.2		12
91.69	odd	6		1274.2.v.e.667.4		12
91.75	odd	6		2366.2.d.r.337.8		12
91.82	odd	6		182.2.m.b.43.3	✓	12
91.89	even	12		2366.2.a.bh.1.2		6
273.173	even	6		1638.2.bj.g.1135.6		12
364.355	even	6		1456.2.cc.d.225.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.3	✓	12	91.82	odd	6
182.2.m.b.127.3	yes	12	7.5	odd	6
1274.2.m.c.491.1		12	7.2	even	3
1274.2.m.c.589.1		12	91.30	even	6
1274.2.o.d.459.6		12	91.17	odd	6
1274.2.o.d.569.3		12	7.6	odd	2
1274.2.o.e.459.4		12	91.4	even	6	inner
1274.2.o.e.569.1		12	1.1	even	1	trivial
1274.2.v.d.361.6		12	7.4	even	3
1274.2.v.d.667.6		12	13.4	even	6
1274.2.v.e.361.4		12	7.3	odd	6
1274.2.v.e.667.4		12	91.69	odd	6
1456.2.cc.d.225.2		12	364.355	even	6
1456.2.cc.d.673.2		12	28.19	even	6
1638.2.bj.g.127.4		12	21.5	even	6
1638.2.bj.g.1135.6		12	273.173	even	6
2366.2.a.bf.1.2		6	91.54	even	12
2366.2.a.bh.1.2		6	91.89	even	12
2366.2.d.r.337.2		12	91.68	odd	6
2366.2.d.r.337.8		12	91.75	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.432757 + 0.749558i) q^{3} -1.00000 q^{4} +(3.21409 + 1.85566i) q^{5} +(0.749558 + 0.432757i) q^{6} +1.00000i q^{8} +(1.12544 + 1.94932i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.432757 + 0.749558i) q^{3} -1.00000 q^{4} +(3.21409 + 1.85566i) q^{5} +(0.749558 + 0.432757i) q^{6} +1.00000i q^{8} +(1.12544 + 1.94932i) q^{9} +(1.85566 - 3.21409i) q^{10} +(5.00118 + 2.88743i) q^{11} +(0.432757 - 0.749558i) q^{12} +(-2.87757 - 2.17246i) q^{13} +(-2.78184 + 1.60610i) q^{15} +1.00000 q^{16} -0.212197 q^{17} +(1.94932 - 1.12544i) q^{18} +(1.85081 - 1.06857i) q^{19} +(-3.21409 - 1.85566i) q^{20} +(2.88743 - 5.00118i) q^{22} -2.47940 q^{23} +(-0.749558 - 0.432757i) q^{24} +(4.38692 + 7.59837i) q^{25} +(-2.17246 + 2.87757i) q^{26} -4.54472 q^{27} +(0.0492830 + 0.0853606i) q^{29} +(1.60610 + 2.78184i) q^{30} +(2.00118 - 1.15538i) q^{31} -1.00000i q^{32} +(-4.32860 + 2.49912i) q^{33} +0.212197i q^{34} +(-1.12544 - 1.94932i) q^{36} +7.87343i q^{37} +(-1.06857 - 1.85081i) q^{38} +(2.87367 - 1.21676i) q^{39} +(-1.85566 + 3.21409i) q^{40} +(-6.51354 + 3.76060i) q^{41} +(2.28987 - 3.96617i) q^{43} +(-5.00118 - 2.88743i) q^{44} +8.35373i q^{45} +2.47940i q^{46} +(-7.92907 - 4.57785i) q^{47} +(-0.432757 + 0.749558i) q^{48} +(7.59837 - 4.38692i) q^{50} +(0.0918298 - 0.159054i) q^{51} +(2.87757 + 2.17246i) q^{52} +(-6.04740 - 10.4744i) q^{53} +4.54472i q^{54} +(10.7162 + 18.5609i) q^{55} +1.84972i q^{57} +(0.0853606 - 0.0492830i) q^{58} -0.231914i q^{59} +(2.78184 - 1.60610i) q^{60} +(4.01605 + 6.95601i) q^{61} +(-1.15538 - 2.00118i) q^{62} -1.00000 q^{64} +(-5.21745 - 12.3223i) q^{65} +(2.49912 + 4.32860i) q^{66} +(11.2323 + 6.48500i) q^{67} +0.212197 q^{68} +(1.07298 - 1.85845i) q^{69} +(6.37721 + 3.68188i) q^{71} +(-1.94932 + 1.12544i) q^{72} +(4.85333 - 2.80207i) q^{73} +7.87343 q^{74} -7.59389 q^{75} +(-1.85081 + 1.06857i) q^{76} +(-1.21676 - 2.87367i) q^{78} +(4.59875 - 7.96526i) q^{79} +(3.21409 + 1.85566i) q^{80} +(-1.40956 + 2.44144i) q^{81} +(3.76060 + 6.51354i) q^{82} +3.17186i q^{83} +(-0.682021 - 0.393765i) q^{85} +(-3.96617 - 2.28987i) q^{86} -0.0853103 q^{87} +(-2.88743 + 5.00118i) q^{88} +11.8167i q^{89} +8.35373 q^{90} +2.47940 q^{92} +2.00000i q^{93} +(-4.57785 + 7.92907i) q^{94} +7.93158 q^{95} +(0.749558 + 0.432757i) q^{96} +(-12.1952 - 7.04093i) q^{97} +12.9985i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} - 12 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q + 2 * q^3 - 12 * q^4 - 6 * q^6 - 6 * q^9	\( 12 q + 2 q^{3} - 12 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} + 18 q^{11} - 2 q^{12} + 8 q^{13} - 6 q^{15} + 12 q^{16} + 8 q^{17} + 12 q^{19} - 2 q^{22} + 12 q^{23} + 6 q^{24} + 12 q^{25} + 2 q^{26} - 40 q^{27} - 10 q^{29} + 14 q^{30} - 18 q^{31} + 12 q^{33} + 6 q^{36} + 4 q^{38} + 24 q^{39} - 2 q^{40} + 24 q^{41} + 26 q^{43} - 18 q^{44} - 48 q^{47} + 2 q^{48} - 12 q^{50} + 18 q^{51} - 8 q^{52} - 18 q^{53} + 6 q^{55} - 24 q^{58} + 6 q^{60} + 28 q^{61} + 2 q^{62} - 12 q^{64} - 4 q^{65} + 42 q^{67} - 8 q^{68} - 32 q^{69} + 48 q^{71} + 48 q^{73} - 96 q^{75} - 12 q^{76} - 8 q^{78} - 22 q^{79} - 34 q^{81} - 6 q^{82} + 54 q^{85} + 6 q^{86} + 4 q^{87} + 2 q^{88} - 12 q^{90} - 12 q^{92} - 8 q^{94} - 64 q^{95} - 6 q^{96} - 60 q^{97}+O(q^{100}) \) 12 * q + 2 * q^3 - 12 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 + 18 * q^11 - 2 * q^12 + 8 * q^13 - 6 * q^15 + 12 * q^16 + 8 * q^17 + 12 * q^19 - 2 * q^22 + 12 * q^23 + 6 * q^24 + 12 * q^25 + 2 * q^26 - 40 * q^27 - 10 * q^29 + 14 * q^30 - 18 * q^31 + 12 * q^33 + 6 * q^36 + 4 * q^38 + 24 * q^39 - 2 * q^40 + 24 * q^41 + 26 * q^43 - 18 * q^44 - 48 * q^47 + 2 * q^48 - 12 * q^50 + 18 * q^51 - 8 * q^52 - 18 * q^53 + 6 * q^55 - 24 * q^58 + 6 * q^60 + 28 * q^61 + 2 * q^62 - 12 * q^64 - 4 * q^65 + 42 * q^67 - 8 * q^68 - 32 * q^69 + 48 * q^71 + 48 * q^73 - 96 * q^75 - 12 * q^76 - 8 * q^78 - 22 * q^79 - 34 * q^81 - 6 * q^82 + 54 * q^85 + 6 * q^86 + 4 * q^87 + 2 * q^88 - 12 * q^90 - 12 * q^92 - 8 * q^94 - 64 * q^95 - 6 * q^96 - 60 * q^97

Introduction

L-functions

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Database

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