LMFDB - Embedded newform 2070.2.j.d.737.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(323,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("2070.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.j (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:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2070.737
Dual form			2070.2.j.d.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.12132 - 0.707107i) q^{5} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.12132 - 0.707107i) q^{5} +(0.707107 + 0.707107i) q^{8} +(2.00000 - 1.00000i) q^{10} -2.82843i q^{11} +(-3.00000 + 3.00000i) q^{13} -1.00000 q^{16} +(-2.82843 + 2.82843i) q^{17} -4.00000i q^{19} +(-0.707107 + 2.12132i) q^{20} +(2.00000 + 2.00000i) q^{22} +(0.707107 + 0.707107i) q^{23} +(4.00000 + 3.00000i) q^{25} -4.24264i q^{26} -9.89949 q^{29} +8.00000 q^{31} +(0.707107 - 0.707107i) q^{32} -4.00000i q^{34} +(7.00000 + 7.00000i) q^{37} +(2.82843 + 2.82843i) q^{38} +(-1.00000 - 2.00000i) q^{40} +7.07107i q^{41} +(2.00000 - 2.00000i) q^{43} -2.82843 q^{44} -1.00000 q^{46} +(2.82843 - 2.82843i) q^{47} -7.00000i q^{49} +(-4.94975 + 0.707107i) q^{50} +(3.00000 + 3.00000i) q^{52} +(-8.48528 - 8.48528i) q^{53} +(-2.00000 + 6.00000i) q^{55} +(7.00000 - 7.00000i) q^{58} +11.3137 q^{59} -4.00000 q^{61} +(-5.65685 + 5.65685i) q^{62} +1.00000i q^{64} +(8.48528 - 4.24264i) q^{65} +(10.0000 + 10.0000i) q^{67} +(2.82843 + 2.82843i) q^{68} -14.1421i q^{71} +(1.00000 - 1.00000i) q^{73} -9.89949 q^{74} -4.00000 q^{76} +4.00000i q^{79} +(2.12132 + 0.707107i) q^{80} +(-5.00000 - 5.00000i) q^{82} +(8.48528 + 8.48528i) q^{83} +(8.00000 - 4.00000i) q^{85} +2.82843i q^{86} +(2.00000 - 2.00000i) q^{88} +9.89949 q^{89} +(0.707107 - 0.707107i) q^{92} +4.00000i q^{94} +(-2.82843 + 8.48528i) q^{95} +(3.00000 + 3.00000i) q^{97} +(4.94975 + 4.94975i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q+O(q^{10}) $ 4 * q	$ 4 q + 8 q^{10} - 12 q^{13} - 4 q^{16} + 8 q^{22} + 16 q^{25} + 32 q^{31} + 28 q^{37} - 4 q^{40} + 8 q^{43} - 4 q^{46} + 12 q^{52} - 8 q^{55} + 28 q^{58} - 16 q^{61} + 40 q^{67} + 4 q^{73} - 16 q^{76} - 20 q^{82} + 32 q^{85} + 8 q^{88} + 12 q^{97}+O(q^{100}) $ 4 * q + 8 * q^10 - 12 * q^13 - 4 * q^16 + 8 * q^22 + 16 * q^25 + 32 * q^31 + 28 * q^37 - 4 * q^40 + 8 * q^43 - 4 * q^46 + 12 * q^52 - 8 * q^55 + 28 * q^58 - 16 * q^61 + 40 * q^67 + 4 * q^73 - 16 * q^76 - 20 * q^82 + 32 * q^85 + 8 * q^88 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−2.12132	−	0.707107i	−0.948683	−	0.316228i
$5$	−2.12132	−	0.707107i	−0.948683	−	0.316228i
$6$		0			0
$7$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$7$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	2.00000	−	1.00000i	0.632456	−	0.316228i
$11$		−	2.82843i		−	0.852803i	−0.904534	−	0.426401i	$-0.859781\pi$
$11$		−	2.82843i		−	0.852803i	0.904534	−	0.426401i	$-0.140219\pi$
$12$		0			0
$13$	−3.00000	+	3.00000i	−0.832050	+	0.832050i	−0.987797	−	0.155747i	$-0.950222\pi$
$13$	−3.00000	+	3.00000i	−0.832050	+	0.832050i	0.155747	+	0.987797i	$0.450222\pi$
$14$		0			0
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−2.82843	+	2.82843i	−0.685994	+	0.685994i	−0.961344	−	0.275350i	$-0.911206\pi$
$17$	−2.82843	+	2.82843i	−0.685994	+	0.685994i	0.275350	+	0.961344i	$0.411206\pi$
$18$		0			0
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	−0.707107	+	2.12132i	−0.158114	+	0.474342i
$21$		0			0
$22$	2.00000	+	2.00000i	0.426401	+	0.426401i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$		0			0
$25$	4.00000	+	3.00000i	0.800000	+	0.600000i
$26$		−	4.24264i		−	0.832050i
$27$		0			0
$28$		0			0
$29$	−9.89949			−1.83829			−0.919145	−	0.393919i	$-0.871119\pi$
$29$	−9.89949			−1.83829			−0.919145	+	0.393919i	$0.871119\pi$
$30$		0			0
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$		−	4.00000i		−	0.685994i
$35$		0			0
$36$		0			0
$37$	7.00000	+	7.00000i	1.15079	+	1.15079i	0.986394	+	0.164399i	$0.0525685\pi$
$37$	7.00000	+	7.00000i	1.15079	+	1.15079i	0.164399	+	0.986394i	$0.447432\pi$
$38$	2.82843	+	2.82843i	0.458831	+	0.458831i
$39$		0			0
$40$	−1.00000	−	2.00000i	−0.158114	−	0.316228i
$41$			7.07107i			1.10432i	0.833740	+	0.552158i	$0.186195\pi$
$41$			7.07107i			1.10432i	−0.833740	+	0.552158i	$0.813805\pi$
$42$		0			0
$43$	2.00000	−	2.00000i	0.304997	−	0.304997i	−0.537968	−	0.842965i	$-0.680808\pi$
$43$	2.00000	−	2.00000i	0.304997	−	0.304997i	0.842965	+	0.537968i	$0.180808\pi$
$44$	−2.82843			−0.426401
$45$		0			0
$46$	−1.00000			−0.147442
$47$	2.82843	−	2.82843i	0.412568	−	0.412568i	−0.470064	−	0.882632i	$-0.655769\pi$
$47$	2.82843	−	2.82843i	0.412568	−	0.412568i	0.882632	+	0.470064i	$0.155769\pi$
$48$		0			0
$49$		−	7.00000i		−	1.00000i
$50$	−4.94975	+	0.707107i	−0.700000	+	0.100000i
$51$		0			0
$52$	3.00000	+	3.00000i	0.416025	+	0.416025i
$53$	−8.48528	−	8.48528i	−1.16554	−	1.16554i	−0.983243	−	0.182300i	$-0.941646\pi$
$53$	−8.48528	−	8.48528i	−1.16554	−	1.16554i	−0.182300	−	0.983243i	$-0.558354\pi$
$54$		0			0
$55$	−2.00000	+	6.00000i	−0.269680	+	0.809040i
$56$		0			0
$57$		0			0
$58$	7.00000	−	7.00000i	0.919145	−	0.919145i
$59$	11.3137			1.47292			0.736460	−	0.676481i	$-0.236496\pi$
$59$	11.3137			1.47292			0.736460	+	0.676481i	$0.236496\pi$
$60$		0			0
$61$	−4.00000			−0.512148			−0.256074	−	0.966657i	$-0.582429\pi$
$61$	−4.00000			−0.512148			−0.256074	+	0.966657i	$0.582429\pi$
$62$	−5.65685	+	5.65685i	−0.718421	+	0.718421i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	8.48528	−	4.24264i	1.05247	−	0.526235i
$66$		0			0
$67$	10.0000	+	10.0000i	1.22169	+	1.22169i	0.967029	+	0.254665i	$0.0819652\pi$
$67$	10.0000	+	10.0000i	1.22169	+	1.22169i	0.254665	+	0.967029i	$0.418035\pi$
$68$	2.82843	+	2.82843i	0.342997	+	0.342997i
$69$		0			0
$70$		0			0
$71$		−	14.1421i		−	1.67836i	−0.543852	−	0.839181i	$-0.683035\pi$
$71$		−	14.1421i		−	1.67836i	0.543852	−	0.839181i	$-0.316965\pi$
$72$		0			0
$73$	1.00000	−	1.00000i	0.117041	−	0.117041i	−0.646160	−	0.763202i	$-0.723626\pi$
$73$	1.00000	−	1.00000i	0.117041	−	0.117041i	0.763202	+	0.646160i	$0.223626\pi$
$74$	−9.89949			−1.15079
$75$		0			0
$76$	−4.00000			−0.458831
$77$		0			0
$78$		0			0
$79$			4.00000i			0.450035i	0.974355	+	0.225018i	$0.0722440\pi$
$79$			4.00000i			0.450035i	−0.974355	+	0.225018i	$0.927756\pi$
$80$	2.12132	+	0.707107i	0.237171	+	0.0790569i
$81$		0			0
$82$	−5.00000	−	5.00000i	−0.552158	−	0.552158i
$83$	8.48528	+	8.48528i	0.931381	+	0.931381i	0.997792	−	0.0664117i	$-0.0211551\pi$
$83$	8.48528	+	8.48528i	0.931381	+	0.931381i	−0.0664117	+	0.997792i	$0.521155\pi$
$84$		0			0
$85$	8.00000	−	4.00000i	0.867722	−	0.433861i
$86$			2.82843i			0.304997i
$87$		0			0
$88$	2.00000	−	2.00000i	0.213201	−	0.213201i
$89$	9.89949			1.04934			0.524672	−	0.851304i	$-0.324188\pi$
$89$	9.89949			1.04934			0.524672	+	0.851304i	$0.324188\pi$
$90$		0			0
$91$		0			0
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$		0			0
$94$			4.00000i			0.412568i
$95$	−2.82843	+	8.48528i	−0.290191	+	0.870572i
$96$		0			0
$97$	3.00000	+	3.00000i	0.304604	+	0.304604i	0.842812	−	0.538208i	$-0.180899\pi$
$97$	3.00000	+	3.00000i	0.304604	+	0.304604i	−0.538208	+	0.842812i	$0.680899\pi$
$98$	4.94975	+	4.94975i	0.500000	+	0.500000i
$99$		0			0
$100$	3.00000	−	4.00000i	0.300000	−	0.400000i
$101$			12.7279i			1.26648i	0.773957	+	0.633238i	$0.218274\pi$
$101$			12.7279i			1.26648i	−0.773957	+	0.633238i	$0.781726\pi$
$102$		0			0
$103$	8.00000	−	8.00000i	0.788263	−	0.788263i	−0.192946	−	0.981209i	$-0.561804\pi$
$103$	8.00000	−	8.00000i	0.788263	−	0.788263i	0.981209	+	0.192946i	$0.0618042\pi$
$104$	−4.24264			−0.416025
$105$		0			0
$106$	12.0000			1.16554
$107$	−5.65685	+	5.65685i	−0.546869	+	0.546869i	−0.925534	−	0.378665i	$-0.876383\pi$
$107$	−5.65685	+	5.65685i	−0.546869	+	0.546869i	0.378665	+	0.925534i	$0.376383\pi$
$108$		0			0
$109$			12.0000i			1.14939i	0.818367	+	0.574696i	$0.194880\pi$
$109$			12.0000i			1.14939i	−0.818367	+	0.574696i	$0.805120\pi$
$110$	−2.82843	−	5.65685i	−0.269680	−	0.539360i
$111$		0			0
$112$		0			0
$113$	9.89949	+	9.89949i	0.931266	+	0.931266i	0.997785	−	0.0665190i	$-0.0211893\pi$
$113$	9.89949	+	9.89949i	0.931266	+	0.931266i	−0.0665190	+	0.997785i	$0.521189\pi$
$114$		0			0
$115$	−1.00000	−	2.00000i	−0.0932505	−	0.186501i
$116$			9.89949i			0.919145i
$117$		0			0
$118$	−8.00000	+	8.00000i	−0.736460	+	0.736460i
$119$		0			0
$120$		0			0
$121$	3.00000			0.272727
$122$	2.82843	−	2.82843i	0.256074	−	0.256074i
$123$		0			0
$124$		−	8.00000i		−	0.718421i
$125$	−6.36396	−	9.19239i	−0.569210	−	0.822192i
$126$		0			0
$127$	−10.0000	−	10.0000i	−0.887357	−	0.887357i	0.106912	−	0.994268i	$-0.465904\pi$
$127$	−10.0000	−	10.0000i	−0.887357	−	0.887357i	−0.994268	+	0.106912i	$0.965904\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−3.00000	+	9.00000i	−0.263117	+	0.789352i
$131$			16.9706i			1.48272i	0.671105	+	0.741362i	$0.265820\pi$
$131$			16.9706i			1.48272i	−0.671105	+	0.741362i	$0.734180\pi$
$132$		0			0
$133$		0			0
$134$	−14.1421			−1.22169
$135$		0			0
$136$	−4.00000			−0.342997
$137$	7.07107	−	7.07107i	0.604122	−	0.604122i	−0.337282	−	0.941404i	$-0.609507\pi$
$137$	7.07107	−	7.07107i	0.604122	−	0.604122i	0.941404	+	0.337282i	$0.109507\pi$
$138$		0			0
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$		0			0
$141$		0			0
$142$	10.0000	+	10.0000i	0.839181	+	0.839181i
$143$	8.48528	+	8.48528i	0.709575	+	0.709575i
$144$		0			0
$145$	21.0000	+	7.00000i	1.74396	+	0.581318i
$146$			1.41421i			0.117041i
$147$		0			0
$148$	7.00000	−	7.00000i	0.575396	−	0.575396i
$149$	18.3848			1.50614			0.753070	−	0.657941i	$-0.228572\pi$
$149$	18.3848			1.50614			0.753070	+	0.657941i	$0.228572\pi$
$150$		0			0
$151$	12.0000			0.976546			0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000			0.976546			0.488273	+	0.872691i	$0.337627\pi$
$152$	2.82843	−	2.82843i	0.229416	−	0.229416i
$153$		0			0
$154$		0			0
$155$	−16.9706	−	5.65685i	−1.36311	−	0.454369i
$156$		0			0
$157$	9.00000	+	9.00000i	0.718278	+	0.718278i	0.968252	−	0.249974i	$-0.0804222\pi$
$157$	9.00000	+	9.00000i	0.718278	+	0.718278i	−0.249974	+	0.968252i	$0.580422\pi$
$158$	−2.82843	−	2.82843i	−0.225018	−	0.225018i
$159$		0			0
$160$	−2.00000	+	1.00000i	−0.158114	+	0.0790569i
$161$		0			0
$162$		0			0
$163$	−12.0000	+	12.0000i	−0.939913	+	0.939913i	−0.998294	−	0.0583818i	$-0.981406\pi$
$163$	−12.0000	+	12.0000i	−0.939913	+	0.939913i	0.0583818	+	0.998294i	$0.481406\pi$
$164$	7.07107			0.552158
$165$		0			0
$166$	−12.0000			−0.931381
$167$	16.9706	−	16.9706i	1.31322	−	1.31322i	0.394195	−	0.919027i	$-0.371024\pi$
$167$	16.9706	−	16.9706i	1.31322	−	1.31322i	0.919027	−	0.394195i	$-0.128976\pi$
$168$		0			0
$169$		−	5.00000i		−	0.384615i
$170$	−2.82843	+	8.48528i	−0.216930	+	0.650791i
$171$		0			0
$172$	−2.00000	−	2.00000i	−0.152499	−	0.152499i
$173$	−1.41421	−	1.41421i	−0.107521	−	0.107521i	0.651300	−	0.758820i	$-0.274224\pi$
$173$	−1.41421	−	1.41421i	−0.107521	−	0.107521i	−0.758820	+	0.651300i	$0.774224\pi$
$174$		0			0
$175$		0			0
$176$			2.82843i			0.213201i
$177$		0			0
$178$	−7.00000	+	7.00000i	−0.524672	+	0.524672i
$179$	−5.65685			−0.422813			−0.211407	−	0.977398i	$-0.567804\pi$
$179$	−5.65685			−0.422813			−0.211407	+	0.977398i	$0.567804\pi$
$180$		0			0
$181$	12.0000			0.891953			0.445976	−	0.895045i	$-0.352856\pi$
$181$	12.0000			0.891953			0.445976	+	0.895045i	$0.352856\pi$
$182$		0			0
$183$		0			0
$184$			1.00000i			0.0737210i
$185$	−9.89949	−	19.7990i	−0.727825	−	1.45565i
$186$		0			0
$187$	8.00000	+	8.00000i	0.585018	+	0.585018i
$188$	−2.82843	−	2.82843i	−0.206284	−	0.206284i
$189$		0			0
$190$	−4.00000	−	8.00000i	−0.290191	−	0.580381i
$191$			5.65685i			0.409316i	0.978834	+	0.204658i	$0.0656082\pi$
$191$			5.65685i			0.409316i	−0.978834	+	0.204658i	$0.934392\pi$
$192$		0			0
$193$	−3.00000	+	3.00000i	−0.215945	+	0.215945i	−0.806787	−	0.590842i	$-0.798796\pi$
$193$	−3.00000	+	3.00000i	−0.215945	+	0.215945i	0.590842	+	0.806787i	$0.298796\pi$
$194$	−4.24264			−0.304604
$195$		0			0
$196$	−7.00000			−0.500000
$197$	−15.5563	+	15.5563i	−1.10834	+	1.10834i	−0.114976	+	0.993368i	$0.536679\pi$
$197$	−15.5563	+	15.5563i	−1.10834	+	1.10834i	−0.993368	+	0.114976i	$0.963321\pi$
$198$		0			0
$199$		−	16.0000i		−	1.13421i	−0.823646	−	0.567105i	$-0.808063\pi$
$199$		−	16.0000i		−	1.13421i	0.823646	−	0.567105i	$-0.191937\pi$
$200$	0.707107	+	4.94975i	0.0500000	+	0.350000i
$201$		0			0
$202$	−9.00000	−	9.00000i	−0.633238	−	0.633238i
$203$		0			0
$204$		0			0
$205$	5.00000	−	15.0000i	0.349215	−	1.04765i
$206$			11.3137i			0.788263i
$207$		0			0
$208$	3.00000	−	3.00000i	0.208013	−	0.208013i
$209$	−11.3137			−0.782586
$210$		0			0
$211$	−24.0000			−1.65223			−0.826114	−	0.563503i	$-0.809453\pi$
$211$	−24.0000			−1.65223			−0.826114	+	0.563503i	$0.809453\pi$
$212$	−8.48528	+	8.48528i	−0.582772	+	0.582772i
$213$		0			0
$214$		−	8.00000i		−	0.546869i
$215$	−5.65685	+	2.82843i	−0.385794	+	0.192897i
$216$		0			0
$217$		0			0
$218$	−8.48528	−	8.48528i	−0.574696	−	0.574696i
$219$		0			0
$220$	6.00000	+	2.00000i	0.404520	+	0.134840i
$221$		−	16.9706i		−	1.14156i
$222$		0			0
$223$	−6.00000	+	6.00000i	−0.401790	+	0.401790i	−0.878863	−	0.477074i	$-0.841698\pi$
$223$	−6.00000	+	6.00000i	−0.401790	+	0.401790i	0.477074	+	0.878863i	$0.341698\pi$
$224$		0			0
$225$		0			0
$226$	−14.0000			−0.931266
$227$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$227$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$228$		0			0
$229$		−	14.0000i		−	0.925146i	−0.886581	−	0.462573i	$-0.846926\pi$
$229$		−	14.0000i		−	0.925146i	0.886581	−	0.462573i	$-0.153074\pi$
$230$	2.12132	+	0.707107i	0.139876	+	0.0466252i
$231$		0			0
$232$	−7.00000	−	7.00000i	−0.459573	−	0.459573i
$233$	16.9706	+	16.9706i	1.11178	+	1.11178i	0.992910	+	0.118869i	$0.0379267\pi$
$233$	16.9706	+	16.9706i	1.11178	+	1.11178i	0.118869	+	0.992910i	$0.462073\pi$
$234$		0			0
$235$	−8.00000	+	4.00000i	−0.521862	+	0.260931i
$236$		−	11.3137i		−	0.736460i
$237$		0			0
$238$		0			0
$239$	19.7990			1.28069			0.640345	−	0.768087i	$-0.278791\pi$
$239$	19.7990			1.28069			0.640345	+	0.768087i	$0.278791\pi$
$240$		0			0
$241$	−18.0000			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$242$	−2.12132	+	2.12132i	−0.136364	+	0.136364i
$243$		0			0
$244$			4.00000i			0.256074i
$245$	−4.94975	+	14.8492i	−0.316228	+	0.948683i
$246$		0			0
$247$	12.0000	+	12.0000i	0.763542	+	0.763542i
$248$	5.65685	+	5.65685i	0.359211	+	0.359211i
$249$		0			0
$250$	11.0000	+	2.00000i	0.695701	+	0.126491i
$251$			14.1421i			0.892644i	0.894873	+	0.446322i	$0.147266\pi$
$251$			14.1421i			0.892644i	−0.894873	+	0.446322i	$0.852734\pi$
$252$		0			0
$253$	2.00000	−	2.00000i	0.125739	−	0.125739i
$254$	14.1421			0.887357
$255$		0			0
$256$	1.00000			0.0625000
$257$	15.5563	−	15.5563i	0.970378	−	0.970378i	−0.0291953	−	0.999574i	$-0.509294\pi$
$257$	15.5563	−	15.5563i	0.970378	−	0.970378i	0.999574	+	0.0291953i	$0.00929448\pi$
$258$		0			0
$259$		0			0
$260$	−4.24264	−	8.48528i	−0.263117	−	0.526235i
$261$		0			0
$262$	−12.0000	−	12.0000i	−0.741362	−	0.741362i
$263$	19.7990	+	19.7990i	1.22086	+	1.22086i	0.967327	+	0.253531i	$0.0815919\pi$
$263$	19.7990	+	19.7990i	1.22086	+	1.22086i	0.253531	+	0.967327i	$0.418408\pi$
$264$		0			0
$265$	12.0000	+	24.0000i	0.737154	+	1.47431i
$266$		0			0
$267$		0			0
$268$	10.0000	−	10.0000i	0.610847	−	0.610847i
$269$	−21.2132			−1.29339			−0.646696	−	0.762748i	$-0.723850\pi$
$269$	−21.2132			−1.29339			−0.646696	+	0.762748i	$0.723850\pi$
$270$		0			0
$271$	−24.0000			−1.45790			−0.728948	−	0.684569i	$-0.759990\pi$
$271$	−24.0000			−1.45790			−0.728948	+	0.684569i	$0.759990\pi$
$272$	2.82843	−	2.82843i	0.171499	−	0.171499i
$273$		0			0
$274$			10.0000i			0.604122i
$275$	8.48528	−	11.3137i	0.511682	−	0.682242i
$276$		0			0
$277$	−3.00000	−	3.00000i	−0.180253	−	0.180253i	0.611213	−	0.791466i	$-0.290682\pi$
$277$	−3.00000	−	3.00000i	−0.180253	−	0.180253i	−0.791466	+	0.611213i	$0.790682\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	9.89949i		−	0.590554i	−0.955412	−	0.295277i	$-0.904588\pi$
$281$		−	9.89949i		−	0.590554i	0.955412	−	0.295277i	$-0.0954120\pi$
$282$		0			0
$283$	6.00000	−	6.00000i	0.356663	−	0.356663i	−0.505918	−	0.862581i	$-0.668846\pi$
$283$	6.00000	−	6.00000i	0.356663	−	0.356663i	0.862581	+	0.505918i	$0.168846\pi$
$284$	−14.1421			−0.839181
$285$		0			0
$286$	−12.0000			−0.709575
$287$		0			0
$288$		0			0
$289$			1.00000i			0.0588235i
$290$	−19.7990	+	9.89949i	−1.16264	+	0.581318i
$291$		0			0
$292$	−1.00000	−	1.00000i	−0.0585206	−	0.0585206i
$293$	4.24264	+	4.24264i	0.247858	+	0.247858i	0.820091	−	0.572233i	$-0.193923\pi$
$293$	4.24264	+	4.24264i	0.247858	+	0.247858i	−0.572233	+	0.820091i	$0.693923\pi$
$294$		0			0
$295$	−24.0000	−	8.00000i	−1.39733	−	0.465778i
$296$			9.89949i			0.575396i
$297$		0			0
$298$	−13.0000	+	13.0000i	−0.753070	+	0.753070i
$299$	−4.24264			−0.245358
$300$		0			0
$301$		0			0
$302$	−8.48528	+	8.48528i	−0.488273	+	0.488273i
$303$		0			0
$304$			4.00000i			0.229416i
$305$	8.48528	+	2.82843i	0.485866	+	0.161955i
$306$		0			0
$307$	12.0000	+	12.0000i	0.684876	+	0.684876i	0.961095	−	0.276219i	$-0.0890814\pi$
$307$	12.0000	+	12.0000i	0.684876	+	0.684876i	−0.276219	+	0.961095i	$0.589081\pi$
$308$		0			0
$309$		0			0
$310$	16.0000	−	8.00000i	0.908739	−	0.454369i
$311$			14.1421i			0.801927i	0.916094	+	0.400963i	$0.131325\pi$
$311$			14.1421i			0.801927i	−0.916094	+	0.400963i	$0.868675\pi$
$312$		0			0
$313$	13.0000	−	13.0000i	0.734803	−	0.734803i	−0.236764	−	0.971567i	$-0.576087\pi$
$313$	13.0000	−	13.0000i	0.734803	−	0.734803i	0.971567	+	0.236764i	$0.0760868\pi$
$314$	−12.7279			−0.718278
$315$		0			0
$316$	4.00000			0.225018
$317$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$317$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$318$		0			0
$319$			28.0000i			1.56770i
$320$	0.707107	−	2.12132i	0.0395285	−	0.118585i
$321$		0			0
$322$		0			0
$323$	11.3137	+	11.3137i	0.629512	+	0.629512i
$324$		0			0
$325$	−21.0000	+	3.00000i	−1.16487	+	0.166410i
$326$		−	16.9706i		−	0.939913i
$327$		0			0
$328$	−5.00000	+	5.00000i	−0.276079	+	0.276079i
$329$		0			0
$330$		0			0
$331$	−16.0000			−0.879440			−0.439720	−	0.898135i	$-0.644922\pi$
$331$	−16.0000			−0.879440			−0.439720	+	0.898135i	$0.644922\pi$
$332$	8.48528	−	8.48528i	0.465690	−	0.465690i
$333$		0			0
$334$			24.0000i			1.31322i
$335$	−14.1421	−	28.2843i	−0.772667	−	1.54533i
$336$		0			0
$337$	21.0000	+	21.0000i	1.14394	+	1.14394i	0.987722	+	0.156221i	$0.0499311\pi$
$337$	21.0000	+	21.0000i	1.14394	+	1.14394i	0.156221	+	0.987722i	$0.450069\pi$
$338$	3.53553	+	3.53553i	0.192308	+	0.192308i
$339$		0			0
$340$	−4.00000	−	8.00000i	−0.216930	−	0.433861i
$341$		−	22.6274i		−	1.22534i
$342$		0			0
$343$		0			0
$344$	2.82843			0.152499
$345$		0			0
$346$	2.00000			0.107521
$347$	8.48528	−	8.48528i	0.455514	−	0.455514i	−0.441666	−	0.897180i	$-0.645612\pi$
$347$	8.48528	−	8.48528i	0.455514	−	0.455514i	0.897180	+	0.441666i	$0.145612\pi$
$348$		0			0
$349$		−	16.0000i		−	0.856460i	−0.903670	−	0.428230i	$-0.859137\pi$
$349$		−	16.0000i		−	0.856460i	0.903670	−	0.428230i	$-0.140863\pi$
$350$		0			0
$351$		0			0
$352$	−2.00000	−	2.00000i	−0.106600	−	0.106600i
$353$	−16.9706	−	16.9706i	−0.903252	−	0.903252i	0.0924641	−	0.995716i	$-0.470526\pi$
$353$	−16.9706	−	16.9706i	−0.903252	−	0.903252i	−0.995716	+	0.0924641i	$0.970526\pi$
$354$		0			0
$355$	−10.0000	+	30.0000i	−0.530745	+	1.59223i
$356$		−	9.89949i		−	0.524672i
$357$		0			0
$358$	4.00000	−	4.00000i	0.211407	−	0.211407i
$359$	−11.3137			−0.597115			−0.298557	−	0.954392i	$-0.596505\pi$
$359$	−11.3137			−0.597115			−0.298557	+	0.954392i	$0.596505\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	−8.48528	+	8.48528i	−0.445976	+	0.445976i
$363$		0			0
$364$		0			0
$365$	−2.82843	+	1.41421i	−0.148047	+	0.0740233i
$366$		0			0
$367$	−20.0000	−	20.0000i	−1.04399	−	1.04399i	−0.998987	−	0.0450047i	$-0.985670\pi$
$367$	−20.0000	−	20.0000i	−1.04399	−	1.04399i	−0.0450047	−	0.998987i	$-0.514330\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$		0			0
$370$	21.0000	+	7.00000i	1.09174	+	0.363913i
$371$		0			0
$372$		0			0
$373$	−11.0000	+	11.0000i	−0.569558	+	0.569558i	−0.932005	−	0.362446i	$-0.881942\pi$
$373$	−11.0000	+	11.0000i	−0.569558	+	0.569558i	0.362446	+	0.932005i	$0.381942\pi$
$374$	−11.3137			−0.585018
$375$		0			0
$376$	4.00000			0.206284
$377$	29.6985	−	29.6985i	1.52955	−	1.52955i
$378$		0			0
$379$		−	24.0000i		−	1.23280i	−0.787434	−	0.616399i	$-0.788591\pi$
$379$		−	24.0000i		−	1.23280i	0.787434	−	0.616399i	$-0.211409\pi$
$380$	8.48528	+	2.82843i	0.435286	+	0.145095i
$381$		0			0
$382$	−4.00000	−	4.00000i	−0.204658	−	0.204658i
$383$	−8.48528	−	8.48528i	−0.433578	−	0.433578i	0.456266	−	0.889843i	$-0.349187\pi$
$383$	−8.48528	−	8.48528i	−0.433578	−	0.433578i	−0.889843	+	0.456266i	$0.849187\pi$
$384$		0			0
$385$		0			0
$386$		−	4.24264i		−	0.215945i
$387$		0			0
$388$	3.00000	−	3.00000i	0.152302	−	0.152302i
$389$	9.89949			0.501924			0.250962	−	0.967997i	$-0.419253\pi$
$389$	9.89949			0.501924			0.250962	+	0.967997i	$0.419253\pi$
$390$		0			0
$391$	−4.00000			−0.202289
$392$	4.94975	−	4.94975i	0.250000	−	0.250000i
$393$		0			0
$394$		−	22.0000i		−	1.10834i
$395$	2.82843	−	8.48528i	0.142314	−	0.426941i
$396$		0			0
$397$	19.0000	+	19.0000i	0.953583	+	0.953583i	0.998969	−	0.0453868i	$-0.0144520\pi$
$397$	19.0000	+	19.0000i	0.953583	+	0.953583i	−0.0453868	+	0.998969i	$0.514452\pi$
$398$	11.3137	+	11.3137i	0.567105	+	0.567105i
$399$		0			0
$400$	−4.00000	−	3.00000i	−0.200000	−	0.150000i
$401$			7.07107i			0.353112i	0.984291	+	0.176556i	$0.0564957\pi$
$401$			7.07107i			0.353112i	−0.984291	+	0.176556i	$0.943504\pi$
$402$		0			0
$403$	−24.0000	+	24.0000i	−1.19553	+	1.19553i
$404$	12.7279			0.633238
$405$		0			0
$406$		0			0
$407$	19.7990	−	19.7990i	0.981399	−	0.981399i
$408$		0			0
$409$		−	32.0000i		−	1.58230i	−0.611623	−	0.791149i	$-0.709483\pi$
$409$		−	32.0000i		−	1.58230i	0.611623	−	0.791149i	$-0.290517\pi$
$410$	7.07107	+	14.1421i	0.349215	+	0.698430i
$411$		0			0
$412$	−8.00000	−	8.00000i	−0.394132	−	0.394132i
$413$		0			0
$414$		0			0
$415$	−12.0000	−	24.0000i	−0.589057	−	1.17811i
$416$			4.24264i			0.208013i
$417$		0			0
$418$	8.00000	−	8.00000i	0.391293	−	0.391293i
$419$	31.1127			1.51995			0.759977	−	0.649950i	$-0.225210\pi$
$419$	31.1127			1.51995			0.759977	+	0.649950i	$0.225210\pi$
$420$		0			0
$421$	−26.0000			−1.26716			−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000			−1.26716			−0.633581	+	0.773676i	$0.718416\pi$
$422$	16.9706	−	16.9706i	0.826114	−	0.826114i
$423$		0			0
$424$		−	12.0000i		−	0.582772i
$425$	−19.7990	+	2.82843i	−0.960392	+	0.137199i
$426$		0			0
$427$		0			0
$428$	5.65685	+	5.65685i	0.273434	+	0.273434i
$429$		0			0
$430$	2.00000	−	6.00000i	0.0964486	−	0.289346i
$431$			11.3137i			0.544962i	0.962161	+	0.272481i	$0.0878442\pi$
$431$			11.3137i			0.544962i	−0.962161	+	0.272481i	$0.912156\pi$
$432$		0			0
$433$	5.00000	−	5.00000i	0.240285	−	0.240285i	−0.576683	−	0.816968i	$-0.695653\pi$
$433$	5.00000	−	5.00000i	0.240285	−	0.240285i	0.816968	+	0.576683i	$0.195653\pi$
$434$		0			0
$435$		0			0
$436$	12.0000			0.574696
$437$	2.82843	−	2.82843i	0.135302	−	0.135302i
$438$		0			0
$439$			4.00000i			0.190910i	0.995434	+	0.0954548i	$0.0304305\pi$
$439$			4.00000i			0.190910i	−0.995434	+	0.0954548i	$0.969569\pi$
$440$	−5.65685	+	2.82843i	−0.269680	+	0.134840i
$441$		0			0
$442$	12.0000	+	12.0000i	0.570782	+	0.570782i
$443$	−2.82843	−	2.82843i	−0.134383	−	0.134383i	0.636716	−	0.771099i	$-0.280292\pi$
$443$	−2.82843	−	2.82843i	−0.134383	−	0.134383i	−0.771099	+	0.636716i	$0.780292\pi$
$444$		0			0
$445$	−21.0000	−	7.00000i	−0.995495	−	0.331832i
$446$		−	8.48528i		−	0.401790i
$447$		0			0
$448$		0			0
$449$	1.41421			0.0667409			0.0333704	−	0.999443i	$-0.489376\pi$
$449$	1.41421			0.0667409			0.0333704	+	0.999443i	$0.489376\pi$
$450$		0			0
$451$	20.0000			0.941763
$452$	9.89949	−	9.89949i	0.465633	−	0.465633i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	15.0000	+	15.0000i	0.701670	+	0.701670i	0.964769	−	0.263099i	$-0.0847444\pi$
$457$	15.0000	+	15.0000i	0.701670	+	0.701670i	−0.263099	+	0.964769i	$0.584744\pi$
$458$	9.89949	+	9.89949i	0.462573	+	0.462573i
$459$		0			0
$460$	−2.00000	+	1.00000i	−0.0932505	+	0.0466252i
$461$		−	35.3553i		−	1.64666i	−0.567561	−	0.823331i	$-0.692113\pi$
$461$		−	35.3553i		−	1.64666i	0.567561	−	0.823331i	$-0.307887\pi$
$462$		0			0
$463$	−30.0000	+	30.0000i	−1.39422	+	1.39422i	−0.578623	+	0.815595i	$0.696410\pi$
$463$	−30.0000	+	30.0000i	−1.39422	+	1.39422i	−0.815595	+	0.578623i	$0.803590\pi$
$464$	9.89949			0.459573
$465$		0			0
$466$	−24.0000			−1.11178
$467$	14.1421	−	14.1421i	0.654420	−	0.654420i	−0.299634	−	0.954054i	$-0.596865\pi$
$467$	14.1421	−	14.1421i	0.654420	−	0.654420i	0.954054	+	0.299634i	$0.0968646\pi$
$468$		0			0
$469$		0			0
$470$	2.82843	−	8.48528i	0.130466	−	0.391397i
$471$		0			0
$472$	8.00000	+	8.00000i	0.368230	+	0.368230i
$473$	−5.65685	−	5.65685i	−0.260102	−	0.260102i
$474$		0			0
$475$	12.0000	−	16.0000i	0.550598	−	0.734130i
$476$		0			0
$477$		0			0
$478$	−14.0000	+	14.0000i	−0.640345	+	0.640345i
$479$	11.3137			0.516937			0.258468	−	0.966020i	$-0.416782\pi$
$479$	11.3137			0.516937			0.258468	+	0.966020i	$0.416782\pi$
$480$		0			0
$481$	−42.0000			−1.91504
$482$	12.7279	−	12.7279i	0.579741	−	0.579741i
$483$		0			0
$484$		−	3.00000i		−	0.136364i
$485$	−4.24264	−	8.48528i	−0.192648	−	0.385297i
$486$		0			0
$487$	2.00000	+	2.00000i	0.0906287	+	0.0906287i	0.750968	−	0.660339i	$-0.229587\pi$
$487$	2.00000	+	2.00000i	0.0906287	+	0.0906287i	−0.660339	+	0.750968i	$0.729587\pi$
$488$	−2.82843	−	2.82843i	−0.128037	−	0.128037i
$489$		0			0
$490$	−7.00000	−	14.0000i	−0.316228	−	0.632456i
$491$		−	5.65685i		−	0.255290i	−0.991820	−	0.127645i	$-0.959258\pi$
$491$		−	5.65685i		−	0.255290i	0.991820	−	0.127645i	$-0.0407419\pi$
$492$		0			0
$493$	28.0000	−	28.0000i	1.26106	−	1.26106i
$494$	−16.9706			−0.763542
$495$		0			0
$496$	−8.00000			−0.359211
$497$		0			0
$498$		0			0
$499$		−	40.0000i		−	1.79065i	−0.445418	−	0.895323i	$-0.646945\pi$
$499$		−	40.0000i		−	1.79065i	0.445418	−	0.895323i	$-0.353055\pi$
$500$	−9.19239	+	6.36396i	−0.411096	+	0.284605i
$501$		0			0
$502$	−10.0000	−	10.0000i	−0.446322	−	0.446322i
$503$	−11.3137	−	11.3137i	−0.504453	−	0.504453i	0.408365	−	0.912819i	$-0.366099\pi$
$503$	−11.3137	−	11.3137i	−0.504453	−	0.504453i	−0.912819	+	0.408365i	$0.866099\pi$
$504$		0			0
$505$	9.00000	−	27.0000i	0.400495	−	1.20148i
$506$			2.82843i			0.125739i
$507$		0			0
$508$	−10.0000	+	10.0000i	−0.443678	+	0.443678i
$509$	−12.7279			−0.564155			−0.282078	−	0.959392i	$-0.591024\pi$
$509$	−12.7279			−0.564155			−0.282078	+	0.959392i	$0.591024\pi$
$510$		0			0
$511$		0			0
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			22.0000i			0.970378i
$515$	−22.6274	+	11.3137i	−0.997083	+	0.498542i
$516$		0			0
$517$	−8.00000	−	8.00000i	−0.351840	−	0.351840i
$518$		0			0
$519$		0			0
$520$	9.00000	+	3.00000i	0.394676	+	0.131559i
$521$		−	7.07107i		−	0.309789i	−0.987931	−	0.154895i	$-0.950496\pi$
$521$		−	7.07107i		−	0.309789i	0.987931	−	0.154895i	$-0.0495038\pi$
$522$		0			0
$523$	6.00000	−	6.00000i	0.262362	−	0.262362i	−0.563651	−	0.826013i	$-0.690604\pi$
$523$	6.00000	−	6.00000i	0.262362	−	0.262362i	0.826013	+	0.563651i	$0.190604\pi$
$524$	16.9706			0.741362
$525$		0			0
$526$	−28.0000			−1.22086
$527$	−22.6274	+	22.6274i	−0.985666	+	0.985666i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$	−25.4558	−	8.48528i	−1.10573	−	0.368577i
$531$		0			0
$532$		0			0
$533$	−21.2132	−	21.2132i	−0.918846	−	0.918846i
$534$		0			0
$535$	16.0000	−	8.00000i	0.691740	−	0.345870i
$536$			14.1421i			0.610847i
$537$		0			0
$538$	15.0000	−	15.0000i	0.646696	−	0.646696i
$539$	−19.7990			−0.852803
$540$		0			0
$541$		0			0			−	1.00000i	$-0.5\pi$
$541$		0			0				1.00000i	$0.5\pi$
$542$	16.9706	−	16.9706i	0.728948	−	0.728948i
$543$		0			0
$544$			4.00000i			0.171499i
$545$	8.48528	−	25.4558i	0.363470	−	1.09041i
$546$		0			0
$547$	4.00000	+	4.00000i	0.171028	+	0.171028i	0.787431	−	0.616403i	$-0.211411\pi$
$547$	4.00000	+	4.00000i	0.171028	+	0.171028i	−0.616403	+	0.787431i	$0.711411\pi$
$548$	−7.07107	−	7.07107i	−0.302061	−	0.302061i
$549$		0			0
$550$	2.00000	+	14.0000i	0.0852803	+	0.596962i
$551$			39.5980i			1.68693i
$552$		0			0
$553$		0			0
$554$	4.24264			0.180253
$555$		0			0
$556$		0			0
$557$	−8.48528	+	8.48528i	−0.359533	+	0.359533i	−0.863641	−	0.504108i	$-0.831821\pi$
$557$	−8.48528	+	8.48528i	−0.359533	+	0.359533i	0.504108	+	0.863641i	$0.331821\pi$
$558$		0			0
$559$			12.0000i			0.507546i
$560$		0			0
$561$		0			0
$562$	7.00000	+	7.00000i	0.295277	+	0.295277i
$563$	2.82843	+	2.82843i	0.119204	+	0.119204i	0.764192	−	0.644988i	$-0.223138\pi$
$563$	2.82843	+	2.82843i	0.119204	+	0.119204i	−0.644988	+	0.764192i	$0.723138\pi$
$564$		0			0
$565$	−14.0000	−	28.0000i	−0.588984	−	1.17797i
$566$			8.48528i			0.356663i
$567$		0			0
$568$	10.0000	−	10.0000i	0.419591	−	0.419591i
$569$	−32.5269			−1.36360			−0.681800	−	0.731539i	$-0.738802\pi$
$569$	−32.5269			−1.36360			−0.681800	+	0.731539i	$0.738802\pi$
$570$		0			0
$571$	8.00000			0.334790			0.167395	−	0.985890i	$-0.446465\pi$
$571$	8.00000			0.334790			0.167395	+	0.985890i	$0.446465\pi$
$572$	8.48528	−	8.48528i	0.354787	−	0.354787i
$573$		0			0
$574$		0			0
$575$	0.707107	+	4.94975i	0.0294884	+	0.206419i
$576$		0			0
$577$	−5.00000	−	5.00000i	−0.208153	−	0.208153i	0.595329	−	0.803482i	$-0.297022\pi$
$577$	−5.00000	−	5.00000i	−0.208153	−	0.208153i	−0.803482	+	0.595329i	$0.797022\pi$
$578$	−0.707107	−	0.707107i	−0.0294118	−	0.0294118i
$579$		0			0
$580$	7.00000	−	21.0000i	0.290659	−	0.871978i
$581$		0			0
$582$		0			0
$583$	−24.0000	+	24.0000i	−0.993978	+	0.993978i
$584$	1.41421			0.0585206
$585$		0			0
$586$	−6.00000			−0.247858
$587$	14.1421	−	14.1421i	0.583708	−	0.583708i	−0.352212	−	0.935920i	$-0.614570\pi$
$587$	14.1421	−	14.1421i	0.583708	−	0.583708i	0.935920	+	0.352212i	$0.114570\pi$
$588$		0			0
$589$		−	32.0000i		−	1.31854i
$590$	22.6274	−	11.3137i	0.931556	−	0.465778i
$591$		0			0
$592$	−7.00000	−	7.00000i	−0.287698	−	0.287698i
$593$	−18.3848	−	18.3848i	−0.754972	−	0.754972i	0.220430	−	0.975403i	$-0.429254\pi$
$593$	−18.3848	−	18.3848i	−0.754972	−	0.754972i	−0.975403	+	0.220430i	$0.929254\pi$
$594$		0			0
$595$		0			0
$596$		−	18.3848i		−	0.753070i
$597$		0			0
$598$	3.00000	−	3.00000i	0.122679	−	0.122679i
$599$	−19.7990			−0.808965			−0.404482	−	0.914546i	$-0.632548\pi$
$599$	−19.7990			−0.808965			−0.404482	+	0.914546i	$0.632548\pi$
$600$		0			0
$601$		0			0			−	1.00000i	$-0.5\pi$
$601$		0			0				1.00000i	$0.5\pi$
$602$		0			0
$603$		0			0
$604$		−	12.0000i		−	0.488273i
$605$	−6.36396	−	2.12132i	−0.258732	−	0.0862439i
$606$		0			0
$607$	2.00000	+	2.00000i	0.0811775	+	0.0811775i	0.746530	−	0.665352i	$-0.231719\pi$
$607$	2.00000	+	2.00000i	0.0811775	+	0.0811775i	−0.665352	+	0.746530i	$0.731719\pi$
$608$	−2.82843	−	2.82843i	−0.114708	−	0.114708i
$609$		0			0
$610$	−8.00000	+	4.00000i	−0.323911	+	0.161955i
$611$			16.9706i			0.686555i
$612$		0			0
$613$	−13.0000	+	13.0000i	−0.525065	+	0.525065i	−0.919097	−	0.394032i	$-0.871080\pi$
$613$	−13.0000	+	13.0000i	−0.525065	+	0.525065i	0.394032	+	0.919097i	$0.371080\pi$
$614$	−16.9706			−0.684876
$615$		0			0
$616$		0			0
$617$	8.48528	−	8.48528i	0.341605	−	0.341605i	−0.515366	−	0.856970i	$-0.672344\pi$
$617$	8.48528	−	8.48528i	0.341605	−	0.341605i	0.856970	+	0.515366i	$0.172344\pi$
$618$		0			0
$619$			44.0000i			1.76851i	0.467005	+	0.884255i	$0.345333\pi$
$619$			44.0000i			1.76851i	−0.467005	+	0.884255i	$0.654667\pi$
$620$	−5.65685	+	16.9706i	−0.227185	+	0.681554i
$621$		0			0
$622$	−10.0000	−	10.0000i	−0.400963	−	0.400963i
$623$		0			0
$624$		0			0
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$			18.3848i			0.734803i
$627$		0			0
$628$	9.00000	−	9.00000i	0.359139	−	0.359139i
$629$	−39.5980			−1.57887
$630$		0			0
$631$	20.0000			0.796187			0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000			0.796187			0.398094	+	0.917345i	$0.369672\pi$
$632$	−2.82843	+	2.82843i	−0.112509	+	0.112509i
$633$		0			0
$634$		0			0
$635$	14.1421	+	28.2843i	0.561214	+	1.12243i
$636$		0			0
$637$	21.0000	+	21.0000i	0.832050	+	0.832050i
$638$	−19.7990	−	19.7990i	−0.783850	−	0.783850i
$639$		0			0
$640$	1.00000	+	2.00000i	0.0395285	+	0.0790569i
$641$			43.8406i			1.73160i	0.500390	+	0.865800i	$0.333190\pi$
$641$			43.8406i			1.73160i	−0.500390	+	0.865800i	$0.666810\pi$
$642$		0			0
$643$	−22.0000	+	22.0000i	−0.867595	+	0.867595i	−0.992206	−	0.124610i	$-0.960232\pi$
$643$	−22.0000	+	22.0000i	−0.867595	+	0.867595i	0.124610	+	0.992206i	$0.460232\pi$
$644$		0			0
$645$		0			0
$646$	−16.0000			−0.629512
$647$	−8.48528	+	8.48528i	−0.333591	+	0.333591i	−0.853948	−	0.520358i	$-0.825799\pi$
$647$	−8.48528	+	8.48528i	−0.333591	+	0.333591i	0.520358	+	0.853948i	$0.325799\pi$
$648$		0			0
$649$		−	32.0000i		−	1.25611i
$650$	12.7279	−	16.9706i	0.499230	−	0.665640i
$651$		0			0
$652$	12.0000	+	12.0000i	0.469956	+	0.469956i
$653$	16.9706	+	16.9706i	0.664109	+	0.664109i	0.956346	−	0.292237i	$-0.0943995\pi$
$653$	16.9706	+	16.9706i	0.664109	+	0.664109i	−0.292237	+	0.956346i	$0.594399\pi$
$654$		0			0
$655$	12.0000	−	36.0000i	0.468879	−	1.40664i
$656$		−	7.07107i		−	0.276079i
$657$		0			0
$658$		0			0
$659$	31.1127			1.21198			0.605989	−	0.795473i	$-0.292777\pi$
$659$	31.1127			1.21198			0.605989	+	0.795473i	$0.292777\pi$
$660$		0			0
$661$	−4.00000			−0.155582			−0.0777910	−	0.996970i	$-0.524787\pi$
$661$	−4.00000			−0.155582			−0.0777910	+	0.996970i	$0.524787\pi$
$662$	11.3137	−	11.3137i	0.439720	−	0.439720i
$663$		0			0
$664$			12.0000i			0.465690i
$665$		0			0
$666$		0			0
$667$	−7.00000	−	7.00000i	−0.271041	−	0.271041i
$668$	−16.9706	−	16.9706i	−0.656611	−	0.656611i
$669$		0			0
$670$	30.0000	+	10.0000i	1.15900	+	0.386334i
$671$			11.3137i			0.436761i
$672$		0			0
$673$	−7.00000	+	7.00000i	−0.269830	+	0.269830i	−0.829032	−	0.559202i	$-0.811108\pi$
$673$	−7.00000	+	7.00000i	−0.269830	+	0.269830i	0.559202	+	0.829032i	$0.311108\pi$
$674$	−29.6985			−1.14394
$675$		0			0
$676$	−5.00000			−0.192308
$677$	−19.7990	+	19.7990i	−0.760937	+	0.760937i	−0.976492	−	0.215555i	$-0.930844\pi$
$677$	−19.7990	+	19.7990i	−0.760937	+	0.760937i	0.215555	+	0.976492i	$0.430844\pi$
$678$		0			0
$679$		0			0
$680$	8.48528	+	2.82843i	0.325396	+	0.108465i
$681$		0			0
$682$	16.0000	+	16.0000i	0.612672	+	0.612672i
$683$	−25.4558	−	25.4558i	−0.974041	−	0.974041i	0.0256307	−	0.999671i	$-0.491841\pi$
$683$	−25.4558	−	25.4558i	−0.974041	−	0.974041i	−0.999671	+	0.0256307i	$0.991841\pi$
$684$		0			0
$685$	−20.0000	+	10.0000i	−0.764161	+	0.382080i
$686$		0			0
$687$		0			0
$688$	−2.00000	+	2.00000i	−0.0762493	+	0.0762493i
$689$	50.9117			1.93958
$690$		0			0
$691$	52.0000			1.97817			0.989087	−	0.147335i	$-0.0470696\pi$
$691$	52.0000			1.97817			0.989087	+	0.147335i	$0.0470696\pi$
$692$	−1.41421	+	1.41421i	−0.0537603	+	0.0537603i
$693$		0			0
$694$			12.0000i			0.455514i
$695$		0			0
$696$		0			0
$697$	−20.0000	−	20.0000i	−0.757554	−	0.757554i
$698$	11.3137	+	11.3137i	0.428230	+	0.428230i
$699$		0			0
$700$		0			0
$701$		−	49.4975i		−	1.86949i	−0.355314	−	0.934747i	$-0.615626\pi$
$701$		−	49.4975i		−	1.86949i	0.355314	−	0.934747i	$-0.384374\pi$
$702$		0			0
$703$	28.0000	−	28.0000i	1.05604	−	1.05604i
$704$	2.82843			0.106600
$705$		0			0
$706$	24.0000			0.903252
$707$		0			0
$708$		0			0
$709$		−	18.0000i		−	0.676004i	−0.941145	−	0.338002i	$-0.890249\pi$
$709$		−	18.0000i		−	0.676004i	0.941145	−	0.338002i	$-0.109751\pi$
$710$	−14.1421	−	28.2843i	−0.530745	−	1.06149i
$711$		0			0
$712$	7.00000	+	7.00000i	0.262336	+	0.262336i
$713$	5.65685	+	5.65685i	0.211851	+	0.211851i
$714$		0			0
$715$	−12.0000	−	24.0000i	−0.448775	−	0.897549i
$716$			5.65685i			0.211407i
$717$		0			0
$718$	8.00000	−	8.00000i	0.298557	−	0.298557i
$719$	19.7990			0.738378			0.369189	−	0.929354i	$-0.379636\pi$
$719$	19.7990			0.738378			0.369189	+	0.929354i	$0.379636\pi$
$720$		0			0
$721$		0			0
$722$	−2.12132	+	2.12132i	−0.0789474	+	0.0789474i
$723$		0			0
$724$		−	12.0000i		−	0.445976i
$725$	−39.5980	−	29.6985i	−1.47063	−	1.10297i
$726$		0			0
$727$	−8.00000	−	8.00000i	−0.296704	−	0.296704i	0.543018	−	0.839721i	$-0.317282\pi$
$727$	−8.00000	−	8.00000i	−0.296704	−	0.296704i	−0.839721	+	0.543018i	$0.817282\pi$
$728$		0			0
$729$		0			0
$730$	1.00000	−	3.00000i	0.0370117	−	0.111035i
$731$			11.3137i			0.418453i
$732$		0			0
$733$	−25.0000	+	25.0000i	−0.923396	+	0.923396i	−0.997268	−	0.0738717i	$-0.976464\pi$
$733$	−25.0000	+	25.0000i	−0.923396	+	0.923396i	0.0738717	+	0.997268i	$0.476464\pi$
$734$	28.2843			1.04399
$735$		0			0
$736$	1.00000			0.0368605
$737$	28.2843	−	28.2843i	1.04186	−	1.04186i
$738$		0			0
$739$			12.0000i			0.441427i	0.975339	+	0.220714i	$0.0708386\pi$
$739$			12.0000i			0.441427i	−0.975339	+	0.220714i	$0.929161\pi$
$740$	−19.7990	+	9.89949i	−0.727825	+	0.363913i
$741$		0			0
$742$		0			0
$743$	2.82843	+	2.82843i	0.103765	+	0.103765i	0.757083	−	0.653318i	$-0.226624\pi$
$743$	2.82843	+	2.82843i	0.103765	+	0.103765i	−0.653318	+	0.757083i	$0.726624\pi$
$744$		0			0
$745$	−39.0000	−	13.0000i	−1.42885	−	0.476283i
$746$		−	15.5563i		−	0.569558i
$747$		0			0
$748$	8.00000	−	8.00000i	0.292509	−	0.292509i
$749$		0			0
$750$		0			0
$751$		0			0			−	1.00000i	$-0.5\pi$
$751$		0			0				1.00000i	$0.5\pi$
$752$	−2.82843	+	2.82843i	−0.103142	+	0.103142i
$753$		0			0
$754$			42.0000i			1.52955i
$755$	−25.4558	−	8.48528i	−0.926433	−	0.308811i
$756$		0			0
$757$	9.00000	+	9.00000i	0.327111	+	0.327111i	0.851487	−	0.524376i	$-0.175701\pi$
$757$	9.00000	+	9.00000i	0.327111	+	0.327111i	−0.524376	+	0.851487i	$0.675701\pi$
$758$	16.9706	+	16.9706i	0.616399	+	0.616399i
$759$		0			0
$760$	−8.00000	+	4.00000i	−0.290191	+	0.145095i
$761$			24.0416i			0.871508i	0.900066	+	0.435754i	$0.143518\pi$
$761$			24.0416i			0.871508i	−0.900066	+	0.435754i	$0.856482\pi$
$762$		0			0
$763$		0			0
$764$	5.65685			0.204658
$765$		0			0
$766$	12.0000			0.433578
$767$	−33.9411	+	33.9411i	−1.22554	+	1.22554i
$768$		0			0
$769$		−	12.0000i		−	0.432731i	−0.976312	−	0.216366i	$-0.930580\pi$
$769$		−	12.0000i		−	0.432731i	0.976312	−	0.216366i	$-0.0694203\pi$
$770$		0			0
$771$		0			0
$772$	3.00000	+	3.00000i	0.107972	+	0.107972i
$773$	2.82843	+	2.82843i	0.101731	+	0.101731i	0.756141	−	0.654409i	$-0.227083\pi$
$773$	2.82843	+	2.82843i	0.101731	+	0.101731i	−0.654409	+	0.756141i	$0.727083\pi$
$774$		0			0
$775$	32.0000	+	24.0000i	1.14947	+	0.862105i
$776$			4.24264i			0.152302i
$777$		0			0
$778$	−7.00000	+	7.00000i	−0.250962	+	0.250962i
$779$	28.2843			1.01339
$780$		0			0
$781$	−40.0000			−1.43131
$782$	2.82843	−	2.82843i	0.101144	−	0.101144i
$783$		0			0
$784$			7.00000i			0.250000i
$785$	−12.7279	−	25.4558i	−0.454279	−	0.908558i
$786$		0			0
$787$	−6.00000	−	6.00000i	−0.213877	−	0.213877i	0.592035	−	0.805912i	$-0.298325\pi$
$787$	−6.00000	−	6.00000i	−0.213877	−	0.213877i	−0.805912	+	0.592035i	$0.798325\pi$
$788$	15.5563	+	15.5563i	0.554172	+	0.554172i
$789$		0			0
$790$	4.00000	+	8.00000i	0.142314	+	0.284627i
$791$		0			0
$792$		0			0
$793$	12.0000	−	12.0000i	0.426132	−	0.426132i
$794$	−26.8701			−0.953583
$795$		0			0
$796$	−16.0000			−0.567105
$797$	4.24264	−	4.24264i	0.150282	−	0.150282i	−0.627962	−	0.778244i	$-0.716111\pi$
$797$	4.24264	−	4.24264i	0.150282	−	0.150282i	0.778244	+	0.627962i	$0.216111\pi$
$798$		0			0
$799$			16.0000i			0.566039i
$800$	4.94975	−	0.707107i	0.175000	−	0.0250000i
$801$		0			0
$802$	−5.00000	−	5.00000i	−0.176556	−	0.176556i
$803$	−2.82843	−	2.82843i	−0.0998130	−	0.0998130i
$804$		0			0
$805$		0			0
$806$		−	33.9411i		−	1.19553i
$807$		0			0
$808$	−9.00000	+	9.00000i	−0.316619	+	0.316619i
$809$	9.89949			0.348048			0.174024	−	0.984741i	$-0.444323\pi$
$809$	9.89949			0.348048			0.174024	+	0.984741i	$0.444323\pi$
$810$		0			0
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$		0			0
$813$		0			0
$814$			28.0000i			0.981399i
$815$	33.9411	−	16.9706i	1.18891	−	0.594453i
$816$		0			0
$817$	−8.00000	−	8.00000i	−0.279885	−	0.279885i
$818$	22.6274	+	22.6274i	0.791149	+	0.791149i
$819$		0			0
$820$	−15.0000	−	5.00000i	−0.523823	−	0.174608i
$821$			12.7279i			0.444208i	0.975023	+	0.222104i	$0.0712924\pi$
$821$			12.7279i			0.444208i	−0.975023	+	0.222104i	$0.928708\pi$
$822$		0			0
$823$	−2.00000	+	2.00000i	−0.0697156	+	0.0697156i	−0.741105	−	0.671389i	$-0.765698\pi$
$823$	−2.00000	+	2.00000i	−0.0697156	+	0.0697156i	0.671389	+	0.741105i	$0.265698\pi$
$824$	11.3137			0.394132
$825$		0			0
$826$		0			0
$827$	−11.3137	+	11.3137i	−0.393416	+	0.393416i	−0.875903	−	0.482487i	$-0.839734\pi$
$827$	−11.3137	+	11.3137i	−0.393416	+	0.393416i	0.482487	+	0.875903i	$0.339734\pi$
$828$		0			0
$829$			16.0000i			0.555703i	0.960624	+	0.277851i	$0.0896223\pi$
$829$			16.0000i			0.555703i	−0.960624	+	0.277851i	$0.910378\pi$
$830$	25.4558	+	8.48528i	0.883585	+	0.294528i
$831$		0			0
$832$	−3.00000	−	3.00000i	−0.104006	−	0.104006i
$833$	19.7990	+	19.7990i	0.685994	+	0.685994i
$834$		0			0
$835$	−48.0000	+	24.0000i	−1.66111	+	0.830554i
$836$			11.3137i			0.391293i
$837$		0			0
$838$	−22.0000	+	22.0000i	−0.759977	+	0.759977i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	69.0000			2.37931
$842$	18.3848	−	18.3848i	0.633581	−	0.633581i
$843$		0			0
$844$			24.0000i			0.826114i
$845$	−3.53553	+	10.6066i	−0.121626	+	0.364878i
$846$		0			0
$847$		0			0
$848$	8.48528	+	8.48528i	0.291386	+	0.291386i
$849$		0			0
$850$	12.0000	−	16.0000i	0.411597	−	0.548795i
$851$			9.89949i			0.339350i
$852$		0			0
$853$	31.0000	−	31.0000i	1.06142	−	1.06142i	0.0634337	−	0.997986i	$-0.479795\pi$
$853$	31.0000	−	31.0000i	1.06142	−	1.06142i	0.997986	−	0.0634337i	$-0.0202051\pi$
$854$		0			0
$855$		0			0
$856$	−8.00000			−0.273434
$857$	−22.6274	+	22.6274i	−0.772938	+	0.772938i	−0.978619	−	0.205681i	$-0.934059\pi$
$857$	−22.6274	+	22.6274i	−0.772938	+	0.772938i	0.205681	+	0.978619i	$0.434059\pi$
$858$		0			0
$859$		−	20.0000i		−	0.682391i	−0.939992	−	0.341196i	$-0.889168\pi$
$859$		−	20.0000i		−	0.682391i	0.939992	−	0.341196i	$-0.110832\pi$
$860$	2.82843	+	5.65685i	0.0964486	+	0.192897i
$861$		0			0
$862$	−8.00000	−	8.00000i	−0.272481	−	0.272481i
$863$	19.7990	+	19.7990i	0.673965	+	0.673965i	0.958628	−	0.284662i	$-0.0918815\pi$
$863$	19.7990	+	19.7990i	0.673965	+	0.673965i	−0.284662	+	0.958628i	$0.591881\pi$
$864$		0			0
$865$	2.00000	+	4.00000i	0.0680020	+	0.136004i
$866$			7.07107i			0.240285i
$867$		0			0
$868$		0			0
$869$	11.3137			0.383791
$870$		0			0
$871$	−60.0000			−2.03302
$872$	−8.48528	+	8.48528i	−0.287348	+	0.287348i
$873$		0			0
$874$			4.00000i			0.135302i
$875$		0			0
$876$		0			0
$877$	1.00000	+	1.00000i	0.0337676	+	0.0337676i	0.723789	−	0.690021i	$-0.242399\pi$
$877$	1.00000	+	1.00000i	0.0337676	+	0.0337676i	−0.690021	+	0.723789i	$0.742399\pi$
$878$	−2.82843	−	2.82843i	−0.0954548	−	0.0954548i
$879$		0			0
$880$	2.00000	−	6.00000i	0.0674200	−	0.202260i
$881$			41.0122i			1.38174i	0.722981	+	0.690868i	$0.242771\pi$
$881$			41.0122i			1.38174i	−0.722981	+	0.690868i	$0.757229\pi$
$882$		0			0
$883$	16.0000	−	16.0000i	0.538443	−	0.538443i	−0.384629	−	0.923071i	$-0.625670\pi$
$883$	16.0000	−	16.0000i	0.538443	−	0.538443i	0.923071	+	0.384629i	$0.125670\pi$
$884$	−16.9706			−0.570782
$885$		0			0
$886$	4.00000			0.134383
$887$	25.4558	−	25.4558i	0.854724	−	0.854724i	−0.135987	−	0.990711i	$-0.543421\pi$
$887$	25.4558	−	25.4558i	0.854724	−	0.854724i	0.990711	+	0.135987i	$0.0434205\pi$
$888$		0			0
$889$		0			0
$890$	19.7990	−	9.89949i	0.663664	−	0.331832i
$891$		0			0
$892$	6.00000	+	6.00000i	0.200895	+	0.200895i
$893$	−11.3137	−	11.3137i	−0.378599	−	0.378599i
$894$		0			0
$895$	12.0000	+	4.00000i	0.401116	+	0.133705i
$896$		0			0
$897$		0			0
$898$	−1.00000	+	1.00000i	−0.0333704	+	0.0333704i
$899$	−79.1960			−2.64133
$900$		0			0
$901$	48.0000			1.59911
$902$	−14.1421	+	14.1421i	−0.470882	+	0.470882i
$903$		0			0
$904$			14.0000i			0.465633i
$905$	−25.4558	−	8.48528i	−0.846181	−	0.282060i
$906$		0			0
$907$	−6.00000	−	6.00000i	−0.199227	−	0.199227i	0.600442	−	0.799668i	$-0.294991\pi$
$907$	−6.00000	−	6.00000i	−0.199227	−	0.199227i	−0.799668	+	0.600442i	$0.794991\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			33.9411i			1.12452i	0.826961	+	0.562260i	$0.190068\pi$
$911$			33.9411i			1.12452i	−0.826961	+	0.562260i	$0.809932\pi$
$912$		0			0
$913$	24.0000	−	24.0000i	0.794284	−	0.794284i
$914$	−21.2132			−0.701670
$915$		0			0
$916$	−14.0000			−0.462573
$917$		0			0
$918$		0			0
$919$			16.0000i			0.527791i	0.964551	+	0.263896i	$0.0850075\pi$
$919$			16.0000i			0.527791i	−0.964551	+	0.263896i	$0.914993\pi$
$920$	0.707107	−	2.12132i	0.0233126	−	0.0699379i
$921$		0			0
$922$	25.0000	+	25.0000i	0.823331	+	0.823331i
$923$	42.4264	+	42.4264i	1.39648	+	1.39648i
$924$		0			0
$925$	7.00000	+	49.0000i	0.230159	+	1.61111i
$926$		−	42.4264i		−	1.39422i
$927$		0			0
$928$	−7.00000	+	7.00000i	−0.229786	+	0.229786i
$929$	35.3553			1.15997			0.579986	−	0.814627i	$-0.303058\pi$
$929$	35.3553			1.15997			0.579986	+	0.814627i	$0.303058\pi$
$930$		0			0
$931$	−28.0000			−0.917663
$932$	16.9706	−	16.9706i	0.555889	−	0.555889i
$933$		0			0
$934$			20.0000i			0.654420i
$935$	−11.3137	−	22.6274i	−0.369998	−	0.739996i
$936$		0			0
$937$	27.0000	+	27.0000i	0.882052	+	0.882052i	0.993743	−	0.111691i	$-0.0356268\pi$
$937$	27.0000	+	27.0000i	0.882052	+	0.882052i	−0.111691	+	0.993743i	$0.535627\pi$
$938$		0			0
$939$		0			0
$940$	4.00000	+	8.00000i	0.130466	+	0.260931i
$941$			43.8406i			1.42916i	0.699552	+	0.714582i	$0.253383\pi$
$941$			43.8406i			1.42916i	−0.699552	+	0.714582i	$0.746617\pi$
$942$		0			0
$943$	−5.00000	+	5.00000i	−0.162822	+	0.162822i
$944$	−11.3137			−0.368230
$945$		0			0
$946$	8.00000			0.260102
$947$	−16.9706	+	16.9706i	−0.551469	+	0.551469i	−0.926865	−	0.375396i	$-0.877507\pi$
$947$	−16.9706	+	16.9706i	−0.551469	+	0.551469i	0.375396	+	0.926865i	$0.377507\pi$
$948$		0			0
$949$			6.00000i			0.194768i
$950$	2.82843	+	19.7990i	0.0917663	+	0.642364i
$951$		0			0
$952$		0			0
$953$	18.3848	+	18.3848i	0.595541	+	0.595541i	0.939123	−	0.343582i	$-0.111640\pi$
$953$	18.3848	+	18.3848i	0.595541	+	0.595541i	−0.343582	+	0.939123i	$0.611640\pi$
$954$		0			0
$955$	4.00000	−	12.0000i	0.129437	−	0.388311i
$956$		−	19.7990i		−	0.640345i
$957$		0			0
$958$	−8.00000	+	8.00000i	−0.258468	+	0.258468i
$959$		0			0
$960$		0			0
$961$	33.0000			1.06452
$962$	29.6985	−	29.6985i	0.957518	−	0.957518i
$963$		0			0
$964$			18.0000i			0.579741i
$965$	8.48528	−	4.24264i	0.273151	−	0.136575i
$966$		0			0
$967$	10.0000	+	10.0000i	0.321578	+	0.321578i	0.849372	−	0.527794i	$-0.176981\pi$
$967$	10.0000	+	10.0000i	0.321578	+	0.321578i	−0.527794	+	0.849372i	$0.676981\pi$
$968$	2.12132	+	2.12132i	0.0681818	+	0.0681818i
$969$		0			0
$970$	9.00000	+	3.00000i	0.288973	+	0.0963242i
$971$			36.7696i			1.17999i	0.807406	+	0.589996i	$0.200871\pi$
$971$			36.7696i			1.17999i	−0.807406	+	0.589996i	$0.799129\pi$
$972$		0			0
$973$		0			0
$974$	−2.82843			−0.0906287
$975$		0			0
$976$	4.00000			0.128037
$977$	−8.48528	+	8.48528i	−0.271468	+	0.271468i	−0.829691	−	0.558223i	$-0.811483\pi$
$977$	−8.48528	+	8.48528i	−0.271468	+	0.271468i	0.558223	+	0.829691i	$0.311483\pi$
$978$		0			0
$979$		−	28.0000i		−	0.894884i
$980$	14.8492	+	4.94975i	0.474342	+	0.158114i
$981$		0			0
$982$	4.00000	+	4.00000i	0.127645	+	0.127645i
$983$	2.82843	+	2.82843i	0.0902128	+	0.0902128i	0.750773	−	0.660560i	$-0.229681\pi$
$983$	2.82843	+	2.82843i	0.0902128	+	0.0902128i	−0.660560	+	0.750773i	$0.729681\pi$
$984$		0			0
$985$	44.0000	−	22.0000i	1.40196	−	0.700978i
$986$			39.5980i			1.26106i
$987$		0			0
$988$	12.0000	−	12.0000i	0.381771	−	0.381771i
$989$	2.82843			0.0899388
$990$		0			0
$991$	4.00000			0.127064			0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000			0.127064			0.0635321	+	0.997980i	$0.479763\pi$
$992$	5.65685	−	5.65685i	0.179605	−	0.179605i
$993$		0			0
$994$		0			0
$995$	−11.3137	+	33.9411i	−0.358669	+	1.07601i
$996$		0			0
$997$	−3.00000	−	3.00000i	−0.0950110	−	0.0950110i	0.658004	−	0.753015i	$-0.271401\pi$
$997$	−3.00000	−	3.00000i	−0.0950110	−	0.0950110i	−0.753015	+	0.658004i	$0.771401\pi$
$998$	28.2843	+	28.2843i	0.895323	+	0.895323i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.j.d.737.1	yes	4
3.2	odd	2	inner	2070.2.j.d.737.2	yes	4
5.3	odd	4	inner	2070.2.j.d.323.2	yes	4
15.8	even	4	inner	2070.2.j.d.323.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.d.323.1	✓	4	15.8	even	4	inner
2070.2.j.d.323.2	yes	4	5.3	odd	4	inner
2070.2.j.d.737.1	yes	4	1.1	even	1	trivial
2070.2.j.d.737.2	yes	4	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.12132 - 0.707107i) q^{5} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.12132 - 0.707107i) q^{5} +(0.707107 + 0.707107i) q^{8} +(2.00000 - 1.00000i) q^{10} -2.82843i q^{11} +(-3.00000 + 3.00000i) q^{13} -1.00000 q^{16} +(-2.82843 + 2.82843i) q^{17} -4.00000i q^{19} +(-0.707107 + 2.12132i) q^{20} +(2.00000 + 2.00000i) q^{22} +(0.707107 + 0.707107i) q^{23} +(4.00000 + 3.00000i) q^{25} -4.24264i q^{26} -9.89949 q^{29} +8.00000 q^{31} +(0.707107 - 0.707107i) q^{32} -4.00000i q^{34} +(7.00000 + 7.00000i) q^{37} +(2.82843 + 2.82843i) q^{38} +(-1.00000 - 2.00000i) q^{40} +7.07107i q^{41} +(2.00000 - 2.00000i) q^{43} -2.82843 q^{44} -1.00000 q^{46} +(2.82843 - 2.82843i) q^{47} -7.00000i q^{49} +(-4.94975 + 0.707107i) q^{50} +(3.00000 + 3.00000i) q^{52} +(-8.48528 - 8.48528i) q^{53} +(-2.00000 + 6.00000i) q^{55} +(7.00000 - 7.00000i) q^{58} +11.3137 q^{59} -4.00000 q^{61} +(-5.65685 + 5.65685i) q^{62} +1.00000i q^{64} +(8.48528 - 4.24264i) q^{65} +(10.0000 + 10.0000i) q^{67} +(2.82843 + 2.82843i) q^{68} -14.1421i q^{71} +(1.00000 - 1.00000i) q^{73} -9.89949 q^{74} -4.00000 q^{76} +4.00000i q^{79} +(2.12132 + 0.707107i) q^{80} +(-5.00000 - 5.00000i) q^{82} +(8.48528 + 8.48528i) q^{83} +(8.00000 - 4.00000i) q^{85} +2.82843i q^{86} +(2.00000 - 2.00000i) q^{88} +9.89949 q^{89} +(0.707107 - 0.707107i) q^{92} +4.00000i q^{94} +(-2.82843 + 8.48528i) q^{95} +(3.00000 + 3.00000i) q^{97} +(4.94975 + 4.94975i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q+O(q^{10}) \) 4 * q	\( 4 q + 8 q^{10} - 12 q^{13} - 4 q^{16} + 8 q^{22} + 16 q^{25} + 32 q^{31} + 28 q^{37} - 4 q^{40} + 8 q^{43} - 4 q^{46} + 12 q^{52} - 8 q^{55} + 28 q^{58} - 16 q^{61} + 40 q^{67} + 4 q^{73} - 16 q^{76} - 20 q^{82} + 32 q^{85} + 8 q^{88} + 12 q^{97}+O(q^{100}) \) 4 * q + 8 * q^10 - 12 * q^13 - 4 * q^16 + 8 * q^22 + 16 * q^25 + 32 * q^31 + 28 * q^37 - 4 * q^40 + 8 * q^43 - 4 * q^46 + 12 * q^52 - 8 * q^55 + 28 * q^58 - 16 * q^61 + 40 * q^67 + 4 * q^73 - 16 * q^76 - 20 * q^82 + 32 * q^85 + 8 * q^88 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more