LMFDB - Embedded newform 650.2.g.d.57.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(57,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("650.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.g (of order $4$, degree $2$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			57.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	650.57
Dual form			650.2.g.d.593.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +2.00000i q^{7} +1.00000 q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +2.00000i q^{7} +1.00000 q^{8} +3.00000i q^{9} +(1.00000 + 1.00000i) q^{11} +(2.00000 - 3.00000i) q^{13} +2.00000i q^{14} +1.00000 q^{16} +(-2.00000 + 2.00000i) q^{17} +3.00000i q^{18} +(3.00000 + 3.00000i) q^{19} +(1.00000 + 1.00000i) q^{22} +(-1.00000 - 1.00000i) q^{23} +(2.00000 - 3.00000i) q^{26} +2.00000i q^{28} +6.00000i q^{29} +(6.00000 - 6.00000i) q^{31} +1.00000 q^{32} +(-2.00000 + 2.00000i) q^{34} +3.00000i q^{36} +2.00000i q^{37} +(3.00000 + 3.00000i) q^{38} +(1.00000 - 1.00000i) q^{41} +(-6.00000 - 6.00000i) q^{43} +(1.00000 + 1.00000i) q^{44} +(-1.00000 - 1.00000i) q^{46} -8.00000i q^{47} +3.00000 q^{49} +(2.00000 - 3.00000i) q^{52} +(5.00000 - 5.00000i) q^{53} +2.00000i q^{56} +6.00000i q^{58} +(-3.00000 + 3.00000i) q^{59} +2.00000 q^{61} +(6.00000 - 6.00000i) q^{62} -6.00000 q^{63} +1.00000 q^{64} -12.0000 q^{67} +(-2.00000 + 2.00000i) q^{68} +(-4.00000 + 4.00000i) q^{71} +3.00000i q^{72} -6.00000 q^{73} +2.00000i q^{74} +(3.00000 + 3.00000i) q^{76} +(-2.00000 + 2.00000i) q^{77} -4.00000i q^{79} -9.00000 q^{81} +(1.00000 - 1.00000i) q^{82} +4.00000i q^{83} +(-6.00000 - 6.00000i) q^{86} +(1.00000 + 1.00000i) q^{88} +(7.00000 - 7.00000i) q^{89} +(6.00000 + 4.00000i) q^{91} +(-1.00000 - 1.00000i) q^{92} -8.00000i q^{94} -2.00000 q^{97} +3.00000 q^{98} +(-3.00000 + 3.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} + 2 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^8	$ 2 q + 2 q^{2} + 2 q^{4} + 2 q^{8} + 2 q^{11} + 4 q^{13} + 2 q^{16} - 4 q^{17} + 6 q^{19} + 2 q^{22} - 2 q^{23} + 4 q^{26} + 12 q^{31} + 2 q^{32} - 4 q^{34} + 6 q^{38} + 2 q^{41} - 12 q^{43} + 2 q^{44} - 2 q^{46} + 6 q^{49} + 4 q^{52} + 10 q^{53} - 6 q^{59} + 4 q^{61} + 12 q^{62} - 12 q^{63} + 2 q^{64} - 24 q^{67} - 4 q^{68} - 8 q^{71} - 12 q^{73} + 6 q^{76} - 4 q^{77} - 18 q^{81} + 2 q^{82} - 12 q^{86} + 2 q^{88} + 14 q^{89} + 12 q^{91} - 2 q^{92} - 4 q^{97} + 6 q^{98} - 6 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^8 + 2 * q^11 + 4 * q^13 + 2 * q^16 - 4 * q^17 + 6 * q^19 + 2 * q^22 - 2 * q^23 + 4 * q^26 + 12 * q^31 + 2 * q^32 - 4 * q^34 + 6 * q^38 + 2 * q^41 - 12 * q^43 + 2 * q^44 - 2 * q^46 + 6 * q^49 + 4 * q^52 + 10 * q^53 - 6 * q^59 + 4 * q^61 + 12 * q^62 - 12 * q^63 + 2 * q^64 - 24 * q^67 - 4 * q^68 - 8 * q^71 - 12 * q^73 + 6 * q^76 - 4 * q^77 - 18 * q^81 + 2 * q^82 - 12 * q^86 + 2 * q^88 + 14 * q^89 + 12 * q^91 - 2 * q^92 - 4 * q^97 + 6 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$3$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$		0			0
$7$			2.00000i			0.755929i	0.925820	+	0.377964i	$0.123376\pi$
$7$			2.00000i			0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$	1.00000			0.353553
$9$			3.00000i			1.00000i
$10$		0			0
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	0.841605	−	0.540094i	$-0.181611\pi$
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	−0.540094	+	0.841605i	$0.681611\pi$
$12$		0			0
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$14$			2.00000i			0.534522i
$15$		0			0
$16$	1.00000			0.250000
$17$	−2.00000	+	2.00000i	−0.485071	+	0.485071i	−0.906747	−	0.421676i	$-0.861442\pi$
$17$	−2.00000	+	2.00000i	−0.485071	+	0.485071i	0.421676	+	0.906747i	$0.361442\pi$
$18$			3.00000i			0.707107i
$19$	3.00000	+	3.00000i	0.688247	+	0.688247i	0.961844	−	0.273597i	$-0.0882135\pi$
$19$	3.00000	+	3.00000i	0.688247	+	0.688247i	−0.273597	+	0.961844i	$0.588214\pi$
$20$		0			0
$21$		0			0
$22$	1.00000	+	1.00000i	0.213201	+	0.213201i
$23$	−1.00000	−	1.00000i	−0.208514	−	0.208514i	0.595121	−	0.803636i	$-0.297104\pi$
$23$	−1.00000	−	1.00000i	−0.208514	−	0.208514i	−0.803636	+	0.595121i	$0.797104\pi$
$24$		0			0
$25$		0			0
$26$	2.00000	−	3.00000i	0.392232	−	0.588348i
$27$		0			0
$28$			2.00000i			0.377964i
$29$			6.00000i			1.11417i	0.830455	+	0.557086i	$0.188081\pi$
$29$			6.00000i			1.11417i	−0.830455	+	0.557086i	$0.811919\pi$
$30$		0			0
$31$	6.00000	−	6.00000i	1.07763	−	1.07763i	0.0809104	−	0.996721i	$-0.474217\pi$
$31$	6.00000	−	6.00000i	1.07763	−	1.07763i	0.996721	−	0.0809104i	$-0.0257828\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−2.00000	+	2.00000i	−0.342997	+	0.342997i
$35$		0			0
$36$			3.00000i			0.500000i
$37$			2.00000i			0.328798i	0.986394	+	0.164399i	$0.0525685\pi$
$37$			2.00000i			0.328798i	−0.986394	+	0.164399i	$0.947432\pi$
$38$	3.00000	+	3.00000i	0.486664	+	0.486664i
$39$		0			0
$40$		0			0
$41$	1.00000	−	1.00000i	0.156174	−	0.156174i	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	1.00000	−	1.00000i	0.156174	−	0.156174i	0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$	−6.00000	−	6.00000i	−0.914991	−	0.914991i	0.0816682	−	0.996660i	$-0.473975\pi$
$43$	−6.00000	−	6.00000i	−0.914991	−	0.914991i	−0.996660	+	0.0816682i	$0.973975\pi$
$44$	1.00000	+	1.00000i	0.150756	+	0.150756i
$45$		0			0
$46$	−1.00000	−	1.00000i	−0.147442	−	0.147442i
$47$		−	8.00000i		−	1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$		−	8.00000i		−	1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$		0			0
$49$	3.00000			0.428571
$50$		0			0
$51$		0			0
$52$	2.00000	−	3.00000i	0.277350	−	0.416025i
$53$	5.00000	−	5.00000i	0.686803	−	0.686803i	−0.274721	−	0.961524i	$-0.588586\pi$
$53$	5.00000	−	5.00000i	0.686803	−	0.686803i	0.961524	+	0.274721i	$0.0885855\pi$
$54$		0			0
$55$		0			0
$56$			2.00000i			0.267261i
$57$		0			0
$58$			6.00000i			0.787839i
$59$	−3.00000	+	3.00000i	−0.390567	+	0.390567i	−0.874889	−	0.484323i	$-0.839066\pi$
$59$	−3.00000	+	3.00000i	−0.390567	+	0.390567i	0.484323	+	0.874889i	$0.339066\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$	6.00000	−	6.00000i	0.762001	−	0.762001i
$63$	−6.00000			−0.755929
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$	−2.00000	+	2.00000i	−0.242536	+	0.242536i
$69$		0			0
$70$		0			0
$71$	−4.00000	+	4.00000i	−0.474713	+	0.474713i	−0.903436	−	0.428723i	$-0.858964\pi$
$71$	−4.00000	+	4.00000i	−0.474713	+	0.474713i	0.428723	+	0.903436i	$0.358964\pi$
$72$			3.00000i			0.353553i
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$			2.00000i			0.232495i
$75$		0			0
$76$	3.00000	+	3.00000i	0.344124	+	0.344124i
$77$	−2.00000	+	2.00000i	−0.227921	+	0.227921i
$78$		0			0
$79$		−	4.00000i		−	0.450035i	−0.974355	−	0.225018i	$-0.927756\pi$
$79$		−	4.00000i		−	0.450035i	0.974355	−	0.225018i	$-0.0722440\pi$
$80$		0			0
$81$	−9.00000			−1.00000
$82$	1.00000	−	1.00000i	0.110432	−	0.110432i
$83$			4.00000i			0.439057i	0.975606	+	0.219529i	$0.0704519\pi$
$83$			4.00000i			0.439057i	−0.975606	+	0.219529i	$0.929548\pi$
$84$		0			0
$85$		0			0
$86$	−6.00000	−	6.00000i	−0.646997	−	0.646997i
$87$		0			0
$88$	1.00000	+	1.00000i	0.106600	+	0.106600i
$89$	7.00000	−	7.00000i	0.741999	−	0.741999i	−0.230964	−	0.972962i	$-0.574188\pi$
$89$	7.00000	−	7.00000i	0.741999	−	0.741999i	0.972962	+	0.230964i	$0.0741879\pi$
$90$		0			0
$91$	6.00000	+	4.00000i	0.628971	+	0.419314i
$92$	−1.00000	−	1.00000i	−0.104257	−	0.104257i
$93$		0			0
$94$		−	8.00000i		−	0.825137i
$95$		0			0
$96$		0			0
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$	3.00000			0.303046
$99$	−3.00000	+	3.00000i	−0.301511	+	0.301511i
$100$		0			0
$101$			10.0000i			0.995037i	0.867453	+	0.497519i	$0.165755\pi$
$101$			10.0000i			0.995037i	−0.867453	+	0.497519i	$0.834245\pi$
$102$		0			0
$103$	−1.00000	−	1.00000i	−0.0985329	−	0.0985329i	0.656122	−	0.754655i	$-0.272196\pi$
$103$	−1.00000	−	1.00000i	−0.0985329	−	0.0985329i	−0.754655	+	0.656122i	$0.772196\pi$
$104$	2.00000	−	3.00000i	0.196116	−	0.294174i
$105$		0			0
$106$	5.00000	−	5.00000i	0.485643	−	0.485643i
$107$	−10.0000	−	10.0000i	−0.966736	−	0.966736i	0.0327278	−	0.999464i	$-0.489581\pi$
$107$	−10.0000	−	10.0000i	−0.966736	−	0.966736i	−0.999464	+	0.0327278i	$0.989581\pi$
$108$		0			0
$109$	−12.0000	−	12.0000i	−1.14939	−	1.14939i	−0.986672	−	0.162719i	$-0.947974\pi$
$109$	−12.0000	−	12.0000i	−1.14939	−	1.14939i	−0.162719	−	0.986672i	$-0.552026\pi$
$110$		0			0
$111$		0			0
$112$			2.00000i			0.188982i
$113$	10.0000	−	10.0000i	0.940721	−	0.940721i	−0.0576178	−	0.998339i	$-0.518350\pi$
$113$	10.0000	−	10.0000i	0.940721	−	0.940721i	0.998339	+	0.0576178i	$0.0183505\pi$
$114$		0			0
$115$		0			0
$116$			6.00000i			0.557086i
$117$	9.00000	+	6.00000i	0.832050	+	0.554700i
$118$	−3.00000	+	3.00000i	−0.276172	+	0.276172i
$119$	−4.00000	−	4.00000i	−0.366679	−	0.366679i
$120$		0			0
$121$		−	9.00000i		−	0.818182i
$122$	2.00000			0.181071
$123$		0			0
$124$	6.00000	−	6.00000i	0.538816	−	0.538816i
$125$		0			0
$126$	−6.00000			−0.534522
$127$	13.0000	−	13.0000i	1.15356	−	1.15356i	0.167731	−	0.985833i	$-0.446356\pi$
$127$	13.0000	−	13.0000i	1.15356	−	1.15356i	0.985833	−	0.167731i	$-0.0536439\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$		0			0
$131$	−18.0000			−1.57267			−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000			−1.57267			−0.786334	+	0.617802i	$0.788023\pi$
$132$		0			0
$133$	−6.00000	+	6.00000i	−0.520266	+	0.520266i
$134$	−12.0000			−1.03664
$135$		0			0
$136$	−2.00000	+	2.00000i	−0.171499	+	0.171499i
$137$			22.0000i			1.87959i	0.341743	+	0.939793i	$0.388983\pi$
$137$			22.0000i			1.87959i	−0.341743	+	0.939793i	$0.611017\pi$
$138$		0			0
$139$		−	14.0000i		−	1.18746i	−0.804663	−	0.593732i	$-0.797654\pi$
$139$		−	14.0000i		−	1.18746i	0.804663	−	0.593732i	$-0.202346\pi$
$140$		0			0
$141$		0			0
$142$	−4.00000	+	4.00000i	−0.335673	+	0.335673i
$143$	5.00000	−	1.00000i	0.418121	−	0.0836242i
$144$			3.00000i			0.250000i
$145$		0			0
$146$	−6.00000			−0.496564
$147$		0			0
$148$			2.00000i			0.164399i
$149$	−2.00000	−	2.00000i	−0.163846	−	0.163846i	0.620422	−	0.784268i	$-0.286961\pi$
$149$	−2.00000	−	2.00000i	−0.163846	−	0.163846i	−0.784268	+	0.620422i	$0.786961\pi$
$150$		0			0
$151$	−4.00000	−	4.00000i	−0.325515	−	0.325515i	0.525363	−	0.850878i	$-0.323930\pi$
$151$	−4.00000	−	4.00000i	−0.325515	−	0.325515i	−0.850878	+	0.525363i	$0.823930\pi$
$152$	3.00000	+	3.00000i	0.243332	+	0.243332i
$153$	−6.00000	−	6.00000i	−0.485071	−	0.485071i
$154$	−2.00000	+	2.00000i	−0.161165	+	0.161165i
$155$		0			0
$156$		0			0
$157$	15.0000	+	15.0000i	1.19713	+	1.19713i	0.975022	+	0.222108i	$0.0712939\pi$
$157$	15.0000	+	15.0000i	1.19713	+	1.19713i	0.222108	+	0.975022i	$0.428706\pi$
$158$		−	4.00000i		−	0.318223i
$159$		0			0
$160$		0			0
$161$	2.00000	−	2.00000i	0.157622	−	0.157622i
$162$	−9.00000			−0.707107
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$	1.00000	−	1.00000i	0.0780869	−	0.0780869i
$165$		0			0
$166$			4.00000i			0.310460i
$167$		−	8.00000i		−	0.619059i	−0.950890	−	0.309529i	$-0.899829\pi$
$167$		−	8.00000i		−	0.619059i	0.950890	−	0.309529i	$-0.100171\pi$
$168$		0			0
$169$	−5.00000	−	12.0000i	−0.384615	−	0.923077i
$170$		0			0
$171$	−9.00000	+	9.00000i	−0.688247	+	0.688247i
$172$	−6.00000	−	6.00000i	−0.457496	−	0.457496i
$173$	9.00000	+	9.00000i	0.684257	+	0.684257i	0.960957	−	0.276699i	$-0.0892406\pi$
$173$	9.00000	+	9.00000i	0.684257	+	0.684257i	−0.276699	+	0.960957i	$0.589241\pi$
$174$		0			0
$175$		0			0
$176$	1.00000	+	1.00000i	0.0753778	+	0.0753778i
$177$		0			0
$178$	7.00000	−	7.00000i	0.524672	−	0.524672i
$179$	10.0000			0.747435			0.373718	−	0.927543i	$-0.378083\pi$
$179$	10.0000			0.747435			0.373718	+	0.927543i	$0.378083\pi$
$180$		0			0
$181$		−	10.0000i		−	0.743294i	−0.928374	−	0.371647i	$-0.878793\pi$
$181$		−	10.0000i		−	0.743294i	0.928374	−	0.371647i	$-0.121207\pi$
$182$	6.00000	+	4.00000i	0.444750	+	0.296500i
$183$		0			0
$184$	−1.00000	−	1.00000i	−0.0737210	−	0.0737210i
$185$		0			0
$186$		0			0
$187$	−4.00000			−0.292509
$188$		−	8.00000i		−	0.583460i
$189$		0			0
$190$		0			0
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$		0			0
$193$	14.0000			1.00774			0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000			1.00774			0.503871	+	0.863779i	$0.331909\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$	3.00000			0.214286
$197$	−22.0000			−1.56744			−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000			−1.56744			−0.783718	+	0.621117i	$0.786679\pi$
$198$	−3.00000	+	3.00000i	−0.213201	+	0.213201i
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$		0			0
$201$		0			0
$202$			10.0000i			0.703598i
$203$	−12.0000			−0.842235
$204$		0			0
$205$		0			0
$206$	−1.00000	−	1.00000i	−0.0696733	−	0.0696733i
$207$	3.00000	−	3.00000i	0.208514	−	0.208514i
$208$	2.00000	−	3.00000i	0.138675	−	0.208013i
$209$			6.00000i			0.415029i
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$	5.00000	−	5.00000i	0.343401	−	0.343401i
$213$		0			0
$214$	−10.0000	−	10.0000i	−0.683586	−	0.683586i
$215$		0			0
$216$		0			0
$217$	12.0000	+	12.0000i	0.814613	+	0.814613i
$218$	−12.0000	−	12.0000i	−0.812743	−	0.812743i
$219$		0			0
$220$		0			0
$221$	2.00000	+	10.0000i	0.134535	+	0.672673i
$222$		0			0
$223$			24.0000i			1.60716i	0.595198	+	0.803579i	$0.297074\pi$
$223$			24.0000i			1.60716i	−0.595198	+	0.803579i	$0.702926\pi$
$224$			2.00000i			0.133631i
$225$		0			0
$226$	10.0000	−	10.0000i	0.665190	−	0.665190i
$227$	−12.0000			−0.796468			−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000			−0.796468			−0.398234	+	0.917284i	$0.630377\pi$
$228$		0			0
$229$	2.00000	−	2.00000i	0.132164	−	0.132164i	−0.637930	−	0.770094i	$-0.720209\pi$
$229$	2.00000	−	2.00000i	0.132164	−	0.132164i	0.770094	+	0.637930i	$0.220209\pi$
$230$		0			0
$231$		0			0
$232$			6.00000i			0.393919i
$233$	14.0000	+	14.0000i	0.917170	+	0.917170i	0.996823	−	0.0796522i	$-0.0253810\pi$
$233$	14.0000	+	14.0000i	0.917170	+	0.917170i	−0.0796522	+	0.996823i	$0.525381\pi$
$234$	9.00000	+	6.00000i	0.588348	+	0.392232i
$235$		0			0
$236$	−3.00000	+	3.00000i	−0.195283	+	0.195283i
$237$		0			0
$238$	−4.00000	−	4.00000i	−0.259281	−	0.259281i
$239$	−2.00000	−	2.00000i	−0.129369	−	0.129369i	0.639457	−	0.768827i	$-0.279159\pi$
$239$	−2.00000	−	2.00000i	−0.129369	−	0.129369i	−0.768827	+	0.639457i	$0.779159\pi$
$240$		0			0
$241$	21.0000	+	21.0000i	1.35273	+	1.35273i	0.882595	+	0.470134i	$0.155794\pi$
$241$	21.0000	+	21.0000i	1.35273	+	1.35273i	0.470134	+	0.882595i	$0.344206\pi$
$242$		−	9.00000i		−	0.578542i
$243$		0			0
$244$	2.00000			0.128037
$245$		0			0
$246$		0			0
$247$	15.0000	−	3.00000i	0.954427	−	0.190885i
$248$	6.00000	−	6.00000i	0.381000	−	0.381000i
$249$		0			0
$250$		0			0
$251$		−	20.0000i		−	1.26239i	−0.775625	−	0.631194i	$-0.782565\pi$
$251$		−	20.0000i		−	1.26239i	0.775625	−	0.631194i	$-0.217435\pi$
$252$	−6.00000			−0.377964
$253$		−	2.00000i		−	0.125739i
$254$	13.0000	−	13.0000i	0.815693	−	0.815693i
$255$		0			0
$256$	1.00000			0.0625000
$257$	18.0000	−	18.0000i	1.12281	−	1.12281i	0.131492	−	0.991317i	$-0.458023\pi$
$257$	18.0000	−	18.0000i	1.12281	−	1.12281i	0.991317	−	0.131492i	$-0.0419767\pi$
$258$		0			0
$259$	−4.00000			−0.248548
$260$		0			0
$261$	−18.0000			−1.11417
$262$	−18.0000			−1.11204
$263$	−15.0000	+	15.0000i	−0.924940	+	0.924940i	−0.997373	−	0.0724336i	$-0.976923\pi$
$263$	−15.0000	+	15.0000i	−0.924940	+	0.924940i	0.0724336	+	0.997373i	$0.476923\pi$
$264$		0			0
$265$		0			0
$266$	−6.00000	+	6.00000i	−0.367884	+	0.367884i
$267$		0			0
$268$	−12.0000			−0.733017
$269$			26.0000i			1.58525i	0.609711	+	0.792624i	$0.291286\pi$
$269$			26.0000i			1.58525i	−0.609711	+	0.792624i	$0.708714\pi$
$270$		0			0
$271$	16.0000	+	16.0000i	0.971931	+	0.971931i	0.999617	−	0.0276859i	$-0.00881382\pi$
$271$	16.0000	+	16.0000i	0.971931	+	0.971931i	−0.0276859	+	0.999617i	$0.508814\pi$
$272$	−2.00000	+	2.00000i	−0.121268	+	0.121268i
$273$		0			0
$274$			22.0000i			1.32907i
$275$		0			0
$276$		0			0
$277$	13.0000	−	13.0000i	0.781094	−	0.781094i	−0.198921	−	0.980015i	$-0.563744\pi$
$277$	13.0000	−	13.0000i	0.781094	−	0.781094i	0.980015	+	0.198921i	$0.0637438\pi$
$278$		−	14.0000i		−	0.839664i
$279$	18.0000	+	18.0000i	1.07763	+	1.07763i
$280$		0			0
$281$	−9.00000	−	9.00000i	−0.536895	−	0.536895i	0.385721	−	0.922616i	$-0.373953\pi$
$281$	−9.00000	−	9.00000i	−0.536895	−	0.536895i	−0.922616	+	0.385721i	$0.873953\pi$
$282$		0			0
$283$	−16.0000	−	16.0000i	−0.951101	−	0.951101i	0.0477577	−	0.998859i	$-0.484792\pi$
$283$	−16.0000	−	16.0000i	−0.951101	−	0.951101i	−0.998859	+	0.0477577i	$0.984792\pi$
$284$	−4.00000	+	4.00000i	−0.237356	+	0.237356i
$285$		0			0
$286$	5.00000	−	1.00000i	0.295656	−	0.0591312i
$287$	2.00000	+	2.00000i	0.118056	+	0.118056i
$288$			3.00000i			0.176777i
$289$			9.00000i			0.529412i
$290$		0			0
$291$		0			0
$292$	−6.00000			−0.351123
$293$	24.0000			1.40209			0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000			1.40209			0.701047	+	0.713115i	$0.252716\pi$
$294$		0			0
$295$		0			0
$296$			2.00000i			0.116248i
$297$		0			0
$298$	−2.00000	−	2.00000i	−0.115857	−	0.115857i
$299$	−5.00000	+	1.00000i	−0.289157	+	0.0578315i
$300$		0			0
$301$	12.0000	−	12.0000i	0.691669	−	0.691669i
$302$	−4.00000	−	4.00000i	−0.230174	−	0.230174i
$303$		0			0
$304$	3.00000	+	3.00000i	0.172062	+	0.172062i
$305$		0			0
$306$	−6.00000	−	6.00000i	−0.342997	−	0.342997i
$307$		−	28.0000i		−	1.59804i	−0.601302	−	0.799022i	$-0.705351\pi$
$307$		−	28.0000i		−	1.59804i	0.601302	−	0.799022i	$-0.294649\pi$
$308$	−2.00000	+	2.00000i	−0.113961	+	0.113961i
$309$		0			0
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$		0			0
$313$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$313$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$314$	15.0000	+	15.0000i	0.846499	+	0.846499i
$315$		0			0
$316$		−	4.00000i		−	0.225018i
$317$	−12.0000			−0.673987			−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000			−0.673987			−0.336994	+	0.941507i	$0.609410\pi$
$318$		0			0
$319$	−6.00000	+	6.00000i	−0.335936	+	0.335936i
$320$		0			0
$321$		0			0
$322$	2.00000	−	2.00000i	0.111456	−	0.111456i
$323$	−12.0000			−0.667698
$324$	−9.00000			−0.500000
$325$		0			0
$326$	4.00000			0.221540
$327$		0			0
$328$	1.00000	−	1.00000i	0.0552158	−	0.0552158i
$329$	16.0000			0.882109
$330$		0			0
$331$	21.0000	−	21.0000i	1.15426	−	1.15426i	0.168576	−	0.985689i	$-0.446083\pi$
$331$	21.0000	−	21.0000i	1.15426	−	1.15426i	0.985689	−	0.168576i	$-0.0539168\pi$
$332$			4.00000i			0.219529i
$333$	−6.00000			−0.328798
$334$		−	8.00000i		−	0.437741i
$335$		0			0
$336$		0			0
$337$	−12.0000	+	12.0000i	−0.653682	+	0.653682i	−0.953878	−	0.300196i	$-0.902948\pi$
$337$	−12.0000	+	12.0000i	−0.653682	+	0.653682i	0.300196	+	0.953878i	$0.402948\pi$
$338$	−5.00000	−	12.0000i	−0.271964	−	0.652714i
$339$		0			0
$340$		0			0
$341$	12.0000			0.649836
$342$	−9.00000	+	9.00000i	−0.486664	+	0.486664i
$343$			20.0000i			1.07990i
$344$	−6.00000	−	6.00000i	−0.323498	−	0.323498i
$345$		0			0
$346$	9.00000	+	9.00000i	0.483843	+	0.483843i
$347$	10.0000	+	10.0000i	0.536828	+	0.536828i	0.922596	−	0.385768i	$-0.126063\pi$
$347$	10.0000	+	10.0000i	0.536828	+	0.536828i	−0.385768	+	0.922596i	$0.626063\pi$
$348$		0			0
$349$	−8.00000	+	8.00000i	−0.428230	+	0.428230i	−0.888025	−	0.459795i	$-0.847923\pi$
$349$	−8.00000	+	8.00000i	−0.428230	+	0.428230i	0.459795	+	0.888025i	$0.347923\pi$
$350$		0			0
$351$		0			0
$352$	1.00000	+	1.00000i	0.0533002	+	0.0533002i
$353$			14.0000i			0.745145i	0.928003	+	0.372572i	$0.121524\pi$
$353$			14.0000i			0.745145i	−0.928003	+	0.372572i	$0.878476\pi$
$354$		0			0
$355$		0			0
$356$	7.00000	−	7.00000i	0.370999	−	0.370999i
$357$		0			0
$358$	10.0000			0.528516
$359$	−18.0000	+	18.0000i	−0.950004	+	0.950004i	−0.998808	−	0.0488047i	$-0.984459\pi$
$359$	−18.0000	+	18.0000i	−0.950004	+	0.950004i	0.0488047	+	0.998808i	$0.484459\pi$
$360$		0			0
$361$		−	1.00000i		−	0.0526316i
$362$		−	10.0000i		−	0.525588i
$363$		0			0
$364$	6.00000	+	4.00000i	0.314485	+	0.209657i
$365$		0			0
$366$		0			0
$367$	−25.0000	−	25.0000i	−1.30499	−	1.30499i	−0.924984	−	0.380005i	$-0.875922\pi$
$367$	−25.0000	−	25.0000i	−1.30499	−	1.30499i	−0.380005	−	0.924984i	$-0.624078\pi$
$368$	−1.00000	−	1.00000i	−0.0521286	−	0.0521286i
$369$	3.00000	+	3.00000i	0.156174	+	0.156174i
$370$		0			0
$371$	10.0000	+	10.0000i	0.519174	+	0.519174i
$372$		0			0
$373$	5.00000	−	5.00000i	0.258890	−	0.258890i	−0.565712	−	0.824603i	$-0.691399\pi$
$373$	5.00000	−	5.00000i	0.258890	−	0.258890i	0.824603	+	0.565712i	$0.191399\pi$
$374$	−4.00000			−0.206835
$375$		0			0
$376$		−	8.00000i		−	0.412568i
$377$	18.0000	+	12.0000i	0.927047	+	0.618031i
$378$		0			0
$379$	3.00000	+	3.00000i	0.154100	+	0.154100i	0.779946	−	0.625847i	$-0.215246\pi$
$379$	3.00000	+	3.00000i	0.154100	+	0.154100i	−0.625847	+	0.779946i	$0.715246\pi$
$380$		0			0
$381$		0			0
$382$	−8.00000			−0.409316
$383$			34.0000i			1.73732i	0.495410	+	0.868659i	$0.335018\pi$
$383$			34.0000i			1.73732i	−0.495410	+	0.868659i	$0.664982\pi$
$384$		0			0
$385$		0			0
$386$	14.0000			0.712581
$387$	18.0000	−	18.0000i	0.914991	−	0.914991i
$388$	−2.00000			−0.101535
$389$	30.0000			1.52106			0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000			1.52106			0.760530	+	0.649303i	$0.224939\pi$
$390$		0			0
$391$	4.00000			0.202289
$392$	3.00000			0.151523
$393$		0			0
$394$	−22.0000			−1.10834
$395$		0			0
$396$	−3.00000	+	3.00000i	−0.150756	+	0.150756i
$397$			32.0000i			1.60603i	0.595956	+	0.803017i	$0.296773\pi$
$397$			32.0000i			1.60603i	−0.595956	+	0.803017i	$0.703227\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−19.0000	−	19.0000i	−0.948815	−	0.948815i	0.0499376	−	0.998752i	$-0.484098\pi$
$401$	−19.0000	−	19.0000i	−0.948815	−	0.948815i	−0.998752	+	0.0499376i	$0.984098\pi$
$402$		0			0
$403$	−6.00000	−	30.0000i	−0.298881	−	1.49441i
$404$			10.0000i			0.497519i
$405$		0			0
$406$	−12.0000			−0.595550
$407$	−2.00000	+	2.00000i	−0.0991363	+	0.0991363i
$408$		0			0
$409$	3.00000	+	3.00000i	0.148340	+	0.148340i	0.777376	−	0.629036i	$-0.216550\pi$
$409$	3.00000	+	3.00000i	0.148340	+	0.148340i	−0.629036	+	0.777376i	$0.716550\pi$
$410$		0			0
$411$		0			0
$412$	−1.00000	−	1.00000i	−0.0492665	−	0.0492665i
$413$	−6.00000	−	6.00000i	−0.295241	−	0.295241i
$414$	3.00000	−	3.00000i	0.147442	−	0.147442i
$415$		0			0
$416$	2.00000	−	3.00000i	0.0980581	−	0.147087i
$417$		0			0
$418$			6.00000i			0.293470i
$419$			6.00000i			0.293119i	0.989202	+	0.146560i	$0.0468200\pi$
$419$			6.00000i			0.293119i	−0.989202	+	0.146560i	$0.953180\pi$
$420$		0			0
$421$	−4.00000	+	4.00000i	−0.194948	+	0.194948i	−0.797830	−	0.602882i	$-0.794019\pi$
$421$	−4.00000	+	4.00000i	−0.194948	+	0.194948i	0.602882	+	0.797830i	$0.294019\pi$
$422$	12.0000			0.584151
$423$	24.0000			1.16692
$424$	5.00000	−	5.00000i	0.242821	−	0.242821i
$425$		0			0
$426$		0			0
$427$			4.00000i			0.193574i
$428$	−10.0000	−	10.0000i	−0.483368	−	0.483368i
$429$		0			0
$430$		0			0
$431$	−4.00000	+	4.00000i	−0.192673	+	0.192673i	−0.796850	−	0.604177i	$-0.793502\pi$
$431$	−4.00000	+	4.00000i	−0.192673	+	0.192673i	0.604177	+	0.796850i	$0.293502\pi$
$432$		0			0
$433$	4.00000	+	4.00000i	0.192228	+	0.192228i	0.796658	−	0.604430i	$-0.206599\pi$
$433$	4.00000	+	4.00000i	0.192228	+	0.192228i	−0.604430	+	0.796658i	$0.706599\pi$
$434$	12.0000	+	12.0000i	0.576018	+	0.576018i
$435$		0			0
$436$	−12.0000	−	12.0000i	−0.574696	−	0.574696i
$437$		−	6.00000i		−	0.287019i
$438$		0			0
$439$	20.0000			0.954548			0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000			0.954548			0.477274	+	0.878755i	$0.341625\pi$
$440$		0			0
$441$			9.00000i			0.428571i
$442$	2.00000	+	10.0000i	0.0951303	+	0.475651i
$443$	10.0000	−	10.0000i	0.475114	−	0.475114i	−0.428451	−	0.903565i	$-0.640940\pi$
$443$	10.0000	−	10.0000i	0.475114	−	0.475114i	0.903565	+	0.428451i	$0.140940\pi$
$444$		0			0
$445$		0			0
$446$			24.0000i			1.13643i
$447$		0			0
$448$			2.00000i			0.0944911i
$449$	−23.0000	+	23.0000i	−1.08544	+	1.08544i	−0.0894454	+	0.995992i	$0.528509\pi$
$449$	−23.0000	+	23.0000i	−1.08544	+	1.08544i	−0.995992	+	0.0894454i	$0.971491\pi$
$450$		0			0
$451$	2.00000			0.0941763
$452$	10.0000	−	10.0000i	0.470360	−	0.470360i
$453$		0			0
$454$	−12.0000			−0.563188
$455$		0			0
$456$		0			0
$457$	−2.00000			−0.0935561			−0.0467780	−	0.998905i	$-0.514895\pi$
$457$	−2.00000			−0.0935561			−0.0467780	+	0.998905i	$0.514895\pi$
$458$	2.00000	−	2.00000i	0.0934539	−	0.0934539i
$459$		0			0
$460$		0			0
$461$	−4.00000	+	4.00000i	−0.186299	+	0.186299i	−0.794094	−	0.607795i	$-0.792054\pi$
$461$	−4.00000	+	4.00000i	−0.186299	+	0.186299i	0.607795	+	0.794094i	$0.292054\pi$
$462$		0			0
$463$	14.0000			0.650635			0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000			0.650635			0.325318	+	0.945605i	$0.394529\pi$
$464$			6.00000i			0.278543i
$465$		0			0
$466$	14.0000	+	14.0000i	0.648537	+	0.648537i
$467$	−22.0000	+	22.0000i	−1.01804	+	1.01804i	−0.0182043	+	0.999834i	$0.505795\pi$
$467$	−22.0000	+	22.0000i	−1.01804	+	1.01804i	−0.999834	+	0.0182043i	$0.994205\pi$
$468$	9.00000	+	6.00000i	0.416025	+	0.277350i
$469$		−	24.0000i		−	1.10822i
$470$		0			0
$471$		0			0
$472$	−3.00000	+	3.00000i	−0.138086	+	0.138086i
$473$		−	12.0000i		−	0.551761i
$474$		0			0
$475$		0			0
$476$	−4.00000	−	4.00000i	−0.183340	−	0.183340i
$477$	15.0000	+	15.0000i	0.686803	+	0.686803i
$478$	−2.00000	−	2.00000i	−0.0914779	−	0.0914779i
$479$	22.0000	−	22.0000i	1.00521	−	1.00521i	0.00521928	−	0.999986i	$-0.498339\pi$
$479$	22.0000	−	22.0000i	1.00521	−	1.00521i	0.999986	−	0.00521928i	$-0.00166136\pi$
$480$		0			0
$481$	6.00000	+	4.00000i	0.273576	+	0.182384i
$482$	21.0000	+	21.0000i	0.956524	+	0.956524i
$483$		0			0
$484$		−	9.00000i		−	0.409091i
$485$		0			0
$486$		0			0
$487$	8.00000			0.362515			0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000			0.362515			0.181257	+	0.983436i	$0.441983\pi$
$488$	2.00000			0.0905357
$489$		0			0
$490$		0			0
$491$			10.0000i			0.451294i	0.974209	+	0.225647i	$0.0724495\pi$
$491$			10.0000i			0.451294i	−0.974209	+	0.225647i	$0.927550\pi$
$492$		0			0
$493$	−12.0000	−	12.0000i	−0.540453	−	0.540453i
$494$	15.0000	−	3.00000i	0.674882	−	0.134976i
$495$		0			0
$496$	6.00000	−	6.00000i	0.269408	−	0.269408i
$497$	−8.00000	−	8.00000i	−0.358849	−	0.358849i
$498$		0			0
$499$	−17.0000	−	17.0000i	−0.761025	−	0.761025i	0.215483	−	0.976508i	$-0.430867\pi$
$499$	−17.0000	−	17.0000i	−0.761025	−	0.761025i	−0.976508	+	0.215483i	$0.930867\pi$
$500$		0			0
$501$		0			0
$502$		−	20.0000i		−	0.892644i
$503$	−15.0000	+	15.0000i	−0.668817	+	0.668817i	−0.957442	−	0.288625i	$-0.906802\pi$
$503$	−15.0000	+	15.0000i	−0.668817	+	0.668817i	0.288625	+	0.957442i	$0.406802\pi$
$504$	−6.00000			−0.267261
$505$		0			0
$506$		−	2.00000i		−	0.0889108i
$507$		0			0
$508$	13.0000	−	13.0000i	0.576782	−	0.576782i
$509$	−22.0000	−	22.0000i	−0.975133	−	0.975133i	0.0245654	−	0.999698i	$-0.492180\pi$
$509$	−22.0000	−	22.0000i	−0.975133	−	0.975133i	−0.999698	+	0.0245654i	$0.992180\pi$
$510$		0			0
$511$		−	12.0000i		−	0.530849i
$512$	1.00000			0.0441942
$513$		0			0
$514$	18.0000	−	18.0000i	0.793946	−	0.793946i
$515$		0			0
$516$		0			0
$517$	8.00000	−	8.00000i	0.351840	−	0.351840i
$518$	−4.00000			−0.175750
$519$		0			0
$520$		0			0
$521$	2.00000			0.0876216			0.0438108	−	0.999040i	$-0.486050\pi$
$521$	2.00000			0.0876216			0.0438108	+	0.999040i	$0.486050\pi$
$522$	−18.0000			−0.787839
$523$	10.0000	−	10.0000i	0.437269	−	0.437269i	−0.453823	−	0.891092i	$-0.649940\pi$
$523$	10.0000	−	10.0000i	0.437269	−	0.437269i	0.891092	+	0.453823i	$0.149940\pi$
$524$	−18.0000			−0.786334
$525$		0			0
$526$	−15.0000	+	15.0000i	−0.654031	+	0.654031i
$527$			24.0000i			1.04546i
$528$		0			0
$529$		−	21.0000i		−	0.913043i
$530$		0			0
$531$	−9.00000	−	9.00000i	−0.390567	−	0.390567i
$532$	−6.00000	+	6.00000i	−0.260133	+	0.260133i
$533$	−1.00000	−	5.00000i	−0.0433148	−	0.216574i
$534$		0			0
$535$		0			0
$536$	−12.0000			−0.518321
$537$		0			0
$538$			26.0000i			1.12094i
$539$	3.00000	+	3.00000i	0.129219	+	0.129219i
$540$		0			0
$541$	6.00000	+	6.00000i	0.257960	+	0.257960i	0.824224	−	0.566264i	$-0.191612\pi$
$541$	6.00000	+	6.00000i	0.257960	+	0.257960i	−0.566264	+	0.824224i	$0.691612\pi$
$542$	16.0000	+	16.0000i	0.687259	+	0.687259i
$543$		0			0
$544$	−2.00000	+	2.00000i	−0.0857493	+	0.0857493i
$545$		0			0
$546$		0			0
$547$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$547$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$548$			22.0000i			0.939793i
$549$			6.00000i			0.256074i
$550$		0			0
$551$	−18.0000	+	18.0000i	−0.766826	+	0.766826i
$552$		0			0
$553$	8.00000			0.340195
$554$	13.0000	−	13.0000i	0.552317	−	0.552317i
$555$		0			0
$556$		−	14.0000i		−	0.593732i
$557$			12.0000i			0.508456i	0.967144	+	0.254228i	$0.0818214\pi$
$557$			12.0000i			0.508456i	−0.967144	+	0.254228i	$0.918179\pi$
$558$	18.0000	+	18.0000i	0.762001	+	0.762001i
$559$	−30.0000	+	6.00000i	−1.26886	+	0.253773i
$560$		0			0
$561$		0			0
$562$	−9.00000	−	9.00000i	−0.379642	−	0.379642i
$563$	−26.0000	−	26.0000i	−1.09577	−	1.09577i	−0.994900	−	0.100870i	$-0.967837\pi$
$563$	−26.0000	−	26.0000i	−1.09577	−	1.09577i	−0.100870	−	0.994900i	$-0.532163\pi$
$564$		0			0
$565$		0			0
$566$	−16.0000	−	16.0000i	−0.672530	−	0.672530i
$567$		−	18.0000i		−	0.755929i
$568$	−4.00000	+	4.00000i	−0.167836	+	0.167836i
$569$	−30.0000			−1.25767			−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000			−1.25767			−0.628833	+	0.777541i	$0.716467\pi$
$570$		0			0
$571$			20.0000i			0.836974i	0.908223	+	0.418487i	$0.137439\pi$
$571$			20.0000i			0.836974i	−0.908223	+	0.418487i	$0.862561\pi$
$572$	5.00000	−	1.00000i	0.209061	−	0.0418121i
$573$		0			0
$574$	2.00000	+	2.00000i	0.0834784	+	0.0834784i
$575$		0			0
$576$			3.00000i			0.125000i
$577$	−2.00000			−0.0832611			−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000			−0.0832611			−0.0416305	+	0.999133i	$0.513255\pi$
$578$			9.00000i			0.374351i
$579$		0			0
$580$		0			0
$581$	−8.00000			−0.331896
$582$		0			0
$583$	10.0000			0.414158
$584$	−6.00000			−0.248282
$585$		0			0
$586$	24.0000			0.991431
$587$	−32.0000			−1.32078			−0.660391	−	0.750922i	$-0.729609\pi$
$587$	−32.0000			−1.32078			−0.660391	+	0.750922i	$0.729609\pi$
$588$		0			0
$589$	36.0000			1.48335
$590$		0			0
$591$		0			0
$592$			2.00000i			0.0821995i
$593$	−6.00000			−0.246390			−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000			−0.246390			−0.123195	+	0.992382i	$0.539314\pi$
$594$		0			0
$595$		0			0
$596$	−2.00000	−	2.00000i	−0.0819232	−	0.0819232i
$597$		0			0
$598$	−5.00000	+	1.00000i	−0.204465	+	0.0408930i
$599$		−	44.0000i		−	1.79779i	−0.438163	−	0.898896i	$-0.644371\pi$
$599$		−	44.0000i		−	1.79779i	0.438163	−	0.898896i	$-0.355629\pi$
$600$		0			0
$601$	−8.00000			−0.326327			−0.163163	−	0.986599i	$-0.552170\pi$
$601$	−8.00000			−0.326327			−0.163163	+	0.986599i	$0.552170\pi$
$602$	12.0000	−	12.0000i	0.489083	−	0.489083i
$603$		−	36.0000i		−	1.46603i
$604$	−4.00000	−	4.00000i	−0.162758	−	0.162758i
$605$		0			0
$606$		0			0
$607$	15.0000	+	15.0000i	0.608831	+	0.608831i	0.942641	−	0.333809i	$-0.108334\pi$
$607$	15.0000	+	15.0000i	0.608831	+	0.608831i	−0.333809	+	0.942641i	$0.608334\pi$
$608$	3.00000	+	3.00000i	0.121666	+	0.121666i
$609$		0			0
$610$		0			0
$611$	−24.0000	−	16.0000i	−0.970936	−	0.647291i
$612$	−6.00000	−	6.00000i	−0.242536	−	0.242536i
$613$			4.00000i			0.161558i	0.996732	+	0.0807792i	$0.0257409\pi$
$613$			4.00000i			0.161558i	−0.996732	+	0.0807792i	$0.974259\pi$
$614$		−	28.0000i		−	1.12999i
$615$		0			0
$616$	−2.00000	+	2.00000i	−0.0805823	+	0.0805823i
$617$	−42.0000			−1.69086			−0.845428	−	0.534089i	$-0.820655\pi$
$617$	−42.0000			−1.69086			−0.845428	+	0.534089i	$0.820655\pi$
$618$		0			0
$619$	7.00000	−	7.00000i	0.281354	−	0.281354i	−0.552295	−	0.833649i	$-0.686248\pi$
$619$	7.00000	−	7.00000i	0.281354	−	0.281354i	0.833649	+	0.552295i	$0.186248\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	14.0000	+	14.0000i	0.560898	+	0.560898i
$624$		0			0
$625$		0			0
$626$		0			0
$627$		0			0
$628$	15.0000	+	15.0000i	0.598565	+	0.598565i
$629$	−4.00000	−	4.00000i	−0.159490	−	0.159490i
$630$		0			0
$631$	−24.0000	−	24.0000i	−0.955425	−	0.955425i	0.0436231	−	0.999048i	$-0.486110\pi$
$631$	−24.0000	−	24.0000i	−0.955425	−	0.955425i	−0.999048	+	0.0436231i	$0.986110\pi$
$632$		−	4.00000i		−	0.159111i
$633$		0			0
$634$	−12.0000			−0.476581
$635$		0			0
$636$		0			0
$637$	6.00000	−	9.00000i	0.237729	−	0.356593i
$638$	−6.00000	+	6.00000i	−0.237542	+	0.237542i
$639$	−12.0000	−	12.0000i	−0.474713	−	0.474713i
$640$		0			0
$641$			30.0000i			1.18493i	0.805597	+	0.592464i	$0.201845\pi$
$641$			30.0000i			1.18493i	−0.805597	+	0.592464i	$0.798155\pi$
$642$		0			0
$643$		−	16.0000i		−	0.630978i	−0.948929	−	0.315489i	$-0.897831\pi$
$643$		−	16.0000i		−	0.630978i	0.948929	−	0.315489i	$-0.102169\pi$
$644$	2.00000	−	2.00000i	0.0788110	−	0.0788110i
$645$		0			0
$646$	−12.0000			−0.472134
$647$	13.0000	−	13.0000i	0.511083	−	0.511083i	−0.403775	−	0.914858i	$-0.632302\pi$
$647$	13.0000	−	13.0000i	0.511083	−	0.511083i	0.914858	+	0.403775i	$0.132302\pi$
$648$	−9.00000			−0.353553
$649$	−6.00000			−0.235521
$650$		0			0
$651$		0			0
$652$	4.00000			0.156652
$653$	−15.0000	+	15.0000i	−0.586995	+	0.586995i	−0.936817	−	0.349821i	$-0.886242\pi$
$653$	−15.0000	+	15.0000i	−0.586995	+	0.586995i	0.349821	+	0.936817i	$0.386242\pi$
$654$		0			0
$655$		0			0
$656$	1.00000	−	1.00000i	0.0390434	−	0.0390434i
$657$		−	18.0000i		−	0.702247i
$658$	16.0000			0.623745
$659$			6.00000i			0.233727i	0.993148	+	0.116863i	$0.0372840\pi$
$659$			6.00000i			0.233727i	−0.993148	+	0.116863i	$0.962716\pi$
$660$		0			0
$661$	−14.0000	−	14.0000i	−0.544537	−	0.544537i	0.380319	−	0.924856i	$-0.375814\pi$
$661$	−14.0000	−	14.0000i	−0.544537	−	0.544537i	−0.924856	+	0.380319i	$0.875814\pi$
$662$	21.0000	−	21.0000i	0.816188	−	0.816188i
$663$		0			0
$664$			4.00000i			0.155230i
$665$		0			0
$666$	−6.00000			−0.232495
$667$	6.00000	−	6.00000i	0.232321	−	0.232321i
$668$		−	8.00000i		−	0.309529i
$669$		0			0
$670$		0			0
$671$	2.00000	+	2.00000i	0.0772091	+	0.0772091i
$672$		0			0
$673$	−26.0000	−	26.0000i	−1.00223	−	1.00223i	−0.999998	−	0.00222883i	$-0.999291\pi$
$673$	−26.0000	−	26.0000i	−1.00223	−	1.00223i	−0.00222883	−	0.999998i	$-0.500709\pi$
$674$	−12.0000	+	12.0000i	−0.462223	+	0.462223i
$675$		0			0
$676$	−5.00000	−	12.0000i	−0.192308	−	0.461538i
$677$	−5.00000	−	5.00000i	−0.192166	−	0.192166i	0.604466	−	0.796631i	$-0.293387\pi$
$677$	−5.00000	−	5.00000i	−0.192166	−	0.192166i	−0.796631	+	0.604466i	$0.793387\pi$
$678$		0			0
$679$		−	4.00000i		−	0.153506i
$680$		0			0
$681$		0			0
$682$	12.0000			0.459504
$683$	−16.0000			−0.612223			−0.306111	−	0.951996i	$-0.599028\pi$
$683$	−16.0000			−0.612223			−0.306111	+	0.951996i	$0.599028\pi$
$684$	−9.00000	+	9.00000i	−0.344124	+	0.344124i
$685$		0			0
$686$			20.0000i			0.763604i
$687$		0			0
$688$	−6.00000	−	6.00000i	−0.228748	−	0.228748i
$689$	−5.00000	−	25.0000i	−0.190485	−	0.952424i
$690$		0			0
$691$	−29.0000	+	29.0000i	−1.10321	+	1.10321i	−0.109191	+	0.994021i	$0.534826\pi$
$691$	−29.0000	+	29.0000i	−1.10321	+	1.10321i	−0.994021	+	0.109191i	$0.965174\pi$
$692$	9.00000	+	9.00000i	0.342129	+	0.342129i
$693$	−6.00000	−	6.00000i	−0.227921	−	0.227921i
$694$	10.0000	+	10.0000i	0.379595	+	0.379595i
$695$		0			0
$696$		0			0
$697$			4.00000i			0.151511i
$698$	−8.00000	+	8.00000i	−0.302804	+	0.302804i
$699$		0			0
$700$		0			0
$701$		−	30.0000i		−	1.13308i	−0.824033	−	0.566542i	$-0.808281\pi$
$701$		−	30.0000i		−	1.13308i	0.824033	−	0.566542i	$-0.191719\pi$
$702$		0			0
$703$	−6.00000	+	6.00000i	−0.226294	+	0.226294i
$704$	1.00000	+	1.00000i	0.0376889	+	0.0376889i
$705$		0			0
$706$			14.0000i			0.526897i
$707$	−20.0000			−0.752177
$708$		0			0
$709$	−18.0000	+	18.0000i	−0.676004	+	0.676004i	−0.959094	−	0.283089i	$-0.908641\pi$
$709$	−18.0000	+	18.0000i	−0.676004	+	0.676004i	0.283089	+	0.959094i	$0.408641\pi$
$710$		0			0
$711$	12.0000			0.450035
$712$	7.00000	−	7.00000i	0.262336	−	0.262336i
$713$	−12.0000			−0.449404
$714$		0			0
$715$		0			0
$716$	10.0000			0.373718
$717$		0			0
$718$	−18.0000	+	18.0000i	−0.671754	+	0.671754i
$719$	20.0000			0.745874			0.372937	−	0.927857i	$-0.378351\pi$
$719$	20.0000			0.745874			0.372937	+	0.927857i	$0.378351\pi$
$720$		0			0
$721$	2.00000	−	2.00000i	0.0744839	−	0.0744839i
$722$		−	1.00000i		−	0.0372161i
$723$		0			0
$724$		−	10.0000i		−	0.371647i
$725$		0			0
$726$		0			0
$727$	3.00000	−	3.00000i	0.111264	−	0.111264i	−0.649283	−	0.760547i	$-0.724931\pi$
$727$	3.00000	−	3.00000i	0.111264	−	0.111264i	0.760547	+	0.649283i	$0.224931\pi$
$728$	6.00000	+	4.00000i	0.222375	+	0.148250i
$729$		−	27.0000i		−	1.00000i
$730$		0			0
$731$	24.0000			0.887672
$732$		0			0
$733$			14.0000i			0.517102i	0.965998	+	0.258551i	$0.0832450\pi$
$733$			14.0000i			0.517102i	−0.965998	+	0.258551i	$0.916755\pi$
$734$	−25.0000	−	25.0000i	−0.922767	−	0.922767i
$735$		0			0
$736$	−1.00000	−	1.00000i	−0.0368605	−	0.0368605i
$737$	−12.0000	−	12.0000i	−0.442026	−	0.442026i
$738$	3.00000	+	3.00000i	0.110432	+	0.110432i
$739$	−3.00000	+	3.00000i	−0.110357	+	0.110357i	−0.760129	−	0.649772i	$-0.774864\pi$
$739$	−3.00000	+	3.00000i	−0.110357	+	0.110357i	0.649772	+	0.760129i	$0.274864\pi$
$740$		0			0
$741$		0			0
$742$	10.0000	+	10.0000i	0.367112	+	0.367112i
$743$		−	6.00000i		−	0.220119i	−0.993925	−	0.110059i	$-0.964896\pi$
$743$		−	6.00000i		−	0.220119i	0.993925	−	0.110059i	$-0.0351041\pi$
$744$		0			0
$745$		0			0
$746$	5.00000	−	5.00000i	0.183063	−	0.183063i
$747$	−12.0000			−0.439057
$748$	−4.00000			−0.146254
$749$	20.0000	−	20.0000i	0.730784	−	0.730784i
$750$		0			0
$751$		−	40.0000i		−	1.45962i	−0.683650	−	0.729810i	$-0.739608\pi$
$751$		−	40.0000i		−	1.45962i	0.683650	−	0.729810i	$-0.260392\pi$
$752$		−	8.00000i		−	0.291730i
$753$		0			0
$754$	18.0000	+	12.0000i	0.655521	+	0.437014i
$755$		0			0
$756$		0			0
$757$	−35.0000	−	35.0000i	−1.27210	−	1.27210i	−0.944986	−	0.327111i	$-0.893925\pi$
$757$	−35.0000	−	35.0000i	−1.27210	−	1.27210i	−0.327111	−	0.944986i	$-0.606075\pi$
$758$	3.00000	+	3.00000i	0.108965	+	0.108965i
$759$		0			0
$760$		0			0
$761$	21.0000	+	21.0000i	0.761249	+	0.761249i	0.976548	−	0.215299i	$-0.0690725\pi$
$761$	21.0000	+	21.0000i	0.761249	+	0.761249i	−0.215299	+	0.976548i	$0.569073\pi$
$762$		0			0
$763$	24.0000	−	24.0000i	0.868858	−	0.868858i
$764$	−8.00000			−0.289430
$765$		0			0
$766$			34.0000i			1.22847i
$767$	3.00000	+	15.0000i	0.108324	+	0.541619i
$768$		0			0
$769$	−7.00000	−	7.00000i	−0.252426	−	0.252426i	0.569538	−	0.821965i	$-0.307122\pi$
$769$	−7.00000	−	7.00000i	−0.252426	−	0.252426i	−0.821965	+	0.569538i	$0.807122\pi$
$770$		0			0
$771$		0			0
$772$	14.0000			0.503871
$773$		−	16.0000i		−	0.575480i	−0.957709	−	0.287740i	$-0.907096\pi$
$773$		−	16.0000i		−	0.575480i	0.957709	−	0.287740i	$-0.0929039\pi$
$774$	18.0000	−	18.0000i	0.646997	−	0.646997i
$775$		0			0
$776$	−2.00000			−0.0717958
$777$		0			0
$778$	30.0000			1.07555
$779$	6.00000			0.214972
$780$		0			0
$781$	−8.00000			−0.286263
$782$	4.00000			0.143040
$783$		0			0
$784$	3.00000			0.107143
$785$		0			0
$786$		0			0
$787$			32.0000i			1.14068i	0.821410	+	0.570338i	$0.193188\pi$
$787$			32.0000i			1.14068i	−0.821410	+	0.570338i	$0.806812\pi$
$788$	−22.0000			−0.783718
$789$		0			0
$790$		0			0
$791$	20.0000	+	20.0000i	0.711118	+	0.711118i
$792$	−3.00000	+	3.00000i	−0.106600	+	0.106600i
$793$	4.00000	−	6.00000i	0.142044	−	0.213066i
$794$			32.0000i			1.13564i
$795$		0			0
$796$		0			0
$797$	−7.00000	+	7.00000i	−0.247953	+	0.247953i	−0.820130	−	0.572177i	$-0.806099\pi$
$797$	−7.00000	+	7.00000i	−0.247953	+	0.247953i	0.572177	+	0.820130i	$0.306099\pi$
$798$		0			0
$799$	16.0000	+	16.0000i	0.566039	+	0.566039i
$800$		0			0
$801$	21.0000	+	21.0000i	0.741999	+	0.741999i
$802$	−19.0000	−	19.0000i	−0.670913	−	0.670913i
$803$	−6.00000	−	6.00000i	−0.211735	−	0.211735i
$804$		0			0
$805$		0			0
$806$	−6.00000	−	30.0000i	−0.211341	−	1.05670i
$807$		0			0
$808$			10.0000i			0.351799i
$809$			36.0000i			1.26569i	0.774277	+	0.632846i	$0.218114\pi$
$809$			36.0000i			1.26569i	−0.774277	+	0.632846i	$0.781886\pi$
$810$		0			0
$811$	−9.00000	+	9.00000i	−0.316033	+	0.316033i	−0.847241	−	0.531208i	$-0.821738\pi$
$811$	−9.00000	+	9.00000i	−0.316033	+	0.316033i	0.531208	+	0.847241i	$0.321738\pi$
$812$	−12.0000			−0.421117
$813$		0			0
$814$	−2.00000	+	2.00000i	−0.0701000	+	0.0701000i
$815$		0			0
$816$		0			0
$817$		−	36.0000i		−	1.25948i
$818$	3.00000	+	3.00000i	0.104893	+	0.104893i
$819$	−12.0000	+	18.0000i	−0.419314	+	0.628971i
$820$		0			0
$821$	16.0000	−	16.0000i	0.558404	−	0.558404i	−0.370449	−	0.928853i	$-0.620796\pi$
$821$	16.0000	−	16.0000i	0.558404	−	0.558404i	0.928853	+	0.370449i	$0.120796\pi$
$822$		0			0
$823$	29.0000	+	29.0000i	1.01088	+	1.01088i	0.999940	+	0.0109363i	$0.00348119\pi$
$823$	29.0000	+	29.0000i	1.01088	+	1.01088i	0.0109363	+	0.999940i	$0.496519\pi$
$824$	−1.00000	−	1.00000i	−0.0348367	−	0.0348367i
$825$		0			0
$826$	−6.00000	−	6.00000i	−0.208767	−	0.208767i
$827$			32.0000i			1.11275i	0.830932	+	0.556375i	$0.187808\pi$
$827$			32.0000i			1.11275i	−0.830932	+	0.556375i	$0.812192\pi$
$828$	3.00000	−	3.00000i	0.104257	−	0.104257i
$829$	30.0000			1.04194			0.520972	−	0.853574i	$-0.325570\pi$
$829$	30.0000			1.04194			0.520972	+	0.853574i	$0.325570\pi$
$830$		0			0
$831$		0			0
$832$	2.00000	−	3.00000i	0.0693375	−	0.104006i
$833$	−6.00000	+	6.00000i	−0.207888	+	0.207888i
$834$		0			0
$835$		0			0
$836$			6.00000i			0.207514i
$837$		0			0
$838$			6.00000i			0.207267i
$839$	−28.0000	+	28.0000i	−0.966667	+	0.966667i	−0.999462	−	0.0327948i	$-0.989559\pi$
$839$	−28.0000	+	28.0000i	−0.966667	+	0.966667i	0.0327948	+	0.999462i	$0.489559\pi$
$840$		0			0
$841$	−7.00000			−0.241379
$842$	−4.00000	+	4.00000i	−0.137849	+	0.137849i
$843$		0			0
$844$	12.0000			0.413057
$845$		0			0
$846$	24.0000			0.825137
$847$	18.0000			0.618487
$848$	5.00000	−	5.00000i	0.171701	−	0.171701i
$849$		0			0
$850$		0			0
$851$	2.00000	−	2.00000i	0.0685591	−	0.0685591i
$852$		0			0
$853$	−26.0000			−0.890223			−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000			−0.890223			−0.445112	+	0.895475i	$0.646836\pi$
$854$			4.00000i			0.136877i
$855$		0			0
$856$	−10.0000	−	10.0000i	−0.341793	−	0.341793i
$857$	8.00000	−	8.00000i	0.273275	−	0.273275i	−0.557142	−	0.830417i	$-0.688102\pi$
$857$	8.00000	−	8.00000i	0.273275	−	0.273275i	0.830417	+	0.557142i	$0.188102\pi$
$858$		0			0
$859$		−	4.00000i		−	0.136478i	−0.997669	−	0.0682391i	$-0.978262\pi$
$859$		−	4.00000i		−	0.136478i	0.997669	−	0.0682391i	$-0.0217381\pi$
$860$		0			0
$861$		0			0
$862$	−4.00000	+	4.00000i	−0.136241	+	0.136241i
$863$			24.0000i			0.816970i	0.912765	+	0.408485i	$0.133943\pi$
$863$			24.0000i			0.816970i	−0.912765	+	0.408485i	$0.866057\pi$
$864$		0			0
$865$		0			0
$866$	4.00000	+	4.00000i	0.135926	+	0.135926i
$867$		0			0
$868$	12.0000	+	12.0000i	0.407307	+	0.407307i
$869$	4.00000	−	4.00000i	0.135691	−	0.135691i
$870$		0			0
$871$	−24.0000	+	36.0000i	−0.813209	+	1.21981i
$872$	−12.0000	−	12.0000i	−0.406371	−	0.406371i
$873$		−	6.00000i		−	0.203069i
$874$		−	6.00000i		−	0.202953i
$875$		0			0
$876$		0			0
$877$	18.0000			0.607817			0.303908	−	0.952701i	$-0.401708\pi$
$877$	18.0000			0.607817			0.303908	+	0.952701i	$0.401708\pi$
$878$	20.0000			0.674967
$879$		0			0
$880$		0			0
$881$		−	50.0000i		−	1.68454i	−0.539054	−	0.842271i	$-0.681218\pi$
$881$		−	50.0000i		−	1.68454i	0.539054	−	0.842271i	$-0.318782\pi$
$882$			9.00000i			0.303046i
$883$	−26.0000	−	26.0000i	−0.874970	−	0.874970i	0.118039	−	0.993009i	$-0.462339\pi$
$883$	−26.0000	−	26.0000i	−0.874970	−	0.874970i	−0.993009	+	0.118039i	$0.962339\pi$
$884$	2.00000	+	10.0000i	0.0672673	+	0.336336i
$885$		0			0
$886$	10.0000	−	10.0000i	0.335957	−	0.335957i
$887$	35.0000	+	35.0000i	1.17518	+	1.17518i	0.980956	+	0.194229i	$0.0622204\pi$
$887$	35.0000	+	35.0000i	1.17518	+	1.17518i	0.194229	+	0.980956i	$0.437780\pi$
$888$		0			0
$889$	26.0000	+	26.0000i	0.872012	+	0.872012i
$890$		0			0
$891$	−9.00000	−	9.00000i	−0.301511	−	0.301511i
$892$			24.0000i			0.803579i
$893$	24.0000	−	24.0000i	0.803129	−	0.803129i
$894$		0			0
$895$		0			0
$896$			2.00000i			0.0668153i
$897$		0			0
$898$	−23.0000	+	23.0000i	−0.767520	+	0.767520i
$899$	36.0000	+	36.0000i	1.20067	+	1.20067i
$900$		0			0
$901$			20.0000i			0.666297i
$902$	2.00000			0.0665927
$903$		0			0
$904$	10.0000	−	10.0000i	0.332595	−	0.332595i
$905$		0			0
$906$		0			0
$907$	−22.0000	+	22.0000i	−0.730498	+	0.730498i	−0.970718	−	0.240220i	$-0.922780\pi$
$907$	−22.0000	+	22.0000i	−0.730498	+	0.730498i	0.240220	+	0.970718i	$0.422780\pi$
$908$	−12.0000			−0.398234
$909$	−30.0000			−0.995037
$910$		0			0
$911$	32.0000			1.06021			0.530104	−	0.847933i	$-0.322153\pi$
$911$	32.0000			1.06021			0.530104	+	0.847933i	$0.322153\pi$
$912$		0			0
$913$	−4.00000	+	4.00000i	−0.132381	+	0.132381i
$914$	−2.00000			−0.0661541
$915$		0			0
$916$	2.00000	−	2.00000i	0.0660819	−	0.0660819i
$917$		−	36.0000i		−	1.18882i
$918$		0			0
$919$			16.0000i			0.527791i	0.964551	+	0.263896i	$0.0850075\pi$
$919$			16.0000i			0.527791i	−0.964551	+	0.263896i	$0.914993\pi$
$920$		0			0
$921$		0			0
$922$	−4.00000	+	4.00000i	−0.131733	+	0.131733i
$923$	4.00000	+	20.0000i	0.131662	+	0.658308i
$924$		0			0
$925$		0			0
$926$	14.0000			0.460069
$927$	3.00000	−	3.00000i	0.0985329	−	0.0985329i
$928$			6.00000i			0.196960i
$929$	13.0000	+	13.0000i	0.426516	+	0.426516i	0.887440	−	0.460924i	$-0.152482\pi$
$929$	13.0000	+	13.0000i	0.426516	+	0.426516i	−0.460924	+	0.887440i	$0.652482\pi$
$930$		0			0
$931$	9.00000	+	9.00000i	0.294963	+	0.294963i
$932$	14.0000	+	14.0000i	0.458585	+	0.458585i
$933$		0			0
$934$	−22.0000	+	22.0000i	−0.719862	+	0.719862i
$935$		0			0
$936$	9.00000	+	6.00000i	0.294174	+	0.196116i
$937$	20.0000	+	20.0000i	0.653372	+	0.653372i	0.953803	−	0.300432i	$-0.0971308\pi$
$937$	20.0000	+	20.0000i	0.653372	+	0.653372i	−0.300432	+	0.953803i	$0.597131\pi$
$938$		−	24.0000i		−	0.783628i
$939$		0			0
$940$		0			0
$941$	−34.0000	+	34.0000i	−1.10837	+	1.10837i	−0.115003	+	0.993365i	$0.536688\pi$
$941$	−34.0000	+	34.0000i	−1.10837	+	1.10837i	−0.993365	+	0.115003i	$0.963312\pi$
$942$		0			0
$943$	−2.00000			−0.0651290
$944$	−3.00000	+	3.00000i	−0.0976417	+	0.0976417i
$945$		0			0
$946$		−	12.0000i		−	0.390154i
$947$			32.0000i			1.03986i	0.854209	+	0.519930i	$0.174042\pi$
$947$			32.0000i			1.03986i	−0.854209	+	0.519930i	$0.825958\pi$
$948$		0			0
$949$	−12.0000	+	18.0000i	−0.389536	+	0.584305i
$950$		0			0
$951$		0			0
$952$	−4.00000	−	4.00000i	−0.129641	−	0.129641i
$953$	4.00000	+	4.00000i	0.129573	+	0.129573i	0.768919	−	0.639346i	$-0.220795\pi$
$953$	4.00000	+	4.00000i	0.129573	+	0.129573i	−0.639346	+	0.768919i	$0.720795\pi$
$954$	15.0000	+	15.0000i	0.485643	+	0.485643i
$955$		0			0
$956$	−2.00000	−	2.00000i	−0.0646846	−	0.0646846i
$957$		0			0
$958$	22.0000	−	22.0000i	0.710788	−	0.710788i
$959$	−44.0000			−1.42083
$960$		0			0
$961$		−	41.0000i		−	1.32258i
$962$	6.00000	+	4.00000i	0.193448	+	0.128965i
$963$	30.0000	−	30.0000i	0.966736	−	0.966736i
$964$	21.0000	+	21.0000i	0.676364	+	0.676364i
$965$		0			0
$966$		0			0
$967$	18.0000			0.578841			0.289420	−	0.957202i	$-0.406537\pi$
$967$	18.0000			0.578841			0.289420	+	0.957202i	$0.406537\pi$
$968$		−	9.00000i		−	0.289271i
$969$		0			0
$970$		0			0
$971$	52.0000			1.66876			0.834380	−	0.551190i	$-0.185826\pi$
$971$	52.0000			1.66876			0.834380	+	0.551190i	$0.185826\pi$
$972$		0			0
$973$	28.0000			0.897639
$974$	8.00000			0.256337
$975$		0			0
$976$	2.00000			0.0640184
$977$	−22.0000			−0.703842			−0.351921	−	0.936030i	$-0.614471\pi$
$977$	−22.0000			−0.703842			−0.351921	+	0.936030i	$0.614471\pi$
$978$		0			0
$979$	14.0000			0.447442
$980$		0			0
$981$	36.0000	−	36.0000i	1.14939	−	1.14939i
$982$			10.0000i			0.319113i
$983$	−6.00000			−0.191370			−0.0956851	−	0.995412i	$-0.530504\pi$
$983$	−6.00000			−0.191370			−0.0956851	+	0.995412i	$0.530504\pi$
$984$		0			0
$985$		0			0
$986$	−12.0000	−	12.0000i	−0.382158	−	0.382158i
$987$		0			0
$988$	15.0000	−	3.00000i	0.477214	−	0.0954427i
$989$			12.0000i			0.381578i
$990$		0			0
$991$	32.0000			1.01651			0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000			1.01651			0.508257	+	0.861206i	$0.330290\pi$
$992$	6.00000	−	6.00000i	0.190500	−	0.190500i
$993$		0			0
$994$	−8.00000	−	8.00000i	−0.253745	−	0.253745i
$995$		0			0
$996$		0			0
$997$	−35.0000	−	35.0000i	−1.10846	−	1.10846i	−0.993353	−	0.115108i	$-0.963279\pi$
$997$	−35.0000	−	35.0000i	−1.10846	−	1.10846i	−0.115108	−	0.993353i	$-0.536721\pi$
$998$	−17.0000	−	17.0000i	−0.538126	−	0.538126i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.g.d.57.1	yes	2
5.2	odd	4		650.2.j.b.343.1	yes	2
5.3	odd	4		650.2.j.c.343.1	yes	2
5.4	even	2		650.2.g.a.57.1	✓	2
13.8	odd	4		650.2.j.c.307.1	yes	2
65.8	even	4	inner	650.2.g.d.593.1	yes	2
65.34	odd	4		650.2.j.b.307.1	yes	2
65.47	even	4		650.2.g.a.593.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.g.a.57.1	✓	2	5.4	even	2
650.2.g.a.593.1	yes	2	65.47	even	4
650.2.g.d.57.1	yes	2	1.1	even	1	trivial
650.2.g.d.593.1	yes	2	65.8	even	4	inner
650.2.j.b.307.1	yes	2	65.34	odd	4
650.2.j.b.343.1	yes	2	5.2	odd	4
650.2.j.c.307.1	yes	2	13.8	odd	4
650.2.j.c.343.1	yes	2	5.3	odd	4

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +2.00000i q^{7} +1.00000 q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +2.00000i q^{7} +1.00000 q^{8} +3.00000i q^{9} +(1.00000 + 1.00000i) q^{11} +(2.00000 - 3.00000i) q^{13} +2.00000i q^{14} +1.00000 q^{16} +(-2.00000 + 2.00000i) q^{17} +3.00000i q^{18} +(3.00000 + 3.00000i) q^{19} +(1.00000 + 1.00000i) q^{22} +(-1.00000 - 1.00000i) q^{23} +(2.00000 - 3.00000i) q^{26} +2.00000i q^{28} +6.00000i q^{29} +(6.00000 - 6.00000i) q^{31} +1.00000 q^{32} +(-2.00000 + 2.00000i) q^{34} +3.00000i q^{36} +2.00000i q^{37} +(3.00000 + 3.00000i) q^{38} +(1.00000 - 1.00000i) q^{41} +(-6.00000 - 6.00000i) q^{43} +(1.00000 + 1.00000i) q^{44} +(-1.00000 - 1.00000i) q^{46} -8.00000i q^{47} +3.00000 q^{49} +(2.00000 - 3.00000i) q^{52} +(5.00000 - 5.00000i) q^{53} +2.00000i q^{56} +6.00000i q^{58} +(-3.00000 + 3.00000i) q^{59} +2.00000 q^{61} +(6.00000 - 6.00000i) q^{62} -6.00000 q^{63} +1.00000 q^{64} -12.0000 q^{67} +(-2.00000 + 2.00000i) q^{68} +(-4.00000 + 4.00000i) q^{71} +3.00000i q^{72} -6.00000 q^{73} +2.00000i q^{74} +(3.00000 + 3.00000i) q^{76} +(-2.00000 + 2.00000i) q^{77} -4.00000i q^{79} -9.00000 q^{81} +(1.00000 - 1.00000i) q^{82} +4.00000i q^{83} +(-6.00000 - 6.00000i) q^{86} +(1.00000 + 1.00000i) q^{88} +(7.00000 - 7.00000i) q^{89} +(6.00000 + 4.00000i) q^{91} +(-1.00000 - 1.00000i) q^{92} -8.00000i q^{94} -2.00000 q^{97} +3.00000 q^{98} +(-3.00000 + 3.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^8	\( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{8} + 2 q^{11} + 4 q^{13} + 2 q^{16} - 4 q^{17} + 6 q^{19} + 2 q^{22} - 2 q^{23} + 4 q^{26} + 12 q^{31} + 2 q^{32} - 4 q^{34} + 6 q^{38} + 2 q^{41} - 12 q^{43} + 2 q^{44} - 2 q^{46} + 6 q^{49} + 4 q^{52} + 10 q^{53} - 6 q^{59} + 4 q^{61} + 12 q^{62} - 12 q^{63} + 2 q^{64} - 24 q^{67} - 4 q^{68} - 8 q^{71} - 12 q^{73} + 6 q^{76} - 4 q^{77} - 18 q^{81} + 2 q^{82} - 12 q^{86} + 2 q^{88} + 14 q^{89} + 12 q^{91} - 2 q^{92} - 4 q^{97} + 6 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^8 + 2 * q^11 + 4 * q^13 + 2 * q^16 - 4 * q^17 + 6 * q^19 + 2 * q^22 - 2 * q^23 + 4 * q^26 + 12 * q^31 + 2 * q^32 - 4 * q^34 + 6 * q^38 + 2 * q^41 - 12 * q^43 + 2 * q^44 - 2 * q^46 + 6 * q^49 + 4 * q^52 + 10 * q^53 - 6 * q^59 + 4 * q^61 + 12 * q^62 - 12 * q^63 + 2 * q^64 - 24 * q^67 - 4 * q^68 - 8 * q^71 - 12 * q^73 + 6 * q^76 - 4 * q^77 - 18 * q^81 + 2 * q^82 - 12 * q^86 + 2 * q^88 + 14 * q^89 + 12 * q^91 - 2 * q^92 - 4 * q^97 + 6 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more