LMFDB - Embedded newform 1320.2.bw.i.1081.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1320,2,Mod(361,1320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1320, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 6]))

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

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

chi := DirichletCharacter("1320.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1320.bw (of order $5$, degree $4$, 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:	$10.5402530668$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 26 x^{14} - 64 x^{13} + 486 x^{12} - 10 x^{11} + 6075 x^{10} + 9130 x^{9} + \cdots + 50410000 $ x^16 - 4x^15 + 26x^14 - 64x^13 + 486x^12 - 10x^11 + 6075x^10 + 9130x^9 + 72165x^8 + 32200x^7 + 420125x^6 + 573200x^5 + 3577025x^4 + 5167000x^3 + 17399000x^2 + 15265000*x + 50410000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			1081.1
Root			$-1.22009 + 3.75505i$ of defining polynomial
Character	$\chi$	$=$	1320.1081
Dual form			1320.2.bw.i.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-1.22009 + 3.75505i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-1.22009 + 3.75505i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(-1.26621 + 3.06541i) q^{11} +(-0.0694794 + 0.0504797i) q^{13} +(0.309017 - 0.951057i) q^{15} +(-5.35028 - 3.88721i) q^{17} +(-0.937528 - 2.88542i) q^{19} -3.94829 q^{21} +0.914119 q^{23} +(0.309017 + 0.951057i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(2.60352 - 8.01280i) q^{29} +(-1.57523 + 1.14447i) q^{31} +(-3.30665 - 0.256975i) q^{33} +(3.19423 - 2.32075i) q^{35} +(0.0984518 - 0.303003i) q^{37} +(-0.0694794 - 0.0504797i) q^{39} +(-1.30597 - 4.01936i) q^{41} +1.47924 q^{43} +1.00000 q^{45} +(-1.95470 - 6.01594i) q^{47} +(-6.94865 - 5.04849i) q^{49} +(2.04362 - 6.28963i) q^{51} +(-10.0698 + 7.31613i) q^{53} +(2.82619 - 1.73571i) q^{55} +(2.45448 - 1.78328i) q^{57} +(-4.11974 + 12.6793i) q^{59} +(1.05271 + 0.764838i) q^{61} +(-1.22009 - 3.75505i) q^{63} +0.0858812 q^{65} -5.14530 q^{67} +(0.282478 + 0.869379i) q^{69} +(-12.0724 - 8.77108i) q^{71} +(-4.98189 + 15.3327i) q^{73} +(-0.809017 + 0.587785i) q^{75} +(-9.96586 - 8.49475i) q^{77} +(4.02020 - 2.92085i) q^{79} +(0.309017 - 0.951057i) q^{81} +(1.58678 + 1.15286i) q^{83} +(2.04362 + 6.28963i) q^{85} +8.42516 q^{87} +13.9622 q^{89} +(-0.104783 - 0.322488i) q^{91} +(-1.57523 - 1.14447i) q^{93} +(-0.937528 + 2.88542i) q^{95} +(-10.1988 + 7.40984i) q^{97} +(-0.777415 - 3.22422i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 16 q - 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} - q^{11} + q^{13} - 4 q^{15} - 3 q^{17} - 2 q^{19} - 6 q^{21} + 10 q^{23} - 4 q^{25} - 4 q^{27} - 5 q^{29} + 3 q^{31} - q^{33} - q^{35} - 25 q^{37} + q^{39} - 2 q^{41} - 2 q^{43} + 16 q^{45} + 14 q^{47} - 8 q^{49} + 2 q^{51} - 11 q^{53} + 4 q^{55} + 8 q^{57} - 7 q^{59} - 3 q^{61} + 4 q^{63} + 6 q^{65} + 32 q^{67} - 15 q^{71} - q^{73} - 4 q^{75} + 9 q^{77} - 15 q^{79} - 4 q^{81} - 17 q^{83} + 2 q^{85} + 26 q^{89} + 36 q^{91} + 3 q^{93} - 2 q^{95} - 45 q^{97} - q^{99}+O(q^{100}) $ 16 * q - 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 - q^11 + q^13 - 4 * q^15 - 3 * q^17 - 2 * q^19 - 6 * q^21 + 10 * q^23 - 4 * q^25 - 4 * q^27 - 5 * q^29 + 3 * q^31 - q^33 - q^35 - 25 * q^37 + q^39 - 2 * q^41 - 2 * q^43 + 16 * q^45 + 14 * q^47 - 8 * q^49 + 2 * q^51 - 11 * q^53 + 4 * q^55 + 8 * q^57 - 7 * q^59 - 3 * q^61 + 4 * q^63 + 6 * q^65 + 32 * q^67 - 15 * q^71 - q^73 - 4 * q^75 + 9 * q^77 - 15 * q^79 - 4 * q^81 - 17 * q^83 + 2 * q^85 + 26 * q^89 + 36 * q^91 + 3 * q^93 - 2 * q^95 - 45 * q^97 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times$.

$n$	$661$	$881$	$991$	$1057$	$1201$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$		0			0
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	−1.22009	+	3.75505i	−0.461150	+	1.41927i	0.402610	+	0.915372i	$0.368103\pi$
$7$	−1.22009	+	3.75505i	−0.461150	+	1.41927i	−0.863760	+	0.503903i	$0.831897\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	−1.26621	+	3.06541i	−0.381777	+	0.924255i
$11$	−1.26621	+	3.06541i	−0.381777	+	0.924255i
$12$		0			0
$13$	−0.0694794	+	0.0504797i	−0.0192701	+	0.0140006i	−0.597379	−	0.801959i	$-0.703791\pi$
$13$	−0.0694794	+	0.0504797i	−0.0192701	+	0.0140006i	0.578109	+	0.815960i	$0.303791\pi$
$14$		0			0
$15$	0.309017	−	0.951057i	0.0797878	−	0.245562i
$16$		0			0
$17$	−5.35028	−	3.88721i	−1.29763	−	0.942786i	−0.297704	−	0.954658i	$-0.596221\pi$
$17$	−5.35028	−	3.88721i	−1.29763	−	0.942786i	−0.999930	+	0.0118725i	$0.996221\pi$
$18$		0			0
$19$	−0.937528	−	2.88542i	−0.215084	−	0.661960i	−0.999148	−	0.0412795i	$-0.986857\pi$
$19$	−0.937528	−	2.88542i	−0.215084	−	0.661960i	0.784064	−	0.620680i	$-0.213143\pi$
$20$		0			0
$21$	−3.94829			−0.861588
$22$		0			0
$23$	0.914119			0.190607			0.0953035	−	0.995448i	$-0.469618\pi$
$23$	0.914119			0.190607			0.0953035	+	0.995448i	$0.469618\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$		0			0
$29$	2.60352	−	8.01280i	0.483461	−	1.48794i	−0.350736	−	0.936474i	$-0.614069\pi$
$29$	2.60352	−	8.01280i	0.483461	−	1.48794i	0.834197	−	0.551466i	$-0.185931\pi$
$30$		0			0
$31$	−1.57523	+	1.14447i	−0.282919	+	0.205553i	−0.720190	−	0.693777i	$-0.755945\pi$
$31$	−1.57523	+	1.14447i	−0.282919	+	0.205553i	0.437271	+	0.899330i	$0.355945\pi$
$32$		0			0
$33$	−3.30665	−	0.256975i	−0.575615	−	0.0447336i
$34$		0			0
$35$	3.19423	−	2.32075i	0.539924	−	0.392278i
$36$		0			0
$37$	0.0984518	−	0.303003i	0.0161854	−	0.0498135i	−0.942638	−	0.333818i	$-0.891663\pi$
$37$	0.0984518	−	0.303003i	0.0161854	−	0.0498135i	0.958823	+	0.284004i	$0.0916630\pi$
$38$		0			0
$39$	−0.0694794	−	0.0504797i	−0.0111256	−	0.00808322i
$40$		0			0
$41$	−1.30597	−	4.01936i	−0.203958	−	0.627719i	−0.999755	−	0.0221546i	$-0.992947\pi$
$41$	−1.30597	−	4.01936i	−0.203958	−	0.627719i	0.795796	−	0.605564i	$-0.207053\pi$
$42$		0			0
$43$	1.47924			0.225582			0.112791	−	0.993619i	$-0.464021\pi$
$43$	1.47924			0.225582			0.112791	+	0.993619i	$0.464021\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	−1.95470	−	6.01594i	−0.285122	−	0.877515i	−0.986362	−	0.164590i	$-0.947370\pi$
$47$	−1.95470	−	6.01594i	−0.285122	−	0.877515i	0.701240	−	0.712925i	$-0.252630\pi$
$48$		0			0
$49$	−6.94865	−	5.04849i	−0.992664	−	0.721213i
$50$		0			0
$51$	2.04362	−	6.28963i	0.286165	−	0.880724i
$52$		0			0
$53$	−10.0698	+	7.31613i	−1.38319	+	1.00495i	−0.386619	+	0.922240i	$0.626357\pi$
$53$	−10.0698	+	7.31613i	−1.38319	+	1.00495i	−0.996574	+	0.0827084i	$0.973643\pi$
$54$		0			0
$55$	2.82619	−	1.73571i	0.381083	−	0.234043i
$56$		0			0
$57$	2.45448	−	1.78328i	0.325104	−	0.236202i
$58$		0			0
$59$	−4.11974	+	12.6793i	−0.536345	+	1.65070i	0.204380	+	0.978892i	$0.434482\pi$
$59$	−4.11974	+	12.6793i	−0.536345	+	1.65070i	−0.740725	+	0.671808i	$0.765518\pi$
$60$		0			0
$61$	1.05271	+	0.764838i	0.134786	+	0.0979274i	0.653135	−	0.757241i	$-0.273453\pi$
$61$	1.05271	+	0.764838i	0.134786	+	0.0979274i	−0.518350	+	0.855169i	$0.673453\pi$
$62$		0			0
$63$	−1.22009	−	3.75505i	−0.153717	−	0.473092i
$64$		0			0
$65$	0.0858812			0.0106523
$66$		0			0
$67$	−5.14530			−0.628598			−0.314299	−	0.949324i	$-0.601769\pi$
$67$	−5.14530			−0.628598			−0.314299	+	0.949324i	$0.601769\pi$
$68$		0			0
$69$	0.282478	+	0.869379i	0.0340064	+	0.104661i
$70$		0			0
$71$	−12.0724	−	8.77108i	−1.43273	−	1.04094i	−0.989501	−	0.144525i	$-0.953834\pi$
$71$	−12.0724	−	8.77108i	−1.43273	−	1.04094i	−0.443224	−	0.896411i	$-0.646166\pi$
$72$		0			0
$73$	−4.98189	+	15.3327i	−0.583086	+	1.79455i	0.0237387	+	0.999718i	$0.492443\pi$
$73$	−4.98189	+	15.3327i	−0.583086	+	1.79455i	−0.606825	+	0.794836i	$0.707557\pi$
$74$		0			0
$75$	−0.809017	+	0.587785i	−0.0934172	+	0.0678716i
$76$		0			0
$77$	−9.96586	−	8.49475i	−1.13571	−	0.968066i
$78$		0			0
$79$	4.02020	−	2.92085i	0.452308	−	0.328621i	−0.338198	−	0.941075i	$-0.609817\pi$
$79$	4.02020	−	2.92085i	0.452308	−	0.328621i	0.790506	+	0.612454i	$0.209817\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	1.58678	+	1.15286i	0.174172	+	0.126543i	0.671456	−	0.741045i	$-0.265669\pi$
$83$	1.58678	+	1.15286i	0.174172	+	0.126543i	−0.497284	+	0.867588i	$0.665669\pi$
$84$		0			0
$85$	2.04362	+	6.28963i	0.221662	+	0.682206i
$86$		0			0
$87$	8.42516			0.903272
$88$		0			0
$89$	13.9622			1.47999			0.739994	−	0.672613i	$-0.234828\pi$
$89$	13.9622			1.47999			0.739994	+	0.672613i	$0.234828\pi$
$90$		0			0
$91$	−0.104783	−	0.322488i	−0.0109842	−	0.0338059i
$92$		0			0
$93$	−1.57523	−	1.14447i	−0.163343	−	0.118676i
$94$		0			0
$95$	−0.937528	+	2.88542i	−0.0961884	+	0.296037i
$96$		0			0
$97$	−10.1988	+	7.40984i	−1.03553	+	0.752355i	−0.969408	−	0.245457i	$-0.921062\pi$
$97$	−10.1988	+	7.40984i	−1.03553	+	0.752355i	−0.0661203	+	0.997812i	$0.521062\pi$
$98$		0			0
$99$	−0.777415	−	3.22422i	−0.0781331	−	0.324047i
$100$		0			0
$101$	8.24730	−	5.99202i	0.820637	−	0.596228i	−0.0962576	−	0.995356i	$-0.530687\pi$
$101$	8.24730	−	5.99202i	0.820637	−	0.596228i	0.916895	+	0.399129i	$0.130687\pi$
$102$		0			0
$103$	0.298540	−	0.918811i	0.0294160	−	0.0905331i	−0.935271	−	0.353933i	$-0.884844\pi$
$103$	0.298540	−	0.918811i	0.0294160	−	0.0905331i	0.964687	+	0.263400i	$0.0848440\pi$
$104$		0			0
$105$	3.19423	+	2.32075i	0.311725	+	0.226482i
$106$		0			0
$107$	0.822923	+	2.53270i	0.0795549	+	0.244845i	0.982922	−	0.184024i	$-0.0589123\pi$
$107$	0.822923	+	2.53270i	0.0795549	+	0.244845i	−0.903367	+	0.428869i	$0.858912\pi$
$108$		0			0
$109$	−18.8494			−1.80545			−0.902724	−	0.430219i	$-0.858436\pi$
$109$	−18.8494			−1.80545			−0.902724	+	0.430219i	$0.858436\pi$
$110$		0			0
$111$	0.318597			0.0302399
$112$		0			0
$113$	0.179451	+	0.552295i	0.0168814	+	0.0519555i	0.959142	−	0.282924i	$-0.0913044\pi$
$113$	0.179451	+	0.552295i	0.0168814	+	0.0519555i	−0.942261	+	0.334879i	$0.891304\pi$
$114$		0			0
$115$	−0.739538	−	0.537306i	−0.0689622	−	0.0501040i
$116$		0			0
$117$	0.0265388	−	0.0816779i	0.00245351	−	0.00755112i
$118$		0			0
$119$	21.1245	−	15.3478i	1.93648	−	1.40693i
$120$		0			0
$121$	−7.79342	−	7.76289i	−0.708493	−	0.705718i
$122$		0			0
$123$	3.41907	−	2.48410i	0.308288	−	0.223984i
$124$		0			0
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	8.77869	+	6.37809i	0.778983	+	0.565964i	0.904674	−	0.426105i	$-0.140115\pi$
$127$	8.77869	+	6.37809i	0.778983	+	0.565964i	−0.125691	+	0.992069i	$0.540115\pi$
$128$		0			0
$129$	0.457110	+	1.40684i	0.0402463	+	0.123865i
$130$		0			0
$131$	17.8718			1.56147			0.780735	−	0.624862i	$-0.214845\pi$
$131$	17.8718			1.56147			0.780735	+	0.624862i	$0.214845\pi$
$132$		0			0
$133$	11.9787			1.03869
$134$		0			0
$135$	0.309017	+	0.951057i	0.0265959	+	0.0818539i
$136$		0			0
$137$	−13.7690	−	10.0038i	−1.17637	−	0.854679i	−0.184608	−	0.982812i	$-0.559102\pi$
$137$	−13.7690	−	10.0038i	−1.17637	−	0.854679i	−0.991757	+	0.128133i	$0.959102\pi$
$138$		0			0
$139$	−4.14100	+	12.7447i	−0.351235	+	1.08099i	0.606926	+	0.794758i	$0.292402\pi$
$139$	−4.14100	+	12.7447i	−0.351235	+	1.08099i	−0.958161	+	0.286231i	$0.907598\pi$
$140$		0			0
$141$	5.11746	−	3.71805i	0.430968	−	0.313117i
$142$		0			0
$143$	−0.0667653	−	0.276900i	−0.00558320	−	0.0231556i
$144$		0			0
$145$	−6.81610	+	4.95219i	−0.566046	+	0.411257i
$146$		0			0
$147$	2.65415	−	8.16863i	0.218910	−	0.673737i
$148$		0			0
$149$	−17.3349	−	12.5945i	−1.42013	−	1.03178i	−0.991750	−	0.128185i	$-0.959085\pi$
$149$	−17.3349	−	12.5945i	−1.42013	−	1.03178i	−0.428379	−	0.903599i	$-0.640915\pi$
$150$		0			0
$151$	−3.15888	−	9.72204i	−0.257066	−	0.791168i	−0.993416	−	0.114567i	$-0.963452\pi$
$151$	−3.15888	−	9.72204i	−0.257066	−	0.791168i	0.736349	−	0.676601i	$-0.236548\pi$
$152$		0			0
$153$	6.61331			0.534654
$154$		0			0
$155$	1.94709			0.156394
$156$		0			0
$157$	1.92635	+	5.92871i	0.153740	+	0.473163i	0.998031	−	0.0627221i	$-0.0199782\pi$
$157$	1.92635	+	5.92871i	0.153740	+	0.473163i	−0.844291	+	0.535885i	$0.819978\pi$
$158$		0			0
$159$	−10.0698	−	7.31613i	−0.798587	−	0.580207i
$160$		0			0
$161$	−1.11531	+	3.43256i	−0.0878985	+	0.270524i
$162$		0			0
$163$	−8.33186	+	6.05345i	−0.652602	+	0.474143i	−0.864156	−	0.503223i	$-0.832147\pi$
$163$	−8.33186	+	6.05345i	−0.652602	+	0.474143i	0.211555	+	0.977366i	$0.432147\pi$
$164$		0			0
$165$	2.52409	+	2.15150i	0.196500	+	0.167494i
$166$		0			0
$167$	−0.931144	+	0.676516i	−0.0720541	+	0.0523504i	−0.623229	−	0.782039i	$-0.714180\pi$
$167$	−0.931144	+	0.676516i	−0.0720541	+	0.0523504i	0.551175	+	0.834390i	$0.314180\pi$
$168$		0			0
$169$	−4.01494	+	12.3567i	−0.308842	+	0.950517i
$170$		0			0
$171$	2.45448	+	1.78328i	0.187699	+	0.136371i
$172$		0			0
$173$	2.84537	+	8.75716i	0.216330	+	0.665795i	0.999057	+	0.0434292i	$0.0138283\pi$
$173$	2.84537	+	8.75716i	0.216330	+	0.665795i	−0.782727	+	0.622366i	$0.786172\pi$
$174$		0			0
$175$	−3.94829			−0.298463
$176$		0			0
$177$	−13.3318			−1.00208
$178$		0			0
$179$	6.72521	+	20.6981i	0.502666	+	1.54705i	0.804659	+	0.593737i	$0.202348\pi$
$179$	6.72521	+	20.6981i	0.502666	+	1.54705i	−0.301993	+	0.953310i	$0.597652\pi$
$180$		0			0
$181$	1.14199	+	0.829705i	0.0848835	+	0.0616715i	0.629418	−	0.777067i	$-0.283294\pi$
$181$	1.14199	+	0.829705i	0.0848835	+	0.0616715i	−0.544534	+	0.838739i	$0.683294\pi$
$182$		0			0
$183$	−0.402099	+	1.23753i	−0.0297240	+	0.0914811i
$184$		0			0
$185$	−0.257750	+	0.187266i	−0.0189502	+	0.0137681i
$186$		0			0
$187$	18.6904	−	11.4788i	1.36678	−	0.839410i
$188$		0			0
$189$	3.19423	−	2.32075i	0.232346	−	0.168810i
$190$		0			0
$191$	5.21104	−	16.0379i	0.377058	−	1.16047i	−0.565022	−	0.825076i	$-0.691132\pi$
$191$	5.21104	−	16.0379i	0.377058	−	1.16047i	0.942080	−	0.335389i	$-0.108868\pi$
$192$		0			0
$193$	13.4893	+	9.80055i	0.970981	+	0.705459i	0.955675	−	0.294424i	$-0.0951277\pi$
$193$	13.4893	+	9.80055i	0.970981	+	0.705459i	0.0153061	+	0.999883i	$0.495128\pi$
$194$		0			0
$195$	0.0265388	+	0.0816779i	0.00190048	+	0.00584907i
$196$		0			0
$197$	−0.528049			−0.0376219			−0.0188110	−	0.999823i	$-0.505988\pi$
$197$	−0.528049			−0.0376219			−0.0188110	+	0.999823i	$0.505988\pi$
$198$		0			0
$199$	−5.84632			−0.414435			−0.207217	−	0.978295i	$-0.566441\pi$
$199$	−5.84632			−0.414435			−0.207217	+	0.978295i	$0.566441\pi$
$200$		0			0
$201$	−1.58998	−	4.89347i	−0.112149	−	0.345159i
$202$		0			0
$203$	26.9119	+	19.5527i	1.88885	+	1.37233i
$204$		0			0
$205$	−1.30597	+	4.01936i	−0.0912129	+	0.280724i
$206$		0			0
$207$	−0.739538	+	0.537306i	−0.0514014	+	0.0373453i
$208$		0			0
$209$	10.0321	+	0.779637i	0.693933	+	0.0539286i
$210$		0			0
$211$	−3.61956	+	2.62977i	−0.249181	+	0.181040i	−0.705364	−	0.708846i	$-0.749216\pi$
$211$	−3.61956	+	2.62977i	−0.249181	+	0.181040i	0.456183	+	0.889886i	$0.349216\pi$
$212$		0			0
$213$	4.61123	−	14.1919i	0.315956	−	0.972414i
$214$		0			0
$215$	−1.19673	−	0.869476i	−0.0816164	−	0.0592978i
$216$		0			0
$217$	−2.37562	−	7.31141i	−0.161268	−	0.496331i
$218$		0			0
$219$	−16.1217			−1.08941
$220$		0			0
$221$	0.567959			0.0382051
$222$		0			0
$223$	4.77362	+	14.6917i	0.319666	+	0.983829i	0.973791	+	0.227444i	$0.0730367\pi$
$223$	4.77362	+	14.6917i	0.319666	+	0.983829i	−0.654126	+	0.756386i	$0.726963\pi$
$224$		0			0
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$		0			0
$227$	1.14267	−	3.51677i	0.0758415	−	0.233416i	−0.905948	−	0.423390i	$-0.860840\pi$
$227$	1.14267	−	3.51677i	0.0758415	−	0.233416i	0.981789	+	0.189973i	$0.0608401\pi$
$228$		0			0
$229$	−11.4362	+	8.30886i	−0.755723	+	0.549065i	−0.897596	−	0.440820i	$-0.854688\pi$
$229$	−11.4362	+	8.30886i	−0.755723	+	0.549065i	0.141872	+	0.989885i	$0.454688\pi$
$230$		0			0
$231$	4.99937	−	12.1031i	0.328934	−	0.796326i
$232$		0			0
$233$	2.95372	−	2.14600i	0.193505	−	0.140589i	−0.486814	−	0.873505i	$-0.661841\pi$
$233$	2.95372	−	2.14600i	0.193505	−	0.140589i	0.680319	+	0.732916i	$0.261841\pi$
$234$		0			0
$235$	−1.95470	+	6.01594i	−0.127510	+	0.392437i
$236$		0			0
$237$	4.02020	+	2.92085i	0.261140	+	0.189730i
$238$		0			0
$239$	−1.76971	−	5.44661i	−0.114473	−	0.352312i	0.877364	−	0.479826i	$-0.159300\pi$
$239$	−1.76971	−	5.44661i	−0.114473	−	0.352312i	−0.991837	+	0.127514i	$0.959300\pi$
$240$		0			0
$241$	29.4347			1.89605			0.948027	−	0.318189i	$-0.103075\pi$
$241$	29.4347			1.89605			0.948027	+	0.318189i	$0.103075\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	2.65415	+	8.16863i	0.169567	+	0.521874i
$246$		0			0
$247$	0.210794	+	0.153151i	0.0134125	+	0.00974474i
$248$		0			0
$249$	−0.606097	+	1.86537i	−0.0384098	+	0.118213i
$250$		0			0
$251$	−21.9279	+	15.9316i	−1.38408	+	1.00559i	−0.387593	+	0.921831i	$0.626693\pi$
$251$	−21.9279	+	15.9316i	−1.38408	+	1.00559i	−0.996486	+	0.0837617i	$0.973307\pi$
$252$		0			0
$253$	−1.15747	+	2.80214i	−0.0727693	+	0.176169i
$254$		0			0
$255$	−5.35028	+	3.88721i	−0.335047	+	0.243426i
$256$		0			0
$257$	−3.11780	+	9.59561i	−0.194483	+	0.598558i	0.805499	+	0.592597i	$0.201897\pi$
$257$	−3.11780	+	9.59561i	−0.194483	+	0.598558i	−0.999982	+	0.00596080i	$0.998103\pi$
$258$		0			0
$259$	1.01767	+	0.739382i	0.0632351	+	0.0459430i
$260$		0			0
$261$	2.60352	+	8.01280i	0.161154	+	0.495980i
$262$		0			0
$263$	11.2194			0.691819			0.345910	−	0.938268i	$-0.387570\pi$
$263$	11.2194			0.691819			0.345910	+	0.938268i	$0.387570\pi$
$264$		0			0
$265$	12.4469			0.764610
$266$		0			0
$267$	4.31455	+	13.2788i	0.264046	+	0.812651i
$268$		0			0
$269$	−11.6283	−	8.44843i	−0.708988	−	0.515110i	0.173859	−	0.984771i	$-0.444376\pi$
$269$	−11.6283	−	8.44843i	−0.708988	−	0.515110i	−0.882847	+	0.469660i	$0.844376\pi$
$270$		0			0
$271$	−0.777147	+	2.39181i	−0.0472083	+	0.145292i	−0.971882	−	0.235468i	$-0.924338\pi$
$271$	−0.777147	+	2.39181i	−0.0472083	+	0.145292i	0.924674	+	0.380760i	$0.124338\pi$
$272$		0			0
$273$	0.274325	−	0.199309i	0.0166029	−	0.0120627i
$274$		0			0
$275$	−3.30665	−	0.256975i	−0.199399	−	0.0154962i
$276$		0			0
$277$	−7.78978	+	5.65961i	−0.468043	+	0.340053i	−0.796678	−	0.604404i	$-0.793411\pi$
$277$	−7.78978	+	5.65961i	−0.468043	+	0.340053i	0.328635	+	0.944457i	$0.393411\pi$
$278$		0			0
$279$	0.601683	−	1.85179i	0.0360218	−	0.110864i
$280$		0			0
$281$	−23.0764	−	16.7660i	−1.37663	−	1.00018i	−0.997187	−	0.0749600i	$-0.976117\pi$
$281$	−23.0764	−	16.7660i	−1.37663	−	1.00018i	−0.379439	−	0.925217i	$-0.623883\pi$
$282$		0			0
$283$	1.62894	+	5.01337i	0.0968307	+	0.298014i	0.987726	−	0.156194i	$-0.0499224\pi$
$283$	1.62894	+	5.01337i	0.0968307	+	0.298014i	−0.890896	+	0.454208i	$0.849922\pi$
$284$		0			0
$285$	−3.03391			−0.179713
$286$		0			0
$287$	16.6863			0.984961
$288$		0			0
$289$	8.26183	+	25.4273i	0.485990	+	1.49572i
$290$		0			0
$291$	−10.1988	−	7.40984i	−0.597862	−	0.434372i
$292$		0			0
$293$	−3.31723	+	10.2094i	−0.193795	+	0.596439i	0.806194	+	0.591651i	$0.201524\pi$
$293$	−3.31723	+	10.2094i	−0.193795	+	0.596439i	−0.999989	+	0.00478722i	$0.998476\pi$
$294$		0			0
$295$	10.7856	−	7.83622i	0.627963	−	0.456242i
$296$		0			0
$297$	2.82619	−	1.73571i	0.163992	−	0.100716i
$298$		0			0
$299$	−0.0635124	+	0.0461444i	−0.00367302	+	0.00266860i
$300$		0			0
$301$	−1.80480	+	5.55462i	−0.104027	+	0.320163i
$302$		0			0
$303$	8.24730	+	5.99202i	0.473795	+	0.344232i
$304$		0			0
$305$	−0.402099	−	1.23753i	−0.0230241	−	0.0708609i
$306$		0			0
$307$	−2.23551			−0.127587			−0.0637937	−	0.997963i	$-0.520320\pi$
$307$	−2.23551			−0.127587			−0.0637937	+	0.997963i	$0.520320\pi$
$308$		0			0
$309$	0.966095			0.0549592
$310$		0			0
$311$	2.32753	+	7.16342i	0.131982	+	0.406200i	0.995108	−	0.0987885i	$-0.0314967\pi$
$311$	2.32753	+	7.16342i	0.131982	+	0.406200i	−0.863126	+	0.504989i	$0.831497\pi$
$312$		0			0
$313$	7.44073	+	5.40601i	0.420575	+	0.305566i	0.777869	−	0.628426i	$-0.216301\pi$
$313$	7.44073	+	5.40601i	0.420575	+	0.305566i	−0.357294	+	0.933992i	$0.616301\pi$
$314$		0			0
$315$	−1.22009	+	3.75505i	−0.0687442	+	0.211573i
$316$		0			0
$317$	−5.32183	+	3.86653i	−0.298904	+	0.217166i	−0.727121	−	0.686510i	$-0.759142\pi$
$317$	−5.32183	+	3.86653i	−0.298904	+	0.217166i	0.428217	+	0.903676i	$0.359142\pi$
$318$		0			0
$319$	21.2659	+	18.1267i	1.19066	+	1.01490i
$320$		0			0
$321$	−2.15444	+	1.56529i	−0.120249	+	0.0873661i
$322$		0			0
$323$	−6.20016	+	19.0821i	−0.344986	+	1.06176i
$324$		0			0
$325$	−0.0694794	−	0.0504797i	−0.00385402	−	0.00280011i
$326$		0			0
$327$	−5.82480	−	17.9269i	−0.322112	−	0.991359i
$328$		0			0
$329$	24.9750			1.37692
$330$		0			0
$331$	−26.5529			−1.45948			−0.729739	−	0.683726i	$-0.760358\pi$
$331$	−26.5529			−1.45948			−0.729739	+	0.683726i	$0.760358\pi$
$332$		0			0
$333$	0.0984518	+	0.303003i	0.00539512	+	0.0166045i
$334$		0			0
$335$	4.16263	+	3.02433i	0.227429	+	0.165237i
$336$		0			0
$337$	5.75706	−	17.7184i	0.313607	−	0.965183i	−0.662717	−	0.748870i	$-0.730597\pi$
$337$	5.75706	−	17.7184i	0.313607	−	0.965183i	0.976324	−	0.216313i	$-0.0694032\pi$
$338$		0			0
$339$	−0.469810	+	0.341337i	−0.0255166	+	0.0185389i
$340$		0			0
$341$	−1.51369	−	6.27785i	−0.0819712	−	0.339965i
$342$		0			0
$343$	5.07565	−	3.68767i	0.274059	−	0.199116i
$344$		0			0
$345$	0.282478	−	0.869379i	0.0152081	−	0.0468058i
$346$		0			0
$347$	8.43742	+	6.13014i	0.452944	+	0.329083i	0.790757	−	0.612130i	$-0.209687\pi$
$347$	8.43742	+	6.13014i	0.452944	+	0.329083i	−0.337813	+	0.941213i	$0.609687\pi$
$348$		0			0
$349$	−0.0548537	−	0.168822i	−0.00293625	−	0.00903685i	0.949578	−	0.313532i	$-0.101512\pi$
$349$	−0.0548537	−	0.168822i	−0.00293625	−	0.00903685i	−0.952514	+	0.304495i	$0.901512\pi$
$350$		0			0
$351$	0.0858812			0.00458400
$352$		0			0
$353$	3.24327			0.172622			0.0863109	−	0.996268i	$-0.472492\pi$
$353$	3.24327			0.172622			0.0863109	+	0.996268i	$0.472492\pi$
$354$		0			0
$355$	4.61123	+	14.1919i	0.244739	+	0.753228i
$356$		0			0
$357$	21.1245	+	15.3478i	1.11802	+	0.812293i
$358$		0			0
$359$	7.88933	−	24.2809i	0.416383	−	1.28149i	−0.494626	−	0.869106i	$-0.664695\pi$
$359$	7.88933	−	24.2809i	0.416383	−	1.28149i	0.911008	−	0.412388i	$-0.135305\pi$
$360$		0			0
$361$	7.92466	−	5.75760i	0.417087	−	0.303032i
$362$		0			0
$363$	4.97465	−	9.81085i	0.261101	−	0.514936i
$364$		0			0
$365$	13.0428	−	9.47611i	0.682689	−	0.496003i
$366$		0			0
$367$	3.26110	−	10.0366i	0.170228	−	0.523908i	−0.829156	−	0.559018i	$-0.811178\pi$
$367$	3.26110	−	10.0366i	0.170228	−	0.523908i	0.999383	+	0.0351104i	$0.0111783\pi$
$368$		0			0
$369$	3.41907	+	2.48410i	0.177990	+	0.129317i
$370$		0			0
$371$	−15.1864	−	46.7389i	−0.788438	−	2.42656i
$372$		0			0
$373$	36.3283			1.88101			0.940503	−	0.339785i	$-0.110354\pi$
$373$	36.3283			1.88101			0.940503	+	0.339785i	$0.110354\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	0.223593	+	0.688149i	0.0115156	+	0.0354415i
$378$		0			0
$379$	2.22372	+	1.61562i	0.114225	+	0.0829890i	0.643431	−	0.765504i	$-0.277510\pi$
$379$	2.22372	+	1.61562i	0.114225	+	0.0829890i	−0.529206	+	0.848493i	$0.677510\pi$
$380$		0			0
$381$	−3.35316	+	10.3200i	−0.171788	+	0.528708i
$382$		0			0
$383$	−16.6288	+	12.0815i	−0.849693	+	0.617338i	−0.925061	−	0.379818i	$-0.875987\pi$
$383$	−16.6288	+	12.0815i	−0.849693	+	0.617338i	0.0753686	+	0.997156i	$0.475987\pi$
$384$		0			0
$385$	3.06946	+	12.7302i	0.156434	+	0.648790i
$386$		0			0
$387$	−1.19673	+	0.869476i	−0.0608332	+	0.0441979i
$388$		0			0
$389$	2.74414	−	8.44559i	0.139133	−	0.428208i	−0.857077	−	0.515189i	$-0.827722\pi$
$389$	2.74414	−	8.44559i	0.139133	−	0.428208i	0.996210	+	0.0869805i	$0.0277218\pi$
$390$		0			0
$391$	−4.89079	−	3.55337i	−0.247338	−	0.179702i
$392$		0			0
$393$	5.52270	+	16.9971i	0.278583	+	0.857392i
$394$		0			0
$395$	−4.96925			−0.250030
$396$		0			0
$397$	0.725442			0.0364089			0.0182045	−	0.999834i	$-0.494205\pi$
$397$	0.725442			0.0364089			0.0182045	+	0.999834i	$0.494205\pi$
$398$		0			0
$399$	3.70163	+	11.3925i	0.185313	+	0.570336i
$400$		0			0
$401$	21.6685	+	15.7431i	1.08207	+	0.786173i	0.978043	−	0.208401i	$-0.0668260\pi$
$401$	21.6685	+	15.7431i	1.08207	+	0.786173i	0.104031	+	0.994574i	$0.466826\pi$
$402$		0			0
$403$	0.0516733	−	0.159034i	0.00257403	−	0.00792205i
$404$		0			0
$405$	−0.809017	+	0.587785i	−0.0402004	+	0.0292073i
$406$		0			0
$407$	0.804168	+	0.685461i	0.0398611	+	0.0339770i
$408$		0			0
$409$	23.1281	−	16.8036i	1.14361	−	0.830884i	0.155995	−	0.987758i	$-0.450142\pi$
$409$	23.1281	−	16.8036i	1.14361	−	0.830884i	0.987619	+	0.156874i	$0.0501417\pi$
$410$		0			0
$411$	5.25929	−	16.1864i	0.259422	−	0.798418i
$412$		0			0
$413$	−42.5848	−	30.9397i	−2.09546	−	1.52244i
$414$		0			0
$415$	−0.606097	−	1.86537i	−0.0297521	−	0.0915676i
$416$		0			0
$417$	−13.4005			−0.656227
$418$		0			0
$419$	2.11693			0.103419			0.0517094	−	0.998662i	$-0.483533\pi$
$419$	2.11693			0.103419			0.0517094	+	0.998662i	$0.483533\pi$
$420$		0			0
$421$	1.27345	+	3.91928i	0.0620643	+	0.191014i	0.977281	−	0.211948i	$-0.0679807\pi$
$421$	1.27345	+	3.91928i	0.0620643	+	0.191014i	−0.915217	+	0.402962i	$0.867981\pi$
$422$		0			0
$423$	5.11746	+	3.71805i	0.248820	+	0.180778i
$424$		0			0
$425$	2.04362	−	6.28963i	0.0991304	−	0.305092i
$426$		0			0
$427$	−4.15640	+	3.01980i	−0.201142	+	0.146138i
$428$		0			0
$429$	0.242716	−	0.149065i	0.0117185	−	0.00719690i
$430$		0			0
$431$	−15.9005	+	11.5524i	−0.765899	+	0.556458i	−0.900714	−	0.434413i	$-0.856956\pi$
$431$	−15.9005	+	11.5524i	−0.765899	+	0.556458i	0.134815	+	0.990871i	$0.456956\pi$
$432$		0			0
$433$	4.09466	−	12.6021i	0.196777	−	0.605616i	−0.803175	−	0.595744i	$-0.796857\pi$
$433$	4.09466	−	12.6021i	0.196777	−	0.605616i	0.999951	−	0.00987269i	$-0.00314263\pi$
$434$		0			0
$435$	−6.81610	−	4.95219i	−0.326807	−	0.237439i
$436$		0			0
$437$	−0.857012	−	2.63761i	−0.0409965	−	0.126174i
$438$		0			0
$439$	6.28501			0.299967			0.149984	−	0.988688i	$-0.452078\pi$
$439$	6.28501			0.299967			0.149984	+	0.988688i	$0.452078\pi$
$440$		0			0
$441$	8.58900			0.409000
$442$		0			0
$443$	11.3500	+	34.9316i	0.539253	+	1.65965i	0.734275	+	0.678852i	$0.237522\pi$
$443$	11.3500	+	34.9316i	0.539253	+	1.65965i	−0.195022	+	0.980799i	$0.562478\pi$
$444$		0			0
$445$	−11.2956	−	8.20676i	−0.535465	−	0.389038i
$446$		0			0
$447$	6.62134	−	20.3784i	0.313178	−	0.963864i
$448$		0			0
$449$	22.4417	−	16.3049i	1.05909	−	0.769475i	0.0851713	−	0.996366i	$-0.472856\pi$
$449$	22.4417	−	16.3049i	1.05909	−	0.769475i	0.973920	+	0.226891i	$0.0728562\pi$
$450$		0			0
$451$	13.9746	+	1.08603i	0.658039	+	0.0511391i
$452$		0			0
$453$	8.27006	−	6.00855i	0.388561	−	0.282306i
$454$		0			0
$455$	−0.104783	+	0.322488i	−0.00491229	+	0.0151185i
$456$		0			0
$457$	−22.5161	−	16.3589i	−1.05326	−	0.765238i	−0.0804301	−	0.996760i	$-0.525629\pi$
$457$	−22.5161	−	16.3589i	−1.05326	−	0.765238i	−0.972830	+	0.231522i	$0.925629\pi$
$458$		0			0
$459$	2.04362	+	6.28963i	0.0953882	+	0.293575i
$460$		0			0
$461$	12.3052			0.573110			0.286555	−	0.958064i	$-0.407490\pi$
$461$	12.3052			0.573110			0.286555	+	0.958064i	$0.407490\pi$
$462$		0			0
$463$	−8.34457			−0.387805			−0.193902	−	0.981021i	$-0.562115\pi$
$463$	−8.34457			−0.387805			−0.193902	+	0.981021i	$0.562115\pi$
$464$		0			0
$465$	0.601683	+	1.85179i	0.0279024	+	0.0858747i
$466$		0			0
$467$	1.54630	+	1.12345i	0.0715540	+	0.0519870i	0.622987	−	0.782232i	$-0.285919\pi$
$467$	1.54630	+	1.12345i	0.0715540	+	0.0519870i	−0.551433	+	0.834219i	$0.685919\pi$
$468$		0			0
$469$	6.27772	−	19.3208i	0.289878	−	0.892153i
$470$		0			0
$471$	−5.04326	+	3.66414i	−0.232381	+	0.168835i
$472$		0			0
$473$	−1.87303	+	4.53447i	−0.0861220	+	0.208495i
$474$		0			0
$475$	2.45448	−	1.78328i	0.112619	−	0.0818227i
$476$		0			0
$477$	3.84632	−	11.8378i	0.176111	−	0.542013i
$478$		0			0
$479$	−22.5641	−	16.3938i	−1.03098	−	0.749051i	−0.0624761	−	0.998046i	$-0.519900\pi$
$479$	−22.5641	−	16.3938i	−1.03098	−	0.749051i	−0.968505	+	0.248995i	$0.919900\pi$
$480$		0			0
$481$	0.00845516	+	0.0260223i	0.000385522	+	0.00118651i
$482$		0			0
$483$	−3.60921			−0.164225
$484$		0			0
$485$	12.6064			0.572426
$486$		0			0
$487$	−2.12136	−	6.52887i	−0.0961280	−	0.295851i	0.891418	−	0.453182i	$-0.149711\pi$
$487$	−2.12136	−	6.52887i	−0.0961280	−	0.295851i	−0.987546	+	0.157330i	$0.949711\pi$
$488$		0			0
$489$	−8.33186	−	6.05345i	−0.376780	−	0.273747i
$490$		0			0
$491$	−3.26165	+	10.0383i	−0.147196	+	0.453024i	−0.997287	−	0.0736128i	$-0.976547\pi$
$491$	−3.26165	+	10.0383i	−0.147196	+	0.453024i	0.850091	+	0.526637i	$0.176547\pi$
$492$		0			0
$493$	−45.0770	+	32.7503i	−2.03016	+	1.47500i
$494$		0			0
$495$	−1.26621	+	3.06541i	−0.0569119	+	0.137780i
$496$		0			0
$497$	47.6652	−	34.6308i	2.13808	−	1.55340i
$498$		0			0
$499$	−3.18478	+	9.80175i	−0.142570	+	0.438787i	−0.996691	−	0.0812891i	$-0.974096\pi$
$499$	−3.18478	+	9.80175i	−0.142570	+	0.438787i	0.854120	+	0.520076i	$0.174096\pi$
$500$		0			0
$501$	−0.931144	−	0.676516i	−0.0416005	−	0.0302245i
$502$		0			0
$503$	7.87459	+	24.2355i	0.351110	+	1.08061i	0.958231	+	0.285997i	$0.0923247\pi$
$503$	7.87459	+	24.2355i	0.351110	+	1.08061i	−0.607120	+	0.794610i	$0.707675\pi$
$504$		0			0
$505$	−10.1942			−0.453637
$506$		0			0
$507$	−12.9926			−0.577023
$508$		0			0
$509$	−0.164446	−	0.506113i	−0.00728894	−	0.0224331i	0.947346	−	0.320212i	$-0.103754\pi$
$509$	−0.164446	−	0.506113i	−0.00728894	−	0.0224331i	−0.954635	+	0.297779i	$0.903754\pi$
$510$		0			0
$511$	−51.4966	−	37.4145i	−2.27807	−	1.65512i
$512$		0			0
$513$	−0.937528	+	2.88542i	−0.0413929	+	0.127394i
$514$		0			0
$515$	−0.781587	+	0.567856i	−0.0344408	+	0.0250227i
$516$		0			0
$517$	20.9163	+	1.62550i	0.919900	+	0.0714895i
$518$		0			0
$519$	−7.44929	+	5.41222i	−0.326987	+	0.237570i
$520$		0			0
$521$	−11.3152	+	34.8247i	−0.495730	+	1.52570i	0.320086	+	0.947388i	$0.396288\pi$
$521$	−11.3152	+	34.8247i	−0.495730	+	1.52570i	−0.815816	+	0.578311i	$0.803712\pi$
$522$		0			0
$523$	−14.0372	−	10.1986i	−0.613805	−	0.445956i	0.236947	−	0.971523i	$-0.423853\pi$
$523$	−14.0372	−	10.1986i	−0.613805	−	0.445956i	−0.850752	+	0.525567i	$0.823853\pi$
$524$		0			0
$525$	−1.22009	−	3.75505i	−0.0532491	−	0.163884i
$526$		0			0
$527$	12.8767			0.560918
$528$		0			0
$529$	−22.1644			−0.963669
$530$		0			0
$531$	−4.11974	−	12.6793i	−0.178782	−	0.550233i
$532$		0			0
$533$	0.293634	+	0.213338i	0.0127187	+	0.00924068i
$534$		0			0
$535$	0.822923	−	2.53270i	0.0355781	−	0.109498i
$536$		0			0
$537$	−17.6068	+	12.7921i	−0.759791	+	0.552021i
$538$		0			0
$539$	24.2741	−	14.9080i	1.04556	−	0.642132i
$540$		0			0
$541$	−6.95892	+	5.05595i	−0.299187	+	0.217372i	−0.727243	−	0.686380i	$-0.759199\pi$
$541$	−6.95892	+	5.05595i	−0.299187	+	0.217372i	0.428056	+	0.903752i	$0.359199\pi$
$542$		0			0
$543$	−0.436202	+	1.34249i	−0.0187192	+	0.0576118i
$544$		0			0
$545$	15.2495	+	11.0794i	0.653217	+	0.474590i
$546$		0			0
$547$	13.3529	+	41.0959i	0.570927	+	1.75713i	0.649648	+	0.760235i	$0.274916\pi$
$547$	13.3529	+	41.0959i	0.570927	+	1.75713i	−0.0787208	+	0.996897i	$0.525084\pi$
$548$		0			0
$549$	−1.30122			−0.0555347
$550$		0			0
$551$	−25.5611			−1.08894
$552$		0			0
$553$	6.06292	+	18.6598i	0.257822	+	0.793493i
$554$		0			0
$555$	−0.257750	−	0.187266i	−0.0109409	−	0.00794902i
$556$		0			0
$557$	−3.35131	+	10.3143i	−0.141999	+	0.437029i	−0.996613	−	0.0822354i	$-0.973794\pi$
$557$	−3.35131	+	10.3143i	−0.141999	+	0.437029i	0.854614	+	0.519265i	$0.173794\pi$
$558$		0			0
$559$	−0.102777	+	0.0746716i	−0.00434699	+	0.00315827i
$560$		0			0
$561$	16.6926	+	14.2285i	0.704763	+	0.600729i
$562$		0			0
$563$	−29.0422	+	21.1004i	−1.22398	+	0.889277i	−0.996425	−	0.0844873i	$-0.973075\pi$
$563$	−29.0422	+	21.1004i	−1.22398	+	0.889277i	−0.227560	+	0.973764i	$0.573075\pi$
$564$		0			0
$565$	0.179451	−	0.552295i	0.00754958	−	0.0232352i
$566$		0			0
$567$	3.19423	+	2.32075i	0.134145	+	0.0974622i
$568$		0			0
$569$	−11.5775	−	35.6318i	−0.485353	−	1.49376i	−0.831468	−	0.555572i	$-0.812499\pi$
$569$	−11.5775	−	35.6318i	−0.485353	−	1.49376i	0.346115	−	0.938192i	$-0.387501\pi$
$570$		0			0
$571$	−16.4296			−0.687558			−0.343779	−	0.939051i	$-0.611707\pi$
$571$	−16.4296			−0.687558			−0.343779	+	0.939051i	$0.611707\pi$
$572$		0			0
$573$	16.8633			0.704474
$574$		0			0
$575$	0.282478	+	0.869379i	0.0117802	+	0.0362556i
$576$		0			0
$577$	−25.7141	−	18.6824i	−1.07049	−	0.777758i	−0.0944910	−	0.995526i	$-0.530122\pi$
$577$	−25.7141	−	18.6824i	−1.07049	−	0.777758i	−0.976001	+	0.217768i	$0.930122\pi$
$578$		0			0
$579$	−5.15245	+	15.8576i	−0.214129	+	0.659020i
$580$		0			0
$581$	−6.26508	+	4.55184i	−0.259919	+	0.188842i
$582$		0			0
$583$	−9.67644	−	40.1318i	−0.400757	−	1.66209i
$584$		0			0
$585$	−0.0694794	+	0.0504797i	−0.00287262	+	0.00208708i
$586$		0			0
$587$	−7.18751	+	22.1209i	−0.296660	+	0.913027i	0.685998	+	0.727603i	$0.259366\pi$
$587$	−7.18751	+	22.1209i	−0.296660	+	0.913027i	−0.982659	+	0.185424i	$0.940634\pi$
$588$		0			0
$589$	4.77909	+	3.47221i	0.196919	+	0.143070i
$590$		0			0
$591$	−0.163176	−	0.502204i	−0.00671217	−	0.0206579i
$592$		0			0
$593$	6.88267			0.282637			0.141319	−	0.989964i	$-0.454866\pi$
$593$	6.88267			0.282637			0.141319	+	0.989964i	$0.454866\pi$
$594$		0			0
$595$	−26.1113			−1.07046
$596$		0			0
$597$	−1.80661	−	5.56018i	−0.0739398	−	0.227563i
$598$		0			0
$599$	19.9880	+	14.5222i	0.816689	+	0.593359i	0.915762	−	0.401721i	$-0.131588\pi$
$599$	19.9880	+	14.5222i	0.816689	+	0.593359i	−0.0990732	+	0.995080i	$0.531588\pi$
$600$		0			0
$601$	9.10396	−	28.0191i	0.371358	−	1.14292i	−0.574545	−	0.818473i	$-0.694821\pi$
$601$	9.10396	−	28.0191i	0.371358	−	1.14292i	0.945903	−	0.324450i	$-0.105179\pi$
$602$		0			0
$603$	4.16263	−	3.02433i	0.169515	−	0.123160i
$604$		0			0
$605$	1.74210	+	10.8612i	0.0708263	+	0.441570i
$606$		0			0
$607$	−15.5194	+	11.2755i	−0.629913	+	0.457659i	−0.856370	−	0.516362i	$-0.827286\pi$
$607$	−15.5194	+	11.2755i	−0.629913	+	0.457659i	0.226457	+	0.974021i	$0.427286\pi$
$608$		0			0
$609$	−10.2794	+	31.6369i	−0.416544	+	1.28199i
$610$		0			0
$611$	0.439494	+	0.319311i	0.0177800	+	0.0129179i
$612$		0			0
$613$	2.15031	+	6.61798i	0.0868503	+	0.267298i	0.985044	−	0.172302i	$-0.0551204\pi$
$613$	2.15031	+	6.61798i	0.0868503	+	0.267298i	−0.898194	+	0.439599i	$0.855120\pi$
$614$		0			0
$615$	−4.22621			−0.170417
$616$		0			0
$617$	−30.1905			−1.21542			−0.607711	−	0.794158i	$-0.707912\pi$
$617$	−30.1905			−1.21542			−0.607711	+	0.794158i	$0.707912\pi$
$618$		0			0
$619$	−2.00016	−	6.15586i	−0.0803932	−	0.247425i	0.902779	−	0.430104i	$-0.141523\pi$
$619$	−2.00016	−	6.15586i	−0.0803932	−	0.247425i	−0.983173	+	0.182679i	$0.941523\pi$
$620$		0			0
$621$	−0.739538	−	0.537306i	−0.0296766	−	0.0215613i
$622$		0			0
$623$	−17.0351	+	52.4287i	−0.682497	+	2.10051i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	2.35860	+	9.78199i	0.0941935	+	0.390655i
$628$		0			0
$629$	−1.70458	+	1.23845i	−0.0679661	+	0.0493803i
$630$		0			0
$631$	11.9849	−	36.8856i	0.477110	−	1.46839i	−0.365981	−	0.930622i	$-0.619266\pi$
$631$	11.9849	−	36.8856i	0.477110	−	1.46839i	0.843091	−	0.537771i	$-0.180734\pi$
$632$		0			0
$633$	−3.61956	−	2.62977i	−0.143865	−	0.104524i
$634$		0			0
$635$	−3.35316	−	10.3200i	−0.133066	−	0.409535i
$636$		0			0
$637$	0.737634			0.0292261
$638$		0			0
$639$	14.9223			0.590315
$640$		0			0
$641$	−6.29036	−	19.3597i	−0.248454	−	0.764664i	−0.995049	−	0.0993847i	$-0.968313\pi$
$641$	−6.29036	−	19.3597i	−0.248454	−	0.764664i	0.746595	−	0.665279i	$-0.231687\pi$
$642$		0			0
$643$	22.5486	+	16.3825i	0.889228	+	0.646062i	0.935677	−	0.352859i	$-0.114790\pi$
$643$	22.5486	+	16.3825i	0.889228	+	0.646062i	−0.0464486	+	0.998921i	$0.514790\pi$
$644$		0			0
$645$	0.457110	−	1.40684i	0.0179987	−	0.0553943i
$646$		0			0
$647$	6.65768	−	4.83709i	0.261741	−	0.190166i	−0.449173	−	0.893445i	$-0.648281\pi$
$647$	6.65768	−	4.83709i	0.261741	−	0.190166i	0.710914	+	0.703279i	$0.248281\pi$
$648$		0			0
$649$	−33.6506	−	28.6833i	−1.32090	−	1.12592i
$650$		0			0
$651$	6.21945	−	4.51870i	0.243760	−	0.177102i
$652$		0			0
$653$	8.52626	−	26.2411i	0.333658	−	1.02689i	−0.633721	−	0.773562i	$-0.718473\pi$
$653$	8.52626	−	26.2411i	0.333658	−	1.02689i	0.967379	−	0.253333i	$-0.0815268\pi$
$654$		0			0
$655$	−14.4586	−	10.5048i	−0.564945	−	0.410457i
$656$		0			0
$657$	−4.98189	−	15.3327i	−0.194362	−	0.598185i
$658$		0			0
$659$	−42.2388			−1.64539			−0.822696	−	0.568482i	$-0.807531\pi$
$659$	−42.2388			−1.64539			−0.822696	+	0.568482i	$0.807531\pi$
$660$		0			0
$661$	8.45304			0.328785			0.164393	−	0.986395i	$-0.447434\pi$
$661$	8.45304			0.328785			0.164393	+	0.986395i	$0.447434\pi$
$662$		0			0
$663$	0.175509	+	0.540161i	0.00681620	+	0.0209781i
$664$		0			0
$665$	−9.69100	−	7.04093i	−0.375801	−	0.273035i
$666$		0			0
$667$	2.37992	−	7.32466i	0.0921511	−	0.283612i
$668$		0			0
$669$	−12.4975	+	9.07997i	−0.483182	+	0.351052i
$670$		0			0
$671$	−3.67749	+	2.25853i	−0.141968	+	0.0871897i
$672$		0			0
$673$	2.79758	−	2.03256i	0.107839	−	0.0783495i	−0.532559	−	0.846393i	$-0.678770\pi$
$673$	2.79758	−	2.03256i	0.107839	−	0.0783495i	0.640398	+	0.768043i	$0.278770\pi$
$674$		0			0
$675$	0.309017	−	0.951057i	0.0118941	−	0.0366062i
$676$		0			0
$677$	−34.9749	−	25.4107i	−1.34419	−	0.976614i	−0.999278	−	0.0379808i	$-0.987907\pi$
$677$	−34.9749	−	25.4107i	−1.34419	−	0.976614i	−0.344916	−	0.938634i	$-0.612093\pi$
$678$		0			0
$679$	−15.3809	−	47.3375i	−0.590265	−	1.81665i
$680$		0			0
$681$	3.69775			0.141698
$682$		0			0
$683$	−25.0818			−0.959728			−0.479864	−	0.877343i	$-0.659314\pi$
$683$	−25.0818			−0.959728			−0.479864	+	0.877343i	$0.659314\pi$
$684$		0			0
$685$	5.25929	+	16.1864i	0.200947	+	0.618452i
$686$		0			0
$687$	−11.4362	−	8.30886i	−0.436317	−	0.317003i
$688$		0			0
$689$	0.330326	−	1.01664i	0.0125844	−	0.0387309i
$690$		0			0
$691$	−16.6160	+	12.0722i	−0.632103	+	0.459250i	−0.857128	−	0.515103i	$-0.827754\pi$
$691$	−16.6160	+	12.0722i	−0.632103	+	0.459250i	0.225025	+	0.974353i	$0.427754\pi$
$692$		0			0
$693$	13.0556	+	1.01461i	0.495943	+	0.0385419i
$694$		0			0
$695$	10.8413	−	7.87664i	0.411233	−	0.298778i
$696$		0			0
$697$	−8.63678	+	26.5813i	−0.327142	+	1.00684i
$698$		0			0
$699$	2.95372	+	2.14600i	0.111720	+	0.0811693i
$700$		0			0
$701$	1.03782	+	3.19409i	0.0391980	+	0.120639i	0.968741	−	0.248075i	$-0.0797980\pi$
$701$	1.03782	+	3.19409i	0.0391980	+	0.120639i	−0.929543	+	0.368714i	$0.879798\pi$
$702$		0			0
$703$	−0.966592			−0.0364557
$704$		0			0
$705$	−6.32553			−0.238233
$706$		0			0
$707$	12.4379	+	38.2798i	0.467774	+	1.43966i
$708$		0			0
$709$	27.7893	+	20.1901i	1.04365	+	0.758255i	0.970994	−	0.239103i	$-0.0768533\pi$
$709$	27.7893	+	20.1901i	1.04365	+	0.758255i	0.0726535	+	0.997357i	$0.476853\pi$
$710$		0			0
$711$	−1.53558	+	4.72603i	−0.0575888	+	0.177240i
$712$		0			0
$713$	−1.43994	+	1.04618i	−0.0539263	+	0.0391798i
$714$		0			0
$715$	−0.108744	+	0.263261i	−0.00406678	+	0.00984539i
$716$		0			0
$717$	4.63316	−	3.36619i	0.173029	−	0.125713i
$718$		0			0
$719$	12.8170	−	39.4466i	0.477992	−	1.47111i	−0.363888	−	0.931443i	$-0.618551\pi$
$719$	12.8170	−	39.4466i	0.477992	−	1.47111i	0.841880	−	0.539665i	$-0.181449\pi$
$720$		0			0
$721$	3.08593	+	2.24206i	0.114926	+	0.0834988i
$722$		0			0
$723$	9.09582	+	27.9941i	0.338277	+	1.04111i
$724$		0			0
$725$	8.42516			0.312903
$726$		0			0
$727$	−13.0120			−0.482589			−0.241295	−	0.970452i	$-0.577572\pi$
$727$	−13.0120			−0.482589			−0.241295	+	0.970452i	$0.577572\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−7.91435	−	5.75011i	−0.292723	−	0.212676i
$732$		0			0
$733$	15.1444	−	46.6097i	0.559372	−	1.72157i	−0.124737	−	0.992190i	$-0.539809\pi$
$733$	15.1444	−	46.6097i	0.559372	−	1.72157i	0.684109	−	0.729380i	$-0.260191\pi$
$734$		0			0
$735$	−6.94865	+	5.04849i	−0.256305	+	0.186216i
$736$		0			0
$737$	6.51503	−	15.7724i	0.239984	−	0.580985i
$738$		0			0
$739$	23.9466	−	17.3982i	0.880891	−	0.640004i	−0.0525964	−	0.998616i	$-0.516750\pi$
$739$	23.9466	−	17.3982i	0.880891	−	0.640004i	0.933487	+	0.358611i	$0.116750\pi$
$740$		0			0
$741$	−0.0805161	+	0.247803i	−0.00295783	+	0.00910327i
$742$		0			0
$743$	−36.9070	−	26.8145i	−1.35399	−	0.983729i	−0.998802	−	0.0489325i	$-0.984418\pi$
$743$	−36.9070	−	26.8145i	−1.35399	−	0.983729i	−0.355184	−	0.934796i	$-0.615582\pi$
$744$		0			0
$745$	6.62134	+	20.3784i	0.242587	+	0.746606i
$746$		0			0
$747$	−1.96137			−0.0717628
$748$		0			0
$749$	−10.5144			−0.384189
$750$		0			0
$751$	−0.177961	−	0.547707i	−0.00649388	−	0.0199861i	0.947757	−	0.318993i	$-0.103345\pi$
$751$	−0.177961	−	0.547707i	−0.00649388	−	0.0199861i	−0.954251	+	0.299007i	$0.903345\pi$
$752$		0			0
$753$	−21.9279	−	15.9316i	−0.799098	−	0.580579i
$754$		0			0
$755$	−3.15888	+	9.72204i	−0.114963	+	0.353821i
$756$		0			0
$757$	31.8217	−	23.1198i	1.15658	−	0.840304i	0.167238	−	0.985917i	$-0.446515\pi$
$757$	31.8217	−	23.1198i	1.15658	−	0.840304i	0.989342	+	0.145613i	$0.0465153\pi$
$758$		0			0
$759$	−3.02268	−	0.234905i	−0.109716	−	0.00852653i
$760$		0			0
$761$	−11.1766	+	8.12025i	−0.405150	+	0.294359i	−0.771635	−	0.636065i	$-0.780561\pi$
$761$	−11.1766	+	8.12025i	−0.405150	+	0.294359i	0.366485	+	0.930424i	$0.380561\pi$
$762$		0			0
$763$	22.9980	−	70.7805i	0.832583	−	2.56243i
$764$		0			0
$765$	−5.35028	−	3.88721i	−0.193440	−	0.140542i
$766$		0			0
$767$	−0.353808	−	1.08891i	−0.0127753	−	0.0393183i
$768$		0			0
$769$	−7.75917			−0.279803			−0.139901	−	0.990165i	$-0.544679\pi$
$769$	−7.75917			−0.279803			−0.139901	+	0.990165i	$0.544679\pi$
$770$		0			0
$771$	−10.0894			−0.363362
$772$		0			0
$773$	−2.57696	−	7.93106i	−0.0926867	−	0.285260i	0.893957	−	0.448152i	$-0.147918\pi$
$773$	−2.57696	−	7.93106i	−0.0926867	−	0.285260i	−0.986644	+	0.162892i	$0.947918\pi$
$774$		0			0
$775$	−1.57523	−	1.14447i	−0.0565838	−	0.0411106i
$776$		0			0
$777$	−0.388716	+	1.19635i	−0.0139451	+	0.0429187i
$778$		0			0
$779$	−10.3731	+	7.53653i	−0.371657	+	0.270024i
$780$		0			0
$781$	42.1731	−	25.9006i	1.50907	−	0.926798i
$782$		0			0
$783$	−6.81610	+	4.95219i	−0.243587	+	0.176977i
$784$		0			0
$785$	1.92635	−	5.92871i	0.0687546	−	0.211605i
$786$		0			0
$787$	−27.4620	−	19.9523i	−0.978913	−	0.711222i	−0.0214478	−	0.999770i	$-0.506828\pi$
$787$	−27.4620	−	19.9523i	−0.978913	−	0.711222i	−0.957465	+	0.288548i	$0.906828\pi$
$788$		0			0
$789$	3.46699	+	10.6703i	0.123428	+	0.379873i
$790$		0			0
$791$	−2.29284			−0.0815240
$792$		0			0
$793$	−0.111750			−0.00396837
$794$		0			0
$795$	3.84632	+	11.8378i	0.136415	+	0.419842i
$796$		0			0
$797$	30.6910	+	22.2984i	1.08713	+	0.789848i	0.978913	−	0.204279i	$-0.0654849\pi$
$797$	30.6910	+	22.2984i	1.08713	+	0.789848i	0.108220	+	0.994127i	$0.465485\pi$
$798$		0			0
$799$	−12.9270	+	39.7853i	−0.457325	+	1.40750i
$800$		0			0
$801$	−11.2956	+	8.20676i	−0.399112	+	0.289972i
$802$		0			0
$803$	−40.6928	−	34.6859i	−1.43602	−	1.22404i
$804$		0			0
$805$	2.91991	−	2.12144i	0.102913	−	0.0747709i
$806$		0			0
$807$	4.44160	−	13.6699i	0.156352	−	0.481202i
$808$		0			0
$809$	−10.8848	−	7.90830i	−0.382690	−	0.278041i	0.379763	−	0.925084i	$-0.376005\pi$
$809$	−10.8848	−	7.90830i	−0.382690	−	0.278041i	−0.762454	+	0.647043i	$0.776005\pi$
$810$		0			0
$811$	4.97313	+	15.3057i	0.174630	+	0.537457i	0.999616	−	0.0276963i	$-0.00881714\pi$
$811$	4.97313	+	15.3057i	0.174630	+	0.537457i	−0.824986	+	0.565153i	$0.808817\pi$
$812$		0			0
$813$	−2.51490			−0.0882014
$814$		0			0
$815$	10.2987			0.360749
$816$		0			0
$817$	−1.38683	−	4.26822i	−0.0485190	−	0.149326i
$818$		0			0
$819$	0.274325	+	0.199309i	0.00958568	+	0.00696441i
$820$		0			0
$821$	−16.2805	+	50.1063i	−0.568194	+	1.74872i	0.0900726	+	0.995935i	$0.471290\pi$
$821$	−16.2805	+	50.1063i	−0.568194	+	1.74872i	−0.658266	+	0.752785i	$0.728710\pi$
$822$		0			0
$823$	43.2641	−	31.4332i	1.50809	−	1.09569i	0.541078	−	0.840972i	$-0.318016\pi$
$823$	43.2641	−	31.4332i	1.50809	−	1.09569i	0.967015	−	0.254721i	$-0.0819837\pi$
$824$		0			0
$825$	−0.777415	−	3.22422i	−0.0270661	−	0.112253i
$826$		0			0
$827$	25.8687	−	18.7947i	0.899544	−	0.653557i	−0.0388051	−	0.999247i	$-0.512355\pi$
$827$	25.8687	−	18.7947i	0.899544	−	0.653557i	0.938349	+	0.345690i	$0.112355\pi$
$828$		0			0
$829$	0.166716	−	0.513099i	0.00579029	−	0.0178207i	−0.948120	−	0.317914i	$-0.897018\pi$
$829$	0.166716	−	0.513099i	0.00579029	−	0.0178207i	0.953910	+	0.300093i	$0.0970177\pi$
$830$		0			0
$831$	−7.78978	−	5.65961i	−0.270224	−	0.196330i
$832$		0			0
$833$	17.5527	+	54.0216i	0.608165	+	1.87174i
$834$		0			0
$835$	1.15096			0.0398305
$836$		0			0
$837$	1.94709			0.0673012
$838$		0			0
$839$	15.9495	+	49.0874i	0.550637	+	1.69469i	0.707195	+	0.707018i	$0.249960\pi$
$839$	15.9495	+	49.0874i	0.550637	+	1.69469i	−0.156558	+	0.987669i	$0.550040\pi$
$840$		0			0
$841$	−33.9652	−	24.6772i	−1.17122	−	0.850938i
$842$		0			0
$843$	8.81442	−	27.1280i	0.303585	−	0.934338i
$844$		0			0
$845$	10.5113	−	7.63687i	0.361598	−	0.262716i
$846$		0			0
$847$	38.6587	−	19.7933i	1.32833	−	0.680104i
$848$		0			0
$849$	−4.26463	+	3.09844i	−0.146362	+	0.106338i
$850$		0			0
$851$	0.0899966	−	0.276981i	0.00308504	−	0.00949479i
$852$		0			0
$853$	34.0606	+	24.7465i	1.16621	+	0.847303i	0.990551	−	0.137147i	$-0.0437934\pi$
$853$	34.0606	+	24.7465i	1.16621	+	0.847303i	0.175662	+	0.984451i	$0.443793\pi$
$854$		0			0
$855$	−0.937528	−	2.88542i	−0.0320628	−	0.0986791i
$856$		0			0
$857$	9.42704			0.322021			0.161011	−	0.986953i	$-0.448525\pi$
$857$	9.42704			0.322021			0.161011	+	0.986953i	$0.448525\pi$
$858$		0			0
$859$	−52.2138			−1.78151			−0.890756	−	0.454481i	$-0.849825\pi$
$859$	−52.2138			−1.78151			−0.890756	+	0.454481i	$0.849825\pi$
$860$		0			0
$861$	5.15635	+	15.8696i	0.175728	+	0.540835i
$862$		0			0
$863$	−31.7129	−	23.0408i	−1.07952	−	0.784317i	−0.101920	−	0.994793i	$-0.532499\pi$
$863$	−31.7129	−	23.0408i	−1.07952	−	0.784317i	−0.977599	+	0.210476i	$0.932499\pi$
$864$		0			0
$865$	2.84537	−	8.75716i	0.0967456	−	0.297752i
$866$		0			0
$867$	−21.6298	+	15.7149i	−0.734585	+	0.533707i
$868$		0			0
$869$	3.86317	+	16.0220i	0.131049	+	0.543508i
$870$		0			0
$871$	0.357492	−	0.259733i	0.0121132	−	0.00880072i
$872$		0			0
$873$	3.89558	−	11.9894i	0.131845	−	0.405779i
$874$		0			0
$875$	3.19423	+	2.32075i	0.107985	+	0.0784556i
$876$		0			0
$877$	−16.2315	−	49.9553i	−0.548098	−	1.68687i	−0.713508	−	0.700647i	$-0.752895\pi$
$877$	−16.2315	−	49.9553i	−0.548098	−	1.68687i	0.165411	−	0.986225i	$-0.447105\pi$
$878$		0			0
$879$	−10.7348			−0.362075
$880$		0			0
$881$	10.5291			0.354734			0.177367	−	0.984145i	$-0.443242\pi$
$881$	10.5291			0.354734			0.177367	+	0.984145i	$0.443242\pi$
$882$		0			0
$883$	−5.01791	−	15.4435i	−0.168866	−	0.519716i	0.830434	−	0.557117i	$-0.188092\pi$
$883$	−5.01791	−	15.4435i	−0.168866	−	0.519716i	−0.999300	+	0.0374003i	$0.988092\pi$
$884$		0			0
$885$	10.7856	+	7.83622i	0.362555	+	0.263412i
$886$		0			0
$887$	−14.2831	+	43.9588i	−0.479579	+	1.47599i	0.360103	+	0.932912i	$0.382741\pi$
$887$	−14.2831	+	43.9588i	−0.479579	+	1.47599i	−0.839682	+	0.543079i	$0.817259\pi$
$888$		0			0
$889$	−34.6608	+	25.1826i	−1.16249	+	0.844596i
$890$		0			0
$891$	2.52409	+	2.15150i	0.0845603	+	0.0720780i
$892$		0			0
$893$	−15.5259	+	11.2802i	−0.519554	+	0.377478i
$894$		0			0
$895$	6.72521	−	20.6981i	0.224799	−	0.691860i
$896$		0			0
$897$	−0.0635124	−	0.0461444i	−0.00212062	−	0.00154072i
$898$		0			0
$899$	5.06928	+	15.6016i	0.169070	+	0.520344i
$900$		0			0
$901$	82.3155			2.74233
$902$		0			0
$903$	−5.84047			−0.194359
$904$		0			0
$905$	−0.436202	−	1.34249i	−0.0144998	−	0.0446259i
$906$		0			0
$907$	4.87350	+	3.54080i	0.161822	+	0.117570i	0.665749	−	0.746176i	$-0.268112\pi$
$907$	4.87350	+	3.54080i	0.161822	+	0.117570i	−0.503927	+	0.863746i	$0.668112\pi$
$908$		0			0
$909$	−3.15019	+	9.69529i	−0.104485	+	0.321572i
$910$		0			0
$911$	16.4254	−	11.9338i	0.544199	−	0.395383i	−0.281443	−	0.959578i	$-0.590813\pi$
$911$	16.4254	−	11.9338i	0.544199	−	0.395383i	0.825642	+	0.564194i	$0.190813\pi$
$912$		0			0
$913$	−5.54320	+	3.40436i	−0.183453	+	0.112668i
$914$		0			0
$915$	1.05271	−	0.764838i	0.0348015	−	0.0252847i
$916$		0			0
$917$	−21.8052	+	67.1096i	−0.720072	+	2.21615i
$918$		0			0
$919$	40.5824	+	29.4848i	1.33869	+	0.972615i	0.999491	+	0.0319003i	$0.0101559\pi$
$919$	40.5824	+	29.4848i	1.33869	+	0.972615i	0.339199	+	0.940715i	$0.389844\pi$
$920$		0			0
$921$	−0.690811	−	2.12610i	−0.0227630	−	0.0700573i
$922$		0			0
$923$	1.28154			0.0421825
$924$		0			0
$925$	0.318597			0.0104754
$926$		0			0
$927$	0.298540	+	0.918811i	0.00980533	+	0.0301777i
$928$		0			0
$929$	3.40956	+	2.47719i	0.111864	+	0.0812740i	0.642311	−	0.766444i	$-0.277976\pi$
$929$	3.40956	+	2.47719i	0.111864	+	0.0812740i	−0.530447	+	0.847718i	$0.677976\pi$
$930$		0			0
$931$	−8.05243	+	24.7828i	−0.263908	+	0.812225i
$932$		0			0
$933$	−6.09357	+	4.42723i	−0.199494	+	0.144941i
$934$		0			0
$935$	−21.8679	−	1.69945i	−0.715158	−	0.0555781i
$936$		0			0
$937$	18.7334	−	13.6106i	0.611994	−	0.444640i	−0.238122	−	0.971235i	$-0.576532\pi$
$937$	18.7334	−	13.6106i	0.611994	−	0.444640i	0.850116	+	0.526595i	$0.176532\pi$
$938$		0			0
$939$	−2.84211	+	8.74710i	−0.0927486	+	0.285451i
$940$		0			0
$941$	−2.72117	−	1.97705i	−0.0887076	−	0.0644498i	0.542547	−	0.840025i	$-0.317460\pi$
$941$	−2.72117	−	1.97705i	−0.0887076	−	0.0644498i	−0.631255	+	0.775575i	$0.717460\pi$
$942$		0			0
$943$	−1.19381	−	3.67418i	−0.0388759	−	0.119648i
$944$		0			0
$945$	−3.94829			−0.128438
$946$		0			0
$947$	−26.6333			−0.865465			−0.432732	−	0.901522i	$-0.642450\pi$
$947$	−26.6333			−0.865465			−0.432732	+	0.901522i	$0.642450\pi$
$948$		0			0
$949$	−0.427851	−	1.31679i	−0.0138886	−	0.0427448i
$950$		0			0
$951$	−5.32183	−	3.86653i	−0.172572	−	0.125381i
$952$		0			0
$953$	−0.987747	+	3.03997i	−0.0319963	+	0.0984744i	−0.965779	−	0.259365i	$-0.916487\pi$
$953$	−0.987747	+	3.03997i	−0.0319963	+	0.0984744i	0.933783	+	0.357840i	$0.116487\pi$
$954$		0			0
$955$	−13.6427	+	9.91200i	−0.441467	+	0.320745i
$956$		0			0
$957$	−10.6680	+	25.8265i	−0.344848	+	0.834853i
$958$		0			0
$959$	54.3640	−	39.4978i	1.75551	−	1.27545i
$960$		0			0
$961$	−8.40800	+	25.8772i	−0.271226	+	0.834747i
$962$		0			0
$963$	−2.15444	−	1.56529i	−0.0694258	−	0.0504408i
$964$		0			0
$965$	−5.15245	−	15.8576i	−0.165863	−	0.510475i
$966$		0			0
$967$	−29.0771			−0.935057			−0.467529	−	0.883978i	$-0.654856\pi$
$967$	−29.0771			−0.935057			−0.467529	+	0.883978i	$0.654856\pi$
$968$		0			0
$969$	−20.0642			−0.644553
$970$		0			0
$971$	−0.507141	−	1.56082i	−0.0162749	−	0.0500891i	0.942589	−	0.333954i	$-0.108383\pi$
$971$	−0.507141	−	1.56082i	−0.0162749	−	0.0500891i	−0.958864	+	0.283865i	$0.908383\pi$
$972$		0			0
$973$	−42.8045	−	31.0993i	−1.37225	−	0.996997i
$974$		0			0
$975$	0.0265388	−	0.0816779i	0.000849920	−	0.00261579i
$976$		0			0
$977$	−33.1809	+	24.1074i	−1.06155	+	0.771263i	−0.974375	−	0.224930i	$-0.927785\pi$
$977$	−33.1809	+	24.1074i	−1.06155	+	0.771263i	−0.0871776	+	0.996193i	$0.527785\pi$
$978$		0			0
$979$	−17.6791	+	42.7998i	−0.565025	+	1.36789i
$980$		0			0
$981$	15.2495	−	11.0794i	0.486880	−	0.353739i
$982$		0			0
$983$	7.35847	−	22.6470i	0.234699	−	0.722328i	−0.762463	−	0.647032i	$-0.776010\pi$
$983$	7.35847	−	22.6470i	0.234699	−	0.722328i	0.997161	−	0.0752958i	$-0.0239901\pi$
$984$		0			0
$985$	0.427201	+	0.310379i	0.0136117	+	0.00988951i
$986$		0			0
$987$	7.71771	+	23.7527i	0.245657	+	0.756056i
$988$		0			0
$989$	1.35220			0.0429975
$990$		0			0
$991$	20.1012			0.638537			0.319268	−	0.947664i	$-0.396563\pi$
$991$	20.1012			0.638537			0.319268	+	0.947664i	$0.396563\pi$
$992$		0			0
$993$	−8.20529	−	25.2533i	−0.260387	−	0.801389i
$994$		0			0
$995$	4.72977	+	3.43638i	0.149944	+	0.108941i
$996$		0			0
$997$	2.74413	−	8.44557i	0.0869076	−	0.267474i	−0.898153	−	0.439683i	$-0.855091\pi$
$997$	2.74413	−	8.44557i	0.0869076	−	0.267474i	0.985060	+	0.172210i	$0.0550906\pi$
$998$		0			0
$999$	−0.257750	+	0.187266i	−0.00815485	+	0.00592485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1320.2.bw.i.1081.1	yes	16
11.4	even	5	inner	1320.2.bw.i.961.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1320.2.bw.i.961.1	✓	16	11.4	even	5	inner
1320.2.bw.i.1081.1	yes	16	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:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.bw (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-1.22009 + 3.75505i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-1.22009 + 3.75505i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(-1.26621 + 3.06541i) q^{11} +(-0.0694794 + 0.0504797i) q^{13} +(0.309017 - 0.951057i) q^{15} +(-5.35028 - 3.88721i) q^{17} +(-0.937528 - 2.88542i) q^{19} -3.94829 q^{21} +0.914119 q^{23} +(0.309017 + 0.951057i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(2.60352 - 8.01280i) q^{29} +(-1.57523 + 1.14447i) q^{31} +(-3.30665 - 0.256975i) q^{33} +(3.19423 - 2.32075i) q^{35} +(0.0984518 - 0.303003i) q^{37} +(-0.0694794 - 0.0504797i) q^{39} +(-1.30597 - 4.01936i) q^{41} +1.47924 q^{43} +1.00000 q^{45} +(-1.95470 - 6.01594i) q^{47} +(-6.94865 - 5.04849i) q^{49} +(2.04362 - 6.28963i) q^{51} +(-10.0698 + 7.31613i) q^{53} +(2.82619 - 1.73571i) q^{55} +(2.45448 - 1.78328i) q^{57} +(-4.11974 + 12.6793i) q^{59} +(1.05271 + 0.764838i) q^{61} +(-1.22009 - 3.75505i) q^{63} +0.0858812 q^{65} -5.14530 q^{67} +(0.282478 + 0.869379i) q^{69} +(-12.0724 - 8.77108i) q^{71} +(-4.98189 + 15.3327i) q^{73} +(-0.809017 + 0.587785i) q^{75} +(-9.96586 - 8.49475i) q^{77} +(4.02020 - 2.92085i) q^{79} +(0.309017 - 0.951057i) q^{81} +(1.58678 + 1.15286i) q^{83} +(2.04362 + 6.28963i) q^{85} +8.42516 q^{87} +13.9622 q^{89} +(-0.104783 - 0.322488i) q^{91} +(-1.57523 - 1.14447i) q^{93} +(-0.937528 + 2.88542i) q^{95} +(-10.1988 + 7.40984i) q^{97} +(-0.777415 - 3.22422i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 16 q - 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} - q^{11} + q^{13} - 4 q^{15} - 3 q^{17} - 2 q^{19} - 6 q^{21} + 10 q^{23} - 4 q^{25} - 4 q^{27} - 5 q^{29} + 3 q^{31} - q^{33} - q^{35} - 25 q^{37} + q^{39} - 2 q^{41} - 2 q^{43} + 16 q^{45} + 14 q^{47} - 8 q^{49} + 2 q^{51} - 11 q^{53} + 4 q^{55} + 8 q^{57} - 7 q^{59} - 3 q^{61} + 4 q^{63} + 6 q^{65} + 32 q^{67} - 15 q^{71} - q^{73} - 4 q^{75} + 9 q^{77} - 15 q^{79} - 4 q^{81} - 17 q^{83} + 2 q^{85} + 26 q^{89} + 36 q^{91} + 3 q^{93} - 2 q^{95} - 45 q^{97} - q^{99}+O(q^{100}) \) 16 * q - 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 - q^11 + q^13 - 4 * q^15 - 3 * q^17 - 2 * q^19 - 6 * q^21 + 10 * q^23 - 4 * q^25 - 4 * q^27 - 5 * q^29 + 3 * q^31 - q^33 - q^35 - 25 * q^37 + q^39 - 2 * q^41 - 2 * q^43 + 16 * q^45 + 14 * q^47 - 8 * q^49 + 2 * q^51 - 11 * q^53 + 4 * q^55 + 8 * q^57 - 7 * q^59 - 3 * q^61 + 4 * q^63 + 6 * q^65 + 32 * q^67 - 15 * q^71 - q^73 - 4 * q^75 + 9 * q^77 - 15 * q^79 - 4 * q^81 - 17 * q^83 + 2 * q^85 + 26 * q^89 + 36 * q^91 + 3 * q^93 - 2 * q^95 - 45 * q^97 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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