LMFDB - Embedded newform 460.2.m.b.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(41,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("460.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.m (of order $11$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.3
Character	$\chi$	$=$	460.121
Dual form			460.2.m.b.441.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.169429 - 0.0497487i) q^{3} +(-0.841254 + 0.540641i) q^{5} +(0.0167209 - 0.116296i) q^{7} +(-2.49753 - 1.60506i) q^{9} +O(q^{10})$	\(q+(-0.169429 - 0.0497487i) q^{3} +(-0.841254 + 0.540641i) q^{5} +(0.0167209 - 0.116296i) q^{7} +(-2.49753 - 1.60506i) q^{9} +(-2.18087 - 4.77544i) q^{11} +(-0.469939 - 3.26850i) q^{13} +(0.169429 - 0.0497487i) q^{15} +(2.47084 - 2.85151i) q^{17} +(4.45395 + 5.14013i) q^{19} +(-0.00861860 + 0.0188721i) q^{21} +(-0.322195 - 4.78500i) q^{23} +(0.415415 - 0.909632i) q^{25} +(0.690212 + 0.796547i) q^{27} +(3.36722 - 3.88598i) q^{29} +(-6.09875 + 1.79076i) q^{31} +(0.131930 + 0.917592i) q^{33} +(0.0488081 + 0.106875i) q^{35} +(-7.87064 - 5.05815i) q^{37} +(-0.0829824 + 0.577156i) q^{39} +(0.642746 - 0.413068i) q^{41} +(-11.0453 - 3.24319i) q^{43} +2.96882 q^{45} +2.37371 q^{47} +(6.70321 + 1.96824i) q^{49} +(-0.560491 + 0.360206i) q^{51} +(-0.334132 + 2.32394i) q^{53} +(4.41646 + 2.83829i) q^{55} +(-0.498912 - 1.09246i) q^{57} +(1.13985 + 7.92780i) q^{59} +(9.33098 - 2.73982i) q^{61} +(-0.228424 + 0.263616i) q^{63} +(2.16242 + 2.49557i) q^{65} +(-5.95950 + 13.0495i) q^{67} +(-0.183458 + 0.826744i) q^{69} +(1.23864 - 2.71224i) q^{71} +(-6.14504 - 7.09176i) q^{73} +(-0.115636 + 0.133451i) q^{75} +(-0.591833 + 0.173778i) q^{77} +(0.499973 + 3.47739i) q^{79} +(3.62256 + 7.93230i) q^{81} +(-4.00000 - 2.57064i) q^{83} +(-0.536966 + 3.73468i) q^{85} +(-0.763826 + 0.490881i) q^{87} +(12.5479 + 3.68441i) q^{89} -0.387972 q^{91} +1.12239 q^{93} +(-6.52587 - 1.91617i) q^{95} +(7.96365 - 5.11793i) q^{97} +(-2.21810 + 15.4272i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) $ 50 * q + 5 * q^5 - q^7 - 25 * q^9	$ 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) $ 50 * q + 5 * q^5 - q^7 - 25 * q^9 - 6 * q^13 + 12 * q^17 + 19 * q^19 + 39 * q^21 - 16 * q^23 - 5 * q^25 + 21 * q^27 - 6 * q^29 + 34 * q^31 + 50 * q^33 - 10 * q^35 + 7 * q^37 - 70 * q^39 - 51 * q^41 - 18 * q^43 - 74 * q^45 + 30 * q^47 - 16 * q^49 - 80 * q^51 - 23 * q^53 - 33 * q^55 + 27 * q^57 - 18 * q^59 + 76 * q^61 + 138 * q^63 + 6 * q^65 + 25 * q^67 - 30 * q^69 - 37 * q^71 + 20 * q^73 + 92 * q^77 + 18 * q^79 + 25 * q^81 - 22 * q^83 - 12 * q^85 - 109 * q^87 + 8 * q^89 + 110 * q^91 + 64 * q^93 + 3 * q^95 - 38 * q^97 - 126 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

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
$3$	−0.169429	−	0.0497487i	−0.0978197	−	0.0287224i	0.232456	−	0.972607i	$-0.425324\pi$
$3$	−0.169429	−	0.0497487i	−0.0978197	−	0.0287224i	−0.330276	+	0.943884i	$0.607142\pi$
$4$		0			0
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$6$		0			0
$7$	0.0167209	−	0.116296i	0.00631991	−	0.0439559i	−0.986417	−	0.164258i	$-0.947477\pi$
$7$	0.0167209	−	0.116296i	0.00631991	−	0.0439559i	0.992737	+	0.120302i	$0.0383862\pi$
$8$		0			0
$9$	−2.49753	−	1.60506i	−0.832510	−	0.535022i
$10$		0			0
$11$	−2.18087	−	4.77544i	−0.657557	−	1.43985i	−0.884781	−	0.466007i	$-0.845692\pi$
$11$	−2.18087	−	4.77544i	−0.657557	−	1.43985i	0.227224	−	0.973843i	$-0.427035\pi$
$12$		0			0
$13$	−0.469939	−	3.26850i	−0.130338	−	0.906518i	−0.945114	−	0.326742i	$-0.894049\pi$
$13$	−0.469939	−	3.26850i	−0.130338	−	0.906518i	0.814776	−	0.579776i	$-0.196860\pi$
$14$		0			0
$15$	0.169429	−	0.0497487i	0.0437463	−	0.0128451i
$16$		0			0
$17$	2.47084	−	2.85151i	0.599268	−	0.691592i	−0.372365	−	0.928086i	$-0.621453\pi$
$17$	2.47084	−	2.85151i	0.599268	−	0.691592i	0.971633	+	0.236494i	$0.0759985\pi$
$18$		0			0
$19$	4.45395	+	5.14013i	1.02181	+	1.17923i	0.983675	+	0.179955i	$0.0575952\pi$
$19$	4.45395	+	5.14013i	1.02181	+	1.17923i	0.0381318	+	0.999273i	$0.487859\pi$
$20$		0			0
$21$	−0.00861860	+	0.0188721i	−0.00188073	+	0.00411823i
$22$		0			0
$23$	−0.322195	−	4.78500i	−0.0671824	−	0.997741i
$23$	−0.322195	−	4.78500i	−0.0671824	−	0.997741i
$24$		0			0
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$		0			0
$27$	0.690212	+	0.796547i	0.132831	+	0.153296i
$28$		0			0
$29$	3.36722	−	3.88598i	0.625277	−	0.721608i	−0.351423	−	0.936217i	$-0.614302\pi$
$29$	3.36722	−	3.88598i	0.625277	−	0.721608i	0.976700	+	0.214609i	$0.0688477\pi$
$30$		0			0
$31$	−6.09875	+	1.79076i	−1.09537	+	0.321629i	−0.779011	−	0.627011i	$-0.784278\pi$
$31$	−6.09875	+	1.79076i	−1.09537	+	0.321629i	−0.316358	+	0.948640i	$0.602460\pi$
$32$		0			0
$33$	0.131930	+	0.917592i	0.0229660	+	0.159732i
$34$		0			0
$35$	0.0488081	+	0.106875i	0.00825007	+	0.0180651i
$36$		0			0
$37$	−7.87064	−	5.05815i	−1.29392	−	0.831555i	−0.301388	−	0.953502i	$-0.597450\pi$
$37$	−7.87064	−	5.05815i	−1.29392	−	0.831555i	−0.992537	+	0.121947i	$0.961086\pi$
$38$		0			0
$39$	−0.0829824	+	0.577156i	−0.0132878	+	0.0924189i
$40$		0			0
$41$	0.642746	−	0.413068i	0.100380	−	0.0645104i	−0.489488	−	0.872010i	$-0.662816\pi$
$41$	0.642746	−	0.413068i	0.100380	−	0.0645104i	0.589868	+	0.807500i	$0.299180\pi$
$42$		0			0
$43$	−11.0453	−	3.24319i	−1.68439	−	0.494582i	−0.707213	−	0.707000i	$-0.750048\pi$
$43$	−11.0453	−	3.24319i	−1.68439	−	0.494582i	−0.977179	+	0.212418i	$0.931866\pi$
$44$		0			0
$45$	2.96882			0.442565
$46$		0			0
$47$	2.37371			0.346241			0.173120	−	0.984901i	$-0.444615\pi$
$47$	2.37371			0.346241			0.173120	+	0.984901i	$0.444615\pi$
$48$		0			0
$49$	6.70321	+	1.96824i	0.957601	+	0.281177i
$50$		0			0
$51$	−0.560491	+	0.360206i	−0.0784844	+	0.0504389i
$52$		0			0
$53$	−0.334132	+	2.32394i	−0.0458965	+	0.319217i	0.953920	+	0.300061i	$0.0970071\pi$
$53$	−0.334132	+	2.32394i	−0.0458965	+	0.319217i	−0.999817	+	0.0191562i	$0.993902\pi$
$54$		0			0
$55$	4.41646	+	2.83829i	0.595516	+	0.382715i
$56$		0			0
$57$	−0.498912	−	1.09246i	−0.0660825	−	0.144700i
$58$		0			0
$59$	1.13985	+	7.92780i	0.148395	+	1.03211i	0.918847	+	0.394613i	$0.129121\pi$
$59$	1.13985	+	7.92780i	0.148395	+	1.03211i	−0.770452	+	0.637498i	$0.779969\pi$
$60$		0			0
$61$	9.33098	−	2.73982i	1.19471	−	0.350798i	0.376882	−	0.926261i	$-0.376996\pi$
$61$	9.33098	−	2.73982i	1.19471	−	0.350798i	0.817828	+	0.575463i	$0.195178\pi$
$62$		0			0
$63$	−0.228424	+	0.263616i	−0.0287788	+	0.0332125i
$64$		0			0
$65$	2.16242	+	2.49557i	0.268215	+	0.309537i
$66$		0			0
$67$	−5.95950	+	13.0495i	−0.728069	+	1.59425i	0.0741705	+	0.997246i	$0.476369\pi$
$67$	−5.95950	+	13.0495i	−0.728069	+	1.59425i	−0.802239	+	0.597003i	$0.796358\pi$
$68$		0			0
$69$	−0.183458	+	0.826744i	−0.0220858	+	0.0995283i
$70$		0			0
$71$	1.23864	−	2.71224i	0.146999	−	0.321883i	−0.821781	−	0.569803i	$-0.807020\pi$
$71$	1.23864	−	2.71224i	0.146999	−	0.321883i	0.968781	+	0.247919i	$0.0797468\pi$
$72$		0			0
$73$	−6.14504	−	7.09176i	−0.719223	−	0.830028i	0.271990	−	0.962300i	$-0.412318\pi$
$73$	−6.14504	−	7.09176i	−0.719223	−	0.830028i	−0.991213	+	0.132272i	$0.957773\pi$
$74$		0			0
$75$	−0.115636	+	0.133451i	−0.0133525	+	0.0154096i
$76$		0			0
$77$	−0.591833	+	0.173778i	−0.0674456	+	0.0198038i
$78$		0			0
$79$	0.499973	+	3.47739i	0.0562513	+	0.391236i	0.998425	+	0.0561103i	$0.0178699\pi$
$79$	0.499973	+	3.47739i	0.0562513	+	0.391236i	−0.942173	+	0.335126i	$0.891221\pi$
$80$		0			0
$81$	3.62256	+	7.93230i	0.402507	+	0.881367i
$82$		0			0
$83$	−4.00000	−	2.57064i	−0.439057	−	0.282165i	0.302380	−	0.953187i	$-0.402219\pi$
$83$	−4.00000	−	2.57064i	−0.439057	−	0.282165i	−0.741437	+	0.671023i	$0.765855\pi$
$84$		0			0
$85$	−0.536966	+	3.73468i	−0.0582421	+	0.405083i
$86$		0			0
$87$	−0.763826	+	0.490881i	−0.0818907	+	0.0526280i
$88$		0			0
$89$	12.5479	+	3.68441i	1.33008	+	0.390547i	0.868120	−	0.496354i	$-0.165328\pi$
$89$	12.5479	+	3.68441i	1.33008	+	0.390547i	0.461960	+	0.886901i	$0.347146\pi$
$90$		0			0
$91$	−0.387972			−0.0406705
$92$		0			0
$93$	1.12239			0.116387
$94$		0			0
$95$	−6.52587	−	1.91617i	−0.669540	−	0.196595i
$96$		0			0
$97$	7.96365	−	5.11793i	0.808586	−	0.519647i	−0.0698213	−	0.997560i	$-0.522243\pi$
$97$	7.96365	−	5.11793i	0.808586	−	0.519647i	0.878407	+	0.477913i	$0.158607\pi$
$98$		0			0
$99$	−2.21810	+	15.4272i	−0.222928	+	1.55050i
$100$		0			0
$101$	−14.8818	−	9.56394i	−1.48079	−	0.951647i	−0.997076	−	0.0764227i	$-0.975650\pi$
$101$	−14.8818	−	9.56394i	−1.48079	−	0.951647i	−0.483717	−	0.875225i	$-0.660713\pi$
$102$		0			0
$103$	7.10957	+	15.5678i	0.700527	+	1.53394i	0.839331	+	0.543621i	$0.182947\pi$
$103$	7.10957	+	15.5678i	0.700527	+	1.53394i	−0.138804	+	0.990320i	$0.544326\pi$
$104$		0			0
$105$	−0.00295260	−	0.0205358i	−0.000288144	−	0.00200409i
$106$		0			0
$107$	7.63888	−	2.24298i	0.738479	−	0.216837i	0.109203	−	0.994019i	$-0.465170\pi$
$107$	7.63888	−	2.24298i	0.738479	−	0.216837i	0.629275	+	0.777183i	$0.283352\pi$
$108$		0			0
$109$	−4.46250	+	5.15000i	−0.427430	+	0.493281i	−0.928086	−	0.372366i	$-0.878547\pi$
$109$	−4.46250	+	5.15000i	−0.427430	+	0.493281i	0.500656	+	0.865646i	$0.333092\pi$
$110$		0			0
$111$	1.08187	+	1.24855i	0.102687	+	0.118507i
$112$		0			0
$113$	7.17389	−	15.7086i	0.674863	−	1.47774i	−0.193133	−	0.981173i	$-0.561865\pi$
$113$	7.17389	−	15.7086i	0.674863	−	1.47774i	0.867996	−	0.496571i	$-0.165408\pi$
$114$		0			0
$115$	2.85801	+	3.85120i	0.266511	+	0.359127i
$116$		0			0
$117$	−4.07246	+	8.91745i	−0.376499	+	0.824418i
$118$		0			0
$119$	−0.290305	−	0.335030i	−0.0266123	−	0.0307122i
$120$		0			0
$121$	−10.8452	+	12.5160i	−0.985925	+	1.13782i
$122$		0			0
$123$	−0.129449	+	0.0380097i	−0.0116720	+	0.00342722i
$124$		0			0
$125$	0.142315	+	0.989821i	0.0127290	+	0.0885323i
$126$		0			0
$127$	−2.68252	−	5.87389i	−0.238035	−	0.521224i	0.752482	−	0.658613i	$-0.228856\pi$
$127$	−2.68252	−	5.87389i	−0.238035	−	0.521224i	−0.990517	+	0.137389i	$0.956129\pi$
$128$		0			0
$129$	1.71005	+	1.09898i	0.150561	+	0.0967597i
$130$		0			0
$131$	1.16005	−	8.06832i	0.101354	−	0.704933i	−0.874263	−	0.485453i	$-0.838655\pi$
$131$	1.16005	−	8.06832i	0.101354	−	0.704933i	0.975617	−	0.219480i	$-0.0704361\pi$
$132$		0			0
$133$	0.672254	−	0.432031i	0.0582918	−	0.0374619i
$134$		0			0
$135$	−1.01129	−	0.296941i	−0.0870379	−	0.0255566i
$136$		0			0
$137$	20.0580			1.71367			0.856836	−	0.515589i	$-0.172427\pi$
$137$	20.0580			1.71367			0.856836	+	0.515589i	$0.172427\pi$
$138$		0			0
$139$	6.03342			0.511748			0.255874	−	0.966710i	$-0.417637\pi$
$139$	6.03342			0.511748			0.255874	+	0.966710i	$0.417637\pi$
$140$		0			0
$141$	−0.402174	−	0.118089i	−0.0338691	−	0.00994488i
$142$		0			0
$143$	−14.5836	+	9.37233i	−1.21954	+	0.783754i
$144$		0			0
$145$	−0.731766	+	5.08955i	−0.0607699	+	0.422664i
$146$		0			0
$147$	−1.03780	−	0.666952i	−0.0855961	−	0.0550093i
$148$		0			0
$149$	6.77344	+	14.8318i	0.554902	+	1.21507i	0.954455	+	0.298355i	$0.0964380\pi$
$149$	6.77344	+	14.8318i	0.554902	+	1.21507i	−0.399553	+	0.916710i	$0.630835\pi$
$150$		0			0
$151$	0.860959	+	5.98810i	0.0700638	+	0.487305i	0.994396	+	0.105717i	$0.0337136\pi$
$151$	0.860959	+	5.98810i	0.0700638	+	0.487305i	−0.924332	+	0.381588i	$0.875377\pi$
$152$		0			0
$153$	−10.7479	+	3.15586i	−0.868913	+	0.255136i
$154$		0			0
$155$	4.16244	−	4.80371i	0.334335	−	0.385844i
$156$		0			0
$157$	−2.80893	−	3.24168i	−0.224177	−	0.258714i	0.632508	−	0.774554i	$-0.282025\pi$
$157$	−2.80893	−	3.24168i	−0.224177	−	0.258714i	−0.856685	+	0.515840i	$0.827480\pi$
$158$		0			0
$159$	0.172224	−	0.377119i	0.0136583	−	0.0299075i
$160$		0			0
$161$	−0.561866	−	0.0425393i	−0.0442812	−	0.00335257i
$162$		0			0
$163$	7.51442	−	16.4543i	0.588575	−	1.28880i	−0.347725	−	0.937597i	$-0.613046\pi$
$163$	7.51442	−	16.4543i	0.588575	−	1.28880i	0.936299	−	0.351203i	$-0.114227\pi$
$164$		0			0
$165$	−0.607074	−	0.700601i	−0.0472607	−	0.0545417i
$166$		0			0
$167$	−13.1551	+	15.1818i	−1.01797	+	1.17480i	−0.0334663	+	0.999440i	$0.510655\pi$
$167$	−13.1551	+	15.1818i	−1.01797	+	1.17480i	−0.984504	+	0.175361i	$0.943891\pi$
$168$		0			0
$169$	2.01119	−	0.590538i	0.154707	−	0.0454260i
$170$		0			0
$171$	−2.87363	−	19.9865i	−0.219752	−	1.52841i
$172$		0			0
$173$	−6.12842	−	13.4194i	−0.465935	−	1.02026i	−0.986094	−	0.166186i	$-0.946855\pi$
$173$	−6.12842	−	13.4194i	−0.465935	−	1.02026i	0.520159	−	0.854069i	$-0.325873\pi$
$174$		0			0
$175$	−0.0988409	−	0.0635212i	−0.00747167	−	0.00480175i
$176$		0			0
$177$	0.201275	−	1.39990i	0.0151288	−	0.105223i
$178$		0			0
$179$	1.68426	−	1.08241i	0.125888	−	0.0809031i	−0.476182	−	0.879347i	$-0.657979\pi$
$179$	1.68426	−	1.08241i	0.125888	−	0.0809031i	0.602069	+	0.798444i	$0.294343\pi$
$180$		0			0
$181$	−1.41296	−	0.414883i	−0.105025	−	0.0308380i	0.228798	−	0.973474i	$-0.426520\pi$
$181$	−1.41296	−	0.414883i	−0.105025	−	0.0308380i	−0.333823	+	0.942636i	$0.608339\pi$
$182$		0			0
$183$	−1.71724			−0.126942
$184$		0			0
$185$	9.35584			0.687855
$186$		0			0
$187$	−19.0058	−	5.58061i	−1.38984	−	0.408094i
$188$		0			0
$189$	0.104177	−	0.0669502i	0.00757773	−	0.00486991i
$190$		0			0
$191$	0.236106	−	1.64215i	0.0170840	−	0.118822i	−0.979495	−	0.201469i	$-0.935428\pi$
$191$	0.236106	−	1.64215i	0.0170840	−	0.118822i	0.996579	+	0.0826473i	$0.0263375\pi$
$192$		0			0
$193$	4.46328	+	2.86837i	0.321274	+	0.206470i	0.691330	−	0.722539i	$-0.257025\pi$
$193$	4.46328	+	2.86837i	0.321274	+	0.206470i	−0.370056	+	0.929009i	$0.620662\pi$
$194$		0			0
$195$	−0.242225	−	0.530398i	−0.0173461	−	0.0379826i
$196$		0			0
$197$	−2.78061	−	19.3396i	−0.198110	−	1.37789i	−0.809762	−	0.586759i	$-0.800404\pi$
$197$	−2.78061	−	19.3396i	−0.198110	−	1.37789i	0.611651	−	0.791127i	$-0.290506\pi$
$198$		0			0
$199$	16.7728	−	4.92493i	1.18899	−	0.349119i	0.373357	−	0.927688i	$-0.378207\pi$
$199$	16.7728	−	4.92493i	1.18899	−	0.349119i	0.815634	+	0.578568i	$0.196388\pi$
$200$		0			0
$201$	1.65891	−	1.91448i	0.117010	−	0.135037i
$202$		0			0
$203$	−0.395622	−	0.456573i	−0.0277672	−	0.0320451i
$204$		0			0
$205$	−0.317391	+	0.694990i	−0.0221676	+	0.0485402i
$206$		0			0
$207$	−6.87554	+	12.4678i	−0.477883	+	0.866573i
$208$		0			0
$209$	14.8329	−	32.4796i	1.02601	−	2.24666i
$210$		0			0
$211$	6.91868	+	7.98458i	0.476301	+	0.549681i	0.942154	−	0.335181i	$-0.108798\pi$
$211$	6.91868	+	7.98458i	0.476301	+	0.549681i	−0.465852	+	0.884863i	$0.654252\pi$
$212$		0			0
$213$	−0.344791	+	0.397910i	−0.0236247	+	0.0272643i
$214$		0			0
$215$	11.0453	−	3.24319i	0.753283	−	0.221184i
$216$		0			0
$217$	0.106282	+	0.739206i	0.00721488	+	0.0501806i
$218$		0			0
$219$	0.688340	+	1.50726i	0.0465137	+	0.101851i
$220$		0			0
$221$	−10.4813	−	6.73591i	−0.705047	−	0.453106i
$222$		0			0
$223$	1.12805	−	7.84573i	0.0755396	−	0.525389i	−0.916556	−	0.399906i	$-0.869043\pi$
$223$	1.12805	−	7.84573i	0.0755396	−	0.525389i	0.992096	−	0.125483i	$-0.0400481\pi$
$224$		0			0
$225$	−2.49753	+	1.60506i	−0.166502	+	0.107004i
$226$		0			0
$227$	10.5626	+	3.10145i	0.701062	+	0.205850i	0.612790	−	0.790246i	$-0.290047\pi$
$227$	10.5626	+	3.10145i	0.701062	+	0.205850i	0.0882723	+	0.996096i	$0.471865\pi$
$228$		0			0
$229$	−28.8188			−1.90440			−0.952199	−	0.305478i	$-0.901184\pi$
$229$	−28.8188			−1.90440			−0.952199	+	0.305478i	$0.901184\pi$
$230$		0			0
$231$	0.108919			0.00716632
$232$		0			0
$233$	3.38799	+	0.994804i	0.221955	+	0.0651718i	0.390819	−	0.920467i	$-0.372192\pi$
$233$	3.38799	+	0.994804i	0.221955	+	0.0651718i	−0.168864	+	0.985639i	$0.554010\pi$
$234$		0			0
$235$	−1.99689	+	1.28332i	−0.130263	+	0.0837147i
$236$		0			0
$237$	0.0882859	−	0.614042i	0.00573478	−	0.0398863i
$238$		0			0
$239$	−16.0467	−	10.3126i	−1.03798	−	0.667067i	−0.0934910	−	0.995620i	$-0.529803\pi$
$239$	−16.0467	−	10.3126i	−1.03798	−	0.667067i	−0.944485	+	0.328553i	$0.893439\pi$
$240$		0			0
$241$	5.90881	+	12.9385i	0.380620	+	0.833441i	0.998873	+	0.0474622i	$0.0151134\pi$
$241$	5.90881	+	12.9385i	0.380620	+	0.833441i	−0.618253	+	0.785979i	$0.712159\pi$
$242$		0			0
$243$	−0.669136	−	4.65394i	−0.0429251	−	0.298550i
$244$		0			0
$245$	−6.70321	+	1.96824i	−0.428252	+	0.125746i
$246$		0			0
$247$	14.7074	−	16.9733i	0.935811	−	1.07998i
$248$		0			0
$249$	0.549828	+	0.634535i	0.0348439	+	0.0402120i
$250$		0			0
$251$	1.97181	−	4.31765i	0.124459	−	0.272528i	−0.837138	−	0.546991i	$-0.815773\pi$
$251$	1.97181	−	4.31765i	0.124459	−	0.272528i	0.961597	+	0.274464i	$0.0885003\pi$
$252$		0			0
$253$	−22.1478	+	11.9741i	−1.39242	+	0.752804i
$254$		0			0
$255$	0.276773	−	0.606048i	0.0173322	−	0.0379522i
$256$		0			0
$257$	−10.3433	−	11.9368i	−0.645195	−	0.744595i	0.335089	−	0.942186i	$-0.391233\pi$
$257$	−10.3433	−	11.9368i	−0.645195	−	0.744595i	−0.980284	+	0.197592i	$0.936688\pi$
$258$		0			0
$259$	−0.719849	+	0.830750i	−0.0447293	+	0.0516203i
$260$		0			0
$261$	−14.6470	+	4.30074i	−0.906625	+	0.266209i
$262$		0			0
$263$	−1.02569	−	7.13382i	−0.0632467	−	0.439890i	−0.996699	−	0.0811883i	$-0.974128\pi$
$263$	−1.02569	−	7.13382i	−0.0632467	−	0.439890i	0.933452	−	0.358702i	$-0.116781\pi$
$264$		0			0
$265$	−0.975326	−	2.13567i	−0.0599138	−	0.131193i
$266$		0			0
$267$	−1.94269	−	1.24849i	−0.118891	−	0.0764063i
$268$		0			0
$269$	−1.52325	+	10.5944i	−0.0928743	+	0.645955i	0.889208	+	0.457503i	$0.151256\pi$
$269$	−1.52325	+	10.5944i	−0.0928743	+	0.645955i	−0.982082	+	0.188452i	$0.939653\pi$
$270$		0			0
$271$	17.3807	−	11.1699i	1.05581	−	0.678525i	0.106959	−	0.994263i	$-0.465889\pi$
$271$	17.3807	−	11.1699i	1.05581	−	0.678525i	0.948846	+	0.315739i	$0.102252\pi$
$272$		0			0
$273$	0.0657336	+	0.0193011i	0.00397838	+	0.00116816i
$274$		0			0
$275$	−5.24986			−0.316579
$276$		0			0
$277$	20.0848			1.20678			0.603390	−	0.797446i	$-0.293816\pi$
$277$	20.0848			1.20678			0.603390	+	0.797446i	$0.293816\pi$
$278$		0			0
$279$	18.1061	+	5.31643i	1.08398	+	0.318286i
$280$		0			0
$281$	18.2204	−	11.7095i	1.08694	−	0.698533i	0.130788	−	0.991410i	$-0.458249\pi$
$281$	18.2204	−	11.7095i	1.08694	−	0.698533i	0.956150	+	0.292878i	$0.0946129\pi$
$282$		0			0
$283$	−1.90826	+	13.2722i	−0.113434	+	0.788952i	0.851102	+	0.525000i	$0.175935\pi$
$283$	−1.90826	+	13.2722i	−0.113434	+	0.788952i	−0.964536	+	0.263951i	$0.914974\pi$
$284$		0			0
$285$	1.01034	+	0.649308i	0.0598475	+	0.0384617i
$286$		0			0
$287$	−0.0372910	−	0.0816560i	−0.00220122	−	0.00482000i
$288$		0			0
$289$	0.393335	+	2.73570i	0.0231373	+	0.160924i
$290$		0			0
$291$	−1.60388	+	0.470942i	−0.0940211	+	0.0276071i
$292$		0			0
$293$	12.6430	−	14.5908i	0.738610	−	0.852401i	−0.254803	−	0.966993i	$-0.582011\pi$
$293$	12.6430	−	14.5908i	0.738610	−	0.852401i	0.993413	+	0.114592i	$0.0365561\pi$
$294$		0			0
$295$	−5.24499	−	6.05304i	−0.305375	−	0.352422i
$296$		0			0
$297$	2.29860	−	5.03323i	0.133378	−	0.292058i
$298$		0			0
$299$	−15.4883	+	3.30175i	−0.895713	+	0.190945i
$300$		0			0
$301$	−0.561859	+	1.23030i	−0.0323850	+	0.0709133i
$302$		0			0
$303$	2.04561	+	2.36075i	0.117517	+	0.135622i
$304$		0			0
$305$	−6.36846	+	7.34960i	−0.364657	+	0.420837i
$306$		0			0
$307$	−7.78252	+	2.28515i	−0.444172	+	0.130421i	−0.496168	−	0.868227i	$-0.665260\pi$
$307$	−7.78252	+	2.28515i	−0.444172	+	0.130421i	0.0519960	+	0.998647i	$0.483442\pi$
$308$		0			0
$309$	−0.430087	−	2.99132i	−0.0244668	−	0.170170i
$310$		0			0
$311$	−8.21679	−	17.9923i	−0.465931	−	1.02025i	−0.986095	−	0.166181i	$-0.946857\pi$
$311$	−8.21679	−	17.9923i	−0.465931	−	1.02025i	0.520164	−	0.854066i	$-0.325871\pi$
$312$		0			0
$313$	3.84528	+	2.47121i	0.217348	+	0.139681i	0.644785	−	0.764364i	$-0.276947\pi$
$313$	3.84528	+	2.47121i	0.217348	+	0.139681i	−0.427437	+	0.904045i	$0.640583\pi$
$314$		0			0
$315$	0.0496413	−	0.345263i	0.00279697	−	0.0194534i
$316$		0			0
$317$	−21.6520	+	13.9149i	−1.21610	+	0.781537i	−0.981668	−	0.190597i	$-0.938958\pi$
$317$	−21.6520	+	13.9149i	−1.21610	+	0.781537i	−0.234427	+	0.972134i	$0.575321\pi$
$318$		0			0
$319$	−25.9007	−	7.60514i	−1.45016	−	0.425806i
$320$		0			0
$321$	−1.40583			−0.0784658
$322$		0			0
$323$	25.6622			1.42788
$324$		0			0
$325$	−3.16835	−	0.930311i	−0.175748	−	0.0516044i
$326$		0			0
$327$	1.01228	−	0.650554i	0.0559793	−	0.0359757i
$328$		0			0
$329$	0.0396905	−	0.276054i	0.00218821	−	0.0152193i
$330$		0			0
$331$	−3.64043	−	2.33956i	−0.200096	−	0.128594i	0.436756	−	0.899580i	$-0.356127\pi$
$331$	−3.64043	−	2.33956i	−0.200096	−	0.128594i	−0.636852	+	0.770986i	$0.719764\pi$
$332$		0			0
$333$	11.5385	+	25.2658i	0.632305	+	1.38456i
$334$		0			0
$335$	−2.04163	−	14.1999i	−0.111546	−	0.775822i
$336$		0			0
$337$	−1.05771	+	0.310570i	−0.0576169	+	0.0169178i	−0.310414	−	0.950601i	$-0.600468\pi$
$337$	−1.05771	+	0.310570i	−0.0576169	+	0.0169178i	0.252797	+	0.967519i	$0.418649\pi$
$338$		0			0
$339$	−1.99695	+	2.30460i	−0.108459	+	0.125169i
$340$		0			0
$341$	21.8522	+	25.2188i	1.18337	+	1.36568i
$342$		0			0
$343$	0.682640	−	1.49477i	0.0368591	−	0.0807101i
$344$		0			0
$345$	−0.292637	−	0.794687i	−0.0157550	−	0.0427845i
$346$		0			0
$347$	3.80546	−	8.33280i	0.204288	−	0.447328i	−0.779562	−	0.626325i	$-0.784558\pi$
$347$	3.80546	−	8.33280i	0.204288	−	0.447328i	0.983850	+	0.178997i	$0.0572854\pi$
$348$		0			0
$349$	−15.1030	−	17.4298i	−0.808446	−	0.932997i	0.190366	−	0.981713i	$-0.439032\pi$
$349$	−15.1030	−	17.4298i	−0.808446	−	0.932997i	−0.998813	+	0.0487164i	$0.984487\pi$
$350$		0			0
$351$	2.27915	−	2.63028i	0.121652	−	0.140394i
$352$		0			0
$353$	−0.991998	+	0.291277i	−0.0527987	+	0.0155031i	−0.308025	−	0.951378i	$-0.599668\pi$
$353$	−0.991998	+	0.291277i	−0.0527987	+	0.0155031i	0.255227	+	0.966881i	$0.417850\pi$
$354$		0			0
$355$	0.424338	+	2.95134i	0.0225215	+	0.156641i
$356$		0			0
$357$	0.0325187	+	0.0712061i	0.00172107	+	0.00376862i
$358$		0			0
$359$	−4.52715	−	2.90942i	−0.238934	−	0.153553i	0.415695	−	0.909504i	$-0.363539\pi$
$359$	−4.52715	−	2.90942i	−0.238934	−	0.153553i	−0.654628	+	0.755951i	$0.727175\pi$
$360$		0			0
$361$	−3.87931	+	26.9812i	−0.204174	+	1.42006i
$362$		0			0
$363$	2.46014	−	1.58103i	0.129124	−	0.0829828i
$364$		0			0
$365$	9.00363	+	2.64371i	0.471272	+	0.138378i
$366$		0			0
$367$	33.1574			1.73080			0.865401	−	0.501080i	$-0.167064\pi$
$367$	33.1574			1.73080			0.865401	+	0.501080i	$0.167064\pi$
$368$		0			0
$369$	−2.26828			−0.118082
$370$		0			0
$371$	0.264679	+	0.0777167i	0.0137414	+	0.00403485i
$372$		0			0
$373$	0.929991	−	0.597669i	0.0481531	−	0.0309461i	−0.516343	−	0.856382i	$-0.672707\pi$
$373$	0.929991	−	0.597669i	0.0481531	−	0.0309461i	0.564496	+	0.825436i	$0.309071\pi$
$374$		0			0
$375$	0.0251302	−	0.174784i	0.00129772	−	0.00902581i
$376$		0			0
$377$	−14.2837	−	9.17957i	−0.735647	−	0.472772i
$378$		0			0
$379$	−4.17514	−	9.14228i	−0.214463	−	0.469607i	0.771573	−	0.636140i	$-0.219470\pi$
$379$	−4.17514	−	9.14228i	−0.214463	−	0.469607i	−0.986036	+	0.166533i	$0.946743\pi$
$380$		0			0
$381$	0.162276	+	1.12866i	0.00831368	+	0.0578229i
$382$		0			0
$383$	13.1113	−	3.84981i	0.669954	−	0.196716i	0.0709715	−	0.997478i	$-0.477390\pi$
$383$	13.1113	−	3.84981i	0.669954	−	0.196716i	0.598983	+	0.800762i	$0.295572\pi$
$384$		0			0
$385$	0.403930	−	0.466160i	0.0205862	−	0.0237577i
$386$		0			0
$387$	22.3804	+	25.8284i	1.13766	+	1.31293i
$388$		0			0
$389$	−2.20823	+	4.83536i	−0.111962	+	0.245162i	−0.957316	−	0.289045i	$-0.906662\pi$
$389$	−2.20823	+	4.83536i	−0.111962	+	0.245162i	0.845354	+	0.534207i	$0.179390\pi$
$390$		0			0
$391$	−14.4405	−	10.9042i	−0.730290	−	0.551451i
$392$		0			0
$393$	−0.597935	+	1.30929i	−0.0301618	+	0.0660451i
$394$		0			0
$395$	−2.30062	−	2.65506i	−0.115757	−	0.133590i
$396$		0			0
$397$	−15.0908	+	17.4157i	−0.757385	+	0.874069i	−0.995262	−	0.0972260i	$-0.969003\pi$
$397$	−15.0908	+	17.4157i	−0.757385	+	0.874069i	0.237877	+	0.971295i	$0.423548\pi$
$398$		0			0
$399$	−0.135392	+	0.0397547i	−0.00677808	+	0.00199022i
$400$		0			0
$401$	4.34593	+	30.2266i	0.217025	+	1.50944i	0.748935	+	0.662643i	$0.230565\pi$
$401$	4.34593	+	30.2266i	0.217025	+	1.50944i	−0.531910	+	0.846801i	$0.678525\pi$
$402$		0			0
$403$	8.71912	+	19.0922i	0.434330	+	0.951050i
$404$		0			0
$405$	−7.33602	−	4.71457i	−0.364530	−	0.234269i
$406$		0			0
$407$	−6.99006	+	48.6169i	−0.346484	+	2.40985i
$408$		0			0
$409$	15.3753	−	9.88108i	0.760257	−	0.488588i	−0.102171	−	0.994767i	$-0.532579\pi$
$409$	15.3753	−	9.88108i	0.760257	−	0.488588i	0.862428	+	0.506179i	$0.168943\pi$
$410$		0			0
$411$	−3.39840	−	0.997861i	−0.167631	−	0.0492209i
$412$		0			0
$413$	0.941034			0.0463053
$414$		0			0
$415$	4.75480			0.233404
$416$		0			0
$417$	−1.02223	−	0.300155i	−0.0500590	−	0.0146986i
$418$		0			0
$419$	2.23972	−	1.43938i	0.109417	−	0.0703183i	−0.484788	−	0.874632i	$-0.661103\pi$
$419$	2.23972	−	1.43938i	0.109417	−	0.0703183i	0.594205	+	0.804314i	$0.297467\pi$
$420$		0			0
$421$	−4.53412	+	31.5355i	−0.220980	+	1.53695i	0.513365	+	0.858170i	$0.328399\pi$
$421$	−4.53412	+	31.5355i	−0.220980	+	1.53695i	−0.734345	+	0.678776i	$0.762511\pi$
$422$		0			0
$423$	−5.92840	−	3.80995i	−0.288249	−	0.185246i
$424$		0			0
$425$	−1.56740	−	3.43212i	−0.0760299	−	0.166482i
$426$		0			0
$427$	−0.162609	−	1.13097i	−0.00786922	−	0.0547316i
$428$		0			0
$429$	2.93715	−	0.862424i	0.141807	−	0.0416382i
$430$		0			0
$431$	5.31845	−	6.13782i	0.256181	−	0.295648i	−0.613061	−	0.790036i	$-0.710062\pi$
$431$	5.31845	−	6.13782i	0.256181	−	0.295648i	0.869242	+	0.494387i	$0.164607\pi$
$432$		0			0
$433$	3.48042	+	4.01662i	0.167258	+	0.193026i	0.833191	−	0.552986i	$-0.186512\pi$
$433$	3.48042	+	4.01662i	0.167258	+	0.193026i	−0.665933	+	0.746012i	$0.731966\pi$
$434$		0			0
$435$	0.377181	−	0.825911i	0.0180844	−	0.0395994i
$436$		0			0
$437$	23.1605	−	22.9683i	1.10792	−	1.09872i
$438$		0			0
$439$	2.52211	−	5.52266i	0.120374	−	0.263582i	−0.839847	−	0.542823i	$-0.817356\pi$
$439$	2.52211	−	5.52266i	0.120374	−	0.263582i	0.960221	+	0.279241i	$0.0900828\pi$
$440$		0			0
$441$	−13.5823	−	15.6748i	−0.646776	−	0.746420i
$442$		0			0
$443$	−19.7240	+	22.7627i	−0.937115	+	1.08149i	0.0594133	+	0.998233i	$0.481077\pi$
$443$	−19.7240	+	22.7627i	−0.937115	+	1.08149i	−0.996528	+	0.0832549i	$0.973468\pi$
$444$		0			0
$445$	−12.5479	+	3.68441i	−0.594830	+	0.174658i
$446$		0			0
$447$	−0.409753	−	2.84989i	−0.0193807	−	0.134795i
$448$		0			0
$449$	−0.859170	−	1.88132i	−0.0405467	−	0.0887850i	0.888275	−	0.459313i	$-0.151904\pi$
$449$	−0.859170	−	1.88132i	−0.0405467	−	0.0887850i	−0.928821	+	0.370528i	$0.879177\pi$
$450$		0			0
$451$	−3.37433	−	2.16855i	−0.158891	−	0.102113i
$452$		0			0
$453$	0.152029	−	1.05739i	0.00714296	−	0.0496804i
$454$		0			0
$455$	0.326383	−	0.209754i	0.0153011	−	0.00983340i
$456$		0			0
$457$	−7.82218	−	2.29680i	−0.365906	−	0.107440i	0.0936105	−	0.995609i	$-0.470159\pi$
$457$	−7.82218	−	2.29680i	−0.365906	−	0.107440i	−0.459517	+	0.888169i	$0.651977\pi$
$458$		0			0
$459$	3.97677			0.185619
$460$		0			0
$461$	6.04565			0.281574			0.140787	−	0.990040i	$-0.455037\pi$
$461$	6.04565			0.281574			0.140787	+	0.990040i	$0.455037\pi$
$462$		0			0
$463$	13.4408	+	3.94657i	0.624647	+	0.183413i	0.578712	−	0.815532i	$-0.303555\pi$
$463$	13.4408	+	3.94657i	0.624647	+	0.183413i	0.0459341	+	0.998944i	$0.485374\pi$
$464$		0			0
$465$	−0.944216	+	0.606811i	−0.0437870	+	0.0281402i
$466$		0			0
$467$	−1.05011	+	7.30366i	−0.0485932	+	0.337973i	0.950993	+	0.309212i	$0.100065\pi$
$467$	−1.05011	+	7.30366i	−0.0485932	+	0.337973i	−0.999586	+	0.0287611i	$0.990844\pi$
$468$		0			0
$469$	1.41796	+	0.911268i	0.0654753	+	0.0420784i
$470$		0			0
$471$	0.314644	+	0.688974i	0.0144980	+	0.0317462i
$472$		0			0
$473$	8.60070	+	59.8192i	0.395460	+	2.75049i
$474$		0			0
$475$	6.52587	−	1.91617i	0.299427	−	0.0879198i
$476$		0			0
$477$	4.56457	−	5.26780i	0.208997	−	0.241196i
$478$		0			0
$479$	13.9830	+	16.1372i	0.638900	+	0.737330i	0.979180	−	0.202995i	$-0.0650674\pi$
$479$	13.9830	+	16.1372i	0.638900	+	0.737330i	−0.340280	+	0.940324i	$0.610522\pi$
$480$		0			0
$481$	−12.8338	+	28.1022i	−0.585172	+	1.28135i
$482$		0			0
$483$	0.0930798	+	0.0351595i	0.00423528	+	0.00159981i
$484$		0			0
$485$	−3.93249	+	8.61095i	−0.178565	+	0.391003i
$486$		0			0
$487$	1.55766	+	1.79764i	0.0705844	+	0.0814588i	0.789943	−	0.613180i	$-0.210110\pi$
$487$	1.55766	+	1.79764i	0.0705844	+	0.0814588i	−0.719359	+	0.694638i	$0.755564\pi$
$488$		0			0
$489$	−2.09174	+	2.41399i	−0.0945917	+	0.109165i
$490$		0			0
$491$	14.0519	−	4.12600i	0.634152	−	0.186204i	0.0511712	−	0.998690i	$-0.483705\pi$
$491$	14.0519	−	4.12600i	0.634152	−	0.186204i	0.582980	+	0.812486i	$0.301886\pi$
$492$		0			0
$493$	−2.76102	−	19.2033i	−0.124350	−	0.864873i
$494$		0			0
$495$	−6.47461	−	14.1774i	−0.291012	−	0.637228i
$496$		0			0
$497$	−0.294712	−	0.189400i	−0.0132197	−	0.00849576i
$498$		0			0
$499$	3.30741	−	23.0035i	0.148060	−	1.02978i	−0.771331	−	0.636434i	$-0.780409\pi$
$499$	3.30741	−	23.0035i	0.148060	−	1.02978i	0.919391	−	0.393345i	$-0.128682\pi$
$500$		0			0
$501$	2.98412	−	1.91778i	0.133321	−	0.0856800i
$502$		0			0
$503$	8.49930	+	2.49562i	0.378965	+	0.111274i	0.465667	−	0.884960i	$-0.345815\pi$
$503$	8.49930	+	2.49562i	0.378965	+	0.111274i	−0.0867017	+	0.996234i	$0.527633\pi$
$504$		0			0
$505$	17.6900			0.787195
$506$		0			0
$507$	−0.370131			−0.0164381
$508$		0			0
$509$	−24.0052	−	7.04855i	−1.06401	−	0.312422i	−0.297545	−	0.954708i	$-0.596168\pi$
$509$	−24.0052	−	7.04855i	−1.06401	−	0.312422i	−0.766465	+	0.642286i	$0.777986\pi$
$510$		0			0
$511$	−0.927497	+	0.596066i	−0.0410301	+	0.0263684i
$512$		0			0
$513$	−1.02019	+	7.09556i	−0.0450424	+	0.313277i
$514$		0			0
$515$	−14.3975	−	9.25274i	−0.634431	−	0.407724i
$516$		0			0
$517$	−5.17675	−	11.3355i	−0.227673	−	0.498535i
$518$		0			0
$519$	0.370733	+	2.57851i	0.0162734	+	0.113184i
$520$		0			0
$521$	19.0192	−	5.58453i	0.833244	−	0.244663i	0.162834	−	0.986653i	$-0.447936\pi$
$521$	19.0192	−	5.58453i	0.833244	−	0.244663i	0.670410	+	0.741991i	$0.266118\pi$
$522$		0			0
$523$	−20.6746	+	23.8598i	−0.904039	+	1.04332i	0.0948166	+	0.995495i	$0.469774\pi$
$523$	−20.6746	+	23.8598i	−0.904039	+	1.04332i	−0.998856	+	0.0478222i	$0.984772\pi$
$524$		0			0
$525$	0.0135864	+	0.0156795i	0.000592958	+	0.000684310i
$526$		0			0
$527$	−9.96272	+	21.8153i	−0.433983	+	0.950290i
$528$		0			0
$529$	−22.7924	+	3.08341i	−0.990973	+	0.134061i
$530$		0			0
$531$	9.87783	−	21.6294i	0.428661	−	0.938637i
$532$		0			0
$533$	−1.65216	−	1.90670i	−0.0715631	−	0.0825882i
$534$		0			0
$535$	−5.21359	+	6.01681i	−0.225403	+	0.260129i
$536$		0			0
$537$	−0.339211	+	0.0996013i	−0.0146380	+	0.00429811i
$538$		0			0
$539$	−5.21962	−	36.3032i	−0.224825	−	1.56369i
$540$		0			0
$541$	7.03120	+	15.3962i	0.302295	+	0.661933i	0.998432	−	0.0559753i	$-0.0178268\pi$
$541$	7.03120	+	15.3962i	0.302295	+	0.661933i	−0.696137	+	0.717909i	$0.745100\pi$
$542$		0			0
$543$	0.218756	+	0.140586i	0.00938772	+	0.00603312i
$544$		0			0
$545$	0.969794	−	6.74507i	0.0415414	−	0.288927i
$546$		0			0
$547$	31.1173	−	19.9979i	1.33048	−	0.855048i	0.334309	−	0.942464i	$-0.391497\pi$
$547$	31.1173	−	19.9979i	1.33048	−	0.855048i	0.996172	+	0.0874153i	$0.0278607\pi$
$548$		0			0
$549$	−27.7020	−	8.13404i	−1.18229	−	0.347152i
$550$		0			0
$551$	34.9719			1.48985
$552$		0			0
$553$	0.412768			0.0175527
$554$		0			0
$555$	−1.58515	−	0.465441i	−0.0672858	−	0.0197569i
$556$		0			0
$557$	−16.3303	+	10.4948i	−0.691935	+	0.444680i	−0.838773	−	0.544481i	$-0.816727\pi$
$557$	−16.3303	+	10.4948i	−0.691935	+	0.444680i	0.146838	+	0.989161i	$0.453090\pi$
$558$		0			0
$559$	−5.40975	+	37.6256i	−0.228808	+	1.59139i
$560$		0			0
$561$	2.94250	+	1.89103i	0.124232	+	0.0798393i
$562$		0			0
$563$	0.781369	+	1.71096i	0.0329308	+	0.0721083i	0.925383	−	0.379034i	$-0.123744\pi$
$563$	0.781369	+	1.71096i	0.0329308	+	0.0721083i	−0.892452	+	0.451143i	$0.851017\pi$
$564$		0			0
$565$	2.45767	+	17.0934i	0.103395	+	0.719127i
$566$		0			0
$567$	0.983071	−	0.288656i	0.0412851	−	0.0121224i
$568$		0			0
$569$	17.3822	−	20.0602i	0.728701	−	0.840966i	−0.263624	−	0.964626i	$-0.584918\pi$
$569$	17.3822	−	20.0602i	0.728701	−	0.840966i	0.992325	+	0.123660i	$0.0394632\pi$
$570$		0			0
$571$	12.1394	+	14.0096i	0.508016	+	0.586282i	0.950590	−	0.310450i	$-0.100480\pi$
$571$	12.1394	+	14.0096i	0.508016	+	0.586282i	−0.442573	+	0.896732i	$0.645934\pi$
$572$		0			0
$573$	−0.121698	+	0.266481i	−0.00508401	+	0.0111324i
$574$		0			0
$575$	−4.48643	−	1.69468i	−0.187097	−	0.0706730i
$576$		0			0
$577$	5.58791	−	12.2358i	0.232628	−	0.509384i	−0.756934	−	0.653491i	$-0.773304\pi$
$577$	5.58791	−	12.2358i	0.232628	−	0.509384i	0.989562	+	0.144107i	$0.0460310\pi$
$578$		0			0
$579$	−0.613509	−	0.708027i	−0.0254966	−	0.0294246i
$580$		0			0
$581$	−0.365840	+	0.422202i	−0.0151776	+	0.0175159i
$582$		0			0
$583$	11.8265	−	3.47258i	0.489804	−	0.143820i
$584$		0			0
$585$	−1.39516	−	9.70357i	−0.0576829	−	0.401193i
$586$		0			0
$587$	−5.56524	−	12.1862i	−0.229702	−	0.502977i	0.759325	−	0.650711i	$-0.225529\pi$
$587$	−5.56524	−	12.1862i	−0.229702	−	0.502977i	−0.989027	+	0.147734i	$0.952802\pi$
$588$		0			0
$589$	−36.3683	−	23.3725i	−1.49853	−	0.963046i
$590$		0			0
$591$	−0.491004	+	3.41501i	−0.0201972	+	0.140475i
$592$		0			0
$593$	3.87787	−	2.49216i	0.159245	−	0.102341i	−0.458591	−	0.888647i	$-0.651646\pi$
$593$	3.87787	−	2.49216i	0.159245	−	0.102341i	0.617836	+	0.786307i	$0.288009\pi$
$594$		0			0
$595$	0.425351	+	0.124894i	0.0174377	+	0.00512017i
$596$		0			0
$597$	−3.08680			−0.126334
$598$		0			0
$599$	−24.6845			−1.00858			−0.504292	−	0.863533i	$-0.668246\pi$
$599$	−24.6845			−1.00858			−0.504292	+	0.863533i	$0.668246\pi$
$600$		0			0
$601$	20.8714	+	6.12839i	0.851361	+	0.249982i	0.678169	−	0.734906i	$-0.262774\pi$
$601$	20.8714	+	6.12839i	0.851361	+	0.249982i	0.173192	+	0.984888i	$0.444592\pi$
$602$		0			0
$603$	35.8293	−	23.0261i	1.45908	−	0.937695i
$604$		0			0
$605$	2.35688	−	16.3925i	0.0958208	−	0.666449i
$606$		0			0
$607$	−29.3822	−	18.8828i	−1.19259	−	0.766429i	−0.214928	−	0.976630i	$-0.568952\pi$
$607$	−29.3822	−	18.8828i	−1.19259	−	0.766429i	−0.977658	+	0.210201i	$0.932588\pi$
$608$		0			0
$609$	0.0443159	+	0.0970382i	0.00179577	+	0.00393219i
$610$		0			0
$611$	−1.11550	−	7.75845i	−0.0451282	−	0.313873i
$612$		0			0
$613$	43.5160	−	12.7774i	1.75759	−	0.516076i	0.765706	−	0.643191i	$-0.222390\pi$
$613$	43.5160	−	12.7774i	1.75759	−	0.516076i	0.991888	+	0.127115i	$0.0405718\pi$
$614$		0			0
$615$	0.0883500	−	0.101961i	0.00356262	−	0.00411148i
$616$		0			0
$617$	1.70615	+	1.96901i	0.0686872	+	0.0792693i	0.789053	−	0.614325i	$-0.210572\pi$
$617$	1.70615	+	1.96901i	0.0686872	+	0.0792693i	−0.720366	+	0.693594i	$0.756026\pi$
$618$		0			0
$619$	10.9853	−	24.0545i	0.441538	−	0.966833i	−0.549776	−	0.835312i	$-0.685287\pi$
$619$	10.9853	−	24.0545i	0.441538	−	0.966833i	0.991313	−	0.131520i	$-0.0419859\pi$
$620$		0			0
$621$	3.58909	−	3.55930i	0.144025	−	0.142830i
$622$		0			0
$623$	0.638297	−	1.39768i	0.0255728	−	0.0559967i
$624$		0			0
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$		0			0
$627$	−4.12894	+	4.76505i	−0.164894	+	0.190298i
$628$		0			0
$629$	−33.8705	+	9.94527i	−1.35050	+	0.396544i
$630$		0			0
$631$	−0.255319	−	1.77578i	−0.0101641	−	0.0706927i	0.984108	−	0.177570i	$-0.0568237\pi$
$631$	−0.255319	−	1.77578i	−0.0101641	−	0.0706927i	−0.994272	+	0.106878i	$0.965915\pi$
$632$		0			0
$633$	−0.774999	−	1.69701i	−0.0308035	−	0.0674502i
$634$		0			0
$635$	5.43234	+	3.49116i	0.215576	+	0.138542i
$636$		0			0
$637$	3.28308	−	22.8343i	0.130081	−	0.904730i
$638$		0			0
$639$	−7.44685	+	4.78580i	−0.294593	+	0.189323i
$640$		0			0
$641$	−37.5220	−	11.0175i	−1.48203	−	0.435164i	−0.562043	−	0.827108i	$-0.689984\pi$
$641$	−37.5220	−	11.0175i	−1.48203	−	0.435164i	−0.919989	+	0.391945i	$0.871803\pi$
$642$		0			0
$643$	2.38873			0.0942023			0.0471011	−	0.998890i	$-0.485002\pi$
$643$	2.38873			0.0942023			0.0471011	+	0.998890i	$0.485002\pi$
$644$		0			0
$645$	−2.03273			−0.0800388
$646$		0			0
$647$	−22.0657	−	6.47909i	−0.867494	−	0.254719i	−0.182445	−	0.983216i	$-0.558401\pi$
$647$	−22.0657	−	6.47909i	−0.867494	−	0.254719i	−0.685049	+	0.728497i	$0.740219\pi$
$648$		0			0
$649$	35.3729	−	22.7328i	1.38851	−	0.892339i
$650$		0			0
$651$	0.0187674	−	0.130530i	0.000735552	−	0.00511588i
$652$		0			0
$653$	−8.18714	−	5.26156i	−0.320388	−	0.205901i	0.370555	−	0.928811i	$-0.379168\pi$
$653$	−8.18714	−	5.26156i	−0.320388	−	0.205901i	−0.690942	+	0.722910i	$0.742804\pi$
$654$		0			0
$655$	3.38617	+	7.41468i	0.132309	+	0.289715i
$656$		0			0
$657$	3.96470	+	27.5751i	0.154678	+	1.07581i
$658$		0			0
$659$	−29.4438	+	8.64548i	−1.14697	+	0.336780i	−0.799356	−	0.600858i	$-0.794826\pi$
$659$	−29.4438	+	8.64548i	−1.14697	+	0.336780i	−0.347612	+	0.937638i	$0.613007\pi$
$660$		0			0
$661$	−0.954163	+	1.10116i	−0.0371126	+	0.0428303i	−0.774002	−	0.633183i	$-0.781748\pi$
$661$	−0.954163	+	1.10116i	−0.0371126	+	0.0428303i	0.736890	+	0.676013i	$0.236294\pi$
$662$		0			0
$663$	1.44073	+	1.66269i	0.0559532	+	0.0645734i
$664$		0			0
$665$	−0.331962	+	0.726895i	−0.0128729	+	0.0281878i
$666$		0			0
$667$	−19.6793	−	14.8601i	−0.761985	−	0.575385i
$668$		0			0
$669$	−0.581439	+	1.27317i	−0.0224797	+	0.0492237i
$670$		0			0
$671$	−33.4335	−	38.5844i	−1.29069	−	1.48953i
$672$		0			0
$673$	−12.2792	+	14.1710i	−0.473328	+	0.546250i	−0.941334	−	0.337475i	$-0.890427\pi$
$673$	−12.2792	+	14.1710i	−0.473328	+	0.546250i	0.468006	+	0.883725i	$0.344973\pi$
$674$		0			0
$675$	1.01129	−	0.296941i	0.0389245	−	0.0114293i
$676$		0			0
$677$	5.04827	+	35.1115i	0.194021	+	1.34944i	0.821232	+	0.570594i	$0.193287\pi$
$677$	5.04827	+	35.1115i	0.194021	+	1.34944i	−0.627212	+	0.778849i	$0.715804\pi$
$678$		0			0
$679$	−0.462037	−	1.01172i	−0.0177314	−	0.0388263i
$680$		0			0
$681$	−1.63531	−	1.05095i	−0.0626651	−	0.0402724i
$682$		0			0
$683$	3.16608	−	22.0206i	0.121147	−	0.842594i	−0.835114	−	0.550077i	$-0.814598\pi$
$683$	3.16608	−	22.0206i	0.121147	−	0.842594i	0.956260	−	0.292517i	$-0.0944927\pi$
$684$		0			0
$685$	−16.8739	+	10.8442i	−0.644718	+	0.414335i
$686$		0			0
$687$	4.88273	+	1.43370i	0.186288	+	0.0546990i
$688$		0			0
$689$	7.75280			0.295358
$690$		0			0
$691$	18.4237			0.700869			0.350434	−	0.936587i	$-0.386034\pi$
$691$	18.4237			0.700869			0.350434	+	0.936587i	$0.386034\pi$
$692$		0			0
$693$	1.75705	+	0.515915i	0.0667446	+	0.0195980i
$694$		0			0
$695$	−5.07563	+	3.26191i	−0.192530	+	0.123731i
$696$		0			0
$697$	0.410260	−	2.85342i	0.0155397	−	0.108081i
$698$		0			0
$699$	−0.524533	−	0.337097i	−0.0198397	−	0.0127502i
$700$		0			0
$701$	0.228329	+	0.499972i	0.00862389	+	0.0188837i	0.913895	−	0.405951i	$-0.133060\pi$
$701$	0.228329	+	0.499972i	0.00862389	+	0.0188837i	−0.905271	+	0.424834i	$0.860332\pi$
$702$		0			0
$703$	−9.05586	−	62.9849i	−0.341548	−	2.37552i
$704$		0			0
$705$	0.402174	−	0.118089i	0.0151467	−	0.00444749i
$706$		0			0
$707$	−1.36109	+	1.57078i	−0.0511890	+	0.0590753i
$708$		0			0
$709$	−0.809348	−	0.934037i	−0.0303957	−	0.0350785i	0.740348	−	0.672224i	$-0.234661\pi$
$709$	−0.809348	−	0.934037i	−0.0303957	−	0.0350785i	−0.770744	+	0.637145i	$0.780115\pi$
$710$		0			0
$711$	4.33273	−	9.48736i	0.162490	−	0.355804i
$712$		0			0
$713$	10.5337	+	28.6055i	0.394492	+	1.07129i
$714$		0			0
$715$	7.20147	−	15.7690i	0.269320	−	0.589728i
$716$		0			0
$717$	2.20574	+	2.54556i	0.0823747	+	0.0950655i
$718$		0			0
$719$	1.53187	−	1.76787i	0.0571290	−	0.0659304i	−0.726466	−	0.687203i	$-0.758838\pi$
$719$	1.53187	−	1.76787i	0.0571290	−	0.0659304i	0.783595	+	0.621272i	$0.213384\pi$
$720$		0			0
$721$	1.92936	−	0.566511i	0.0718531	−	0.0210980i
$722$		0			0
$723$	−0.357448	−	2.48611i	−0.0132936	−	0.0924593i
$724$		0			0
$725$	−2.13602	−	4.67722i	−0.0793296	−	0.173708i
$726$		0			0
$727$	8.06574	+	5.18353i	0.299142	+	0.192247i	0.681598	−	0.731727i	$-0.261285\pi$
$727$	8.06574	+	5.18353i	0.299142	+	0.192247i	−0.382456	+	0.923974i	$0.624922\pi$
$728$		0			0
$729$	3.60495	−	25.0729i	0.133517	−	0.928628i
$730$		0			0
$731$	−36.5392	+	23.4823i	−1.35145	+	0.868525i
$732$		0			0
$733$	20.9805	+	6.16042i	0.774931	+	0.227540i	0.645205	−	0.764010i	$-0.276772\pi$
$733$	20.9805	+	6.16042i	0.774931	+	0.227540i	0.129726	+	0.991550i	$0.458590\pi$
$734$		0			0
$735$	1.23363			0.0455032
$736$		0			0
$737$	75.3139			2.77422
$738$		0			0
$739$	37.4526	+	10.9971i	1.37772	+	0.404534i	0.884974	−	0.465641i	$-0.154176\pi$
$739$	37.4526	+	10.9971i	1.37772	+	0.404534i	0.492743	+	0.870175i	$0.335994\pi$
$740$		0			0
$741$	−3.33626	+	2.14408i	−0.122560	+	0.0787648i
$742$		0			0
$743$	−7.36942	+	51.2555i	−0.270358	+	1.88038i	0.174318	+	0.984689i	$0.444228\pi$
$743$	−7.36942	+	51.2555i	−0.270358	+	1.88038i	−0.444676	+	0.895692i	$0.646681\pi$
$744$		0			0
$745$	−13.7168	−	8.81527i	−0.502546	−	0.322967i
$746$		0			0
$747$	5.86406	+	12.8405i	0.214555	+	0.469809i
$748$		0			0
$749$	−0.133121	−	0.925880i	−0.00486415	−	0.0338309i
$750$		0			0
$751$	−19.6100	+	5.75801i	−0.715579	+	0.210113i	−0.619202	−	0.785232i	$-0.712544\pi$
$751$	−19.6100	+	5.75801i	−0.715579	+	0.210113i	−0.0963770	+	0.995345i	$0.530725\pi$
$752$		0			0
$753$	−0.548878	+	0.633439i	−0.0200022	+	0.0230838i
$754$		0			0
$755$	−3.96170	−	4.57204i	−0.144181	−	0.166394i
$756$		0			0
$757$	19.9340	−	43.6494i	0.724513	−	1.58646i	−0.0829555	−	0.996553i	$-0.526436\pi$
$757$	19.9340	−	43.6494i	0.724513	−	1.58646i	0.807469	−	0.589910i	$-0.200837\pi$
$758$		0			0
$759$	4.34817	−	0.926928i	0.157828	−	0.0336453i
$760$		0			0
$761$	7.45300	−	16.3198i	0.270171	−	0.591592i	−0.725109	−	0.688634i	$-0.758211\pi$
$761$	7.45300	−	16.3198i	0.270171	−	0.591592i	0.995280	+	0.0970419i	$0.0309381\pi$
$762$		0			0
$763$	0.524310	+	0.605086i	0.0189813	+	0.0219056i
$764$		0			0
$765$	7.33549	−	8.46561i	0.265215	−	0.306075i
$766$		0			0
$767$	25.3763	−	7.45116i	0.916285	−	0.269046i
$768$		0			0
$769$	−3.25984	−	22.6727i	−0.117553	−	0.817597i	−0.960236	−	0.279188i	$-0.909935\pi$
$769$	−3.25984	−	22.6727i	−0.117553	−	0.817597i	0.842684	−	0.538409i	$-0.180974\pi$
$770$		0			0
$771$	1.15861	+	2.53699i	0.0417262	+	0.0913676i
$772$		0			0
$773$	−36.7847	−	23.6401i	−1.32305	−	0.850275i	−0.327535	−	0.944839i	$-0.606218\pi$
$773$	−36.7847	−	23.6401i	−1.32305	−	0.850275i	−0.995519	+	0.0945639i	$0.969854\pi$
$774$		0			0
$775$	−0.904585	+	6.29153i	−0.0324937	+	0.225998i
$776$		0			0
$777$	0.163292	−	0.104941i	0.00585806	−	0.00376475i
$778$		0			0
$779$	4.98599	+	1.46402i	0.178641	+	0.0524539i
$780$		0			0
$781$	−15.6534			−0.560124
$782$		0			0
$783$	5.41946			0.193676
$784$		0			0
$785$	4.11561	+	1.20845i	0.146892	+	0.0431315i
$786$		0			0
$787$	−42.4114	+	27.2562i	−1.51180	+	0.971577i	−0.518621	+	0.855004i	$0.673554\pi$
$787$	−42.4114	+	27.2562i	−1.51180	+	0.971577i	−0.993182	+	0.116573i	$0.962809\pi$
$788$		0			0
$789$	−0.181118	+	1.25970i	−0.00644796	+	0.0448465i
$790$		0			0
$791$	−1.70690	−	1.09696i	−0.0606905	−	0.0390034i
$792$		0			0
$793$	−13.3401	−	29.2107i	−0.473720	−	1.03730i
$794$		0			0
$795$	0.0590015	+	0.410364i	0.00209257	+	0.0145541i
$796$		0			0
$797$	17.6717	−	5.18887i	0.625962	−	0.183799i	0.0466587	−	0.998911i	$-0.485143\pi$
$797$	17.6717	−	5.18887i	0.625962	−	0.183799i	0.579304	+	0.815112i	$0.303325\pi$
$798$		0			0
$799$	5.86506	−	6.76864i	0.207491	−	0.239457i
$800$		0			0
$801$	−25.4252	−	29.3422i	−0.898354	−	1.03676i
$802$		0			0
$803$	−20.4647	+	44.8115i	−0.722185	+	1.58136i
$804$		0			0
$805$	0.495670	−	0.267981i	0.0174701	−	0.00944509i
$806$		0			0
$807$	0.785143	−	1.71922i	0.0276383	−	0.0605195i
$808$		0			0
$809$	11.2080	+	12.9347i	0.394051	+	0.454759i	0.917758	−	0.397139i	$-0.129997\pi$
$809$	11.2080	+	12.9347i	0.394051	+	0.454759i	−0.523707	+	0.851898i	$0.675452\pi$
$810$		0			0
$811$	6.58161	−	7.59559i	0.231112	−	0.266717i	−0.628335	−	0.777943i	$-0.716263\pi$
$811$	6.58161	−	7.59559i	0.231112	−	0.266717i	0.859446	+	0.511226i	$0.170809\pi$
$812$		0			0
$813$	−3.50049	+	1.02784i	−0.122767	+	0.0360478i
$814$		0			0
$815$	2.57433	+	17.9048i	0.0901747	+	0.627179i
$816$		0			0
$817$	−32.5248	−	71.2193i	−1.13790	−	2.49165i
$818$		0			0
$819$	0.968972	+	0.622721i	0.0338586	+	0.0217596i
$820$		0			0
$821$	−1.83200	+	12.7419i	−0.0639373	+	0.444694i	0.932556	+	0.361025i	$0.117573\pi$
$821$	−1.83200	+	12.7419i	−0.0639373	+	0.444694i	−0.996494	+	0.0836692i	$0.973336\pi$
$822$		0			0
$823$	−26.8518	+	17.2566i	−0.935995	+	0.601527i	−0.917257	−	0.398297i	$-0.869601\pi$
$823$	−26.8518	+	17.2566i	−0.935995	+	0.601527i	−0.0187385	+	0.999824i	$0.505965\pi$
$824$		0			0
$825$	0.889477	+	0.261174i	0.0309676	+	0.00909291i
$826$		0			0
$827$	−20.7398			−0.721195			−0.360598	−	0.932721i	$-0.617427\pi$
$827$	−20.7398			−0.721195			−0.360598	+	0.932721i	$0.617427\pi$
$828$		0			0
$829$	44.7490			1.55420			0.777099	−	0.629378i	$-0.216690\pi$
$829$	44.7490			1.55420			0.777099	+	0.629378i	$0.216690\pi$
$830$		0			0
$831$	−3.40295	−	0.999195i	−0.118047	−	0.0346617i
$832$		0			0
$833$	22.1750	−	14.2510i	0.768319	−	0.493769i
$834$		0			0
$835$	2.85887	−	19.8839i	0.0989353	−	0.688110i
$836$		0			0
$837$	−5.63585	−	3.62194i	−0.194804	−	0.125193i
$838$		0			0
$839$	8.29463	+	18.1627i	0.286363	+	0.627047i	0.997074	−	0.0764367i	$-0.0243543\pi$
$839$	8.29463	+	18.1627i	0.286363	+	0.627047i	−0.710712	+	0.703483i	$0.751627\pi$
$840$		0			0
$841$	0.364473	+	2.53496i	0.0125680	+	0.0874125i
$842$		0			0
$843$	−3.66959	+	1.07749i	−0.126387	+	0.0371107i
$844$		0			0
$845$	−1.37265	+	1.58412i	−0.0472206	+	0.0544955i
$846$		0			0
$847$	1.27422	+	1.47053i	0.0437829	+	0.0505281i
$848$		0			0
$849$	0.983590	−	2.15376i	0.0337567	−	0.0739169i
$850$		0			0
$851$	−21.6673	+	39.2907i	−0.742747	+	1.34687i
$852$		0			0
$853$	11.4674	−	25.1100i	0.392635	−	0.859751i	−0.605329	−	0.795975i	$-0.706958\pi$
$853$	11.4674	−	25.1100i	0.392635	−	0.859751i	0.997964	−	0.0637758i	$-0.0203143\pi$
$854$		0			0
$855$	13.2230	+	15.2601i	0.452216	+	0.521885i
$856$		0			0
$857$	−21.7962	+	25.1541i	−0.744542	+	0.859248i	−0.994027	−	0.109131i	$-0.965193\pi$
$857$	−21.7962	+	25.1541i	−0.744542	+	0.859248i	0.249485	+	0.968379i	$0.419739\pi$
$858$		0			0
$859$	−32.4888	+	9.53959i	−1.10851	+	0.325486i	−0.784226	−	0.620475i	$-0.786940\pi$
$859$	−32.4888	+	9.53959i	−1.10851	+	0.325486i	−0.324279	+	0.945961i	$0.605122\pi$
$860$		0			0
$861$	0.00225589	+	0.0156900i	7.68805e−5	+	0.000534715i
$862$		0			0
$863$	−0.432805	−	0.947711i	−0.0147328	−	0.0322604i	0.902123	−	0.431480i	$-0.142008\pi$
$863$	−0.432805	−	0.947711i	−0.0147328	−	0.0322604i	−0.916855	+	0.399219i	$0.869281\pi$
$864$		0			0
$865$	12.4106	+	7.97582i	0.421973	+	0.271186i
$866$		0			0
$867$	0.0694556	−	0.483074i	0.00235884	−	0.0164061i
$868$		0			0
$869$	15.5157	−	9.97132i	0.526333	−	0.338254i
$870$		0			0
$871$	45.4528	+	13.3461i	1.54011	+	0.452217i
$872$		0			0
$873$	−28.1040			−0.951178
$874$		0			0
$875$	0.117492			0.00397197
$876$		0			0
$877$	−24.0396	−	7.05866i	−0.811760	−	0.238354i	−0.150596	−	0.988595i	$-0.548119\pi$
$877$	−24.0396	−	7.05866i	−0.811760	−	0.238354i	−0.661164	+	0.750241i	$0.729937\pi$
$878$		0			0
$879$	−2.86795	+	1.84312i	−0.0967336	+	0.0621669i
$880$		0			0
$881$	3.25896	−	22.6665i	0.109797	−	0.763655i	−0.858312	−	0.513128i	$-0.828487\pi$
$881$	3.25896	−	22.6665i	0.109797	−	0.763655i	0.968109	−	0.250528i	$-0.0806041\pi$
$882$		0			0
$883$	−3.87205	−	2.48841i	−0.130305	−	0.0837418i	0.473865	−	0.880598i	$-0.342859\pi$
$883$	−3.87205	−	2.48841i	−0.130305	−	0.0837418i	−0.604169	+	0.796856i	$0.706495\pi$
$884$		0			0
$885$	0.587520	+	1.28649i	0.0197493	+	0.0432449i
$886$		0			0
$887$	3.77305	+	26.2421i	0.126687	+	0.881125i	0.949713	+	0.313122i	$0.101375\pi$
$887$	3.77305	+	26.2421i	0.126687	+	0.881125i	−0.823026	+	0.568003i	$0.807716\pi$
$888$		0			0
$889$	−0.727967	+	0.213750i	−0.0244152	+	0.00716896i
$890$		0			0
$891$	29.9799	−	34.5987i	1.00436	−	1.15910i
$892$		0			0
$893$	10.5724	+	12.2012i	0.353791	+	0.408297i
$894$		0			0
$895$	−0.831697	+	1.82116i	−0.0278006	+	0.0608747i
$896$		0			0
$897$	2.78842	+	0.211114i	0.0931028	+	0.00704888i
$898$		0			0
$899$	−13.5770	+	29.7295i	−0.452818	+	0.991534i
$900$		0			0
$901$	5.80113	+	6.69487i	0.193264	+	0.223038i
$902$		0			0
$903$	0.156401	−	0.180496i	0.00520470	−	0.00600654i
$904$		0			0
$905$	1.41296	−	0.414883i	0.0469684	−	0.0137912i
$906$		0			0
$907$	5.61868	+	39.0788i	0.186565	+	1.29759i	0.840820	+	0.541315i	$0.182073\pi$
$907$	5.61868	+	39.0788i	0.186565	+	1.29759i	−0.654255	+	0.756274i	$0.727018\pi$
$908$		0			0
$909$	21.8169	+	47.7724i	0.723622	+	1.58451i
$910$		0			0
$911$	−2.54305	−	1.63432i	−0.0842549	−	0.0541474i	0.497835	−	0.867272i	$-0.334128\pi$
$911$	−2.54305	−	1.63432i	−0.0842549	−	0.0541474i	−0.582090	+	0.813124i	$0.697765\pi$
$912$		0			0
$913$	−3.55247	+	24.7080i	−0.117570	+	0.817715i
$914$		0			0
$915$	1.44463	−	0.928409i	0.0477581	−	0.0306923i
$916$		0			0
$917$	−0.918920	−	0.269819i	−0.0303454	−	0.00891022i
$918$		0			0
$919$	2.56432			0.0845890			0.0422945	−	0.999105i	$-0.486533\pi$
$919$	2.56432			0.0845890			0.0422945	+	0.999105i	$0.486533\pi$
$920$		0			0
$921$	1.43226			0.0471947
$922$		0			0
$923$	−9.44702	−	2.77390i	−0.310952	−	0.0913039i
$924$		0			0
$925$	−7.87064	+	5.05815i	−0.258785	+	0.166311i
$926$		0			0
$927$	7.23095	−	50.2924i	0.237496	−	1.65182i
$928$		0			0
$929$	48.7184	+	31.3094i	1.59840	+	1.02723i	0.967998	+	0.250959i	$0.0807458\pi$
$929$	48.7184	+	31.3094i	1.59840	+	1.02723i	0.630401	+	0.776270i	$0.282891\pi$
$930$		0			0
$931$	19.7387	+	43.2218i	0.646911	+	1.41654i
$932$		0			0
$933$	0.497067	+	3.45718i	0.0162732	+	0.113183i
$934$		0			0
$935$	19.0058	−	5.58061i	0.621556	−	0.182505i
$936$		0			0
$937$	−5.10070	+	5.88652i	−0.166633	+	0.192304i	−0.832924	−	0.553387i	$-0.813335\pi$
$937$	−5.10070	+	5.88652i	−0.166633	+	0.192304i	0.666292	+	0.745691i	$0.267881\pi$
$938$		0			0
$939$	−0.528561	−	0.609992i	−0.0172490	−	0.0199064i
$940$		0			0
$941$	11.9185	−	26.0980i	0.388533	−	0.850770i	−0.609772	−	0.792577i	$-0.708739\pi$
$941$	11.9185	−	26.0980i	0.388533	−	0.850770i	0.998305	−	0.0581927i	$-0.0185338\pi$
$942$		0			0
$943$	−2.18362	−	2.94245i	−0.0711084	−	0.0958194i
$944$		0			0
$945$	−0.0514429	+	0.112644i	−0.00167344	+	0.00366432i
$946$		0			0
$947$	35.4469	+	40.9079i	1.15187	+	1.32933i	0.935627	+	0.352990i	$0.114835\pi$
$947$	35.4469	+	40.9079i	1.15187	+	1.32933i	0.216244	+	0.976339i	$0.430619\pi$
$948$		0			0
$949$	−20.2916	+	23.4177i	−0.658693	+	0.760172i
$950$		0			0
$951$	4.36071	−	1.28042i	0.141406	−	0.0415205i
$952$		0			0
$953$	−3.57085	−	24.8358i	−0.115671	−	0.804512i	−0.962234	−	0.272223i	$-0.912241\pi$
$953$	−3.57085	−	24.8358i	−0.115671	−	0.804512i	0.846563	−	0.532289i	$-0.178668\pi$
$954$		0			0
$955$	0.689189	+	1.50911i	0.0223016	+	0.0488338i
$956$		0			0
$957$	4.00998	+	2.57706i	0.129624	+	0.0833044i
$958$		0			0
$959$	0.335388	−	2.33268i	0.0108303	−	0.0753261i
$960$		0			0
$961$	7.90912	−	5.08289i	0.255133	−	0.163964i
$962$		0			0
$963$	−22.6785	−	6.65900i	−0.730803	−	0.214583i
$964$		0			0
$965$	−5.30551			−0.170790
$966$		0			0
$967$	−33.0753			−1.06363			−0.531815	−	0.846860i	$-0.678490\pi$
$967$	−33.0753			−1.06363			−0.531815	+	0.846860i	$0.678490\pi$
$968$		0			0
$969$	−4.34790	−	1.27666i	−0.139675	−	0.0410122i
$970$		0			0
$971$	−37.9586	+	24.3945i	−1.21815	+	0.782857i	−0.982004	−	0.188860i	$-0.939521\pi$
$971$	−37.9586	+	24.3945i	−1.21815	+	0.782857i	−0.236146	+	0.971718i	$0.575884\pi$
$972$		0			0
$973$	0.100884	−	0.701665i	0.00323420	−	0.0224943i
$974$		0			0
$975$	0.490527	+	0.315243i	0.0157094	+	0.0100958i
$976$		0			0
$977$	17.9478	+	39.3001i	0.574200	+	1.25732i	0.944531	+	0.328422i	$0.106517\pi$
$977$	17.9478	+	39.3001i	0.574200	+	1.25732i	−0.370332	+	0.928900i	$0.620756\pi$
$978$		0			0
$979$	−9.77077	−	67.9572i	−0.312275	−	2.17192i
$980$		0			0
$981$	19.4113	−	5.69968i	0.619756	−	0.181977i
$982$		0			0
$983$	8.34058	−	9.62554i	0.266023	−	0.307007i	−0.606984	−	0.794714i	$-0.707621\pi$
$983$	8.34058	−	9.62554i	0.266023	−	0.307007i	0.873008	+	0.487707i	$0.162166\pi$
$984$		0			0
$985$	12.7950	+	14.7662i	0.407681	+	0.470489i
$986$		0			0
$987$	−0.0204580	+	0.0447968i	−0.000651186	+	0.00142590i
$988$		0			0
$989$	−11.9599	+	53.8967i	−0.380303	+	1.71381i
$990$		0			0
$991$	−13.8009	+	30.2198i	−0.438400	+	0.959963i	0.553489	+	0.832857i	$0.313296\pi$
$991$	−13.8009	+	30.2198i	−0.438400	+	0.959963i	−0.991889	+	0.127106i	$0.959431\pi$
$992$		0			0
$993$	0.500403	+	0.577495i	0.0158798	+	0.0183263i
$994$		0			0
$995$	−11.4475	+	13.2112i	−0.362912	+	0.418822i
$996$		0			0
$997$	15.5244	−	4.55837i	0.491662	−	0.144365i	−0.0264977	−	0.999649i	$-0.508435\pi$
$997$	15.5244	−	4.55837i	0.491662	−	0.144365i	0.518160	+	0.855284i	$0.326617\pi$
$998$		0			0
$999$	−1.40335	−	9.76053i	−0.0444001	−	0.308809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.m.b.121.3	✓	50
23.4	even	11	inner	460.2.m.b.441.3	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.b.121.3	✓	50	1.1	even	1	trivial
460.2.m.b.441.3	yes	50	23.4	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.169429 - 0.0497487i) q^{3} +(-0.841254 + 0.540641i) q^{5} +(0.0167209 - 0.116296i) q^{7} +(-2.49753 - 1.60506i) q^{9} +O(q^{10})\)	\(q+(-0.169429 - 0.0497487i) q^{3} +(-0.841254 + 0.540641i) q^{5} +(0.0167209 - 0.116296i) q^{7} +(-2.49753 - 1.60506i) q^{9} +(-2.18087 - 4.77544i) q^{11} +(-0.469939 - 3.26850i) q^{13} +(0.169429 - 0.0497487i) q^{15} +(2.47084 - 2.85151i) q^{17} +(4.45395 + 5.14013i) q^{19} +(-0.00861860 + 0.0188721i) q^{21} +(-0.322195 - 4.78500i) q^{23} +(0.415415 - 0.909632i) q^{25} +(0.690212 + 0.796547i) q^{27} +(3.36722 - 3.88598i) q^{29} +(-6.09875 + 1.79076i) q^{31} +(0.131930 + 0.917592i) q^{33} +(0.0488081 + 0.106875i) q^{35} +(-7.87064 - 5.05815i) q^{37} +(-0.0829824 + 0.577156i) q^{39} +(0.642746 - 0.413068i) q^{41} +(-11.0453 - 3.24319i) q^{43} +2.96882 q^{45} +2.37371 q^{47} +(6.70321 + 1.96824i) q^{49} +(-0.560491 + 0.360206i) q^{51} +(-0.334132 + 2.32394i) q^{53} +(4.41646 + 2.83829i) q^{55} +(-0.498912 - 1.09246i) q^{57} +(1.13985 + 7.92780i) q^{59} +(9.33098 - 2.73982i) q^{61} +(-0.228424 + 0.263616i) q^{63} +(2.16242 + 2.49557i) q^{65} +(-5.95950 + 13.0495i) q^{67} +(-0.183458 + 0.826744i) q^{69} +(1.23864 - 2.71224i) q^{71} +(-6.14504 - 7.09176i) q^{73} +(-0.115636 + 0.133451i) q^{75} +(-0.591833 + 0.173778i) q^{77} +(0.499973 + 3.47739i) q^{79} +(3.62256 + 7.93230i) q^{81} +(-4.00000 - 2.57064i) q^{83} +(-0.536966 + 3.73468i) q^{85} +(-0.763826 + 0.490881i) q^{87} +(12.5479 + 3.68441i) q^{89} -0.387972 q^{91} +1.12239 q^{93} +(-6.52587 - 1.91617i) q^{95} +(7.96365 - 5.11793i) q^{97} +(-2.21810 + 15.4272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) \) 50 * q + 5 * q^5 - q^7 - 25 * q^9	\( 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) \) 50 * q + 5 * q^5 - q^7 - 25 * q^9 - 6 * q^13 + 12 * q^17 + 19 * q^19 + 39 * q^21 - 16 * q^23 - 5 * q^25 + 21 * q^27 - 6 * q^29 + 34 * q^31 + 50 * q^33 - 10 * q^35 + 7 * q^37 - 70 * q^39 - 51 * q^41 - 18 * q^43 - 74 * q^45 + 30 * q^47 - 16 * q^49 - 80 * q^51 - 23 * q^53 - 33 * q^55 + 27 * q^57 - 18 * q^59 + 76 * q^61 + 138 * q^63 + 6 * q^65 + 25 * q^67 - 30 * q^69 - 37 * q^71 + 20 * q^73 + 92 * q^77 + 18 * q^79 + 25 * q^81 - 22 * q^83 - 12 * q^85 - 109 * q^87 + 8 * q^89 + 110 * q^91 + 64 * q^93 + 3 * q^95 - 38 * q^97 - 126 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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