LMFDB - Embedded newform 1274.2.o.d.459.3

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			459.3
Root			$0.500000 + 1.69027i$ of defining polynomial
Character	$\chi$	$=$	1274.459
Dual form			1274.2.o.d.569.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.27815 + 2.21381i) q^{3} -1.00000 q^{4} +(3.02030 - 1.74377i) q^{5} +(2.21381 - 1.27815i) q^{6} +1.00000i q^{8} +(-1.76732 + 3.06108i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.27815 + 2.21381i) q^{3} -1.00000 q^{4} +(3.02030 - 1.74377i) q^{5} +(2.21381 - 1.27815i) q^{6} +1.00000i q^{8} +(-1.76732 + 3.06108i) q^{9} +(-1.74377 - 3.02030i) q^{10} +(2.32244 - 1.34086i) q^{11} +(-1.27815 - 2.21381i) q^{12} +(-3.15338 - 1.74819i) q^{13} +(7.72076 + 4.45758i) q^{15} +1.00000 q^{16} +5.91517 q^{17} +(3.06108 + 1.76732i) q^{18} +(-4.50154 - 2.59896i) q^{19} +(-3.02030 + 1.74377i) q^{20} +(-1.34086 - 2.32244i) q^{22} +7.05268 q^{23} +(-2.21381 + 1.27815i) q^{24} +(3.58146 - 6.20327i) q^{25} +(-1.74819 + 3.15338i) q^{26} -1.36668 q^{27} +(-3.56639 + 6.17717i) q^{29} +(4.45758 - 7.72076i) q^{30} +(0.677564 + 0.391192i) q^{31} -1.00000i q^{32} +(5.93683 + 3.42763i) q^{33} -5.91517i q^{34} +(1.76732 - 3.06108i) q^{36} -7.81450i q^{37} +(-2.59896 + 4.50154i) q^{38} +(-0.160313 - 9.21545i) q^{39} +(1.74377 + 3.02030i) q^{40} +(0.136579 + 0.0788541i) q^{41} +(-0.165101 - 0.285963i) q^{43} +(-2.32244 + 1.34086i) q^{44} +12.3272i q^{45} -7.05268i q^{46} +(1.38704 - 0.800806i) q^{47} +(1.27815 + 2.21381i) q^{48} +(-6.20327 - 3.58146i) q^{50} +(7.56045 + 13.0951i) q^{51} +(3.15338 + 1.74819i) q^{52} +(-1.96300 + 3.40002i) q^{53} +1.36668i q^{54} +(4.67630 - 8.09958i) q^{55} -13.2874i q^{57} +(6.17717 + 3.56639i) q^{58} +9.54021i q^{59} +(-7.72076 - 4.45758i) q^{60} +(-7.70525 + 13.3459i) q^{61} +(0.391192 - 0.677564i) q^{62} -1.00000 q^{64} +(-12.5726 + 0.218714i) q^{65} +(3.42763 - 5.93683i) q^{66} +(-0.837243 + 0.483382i) q^{67} -5.91517 q^{68} +(9.01435 + 15.6133i) q^{69} +(3.62568 - 2.09329i) q^{71} +(-3.06108 - 1.76732i) q^{72} +(-13.0216 - 7.51803i) q^{73} -7.81450 q^{74} +18.3105 q^{75} +(4.50154 + 2.59896i) q^{76} +(-9.21545 + 0.160313i) q^{78} +(0.146678 + 0.254054i) q^{79} +(3.02030 - 1.74377i) q^{80} +(3.55514 + 6.15768i) q^{81} +(0.0788541 - 0.136579i) q^{82} +2.87495i q^{83} +(17.8656 - 10.3147i) q^{85} +(-0.285963 + 0.165101i) q^{86} -18.2335 q^{87} +(1.34086 + 2.32244i) q^{88} -5.21325i q^{89} +12.3272 q^{90} -7.05268 q^{92} +2.00000i q^{93} +(-0.800806 - 1.38704i) q^{94} -18.1280 q^{95} +(2.21381 - 1.27815i) q^{96} +(-2.73617 + 1.57973i) q^{97} +9.47889i 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 $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.27815	+	2.21381i	0.737938	+	1.27815i	0.953422	+	0.301639i	$0.0975337\pi$
$3$	1.27815	+	2.21381i	0.737938	+	1.27815i	−0.215484	+	0.976507i	$0.569133\pi$
$4$	−1.00000			−0.500000
$5$	3.02030	−	1.74377i	1.35072	−	0.779837i	0.362367	−	0.932035i	$-0.381969\pi$
$5$	3.02030	−	1.74377i	1.35072	−	0.779837i	0.988350	+	0.152198i	$0.0486352\pi$
$6$	2.21381	−	1.27815i	0.903786	−	0.521801i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−1.76732	+	3.06108i	−0.589105	+	1.02036i
$10$	−1.74377	−	3.02030i	−0.551428	−	0.955101i
$11$	2.32244	−	1.34086i	0.700241	−	0.404284i	−0.107196	−	0.994238i	$-0.534187\pi$
$11$	2.32244	−	1.34086i	0.700241	−	0.404284i	0.807437	+	0.589954i	$0.200854\pi$
$12$	−1.27815	−	2.21381i	−0.368969	−	0.639073i
$13$	−3.15338	−	1.74819i	−0.874591	−	0.484861i
$13$	−3.15338	−	1.74819i	−0.874591	−	0.484861i
$14$		0			0
$15$	7.72076	+	4.45758i	1.99349	+	1.15094i
$16$	1.00000			0.250000
$17$	5.91517			1.43464			0.717319	−	0.696745i	$-0.245369\pi$
$17$	5.91517			1.43464			0.717319	+	0.696745i	$0.245369\pi$
$18$	3.06108	+	1.76732i	0.721504	+	0.416560i
$19$	−4.50154	−	2.59896i	−1.03272	−	0.596243i	−0.114960	−	0.993370i	$-0.536674\pi$
$19$	−4.50154	−	2.59896i	−1.03272	−	0.596243i	−0.917764	+	0.397127i	$0.870007\pi$
$20$	−3.02030	+	1.74377i	−0.675359	+	0.389919i
$21$		0			0
$22$	−1.34086	−	2.32244i	−0.285872	−	0.495145i
$23$	7.05268			1.47058			0.735292	−	0.677750i	$-0.237045\pi$
$23$	7.05268			1.47058			0.735292	+	0.677750i	$0.237045\pi$
$24$	−2.21381	+	1.27815i	−0.451893	+	0.260901i
$25$	3.58146	−	6.20327i	0.716292	−	1.24065i
$26$	−1.74819	+	3.15338i	−0.342849	+	0.618429i
$27$	−1.36668			−0.263017
$28$		0			0
$29$	−3.56639	+	6.17717i	−0.662262	+	1.14707i	0.317758	+	0.948172i	$0.397070\pi$
$29$	−3.56639	+	6.17717i	−0.662262	+	1.14707i	−0.980020	+	0.198900i	$0.936263\pi$
$30$	4.45758	−	7.72076i	0.813840	−	1.40961i
$31$	0.677564	+	0.391192i	0.121694	+	0.0702601i	0.559611	−	0.828755i	$-0.310950\pi$
$31$	0.677564	+	0.391192i	0.121694	+	0.0702601i	−0.437917	+	0.899015i	$0.644284\pi$
$32$		−	1.00000i		−	0.176777i
$33$	5.93683	+	3.42763i	1.03347	+	0.596674i
$34$		−	5.91517i		−	1.01444i
$35$		0			0
$36$	1.76732	−	3.06108i	0.294553	−	0.510180i
$37$		−	7.81450i		−	1.28470i	−0.766413	−	0.642348i	$-0.777960\pi$
$37$		−	7.81450i		−	1.28470i	0.766413	−	0.642348i	$-0.222040\pi$
$38$	−2.59896	+	4.50154i	−0.421608	+	0.730246i
$39$	−0.160313	−	9.21545i	−0.0256706	−	1.47565i
$40$	1.74377	+	3.02030i	0.275714	+	0.477551i
$41$	0.136579	+	0.0788541i	0.0213301	+	0.0123149i	0.510627	−	0.859802i	$-0.329413\pi$
$41$	0.136579	+	0.0788541i	0.0213301	+	0.0123149i	−0.489297	+	0.872117i	$0.662747\pi$
$42$		0			0
$43$	−0.165101	−	0.285963i	−0.0251777	−	0.0436090i	0.853162	−	0.521646i	$-0.174682\pi$
$43$	−0.165101	−	0.285963i	−0.0251777	−	0.0436090i	−0.878340	+	0.478037i	$0.841348\pi$
$44$	−2.32244	+	1.34086i	−0.350120	+	0.202142i
$45$			12.3272i			1.83762i
$46$		−	7.05268i		−	1.03986i
$47$	1.38704	−	0.800806i	0.202320	−	0.116810i	−0.395417	−	0.918502i	$-0.629400\pi$
$47$	1.38704	−	0.800806i	0.202320	−	0.116810i	0.597737	+	0.801692i	$0.296067\pi$
$48$	1.27815	+	2.21381i	0.184485	+	0.319537i
$49$		0			0
$50$	−6.20327	−	3.58146i	−0.877275	−	0.506495i
$51$	7.56045	+	13.0951i	1.05867	+	1.83368i
$52$	3.15338	+	1.74819i	0.437296	+	0.242431i
$53$	−1.96300	+	3.40002i	−0.269639	+	0.467029i	−0.968769	−	0.247966i	$-0.920238\pi$
$53$	−1.96300	+	3.40002i	−0.269639	+	0.467029i	0.699129	+	0.714995i	$0.253571\pi$
$54$			1.36668i			0.185981i
$55$	4.67630	−	8.09958i	0.630552	−	1.09215i
$56$		0			0
$57$		−	13.2874i		−	1.75996i
$58$	6.17717	+	3.56639i	0.811102	+	0.468290i
$59$			9.54021i			1.24203i	0.783799	+	0.621015i	$0.213279\pi$
$59$			9.54021i			1.24203i	−0.783799	+	0.621015i	$0.786721\pi$
$60$	−7.72076	−	4.45758i	−0.996746	−	0.575471i
$61$	−7.70525	+	13.3459i	−0.986556	+	1.70877i	−0.351752	+	0.936093i	$0.614414\pi$
$61$	−7.70525	+	13.3459i	−0.986556	+	1.70877i	−0.634805	+	0.772673i	$0.718919\pi$
$62$	0.391192	−	0.677564i	0.0496814	−	0.0860507i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−12.5726	+	0.218714i	−1.55944	+	0.0271281i
$66$	3.42763	−	5.93683i	0.421912	−	0.730773i
$67$	−0.837243	+	0.483382i	−0.102286	+	0.0590546i	−0.550270	−	0.834987i	$-0.685475\pi$
$67$	−0.837243	+	0.483382i	−0.102286	+	0.0590546i	0.447985	+	0.894041i	$0.352142\pi$
$68$	−5.91517			−0.717319
$69$	9.01435	+	15.6133i	1.08520	+	1.87962i
$70$		0			0
$71$	3.62568	−	2.09329i	0.430289	−	0.248428i	−0.269181	−	0.963090i	$-0.586753\pi$
$71$	3.62568	−	2.09329i	0.430289	−	0.248428i	0.699470	+	0.714662i	$0.253420\pi$
$72$	−3.06108	−	1.76732i	−0.360752	−	0.208280i
$73$	−13.0216	−	7.51803i	−1.52406	−	0.879919i	−0.999594	−	0.0284901i	$-0.990930\pi$
$73$	−13.0216	−	7.51803i	−1.52406	−	0.879919i	−0.524470	−	0.851429i	$-0.675737\pi$
$74$	−7.81450			−0.908417
$75$	18.3105			2.11432
$76$	4.50154	+	2.59896i	0.516362	+	0.298122i
$77$		0			0
$78$	−9.21545	+	0.160313i	−1.04344	+	0.0181518i
$79$	0.146678	+	0.254054i	0.0165026	+	0.0285833i	0.874159	−	0.485640i	$-0.161413\pi$
$79$	0.146678	+	0.254054i	0.0165026	+	0.0285833i	−0.857656	+	0.514224i	$0.828080\pi$
$80$	3.02030	−	1.74377i	0.337679	−	0.194959i
$81$	3.55514	+	6.15768i	0.395015	+	0.684186i
$82$	0.0788541	−	0.136579i	0.00870797	−	0.0150827i
$83$			2.87495i			0.315566i	0.987474	+	0.157783i	$0.0504347\pi$
$83$			2.87495i			0.315566i	−0.987474	+	0.157783i	$0.949565\pi$
$84$		0			0
$85$	17.8656	−	10.3147i	1.93779	−	1.11878i
$86$	−0.285963	+	0.165101i	−0.0308362	+	0.0178033i
$87$	−18.2335			−1.95483
$88$	1.34086	+	2.32244i	0.142936	+	0.247573i
$89$		−	5.21325i		−	0.552603i	−0.961071	−	0.276302i	$-0.910891\pi$
$89$		−	5.21325i		−	0.552603i	0.961071	−	0.276302i	$-0.0891089\pi$
$90$	12.3272			1.29940
$91$		0			0
$92$	−7.05268			−0.735292
$93$			2.00000i			0.207390i
$94$	−0.800806	−	1.38704i	−0.0825968	−	0.143062i
$95$	−18.1280			−1.85989
$96$	2.21381	−	1.27815i	0.225946	−	0.130450i
$97$	−2.73617	+	1.57973i	−0.277816	+	0.160397i	−0.632434	−	0.774614i	$-0.717944\pi$
$97$	−2.73617	+	1.57973i	−0.277816	+	0.160397i	0.354618	+	0.935011i	$0.384611\pi$
$98$		0			0
$99$			9.47889i			0.952664i
$100$	−3.58146	+	6.20327i	−0.358146	+	0.620327i
$101$	1.89325	+	3.27921i	0.188386	+	0.326293i	0.944712	−	0.327901i	$-0.106341\pi$
$101$	1.89325	+	3.27921i	0.188386	+	0.326293i	−0.756327	+	0.654194i	$0.773008\pi$
$102$	13.0951	−	7.56045i	1.29661	−	0.748596i
$103$	3.40419	+	5.89623i	0.335425	+	0.580973i	0.983566	−	0.180547i	$-0.0577867\pi$
$103$	3.40419	+	5.89623i	0.335425	+	0.580973i	−0.648141	+	0.761520i	$0.724453\pi$
$104$	1.74819	−	3.15338i	0.171424	−	0.309215i
$105$		0			0
$106$	3.40002	+	1.96300i	0.330240	+	0.190664i
$107$	14.3017			1.38259			0.691297	−	0.722571i	$-0.257040\pi$
$107$	14.3017			1.38259			0.691297	+	0.722571i	$0.257040\pi$
$108$	1.36668			0.131508
$109$	3.96353	+	2.28834i	0.379637	+	0.219184i	0.677660	−	0.735375i	$-0.262994\pi$
$109$	3.96353	+	2.28834i	0.379637	+	0.219184i	−0.298023	+	0.954559i	$0.596327\pi$
$110$	−8.09958	−	4.67630i	−0.772265	−	0.445867i
$111$	17.2999	−	9.98808i	1.64203	−	0.948026i
$112$		0			0
$113$	1.50648	+	2.60930i	0.141718	+	0.245463i	0.928144	−	0.372222i	$-0.121404\pi$
$113$	1.50648	+	2.60930i	0.141718	+	0.245463i	−0.786426	+	0.617685i	$0.788071\pi$
$114$	−13.2874			−1.24448
$115$	21.3012	−	12.2982i	1.98634	−	1.14682i
$116$	3.56639	−	6.17717i	0.331131	−	0.573536i
$117$	10.9244	−	6.56315i	1.00996	−	0.606764i
$118$	9.54021			0.878248
$119$		0			0
$120$	−4.45758	+	7.72076i	−0.406920	+	0.704806i
$121$	−1.90419	+	3.29816i	−0.173108	+	0.299833i
$122$	13.3459	+	7.70525i	1.20828	+	0.697601i
$123$			0.403148i			0.0363506i
$124$	−0.677564	−	0.391192i	−0.0608470	−	0.0351300i
$125$		−	7.54326i		−	0.674689i
$126$		0			0
$127$	5.56278	−	9.63501i	0.493616	−	0.854969i	−0.506356	−	0.862324i	$-0.669008\pi$
$127$	5.56278	−	9.63501i	0.493616	−	0.854969i	0.999973	+	0.00735543i	$0.00234133\pi$
$128$			1.00000i			0.0883883i
$129$	0.422047	−	0.731006i	0.0371591	−	0.0643615i
$130$	0.218714	+	12.5726i	0.0191825	+	1.10269i
$131$	−7.45584	−	12.9139i	−0.651420	−	1.12829i	−0.982779	−	0.184787i	$-0.940840\pi$
$131$	−7.45584	−	12.9139i	−0.651420	−	1.12829i	0.331359	−	0.943505i	$-0.392493\pi$
$132$	−5.93683	−	3.42763i	−0.516734	−	0.298337i
$133$		0			0
$134$	0.483382	+	0.837243i	0.0417579	+	0.0723268i
$135$	−4.12776	+	2.38317i	−0.355261	+	0.205110i
$136$			5.91517i			0.507221i
$137$		−	15.4617i		−	1.32098i	−0.750833	−	0.660492i	$-0.770348\pi$
$137$		−	15.4617i		−	1.32098i	0.750833	−	0.660492i	$-0.229652\pi$
$138$	15.6133	−	9.01435i	1.32909	−	0.767353i
$139$	−7.15110	−	12.3861i	−0.606548	−	1.05057i	−0.991805	−	0.127763i	$-0.959220\pi$
$139$	−7.15110	−	12.3861i	−0.606548	−	1.05057i	0.385256	−	0.922810i	$-0.374113\pi$
$140$		0			0
$141$	3.54567	+	2.04709i	0.298599	+	0.172396i
$142$	−2.09329	−	3.62568i	−0.175665	−	0.304260i
$143$	−9.66761	+	0.168179i	−0.808446	+	0.0140638i
$144$	−1.76732	+	3.06108i	−0.147276	+	0.255090i
$145$			24.8758i			2.06583i
$146$	−7.51803	+	13.0216i	−0.622197	+	1.07768i
$147$		0			0
$148$			7.81450i			0.642348i
$149$	3.08060	+	1.77859i	0.252373	+	0.145708i	0.620850	−	0.783929i	$-0.286787\pi$
$149$	3.08060	+	1.77859i	0.252373	+	0.145708i	−0.368477	+	0.929637i	$0.620121\pi$
$150$		−	18.3105i		−	1.49505i
$151$	−8.25097	−	4.76370i	−0.671454	−	0.387664i	0.125173	−	0.992135i	$-0.460051\pi$
$151$	−8.25097	−	4.76370i	−0.671454	−	0.387664i	−0.796627	+	0.604471i	$0.793385\pi$
$152$	2.59896	−	4.50154i	0.210804	−	0.365123i
$153$	−10.4540	+	18.1068i	−0.845153	+	1.46385i
$154$		0			0
$155$	2.72859			0.219166
$156$	0.160313	+	9.21545i	0.0128353	+	0.737826i
$157$	−10.4173	+	18.0432i	−0.831388	+	1.44001i	0.0655497	+	0.997849i	$0.479120\pi$
$157$	−10.4173	+	18.0432i	−0.831388	+	1.44001i	−0.896938	+	0.442157i	$0.854213\pi$
$158$	0.254054	−	0.146678i	0.0202115	−	0.0116691i
$159$	−10.0360			−0.795909
$160$	−1.74377	−	3.02030i	−0.137857	−	0.238775i
$161$		0			0
$162$	6.15768	−	3.55514i	0.483793	−	0.279318i
$163$	−5.46119	−	3.15302i	−0.427753	−	0.246963i	0.270636	−	0.962682i	$-0.412766\pi$
$163$	−5.46119	−	3.15302i	−0.427753	−	0.246963i	−0.698389	+	0.715718i	$0.746099\pi$
$164$	−0.136579	−	0.0788541i	−0.0106650	−	0.00615747i
$165$	23.9080			1.86123
$166$	2.87495			0.223139
$167$	5.77528	+	3.33436i	0.446904	+	0.258020i	0.706522	−	0.707691i	$-0.250263\pi$
$167$	5.77528	+	3.33436i	0.446904	+	0.258020i	−0.259618	+	0.965711i	$0.583597\pi$
$168$		0			0
$169$	6.88765	+	11.0254i	0.529819	+	0.848111i
$170$	−10.3147	−	17.8656i	−0.791100	−	1.37023i
$171$	15.9113	−	9.18638i	1.21677	−	0.702500i
$172$	0.165101	+	0.285963i	0.0125888	+	0.0218045i
$173$	−10.6596	+	18.4630i	−0.810434	+	1.40371i	0.102126	+	0.994771i	$0.467435\pi$
$173$	−10.6596	+	18.4630i	−0.810434	+	1.40371i	−0.912560	+	0.408942i	$0.865898\pi$
$174$			18.2335i			1.38228i
$175$		0			0
$176$	2.32244	−	1.34086i	0.175060	−	0.101071i
$177$	−21.1203	+	12.1938i	−1.58750	+	0.916541i
$178$	−5.21325			−0.390750
$179$	7.71921	+	13.3701i	0.576961	+	0.999325i	0.995826	+	0.0912768i	$0.0290948\pi$
$179$	7.71921	+	13.3701i	0.576961	+	0.999325i	−0.418865	+	0.908049i	$0.637572\pi$
$180$		−	12.3272i		−	0.918812i
$181$	−13.2818			−0.987231			−0.493616	−	0.869680i	$-0.664325\pi$
$181$	−13.2818			−0.987231			−0.493616	+	0.869680i	$0.664325\pi$
$182$		0			0
$183$	−39.3938			−2.91207
$184$			7.05268i			0.519930i
$185$	−13.6267	−	23.6021i	−1.00185	−	1.73526i
$186$	2.00000			0.146647
$187$	13.7376	−	7.93141i	1.00459	−	0.580002i
$188$	−1.38704	+	0.800806i	−0.101160	+	0.0584048i
$189$		0			0
$190$			18.1280i			1.31514i
$191$	5.96230	−	10.3270i	0.431417	−	0.747235i	−0.565579	−	0.824694i	$-0.691347\pi$
$191$	5.96230	−	10.3270i	0.431417	−	0.747235i	0.996996	+	0.0774587i	$0.0246806\pi$
$192$	−1.27815	−	2.21381i	−0.0922423	−	0.159768i
$193$	−4.63268	+	2.67468i	−0.333467	+	0.192528i	−0.657380	−	0.753560i	$-0.728335\pi$
$193$	−4.63268	+	2.67468i	−0.333467	+	0.192528i	0.323912	+	0.946087i	$0.395002\pi$
$194$	1.57973	+	2.73617i	0.113418	+	0.196446i
$195$	−16.5538	−	27.5538i	−1.18544	−	1.97317i
$196$		0			0
$197$	−11.4261	−	6.59688i	−0.814079	−	0.470009i	0.0342916	−	0.999412i	$-0.489083\pi$
$197$	−11.4261	−	6.59688i	−0.814079	−	0.470009i	−0.848370	+	0.529403i	$0.822416\pi$
$198$	9.47889			0.673635
$199$	−20.0516			−1.42142			−0.710709	−	0.703486i	$-0.751626\pi$
$199$	−20.0516			−1.42142			−0.710709	+	0.703486i	$0.751626\pi$
$200$	6.20327	+	3.58146i	0.438637	+	0.253247i
$201$	−2.14024	−	1.23567i	−0.150961	−	0.0871572i
$202$	3.27921	−	1.89325i	0.230724	−	0.133209i
$203$		0			0
$204$	−7.56045	−	13.0951i	−0.529337	−	0.916839i
$205$	0.550013			0.0384146
$206$	5.89623	−	3.40419i	0.410810	−	0.237181i
$207$	−12.4643	+	21.5888i	−0.866329	+	1.50053i
$208$	−3.15338	−	1.74819i	−0.218648	−	0.121215i
$209$	−13.9394			−0.964207
$210$		0			0
$211$	3.98072	−	6.89481i	0.274044	−	0.474658i	−0.695849	−	0.718188i	$-0.744972\pi$
$211$	3.98072	−	6.89481i	0.274044	−	0.474658i	0.969893	+	0.243530i	$0.0783053\pi$
$212$	1.96300	−	3.40002i	0.134820	−	0.233515i
$213$	9.26830	+	5.35106i	0.635054	+	0.366648i
$214$		−	14.3017i		−	0.977642i
$215$	−0.997308	−	0.575796i	−0.0680158	−	0.0392690i
$216$		−	1.36668i		−	0.0929905i
$217$		0			0
$218$	2.28834	−	3.96353i	0.154986	−	0.268444i
$219$		−	38.4366i		−	2.59730i
$220$	−4.67630	+	8.09958i	−0.315276	+	0.546074i
$221$	−18.6528	−	10.3408i	−1.25472	−	0.695601i
$222$	−9.98808	−	17.2999i	−0.670356	−	1.16109i
$223$	−18.6557	−	10.7709i	−1.24928	−	0.721271i	−0.278312	−	0.960491i	$-0.589775\pi$
$223$	−18.6557	−	10.7709i	−1.24928	−	0.721271i	−0.970965	+	0.239220i	$0.923108\pi$
$224$		0			0
$225$	12.6591	+	21.9263i	0.843943	+	1.46175i
$226$	2.60930	−	1.50648i	0.173568	−	0.100210i
$227$			3.65771i			0.242771i	0.992605	+	0.121385i	$0.0387337\pi$
$227$			3.65771i			0.242771i	−0.992605	+	0.121385i	$0.961266\pi$
$228$			13.2874i			0.879981i
$229$	−8.44160	+	4.87376i	−0.557837	+	0.322067i	−0.752277	−	0.658847i	$-0.771044\pi$
$229$	−8.44160	+	4.87376i	−0.557837	+	0.322067i	0.194440	+	0.980914i	$0.437711\pi$
$230$	−12.2982	−	21.3012i	−0.810922	−	1.40456i
$231$		0			0
$232$	−6.17717	−	3.56639i	−0.405551	−	0.234145i
$233$	1.36448	+	2.36334i	0.0893897	+	0.154828i	0.907253	−	0.420585i	$-0.138175\pi$
$233$	1.36448	+	2.36334i	0.0893897	+	0.154828i	−0.817864	+	0.575412i	$0.804842\pi$
$234$	−6.56315	−	10.9244i	−0.429047	−	0.714149i
$235$	2.79284	−	4.83734i	0.182185	−	0.315553i
$236$		−	9.54021i		−	0.621015i
$237$	−0.374952	+	0.649436i	−0.0243558	+	0.0421854i
$238$		0			0
$239$		−	12.2347i		−	0.791400i	−0.918380	−	0.395700i	$-0.870502\pi$
$239$		−	12.2347i		−	0.791400i	0.918380	−	0.395700i	$-0.129498\pi$
$240$	7.72076	+	4.45758i	0.498373	+	0.287736i
$241$		−	24.2176i		−	1.56000i	−0.625782	−	0.779998i	$-0.715220\pi$
$241$		−	24.2176i		−	1.56000i	0.625782	−	0.779998i	$-0.284780\pi$
$242$	3.29816	+	1.90419i	0.212014	+	0.122406i
$243$	−11.1380	+	19.2916i	−0.714502	+	1.23755i
$244$	7.70525	−	13.3459i	0.493278	−	0.854383i
$245$		0			0
$246$	0.403148			0.0257038
$247$	9.65158	+	16.0651i	0.614116	+	1.02220i
$248$	−0.391192	+	0.677564i	−0.0248407	+	0.0430253i
$249$	−6.36460	+	3.67460i	−0.403340	+	0.232868i
$250$	−7.54326			−0.477077
$251$	1.00685	+	1.74392i	0.0635521	+	0.110075i	0.896051	−	0.443952i	$-0.146424\pi$
$251$	1.00685	+	1.74392i	0.0635521	+	0.110075i	−0.832499	+	0.554027i	$0.813090\pi$
$252$		0			0
$253$	16.3794	−	9.45665i	1.02976	−	0.594534i
$254$	−9.63501	−	5.56278i	−0.604554	−	0.349040i
$255$	45.6696	+	26.3673i	2.85994	+	1.65119i
$256$	1.00000			0.0625000
$257$	2.14218			0.133625			0.0668127	−	0.997766i	$-0.478717\pi$
$257$	2.14218			0.133625			0.0668127	+	0.997766i	$0.478717\pi$
$258$	−0.731006	−	0.422047i	−0.0455105	−	0.0262755i
$259$		0			0
$260$	12.5726	−	0.218714i	0.779719	−	0.0135641i
$261$	−12.6059	−	21.8340i	−0.780284	−	1.35149i
$262$	−12.9139	+	7.45584i	−0.797823	+	0.460623i
$263$	5.43131	+	9.40731i	0.334909	+	0.580080i	0.983467	−	0.181085i	$-0.0579610\pi$
$263$	5.43131	+	9.40731i	0.334909	+	0.580080i	−0.648558	+	0.761165i	$0.724628\pi$
$264$	−3.42763	+	5.93683i	−0.210956	+	0.365386i
$265$			13.6921i			0.841099i
$266$		0			0
$267$	11.5412	−	6.66330i	0.706308	−	0.407787i
$268$	0.837243	−	0.483382i	0.0511428	−	0.0295273i
$269$	−14.8051			−0.902686			−0.451343	−	0.892351i	$-0.649055\pi$
$269$	−14.8051			−0.902686			−0.451343	+	0.892351i	$0.649055\pi$
$270$	2.38317	+	4.12776i	0.145035	+	0.251208i
$271$		−	0.0646361i		−	0.00392636i	−0.999998	−	0.00196318i	$-0.999375\pi$
$271$		−	0.0646361i		−	0.00392636i	0.999998	−	0.00196318i	$-0.000624900\pi$
$272$	5.91517			0.358660
$273$		0			0
$274$	−15.4617			−0.934077
$275$		−	19.2089i		−	1.15834i
$276$	−9.01435	−	15.6133i	−0.542600	−	0.939811i
$277$	−4.25115			−0.255427			−0.127713	−	0.991811i	$-0.540764\pi$
$277$	−4.25115			−0.255427			−0.127713	+	0.991811i	$0.540764\pi$
$278$	−12.3861	+	7.15110i	−0.742867	+	0.428895i
$279$	−2.39494	+	1.38272i	−0.143381	+	0.0827812i
$280$		0			0
$281$			11.0454i			0.658916i	0.944170	+	0.329458i	$0.106866\pi$
$281$			11.0454i			0.658916i	−0.944170	+	0.329458i	$0.893134\pi$
$282$	2.04709	−	3.54567i	0.121903	−	0.211142i
$283$	5.64271	+	9.77346i	0.335424	+	0.580972i	0.983566	−	0.180548i	$-0.0577870\pi$
$283$	5.64271	+	9.77346i	0.335424	+	0.580972i	−0.648142	+	0.761520i	$0.724454\pi$
$284$	−3.62568	+	2.09329i	−0.215145	+	0.124214i
$285$	−23.1702	−	40.1320i	−1.37248	−	2.37721i
$286$	0.168179	+	9.66761i	0.00994461	+	0.571658i
$287$		0			0
$288$	3.06108	+	1.76732i	0.180376	+	0.104140i
$289$	17.9892			1.05819
$290$	24.8758			1.46076
$291$	−6.99445	−	4.03825i	−0.410022	−	0.236726i
$292$	13.0216	+	7.51803i	0.762032	+	0.439959i
$293$	−22.5549	+	13.0221i	−1.31767	+	0.760758i	−0.983354	−	0.181703i	$-0.941839\pi$
$293$	−22.5549	+	13.0221i	−1.31767	+	0.760758i	−0.334318	+	0.942460i	$0.608506\pi$
$294$		0			0
$295$	16.6359	+	28.8143i	0.968581	+	1.67763i
$296$	7.81450			0.454209
$297$	−3.17402	+	1.83252i	−0.184175	+	0.106334i
$298$	1.77859	−	3.08060i	0.103031	−	0.178455i
$299$	−22.2398	−	12.3294i	−1.28616	−	0.713029i
$300$	−18.3105			−1.05716
$301$		0			0
$302$	−4.76370	+	8.25097i	−0.274120	+	0.474790i
$303$	−4.83970	+	8.38261i	−0.278034	+	0.481569i
$304$	−4.50154	−	2.59896i	−0.258181	−	0.149061i
$305$			53.7447i			3.07741i
$306$	18.1068	+	10.4540i	1.03510	+	0.597614i
$307$			25.0551i			1.42997i	0.699139	+	0.714986i	$0.253567\pi$
$307$			25.0551i			1.42997i	−0.699139	+	0.714986i	$0.746433\pi$
$308$		0			0
$309$	−8.70211	+	15.0725i	−0.495046	+	0.857445i
$310$		−	2.72859i		−	0.154974i
$311$	16.2165	−	28.0878i	0.919554	−	1.59271i	0.119460	−	0.992839i	$-0.461884\pi$
$311$	16.2165	−	28.0878i	0.919554	−	1.59271i	0.800094	−	0.599875i	$-0.204783\pi$
$312$	9.21545	−	0.160313i	0.521722	−	0.00907592i
$313$	−1.11259	−	1.92705i	−0.0628870	−	0.108924i	0.832868	−	0.553472i	$-0.186697\pi$
$313$	−1.11259	−	1.92705i	−0.0628870	−	0.108924i	−0.895755	+	0.444549i	$0.853364\pi$
$314$	18.0432	+	10.4173i	1.01824	+	0.587880i
$315$		0			0
$316$	−0.146678	−	0.254054i	−0.00825129	−	0.0142917i
$317$	−3.32340	+	1.91877i	−0.186661	+	0.107769i	−0.590418	−	0.807097i	$-0.701037\pi$
$317$	−3.32340	+	1.91877i	−0.186661	+	0.107769i	0.403758	+	0.914866i	$0.367704\pi$
$318$			10.0360i			0.562793i
$319$			19.1281i			1.07097i
$320$	−3.02030	+	1.74377i	−0.168840	+	0.0974796i
$321$	18.2796	+	31.6612i	1.02027	+	1.76716i
$322$		0			0
$323$	−26.6273	−	15.3733i	−1.48158	−	0.855393i
$324$	−3.55514	−	6.15768i	−0.197508	−	0.342093i
$325$	−22.1382	+	13.3002i	−1.22801	+	0.737763i
$326$	−3.15302	+	5.46119i	−0.174629	+	0.302467i
$327$			11.6994i			0.646976i
$328$	−0.0788541	+	0.136579i	−0.00435399	+	0.00754133i
$329$		0			0
$330$		−	23.9080i		−	1.31609i
$331$	−5.26859	−	3.04182i	−0.289588	−	0.167194i	0.348168	−	0.937432i	$-0.386804\pi$
$331$	−5.26859	−	3.04182i	−0.289588	−	0.167194i	−0.637756	+	0.770238i	$0.720137\pi$
$332$		−	2.87495i		−	0.157783i
$333$	23.9208	+	13.8107i	1.31085	+	0.756821i
$334$	3.33436	−	5.77528i	0.182448	−	0.316009i
$335$	−1.68581	+	2.91992i	−0.0921059	+	0.159532i
$336$		0			0
$337$	−19.3746			−1.05540			−0.527700	−	0.849431i	$-0.676946\pi$
$337$	−19.3746			−1.05540			−0.527700	+	0.849431i	$0.676946\pi$
$338$	11.0254	−	6.88765i	0.599705	−	0.374639i
$339$	−3.85101	+	6.67015i	−0.209158	+	0.362273i
$340$	−17.8656	+	10.3147i	−0.968896	+	0.559392i
$341$	2.09813			0.113620
$342$	−9.18638	−	15.9113i	−0.496743	−	0.860383i
$343$		0			0
$344$	0.285963	−	0.165101i	0.0154181	−	0.00890165i
$345$	54.4520	+	31.4379i	2.93160	+	1.69256i
$346$	18.4630	+	10.6596i	0.992575	+	0.573064i
$347$	−9.02056			−0.484249			−0.242124	−	0.970245i	$-0.577844\pi$
$347$	−9.02056			−0.484249			−0.242124	+	0.970245i	$0.577844\pi$
$348$	18.2335			0.977417
$349$	6.04213	+	3.48843i	0.323428	+	0.186731i	0.652919	−	0.757427i	$-0.273544\pi$
$349$	6.04213	+	3.48843i	0.323428	+	0.186731i	−0.329492	+	0.944159i	$0.606877\pi$
$350$		0			0
$351$	4.30965	+	2.38921i	0.230032	+	0.127527i
$352$	−1.34086	−	2.32244i	−0.0714680	−	0.123786i
$353$	21.6841	−	12.5193i	1.15413	−	0.666335i	0.204237	−	0.978922i	$-0.434529\pi$
$353$	21.6841	−	12.5193i	1.15413	−	0.666335i	0.949889	+	0.312587i	$0.101195\pi$
$354$	12.1938	+	21.1203i	0.648093	+	1.12253i
$355$	7.30042	−	12.6447i	0.387466	−	0.671111i
$356$			5.21325i			0.276302i
$357$		0			0
$358$	13.3701	−	7.71921i	0.706630	−	0.407973i
$359$	−32.5703	+	18.8045i	−1.71900	+	0.992463i	−0.798225	+	0.602359i	$0.794228\pi$
$359$	−32.5703	+	18.8045i	−1.71900	+	0.992463i	−0.920771	+	0.390104i	$0.872439\pi$
$360$	−12.3272			−0.649698
$361$	4.00922	+	6.94418i	0.211012	+	0.365483i
$362$			13.2818i			0.698078i
$363$	−9.73535			−0.510973
$364$		0			0
$365$	−52.4388			−2.74477
$366$			39.3938i			2.05914i
$367$	−10.5455	−	18.2653i	−0.550470	−	0.953442i	−0.998241	−	0.0592934i	$-0.981115\pi$
$367$	−10.5455	−	18.2653i	−0.550470	−	0.953442i	0.447771	−	0.894148i	$-0.352218\pi$
$368$	7.05268			0.367646
$369$	−0.482757	+	0.278720i	−0.0251313	+	0.0145096i
$370$	−23.6021	+	13.6267i	−1.22702	+	0.708418i
$371$		0			0
$372$		−	2.00000i		−	0.103695i
$373$	−7.04708	+	12.2059i	−0.364884	+	0.631998i	−0.988758	−	0.149528i	$-0.952225\pi$
$373$	−7.04708	+	12.2059i	−0.364884	+	0.631998i	0.623874	+	0.781525i	$0.285558\pi$
$374$	−7.93141	−	13.7376i	−0.410123	−	0.710354i
$375$	16.6994	−	9.64138i	0.862352	−	0.497879i
$376$	0.800806	+	1.38704i	0.0412984	+	0.0715309i
$377$	22.0451	−	13.2443i	1.13538	−	0.682114i
$378$		0			0
$379$	28.6773	+	16.5568i	1.47305	+	0.850467i	0.999540	−	0.0303204i	$-0.00965277\pi$
$379$	28.6773	+	16.5568i	1.47305	+	0.850467i	0.473512	+	0.880787i	$0.342986\pi$
$380$	18.1280			0.929945
$381$	28.4402			1.45703
$382$	−10.3270	−	5.96230i	−0.528375	−	0.305058i
$383$	22.4578	+	12.9660i	1.14754	+	0.662534i	0.948287	−	0.317414i	$-0.102814\pi$
$383$	22.4578	+	12.9660i	1.14754	+	0.662534i	0.199255	+	0.979948i	$0.436148\pi$
$384$	−2.21381	+	1.27815i	−0.112973	+	0.0652251i
$385$		0			0
$386$	2.67468	+	4.63268i	0.136138	+	0.235797i
$387$	1.16714			0.0593292
$388$	2.73617	−	1.57973i	0.138908	−	0.0801986i
$389$	15.2824	−	26.4698i	0.774847	−	1.34207i	−0.160034	−	0.987111i	$-0.551160\pi$
$389$	15.2824	−	26.4698i	0.774847	−	1.34207i	0.934881	−	0.354962i	$-0.115506\pi$
$390$	−27.5538	+	16.5538i	−1.39524	+	0.838234i
$391$	41.7178			2.10976
$392$		0			0
$393$	19.0593	−	33.0117i	0.961415	−	1.66522i
$394$	−6.59688	+	11.4261i	−0.332346	+	0.575641i
$395$	0.886023	+	0.511546i	0.0445807	+	0.0257387i
$396$		−	9.47889i		−	0.476332i
$397$	−19.4521	−	11.2307i	−0.976275	−	0.563653i	−0.0751317	−	0.997174i	$-0.523938\pi$
$397$	−19.4521	−	11.2307i	−0.976275	−	0.563653i	−0.901144	+	0.433521i	$0.857271\pi$
$398$			20.0516i			1.00509i
$399$		0			0
$400$	3.58146	−	6.20327i	0.179073	−	0.310163i
$401$			17.0288i			0.850376i	0.905105	+	0.425188i	$0.139792\pi$
$401$			17.0288i			0.850376i	−0.905105	+	0.425188i	$0.860208\pi$
$402$	−1.23567	+	2.14024i	−0.0616295	+	0.106745i
$403$	−1.45274	−	2.41809i	−0.0723661	−	0.120454i
$404$	−1.89325	−	3.27921i	−0.0941928	−	0.163147i
$405$	21.4751	+	12.3987i	1.06711	+	0.616095i
$406$		0			0
$407$	−10.4781	−	18.1487i	−0.519382	−	0.899597i
$408$	−13.0951	+	7.56045i	−0.648303	+	0.374298i
$409$			5.13532i			0.253925i	0.991908	+	0.126963i	$0.0405228\pi$
$409$			5.13532i			0.253925i	−0.991908	+	0.126963i	$0.959477\pi$
$410$		−	0.550013i		−	0.0271632i
$411$	34.2294	−	19.7623i	1.68841	−	0.974804i
$412$	−3.40419	−	5.89623i	−0.167713	−	0.290487i
$413$		0			0
$414$	21.5888	+	12.4643i	1.06103	+	0.612587i
$415$	5.01324	+	8.68319i	0.246090	+	0.426241i
$416$	−1.74819	+	3.15338i	−0.0857122	+	0.154607i
$417$	18.2803	−	31.6624i	0.895190	−	1.55052i
$418$			13.9394i			0.681797i
$419$	15.9418	−	27.6120i	0.778808	−	1.34893i	−0.153822	−	0.988099i	$-0.549158\pi$
$419$	15.9418	−	27.6120i	0.778808	−	1.34893i	0.932629	−	0.360836i	$-0.117509\pi$
$420$		0			0
$421$			14.7648i			0.719594i	0.933031	+	0.359797i	$0.117154\pi$
$421$			14.7648i			0.719594i	−0.933031	+	0.359797i	$0.882846\pi$
$422$	−6.89481	−	3.98072i	−0.335634	−	0.193778i
$423$			5.66111i			0.275252i
$424$	−3.40002	−	1.96300i	−0.165120	−	0.0953319i
$425$	21.1849	−	36.6934i	1.02762	−	1.77989i
$426$	5.35106	−	9.26830i	0.259260	−	0.449051i
$427$		0			0
$428$	−14.3017			−0.691297
$429$	−12.7289	−	21.1873i	−0.614559	−	1.02293i
$430$	−0.575796	+	0.997308i	−0.0277674	+	0.0480945i
$431$	−30.4051	+	17.5544i	−1.46456	+	0.845565i	−0.999217	−	0.0395640i	$-0.987403\pi$
$431$	−30.4051	+	17.5544i	−1.46456	+	0.845565i	−0.465345	+	0.885129i	$0.654070\pi$
$432$	−1.36668			−0.0657542
$433$	−1.98625	−	3.44029i	−0.0954533	−	0.165330i	0.814344	−	0.580382i	$-0.197097\pi$
$433$	−1.98625	−	3.44029i	−0.0954533	−	0.165330i	−0.909798	+	0.415052i	$0.863763\pi$
$434$		0			0
$435$	−55.0705	+	31.7950i	−2.64043	+	1.52445i
$436$	−3.96353	−	2.28834i	−0.189819	−	0.109592i
$437$	−31.7479	−	18.3296i	−1.51871	−	0.876826i
$438$	−38.4366			−1.83657
$439$	−5.75277			−0.274565			−0.137282	−	0.990532i	$-0.543837\pi$
$439$	−5.75277			−0.274565			−0.137282	+	0.990532i	$0.543837\pi$
$440$	8.09958	+	4.67630i	0.386133	+	0.222934i
$441$		0			0
$442$	−10.3408	+	18.6528i	−0.491864	+	0.887222i
$443$	13.5402	+	23.4523i	0.643315	+	1.11425i	0.984688	+	0.174326i	$0.0557747\pi$
$443$	13.5402	+	23.4523i	0.643315	+	1.11425i	−0.341373	+	0.939928i	$0.610892\pi$
$444$	−17.2999	+	9.98808i	−0.821015	+	0.474013i
$445$	−9.09070	−	15.7456i	−0.430941	−	0.746411i
$446$	−10.7709	+	18.6557i	−0.510015	+	0.883373i
$447$			9.09318i			0.430092i
$448$		0			0
$449$	7.14396	−	4.12457i	0.337145	−	0.194650i	−0.321864	−	0.946786i	$-0.604309\pi$
$449$	7.14396	−	4.12457i	0.337145	−	0.194650i	0.659009	+	0.752135i	$0.270976\pi$
$450$	21.9263	−	12.6591i	1.03361	−	0.596757i
$451$	0.422929			0.0199149
$452$	−1.50648	−	2.60930i	−0.0708590	−	0.122731i
$453$		−	24.3548i		−	1.14429i
$454$	3.65771			0.171665
$455$		0			0
$456$	13.2874			0.622241
$457$		−	38.6967i		−	1.81015i	−0.425247	−	0.905077i	$-0.639813\pi$
$457$		−	38.6967i		−	1.81015i	0.425247	−	0.905077i	$-0.360187\pi$
$458$	4.87376	+	8.44160i	0.227736	+	0.394450i
$459$	−8.08411			−0.377334
$460$	−21.3012	+	12.2982i	−0.993172	+	0.573408i
$461$	11.3751	−	6.56742i	0.529792	−	0.305875i	−0.211140	−	0.977456i	$-0.567718\pi$
$461$	11.3751	−	6.56742i	0.529792	−	0.305875i	0.740932	+	0.671581i	$0.234384\pi$
$462$		0			0
$463$			6.98417i			0.324582i	0.986743	+	0.162291i	$0.0518883\pi$
$463$			6.98417i			0.324582i	−0.986743	+	0.162291i	$0.948112\pi$
$464$	−3.56639	+	6.17717i	−0.165566	+	0.286768i
$465$	3.48754	+	6.04059i	0.161731	+	0.280126i
$466$	2.36334	−	1.36448i	0.109480	−	0.0632081i
$467$	−2.81345	−	4.87305i	−0.130191	−	0.225498i	0.793559	−	0.608493i	$-0.208226\pi$
$467$	−2.81345	−	4.87305i	−0.130191	−	0.225498i	−0.923750	+	0.382996i	$0.874892\pi$
$468$	−10.9244	+	6.56315i	−0.504980	+	0.303382i
$469$		0			0
$470$	−4.83734	−	2.79284i	−0.223130	−	0.128824i
$471$	−53.2591			−2.45405
$472$	−9.54021			−0.439124
$473$	−0.766873	−	0.442755i	−0.0352609	−	0.0203579i
$474$	0.649436	+	0.374952i	0.0298296	+	0.0172221i
$475$	−32.2441	+	18.6162i	−1.47946	+	0.854168i
$476$		0			0
$477$	−6.93850	−	12.0178i	−0.317692	−	0.550259i
$478$	−12.2347			−0.559604
$479$	−21.7538	+	12.5596i	−0.993956	+	0.573861i	−0.906454	−	0.422304i	$-0.861222\pi$
$479$	−21.7538	+	12.5596i	−0.993956	+	0.573861i	−0.0875014	+	0.996164i	$0.527888\pi$
$480$	4.45758	−	7.72076i	0.203460	−	0.352403i
$481$	−13.6612	+	24.6421i	−0.622899	+	1.12358i
$482$	−24.2176			−1.10308
$483$		0			0
$484$	1.90419	−	3.29816i	0.0865542	−	0.149916i
$485$	−5.50936	+	9.54249i	−0.250167	+	0.433302i
$486$	19.2916	+	11.1380i	0.875083	+	0.505229i
$487$		−	17.6758i		−	0.800968i	−0.916304	−	0.400484i	$-0.868842\pi$
$487$		−	17.6758i		−	0.800968i	0.916304	−	0.400484i	$-0.131158\pi$
$488$	−13.3459	−	7.70525i	−0.604140	−	0.348800i
$489$		−	16.1201i		−	0.728975i
$490$		0			0
$491$	15.9975	−	27.7084i	0.721956	−	1.25046i	−0.238259	−	0.971202i	$-0.576577\pi$
$491$	15.9975	−	27.7084i	0.721956	−	1.25046i	0.960215	−	0.279262i	$-0.0900898\pi$
$492$		−	0.403148i		−	0.0181753i
$493$	−21.0958	+	36.5390i	−0.950107	+	1.64563i
$494$	16.0651	−	9.65158i	0.722802	−	0.434245i
$495$	16.5290	+	28.6290i	0.742923	+	1.28678i
$496$	0.677564	+	0.391192i	0.0304235	+	0.0175650i
$497$		0			0
$498$	3.67460	+	6.36460i	0.164663	+	0.285204i
$499$	10.0819	−	5.82079i	0.451328	−	0.260574i	−0.257063	−	0.966395i	$-0.582755\pi$
$499$	10.0819	−	5.82079i	0.451328	−	0.260574i	0.708391	+	0.705820i	$0.249421\pi$
$500$			7.54326i			0.337345i
$501$			17.0472i			0.761612i
$502$	1.74392	−	1.00685i	0.0778351	−	0.0449381i
$503$	−7.51764	−	13.0209i	−0.335195	−	0.580574i	0.648327	−	0.761362i	$-0.275469\pi$
$503$	−7.51764	−	13.0209i	−0.335195	−	0.580574i	−0.983522	+	0.180787i	$0.942135\pi$
$504$		0			0
$505$	11.4364	+	6.60278i	0.508911	+	0.293820i
$506$	−9.45665	−	16.3794i	−0.420399	−	0.728153i
$507$	−15.6048	+	29.3401i	−0.693036	+	1.30304i
$508$	−5.56278	+	9.63501i	−0.246808	+	0.427484i
$509$		−	2.56096i		−	0.113513i	−0.998388	−	0.0567563i	$-0.981924\pi$
$509$		−	2.56096i		−	0.113513i	0.998388	−	0.0567563i	$-0.0180758\pi$
$510$	26.3673	−	45.6696i	1.16757	−	2.02228i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	6.15214	+	3.55194i	0.271624	+	0.156822i
$514$		−	2.14218i		−	0.0944874i
$515$	20.5633	+	11.8722i	0.906129	+	0.523154i
$516$	−0.422047	+	0.731006i	−0.0185796	+	0.0321807i
$517$	2.14754	−	3.71964i	0.0944485	−	0.163590i
$518$		0			0
$519$	−54.4981			−2.39220
$520$	−0.218714	−	12.5726i	−0.00959124	−	0.551345i
$521$	15.5272	−	26.8939i	0.680259	−	1.17824i	−0.294643	−	0.955607i	$-0.595201\pi$
$521$	15.5272	−	26.8939i	0.680259	−	1.17824i	0.974902	−	0.222636i	$-0.0714660\pi$
$522$	−21.8340	+	12.6059i	−0.955649	+	0.551744i
$523$	−4.36360			−0.190807			−0.0954035	−	0.995439i	$-0.530414\pi$
$523$	−4.36360			−0.190807			−0.0954035	+	0.995439i	$0.530414\pi$
$524$	7.45584	+	12.9139i	0.325710	+	0.564146i
$525$		0			0
$526$	9.40731	−	5.43131i	0.410178	−	0.236817i
$527$	4.00790	+	2.31396i	0.174587	+	0.100798i
$528$	5.93683	+	3.42763i	0.258367	+	0.149168i
$529$	26.7402			1.16262
$530$	13.6921			0.594747
$531$	−29.2034	−	16.8606i	−1.26732	−	0.731686i
$532$		0			0
$533$	−0.292835	−	0.487424i	−0.0126841	−	0.0211127i
$534$	−6.66330	−	11.5412i	−0.288349	−	0.499435i
$535$	43.1953	−	24.9388i	1.86749	−	1.07820i
$536$	−0.483382	−	0.837243i	−0.0208789	−	0.0361634i
$537$	−19.7326	+	34.1778i	−0.851523	+	1.47488i
$538$			14.8051i			0.638295i
$539$		0			0
$540$	4.12776	−	2.38317i	0.177631	−	0.102555i
$541$	−14.9121	+	8.60953i	−0.641123	+	0.370152i	−0.785047	−	0.619436i	$-0.787361\pi$
$541$	−14.9121	+	8.60953i	−0.641123	+	0.370152i	0.143924	+	0.989589i	$0.454028\pi$
$542$	−0.0646361			−0.00277636
$543$	−16.9761	−	29.4035i	−0.728516	−	1.26183i
$544$		−	5.91517i		−	0.253611i
$545$	15.9614			0.683710
$546$		0			0
$547$	42.8331			1.83141			0.915706	−	0.401849i	$-0.131632\pi$
$547$	42.8331			1.83141			0.915706	+	0.401849i	$0.131632\pi$
$548$			15.4617i			0.660492i
$549$	−27.2352	−	47.1728i	−1.16237	−	2.01329i
$550$	−19.2089			−0.819071
$551$	32.1085	−	18.5378i	1.36787	−	0.789739i
$552$	−15.6133	+	9.01435i	−0.664547	+	0.383676i
$553$		0			0
$554$			4.25115i			0.180614i
$555$	34.8338	−	60.3339i	1.47861	−	2.56103i
$556$	7.15110	+	12.3861i	0.303274	+	0.525286i
$557$	20.9756	−	12.1103i	0.888765	−	0.513129i	0.0152269	−	0.999884i	$-0.495153\pi$
$557$	20.9756	−	12.1103i	0.888765	−	0.513129i	0.873538	+	0.486755i	$0.161820\pi$
$558$	1.38272	+	2.39494i	0.0585351	+	0.101386i
$559$	0.0207080	+	1.19038i	0.000875853	+	0.0503477i
$560$		0			0
$561$	35.1173	+	20.2750i	1.48265	+	0.856011i
$562$	11.0454			0.465924
$563$	13.2481			0.558341			0.279170	−	0.960242i	$-0.409941\pi$
$563$	13.2481			0.558341			0.279170	+	0.960242i	$0.409941\pi$
$564$	−3.54567	−	2.04709i	−0.149300	−	0.0861982i
$565$	9.10005	+	5.25391i	0.382842	+	0.221034i
$566$	9.77346	−	5.64271i	0.410809	−	0.237181i
$567$		0			0
$568$	2.09329	+	3.62568i	0.0878324	+	0.152130i
$569$	24.9921			1.04772			0.523861	−	0.851804i	$-0.324491\pi$
$569$	24.9921			1.04772			0.523861	+	0.851804i	$0.324491\pi$
$570$	−40.1320	+	23.1702i	−1.68094	+	0.970493i
$571$	−11.2638	+	19.5095i	−0.471375	+	0.816445i	−0.999464	−	0.0327437i	$-0.989575\pi$
$571$	−11.2638	+	19.5095i	−0.471375	+	0.816445i	0.528089	+	0.849189i	$0.322909\pi$
$572$	9.66761	−	0.168179i	0.404223	−	0.00703190i
$573$	30.4827			1.27344
$574$		0			0
$575$	25.2589	−	43.7496i	1.05337	−	1.82449i
$576$	1.76732	−	3.06108i	0.0736382	−	0.127545i
$577$	11.2452	+	6.49240i	0.468142	+	0.270282i	0.715462	−	0.698652i	$-0.246216\pi$
$577$	11.2452	+	6.49240i	0.468142	+	0.270282i	−0.247319	+	0.968934i	$0.579550\pi$
$578$		−	17.9892i		−	0.748252i
$579$	−11.8425	−	6.83726i	−0.492157	−	0.284147i
$580$		−	24.8758i		−	1.03291i
$581$		0			0
$582$	−4.03825	+	6.99445i	−0.167391	+	0.289929i
$583$			10.5285i			0.436044i
$584$	7.51803	−	13.0216i	0.311098	−	0.538838i
$585$	21.5502	−	38.8723i	0.890993	−	1.60717i
$586$	13.0221	+	22.5549i	0.537937	+	0.931734i
$587$	3.02617	+	1.74716i	0.124903	+	0.0721131i	0.561150	−	0.827714i	$-0.310359\pi$
$587$	3.02617	+	1.74716i	0.124903	+	0.0721131i	−0.436246	+	0.899827i	$0.643692\pi$
$588$		0			0
$589$	−2.03339	−	3.52193i	−0.0837842	−	0.145118i
$590$	28.8143	−	16.6359i	1.18626	−	0.684890i
$591$		−	33.7271i		−	1.38735i
$592$		−	7.81450i		−	0.321174i
$593$	−20.1039	+	11.6070i	−0.825568	+	0.476642i	−0.852333	−	0.523000i	$-0.824813\pi$
$593$	−20.1039	+	11.6070i	−0.825568	+	0.476642i	0.0267650	+	0.999642i	$0.491479\pi$
$594$	1.83252	+	3.17402i	0.0751892	+	0.130231i
$595$		0			0
$596$	−3.08060	−	1.77859i	−0.126186	−	0.0728538i
$597$	−25.6288	−	44.3904i	−1.04892	−	1.81678i
$598$	−12.3294	+	22.2398i	−0.504188	+	0.909453i
$599$	−9.18226	+	15.9041i	−0.375177	+	0.649826i	−0.990354	−	0.138564i	$-0.955751\pi$
$599$	−9.18226	+	15.9041i	−0.375177	+	0.649826i	0.615177	+	0.788389i	$0.289085\pi$
$600$			18.3105i			0.747524i
$601$	2.37983	−	4.12198i	0.0970751	−	0.168139i	−0.813398	−	0.581708i	$-0.802385\pi$
$601$	2.37983	−	4.12198i	0.0970751	−	0.168139i	0.910473	+	0.413569i	$0.135718\pi$
$602$		0			0
$603$		−	3.41716i		−	0.139157i
$604$	8.25097	+	4.76370i	0.335727	+	0.193832i
$605$			13.2819i			0.539986i
$606$	8.38261	+	4.83970i	0.340520	+	0.196600i
$607$	−10.4828	+	18.1568i	−0.425484	+	0.736960i	−0.996466	−	0.0840029i	$-0.973230\pi$
$607$	−10.4828	+	18.1568i	−0.425484	+	0.736960i	0.570981	+	0.820963i	$0.306563\pi$
$608$	−2.59896	+	4.50154i	−0.105402	+	0.182561i
$609$		0			0
$610$	53.7447			2.17606
$611$	−5.77382	+	0.100442i	−0.233584	+	0.00406344i
$612$	10.4540	−	18.1068i	0.422577	−	0.731924i
$613$	25.3853	−	14.6562i	1.02530	−	0.591959i	0.109667	−	0.993968i	$-0.465022\pi$
$613$	25.3853	−	14.6562i	1.02530	−	0.591959i	0.915635	+	0.402010i	$0.131688\pi$
$614$	25.0551			1.01114
$615$	0.702997	+	1.21763i	0.0283476	+	0.0490994i
$616$		0			0
$617$	−4.55827	+	2.63172i	−0.183509	+	0.105949i	−0.588940	−	0.808177i	$-0.700455\pi$
$617$	−4.55827	+	2.63172i	−0.183509	+	0.105949i	0.405431	+	0.914125i	$0.367121\pi$
$618$	15.0725	+	8.70211i	0.606305	+	0.350050i
$619$	9.49712	+	5.48317i	0.381722	+	0.220387i	0.678567	−	0.734538i	$-0.262601\pi$
$619$	9.49712	+	5.48317i	0.381722	+	0.220387i	−0.296845	+	0.954926i	$0.595935\pi$
$620$	−2.72859			−0.109583
$621$	−9.63872			−0.386788
$622$	−28.0878	−	16.2165i	−1.12622	−	0.650223i
$623$		0			0
$624$	−0.160313	−	9.21545i	−0.00641765	−	0.368913i
$625$	4.75360	+	8.23348i	0.190144	+	0.329339i
$626$	−1.92705	+	1.11259i	−0.0770206	+	0.0444678i
$627$	−17.8166	−	30.8592i	−0.711525	−	1.23240i
$628$	10.4173	−	18.0432i	0.415694	−	0.720003i
$629$		−	46.2241i		−	1.84307i
$630$		0			0
$631$	−21.0642	+	12.1614i	−0.838553	+	0.484139i	−0.856772	−	0.515695i	$-0.827534\pi$
$631$	−21.0642	+	12.1614i	−0.838553	+	0.484139i	0.0182188	+	0.999834i	$0.494200\pi$
$632$	−0.254054	+	0.146678i	−0.0101057	+	0.00583454i
$633$	20.3518			0.808910
$634$	1.91877	+	3.32340i	0.0762039	+	0.131989i
$635$		−	38.8008i		−	1.53976i
$636$	10.0360			0.397954
$637$		0			0
$638$	19.1281			0.757289
$639$			14.7980i			0.585400i
$640$	1.74377	+	3.02030i	0.0689285	+	0.119388i
$641$	−1.30118			−0.0513937			−0.0256968	−	0.999670i	$-0.508180\pi$
$641$	−1.30118			−0.0513937			−0.0256968	+	0.999670i	$0.508180\pi$
$642$	31.6612	−	18.2796i	1.24957	−	0.721439i
$643$	4.87547	−	2.81485i	0.192270	−	0.111007i	−0.400775	−	0.916177i	$-0.631259\pi$
$643$	4.87547	−	2.81485i	0.192270	−	0.111007i	0.593045	+	0.805170i	$0.297926\pi$
$644$		0			0
$645$		−	2.94381i		−	0.115912i
$646$	−15.3733	+	26.6273i	−0.604854	+	1.04764i
$647$	−5.90635	−	10.2301i	−0.232202	−	0.402186i	0.726254	−	0.687427i	$-0.241260\pi$
$647$	−5.90635	−	10.2301i	−0.232202	−	0.402186i	−0.958456	+	0.285241i	$0.907927\pi$
$648$	−6.15768	+	3.55514i	−0.241896	+	0.139659i
$649$	12.7921	+	22.1565i	0.502133	+	0.869720i
$650$	13.3002	+	22.1382i	0.521677	+	0.868332i
$651$		0			0
$652$	5.46119	+	3.15302i	0.213877	+	0.123482i
$653$	−3.12013			−0.122100			−0.0610500	−	0.998135i	$-0.519445\pi$
$653$	−3.12013			−0.122100			−0.0610500	+	0.998135i	$0.519445\pi$
$654$	11.6994			0.457481
$655$	−45.0377	−	26.0025i	−1.75977	−	1.01600i
$656$	0.136579	+	0.0788541i	0.00533252	+	0.00307873i
$657$	46.0266	−	26.5735i	1.79567	−	1.03673i
$658$		0			0
$659$	−18.7533	−	32.4817i	−0.730526	−	1.26531i	−0.956659	−	0.291211i	$-0.905942\pi$
$659$	−18.7533	−	32.4817i	−0.730526	−	1.26531i	0.226133	−	0.974096i	$-0.427392\pi$
$660$	−23.9080			−0.930616
$661$	−30.9817	+	17.8873i	−1.20505	+	0.695735i	−0.961673	−	0.274198i	$-0.911588\pi$
$661$	−30.9817	+	17.8873i	−1.20505	+	0.695735i	−0.243375	+	0.969932i	$0.578254\pi$
$662$	−3.04182	+	5.26859i	−0.118224	+	0.204770i
$663$	−0.948277	−	54.5109i	−0.0368280	−	2.11703i
$664$	−2.87495			−0.111570
$665$		0			0
$666$	13.8107	−	23.9208i	0.535153	−	0.926913i
$667$	−25.1526	+	43.5656i	−0.973913	+	1.68687i
$668$	−5.77528	−	3.33436i	−0.223452	−	0.129010i
$669$		−	55.0670i		−	2.12901i
$670$	2.91992	+	1.68581i	0.112806	+	0.0651287i
$671$			41.3266i			1.59540i
$672$		0			0
$673$	−4.31081	+	7.46655i	−0.166170	+	0.287814i	−0.937070	−	0.349141i	$-0.886473\pi$
$673$	−4.31081	+	7.46655i	−0.166170	+	0.287814i	0.770900	+	0.636956i	$0.219807\pi$
$674$			19.3746i			0.746281i
$675$	−4.89469	+	8.47785i	−0.188397	+	0.326313i
$676$	−6.88765	−	11.0254i	−0.264910	−	0.424055i
$677$	7.77753	+	13.4711i	0.298915	+	0.517735i	0.975888	−	0.218272i	$-0.0700421\pi$
$677$	7.77753	+	13.4711i	0.298915	+	0.517735i	−0.676973	+	0.736008i	$0.736709\pi$
$678$	6.67015	+	3.85101i	0.256165	+	0.147897i
$679$		0			0
$680$	10.3147	+	17.8656i	0.395550	+	0.685113i
$681$	−8.09750	+	4.67509i	−0.310297	+	0.179150i
$682$		−	2.09813i		−	0.0803416i
$683$		−	8.89795i		−	0.340471i	−0.985403	−	0.170235i	$-0.945547\pi$
$683$		−	8.89795i		−	0.340471i	0.985403	−	0.170235i	$-0.0544528\pi$
$684$	−15.9113	+	9.18638i	−0.608383	+	0.351250i
$685$	−26.9617	−	46.6990i	−1.03015	−	1.78428i
$686$		0			0
$687$	−21.5792	−	12.4588i	−0.823298	−	0.475331i
$688$	−0.165101	−	0.285963i	−0.00629442	−	0.0109023i
$689$	12.1340	−	7.28987i	0.462269	−	0.277722i
$690$	31.4379	−	54.4520i	1.19682	−	2.07295i
$691$			38.1797i			1.45243i	0.687470	+	0.726213i	$0.258721\pi$
$691$			38.1797i			1.45243i	−0.687470	+	0.726213i	$0.741279\pi$
$692$	10.6596	−	18.4630i	0.405217	−	0.701857i
$693$		0			0
$694$			9.02056i			0.342416i
$695$	−43.1969	−	24.9397i	−1.63855	−	0.946018i
$696$		−	18.2335i		−	0.691138i
$697$	0.807889	+	0.466435i	0.0306010	+	0.0176675i
$698$	3.48843	−	6.04213i	0.132039	−	0.228698i
$699$	−3.48800	+	6.04139i	−0.131928	+	0.228506i
$700$		0			0
$701$	44.0952			1.66545			0.832727	−	0.553684i	$-0.186779\pi$
$701$	44.0952			1.66545			0.832727	+	0.553684i	$0.186779\pi$
$702$	2.38921	−	4.30965i	0.0901749	−	0.162657i
$703$	−20.3096	+	35.1773i	−0.765991	+	1.32674i
$704$	−2.32244	+	1.34086i	−0.0875301	+	0.0505355i
$705$	14.2786			0.537765
$706$	−12.5193	−	21.6841i	−0.471170	−	0.816090i
$707$		0			0
$708$	21.1203	−	12.1938i	0.793748	−	0.458271i
$709$	−10.6207	−	6.13185i	−0.398868	−	0.230287i	0.287127	−	0.957892i	$-0.407300\pi$
$709$	−10.6207	−	6.13185i	−0.398868	−	0.230287i	−0.685995	+	0.727606i	$0.740633\pi$
$710$	−12.6447	−	7.30042i	−0.474547	−	0.273980i
$711$	−1.03691			−0.0388870
$712$	5.21325			0.195375
$713$	4.77864	+	2.75895i	0.178961	+	0.103323i
$714$		0			0
$715$	−28.9058	+	17.3660i	−1.08101	+	0.649453i
$716$	−7.71921	−	13.3701i	−0.288480	−	0.499663i
$717$	27.0855	−	15.6378i	1.01152	−	0.584004i
$718$	18.8045	+	32.5703i	0.701777	+	1.21551i
$719$	13.5967	−	23.5501i	0.507070	−	0.878272i	−0.492896	−	0.870088i	$-0.664062\pi$
$719$	13.5967	−	23.5501i	0.507070	−	0.878272i	0.999967	−	0.00818343i	$-0.00260489\pi$
$720$			12.3272i			0.459406i
$721$		0			0
$722$	6.94418	−	4.00922i	0.258436	−	0.149208i
$723$	53.6134	−	30.9537i	1.99390	−	1.15118i
$724$	13.2818			0.493616
$725$	25.5458	+	44.2466i	0.948746	+	1.64328i
$726$			9.73535i			0.361313i
$727$	−18.5289			−0.687200			−0.343600	−	0.939116i	$-0.611646\pi$
$727$	−18.5289			−0.687200			−0.343600	+	0.939116i	$0.611646\pi$
$728$		0			0
$729$	−35.6131			−1.31900
$730$			52.4388i			1.94085i
$731$	−0.976600	−	1.69152i	−0.0361209	−	0.0625632i
$732$	39.3938			1.45604
$733$	44.0795	−	25.4493i	1.62811	−	0.939992i	0.643459	−	0.765480i	$-0.277499\pi$
$733$	44.0795	−	25.4493i	1.62811	−	0.939992i	0.984655	−	0.174512i	$-0.0558347\pi$
$734$	−18.2653	+	10.5455i	−0.674185	+	0.389241i
$735$		0			0
$736$		−	7.05268i		−	0.259965i
$737$	−1.29630	+	2.24525i	−0.0477497	+	0.0827049i
$738$	0.278720	+	0.482757i	0.0102598	+	0.0177705i
$739$	7.43889	−	4.29485i	0.273644	−	0.157988i	−0.356898	−	0.934143i	$-0.616166\pi$
$739$	7.43889	−	4.29485i	0.273644	−	0.157988i	0.630542	+	0.776155i	$0.282832\pi$
$740$	13.6267	+	23.6021i	0.500927	+	0.867631i
$741$	−23.2290	+	41.9003i	−0.853337	+	1.53925i
$742$		0			0
$743$	33.0711	+	19.0936i	1.21326	+	0.700477i	0.963468	−	0.267822i	$-0.0863039\pi$
$743$	33.0711	+	19.0936i	1.21326	+	0.700477i	0.249794	+	0.968299i	$0.419637\pi$
$744$	−2.00000			−0.0733236
$745$	12.4058			0.454512
$746$	12.2059	+	7.04708i	0.446890	+	0.258012i
$747$	−8.80044	−	5.08094i	−0.321991	−	0.185902i
$748$	−13.7376	+	7.93141i	−0.502296	+	0.290001i
$749$		0			0
$750$	−9.64138	−	16.6994i	−0.352054	−	0.609775i
$751$	2.84971			0.103987			0.0519937	−	0.998647i	$-0.483442\pi$
$751$	2.84971			0.103987			0.0519937	+	0.998647i	$0.483442\pi$
$752$	1.38704	−	0.800806i	0.0505800	−	0.0292024i
$753$	−2.57381	+	4.45798i	−0.0937950	+	0.162458i
$754$	−13.2443	−	22.0451i	−0.482327	−	0.802834i
$755$	−33.2272			−1.20926
$756$		0			0
$757$	−9.63950	+	16.6961i	−0.350354	+	0.606830i	−0.986311	−	0.164894i	$-0.947272\pi$
$757$	−9.63950	+	16.6961i	−0.350354	+	0.606830i	0.635958	+	0.771724i	$0.280605\pi$
$758$	16.5568	−	28.6773i	0.601371	−	1.04161i
$759$	41.8705	+	24.1740i	1.51980	+	0.877459i
$760$		−	18.1280i		−	0.657570i
$761$	10.0320	+	5.79199i	0.363660	+	0.209959i	0.670685	−	0.741742i	$-0.266000\pi$
$761$	10.0320	+	5.79199i	0.363660	+	0.209959i	−0.307025	+	0.951701i	$0.599334\pi$
$762$		−	28.4402i		−	1.03028i
$763$		0			0
$764$	−5.96230	+	10.3270i	−0.215708	+	0.373618i
$765$			72.9172i			2.63633i
$766$	12.9660	−	22.4578i	0.468482	−	0.811435i
$767$	16.6781	−	30.0839i	0.602212	−	1.08627i
$768$	1.27815	+	2.21381i	0.0461211	+	0.0798841i
$769$	21.1486	+	12.2102i	0.762639	+	0.440310i	0.830242	−	0.557403i	$-0.188202\pi$
$769$	21.1486	+	12.2102i	0.762639	+	0.440310i	−0.0676036	+	0.997712i	$0.521535\pi$
$770$		0			0
$771$	2.73802	+	4.74238i	0.0986072	+	0.170793i
$772$	4.63268	−	2.67468i	0.166734	−	0.0962638i
$773$			6.98615i			0.251275i	0.992076	+	0.125637i	$0.0400975\pi$
$773$			6.98615i			0.251275i	−0.992076	+	0.125637i	$0.959902\pi$
$774$		−	1.16714i		−	0.0419521i
$775$	4.85333	−	2.80207i	0.174337	−	0.100653i
$776$	−1.57973	−	2.73617i	−0.0567089	−	0.0982228i
$777$		0			0
$778$	−26.4698	−	15.2824i	−0.948989	−	0.547899i
$779$	−0.409878	−	0.709929i	−0.0146854	−	0.0254358i
$780$	16.5538	+	27.5538i	0.592721	+	0.986586i
$781$	5.61361	−	9.72306i	0.200871	−	0.347918i
$782$		−	41.7178i		−	1.49182i
$783$	4.87410	−	8.44219i	0.174186	−	0.301699i
$784$		0			0
$785$			72.6612i			2.59339i
$786$	−33.0117	−	19.0593i	−1.17749	−	0.679823i
$787$		−	17.3473i		−	0.618364i	−0.951003	−	0.309182i	$-0.899945\pi$
$787$		−	17.3473i		−	0.618364i	0.951003	−	0.309182i	$-0.100055\pi$
$788$	11.4261	+	6.59688i	0.407039	+	0.235004i
$789$	−13.8840	+	24.0478i	−0.494284	+	0.856126i
$790$	0.511546	−	0.886023i	0.0182000	−	0.0315233i
$791$		0			0
$792$	−9.47889			−0.336818
$793$	47.6288	−	28.6144i	1.69135	−	1.01613i
$794$	−11.2307	+	19.4521i	−0.398563	+	0.690331i
$795$	−30.3118	+	17.5005i	−1.07505	+	0.620679i
$796$	20.0516			0.710709
$797$	20.1670	+	34.9303i	0.714353	+	1.23729i	0.963209	+	0.268754i	$0.0866120\pi$
$797$	20.1670	+	34.9303i	0.714353	+	1.23729i	−0.248856	+	0.968540i	$0.580055\pi$
$798$		0			0
$799$	8.20455	−	4.73690i	0.290256	−	0.167579i
$800$	−6.20327	−	3.58146i	−0.219319	−	0.126624i
$801$	15.9582	+	9.21346i	0.563855	+	0.325542i
$802$	17.0288			0.601307
$803$	−40.3225			−1.42295
$804$	2.14024	+	1.23567i	0.0754804	+	0.0435786i
$805$		0			0
$806$	−2.41809	+	1.45274i	−0.0851735	+	0.0511706i
$807$	−18.9231	−	32.7758i	−0.666126	−	1.15376i
$808$	−3.27921	+	1.89325i	−0.115362	+	0.0666043i
$809$	−1.35525	−	2.34736i	−0.0476481	−	0.0825289i	0.841218	−	0.540697i	$-0.181839\pi$
$809$	−1.35525	−	2.34736i	−0.0476481	−	0.0825289i	−0.888866	+	0.458168i	$0.848506\pi$
$810$	12.3987	−	21.4751i	0.435645	−	0.754559i
$811$		−	29.7449i		−	1.04448i	−0.852797	−	0.522242i	$-0.825096\pi$
$811$		−	29.7449i		−	1.04448i	0.852797	−	0.522242i	$-0.174904\pi$
$812$		0			0
$813$	0.143092	−	0.0826144i	0.00501847	−	0.00289741i
$814$	−18.1487	+	10.4781i	−0.636111	+	0.367259i
$815$	−21.9925			−0.770365
$816$	7.56045	+	13.0951i	0.264669	+	0.458419i
$817$			1.71637i			0.0600481i
$818$	5.13532			0.179552
$819$		0			0
$820$	−0.550013			−0.0192073
$821$		−	17.3317i		−	0.604880i	−0.953168	−	0.302440i	$-0.902199\pi$
$821$		−	17.3317i		−	0.604880i	0.953168	−	0.302440i	$-0.0978011\pi$
$822$	−19.7623	−	34.2294i	−0.689291	−	1.19389i
$823$	−11.4589			−0.399432			−0.199716	−	0.979854i	$-0.564002\pi$
$823$	−11.4589			−0.399432			−0.199716	+	0.979854i	$0.564002\pi$
$824$	−5.89623	+	3.40419i	−0.205405	+	0.118591i
$825$	42.5250	−	24.5518i	1.48053	−	0.854785i
$826$		0			0
$827$			5.41259i			0.188214i	0.995562	+	0.0941070i	$0.0299996\pi$
$827$			5.41259i			0.188214i	−0.995562	+	0.0941070i	$0.970000\pi$
$828$	12.4643	−	21.5888i	0.433165	−	0.750263i
$829$	17.4347	+	30.1978i	0.605533	+	1.04881i	0.991967	+	0.126497i	$0.0403734\pi$
$829$	17.4347	+	30.1978i	0.605533	+	1.04881i	−0.386434	+	0.922317i	$0.626293\pi$
$830$	8.68319	−	5.01324i	0.301398	−	0.174012i
$831$	−5.43359	−	9.41126i	−0.188489	−	0.326473i
$832$	3.15338	+	1.74819i	0.109324	+	0.0606076i
$833$		0			0
$834$	−31.6624	−	18.2803i	−1.09638	−	0.632995i
$835$	23.2574			0.804855
$836$	13.9394			0.482103
$837$	−0.926009	−	0.534632i	−0.0320076	−	0.0184796i
$838$	−27.6120	−	15.9418i	−0.953841	−	0.550700i
$839$	21.4211	−	12.3675i	0.739540	−	0.426973i	−0.0823623	−	0.996602i	$-0.526246\pi$
$839$	21.4211	−	12.3675i	0.739540	−	0.426973i	0.821902	+	0.569629i	$0.192913\pi$
$840$		0			0
$841$	−10.9383	−	18.9457i	−0.377183	−	0.653300i
$842$	14.7648			0.508830
$843$	−24.4526	+	14.1177i	−0.842191	+	0.486239i
$844$	−3.98072	+	6.89481i	−0.137022	+	0.237329i
$845$	40.0286	+	21.2896i	1.37702	+	0.732385i
$846$	5.66111			0.194633
$847$		0			0
$848$	−1.96300	+	3.40002i	−0.0674099	+	0.116757i
$849$	−14.4244	+	24.9838i	−0.495045	+	0.857443i
$850$	−36.6934	−	21.1849i	−1.25857	−	0.726637i
$851$		−	55.1132i		−	1.88925i
$852$	−9.26830	−	5.35106i	−0.317527	−	0.183324i
$853$			6.14219i			0.210304i	0.994456	+	0.105152i	$0.0335330\pi$
$853$			6.14219i			0.210304i	−0.994456	+	0.105152i	$0.966467\pi$
$854$		0			0
$855$	32.0378	−	55.4912i	1.09567	−	1.89776i
$856$			14.3017i			0.488821i
$857$	−16.1036	+	27.8923i	−0.550088	+	0.952781i	0.448179	+	0.893944i	$0.352073\pi$
$857$	−16.1036	+	27.8923i	−0.550088	+	0.952781i	−0.998268	+	0.0588374i	$0.981261\pi$
$858$	−21.1873	+	12.7289i	−0.723324	+	0.434559i
$859$	8.68571	+	15.0441i	0.296352	+	0.513298i	0.975299	−	0.220891i	$-0.0708964\pi$
$859$	8.68571	+	15.0441i	0.296352	+	0.513298i	−0.678946	+	0.734188i	$0.737563\pi$
$860$	0.997308	+	0.575796i	0.0340079	+	0.0196345i
$861$		0			0
$862$	17.5544	+	30.4051i	0.597905	+	1.03560i
$863$	−0.267862	+	0.154650i	−0.00911812	+	0.00526435i	−0.504552	−	0.863381i	$-0.668342\pi$
$863$	−0.267862	+	0.154650i	−0.00911812	+	0.00526435i	0.495434	+	0.868646i	$0.335009\pi$
$864$			1.36668i			0.0464952i
$865$			74.3515i			2.52803i
$866$	−3.44029	+	1.98625i	−0.116906	+	0.0674957i
$867$	22.9928	+	39.8247i	0.780877	+	1.35252i
$868$		0			0
$869$	0.681301	+	0.393350i	0.0231116	+	0.0133435i
$870$	31.7950	+	55.0705i	1.07795	+	1.86707i
$871$	3.48519	−	0.0606287i	0.118091	−	0.00205433i
$872$	−2.28834	+	3.96353i	−0.0774931	+	0.134222i
$873$		−	11.1675i		−	0.377963i
$874$	−18.3296	+	31.7479i	−0.620010	+	1.07389i
$875$		0			0
$876$			38.4366i			1.29865i
$877$	18.8921	+	10.9074i	0.637942	+	0.368316i	0.783822	−	0.620986i	$-0.213268\pi$
$877$	18.8921	+	10.9074i	0.637942	+	0.368316i	−0.145879	+	0.989302i	$0.546601\pi$
$878$			5.75277i			0.194147i
$879$	−57.6569	−	33.2882i	−1.94472	−	1.12278i
$880$	4.67630	−	8.09958i	0.157638	−	0.273037i
$881$	−5.18132	+	8.97430i	−0.174563	+	0.302352i	−0.940010	−	0.341147i	$-0.889185\pi$
$881$	−5.18132	+	8.97430i	−0.174563	+	0.302352i	0.765447	+	0.643499i	$0.222518\pi$
$882$		0			0
$883$	47.4366			1.59637			0.798184	−	0.602414i	$-0.205794\pi$
$883$	47.4366			1.59637			0.798184	+	0.602414i	$0.205794\pi$
$884$	18.6528	+	10.3408i	0.627361	+	0.347800i
$885$	−42.5263	+	73.6577i	−1.42951	+	2.47598i
$886$	23.4523	−	13.5402i	0.787897	−	0.454892i
$887$	20.3479			0.683216			0.341608	−	0.939843i	$-0.389028\pi$
$887$	20.3479			0.683216			0.341608	+	0.939843i	$0.389028\pi$
$888$	9.98808	+	17.2999i	0.335178	+	0.580545i
$889$		0			0
$890$	−15.7456	+	9.09070i	−0.527792	+	0.304721i
$891$	16.5132	+	9.53388i	0.553212	+	0.319397i
$892$	18.6557	+	10.7709i	0.624639	+	0.360635i
$893$	−8.32506			−0.278588
$894$	9.09318			0.304121
$895$	46.6286	+	26.9210i	1.55862	+	0.899871i
$896$		0			0
$897$	−1.13063	−	64.9936i	−0.0377508	−	2.17007i
$898$	−4.12457	−	7.14396i	−0.137639	−	0.238397i
$899$	−4.83291	+	2.79028i	−0.161187	+	0.0930612i
$900$	−12.6591	−	21.9263i	−0.421971	−	0.730876i
$901$	−11.6115	+	20.1117i	−0.386835	+	0.670018i
$902$		−	0.422929i		−	0.0140820i
$903$		0			0
$904$	−2.60930	+	1.50648i	−0.0867842	+	0.0501049i
$905$	−40.1151	+	23.1605i	−1.33347	+	0.769880i
$906$	−24.3548			−0.809135
$907$	−8.50650	−	14.7337i	−0.282454	−	0.489224i	0.689535	−	0.724253i	$-0.257815\pi$
$907$	−8.50650	−	14.7337i	−0.282454	−	0.489224i	−0.971989	+	0.235028i	$0.924482\pi$
$908$		−	3.65771i		−	0.121385i
$909$	−13.3839			−0.443916
$910$		0			0
$911$	12.8289			0.425040			0.212520	−	0.977157i	$-0.431833\pi$
$911$	12.8289			0.425040			0.212520	+	0.977157i	$0.431833\pi$
$912$		−	13.2874i		−	0.439991i
$913$	3.85490	+	6.67688i	0.127579	+	0.220973i
$914$	−38.6967			−1.27997
$915$	−118.981	+	68.6936i	−3.93338	+	2.27094i
$916$	8.44160	−	4.87376i	0.278918	−	0.161034i
$917$		0			0
$918$			8.08411i			0.266815i
$919$	19.2883	−	33.4082i	0.636261	−	1.10204i	−0.349986	−	0.936755i	$-0.613814\pi$
$919$	19.2883	−	33.4082i	0.636261	−	1.10204i	0.986247	−	0.165281i	$-0.0528531\pi$
$920$	12.2982	+	21.3012i	0.405461	+	0.702279i
$921$	−55.4674	+	32.0241i	−1.82771	+	1.05523i
$922$	−6.56742	−	11.3751i	−0.216286	−	0.374619i
$923$	−15.0926	+	0.262553i	−0.496780	+	0.00864203i
$924$		0			0
$925$	−48.4755	−	27.9873i	−1.59386	−	0.920217i
$926$	6.98417			0.229514
$927$	−24.0651			−0.790403
$928$	6.17717	+	3.56639i	0.202776	+	0.117073i
$929$	3.76685	+	2.17479i	0.123586	+	0.0713526i	0.560519	−	0.828142i	$-0.310602\pi$
$929$	3.76685	+	2.17479i	0.123586	+	0.0713526i	−0.436932	+	0.899494i	$0.643935\pi$
$930$	6.04059	−	3.48754i	0.198079	−	0.114361i
$931$		0			0
$932$	−1.36448	−	2.36334i	−0.0446949	−	0.0774138i
$933$	82.9083			2.71430
$934$	−4.87305	+	2.81345i	−0.159451	+	0.0920591i
$935$	27.6611	−	47.9104i	0.904614	−	1.56684i
$936$	6.56315	+	10.9244i	0.214523	+	0.357075i
$937$	−13.5931			−0.444068			−0.222034	−	0.975039i	$-0.571270\pi$
$937$	−13.5931			−0.444068			−0.222034	+	0.975039i	$0.571270\pi$
$938$		0			0
$939$	2.84409	−	4.92611i	0.0928135	−	0.160758i
$940$	−2.79284	+	4.83734i	−0.0910924	+	0.157777i
$941$	21.2738	+	12.2824i	0.693506	+	0.400396i	0.804924	−	0.593377i	$-0.202206\pi$
$941$	21.2738	+	12.2824i	0.693506	+	0.400396i	−0.111418	+	0.993774i	$0.535539\pi$
$942$			53.2591i			1.73528i
$943$	0.963249	+	0.556132i	0.0313677	+	0.0181102i
$944$			9.54021i			0.310508i
$945$		0			0
$946$	−0.442755	+	0.766873i	−0.0143952	+	0.0249332i
$947$			2.09781i			0.0681697i	0.999419	+	0.0340848i	$0.0108516\pi$
$947$			2.09781i			0.0681697i	−0.999419	+	0.0340848i	$0.989148\pi$
$948$	0.374952	−	0.649436i	0.0121779	−	0.0210927i
$949$	27.9192	+	46.4715i	0.906295	+	1.50853i
$950$	18.6162	+	32.2441i	0.603988	+	1.04614i
$951$	−8.49558	−	4.90493i	−0.275488	−	0.159053i
$952$		0			0
$953$	−20.1699	−	34.9353i	−0.653367	−	1.13166i	−0.982301	−	0.187311i	$-0.940023\pi$
$953$	−20.1699	−	34.9353i	−0.653367	−	1.13166i	0.328934	−	0.944353i	$-0.393311\pi$
$954$	−12.0178	+	6.93850i	−0.389092	+	0.224642i
$955$		−	41.5875i		−	1.34574i
$956$			12.2347i			0.395700i
$957$	−42.3461	+	24.4485i	−1.36885	+	0.790309i
$958$	12.5596	+	21.7538i	0.405781	+	0.702833i
$959$		0			0
$960$	−7.72076	−	4.45758i	−0.249186	−	0.143868i
$961$	−15.1939	−	26.3167i	−0.490127	−	0.848925i
$962$	24.6421	+	13.6612i	0.794494	+	0.440456i
$963$	−25.2756	+	43.7786i	−0.814494	+	1.41074i
$964$			24.2176i			0.779998i
$965$	−9.32804	+	16.1566i	−0.300280	+	0.520101i
$966$		0			0
$967$		−	2.90536i		−	0.0934300i	−0.998908	−	0.0467150i	$-0.985125\pi$
$967$		−	2.90536i		−	0.0934300i	0.998908	−	0.0467150i	$-0.0148753\pi$
$968$	−3.29816	−	1.90419i	−0.106007	−	0.0612031i
$969$		−	78.5973i		−	2.52491i
$970$	9.54249	+	5.50936i	0.306391	+	0.176895i
$971$	5.87760	−	10.1803i	0.188621	−	0.326701i	−0.756170	−	0.654376i	$-0.772932\pi$
$971$	5.87760	−	10.1803i	0.188621	−	0.326701i	0.944791	+	0.327674i	$0.106265\pi$
$972$	11.1380	−	19.2916i	0.357251	−	0.618777i
$973$		0			0
$974$	−17.6758			−0.566370
$975$	−57.7401	−	32.0103i	−1.84916	−	1.02515i
$976$	−7.70525	+	13.3459i	−0.246639	+	0.427191i
$977$	−17.3989	+	10.0452i	−0.556639	+	0.321375i	−0.751795	−	0.659397i	$-0.770812\pi$
$977$	−17.3989	+	10.0452i	−0.556639	+	0.321375i	0.195157	+	0.980772i	$0.437478\pi$
$978$	−16.1201			−0.515463
$979$	−6.99023	−	12.1074i	−0.223409	−	0.386955i
$980$		0			0
$981$	−14.0096	+	8.08845i	−0.447292	+	0.258244i
$982$	−27.7084	−	15.9975i	−0.884211	−	0.510500i
$983$	26.6768	+	15.4019i	0.850858	+	0.491243i	0.860940	−	0.508706i	$-0.169876\pi$
$983$	26.6768	+	15.4019i	0.850858	+	0.491243i	−0.0100819	+	0.999949i	$0.503209\pi$
$984$	−0.403148			−0.0128519
$985$	−46.0138			−1.46612
$986$	36.5390	+	21.0958i	1.16364	+	0.671827i
$987$		0			0
$988$	−9.65158	−	16.0651i	−0.307058	−	0.511098i
$989$	−1.16440	−	2.01681i	−0.0370259	−	0.0641307i
$990$	28.6290	−	16.5290i	0.909891	−	0.525326i
$991$	21.3229	+	36.9323i	0.677343	+	1.17319i	0.975778	+	0.218762i	$0.0702019\pi$
$991$	21.3229	+	36.9323i	0.677343	+	1.17319i	−0.298435	+	0.954430i	$0.596465\pi$
$992$	0.391192	−	0.677564i	0.0124203	−	0.0215127i
$993$		−	15.5516i		−	0.493514i
$994$		0			0
$995$	−60.5616	+	34.9653i	−1.91993	+	1.10847i
$996$	6.36460	−	3.67460i	0.201670	−	0.116434i
$997$	−31.5540			−0.999326			−0.499663	−	0.866220i	$-0.666543\pi$
$997$	−31.5540			−0.999326			−0.499663	+	0.866220i	$0.666543\pi$
$998$	−5.82079	−	10.0819i	−0.184254	−	0.319137i
$999$			10.6799i			0.337897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.o.d.459.3		12
7.2	even	3		1274.2.v.e.667.1		12
7.3	odd	6		1274.2.m.c.589.4		12
7.4	even	3		182.2.m.b.43.6	✓	12
7.5	odd	6		1274.2.v.d.667.3		12
7.6	odd	2		1274.2.o.e.459.1		12
13.10	even	6		1274.2.v.e.361.1		12
21.11	odd	6		1638.2.bj.g.1135.1		12
28.11	odd	6		1456.2.cc.d.225.1		12
91.4	even	6		2366.2.d.r.337.7		12
91.10	odd	6		1274.2.m.c.491.4		12
91.23	even	6	inner	1274.2.o.d.569.6		12
91.32	odd	12		2366.2.a.bf.1.1		6
91.46	odd	12		2366.2.a.bh.1.1		6
91.62	odd	6		1274.2.v.d.361.3		12
91.74	even	3		2366.2.d.r.337.1		12
91.75	odd	6		1274.2.o.e.569.4		12
91.88	even	6		182.2.m.b.127.6	yes	12
273.179	odd	6		1638.2.bj.g.127.3		12
364.179	odd	6		1456.2.cc.d.673.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.6	✓	12	7.4	even	3
182.2.m.b.127.6	yes	12	91.88	even	6
1274.2.m.c.491.4		12	91.10	odd	6
1274.2.m.c.589.4		12	7.3	odd	6
1274.2.o.d.459.3		12	1.1	even	1	trivial
1274.2.o.d.569.6		12	91.23	even	6	inner
1274.2.o.e.459.1		12	7.6	odd	2
1274.2.o.e.569.4		12	91.75	odd	6
1274.2.v.d.361.3		12	91.62	odd	6
1274.2.v.d.667.3		12	7.5	odd	6
1274.2.v.e.361.1		12	13.10	even	6
1274.2.v.e.667.1		12	7.2	even	3
1456.2.cc.d.225.1		12	28.11	odd	6
1456.2.cc.d.673.1		12	364.179	odd	6
1638.2.bj.g.127.3		12	273.179	odd	6
1638.2.bj.g.1135.1		12	21.11	odd	6
2366.2.a.bf.1.1		6	91.32	odd	12
2366.2.a.bh.1.1		6	91.46	odd	12
2366.2.d.r.337.1		12	91.74	even	3
2366.2.d.r.337.7		12	91.4	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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.27815 + 2.21381i) q^{3} -1.00000 q^{4} +(3.02030 - 1.74377i) q^{5} +(2.21381 - 1.27815i) q^{6} +1.00000i q^{8} +(-1.76732 + 3.06108i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.27815 + 2.21381i) q^{3} -1.00000 q^{4} +(3.02030 - 1.74377i) q^{5} +(2.21381 - 1.27815i) q^{6} +1.00000i q^{8} +(-1.76732 + 3.06108i) q^{9} +(-1.74377 - 3.02030i) q^{10} +(2.32244 - 1.34086i) q^{11} +(-1.27815 - 2.21381i) q^{12} +(-3.15338 - 1.74819i) q^{13} +(7.72076 + 4.45758i) q^{15} +1.00000 q^{16} +5.91517 q^{17} +(3.06108 + 1.76732i) q^{18} +(-4.50154 - 2.59896i) q^{19} +(-3.02030 + 1.74377i) q^{20} +(-1.34086 - 2.32244i) q^{22} +7.05268 q^{23} +(-2.21381 + 1.27815i) q^{24} +(3.58146 - 6.20327i) q^{25} +(-1.74819 + 3.15338i) q^{26} -1.36668 q^{27} +(-3.56639 + 6.17717i) q^{29} +(4.45758 - 7.72076i) q^{30} +(0.677564 + 0.391192i) q^{31} -1.00000i q^{32} +(5.93683 + 3.42763i) q^{33} -5.91517i q^{34} +(1.76732 - 3.06108i) q^{36} -7.81450i q^{37} +(-2.59896 + 4.50154i) q^{38} +(-0.160313 - 9.21545i) q^{39} +(1.74377 + 3.02030i) q^{40} +(0.136579 + 0.0788541i) q^{41} +(-0.165101 - 0.285963i) q^{43} +(-2.32244 + 1.34086i) q^{44} +12.3272i q^{45} -7.05268i q^{46} +(1.38704 - 0.800806i) q^{47} +(1.27815 + 2.21381i) q^{48} +(-6.20327 - 3.58146i) q^{50} +(7.56045 + 13.0951i) q^{51} +(3.15338 + 1.74819i) q^{52} +(-1.96300 + 3.40002i) q^{53} +1.36668i q^{54} +(4.67630 - 8.09958i) q^{55} -13.2874i q^{57} +(6.17717 + 3.56639i) q^{58} +9.54021i q^{59} +(-7.72076 - 4.45758i) q^{60} +(-7.70525 + 13.3459i) q^{61} +(0.391192 - 0.677564i) q^{62} -1.00000 q^{64} +(-12.5726 + 0.218714i) q^{65} +(3.42763 - 5.93683i) q^{66} +(-0.837243 + 0.483382i) q^{67} -5.91517 q^{68} +(9.01435 + 15.6133i) q^{69} +(3.62568 - 2.09329i) q^{71} +(-3.06108 - 1.76732i) q^{72} +(-13.0216 - 7.51803i) q^{73} -7.81450 q^{74} +18.3105 q^{75} +(4.50154 + 2.59896i) q^{76} +(-9.21545 + 0.160313i) q^{78} +(0.146678 + 0.254054i) q^{79} +(3.02030 - 1.74377i) q^{80} +(3.55514 + 6.15768i) q^{81} +(0.0788541 - 0.136579i) q^{82} +2.87495i q^{83} +(17.8656 - 10.3147i) q^{85} +(-0.285963 + 0.165101i) q^{86} -18.2335 q^{87} +(1.34086 + 2.32244i) q^{88} -5.21325i q^{89} +12.3272 q^{90} -7.05268 q^{92} +2.00000i q^{93} +(-0.800806 - 1.38704i) q^{94} -18.1280 q^{95} +(2.21381 - 1.27815i) q^{96} +(-2.73617 + 1.57973i) q^{97} +9.47889i 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more