LMFDB - Embedded newform 1360.2.bt.b.81.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1360,2,Mod(81,1360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1360, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

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

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

chi := DirichletCharacter("1360.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1360 = 2^{4} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1360.bt (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.8596546749$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.23045668864.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 26x^{6} + 237x^{4} + 892x^{2} + 1156 $ x^8 + 26x^6 + 237x^4 + 892*x^2 + 1156
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.4
Root			$-2.26843i$ of defining polynomial
Character	$\chi$	$=$	1360.81
Dual form			1360.2.bt.b.1041.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.31113 + 2.31113i) q^{3} +(0.707107 + 0.707107i) q^{5} +(3.26843 - 3.26843i) q^{7} +7.68265i q^{9} +O(q^{10})$	\(q+(2.31113 + 2.31113i) q^{3} +(0.707107 + 0.707107i) q^{5} +(3.26843 - 3.26843i) q^{7} +7.68265i q^{9} +(1.82843 - 1.82843i) q^{11} -0.145782 q^{13} +3.26843i q^{15} +(-3.31113 - 2.45691i) q^{17} +2.06038i q^{19} +15.1075 q^{21} +(3.41421 - 3.41421i) q^{23} +1.00000i q^{25} +(-10.8222 + 10.8222i) q^{27} +(2.10308 + 2.10308i) q^{29} +(2.78573 + 2.78573i) q^{31} +8.45147 q^{33} +4.62226 q^{35} +(-2.44000 - 2.44000i) q^{37} +(-0.336921 - 0.336921i) q^{39} +(-5.53686 + 5.53686i) q^{41} -0.622260i q^{43} +(-5.43245 + 5.43245i) q^{45} -8.47648 q^{47} -14.3653i q^{49} +(-1.97421 - 13.3307i) q^{51} +6.68265i q^{53} +2.58579 q^{55} +(-4.76182 + 4.76182i) q^{57} -5.71724i q^{59} +(2.63995 - 2.63995i) q^{61} +(25.1102 + 25.1102i) q^{63} +(-0.103083 - 0.103083i) q^{65} -1.58767 q^{67} +15.7814 q^{69} +(-1.83653 - 1.83653i) q^{71} +(-5.82220 - 5.82220i) q^{73} +(-2.31113 + 2.31113i) q^{75} -11.9522i q^{77} +(-3.29344 + 3.29344i) q^{79} -26.9751 q^{81} -8.91382i q^{83} +(-0.604023 - 4.07862i) q^{85} +9.72100i q^{87} -15.9787 q^{89} +(-0.476478 + 0.476478i) q^{91} +12.8764i q^{93} +(-1.45691 + 1.45691i) q^{95} +(12.5814 + 12.5814i) q^{97} +(14.0472 + 14.0472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^7	$ 8 q + 4 q^{7} - 8 q^{11} - 12 q^{13} - 8 q^{17} + 16 q^{21} + 16 q^{23} - 12 q^{27} + 24 q^{29} - 4 q^{31} + 16 q^{33} - 20 q^{37} + 4 q^{39} - 8 q^{45} - 20 q^{47} - 4 q^{51} + 32 q^{55} + 40 q^{57} - 16 q^{61} + 64 q^{63} - 8 q^{65} + 16 q^{67} + 8 q^{69} - 4 q^{71} + 28 q^{73} - 8 q^{79} - 8 q^{81} + 8 q^{85} - 44 q^{89} + 44 q^{91} - 4 q^{95} + 20 q^{97} + 4 q^{99}+O(q^{100}) $ 8 * q + 4 * q^7 - 8 * q^11 - 12 * q^13 - 8 * q^17 + 16 * q^21 + 16 * q^23 - 12 * q^27 + 24 * q^29 - 4 * q^31 + 16 * q^33 - 20 * q^37 + 4 * q^39 - 8 * q^45 - 20 * q^47 - 4 * q^51 + 32 * q^55 + 40 * q^57 - 16 * q^61 + 64 * q^63 - 8 * q^65 + 16 * q^67 + 8 * q^69 - 4 * q^71 + 28 * q^73 - 8 * q^79 - 8 * q^81 + 8 * q^85 - 44 * q^89 + 44 * q^91 - 4 * q^95 + 20 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1360\mathbb{Z}\right)^\times$.

$n$	$241$	$341$	$511$	$817$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	2.31113	+	2.31113i	1.33433	+	1.33433i	0.901451	+	0.432880i	$0.142503\pi$
$3$	2.31113	+	2.31113i	1.33433	+	1.33433i	0.432880	+	0.901451i	$0.357497\pi$
$4$		0			0
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$		0			0
$7$	3.26843	−	3.26843i	1.23535	−	1.23535i	0.273471	−	0.961880i	$-0.411828\pi$
$7$	3.26843	−	3.26843i	1.23535	−	1.23535i	0.961880	−	0.273471i	$-0.0881717\pi$
$8$		0			0
$9$			7.68265i			2.56088i
$10$		0			0
$11$	1.82843	−	1.82843i	0.551292	−	0.551292i	−0.375522	−	0.926813i	$-0.622537\pi$
$11$	1.82843	−	1.82843i	0.551292	−	0.551292i	0.926813	+	0.375522i	$0.122537\pi$
$12$		0			0
$13$	−0.145782			−0.0404326			−0.0202163	−	0.999796i	$-0.506435\pi$
$13$	−0.145782			−0.0404326			−0.0202163	+	0.999796i	$0.506435\pi$
$14$		0			0
$15$			3.26843i			0.843905i
$16$		0			0
$17$	−3.31113	−	2.45691i	−0.803067	−	0.595889i
$17$	−3.31113	−	2.45691i	−0.803067	−	0.595889i
$18$		0			0
$19$			2.06038i			0.472685i	0.971670	+	0.236342i	$0.0759487\pi$
$19$			2.06038i			0.472685i	−0.971670	+	0.236342i	$0.924051\pi$
$20$		0			0
$21$	15.1075			3.29674
$22$		0			0
$23$	3.41421	−	3.41421i	0.711913	−	0.711913i	−0.255022	−	0.966935i	$-0.582083\pi$
$23$	3.41421	−	3.41421i	0.711913	−	0.711913i	0.966935	+	0.255022i	$0.0820828\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	−10.8222	+	10.8222i	−2.08273	+	2.08273i
$28$		0			0
$29$	2.10308	+	2.10308i	0.390533	+	0.390533i	0.874877	−	0.484345i	$-0.160942\pi$
$29$	2.10308	+	2.10308i	0.390533	+	0.390533i	−0.484345	+	0.874877i	$0.660942\pi$
$30$		0			0
$31$	2.78573	+	2.78573i	0.500332	+	0.500332i	0.911541	−	0.411209i	$-0.134893\pi$
$31$	2.78573	+	2.78573i	0.500332	+	0.500332i	−0.411209	+	0.911541i	$0.634893\pi$
$32$		0			0
$33$	8.45147			1.47121
$34$		0			0
$35$	4.62226			0.781305
$36$		0			0
$37$	−2.44000	−	2.44000i	−0.401134	−	0.401134i	0.477498	−	0.878633i	$-0.341544\pi$
$37$	−2.44000	−	2.44000i	−0.401134	−	0.401134i	−0.878633	+	0.477498i	$0.841544\pi$
$38$		0			0
$39$	−0.336921	−	0.336921i	−0.0539505	−	0.0539505i
$40$		0			0
$41$	−5.53686	+	5.53686i	−0.864713	+	0.864713i	−0.991881	−	0.127168i	$-0.959411\pi$
$41$	−5.53686	+	5.53686i	−0.864713	+	0.864713i	0.127168	+	0.991881i	$0.459411\pi$
$42$		0			0
$43$		−	0.622260i		−	0.0948938i	−0.998874	−	0.0474469i	$-0.984892\pi$
$43$		−	0.622260i		−	0.0948938i	0.998874	−	0.0474469i	$-0.0151085\pi$
$44$		0			0
$45$	−5.43245	+	5.43245i	−0.809822	+	0.809822i
$46$		0			0
$47$	−8.47648			−1.23642			−0.618211	−	0.786012i	$-0.712142\pi$
$47$	−8.47648			−1.23642			−0.618211	+	0.786012i	$0.712142\pi$
$48$		0			0
$49$		−	14.3653i		−	2.05218i
$50$		0			0
$51$	−1.97421	−	13.3307i	−0.276445	−	1.86667i
$52$		0			0
$53$			6.68265i			0.917932i	0.888454	+	0.458966i	$0.151780\pi$
$53$			6.68265i			0.917932i	−0.888454	+	0.458966i	$0.848220\pi$
$54$		0			0
$55$	2.58579			0.348667
$56$		0			0
$57$	−4.76182	+	4.76182i	−0.630718	+	0.630718i
$58$		0			0
$59$		−	5.71724i		−	0.744321i	−0.928168	−	0.372161i	$-0.878617\pi$
$59$		−	5.71724i		−	0.744321i	0.928168	−	0.372161i	$-0.121383\pi$
$60$		0			0
$61$	2.63995	−	2.63995i	0.338011	−	0.338011i	−0.517608	−	0.855618i	$-0.673177\pi$
$61$	2.63995	−	2.63995i	0.338011	−	0.338011i	0.855618	+	0.517608i	$0.173177\pi$
$62$		0			0
$63$	25.1102	+	25.1102i	3.16359	+	3.16359i
$64$		0			0
$65$	−0.103083	−	0.103083i	−0.0127859	−	0.0127859i
$66$		0			0
$67$	−1.58767			−0.193964			−0.0969822	−	0.995286i	$-0.530919\pi$
$67$	−1.58767			−0.193964			−0.0969822	+	0.995286i	$0.530919\pi$
$68$		0			0
$69$	15.7814			1.89986
$70$		0			0
$71$	−1.83653	−	1.83653i	−0.217956	−	0.217956i	0.589680	−	0.807637i	$-0.299254\pi$
$71$	−1.83653	−	1.83653i	−0.217956	−	0.217956i	−0.807637	+	0.589680i	$0.799254\pi$
$72$		0			0
$73$	−5.82220	−	5.82220i	−0.681437	−	0.681437i	0.278887	−	0.960324i	$-0.410035\pi$
$73$	−5.82220	−	5.82220i	−0.681437	−	0.681437i	−0.960324	+	0.278887i	$0.910035\pi$
$74$		0			0
$75$	−2.31113	+	2.31113i	−0.266866	+	0.266866i
$76$		0			0
$77$		−	11.9522i		−	1.36208i
$78$		0			0
$79$	−3.29344	+	3.29344i	−0.370541	+	0.370541i	−0.867674	−	0.497133i	$-0.834386\pi$
$79$	−3.29344	+	3.29344i	−0.370541	+	0.370541i	0.497133	+	0.867674i	$0.334386\pi$
$80$		0			0
$81$	−26.9751			−2.99723
$82$		0			0
$83$		−	8.91382i		−	0.978419i	−0.872166	−	0.489210i	$-0.837285\pi$
$83$		−	8.91382i		−	0.978419i	0.872166	−	0.489210i	$-0.162715\pi$
$84$		0			0
$85$	−0.604023	−	4.07862i	−0.0655155	−	0.442389i
$86$		0			0
$87$			9.72100i			1.04220i
$88$		0			0
$89$	−15.9787			−1.69374			−0.846872	−	0.531797i	$-0.821517\pi$
$89$	−15.9787			−1.69374			−0.846872	+	0.531797i	$0.821517\pi$
$90$		0			0
$91$	−0.476478	+	0.476478i	−0.0499485	+	0.0499485i
$92$		0			0
$93$			12.8764i			1.33522i
$94$		0			0
$95$	−1.45691	+	1.45691i	−0.149476	+	0.149476i
$96$		0			0
$97$	12.5814	+	12.5814i	1.27745	+	1.27745i	0.942089	+	0.335363i	$0.108859\pi$
$97$	12.5814	+	12.5814i	1.27745	+	1.27745i	0.335363	+	0.942089i	$0.391141\pi$
$98$		0			0
$99$	14.0472	+	14.0472i	1.41179	+	1.41179i
$100$		0			0
$101$	7.65685			0.761885			0.380943	−	0.924599i	$-0.375599\pi$
$101$	7.65685			0.761885			0.380943	+	0.924599i	$0.375599\pi$
$102$		0			0
$103$	−8.07295			−0.795451			−0.397726	−	0.917504i	$-0.630200\pi$
$103$	−8.07295			−0.795451			−0.397726	+	0.917504i	$0.630200\pi$
$104$		0			0
$105$	10.6826	+	10.6826i	1.04252	+	1.04252i
$106$		0			0
$107$	−1.68265	−	1.68265i	−0.162667	−	0.162667i	0.621080	−	0.783747i	$-0.286694\pi$
$107$	−1.68265	−	1.68265i	−0.162667	−	0.162667i	−0.783747	+	0.621080i	$0.786694\pi$
$108$		0			0
$109$	−2.10308	+	2.10308i	−0.201439	+	0.201439i	−0.800616	−	0.599177i	$-0.795494\pi$
$109$	−2.10308	+	2.10308i	−0.201439	+	0.201439i	0.599177	+	0.800616i	$0.295494\pi$
$110$		0			0
$111$		−	11.2783i		−	1.07049i
$112$		0			0
$113$	−7.19994	+	7.19994i	−0.677314	+	0.677314i	−0.959391	−	0.282078i	$-0.908976\pi$
$113$	−7.19994	+	7.19994i	−0.677314	+	0.677314i	0.282078	+	0.959391i	$0.408976\pi$
$114$		0			0
$115$	4.82843			0.450253
$116$		0			0
$117$		−	1.11999i		−	0.103543i
$118$		0			0
$119$	−18.8525	+	2.79195i	−1.72820	+	0.255938i
$120$		0			0
$121$			4.31371i			0.392155i
$122$		0			0
$123$	−25.5928			−2.30763
$124$		0			0
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$		−	11.1841i		−	0.992432i	−0.868199	−	0.496216i	$-0.834722\pi$
$127$		−	11.1841i		−	0.992432i	0.868199	−	0.496216i	$-0.165278\pi$
$128$		0			0
$129$	1.43812	−	1.43812i	0.126620	−	0.126620i
$130$		0			0
$131$	−10.5715	−	10.5715i	−0.923633	−	0.923633i	0.0736515	−	0.997284i	$-0.476535\pi$
$131$	−10.5715	−	10.5715i	−0.923633	−	0.923633i	−0.997284	+	0.0736515i	$0.976535\pi$
$132$		0			0
$133$	6.73423	+	6.73423i	0.583932	+	0.583932i
$134$		0			0
$135$	−15.3049			−1.31724
$136$		0			0
$137$	−14.1583			−1.20963			−0.604815	−	0.796366i	$-0.706753\pi$
$137$	−14.1583			−1.20963			−0.604815	+	0.796366i	$0.706753\pi$
$138$		0			0
$139$	15.0729	+	15.0729i	1.27847	+	1.27847i	0.941524	+	0.336947i	$0.109394\pi$
$139$	15.0729	+	15.0729i	1.27847	+	1.27847i	0.336947	+	0.941524i	$0.390606\pi$
$140$		0			0
$141$	−19.5902	−	19.5902i	−1.64980	−	1.64980i
$142$		0			0
$143$	−0.266552	+	0.266552i	−0.0222902	+	0.0222902i
$144$		0			0
$145$			2.97421i			0.246995i
$146$		0			0
$147$	33.2001	−	33.2001i	2.73829	−	2.73829i
$148$		0			0
$149$	−10.2791			−0.842098			−0.421049	−	0.907038i	$-0.638338\pi$
$149$	−10.2791			−0.842098			−0.421049	+	0.907038i	$0.638338\pi$
$150$		0			0
$151$			6.53686i			0.531962i	0.963978	+	0.265981i	$0.0856959\pi$
$151$			6.53686i			0.531962i	−0.963978	+	0.265981i	$0.914304\pi$
$152$		0			0
$153$	18.8756	−	25.4382i	1.52600	−	2.05656i
$154$		0			0
$155$			3.93962i			0.316438i
$156$		0			0
$157$	12.4337			0.992317			0.496159	−	0.868232i	$-0.334743\pi$
$157$	12.4337			0.992317			0.496159	+	0.868232i	$0.334743\pi$
$158$		0			0
$159$	−15.4445	+	15.4445i	−1.22483	+	1.22483i
$160$		0			0
$161$		−	22.3182i		−	1.75892i
$162$		0			0
$163$	0.562654	−	0.562654i	0.0440705	−	0.0440705i	−0.684728	−	0.728799i	$-0.740079\pi$
$163$	0.562654	−	0.562654i	0.0440705	−	0.0440705i	0.728799	+	0.684728i	$0.240079\pi$
$164$		0			0
$165$	5.97609	+	5.97609i	0.465238	+	0.465238i
$166$		0			0
$167$	3.36263	+	3.36263i	0.260208	+	0.260208i	0.825139	−	0.564930i	$-0.191097\pi$
$167$	3.36263	+	3.36263i	0.260208	+	0.260208i	−0.564930	+	0.825139i	$0.691097\pi$
$168$		0			0
$169$	−12.9787			−0.998365
$170$		0			0
$171$	−15.8292			−1.21049
$172$		0			0
$173$	9.00188	+	9.00188i	0.684400	+	0.684400i	0.960989	−	0.276588i	$-0.0892038\pi$
$173$	9.00188	+	9.00188i	0.684400	+	0.684400i	−0.276588	+	0.960989i	$0.589204\pi$
$174$		0			0
$175$	3.26843	+	3.26843i	0.247070	+	0.247070i
$176$		0			0
$177$	13.2133	−	13.2133i	0.993171	−	0.993171i
$178$		0			0
$179$		−	0.170794i		−	0.0127658i	−0.999980	−	0.00638288i	$-0.997968\pi$
$179$		−	0.170794i		−	0.0127658i	0.999980	−	0.00638288i	$-0.00203175\pi$
$180$		0			0
$181$	3.32882	−	3.32882i	0.247429	−	0.247429i	−0.572486	−	0.819915i	$-0.694021\pi$
$181$	3.32882	−	3.32882i	0.247429	−	0.247429i	0.819915	+	0.572486i	$0.194021\pi$
$182$		0			0
$183$	12.2025			0.902036
$184$		0			0
$185$		−	3.45069i		−	0.253700i
$186$		0			0
$187$	−10.5464	+	1.56188i	−0.771232	+	0.114216i
$188$		0			0
$189$			70.7433i			5.14581i
$190$		0			0
$191$	−4.79461			−0.346926			−0.173463	−	0.984840i	$-0.555496\pi$
$191$	−4.79461			−0.346926			−0.173463	+	0.984840i	$0.555496\pi$
$192$		0			0
$193$	10.6819	−	10.6819i	0.768898	−	0.768898i	−0.209015	−	0.977912i	$-0.567026\pi$
$193$	10.6819	−	10.6819i	0.768898	−	0.768898i	0.977912	+	0.209015i	$0.0670257\pi$
$194$		0			0
$195$		−	0.476478i		−	0.0341213i
$196$		0			0
$197$	4.85610	−	4.85610i	0.345983	−	0.345983i	−0.512628	−	0.858611i	$-0.671328\pi$
$197$	4.85610	−	4.85610i	0.345983	−	0.345983i	0.858611	+	0.512628i	$0.171328\pi$
$198$		0			0
$199$	2.12810	+	2.12810i	0.150857	+	0.150857i	0.778501	−	0.627644i	$-0.215981\pi$
$199$	2.12810	+	2.12810i	0.150857	+	0.150857i	−0.627644	+	0.778501i	$0.715981\pi$
$200$		0			0
$201$	−3.66930	−	3.66930i	−0.258813	−	0.258813i
$202$		0			0
$203$	13.7476			0.964890
$204$		0			0
$205$	−7.83031			−0.546892
$206$		0			0
$207$	26.2302	+	26.2302i	1.82312	+	1.82312i
$208$		0			0
$209$	3.76726	+	3.76726i	0.260587	+	0.260587i
$210$		0			0
$211$	1.47648	−	1.47648i	0.101645	−	0.101645i	−0.654456	−	0.756100i	$-0.727102\pi$
$211$	1.47648	−	1.47648i	0.101645	−	0.101645i	0.756100	+	0.654456i	$0.227102\pi$
$212$		0			0
$213$		−	8.48893i		−	0.581652i
$214$		0			0
$215$	0.440004	−	0.440004i	0.0300081	−	0.0300081i
$216$		0			0
$217$	18.2099			1.23617
$218$		0			0
$219$		−	26.9117i		−	1.81853i
$220$		0			0
$221$	0.482703	+	0.358173i	0.0324701	+	0.0240934i
$222$		0			0
$223$		−	22.6186i		−	1.51465i	−0.653036	−	0.757327i	$-0.726505\pi$
$223$		−	22.6186i		−	1.51465i	0.653036	−	0.757327i	$-0.273495\pi$
$224$		0			0
$225$	−7.68265			−0.512176
$226$		0			0
$227$	8.29868	−	8.29868i	0.550803	−	0.550803i	−0.375870	−	0.926673i	$-0.622656\pi$
$227$	8.29868	−	8.29868i	0.550803	−	0.550803i	0.926673	+	0.375870i	$0.122656\pi$
$228$		0			0
$229$		−	25.8897i		−	1.71084i	−0.517935	−	0.855420i	$-0.673299\pi$
$229$		−	25.8897i		−	1.71084i	0.517935	−	0.855420i	$-0.326701\pi$
$230$		0			0
$231$	27.6230	−	27.6230i	1.81746	−	1.81746i
$232$		0			0
$233$	9.65141	+	9.65141i	0.632285	+	0.632285i	0.948641	−	0.316356i	$-0.102459\pi$
$233$	9.65141	+	9.65141i	0.632285	+	0.632285i	−0.316356	+	0.948641i	$0.602459\pi$
$234$		0			0
$235$	−5.99378	−	5.99378i	−0.390991	−	0.390991i
$236$		0			0
$237$	−15.2232			−0.988850
$238$		0			0
$239$	25.4736			1.64775			0.823875	−	0.566771i	$-0.191808\pi$
$239$	25.4736			1.64775			0.823875	+	0.566771i	$0.191808\pi$
$240$		0			0
$241$	5.65763	+	5.65763i	0.364440	+	0.364440i	0.865445	−	0.501005i	$-0.167036\pi$
$241$	5.65763	+	5.65763i	0.364440	+	0.364440i	−0.501005	+	0.865445i	$0.667036\pi$
$242$		0			0
$243$	−29.8764	−	29.8764i	−1.91657	−	1.91657i
$244$		0			0
$245$	10.1578	−	10.1578i	0.648958	−	0.648958i
$246$		0			0
$247$		−	0.300367i		−	0.0191119i
$248$		0			0
$249$	20.6010	−	20.6010i	1.30554	−	1.30554i
$250$		0			0
$251$	−8.60981			−0.543446			−0.271723	−	0.962375i	$-0.587594\pi$
$251$	−8.60981			−0.543446			−0.271723	+	0.962375i	$0.587594\pi$
$252$		0			0
$253$		−	12.4853i		−	0.784943i
$254$		0			0
$255$	8.03025	−	10.8222i	0.502874	−	0.677713i
$256$		0			0
$257$		−	13.7976i		−	0.860670i	−0.902669	−	0.430335i	$-0.858395\pi$
$257$		−	13.7976i		−	0.860670i	0.902669	−	0.430335i	$-0.141605\pi$
$258$		0			0
$259$	−15.9500			−0.991083
$260$		0			0
$261$	−16.1572	+	16.1572i	−1.00011	+	1.00011i
$262$		0			0
$263$			22.3271i			1.37674i	0.725357	+	0.688372i	$0.241675\pi$
$263$			22.3271i			1.37674i	−0.725357	+	0.688372i	$0.758325\pi$
$264$		0			0
$265$	−4.72534	+	4.72534i	−0.290276	+	0.290276i
$266$		0			0
$267$	−36.9290	−	36.9290i	−2.26002	−	2.26002i
$268$		0			0
$269$	11.2747	+	11.2747i	0.687428	+	0.687428i	0.961663	−	0.274235i	$-0.0884246\pi$
$269$	11.2747	+	11.2747i	0.687428	+	0.687428i	−0.274235	+	0.961663i	$0.588425\pi$
$270$		0			0
$271$	30.8765			1.87561			0.937806	−	0.347159i	$-0.112854\pi$
$271$	30.8765			1.87561			0.937806	+	0.347159i	$0.112854\pi$
$272$		0			0
$273$	−2.20241			−0.133296
$274$		0			0
$275$	1.82843	+	1.82843i	0.110258	+	0.110258i
$276$		0			0
$277$	−19.7325	−	19.7325i	−1.18561	−	1.18561i	−0.978269	−	0.207340i	$-0.933519\pi$
$277$	−19.7325	−	19.7325i	−1.18561	−	1.18561i	−0.207340	−	0.978269i	$-0.566481\pi$
$278$		0			0
$279$	−21.4018	+	21.4018i	−1.28129	+	1.28129i
$280$		0			0
$281$		−	10.2879i		−	0.613726i	−0.951754	−	0.306863i	$-0.900721\pi$
$281$		−	10.2879i		−	0.613726i	0.951754	−	0.306863i	$-0.0992793\pi$
$282$		0			0
$283$	8.51730	−	8.51730i	0.506301	−	0.506301i	−0.407088	−	0.913389i	$-0.633456\pi$
$283$	8.51730	−	8.51730i	0.506301	−	0.506301i	0.913389	+	0.407088i	$0.133456\pi$
$284$		0			0
$285$	−6.73423			−0.398901
$286$		0			0
$287$			36.1937i			2.13645i
$288$		0			0
$289$	4.92717	+	16.2703i	0.289833	+	0.957077i
$290$		0			0
$291$			58.1547i			3.40909i
$292$		0			0
$293$	−30.6024			−1.78781			−0.893906	−	0.448255i	$-0.852046\pi$
$293$	−30.6024			−1.78781			−0.893906	+	0.448255i	$0.852046\pi$
$294$		0			0
$295$	4.04270	−	4.04270i	0.235375	−	0.235375i
$296$		0			0
$297$			39.5752i			2.29639i
$298$		0			0
$299$	−0.497731	+	0.497731i	−0.0287845	+	0.0287845i
$300$		0			0
$301$	−2.03382	−	2.03382i	−0.117227	−	0.117227i
$302$		0			0
$303$	17.6960	+	17.6960i	1.01661	+	1.01661i
$304$		0			0
$305$	3.73345			0.213777
$306$		0			0
$307$	13.6268			0.777722			0.388861	−	0.921296i	$-0.372869\pi$
$307$	13.6268			0.777722			0.388861	+	0.921296i	$0.372869\pi$
$308$		0			0
$309$	−18.6576	−	18.6576i	−1.06140	−	1.06140i
$310$		0			0
$311$	−8.72792	−	8.72792i	−0.494915	−	0.494915i	0.414936	−	0.909851i	$-0.363804\pi$
$311$	−8.72792	−	8.72792i	−0.494915	−	0.494915i	−0.909851	+	0.414936i	$0.863804\pi$
$312$		0			0
$313$	−8.73345	+	8.73345i	−0.493644	+	0.493644i	−0.909452	−	0.415809i	$-0.863499\pi$
$313$	−8.73345	+	8.73345i	−0.493644	+	0.493644i	0.415809	+	0.909452i	$0.363499\pi$
$314$		0			0
$315$			35.5112i			2.00083i
$316$		0			0
$317$	11.3288	−	11.3288i	0.636290	−	0.636290i	−0.313348	−	0.949638i	$-0.601451\pi$
$317$	11.3288	−	11.3288i	0.636290	−	0.636290i	0.949638	+	0.313348i	$0.101451\pi$
$318$		0			0
$319$	7.69067			0.430595
$320$		0			0
$321$		−	7.77762i		−	0.434105i
$322$		0			0
$323$	5.06218	−	6.82220i	0.281667	−	0.379597i
$324$		0			0
$325$		−	0.145782i		−	0.00808653i
$326$		0			0
$327$	−9.72100			−0.537572
$328$		0			0
$329$	−27.7048	+	27.7048i	−1.52741	+	1.52741i
$330$		0			0
$331$		−	10.5494i		−	0.579849i	−0.957050	−	0.289924i	$-0.906370\pi$
$331$		−	10.5494i		−	0.579849i	0.957050	−	0.289924i	$-0.0936302\pi$
$332$		0			0
$333$	18.7457	−	18.7457i	1.02726	−	1.02726i
$334$		0			0
$335$	−1.12265	−	1.12265i	−0.0613369	−	0.0613369i
$336$		0			0
$337$	8.95840	+	8.95840i	0.487995	+	0.487995i	0.907673	−	0.419678i	$-0.137857\pi$
$337$	8.95840	+	8.95840i	0.487995	+	0.487995i	−0.419678	+	0.907673i	$0.637857\pi$
$338$		0			0
$339$	−33.2800			−1.80752
$340$		0			0
$341$	10.1870			0.551657
$342$		0			0
$343$	−24.0729	−	24.0729i	−1.29982	−	1.29982i
$344$		0			0
$345$	11.1591	+	11.1591i	0.600787	+	0.600787i
$346$		0			0
$347$	−2.59024	+	2.59024i	−0.139052	+	0.139052i	−0.773206	−	0.634155i	$-0.781348\pi$
$347$	−2.59024	+	2.59024i	−0.139052	+	0.139052i	0.634155	+	0.773206i	$0.281348\pi$
$348$		0			0
$349$			28.5120i			1.52621i	0.646274	+	0.763105i	$0.276326\pi$
$349$			28.5120i			1.52621i	−0.646274	+	0.763105i	$0.723674\pi$
$350$		0			0
$351$	1.57768	−	1.57768i	0.0842104	−	0.0842104i
$352$		0			0
$353$	−9.22691			−0.491099			−0.245550	−	0.969384i	$-0.578968\pi$
$353$	−9.22691			−0.491099			−0.245550	+	0.969384i	$0.578968\pi$
$354$		0			0
$355$		−	2.59725i		−	0.137848i
$356$		0			0
$357$	−50.0230	−	37.1179i	−2.64750	−	1.96449i
$358$		0			0
$359$		−	23.1576i		−	1.22221i	−0.791550	−	0.611105i	$-0.790725\pi$
$359$		−	23.1576i		−	1.22221i	0.791550	−	0.611105i	$-0.209275\pi$
$360$		0			0
$361$	14.7548			0.776569
$362$		0			0
$363$	−9.96954	+	9.96954i	−0.523265	+	0.523265i
$364$		0			0
$365$		−	8.23384i		−	0.430979i
$366$		0			0
$367$	5.65951	−	5.65951i	0.295424	−	0.295424i	−0.543794	−	0.839219i	$-0.683013\pi$
$367$	5.65951	−	5.65951i	0.295424	−	0.295424i	0.839219	+	0.543794i	$0.183013\pi$
$368$		0			0
$369$	−42.5378	−	42.5378i	−2.21443	−	2.21443i
$370$		0			0
$371$	21.8418	+	21.8418i	1.13397	+	1.13397i
$372$		0			0
$373$	−16.1245			−0.834896			−0.417448	−	0.908701i	$-0.637075\pi$
$373$	−16.1245			−0.834896			−0.417448	+	0.908701i	$0.637075\pi$
$374$		0			0
$375$	−3.26843			−0.168781
$376$		0			0
$377$	−0.306592	−	0.306592i	−0.0157903	−	0.0157903i
$378$		0			0
$379$	−23.6577	−	23.6577i	−1.21522	−	1.21522i	−0.969288	−	0.245929i	$-0.920907\pi$
$379$	−23.6577	−	23.6577i	−1.21522	−	1.21522i	−0.245929	−	0.969288i	$-0.579093\pi$
$380$		0			0
$381$	25.8480	−	25.8480i	1.32423	−	1.32423i
$382$		0			0
$383$		−	17.5273i		−	0.895602i	−0.894133	−	0.447801i	$-0.852207\pi$
$383$		−	17.5273i		−	0.895602i	0.894133	−	0.447801i	$-0.147793\pi$
$384$		0			0
$385$	8.45147	−	8.45147i	0.430727	−	0.430727i
$386$		0			0
$387$	4.78061			0.243012
$388$		0			0
$389$			5.39395i			0.273484i	0.990607	+	0.136742i	$0.0436631\pi$
$389$			5.39395i			0.273484i	−0.990607	+	0.136742i	$0.956337\pi$
$390$		0			0
$391$	−19.6933	+	2.91648i	−0.995934	+	0.147493i
$392$		0			0
$393$		−	48.8640i		−	2.46486i
$394$		0			0
$395$	−4.65763			−0.234351
$396$		0			0
$397$	22.1572	−	22.1572i	1.11204	−	1.11204i	0.119166	−	0.992874i	$-0.461978\pi$
$397$	22.1572	−	22.1572i	1.11204	−	1.11204i	0.992874	−	0.119166i	$-0.0380220\pi$
$398$		0			0
$399$			31.1274i			1.55832i
$400$		0			0
$401$	−27.5332	+	27.5332i	−1.37494	+	1.37494i	−0.521994	+	0.852949i	$0.674812\pi$
$401$	−27.5332	+	27.5332i	−1.37494	+	1.37494i	−0.852949	+	0.521994i	$0.825188\pi$
$402$		0			0
$403$	−0.406109	−	0.406109i	−0.0202297	−	0.0202297i
$404$		0			0
$405$	−19.0743	−	19.0743i	−0.947808	−	0.947808i
$406$		0			0
$407$	−8.92274			−0.442284
$408$		0			0
$409$	16.6326			0.822430			0.411215	−	0.911538i	$-0.365105\pi$
$409$	16.6326			0.822430			0.411215	+	0.911538i	$0.365105\pi$
$410$		0			0
$411$	−32.7218	−	32.7218i	−1.61405	−	1.61405i
$412$		0			0
$413$	−18.6864	−	18.6864i	−0.919498	−	0.919498i
$414$		0			0
$415$	6.30303	−	6.30303i	0.309403	−	0.309403i
$416$		0			0
$417$			69.6711i			3.41181i
$418$		0			0
$419$	−20.3049	+	20.3049i	−0.991960	+	0.991960i	−0.999968	−	0.00800839i	$-0.997451\pi$
$419$	−20.3049	+	20.3049i	−0.991960	+	0.991960i	0.00800839	+	0.999968i	$0.497451\pi$
$420$		0			0
$421$	28.5974			1.39375			0.696875	−	0.717193i	$-0.254573\pi$
$421$	28.5974			1.39375			0.696875	+	0.717193i	$0.254573\pi$
$422$		0			0
$423$		−	65.1218i		−	3.16633i
$424$		0			0
$425$	2.45691	−	3.31113i	0.119178	−	0.160613i
$426$		0			0
$427$		−	17.2570i		−	0.835123i
$428$		0			0
$429$	−1.23207			−0.0594850
$430$		0			0
$431$	−1.39800	+	1.39800i	−0.0673395	+	0.0673395i	−0.739974	−	0.672635i	$-0.765162\pi$
$431$	−1.39800	+	1.39800i	−0.0673395	+	0.0673395i	0.672635	+	0.739974i	$0.265162\pi$
$432$		0			0
$433$		−	35.6444i		−	1.71296i	−0.516180	−	0.856480i	$-0.672646\pi$
$433$		−	35.6444i		−	1.71296i	0.516180	−	0.856480i	$-0.327354\pi$
$434$		0			0
$435$	−6.87378	+	6.87378i	−0.329573	+	0.329573i
$436$		0			0
$437$	7.03459	+	7.03459i	0.336510	+	0.336510i
$438$		0			0
$439$	10.9165	+	10.9165i	0.521015	+	0.521015i	0.917878	−	0.396863i	$-0.129901\pi$
$439$	10.9165	+	10.9165i	0.521015	+	0.521015i	−0.396863	+	0.917878i	$0.629901\pi$
$440$		0			0
$441$	110.363			5.25540
$442$		0			0
$443$	8.63471			0.410247			0.205124	−	0.978736i	$-0.434240\pi$
$443$	8.63471			0.410247			0.205124	+	0.978736i	$0.434240\pi$
$444$		0			0
$445$	−11.2987	−	11.2987i	−0.535609	−	0.535609i
$446$		0			0
$447$	−23.7564	−	23.7564i	−1.12364	−	1.12364i
$448$		0			0
$449$	5.98677	−	5.98677i	0.282533	−	0.282533i	−0.551585	−	0.834119i	$-0.685977\pi$
$449$	5.98677	−	5.98677i	0.282533	−	0.282533i	0.834119	+	0.551585i	$0.185977\pi$
$450$		0			0
$451$			20.2475i			0.953418i
$452$		0			0
$453$	−15.1075	+	15.1075i	−0.709814	+	0.709814i
$454$		0			0
$455$	−0.673842			−0.0315902
$456$		0			0
$457$			33.1305i			1.54978i	0.632097	+	0.774889i	$0.282194\pi$
$457$			33.1305i			1.54978i	−0.632097	+	0.774889i	$0.717806\pi$
$458$		0			0
$459$	62.4229	−	9.24452i	2.91365	−	0.431497i
$460$		0			0
$461$			12.8035i			0.596320i	0.954516	+	0.298160i	$0.0963729\pi$
$461$			12.8035i			0.596320i	−0.954516	+	0.298160i	$0.903627\pi$
$462$		0			0
$463$	−25.9877			−1.20775			−0.603875	−	0.797079i	$-0.706377\pi$
$463$	−25.9877			−1.20775			−0.603875	+	0.797079i	$0.706377\pi$
$464$		0			0
$465$	−9.10496	+	9.10496i	−0.422233	+	0.422233i
$466$		0			0
$467$			11.1805i			0.517371i	0.965962	+	0.258686i	$0.0832894\pi$
$467$			11.1805i			0.517371i	−0.965962	+	0.258686i	$0.916711\pi$
$468$		0			0
$469$	−5.18918	+	5.18918i	−0.239614	+	0.239614i
$470$		0			0
$471$	28.7359	+	28.7359i	1.32408	+	1.32408i
$472$		0			0
$473$	−1.13776	−	1.13776i	−0.0523142	−	0.0523142i
$474$		0			0
$475$	−2.06038			−0.0945369
$476$		0			0
$477$	−51.3404			−2.35072
$478$		0			0
$479$	7.57878	+	7.57878i	0.346283	+	0.346283i	0.858723	−	0.512440i	$-0.171258\pi$
$479$	7.57878	+	7.57878i	0.346283	+	0.346283i	−0.512440	+	0.858723i	$0.671258\pi$
$480$		0			0
$481$	0.355709	+	0.355709i	0.0162189	+	0.0162189i
$482$		0			0
$483$	51.5804	−	51.5804i	2.34699	−	2.34699i
$484$		0			0
$485$			17.7928i			0.807931i
$486$		0			0
$487$	19.9761	−	19.9761i	0.905203	−	0.905203i	−0.0906773	−	0.995880i	$-0.528903\pi$
$487$	19.9761	−	19.9761i	0.905203	−	0.905203i	0.995880	+	0.0906773i	$0.0289032\pi$
$488$		0			0
$489$	2.60073			0.117609
$490$		0			0
$491$		−	9.08253i		−	0.409889i	−0.978774	−	0.204944i	$-0.934299\pi$
$491$		−	9.08253i		−	0.409889i	0.978774	−	0.204944i	$-0.0657014\pi$
$492$		0			0
$493$	−1.79649	−	12.1307i	−0.0809099	−	0.546338i
$494$		0			0
$495$			19.8657i			0.892896i
$496$		0			0
$497$	−12.0052			−0.538505
$498$		0			0
$499$	2.62304	−	2.62304i	0.117423	−	0.117423i	−0.645953	−	0.763377i	$-0.723540\pi$
$499$	2.62304	−	2.62304i	0.117423	−	0.117423i	0.763377	+	0.645953i	$0.223540\pi$
$500$		0			0
$501$			15.5430i			0.694408i
$502$		0			0
$503$	−2.84354	+	2.84354i	−0.126787	+	0.126787i	−0.767653	−	0.640866i	$-0.778575\pi$
$503$	−2.84354	+	2.84354i	−0.126787	+	0.126787i	0.640866	+	0.767653i	$0.278575\pi$
$504$		0			0
$505$	5.41421	+	5.41421i	0.240929	+	0.240929i
$506$		0			0
$507$	−29.9956	−	29.9956i	−1.33215	−	1.33215i
$508$		0			0
$509$	21.0221			0.931790			0.465895	−	0.884840i	$-0.345732\pi$
$509$	21.0221			0.931790			0.465895	+	0.884840i	$0.345732\pi$
$510$		0			0
$511$	−38.0589			−1.68363
$512$		0			0
$513$	−22.2979	−	22.2979i	−0.984476	−	0.984476i
$514$		0			0
$515$	−5.70844	−	5.70844i	−0.251544	−	0.251544i
$516$		0			0
$517$	−15.4986	+	15.4986i	−0.681629	+	0.681629i
$518$		0			0
$519$			41.6090i			1.82643i
$520$		0			0
$521$	−3.14578	+	3.14578i	−0.137819	+	0.137819i	−0.772651	−	0.634831i	$-0.781070\pi$
$521$	−3.14578	+	3.14578i	−0.137819	+	0.137819i	0.634831	+	0.772651i	$0.281070\pi$
$522$		0			0
$523$	2.55823			0.111864			0.0559318	−	0.998435i	$-0.482187\pi$
$523$	2.55823			0.111864			0.0559318	+	0.998435i	$0.482187\pi$
$524$		0			0
$525$			15.1075i			0.659347i
$526$		0			0
$527$	−2.37962	−	16.0682i	−0.103658	−	0.699942i
$528$		0			0
$529$		−	0.313708i		−	0.0136395i
$530$		0			0
$531$	43.9235			1.90612
$532$		0			0
$533$	0.807175	−	0.807175i	0.0349626	−	0.0349626i
$534$		0			0
$535$		−	2.37962i		−	0.102880i
$536$		0			0
$537$	0.394728	−	0.394728i	0.0170338	−	0.0170338i
$538$		0			0
$539$	−26.2659	−	26.2659i	−1.13135	−	1.13135i
$540$		0			0
$541$	−20.3318	−	20.3318i	−0.874132	−	0.874132i	0.118787	−	0.992920i	$-0.462099\pi$
$541$	−20.3318	−	20.3318i	−0.874132	−	0.874132i	−0.992920	+	0.118787i	$0.962099\pi$
$542$		0			0
$543$	15.3867			0.660305
$544$		0			0
$545$	−2.97421			−0.127401
$546$		0			0
$547$	7.93417	+	7.93417i	0.339241	+	0.339241i	0.856081	−	0.516841i	$-0.172892\pi$
$547$	7.93417	+	7.93417i	0.339241	+	0.339241i	−0.516841	+	0.856081i	$0.672892\pi$
$548$		0			0
$549$	20.2818	+	20.2818i	0.865605	+	0.865605i
$550$		0			0
$551$	−4.33316	+	4.33316i	−0.184599	+	0.184599i
$552$		0			0
$553$			21.5288i			0.915497i
$554$		0			0
$555$	7.97499	−	7.97499i	0.338519	−	0.338519i
$556$		0			0
$557$	37.4862			1.58834			0.794170	−	0.607696i	$-0.207906\pi$
$557$	37.4862			1.58834			0.794170	+	0.607696i	$0.207906\pi$
$558$		0			0
$559$			0.0907143i			0.00383681i
$560$		0			0
$561$	−27.9839	−	20.7645i	−1.18148	−	0.876678i
$562$		0			0
$563$			21.9751i			0.926140i	0.886322	+	0.463070i	$0.153252\pi$
$563$			21.9751i			0.926140i	−0.886322	+	0.463070i	$0.846748\pi$
$564$		0			0
$565$	−10.1823			−0.428371
$566$		0			0
$567$	−88.1663	+	88.1663i	−3.70264	+	3.70264i
$568$		0			0
$569$			15.3425i			0.643190i	0.946877	+	0.321595i	$0.104219\pi$
$569$			15.3425i			0.643190i	−0.946877	+	0.321595i	$0.895781\pi$
$570$		0			0
$571$	−1.57068	+	1.57068i	−0.0657308	+	0.0657308i	−0.739208	−	0.673477i	$-0.764800\pi$
$571$	−1.57068	+	1.57068i	−0.0657308	+	0.0657308i	0.673477	+	0.739208i	$0.264800\pi$
$572$		0			0
$573$	−11.0810	−	11.0810i	−0.462914	−	0.462914i
$574$		0			0
$575$	3.41421	+	3.41421i	0.142383	+	0.142383i
$576$		0			0
$577$	1.36685			0.0569026			0.0284513	−	0.999595i	$-0.490942\pi$
$577$	1.36685			0.0569026			0.0284513	+	0.999595i	$0.490942\pi$
$578$		0			0
$579$	49.3744			2.05193
$580$		0			0
$581$	−29.1342	−	29.1342i	−1.20869	−	1.20869i
$582$		0			0
$583$	12.2187	+	12.2187i	0.506048	+	0.506048i
$584$		0			0
$585$	0.791953	−	0.791953i	0.0327432	−	0.0327432i
$586$		0			0
$587$			36.4050i			1.50260i	0.659963	+	0.751298i	$0.270572\pi$
$587$			36.4050i			1.50260i	−0.659963	+	0.751298i	$0.729428\pi$
$588$		0			0
$589$	−5.73967	+	5.73967i	−0.236499	+	0.236499i
$590$		0			0
$591$	22.4461			0.923311
$592$		0			0
$593$			20.7822i			0.853421i	0.904388	+	0.426711i	$0.140328\pi$
$593$			20.7822i			0.853421i	−0.904388	+	0.426711i	$0.859672\pi$
$594$		0			0
$595$	−15.3049	−	11.3565i	−0.627440	−	0.465571i
$596$		0			0
$597$			9.83661i			0.402586i
$598$		0			0
$599$	−11.2961			−0.461546			−0.230773	−	0.973008i	$-0.574126\pi$
$599$	−11.2961			−0.461546			−0.230773	+	0.973008i	$0.574126\pi$
$600$		0			0
$601$	−30.6356	+	30.6356i	−1.24965	+	1.24965i	−0.293779	+	0.955873i	$0.594913\pi$
$601$	−30.6356	+	30.6356i	−1.24965	+	1.24965i	−0.955873	+	0.293779i	$0.905087\pi$
$602$		0			0
$603$		−	12.1975i		−	0.496720i
$604$		0			0
$605$	−3.05025	+	3.05025i	−0.124010	+	0.124010i
$606$		0			0
$607$	28.6035	+	28.6035i	1.16098	+	1.16098i	0.984261	+	0.176719i	$0.0565484\pi$
$607$	28.6035	+	28.6035i	1.16098	+	1.16098i	0.176719	+	0.984261i	$0.443452\pi$
$608$		0			0
$609$	31.7724	+	31.7724i	1.28748	+	1.28748i
$610$		0			0
$611$	1.23572			0.0499918
$612$		0			0
$613$	−6.73799			−0.272145			−0.136072	−	0.990699i	$-0.543448\pi$
$613$	−6.73799			−0.272145			−0.136072	+	0.990699i	$0.543448\pi$
$614$		0			0
$615$	−18.0969	−	18.0969i	−0.729736	−	0.729736i
$616$		0			0
$617$	17.4915	+	17.4915i	0.704182	+	0.704182i	0.965305	−	0.261124i	$-0.0840931\pi$
$617$	17.4915	+	17.4915i	0.704182	+	0.704182i	−0.261124	+	0.965305i	$0.584093\pi$
$618$		0			0
$619$	−15.9442	+	15.9442i	−0.640850	+	0.640850i	−0.950764	−	0.309915i	$-0.899699\pi$
$619$	−15.9442	+	15.9442i	−0.640850	+	0.640850i	0.309915	+	0.950764i	$0.399699\pi$
$620$		0			0
$621$			73.8986i			2.96545i
$622$		0			0
$623$	−52.2254	+	52.2254i	−2.09237	+	2.09237i
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$			17.4133i			0.695419i
$628$		0			0
$629$	2.08430	+	14.0740i	0.0831063	+	0.561169i
$630$		0			0
$631$		−	5.83297i		−	0.232207i	−0.993237	−	0.116103i	$-0.962960\pi$
$631$		−	5.83297i		−	0.232207i	0.993237	−	0.116103i	$-0.0370404\pi$
$632$		0			0
$633$	6.82467			0.271256
$634$		0			0
$635$	7.90838	−	7.90838i	0.313834	−	0.313834i
$636$		0			0
$637$			2.09420i			0.0829752i
$638$		0			0
$639$	14.1094	−	14.1094i	0.558160	−	0.558160i
$640$		0			0
$641$	8.08629	+	8.08629i	0.319389	+	0.319389i	0.848532	−	0.529143i	$-0.177487\pi$
$641$	8.08629	+	8.08629i	0.319389	+	0.319389i	−0.529143	+	0.848532i	$0.677487\pi$
$642$		0			0
$643$	2.42192	+	2.42192i	0.0955110	+	0.0955110i	0.753248	−	0.657737i	$-0.228486\pi$
$643$	2.42192	+	2.42192i	0.0955110	+	0.0955110i	−0.657737	+	0.753248i	$0.728486\pi$
$644$		0			0
$645$	2.03382			0.0800814
$646$		0			0
$647$	−32.9671			−1.29607			−0.648035	−	0.761611i	$-0.724409\pi$
$647$	−32.9671			−1.29607			−0.648035	+	0.761611i	$0.724409\pi$
$648$		0			0
$649$	−10.4536	−	10.4536i	−0.410338	−	0.410338i
$650$		0			0
$651$	42.0855	+	42.0855i	1.64946	+	1.64946i
$652$		0			0
$653$	2.47382	−	2.47382i	0.0968080	−	0.0968080i	−0.657044	−	0.753852i	$-0.728193\pi$
$653$	2.47382	−	2.47382i	0.0968080	−	0.0968080i	0.753852	+	0.657044i	$0.228193\pi$
$654$		0			0
$655$		−	14.9503i		−	0.584156i
$656$		0			0
$657$	44.7299	−	44.7299i	1.74508	−	1.74508i
$658$		0			0
$659$	−38.0355			−1.48165			−0.740826	−	0.671697i	$-0.765566\pi$
$659$	−38.0355			−1.48165			−0.740826	+	0.671697i	$0.765566\pi$
$660$		0			0
$661$			16.7077i			0.649853i	0.945739	+	0.324926i	$0.105339\pi$
$661$			16.7077i			0.649853i	−0.945739	+	0.324926i	$0.894661\pi$
$662$		0			0
$663$	0.287804	+	1.94337i	0.0111774	+	0.0754744i
$664$		0			0
$665$			9.52364i			0.369311i
$666$		0			0
$667$	14.3608			0.556051
$668$		0			0
$669$	52.2746	−	52.2746i	2.02105	−	2.02105i
$670$		0			0
$671$		−	9.65390i		−	0.372685i
$672$		0			0
$673$	21.0829	−	21.0829i	0.812687	−	0.812687i	−0.172349	−	0.985036i	$-0.555136\pi$
$673$	21.0829	−	21.0829i	0.812687	−	0.812687i	0.985036	+	0.172349i	$0.0551356\pi$
$674$		0			0
$675$	−10.8222	−	10.8222i	−0.416547	−	0.416547i
$676$		0			0
$677$	7.32517	+	7.32517i	0.281529	+	0.281529i	0.833719	−	0.552189i	$-0.186208\pi$
$677$	7.32517	+	7.32517i	0.281529	+	0.281529i	−0.552189	+	0.833719i	$0.686208\pi$
$678$		0			0
$679$	82.2432			3.15620
$680$		0			0
$681$	38.3587			1.46991
$682$		0			0
$683$	20.1403	+	20.1403i	0.770649	+	0.770649i	0.978220	−	0.207571i	$-0.0665559\pi$
$683$	20.1403	+	20.1403i	0.770649	+	0.770649i	−0.207571	+	0.978220i	$0.566556\pi$
$684$		0			0
$685$	−10.0115	−	10.0115i	−0.382518	−	0.382518i
$686$		0			0
$687$	59.8345	−	59.8345i	2.28283	−	2.28283i
$688$		0			0
$689$		−	0.974209i		−	0.0371144i
$690$		0			0
$691$	−34.6090	+	34.6090i	−1.31659	+	1.31659i	−0.400132	+	0.916457i	$0.631036\pi$
$691$	−34.6090	+	34.6090i	−1.31659	+	1.31659i	−0.916457	+	0.400132i	$0.868964\pi$
$692$		0			0
$693$	91.8243			3.48812
$694$		0			0
$695$			21.3164i			0.808576i
$696$		0			0
$697$	31.9369	−	4.72969i	1.20969	−	0.179150i
$698$		0			0
$699$			44.6113i			1.68736i
$700$		0			0
$701$	−8.53155			−0.322232			−0.161116	−	0.986935i	$-0.551509\pi$
$701$	−8.53155			−0.322232			−0.161116	+	0.986935i	$0.551509\pi$
$702$		0			0
$703$	5.02735	−	5.02735i	0.189610	−	0.189610i
$704$		0			0
$705$		−	27.7048i		−	1.04342i
$706$		0			0
$707$	25.0259	−	25.0259i	0.941196	−	0.941196i
$708$		0			0
$709$	9.95226	+	9.95226i	0.373765	+	0.373765i	0.868846	−	0.495082i	$-0.164862\pi$
$709$	9.95226	+	9.95226i	0.373765	+	0.373765i	−0.495082	+	0.868846i	$0.664862\pi$
$710$		0			0
$711$	−25.3024	−	25.3024i	−0.948913	−	0.948913i
$712$		0			0
$713$	19.0221			0.712385
$714$		0			0
$715$	−0.376961			−0.0140975
$716$		0			0
$717$	58.8728	+	58.8728i	2.19865	+	2.19865i
$718$		0			0
$719$	−2.74660	−	2.74660i	−0.102431	−	0.102431i	0.654034	−	0.756465i	$-0.273075\pi$
$719$	−2.74660	−	2.74660i	−0.102431	−	0.102431i	−0.756465	+	0.654034i	$0.773075\pi$
$720$		0			0
$721$	−26.3859	+	26.3859i	−0.982661	+	0.982661i
$722$		0			0
$723$			26.1511i			0.972568i
$724$		0			0
$725$	−2.10308	+	2.10308i	−0.0781066	+	0.0781066i
$726$		0			0
$727$	43.7477			1.62251			0.811256	−	0.584691i	$-0.198784\pi$
$727$	43.7477			1.62251			0.811256	+	0.584691i	$0.198784\pi$
$728$		0			0
$729$		−	57.1710i		−	2.11745i
$730$		0			0
$731$	−1.52884	+	2.06038i	−0.0565461	+	0.0762061i
$732$		0			0
$733$			27.1945i			1.00445i	0.864737	+	0.502226i	$0.167485\pi$
$733$			27.1945i			1.00445i	−0.864737	+	0.502226i	$0.832515\pi$
$734$		0			0
$735$	46.9520			1.73185
$736$		0			0
$737$	−2.90293	+	2.90293i	−0.106931	+	0.106931i
$738$		0			0
$739$		−	14.5227i		−	0.534228i	−0.963665	−	0.267114i	$-0.913930\pi$
$739$		−	14.5227i		−	0.534228i	0.963665	−	0.267114i	$-0.0860700\pi$
$740$		0			0
$741$	0.694187	−	0.694187i	0.0255016	−	0.0255016i
$742$		0			0
$743$	−36.1912	−	36.1912i	−1.32773	−	1.32773i	−0.907351	−	0.420375i	$-0.861899\pi$
$743$	−36.1912	−	36.1912i	−1.32773	−	1.32773i	−0.420375	−	0.907351i	$-0.638101\pi$
$744$		0			0
$745$	−7.26843	−	7.26843i	−0.266295	−	0.266295i
$746$		0			0
$747$	68.4817			2.50562
$748$		0			0
$749$	−10.9992			−0.401903
$750$		0			0
$751$	−12.4234	−	12.4234i	−0.453337	−	0.453337i	0.443124	−	0.896461i	$-0.353870\pi$
$751$	−12.4234	−	12.4234i	−0.453337	−	0.453337i	−0.896461	+	0.443124i	$0.853870\pi$
$752$		0			0
$753$	−19.8984	−	19.8984i	−0.725138	−	0.725138i
$754$		0			0
$755$	−4.62226	+	4.62226i	−0.168221	+	0.168221i
$756$		0			0
$757$		−	37.5091i		−	1.36329i	−0.731682	−	0.681646i	$-0.761265\pi$
$757$		−	37.5091i		−	1.36329i	0.731682	−	0.681646i	$-0.238735\pi$
$758$		0			0
$759$	28.8551	−	28.8551i	1.04737	−	1.04737i
$760$		0			0
$761$	−31.7851			−1.15221			−0.576105	−	0.817375i	$-0.695428\pi$
$761$	−31.7851			−1.15221			−0.576105	+	0.817375i	$0.695428\pi$
$762$		0			0
$763$			13.7476i			0.497695i
$764$		0			0
$765$	31.3346	−	4.64050i	1.13291	−	0.167778i
$766$		0			0
$767$			0.833470i			0.0300949i
$768$		0			0
$769$	−31.9023			−1.15043			−0.575213	−	0.818004i	$-0.695081\pi$
$769$	−31.9023			−1.15043			−0.575213	+	0.818004i	$0.695081\pi$
$770$		0			0
$771$	31.8880	−	31.8880i	1.14842	−	1.14842i
$772$		0			0
$773$		−	27.0913i		−	0.974408i	−0.873288	−	0.487204i	$-0.838017\pi$
$773$		−	27.0913i		−	0.974408i	0.873288	−	0.487204i	$-0.161983\pi$
$774$		0			0
$775$	−2.78573	+	2.78573i	−0.100066	+	0.100066i
$776$		0			0
$777$	−36.8625	−	36.8625i	−1.32243	−	1.32243i
$778$		0			0
$779$	−11.4081	−	11.4081i	−0.408736	−	0.408736i
$780$		0			0
$781$	−6.71593			−0.240315
$782$		0			0
$783$	−45.5200			−1.62675
$784$		0			0
$785$	8.79195	+	8.79195i	0.313798	+	0.313798i
$786$		0			0
$787$	37.0771	+	37.0771i	1.32166	+	1.32166i	0.912436	+	0.409219i	$0.134199\pi$
$787$	37.0771	+	37.0771i	1.32166	+	1.32166i	0.409219	+	0.912436i	$0.365801\pi$
$788$		0			0
$789$	−51.6007	+	51.6007i	−1.83703	+	1.83703i
$790$		0			0
$791$			47.0650i			1.67344i
$792$		0			0
$793$	−0.384857	+	0.384857i	−0.0136667	+	0.0136667i
$794$		0			0
$795$	−21.8418			−0.774648
$796$		0			0
$797$		−	34.4375i		−	1.21984i	−0.792464	−	0.609919i	$-0.791202\pi$
$797$		−	34.4375i		−	1.21984i	0.792464	−	0.609919i	$-0.208798\pi$
$798$		0			0
$799$	28.0667	+	20.8260i	0.992929	+	0.736770i
$800$		0			0
$801$		−	122.759i		−	4.33748i
$802$		0			0
$803$	−21.2909			−0.751341
$804$		0			0
$805$	15.7814	−	15.7814i	0.556221	−	0.556221i
$806$		0			0
$807$			52.1144i			1.83451i
$808$		0			0
$809$	−4.90215	+	4.90215i	−0.172351	+	0.172351i	−0.788011	−	0.615661i	$-0.788889\pi$
$809$	−4.90215	+	4.90215i	−0.172351	+	0.172351i	0.615661	+	0.788011i	$0.288889\pi$
$810$		0			0
$811$	16.9360	+	16.9360i	0.594702	+	0.594702i	0.938898	−	0.344196i	$-0.111848\pi$
$811$	16.9360	+	16.9360i	0.594702	+	0.594702i	−0.344196	+	0.938898i	$0.611848\pi$
$812$		0			0
$813$	71.3596	+	71.3596i	2.50269	+	2.50269i
$814$		0			0
$815$	0.795713			0.0278726
$816$		0			0
$817$	1.28210			0.0448549
$818$		0			0
$819$	−3.66061	−	3.66061i	−0.127912	−	0.127912i
$820$		0			0
$821$	14.1244	+	14.1244i	0.492947	+	0.492947i	0.909233	−	0.416287i	$-0.136669\pi$
$821$	14.1244	+	14.1244i	0.492947	+	0.492947i	−0.416287	+	0.909233i	$0.636669\pi$
$822$		0			0
$823$	−4.17345	+	4.17345i	−0.145477	+	0.145477i	−0.776094	−	0.630617i	$-0.782802\pi$
$823$	−4.17345	+	4.17345i	−0.145477	+	0.145477i	0.630617	+	0.776094i	$0.282802\pi$
$824$		0			0
$825$			8.45147i			0.294242i
$826$		0			0
$827$	18.0258	−	18.0258i	0.626818	−	0.626818i	−0.320448	−	0.947266i	$-0.603833\pi$
$827$	18.0258	−	18.0258i	0.626818	−	0.626818i	0.947266	+	0.320448i	$0.103833\pi$
$828$		0			0
$829$	18.4375			0.640359			0.320180	−	0.947357i	$-0.396257\pi$
$829$	18.4375			0.640359			0.320180	+	0.947357i	$0.396257\pi$
$830$		0			0
$831$		−	91.2086i		−	3.16399i
$832$		0			0
$833$	−35.2943	+	47.5653i	−1.22287	+	1.64804i
$834$		0			0
$835$			4.75548i			0.164570i
$836$		0			0
$837$	−60.2954			−2.08412
$838$		0			0
$839$	−8.28424	+	8.28424i	−0.286004	+	0.286004i	−0.835498	−	0.549494i	$-0.814821\pi$
$839$	−8.28424	+	8.28424i	−0.286004	+	0.286004i	0.549494	+	0.835498i	$0.314821\pi$
$840$		0			0
$841$		−	20.1541i		−	0.694968i
$842$		0			0
$843$	23.7767	−	23.7767i	0.818914	−	0.818914i
$844$		0			0
$845$	−9.17736	−	9.17736i	−0.315711	−	0.315711i
$846$		0			0
$847$	14.0991	+	14.0991i	0.484449	+	0.484449i
$848$		0			0
$849$	39.3692			1.35115
$850$		0			0
$851$	−16.6614			−0.571145
$852$		0			0
$853$	9.64915	+	9.64915i	0.330381	+	0.330381i	0.852731	−	0.522350i	$-0.174945\pi$
$853$	9.64915	+	9.64915i	0.330381	+	0.330381i	−0.522350	+	0.852731i	$0.674945\pi$
$854$		0			0
$855$	−11.1929	−	11.1929i	−0.382790	−	0.382790i
$856$		0			0
$857$	22.9313	−	22.9313i	0.783318	−	0.783318i	−0.197071	−	0.980389i	$-0.563143\pi$
$857$	22.9313	−	22.9313i	0.783318	−	0.783318i	0.980389	+	0.197071i	$0.0631429\pi$
$858$		0			0
$859$			14.1902i			0.484164i	0.970256	+	0.242082i	$0.0778304\pi$
$859$			14.1902i			0.484164i	−0.970256	+	0.242082i	$0.922170\pi$
$860$		0			0
$861$	−83.6484	+	83.6484i	−2.85073	+	2.85073i
$862$		0			0
$863$	52.0480			1.77174			0.885868	−	0.463937i	$-0.153564\pi$
$863$	52.0480			1.77174			0.885868	+	0.463937i	$0.153564\pi$
$864$		0			0
$865$			12.7306i			0.432853i
$866$		0			0
$867$	−26.2155	+	48.9901i	−0.890325	+	1.66379i
$868$		0			0
$869$			12.0436i			0.408553i
$870$		0			0
$871$	0.231453			0.00784249
$872$		0			0
$873$	−96.6588	+	96.6588i	−3.27140	+	3.27140i
$874$		0			0
$875$			4.62226i			0.156261i
$876$		0			0
$877$	3.85156	−	3.85156i	0.130058	−	0.130058i	−0.639081	−	0.769139i	$-0.720685\pi$
$877$	3.85156	−	3.85156i	0.130058	−	0.130058i	0.769139	+	0.639081i	$0.220685\pi$
$878$		0			0
$879$	−70.7261	−	70.7261i	−2.38553	−	2.38553i
$880$		0			0
$881$	12.6672	+	12.6672i	0.426769	+	0.426769i	0.887526	−	0.460757i	$-0.152422\pi$
$881$	12.6672	+	12.6672i	0.426769	+	0.426769i	−0.460757	+	0.887526i	$0.652422\pi$
$882$		0			0
$883$	−15.1362			−0.509374			−0.254687	−	0.967024i	$-0.581972\pi$
$883$	−15.1362			−0.509374			−0.254687	+	0.967024i	$0.581972\pi$
$884$		0			0
$885$	18.6864			0.628137
$886$		0			0
$887$	29.5122	+	29.5122i	0.990922	+	0.990922i	0.999959	−	0.00903736i	$-0.00287672\pi$
$887$	29.5122	+	29.5122i	0.990922	+	0.990922i	−0.00903736	+	0.999959i	$0.502877\pi$
$888$		0			0
$889$	−36.5546	−	36.5546i	−1.22600	−	1.22600i
$890$		0			0
$891$	−49.3220	+	49.3220i	−1.65235	+	1.65235i
$892$		0			0
$893$		−	17.4648i		−	0.584438i
$894$		0			0
$895$	0.120770	−	0.120770i	0.00403689	−	0.00403689i
$896$		0			0
$897$	−2.30064			−0.0768162
$898$		0			0
$899$			11.7172i			0.390792i
$900$		0			0
$901$	16.4187	−	22.1271i	0.546985	−	0.737161i
$902$		0			0
$903$		−	9.40082i		−	0.312840i
$904$		0			0
$905$	4.70766			0.156488
$906$		0			0
$907$	9.65865	−	9.65865i	0.320710	−	0.320710i	−0.528329	−	0.849040i	$-0.677181\pi$
$907$	9.65865	−	9.65865i	0.320710	−	0.320710i	0.849040	+	0.528329i	$0.177181\pi$
$908$		0			0
$909$			58.8249i			1.95110i
$910$		0			0
$911$	−0.866458	+	0.866458i	−0.0287070	+	0.0287070i	−0.721315	−	0.692608i	$-0.756462\pi$
$911$	−0.866458	+	0.866458i	−0.0287070	+	0.0287070i	0.692608	+	0.721315i	$0.256462\pi$
$912$		0			0
$913$	−16.2983	−	16.2983i	−0.539394	−	0.539394i
$914$		0			0
$915$	8.62848	+	8.62848i	0.285249	+	0.285249i
$916$		0			0
$917$	−69.1042			−2.28202
$918$		0			0
$919$	−21.7152			−0.716317			−0.358158	−	0.933661i	$-0.616595\pi$
$919$	−21.7152			−0.716317			−0.358158	+	0.933661i	$0.616595\pi$
$920$		0			0
$921$	31.4933	+	31.4933i	1.03774	+	1.03774i
$922$		0			0
$923$	0.267733	+	0.267733i	0.00881255	+	0.00881255i
$924$		0			0
$925$	2.44000	−	2.44000i	0.0802269	−	0.0802269i
$926$		0			0
$927$		−	62.0216i		−	2.03706i
$928$		0			0
$929$	−14.9022	+	14.9022i	−0.488924	+	0.488924i	−0.907967	−	0.419043i	$-0.862366\pi$
$929$	−14.9022	+	14.9022i	−0.488924	+	0.488924i	0.419043	+	0.907967i	$0.362366\pi$
$930$		0			0
$931$	29.5980			0.970036
$932$		0			0
$933$		−	40.3427i		−	1.32076i
$934$		0			0
$935$	−8.56188	−	6.35305i	−0.280003	−	0.207767i
$936$		0			0
$937$			48.3234i			1.57866i	0.613971	+	0.789328i	$0.289571\pi$
$937$			48.3234i			1.57866i	−0.613971	+	0.789328i	$0.710429\pi$
$938$		0			0
$939$	−40.3683			−1.31737
$940$		0			0
$941$	11.0045	−	11.0045i	0.358735	−	0.358735i	−0.504611	−	0.863347i	$-0.668364\pi$
$941$	11.0045	−	11.0045i	0.358735	−	0.358735i	0.863347	+	0.504611i	$0.168364\pi$
$942$		0			0
$943$			37.8081i			1.23120i
$944$		0			0
$945$	−50.0230	+	50.0230i	−1.62725	+	1.62725i
$946$		0			0
$947$	−21.4879	−	21.4879i	−0.698262	−	0.698262i	0.265774	−	0.964035i	$-0.414373\pi$
$947$	−21.4879	−	21.4879i	−0.698262	−	0.698262i	−0.964035	+	0.265774i	$0.914373\pi$
$948$		0			0
$949$	0.848772	+	0.848772i	0.0275523	+	0.0275523i
$950$		0			0
$951$	52.3647			1.69804
$952$		0			0
$953$	−18.6150			−0.602998			−0.301499	−	0.953467i	$-0.597487\pi$
$953$	−18.6150			−0.602998			−0.301499	+	0.953467i	$0.597487\pi$
$954$		0			0
$955$	−3.39030	−	3.39030i	−0.109708	−	0.109708i
$956$		0			0
$957$	17.7741	+	17.7741i	0.574556	+	0.574556i
$958$		0			0
$959$	−46.2756	+	46.2756i	−1.49432	+	1.49432i
$960$		0			0
$961$		−	15.4794i		−	0.499337i
$962$		0			0
$963$	12.9272	−	12.9272i	0.416572	−	0.416572i
$964$		0			0
$965$	15.1064			0.486294
$966$		0			0
$967$		−	24.1990i		−	0.778188i	−0.921198	−	0.389094i	$-0.872788\pi$
$967$		−	24.1990i		−	0.778188i	0.921198	−	0.389094i	$-0.127212\pi$
$968$		0			0
$969$	27.4664	−	4.06763i	0.882347	−	0.130671i
$970$		0			0
$971$		−	23.8896i		−	0.766653i	−0.923613	−	0.383327i	$-0.874778\pi$
$971$		−	23.8896i		−	0.766653i	0.923613	−	0.383327i	$-0.125222\pi$
$972$		0			0
$973$	98.5298			3.15872
$974$		0			0
$975$	0.336921	−	0.336921i	0.0107901	−	0.0107901i
$976$		0			0
$977$			23.3337i			0.746510i	0.927729	+	0.373255i	$0.121758\pi$
$977$			23.3337i			0.746510i	−0.927729	+	0.373255i	$0.878242\pi$
$978$		0			0
$979$	−29.2160	+	29.2160i	−0.933747	+	0.933747i
$980$		0			0
$981$	−16.1572	−	16.1572i	−0.515861	−	0.515861i
$982$		0			0
$983$	−37.4373	−	37.4373i	−1.19406	−	1.19406i	−0.975916	−	0.218147i	$-0.929999\pi$
$983$	−37.4373	−	37.4373i	−1.19406	−	1.19406i	−0.218147	−	0.975916i	$-0.570001\pi$
$984$		0			0
$985$	6.86756			0.218819
$986$		0			0
$987$	−128.059			−4.07615
$988$		0			0
$989$	−2.12453	−	2.12453i	−0.0675561	−	0.0675561i
$990$		0			0
$991$	−39.1164	−	39.1164i	−1.24257	−	1.24257i	−0.958929	−	0.283645i	$-0.908456\pi$
$991$	−39.1164	−	39.1164i	−1.24257	−	1.24257i	−0.283645	−	0.958929i	$-0.591544\pi$
$992$		0			0
$993$	24.3811	−	24.3811i	0.773711	−	0.773711i
$994$		0			0
$995$			3.00958i			0.0954102i
$996$		0			0
$997$	36.7958	−	36.7958i	1.16534	−	1.16534i	0.182045	−	0.983290i	$-0.441728\pi$
$997$	36.7958	−	36.7958i	1.16534	−	1.16534i	0.983290	−	0.182045i	$-0.0582718\pi$
$998$		0			0
$999$	52.8124			1.67091

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1360.2.bt.b.81.4		8
4.3	odd	2		170.2.h.b.81.1	yes	8
12.11	even	2		1530.2.q.g.1441.1		8
17.4	even	4	inner	1360.2.bt.b.1041.4		8
20.3	even	4		850.2.g.l.149.4		8
20.7	even	4		850.2.g.i.149.1		8
20.19	odd	2		850.2.h.n.251.4		8
68.15	odd	8		2890.2.a.be.1.4		4
68.19	odd	8		2890.2.a.bd.1.1		4
68.43	odd	8		2890.2.b.o.2311.1		8
68.55	odd	4		170.2.h.b.21.1	✓	8
68.59	odd	8		2890.2.b.o.2311.8		8
204.191	even	4		1530.2.q.g.361.1		8
340.123	even	4		850.2.g.i.599.1		8
340.259	odd	4		850.2.h.n.701.4		8
340.327	even	4		850.2.g.l.599.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.h.b.21.1	✓	8	68.55	odd	4
170.2.h.b.81.1	yes	8	4.3	odd	2
850.2.g.i.149.1		8	20.7	even	4
850.2.g.i.599.1		8	340.123	even	4
850.2.g.l.149.4		8	20.3	even	4
850.2.g.l.599.4		8	340.327	even	4
850.2.h.n.251.4		8	20.19	odd	2
850.2.h.n.701.4		8	340.259	odd	4
1360.2.bt.b.81.4		8	1.1	even	1	trivial
1360.2.bt.b.1041.4		8	17.4	even	4	inner
1530.2.q.g.361.1		8	204.191	even	4
1530.2.q.g.1441.1		8	12.11	even	2
2890.2.a.bd.1.1		4	68.19	odd	8
2890.2.a.be.1.4		4	68.15	odd	8
2890.2.b.o.2311.1		8	68.43	odd	8
2890.2.b.o.2311.8		8	68.59	odd	8

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:	\( N \)	\(=\)	\( 1360 = 2^{4} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1360.bt (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.31113 + 2.31113i) q^{3} +(0.707107 + 0.707107i) q^{5} +(3.26843 - 3.26843i) q^{7} +7.68265i q^{9} +O(q^{10})\)	\(q+(2.31113 + 2.31113i) q^{3} +(0.707107 + 0.707107i) q^{5} +(3.26843 - 3.26843i) q^{7} +7.68265i q^{9} +(1.82843 - 1.82843i) q^{11} -0.145782 q^{13} +3.26843i q^{15} +(-3.31113 - 2.45691i) q^{17} +2.06038i q^{19} +15.1075 q^{21} +(3.41421 - 3.41421i) q^{23} +1.00000i q^{25} +(-10.8222 + 10.8222i) q^{27} +(2.10308 + 2.10308i) q^{29} +(2.78573 + 2.78573i) q^{31} +8.45147 q^{33} +4.62226 q^{35} +(-2.44000 - 2.44000i) q^{37} +(-0.336921 - 0.336921i) q^{39} +(-5.53686 + 5.53686i) q^{41} -0.622260i q^{43} +(-5.43245 + 5.43245i) q^{45} -8.47648 q^{47} -14.3653i q^{49} +(-1.97421 - 13.3307i) q^{51} +6.68265i q^{53} +2.58579 q^{55} +(-4.76182 + 4.76182i) q^{57} -5.71724i q^{59} +(2.63995 - 2.63995i) q^{61} +(25.1102 + 25.1102i) q^{63} +(-0.103083 - 0.103083i) q^{65} -1.58767 q^{67} +15.7814 q^{69} +(-1.83653 - 1.83653i) q^{71} +(-5.82220 - 5.82220i) q^{73} +(-2.31113 + 2.31113i) q^{75} -11.9522i q^{77} +(-3.29344 + 3.29344i) q^{79} -26.9751 q^{81} -8.91382i q^{83} +(-0.604023 - 4.07862i) q^{85} +9.72100i q^{87} -15.9787 q^{89} +(-0.476478 + 0.476478i) q^{91} +12.8764i q^{93} +(-1.45691 + 1.45691i) q^{95} +(12.5814 + 12.5814i) q^{97} +(14.0472 + 14.0472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^7	\( 8 q + 4 q^{7} - 8 q^{11} - 12 q^{13} - 8 q^{17} + 16 q^{21} + 16 q^{23} - 12 q^{27} + 24 q^{29} - 4 q^{31} + 16 q^{33} - 20 q^{37} + 4 q^{39} - 8 q^{45} - 20 q^{47} - 4 q^{51} + 32 q^{55} + 40 q^{57} - 16 q^{61} + 64 q^{63} - 8 q^{65} + 16 q^{67} + 8 q^{69} - 4 q^{71} + 28 q^{73} - 8 q^{79} - 8 q^{81} + 8 q^{85} - 44 q^{89} + 44 q^{91} - 4 q^{95} + 20 q^{97} + 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^7 - 8 * q^11 - 12 * q^13 - 8 * q^17 + 16 * q^21 + 16 * q^23 - 12 * q^27 + 24 * q^29 - 4 * q^31 + 16 * q^33 - 20 * q^37 + 4 * q^39 - 8 * q^45 - 20 * q^47 - 4 * q^51 + 32 * q^55 + 40 * q^57 - 16 * q^61 + 64 * q^63 - 8 * q^65 + 16 * q^67 + 8 * q^69 - 4 * q^71 + 28 * q^73 - 8 * q^79 - 8 * q^81 + 8 * q^85 - 44 * q^89 + 44 * q^91 - 4 * q^95 + 20 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more