LMFDB - Embedded newform 1008.2.q.i.625.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(529,1008)]

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, 4, 4]))

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

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

chi := DirichletCharacter("1008.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.q (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			625.3
Root			$0.247934 + 0.429435i$ of defining polynomial
Character	$\chi$	$=$	1008.625
Dual form			1008.2.q.i.529.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.221298 - 1.71786i) q^{3} +(1.84629 + 3.19787i) q^{5} +(-0.926641 + 2.47817i) q^{7} +(-2.90205 - 0.760316i) q^{9} +O(q^{10})$	\(q+(0.221298 - 1.71786i) q^{3} +(1.84629 + 3.19787i) q^{5} +(-0.926641 + 2.47817i) q^{7} +(-2.90205 - 0.760316i) q^{9} +(-0.446284 + 0.772987i) q^{11} +(0.598355 - 1.03638i) q^{13} +(5.90205 - 2.46398i) q^{15} +(-0.124991 - 0.216492i) q^{17} +(-1.40414 + 2.43204i) q^{19} +(4.05208 + 2.14025i) q^{21} +(1.23886 + 2.14576i) q^{23} +(-4.31757 + 7.47825i) q^{25} +(-1.94833 + 4.81705i) q^{27} +(2.07128 + 3.58755i) q^{29} -3.58515 q^{31} +(1.22912 + 0.937712i) q^{33} +(-9.63571 + 1.61215i) q^{35} +(-2.36568 + 4.09747i) q^{37} +(-1.64794 - 1.25724i) q^{39} +(-2.39093 + 4.14121i) q^{41} +(4.98928 + 8.64169i) q^{43} +(-2.92664 - 10.6841i) q^{45} +10.1731 q^{47} +(-5.28267 - 4.59275i) q^{49} +(-0.399562 + 0.166808i) q^{51} +(-4.94465 - 8.56438i) q^{53} -3.29588 q^{55} +(3.86715 + 2.95031i) q^{57} -1.81237 q^{59} +10.8041 q^{61} +(4.57336 - 6.48725i) q^{63} +4.41895 q^{65} -1.02937 q^{67} +(3.96027 - 1.65332i) q^{69} +4.94533 q^{71} +(-0.915262 - 1.58528i) q^{73} +(11.8911 + 9.07189i) q^{75} +(-1.50205 - 1.82225i) q^{77} +1.79912 q^{79} +(7.84384 + 4.41296i) q^{81} +(-6.16156 - 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +(6.62127 - 2.76423i) q^{87} +(-1.20370 + 2.08488i) q^{89} +(2.01387 + 2.44318i) q^{91} +(-0.793387 + 6.15877i) q^{93} -10.3698 q^{95} +(5.52210 + 9.56456i) q^{97} +(1.88286 - 1.90393i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} + 4 q^{5} + 4 q^{7} + 11 q^{9}+O(q^{10}) $ 10 * q + q^3 + 4 * q^5 + 4 * q^7 + 11 * q^9	$ 10 q + q^{3} + 4 q^{5} + 4 q^{7} + 11 q^{9} - 4 q^{11} - 8 q^{13} + 19 q^{15} + 12 q^{17} - q^{19} + 13 q^{21} - 3 q^{23} - q^{25} + 7 q^{27} + 7 q^{29} - 6 q^{31} + 14 q^{33} - 5 q^{35} - 2 q^{39} + 5 q^{41} + 7 q^{43} - 16 q^{45} + 54 q^{47} - 8 q^{49} + 9 q^{51} - 21 q^{53} - 4 q^{55} - 4 q^{57} + 60 q^{59} + 28 q^{61} + 59 q^{63} + 22 q^{65} - 4 q^{67} + 15 q^{69} + 6 q^{71} + 15 q^{73} + 14 q^{75} + 11 q^{77} - 8 q^{79} + 23 q^{81} - 9 q^{83} - 6 q^{85} - 2 q^{87} + 28 q^{89} + 4 q^{91} - 6 q^{93} - 28 q^{95} - 12 q^{97} - 35 q^{99}+O(q^{100}) $ 10 * q + q^3 + 4 * q^5 + 4 * q^7 + 11 * q^9 - 4 * q^11 - 8 * q^13 + 19 * q^15 + 12 * q^17 - q^19 + 13 * q^21 - 3 * q^23 - q^25 + 7 * q^27 + 7 * q^29 - 6 * q^31 + 14 * q^33 - 5 * q^35 - 2 * q^39 + 5 * q^41 + 7 * q^43 - 16 * q^45 + 54 * q^47 - 8 * q^49 + 9 * q^51 - 21 * q^53 - 4 * q^55 - 4 * q^57 + 60 * q^59 + 28 * q^61 + 59 * q^63 + 22 * q^65 - 4 * q^67 + 15 * q^69 + 6 * q^71 + 15 * q^73 + 14 * q^75 + 11 * q^77 - 8 * q^79 + 23 * q^81 - 9 * q^83 - 6 * q^85 - 2 * q^87 + 28 * q^89 + 4 * q^91 - 6 * q^93 - 28 * q^95 - 12 * q^97 - 35 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	0.221298	−	1.71786i	0.127767	−	0.991804i
$3$	0.221298	−	1.71786i	0.127767	−	0.991804i
$4$		0			0
$5$	1.84629	+	3.19787i	0.825686	+	1.43013i	0.901394	+	0.433000i	$0.142545\pi$
$5$	1.84629	+	3.19787i	0.825686	+	1.43013i	−0.0757082	+	0.997130i	$0.524122\pi$
$6$		0			0
$7$	−0.926641	+	2.47817i	−0.350238	+	0.936661i
$7$	−0.926641	+	2.47817i	−0.350238	+	0.936661i
$8$		0			0
$9$	−2.90205	−	0.760316i	−0.967351	−	0.253439i
$10$		0			0
$11$	−0.446284	+	0.772987i	−0.134560	+	0.233064i	−0.925429	−	0.378921i	$-0.876295\pi$
$11$	−0.446284	+	0.772987i	−0.134560	+	0.233064i	0.790869	+	0.611985i	$0.209629\pi$
$12$		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	0.850470	−	0.526024i	$-0.176318\pi$
$17$	−0.124991	−	0.216492i	−0.0303149	−	0.0525069i	−0.880785	+	0.473517i	$0.842984\pi$
$18$		0			0
$19$	−1.40414	+	2.43204i	−0.322131	+	0.557948i	−0.980928	−	0.194374i	$-0.937733\pi$
$19$	−1.40414	+	2.43204i	−0.322131	+	0.557948i	0.658796	+	0.752321i	$0.271066\pi$
$20$		0			0
$21$	4.05208	+	2.14025i	0.884236	+	0.467041i
$22$		0			0
$23$	1.23886	+	2.14576i	0.258320	+	0.447423i	0.965792	−	0.259318i	$-0.0834979\pi$
$23$	1.23886	+	2.14576i	0.258320	+	0.447423i	−0.707472	+	0.706741i	$0.750165\pi$
$24$		0			0
$25$	−4.31757	+	7.47825i	−0.863514	+	1.49565i
$26$		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
$31$	−3.58515			−0.643912			−0.321956	−	0.946755i	$-0.604340\pi$
$31$	−3.58515			−0.643912			−0.321956	+	0.946755i	$0.604340\pi$
$32$		0			0
$33$	1.22912	+	0.937712i	0.213962	+	0.163235i
$34$		0			0
$35$	−9.63571	+	1.61215i	−1.62873	+	0.272502i
$36$		0			0
$37$	−2.36568	+	4.09747i	−0.388915	+	0.673621i	−0.992304	−	0.123826i	$-0.960483\pi$
$37$	−2.36568	+	4.09747i	−0.388915	+	0.673621i	0.603389	+	0.797447i	$0.293817\pi$
$38$		0			0
$39$	−1.64794	−	1.25724i	−0.263882	−	0.201319i
$40$		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
$45$	−2.92664	−	10.6841i	−0.436278	−	1.59270i
$46$		0			0
$47$	10.1731			1.48389			0.741947	−	0.670459i	$-0.233903\pi$
$47$	10.1731			1.48389			0.741947	+	0.670459i	$0.233903\pi$
$48$		0			0
$49$	−5.28267	−	4.59275i	−0.754667	−	0.656108i
$50$		0			0
$51$	−0.399562	+	0.166808i	−0.0559498	+	0.0233578i
$52$		0			0
$53$	−4.94465	−	8.56438i	−0.679199	−	1.17641i	−0.975222	−	0.221227i	$-0.928994\pi$
$53$	−4.94465	−	8.56438i	−0.679199	−	1.17641i	0.296023	−	0.955181i	$-0.404339\pi$
$54$		0			0
$55$	−3.29588			−0.444416
$56$		0			0
$57$	3.86715	+	2.95031i	0.512217	+	0.390778i
$58$		0			0
$59$	−1.81237			−0.235951			−0.117975	−	0.993017i	$-0.537640\pi$
$59$	−1.81237			−0.235951			−0.117975	+	0.993017i	$0.537640\pi$
$60$		0			0
$61$	10.8041			1.38332			0.691662	−	0.722221i	$-0.256879\pi$
$61$	10.8041			1.38332			0.691662	+	0.722221i	$0.256879\pi$
$62$		0			0
$63$	4.57336	−	6.48725i	0.576189	−	0.817316i
$64$		0			0
$65$	4.41895			0.548103
$66$		0			0
$67$	−1.02937			−0.125757			−0.0628787	−	0.998021i	$-0.520028\pi$
$67$	−1.02937			−0.125757			−0.0628787	+	0.998021i	$0.520028\pi$
$68$		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	0.807480	−	0.589894i	$-0.200831\pi$
$73$	−0.915262	−	1.58528i	−0.107123	−	0.185543i	−0.914604	+	0.404351i	$0.867497\pi$
$74$		0			0
$75$	11.8911	+	9.07189i	1.37306	+	1.04753i
$76$		0			0
$77$	−1.50205	−	1.82225i	−0.171174	−	0.207665i
$78$		0			0
$79$	1.79912			0.202417			0.101209	−	0.994865i	$-0.467729\pi$
$79$	1.79912			0.202417			0.101209	+	0.994865i	$0.467729\pi$
$80$		0			0
$81$	7.84384	+	4.41296i	0.871538	+	0.490329i
$82$		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
$87$	6.62127	−	2.76423i	0.709875	−	0.296357i
$88$		0			0
$89$	−1.20370	+	2.08488i	−0.127592	+	0.220997i	−0.922743	−	0.385415i	$-0.874058\pi$
$89$	−1.20370	+	2.08488i	−0.127592	+	0.220997i	0.795151	+	0.606412i	$0.207392\pi$
$90$		0			0
$91$	2.01387	+	2.44318i	0.211111	+	0.256115i
$92$		0			0
$93$	−0.793387	+	6.15877i	−0.0822704	+	0.638634i
$94$		0			0
$95$	−10.3698			−1.06392
$96$		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
$101$	1.29982	−	2.25136i	0.129337	−	0.224018i	−0.794083	−	0.607810i	$-0.792048\pi$
$101$	1.29982	−	2.25136i	0.129337	−	0.224018i	0.923420	+	0.383791i	$0.125382\pi$
$102$		0			0
$103$	4.85578	+	8.41045i	0.478454	+	0.828706i	0.999695	−	0.0247032i	$-0.00786408\pi$
$103$	4.85578	+	8.41045i	0.478454	+	0.828706i	−0.521241	+	0.853409i	$0.674531\pi$
$104$		0			0
$105$	0.637069	+	16.9095i	0.0621716	+	1.65020i
$106$		0			0
$107$	5.45025	−	9.44012i	0.526896	−	0.912610i	−0.472613	−	0.881270i	$-0.656689\pi$
$107$	5.45025	−	9.44012i	0.526896	−	0.912610i	0.999509	−	0.0313403i	$-0.00997757\pi$
$108$		0			0
$109$	−1.06096	−	1.83764i	−0.101622	−	0.176014i	0.810731	−	0.585419i	$-0.199070\pi$
$109$	−1.06096	−	1.83764i	−0.101622	−	0.176014i	−0.912353	+	0.409404i	$0.865737\pi$
$110$		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
$115$	−4.57458	+	7.92341i	−0.426582	+	0.738861i
$116$		0			0
$117$	−2.52444	+	2.55270i	−0.233384	+	0.235997i
$118$		0			0
$119$	0.652326	−	0.109140i	0.0597986	−	0.0100049i
$120$		0			0
$121$	5.10166	+	8.83634i	0.463787	+	0.803303i
$122$		0			0
$123$	6.58489	+	5.02371i	0.593740	+	0.452973i
$124$		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
$129$	15.9493	−	6.65848i	1.40426	−	0.586246i
$130$		0			0
$131$	−7.51444	−	13.0154i	−0.656540	−	1.13716i	−0.981505	−	0.191435i	$-0.938686\pi$
$131$	−7.51444	−	13.0154i	−0.656540	−	1.13716i	0.324965	−	0.945726i	$-0.394647\pi$
$132$		0			0
$133$	−4.72587	−	5.73332i	−0.409785	−	0.497142i
$134$		0			0
$135$	−19.0015	+	2.66316i	−1.63539	+	0.229209i
$136$		0			0
$137$	0.244246	−	0.423047i	0.0208674	−	0.0361433i	−0.855403	−	0.517963i	$-0.826691\pi$
$137$	0.244246	−	0.423047i	0.0208674	−	0.0361433i	0.876271	+	0.481819i	$0.160024\pi$
$138$		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
$147$	−9.05873	+	8.05850i	−0.747152	+	0.664654i
$148$		0			0
$149$	−10.5120	−	18.2073i	−0.861175	−	1.49160i	−0.870796	−	0.491645i	$-0.836396\pi$
$149$	−10.5120	−	18.2073i	−0.861175	−	1.49160i	0.00962096	−	0.999954i	$-0.496938\pi$
$150$		0			0
$151$	0.749191	−	1.29764i	0.0609683	−	0.105600i	−0.833930	−	0.551870i	$-0.813914\pi$
$151$	0.749191	−	1.29764i	0.0609683	−	0.105600i	0.894898	+	0.446270i	$0.147248\pi$
$152$		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
$157$	−16.6796			−1.33118			−0.665590	−	0.746317i	$-0.731820\pi$
$157$	−16.6796			−1.33118			−0.665590	+	0.746317i	$0.731820\pi$
$158$		0			0
$159$	−15.8066	+	6.59890i	−1.25355	+	0.523327i
$160$		0			0
$161$	−6.46555	+	1.08175i	−0.509557	+	0.0852537i
$162$		0			0
$163$	3.34135	−	5.78738i	0.261714	−	0.453303i	−0.704983	−	0.709224i	$-0.749046\pi$
$163$	3.34135	−	5.78738i	0.261714	−	0.453303i	0.966698	+	0.255921i	$0.0823788\pi$
$164$		0			0
$165$	−0.729372	+	5.66184i	−0.0567815	+	0.440774i
$166$		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
$171$	5.92400	−	5.99031i	0.453020	−	0.458091i
$172$		0			0
$173$	−3.88685			−0.295511			−0.147756	−	0.989024i	$-0.547205\pi$
$173$	−3.88685			−0.295511			−0.147756	+	0.989024i	$0.547205\pi$
$174$		0			0
$175$	−14.5316	−	17.6293i	−1.09848	−	1.33265i
$176$		0			0
$177$	−0.401075	+	3.11339i	−0.0301466	+	0.234017i
$178$		0			0
$179$	−3.66758	−	6.35244i	−0.274128	−	0.474804i	0.695787	−	0.718248i	$-0.255056\pi$
$179$	−3.66758	−	6.35244i	−0.274128	−	0.474804i	−0.969915	+	0.243445i	$0.921723\pi$
$180$		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
$185$	−17.4709			−1.28449
$186$		0			0
$187$	0.223127			0.0163167
$188$		0			0
$189$	−10.1321	−	9.29198i	−0.737000	−	0.675892i
$190$		0			0
$191$	23.8459			1.72543			0.862715	−	0.505690i	$-0.168762\pi$
$191$	23.8459			1.72543			0.862715	+	0.505690i	$0.168762\pi$
$192$		0			0
$193$	5.93456			0.427179			0.213589	−	0.976924i	$-0.431485\pi$
$193$	5.93456			0.427179			0.213589	+	0.976924i	$0.431485\pi$
$194$		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	−0.998326	−	0.0578402i	$-0.981579\pi$
$199$	−7.74818	−	13.4202i	−0.549254	−	0.951336i	0.449072	−	0.893496i	$-0.351755\pi$
$200$		0			0
$201$	−0.227798	+	1.76831i	−0.0160676	+	0.124727i
$202$		0			0
$203$	−10.8099	+	1.80860i	−0.758707	+	0.126939i
$204$		0			0
$205$	−17.6574			−1.23325
$206$		0			0
$207$	−1.96377	−	7.16905i	−0.136492	−	0.498283i
$208$		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
$213$	1.09439	−	8.49536i	0.0749866	−	0.582093i
$214$		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
$219$	−2.92583	+	1.22147i	−0.197709	+	0.0825392i
$220$		0			0
$221$	−0.299157			−0.0201235
$222$		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
$227$	−8.03818	+	13.9225i	−0.533513	+	0.924072i	0.465721	+	0.884932i	$0.345795\pi$
$227$	−8.03818	+	13.9225i	−0.533513	+	0.924072i	−0.999234	+	0.0391399i	$0.987538\pi$
$228$		0			0
$229$	4.98420	+	8.63289i	0.329365	+	0.570477i	0.982386	−	0.186863i	$-0.0598319\pi$
$229$	4.98420	+	8.63289i	0.329365	+	0.570477i	−0.653021	+	0.757340i	$0.726499\pi$
$230$		0			0
$231$	−3.46276	+	2.17704i	−0.227833	+	0.143239i
$232$		0			0
$233$	8.27045	−	14.3248i	0.541815	−	0.938451i	−0.456985	−	0.889474i	$-0.651071\pi$
$233$	8.27045	−	14.3248i	0.541815	−	0.938451i	0.998800	−	0.0489765i	$-0.0155959\pi$
$234$		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
$241$	−8.36004	+	14.4800i	−0.538517	+	0.932739i	0.460467	+	0.887677i	$0.347682\pi$
$241$	−8.36004	+	14.4800i	−0.538517	+	0.932739i	−0.998984	+	0.0450623i	$0.985651\pi$
$242$		0			0
$243$	9.31665	−	12.4980i	0.597664	−	0.801747i
$244$		0			0
$245$	4.93368	−	25.3728i	0.315201	−	1.62101i
$246$		0			0
$247$	1.68035	+	2.91045i	0.106918	+	0.185187i
$248$		0			0
$249$	−19.6967	+	8.22294i	−1.24823	+	0.521108i
$250$		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
$255$	−1.27114	−	0.969769i	−0.0796017	−	0.0607293i
$256$		0			0
$257$	8.55986	+	14.8261i	0.533950	+	0.924828i	0.999213	+	0.0396557i	$0.0126261\pi$
$257$	8.55986	+	14.8261i	0.533950	+	0.924828i	−0.465264	+	0.885172i	$0.654041\pi$
$258$		0			0
$259$	−7.96211	−	9.65945i	−0.494741	−	0.600209i
$260$		0			0
$261$	−3.28328	−	11.9861i	−0.203230	−	0.741921i
$262$		0			0
$263$	10.2763	−	17.7991i	0.633666	−	1.09754i	−0.353130	−	0.935574i	$-0.614883\pi$
$263$	10.2763	−	17.7991i	0.633666	−	1.09754i	0.986796	−	0.161967i	$-0.0517838\pi$
$264$		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	0.992052	+	0.125827i	$0.0401585\pi$
$269$	9.92267	+	17.1866i	0.604996	+	1.04788i	−0.387057	+	0.922056i	$0.626508\pi$
$270$		0			0
$271$	−5.32056	+	9.21548i	−0.323201	+	0.559801i	−0.981147	−	0.193265i	$-0.938092\pi$
$271$	−5.32056	+	9.21548i	−0.323201	+	0.559801i	0.657946	+	0.753065i	$0.271426\pi$
$272$		0			0
$273$	4.64270	−	2.91887i	0.280989	−	0.176658i
$274$		0			0
$275$	−3.85373	−	6.67485i	−0.232388	−	0.402509i
$276$		0			0
$277$	12.4407	−	21.5479i	0.747487	−	1.29469i	−0.201536	−	0.979481i	$-0.564593\pi$
$277$	12.4407	−	21.5479i	0.747487	−	1.29469i	0.949024	−	0.315205i	$-0.102073\pi$
$278$		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
$283$	−6.32179			−0.375791			−0.187896	−	0.982189i	$-0.560167\pi$
$283$	−6.32179			−0.375791			−0.187896	+	0.982189i	$0.560167\pi$
$284$		0			0
$285$	−2.29481	+	17.8138i	−0.135933	+	1.05520i
$286$		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
$291$	17.6526	−	7.36955i	1.03481	−	0.432011i
$292$		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
$297$	−2.85401	−	3.65581i	−0.165606	−	0.212132i
$298$		0			0
$299$	2.96511			0.171477
$300$		0			0
$301$	−26.0389	+	4.35655i	−1.50086	+	0.251108i
$302$		0			0
$303$	−3.57986	−	2.73113i	−0.205657	−	0.156899i
$304$		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
$311$	15.1003			0.856258			0.428129	−	0.903718i	$-0.359173\pi$
$311$	15.1003			0.856258			0.428129	+	0.903718i	$0.359173\pi$
$312$		0			0
$313$	−25.4785			−1.44013			−0.720064	−	0.693908i	$-0.755888\pi$
$313$	−25.4785			−1.44013			−0.720064	+	0.693908i	$0.755888\pi$
$314$		0			0
$315$	29.1891	+	2.64766i	1.64462	+	0.149178i
$316$		0			0
$317$	32.5209			1.82656			0.913278	−	0.407337i	$-0.133543\pi$
$317$	32.5209			1.82656			0.913278	+	0.407337i	$0.133543\pi$
$318$		0			0
$319$	−3.69751			−0.207021
$320$		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
$327$	−3.39159	+	1.41591i	−0.187556	+	0.0783003i
$328$		0			0
$329$	−9.42678	+	25.2106i	−0.519715	+	1.38991i
$330$		0			0
$331$	−18.0948			−0.994582			−0.497291	−	0.867584i	$-0.665672\pi$
$331$	−18.0948			−0.994582			−0.497291	+	0.867584i	$0.665672\pi$
$332$		0			0
$333$	9.98070	−	10.0924i	0.546939	−	0.553062i
$334$		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
$339$	−21.7938	−	16.6268i	−1.18368	−	0.903045i
$340$		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
$345$	12.5989	+	9.61190i	0.678303	+	0.517488i
$346$		0			0
$347$	−10.7489			−0.577030			−0.288515	−	0.957475i	$-0.593162\pi$
$347$	−10.7489			−0.577030			−0.288515	+	0.957475i	$0.593162\pi$
$348$		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
$353$	−8.40960	+	14.5658i	−0.447598	+	0.775262i	−0.998229	−	0.0594866i	$-0.981054\pi$
$353$	−8.40960	+	14.5658i	−0.447598	+	0.775262i	0.550631	+	0.834748i	$0.314387\pi$
$354$		0			0
$355$	9.13051	+	15.8145i	0.484597	+	0.839347i
$356$		0			0
$357$	−0.0431288	−	1.14475i	−0.00228262	−	0.0605868i
$358$		0			0
$359$	−11.8921	+	20.5978i	−0.627642	+	1.08711i	0.360382	+	0.932805i	$0.382646\pi$
$359$	−11.8921	+	20.5978i	−0.627642	+	1.08711i	−0.988024	+	0.154303i	$0.950687\pi$
$360$		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
$367$	−0.344992	+	0.597544i	−0.0180084	+	0.0311915i	−0.874889	−	0.484323i	$-0.839066\pi$
$367$	−0.344992	+	0.597544i	−0.0180084	+	0.0311915i	0.856881	+	0.515515i	$0.172399\pi$
$368$		0			0
$369$	10.0872	−	10.2002i	0.525121	−	0.530999i
$370$		0			0
$371$	25.8059	−	4.31757i	1.33978	−	0.224157i
$372$		0			0
$373$	1.88006	+	3.25636i	0.0973457	+	0.168608i	0.910585	−	0.413321i	$-0.135631\pi$
$373$	1.88006	+	3.25636i	0.0973457	+	0.168608i	−0.813239	+	0.581929i	$0.802298\pi$
$374$		0			0
$375$	−2.97050	+	23.0589i	−0.153396	+	1.19075i
$376$		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
$381$	0.280930	−	2.18075i	0.0143925	−	0.111723i
$382$		0			0
$383$	−0.536335	−	0.928960i	−0.0274055	−	0.0474676i	0.851997	−	0.523546i	$-0.175391\pi$
$383$	−0.536335	−	0.928960i	−0.0274055	−	0.0474676i	−0.879403	+	0.476078i	$0.842058\pi$
$384$		0			0
$385$	3.05410	−	8.16775i	0.155651	−	0.416267i
$386$		0			0
$387$	−7.90875	−	28.8721i	−0.402024	−	1.46765i
$388$		0			0
$389$	11.8718	−	20.5626i	0.601925	−	1.04256i	−0.390605	−	0.920559i	$-0.627734\pi$
$389$	11.8718	−	20.5626i	0.601925	−	1.04256i	0.992529	−	0.122006i	$-0.0389326\pi$
$390$		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	−0.866428	−	0.499302i	$-0.833590\pi$
$397$	−0.0160489	+	0.0277975i	−0.000805471	+	0.00139512i	0.865622	+	0.500697i	$0.166923\pi$
$398$		0			0
$399$	−10.8948	+	6.84959i	−0.545424	+	0.342909i
$400$		0			0
$401$	−12.2628	−	21.2398i	−0.612374	−	1.06066i	−0.990839	−	0.135048i	$-0.956881\pi$
$401$	−12.2628	−	21.2398i	−0.612374	−	1.06066i	0.378465	−	0.925616i	$-0.376452\pi$
$402$		0			0
$403$	−2.14519	+	3.71558i	−0.106860	+	0.185086i
$404$		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
$409$	26.7897			1.32467			0.662333	−	0.749210i	$-0.269567\pi$
$409$	26.7897			1.32467			0.662333	+	0.749210i	$0.269567\pi$
$410$		0			0
$411$	−0.672682	−	0.513199i	−0.0331810	−	0.0253143i
$412$		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
$417$	−13.5912	−	10.3689i	−0.665564	−	0.507769i
$418$		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
$423$	−29.5228	−	7.73475i	−1.43545	−	0.376076i
$424$		0			0
$425$	2.15864			0.104709
$426$		0			0
$427$	−10.0115	+	26.7744i	−0.484492	+	1.29571i
$428$		0			0
$429$	1.70728	−	0.712750i	0.0824281	−	0.0344119i
$430$		0			0
$431$	7.95192	+	13.7731i	0.383031	+	0.663428i	0.991494	−	0.130154i	$-0.0415471\pi$
$431$	7.95192	+	13.7731i	0.383031	+	0.663428i	−0.608463	+	0.793582i	$0.708214\pi$
$432$		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
$437$	−6.95811			−0.332851
$438$		0			0
$439$	15.5447			0.741909			0.370954	−	0.928651i	$-0.379031\pi$
$439$	15.5447			0.741909			0.370954	+	0.928651i	$0.379031\pi$
$440$		0			0
$441$	11.8387	+	17.3449i	0.563745	+	0.825949i
$442$		0			0
$443$	−1.79005			−0.0850480			−0.0425240	−	0.999095i	$-0.513540\pi$
$443$	−1.79005			−0.0850480			−0.0425240	+	0.999095i	$0.513540\pi$
$444$		0			0
$445$	−8.88955			−0.421405
$446$		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
$453$	−2.06336	−	1.57417i	−0.0969450	−	0.0739608i
$454$		0			0
$455$	−4.09478	+	10.9509i	−0.191966	+	0.513387i
$456$		0			0
$457$	2.56917			0.120181			0.0600905	−	0.998193i	$-0.480861\pi$
$457$	2.56917			0.120181			0.0600905	+	0.998193i	$0.480861\pi$
$458$		0			0
$459$	1.28638	−	0.180293i	0.0600429	−	0.00841535i
$460$		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
$465$	−21.1597	+	8.83372i	−0.981259	+	0.409654i
$466$		0			0
$467$	4.35022	−	7.53480i	0.201304	−	0.348669i	−0.747645	−	0.664099i	$-0.768815\pi$
$467$	4.35022	−	7.53480i	0.201304	−	0.348669i	0.948949	+	0.315430i	$0.102149\pi$
$468$		0			0
$469$	0.953856	−	2.55095i	0.0440450	−	0.117792i
$470$		0			0
$471$	−3.69117	+	28.6532i	−0.170080	+	1.32027i
$472$		0			0
$473$	−8.90655			−0.409524
$474$		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
$479$	−8.88370	+	15.3870i	−0.405907	+	0.703051i	−0.994427	−	0.105432i	$-0.966378\pi$
$479$	−8.88370	+	15.3870i	−0.405907	+	0.703051i	0.588520	+	0.808483i	$0.299711\pi$
$480$		0			0
$481$	2.83103	+	4.90349i	0.129084	+	0.223580i
$482$		0			0
$483$	0.427472	+	11.3463i	0.0194507	+	0.516273i
$484$		0			0
$485$	−20.3908	+	35.3179i	−0.925898	+	1.60370i
$486$		0			0
$487$	−8.32763	−	14.4239i	−0.377361	−	0.653608i	0.613316	−	0.789837i	$-0.289835\pi$
$487$	−8.32763	−	14.4239i	−0.377361	−	0.653608i	−0.990677	+	0.136229i	$0.956502\pi$
$488$		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
$493$	0.517784	−	0.896827i	0.0233198	−	0.0403911i
$494$		0			0
$495$	9.56482	+	2.50591i	0.429907	+	0.112632i
$496$		0			0
$497$	−4.58255	+	12.2554i	−0.205555	+	0.549729i
$498$		0			0
$499$	5.57296	+	9.65264i	0.249480	+	0.432112i	0.963382	−	0.268134i	$-0.0864071\pi$
$499$	5.57296	+	9.65264i	0.249480	+	0.432112i	−0.713902	+	0.700246i	$0.753074\pi$
$500$		0			0
$501$	24.2789	+	18.5227i	1.08470	+	0.827533i
$502$		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
$507$	18.4896	−	7.71899i	0.821151	−	0.342812i
$508$		0			0
$509$	−15.5411	−	26.9180i	−0.688848	−	1.19312i	−0.972211	−	0.234107i	$-0.924783\pi$
$509$	−15.5411	−	26.9180i	−0.688848	−	1.19312i	0.283362	−	0.959013i	$-0.408550\pi$
$510$		0			0
$511$	4.77672	−	0.799190i	0.211310	−	0.0353541i
$512$		0			0
$513$	−8.97952	−	11.5022i	−0.396456	−	0.507835i
$514$		0			0
$515$	−17.9303	+	31.0563i	−0.790105	+	1.36850i
$516$		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	0.809174	−	0.587570i	$-0.199915\pi$
$521$	−2.37986	−	4.12203i	−0.104263	−	0.180590i	−0.913437	+	0.406980i	$0.866582\pi$
$522$		0			0
$523$	−20.1258	+	34.8588i	−0.880038	+	1.52427i	−0.0287402	+	0.999587i	$0.509150\pi$
$523$	−20.1258	+	34.8588i	−0.880038	+	1.52427i	−0.851298	+	0.524683i	$0.824184\pi$
$524$		0			0
$525$	−33.5005	+	21.0618i	−1.46208	+	0.919211i
$526$		0			0
$527$	0.448113	+	0.776154i	0.0195201	+	0.0338098i
$528$		0			0
$529$	8.43046	−	14.6020i	0.366542	−	0.634869i
$530$		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
$535$	40.2510			1.74020
$536$		0			0
$537$	−11.7242	+	4.89459i	−0.505937	+	0.211217i
$538$		0			0
$539$	5.90771	−	2.03376i	0.254463	−	0.0876003i
$540$		0			0
$541$	12.0547	−	20.8794i	0.518273	−	0.897675i	−0.481502	−	0.876445i	$-0.659908\pi$
$541$	12.0547	−	20.8794i	0.518273	−	0.897675i	0.999775	−	0.0212301i	$-0.00675826\pi$
$542$		0			0
$543$	2.49105	−	19.3371i	0.106901	−	0.829836i
$544$		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
$549$	−31.3541	−	8.21454i	−1.33816	−	0.350588i
$550$		0			0
$551$	−11.6334			−0.495600
$552$		0			0
$553$	−1.66714	+	4.45854i	−0.0708941	+	0.189596i
$554$		0			0
$555$	−3.86628	+	30.0125i	−0.164114	+	1.27396i
$556$		0			0
$557$	4.03845	+	6.99479i	0.171114	+	0.296379i	0.938810	−	0.344436i	$-0.111930\pi$
$557$	4.03845	+	6.99479i	0.171114	+	0.296379i	−0.767695	+	0.640815i	$0.778597\pi$
$558$		0			0
$559$	11.9415			0.505070
$560$		0			0
$561$	0.0493776	−	0.383300i	0.00208472	−	0.0161829i
$562$		0			0
$563$	−45.2127			−1.90549			−0.952744	−	0.303774i	$-0.901753\pi$
$563$	−45.2127			−1.90549			−0.952744	+	0.303774i	$0.901753\pi$
$564$		0			0
$565$	58.4401			2.45859
$566$		0			0
$567$	−18.2045	+	15.3491i	−0.764517	+	0.644604i
$568$		0			0
$569$	22.4299			0.940309			0.470155	−	0.882584i	$-0.344198\pi$
$569$	22.4299			0.940309			0.470155	+	0.882584i	$0.344198\pi$
$570$		0			0
$571$	21.8269			0.913426			0.456713	−	0.889614i	$-0.349027\pi$
$571$	21.8269			0.913426			0.456713	+	0.889614i	$0.349027\pi$
$572$		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	−0.977807	−	0.209508i	$-0.932814\pi$
$577$	−16.1022	−	27.8898i	−0.670342	−	1.16107i	0.307465	−	0.951559i	$-0.400519\pi$
$578$		0			0
$579$	1.31331	−	10.1947i	0.0545791	−	0.423678i
$580$		0			0
$581$	32.1569	−	5.38016i	1.33409	−	0.223207i
$582$		0			0
$583$	8.82687			0.365571
$584$		0			0
$585$	−12.8240	−	3.35980i	−0.530209	−	0.138911i
$586$		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
$591$	−3.42309	+	26.5721i	−0.140807	+	1.09303i
$592$		0			0
$593$	−14.4202	+	24.9766i	−0.592168	+	1.02566i	0.401772	+	0.915740i	$0.368394\pi$
$593$	−14.4202	+	24.9766i	−0.592168	+	1.02566i	−0.993940	+	0.109925i	$0.964939\pi$
$594$		0			0
$595$	1.55340	+	1.88455i	0.0636831	+	0.0772589i
$596$		0			0
$597$	−24.7687	+	10.3404i	−1.01372	+	0.423204i
$598$		0			0
$599$	46.9989			1.92032			0.960161	−	0.279447i	$-0.0901511\pi$
$599$	46.9989			1.92032			0.960161	+	0.279447i	$0.0901511\pi$
$600$		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
$605$	−18.8383	+	32.6289i	−0.765885	+	1.32655i
$606$		0			0
$607$	−14.3266	−	24.8144i	−0.581500	−	1.00719i	−0.995302	−	0.0968200i	$-0.969133\pi$
$607$	−14.3266	−	24.8144i	−0.581500	−	1.00719i	0.413802	−	0.910367i	$-0.364200\pi$
$608$		0			0
$609$	0.714701	+	18.9701i	0.0289611	+	0.768707i
$610$		0			0
$611$	6.08711	−	10.5432i	0.246258	−	0.426531i
$612$		0			0
$613$	14.6734	+	25.4151i	0.592653	+	1.02651i	0.993873	+	0.110524i	$0.0352529\pi$
$613$	14.6734	+	25.4151i	0.592653	+	1.02651i	−0.401220	+	0.915982i	$0.631414\pi$
$614$		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
$619$	11.3565	−	19.6700i	0.456456	−	0.790605i	−0.542315	−	0.840175i	$-0.682452\pi$
$619$	11.3565	−	19.6700i	0.456456	−	0.790605i	0.998771	+	0.0495708i	$0.0157853\pi$
$620$		0			0
$621$	−12.7500	+	1.78698i	−0.511639	+	0.0717090i
$622$		0			0
$623$	−4.05128	−	4.91492i	−0.162311	−	0.196912i
$624$		0			0
$625$	−3.19498	−	5.53387i	−0.127799	−	0.221355i
$626$		0			0
$627$	−4.00640	+	1.67258i	−0.160000	+	0.0667965i
$628$		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
$633$	2.12590	+	1.62188i	0.0844968	+	0.0644639i
$634$		0			0
$635$	2.34380	+	4.05958i	0.0930107	+	0.161099i
$636$		0			0
$637$	−7.92076	+	2.72677i	−0.313832	+	0.108038i
$638$		0			0
$639$	−14.3516	−	3.76002i	−0.567741	−	0.148744i
$640$		0			0
$641$	14.2363	−	24.6580i	0.562301	−	0.973933i	−0.434995	−	0.900433i	$-0.643250\pi$
$641$	14.2363	−	24.6580i	0.562301	−	0.973933i	0.997295	−	0.0735002i	$-0.0234169\pi$
$642$		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	0.830933	−	0.556372i	$-0.187807\pi$
$647$	−1.68809	−	2.92386i	−0.0663657	−	0.114949i	−0.897299	+	0.441423i	$0.854474\pi$
$648$		0			0
$649$	0.808833	−	1.40094i	0.0317495	−	0.0549917i
$650$		0			0
$651$	−14.5273	−	7.67312i	−0.569370	−	0.300733i
$652$		0			0
$653$	9.17255	+	15.8873i	0.358950	+	0.621719i	0.987786	−	0.155819i	$-0.0498017\pi$
$653$	9.17255	+	15.8873i	0.358950	+	0.621719i	−0.628836	+	0.777538i	$0.716468\pi$
$654$		0			0
$655$	27.7477	−	48.0604i	1.08419	−	1.87787i
$656$		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
$661$	39.0141			1.51747			0.758737	−	0.651397i	$-0.225817\pi$
$661$	39.0141			1.51747			0.758737	+	0.651397i	$0.225817\pi$
$662$		0			0
$663$	−0.0662030	+	0.513909i	−0.00257111	+	0.0199586i
$664$		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
$669$	8.70051	−	3.63227i	0.336381	−	0.140432i
$670$		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
$675$	−27.6111	−	35.3681i	−1.06275	−	1.36132i
$676$		0			0
$677$	−23.3915			−0.899010			−0.449505	−	0.893278i	$-0.648400\pi$
$677$	−23.3915			−0.899010			−0.449505	+	0.893278i	$0.648400\pi$
$678$		0			0
$679$	−28.8196	+	4.82180i	−1.10600	+	0.185044i
$680$		0			0
$681$	22.1381	+	16.8895i	0.848333	+	0.647206i
$682$		0			0
$683$	15.1632	+	26.2634i	0.580204	+	1.00494i	0.995455	+	0.0952356i	$0.0303604\pi$
$683$	15.1632	+	26.2634i	0.580204	+	1.00494i	−0.415251	+	0.909707i	$0.636306\pi$
$684$		0			0
$685$	1.80380			0.0689196
$686$		0			0
$687$	15.9330	−	6.65169i	0.607884	−	0.253778i
$688$		0			0
$689$	−11.8346			−0.450863
$690$		0			0
$691$	4.11330			0.156477			0.0782387	−	0.996935i	$-0.475070\pi$
$691$	4.11330			0.156477			0.0782387	+	0.996935i	$0.475070\pi$
$692$		0			0
$693$	2.97354	+	6.43030i	0.112955	+	0.244267i
$694$		0			0
$695$	36.4448			1.38243
$696$		0			0
$697$	1.19538			0.0452784
$698$		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
$705$	60.0420	−	25.0662i	2.26131	−	0.944047i
$706$		0			0
$707$	4.37478	+	5.30738i	0.164531	+	0.199605i
$708$		0			0
$709$	−42.4617			−1.59468			−0.797342	−	0.603528i	$-0.793761\pi$
$709$	−42.4617			−1.59468			−0.797342	+	0.603528i	$0.793761\pi$
$710$		0			0
$711$	−5.22115	−	1.36790i	−0.195809	−	0.0513004i
$712$		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
$717$	−30.3282	−	23.1378i	−1.13263	−	0.864097i
$718$		0			0
$719$	5.57126	−	9.64970i	0.207773	−	0.359873i	−0.743240	−	0.669025i	$-0.766712\pi$
$719$	5.57126	−	9.64970i	0.207773	−	0.359873i	0.951013	+	0.309152i	$0.100045\pi$
$720$		0			0
$721$	−25.3421	+	4.23997i	−0.943789	+	0.157905i
$722$		0			0
$723$	23.0245	+	17.5657i	0.856290	+	0.653277i
$724$		0			0
$725$	−35.7715			−1.32852
$726$		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
$731$	1.24724	−	2.16028i	0.0461307	−	0.0799007i
$732$		0			0
$733$	12.5264	+	21.6964i	0.462674	+	0.801375i	0.999093	−	0.0425768i	$-0.0135567\pi$
$733$	12.5264	+	21.6964i	0.462674	+	0.801375i	−0.536419	+	0.843952i	$0.680223\pi$
$734$		0			0
$735$	−42.4950	−	14.0903i	−1.56745	−	0.519729i
$736$		0			0
$737$	0.459391	−	0.795689i	0.0169219	−	0.0293096i
$738$		0			0
$739$	−13.7608	−	23.8344i	−0.506198	−	0.876761i	−0.999974	−	0.00717223i	$-0.997717\pi$
$739$	−13.7608	−	23.8344i	−0.506198	−	0.876761i	0.493776	−	0.869589i	$-0.335616\pi$
$740$		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
$745$	38.8163	−	67.2318i	1.42212	−	2.46318i
$746$		0			0
$747$	9.76698	+	35.6558i	0.357355	+	1.30458i
$748$		0			0
$749$	18.3438	+	22.2543i	0.670268	+	0.813153i
$750$		0			0
$751$	−26.1297	−	45.2580i	−0.953486	−	1.65149i	−0.737795	−	0.675025i	$-0.764133\pi$
$751$	−26.1297	−	45.2580i	−0.953486	−	1.65149i	−0.215692	−	0.976461i	$-0.569201\pi$
$752$		0			0
$753$	1.88789	−	14.6550i	0.0687986	−	0.534058i
$754$		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
$759$	−0.489408	+	3.79909i	−0.0177644	+	0.137898i
$760$		0			0
$761$	8.62550	+	14.9398i	0.312674	+	0.541568i	0.978940	−	0.204146i	$-0.0654419\pi$
$761$	8.62550	+	14.9398i	0.312674	+	0.541568i	−0.666266	+	0.745714i	$0.732109\pi$
$762$		0			0
$763$	5.53713	−	0.926414i	0.200457	−	0.0335384i
$764$		0			0
$765$	−1.94722	+	1.96902i	−0.0704020	+	0.0711901i
$766$		0			0
$767$	−1.08444	+	1.87831i	−0.0391570	+	0.0678218i
$768$		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	0.723254	−	0.690582i	$-0.242646\pi$
$773$	−6.57357	−	11.3858i	−0.236435	−	0.409517i	−0.959689	+	0.281065i	$0.909312\pi$
$774$		0			0
$775$	15.4791	−	26.8106i	0.556027	−	0.963066i
$776$		0			0
$777$	−18.3555	+	11.5401i	−0.658501	+	0.414000i
$778$		0			0
$779$	−6.71439	−	11.6297i	−0.240568	−	0.416676i
$780$		0			0
$781$	−2.20702	+	3.82268i	−0.0789735	+	0.136786i
$782$		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
$787$	28.1301			1.00273			0.501364	−	0.865236i	$-0.332832\pi$
$787$	28.1301			1.00273			0.501364	+	0.865236i	$0.332832\pi$
$788$		0			0
$789$	−28.3022	−	21.5922i	−1.00758	−	0.768701i
$790$		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
$795$	−50.2860	−	38.3639i	−1.78346	−	1.36063i
$796$		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
$801$	5.07838	−	5.13523i	0.179436	−	0.181444i
$802$		0			0
$803$	1.63387			0.0576580
$804$		0			0
$805$	−15.3966	−	18.6788i	−0.542658	−	0.658340i
$806$		0			0
$807$	31.7199	−	13.2423i	1.11659	−	0.466153i
$808$		0			0
$809$	15.9353	+	27.6007i	0.560254	+	0.970388i	0.997474	+	0.0710338i	$0.0226298\pi$
$809$	15.9353	+	27.6007i	0.560254	+	0.970388i	−0.437220	+	0.899355i	$0.644037\pi$
$810$		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
$815$	24.6764			0.864375
$816$		0			0
$817$	−28.0226			−0.980385
$818$		0			0
$819$	−3.98677	−	8.62143i	−0.139309	−	0.301257i
$820$		0			0
$821$	−16.3935			−0.572139			−0.286069	−	0.958209i	$-0.592349\pi$
$821$	−16.3935			−0.572139			−0.286069	+	0.958209i	$0.592349\pi$
$822$		0			0
$823$	26.3780			0.919478			0.459739	−	0.888054i	$-0.347943\pi$
$823$	26.3780			0.919478			0.459739	+	0.888054i	$0.347943\pi$
$824$		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	0.996160	−	0.0875485i	$-0.0279033\pi$
$829$	12.1579	+	21.0581i	0.422261	+	0.731377i	−0.573899	+	0.818926i	$0.694570\pi$
$830$		0			0
$831$	−34.2630	−	26.1398i	−1.18857	−	0.906779i
$832$		0			0
$833$	−0.334004	+	1.71771i	−0.0115725	+	0.0595151i
$834$		0			0
$835$	−65.1038			−2.25301
$836$		0			0
$837$	6.98506	−	17.2698i	0.241439	−	0.596933i
$838$		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
$843$	−21.8570	+	9.12480i	−0.752794	+	0.314275i
$844$		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
$849$	−1.39900	+	10.8599i	−0.0480135	+	0.372711i
$850$		0			0
$851$	−11.7230			−0.401858
$852$		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
$857$	12.6934	−	21.9856i	0.433598	−	0.751015i	−0.563582	−	0.826060i	$-0.690577\pi$
$857$	12.6934	−	21.9856i	0.433598	−	0.751015i	0.997180	+	0.0750458i	$0.0239103\pi$
$858$		0			0
$859$	−2.97891	−	5.15963i	−0.101639	−	0.176044i	0.810721	−	0.585433i	$-0.199075\pi$
$859$	−2.97891	−	5.15963i	−0.101639	−	0.176044i	−0.912360	+	0.409388i	$0.865742\pi$
$860$		0			0
$861$	−18.5515	+	11.6633i	−0.632232	+	0.397485i
$862$		0			0
$863$	−8.19545	+	14.1949i	−0.278977	+	0.483201i	−0.971131	−	0.238548i	$-0.923328\pi$
$863$	−8.19545	+	14.1949i	−0.278977	+	0.483201i	0.692154	+	0.721750i	$0.256662\pi$
$864$		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
$871$	−0.615929	+	1.06682i	−0.0208700	+	0.0361478i
$872$		0			0
$873$	−8.75335	−	31.9554i	−0.296256	−	1.08153i
$874$		0			0
$875$	12.4384	−	33.2646i	0.420493	−	1.12455i
$876$		0			0
$877$	−17.6270	−	30.5308i	−0.595220	−	1.03095i	−0.993516	−	0.113695i	$-0.963731\pi$
$877$	−17.6270	−	30.5308i	−0.595220	−	1.03095i	0.398295	−	0.917257i	$-0.369602\pi$
$878$		0			0
$879$	3.62188	+	2.76318i	0.122163	+	0.0931998i
$880$		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
$885$	−10.6967	+	4.46564i	−0.359566	+	0.150111i
$886$		0			0
$887$	−7.95282	−	13.7747i	−0.267030	−	0.462509i	0.701064	−	0.713099i	$-0.252709\pi$
$887$	−7.95282	−	13.7747i	−0.267030	−	0.462509i	−0.968093	+	0.250590i	$0.919376\pi$
$888$		0			0
$889$	−1.17634	+	3.14595i	−0.0394531	+	0.105512i
$890$		0			0
$891$	−6.91174	+	4.09375i	−0.231552	+	0.137146i
$892$		0			0
$893$	−14.2844	+	24.7413i	−0.478009	+	0.827935i
$894$		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
$903$	1.72157	+	45.6951i	0.0572903	+	1.52064i
$904$		0			0
$905$	20.7829	+	35.9970i	0.690846	+	1.19658i
$906$		0			0
$907$	−8.54624	+	14.8025i	−0.283773	+	0.491510i	−0.972311	−	0.233691i	$-0.924920\pi$
$907$	−8.54624	+	14.8025i	−0.283773	+	0.491510i	0.688538	+	0.725201i	$0.258253\pi$
$908$		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
$913$	10.9992			0.364021
$914$		0			0
$915$	63.7664	−	26.6211i	2.10805	−	0.880065i
$916$		0			0
$917$	39.2176	−	6.56148i	1.29508	−	0.216679i
$918$		0			0
$919$	−11.8283	+	20.4873i	−0.390181	+	0.675813i	−0.992473	−	0.122462i	$-0.960921\pi$
$919$	−11.8283	+	20.4873i	−0.390181	+	0.675813i	0.602292	+	0.798276i	$0.294254\pi$
$920$		0			0
$921$	0.618519	−	4.80133i	0.0203809	−	0.158209i
$922$		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
$927$	−7.69712	−	28.0995i	−0.252807	−	0.922909i
$928$		0			0
$929$	12.6176			0.413970			0.206985	−	0.978344i	$-0.433635\pi$
$929$	12.6176			0.413970			0.206985	+	0.978344i	$0.433635\pi$
$930$		0			0
$931$	18.5873	−	6.39880i	0.609176	−	0.209712i
$932$		0			0
$933$	3.34166	−	25.9401i	0.109401	−	0.849240i
$934$		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
$941$	50.9397			1.66059			0.830294	−	0.557326i	$-0.188173\pi$
$941$	50.9397			1.66059			0.830294	+	0.557326i	$0.188173\pi$
$942$		0			0
$943$	−11.8481			−0.385827
$944$		0			0
$945$	11.0078	−	49.5567i	0.358083	−	1.61208i
$946$		0			0
$947$	−27.6798			−0.899474			−0.449737	−	0.893161i	$-0.648482\pi$
$947$	−27.6798			−0.899474			−0.449737	+	0.893161i	$0.648482\pi$
$948$		0			0
$949$	−2.19061			−0.0711102
$950$		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
$957$	−0.818252	+	6.35179i	−0.0264503	+	0.205324i
$958$		0			0
$959$	0.822054	+	0.997297i	0.0265455	+	0.0322044i
$960$		0			0
$961$	−18.1467			−0.585378
$962$		0			0
$963$	−22.9944	+	23.2518i	−0.740984	+	0.749279i
$964$		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
$969$	0.155356	−	1.20597i	0.00499075	−	0.0387413i
$970$		0			0
$971$	−19.7416	+	34.1935i	−0.633538	+	1.09732i	0.353285	+	0.935516i	$0.385065\pi$
$971$	−19.7416	+	34.1935i	−0.633538	+	1.09732i	−0.986823	+	0.161804i	$0.948269\pi$
$972$		0			0
$973$	16.6092	+	20.1499i	0.532466	+	0.645975i
$974$		0			0
$975$	16.5170	−	6.89549i	0.528968	−	0.220833i
$976$		0			0
$977$	11.9156			0.381215			0.190608	−	0.981666i	$-0.438954\pi$
$977$	11.9156			0.381215			0.190608	+	0.981666i	$0.438954\pi$
$978$		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
$983$	−9.23896	+	16.0024i	−0.294677	+	0.510396i	−0.974910	−	0.222601i	$-0.928545\pi$
$983$	−9.23896	+	16.0024i	−0.294677	+	0.510396i	0.680233	+	0.732996i	$0.261879\pi$
$984$		0			0
$985$	−28.5588	−	49.4653i	−0.909959	−	1.57609i
$986$		0			0
$987$	41.2220	+	21.7729i	1.31211	+	0.693039i
$988$		0			0
$989$	−12.3620	+	21.4117i	−0.393090	+	0.680851i
$990$		0			0
$991$	6.34850	+	10.9959i	0.201667	+	0.349297i	0.949066	−	0.315079i	$-0.102031\pi$
$991$	6.34850	+	10.9959i	0.201667	+	0.349297i	−0.747399	+	0.664376i	$0.768698\pi$
$992$		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
$997$	−20.9767	+	36.3327i	−0.664338	+	1.15067i	0.315127	+	0.949050i	$0.397953\pi$
$997$	−20.9767	+	36.3327i	−0.664338	+	1.15067i	−0.979464	+	0.201617i	$0.935380\pi$
$998$		0			0
$999$	−15.1286	−	19.3788i	−0.478648	−	0.613119i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.3	✓	10	28.11	odd	6
63.2.g.b.16.3	yes	10	36.7	odd	6
63.2.h.b.25.3	yes	10	252.151	odd	6
63.2.h.b.58.3	yes	10	4.3	odd	2
189.2.g.b.100.3		10	36.11	even	6
189.2.g.b.172.3		10	84.11	even	6
189.2.h.b.37.3		10	12.11	even	2
189.2.h.b.46.3		10	252.11	even	6
441.2.f.e.148.3		10	28.23	odd	6
441.2.f.e.295.3		10	252.79	odd	6
441.2.f.f.148.3		10	28.19	even	6
441.2.f.f.295.3		10	252.187	even	6
441.2.g.f.67.3		10	28.3	even	6
441.2.g.f.79.3		10	252.223	even	6
441.2.h.f.214.3		10	252.115	even	6
441.2.h.f.373.3		10	28.27	even	2
567.2.e.e.163.3		10	36.23	even	6
567.2.e.e.487.3		10	252.95	even	6
567.2.e.f.163.3		10	36.31	odd	6
567.2.e.f.487.3		10	252.67	odd	6
1008.2.q.i.529.3		10	63.25	even	3	inner
1008.2.q.i.625.3		10	1.1	even	1	trivial
1008.2.t.i.193.1		10	7.4	even	3
1008.2.t.i.961.1		10	9.7	even	3
1323.2.f.e.442.3		10	84.23	even	6
1323.2.f.e.883.3		10	252.191	even	6
1323.2.f.f.442.3		10	84.47	odd	6
1323.2.f.f.883.3		10	252.47	odd	6
1323.2.g.f.361.3		10	84.59	odd	6
1323.2.g.f.667.3		10	252.83	odd	6
1323.2.h.f.226.3		10	84.83	odd	2
1323.2.h.f.802.3		10	252.227	odd	6
3024.2.q.i.2305.1		10	3.2	odd	2
3024.2.q.i.2881.1		10	63.11	odd	6
3024.2.t.i.289.5		10	9.2	odd	6
3024.2.t.i.1873.5		10	21.11	odd	6
3969.2.a.z.1.3		5	252.247	odd	6
3969.2.a.ba.1.3		5	252.103	even	6
3969.2.a.bb.1.3		5	252.131	odd	6
3969.2.a.bc.1.3		5	252.23	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.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.221298 - 1.71786i) q^{3} +(1.84629 + 3.19787i) q^{5} +(-0.926641 + 2.47817i) q^{7} +(-2.90205 - 0.760316i) q^{9} +O(q^{10})\)	\(q+(0.221298 - 1.71786i) q^{3} +(1.84629 + 3.19787i) q^{5} +(-0.926641 + 2.47817i) q^{7} +(-2.90205 - 0.760316i) q^{9} +(-0.446284 + 0.772987i) q^{11} +(0.598355 - 1.03638i) q^{13} +(5.90205 - 2.46398i) q^{15} +(-0.124991 - 0.216492i) q^{17} +(-1.40414 + 2.43204i) q^{19} +(4.05208 + 2.14025i) q^{21} +(1.23886 + 2.14576i) q^{23} +(-4.31757 + 7.47825i) q^{25} +(-1.94833 + 4.81705i) q^{27} +(2.07128 + 3.58755i) q^{29} -3.58515 q^{31} +(1.22912 + 0.937712i) q^{33} +(-9.63571 + 1.61215i) q^{35} +(-2.36568 + 4.09747i) q^{37} +(-1.64794 - 1.25724i) q^{39} +(-2.39093 + 4.14121i) q^{41} +(4.98928 + 8.64169i) q^{43} +(-2.92664 - 10.6841i) q^{45} +10.1731 q^{47} +(-5.28267 - 4.59275i) q^{49} +(-0.399562 + 0.166808i) q^{51} +(-4.94465 - 8.56438i) q^{53} -3.29588 q^{55} +(3.86715 + 2.95031i) q^{57} -1.81237 q^{59} +10.8041 q^{61} +(4.57336 - 6.48725i) q^{63} +4.41895 q^{65} -1.02937 q^{67} +(3.96027 - 1.65332i) q^{69} +4.94533 q^{71} +(-0.915262 - 1.58528i) q^{73} +(11.8911 + 9.07189i) q^{75} +(-1.50205 - 1.82225i) q^{77} +1.79912 q^{79} +(7.84384 + 4.41296i) q^{81} +(-6.16156 - 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +(6.62127 - 2.76423i) q^{87} +(-1.20370 + 2.08488i) q^{89} +(2.01387 + 2.44318i) q^{91} +(-0.793387 + 6.15877i) q^{93} -10.3698 q^{95} +(5.52210 + 9.56456i) q^{97} +(1.88286 - 1.90393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 4 q^{5} + 4 q^{7} + 11 q^{9}+O(q^{10}) \) 10 * q + q^3 + 4 * q^5 + 4 * q^7 + 11 * q^9	\( 10 q + q^{3} + 4 q^{5} + 4 q^{7} + 11 q^{9} - 4 q^{11} - 8 q^{13} + 19 q^{15} + 12 q^{17} - q^{19} + 13 q^{21} - 3 q^{23} - q^{25} + 7 q^{27} + 7 q^{29} - 6 q^{31} + 14 q^{33} - 5 q^{35} - 2 q^{39} + 5 q^{41} + 7 q^{43} - 16 q^{45} + 54 q^{47} - 8 q^{49} + 9 q^{51} - 21 q^{53} - 4 q^{55} - 4 q^{57} + 60 q^{59} + 28 q^{61} + 59 q^{63} + 22 q^{65} - 4 q^{67} + 15 q^{69} + 6 q^{71} + 15 q^{73} + 14 q^{75} + 11 q^{77} - 8 q^{79} + 23 q^{81} - 9 q^{83} - 6 q^{85} - 2 q^{87} + 28 q^{89} + 4 q^{91} - 6 q^{93} - 28 q^{95} - 12 q^{97} - 35 q^{99}+O(q^{100}) \) 10 * q + q^3 + 4 * q^5 + 4 * q^7 + 11 * q^9 - 4 * q^11 - 8 * q^13 + 19 * q^15 + 12 * q^17 - q^19 + 13 * q^21 - 3 * q^23 - q^25 + 7 * q^27 + 7 * q^29 - 6 * q^31 + 14 * q^33 - 5 * q^35 - 2 * q^39 + 5 * q^41 + 7 * q^43 - 16 * q^45 + 54 * q^47 - 8 * q^49 + 9 * q^51 - 21 * q^53 - 4 * q^55 - 4 * q^57 + 60 * q^59 + 28 * q^61 + 59 * q^63 + 22 * q^65 - 4 * q^67 + 15 * q^69 + 6 * q^71 + 15 * q^73 + 14 * q^75 + 11 * q^77 - 8 * q^79 + 23 * q^81 - 9 * q^83 - 6 * q^85 - 2 * q^87 + 28 * q^89 + 4 * q^91 - 6 * q^93 - 28 * q^95 - 12 * q^97 - 35 * q^99

Introduction

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