LMFDB - Embedded newform 4020.2.q.k.3781.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4020,2,Mod(841,4020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4020, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4020.q (of order $3$, 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:	$32.0998616126$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 11 x^{12} - 8 x^{11} + 88 x^{10} - 57 x^{9} + 270 x^{8} + 17 x^{7} + 458 x^{6} + \cdots + 4 $ x^14 - x^13 + 11x^12 - 8x^11 + 88x^10 - 57x^9 + 270x^8 + 17x^7 + 458x^6 - 101x^5 + 189x^4 - 30x^3 + 54x^2 - 12x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3781.1
Root			$0.295122 + 0.511167i$ of defining polynomial
Character	$\chi$	$=$	4020.3781
Dual form			4020.2.q.k.841.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} +1.00000 q^{5} +(-1.59463 - 2.76199i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} +1.00000 q^{5} +(-1.59463 - 2.76199i) q^{7} +1.00000 q^{9} +(2.11819 + 3.66882i) q^{11} +(1.09024 - 1.88836i) q^{13} -1.00000 q^{15} +(-2.56215 + 4.43778i) q^{17} +(-0.325805 + 0.564312i) q^{19} +(1.59463 + 2.76199i) q^{21} +(4.02246 - 6.96710i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-3.94885 - 6.83962i) q^{29} +(4.23779 + 7.34007i) q^{31} +(-2.11819 - 3.66882i) q^{33} +(-1.59463 - 2.76199i) q^{35} +(-1.75252 + 3.03546i) q^{37} +(-1.09024 + 1.88836i) q^{39} +(0.135436 + 0.234583i) q^{41} +8.32328 q^{43} +1.00000 q^{45} +(-0.171569 - 0.297167i) q^{47} +(-1.58571 + 2.74654i) q^{49} +(2.56215 - 4.43778i) q^{51} +7.89678 q^{53} +(2.11819 + 3.66882i) q^{55} +(0.325805 - 0.564312i) q^{57} -4.39987 q^{59} +(-7.05670 + 12.2226i) q^{61} +(-1.59463 - 2.76199i) q^{63} +(1.09024 - 1.88836i) q^{65} +(5.59464 + 5.97495i) q^{67} +(-4.02246 + 6.96710i) q^{69} +(1.45116 + 2.51348i) q^{71} +(3.18520 - 5.51693i) q^{73} -1.00000 q^{75} +(6.75549 - 11.7008i) q^{77} +(0.598566 + 1.03675i) q^{79} +1.00000 q^{81} +(0.963958 - 1.66962i) q^{83} +(-2.56215 + 4.43778i) q^{85} +(3.94885 + 6.83962i) q^{87} -3.23796 q^{89} -6.95417 q^{91} +(-4.23779 - 7.34007i) q^{93} +(-0.325805 + 0.564312i) q^{95} +(5.58794 - 9.67860i) q^{97} +(2.11819 + 3.66882i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9	$ 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9} + 6 q^{11} + 9 q^{13} - 14 q^{15} - 12 q^{17} + 14 q^{19} - 3 q^{21} + 6 q^{23} + 14 q^{25} - 14 q^{27} - q^{29} + 7 q^{31} - 6 q^{33} + 3 q^{35} - 2 q^{37} - 9 q^{39} - 18 q^{41} - 6 q^{43} + 14 q^{45} + 7 q^{47} + 12 q^{51} - 12 q^{53} + 6 q^{55} - 14 q^{57} - 2 q^{59} + 3 q^{63} + 9 q^{65} + 25 q^{67} - 6 q^{69} + 22 q^{71} - 15 q^{73} - 14 q^{75} + q^{77} + 9 q^{79} + 14 q^{81} - q^{83} - 12 q^{85} + q^{87} - 12 q^{89} - 38 q^{91} - 7 q^{93} + 14 q^{95} + 16 q^{97} + 6 q^{99}+O(q^{100}) $ 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9 + 6 * q^11 + 9 * q^13 - 14 * q^15 - 12 * q^17 + 14 * q^19 - 3 * q^21 + 6 * q^23 + 14 * q^25 - 14 * q^27 - q^29 + 7 * q^31 - 6 * q^33 + 3 * q^35 - 2 * q^37 - 9 * q^39 - 18 * q^41 - 6 * q^43 + 14 * q^45 + 7 * q^47 + 12 * q^51 - 12 * q^53 + 6 * q^55 - 14 * q^57 - 2 * q^59 + 3 * q^63 + 9 * q^65 + 25 * q^67 - 6 * q^69 + 22 * q^71 - 15 * q^73 - 14 * q^75 + q^77 + 9 * q^79 + 14 * q^81 - q^83 - 12 * q^85 + q^87 - 12 * q^89 - 38 * q^91 - 7 * q^93 + 14 * q^95 + 16 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times$.

$n$	$1141$	$2011$	$2681$	$3217$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−1.59463	−	2.76199i	−0.602715	−	1.04393i	−0.992408	−	0.122988i	$-0.960752\pi$
$7$	−1.59463	−	2.76199i	−0.602715	−	1.04393i	0.389693	−	0.920945i	$-0.372581\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	2.11819	+	3.66882i	0.638660	+	1.10619i	0.985727	+	0.168351i	$0.0538441\pi$
$11$	2.11819	+	3.66882i	0.638660	+	1.10619i	−0.347068	+	0.937840i	$0.612823\pi$
$12$		0			0
$13$	1.09024	−	1.88836i	0.302380	−	0.523737i	−0.674295	−	0.738462i	$-0.735552\pi$
$13$	1.09024	−	1.88836i	0.302380	−	0.523737i	0.976674	+	0.214725i	$0.0688857\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	−2.56215	+	4.43778i	−0.621413	+	1.07632i	0.367810	+	0.929901i	$0.380108\pi$
$17$	−2.56215	+	4.43778i	−0.621413	+	1.07632i	−0.989223	+	0.146418i	$0.953225\pi$
$18$		0			0
$19$	−0.325805	+	0.564312i	−0.0747449	+	0.129462i	−0.900975	−	0.433870i	$-0.857148\pi$
$19$	−0.325805	+	0.564312i	−0.0747449	+	0.129462i	0.826230	+	0.563332i	$0.190481\pi$
$20$		0			0
$21$	1.59463	+	2.76199i	0.347978	+	0.602715i
$22$		0			0
$23$	4.02246	−	6.96710i	0.838741	−	1.45274i	−0.0522075	−	0.998636i	$-0.516626\pi$
$23$	4.02246	−	6.96710i	0.838741	−	1.45274i	0.890948	−	0.454105i	$-0.150041\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−3.94885	−	6.83962i	−0.733284	−	1.27008i	−0.955472	−	0.295081i	$-0.904653\pi$
$29$	−3.94885	−	6.83962i	−0.733284	−	1.27008i	0.222188	−	0.975004i	$-0.428680\pi$
$30$		0			0
$31$	4.23779	+	7.34007i	0.761129	+	1.31831i	0.942269	+	0.334857i	$0.108688\pi$
$31$	4.23779	+	7.34007i	0.761129	+	1.31831i	−0.181139	+	0.983457i	$0.557979\pi$
$32$		0			0
$33$	−2.11819	−	3.66882i	−0.368730	−	0.638660i
$34$		0			0
$35$	−1.59463	−	2.76199i	−0.269542	−	0.466861i
$36$		0			0
$37$	−1.75252	+	3.03546i	−0.288113	+	0.499026i	−0.973359	−	0.229285i	$-0.926361\pi$
$37$	−1.75252	+	3.03546i	−0.288113	+	0.499026i	0.685246	+	0.728311i	$0.259694\pi$
$38$		0			0
$39$	−1.09024	+	1.88836i	−0.174579	+	0.302380i
$40$		0			0
$41$	0.135436	+	0.234583i	0.0211516	+	0.0366356i	0.876407	−	0.481570i	$-0.159933\pi$
$41$	0.135436	+	0.234583i	0.0211516	+	0.0366356i	−0.855256	+	0.518206i	$0.826600\pi$
$42$		0			0
$43$	8.32328			1.26929			0.634644	−	0.772804i	$-0.281147\pi$
$43$	8.32328			1.26929			0.634644	+	0.772804i	$0.281147\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	−0.171569	−	0.297167i	−0.0250260	−	0.0433462i	0.853241	−	0.521517i	$-0.174634\pi$
$47$	−0.171569	−	0.297167i	−0.0250260	−	0.0433462i	−0.878267	+	0.478170i	$0.841300\pi$
$48$		0			0
$49$	−1.58571	+	2.74654i	−0.226530	+	0.392362i
$50$		0			0
$51$	2.56215	−	4.43778i	0.358773	−	0.621413i
$52$		0			0
$53$	7.89678			1.08471			0.542353	−	0.840151i	$-0.317534\pi$
$53$	7.89678			1.08471			0.542353	+	0.840151i	$0.317534\pi$
$54$		0			0
$55$	2.11819	+	3.66882i	0.285617	+	0.494704i
$56$		0			0
$57$	0.325805	−	0.564312i	0.0431540	−	0.0747449i
$58$		0			0
$59$	−4.39987			−0.572814			−0.286407	−	0.958108i	$-0.592461\pi$
$59$	−4.39987			−0.572814			−0.286407	+	0.958108i	$0.592461\pi$
$60$		0			0
$61$	−7.05670	+	12.2226i	−0.903518	+	1.56494i	−0.0806243	+	0.996745i	$0.525691\pi$
$61$	−7.05670	+	12.2226i	−0.903518	+	1.56494i	−0.822894	+	0.568195i	$0.807642\pi$
$62$		0			0
$63$	−1.59463	−	2.76199i	−0.200905	−	0.347978i
$64$		0			0
$65$	1.09024	−	1.88836i	0.135228	−	0.234222i
$66$		0			0
$67$	5.59464	+	5.97495i	0.683493	+	0.729957i
$67$	5.59464	+	5.97495i	0.683493	+	0.729957i
$68$		0			0
$69$	−4.02246	+	6.96710i	−0.484247	+	0.838741i
$70$		0			0
$71$	1.45116	+	2.51348i	0.172221	+	0.298295i	0.939196	−	0.343382i	$-0.111572\pi$
$71$	1.45116	+	2.51348i	0.172221	+	0.298295i	−0.766975	+	0.641677i	$0.778239\pi$
$72$		0			0
$73$	3.18520	−	5.51693i	0.372800	−	0.645708i	−0.617195	−	0.786810i	$-0.711731\pi$
$73$	3.18520	−	5.51693i	0.372800	−	0.645708i	0.989995	+	0.141102i	$0.0450646\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	6.75549	−	11.7008i	0.769859	−	1.33344i
$78$		0			0
$79$	0.598566	+	1.03675i	0.0673440	+	0.116643i	0.897731	−	0.440543i	$-0.145214\pi$
$79$	0.598566	+	1.03675i	0.0673440	+	0.116643i	−0.830387	+	0.557187i	$0.811881\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	0.963958	−	1.66962i	0.105808	−	0.183265i	−0.808260	−	0.588826i	$-0.799590\pi$
$83$	0.963958	−	1.66962i	0.105808	−	0.183265i	0.914068	+	0.405561i	$0.132924\pi$
$84$		0			0
$85$	−2.56215	+	4.43778i	−0.277904	+	0.481345i
$86$		0			0
$87$	3.94885	+	6.83962i	0.423362	+	0.733284i
$88$		0			0
$89$	−3.23796			−0.343223			−0.171612	−	0.985165i	$-0.554897\pi$
$89$	−3.23796			−0.343223			−0.171612	+	0.985165i	$0.554897\pi$
$90$		0			0
$91$	−6.95417			−0.728995
$92$		0			0
$93$	−4.23779	−	7.34007i	−0.439438	−	0.761129i
$94$		0			0
$95$	−0.325805	+	0.564312i	−0.0334269	+	0.0578971i
$96$		0			0
$97$	5.58794	−	9.67860i	0.567370	−	0.982713i	−0.429455	−	0.903088i	$-0.641294\pi$
$97$	5.58794	−	9.67860i	0.567370	−	0.982713i	0.996825	−	0.0796248i	$-0.0253722\pi$
$98$		0			0
$99$	2.11819	+	3.66882i	0.212887	+	0.368730i
$100$		0			0
$101$	−7.11803	−	12.3288i	−0.708270	−	1.22676i	−0.965498	−	0.260409i	$-0.916142\pi$
$101$	−7.11803	−	12.3288i	−0.708270	−	1.22676i	0.257228	−	0.966351i	$-0.417191\pi$
$102$		0			0
$103$	5.69947	+	9.87177i	0.561585	+	0.972694i	0.997358	+	0.0726378i	$0.0231417\pi$
$103$	5.69947	+	9.87177i	0.561585	+	0.972694i	−0.435773	+	0.900057i	$0.643525\pi$
$104$		0			0
$105$	1.59463	+	2.76199i	0.155620	+	0.269542i
$106$		0			0
$107$	8.78848			0.849615			0.424807	−	0.905284i	$-0.360342\pi$
$107$	8.78848			0.849615			0.424807	+	0.905284i	$0.360342\pi$
$108$		0			0
$109$	2.52859			0.242195			0.121098	−	0.992641i	$-0.461359\pi$
$109$	2.52859			0.242195			0.121098	+	0.992641i	$0.461359\pi$
$110$		0			0
$111$	1.75252	−	3.03546i	0.166342	−	0.288113i
$112$		0			0
$113$	−8.82932	−	15.2928i	−0.830593	−	1.43863i	−0.897569	−	0.440874i	$-0.854669\pi$
$113$	−8.82932	−	15.2928i	−0.830593	−	1.43863i	0.0669763	−	0.997755i	$-0.478665\pi$
$114$		0			0
$115$	4.02246	−	6.96710i	0.375096	−	0.649686i
$116$		0			0
$117$	1.09024	−	1.88836i	0.100793	−	0.174579i
$118$		0			0
$119$	16.3428			1.49814
$120$		0			0
$121$	−3.47349	+	6.01627i	−0.315772	+	0.546933i
$122$		0			0
$123$	−0.135436	−	0.234583i	−0.0122119	−	0.0211516i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−5.93915	−	10.2869i	−0.527015	−	0.912816i	−0.999504	−	0.0314799i	$-0.989978\pi$
$127$	−5.93915	−	10.2869i	−0.527015	−	0.912816i	0.472490	−	0.881336i	$-0.343355\pi$
$128$		0			0
$129$	−8.32328			−0.732824
$130$		0			0
$131$	1.93949			0.169454			0.0847271	−	0.996404i	$-0.472998\pi$
$131$	1.93949			0.169454			0.0847271	+	0.996404i	$0.472998\pi$
$132$		0			0
$133$	2.07816			0.180199
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	−15.7104			−1.34223			−0.671115	−	0.741353i	$-0.734184\pi$
$137$	−15.7104			−1.34223			−0.671115	+	0.741353i	$0.734184\pi$
$138$		0			0
$139$	15.1789			1.28746			0.643730	−	0.765253i	$-0.277386\pi$
$139$	15.1789			1.28746			0.643730	+	0.765253i	$0.277386\pi$
$140$		0			0
$141$	0.171569	+	0.297167i	0.0144487	+	0.0250260i
$142$		0			0
$143$	9.23740			0.772470
$144$		0			0
$145$	−3.94885	−	6.83962i	−0.327934	−	0.567999i
$146$		0			0
$147$	1.58571	−	2.74654i	0.130787	−	0.226530i
$148$		0			0
$149$	10.2647			0.840916			0.420458	−	0.907312i	$-0.361869\pi$
$149$	10.2647			0.840916			0.420458	+	0.907312i	$0.361869\pi$
$150$		0			0
$151$	8.87873	−	15.3784i	0.722541	−	1.25148i	−0.237437	−	0.971403i	$-0.576307\pi$
$151$	8.87873	−	15.3784i	0.722541	−	1.25148i	0.959978	−	0.280075i	$-0.0903594\pi$
$152$		0			0
$153$	−2.56215	+	4.43778i	−0.207138	+	0.358773i
$154$		0			0
$155$	4.23779	+	7.34007i	0.340387	+	0.589568i
$156$		0			0
$157$	11.3542	−	19.6661i	0.906167	−	1.56953i	0.0868237	−	0.996224i	$-0.472328\pi$
$157$	11.3542	−	19.6661i	0.906167	−	1.56953i	0.819343	−	0.573303i	$-0.194338\pi$
$158$		0			0
$159$	−7.89678			−0.626255
$160$		0			0
$161$	−25.6574			−2.02209
$162$		0			0
$163$	−3.63817	−	6.30150i	−0.284964	−	0.493571i	0.687637	−	0.726055i	$-0.258648\pi$
$163$	−3.63817	−	6.30150i	−0.284964	−	0.493571i	−0.972600	+	0.232484i	$0.925315\pi$
$164$		0			0
$165$	−2.11819	−	3.66882i	−0.164901	−	0.285617i
$166$		0			0
$167$	8.49804	+	14.7190i	0.657598	+	1.13899i	0.981236	+	0.192812i	$0.0617607\pi$
$167$	8.49804	+	14.7190i	0.657598	+	1.13899i	−0.323638	+	0.946181i	$0.604906\pi$
$168$		0			0
$169$	4.12273	+	7.14078i	0.317133	+	0.549291i
$170$		0			0
$171$	−0.325805	+	0.564312i	−0.0249150	+	0.0431540i
$172$		0			0
$173$	4.74878	−	8.22513i	0.361043	−	0.625345i	−0.627090	−	0.778947i	$-0.715754\pi$
$173$	4.74878	−	8.22513i	0.361043	−	0.625345i	0.988133	+	0.153602i	$0.0490873\pi$
$174$		0			0
$175$	−1.59463	−	2.76199i	−0.120543	−	0.208787i
$176$		0			0
$177$	4.39987			0.330714
$178$		0			0
$179$	2.79245			0.208717			0.104359	−	0.994540i	$-0.466721\pi$
$179$	2.79245			0.208717			0.104359	+	0.994540i	$0.466721\pi$
$180$		0			0
$181$	0.424877	+	0.735909i	0.0315809	+	0.0546997i	0.881384	−	0.472401i	$-0.156612\pi$
$181$	0.424877	+	0.735909i	0.0315809	+	0.0546997i	−0.849803	+	0.527100i	$0.823279\pi$
$182$		0			0
$183$	7.05670	−	12.2226i	0.521647	−	0.903518i
$184$		0			0
$185$	−1.75252	+	3.03546i	−0.128848	+	0.223171i
$186$		0			0
$187$	−21.7085			−1.58749
$188$		0			0
$189$	1.59463	+	2.76199i	0.115993	+	0.200905i
$190$		0			0
$191$	7.32457	−	12.6865i	0.529987	−	0.917965i	−0.469401	−	0.882985i	$-0.655530\pi$
$191$	7.32457	−	12.6865i	0.529987	−	0.917965i	0.999388	−	0.0349798i	$-0.0111367\pi$
$192$		0			0
$193$	17.5891			1.26609			0.633047	−	0.774113i	$-0.281804\pi$
$193$	17.5891			1.26609			0.633047	+	0.774113i	$0.281804\pi$
$194$		0			0
$195$	−1.09024	+	1.88836i	−0.0780741	+	0.135228i
$196$		0			0
$197$	11.2607	+	19.5041i	0.802293	+	1.38961i	0.918103	+	0.396341i	$0.129720\pi$
$197$	11.2607	+	19.5041i	0.802293	+	1.38961i	−0.115811	+	0.993271i	$0.536947\pi$
$198$		0			0
$199$	−0.782789	+	1.35583i	−0.0554904	+	0.0961123i	−0.892436	−	0.451173i	$-0.851006\pi$
$199$	−0.782789	+	1.35583i	−0.0554904	+	0.0961123i	0.836946	+	0.547286i	$0.184339\pi$
$200$		0			0
$201$	−5.59464	−	5.97495i	−0.394615	−	0.421441i
$202$		0			0
$203$	−12.5940	+	21.8134i	−0.883922	+	1.53100i
$204$		0			0
$205$	0.135436	+	0.234583i	0.00945928	+	0.0163840i
$206$		0			0
$207$	4.02246	−	6.96710i	0.279580	−	0.484247i
$208$		0			0
$209$	−2.76048			−0.190946
$210$		0			0
$211$	10.6933	−	18.5213i	0.736156	−	1.27506i	−0.218058	−	0.975936i	$-0.569972\pi$
$211$	10.6933	−	18.5213i	0.736156	−	1.27506i	0.954214	−	0.299124i	$-0.0966946\pi$
$212$		0			0
$213$	−1.45116	−	2.51348i	−0.0994316	−	0.172221i
$214$		0			0
$215$	8.32328			0.567643
$216$		0			0
$217$	13.5154	−	23.4094i	0.917488	−	1.58914i
$218$		0			0
$219$	−3.18520	+	5.51693i	−0.215236	+	0.372800i
$220$		0			0
$221$	5.58675	+	9.67653i	0.375805	+	0.650914i
$222$		0			0
$223$	14.6790			0.982979			0.491490	−	0.870883i	$-0.336453\pi$
$223$	14.6790			0.982979			0.491490	+	0.870883i	$0.336453\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	11.3434	+	19.6473i	0.752888	+	1.30404i	0.946417	+	0.322946i	$0.104673\pi$
$227$	11.3434	+	19.6473i	0.752888	+	1.30404i	−0.193529	+	0.981094i	$0.561994\pi$
$228$		0			0
$229$	−0.410433	+	0.710890i	−0.0271221	+	0.0469769i	−0.879268	−	0.476328i	$-0.841968\pi$
$229$	−0.410433	+	0.710890i	−0.0271221	+	0.0469769i	0.852146	+	0.523305i	$0.175301\pi$
$230$		0			0
$231$	−6.75549	+	11.7008i	−0.444478	+	0.769859i
$232$		0			0
$233$	−10.2133	−	17.6899i	−0.669093	−	1.15890i	−0.978158	−	0.207862i	$-0.933349\pi$
$233$	−10.2133	−	17.6899i	−0.669093	−	1.15890i	0.309065	−	0.951041i	$-0.399984\pi$
$234$		0			0
$235$	−0.171569	−	0.297167i	−0.0111919	−	0.0193850i
$236$		0			0
$237$	−0.598566	−	1.03675i	−0.0388811	−	0.0673440i
$238$		0			0
$239$	13.4875	+	23.3611i	0.872436	+	1.51110i	0.859470	+	0.511187i	$0.170794\pi$
$239$	13.4875	+	23.3611i	0.872436	+	1.51110i	0.0129662	+	0.999916i	$0.495873\pi$
$240$		0			0
$241$	−4.12596			−0.265776			−0.132888	−	0.991131i	$-0.542425\pi$
$241$	−4.12596			−0.265776			−0.132888	+	0.991131i	$0.542425\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−1.58571	+	2.74654i	−0.101307	+	0.175470i
$246$		0			0
$247$	0.710415	+	1.23048i	0.0452027	+	0.0782933i
$248$		0			0
$249$	−0.963958	+	1.66962i	−0.0610884	+	0.105808i
$250$		0			0
$251$	2.26482	−	3.92278i	0.142954	−	0.247604i	−0.785654	−	0.618666i	$-0.787673\pi$
$251$	2.26482	−	3.92278i	0.142954	−	0.247604i	0.928608	+	0.371063i	$0.121007\pi$
$252$		0			0
$253$	34.0814			2.14268
$254$		0			0
$255$	2.56215	−	4.43778i	0.160448	−	0.277904i
$256$		0			0
$257$	−1.27099	−	2.20142i	−0.0792821	−	0.137321i	0.823658	−	0.567086i	$-0.191929\pi$
$257$	−1.27099	−	2.20142i	−0.0792821	−	0.137321i	−0.902940	+	0.429766i	$0.858596\pi$
$258$		0			0
$259$	11.1785			0.694599
$260$		0			0
$261$	−3.94885	−	6.83962i	−0.244428	−	0.423362i
$262$		0			0
$263$	22.9781			1.41689			0.708446	−	0.705765i	$-0.249397\pi$
$263$	22.9781			1.41689			0.708446	+	0.705765i	$0.249397\pi$
$264$		0			0
$265$	7.89678			0.485095
$266$		0			0
$267$	3.23796			0.198160
$268$		0			0
$269$	12.7893			0.779777			0.389889	−	0.920862i	$-0.372513\pi$
$269$	12.7893			0.779777			0.389889	+	0.920862i	$0.372513\pi$
$270$		0			0
$271$	−3.91554			−0.237852			−0.118926	−	0.992903i	$-0.537945\pi$
$271$	−3.91554			−0.237852			−0.118926	+	0.992903i	$0.537945\pi$
$272$		0			0
$273$	6.95417			0.420885
$274$		0			0
$275$	2.11819	+	3.66882i	0.127732	+	0.221238i
$276$		0			0
$277$	21.4499			1.28880			0.644401	−	0.764688i	$-0.277107\pi$
$277$	21.4499			1.28880			0.644401	+	0.764688i	$0.277107\pi$
$278$		0			0
$279$	4.23779	+	7.34007i	0.253710	+	0.439438i
$280$		0			0
$281$	−3.76695	+	6.52455i	−0.224717	+	0.389222i	−0.956235	−	0.292601i	$-0.905479\pi$
$281$	−3.76695	+	6.52455i	−0.224717	+	0.389222i	0.731517	+	0.681823i	$0.238813\pi$
$282$		0			0
$283$	2.37594			0.141235			0.0706175	−	0.997503i	$-0.477503\pi$
$283$	2.37594			0.141235			0.0706175	+	0.997503i	$0.477503\pi$
$284$		0			0
$285$	0.325805	−	0.564312i	0.0192990	−	0.0334269i
$286$		0			0
$287$	0.431943	−	0.748146i	0.0254968	−	0.0441617i
$288$		0			0
$289$	−4.62925	−	8.01810i	−0.272309	−	0.471653i
$290$		0			0
$291$	−5.58794	+	9.67860i	−0.327571	+	0.567370i
$292$		0			0
$293$	−0.957295			−0.0559258			−0.0279629	−	0.999609i	$-0.508902\pi$
$293$	−0.957295			−0.0559258			−0.0279629	+	0.999609i	$0.508902\pi$
$294$		0			0
$295$	−4.39987			−0.256170
$296$		0			0
$297$	−2.11819	−	3.66882i	−0.122910	−	0.212887i
$298$		0			0
$299$	−8.77093	−	15.1917i	−0.507236	−	0.878559i
$300$		0			0
$301$	−13.2726	−	22.9888i	−0.765019	−	1.32505i
$302$		0			0
$303$	7.11803	+	12.3288i	0.408920	+	0.708270i
$304$		0			0
$305$	−7.05670	+	12.2226i	−0.404066	+	0.699862i
$306$		0			0
$307$	−13.7000	+	23.7291i	−0.781900	+	1.35429i	0.148934	+	0.988847i	$0.452416\pi$
$307$	−13.7000	+	23.7291i	−0.781900	+	1.35429i	−0.930834	+	0.365443i	$0.880917\pi$
$308$		0			0
$309$	−5.69947	−	9.87177i	−0.324231	−	0.561585i
$310$		0			0
$311$	−7.11121			−0.403240			−0.201620	−	0.979464i	$-0.564621\pi$
$311$	−7.11121			−0.403240			−0.201620	+	0.979464i	$0.564621\pi$
$312$		0			0
$313$	−23.4103			−1.32323			−0.661616	−	0.749843i	$-0.730129\pi$
$313$	−23.4103			−1.32323			−0.661616	+	0.749843i	$0.730129\pi$
$314$		0			0
$315$	−1.59463	−	2.76199i	−0.0898474	−	0.155620i
$316$		0			0
$317$	0.400887	−	0.694356i	0.0225160	−	0.0389989i	−0.854548	−	0.519373i	$-0.826166\pi$
$317$	0.400887	−	0.694356i	0.0225160	−	0.0389989i	0.877064	+	0.480374i	$0.159499\pi$
$318$		0			0
$319$	16.7289	−	28.9753i	0.936637	−	1.62230i
$320$		0			0
$321$	−8.78848			−0.490525
$322$		0			0
$323$	−1.66953	−	2.89170i	−0.0928949	−	0.160899i
$324$		0			0
$325$	1.09024	−	1.88836i	0.0604759	−	0.104747i
$326$		0			0
$327$	−2.52859			−0.139831
$328$		0			0
$329$	−0.547180	+	0.947744i	−0.0301670	+	0.0522508i
$330$		0			0
$331$	−6.38166	−	11.0534i	−0.350768	−	0.607547i	0.635617	−	0.772005i	$-0.280746\pi$
$331$	−6.38166	−	11.0534i	−0.350768	−	0.607547i	−0.986384	+	0.164458i	$0.947413\pi$
$332$		0			0
$333$	−1.75252	+	3.03546i	−0.0960376	+	0.166342i
$334$		0			0
$335$	5.59464	+	5.97495i	0.305668	+	0.326447i
$336$		0			0
$337$	8.07382	−	13.9843i	0.439809	−	0.761772i	−0.557865	−	0.829931i	$-0.688379\pi$
$337$	8.07382	−	13.9843i	0.439809	−	0.761772i	0.997674	+	0.0681599i	$0.0217128\pi$
$338$		0			0
$339$	8.82932	+	15.2928i	0.479543	+	0.830593i
$340$		0			0
$341$	−17.9529	+	31.0954i	−0.972205	+	1.68391i
$342$		0			0
$343$	−12.2103			−0.659297
$344$		0			0
$345$	−4.02246	+	6.96710i	−0.216562	+	0.375096i
$346$		0			0
$347$	−2.53654	−	4.39341i	−0.136169	−	0.235851i	0.789875	−	0.613268i	$-0.210146\pi$
$347$	−2.53654	−	4.39341i	−0.136169	−	0.235851i	−0.926043	+	0.377417i	$0.876812\pi$
$348$		0			0
$349$	4.95651			0.265316			0.132658	−	0.991162i	$-0.457649\pi$
$349$	4.95651			0.265316			0.132658	+	0.991162i	$0.457649\pi$
$350$		0			0
$351$	−1.09024	+	1.88836i	−0.0581930	+	0.100793i
$352$		0			0
$353$	−0.676718	+	1.17211i	−0.0360181	+	0.0623851i	−0.883473	−	0.468483i	$-0.844801\pi$
$353$	−0.676718	+	1.17211i	−0.0360181	+	0.0623851i	0.847454	+	0.530868i	$0.178134\pi$
$354$		0			0
$355$	1.45116	+	2.51348i	0.0770194	+	0.133402i
$356$		0			0
$357$	−16.3428			−0.864952
$358$		0			0
$359$	−21.5436			−1.13703			−0.568514	−	0.822674i	$-0.692481\pi$
$359$	−21.5436			−1.13703			−0.568514	+	0.822674i	$0.692481\pi$
$360$		0			0
$361$	9.28770	+	16.0868i	0.488826	+	0.846672i
$362$		0			0
$363$	3.47349	−	6.01627i	0.182311	−	0.315772i
$364$		0			0
$365$	3.18520	−	5.51693i	0.166721	−	0.288769i
$366$		0			0
$367$	8.20139	+	14.2052i	0.428109	+	0.741507i	0.996705	−	0.0811103i	$-0.0258466\pi$
$367$	8.20139	+	14.2052i	0.428109	+	0.741507i	−0.568596	+	0.822617i	$0.692513\pi$
$368$		0			0
$369$	0.135436	+	0.234583i	0.00705053	+	0.0122119i
$370$		0			0
$371$	−12.5925	−	21.8108i	−0.653768	−	1.13236i
$372$		0			0
$373$	12.8529	+	22.2619i	0.665498	+	1.15268i	0.979150	+	0.203139i	$0.0651142\pi$
$373$	12.8529	+	22.2619i	0.665498	+	1.15268i	−0.313652	+	0.949538i	$0.601552\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	−17.2209			−0.886920
$378$		0			0
$379$	11.7431	−	20.3397i	0.603204	−	1.04478i	−0.389129	−	0.921183i	$-0.627224\pi$
$379$	11.7431	−	20.3397i	0.603204	−	1.04478i	0.992333	−	0.123597i	$-0.0394428\pi$
$380$		0			0
$381$	5.93915	+	10.2869i	0.304272	+	0.527015i
$382$		0			0
$383$	15.5127	−	26.8688i	0.792663	−	1.37293i	−0.131650	−	0.991296i	$-0.542027\pi$
$383$	15.5127	−	26.8688i	0.792663	−	1.37293i	0.924313	−	0.381636i	$-0.124639\pi$
$384$		0			0
$385$	6.75549	−	11.7008i	0.344292	−	0.596330i
$386$		0			0
$387$	8.32328			0.423096
$388$		0			0
$389$	5.23358	−	9.06483i	0.265353	−	0.459605i	−0.702303	−	0.711878i	$-0.747845\pi$
$389$	5.23358	−	9.06483i	0.265353	−	0.459605i	0.967656	+	0.252273i	$0.0811782\pi$
$390$		0			0
$391$	20.6123	+	35.7016i	1.04241	+	1.80551i
$392$		0			0
$393$	−1.93949			−0.0978345
$394$		0			0
$395$	0.598566	+	1.03675i	0.0301171	+	0.0521644i
$396$		0			0
$397$	−5.59361			−0.280735			−0.140368	−	0.990099i	$-0.544828\pi$
$397$	−5.59361			−0.280735			−0.140368	+	0.990099i	$0.544828\pi$
$398$		0			0
$399$	−2.07816			−0.104038
$400$		0			0
$401$	−21.0340			−1.05039			−0.525193	−	0.850983i	$-0.676007\pi$
$401$	−21.0340			−1.05039			−0.525193	+	0.850983i	$0.676007\pi$
$402$		0			0
$403$	18.4809			0.920600
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	−14.8487			−0.736024
$408$		0			0
$409$	13.6119	+	23.5765i	0.673066	+	1.16579i	0.977030	+	0.213102i	$0.0683566\pi$
$409$	13.6119	+	23.5765i	0.673066	+	1.16579i	−0.303964	+	0.952684i	$0.598310\pi$
$410$		0			0
$411$	15.7104			0.774937
$412$		0			0
$413$	7.01617	+	12.1524i	0.345243	+	0.597979i
$414$		0			0
$415$	0.963958	−	1.66962i	0.0473188	−	0.0819586i
$416$		0			0
$417$	−15.1789			−0.743315
$418$		0			0
$419$	3.91227	−	6.77625i	0.191127	−	0.331042i	−0.754497	−	0.656303i	$-0.772119\pi$
$419$	3.91227	−	6.77625i	0.191127	−	0.331042i	0.945624	+	0.325262i	$0.105452\pi$
$420$		0			0
$421$	−2.08243	+	3.60688i	−0.101492	+	0.175789i	−0.912299	−	0.409524i	$-0.865695\pi$
$421$	−2.08243	+	3.60688i	−0.101492	+	0.175789i	0.810808	+	0.585313i	$0.199028\pi$
$422$		0			0
$423$	−0.171569	−	0.297167i	−0.00834199	−	0.0144487i
$424$		0			0
$425$	−2.56215	+	4.43778i	−0.124283	+	0.215264i
$426$		0			0
$427$	45.0114			2.17826
$428$		0			0
$429$	−9.23740			−0.445986
$430$		0			0
$431$	3.27726	+	5.67638i	0.157860	+	0.273422i	0.934097	−	0.357020i	$-0.116207\pi$
$431$	3.27726	+	5.67638i	0.157860	+	0.273422i	−0.776237	+	0.630442i	$0.782874\pi$
$432$		0			0
$433$	−18.2476	−	31.6057i	−0.876922	−	1.51887i	−0.854701	−	0.519121i	$-0.826260\pi$
$433$	−18.2476	−	31.6057i	−0.876922	−	1.51887i	−0.0222211	−	0.999753i	$-0.507074\pi$
$434$		0			0
$435$	3.94885	+	6.83962i	0.189333	+	0.327934i
$436$		0			0
$437$	2.62108	+	4.53984i	0.125383	+	0.217170i
$438$		0			0
$439$	−13.4752	+	23.3397i	−0.643136	+	1.11394i	0.341593	+	0.939848i	$0.389034\pi$
$439$	−13.4752	+	23.3397i	−0.643136	+	1.11394i	−0.984729	+	0.174096i	$0.944300\pi$
$440$		0			0
$441$	−1.58571	+	2.74654i	−0.0755101	+	0.130787i
$442$		0			0
$443$	−15.6017	−	27.0229i	−0.741257	−	1.28390i	−0.951923	−	0.306337i	$-0.900896\pi$
$443$	−15.6017	−	27.0229i	−0.741257	−	1.28390i	0.210666	−	0.977558i	$-0.432437\pi$
$444$		0			0
$445$	−3.23796			−0.153494
$446$		0			0
$447$	−10.2647			−0.485503
$448$		0			0
$449$	−8.51529	−	14.7489i	−0.401861	−	0.696044i	0.592089	−	0.805872i	$-0.298303\pi$
$449$	−8.51529	−	14.7489i	−0.401861	−	0.696044i	−0.993951	+	0.109828i	$0.964970\pi$
$450$		0			0
$451$	−0.573761	+	0.993783i	−0.0270173	+	0.0467954i
$452$		0			0
$453$	−8.87873	+	15.3784i	−0.417159	+	0.722541i
$454$		0			0
$455$	−6.95417			−0.326016
$456$		0			0
$457$	−0.837395	−	1.45041i	−0.0391717	−	0.0678474i	0.845775	−	0.533540i	$-0.179139\pi$
$457$	−0.837395	−	1.45041i	−0.0391717	−	0.0678474i	−0.884947	+	0.465693i	$0.845805\pi$
$458$		0			0
$459$	2.56215	−	4.43778i	0.119591	−	0.207138i
$460$		0			0
$461$	−35.3135			−1.64471			−0.822357	−	0.568972i	$-0.807341\pi$
$461$	−35.3135			−1.64471			−0.822357	+	0.568972i	$0.807341\pi$
$462$		0			0
$463$	8.00755	−	13.8695i	0.372143	−	0.644570i	−0.617752	−	0.786373i	$-0.711957\pi$
$463$	8.00755	−	13.8695i	0.372143	−	0.644570i	0.989895	+	0.141803i	$0.0452899\pi$
$464$		0			0
$465$	−4.23779	−	7.34007i	−0.196523	−	0.340387i
$466$		0			0
$467$	−3.66214	+	6.34301i	−0.169464	+	0.293519i	−0.938231	−	0.346008i	$-0.887537\pi$
$467$	−3.66214	+	6.34301i	−0.169464	+	0.293519i	0.768768	+	0.639528i	$0.220870\pi$
$468$		0			0
$469$	7.58135	−	24.9802i	0.350074	−	1.15348i
$470$		0			0
$471$	−11.3542	+	19.6661i	−0.523176	+	0.906167i
$472$		0			0
$473$	17.6303	+	30.5366i	0.810643	+	1.40408i
$474$		0			0
$475$	−0.325805	+	0.564312i	−0.0149490	+	0.0258924i
$476$		0			0
$477$	7.89678			0.361569
$478$		0			0
$479$	15.2111	−	26.3464i	0.695012	−	1.20380i	−0.275164	−	0.961397i	$-0.588732\pi$
$479$	15.2111	−	26.3464i	0.695012	−	1.20380i	0.970177	−	0.242399i	$-0.0779344\pi$
$480$		0			0
$481$	3.82136	+	6.61878i	0.174239	+	0.301790i
$482$		0			0
$483$	25.6574			1.16745
$484$		0			0
$485$	5.58794	−	9.67860i	0.253735	−	0.439483i
$486$		0			0
$487$	1.39290	−	2.41258i	0.0631185	−	0.109324i	−0.832739	−	0.553665i	$-0.813229\pi$
$487$	1.39290	−	2.41258i	0.0631185	−	0.109324i	0.895858	+	0.444341i	$0.146562\pi$
$488$		0			0
$489$	3.63817	+	6.30150i	0.164524	+	0.284964i
$490$		0			0
$491$	8.67676			0.391577			0.195788	−	0.980646i	$-0.437273\pi$
$491$	8.67676			0.391577			0.195788	+	0.980646i	$0.437273\pi$
$492$		0			0
$493$	40.4703			1.82269
$494$		0			0
$495$	2.11819	+	3.66882i	0.0952057	+	0.164901i
$496$		0			0
$497$	4.62813	−	8.01615i	0.207600	−	0.359574i
$498$		0			0
$499$	2.35666	−	4.08185i	0.105499	−	0.182729i	−0.808443	−	0.588574i	$-0.799690\pi$
$499$	2.35666	−	4.08185i	0.105499	−	0.182729i	0.913942	+	0.405845i	$0.133023\pi$
$500$		0			0
$501$	−8.49804	−	14.7190i	−0.379664	−	0.657598i
$502$		0			0
$503$	7.84252	+	13.5836i	0.349681	+	0.605665i	0.986193	−	0.165602i	$-0.0529568\pi$
$503$	7.84252	+	13.5836i	0.349681	+	0.605665i	−0.636512	+	0.771267i	$0.719623\pi$
$504$		0			0
$505$	−7.11803	−	12.3288i	−0.316748	−	0.548624i
$506$		0			0
$507$	−4.12273	−	7.14078i	−0.183097	−	0.317133i
$508$		0			0
$509$	−1.49842			−0.0664163			−0.0332082	−	0.999448i	$-0.510572\pi$
$509$	−1.49842			−0.0664163			−0.0332082	+	0.999448i	$0.510572\pi$
$510$		0			0
$511$	−20.3169			−0.898767
$512$		0			0
$513$	0.325805	−	0.564312i	0.0143847	−	0.0249150i
$514$		0			0
$515$	5.69947	+	9.87177i	0.251149	+	0.435002i
$516$		0			0
$517$	0.726834	−	1.25891i	0.0319661	−	0.0553670i
$518$		0			0
$519$	−4.74878	+	8.22513i	−0.208448	+	0.361043i
$520$		0			0
$521$	17.8113			0.780328			0.390164	−	0.920745i	$-0.372418\pi$
$521$	17.8113			0.780328			0.390164	+	0.920745i	$0.372418\pi$
$522$		0			0
$523$	0.689611	−	1.19444i	0.0301546	−	0.0522293i	−0.850554	−	0.525887i	$-0.823733\pi$
$523$	0.689611	−	1.19444i	0.0301546	−	0.0522293i	0.880709	+	0.473658i	$0.157067\pi$
$524$		0			0
$525$	1.59463	+	2.76199i	0.0695955	+	0.120543i
$526$		0			0
$527$	−43.4315			−1.89190
$528$		0			0
$529$	−20.8603	−	36.1312i	−0.906972	−	1.57092i
$530$		0			0
$531$	−4.39987			−0.190938
$532$		0			0
$533$	0.590635			0.0255832
$534$		0			0
$535$	8.78848			0.379959
$536$		0			0
$537$	−2.79245			−0.120503
$538$		0			0
$539$	−13.4354			−0.578703
$540$		0			0
$541$	34.7368			1.49345			0.746726	−	0.665132i	$-0.231625\pi$
$541$	34.7368			1.49345			0.746726	+	0.665132i	$0.231625\pi$
$542$		0			0
$543$	−0.424877	−	0.735909i	−0.0182332	−	0.0315809i
$544$		0			0
$545$	2.52859			0.108313
$546$		0			0
$547$	12.7913	+	22.1552i	0.546917	+	0.947289i	0.998484	+	0.0550511i	$0.0175322\pi$
$547$	12.7913	+	22.1552i	0.546917	+	0.947289i	−0.451566	+	0.892238i	$0.649134\pi$
$548$		0			0
$549$	−7.05670	+	12.2226i	−0.301173	+	0.521647i
$550$		0			0
$551$	5.14623			0.219237
$552$		0			0
$553$	1.90899	−	3.30646i	0.0811784	−	0.140605i
$554$		0			0
$555$	1.75252	−	3.03546i	0.0743904	−	0.128848i
$556$		0			0
$557$	−5.78484	−	10.0196i	−0.245112	−	0.424546i	0.717051	−	0.697020i	$-0.245491\pi$
$557$	−5.78484	−	10.0196i	−0.245112	−	0.424546i	−0.962163	+	0.272474i	$0.912158\pi$
$558$		0			0
$559$	9.07442	−	15.7173i	0.383807	−	0.664773i
$560$		0			0
$561$	21.7085			0.916536
$562$		0			0
$563$	−22.9163			−0.965809			−0.482904	−	0.875673i	$-0.660418\pi$
$563$	−22.9163			−0.965809			−0.482904	+	0.875673i	$0.660418\pi$
$564$		0			0
$565$	−8.82932	−	15.2928i	−0.371452	−	0.643374i
$566$		0			0
$567$	−1.59463	−	2.76199i	−0.0669683	−	0.115993i
$568$		0			0
$569$	−6.47148	−	11.2089i	−0.271299	−	0.469903i	0.697896	−	0.716199i	$-0.254120\pi$
$569$	−6.47148	−	11.2089i	−0.271299	−	0.469903i	−0.969195	+	0.246296i	$0.920786\pi$
$570$		0			0
$571$	−6.16229	−	10.6734i	−0.257884	−	0.446668i	0.707791	−	0.706422i	$-0.249692\pi$
$571$	−6.16229	−	10.6734i	−0.257884	−	0.446668i	−0.965675	+	0.259754i	$0.916359\pi$
$572$		0			0
$573$	−7.32457	+	12.6865i	−0.305988	+	0.529987i
$574$		0			0
$575$	4.02246	−	6.96710i	0.167748	−	0.290548i
$576$		0			0
$577$	−2.13548	−	3.69876i	−0.0889012	−	0.153981i	0.818146	−	0.575011i	$-0.195002\pi$
$577$	−2.13548	−	3.69876i	−0.0889012	−	0.153981i	−0.907047	+	0.421030i	$0.861669\pi$
$578$		0			0
$579$	−17.5891			−0.730980
$580$		0			0
$581$	−6.14864			−0.255089
$582$		0			0
$583$	16.7269	+	28.9719i	0.692758	+	1.19989i
$584$		0			0
$585$	1.09024	−	1.88836i	0.0450761	−	0.0780741i
$586$		0			0
$587$	7.02283	−	12.1639i	0.289863	−	0.502058i	−0.683914	−	0.729563i	$-0.739723\pi$
$587$	7.02283	−	12.1639i	0.289863	−	0.502058i	0.973777	+	0.227505i	$0.0730568\pi$
$588$		0			0
$589$	−5.52278			−0.227562
$590$		0			0
$591$	−11.2607	−	19.5041i	−0.463204	−	0.802293i
$592$		0			0
$593$	−19.6100	+	33.9655i	−0.805286	+	1.39480i	0.110813	+	0.993841i	$0.464655\pi$
$593$	−19.6100	+	33.9655i	−0.805286	+	1.39480i	−0.916098	+	0.400954i	$0.868679\pi$
$594$		0			0
$595$	16.3428			0.669989
$596$		0			0
$597$	0.782789	−	1.35583i	0.0320374	−	0.0554904i
$598$		0			0
$599$	22.7801	+	39.4562i	0.930768	+	1.61214i	0.782012	+	0.623263i	$0.214193\pi$
$599$	22.7801	+	39.4562i	0.930768	+	1.61214i	0.148756	+	0.988874i	$0.452473\pi$
$600$		0			0
$601$	0.697116	−	1.20744i	0.0284360	−	0.0492525i	−0.851457	−	0.524424i	$-0.824281\pi$
$601$	0.697116	−	1.20744i	0.0284360	−	0.0492525i	0.879893	+	0.475172i	$0.157614\pi$
$602$		0			0
$603$	5.59464	+	5.97495i	0.227831	+	0.243319i
$604$		0			0
$605$	−3.47349	+	6.01627i	−0.141218	+	0.244596i
$606$		0			0
$607$	−15.9376	−	27.6047i	−0.646886	−	1.12044i	−0.983862	−	0.178926i	$-0.942738\pi$
$607$	−15.9376	−	27.6047i	−0.646886	−	1.12044i	0.336977	−	0.941513i	$-0.390596\pi$
$608$		0			0
$609$	12.5940	−	21.8134i	0.510333	−	0.883922i
$610$		0			0
$611$	−0.748210			−0.0302693
$612$		0			0
$613$	16.1889	−	28.0400i	0.653863	−	1.13252i	−0.328315	−	0.944568i	$-0.606481\pi$
$613$	16.1889	−	28.0400i	0.653863	−	1.13252i	0.982178	−	0.187955i	$-0.0601861\pi$
$614$		0			0
$615$	−0.135436	−	0.234583i	−0.00546132	−	0.00945928i
$616$		0			0
$617$	−46.7023			−1.88016			−0.940081	−	0.340951i	$-0.889251\pi$
$617$	−46.7023			−1.88016			−0.940081	+	0.340951i	$0.889251\pi$
$618$		0			0
$619$	−2.04658	+	3.54477i	−0.0822588	+	0.142476i	−0.904220	−	0.427067i	$-0.859547\pi$
$619$	−2.04658	+	3.54477i	−0.0822588	+	0.142476i	0.821961	+	0.569544i	$0.192880\pi$
$620$		0			0
$621$	−4.02246	+	6.96710i	−0.161416	+	0.279580i
$622$		0			0
$623$	5.16336	+	8.94321i	0.206866	+	0.358302i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	2.76048			0.110243
$628$		0			0
$629$	−8.98045	−	15.5546i	−0.358074	−	0.620203i
$630$		0			0
$631$	−8.16830	+	14.1479i	−0.325175	+	0.563219i	−0.981548	−	0.191217i	$-0.938756\pi$
$631$	−8.16830	+	14.1479i	−0.325175	+	0.563219i	0.656373	+	0.754437i	$0.272090\pi$
$632$		0			0
$633$	−10.6933	+	18.5213i	−0.425020	+	0.736156i
$634$		0			0
$635$	−5.93915	−	10.2869i	−0.235688	−	0.408224i
$636$		0			0
$637$	3.45763	+	5.98879i	0.136996	+	0.237285i
$638$		0			0
$639$	1.45116	+	2.51348i	0.0574069	+	0.0994316i
$640$		0			0
$641$	−19.3268	−	33.4750i	−0.763363	−	1.32218i	−0.941108	−	0.338106i	$-0.890214\pi$
$641$	−19.3268	−	33.4750i	−0.763363	−	1.32218i	0.177745	−	0.984077i	$-0.443120\pi$
$642$		0			0
$643$	−4.00953			−0.158120			−0.0790602	−	0.996870i	$-0.525192\pi$
$643$	−4.00953			−0.158120			−0.0790602	+	0.996870i	$0.525192\pi$
$644$		0			0
$645$	−8.32328			−0.327729
$646$		0			0
$647$	19.7253	−	34.1652i	0.775482	−	1.34317i	−0.159041	−	0.987272i	$-0.550840\pi$
$647$	19.7253	−	34.1652i	0.775482	−	1.34317i	0.934523	−	0.355902i	$-0.115826\pi$
$648$		0			0
$649$	−9.31977	−	16.1423i	−0.365833	−	0.633641i
$650$		0			0
$651$	−13.5154	+	23.4094i	−0.529712	+	0.917488i
$652$		0			0
$653$	−0.542419	+	0.939496i	−0.0212265	+	0.0367653i	−0.876444	−	0.481505i	$-0.840090\pi$
$653$	−0.542419	+	0.939496i	−0.0212265	+	0.0367653i	0.855217	+	0.518270i	$0.173424\pi$
$654$		0			0
$655$	1.93949			0.0757823
$656$		0			0
$657$	3.18520	−	5.51693i	0.124267	−	0.215236i
$658$		0			0
$659$	−8.14677	−	14.1106i	−0.317353	−	0.549672i	0.662582	−	0.748990i	$-0.269461\pi$
$659$	−8.14677	−	14.1106i	−0.317353	−	0.549672i	−0.979935	+	0.199318i	$0.936127\pi$
$660$		0			0
$661$	−24.1025			−0.937479			−0.468740	−	0.883336i	$-0.655292\pi$
$661$	−24.1025			−0.937479			−0.468740	+	0.883336i	$0.655292\pi$
$662$		0			0
$663$	−5.58675	−	9.67653i	−0.216971	−	0.375805i
$664$		0			0
$665$	2.07816			0.0805876
$666$		0			0
$667$	−63.5364			−2.46014
$668$		0			0
$669$	−14.6790			−0.567523
$670$		0			0
$671$	−59.7899			−2.30816
$672$		0			0
$673$	−14.9779			−0.577356			−0.288678	−	0.957426i	$-0.593216\pi$
$673$	−14.9779			−0.577356			−0.288678	+	0.957426i	$0.593216\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	16.9425	+	29.3452i	0.651152	+	1.12783i	0.982844	+	0.184441i	$0.0590475\pi$
$677$	16.9425	+	29.3452i	0.651152	+	1.12783i	−0.331691	+	0.943388i	$0.607619\pi$
$678$		0			0
$679$	−35.6429			−1.36785
$680$		0			0
$681$	−11.3434	−	19.6473i	−0.434680	−	0.752888i
$682$		0			0
$683$	−14.5645	+	25.2264i	−0.557294	+	0.965262i	0.440427	+	0.897789i	$0.354827\pi$
$683$	−14.5645	+	25.2264i	−0.557294	+	0.965262i	−0.997721	+	0.0674735i	$0.978506\pi$
$684$		0			0
$685$	−15.7104			−0.600264
$686$		0			0
$687$	0.410433	−	0.710890i	0.0156590	−	0.0271221i
$688$		0			0
$689$	8.60942	−	14.9120i	0.327993	−	0.568100i
$690$		0			0
$691$	−4.89874	−	8.48487i	−0.186357	−	0.322780i	0.757676	−	0.652631i	$-0.226335\pi$
$691$	−4.89874	−	8.48487i	−0.186357	−	0.322780i	−0.944033	+	0.329851i	$0.893001\pi$
$692$		0			0
$693$	6.75549	−	11.7008i	0.256620	−	0.444478i
$694$		0			0
$695$	15.1789			0.575770
$696$		0			0
$697$	−1.38803			−0.0525755
$698$		0			0
$699$	10.2133	+	17.6899i	0.386301	+	0.669093i
$700$		0			0
$701$	9.65402	+	16.7213i	0.364627	+	0.631553i	0.988716	−	0.149800i	$-0.0478630\pi$
$701$	9.65402	+	16.7213i	0.364627	+	0.631553i	−0.624089	+	0.781353i	$0.714530\pi$
$702$		0			0
$703$	−1.14196	−	1.97794i	−0.0430699	−	0.0745993i
$704$		0			0
$705$	0.171569	+	0.297167i	0.00646167	+	0.0111919i
$706$		0			0
$707$	−22.7013	+	39.3198i	−0.853770	+	1.47877i
$708$		0			0
$709$	−13.2319	+	22.9182i	−0.496933	+	0.860712i	−0.999994	−	0.00353836i	$-0.998874\pi$
$709$	−13.2319	+	22.9182i	−0.496933	+	0.860712i	0.503061	+	0.864251i	$0.332207\pi$
$710$		0			0
$711$	0.598566	+	1.03675i	0.0224480	+	0.0388811i
$712$		0			0
$713$	68.1853			2.55356
$714$		0			0
$715$	9.23740			0.345459
$716$		0			0
$717$	−13.4875	−	23.3611i	−0.503701	−	0.872436i
$718$		0			0
$719$	−6.78309	+	11.7487i	−0.252967	+	0.438151i	−0.964341	−	0.264662i	$-0.914740\pi$
$719$	−6.78309	+	11.7487i	−0.252967	+	0.438151i	0.711375	+	0.702813i	$0.248073\pi$
$720$		0			0
$721$	18.1771	−	31.4837i	0.676952	−	1.17251i
$722$		0			0
$723$	4.12596			0.153446
$724$		0			0
$725$	−3.94885	−	6.83962i	−0.146657	−	0.254017i
$726$		0			0
$727$	−16.1213	+	27.9229i	−0.597906	+	1.03560i	0.395224	+	0.918585i	$0.370667\pi$
$727$	−16.1213	+	27.9229i	−0.597906	+	1.03560i	−0.993130	+	0.117018i	$0.962666\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−21.3255	+	36.9369i	−0.788753	+	1.36616i
$732$		0			0
$733$	12.6254	+	21.8679i	0.466330	+	0.807708i	0.999260	−	0.0384513i	$-0.0122424\pi$
$733$	12.6254	+	21.8679i	0.466330	+	0.807708i	−0.532930	+	0.846159i	$0.678909\pi$
$734$		0			0
$735$	1.58571	−	2.74654i	0.0584899	−	0.101307i
$736$		0			0
$737$	−10.0705	+	33.1818i	−0.370952	+	1.22227i
$738$		0			0
$739$	−26.7641	+	46.3568i	−0.984534	+	1.70526i	−0.340544	+	0.940229i	$0.610611\pi$
$739$	−26.7641	+	46.3568i	−0.984534	+	1.70526i	−0.643990	+	0.765034i	$0.722722\pi$
$740$		0			0
$741$	−0.710415	−	1.23048i	−0.0260978	−	0.0452027i
$742$		0			0
$743$	−7.08937	+	12.2792i	−0.260084	+	0.450478i	−0.966264	−	0.257554i	$-0.917084\pi$
$743$	−7.08937	+	12.2792i	−0.260084	+	0.450478i	0.706180	+	0.708032i	$0.250417\pi$
$744$		0			0
$745$	10.2647			0.376069
$746$		0			0
$747$	0.963958	−	1.66962i	0.0352694	−	0.0610884i
$748$		0			0
$749$	−14.0144	−	24.2737i	−0.512075	−	0.886941i
$750$		0			0
$751$	−28.8789			−1.05381			−0.526904	−	0.849925i	$-0.676647\pi$
$751$	−28.8789			−1.05381			−0.526904	+	0.849925i	$0.676647\pi$
$752$		0			0
$753$	−2.26482	+	3.92278i	−0.0825345	+	0.142954i
$754$		0			0
$755$	8.87873	−	15.3784i	0.323130	−	0.559678i
$756$		0			0
$757$	20.5487	+	35.5915i	0.746857	+	1.29359i	0.949322	+	0.314304i	$0.101771\pi$
$757$	20.5487	+	35.5915i	0.746857	+	1.29359i	−0.202466	+	0.979289i	$0.564895\pi$
$758$		0			0
$759$	−34.0814			−1.23708
$760$		0			0
$761$	19.8369			0.719087			0.359544	−	0.933128i	$-0.382932\pi$
$761$	19.8369			0.719087			0.359544	+	0.933128i	$0.382932\pi$
$762$		0			0
$763$	−4.03218	−	6.98394i	−0.145975	−	0.252836i
$764$		0			0
$765$	−2.56215	+	4.43778i	−0.0926348	+	0.160448i
$766$		0			0
$767$	−4.79693	+	8.30853i	−0.173207	+	0.300004i
$768$		0			0
$769$	10.9558	+	18.9760i	0.395077	+	0.684293i	0.993111	−	0.117178i	$-0.0373847\pi$
$769$	10.9558	+	18.9760i	0.395077	+	0.684293i	−0.598034	+	0.801470i	$0.704051\pi$
$770$		0			0
$771$	1.27099	+	2.20142i	0.0457736	+	0.0792821i
$772$		0			0
$773$	−23.4893	−	40.6847i	−0.844852	−	1.46333i	−0.885749	−	0.464164i	$-0.846355\pi$
$773$	−23.4893	−	40.6847i	−0.844852	−	1.46333i	0.0408971	−	0.999163i	$-0.486978\pi$
$774$		0			0
$775$	4.23779	+	7.34007i	0.152226	+	0.263663i
$776$		0			0
$777$	−11.1785			−0.401027
$778$		0			0
$779$	−0.176504			−0.00632389
$780$		0			0
$781$	−6.14766	+	10.6481i	−0.219981	+	0.381018i
$782$		0			0
$783$	3.94885	+	6.83962i	0.141121	+	0.244428i
$784$		0			0
$785$	11.3542	−	19.6661i	0.405250	−	0.701914i
$786$		0			0
$787$	6.55363	−	11.3512i	0.233612	−	0.404627i	−0.725257	−	0.688479i	$-0.758279\pi$
$787$	6.55363	−	11.3512i	0.233612	−	0.404627i	0.958868	+	0.283851i	$0.0916123\pi$
$788$		0			0
$789$	−22.9781			−0.818043
$790$		0			0
$791$	−28.1591	+	48.7729i	−1.00122	+	1.73417i
$792$		0			0
$793$	15.3871	+	26.6512i	0.546411	+	0.946411i
$794$		0			0
$795$	−7.89678			−0.280070
$796$		0			0
$797$	−16.5500	−	28.6655i	−0.586232	−	1.01538i	−0.994721	−	0.102620i	$-0.967277\pi$
$797$	−16.5500	−	28.6655i	−0.586232	−	1.01538i	0.408489	−	0.912763i	$-0.366056\pi$
$798$		0			0
$799$	1.75835			0.0622058
$800$		0			0
$801$	−3.23796			−0.114408
$802$		0			0
$803$	26.9875			0.952368
$804$		0			0
$805$	−25.6574			−0.904304
$806$		0			0
$807$	−12.7893			−0.450205
$808$		0			0
$809$	1.26662			0.0445319			0.0222659	−	0.999752i	$-0.492912\pi$
$809$	1.26662			0.0445319			0.0222659	+	0.999752i	$0.492912\pi$
$810$		0			0
$811$	21.1554	+	36.6423i	0.742868	+	1.28668i	0.951184	+	0.308623i	$0.0998682\pi$
$811$	21.1554	+	36.6423i	0.742868	+	1.28668i	−0.208317	+	0.978061i	$0.566798\pi$
$812$		0			0
$813$	3.91554			0.137324
$814$		0			0
$815$	−3.63817	−	6.30150i	−0.127440	−	0.220732i
$816$		0			0
$817$	−2.71177	+	4.69692i	−0.0948728	+	0.164325i
$818$		0			0
$819$	−6.95417			−0.242998
$820$		0			0
$821$	−24.1089	+	41.7579i	−0.841408	+	1.45736i	0.0472972	+	0.998881i	$0.484939\pi$
$821$	−24.1089	+	41.7579i	−0.841408	+	1.45736i	−0.888705	+	0.458480i	$0.848394\pi$
$822$		0			0
$823$	−2.26099	+	3.91615i	−0.0788132	+	0.136508i	−0.902738	−	0.430190i	$-0.858446\pi$
$823$	−2.26099	+	3.91615i	−0.0788132	+	0.136508i	0.823925	+	0.566699i	$0.191780\pi$
$824$		0			0
$825$	−2.11819	−	3.66882i	−0.0737461	−	0.127732i
$826$		0			0
$827$	−13.5058	+	23.3928i	−0.469644	+	0.813448i	−0.999398	−	0.0347040i	$-0.988951\pi$
$827$	−13.5058	+	23.3928i	−0.469644	+	0.813448i	0.529753	+	0.848152i	$0.322284\pi$
$828$		0			0
$829$	10.6720			0.370655			0.185327	−	0.982677i	$-0.440665\pi$
$829$	10.6720			0.370655			0.185327	+	0.982677i	$0.440665\pi$
$830$		0			0
$831$	−21.4499			−0.744090
$832$		0			0
$833$	−8.12568	−	14.0741i	−0.281538	−	0.487638i
$834$		0			0
$835$	8.49804	+	14.7190i	0.294087	+	0.509373i
$836$		0			0
$837$	−4.23779	−	7.34007i	−0.146479	−	0.253710i
$838$		0			0
$839$	12.2783	+	21.2666i	0.423893	+	0.734205i	0.996316	−	0.0857537i	$-0.0273298\pi$
$839$	12.2783	+	21.2666i	0.423893	+	0.734205i	−0.572423	+	0.819958i	$0.693996\pi$
$840$		0			0
$841$	−16.6869	+	28.9025i	−0.575410	+	0.996640i
$842$		0			0
$843$	3.76695	−	6.52455i	0.129741	−	0.224717i
$844$		0			0
$845$	4.12273	+	7.14078i	0.141826	+	0.245650i
$846$		0			0
$847$	22.1558			0.761282
$848$		0			0
$849$	−2.37594			−0.0815421
$850$		0			0
$851$	14.0989	+	24.4200i	0.483304	+	0.837107i
$852$		0			0
$853$	−4.10124	+	7.10356i	−0.140424	+	0.243221i	−0.927656	−	0.373435i	$-0.878180\pi$
$853$	−4.10124	+	7.10356i	−0.140424	+	0.243221i	0.787232	+	0.616656i	$0.211513\pi$
$854$		0			0
$855$	−0.325805	+	0.564312i	−0.0111423	+	0.0192990i
$856$		0			0
$857$	6.95877			0.237707			0.118854	−	0.992912i	$-0.462078\pi$
$857$	6.95877			0.237707			0.118854	+	0.992912i	$0.462078\pi$
$858$		0			0
$859$	−2.47836	−	4.29264i	−0.0845605	−	0.146463i	0.820643	−	0.571441i	$-0.193615\pi$
$859$	−2.47836	−	4.29264i	−0.0845605	−	0.146463i	−0.905204	+	0.424978i	$0.860282\pi$
$860$		0			0
$861$	−0.431943	+	0.748146i	−0.0147206	+	0.0254968i
$862$		0			0
$863$	−26.2711			−0.894278			−0.447139	−	0.894465i	$-0.647557\pi$
$863$	−26.2711			−0.894278			−0.447139	+	0.894465i	$0.647557\pi$
$864$		0			0
$865$	4.74878	−	8.22513i	0.161463	−	0.279663i
$866$		0			0
$867$	4.62925	+	8.01810i	0.157218	+	0.272309i
$868$		0			0
$869$	−2.53576	+	4.39206i	−0.0860198	+	0.148991i
$870$		0			0
$871$	17.3824	−	4.05052i	0.588980	−	0.137247i
$872$		0			0
$873$	5.58794	−	9.67860i	0.189123	−	0.327571i
$874$		0			0
$875$	−1.59463	−	2.76199i	−0.0539085	−	0.0933722i
$876$		0			0
$877$	14.2783	−	24.7307i	0.482143	−	0.835097i	−0.517647	−	0.855594i	$-0.673192\pi$
$877$	14.2783	−	24.7307i	0.482143	−	0.835097i	0.999790	+	0.0204979i	$0.00652516\pi$
$878$		0			0
$879$	0.957295			0.0322888
$880$		0			0
$881$	−25.0945	+	43.4649i	−0.845454	+	1.46437i	0.0397724	+	0.999209i	$0.487337\pi$
$881$	−25.0945	+	43.4649i	−0.845454	+	1.46437i	−0.885226	+	0.465160i	$0.845997\pi$
$882$		0			0
$883$	−22.6670	−	39.2604i	−0.762805	−	1.32122i	−0.941399	−	0.337295i	$-0.890488\pi$
$883$	−22.6670	−	39.2604i	−0.762805	−	1.32122i	0.178594	−	0.983923i	$-0.442845\pi$
$884$		0			0
$885$	4.39987			0.147900
$886$		0			0
$887$	−24.2008	+	41.9170i	−0.812583	+	1.40743i	0.0984678	+	0.995140i	$0.468606\pi$
$887$	−24.2008	+	41.9170i	−0.812583	+	1.40743i	−0.911051	+	0.412294i	$0.864727\pi$
$888$		0			0
$889$	−18.9415	+	32.8077i	−0.635279	+	1.10034i
$890$		0			0
$891$	2.11819	+	3.66882i	0.0709622	+	0.122910i
$892$		0			0
$893$	0.223593			0.00748225
$894$		0			0
$895$	2.79245			0.0933412
$896$		0			0
$897$	8.77093	+	15.1917i	0.292853	+	0.507236i
$898$		0			0
$899$	33.4688	−	57.9697i	1.11625	−	1.93340i
$900$		0			0
$901$	−20.2327	+	35.0441i	−0.674050	+	1.16749i
$902$		0			0
$903$	13.2726	+	22.9888i	0.441684	+	0.765019i
$904$		0			0
$905$	0.424877	+	0.735909i	0.0141234	+	0.0244625i
$906$		0			0
$907$	−3.03951	−	5.26458i	−0.100925	−	0.174807i	0.811141	−	0.584851i	$-0.198847\pi$
$907$	−3.03951	−	5.26458i	−0.100925	−	0.174807i	−0.912066	+	0.410043i	$0.865514\pi$
$908$		0			0
$909$	−7.11803	−	12.3288i	−0.236090	−	0.408920i
$910$		0			0
$911$	23.6693			0.784198			0.392099	−	0.919923i	$-0.371749\pi$
$911$	23.6693			0.784198			0.392099	+	0.919923i	$0.371749\pi$
$912$		0			0
$913$	8.16740			0.270302
$914$		0			0
$915$	7.05670	−	12.2226i	0.233287	−	0.404066i
$916$		0			0
$917$	−3.09278	−	5.35685i	−0.102133	−	0.176899i
$918$		0			0
$919$	−17.0526	+	29.5360i	−0.562514	+	0.974303i	0.434762	+	0.900545i	$0.356832\pi$
$919$	−17.0526	+	29.5360i	−0.562514	+	0.974303i	−0.997276	+	0.0737576i	$0.976501\pi$
$920$		0			0
$921$	13.7000	−	23.7291i	0.451430	−	0.781900i
$922$		0			0
$923$	6.32847			0.208304
$924$		0			0
$925$	−1.75252	+	3.03546i	−0.0576226	+	0.0998052i
$926$		0			0
$927$	5.69947	+	9.87177i	0.187195	+	0.324231i
$928$		0			0
$929$	31.3625			1.02897			0.514485	−	0.857499i	$-0.327983\pi$
$929$	31.3625			1.02897			0.514485	+	0.857499i	$0.327983\pi$
$930$		0			0
$931$	−1.03327	−	1.78967i	−0.0338640	−	0.0586541i
$932$		0			0
$933$	7.11121			0.232811
$934$		0			0
$935$	−21.7085			−0.709945
$936$		0			0
$937$	22.0357			0.719873			0.359937	−	0.932977i	$-0.382798\pi$
$937$	22.0357			0.719873			0.359937	+	0.932977i	$0.382798\pi$
$938$		0			0
$939$	23.4103			0.763968
$940$		0			0
$941$	−40.4555			−1.31881			−0.659407	−	0.751787i	$-0.729192\pi$
$941$	−40.4555			−1.31881			−0.659407	+	0.751787i	$0.729192\pi$
$942$		0			0
$943$	2.17915			0.0709628
$944$		0			0
$945$	1.59463	+	2.76199i	0.0518734	+	0.0898474i
$946$		0			0
$947$	20.1940			0.656217			0.328108	−	0.944640i	$-0.393589\pi$
$947$	20.1940			0.656217			0.328108	+	0.944640i	$0.393589\pi$
$948$		0			0
$949$	−6.94530	−	12.0296i	−0.225454	−	0.390498i
$950$		0			0
$951$	−0.400887	+	0.694356i	−0.0129996	+	0.0225160i
$952$		0			0
$953$	−27.8758			−0.902987			−0.451494	−	0.892274i	$-0.649109\pi$
$953$	−27.8758			−0.902987			−0.451494	+	0.892274i	$0.649109\pi$
$954$		0			0
$955$	7.32457	−	12.6865i	0.237018	−	0.410526i
$956$		0			0
$957$	−16.7289	+	28.9753i	−0.540768	+	0.936637i
$958$		0			0
$959$	25.0523	+	43.3919i	0.808982	+	1.40120i
$960$		0			0
$961$	−20.4177	+	35.3645i	−0.658636	+	1.14079i
$962$		0			0
$963$	8.78848			0.283205
$964$		0			0
$965$	17.5891			0.566214
$966$		0			0
$967$	16.6919	+	28.9112i	0.536775	+	0.929721i	0.999075	+	0.0429979i	$0.0136909\pi$
$967$	16.6919	+	28.9112i	0.536775	+	0.929721i	−0.462300	+	0.886723i	$0.652976\pi$
$968$		0			0
$969$	1.66953	+	2.89170i	0.0536329	+	0.0928949i
$970$		0			0
$971$	−13.5874	−	23.5341i	−0.436041	−	0.755245i	0.561339	−	0.827586i	$-0.310286\pi$
$971$	−13.5874	−	23.5341i	−0.436041	−	0.755245i	−0.997380	+	0.0723410i	$0.976953\pi$
$972$		0			0
$973$	−24.2048	−	41.9240i	−0.775971	−	1.34402i
$974$		0			0
$975$	−1.09024	+	1.88836i	−0.0349158	+	0.0604759i
$976$		0			0
$977$	−29.5283	+	51.1446i	−0.944695	+	1.63626i	−0.188335	+	0.982105i	$0.560309\pi$
$977$	−29.5283	+	51.1446i	−0.944695	+	1.63626i	−0.756360	+	0.654155i	$0.773024\pi$
$978$		0			0
$979$	−6.85863	−	11.8795i	−0.219203	−	0.379670i
$980$		0			0
$981$	2.52859			0.0807317
$982$		0			0
$983$	−27.7979			−0.886615			−0.443308	−	0.896370i	$-0.646195\pi$
$983$	−27.7979			−0.886615			−0.443308	+	0.896370i	$0.646195\pi$
$984$		0			0
$985$	11.2607	+	19.5041i	0.358796	+	0.621453i
$986$		0			0
$987$	0.547180	−	0.947744i	0.0174169	−	0.0301670i
$988$		0			0
$989$	33.4801	−	57.9892i	1.06460	−	1.84395i
$990$		0			0
$991$	−8.19672			−0.260377			−0.130189	−	0.991489i	$-0.541558\pi$
$991$	−8.19672			−0.260377			−0.130189	+	0.991489i	$0.541558\pi$
$992$		0			0
$993$	6.38166	+	11.0534i	0.202516	+	0.350768i
$994$		0			0
$995$	−0.782789	+	1.35583i	−0.0248161	+	0.0429827i
$996$		0			0
$997$	9.27572			0.293765			0.146883	−	0.989154i	$-0.453076\pi$
$997$	9.27572			0.293765			0.146883	+	0.989154i	$0.453076\pi$
$998$		0			0
$999$	1.75252	−	3.03546i	0.0554473	−	0.0960376i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.k.3781.1	yes	14
67.37	even	3	inner	4020.2.q.k.841.1	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.k.841.1	✓	14	67.37	even	3	inner
4020.2.q.k.3781.1	yes	14	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4020.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(-1.59463 - 2.76199i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(-1.59463 - 2.76199i) q^{7} +1.00000 q^{9} +(2.11819 + 3.66882i) q^{11} +(1.09024 - 1.88836i) q^{13} -1.00000 q^{15} +(-2.56215 + 4.43778i) q^{17} +(-0.325805 + 0.564312i) q^{19} +(1.59463 + 2.76199i) q^{21} +(4.02246 - 6.96710i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-3.94885 - 6.83962i) q^{29} +(4.23779 + 7.34007i) q^{31} +(-2.11819 - 3.66882i) q^{33} +(-1.59463 - 2.76199i) q^{35} +(-1.75252 + 3.03546i) q^{37} +(-1.09024 + 1.88836i) q^{39} +(0.135436 + 0.234583i) q^{41} +8.32328 q^{43} +1.00000 q^{45} +(-0.171569 - 0.297167i) q^{47} +(-1.58571 + 2.74654i) q^{49} +(2.56215 - 4.43778i) q^{51} +7.89678 q^{53} +(2.11819 + 3.66882i) q^{55} +(0.325805 - 0.564312i) q^{57} -4.39987 q^{59} +(-7.05670 + 12.2226i) q^{61} +(-1.59463 - 2.76199i) q^{63} +(1.09024 - 1.88836i) q^{65} +(5.59464 + 5.97495i) q^{67} +(-4.02246 + 6.96710i) q^{69} +(1.45116 + 2.51348i) q^{71} +(3.18520 - 5.51693i) q^{73} -1.00000 q^{75} +(6.75549 - 11.7008i) q^{77} +(0.598566 + 1.03675i) q^{79} +1.00000 q^{81} +(0.963958 - 1.66962i) q^{83} +(-2.56215 + 4.43778i) q^{85} +(3.94885 + 6.83962i) q^{87} -3.23796 q^{89} -6.95417 q^{91} +(-4.23779 - 7.34007i) q^{93} +(-0.325805 + 0.564312i) q^{95} +(5.58794 - 9.67860i) q^{97} +(2.11819 + 3.66882i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9	\( 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9} + 6 q^{11} + 9 q^{13} - 14 q^{15} - 12 q^{17} + 14 q^{19} - 3 q^{21} + 6 q^{23} + 14 q^{25} - 14 q^{27} - q^{29} + 7 q^{31} - 6 q^{33} + 3 q^{35} - 2 q^{37} - 9 q^{39} - 18 q^{41} - 6 q^{43} + 14 q^{45} + 7 q^{47} + 12 q^{51} - 12 q^{53} + 6 q^{55} - 14 q^{57} - 2 q^{59} + 3 q^{63} + 9 q^{65} + 25 q^{67} - 6 q^{69} + 22 q^{71} - 15 q^{73} - 14 q^{75} + q^{77} + 9 q^{79} + 14 q^{81} - q^{83} - 12 q^{85} + q^{87} - 12 q^{89} - 38 q^{91} - 7 q^{93} + 14 q^{95} + 16 q^{97} + 6 q^{99}+O(q^{100}) \) 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9 + 6 * q^11 + 9 * q^13 - 14 * q^15 - 12 * q^17 + 14 * q^19 - 3 * q^21 + 6 * q^23 + 14 * q^25 - 14 * q^27 - q^29 + 7 * q^31 - 6 * q^33 + 3 * q^35 - 2 * q^37 - 9 * q^39 - 18 * q^41 - 6 * q^43 + 14 * q^45 + 7 * q^47 + 12 * q^51 - 12 * q^53 + 6 * q^55 - 14 * q^57 - 2 * q^59 + 3 * q^63 + 9 * q^65 + 25 * q^67 - 6 * q^69 + 22 * q^71 - 15 * q^73 - 14 * q^75 + q^77 + 9 * q^79 + 14 * q^81 - q^83 - 12 * q^85 + q^87 - 12 * q^89 - 38 * q^91 - 7 * q^93 + 14 * q^95 + 16 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more