LMFDB - Embedded newform 1008.2.t.i.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(193,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("1008.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.t (of order $3$, 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.1
Root			$0.247934 - 0.429435i$ of defining polynomial
Character	$\chi$	$=$	1008.193
Dual form			1008.2.t.i.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59836 + 0.667278i) q^{3} -3.69258 q^{5} +(2.60948 + 0.436591i) q^{7} +(2.10948 - 2.13309i) q^{9} +O(q^{10})$	\(q+(-1.59836 + 0.667278i) q^{3} -3.69258 q^{5} +(2.60948 + 0.436591i) q^{7} +(2.10948 - 2.13309i) q^{9} +0.892568 q^{11} +(0.598355 - 1.03638i) q^{13} +(5.90205 - 2.46398i) q^{15} +(-0.124991 + 0.216492i) q^{17} +(-1.40414 - 2.43204i) q^{19} +(-4.46220 + 1.04342i) q^{21} -2.47772 q^{23} +8.63514 q^{25} +(-1.94833 + 4.81705i) q^{27} +(2.07128 + 3.58755i) q^{29} +(1.79257 + 3.10483i) q^{31} +(-1.42664 + 0.595591i) q^{33} +(-9.63571 - 1.61215i) q^{35} +(-2.36568 - 4.09747i) q^{37} +(-0.264830 + 2.05578i) q^{39} +(-2.39093 + 4.14121i) q^{41} +(4.98928 + 8.64169i) q^{43} +(-7.78942 + 7.87662i) q^{45} +(-5.08653 + 8.81013i) q^{47} +(6.61878 + 2.27855i) q^{49} +(0.0553208 - 0.429435i) q^{51} +(-4.94465 + 8.56438i) q^{53} -3.29588 q^{55} +(3.86715 + 2.95031i) q^{57} +(0.906186 + 1.56956i) q^{59} +(-5.40205 + 9.35663i) q^{61} +(6.43594 - 4.64529i) q^{63} +(-2.20948 + 3.82692i) q^{65} +(0.514685 + 0.891460i) q^{67} +(3.96027 - 1.65332i) q^{69} +4.94533 q^{71} +(-0.915262 + 1.58528i) q^{73} +(-13.8020 + 5.76204i) q^{75} +(2.32914 + 0.389687i) q^{77} +(-0.899562 + 1.55809i) q^{79} +(-0.100184 - 8.99944i) q^{81} +(-6.16156 - 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +(-5.70453 - 4.35207i) q^{87} +(-1.20370 - 2.08488i) q^{89} +(2.01387 - 2.44318i) q^{91} +(-4.93695 - 3.76648i) q^{93} +(5.18489 + 8.98049i) q^{95} +(5.52210 + 9.56456i) q^{97} +(1.88286 - 1.90393i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{3} - 8 q^{5} + q^{7} - 4 q^{9}+O(q^{10}) $ 10 * q - 2 * q^3 - 8 * q^5 + q^7 - 4 * q^9	$ 10 q - 2 q^{3} - 8 q^{5} + q^{7} - 4 q^{9} + 8 q^{11} - 8 q^{13} + 19 q^{15} + 12 q^{17} - q^{19} - 2 q^{21} + 6 q^{23} + 2 q^{25} + 7 q^{27} + 7 q^{29} + 3 q^{31} - q^{33} - 5 q^{35} - 20 q^{39} + 5 q^{41} + 7 q^{43} - q^{45} - 27 q^{47} + 25 q^{49} - 24 q^{51} - 21 q^{53} - 4 q^{55} - 4 q^{57} - 30 q^{59} - 14 q^{61} + 35 q^{63} - 11 q^{65} + 2 q^{67} + 15 q^{69} + 6 q^{71} + 15 q^{73} - 31 q^{75} - 31 q^{77} + 4 q^{79} + 8 q^{81} - 9 q^{83} - 6 q^{85} - 32 q^{87} + 28 q^{89} + 4 q^{91} - 12 q^{93} + 14 q^{95} - 12 q^{97} - 35 q^{99}+O(q^{100}) $ 10 * q - 2 * q^3 - 8 * q^5 + q^7 - 4 * q^9 + 8 * q^11 - 8 * q^13 + 19 * q^15 + 12 * q^17 - q^19 - 2 * q^21 + 6 * q^23 + 2 * q^25 + 7 * q^27 + 7 * q^29 + 3 * q^31 - q^33 - 5 * q^35 - 20 * q^39 + 5 * q^41 + 7 * q^43 - q^45 - 27 * q^47 + 25 * q^49 - 24 * q^51 - 21 * q^53 - 4 * q^55 - 4 * q^57 - 30 * q^59 - 14 * q^61 + 35 * q^63 - 11 * q^65 + 2 * q^67 + 15 * q^69 + 6 * q^71 + 15 * q^73 - 31 * q^75 - 31 * q^77 + 4 * q^79 + 8 * q^81 - 9 * q^83 - 6 * q^85 - 32 * q^87 + 28 * q^89 + 4 * q^91 - 12 * q^93 + 14 * q^95 - 12 * q^97 - 35 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.59836	+	0.667278i	−0.922811	+	0.385253i
$3$	−1.59836	+	0.667278i	−0.922811	+	0.385253i
$4$		0			0
$5$	−3.69258			−1.65137			−0.825686	−	0.564130i	$-0.809212\pi$
$5$	−3.69258			−1.65137			−0.825686	+	0.564130i	$0.809212\pi$
$6$		0			0
$7$	2.60948	+	0.436591i	0.986291	+	0.165016i
$7$	2.60948	+	0.436591i	0.986291	+	0.165016i
$8$		0			0
$9$	2.10948	−	2.13309i	0.703160	−	0.711031i
$10$		0			0
$11$	0.892568			0.269119			0.134560	−	0.990905i	$-0.457038\pi$
$11$	0.892568			0.269119			0.134560	+	0.990905i	$0.457038\pi$
$12$		0			0
$13$	0.598355	−	1.03638i	0.165954	−	0.287441i	−0.771040	−	0.636787i	$-0.780263\pi$
$13$	0.598355	−	1.03638i	0.165954	−	0.287441i	0.936994	+	0.349346i	$0.113596\pi$
$14$		0			0
$15$	5.90205	−	2.46398i	1.52390	−	0.636196i
$16$		0			0
$17$	−0.124991	+	0.216492i	−0.0303149	+	0.0525069i	−0.880785	−	0.473517i	$-0.842984\pi$
$17$	−0.124991	+	0.216492i	−0.0303149	+	0.0525069i	0.850470	+	0.526024i	$0.176318\pi$
$18$		0			0
$19$	−1.40414	−	2.43204i	−0.322131	−	0.557948i	0.658796	−	0.752321i	$-0.271066\pi$
$19$	−1.40414	−	2.43204i	−0.322131	−	0.557948i	−0.980928	+	0.194374i	$0.937733\pi$
$20$		0			0
$21$	−4.46220	+	1.04342i	−0.973733	+	0.227693i
$22$		0			0
$23$	−2.47772			−0.516639			−0.258320	−	0.966059i	$-0.583169\pi$
$23$	−2.47772			−0.516639			−0.258320	+	0.966059i	$0.583169\pi$
$24$		0			0
$25$	8.63514			1.72703
$26$		0			0
$27$	−1.94833	+	4.81705i	−0.374957	+	0.927042i
$28$		0			0
$29$	2.07128	+	3.58755i	0.384626	+	0.666192i	0.991717	−	0.128440i	$-0.0409970\pi$
$29$	2.07128	+	3.58755i	0.384626	+	0.666192i	−0.607091	+	0.794632i	$0.707664\pi$
$30$		0			0
$31$	1.79257	+	3.10483i	0.321956	+	0.557644i	0.980892	−	0.194555i	$-0.0623264\pi$
$31$	1.79257	+	3.10483i	0.321956	+	0.557644i	−0.658936	+	0.752199i	$0.728993\pi$
$32$		0			0
$33$	−1.42664	+	0.595591i	−0.248346	+	0.103679i
$34$		0			0
$35$	−9.63571	−	1.61215i	−1.62873	−	0.272502i
$36$		0			0
$37$	−2.36568	−	4.09747i	−0.388915	−	0.673621i	0.603389	−	0.797447i	$-0.293817\pi$
$37$	−2.36568	−	4.09747i	−0.388915	−	0.673621i	−0.992304	+	0.123826i	$0.960483\pi$
$38$		0			0
$39$	−0.264830	+	2.05578i	−0.0424067	+	0.329188i
$40$		0			0
$41$	−2.39093	+	4.14121i	−0.373400	+	0.646748i	−0.990086	−	0.140461i	$-0.955142\pi$
$41$	−2.39093	+	4.14121i	−0.373400	+	0.646748i	0.616686	+	0.787209i	$0.288475\pi$
$42$		0			0
$43$	4.98928	+	8.64169i	0.760859	+	1.31785i	0.942408	+	0.334464i	$0.108555\pi$
$43$	4.98928	+	8.64169i	0.760859	+	1.31785i	−0.181550	+	0.983382i	$0.558111\pi$
$44$		0			0
$45$	−7.78942	+	7.87662i	−1.16118	+	1.17418i
$46$		0			0
$47$	−5.08653	+	8.81013i	−0.741947	+	1.28509i	0.209661	+	0.977774i	$0.432764\pi$
$47$	−5.08653	+	8.81013i	−0.741947	+	1.28509i	−0.951608	+	0.307316i	$0.900569\pi$
$48$		0			0
$49$	6.61878	+	2.27855i	0.945540	+	0.325507i
$50$		0			0
$51$	0.0553208	−	0.429435i	0.00774646	−	0.0601329i
$52$		0			0
$53$	−4.94465	+	8.56438i	−0.679199	+	1.17641i	0.296023	+	0.955181i	$0.404339\pi$
$53$	−4.94465	+	8.56438i	−0.679199	+	1.17641i	−0.975222	+	0.221227i	$0.928994\pi$
$54$		0			0
$55$	−3.29588			−0.444416
$56$		0			0
$57$	3.86715	+	2.95031i	0.512217	+	0.390778i
$58$		0			0
$59$	0.906186	+	1.56956i	0.117975	+	0.204339i	0.918965	−	0.394339i	$-0.129026\pi$
$59$	0.906186	+	1.56956i	0.117975	+	0.204339i	−0.800990	+	0.598678i	$0.795693\pi$
$60$		0			0
$61$	−5.40205	+	9.35663i	−0.691662	+	1.19799i	0.279631	+	0.960108i	$0.409788\pi$
$61$	−5.40205	+	9.35663i	−0.691662	+	1.19799i	−0.971293	+	0.237886i	$0.923545\pi$
$62$		0			0
$63$	6.43594	−	4.64529i	0.810852	−	0.585251i
$64$		0			0
$65$	−2.20948	+	3.82692i	−0.274052	+	0.474671i
$66$		0			0
$67$	0.514685	+	0.891460i	0.0628787	+	0.108909i	0.895751	−	0.444556i	$-0.146639\pi$
$67$	0.514685	+	0.891460i	0.0628787	+	0.108909i	−0.832872	+	0.553465i	$0.813305\pi$
$68$		0			0
$69$	3.96027	−	1.65332i	0.476761	−	0.199037i
$70$		0			0
$71$	4.94533			0.586903			0.293451	−	0.955974i	$-0.405196\pi$
$71$	4.94533			0.586903			0.293451	+	0.955974i	$0.405196\pi$
$72$		0			0
$73$	−0.915262	+	1.58528i	−0.107123	+	0.185543i	−0.914604	−	0.404351i	$-0.867497\pi$
$73$	−0.915262	+	1.58528i	−0.107123	+	0.185543i	0.807480	+	0.589894i	$0.200831\pi$
$74$		0			0
$75$	−13.8020	+	5.76204i	−1.59372	+	0.665343i
$76$		0			0
$77$	2.32914	+	0.389687i	0.265430	+	0.0444090i
$78$		0			0
$79$	−0.899562	+	1.55809i	−0.101209	+	0.175298i	−0.912183	−	0.409783i	$-0.865604\pi$
$79$	−0.899562	+	1.55809i	−0.101209	+	0.175298i	0.810974	+	0.585082i	$0.198938\pi$
$80$		0			0
$81$	−0.100184	−	8.99944i	−0.0111316	−	0.999938i
$82$		0			0
$83$	−6.16156	−	10.6721i	−0.676319	−	1.17142i	−0.976082	−	0.217405i	$-0.930241\pi$
$83$	−6.16156	−	10.6721i	−0.676319	−	1.17142i	0.299763	−	0.954014i	$-0.403092\pi$
$84$		0			0
$85$	0.461541	−	0.799412i	0.0500611	−	0.0867084i
$86$		0			0
$87$	−5.70453	−	4.35207i	−0.611590	−	0.466591i
$88$		0			0
$89$	−1.20370	−	2.08488i	−0.127592	−	0.220997i	0.795151	−	0.606412i	$-0.207392\pi$
$89$	−1.20370	−	2.08488i	−0.127592	−	0.220997i	−0.922743	+	0.385415i	$0.874058\pi$
$90$		0			0
$91$	2.01387	−	2.44318i	0.211111	−	0.256115i
$92$		0			0
$93$	−4.93695	−	3.76648i	−0.511938	−	0.390565i
$94$		0			0
$95$	5.18489	+	8.98049i	0.531958	+	0.921379i
$96$		0			0
$97$	5.52210	+	9.56456i	0.560684	+	0.971134i	0.997437	+	0.0715522i	$0.0227952\pi$
$97$	5.52210	+	9.56456i	0.560684	+	0.971134i	−0.436752	+	0.899582i	$0.643871\pi$
$98$		0			0
$99$	1.88286	−	1.90393i	0.189234	−	0.191352i
$100$		0			0
$101$	−2.59964			−0.258674			−0.129337	−	0.991601i	$-0.541285\pi$
$101$	−2.59964			−0.258674			−0.129337	+	0.991601i	$0.541285\pi$
$102$		0			0
$103$	−9.71155			−0.956908			−0.478454	−	0.878113i	$-0.658803\pi$
$103$	−9.71155			−0.956908			−0.478454	+	0.878113i	$0.658803\pi$
$104$		0			0
$105$	16.4770	−	3.85292i	1.60799	−	0.376006i
$106$		0			0
$107$	5.45025	+	9.44012i	0.526896	+	0.912610i	0.999509	+	0.0313403i	$0.00997757\pi$
$107$	5.45025	+	9.44012i	0.526896	+	0.912610i	−0.472613	+	0.881270i	$0.656689\pi$
$108$		0			0
$109$	−1.06096	+	1.83764i	−0.101622	+	0.176014i	−0.912353	−	0.409404i	$-0.865737\pi$
$109$	−1.06096	+	1.83764i	−0.101622	+	0.176014i	0.810731	+	0.585419i	$0.199070\pi$
$110$		0			0
$111$	6.51535	+	4.97066i	0.618410	+	0.471794i
$112$		0			0
$113$	7.91318	−	13.7060i	0.744409	−	1.28935i	−0.206061	−	0.978539i	$-0.566065\pi$
$113$	7.91318	−	13.7060i	0.744409	−	1.28935i	0.950470	−	0.310816i	$-0.100602\pi$
$114$		0			0
$115$	9.14916			0.853164
$116$		0			0
$117$	−0.948482	−	3.46258i	−0.0876872	−	0.320115i
$118$		0			0
$119$	−0.420681	+	0.510360i	−0.0385638	+	0.0467847i
$120$		0			0
$121$	−10.2033			−0.927575
$122$		0			0
$123$	1.05822	−	8.21454i	0.0954162	−	0.740680i
$124$		0			0
$125$	−13.4230			−1.20059
$126$		0			0
$127$	1.26946			0.112647			0.0563233	−	0.998413i	$-0.482062\pi$
$127$	1.26946			0.112647			0.0563233	+	0.998413i	$0.482062\pi$
$128$		0			0
$129$	−13.7411	−	10.4833i	−1.20983	−	0.923000i
$130$		0			0
$131$	15.0289			1.31308			0.656540	−	0.754291i	$-0.272019\pi$
$131$	15.0289			1.31308			0.656540	+	0.754291i	$0.272019\pi$
$132$		0			0
$133$	−2.60226	−	6.95939i	−0.225645	−	0.603455i
$134$		0			0
$135$	7.19437	−	17.7873i	0.619193	−	1.53089i
$136$		0			0
$137$	−0.488493			−0.0417347			−0.0208674	−	0.999782i	$-0.506643\pi$
$137$	−0.488493			−0.0417347			−0.0208674	+	0.999782i	$0.506643\pi$
$138$		0			0
$139$	4.93487	−	8.54745i	0.418570	−	0.724985i	−0.577226	−	0.816585i	$-0.695865\pi$
$139$	4.93487	−	8.54745i	0.418570	−	0.724985i	0.995796	+	0.0915997i	$0.0291980\pi$
$140$		0			0
$141$	2.25128	−	17.4759i	0.189592	−	1.47173i
$142$		0			0
$143$	0.534073	−	0.925042i	0.0446614	−	0.0773559i
$144$		0			0
$145$	−7.64835	−	13.2473i	−0.635161	−	1.10013i
$146$		0			0
$147$	−12.0996	+	0.774629i	−0.997957	+	0.0638903i
$148$		0			0
$149$	21.0240			1.72235			0.861175	−	0.508309i	$-0.169729\pi$
$149$	21.0240			1.72235			0.861175	+	0.508309i	$0.169729\pi$
$150$		0			0
$151$	−1.49838			−0.121937			−0.0609683	−	0.998140i	$-0.519419\pi$
$151$	−1.49838			−0.121937			−0.0609683	+	0.998140i	$0.519419\pi$
$152$		0			0
$153$	0.198130	+	0.723303i	0.0160179	+	0.0584756i
$154$		0			0
$155$	−6.61922	−	11.4648i	−0.531669	−	0.920877i
$156$		0			0
$157$	8.33982	+	14.4450i	0.665590	+	1.15284i	0.979125	+	0.203259i	$0.0651534\pi$
$157$	8.33982	+	14.4450i	0.665590	+	1.15284i	−0.313535	+	0.949577i	$0.601513\pi$
$158$		0			0
$159$	2.18848	−	16.9884i	0.173558	−	1.34727i
$160$		0			0
$161$	−6.46555	−	1.08175i	−0.509557	−	0.0852537i
$162$		0			0
$163$	3.34135	+	5.78738i	0.261714	+	0.453303i	0.966698	−	0.255921i	$-0.0823788\pi$
$163$	3.34135	+	5.78738i	0.261714	+	0.453303i	−0.704983	+	0.709224i	$0.749046\pi$
$164$		0			0
$165$	5.26799	−	2.19927i	0.410112	−	0.171213i
$166$		0			0
$167$	−8.81549	+	15.2689i	−0.682163	+	1.18154i	0.292156	+	0.956371i	$0.405627\pi$
$167$	−8.81549	+	15.2689i	−0.682163	+	1.18154i	−0.974319	+	0.225170i	$0.927706\pi$
$168$		0			0
$169$	5.78394	+	10.0181i	0.444919	+	0.770622i
$170$		0			0
$171$	−8.14976	−	2.13518i	−0.623228	−	0.163281i
$172$		0			0
$173$	1.94342	−	3.36611i	0.147756	−	0.255920i	−0.782642	−	0.622472i	$-0.786128\pi$
$173$	1.94342	−	3.36611i	0.147756	−	0.255920i	0.930398	+	0.366552i	$0.119462\pi$
$174$		0			0
$175$	22.5332	+	3.77002i	1.70335	+	0.284987i
$176$		0			0
$177$	−2.49574	−	1.90404i	−0.187591	−	0.143116i
$178$		0			0
$179$	−3.66758	+	6.35244i	−0.274128	+	0.474804i	−0.969915	−	0.243445i	$-0.921723\pi$
$179$	−3.66758	+	6.35244i	−0.274128	+	0.474804i	0.695787	+	0.718248i	$0.255056\pi$
$180$		0			0
$181$	11.2566			0.836693			0.418346	−	0.908288i	$-0.362610\pi$
$181$	11.2566			0.836693			0.418346	+	0.908288i	$0.362610\pi$
$182$		0			0
$183$	2.39093	−	18.5599i	0.176743	−	1.37199i
$184$		0			0
$185$	8.73545	+	15.1302i	0.642243	+	1.11240i
$186$		0			0
$187$	−0.111563	+	0.193234i	−0.00815833	+	0.0141306i
$188$		0			0
$189$	−7.18722	+	11.7194i	−0.522793	+	0.852460i
$190$		0			0
$191$	−11.9230	+	20.6512i	−0.862715	+	1.49427i	0.00658302	+	0.999978i	$0.497905\pi$
$191$	−11.9230	+	20.6512i	−0.862715	+	1.49427i	−0.869298	+	0.494288i	$0.835429\pi$
$192$		0			0
$193$	−2.96728	−	5.13948i	−0.213589	−	0.369948i	0.739246	−	0.673436i	$-0.235182\pi$
$193$	−2.96728	−	5.13948i	−0.213589	−	0.369948i	−0.952835	+	0.303488i	$0.901849\pi$
$194$		0			0
$195$	0.977905	−	7.59112i	0.0700293	−	0.543611i
$196$		0			0
$197$	−15.4682			−1.10206			−0.551032	−	0.834484i	$-0.685766\pi$
$197$	−15.4682			−1.10206			−0.551032	+	0.834484i	$0.685766\pi$
$198$		0			0
$199$	−7.74818	+	13.4202i	−0.549254	+	0.951336i	0.449072	+	0.893496i	$0.351755\pi$
$199$	−7.74818	+	13.4202i	−0.549254	+	0.951336i	−0.998326	+	0.0578402i	$0.981579\pi$
$200$		0			0
$201$	−1.41750	−	1.08143i	−0.0999828	−	0.0762784i
$202$		0			0
$203$	3.83866	+	10.2660i	0.269421	+	0.720529i
$204$		0			0
$205$	8.82870	−	15.2917i	0.616623	−	1.06802i
$206$		0			0
$207$	−5.22669	+	5.28520i	−0.363280	+	0.367347i
$208$		0			0
$209$	−1.25329	−	2.17076i	−0.0866918	−	0.150155i
$210$		0			0
$211$	−0.771898	+	1.33697i	−0.0531397	+	0.0920406i	−0.891372	−	0.453273i	$-0.850256\pi$
$211$	−0.771898	+	1.33697i	−0.0531397	+	0.0920406i	0.838232	+	0.545314i	$0.183590\pi$
$212$		0			0
$213$	−7.90440	+	3.29991i	−0.541600	+	0.226106i
$214$		0			0
$215$	−18.4233	−	31.9101i	−1.25646	−	2.17625i
$216$		0			0
$217$	3.32215	+	8.88461i	0.225522	+	0.603127i
$218$		0			0
$219$	0.405092	−	3.14458i	0.0273736	−	0.212491i
$220$		0			0
$221$	0.149579	+	0.259078i	0.0100617	+	0.0174275i
$222$		0			0
$223$	2.72171	+	4.71414i	0.182259	+	0.315682i	0.942649	−	0.333784i	$-0.108326\pi$
$223$	2.72171	+	4.71414i	0.182259	+	0.315682i	−0.760390	+	0.649466i	$0.774992\pi$
$224$		0			0
$225$	18.2157	−	18.4196i	1.21438	−	1.22797i
$226$		0			0
$227$	16.0764			1.06703			0.533513	−	0.845792i	$-0.320872\pi$
$227$	16.0764			1.06703			0.533513	+	0.845792i	$0.320872\pi$
$228$		0			0
$229$	−9.96840			−0.658730			−0.329365	−	0.944203i	$-0.606835\pi$
$229$	−9.96840			−0.658730			−0.329365	+	0.944203i	$0.606835\pi$
$230$		0			0
$231$	−3.98282	+	0.931325i	−0.262050	+	0.0612767i
$232$		0			0
$233$	8.27045	+	14.3248i	0.541815	+	0.938451i	0.998800	+	0.0489765i	$0.0155959\pi$
$233$	8.27045	+	14.3248i	0.541815	+	0.938451i	−0.456985	+	0.889474i	$0.651071\pi$
$234$		0			0
$235$	18.7824	−	32.5321i	1.22523	−	2.12216i
$236$		0			0
$237$	0.398143	−	3.09063i	0.0258621	−	0.200758i
$238$		0			0
$239$	11.0119	−	19.0732i	0.712303	−	1.23375i	−0.251687	−	0.967809i	$-0.580985\pi$
$239$	11.0119	−	19.0732i	0.712303	−	1.23375i	0.963990	−	0.265937i	$-0.0856813\pi$
$240$		0			0
$241$	16.7201			1.07703			0.538517	−	0.842615i	$-0.318985\pi$
$241$	16.7201			1.07703			0.538517	+	0.842615i	$0.318985\pi$
$242$		0			0
$243$	6.16526	+	14.3175i	0.395502	+	0.918465i
$244$		0			0
$245$	−24.4404	−	8.41373i	−1.56144	−	0.537533i
$246$		0			0
$247$	−3.36069			−0.213836
$248$		0			0
$249$	16.9696	+	12.9464i	1.07541	+	0.820444i
$250$		0			0
$251$	8.53099			0.538471			0.269236	−	0.963074i	$-0.413229\pi$
$251$	8.53099			0.538471			0.269236	+	0.963074i	$0.413229\pi$
$252$		0			0
$253$	−2.21153			−0.139038
$254$		0			0
$255$	−0.204276	+	1.58572i	−0.0127923	+	0.0993017i
$256$		0			0
$257$	−17.1197			−1.06790			−0.533950	−	0.845516i	$-0.679293\pi$
$257$	−17.1197			−1.06790			−0.533950	+	0.845516i	$0.679293\pi$
$258$		0			0
$259$	−4.38427	−	11.7251i	−0.272425	−	0.728563i
$260$		0			0
$261$	12.0219	+	3.14965i	0.744137	+	0.194958i
$262$		0			0
$263$	−20.5527			−1.26733			−0.633666	−	0.773607i	$-0.718451\pi$
$263$	−20.5527			−1.26733			−0.633666	+	0.773607i	$0.718451\pi$
$264$		0			0
$265$	18.2585	−	31.6246i	1.12161	−	1.94269i
$266$		0			0
$267$	3.31514	+	2.52917i	0.202883	+	0.154783i
$268$		0			0
$269$	9.92267	−	17.1866i	0.604996	−	1.04788i	−0.387057	−	0.922056i	$-0.626508\pi$
$269$	9.92267	−	17.1866i	0.604996	−	1.04788i	0.992052	−	0.125827i	$-0.0401585\pi$
$270$		0			0
$271$	−5.32056	−	9.21548i	−0.323201	−	0.559801i	0.657946	−	0.753065i	$-0.271426\pi$
$271$	−5.32056	−	9.21548i	−0.323201	−	0.559801i	−0.981147	+	0.193265i	$0.938092\pi$
$272$		0			0
$273$	−1.58860	+	5.24889i	−0.0961466	+	0.317677i
$274$		0			0
$275$	7.70745			0.464777
$276$		0			0
$277$	−24.8813			−1.49497			−0.747487	−	0.664276i	$-0.768740\pi$
$277$	−24.8813			−1.49497			−0.747487	+	0.664276i	$0.768740\pi$
$278$		0			0
$279$	10.4043	+	2.72585i	0.622889	+	0.163192i
$280$		0			0
$281$	−6.83733	−	11.8426i	−0.407881	−	0.706470i	0.586771	−	0.809753i	$-0.300399\pi$
$281$	−6.83733	−	11.8426i	−0.407881	−	0.706470i	−0.994652	+	0.103282i	$0.967065\pi$
$282$		0			0
$283$	3.16089	+	5.47483i	0.187896	+	0.325445i	0.944548	−	0.328372i	$-0.106500\pi$
$283$	3.16089	+	5.47483i	0.187896	+	0.325445i	−0.756653	+	0.653817i	$0.773167\pi$
$284$		0			0
$285$	−14.2798	−	10.8943i	−0.845861	−	0.645320i
$286$		0			0
$287$	−8.04710	+	9.76255i	−0.475005	+	0.576265i
$288$		0			0
$289$	8.46875	+	14.6683i	0.498162	+	0.862842i
$290$		0			0
$291$	−15.2085	−	11.6028i	−0.891538	−	0.680168i
$292$		0			0
$293$	−1.31508	+	2.27778i	−0.0768277	+	0.133069i	−0.901880	−	0.431987i	$-0.857812\pi$
$293$	−1.31508	+	2.27778i	−0.0768277	+	0.133069i	0.825052	+	0.565057i	$0.191146\pi$
$294$		0			0
$295$	−3.34616	−	5.79573i	−0.194821	−	0.337440i
$296$		0			0
$297$	−1.73902	+	4.29955i	−0.100908	+	0.249485i
$298$		0			0
$299$	−1.48255	+	2.56786i	−0.0857384	+	0.148503i
$300$		0			0
$301$	9.24656	+	24.7286i	0.532963	+	1.42533i
$302$		0			0
$303$	4.15515	−	1.73468i	0.238707	−	0.0996550i
$304$		0			0
$305$	19.9475	−	34.5501i	1.14219	−	1.97833i
$306$		0			0
$307$	2.79496			0.159517			0.0797583	−	0.996814i	$-0.474585\pi$
$307$	2.79496			0.159517			0.0797583	+	0.996814i	$0.474585\pi$
$308$		0			0
$309$	15.5225	−	6.48030i	0.883045	−	0.368652i
$310$		0			0
$311$	−7.55013	−	13.0772i	−0.428129	−	0.741541i	0.568578	−	0.822629i	$-0.307494\pi$
$311$	−7.55013	−	13.0772i	−0.428129	−	0.741541i	−0.996707	+	0.0810885i	$0.974160\pi$
$312$		0			0
$313$	12.7392	−	22.0650i	0.720064	−	1.24719i	−0.240910	−	0.970548i	$-0.577446\pi$
$313$	12.7392	−	22.0650i	0.720064	−	1.24719i	0.960974	−	0.276640i	$-0.0892209\pi$
$314$		0			0
$315$	−23.7652	+	17.1531i	−1.33902	+	0.966467i
$316$		0			0
$317$	−16.2605	+	28.1639i	−0.913278	+	1.58184i	−0.103875	+	0.994590i	$0.533124\pi$
$317$	−16.2605	+	28.1639i	−0.913278	+	1.58184i	−0.809403	+	0.587253i	$0.800209\pi$
$318$		0			0
$319$	1.84875	+	3.20214i	0.103510	+	0.179285i
$320$		0			0
$321$	−15.0106	−	11.4518i	−0.837811	−	0.639179i
$322$		0			0
$323$	0.702021			0.0390615
$324$		0			0
$325$	5.16688	−	8.94931i	0.286607	−	0.496418i
$326$		0			0
$327$	0.469578	−	3.64516i	0.0259677	−	0.201578i
$328$		0			0
$329$	−17.1196	+	20.7691i	−0.943836	+	1.14504i
$330$		0			0
$331$	9.04741	−	15.6706i	0.497291	−	0.861333i	−0.502704	−	0.864458i	$-0.667662\pi$
$331$	9.04741	−	15.6706i	0.497291	−	0.861333i	0.999995	+	0.00312545i	$0.000994863\pi$
$332$		0			0
$333$	−13.7307	−	3.59733i	−0.752435	−	0.197132i
$334$		0			0
$335$	−1.90051	−	3.29179i	−0.103836	−	0.179850i
$336$		0			0
$337$	−12.5086	+	21.6656i	−0.681389	+	1.18020i	0.293168	+	0.956061i	$0.405290\pi$
$337$	−12.5086	+	21.6656i	−0.681389	+	1.18020i	−0.974557	+	0.224139i	$0.928043\pi$
$338$		0			0
$339$	−3.50234	+	27.1874i	−0.190221	+	1.47662i
$340$		0			0
$341$	1.59999	+	2.77127i	0.0866446	+	0.150073i
$342$		0			0
$343$	16.2768	+	8.83553i	0.878863	+	0.477074i
$344$		0			0
$345$	−14.6236	+	6.10503i	−0.787309	+	0.328684i
$346$		0			0
$347$	5.37444	+	9.30881i	0.288515	+	0.499723i	0.973456	−	0.228876i	$-0.0735051\pi$
$347$	5.37444	+	9.30881i	0.288515	+	0.499723i	−0.684940	+	0.728599i	$0.740172\pi$
$348$		0			0
$349$	−1.64301	−	2.84577i	−0.0879482	−	0.152331i	0.818695	−	0.574228i	$-0.194698\pi$
$349$	−1.64301	−	2.84577i	−0.0879482	−	0.152331i	−0.906644	+	0.421897i	$0.861364\pi$
$350$		0			0
$351$	3.82651	+	4.90153i	0.204244	+	0.261624i
$352$		0			0
$353$	16.8192			0.895195			0.447598	−	0.894235i	$-0.352280\pi$
$353$	16.8192			0.895195			0.447598	+	0.894235i	$0.352280\pi$
$354$		0			0
$355$	−18.2610			−0.969195
$356$		0			0
$357$	0.331846	−	1.09645i	0.0175631	−	0.0580302i
$358$		0			0
$359$	−11.8921	−	20.5978i	−0.627642	−	1.08711i	−0.988024	−	0.154303i	$-0.950687\pi$
$359$	−11.8921	−	20.5978i	−0.627642	−	1.08711i	0.360382	−	0.932805i	$-0.382646\pi$
$360$		0			0
$361$	5.55680	−	9.62466i	0.292463	−	0.506561i
$362$		0			0
$363$	16.3085	−	6.80845i	0.855976	−	0.357351i
$364$		0			0
$365$	3.37968	−	5.85377i	0.176900	−	0.306401i
$366$		0			0
$367$	0.689984			0.0360169			0.0180084	−	0.999838i	$-0.494267\pi$
$367$	0.689984			0.0360169			0.0180084	+	0.999838i	$0.494267\pi$
$368$		0			0
$369$	3.78998	+	13.8359i	0.197298	+	0.720267i
$370$		0			0
$371$	−16.6421	+	20.1898i	−0.864014	+	1.04820i
$372$		0			0
$373$	−3.76012			−0.194691			−0.0973457	−	0.995251i	$-0.531035\pi$
$373$	−3.76012			−0.194691			−0.0973457	+	0.995251i	$0.531035\pi$
$374$		0			0
$375$	21.4548	−	8.95690i	1.10792	−	0.462532i
$376$		0			0
$377$	4.95744			0.255321
$378$		0			0
$379$	−32.8735			−1.68860			−0.844300	−	0.535872i	$-0.819983\pi$
$379$	−32.8735			−1.68860			−0.844300	+	0.535872i	$0.819983\pi$
$380$		0			0
$381$	−2.02905	+	0.847085i	−0.103952	+	0.0433975i
$382$		0			0
$383$	1.07267			0.0548109			0.0274055	−	0.999624i	$-0.491275\pi$
$383$	1.07267			0.0548109			0.0274055	+	0.999624i	$0.491275\pi$
$384$		0			0
$385$	−8.60053	−	1.43895i	−0.438324	−	0.0733357i
$386$		0			0
$387$	28.9583	+	7.58687i	1.47204	+	0.385662i
$388$		0			0
$389$	−23.7436			−1.20385			−0.601925	−	0.798553i	$-0.705599\pi$
$389$	−23.7436			−1.20385			−0.601925	+	0.798553i	$0.705599\pi$
$390$		0			0
$391$	0.309693	−	0.536405i	0.0156619	−	0.0271271i
$392$		0			0
$393$	−24.0215	+	10.0284i	−1.21172	+	0.505868i
$394$		0			0
$395$	3.32170	−	5.75336i	0.167133	−	0.289483i
$396$		0			0
$397$	−0.0160489	−	0.0277975i	−0.000805471	−	0.00139512i	0.865622	−	0.500697i	$-0.166923\pi$
$397$	−0.0160489	−	0.0277975i	−0.000805471	−	0.00139512i	−0.866428	+	0.499302i	$0.833590\pi$
$398$		0			0
$399$	8.80319	+	9.38714i	0.440711	+	0.469945i
$400$		0			0
$401$	24.5256			1.22475			0.612374	−	0.790568i	$-0.290215\pi$
$401$	24.5256			1.22475			0.612374	+	0.790568i	$0.290215\pi$
$402$		0			0
$403$	4.29039			0.213719
$404$		0			0
$405$	0.369938	+	33.2312i	0.0183824	+	1.65127i
$406$		0			0
$407$	−2.11153	−	3.65728i	−0.104665	−	0.181284i
$408$		0			0
$409$	−13.3948	−	23.2006i	−0.662333	−	1.14719i	−0.980001	−	0.198992i	$-0.936233\pi$
$409$	−13.3948	−	23.2006i	−0.662333	−	1.14719i	0.317669	−	0.948202i	$-0.397100\pi$
$410$		0			0
$411$	0.780785	−	0.325960i	0.0385133	−	0.0160784i
$412$		0			0
$413$	1.67942	+	4.49137i	0.0826388	+	0.221006i
$414$		0			0
$415$	22.7520	+	39.4077i	1.11685	+	1.93445i
$416$		0			0
$417$	−2.18416	+	16.9548i	−0.106959	+	0.830280i
$418$		0			0
$419$	10.5262	−	18.2320i	0.514240	−	0.890689i	−0.485624	−	0.874168i	$-0.661407\pi$
$419$	10.5262	−	18.2320i	0.514240	−	0.890689i	0.999864	−	0.0165215i	$-0.00525920\pi$
$420$		0			0
$421$	−7.44533	−	12.8957i	−0.362863	−	0.628498i	0.625568	−	0.780170i	$-0.284867\pi$
$421$	−7.44533	−	12.8957i	−0.362863	−	0.628498i	−0.988431	+	0.151672i	$0.951534\pi$
$422$		0			0
$423$	8.06290	+	29.4349i	0.392032	+	1.43117i
$424$		0			0
$425$	−1.07932	+	1.86944i	−0.0523547	+	0.0906809i
$426$		0			0
$427$	−18.1816	+	22.0575i	−0.879868	+	1.06744i
$428$		0			0
$429$	−0.236379	+	1.83492i	−0.0114125	+	0.0885908i
$430$		0			0
$431$	7.95192	−	13.7731i	0.383031	−	0.663428i	−0.608463	−	0.793582i	$-0.708214\pi$
$431$	7.95192	−	13.7731i	0.383031	−	0.663428i	0.991494	+	0.130154i	$0.0415471\pi$
$432$		0			0
$433$	−16.3658			−0.786490			−0.393245	−	0.919434i	$-0.628648\pi$
$433$	−16.3658			−0.786490			−0.393245	+	0.919434i	$0.628648\pi$
$434$		0			0
$435$	21.0644	+	16.0704i	1.00996	+	0.770515i
$436$		0			0
$437$	3.47905	+	6.02590i	0.166426	+	0.288258i
$438$		0			0
$439$	−7.77236	+	13.4621i	−0.370954	+	0.642512i	−0.989713	−	0.143070i	$-0.954303\pi$
$439$	−7.77236	+	13.4621i	−0.370954	+	0.642512i	0.618758	+	0.785582i	$0.287636\pi$
$440$		0			0
$441$	18.8225	−	9.31192i	0.896312	−	0.443425i
$442$		0			0
$443$	0.895027	−	1.55023i	0.0425240	−	0.0736537i	−0.843980	−	0.536375i	$-0.819793\pi$
$443$	0.895027	−	1.55023i	0.0425240	−	0.0736537i	0.886504	+	0.462721i	$0.153127\pi$
$444$		0			0
$445$	4.44477	+	7.69857i	0.210702	+	0.364947i
$446$		0			0
$447$	−33.6038	+	14.0288i	−1.58940	+	0.663540i
$448$		0			0
$449$	13.5666			0.640250			0.320125	−	0.947375i	$-0.396275\pi$
$449$	13.5666			0.640250			0.320125	+	0.947375i	$0.396275\pi$
$450$		0			0
$451$	−2.13407	+	3.69631i	−0.100489	+	0.174053i
$452$		0			0
$453$	2.39495	−	0.999837i	0.112524	−	0.0469764i
$454$		0			0
$455$	−7.43638	+	9.02164i	−0.348623	+	0.422941i
$456$		0			0
$457$	−1.28459	+	2.22497i	−0.0600905	+	0.104080i	−0.894506	−	0.447057i	$-0.852472\pi$
$457$	−1.28459	+	2.22497i	−0.0600905	+	0.104080i	0.834415	+	0.551136i	$0.185806\pi$
$458$		0			0
$459$	−0.799326	−	1.02389i	−0.0373094	−	0.0477910i
$460$		0			0
$461$	18.0934	+	31.3388i	0.842695	+	1.45959i	0.887608	+	0.460600i	$0.152366\pi$
$461$	18.0934	+	31.3388i	0.842695	+	1.45959i	−0.0449122	+	0.998991i	$0.514301\pi$
$462$		0			0
$463$	−8.19224	+	14.1894i	−0.380726	+	0.659436i	−0.991166	−	0.132626i	$-0.957659\pi$
$463$	−8.19224	+	14.1894i	−0.380726	+	0.659436i	0.610440	+	0.792062i	$0.290992\pi$
$464$		0			0
$465$	18.2301	+	13.9080i	0.845400	+	0.644968i
$466$		0			0
$467$	4.35022	+	7.53480i	0.201304	+	0.348669i	0.948949	−	0.315430i	$-0.102149\pi$
$467$	4.35022	+	7.53480i	0.201304	+	0.348669i	−0.747645	+	0.664099i	$0.768815\pi$
$468$		0			0
$469$	0.953856	+	2.55095i	0.0440450	+	0.117792i
$470$		0			0
$471$	−22.9688	−	17.5233i	−1.05835	−	0.807429i
$472$		0			0
$473$	4.45328	+	7.71330i	0.204762	+	0.354658i
$474$		0			0
$475$	−12.1249	−	21.0010i	−0.556330	−	0.963591i
$476$		0			0
$477$	7.83799	+	28.6138i	0.358877	+	1.31014i
$478$		0			0
$479$	17.7674			0.811813			0.405907	−	0.913915i	$-0.366956\pi$
$479$	17.7674			0.811813			0.405907	+	0.913915i	$0.366956\pi$
$480$		0			0
$481$	−5.66207			−0.258168
$482$		0			0
$483$	11.0561	−	2.58530i	0.503069	−	0.117635i
$484$		0			0
$485$	−20.3908	−	35.3179i	−0.925898	−	1.60370i
$486$		0			0
$487$	−8.32763	+	14.4239i	−0.377361	+	0.653608i	−0.990677	−	0.136229i	$-0.956502\pi$
$487$	−8.32763	+	14.4239i	−0.377361	+	0.653608i	0.613316	+	0.789837i	$0.289835\pi$
$488$		0			0
$489$	−9.20245	−	7.02068i	−0.416149	−	0.317486i
$490$		0			0
$491$	3.21021	−	5.56025i	0.144875	−	0.250930i	−0.784451	−	0.620190i	$-0.787055\pi$
$491$	3.21021	−	5.56025i	0.144875	−	0.250930i	0.929326	+	0.369260i	$0.120389\pi$
$492$		0			0
$493$	−1.03557			−0.0466396
$494$		0			0
$495$	−6.95259	+	7.03042i	−0.312496	+	0.315994i
$496$		0			0
$497$	12.9047	+	2.15909i	0.578857	+	0.0968483i
$498$		0			0
$499$	−11.1459			−0.498960			−0.249480	−	0.968380i	$-0.580260\pi$
$499$	−11.1459			−0.498960			−0.249480	+	0.968380i	$0.580260\pi$
$500$		0			0
$501$	3.90170	−	30.2875i	0.174315	−	1.35314i
$502$		0			0
$503$	17.7223			0.790200			0.395100	−	0.918638i	$-0.370710\pi$
$503$	17.7223			0.790200			0.395100	+	0.918638i	$0.370710\pi$
$504$		0			0
$505$	9.59939			0.427167
$506$		0			0
$507$	−15.9296	−	12.1530i	−0.707460	−	0.539732i
$508$		0			0
$509$	31.0823			1.37770			0.688848	−	0.724906i	$-0.258117\pi$
$509$	31.0823			1.37770			0.688848	+	0.724906i	$0.258117\pi$
$510$		0			0
$511$	−3.08048	+	3.73716i	−0.136272	+	0.165322i
$512$		0			0
$513$	14.4510	−	2.02539i	0.638026	−	0.0894230i
$514$		0			0
$515$	35.8607			1.58021
$516$		0			0
$517$	−4.54008	+	7.86365i	−0.199672	+	0.345843i
$518$		0			0
$519$	−0.860152	+	6.67704i	−0.0377565	+	0.293089i
$520$		0			0
$521$	−2.37986	+	4.12203i	−0.104263	+	0.180590i	−0.913437	−	0.406980i	$-0.866582\pi$
$521$	−2.37986	+	4.12203i	−0.104263	+	0.180590i	0.809174	+	0.587570i	$0.199915\pi$
$522$		0			0
$523$	−20.1258	−	34.8588i	−0.880038	−	1.52427i	−0.851298	−	0.524683i	$-0.824184\pi$
$523$	−20.1258	−	34.8588i	−0.880038	−	1.52427i	−0.0287402	−	0.999587i	$-0.509150\pi$
$524$		0			0
$525$	−38.5318	+	9.01009i	−1.68166	+	0.393233i
$526$		0			0
$527$	−0.896226			−0.0390402
$528$		0			0
$529$	−16.8609			−0.733084
$530$		0			0
$531$	5.25960	+	1.37798i	0.228247	+	0.0597991i
$532$		0			0
$533$	2.86125	+	4.95583i	0.123935	+	0.214661i
$534$		0			0
$535$	−20.1255	−	34.8584i	−0.870101	−	1.50706i
$536$		0			0
$537$	1.62326	−	12.6008i	0.0700488	−	0.543763i
$538$		0			0
$539$	5.90771	+	2.03376i	0.254463	+	0.0876003i
$540$		0			0
$541$	12.0547	+	20.8794i	0.518273	+	0.897675i	0.999775	+	0.0212301i	$0.00675826\pi$
$541$	12.0547	+	20.8794i	0.518273	+	0.897675i	−0.481502	+	0.876445i	$0.659908\pi$
$542$		0			0
$543$	−17.9920	+	7.51125i	−0.772109	+	0.322339i
$544$		0			0
$545$	3.91769	−	6.78564i	0.167815	−	0.290665i
$546$		0			0
$547$	6.17751	+	10.6998i	0.264131	+	0.457489i	0.967336	−	0.253499i	$-0.0815814\pi$
$547$	6.17751	+	10.6998i	0.264131	+	0.457489i	−0.703204	+	0.710988i	$0.748248\pi$
$548$		0			0
$549$	8.56305	+	31.2607i	0.365462	+	1.33418i
$550$		0			0
$551$	5.81671	−	10.0748i	0.247800	−	0.429203i
$552$		0			0
$553$	−3.02763	+	3.67306i	−0.128748	+	0.156194i
$554$		0			0
$555$	−24.0584	−	18.3545i	−1.02122	−	0.779107i
$556$		0			0
$557$	4.03845	−	6.99479i	0.171114	−	0.296379i	−0.767695	−	0.640815i	$-0.778597\pi$
$557$	4.03845	−	6.99479i	0.171114	−	0.296379i	0.938810	+	0.344436i	$0.111930\pi$
$558$		0			0
$559$	11.9415			0.505070
$560$		0			0
$561$	0.0493776	−	0.383300i	0.00208472	−	0.0161829i
$562$		0			0
$563$	22.6064	+	39.1554i	0.952744	+	1.65020i	0.739448	+	0.673214i	$0.235087\pi$
$563$	22.6064	+	39.1554i	0.952744	+	1.65020i	0.213296	+	0.976988i	$0.431580\pi$
$564$		0			0
$565$	−29.2200	+	50.6106i	−1.22930	+	2.12920i
$566$		0			0
$567$	3.66765	−	23.5276i	0.154027	−	0.988067i
$568$		0			0
$569$	−11.2149	+	19.4248i	−0.470155	+	0.814332i	−0.999418	−	0.0341263i	$-0.989135\pi$
$569$	−11.2149	+	19.4248i	−0.470155	+	0.814332i	0.529263	+	0.848458i	$0.322468\pi$
$570$		0			0
$571$	−10.9134	−	18.9026i	−0.456713	−	0.791050i	0.542072	−	0.840332i	$-0.317640\pi$
$571$	−10.9134	−	18.9026i	−0.456713	−	0.791050i	−0.998785	+	0.0492820i	$0.984307\pi$
$572$		0			0
$573$	5.27706	−	40.9638i	0.220452	−	1.71129i
$574$		0			0
$575$	−21.3954			−0.892251
$576$		0			0
$577$	−16.1022	+	27.8898i	−0.670342	+	1.16107i	0.307465	+	0.951559i	$0.400519\pi$
$577$	−16.1022	+	27.8898i	−0.670342	+	1.16107i	−0.977807	+	0.209508i	$0.932814\pi$
$578$		0			0
$579$	8.17222	+	6.23471i	0.339626	+	0.259106i
$580$		0			0
$581$	−11.4191	−	30.5388i	−0.473744	−	1.26696i
$582$		0			0
$583$	−4.41343	+	7.64429i	−0.182786	+	0.316594i
$584$		0			0
$585$	3.50234	+	12.7858i	0.144804	+	0.528629i
$586$		0			0
$587$	9.72304	+	16.8408i	0.401313	+	0.695094i	0.993885	−	0.110424i	$-0.0352208\pi$
$587$	9.72304	+	16.8408i	0.401313	+	0.695094i	−0.592572	+	0.805518i	$0.701887\pi$
$588$		0			0
$589$	5.03404	−	8.71921i	0.207424	−	0.359269i
$590$		0			0
$591$	24.7237	−	10.3216i	1.01700	−	0.424574i
$592$		0			0
$593$	−14.4202	−	24.9766i	−0.592168	−	1.02566i	−0.993940	−	0.109925i	$-0.964939\pi$
$593$	−14.4202	−	24.9766i	−0.592168	−	1.02566i	0.401772	−	0.915740i	$-0.368394\pi$
$594$		0			0
$595$	1.55340	−	1.88455i	0.0636831	−	0.0772589i
$596$		0			0
$597$	3.42932	−	26.6205i	0.140353	−	1.08950i
$598$		0			0
$599$	−23.4994	−	40.7022i	−0.960161	−	1.66305i	−0.722089	−	0.691800i	$-0.756818\pi$
$599$	−23.4994	−	40.7022i	−0.960161	−	1.66305i	−0.238072	−	0.971247i	$-0.576516\pi$
$600$		0			0
$601$	−7.80843	−	13.5246i	−0.318512	−	0.551680i	0.661665	−	0.749799i	$-0.269850\pi$
$601$	−7.80843	−	13.5246i	−0.318512	−	0.551680i	−0.980178	+	0.198119i	$0.936517\pi$
$602$		0			0
$603$	2.98729	+	0.782646i	0.121652	+	0.0318718i
$604$		0			0
$605$	37.6766			1.53177
$606$		0			0
$607$	28.6532			1.16300			0.581500	−	0.813547i	$-0.302466\pi$
$607$	28.6532			1.16300			0.581500	+	0.813547i	$0.302466\pi$
$608$		0			0
$609$	−12.9858	−	13.8472i	−0.526211	−	0.561116i
$610$		0			0
$611$	6.08711	+	10.5432i	0.246258	+	0.426531i
$612$		0			0
$613$	14.6734	−	25.4151i	0.592653	−	1.02651i	−0.401220	−	0.915982i	$-0.631414\pi$
$613$	14.6734	−	25.4151i	0.592653	−	1.02651i	0.993873	−	0.110524i	$-0.0352529\pi$
$614$		0			0
$615$	−3.90755	+	30.3328i	−0.157568	+	1.22314i
$616$		0			0
$617$	2.06401	−	3.57497i	0.0830938	−	0.143923i	−0.821484	−	0.570232i	$-0.806853\pi$
$617$	2.06401	−	3.57497i	0.0830938	−	0.143923i	0.904577	+	0.426310i	$0.140187\pi$
$618$		0			0
$619$	−22.7130			−0.912912			−0.456456	−	0.889746i	$-0.650881\pi$
$619$	−22.7130			−0.912912			−0.456456	+	0.889746i	$0.650881\pi$
$620$		0			0
$621$	4.82742	−	11.9353i	0.193718	−	0.478947i
$622$		0			0
$623$	−2.23080	−	5.96597i	−0.0893753	−	0.239022i
$624$		0			0
$625$	6.38996			0.255598
$626$		0			0
$627$	3.45170	+	2.63335i	0.137848	+	0.105166i
$628$		0			0
$629$	1.18276			0.0471597
$630$		0			0
$631$	38.6411			1.53828			0.769138	−	0.639082i	$-0.220686\pi$
$631$	38.6411			1.53828			0.769138	+	0.639082i	$0.220686\pi$
$632$		0			0
$633$	0.341639	−	2.65202i	0.0135789	−	0.105408i
$634$		0			0
$635$	−4.68759			−0.186021
$636$		0			0
$637$	6.32183	−	5.49620i	0.250480	−	0.217767i
$638$		0			0
$639$	10.4321	−	10.5489i	0.412687	−	0.417306i
$640$		0			0
$641$	−28.4726			−1.12460			−0.562301	−	0.826933i	$-0.690084\pi$
$641$	−28.4726			−1.12460			−0.562301	+	0.826933i	$0.690084\pi$
$642$		0			0
$643$	8.52125	−	14.7592i	0.336045	−	0.582048i	−0.647640	−	0.761947i	$-0.724244\pi$
$643$	8.52125	−	14.7592i	0.336045	−	0.582048i	0.983685	+	0.179899i	$0.0575771\pi$
$644$		0			0
$645$	50.7400	+	38.7103i	1.99788	+	1.52422i
$646$		0			0
$647$	−1.68809	+	2.92386i	−0.0663657	+	0.114949i	−0.897299	−	0.441423i	$-0.854474\pi$
$647$	−1.68809	+	2.92386i	−0.0663657	+	0.114949i	0.830933	+	0.556372i	$0.187807\pi$
$648$		0			0
$649$	0.808833	+	1.40094i	0.0317495	+	0.0549917i
$650$		0			0
$651$	−11.2385	−	11.9840i	−0.440471	−	0.469689i
$652$		0			0
$653$	−18.3451			−0.717899			−0.358950	−	0.933357i	$-0.616865\pi$
$653$	−18.3451			−0.717899			−0.358950	+	0.933357i	$0.616865\pi$
$654$		0			0
$655$	−55.4954			−2.16838
$656$		0			0
$657$	1.45083	+	5.29646i	0.0566021	+	0.206635i
$658$		0			0
$659$	13.9248	+	24.1184i	0.542432	+	0.939519i	0.998764	+	0.0497098i	$0.0158297\pi$
$659$	13.9248	+	24.1184i	0.542432	+	0.939519i	−0.456332	+	0.889810i	$0.650837\pi$
$660$		0			0
$661$	−19.5071	−	33.7872i	−0.758737	−	1.31417i	−0.943495	−	0.331387i	$-0.892484\pi$
$661$	−19.5071	−	33.7872i	−0.758737	−	1.31417i	0.184758	−	0.982784i	$-0.440850\pi$
$662$		0			0
$663$	−0.411957	−	0.314288i	−0.0159991	−	0.0122059i
$664$		0			0
$665$	9.60906	+	25.6981i	0.372624	+	0.996529i
$666$		0			0
$667$	−5.13203	−	8.88894i	−0.198713	−	0.344181i
$668$		0			0
$669$	−7.49590	−	5.71873i	−0.289808	−	0.221099i
$670$		0			0
$671$	−4.82170	+	8.35143i	−0.186140	+	0.322404i
$672$		0			0
$673$	24.6154	+	42.6352i	0.948856	+	1.64347i	0.747841	+	0.663878i	$0.231090\pi$
$673$	24.6154	+	42.6352i	0.948856	+	1.64347i	0.201014	+	0.979588i	$0.435576\pi$
$674$		0			0
$675$	−16.8241	+	41.5959i	−0.647561	+	1.60103i
$676$		0			0
$677$	11.6958	−	20.2577i	0.449505	−	0.778565i	−0.548849	−	0.835922i	$-0.684934\pi$
$677$	11.6958	−	20.2577i	0.449505	−	0.778565i	0.998354	+	0.0573564i	$0.0182671\pi$
$678$		0			0
$679$	10.2340	+	27.3694i	0.392745	+	1.05034i
$680$		0			0
$681$	−25.6958	+	10.7274i	−0.984663	+	0.411075i
$682$		0			0
$683$	15.1632	−	26.2634i	0.580204	−	1.00494i	−0.415251	−	0.909707i	$-0.636306\pi$
$683$	15.1632	−	26.2634i	0.580204	−	1.00494i	0.995455	−	0.0952356i	$-0.0303604\pi$
$684$		0			0
$685$	1.80380			0.0689196
$686$		0			0
$687$	15.9330	−	6.65169i	0.607884	−	0.253778i
$688$		0			0
$689$	5.91731	+	10.2491i	0.225432	+	0.390459i
$690$		0			0
$691$	−2.05665	+	3.56223i	−0.0782387	+	0.135513i	−0.902490	−	0.430711i	$-0.858263\pi$
$691$	−2.05665	+	3.56223i	−0.0782387	+	0.135513i	0.824251	+	0.566224i	$0.191596\pi$
$692$		0			0
$693$	5.74451	−	4.14624i	0.218216	−	0.157503i
$694$		0			0
$695$	−18.2224	+	31.5621i	−0.691215	+	1.19722i
$696$		0			0
$697$	−0.597691	−	1.03523i	−0.0226392	−	0.0392122i
$698$		0			0
$699$	−22.7778	−	17.3775i	−0.861534	−	0.657277i
$700$		0			0
$701$	29.1835			1.10225			0.551123	−	0.834424i	$-0.314200\pi$
$701$	29.1835			1.10225			0.551123	+	0.834424i	$0.314200\pi$
$702$		0			0
$703$	−6.64347	+	11.5068i	−0.250563	+	0.433988i
$704$		0			0
$705$	−8.31303	+	64.5310i	−0.313087	+	2.43038i
$706$		0			0
$707$	−6.78372	−	1.13498i	−0.255128	−	0.0426853i
$708$		0			0
$709$	21.2309	−	36.7729i	0.797342	−	1.38104i	−0.123999	−	0.992282i	$-0.539572\pi$
$709$	21.2309	−	36.7729i	0.797342	−	1.38104i	0.921341	−	0.388755i	$-0.127095\pi$
$710$		0			0
$711$	1.42594	+	5.20560i	0.0534768	+	0.195225i
$712$		0			0
$713$	−4.44149	−	7.69288i	−0.166335	−	0.288101i
$714$		0			0
$715$	−1.97211	+	3.41579i	−0.0737526	+	0.127743i
$716$		0			0
$717$	−4.87385	+	37.8339i	−0.182017	+	1.41293i
$718$		0			0
$719$	5.57126	+	9.64970i	0.207773	+	0.359873i	0.951013	−	0.309152i	$-0.100045\pi$
$719$	5.57126	+	9.64970i	0.207773	+	0.359873i	−0.743240	+	0.669025i	$0.766712\pi$
$720$		0			0
$721$	−25.3421	−	4.23997i	−0.943789	−	0.157905i
$722$		0			0
$723$	−26.7246	+	11.1569i	−0.993899	+	0.414931i
$724$		0			0
$725$	17.8858	+	30.9790i	0.664260	+	1.15053i
$726$		0			0
$727$	14.3410	+	24.8393i	0.531878	+	0.921239i	0.999308	+	0.0372089i	$0.0118467\pi$
$727$	14.3410	+	24.8393i	0.531878	+	0.921239i	−0.467430	+	0.884030i	$0.654820\pi$
$728$		0			0
$729$	−19.4080	−	18.7704i	−0.718815	−	0.695202i
$730$		0			0
$731$	−2.49447			−0.0922614
$732$		0			0
$733$	−25.0528			−0.925348			−0.462674	−	0.886529i	$-0.653110\pi$
$733$	−25.0528			−0.925348			−0.462674	+	0.886529i	$0.653110\pi$
$734$		0			0
$735$	44.6787	−	2.86038i	1.64800	−	0.105507i
$736$		0			0
$737$	0.459391	+	0.795689i	0.0169219	+	0.0293096i
$738$		0			0
$739$	−13.7608	+	23.8344i	−0.506198	+	0.876761i	0.493776	+	0.869589i	$0.335616\pi$
$739$	−13.7608	+	23.8344i	−0.506198	+	0.876761i	−0.999974	+	0.00717223i	$0.997717\pi$
$740$		0			0
$741$	5.37158	−	2.24252i	0.197330	−	0.0823809i
$742$		0			0
$743$	7.00608	−	12.1349i	0.257028	−	0.445186i	−0.708416	−	0.705795i	$-0.750590\pi$
$743$	7.00608	−	12.1349i	0.257028	−	0.445186i	0.965444	+	0.260609i	$0.0839233\pi$
$744$		0			0
$745$	−77.6326			−2.84424
$746$		0			0
$747$	−35.7623	−	9.36947i	−1.30848	−	0.342811i
$748$		0			0
$749$	10.1009	+	27.0133i	0.369077	+	0.987046i
$750$		0			0
$751$	52.2594			1.90697			0.953486	−	0.301436i	$-0.0974660\pi$
$751$	52.2594			1.90697			0.953486	+	0.301436i	$0.0974660\pi$
$752$		0			0
$753$	−13.6356	+	5.69254i	−0.496907	+	0.207448i
$754$		0			0
$755$	5.53289			0.201363
$756$		0			0
$757$	−43.3447			−1.57539			−0.787694	−	0.616066i	$-0.788725\pi$
$757$	−43.3447			−1.57539			−0.787694	+	0.616066i	$0.788725\pi$
$758$		0			0
$759$	3.53481	−	1.47571i	0.128306	−	0.0535647i
$760$		0			0
$761$	−17.2510			−0.625348			−0.312674	−	0.949860i	$-0.601225\pi$
$761$	−17.2510			−0.625348			−0.312674	+	0.949860i	$0.601225\pi$
$762$		0			0
$763$	−3.57086	+	4.33209i	−0.129274	+	0.156832i
$764$		0			0
$765$	−0.731610	−	2.67085i	−0.0264514	−	0.0965650i
$766$		0			0
$767$	2.16889			0.0783139
$768$		0			0
$769$	−10.6727	+	18.4856i	−0.384867	+	0.666609i	−0.991751	−	0.128182i	$-0.959086\pi$
$769$	−10.6727	+	18.4856i	−0.384867	+	0.666609i	0.606884	+	0.794790i	$0.292419\pi$
$770$		0			0
$771$	27.3634	−	11.4236i	0.985469	−	0.411411i
$772$		0			0
$773$	−6.57357	+	11.3858i	−0.236435	+	0.409517i	−0.959689	−	0.281065i	$-0.909312\pi$
$773$	−6.57357	+	11.3858i	−0.236435	+	0.409517i	0.723254	+	0.690582i	$0.242646\pi$
$774$		0			0
$775$	15.4791	+	26.8106i	0.556027	+	0.963066i
$776$		0			0
$777$	14.8315	+	15.8154i	0.532078	+	0.567373i
$778$		0			0
$779$	13.4288			0.481136
$780$		0			0
$781$	4.41405			0.157947
$782$		0			0
$783$	−21.3170	+	2.98769i	−0.761807	+	0.106771i
$784$		0			0
$785$	−30.7954	−	53.3393i	−1.09914	−	1.90376i
$786$		0			0
$787$	−14.0650	−	24.3614i	−0.501364	−	0.868389i	−0.999999	−	0.00157623i	$-0.999498\pi$
$787$	−14.0650	−	24.3614i	−0.501364	−	0.868389i	0.498634	−	0.866812i	$-0.333835\pi$
$788$		0			0
$789$	32.8505	−	13.7143i	1.16951	−	0.488243i
$790$		0			0
$791$	26.6332	−	32.3108i	0.946968	−	1.14884i
$792$		0			0
$793$	6.46470	+	11.1972i	0.229568	+	0.397624i
$794$		0			0
$795$	−8.08114	+	62.7309i	−0.286609	+	2.22484i
$796$		0			0
$797$	12.8683	−	22.2885i	0.455817	−	0.789499i	−0.542917	−	0.839786i	$-0.682680\pi$
$797$	12.8683	−	22.2885i	0.455817	−	0.789499i	0.998735	+	0.0502873i	$0.0160137\pi$
$798$		0			0
$799$	−1.27155	−	2.20238i	−0.0449841	−	0.0779147i
$800$		0			0
$801$	−6.98643	−	1.83039i	−0.246853	−	0.0646737i
$802$		0			0
$803$	−0.816934	+	1.41497i	−0.0288290	+	0.0499333i
$804$		0			0
$805$	23.8746	+	3.99444i	0.841468	+	0.140786i
$806$		0			0
$807$	−4.39173	+	34.0914i	−0.154596	+	1.20007i
$808$		0			0
$809$	15.9353	−	27.6007i	0.560254	−	0.970388i	−0.437220	−	0.899355i	$-0.644037\pi$
$809$	15.9353	−	27.6007i	0.560254	−	0.970388i	0.997474	−	0.0710338i	$-0.0226298\pi$
$810$		0			0
$811$	−43.3860			−1.52349			−0.761744	−	0.647878i	$-0.775657\pi$
$811$	−43.3860			−1.52349			−0.761744	+	0.647878i	$0.775657\pi$
$812$		0			0
$813$	14.6534	+	11.1793i	0.513918	+	0.392076i
$814$		0			0
$815$	−12.3382	−	21.3704i	−0.432188	−	0.748571i
$816$		0			0
$817$	14.0113	−	24.2682i	0.490193	−	0.849039i
$818$		0			0
$819$	−0.963315	−	9.44962i	−0.0336610	−	0.330197i
$820$		0			0
$821$	8.19677	−	14.1972i	0.286069	−	0.495487i	−0.686799	−	0.726848i	$-0.740985\pi$
$821$	8.19677	−	14.1972i	0.286069	−	0.495487i	0.972868	+	0.231361i	$0.0743179\pi$
$822$		0			0
$823$	−13.1890	−	22.8440i	−0.459739	−	0.796292i	0.539208	−	0.842173i	$-0.318724\pi$
$823$	−13.1890	−	22.8440i	−0.459739	−	0.796292i	−0.998947	+	0.0458812i	$0.985390\pi$
$824$		0			0
$825$	−12.3193	+	5.14301i	−0.428901	+	0.179057i
$826$		0			0
$827$	−36.7225			−1.27697			−0.638484	−	0.769635i	$-0.720438\pi$
$827$	−36.7225			−1.27697			−0.638484	+	0.769635i	$0.720438\pi$
$828$		0			0
$829$	12.1579	−	21.0581i	0.422261	−	0.731377i	−0.573899	−	0.818926i	$-0.694570\pi$
$829$	12.1579	−	21.0581i	0.422261	−	0.731377i	0.996160	+	0.0875485i	$0.0279033\pi$
$830$		0			0
$831$	39.7692	−	16.6028i	1.37958	−	0.575944i
$832$		0			0
$833$	−1.32058	+	1.14811i	−0.0457553	+	0.0397797i
$834$		0			0
$835$	32.5519	−	56.3815i	1.12650	−	1.95116i
$836$		0			0
$837$	−18.4487	+	2.58568i	−0.637679	+	0.0893743i
$838$		0			0
$839$	12.8405	+	22.2404i	0.443303	+	0.767824i	0.997932	−	0.0642741i	$-0.0204732\pi$
$839$	12.8405	+	22.2404i	0.443303	+	0.767824i	−0.554629	+	0.832098i	$0.687140\pi$
$840$		0			0
$841$	5.91963	−	10.2531i	0.204125	−	0.353555i
$842$		0			0
$843$	18.8308	+	14.3663i	0.648567	+	0.494801i
$844$		0			0
$845$	−21.3577	−	36.9926i	−0.734726	−	1.27258i
$846$		0			0
$847$	−26.6254	−	4.45468i	−0.914859	−	0.153065i
$848$		0			0
$849$	−8.70546	−	6.64153i	−0.298771	−	0.227937i
$850$		0			0
$851$	5.86148	+	10.1524i	0.200929	+	0.348019i
$852$		0			0
$853$	14.4872	+	25.0925i	0.496031	+	0.859150i	0.999990	−	0.00457743i	$-0.00145705\pi$
$853$	14.4872	+	25.0925i	0.496031	+	0.859150i	−0.503959	+	0.863728i	$0.668124\pi$
$854$		0			0
$855$	30.0937	+	7.88431i	1.02918	+	0.269638i
$856$		0			0
$857$	−25.3868			−0.867197			−0.433598	−	0.901106i	$-0.642756\pi$
$857$	−25.3868			−0.867197			−0.433598	+	0.901106i	$0.642756\pi$
$858$		0			0
$859$	5.95783			0.203279			0.101639	−	0.994821i	$-0.467591\pi$
$859$	5.95783			0.203279			0.101639	+	0.994821i	$0.467591\pi$
$860$		0			0
$861$	6.34779	−	20.9737i	0.216332	−	0.714781i
$862$		0			0
$863$	−8.19545	−	14.1949i	−0.278977	−	0.483201i	0.692154	−	0.721750i	$-0.256662\pi$
$863$	−8.19545	−	14.1949i	−0.278977	−	0.483201i	−0.971131	+	0.238548i	$0.923328\pi$
$864$		0			0
$865$	−7.17624	+	12.4296i	−0.244000	+	0.422620i
$866$		0			0
$867$	−23.3239	−	17.7942i	−0.792122	−	0.604322i
$868$		0			0
$869$	−0.802920	+	1.39070i	−0.0272372	+	0.0471762i
$870$		0			0
$871$	1.23186			0.0417399
$872$		0			0
$873$	32.0509	+	8.39709i	1.08476	+	0.284198i
$874$		0			0
$875$	−35.0272	−	5.86038i	−1.18413	−	0.198117i
$876$		0			0
$877$	35.2539			1.19044			0.595220	−	0.803563i	$-0.297065\pi$
$877$	35.2539			1.19044			0.595220	+	0.803563i	$0.297065\pi$
$878$		0			0
$879$	0.582049	−	4.51823i	0.0196320	−	0.152396i
$880$		0			0
$881$	26.2582			0.884661			0.442331	−	0.896852i	$-0.354152\pi$
$881$	26.2582			0.884661			0.442331	+	0.896852i	$0.354152\pi$
$882$		0			0
$883$	−10.0087			−0.336821			−0.168410	−	0.985717i	$-0.553863\pi$
$883$	−10.0087			−0.336821			−0.168410	+	0.985717i	$0.553863\pi$
$884$		0			0
$885$	9.21572	+	7.03081i	0.309783	+	0.236338i
$886$		0			0
$887$	15.9056			0.534059			0.267030	−	0.963688i	$-0.413958\pi$
$887$	15.9056			0.534059			0.267030	+	0.963688i	$0.413958\pi$
$888$		0			0
$889$	3.31264	+	0.554236i	0.111102	+	0.0185885i
$890$		0			0
$891$	−0.0894212	−	8.03262i	−0.00299572	−	0.269103i
$892$		0			0
$893$	28.5688			0.956017
$894$		0			0
$895$	13.5428	−	23.4569i	0.452687	−	0.784077i
$896$		0			0
$897$	0.656173	−	5.09363i	0.0219090	−	0.170071i
$898$		0			0
$899$	−7.42583	+	12.8619i	−0.247665	+	0.428969i
$900$		0			0
$901$	−1.23608	−	2.14095i	−0.0411797	−	0.0713253i
$902$		0			0
$903$	−31.2801	−	33.3551i	−1.04094	−	1.10999i
$904$		0			0
$905$	−41.5657			−1.38169
$906$		0			0
$907$	17.0925			0.567547			0.283773	−	0.958891i	$-0.408414\pi$
$907$	17.0925			0.567547			0.283773	+	0.958891i	$0.408414\pi$
$908$		0			0
$909$	−5.48390	+	5.54528i	−0.181889	+	0.183925i
$910$		0			0
$911$	−14.9435	−	25.8829i	−0.495099	−	0.857537i	0.504885	−	0.863187i	$-0.331535\pi$
$911$	−14.9435	−	25.8829i	−0.495099	−	0.857537i	−0.999984	+	0.00564955i	$0.998202\pi$
$912$		0			0
$913$	−5.49961	−	9.52561i	−0.182011	−	0.315252i
$914$		0			0
$915$	−8.82870	+	68.5339i	−0.291868	+	2.26566i
$916$		0			0
$917$	39.2176	+	6.56148i	1.29508	+	0.216679i
$918$		0			0
$919$	−11.8283	−	20.4873i	−0.390181	−	0.675813i	0.602292	−	0.798276i	$-0.294254\pi$
$919$	−11.8283	−	20.4873i	−0.390181	−	0.675813i	−0.992473	+	0.122462i	$0.960921\pi$
$920$		0			0
$921$	−4.46734	+	1.86501i	−0.147204	+	0.0614543i
$922$		0			0
$923$	2.95907	−	5.12525i	0.0973989	−	0.168700i
$924$		0			0
$925$	−20.4280	−	35.3823i	−0.671667	−	1.16336i
$926$		0			0
$927$	−20.4863	+	20.7157i	−0.672859	+	0.680391i
$928$		0			0
$929$	−6.30880	+	10.9272i	−0.206985	+	0.358509i	−0.950763	−	0.309918i	$-0.899698\pi$
$929$	−6.30880	+	10.9272i	−0.206985	+	0.358509i	0.743778	+	0.668426i	$0.233032\pi$
$930$		0			0
$931$	−3.75215	−	19.2965i	−0.122972	−	0.632417i
$932$		0			0
$933$	20.7939	+	15.8640i	0.680763	+	0.519364i
$934$		0			0
$935$	0.411957	−	0.713530i	0.0134724	−	0.0233349i
$936$		0			0
$937$	−26.3440			−0.860622			−0.430311	−	0.902681i	$-0.641596\pi$
$937$	−26.3440			−0.860622			−0.430311	+	0.902681i	$0.641596\pi$
$938$		0			0
$939$	−5.63834	+	43.7683i	−0.184000	+	1.42833i
$940$		0			0
$941$	−25.4699	−	44.1151i	−0.830294	−	1.43811i	−0.897805	−	0.440392i	$-0.854839\pi$
$941$	−25.4699	−	44.1151i	−0.830294	−	1.43811i	0.0675118	−	0.997718i	$-0.478494\pi$
$942$		0			0
$943$	5.92404	−	10.2607i	0.192913	−	0.334136i
$944$		0			0
$945$	26.5394	−	43.2747i	0.863326	−	1.40773i
$946$		0			0
$947$	13.8399	−	23.9714i	0.449737	−	0.778967i	−0.548632	−	0.836064i	$-0.684851\pi$
$947$	13.8399	−	23.9714i	0.449737	−	0.778967i	0.998369	+	0.0570968i	$0.0181844\pi$
$948$		0			0
$949$	1.09530	+	1.89712i	0.0355551	+	0.0615832i
$950$		0			0
$951$	7.19682	−	55.8662i	0.233373	−	1.81159i
$952$		0			0
$953$	−27.4017			−0.887628			−0.443814	−	0.896119i	$-0.646375\pi$
$953$	−27.4017			−0.887628			−0.443814	+	0.896119i	$0.646375\pi$
$954$		0			0
$955$	44.0265	−	76.2561i	1.42466	−	2.46759i
$956$		0			0
$957$	−5.09168	−	3.88452i	−0.164591	−	0.125569i
$958$		0			0
$959$	−1.27471	−	0.213271i	−0.0411626	−	0.00688689i
$960$		0			0
$961$	9.07336	−	15.7155i	0.292689	−	0.506952i
$962$		0			0
$963$	31.6339	+	8.28783i	1.01939	+	0.267072i
$964$		0			0
$965$	10.9569	+	18.9779i	0.352715	+	0.610921i
$966$		0			0
$967$	−9.09069	+	15.7455i	−0.292337	+	0.506342i	−0.974362	−	0.224986i	$-0.927766\pi$
$967$	−9.09069	+	15.7455i	−0.292337	+	0.506342i	0.682025	+	0.731329i	$0.261100\pi$
$968$		0			0
$969$	−1.12208	+	0.468443i	−0.0360464	+	0.0150486i
$970$		0			0
$971$	−19.7416	−	34.1935i	−0.633538	−	1.09732i	−0.986823	−	0.161804i	$-0.948269\pi$
$971$	−19.7416	−	34.1935i	−0.633538	−	1.09732i	0.353285	−	0.935516i	$-0.385065\pi$
$972$		0			0
$973$	16.6092	−	20.1499i	0.532466	−	0.645975i
$974$		0			0
$975$	−2.28684	+	17.7519i	−0.0732376	+	0.568516i
$976$		0			0
$977$	−5.95782	−	10.3193i	−0.190608	−	0.330142i	0.754844	−	0.655904i	$-0.227712\pi$
$977$	−5.95782	−	10.3193i	−0.190608	−	0.330142i	−0.945452	+	0.325762i	$0.894379\pi$
$978$		0			0
$979$	−1.07439	−	1.86090i	−0.0343376	−	0.0594745i
$980$		0			0
$981$	1.68178	+	6.13961i	0.0536952	+	0.196023i
$982$		0			0
$983$	18.4779			0.589354			0.294677	−	0.955597i	$-0.404788\pi$
$983$	18.4779			0.589354			0.294677	+	0.955597i	$0.404788\pi$
$984$		0			0
$985$	57.1176			1.81992
$986$		0			0
$987$	13.5045	−	44.6200i	0.429852	−	1.42027i
$988$		0			0
$989$	−12.3620	−	21.4117i	−0.393090	−	0.680851i
$990$		0			0
$991$	6.34850	−	10.9959i	0.201667	−	0.349297i	−0.747399	−	0.664376i	$-0.768698\pi$
$991$	6.34850	−	10.9959i	0.201667	−	0.349297i	0.949066	+	0.315079i	$0.102031\pi$
$992$		0			0
$993$	−4.00435	+	31.0843i	−0.127074	+	0.986430i
$994$		0			0
$995$	28.6108	−	49.5553i	0.907023	−	1.57101i
$996$		0			0
$997$	41.9533			1.32868			0.664338	−	0.747432i	$-0.268714\pi$
$997$	41.9533			1.32868			0.664338	+	0.747432i	$0.268714\pi$
$998$		0			0
$999$	24.3469	−	3.41235i	0.770301	−	0.107962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.t.i.193.1		10
3.2	odd	2		3024.2.t.i.1873.5		10
4.3	odd	2		63.2.g.b.4.3	✓	10
7.2	even	3		1008.2.q.i.625.3		10
9.2	odd	6		3024.2.q.i.2881.1		10
9.7	even	3		1008.2.q.i.529.3		10
12.11	even	2		189.2.g.b.172.3		10
21.2	odd	6		3024.2.q.i.2305.1		10
28.3	even	6		441.2.f.f.148.3		10
28.11	odd	6		441.2.f.e.148.3		10
28.19	even	6		441.2.h.f.373.3		10
28.23	odd	6		63.2.h.b.58.3	yes	10
28.27	even	2		441.2.g.f.67.3		10
36.7	odd	6		63.2.h.b.25.3	yes	10
36.11	even	6		189.2.h.b.46.3		10
36.23	even	6		567.2.e.e.487.3		10
36.31	odd	6		567.2.e.f.487.3		10
63.2	odd	6		3024.2.t.i.289.5		10
63.16	even	3	inner	1008.2.t.i.961.1		10
84.11	even	6		1323.2.f.e.442.3		10
84.23	even	6		189.2.h.b.37.3		10
84.47	odd	6		1323.2.h.f.226.3		10
84.59	odd	6		1323.2.f.f.442.3		10
84.83	odd	2		1323.2.g.f.361.3		10
252.11	even	6		1323.2.f.e.883.3		10
252.23	even	6		567.2.e.e.163.3		10
252.31	even	6		3969.2.a.ba.1.3		5
252.47	odd	6		1323.2.g.f.667.3		10
252.59	odd	6		3969.2.a.bb.1.3		5
252.67	odd	6		3969.2.a.z.1.3		5
252.79	odd	6		63.2.g.b.16.3	yes	10
252.83	odd	6		1323.2.h.f.802.3		10
252.95	even	6		3969.2.a.bc.1.3		5
252.115	even	6		441.2.f.f.295.3		10
252.151	odd	6		441.2.f.e.295.3		10
252.187	even	6		441.2.g.f.79.3		10
252.191	even	6		189.2.g.b.100.3		10
252.223	even	6		441.2.h.f.214.3		10
252.227	odd	6		1323.2.f.f.883.3		10
252.247	odd	6		567.2.e.f.163.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.3	✓	10	4.3	odd	2
63.2.g.b.16.3	yes	10	252.79	odd	6
63.2.h.b.25.3	yes	10	36.7	odd	6
63.2.h.b.58.3	yes	10	28.23	odd	6
189.2.g.b.100.3		10	252.191	even	6
189.2.g.b.172.3		10	12.11	even	2
189.2.h.b.37.3		10	84.23	even	6
189.2.h.b.46.3		10	36.11	even	6
441.2.f.e.148.3		10	28.11	odd	6
441.2.f.e.295.3		10	252.151	odd	6
441.2.f.f.148.3		10	28.3	even	6
441.2.f.f.295.3		10	252.115	even	6
441.2.g.f.67.3		10	28.27	even	2
441.2.g.f.79.3		10	252.187	even	6
441.2.h.f.214.3		10	252.223	even	6
441.2.h.f.373.3		10	28.19	even	6
567.2.e.e.163.3		10	252.23	even	6
567.2.e.e.487.3		10	36.23	even	6
567.2.e.f.163.3		10	252.247	odd	6
567.2.e.f.487.3		10	36.31	odd	6
1008.2.q.i.529.3		10	9.7	even	3
1008.2.q.i.625.3		10	7.2	even	3
1008.2.t.i.193.1		10	1.1	even	1	trivial
1008.2.t.i.961.1		10	63.16	even	3	inner
1323.2.f.e.442.3		10	84.11	even	6
1323.2.f.e.883.3		10	252.11	even	6
1323.2.f.f.442.3		10	84.59	odd	6
1323.2.f.f.883.3		10	252.227	odd	6
1323.2.g.f.361.3		10	84.83	odd	2
1323.2.g.f.667.3		10	252.47	odd	6
1323.2.h.f.226.3		10	84.47	odd	6
1323.2.h.f.802.3		10	252.83	odd	6
3024.2.q.i.2305.1		10	21.2	odd	6
3024.2.q.i.2881.1		10	9.2	odd	6
3024.2.t.i.289.5		10	63.2	odd	6
3024.2.t.i.1873.5		10	3.2	odd	2
3969.2.a.z.1.3		5	252.67	odd	6
3969.2.a.ba.1.3		5	252.31	even	6
3969.2.a.bb.1.3		5	252.59	odd	6
3969.2.a.bc.1.3		5	252.95	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.59836 + 0.667278i) q^{3} -3.69258 q^{5} +(2.60948 + 0.436591i) q^{7} +(2.10948 - 2.13309i) q^{9} +O(q^{10})\)	\(q+(-1.59836 + 0.667278i) q^{3} -3.69258 q^{5} +(2.60948 + 0.436591i) q^{7} +(2.10948 - 2.13309i) q^{9} +0.892568 q^{11} +(0.598355 - 1.03638i) q^{13} +(5.90205 - 2.46398i) q^{15} +(-0.124991 + 0.216492i) q^{17} +(-1.40414 - 2.43204i) q^{19} +(-4.46220 + 1.04342i) q^{21} -2.47772 q^{23} +8.63514 q^{25} +(-1.94833 + 4.81705i) q^{27} +(2.07128 + 3.58755i) q^{29} +(1.79257 + 3.10483i) q^{31} +(-1.42664 + 0.595591i) q^{33} +(-9.63571 - 1.61215i) q^{35} +(-2.36568 - 4.09747i) q^{37} +(-0.264830 + 2.05578i) q^{39} +(-2.39093 + 4.14121i) q^{41} +(4.98928 + 8.64169i) q^{43} +(-7.78942 + 7.87662i) q^{45} +(-5.08653 + 8.81013i) q^{47} +(6.61878 + 2.27855i) q^{49} +(0.0553208 - 0.429435i) q^{51} +(-4.94465 + 8.56438i) q^{53} -3.29588 q^{55} +(3.86715 + 2.95031i) q^{57} +(0.906186 + 1.56956i) q^{59} +(-5.40205 + 9.35663i) q^{61} +(6.43594 - 4.64529i) q^{63} +(-2.20948 + 3.82692i) q^{65} +(0.514685 + 0.891460i) q^{67} +(3.96027 - 1.65332i) q^{69} +4.94533 q^{71} +(-0.915262 + 1.58528i) q^{73} +(-13.8020 + 5.76204i) q^{75} +(2.32914 + 0.389687i) q^{77} +(-0.899562 + 1.55809i) q^{79} +(-0.100184 - 8.99944i) q^{81} +(-6.16156 - 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +(-5.70453 - 4.35207i) q^{87} +(-1.20370 - 2.08488i) q^{89} +(2.01387 - 2.44318i) q^{91} +(-4.93695 - 3.76648i) q^{93} +(5.18489 + 8.98049i) q^{95} +(5.52210 + 9.56456i) q^{97} +(1.88286 - 1.90393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{3} - 8 q^{5} + q^{7} - 4 q^{9}+O(q^{10}) \) 10 * q - 2 * q^3 - 8 * q^5 + q^7 - 4 * q^9	\( 10 q - 2 q^{3} - 8 q^{5} + q^{7} - 4 q^{9} + 8 q^{11} - 8 q^{13} + 19 q^{15} + 12 q^{17} - q^{19} - 2 q^{21} + 6 q^{23} + 2 q^{25} + 7 q^{27} + 7 q^{29} + 3 q^{31} - q^{33} - 5 q^{35} - 20 q^{39} + 5 q^{41} + 7 q^{43} - q^{45} - 27 q^{47} + 25 q^{49} - 24 q^{51} - 21 q^{53} - 4 q^{55} - 4 q^{57} - 30 q^{59} - 14 q^{61} + 35 q^{63} - 11 q^{65} + 2 q^{67} + 15 q^{69} + 6 q^{71} + 15 q^{73} - 31 q^{75} - 31 q^{77} + 4 q^{79} + 8 q^{81} - 9 q^{83} - 6 q^{85} - 32 q^{87} + 28 q^{89} + 4 q^{91} - 12 q^{93} + 14 q^{95} - 12 q^{97} - 35 q^{99}+O(q^{100}) \) 10 * q - 2 * q^3 - 8 * q^5 + q^7 - 4 * q^9 + 8 * q^11 - 8 * q^13 + 19 * q^15 + 12 * q^17 - q^19 - 2 * q^21 + 6 * q^23 + 2 * q^25 + 7 * q^27 + 7 * q^29 + 3 * q^31 - q^33 - 5 * q^35 - 20 * q^39 + 5 * q^41 + 7 * q^43 - q^45 - 27 * q^47 + 25 * q^49 - 24 * q^51 - 21 * q^53 - 4 * q^55 - 4 * q^57 - 30 * q^59 - 14 * q^61 + 35 * q^63 - 11 * q^65 + 2 * q^67 + 15 * q^69 + 6 * q^71 + 15 * q^73 - 31 * q^75 - 31 * q^77 + 4 * q^79 + 8 * q^81 - 9 * q^83 - 6 * q^85 - 32 * q^87 + 28 * q^89 + 4 * q^91 - 12 * q^93 + 14 * q^95 - 12 * q^97 - 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more