LMFDB - Embedded newform 1274.2.v.e.361.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1274,2,Mod(361,1274)]

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, 5]))

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

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

chi := DirichletCharacter("1274.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.v (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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.4
Root			$0.500000 + 1.73154i$ of defining polynomial
Character	$\chi$	$=$	1274.361
Dual form			1274.2.v.e.667.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} -0.865515 q^{3} +(0.500000 + 0.866025i) q^{4} +(3.21409 - 1.85566i) q^{5} +(-0.749558 - 0.432757i) q^{6} +1.00000i q^{8} -2.25088 q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} -0.865515 q^{3} +(0.500000 + 0.866025i) q^{4} +(3.21409 - 1.85566i) q^{5} +(-0.749558 - 0.432757i) q^{6} +1.00000i q^{8} -2.25088 q^{9} +3.71131 q^{10} -5.77486i q^{11} +(-0.432757 - 0.749558i) q^{12} +(2.87757 + 2.17246i) q^{13} +(-2.78184 + 1.60610i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.106098 - 0.183768i) q^{17} +(-1.94932 - 1.12544i) q^{18} -2.13714i q^{19} +(3.21409 + 1.85566i) q^{20} +(2.88743 - 5.00118i) q^{22} +(1.23970 - 2.14722i) q^{23} -0.865515i q^{24} +(4.38692 - 7.59837i) q^{25} +(1.40582 + 3.32019i) q^{26} +4.54472 q^{27} +(0.0492830 + 0.0853606i) q^{29} -3.21220 q^{30} +(2.00118 + 1.15538i) q^{31} +(-0.866025 + 0.500000i) q^{32} +4.99823i q^{33} -0.212197i q^{34} +(-1.12544 - 1.94932i) q^{36} +(-6.81859 - 3.93672i) q^{37} +(1.06857 - 1.85081i) q^{38} +(-2.49058 - 1.88029i) 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} +(-7.23455 + 4.17687i) q^{45} +(2.14722 - 1.23970i) 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} +(-0.442616 + 3.57828i) q^{52} +(-6.04740 + 10.4744i) q^{53} +(3.93584 + 2.27236i) q^{54} +(-10.7162 - 18.5609i) q^{55} +1.84972i q^{57} +0.0985660i q^{58} +(0.200843 - 0.115957i) q^{59} +(-2.78184 - 1.60610i) q^{60} +8.03211 q^{61} +(1.15538 + 2.00118i) q^{62} -1.00000 q^{64} +(13.2801 + 1.64269i) q^{65} +(-2.49912 + 4.32860i) q^{66} -12.9700i q^{67} +(0.106098 - 0.183768i) q^{68} +(-1.07298 + 1.85845i) q^{69} +(6.37721 + 3.68188i) q^{71} -2.25088i q^{72} +(4.85333 + 2.80207i) q^{73} +(-3.93672 - 6.81859i) q^{74} +(-3.79695 + 6.57650i) q^{75} +(1.85081 - 1.06857i) q^{76} +(-1.21676 - 2.87367i) q^{78} +(4.59875 + 7.96526i) q^{79} +3.71131i q^{80} +2.81913 q^{81} +7.52119 q^{82} -3.17186i q^{83} +(-0.682021 - 0.393765i) q^{85} +(3.96617 - 2.28987i) q^{86} +(-0.0426552 - 0.0738809i) q^{87} +5.77486 q^{88} +(10.2335 + 5.90833i) q^{89} -8.35373 q^{90} +2.47940 q^{92} +(-1.73205 - 1.00000i) q^{93} -9.15570 q^{94} +(-3.96579 - 6.86895i) 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 + 4 q^{3} + 6 q^{4} + 6 q^{6} + 12 q^{9}+O(q^{10}) $ 12 * q + 4 * q^3 + 6 * q^4 + 6 * q^6 + 12 * q^9	$ 12 q + 4 q^{3} + 6 q^{4} + 6 q^{6} + 12 q^{9} + 4 q^{10} + 2 q^{12} - 8 q^{13} - 6 q^{15} - 6 q^{16} + 4 q^{17} - 2 q^{22} - 6 q^{23} + 12 q^{25} + 16 q^{26} + 40 q^{27} - 10 q^{29} - 28 q^{30} - 18 q^{31} + 6 q^{36} + 6 q^{37} - 4 q^{38} + 30 q^{39} + 2 q^{40} - 24 q^{41} + 26 q^{43} + 18 q^{44} - 72 q^{45} + 6 q^{46} - 48 q^{47} - 2 q^{48} - 12 q^{50} + 18 q^{51} - 4 q^{52} - 18 q^{53} + 36 q^{54} - 6 q^{55} - 6 q^{59} - 6 q^{60} + 56 q^{61} - 2 q^{62} - 12 q^{64} + 38 q^{65} - 4 q^{68} + 32 q^{69} + 48 q^{71} + 48 q^{73} - 48 q^{75} + 12 q^{76} - 8 q^{78} - 22 q^{79} + 68 q^{81} - 12 q^{82} + 54 q^{85} - 6 q^{86} + 2 q^{87} - 4 q^{88} - 12 q^{89} + 12 q^{90} - 12 q^{92} - 16 q^{94} + 32 q^{95} - 6 q^{96} + 60 q^{97}+O(q^{100}) $ 12 * q + 4 * q^3 + 6 * q^4 + 6 * q^6 + 12 * q^9 + 4 * q^10 + 2 * q^12 - 8 * q^13 - 6 * q^15 - 6 * q^16 + 4 * q^17 - 2 * q^22 - 6 * q^23 + 12 * q^25 + 16 * q^26 + 40 * q^27 - 10 * q^29 - 28 * q^30 - 18 * q^31 + 6 * q^36 + 6 * q^37 - 4 * q^38 + 30 * q^39 + 2 * q^40 - 24 * q^41 + 26 * q^43 + 18 * q^44 - 72 * q^45 + 6 * q^46 - 48 * q^47 - 2 * q^48 - 12 * q^50 + 18 * q^51 - 4 * q^52 - 18 * q^53 + 36 * q^54 - 6 * q^55 - 6 * q^59 - 6 * q^60 + 56 * q^61 - 2 * q^62 - 12 * q^64 + 38 * q^65 - 4 * q^68 + 32 * q^69 + 48 * q^71 + 48 * q^73 - 48 * q^75 + 12 * q^76 - 8 * q^78 - 22 * q^79 + 68 * q^81 - 12 * q^82 + 54 * q^85 - 6 * q^86 + 2 * q^87 - 4 * q^88 - 12 * q^89 + 12 * q^90 - 12 * q^92 - 16 * q^94 + 32 * q^95 - 6 * q^96 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$885$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.865515			−0.499705			−0.249853	−	0.968284i	$-0.580382\pi$
$3$	−0.865515			−0.499705			−0.249853	+	0.968284i	$0.580382\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	3.21409	−	1.85566i	1.43739	−	0.829875i	0.439718	−	0.898136i	$-0.355078\pi$
$5$	3.21409	−	1.85566i	1.43739	−	0.829875i	0.997667	+	0.0682612i	$0.0217451\pi$
$6$	−0.749558	−	0.432757i	−0.306006	−	0.176673i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−2.25088			−0.750295
$10$	3.71131			1.17362
$11$		−	5.77486i		−	1.74119i	−0.492003	−	0.870594i	$-0.663735\pi$
$11$		−	5.77486i		−	1.74119i	0.492003	−	0.870594i	$-0.336265\pi$
$12$	−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
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.106098	−	0.183768i	−0.0257327	−	0.0445703i	0.852872	−	0.522120i	$-0.174859\pi$
$17$	−0.106098	−	0.183768i	−0.0257327	−	0.0445703i	−0.878605	+	0.477549i	$0.841525\pi$
$18$	−1.94932	−	1.12544i	−0.459460	−	0.265269i
$19$		−	2.13714i		−	0.490293i	−0.969486	−	0.245146i	$-0.921164\pi$
$19$		−	2.13714i		−	0.490293i	0.969486	−	0.245146i	$-0.0788360\pi$
$20$	3.21409	+	1.85566i	0.718693	+	0.414937i
$21$		0			0
$22$	2.88743	−	5.00118i	0.615603	−	1.06626i
$23$	1.23970	−	2.14722i	0.258495	−	0.447727i	−0.707344	−	0.706870i	$-0.750107\pi$
$23$	1.23970	−	2.14722i	0.258495	−	0.447727i	0.965839	+	0.259143i	$0.0834400\pi$
$24$		−	0.865515i		−	0.176673i
$25$	4.38692	−	7.59837i	0.877384	−	1.51967i
$26$	1.40582	+	3.32019i	0.275705	+	0.651143i
$27$	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	$0.830420\pi$
$30$	−3.21220			−0.586464
$31$	2.00118	+	1.15538i	0.359422	+	0.207513i	0.668827	−	0.743418i	$-0.266797\pi$
$31$	2.00118	+	1.15538i	0.359422	+	0.207513i	−0.309405	+	0.950930i	$0.600130\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$			4.99823i			0.870080i
$34$		−	0.212197i		−	0.0363915i
$35$		0			0
$36$	−1.12544	−	1.94932i	−0.187574	−	0.324887i
$37$	−6.81859	−	3.93672i	−1.12097	−	0.647192i	−0.179321	−	0.983791i	$-0.557390\pi$
$37$	−6.81859	−	3.93672i	−1.12097	−	0.647192i	−0.941648	+	0.336599i	$0.890723\pi$
$38$	1.06857	−	1.85081i	0.173345	−	0.300242i
$39$	−2.49058	−	1.88029i	−0.398812	−	0.301088i
$40$	1.85566	+	3.21409i	0.293405	+	0.508192i
$41$	6.51354	−	3.76060i	1.01724	−	0.587306i	0.103940	−	0.994584i	$-0.466855\pi$
$41$	6.51354	−	3.76060i	1.01724	−	0.587306i	0.913305	+	0.407277i	$0.133522\pi$
$42$		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
$45$	−7.23455	+	4.17687i	−1.07846	+	0.622651i
$46$	2.14722	−	1.23970i	0.316591	−	0.182784i
$47$	−7.92907	+	4.57785i	−1.15657	+	0.667748i	−0.950480	−	0.310785i	$-0.899408\pi$
$47$	−7.92907	+	4.57785i	−1.15657	+	0.667748i	−0.206093	+	0.978532i	$0.566075\pi$
$48$	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
$52$	−0.442616	+	3.57828i	−0.0613798	+	0.496218i
$53$	−6.04740	+	10.4744i	−0.830674	+	1.43877i	0.0668303	+	0.997764i	$0.478711\pi$
$53$	−6.04740	+	10.4744i	−0.830674	+	1.43877i	−0.897504	+	0.441005i	$0.854622\pi$
$54$	3.93584	+	2.27236i	0.535600	+	0.309229i
$55$	−10.7162	−	18.5609i	−1.44497	−	2.50276i
$56$		0			0
$57$			1.84972i			0.245002i
$58$			0.0985660i			0.0129423i
$59$	0.200843	−	0.115957i	0.0261476	−	0.0150963i	−0.486869	−	0.873475i	$-0.661861\pi$
$59$	0.200843	−	0.115957i	0.0261476	−	0.0150963i	0.513017	+	0.858379i	$0.328528\pi$
$60$	−2.78184	−	1.60610i	−0.359135	−	0.207346i
$61$	8.03211			1.02841			0.514203	−	0.857668i	$-0.328088\pi$
$61$	8.03211			1.02841			0.514203	+	0.857668i	$0.328088\pi$
$62$	1.15538	+	2.00118i	0.146734	+	0.254150i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	13.2801	+	1.64269i	1.64720	+	0.203750i
$66$	−2.49912	+	4.32860i	−0.307620	+	0.532813i
$67$		−	12.9700i		−	1.58454i	−0.610172	−	0.792269i	$-0.708900\pi$
$67$		−	12.9700i		−	1.58454i	0.610172	−	0.792269i	$-0.291100\pi$
$68$	0.106098	−	0.183768i	0.0128663	−	0.0222851i
$69$	−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	$0.522722\pi$
$72$		−	2.25088i		−	0.265269i
$73$	4.85333	+	2.80207i	0.568039	+	0.327958i	0.756366	−	0.654149i	$-0.226973\pi$
$73$	4.85333	+	2.80207i	0.568039	+	0.327958i	−0.188327	+	0.982106i	$0.560306\pi$
$74$	−3.93672	−	6.81859i	−0.457634	−	0.792645i
$75$	−3.79695	+	6.57650i	−0.438434	+	0.759389i
$76$	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	0.999796	+	0.0202088i	$0.00643311\pi$
$79$	4.59875	+	7.96526i	0.517399	+	0.896162i	−0.482397	+	0.875953i	$0.660234\pi$
$80$			3.71131i			0.414937i
$81$	2.81913			0.313237
$82$	7.52119			0.830577
$83$		−	3.17186i		−	0.348157i	−0.984732	−	0.174078i	$-0.944305\pi$
$83$		−	3.17186i		−	0.348157i	0.984732	−	0.174078i	$-0.0556946\pi$
$84$		0			0
$85$	−0.682021	−	0.393765i	−0.0739755	−	0.0427098i
$86$	3.96617	−	2.28987i	0.427683	−	0.246923i
$87$	−0.0426552	−	0.0738809i	−0.00457311	−	0.00792087i
$88$	5.77486			0.615603
$89$	10.2335	+	5.90833i	1.08475	+	0.626282i	0.932174	−	0.362010i	$-0.117909\pi$
$89$	10.2335	+	5.90833i	1.08475	+	0.626282i	0.152577	+	0.988292i	$0.451243\pi$
$90$	−8.35373			−0.880561
$91$		0			0
$92$	2.47940			0.258495
$93$	−1.73205	−	1.00000i	−0.179605	−	0.103695i
$94$	−9.15570			−0.944338
$95$	−3.96579	−	6.86895i	−0.406882	−	0.704740i
$96$	0.749558	−	0.432757i	0.0765014	−	0.0441681i
$97$	12.1952	+	7.04093i	1.23824	+	0.714898i	0.968734	−	0.248101i	$-0.0798064\pi$
$97$	12.1952	+	7.04093i	1.23824	+	0.714898i	0.269506	+	0.962999i	$0.413140\pi$
$98$		0			0
$99$			12.9985i			1.30640i
$100$	8.77384			0.877384
$101$	6.15243			0.612190			0.306095	−	0.952001i	$-0.400977\pi$
$101$	6.15243			0.612190			0.306095	+	0.952001i	$0.400977\pi$
$102$			0.183660i			0.0181850i
$103$	−9.67453	−	16.7568i	−0.953260	−	1.65109i	−0.738301	−	0.674471i	$-0.764372\pi$
$103$	−9.67453	−	16.7568i	−0.953260	−	1.65109i	−0.214959	−	0.976623i	$-0.568962\pi$
$104$	−2.17246	+	2.87757i	−0.213027	+	0.282169i
$105$		0			0
$106$	−10.4744	+	6.04740i	−1.01736	+	0.587375i
$107$	−5.82506	+	10.0893i	−0.563130	+	0.975369i	0.434091	+	0.900869i	$0.357070\pi$
$107$	−5.82506	+	10.0893i	−0.563130	+	0.975369i	−0.997221	+	0.0745005i	$0.976264\pi$
$108$	2.27236	+	3.93584i	0.218658	+	0.378727i
$109$	−4.96499	−	2.86654i	−0.475559	−	0.274564i	0.243005	−	0.970025i	$-0.421867\pi$
$109$	−4.96499	−	2.86654i	−0.475559	−	0.274564i	−0.718564	+	0.695461i	$0.755200\pi$
$110$		−	21.4323i		−	2.04349i
$111$	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	$0.883403\pi$
$114$	−0.924862	+	1.60191i	−0.0866213	+	0.150032i
$115$		−	9.20183i		−	0.858075i
$116$	−0.0492830	+	0.0853606i	−0.00457581	+	0.00792554i
$117$	−6.47708	−	4.88995i	−0.598807	−	0.452076i
$118$	0.231914			0.0213494
$119$		0			0
$120$	−1.60610	−	2.78184i	−0.146616	−	0.253946i
$121$	−22.3491			−2.03173
$122$	6.95601	+	4.01605i	0.629768	+	0.363597i
$123$	−5.63757	+	3.25485i	−0.508323	+	0.293480i
$124$			2.31076i			0.207513i
$125$		−	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	$-0.341863\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−1.98191	+	3.43278i	−0.174498	+	0.302239i
$130$	10.6796	+	8.06267i	0.936661	+	0.707143i
$131$	2.56429	+	4.44149i	0.224043	+	0.388055i	0.956032	−	0.293262i	$-0.0947409\pi$
$131$	2.56429	+	4.44149i	0.224043	+	0.388055i	−0.731989	+	0.681317i	$0.761408\pi$
$132$	−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
$136$	0.183768	−	0.106098i	0.0157580	−	0.00909787i
$137$	8.13482	−	4.69664i	0.695005	−	0.401261i	−0.110479	−	0.993878i	$-0.535239\pi$
$137$	8.13482	−	4.69664i	0.695005	−	0.401261i	0.805484	+	0.592617i	$0.201905\pi$
$138$	−1.85845	+	1.07298i	−0.158202	+	0.0913380i
$139$	−7.57063	+	13.1127i	−0.642133	+	1.11221i	0.342823	+	0.939400i	$0.388617\pi$
$139$	−7.57063	+	13.1127i	−0.642133	+	1.11221i	−0.984956	+	0.172806i	$0.944717\pi$
$140$		0			0
$141$	6.86273	−	3.96220i	0.577946	−	0.333677i
$142$	3.68188	+	6.37721i	0.308977	+	0.535164i
$143$	12.5456	−	16.6176i	1.04912	−	1.38963i
$144$	1.12544	−	1.94932i	0.0937868	−	0.162444i
$145$	0.316800	+	0.182905i	0.0263088	+	0.0151894i
$146$	2.80207	+	4.85333i	0.231901	+	0.401664i
$147$		0			0
$148$		−	7.87343i		−	0.647192i
$149$			20.6027i			1.68784i	0.536470	+	0.843919i	$0.319757\pi$
$149$			20.6027i			1.68784i	−0.536470	+	0.843919i	$0.680243\pi$
$150$	−6.57650	+	3.79695i	−0.536969	+	0.310019i
$151$	10.3410	+	5.97036i	0.841535	+	0.485861i	0.857786	−	0.514007i	$-0.171840\pi$
$151$	10.3410	+	5.97036i	0.841535	+	0.485861i	−0.0162505	+	0.999868i	$0.505173\pi$
$152$	2.13714			0.173345
$153$	0.238815	+	0.413640i	0.0193071	+	0.0334408i
$154$		0			0
$155$	8.57596			0.688838
$156$	0.383091	−	3.09706i	0.0306718	−	0.247963i
$157$	−4.67011	+	8.08887i	−0.372715	+	0.645562i	−0.989982	−	0.141192i	$-0.954907\pi$
$157$	−4.67011	+	8.08887i	−0.372715	+	0.645562i	0.617267	+	0.786754i	$0.288240\pi$
$158$			9.19749i			0.731713i
$159$	5.23411	−	9.06575i	0.415092	−	0.718961i
$160$	−1.85566	+	3.21409i	−0.146703	+	0.254096i
$161$		0			0
$162$	2.44144	+	1.40956i	0.191817	+	0.110746i
$163$		−	4.47730i		−	0.350689i	−0.984507	−	0.175345i	$-0.943896\pi$
$163$		−	4.47730i		−	0.350689i	0.984507	−	0.175345i	$-0.0561040\pi$
$164$	6.51354	+	3.76060i	0.508622	+	0.293653i
$165$	9.27500	+	16.0648i	0.722058	+	1.25064i
$166$	1.58593	−	2.74691i	0.123092	−	0.213202i
$167$	12.7365	−	7.35342i	0.985579	−	0.569025i	0.0816295	−	0.996663i	$-0.473988\pi$
$167$	12.7365	−	7.35342i	0.985579	−	0.569025i	0.903950	+	0.427638i	$0.140654\pi$
$168$		0			0
$169$	3.56086	+	12.5028i	0.273912	+	0.961755i
$170$	−0.393765	−	0.682021i	−0.0302004	−	0.0523086i
$171$			4.81045i			0.367864i
$172$	4.57973			0.349201
$173$	−13.7657			−1.04659			−0.523294	−	0.852152i	$-0.675297\pi$
$173$	−13.7657			−1.04659			−0.523294	+	0.852152i	$0.675297\pi$
$174$		−	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
$178$	5.90833	+	10.2335i	0.442848	+	0.767035i
$179$	−15.2787			−1.14198			−0.570992	−	0.820955i	$-0.693441\pi$
$179$	−15.2787			−1.14198			−0.570992	+	0.820955i	$0.693441\pi$
$180$	−7.23455	−	4.17687i	−0.539231	−	0.311325i
$181$	−1.66748			−0.123943			−0.0619713	−	0.998078i	$-0.519739\pi$
$181$	−1.66748			−0.123943			−0.0619713	+	0.998078i	$0.519739\pi$
$182$		0			0
$183$	−6.95191			−0.513900
$184$	2.14722	+	1.23970i	0.158295	+	0.0913919i
$185$	−29.2208			−2.14835
$186$	−1.00000	−	1.73205i	−0.0733236	−	0.127000i
$187$	−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
$191$	0.120976			0.00875351			0.00437676	−	0.999990i	$-0.498607\pi$
$191$	0.120976			0.00875351			0.00437676	+	0.999990i	$0.498607\pi$
$192$	0.865515			0.0624632
$193$		−	2.75550i		−	0.198345i	−0.995070	−	0.0991725i	$-0.968380\pi$
$193$		−	2.75550i		−	0.198345i	0.995070	−	0.0991725i	$-0.0316196\pi$
$194$	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	$0.514462\pi$
$198$	−6.49927	+	11.2571i	−0.461883	+	0.800005i
$199$	2.65320	+	4.59548i	0.188080	+	0.325765i	0.944610	−	0.328194i	$-0.106440\pi$
$199$	2.65320	+	4.59548i	0.188080	+	0.325765i	−0.756530	+	0.653959i	$0.773107\pi$
$200$	7.59837	+	4.38692i	0.537286	+	0.310202i
$201$			11.2257i			0.791802i
$202$	5.32816	+	3.07622i	0.374888	+	0.216442i
$203$		0			0
$204$	−0.0918298	+	0.159054i	−0.00642937	+	0.0111360i
$205$	13.9567	−	24.1738i	0.974782	−	1.68837i
$206$		−	19.3491i		−	1.34811i
$207$	−2.79042	+	4.83315i	−0.193948	+	0.335927i
$208$	−3.32019	+	1.40582i	−0.230214	+	0.0974763i
$209$	−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	$-0.377947\pi$
$212$	−12.0948			−0.830674
$213$	−5.51957	−	3.18673i	−0.378195	−	0.218351i
$214$	−10.0893	+	5.82506i	−0.689690	+	0.398193i
$215$		−	16.9968i		−	1.15917i
$216$			4.54472i			0.309229i
$217$		0			0
$218$	−2.86654	−	4.96499i	−0.194146	−	0.336271i
$219$	−4.20063	−	2.42524i	−0.283852	−	0.163882i
$220$	10.7162	−	18.5609i	0.722484	−	1.25138i
$221$	0.0939218	−	0.759300i	0.00631786	−	0.0510761i
$222$	3.40729	+	5.90159i	0.228682	+	0.396089i
$223$	−14.2362	+	8.21925i	−0.953324	+	0.550402i	−0.894112	−	0.447844i	$-0.852192\pi$
$223$	−14.2362	+	8.21925i	−0.953324	+	0.550402i	−0.0592118	+	0.998245i	$0.518859\pi$
$224$		0			0
$225$	−9.87445	+	17.1031i	−0.658297	+	1.14020i
$226$	−14.3062	+	8.25971i	−0.951637	+	0.549428i
$227$	4.87655	−	2.81547i	0.323668	−	0.186870i	−0.329359	−	0.944205i	$-0.606832\pi$
$227$	4.87655	−	2.81547i	0.323668	−	0.186870i	0.653026	+	0.757335i	$0.273499\pi$
$228$	−1.60191	+	0.924862i	−0.106089	+	0.0612505i
$229$	−24.0084	+	13.8613i	−1.58652	+	0.915978i	−0.592646	+	0.805463i	$0.701917\pi$
$229$	−24.0084	+	13.8613i	−1.58652	+	0.915978i	−0.993874	+	0.110515i	$0.964750\pi$
$230$	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	0.980943	+	0.194296i	$0.0622422\pi$
$233$	10.0552	+	17.4161i	0.658737	+	1.14097i	−0.322206	+	0.946669i	$0.604425\pi$
$234$	−3.16435	−	7.47336i	−0.206860	−	0.488549i
$235$	−16.9898	+	29.4272i	−1.10829	+	1.91962i
$236$	0.200843	+	0.115957i	0.0130738	+	0.00754816i
$237$	−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	$-0.0687858\pi$
$240$		−	3.21220i		−	0.207346i
$241$	−1.40025	+	0.808433i	−0.0901978	+	0.0520757i	−0.544420	−	0.838812i	$-0.683250\pi$
$241$	−1.40025	+	0.808433i	−0.0901978	+	0.0520757i	0.454223	+	0.890888i	$0.349917\pi$
$242$	−19.3549	−	11.1745i	−1.24418	−	0.718326i
$243$	−16.0742			−1.03116
$244$	4.01605	+	6.95601i	0.257102	+	0.445313i
$245$		0			0
$246$	−6.50970			−0.415044
$247$	4.64284	−	6.14977i	0.295417	−	0.391300i
$248$	−1.15538	+	2.00118i	−0.0733668	+	0.127075i
$249$			2.74529i			0.173976i
$250$	7.00296	−	12.1295i	0.442906	−	0.767136i
$251$	0.253506	−	0.439085i	0.0160011	−	0.0277148i	−0.857914	−	0.513793i	$-0.828240\pi$
$251$	0.253506	−	0.439085i	0.0160011	−	0.0277148i	0.873915	+	0.486079i	$0.161573\pi$
$252$		0			0
$253$	−12.3999	−	7.15910i	−0.779576	−	0.450089i
$254$		−	11.7884i		−	0.739670i
$255$	0.590299	+	0.340809i	0.0369660	+	0.0213423i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.82032	+	8.34903i	−0.300683	+	0.520798i	−0.976291	−	0.216463i	$-0.930548\pi$
$257$	−4.82032	+	8.34903i	−0.300683	+	0.520798i	0.675608	+	0.737261i	$0.263881\pi$
$258$	−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
$262$			5.12859i			0.316845i
$263$	−7.34617			−0.452985			−0.226492	−	0.974013i	$-0.572726\pi$
$263$	−7.34617			−0.452985			−0.226492	+	0.974013i	$0.572726\pi$
$264$	−4.99823			−0.307620
$265$			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
$269$	−11.1770	−	19.3592i	−0.681476	−	1.18035i	−0.974530	−	0.224255i	$-0.928005\pi$
$269$	−11.1770	−	19.3592i	−0.681476	−	1.18035i	0.293055	−	0.956096i	$-0.405328\pi$
$270$	16.8669			1.02649
$271$	8.32891	+	4.80870i	0.505945	+	0.292108i	0.731165	−	0.682200i	$-0.238977\pi$
$271$	8.32891	+	4.80870i	0.505945	+	0.292108i	−0.225220	+	0.974308i	$0.572310\pi$
$272$	0.212197			0.0128663
$273$		0			0
$274$	9.39328			0.567469
$275$	−43.8796	−	25.3339i	−2.64604	−	1.52769i
$276$	−2.14596			−0.129171
$277$	5.08945	+	8.81518i	0.305795	+	0.529653i	0.977438	−	0.211222i	$-0.0677444\pi$
$277$	5.08945	+	8.81518i	0.305795	+	0.529653i	−0.671643	+	0.740875i	$0.734411\pi$
$278$	−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	$-0.138894\pi$
$282$	7.92439			0.471891
$283$	−18.9326			−1.12543			−0.562714	−	0.826652i	$-0.690243\pi$
$283$	−18.9326			−1.12543			−0.562714	+	0.826652i	$0.690243\pi$
$284$			7.36377i			0.436959i
$285$	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
$289$	8.47749	−	14.6834i	0.498676	−	0.863732i
$290$	0.182905	+	0.316800i	0.0107405	+	0.0186031i
$291$	−10.5552	−	6.09403i	−0.618755	−	0.357238i
$292$			5.60414i			0.327958i
$293$	3.16950	+	1.82991i	0.185164	+	0.106905i	0.589717	−	0.807610i	$-0.299239\pi$
$293$	3.16950	+	1.82991i	0.185164	+	0.106905i	−0.404553	+	0.914515i	$0.632573\pi$
$294$		0			0
$295$	0.430353	−	0.745393i	0.0250561	−	0.0433985i
$296$	3.93672	−	6.81859i	0.228817	−	0.396323i
$297$		−	26.2451i		−	1.52290i
$298$	−10.3013	+	17.8425i	−0.596741	+	1.03359i
$299$	8.23207	−	3.48560i	0.476073	−	0.201577i
$300$	−7.59389			−0.438434
$301$		0			0
$302$	5.97036	+	10.3410i	0.343555	+	0.595055i
$303$	−5.32502			−0.305915
$304$	1.85081	+	1.06857i	0.106151	+	0.0612866i
$305$	25.8159	−	14.9048i	1.47822	−	0.853448i
$306$			0.477631i			0.0273043i
$307$			19.6987i			1.12426i	0.827048	+	0.562132i	$0.190019\pi$
$307$			19.6987i			1.12426i	−0.827048	+	0.562132i	$0.809981\pi$
$308$		0			0
$309$	8.37345	+	14.5032i	0.476349	+	0.825061i
$310$	7.42700	+	4.28798i	0.421825	+	0.243541i
$311$	−8.48425	+	14.6952i	−0.481098	+	0.833286i	−0.999765	−	0.0216906i	$-0.993095\pi$
$311$	−8.48425	+	14.6952i	−0.481098	+	0.833286i	0.518667	+	0.854976i	$0.326428\pi$
$312$	1.88029	−	2.49058i	0.106451	−	0.141002i
$313$	2.26897	+	3.92997i	0.128250	+	0.222135i	0.922999	−	0.384803i	$-0.125731\pi$
$313$	2.26897	+	3.92997i	0.128250	+	0.222135i	−0.794749	+	0.606939i	$0.792397\pi$
$314$	−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	$-0.972494\pi$
$317$	−25.2763	+	14.5933i	−1.41966	+	0.819641i	−0.423392	+	0.905947i	$0.639161\pi$
$318$	9.06575	−	5.23411i	0.508382	−	0.293515i
$319$	0.492946	−	0.284603i	0.0275997	−	0.0159347i
$320$	−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
$325$	29.1308	−	12.3345i	1.61589	−	0.684194i
$326$	2.23865	−	3.87746i	0.123987	−	0.214752i
$327$	4.29727	+	2.48103i	0.237640	+	0.137201i
$328$	3.76060	+	6.51354i	0.207644	+	0.359650i
$329$		0			0
$330$			18.5500i			1.02114i
$331$		−	4.80542i		−	0.264130i	−0.991241	−	0.132065i	$-0.957839\pi$
$331$		−	4.80542i		−	0.264130i	0.991241	−	0.132065i	$-0.0421607\pi$
$332$	2.74691	−	1.58593i	0.150756	−	0.0870392i
$333$	15.3479	+	8.86109i	0.841057	+	0.485585i
$334$	14.7068			0.804722
$335$	−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	$0.339568\pi$
$338$	−3.16761	+	12.6082i	−0.172295	+	0.685795i
$339$	7.14890	−	12.3823i	0.388275	−	0.672512i
$340$		−	0.787529i		−	0.0427098i
$341$	6.67217	−	11.5565i	0.361318	−	0.625822i
$342$	−2.40522	+	4.16597i	−0.130060	+	0.225270i
$343$		0			0
$344$	3.96617	+	2.28987i	0.213841	+	0.123461i
$345$			7.96432i			0.428784i
$346$	−11.9215	−	6.88286i	−0.640902	−	0.370025i
$347$	8.35240	+	14.4668i	0.448380	+	0.776617i	0.998281	−	0.0586128i	$-0.0186677\pi$
$347$	8.35240	+	14.4668i	0.448380	+	0.776617i	−0.549901	+	0.835230i	$0.685334\pi$
$348$	0.0426552	−	0.0738809i	0.00228656	−	0.00396043i
$349$	0.0173616	−	0.0100237i	0.000929347	−	0.000536559i	−0.499535	−	0.866294i	$-0.666496\pi$
$349$	0.0173616	−	0.0100237i	0.000929347	−	0.000536559i	0.500465	+	0.865757i	$0.333163\pi$
$350$		0			0
$351$	13.0778	+	9.87321i	0.698039	+	0.526993i
$352$	2.88743	+	5.00118i	0.153901	+	0.266564i
$353$			29.8258i			1.58747i	0.608265	+	0.793734i	$0.291866\pi$
$353$			29.8258i			1.58747i	−0.608265	+	0.793734i	$0.708134\pi$
$354$	−0.200725			−0.0106684
$355$	27.3292			1.45049
$356$			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	$-0.505907\pi$
$359$	15.8786	−	9.16753i	0.838042	−	0.483844i	0.856598	+	0.515984i	$0.172574\pi$
$360$	−4.17687	−	7.23455i	−0.220140	−	0.381294i
$361$	14.4326			0.759613
$362$	−1.44408	−	0.833739i	−0.0758991	−	0.0438204i
$363$	19.3434			1.01527
$364$		0			0
$365$	20.7987			1.08866
$366$	−6.02053	−	3.47596i	−0.314698	−	0.181691i
$367$	1.34485			0.0702007			0.0351004	−	0.999384i	$-0.488825\pi$
$367$	1.34485			0.0702007			0.0351004	+	0.999384i	$0.488825\pi$
$368$	1.23970	+	2.14722i	0.0646238	+	0.111932i
$369$	−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
$373$	−11.0715			−0.573261			−0.286630	−	0.958041i	$-0.592535\pi$
$373$	−11.0715			−0.573261			−0.286630	+	0.958041i	$0.592535\pi$
$374$	−1.22541			−0.0633644
$375$			12.1223i			0.625994i
$376$	−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	$0.191231\pi$
$380$	3.96579	−	6.86895i	0.203441	−	0.352370i
$381$	5.10152	+	8.83608i	0.261359	+	0.452686i
$382$	0.104768	+	0.0604880i	0.00536041	+	0.00309483i
$383$		−	16.5771i		−	0.847051i	−0.905884	−	0.423525i	$-0.860792\pi$
$383$		−	16.5771i		−	0.847051i	0.905884	−	0.423525i	$-0.139208\pi$
$384$	0.749558	+	0.432757i	0.0382507	+	0.0220841i
$385$		0			0
$386$	1.37775	−	2.38633i	0.0701256	−	0.121461i
$387$	−5.15422	+	8.92738i	−0.262004	+	0.453804i
$388$			14.0819i			0.714898i
$389$	0.585065	−	1.01336i	0.0296640	−	0.0513795i	−0.850812	−	0.525470i	$-0.823890\pi$
$389$	0.585065	−	1.01336i	0.0296640	−	0.0513795i	0.880476	+	0.474090i	$0.157223\pi$
$390$	−9.24333	−	6.97836i	−0.468054	−	0.353363i
$391$	−0.526121			−0.0266071
$392$		0			0
$393$	−2.21944	−	3.84418i	−0.111956	−	0.193913i
$394$	−15.1253			−0.762003
$395$	29.5616	+	17.0674i	1.48740	+	0.858753i
$396$	−11.2571	+	6.49927i	−0.565689	+	0.326601i
$397$		−	26.1975i		−	1.31481i	−0.753536	−	0.657406i	$-0.771654\pi$
$397$		−	26.1975i		−	1.31481i	0.753536	−	0.657406i	$-0.228346\pi$
$398$			5.30640i			0.265986i
$399$		0			0
$400$	4.38692	+	7.59837i	0.219346	+	0.379919i
$401$	9.84559	+	5.68436i	0.491665	+	0.283863i	0.725265	−	0.688470i	$-0.241717\pi$
$401$	9.84559	+	5.68436i	0.491665	+	0.283863i	−0.233600	+	0.972333i	$0.575051\pi$
$402$	−5.61286	+	9.72176i	−0.279944	+	0.484878i
$403$	3.24852	+	7.67217i	0.161821	+	0.382178i
$404$	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
$409$	20.2056	−	11.6657i	0.999102	−	0.576832i	0.0911196	−	0.995840i	$-0.470955\pi$
$409$	20.2056	−	11.6657i	0.999102	−	0.576832i	0.907982	+	0.419008i	$0.137622\pi$
$410$	24.1738	−	13.9567i	1.19386	−	0.689275i
$411$	−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
$416$	−3.57828	−	0.442616i	−0.175440	−	0.0217010i
$417$	6.55250	−	11.3493i	0.320877	−	0.555775i
$418$	−10.6882	−	6.17084i	−0.522777	−	0.301826i
$419$	6.33402	+	10.9709i	0.309437	+	0.535961i	0.978239	−	0.207479i	$-0.0665260\pi$
$419$	6.33402	+	10.9709i	0.309437	+	0.535961i	−0.668802	+	0.743441i	$0.733193\pi$
$420$		0			0
$421$		−	27.6625i		−	1.34819i	−0.738646	−	0.674094i	$-0.764534\pi$
$421$		−	27.6625i		−	1.34819i	0.738646	−	0.674094i	$-0.235466\pi$
$422$		−	17.8982i		−	0.871271i
$423$	17.8474	−	10.3042i	0.867771	−	0.501008i
$424$	−10.4744	−	6.04740i	−0.508682	−	0.293688i
$425$	−1.86178			−0.0903098
$426$	−3.18673	−	5.51957i	−0.154397	−	0.267424i
$427$		0			0
$428$	−11.6501			−0.563130
$429$	−10.8584	+	14.3828i	−0.524251	+	0.694407i
$430$	8.49841	−	14.7197i	0.409830	−	0.709846i
$431$			6.41393i			0.308948i	0.987997	+	0.154474i	$0.0493683\pi$
$431$			6.41393i			0.308948i	−0.987997	+	0.154474i	$0.950632\pi$
$432$	−2.27236	+	3.93584i	−0.109329	+	0.189363i
$433$	−0.0325135	+	0.0563150i	−0.00156250	+	0.00270633i	−0.866806	−	0.498646i	$-0.833831\pi$
$433$	−0.0325135	+	0.0563150i	−0.00156250	+	0.00270633i	0.865243	+	0.501353i	$0.167164\pi$
$434$		0			0
$435$	−0.274195	−	0.158307i	−0.0131467	−	0.00759022i
$436$		−	5.73307i		−	0.274564i
$437$	−4.58891	−	2.64941i	−0.219517	−	0.126738i
$438$	−2.42524	−	4.20063i	−0.115882	−	0.200714i
$439$	18.3889	−	31.8505i	0.877655	−	1.52014i	0.0237469	−	0.999718i	$-0.492440\pi$
$439$	18.3889	−	31.8505i	0.877655	−	1.52014i	0.853908	−	0.520424i	$-0.174226\pi$
$440$	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	0.948872	−	0.315662i	$-0.102227\pi$
$443$	4.23191	+	7.32989i	0.201064	+	0.348254i	−0.747807	+	0.663916i	$0.768893\pi$
$444$			6.81457i			0.323405i
$445$	43.8553			2.07894
$446$	−16.4385			−0.778385
$447$		−	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
$451$	−21.7169	−	37.6148i	−1.02261	−	1.77121i
$452$	−16.5194			−0.777008
$453$	−8.95026	−	5.16743i	−0.420520	−	0.242787i
$454$	5.63095			0.264274
$455$		0			0
$456$	−1.84972			−0.0866213
$457$	14.1310	+	8.15851i	0.661018	+	0.381639i	0.792665	−	0.609658i	$-0.208693\pi$
$457$	14.1310	+	8.15851i	0.661018	+	0.381639i	−0.131647	+	0.991297i	$0.542026\pi$
$458$	−27.7225			−1.29539
$459$	−0.482188	−	0.835174i	−0.0225066	−	0.0389826i
$460$	7.96901	−	4.60091i	0.371557	−	0.214519i
$461$	16.6951	+	9.63892i	0.777568	+	0.448929i	0.835568	−	0.549387i	$-0.185139\pi$
$461$	16.6951	+	9.63892i	0.777568	+	0.448929i	−0.0579996	+	0.998317i	$0.518472\pi$
$462$		0			0
$463$			2.70218i			0.125581i	0.998027	+	0.0627904i	$0.0200000\pi$
$463$			2.70218i			0.125581i	−0.998027	+	0.0627904i	$0.980000\pi$
$464$	−0.0985660			−0.00457581
$465$	−7.42263			−0.344216
$466$			20.1104i			0.931594i
$467$	9.19528	+	15.9267i	0.425507	+	0.736999i	0.996468	−	0.0839779i	$-0.0267625\pi$
$467$	9.19528	+	15.9267i	0.425507	+	0.736999i	−0.570961	+	0.820977i	$0.693429\pi$
$468$	0.996277	−	8.05429i	0.0460529	−	0.372310i
$469$		0			0
$470$	−29.4272	+	16.9898i	−1.35738	+	0.783682i
$471$	4.04205	−	7.00104i	0.186248	−	0.322591i
$472$	0.115957	+	0.200843i	0.00533735	+	0.00924457i
$473$	−22.9041	−	13.2237i	−1.05313	−	0.608025i
$474$		−	7.96057i		−	0.365641i
$475$	−16.2388	−	9.37545i	−0.745085	−	0.430175i
$476$		0			0
$477$	13.6120	−	23.5767i	0.623250	−	1.07950i
$478$	3.31484	−	5.74147i	0.151617	−	0.262609i
$479$			40.8708i			1.86743i	0.358012	+	0.933717i	$0.383455\pi$
$479$			40.8708i			1.86743i	−0.358012	+	0.933717i	$0.616545\pi$
$480$	1.60610	−	2.78184i	0.0733080	−	0.126973i
$481$	−11.0687	−	26.1413i	−0.504687	−	1.19194i
$482$	−1.61687			−0.0736462
$483$		0			0
$484$	−11.1745	−	19.3549i	−0.507933	−	0.879766i
$485$	52.2622			2.37310
$486$	−13.9206	−	8.03708i	−0.631452	−	0.364569i
$487$	−15.2674	+	8.81466i	−0.691834	+	0.399430i	−0.804299	−	0.594225i	$-0.797459\pi$
$487$	−15.2674	+	8.81466i	−0.691834	+	0.399430i	0.112465	+	0.993656i	$0.464125\pi$
$488$			8.03211i			0.363597i
$489$			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	$0.973259\pi$
$492$	−5.63757	−	3.25485i	−0.254161	−	0.146740i
$493$	0.0104577	−	0.0181133i	0.000470991	−	0.000815781i
$494$	7.09570	−	3.00444i	0.319251	−	0.135176i
$495$	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	$-0.681687\pi$
$499$	−1.82508	+	1.05371i	−0.0817017	+	0.0471705i	0.458593	+	0.888647i	$0.348354\pi$
$500$	12.1295	−	7.00296i	0.542447	−	0.313182i
$501$	−11.0236	+	6.36449i	−0.492499	+	0.284345i
$502$	0.439085	−	0.253506i	0.0195973	−	0.0113145i
$503$	−10.8942	+	18.8693i	−0.485749	+	0.841342i	−0.999866	−	0.0163784i	$-0.994786\pi$
$503$	−10.8942	+	18.8693i	−0.485749	+	0.841342i	0.514117	+	0.857720i	$0.328120\pi$
$504$		0			0
$505$	19.7745	−	11.4168i	0.879953	−	0.508041i
$506$	−7.15910	−	12.3999i	−0.318261	−	0.551244i
$507$	−3.08198	−	10.8214i	−0.136875	−	0.480594i
$508$	5.89420	−	10.2090i	0.261513	−	0.452953i
$509$	10.5636	+	6.09887i	0.468221	+	0.270328i	0.715495	−	0.698618i	$-0.246201\pi$
$509$	10.5636	+	6.09887i	0.468221	+	0.270328i	−0.247273	+	0.968946i	$0.579535\pi$
$510$	0.340809	+	0.590299i	0.0150913	+	0.0261389i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		−	9.71268i		−	0.428826i
$514$	−8.34903	+	4.82032i	−0.368260	+	0.212615i
$515$	−62.1896	−	35.9052i	−2.74040	−	1.58217i
$516$	−3.96383			−0.174498
$517$	26.4365	+	45.7893i	1.16267	+	2.01381i
$518$		0			0
$519$	11.9144			0.522986
$520$	−1.64269	+	13.2801i	−0.0720366	+	0.582372i
$521$	13.4883	−	23.3624i	0.590932	−	1.02352i	−0.403175	−	0.915123i	$-0.632094\pi$
$521$	13.4883	−	23.3624i	0.590932	−	1.02352i	0.994107	−	0.108401i	$-0.0345731\pi$
$522$		−	0.221861i		−	0.00971057i
$523$	1.87683	−	3.25076i	0.0820679	−	0.142146i	−0.822070	−	0.569386i	$-0.807181\pi$
$523$	1.87683	−	3.25076i	0.0820679	−	0.142146i	0.904138	+	0.427241i	$0.140514\pi$
$524$	−2.56429	+	4.44149i	−0.112022	+	0.194027i
$525$		0			0
$526$	−6.36197	−	3.67309i	−0.277395	−	0.160154i
$527$		−	0.490337i		−	0.0213594i
$528$	−4.32860	−	2.49912i	−0.188378	−	0.108760i
$529$	8.42629	+	14.5948i	0.366360	+	0.634555i
$530$	−22.4438	+	38.8738i	−0.974896	+	1.68857i
$531$	−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
$535$			43.2372i			1.86931i
$536$	12.9700			0.560219
$537$	13.2240			0.570656
$538$		−	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	$-0.666574\pi$
$541$	0.0117524	−	0.00678524i	0.000505274	−	0.000291720i	0.500253	+	0.865880i	$0.333240\pi$
$542$	4.80870	+	8.32891i	0.206551	+	0.357757i
$543$	1.44323			0.0619348
$544$	0.183768	+	0.106098i	0.00787899	+	0.00454894i
$545$	−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	$0.566220\pi$
$548$	8.13482	+	4.69664i	0.347502	+	0.200631i
$549$	−18.0793			−0.771608
$550$	−25.3339	−	43.8796i	−1.08024	−	1.87103i
$551$	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
$555$	25.2910			1.07354
$556$	−15.1413			−0.642133
$557$		−	24.9582i		−	1.05751i	−0.848773	−	0.528757i	$-0.822658\pi$
$557$		−	24.9582i		−	1.05751i	0.848773	−	0.528757i	$-0.177342\pi$
$558$	−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
$562$	7.08461	−	12.2709i	0.298846	−	0.517617i
$563$	7.94970	+	13.7693i	0.335040	+	0.580306i	0.983492	−	0.180949i	$-0.0579169\pi$
$563$	7.94970	+	13.7693i	0.335040	+	0.580306i	−0.648453	+	0.761255i	$0.724584\pi$
$564$	6.86273	+	3.96220i	0.288973	+	0.166839i
$565$			61.3088i			2.57928i
$566$	−16.3961	−	9.46631i	−0.689181	−	0.397899i
$567$		0			0
$568$	−3.68188	+	6.37721i	−0.154488	+	0.267582i
$569$	−8.95465	+	15.5099i	−0.375398	+	0.650209i	−0.990387	−	0.138327i	$-0.955827\pi$
$569$	−8.95465	+	15.5099i	−0.375398	+	0.650209i	0.614988	+	0.788536i	$0.289161\pi$
$570$			6.86490i			0.287539i
$571$	6.25615	−	10.8360i	0.261812	−	0.453471i	−0.704912	−	0.709295i	$-0.749013\pi$
$571$	6.25615	−	10.8360i	0.261812	−	0.453471i	0.966723	+	0.255824i	$0.0823467\pi$
$572$	20.6641	+	2.55605i	0.864009	+	0.106874i
$573$	−0.104707			−0.00437418
$574$		0			0
$575$	−10.8769	−	18.8394i	−0.453599	−	0.785657i
$576$	2.25088			0.0937868
$577$	19.1314	+	11.0455i	0.796450	+	0.459831i	0.842228	−	0.539121i	$-0.181243\pi$
$577$	19.1314	+	11.0455i	0.796450	+	0.459831i	−0.0457781	+	0.998952i	$0.514577\pi$
$578$	14.6834	−	8.47749i	0.610750	−	0.352617i
$579$			2.38492i			0.0991141i
$580$			0.365809i			0.0151894i
$581$		0			0
$582$	−6.09403	−	10.5552i	−0.252606	−	0.437526i
$583$	60.4883	+	34.9229i	2.50517	+	1.44636i
$584$	−2.80207	+	4.85333i	−0.115951	+	0.200832i
$585$	−29.8920	−	3.69750i	−1.23588	−	0.152873i
$586$	1.82991	+	3.16950i	0.0755929	+	0.130931i
$587$	−18.3007	+	10.5659i	−0.755352	+	0.436102i	−0.827624	−	0.561282i	$-0.810308\pi$
$587$	−18.3007	+	10.5659i	−0.755352	+	0.436102i	0.0722727	+	0.997385i	$0.476975\pi$
$588$		0			0
$589$	2.46921	−	4.27679i	0.101742	−	0.176222i
$590$	0.745393	−	0.430353i	0.0306873	−	0.0177173i
$591$	11.3373	−	6.54560i	0.466355	−	0.269250i
$592$	6.81859	−	3.93672i	0.280242	−	0.161798i
$593$	7.75520	−	4.47747i	0.318468	−	0.183867i	−0.332242	−	0.943194i	$-0.607805\pi$
$593$	7.75520	−	4.47747i	0.318468	−	0.183867i	0.650709	+	0.759327i	$0.274472\pi$
$594$	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
$598$	8.87198	+	1.09742i	0.362802	+	0.0448769i
$599$	−20.8998	+	36.1995i	−0.853942	+	1.47907i	0.0236813	+	0.999720i	$0.492461\pi$
$599$	−20.8998	+	36.1995i	−0.853942	+	1.47907i	−0.877623	+	0.479351i	$0.840872\pi$
$600$	−6.57650	−	3.79695i	−0.268485	−	0.155010i
$601$	−7.64481	−	13.2412i	−0.311838	−	0.540120i	0.666922	−	0.745127i	$-0.267611\pi$
$601$	−7.64481	−	13.2412i	−0.311838	−	0.540120i	−0.978760	+	0.205008i	$0.934278\pi$
$602$		0			0
$603$			29.1940i			1.18887i
$604$			11.9407i			0.485861i
$605$	−71.8319	+	41.4722i	−2.92038	+	1.68608i
$606$	−4.61161	−	2.66251i	−0.187334	−	0.108157i
$607$	14.6087			0.592948			0.296474	−	0.955041i	$-0.404189\pi$
$607$	14.6087			0.592948			0.296474	+	0.955041i	$0.404189\pi$
$608$	1.06857	+	1.85081i	0.0433362	+	0.0750604i
$609$		0			0
$610$	29.8097			1.20696
$611$	−32.7617	−	4.05246i	−1.32539	−	0.163945i
$612$	−0.238815	+	0.413640i	−0.00965354	+	0.0167204i
$613$		−	39.2163i		−	1.58393i	−0.610566	−	0.791965i	$-0.709058\pi$
$613$		−	39.2163i		−	1.58393i	0.610566	−	0.791965i	$-0.290942\pi$
$614$	−9.84935	+	17.0596i	−0.397487	+	0.688468i
$615$	−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	$0.606342\pi$
$618$			16.7469i			0.673659i
$619$	37.8518	+	21.8537i	1.52139	+	0.878376i	0.999681	+	0.0252541i	$0.00803947\pi$
$619$	37.8518	+	21.8537i	1.52139	+	0.878376i	0.521711	+	0.853122i	$0.325294\pi$
$620$	4.28798	+	7.42700i	0.172210	+	0.298276i
$621$	5.63409	−	9.75852i	0.226088	−	0.391596i
$622$	−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
$626$			4.53794i			0.181373i
$627$	10.6819			0.426594
$628$	−9.34022			−0.372715
$629$			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
$633$	7.74558	+	13.4157i	0.307859	+	0.533228i
$634$	−29.1866			−1.15915
$635$	−37.8890	−	21.8752i	−1.50358	−	0.868091i
$636$	10.4682			0.415092
$637$		0			0
$638$	0.569205			0.0225350
$639$	−14.3544	−	8.28749i	−0.567850	−	0.327848i
$640$	−3.71131			−0.146703
$641$	−3.61897	−	6.26824i	−0.142941	−	0.247581i	0.785662	−	0.618656i	$-0.212323\pi$
$641$	−3.61897	−	6.26824i	−0.142941	−	0.247581i	−0.928603	+	0.371075i	$0.878989\pi$
$642$	8.73244	−	5.04168i	0.344642	−	0.198979i
$643$	34.7898	+	20.0859i	1.37198	+	0.792111i	0.991177	−	0.132547i	$-0.0423154\pi$
$643$	34.7898	+	20.0859i	1.37198	+	0.792111i	0.380800	+	0.924658i	$0.375649\pi$
$644$		0			0
$645$			14.7110i			0.579245i
$646$	−0.453494			−0.0178425
$647$	−14.5512			−0.572068			−0.286034	−	0.958220i	$-0.592337\pi$
$647$	−14.5512			−0.572068			−0.286034	+	0.958220i	$0.592337\pi$
$648$			2.81913i			0.110746i
$649$	−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
$653$	24.8634	−	43.0646i	0.972978	−	1.68525i	0.286527	−	0.958072i	$-0.407499\pi$
$653$	24.8634	−	43.0646i	0.972978	−	1.68525i	0.686451	−	0.727176i	$-0.259168\pi$
$654$	2.48103	+	4.29727i	0.0970159	+	0.168037i
$655$	16.4838	+	9.51690i	0.644074	+	0.371856i
$656$			7.52119i			0.293653i
$657$	−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	$-0.0443532\pi$
$660$	−9.27500	+	16.0648i	−0.361029	+	0.625320i
$661$		−	24.8712i		−	0.967379i	−0.875240	−	0.483689i	$-0.839296\pi$
$661$		−	24.8712i		−	0.967379i	0.875240	−	0.483689i	$-0.160704\pi$
$662$	2.40271	−	4.16161i	0.0933839	−	0.161746i
$663$	−0.0812907	+	0.657186i	−0.00315707	+	0.0255230i
$664$	3.17186			0.123092
$665$		0			0
$666$	8.86109	+	15.3479i	0.343360	+	0.594717i
$667$	0.244384			0.00946260
$668$	12.7365	+	7.35342i	0.492790	+	0.284512i
$669$	12.3216	−	7.11388i	0.476381	−	0.275039i
$670$		−	48.1357i		−	1.85964i
$671$		−	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	$0.970341\pi$
$674$	15.3557	+	8.86562i	0.591480	+	0.341491i
$675$	19.9373	−	34.5325i	0.767388	−	1.32916i
$676$	−9.04732	+	9.33520i	−0.347974	+	0.359046i
$677$	−7.19675	−	12.4651i	−0.276594	−	0.479074i	0.693942	−	0.720031i	$-0.255872\pi$
$677$	−7.19675	−	12.4651i	−0.276594	−	0.479074i	−0.970536	+	0.240956i	$0.922539\pi$
$678$	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
$682$	11.5565	−	6.67217i	0.442523	−	0.255491i
$683$	36.6968	−	21.1869i	1.40416	−	0.810694i	0.409346	−	0.912379i	$-0.365757\pi$
$683$	36.6968	−	21.1869i	1.40416	−	0.810694i	0.994817	+	0.101686i	$0.0324235\pi$
$684$	−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
$689$	−40.1570	+	17.0032i	−1.52986	+	0.647768i
$690$	−3.98216	+	6.89730i	−0.151598	+	0.262576i
$691$	19.8651	+	11.4691i	0.755703	+	0.436305i	0.827751	−	0.561096i	$-0.189620\pi$
$691$	19.8651	+	11.4691i	0.755703	+	0.436305i	−0.0720480	+	0.997401i	$0.522953\pi$
$692$	−6.88286	−	11.9215i	−0.261647	−	0.453186i
$693$		0			0
$694$			16.7048i			0.634105i
$695$			56.1940i			2.13156i
$696$	0.0738809	−	0.0426552i	0.00280045	−	0.00161684i
$697$	−1.38215	−	0.797987i	−0.0523528	−	0.0302259i
$698$	0.0200475			0.000758808
$699$	−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	$0.489737\pi$
$702$	6.38907	+	15.0893i	0.241140	+	0.569510i
$703$	−8.41330	+	14.5723i	−0.317314	+	0.549603i
$704$			5.77486i			0.217648i
$705$	14.7050	−	25.4697i	0.553821	−	0.959245i
$706$	−14.9129	+	25.8299i	−0.561255	+	0.972122i
$707$		0			0
$708$	−0.173833	−	0.100363i	−0.00653304	−	0.00377186i
$709$			18.2131i			0.684009i	0.939698	+	0.342005i	$0.111106\pi$
$709$			18.2131i			0.684009i	−0.939698	+	0.342005i	$0.888894\pi$
$710$	23.6678	+	13.6646i	0.888237	+	0.512824i
$711$	−10.3512	−	17.9289i	−0.388202	−	0.672385i
$712$	−5.90833	+	10.2335i	−0.221424	+	0.383518i
$713$	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
$717$			5.73808i			0.214293i
$718$	18.3351			0.684258
$719$	−3.58214			−0.133591			−0.0667956	−	0.997767i	$-0.521278\pi$
$719$	−3.58214			−0.133591			−0.0667956	+	0.997767i	$0.521278\pi$
$720$		−	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
$724$	−0.833739	−	1.44408i	−0.0309857	−	0.0536688i
$725$	0.864802			0.0321180
$726$	16.7519	+	9.67172i	0.621722	+	0.358951i
$727$	3.21747			0.119329			0.0596647	−	0.998218i	$-0.480997\pi$
$727$	3.21747			0.119329			0.0596647	+	0.998218i	$0.480997\pi$
$728$		0			0
$729$	5.45503			0.202038
$730$	18.0122	+	10.3994i	0.666662	+	0.384898i
$731$	−0.971806			−0.0359435
$732$	−3.47596	−	6.02053i	−0.128475	−	0.222525i
$733$	4.15028	−	2.39616i	0.153294	−	0.0885043i	−0.421391	−	0.906879i	$-0.638458\pi$
$733$	4.15028	−	2.39616i	0.153294	−	0.0885043i	0.574685	+	0.818375i	$0.305125\pi$
$734$	1.16468	+	0.672426i	0.0429890	+	0.0248197i
$735$		0			0
$736$			2.47940i			0.0913919i
$737$	−74.9000			−2.75898
$738$	−16.9293			−0.623177
$739$			11.1989i			0.411958i	0.978556	+	0.205979i	$0.0660379\pi$
$739$			11.1989i			0.411958i	−0.978556	+	0.205979i	$0.933962\pi$
$740$	−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	$0.580934\pi$
$744$	1.00000	−	1.73205i	0.0366618	−	0.0635001i
$745$	38.2315	+	66.2189i	1.40069	+	2.42607i
$746$	−9.58821	−	5.53575i	−0.351049	−	0.202678i
$747$			7.13948i			0.261220i
$748$	−1.06124	−	0.612704i	−0.0388026	−	0.0224027i
$749$		0			0
$750$	−6.06116	+	10.4982i	−0.221322	+	0.383342i
$751$	−0.920125	+	1.59370i	−0.0335758	+	0.0581551i	−0.882325	−	0.470641i	$-0.844023\pi$
$751$	−0.920125	+	1.59370i	−0.0335758	+	0.0581551i	0.848749	+	0.528796i	$0.177356\pi$
$752$		−	9.15570i		−	0.333874i
$753$	−0.219413	+	0.380034i	−0.00799585	+	0.0138492i
$754$	−0.214130	+	0.283631i	−0.00779817	+	0.0103292i
$755$	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	$0.707493\pi$
$758$	16.8105			0.610583
$759$	10.7323	+	6.19631i	0.389558	+	0.224912i
$760$	6.86895	−	3.96579i	0.249163	−	0.143854i
$761$			14.1313i			0.512260i	0.966642	+	0.256130i	$0.0824475\pi$
$761$			14.1313i			0.512260i	−0.966642	+	0.256130i	$0.917553\pi$
$762$			10.2030i			0.369617i
$763$		0			0
$764$	0.0604880	+	0.104768i	0.00218838	+	0.00379038i
$765$	1.53515	+	0.886319i	0.0555034	+	0.0320449i
$766$	8.28855	−	14.3562i	0.299478	−	0.518710i
$767$	0.829853	+	0.102649i	0.0299643	+	0.00370644i
$768$	0.432757	+	0.749558i	0.0156158	+	0.0270473i
$769$	−26.5219	+	15.3124i	−0.956405	+	0.552181i	−0.895065	−	0.445936i	$-0.852871\pi$
$769$	−26.5219	+	15.3124i	−0.956405	+	0.552181i	−0.0613401	+	0.998117i	$0.519537\pi$
$770$		0			0
$771$	4.17206	−	7.22621i	0.150253	−	0.260246i
$772$	2.38633	−	1.37775i	0.0858859	−	0.0495863i
$773$	8.48254	−	4.89740i	0.305096	−	0.176147i	−0.339634	−	0.940558i	$-0.610303\pi$
$773$	8.48254	−	4.89740i	0.305096	−	0.176147i	0.644730	+	0.764411i	$0.276970\pi$
$774$	−8.92738	+	5.15422i	−0.320888	+	0.185265i
$775$	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
$780$	−4.51578	−	10.6651i	−0.161691	−	0.381872i
$781$	21.2624	−	36.8275i	0.760828	−	1.31779i
$782$	−0.455634	−	0.263061i	−0.0162934	−	0.00940702i
$783$	0.223977	+	0.387940i	0.00800430	+	0.0138638i
$784$		0			0
$785$			34.6645i			1.23723i
$786$		−	4.43887i		−	0.158329i
$787$	−17.8665	+	10.3152i	−0.636873	+	0.367699i	−0.783409	−	0.621507i	$-0.786521\pi$
$787$	−17.8665	+	10.3152i	−0.636873	+	0.367699i	0.146536	+	0.989205i	$0.453188\pi$
$788$	−13.0989	−	7.56267i	−0.466630	−	0.269409i
$789$	6.35822			0.226359
$790$	17.0674	+	29.5616i	0.607230	+	1.05175i
$791$		0			0
$792$	−12.9985			−0.461883
$793$	23.1130	+	17.4494i	0.820766	+	0.619647i
$794$	13.0987	−	22.6877i	0.464856	−	0.805155i
$795$		−	38.8509i		−	1.37790i
$796$	−2.65320	+	4.59548i	−0.0940402	+	0.162882i
$797$	3.88584	−	6.73047i	0.137643	−	0.238405i	−0.788961	−	0.614444i	$-0.789381\pi$
$797$	3.88584	−	6.73047i	0.137643	−	0.238405i	0.926604	+	0.376038i	$0.122714\pi$
$798$		0			0
$799$	1.68252	+	0.971406i	0.0595234	+	0.0343659i
$800$			8.77384i			0.310202i
$801$	−23.0345	−	13.2990i	−0.813883	−	0.469896i
$802$	5.68436	+	9.84559i	0.200722	+	0.347660i
$803$	16.1816	−	28.0273i	0.571036	−	0.989063i
$804$	−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
$808$			6.15243i			0.216442i
$809$	42.5430			1.49573			0.747866	−	0.663850i	$-0.231078\pi$
$809$	42.5430			1.49573			0.747866	+	0.663850i	$0.231078\pi$
$810$	10.4627			0.367621
$811$		−	22.1131i		−	0.776494i	−0.921555	−	0.388247i	$-0.873081\pi$
$811$		−	22.1131i		−	0.776494i	0.921555	−	0.388247i	$-0.126919\pi$
$812$		0			0
$813$	−7.20880	−	4.16200i	−0.252824	−	0.145968i
$814$	−39.3764	+	22.7340i	−1.38014	+	0.796826i
$815$	−8.30833	−	14.3905i	−0.291028	−	0.504076i
$816$	−0.183660			−0.00642937
$817$	−8.47624	−	4.89376i	−0.296546	−	0.171211i
$818$	23.3314			0.815763
$819$		0			0
$820$	27.9135			0.974782
$821$	−21.0920	−	12.1775i	−0.736115	−	0.424996i	0.0845401	−	0.996420i	$-0.473058\pi$
$821$	−21.0920	−	12.1775i	−0.736115	−	0.424996i	−0.820655	+	0.571424i	$0.806391\pi$
$822$	−8.13003			−0.283567
$823$	−2.37957	−	4.12153i	−0.0829465	−	0.143668i	0.821568	−	0.570111i	$-0.193100\pi$
$823$	−2.37957	−	4.12153i	−0.0829465	−	0.143668i	−0.904514	+	0.426443i	$0.859766\pi$
$824$	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	$0.961145\pi$
$828$	−5.58084			−0.193948
$829$	5.75238			0.199788			0.0998941	−	0.994998i	$-0.468150\pi$
$829$	5.75238			0.199788			0.0998941	+	0.994998i	$0.468150\pi$
$830$		−	11.7718i		−	0.408604i
$831$	−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
$835$	27.2908	−	47.2691i	0.944438	−	1.63582i
$836$	−6.17084	−	10.6882i	−0.213423	−	0.369659i
$837$	9.09480	+	5.25088i	0.314362	+	0.181497i
$838$			12.6680i			0.437610i
$839$	−35.6863	−	20.6035i	−1.23203	−	0.711311i	−0.264575	−	0.964365i	$-0.585232\pi$
$839$	−35.6863	−	20.6035i	−1.23203	−	0.711311i	−0.967452	+	0.253054i	$0.918565\pi$
$840$		0			0
$841$	14.4951	−	25.1063i	0.499832	−	0.865735i
$842$	13.8312	−	23.9564i	0.476656	−	0.825593i
$843$			12.2637i			0.422384i
$844$	8.94910	−	15.5003i	0.308041	−	0.533542i
$845$	34.6459	+	33.5774i	1.19185	+	1.15510i
$846$	20.6084			0.708532
$847$		0			0
$848$	−6.04740	−	10.4744i	−0.207669	−	0.359692i
$849$	16.3865			0.562382
$850$	−1.61235	−	0.930892i	−0.0553032	−	0.0319293i
$851$	−16.9060	+	9.76069i	−0.579530	+	0.334592i
$852$		−	6.37345i		−	0.218351i
$853$		−	2.38939i		−	0.0818113i	−0.999163	−	0.0409056i	$-0.986976\pi$
$853$		−	2.38939i		−	0.0818113i	0.999163	−	0.0409056i	$-0.0130243\pi$
$854$		0			0
$855$	8.92654	+	15.4612i	0.305281	+	0.528762i
$856$	−10.0893	−	5.82506i	−0.344845	−	0.199096i
$857$	6.90186	−	11.9544i	0.235763	−	0.408353i	−0.723731	−	0.690082i	$-0.757574\pi$
$857$	6.90186	−	11.9544i	0.235763	−	0.408353i	0.959494	+	0.281729i	$0.0909078\pi$
$858$	−16.5951	+	7.02663i	−0.566547	+	0.239885i
$859$	18.8638	+	32.6730i	0.643624	+	1.11479i	0.984617	+	0.174724i	$0.0559032\pi$
$859$	18.8638	+	32.6730i	0.643624	+	1.11479i	−0.340994	+	0.940066i	$0.610763\pi$
$860$	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	$-0.523655\pi$
$863$	22.0992	−	12.7590i	0.752267	−	0.434322i	0.826513	+	0.562918i	$0.190321\pi$
$864$	−3.93584	+	2.27236i	−0.133900	+	0.0773072i
$865$	−44.2443	+	25.5444i	−1.50435	+	0.868537i
$866$	−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
$871$	28.1768	−	37.3221i	0.954733	−	1.26461i
$872$	2.86654	−	4.96499i	0.0970732	−	0.168136i
$873$	−27.4501	−	15.8483i	−0.929045	−	0.536384i
$874$	−2.64941	−	4.58891i	−0.0896175	−	0.155222i
$875$		0			0
$876$		−	4.85047i		−	0.163882i
$877$		−	12.4391i		−	0.420039i	−0.977697	−	0.210019i	$-0.932647\pi$
$877$		−	12.4391i		−	0.420039i	0.977697	−	0.210019i	$-0.0673527\pi$
$878$	31.8505	−	18.3889i	1.07490	−	0.620596i
$879$	−2.74325	−	1.58382i	−0.0925275	−	0.0534208i
$880$	21.4323			0.722484
$881$	−11.2710	−	19.5219i	−0.379728	−	0.657709i	0.611294	−	0.791404i	$-0.290649\pi$
$881$	−11.2710	−	19.5219i	−0.379728	−	0.657709i	−0.991023	+	0.133694i	$0.957316\pi$
$882$		0			0
$883$	−15.1548			−0.509998			−0.254999	−	0.966941i	$-0.582075\pi$
$883$	−15.1548			−0.509998			−0.254999	+	0.966941i	$0.582075\pi$
$884$	0.704534	−	0.298312i	0.0236961	−	0.0100333i
$885$	−0.372477	+	0.645149i	−0.0125207	+	0.0216864i
$886$			8.46383i			0.284348i
$887$	−20.8875	+	36.1781i	−0.701332	+	1.21474i	0.266667	+	0.963789i	$0.414078\pi$
$887$	−20.8875	+	36.1781i	−0.701332	+	1.21474i	−0.967999	+	0.250954i	$0.919256\pi$
$888$	−3.40729	+	5.90159i	−0.114341	+	0.198044i
$889$		0			0
$890$	37.9798	+	21.9277i	1.27309	+	0.735017i
$891$		−	16.2801i		−	0.545404i
$892$	−14.2362	−	8.21925i	−0.476662	−	0.275201i
$893$	9.78349	+	16.9455i	0.327392	+	0.567060i
$894$	8.91597	−	15.4429i	0.298195	−	0.516488i
$895$	−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
$899$			0.227763i			0.00759631i
$900$	−19.7489			−0.658297
$901$	2.56648			0.0855018
$902$		−	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
$906$	−5.16743	−	8.95026i	−0.171676	−	0.297352i
$907$	−4.28751			−0.142365			−0.0711823	−	0.997463i	$-0.522677\pi$
$907$	−4.28751			−0.142365			−0.0711823	+	0.997463i	$0.522677\pi$
$908$	4.87655	+	2.81547i	0.161834	+	0.0934348i
$909$	−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	$0.520453\pi$
$912$	−1.60191	−	0.924862i	−0.0530445	−	0.0306252i
$913$	−18.3171			−0.606206
$914$	8.15851	+	14.1310i	0.269859	+	0.467410i
$915$	−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
$919$	45.9047			1.51426			0.757129	−	0.653266i	$-0.226601\pi$
$919$	45.9047			1.51426			0.757129	+	0.653266i	$0.226601\pi$
$920$	9.20183			0.303375
$921$		−	17.0495i		−	0.561801i
$922$	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
$926$	−1.35109	+	2.34015i	−0.0443995	+	0.0769022i
$927$	21.7762	+	37.7176i	0.715226	+	1.23881i
$928$	−0.0853606	−	0.0492830i	−0.00280210	−	0.00161779i
$929$		−	9.83612i		−	0.322713i	−0.986896	−	0.161356i	$-0.948413\pi$
$929$		−	9.83612i		−	0.322713i	0.986896	−	0.161356i	$-0.0515869\pi$
$930$	−6.42818	−	3.71131i	−0.210788	−	0.121699i
$931$		0			0
$932$	−10.0552	+	17.4161i	−0.329368	+	0.570483i
$933$	7.34325	−	12.7189i	0.240407	−	0.416397i
$934$			18.3906i			0.601758i
$935$	−2.27394	+	3.93858i	−0.0743657	+	0.128805i
$936$	4.88995	−	6.47708i	0.159833	−	0.211710i
$937$	21.5135			0.702815			0.351407	−	0.936223i	$-0.385703\pi$
$937$	21.5135			0.702815			0.351407	+	0.936223i	$0.385703\pi$
$938$		0			0
$939$	−1.96383	−	3.40145i	−0.0640871	−	0.111002i
$940$	−33.9797			−1.10829
$941$	−5.55854	−	3.20923i	−0.181203	−	0.104618i	0.406655	−	0.913582i	$-0.366695\pi$
$941$	−5.55854	−	3.20923i	−0.181203	−	0.104618i	−0.587858	+	0.808964i	$0.700029\pi$
$942$	7.00104	−	4.04205i	0.228106	−	0.131697i
$943$		−	18.6480i		−	0.607264i
$944$			0.231914i			0.00754816i
$945$		0			0
$946$	−13.2237	−	22.9041i	−0.429939	−	0.744675i
$947$	−6.55812	−	3.78633i	−0.213110	−	0.123039i	0.389646	−	0.920965i	$-0.372597\pi$
$947$	−6.55812	−	3.78633i	−0.213110	−	0.123039i	−0.602756	+	0.797926i	$0.705931\pi$
$948$	3.98028	−	6.89405i	0.129274	−	0.223908i
$949$	7.87844	+	18.6068i	0.255745	+	0.604003i
$950$	−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
$955$	0.388828	−	0.224490i	0.0125822	−	0.00726432i
$956$	5.74147	−	3.31484i	0.185692	−	0.107210i
$957$	−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
$962$	3.48491	−	28.1733i	0.112358	−	0.908345i
$963$	13.1115	−	22.7098i	0.422513	−	0.731814i
$964$	−1.40025	−	0.808433i	−0.0450989	−	0.0260379i
$965$	−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	$-0.174351\pi$
$968$		−	22.3491i		−	0.718326i
$969$	0.339920	−	0.196253i	0.0109198	−	0.00630455i
$970$	45.2604	+	26.1311i	1.45322	+	0.839019i
$971$	34.4065			1.10416			0.552079	−	0.833792i	$-0.313835\pi$
$971$	34.4065			1.10416			0.552079	+	0.833792i	$0.313835\pi$
$972$	−8.03708	−	13.9206i	−0.257789	−	0.446504i
$973$		0			0
$974$	−17.6293			−0.564880
$975$	−25.2132	+	10.6757i	−0.807468	+	0.341895i
$976$	−4.01605	+	6.95601i	−0.128551	+	0.222656i
$977$			23.1484i			0.740583i	0.928916	+	0.370291i	$0.120742\pi$
$977$			23.1484i			0.740583i	−0.928916	+	0.370291i	$0.879258\pi$
$978$	−1.93759	+	3.35600i	−0.0619571	+	0.107313i
$979$	34.1198	−	59.0972i	1.09047	−	1.88876i
$980$		0			0
$981$	11.1756	+	6.45224i	0.356810	+	0.206004i
$982$		−	18.8599i		−	0.601845i
$983$	−40.7534	−	23.5290i	−1.29983	−	0.750458i	−0.319456	−	0.947601i	$-0.603500\pi$
$983$	−40.7534	−	23.5290i	−1.29983	−	0.750458i	−0.980375	+	0.197143i	$0.936834\pi$
$984$	−3.25485	−	5.63757i	−0.103761	−	0.179719i
$985$	−28.0674	+	48.6142i	−0.894303	+	1.54898i
$986$	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
$990$			48.2417i			1.53322i
$991$	−11.9010			−0.378049			−0.189025	−	0.981972i	$-0.560533\pi$
$991$	−11.9010			−0.378049			−0.189025	+	0.981972i	$0.560533\pi$
$992$	−2.31076			−0.0733668
$993$			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
$997$	−6.50714	−	11.2707i	−0.206083	−	0.356946i	0.744394	−	0.667740i	$-0.232738\pi$
$997$	−6.50714	−	11.2707i	−0.206083	−	0.356946i	−0.950477	+	0.310794i	$0.899405\pi$
$998$	−2.10742			−0.0667092
$999$	−30.9886	−	17.8913i	−0.980435	−	0.566055i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.v.e.361.4		12
7.2	even	3		1274.2.o.d.569.3		12
7.3	odd	6		1274.2.m.c.491.1		12
7.4	even	3		182.2.m.b.127.3	yes	12
7.5	odd	6		1274.2.o.e.569.1		12
7.6	odd	2		1274.2.v.d.361.6		12
13.4	even	6		1274.2.o.d.459.6		12
21.11	odd	6		1638.2.bj.g.127.4		12
28.11	odd	6		1456.2.cc.d.673.2		12
91.4	even	6		182.2.m.b.43.3	✓	12
91.11	odd	12		2366.2.a.bh.1.2		6
91.17	odd	6		1274.2.m.c.589.1		12
91.30	even	6	inner	1274.2.v.e.667.4		12
91.67	odd	12		2366.2.a.bf.1.2		6
91.69	odd	6		1274.2.o.e.459.4		12
91.81	even	3		2366.2.d.r.337.2		12
91.82	odd	6		1274.2.v.d.667.6		12
91.88	even	6		2366.2.d.r.337.8		12
273.95	odd	6		1638.2.bj.g.1135.6		12
364.95	odd	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	91.4	even	6
182.2.m.b.127.3	yes	12	7.4	even	3
1274.2.m.c.491.1		12	7.3	odd	6
1274.2.m.c.589.1		12	91.17	odd	6
1274.2.o.d.459.6		12	13.4	even	6
1274.2.o.d.569.3		12	7.2	even	3
1274.2.o.e.459.4		12	91.69	odd	6
1274.2.o.e.569.1		12	7.5	odd	6
1274.2.v.d.361.6		12	7.6	odd	2
1274.2.v.d.667.6		12	91.82	odd	6
1274.2.v.e.361.4		12	1.1	even	1	trivial
1274.2.v.e.667.4		12	91.30	even	6	inner
1456.2.cc.d.225.2		12	364.95	odd	6
1456.2.cc.d.673.2		12	28.11	odd	6
1638.2.bj.g.127.4		12	21.11	odd	6
1638.2.bj.g.1135.6		12	273.95	odd	6
2366.2.a.bf.1.2		6	91.67	odd	12
2366.2.a.bh.1.2		6	91.11	odd	12
2366.2.d.r.337.2		12	91.81	even	3
2366.2.d.r.337.8		12	91.88	even	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.v (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} -0.865515 q^{3} +(0.500000 + 0.866025i) q^{4} +(3.21409 - 1.85566i) q^{5} +(-0.749558 - 0.432757i) q^{6} +1.00000i q^{8} -2.25088 q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} -0.865515 q^{3} +(0.500000 + 0.866025i) q^{4} +(3.21409 - 1.85566i) q^{5} +(-0.749558 - 0.432757i) q^{6} +1.00000i q^{8} -2.25088 q^{9} +3.71131 q^{10} -5.77486i q^{11} +(-0.432757 - 0.749558i) q^{12} +(2.87757 + 2.17246i) q^{13} +(-2.78184 + 1.60610i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.106098 - 0.183768i) q^{17} +(-1.94932 - 1.12544i) q^{18} -2.13714i q^{19} +(3.21409 + 1.85566i) q^{20} +(2.88743 - 5.00118i) q^{22} +(1.23970 - 2.14722i) q^{23} -0.865515i q^{24} +(4.38692 - 7.59837i) q^{25} +(1.40582 + 3.32019i) q^{26} +4.54472 q^{27} +(0.0492830 + 0.0853606i) q^{29} -3.21220 q^{30} +(2.00118 + 1.15538i) q^{31} +(-0.866025 + 0.500000i) q^{32} +4.99823i q^{33} -0.212197i q^{34} +(-1.12544 - 1.94932i) q^{36} +(-6.81859 - 3.93672i) q^{37} +(1.06857 - 1.85081i) q^{38} +(-2.49058 - 1.88029i) 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} +(-7.23455 + 4.17687i) q^{45} +(2.14722 - 1.23970i) 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} +(-0.442616 + 3.57828i) q^{52} +(-6.04740 + 10.4744i) q^{53} +(3.93584 + 2.27236i) q^{54} +(-10.7162 - 18.5609i) q^{55} +1.84972i q^{57} +0.0985660i q^{58} +(0.200843 - 0.115957i) q^{59} +(-2.78184 - 1.60610i) q^{60} +8.03211 q^{61} +(1.15538 + 2.00118i) q^{62} -1.00000 q^{64} +(13.2801 + 1.64269i) q^{65} +(-2.49912 + 4.32860i) q^{66} -12.9700i q^{67} +(0.106098 - 0.183768i) q^{68} +(-1.07298 + 1.85845i) q^{69} +(6.37721 + 3.68188i) q^{71} -2.25088i q^{72} +(4.85333 + 2.80207i) q^{73} +(-3.93672 - 6.81859i) q^{74} +(-3.79695 + 6.57650i) q^{75} +(1.85081 - 1.06857i) q^{76} +(-1.21676 - 2.87367i) q^{78} +(4.59875 + 7.96526i) q^{79} +3.71131i q^{80} +2.81913 q^{81} +7.52119 q^{82} -3.17186i q^{83} +(-0.682021 - 0.393765i) q^{85} +(3.96617 - 2.28987i) q^{86} +(-0.0426552 - 0.0738809i) q^{87} +5.77486 q^{88} +(10.2335 + 5.90833i) q^{89} -8.35373 q^{90} +2.47940 q^{92} +(-1.73205 - 1.00000i) q^{93} -9.15570 q^{94} +(-3.96579 - 6.86895i) q^{95} +(0.749558 - 0.432757i) q^{96} +(12.1952 + 7.04093i) q^{97} +12.9985i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} + 6 q^{4} + 6 q^{6} + 12 q^{9}+O(q^{10}) \) 12 * q + 4 * q^3 + 6 * q^4 + 6 * q^6 + 12 * q^9	\( 12 q + 4 q^{3} + 6 q^{4} + 6 q^{6} + 12 q^{9} + 4 q^{10} + 2 q^{12} - 8 q^{13} - 6 q^{15} - 6 q^{16} + 4 q^{17} - 2 q^{22} - 6 q^{23} + 12 q^{25} + 16 q^{26} + 40 q^{27} - 10 q^{29} - 28 q^{30} - 18 q^{31} + 6 q^{36} + 6 q^{37} - 4 q^{38} + 30 q^{39} + 2 q^{40} - 24 q^{41} + 26 q^{43} + 18 q^{44} - 72 q^{45} + 6 q^{46} - 48 q^{47} - 2 q^{48} - 12 q^{50} + 18 q^{51} - 4 q^{52} - 18 q^{53} + 36 q^{54} - 6 q^{55} - 6 q^{59} - 6 q^{60} + 56 q^{61} - 2 q^{62} - 12 q^{64} + 38 q^{65} - 4 q^{68} + 32 q^{69} + 48 q^{71} + 48 q^{73} - 48 q^{75} + 12 q^{76} - 8 q^{78} - 22 q^{79} + 68 q^{81} - 12 q^{82} + 54 q^{85} - 6 q^{86} + 2 q^{87} - 4 q^{88} - 12 q^{89} + 12 q^{90} - 12 q^{92} - 16 q^{94} + 32 q^{95} - 6 q^{96} + 60 q^{97}+O(q^{100}) \) 12 * q + 4 * q^3 + 6 * q^4 + 6 * q^6 + 12 * q^9 + 4 * q^10 + 2 * q^12 - 8 * q^13 - 6 * q^15 - 6 * q^16 + 4 * q^17 - 2 * q^22 - 6 * q^23 + 12 * q^25 + 16 * q^26 + 40 * q^27 - 10 * q^29 - 28 * q^30 - 18 * q^31 + 6 * q^36 + 6 * q^37 - 4 * q^38 + 30 * q^39 + 2 * q^40 - 24 * q^41 + 26 * q^43 + 18 * q^44 - 72 * q^45 + 6 * q^46 - 48 * q^47 - 2 * q^48 - 12 * q^50 + 18 * q^51 - 4 * q^52 - 18 * q^53 + 36 * q^54 - 6 * q^55 - 6 * q^59 - 6 * q^60 + 56 * q^61 - 2 * q^62 - 12 * q^64 + 38 * q^65 - 4 * q^68 + 32 * q^69 + 48 * q^71 + 48 * q^73 - 48 * q^75 + 12 * q^76 - 8 * q^78 - 22 * q^79 + 68 * q^81 - 12 * q^82 + 54 * q^85 - 6 * q^86 + 2 * q^87 - 4 * q^88 - 12 * q^89 + 12 * q^90 - 12 * q^92 - 16 * q^94 + 32 * q^95 - 6 * q^96 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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