LMFDB - Embedded newform 693.2.by.b.478.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(37,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 10, 6]))

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

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

chi := DirichletCharacter("693.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.by (of order $15$, degree $8$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			478.2
Character	$\chi$	$=$	693.478
Dual form			693.2.by.b.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.659236 - 0.140125i) q^{2} +(-1.41213 - 0.628722i) q^{4} +(-1.13022 - 1.25524i) q^{5} +(2.51637 - 0.817238i) q^{7} +(1.93333 + 1.40464i) q^{8} +O(q^{10})$	\(q+(-0.659236 - 0.140125i) q^{2} +(-1.41213 - 0.628722i) q^{4} +(-1.13022 - 1.25524i) q^{5} +(2.51637 - 0.817238i) q^{7} +(1.93333 + 1.40464i) q^{8} +(0.569194 + 0.985873i) q^{10} +(2.63784 + 2.01042i) q^{11} +(-1.22798 - 3.77933i) q^{13} +(-1.77340 + 0.186146i) q^{14} +(0.990954 + 1.10057i) q^{16} +(-2.51278 + 0.534107i) q^{17} +(0.305292 - 0.135925i) q^{19} +(0.806829 + 2.48316i) q^{20} +(-1.45725 - 1.69497i) q^{22} +(2.11859 - 3.66950i) q^{23} +(0.224419 - 2.13520i) q^{25} +(0.279950 + 2.66354i) q^{26} +(-4.06727 - 0.428050i) q^{28} +(2.51823 - 1.82960i) q^{29} +(-5.11813 + 5.68426i) q^{31} +(-2.88878 - 5.00351i) q^{32} +1.73135 q^{34} +(-3.86989 - 2.23499i) q^{35} +(-1.06012 - 10.0863i) q^{37} +(-0.220306 + 0.0468275i) q^{38} +(-0.421925 - 4.01435i) q^{40} +(-8.76494 - 6.36810i) q^{41} -6.26797 q^{43} +(-2.46099 - 4.49745i) q^{44} +(-1.91084 + 2.12220i) q^{46} +(2.15968 - 0.961554i) q^{47} +(5.66425 - 4.11295i) q^{49} +(-0.447141 + 1.37616i) q^{50} +(-0.642079 + 6.10898i) q^{52} +(2.93539 - 3.26008i) q^{53} +(-0.457796 - 5.58335i) q^{55} +(6.01289 + 1.95462i) q^{56} +(-1.91648 + 0.853273i) q^{58} +(0.0319655 + 0.0142320i) q^{59} +(-2.74836 - 3.05237i) q^{61} +(4.17056 - 3.03009i) q^{62} +(0.287989 + 0.886339i) q^{64} +(-3.35608 + 5.81290i) q^{65} +(-2.72981 - 4.72817i) q^{67} +(3.88418 + 0.825608i) q^{68} +(2.23800 + 2.01566i) q^{70} +(-2.91440 + 8.96959i) q^{71} +(-0.273807 - 0.121907i) q^{73} +(-0.714481 + 6.79783i) q^{74} -0.516572 q^{76} +(8.28078 + 2.90321i) q^{77} +(13.9247 + 2.95979i) q^{79} +(0.261475 - 2.48777i) q^{80} +(4.88583 + 5.42627i) q^{82} +(1.43515 - 4.41695i) q^{83} +(3.51043 + 2.55048i) q^{85} +(4.13208 + 0.878300i) q^{86} +(2.27589 + 7.59203i) q^{88} +(6.99890 - 12.1225i) q^{89} +(-6.17866 - 8.50664i) q^{91} +(-5.29882 + 3.84982i) q^{92} +(-1.55848 + 0.331265i) q^{94} +(-0.515666 - 0.229589i) q^{95} +(-1.02232 - 3.14637i) q^{97} +(-4.31040 + 1.91770i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 3 q^{2} - 3 q^{4} - 4 q^{5} - 2 q^{7} + 38 q^{8}+O(q^{10}) $ 40 * q + 3 * q^2 - 3 * q^4 - 4 * q^5 - 2 * q^7 + 38 * q^8	$ 40 q + 3 q^{2} - 3 q^{4} - 4 q^{5} - 2 q^{7} + 38 q^{8} + 14 q^{10} + 9 q^{11} + 6 q^{13} + 3 q^{14} - 5 q^{16} + 7 q^{17} - 4 q^{19} + 30 q^{20} + 44 q^{22} + 14 q^{23} + 21 q^{25} + 16 q^{28} - 17 q^{31} + 30 q^{32} + 48 q^{34} + 14 q^{35} + 24 q^{37} - 12 q^{38} + 10 q^{40} - 60 q^{41} - 72 q^{43} - 18 q^{44} + 8 q^{46} - 13 q^{47} - 10 q^{49} - 6 q^{50} + 2 q^{52} - 33 q^{53} - 6 q^{55} - 24 q^{56} - 17 q^{58} - 21 q^{59} + 52 q^{62} + 94 q^{64} + 40 q^{65} - 38 q^{67} + 23 q^{68} - 3 q^{70} - 20 q^{71} + 11 q^{73} + 41 q^{74} - 96 q^{76} - 36 q^{77} + 21 q^{79} - 12 q^{80} + 6 q^{82} + 46 q^{83} - 78 q^{85} - 7 q^{86} + 32 q^{88} + 10 q^{89} - 14 q^{91} + 110 q^{92} + 37 q^{94} - 7 q^{95} - 54 q^{97} - 116 q^{98}+O(q^{100}) $ 40 * q + 3 * q^2 - 3 * q^4 - 4 * q^5 - 2 * q^7 + 38 * q^8 + 14 * q^10 + 9 * q^11 + 6 * q^13 + 3 * q^14 - 5 * q^16 + 7 * q^17 - 4 * q^19 + 30 * q^20 + 44 * q^22 + 14 * q^23 + 21 * q^25 + 16 * q^28 - 17 * q^31 + 30 * q^32 + 48 * q^34 + 14 * q^35 + 24 * q^37 - 12 * q^38 + 10 * q^40 - 60 * q^41 - 72 * q^43 - 18 * q^44 + 8 * q^46 - 13 * q^47 - 10 * q^49 - 6 * q^50 + 2 * q^52 - 33 * q^53 - 6 * q^55 - 24 * q^56 - 17 * q^58 - 21 * q^59 + 52 * q^62 + 94 * q^64 + 40 * q^65 - 38 * q^67 + 23 * q^68 - 3 * q^70 - 20 * q^71 + 11 * q^73 + 41 * q^74 - 96 * q^76 - 36 * q^77 + 21 * q^79 - 12 * q^80 + 6 * q^82 + 46 * q^83 - 78 * q^85 - 7 * q^86 + 32 * q^88 + 10 * q^89 - 14 * q^91 + 110 * q^92 + 37 * q^94 - 7 * q^95 - 54 * q^97 - 116 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.659236	−	0.140125i	−0.466150	−	0.0990833i	−0.0311523	−	0.999515i	$-0.509918\pi$
$2$	−0.659236	−	0.140125i	−0.466150	−	0.0990833i	−0.434998	+	0.900431i	$0.643251\pi$
$3$		0			0
$3$		0			0
$4$	−1.41213	−	0.628722i	−0.706067	−	0.314361i
$5$	−1.13022	−	1.25524i	−0.505451	−	0.561361i	0.435375	−	0.900249i	$-0.356616\pi$
$5$	−1.13022	−	1.25524i	−0.505451	−	0.561361i	−0.940827	+	0.338888i	$0.889949\pi$
$6$		0			0
$7$	2.51637	−	0.817238i	0.951099	−	0.308887i
$7$	2.51637	−	0.817238i	0.951099	−	0.308887i
$8$	1.93333	+	1.40464i	0.683534	+	0.496617i
$9$		0			0
$10$	0.569194	+	0.985873i	0.179995	+	0.311760i
$11$	2.63784	+	2.01042i	0.795340	+	0.606164i
$11$	2.63784	+	2.01042i	0.795340	+	0.606164i
$12$		0			0
$13$	−1.22798	−	3.77933i	−0.340580	−	1.04820i	−0.963908	−	0.266237i	$-0.914220\pi$
$13$	−1.22798	−	3.77933i	−0.340580	−	1.04820i	0.623328	−	0.781961i	$-0.285780\pi$
$14$	−1.77340	+	0.186146i	−0.473961	+	0.0497497i
$15$		0			0
$16$	0.990954	+	1.10057i	0.247738	+	0.275141i
$17$	−2.51278	+	0.534107i	−0.609438	+	0.129540i	−0.502284	−	0.864703i	$-0.667507\pi$
$17$	−2.51278	+	0.534107i	−0.609438	+	0.129540i	−0.107153	+	0.994243i	$0.534174\pi$
$18$		0			0
$19$	0.305292	−	0.135925i	0.0700388	−	0.0311833i	−0.371418	−	0.928466i	$-0.621128\pi$
$19$	0.305292	−	0.135925i	0.0700388	−	0.0311833i	0.441457	+	0.897282i	$0.354462\pi$
$20$	0.806829	+	2.48316i	0.180412	+	0.555252i
$21$		0			0
$22$	−1.45725	−	1.69497i	−0.310687	−	0.361368i
$23$	2.11859	−	3.66950i	0.441756	−	0.765143i	−0.556064	−	0.831139i	$-0.687689\pi$
$23$	2.11859	−	3.66950i	0.441756	−	0.765143i	0.997820	+	0.0659962i	$0.0210225\pi$
$24$		0			0
$25$	0.224419	−	2.13520i	0.0448838	−	0.427041i
$26$	0.279950	+	2.66354i	0.0549026	+	0.522364i
$27$		0			0
$28$	−4.06727	−	0.428050i	−0.768641	−	0.0808939i
$29$	2.51823	−	1.82960i	0.467624	−	0.339749i	−0.328891	−	0.944368i	$-0.606675\pi$
$29$	2.51823	−	1.82960i	0.467624	−	0.339749i	0.796515	+	0.604619i	$0.206675\pi$
$30$		0			0
$31$	−5.11813	+	5.68426i	−0.919243	+	1.02092i	0.0804649	+	0.996757i	$0.474360\pi$
$31$	−5.11813	+	5.68426i	−0.919243	+	1.02092i	−0.999708	+	0.0241654i	$0.992307\pi$
$32$	−2.88878	−	5.00351i	−0.510669	−	0.884504i
$33$		0			0
$34$	1.73135			0.296925
$35$	−3.86989	−	2.23499i	−0.654131	−	0.377782i
$36$		0			0
$37$	−1.06012	−	10.0863i	−0.174282	−	1.65818i	−0.636395	−	0.771364i	$-0.719575\pi$
$37$	−1.06012	−	10.0863i	−0.174282	−	1.65818i	0.462112	−	0.886821i	$-0.347092\pi$
$38$	−0.220306	+	0.0468275i	−0.0357383	+	0.00759642i
$39$		0			0
$40$	−0.421925	−	4.01435i	−0.0667123	−	0.634725i
$41$	−8.76494	−	6.36810i	−1.36885	−	0.994530i	−0.997826	−	0.0659081i	$-0.979006\pi$
$41$	−8.76494	−	6.36810i	−1.36885	−	0.994530i	−0.371027	−	0.928622i	$-0.620994\pi$
$42$		0			0
$43$	−6.26797			−0.955857			−0.477928	−	0.878399i	$-0.658612\pi$
$43$	−6.26797			−0.955857			−0.477928	+	0.878399i	$0.658612\pi$
$44$	−2.46099	−	4.49745i	−0.371009	−	0.678016i
$45$		0			0
$46$	−1.91084	+	2.12220i	−0.281738	+	0.312901i
$47$	2.15968	−	0.961554i	0.315022	−	0.140257i	−0.243134	−	0.969993i	$-0.578176\pi$
$47$	2.15968	−	0.961554i	0.315022	−	0.140257i	0.558157	+	0.829736i	$0.311509\pi$
$48$		0			0
$49$	5.66425	−	4.11295i	0.809178	−	0.587564i
$50$	−0.447141	+	1.37616i	−0.0632352	+	0.194618i
$51$		0			0
$52$	−0.642079	+	6.10898i	−0.0890404	+	0.847162i
$53$	2.93539	−	3.26008i	0.403207	−	0.447807i	−0.507009	−	0.861941i	$-0.669249\pi$
$53$	2.93539	−	3.26008i	0.403207	−	0.447807i	0.910216	+	0.414134i	$0.135915\pi$
$54$		0			0
$55$	−0.457796	−	5.58335i	−0.0617292	−	0.752859i
$56$	6.01289	+	1.95462i	0.803507	+	0.261197i
$57$		0			0
$58$	−1.91648	+	0.853273i	−0.251647	+	0.112040i
$59$	0.0319655	+	0.0142320i	0.00416155	+	0.00185284i	0.408816	−	0.912617i	$-0.365942\pi$
$59$	0.0319655	+	0.0142320i	0.00416155	+	0.00185284i	−0.404655	+	0.914470i	$0.632608\pi$
$60$		0			0
$61$	−2.74836	−	3.05237i	−0.351892	−	0.390815i	0.541048	−	0.840992i	$-0.318028\pi$
$61$	−2.74836	−	3.05237i	−0.351892	−	0.390815i	−0.892940	+	0.450176i	$0.851361\pi$
$62$	4.17056	−	3.03009i	0.529662	−	0.384822i
$63$		0			0
$64$	0.287989	+	0.886339i	0.0359986	+	0.110792i
$65$	−3.35608	+	5.81290i	−0.416270	+	0.721001i
$66$		0			0
$67$	−2.72981	−	4.72817i	−0.333499	−	0.577637i	0.649696	−	0.760194i	$-0.274896\pi$
$67$	−2.72981	−	4.72817i	−0.333499	−	0.577637i	−0.983195	+	0.182557i	$0.941563\pi$
$68$	3.88418	+	0.825608i	0.471026	+	0.100120i
$69$		0			0
$70$	2.23800	+	2.01566i	0.267492	+	0.240917i
$71$	−2.91440	+	8.96959i	−0.345875	+	1.06449i	0.615238	+	0.788341i	$0.289060\pi$
$71$	−2.91440	+	8.96959i	−0.345875	+	1.06449i	−0.961114	+	0.276154i	$0.910940\pi$
$72$		0			0
$73$	−0.273807	−	0.121907i	−0.0320467	−	0.0142681i	0.390651	−	0.920539i	$-0.372250\pi$
$73$	−0.273807	−	0.121907i	−0.0320467	−	0.0142681i	−0.422697	+	0.906271i	$0.638917\pi$
$74$	−0.714481	+	6.79783i	−0.0830567	+	0.790232i
$75$		0			0
$76$	−0.516572			−0.0592548
$77$	8.28078	+	2.90321i	0.943683	+	0.330852i
$78$		0			0
$79$	13.9247	+	2.95979i	1.56666	+	0.333003i	0.907845	−	0.419306i	$-0.137727\pi$
$79$	13.9247	+	2.95979i	1.56666	+	0.333003i	0.658810	+	0.752309i	$0.271060\pi$
$80$	0.261475	−	2.48777i	0.0292338	−	0.278141i
$81$		0			0
$82$	4.88583	+	5.42627i	0.539550	+	0.599231i
$83$	1.43515	−	4.41695i	0.157528	−	0.484823i	−0.840880	−	0.541222i	$-0.817962\pi$
$83$	1.43515	−	4.41695i	0.157528	−	0.484823i	0.998408	+	0.0563991i	$0.0179619\pi$
$84$		0			0
$85$	3.51043	+	2.55048i	0.380760	+	0.276638i
$86$	4.13208	+	0.878300i	0.445573	+	0.0947095i
$87$		0			0
$88$	2.27589	+	7.59203i	0.242611	+	0.809313i
$89$	6.99890	−	12.1225i	0.741882	−	1.28498i	−0.209755	−	0.977754i	$-0.567267\pi$
$89$	6.99890	−	12.1225i	0.741882	−	1.28498i	0.951637	−	0.307224i	$-0.0994000\pi$
$90$		0			0
$91$	−6.17866	−	8.50664i	−0.647700	−	0.891739i
$92$	−5.29882	+	3.84982i	−0.552440	+	0.401371i
$93$		0			0
$94$	−1.55848	+	0.331265i	−0.160745	+	0.0341674i
$95$	−0.515666	−	0.229589i	−0.0529063	−	0.0235554i
$96$		0			0
$97$	−1.02232	−	3.14637i	−0.103801	−	0.319465i	0.885646	−	0.464360i	$-0.153716\pi$
$97$	−1.02232	−	3.14637i	−0.103801	−	0.319465i	−0.989447	+	0.144895i	$0.953716\pi$
$98$	−4.31040	+	1.91770i	−0.435416	+	0.193717i
$99$		0			0
$100$	−1.65936	+	2.87410i	−0.165936	+	0.287410i
$101$	−6.16373	+	6.84552i	−0.613314	+	0.681155i	−0.967166	−	0.254147i	$-0.918205\pi$
$101$	−6.16373	+	6.84552i	−0.613314	+	0.681155i	0.353851	+	0.935302i	$0.384872\pi$
$102$		0			0
$103$	1.74351	+	16.5884i	0.171793	+	1.63450i	0.652620	+	0.757685i	$0.273670\pi$
$103$	1.74351	+	16.5884i	0.171793	+	1.63450i	−0.480828	+	0.876815i	$0.659664\pi$
$104$	2.93453	−	9.03155i	0.287754	−	0.885616i
$105$		0			0
$106$	−2.39194	+	1.73784i	−0.232326	+	0.168794i
$107$	−1.22455	+	0.545203i	−0.118381	+	0.0527068i	−0.465073	−	0.885273i	$-0.653972\pi$
$107$	−1.22455	+	0.545203i	−0.118381	+	0.0527068i	0.346691	+	0.937979i	$0.387305\pi$
$108$		0			0
$109$	3.16671	+	5.48491i	0.303316	+	0.525359i	0.976885	−	0.213765i	$-0.0685728\pi$
$109$	3.16671	+	5.48491i	0.303316	+	0.525359i	−0.673569	+	0.739124i	$0.735240\pi$
$110$	−0.480571	+	3.74490i	−0.0458207	+	0.357062i
$111$		0			0
$112$	3.39303	+	1.95959i	0.320611	+	0.185164i
$113$	−12.3099	−	8.94367i	−1.15802	−	0.841349i	−0.168492	−	0.985703i	$-0.553890\pi$
$113$	−12.3099	−	8.94367i	−1.15802	−	0.841349i	−0.989526	+	0.144354i	$0.953890\pi$
$114$		0			0
$115$	−7.00058	+	1.48802i	−0.652807	+	0.138758i
$116$	−4.70639	+	1.00037i	−0.436978	+	0.0928824i
$117$		0			0
$118$	−0.0190786	−	0.0138614i	−0.00175632	−	0.00127604i
$119$	−5.88658	+	3.39755i	−0.539622	+	0.311452i
$120$		0			0
$121$	2.91644	+	10.6063i	0.265131	+	0.964212i
$122$	1.38411	+	2.39734i	0.125311	+	0.217045i
$123$		0			0
$124$	10.8013	−	4.80905i	0.969985	−	0.431865i
$125$	−9.76636	+	7.09568i	−0.873530	+	0.634657i
$126$		0			0
$127$	1.68911	−	5.19854i	0.149884	−	0.461296i	−0.847723	−	0.530440i	$-0.822027\pi$
$127$	1.68911	−	5.19854i	0.149884	−	0.461296i	0.997607	+	0.0691441i	$0.0220268\pi$
$128$	1.14218	+	10.8672i	0.100956	+	0.960530i
$129$		0			0
$130$	3.02698	−	3.36180i	0.265484	−	0.294850i
$131$	2.46819	−	4.27502i	0.215646	−	0.373510i	−0.737826	−	0.674991i	$-0.764147\pi$
$131$	2.46819	−	4.27502i	0.215646	−	0.373510i	0.953472	+	0.301481i	$0.0974808\pi$
$132$		0			0
$133$	0.657145	−	0.591533i	0.0569817	−	0.0512924i
$134$	1.13705	+	3.49949i	0.0982265	+	0.302310i
$135$		0			0
$136$	−5.60825	−	2.49695i	−0.480903	−	0.214112i
$137$	1.59960	−	0.340006i	0.136663	−	0.0290487i	−0.139072	−	0.990282i	$-0.544412\pi$
$137$	1.59960	−	0.340006i	0.136663	−	0.0290487i	0.275735	+	0.961234i	$0.411079\pi$
$138$		0			0
$139$	7.16508	−	5.20573i	0.607734	−	0.441545i	−0.240882	−	0.970554i	$-0.577437\pi$
$139$	7.16508	−	5.20573i	0.607734	−	0.441545i	0.848616	+	0.529010i	$0.177437\pi$
$140$	4.05962	+	5.58919i	0.343100	+	0.472373i
$141$		0			0
$142$	3.17814	−	5.50470i	0.266704	−	0.461944i
$143$	4.35882	−	12.4380i	0.364502	−	1.04012i
$144$		0			0
$145$	−5.14276	−	1.09313i	−0.427083	−	0.0907793i
$146$	0.163422	+	0.118733i	0.0135249	+	0.00982639i
$147$		0			0
$148$	−4.84448	+	14.9098i	−0.398214	+	1.22558i
$149$	3.20622	+	3.56086i	0.262663	+	0.291717i	0.860022	−	0.510257i	$-0.170450\pi$
$149$	3.20622	+	3.56086i	0.262663	+	0.291717i	−0.597359	+	0.801974i	$0.703783\pi$
$150$		0			0
$151$	1.68058	−	15.9897i	0.136764	−	1.30122i	−0.683802	−	0.729668i	$-0.739675\pi$
$151$	1.68058	−	15.9897i	0.136764	−	1.30122i	0.820566	−	0.571552i	$-0.193659\pi$
$152$	0.781155	+	0.166040i	0.0633600	+	0.0134676i
$153$		0			0
$154$	−5.05218	−	3.07425i	−0.407116	−	0.247730i
$155$	12.9197			1.03774
$156$		0			0
$157$	−0.712751	+	6.78137i	−0.0568837	+	0.541212i	0.928557	+	0.371191i	$0.121050\pi$
$157$	−0.712751	+	6.78137i	−0.0568837	+	0.541212i	−0.985440	+	0.170022i	$0.945616\pi$
$158$	−8.76495	−	3.90241i	−0.697302	−	0.310459i
$159$		0			0
$160$	−3.01565	+	9.28120i	−0.238408	+	0.733743i
$161$	2.33230	−	10.9652i	0.183811	−	0.864179i
$162$		0			0
$163$	13.4196	+	2.85242i	1.05110	+	0.223419i	0.700904	−	0.713256i	$-0.252780\pi$
$163$	13.4196	+	2.85242i	1.05110	+	0.223419i	0.350200	+	0.936675i	$0.386114\pi$
$164$	8.37349	+	14.5033i	0.653860	+	1.13252i
$165$		0			0
$166$	−1.56503	+	2.71071i	−0.121470	+	0.210392i
$167$	6.04406	+	18.6017i	0.467703	+	1.43944i	0.855551	+	0.517719i	$0.173219\pi$
$167$	6.04406	+	18.6017i	0.467703	+	1.43944i	−0.387847	+	0.921724i	$0.626781\pi$
$168$		0			0
$169$	−2.25818	+	1.64066i	−0.173706	+	0.126205i
$170$	−1.95682	−	2.17327i	−0.150081	−	0.166682i
$171$		0			0
$172$	8.85121	+	3.94081i	0.674899	+	0.300484i
$173$	−3.36136	+	1.49657i	−0.255559	+	0.113782i	−0.530518	−	0.847674i	$-0.678003\pi$
$173$	−3.36136	+	1.49657i	−0.255559	+	0.113782i	0.274959	+	0.961456i	$0.411336\pi$
$174$		0			0
$175$	−1.18025	−	5.55637i	−0.0892183	−	0.420022i
$176$	0.401385	+	4.89535i	0.0302555	+	0.369001i
$177$		0			0
$178$	−6.31259	+	7.01084i	−0.473149	+	0.525485i
$179$	2.06293	−	19.6275i	0.154191	−	1.46703i	−0.594493	−	0.804101i	$-0.702647\pi$
$179$	2.06293	−	19.6275i	0.154191	−	1.46703i	0.748684	−	0.662927i	$-0.230686\pi$
$180$		0			0
$181$	−0.683681	+	2.10415i	−0.0508176	+	0.156400i	−0.973245	−	0.229770i	$-0.926202\pi$
$181$	−0.683681	+	2.10415i	−0.0508176	+	0.156400i	0.922427	+	0.386171i	$0.126202\pi$
$182$	2.88120	+	6.47367i	0.213569	+	0.479861i
$183$		0			0
$184$	9.25026	−	4.11848i	0.681938	−	0.303618i
$185$	−11.4626	+	12.7305i	−0.842749	+	0.935967i
$186$		0			0
$187$	−7.70209	−	3.64284i	−0.563232	−	0.266391i
$188$	−3.65431			−0.266518
$189$		0			0
$190$	0.307775	+	0.223611i	0.0223283	+	0.0162225i
$191$	0.899407	+	8.55728i	0.0650788	+	0.619183i	0.977646	+	0.210257i	$0.0674300\pi$
$191$	0.899407	+	8.55728i	0.0650788	+	0.619183i	−0.912567	+	0.408926i	$0.865903\pi$
$192$		0			0
$193$	−0.249950	+	0.0531286i	−0.0179918	+	0.00382428i	−0.216899	−	0.976194i	$-0.569594\pi$
$193$	−0.249950	+	0.0531286i	−0.0179918	+	0.00382428i	0.198907	+	0.980018i	$0.436261\pi$
$194$	0.233064	+	2.21745i	0.0167330	+	0.159204i
$195$		0			0
$196$	−10.5846	+	2.24679i	−0.756041	+	0.160485i
$197$	9.76587			0.695789			0.347895	−	0.937534i	$-0.386897\pi$
$197$	9.76587			0.695789			0.347895	+	0.937534i	$0.386897\pi$
$198$		0			0
$199$	0.176993	+	0.306561i	0.0125467	+	0.0217315i	0.872231	−	0.489095i	$-0.162673\pi$
$199$	0.176993	+	0.306561i	0.0125467	+	0.0217315i	−0.859684	+	0.510826i	$0.829339\pi$
$200$	3.43308	−	3.81282i	0.242755	−	0.269607i
$201$		0			0
$202$	5.02259	−	3.64912i	0.353388	−	0.256751i
$203$	4.84159	−	6.66195i	0.339813	−	0.467577i
$204$		0			0
$205$	1.91284	+	18.1995i	0.133599	+	1.27111i
$206$	1.17506	−	11.1800i	0.0818704	−	0.778945i
$207$		0			0
$208$	2.94253	−	5.09661i	0.204028	−	0.353386i
$209$	1.07858	+	0.255216i	0.0746068	+	0.0176537i
$210$		0			0
$211$	4.60636	+	14.1769i	0.317115	+	0.975979i	0.974875	+	0.222751i	$0.0715039\pi$
$211$	4.60636	+	14.1769i	0.317115	+	0.975979i	−0.657761	+	0.753227i	$0.728496\pi$
$212$	−6.19486	+	2.75813i	−0.425464	+	0.189429i
$213$		0			0
$214$	0.883662	−	0.187828i	0.0604059	−	0.0128397i
$215$	7.08421	+	7.86782i	0.483139	+	0.536581i
$216$		0			0
$217$	−8.23372	+	18.4864i	−0.558941	+	1.25494i
$218$	−1.31904	−	4.05959i	−0.0893366	−	0.274950i
$219$		0			0
$220$	−2.86391	+	8.17226i	−0.193085	+	0.550974i
$221$	5.10420	+	8.84073i	0.343346	+	0.594692i
$222$		0			0
$223$	−23.1818	−	16.8425i	−1.55237	−	1.12786i	−0.941938	−	0.335788i	$-0.890997\pi$
$223$	−23.1818	−	16.8425i	−1.55237	−	1.12786i	−0.610428	−	0.792072i	$-0.709003\pi$
$224$	−11.3583	−	10.2299i	−0.758908	−	0.683512i
$225$		0			0
$226$	6.86190	+	7.62091i	0.456447	+	0.506936i
$227$	19.2446	+	8.56826i	1.27731	+	0.568695i	0.929484	−	0.368863i	$-0.120253\pi$
$227$	19.2446	+	8.56826i	1.27731	+	0.568695i	0.347827	+	0.937559i	$0.386920\pi$
$228$		0			0
$229$	7.06001	+	1.50065i	0.466539	+	0.0991658i	0.435182	−	0.900342i	$-0.356684\pi$
$229$	7.06001	+	1.50065i	0.466539	+	0.0991658i	0.0313564	+	0.999508i	$0.490017\pi$
$230$	4.82354			0.318055
$231$		0			0
$232$	7.43851			0.488362
$233$	25.1228	+	5.34001i	1.64585	+	0.349836i	0.935312	−	0.353825i	$-0.115119\pi$
$233$	25.1228	+	5.34001i	1.64585	+	0.349836i	0.710536	+	0.703661i	$0.248452\pi$
$234$		0			0
$235$	−3.64791	−	1.62415i	−0.237963	−	0.105948i
$236$	−0.0361916	−	0.0401949i	−0.00235587	−	0.00261646i
$237$		0			0
$238$	4.35673	−	1.41493i	0.282405	−	0.0917162i
$239$	−7.01845	−	5.09920i	−0.453986	−	0.329840i	0.337182	−	0.941440i	$-0.390526\pi$
$239$	−7.01845	−	5.09920i	−0.453986	−	0.329840i	−0.791167	+	0.611600i	$0.790526\pi$
$240$		0			0
$241$	11.0355	+	19.1141i	0.710862	+	1.23125i	0.964534	+	0.263959i	$0.0850284\pi$
$241$	11.0355	+	19.1141i	0.710862	+	1.23125i	−0.253672	+	0.967290i	$0.581638\pi$
$242$	−0.436411	−	7.40075i	−0.0280536	−	0.475738i
$243$		0			0
$244$	1.96196	+	6.03830i	0.125602	+	0.386563i
$245$	−11.5646	−	2.46144i	−0.738835	−	0.157256i
$246$		0			0
$247$	−0.888596	−	0.986886i	−0.0565400	−	0.0627941i
$248$	−17.8794	+	3.80038i	−1.13534	+	0.241324i
$249$		0			0
$250$	7.43262	−	3.30922i	0.470080	−	0.209293i
$251$	−5.32569	−	16.3908i	−0.336155	−	1.03458i	−0.966150	−	0.257980i	$-0.916943\pi$
$251$	−5.32569	−	16.3908i	−0.336155	−	1.03458i	0.629995	−	0.776599i	$-0.283057\pi$
$252$		0			0
$253$	12.9657	−	5.42032i	0.815148	−	0.340773i
$254$	−1.84197	+	3.19038i	−0.115575	+	0.200182i
$255$		0			0
$256$	0.964622	−	9.17777i	0.0602889	−	0.573610i
$257$	−0.599439	−	5.70328i	−0.0373920	−	0.355761i	−0.997181	−	0.0750376i	$-0.976092\pi$
$257$	−0.599439	−	5.70328i	−0.0373920	−	0.355761i	0.959789	−	0.280723i	$-0.0905744\pi$
$258$		0			0
$259$	−10.9106	−	24.5146i	−0.677951	−	1.52326i
$260$	8.39393	−	6.09855i	0.520569	−	0.378216i
$261$		0			0
$262$	−2.22616	+	2.47240i	−0.137532	+	0.152745i
$263$	11.2982	+	19.5691i	0.696679	+	1.20668i	0.969612	+	0.244650i	$0.0786729\pi$
$263$	11.2982	+	19.5691i	0.696679	+	1.20668i	−0.272933	+	0.962033i	$0.587994\pi$
$264$		0			0
$265$	−7.40984			−0.455183
$266$	−0.516102	+	0.297878i	−0.0316443	+	0.0182640i
$267$		0			0
$268$	0.882149	+	8.39309i	0.0538859	+	0.512690i
$269$	−15.9050	+	3.38071i	−0.969744	+	0.206125i	−0.665441	−	0.746450i	$-0.731757\pi$
$269$	−15.9050	+	3.38071i	−0.969744	+	0.206125i	−0.304302	+	0.952575i	$0.598423\pi$
$270$		0			0
$271$	−0.738626	−	7.02755i	−0.0448683	−	0.426894i	−0.993781	−	0.111354i	$-0.964481\pi$
$271$	−0.738626	−	7.02755i	−0.0448683	−	0.426894i	0.948912	−	0.315539i	$-0.102185\pi$
$272$	−3.07786	−	2.23620i	−0.186623	−	0.135590i
$273$		0			0
$274$	−1.10216			−0.0665839
$275$	4.88463	−	5.18116i	0.294554	−	0.312436i
$276$		0			0
$277$	7.95588	−	8.83591i	0.478023	−	0.530898i	−0.455107	−	0.890437i	$-0.650399\pi$
$277$	7.95588	−	8.83591i	0.478023	−	0.530898i	0.933130	+	0.359538i	$0.117066\pi$
$278$	−5.45293	+	2.42780i	−0.327045	+	0.145610i
$279$		0			0
$280$	−4.34240	−	9.75679i	−0.259508	−	0.583080i
$281$	−3.21105	+	9.88261i	−0.191555	+	0.589547i	0.808444	+	0.588573i	$0.200310\pi$
$281$	−3.21105	+	9.88261i	−0.191555	+	0.589547i	−1.00000		0.000973981i	$0.999690\pi$
$282$		0			0
$283$	2.12197	−	20.1892i	0.126138	−	1.20012i	−0.730027	−	0.683419i	$-0.760492\pi$
$283$	2.12197	−	20.1892i	0.126138	−	1.20012i	0.856165	−	0.516703i	$-0.172841\pi$
$284$	9.75490	−	10.8339i	0.578847	−	0.642875i
$285$		0			0
$286$	−4.61637	+	7.58882i	−0.272972	+	0.448737i
$287$	−27.2601	−	8.86146i	−1.60911	−	0.523076i
$288$		0			0
$289$	−9.50150	+	4.23034i	−0.558912	+	0.248844i
$290$	3.23712	+	1.44126i	0.190090	+	0.0846336i
$291$		0			0
$292$	0.310007	+	0.344298i	0.0181418	+	0.0201485i
$293$	19.3158	−	14.0337i	1.12844	−	0.819860i	0.142973	−	0.989727i	$-0.454334\pi$
$293$	19.3158	−	14.0337i	1.12844	−	0.819860i	0.985467	+	0.169866i	$0.0543336\pi$
$294$		0			0
$295$	−0.0182636	−	0.0562097i	−0.00106335	−	0.00327266i
$296$	12.1182	−	20.9893i	0.704354	−	1.21998i
$297$		0			0
$298$	−1.61469	−	2.79672i	−0.0935364	−	0.162010i
$299$	−16.4698	−	3.50077i	−0.952474	−	0.202455i
$300$		0			0
$301$	−15.7725	+	5.12242i	−0.909114	+	0.295252i
$302$	−3.34845	+	10.3055i	−0.192682	+	0.593013i
$303$		0			0
$304$	0.452124	+	0.201299i	0.0259311	+	0.0115453i
$305$	−0.725189	+	6.89971i	−0.0415242	+	0.395076i
$306$		0			0
$307$	8.73868			0.498743			0.249372	−	0.968408i	$-0.419776\pi$
$307$	8.73868			0.498743			0.249372	+	0.968408i	$0.419776\pi$
$308$	−9.86826	−	9.30603i	−0.562296	−	0.530261i
$309$		0			0
$310$	−8.51716	−	1.81038i	−0.483742	−	0.102823i
$311$	0.273671	−	2.60381i	0.0155185	−	0.147648i	−0.984019	−	0.178064i	$-0.943017\pi$
$311$	0.273671	−	2.60381i	0.0155185	−	0.147648i	0.999537	+	0.0304159i	$0.00968317\pi$
$312$		0			0
$313$	−15.2251	−	16.9092i	−0.860574	−	0.955764i	0.138829	−	0.990316i	$-0.455666\pi$
$313$	−15.2251	−	16.9092i	−0.860574	−	0.955764i	−0.999403	+	0.0345523i	$0.988999\pi$
$314$	1.42011	−	4.37065i	0.0801415	−	0.246650i
$315$		0			0
$316$	−17.8027	−	12.9344i	−1.00148	−	0.727618i
$317$	4.39006	+	0.933136i	0.246570	+	0.0524101i	0.329539	−	0.944142i	$-0.393107\pi$
$317$	4.39006	+	0.933136i	0.246570	+	0.0524101i	−0.0829685	+	0.996552i	$0.526440\pi$
$318$		0			0
$319$	10.3210	+	0.236492i	0.577863	+	0.0132410i
$320$	0.787077	−	1.36326i	0.0439989	−	0.0762084i
$321$		0			0
$322$	−3.07403	+	6.90185i	−0.171309	+	0.384625i
$323$	−0.694532	+	0.504607i	−0.0386448	+	0.0280771i
$324$		0			0
$325$	−8.34522	+	1.77383i	−0.462910	+	0.0983945i
$326$	−8.44699	−	3.76084i	−0.467835	−	0.208294i
$327$		0			0
$328$	−8.00057	−	24.6232i	−0.441758	−	1.35959i
$329$	4.64875	−	4.18460i	0.256294	−	0.230705i
$330$		0			0
$331$	6.90068	−	11.9523i	0.379296	−	0.656960i	−0.611664	−	0.791118i	$-0.709500\pi$
$331$	6.90068	−	11.9523i	0.379296	−	0.656960i	0.990960	+	0.134158i	$0.0428330\pi$
$332$	−4.80366	+	5.33500i	−0.263635	+	0.292796i
$333$		0			0
$334$	−1.37790	−	13.1098i	−0.0753953	−	0.717338i
$335$	−2.84969	+	8.77045i	−0.155695	+	0.479181i
$336$		0			0
$337$	9.10560	−	6.61560i	0.496013	−	0.360375i	−0.311479	−	0.950253i	$-0.600824\pi$
$337$	9.10560	−	6.61560i	0.496013	−	0.360375i	0.807492	+	0.589878i	$0.200824\pi$
$338$	1.71857	−	0.765158i	0.0934780	−	0.0416191i
$339$		0			0
$340$	−3.35366	−	5.80870i	−0.181877	−	0.315021i
$341$	−24.9286	+	4.70461i	−1.34996	+	0.254769i
$342$		0			0
$343$	10.8921	−	14.9787i	0.588118	−	0.808775i
$344$	−12.1180	−	8.80427i	−0.653361	−	0.474695i
$345$		0			0
$346$	2.42564	−	0.515585i	0.130403	−	0.0277180i
$347$	−15.1016	+	3.20994i	−0.810696	+	0.172319i	−0.594567	−	0.804046i	$-0.702677\pi$
$347$	−15.1016	+	3.20994i	−0.810696	+	0.172319i	−0.216129	+	0.976365i	$0.569343\pi$
$348$		0			0
$349$	8.01108	+	5.82039i	0.428823	+	0.311558i	0.781178	−	0.624308i	$-0.214619\pi$
$349$	8.01108	+	5.82039i	0.428823	+	0.311558i	−0.352355	+	0.935866i	$0.614619\pi$
$350$	−0.000524251		3.82834i	−2.80224e−5		0.204633i
$351$		0			0
$352$	2.43900	−	19.0061i	0.129999	−	1.01303i
$353$	4.91732	+	8.51704i	0.261722	+	0.453316i	0.966700	−	0.255913i	$-0.0823762\pi$
$353$	4.91732	+	8.51704i	0.261722	+	0.453316i	−0.704977	+	0.709230i	$0.749043\pi$
$354$		0			0
$355$	14.5529	−	6.47938i	0.772389	−	0.343890i
$356$	−17.5050	+	12.7182i	−0.927765	+	0.674061i
$357$		0			0
$358$	−4.11026	+	12.6501i	−0.217234	+	0.668578i
$359$	0.319789	+	3.04259i	0.0168778	+	0.160582i	0.999714	−	0.0238963i	$-0.00760716\pi$
$359$	0.319789	+	3.04259i	0.0168778	+	0.160582i	−0.982837	+	0.184478i	$0.940940\pi$
$360$		0			0
$361$	−12.6388	+	14.0368i	−0.665198	+	0.738777i
$362$	0.745552	−	1.29133i	0.0391853	−	0.0678710i
$363$		0			0
$364$	3.37677	+	15.8972i	0.176991	+	0.833239i
$365$	0.156441	+	0.481476i	0.00818851	+	0.0252016i
$366$		0			0
$367$	−7.01601	−	3.12373i	−0.366233	−	0.163057i	0.215366	−	0.976534i	$-0.430906\pi$
$367$	−7.01601	−	3.12373i	−0.366233	−	0.163057i	−0.581598	+	0.813476i	$0.697572\pi$
$368$	6.13794	−	1.30466i	0.319962	−	0.0680101i
$369$		0			0
$370$	9.34044	−	6.78623i	0.485586	−	0.352799i
$371$	4.72228	−	10.6025i	0.245168	−	0.550454i
$372$		0			0
$373$	3.34422	−	5.79236i	0.173157	−	0.299917i	−0.766365	−	0.642406i	$-0.777936\pi$
$373$	3.34422	−	5.79236i	0.173157	−	0.299917i	0.939522	+	0.342488i	$0.111270\pi$
$374$	4.56704	+	3.48075i	0.236156	+	0.179985i
$375$		0			0
$376$	5.52602	+	1.17459i	0.284983	+	0.0605749i
$377$	−10.0070	−	7.27052i	−0.515387	−	0.374451i
$378$		0			0
$379$	−4.17467	+	12.8483i	−0.214438	+	0.659973i	0.784755	+	0.619806i	$0.212789\pi$
$379$	−4.17467	+	12.8483i	−0.214438	+	0.659973i	−0.999193	+	0.0401666i	$0.987211\pi$
$380$	0.583842	+	0.648422i	0.0299504	+	0.0332633i
$381$		0			0
$382$	0.606168	−	5.76730i	0.0310142	−	0.295081i
$383$	0.490256	+	0.104207i	0.0250509	+	0.00532473i	0.220420	−	0.975405i	$-0.429257\pi$
$383$	0.490256	+	0.104207i	0.0250509	+	0.00532473i	−0.195369	+	0.980730i	$0.562591\pi$
$384$		0			0
$385$	−5.71491	−	13.6757i	−0.291259	−	0.696976i
$386$	0.172221			0.00876582
$387$		0			0
$388$	−0.534544	+	5.08585i	−0.0271374	+	0.258195i
$389$	17.0893	+	7.60865i	0.866463	+	0.385774i	0.791323	−	0.611399i	$-0.209393\pi$
$389$	17.0893	+	7.60865i	0.866463	+	0.385774i	0.0751402	+	0.997173i	$0.476060\pi$
$390$		0			0
$391$	−3.36363	+	10.3522i	−0.170106	+	0.523532i
$392$	16.7281	+	0.00458146i	0.844895	+	0.000231399i
$393$		0			0
$394$	−6.43802	−	1.36844i	−0.324343	−	0.0689411i
$395$	−12.0228	−	20.8241i	−0.604934	−	1.04778i
$396$		0			0
$397$	−2.36033	+	4.08821i	−0.118461	+	0.205181i	−0.919158	−	0.393889i	$-0.871130\pi$
$397$	−2.36033	+	4.08821i	−0.118461	+	0.205181i	0.800697	+	0.599070i	$0.204463\pi$
$398$	−0.0737234	−	0.226897i	−0.00369542	−	0.0113733i
$399$		0			0
$400$	2.57232	−	1.86890i	0.128616	−	0.0934450i
$401$	−11.3134	−	12.5648i	−0.564965	−	0.627458i	0.391193	−	0.920309i	$-0.372063\pi$
$401$	−11.3134	−	12.5648i	−0.564965	−	0.627458i	−0.956158	+	0.292851i	$0.905396\pi$
$402$		0			0
$403$	27.7676	+	12.3629i	1.38320	+	0.615842i
$404$	13.0079	−	5.79151i	0.647169	−	0.288138i
$405$		0			0
$406$	−4.12526	+	3.71337i	−0.204733	+	0.184292i
$407$	17.4813	−	28.7375i	0.866518	−	1.42446i
$408$		0			0
$409$	−17.0587	+	18.9456i	−0.843496	+	0.936797i	−0.998694	−	0.0510860i	$-0.983732\pi$
$409$	−17.0587	+	18.9456i	−0.843496	+	0.936797i	0.155198	+	0.987883i	$0.450398\pi$
$410$	1.28919	−	12.2658i	0.0636684	−	0.605765i
$411$		0			0
$412$	7.96741	−	24.5212i	0.392526	−	1.20807i
$413$	0.0920680	+	0.00968948i	0.00453037	+	0.000476788i
$414$		0			0
$415$	−7.16637	+	3.19067i	−0.351783	+	0.156624i
$416$	−15.3626	+	17.0619i	−0.753212	+	0.836526i
$417$		0			0
$418$	−0.675276	−	0.319383i	−0.0330288	−	0.0156216i
$419$	22.6624			1.10713			0.553565	−	0.832806i	$-0.313267\pi$
$419$	22.6624			1.10713			0.553565	+	0.832806i	$0.313267\pi$
$420$		0			0
$421$	15.1994	+	11.0430i	0.740774	+	0.538204i	0.892954	−	0.450149i	$-0.148629\pi$
$421$	15.1994	+	11.0430i	0.740774	+	0.538204i	−0.152179	+	0.988353i	$0.548629\pi$
$422$	−1.05014	−	9.99140i	−0.0511199	−	0.486374i
$423$		0			0
$424$	10.2543	−	2.17963i	0.497994	−	0.105852i
$425$	0.576513	+	5.48515i	0.0279650	+	0.266069i
$426$		0			0
$427$	−9.41041	−	5.43482i	−0.455401	−	0.263009i
$428$	2.07200			0.100154
$429$		0			0
$430$	−3.56769	−	6.17942i	−0.172049	−	0.297998i
$431$	−22.9484	+	25.4867i	−1.10538	+	1.22765i	−0.133786	+	0.991010i	$0.542714\pi$
$431$	−22.9484	+	25.4867i	−1.10538	+	1.22765i	−0.971597	+	0.236642i	$0.923953\pi$
$432$		0			0
$433$	−2.57803	+	1.87305i	−0.123892	+	0.0900130i	−0.648006	−	0.761635i	$-0.724397\pi$
$433$	−2.57803	+	1.87305i	−0.123892	+	0.0900130i	0.524114	+	0.851648i	$0.324397\pi$
$434$	8.01838	−	11.0332i	0.384895	−	0.529609i
$435$		0			0
$436$	−1.02334	−	9.73641i	−0.0490090	−	0.466289i
$437$	0.148012	−	1.40824i	0.00708035	−	0.0673651i
$438$		0			0
$439$	−6.18390	+	10.7108i	−0.295141	+	0.511200i	−0.975018	−	0.222127i	$-0.928700\pi$
$439$	−6.18390	+	10.7108i	−0.295141	+	0.511200i	0.679877	+	0.733327i	$0.262033\pi$
$440$	6.95755	−	11.4375i	0.331688	−	0.545261i
$441$		0			0
$442$	−2.12607	−	6.54336i	−0.101127	−	0.311236i
$443$	4.66181	−	2.07557i	0.221489	−	0.0986133i	−0.292992	−	0.956115i	$-0.594651\pi$
$443$	4.66181	−	2.07557i	0.221489	−	0.0986133i	0.514482	+	0.857501i	$0.327984\pi$
$444$		0			0
$445$	−23.1269	+	4.91578i	−1.09632	+	0.233030i
$446$	12.9222	+	14.3516i	0.611884	+	0.679566i
$447$		0			0
$448$	1.44904	+	1.99500i	0.0684606	+	0.0942550i
$449$	0.378022	+	1.16343i	0.0178400	+	0.0549057i	0.959580	−	0.281435i	$-0.0908105\pi$
$449$	0.378022	+	1.16343i	0.0178400	+	0.0549057i	−0.941740	+	0.336341i	$0.890810\pi$
$450$		0			0
$451$	−10.3180	−	34.4192i	−0.485855	−	1.62074i
$452$	11.7601	+	20.3692i	0.553150	+	0.958085i
$453$		0			0
$454$	−11.4861	−	8.34516i	−0.539071	−	0.391658i
$455$	−3.69462	+	17.3701i	−0.173206	+	0.814324i
$456$		0			0
$457$	3.43531	+	3.81530i	0.160697	+	0.178472i	0.818116	−	0.575053i	$-0.195019\pi$
$457$	3.43531	+	3.81530i	0.160697	+	0.178472i	−0.657419	+	0.753525i	$0.728352\pi$
$458$	−4.44394	−	1.97857i	−0.207652	−	0.0924524i
$459$		0			0
$460$	10.8213	+	2.30014i	0.504546	+	0.107245i
$461$	−22.7757			−1.06077			−0.530386	−	0.847757i	$-0.677953\pi$
$461$	−22.7757			−1.06077			−0.530386	+	0.847757i	$0.677953\pi$
$462$		0			0
$463$	29.8445			1.38699			0.693496	−	0.720460i	$-0.256069\pi$
$463$	29.8445			1.38699			0.693496	+	0.720460i	$0.256069\pi$
$464$	4.50905	+	0.958428i	0.209327	+	0.0444939i
$465$		0			0
$466$	−15.8136	−	7.04066i	−0.732550	−	0.326152i
$467$	−1.03715	−	1.15187i	−0.0479936	−	0.0533022i	0.718670	−	0.695351i	$-0.244751\pi$
$467$	−1.03715	−	1.15187i	−0.0479936	−	0.0533022i	−0.766664	+	0.642049i	$0.778085\pi$
$468$		0			0
$469$	−10.7332	−	9.66692i	−0.495615	−	0.446377i
$470$	2.17725	+	1.58186i	0.100429	+	0.0729660i
$471$		0			0
$472$	0.0418089	+	0.0724152i	0.00192441	+	0.00333318i
$473$	−16.5339	−	12.6012i	−0.760231	−	0.579406i
$474$		0			0
$475$	−0.221714	−	0.682364i	−0.0101729	−	0.0313090i
$476$	10.4488	−	1.09676i	0.478918	−	0.0502700i
$477$		0			0
$478$	3.91229	+	4.34504i	0.178944	+	0.198737i
$479$	−11.4888	+	2.44202i	−0.524937	+	0.111579i	−0.462755	−	0.886486i	$-0.653139\pi$
$479$	−11.4888	+	2.44202i	−0.524937	+	0.111579i	−0.0621816	+	0.998065i	$0.519806\pi$
$480$		0			0
$481$	−36.8178	+	16.3923i	−1.67875	+	0.747427i
$482$	−4.59667	−	14.1471i	−0.209372	−	0.644382i
$483$		0			0
$484$	2.55004	−	16.8112i	0.115911	−	0.764145i
$485$	−2.79400	+	4.83936i	−0.126869	+	0.219744i
$486$		0			0
$487$	−0.767648	+	7.30368i	−0.0347854	+	0.330961i	0.963265	+	0.268552i	$0.0865451\pi$
$487$	−0.767648	+	7.30368i	−0.0347854	+	0.330961i	−0.998051	+	0.0624094i	$0.980122\pi$
$488$	−1.02599	−	9.76169i	−0.0464446	−	0.441891i
$489$		0			0
$490$	7.27890	+	3.24316i	0.328827	+	0.146511i
$491$	−10.4859	+	7.61845i	−0.473222	+	0.343816i	−0.798696	−	0.601735i	$-0.794476\pi$
$491$	−10.4859	+	7.61845i	−0.473222	+	0.343816i	0.325474	+	0.945551i	$0.394476\pi$
$492$		0			0
$493$	−5.35055	+	5.94239i	−0.240977	+	0.267632i
$494$	0.447507	+	0.775106i	0.0201343	+	0.0348737i
$495$		0			0
$496$	−11.3277			−0.508630
$497$	−0.00341699	+	24.9526i	−0.000153273	+	1.11928i
$498$		0			0
$499$	−0.457159	−	4.34958i	−0.0204653	−	0.194714i	0.979512	−	0.201383i	$-0.0645437\pi$
$499$	−0.457159	−	4.34958i	−0.0204653	−	0.194714i	−0.999978	+	0.00666940i	$0.997877\pi$
$500$	18.2526	−	3.87971i	0.816282	−	0.173506i
$501$		0			0
$502$	1.21413	+	11.5517i	0.0541893	+	0.515577i
$503$	25.8970	+	18.8153i	1.15469	+	0.838931i	0.989097	−	0.147263i	$-0.0470464\pi$
$503$	25.8970	+	18.8153i	1.15469	+	0.838931i	0.165592	+	0.986194i	$0.447046\pi$
$504$		0			0
$505$	15.5592			0.692374
$506$	−9.30700	+	1.75645i	−0.413746	+	0.0780837i
$507$		0			0
$508$	−5.65368	+	6.27905i	−0.250842	+	0.278588i
$509$	19.7525	−	8.79440i	0.875516	−	0.389805i	0.0807597	−	0.996734i	$-0.474265\pi$
$509$	19.7525	−	8.79440i	0.875516	−	0.389805i	0.794756	+	0.606929i	$0.207599\pi$
$510$		0			0
$511$	−0.788628	−	0.0829973i	−0.0348869	−	0.00367159i
$512$	4.83132	−	14.8693i	0.213516	−	0.657135i
$513$		0			0
$514$	−0.404000	+	3.84381i	−0.0178197	+	0.169543i
$515$	18.8518	−	20.9371i	0.830711	−	0.922598i
$516$		0			0
$517$	7.63004	+	1.80544i	0.335569	+	0.0794032i
$518$	3.75755	+	17.6898i	0.165097	+	0.777244i
$519$		0			0
$520$	−14.6534	+	6.52413i	−0.642596	+	0.286102i
$521$	−1.34423	−	0.598491i	−0.0588919	−	0.0262204i	0.377079	−	0.926181i	$-0.376928\pi$
$521$	−1.34423	−	0.598491i	−0.0588919	−	0.0262204i	−0.435971	+	0.899961i	$0.643595\pi$
$522$		0			0
$523$	23.1035	+	25.6590i	1.01025	+	1.12199i	0.992512	+	0.122149i	$0.0389786\pi$
$523$	23.1035	+	25.6590i	1.01025	+	1.12199i	0.0177343	+	0.999843i	$0.494355\pi$
$524$	−6.17321	+	4.48510i	−0.269678	+	0.195932i
$525$		0			0
$526$	−4.70608	−	14.4838i	−0.205195	−	0.631525i
$527$	9.82471	−	17.0169i	0.427971	−	0.741267i
$528$		0			0
$529$	2.52319	+	4.37030i	0.109704	+	0.190013i
$530$	4.88484	+	1.03830i	0.212184	+	0.0451011i
$531$		0			0
$532$	−1.29989	+	0.422162i	−0.0563572	+	0.0183030i
$533$	−13.3040	+	40.9455i	−0.576260	+	1.77355i
$534$		0			0
$535$	2.06837	+	0.920898i	0.0894235	+	0.0398139i
$536$	1.36378	−	12.9755i	0.0589063	−	0.560456i
$537$		0			0
$538$	10.9589			0.472470
$539$	23.2101	+	0.538191i	0.999731	+	0.0231815i
$540$		0			0
$541$	5.98408	+	1.27195i	0.257276	+	0.0546856i	0.334744	−	0.942309i	$-0.391350\pi$
$541$	5.98408	+	1.27195i	0.257276	+	0.0546856i	−0.0774681	+	0.996995i	$0.524684\pi$
$542$	−0.497807	+	4.73632i	−0.0213827	+	0.203442i
$543$		0			0
$544$	9.93126	+	11.0298i	0.425799	+	0.472898i
$545$	3.30579	−	10.1742i	0.141604	−	0.435813i
$546$		0			0
$547$	20.2909	+	14.7422i	0.867575	+	0.630330i	0.929935	−	0.367724i	$-0.119863\pi$
$547$	20.2909	+	14.7422i	0.867575	+	0.630330i	−0.0623603	+	0.998054i	$0.519863\pi$
$548$	−2.47262	−	0.525572i	−0.105625	−	0.0224513i
$549$		0			0
$550$	−3.94614	+	2.73115i	−0.168264	+	0.116457i
$551$	0.520108	−	0.900853i	0.0221573	−	0.0383776i
$552$		0			0
$553$	37.4587	−	3.93188i	1.59290	−	0.167200i
$554$	−6.48294	+	4.71013i	−0.275434	+	0.200114i
$555$		0			0
$556$	−13.3910	+	2.84635i	−0.567905	+	0.120712i
$557$	28.0427	+	12.4854i	1.18821	+	0.529023i	0.903082	−	0.429468i	$-0.141299\pi$
$557$	28.0427	+	12.4854i	1.18821	+	0.529023i	0.285123	+	0.958491i	$0.407965\pi$
$558$		0			0
$559$	7.69694	+	23.6887i	0.325546	+	1.00193i
$560$	−1.37513	−	6.47384i	−0.0581099	−	0.273570i
$561$		0			0
$562$	3.50164	−	6.06502i	0.147708	−	0.255838i
$563$	11.6914	−	12.9846i	0.492733	−	0.547235i	−0.444573	−	0.895742i	$-0.646645\pi$
$563$	11.6914	−	12.9846i	0.492733	−	0.547235i	0.937306	+	0.348507i	$0.113311\pi$
$564$		0			0
$565$	2.68649	+	25.5602i	0.113021	+	1.07533i
$566$	−4.22789	+	13.0121i	−0.177711	+	0.546939i
$567$		0			0
$568$	−18.2336	+	13.2475i	−0.765063	+	0.555851i
$569$	−21.3265	+	9.49519i	−0.894055	+	0.398059i	−0.801742	−	0.597671i	$-0.796093\pi$
$569$	−21.3265	+	9.49519i	−0.894055	+	0.398059i	−0.0923138	+	0.995730i	$0.529426\pi$
$570$		0			0
$571$	−7.38432	−	12.7900i	−0.309024	−	0.535245i	0.669125	−	0.743150i	$-0.266669\pi$
$571$	−7.38432	−	12.7900i	−0.309024	−	0.535245i	−0.978149	+	0.207905i	$0.933336\pi$
$572$	−13.9753	+	14.8237i	−0.584336	+	0.619809i
$573$		0			0
$574$	16.7291	+	9.66162i	0.698260	+	0.403268i
$575$	−7.35967	−	5.34712i	−0.306920	−	0.222990i
$576$		0			0
$577$	35.4430	−	7.53363i	1.47551	−	0.313629i	0.601240	−	0.799069i	$-0.294674\pi$
$577$	35.4430	−	7.53363i	1.47551	−	0.313629i	0.874270	+	0.485439i	$0.161340\pi$
$578$	6.85651	−	1.45740i	0.285193	−	0.0606197i
$579$		0			0
$580$	6.57499	+	4.77701i	0.273011	+	0.198354i
$581$	0.00168265	−	12.2875i	6.98079e−5	−	0.509773i
$582$		0			0
$583$	14.2972	−	2.69823i	0.592131	−	0.111749i
$584$	−0.358123	−	0.620288i	−0.0148193	−	0.0256677i
$585$		0			0
$586$	−14.7001	+	6.54493i	−0.607258	+	0.270368i
$587$	−14.7176	+	10.6930i	−0.607461	+	0.441346i	−0.848519	−	0.529164i	$-0.822506\pi$
$587$	−14.7176	+	10.6930i	−0.607461	+	0.441346i	0.241058	+	0.970511i	$0.422506\pi$
$588$		0			0
$589$	−0.789892	+	2.43104i	−0.0325469	+	0.100169i
$590$	0.00416367	+	0.0396147i	0.000171416	+	0.00163091i
$591$		0			0
$592$	10.0502	−	11.1618i	0.413059	−	0.458748i
$593$	−21.2413	+	36.7910i	−0.872276	+	1.51083i	−0.0126393	+	0.999920i	$0.504023\pi$
$593$	−21.2413	+	36.7910i	−0.872276	+	1.51083i	−0.859637	+	0.510906i	$0.829310\pi$
$594$		0			0
$595$	10.9179	+	3.54909i	0.447590	+	0.145499i
$596$	−2.28881	−	7.04423i	−0.0937533	−	0.288543i
$597$		0			0
$598$	10.3670	+	4.61567i	0.423936	+	0.188749i
$599$	−17.2038	+	3.65677i	−0.702927	+	0.149412i	−0.545490	−	0.838117i	$-0.683656\pi$
$599$	−17.2038	+	3.65677i	−0.702927	+	0.149412i	−0.157437	+	0.987529i	$0.550323\pi$
$600$		0			0
$601$	−24.8322	+	18.0416i	−1.01293	+	0.735934i	−0.964821	−	0.262909i	$-0.915318\pi$
$601$	−24.8322	+	18.0416i	−1.01293	+	0.735934i	−0.0481049	+	0.998842i	$0.515318\pi$
$602$	11.1156	−	1.16676i	0.453039	−	0.0475536i
$603$		0			0
$604$	−12.4263	+	21.5229i	−0.505617	+	0.875755i
$605$	10.0173	−	15.6484i	0.407260	−	0.636197i
$606$		0			0
$607$	−34.6965	−	7.37497i	−1.40829	−	0.299341i	−0.559832	−	0.828606i	$-0.689134\pi$
$607$	−34.6965	−	7.37497i	−1.40829	−	0.299341i	−0.848456	+	0.529266i	$0.822468\pi$
$608$	−1.56202	−	1.13488i	−0.0633484	−	0.0460253i
$609$		0			0
$610$	1.44489	−	4.44692i	0.0585020	−	0.180051i
$611$	−6.28607	−	6.98139i	−0.254307	−	0.282437i
$612$		0			0
$613$	−1.43644	+	13.6668i	−0.0580172	+	0.551997i	0.926449	+	0.376421i	$0.122845\pi$
$613$	−1.43644	+	13.6668i	−0.0580172	+	0.551997i	−0.984466	+	0.175576i	$0.943821\pi$
$614$	−5.76086	−	1.22451i	−0.232489	−	0.0494171i
$615$		0			0
$616$	11.9315	+	17.2444i	0.480733	+	0.694797i
$617$	−2.42135			−0.0974798			−0.0487399	−	0.998812i	$-0.515521\pi$
$617$	−2.42135			−0.0974798			−0.0487399	+	0.998812i	$0.515521\pi$
$618$		0			0
$619$	1.45422	−	13.8360i	0.0584499	−	0.556114i	−0.925635	−	0.378417i	$-0.876469\pi$
$619$	1.45422	−	13.8360i	0.0584499	−	0.556114i	0.984085	−	0.177697i	$-0.0568648\pi$
$620$	−18.2444	−	8.12293i	−0.732713	−	0.326225i
$621$		0			0
$622$	−0.545273	+	1.67818i	−0.0218634	+	0.0672887i
$623$	7.70491	−	36.2244i	0.308691	−	1.45130i
$624$		0			0
$625$	9.44472	+	2.00754i	0.377789	+	0.0803015i
$626$	7.66754	+	13.2806i	0.306457	+	0.530798i
$627$		0			0
$628$	5.27010	−	9.12808i	0.210300	−	0.364250i
$629$	8.05102	+	24.7785i	0.321015	+	0.987984i
$630$		0			0
$631$	−31.3804	+	22.7992i	−1.24923	+	0.907620i	−0.998177	−	0.0603525i	$-0.980778\pi$
$631$	−31.3804	+	22.7992i	−1.24923	+	0.907620i	−0.251055	+	0.967973i	$0.580778\pi$
$632$	22.7636	+	25.2816i	0.905488	+	1.00565i
$633$		0			0
$634$	−2.76333	−	1.23031i	−0.109746	−	0.0488620i
$635$	−8.43449	+	3.75527i	−0.334712	+	0.149024i
$636$		0			0
$637$	−22.4997	−	16.3564i	−0.891473	−	0.648066i
$638$	−6.77082	−	1.60213i	−0.268059	−	0.0634289i
$639$		0			0
$640$	12.3500	−	13.7160i	0.488175	−	0.542174i
$641$	−2.64384	+	25.1545i	−0.104426	+	0.993543i	0.809351	+	0.587326i	$0.199819\pi$
$641$	−2.64384	+	25.1545i	−0.104426	+	0.993543i	−0.913776	+	0.406218i	$0.866848\pi$
$642$		0			0
$643$	−0.0277191	+	0.0853105i	−0.00109313	+	0.00336432i	−0.951602	−	0.307334i	$-0.900563\pi$
$643$	−0.0277191	+	0.0853105i	−0.00109313	+	0.00336432i	0.950508	+	0.310699i	$0.100563\pi$
$644$	−10.1876	+	14.0180i	−0.401447	+	0.552385i
$645$		0			0
$646$	0.528569	−	0.235334i	0.0207963	−	0.00925909i
$647$	2.90392	−	3.22513i	0.114165	−	0.126793i	−0.683353	−	0.730088i	$-0.739479\pi$
$647$	2.90392	−	3.22513i	0.114165	−	0.126793i	0.797518	+	0.603295i	$0.206146\pi$
$648$		0			0
$649$	0.0557078	+	0.101806i	0.00218672	+	0.00399622i
$650$	5.75003			0.225535
$651$		0			0
$652$	−17.1569	−	12.4652i	−0.671915	−	0.488175i
$653$	−2.21857	−	21.1083i	−0.0868195	−	0.826032i	−0.948115	−	0.317928i	$-0.897013\pi$
$653$	−2.21857	−	21.1083i	−0.0868195	−	0.826032i	0.861295	−	0.508104i	$-0.169654\pi$
$654$		0			0
$655$	−8.15578	+	1.73357i	−0.318673	+	0.0677360i
$656$	−1.67714	−	15.9569i	−0.0654812	−	0.623012i
$657$		0			0
$658$	−3.65099	+	2.10723i	−0.142331	+	0.0821486i
$659$	25.4606			0.991805			0.495902	−	0.868378i	$-0.334837\pi$
$659$	25.4606			0.991805			0.495902	+	0.868378i	$0.334837\pi$
$660$		0			0
$661$	−4.77124	−	8.26403i	−0.185580	−	0.321433i	0.758192	−	0.652031i	$-0.226083\pi$
$661$	−4.77124	−	8.26403i	−0.185580	−	0.321433i	−0.943772	+	0.330598i	$0.892750\pi$
$662$	−6.22400	+	6.91245i	−0.241903	+	0.268660i
$663$		0			0
$664$	8.97885	−	6.52352i	0.348447	−	0.253162i
$665$	−1.48524	−	0.156310i	−0.0575950	−	0.00606146i
$666$		0			0
$667$	−1.37863	−	13.1168i	−0.0533809	−	0.507885i
$668$	3.16029	−	30.0681i	0.122275	−	1.16337i
$669$		0			0
$670$	3.10758	−	5.38249i	0.120056	−	0.207944i
$671$	−1.11322	−	13.5770i	−0.0429754	−	0.524135i
$672$		0			0
$673$	5.11101	+	15.7301i	0.197015	+	0.606350i	0.999947	+	0.0102793i	$0.00327207\pi$
$673$	5.11101	+	15.7301i	0.197015	+	0.606350i	−0.802932	+	0.596070i	$0.796728\pi$
$674$	−6.92975	+	3.08532i	−0.266924	+	0.118842i
$675$		0			0
$676$	4.22037	−	0.897068i	0.162322	−	0.0345026i
$677$	1.62842	+	1.80854i	0.0625852	+	0.0695079i	0.773624	−	0.633645i	$-0.218442\pi$
$677$	1.62842	+	1.80854i	0.0625852	+	0.0695079i	−0.711039	+	0.703152i	$0.751775\pi$
$678$		0			0
$679$	−5.14386	−	7.08196i	−0.197403	−	0.271781i
$680$	3.20430	+	9.86181i	0.122879	+	0.378183i
$681$		0			0
$682$	17.0930	+	0.391665i	0.654526	+	0.0149976i
$683$	−2.64045	−	4.57339i	−0.101034	−	0.174996i	0.811077	−	0.584939i	$-0.198882\pi$
$683$	−2.64045	−	4.57339i	−0.101034	−	0.174996i	−0.912111	+	0.409944i	$0.865548\pi$
$684$		0			0
$685$	−2.23470	−	1.62360i	−0.0853834	−	0.0620347i
$686$	−9.27936	+	8.34827i	−0.354287	+	0.318738i
$687$		0			0
$688$	−6.21127	−	6.89832i	−0.236803	−	0.262996i
$689$	−15.9255	−	7.09051i	−0.606715	−	0.270127i
$690$		0			0
$691$	20.6370	+	4.38653i	0.785069	+	0.166872i	0.582970	−	0.812494i	$-0.301890\pi$
$691$	20.6370	+	4.38653i	0.785069	+	0.166872i	0.202099	+	0.979365i	$0.435224\pi$
$692$	5.68761			0.216211
$693$		0			0
$694$	10.4053			0.394980
$695$	−14.6326	−	3.11025i	−0.555046	−	0.117979i
$696$		0			0
$697$	25.4256	+	11.3202i	0.963062	+	0.428783i
$698$	−4.46561	−	4.95957i	−0.169026	−	0.187722i
$699$		0			0
$700$	−1.82675	+	8.58838i	−0.0690445	+	0.324610i
$701$	22.7280	+	16.5128i	0.858423	+	0.623681i	0.927456	−	0.373934i	$-0.121991\pi$
$701$	22.7280	+	16.5128i	0.858423	+	0.623681i	−0.0690324	+	0.997614i	$0.521991\pi$
$702$		0			0
$703$	−1.69463	−	2.93518i	−0.0639141	−	0.110703i
$704$	−1.02224	+	2.91700i	−0.0385272	+	0.109939i
$705$		0			0
$706$	−2.04822	−	6.30378i	−0.0770859	−	0.237246i
$707$	−9.91582	+	22.2631i	−0.372923	+	0.837290i
$708$		0			0
$709$	−3.41227	−	3.78971i	−0.128150	−	0.142325i	0.675655	−	0.737218i	$-0.263861\pi$
$709$	−3.41227	−	3.78971i	−0.128150	−	0.142325i	−0.803805	+	0.594893i	$0.797194\pi$
$710$	−10.5017	+	2.23221i	−0.394123	+	0.0837735i
$711$		0			0
$712$	30.5589	−	13.6057i	1.14524	−	0.509895i
$713$	10.0152	+	30.8235i	0.375071	+	1.15435i
$714$		0			0
$715$	−20.5392	+	8.58640i	−0.768121	+	0.321113i
$716$	−15.2534	+	26.4196i	−0.570046	+	0.987348i
$717$		0			0
$718$	0.215527	−	2.05060i	0.00804338	−	0.0765276i
$719$	2.51282	+	23.9079i	0.0937123	+	0.891613i	0.935862	+	0.352368i	$0.114623\pi$
$719$	2.51282	+	23.9079i	0.0937123	+	0.891613i	−0.842149	+	0.539244i	$0.818710\pi$
$720$		0			0
$721$	17.9439	+	40.3176i	0.668267	+	1.50151i
$722$	10.2988	−	7.48254i	0.383283	−	0.278471i
$723$		0			0
$724$	2.28838	−	2.54150i	0.0850468	−	0.0944541i
$725$	−3.34144	−	5.78754i	−0.124098	−	0.214944i
$726$		0			0
$727$	14.6738			0.544221			0.272111	−	0.962266i	$-0.412278\pi$
$727$	14.6738			0.544221			0.272111	+	0.962266i	$0.412278\pi$
$728$	0.00344059	−	25.1249i	0.000127517	−	0.931192i
$729$		0			0
$730$	−0.0356648	−	0.339328i	−0.00132001	−	0.0125591i
$731$	15.7500	−	3.34777i	0.582535	−	0.123822i
$732$		0			0
$733$	−5.07226	−	48.2593i	−0.187348	−	1.78250i	−0.534977	−	0.844867i	$-0.679680\pi$
$733$	−5.07226	−	48.2593i	−0.187348	−	1.78250i	0.347628	−	0.937632i	$-0.386987\pi$
$734$	4.18750	+	3.04239i	0.154563	+	0.112297i
$735$		0			0
$736$	−24.4805			−0.902363
$737$	2.30478	−	17.9602i	0.0848977	−	0.661573i
$738$		0			0
$739$	−7.55017	+	8.38531i	−0.277737	+	0.308459i	−0.865833	−	0.500333i	$-0.833211\pi$
$739$	−7.55017	+	8.38531i	−0.277737	+	0.308459i	0.588096	+	0.808791i	$0.299878\pi$
$740$	24.1907	−	10.7704i	0.889268	−	0.395928i
$741$		0			0
$742$	−4.59877	+	6.32784i	−0.168826	+	0.232302i
$743$	−1.07005	+	3.29327i	−0.0392562	+	0.120818i	−0.968764	−	0.247984i	$-0.920232\pi$
$743$	−1.07005	+	3.29327i	−0.0392562	+	0.120818i	0.929508	+	0.368802i	$0.120232\pi$
$744$		0			0
$745$	0.845999	−	8.04914i	0.0309950	−	0.294898i
$746$	−3.01629	+	3.34993i	−0.110434	+	0.122650i
$747$		0			0
$748$	8.58604	+	9.98665i	0.313937	+	0.365148i
$749$	−2.63585	+	2.37268i	−0.0963119	+	0.0866957i
$750$		0			0
$751$	1.95566	−	0.870716i	0.0713630	−	0.0317729i	−0.370745	−	0.928735i	$-0.620898\pi$
$751$	1.95566	−	0.870716i	0.0713630	−	0.0317729i	0.442108	+	0.896962i	$0.354231\pi$
$752$	3.19840	+	1.42402i	0.116634	+	0.0519287i
$753$		0			0
$754$	5.57820	+	6.19522i	0.203146	+	0.225617i
$755$	−21.9703	+	15.9624i	−0.799581	+	0.580930i
$756$		0			0
$757$	−11.3705	−	34.9949i	−0.413269	−	1.27191i	−0.913790	−	0.406186i	$-0.866858\pi$
$757$	−11.3705	−	34.9949i	−0.413269	−	1.27191i	0.500522	−	0.865724i	$-0.333142\pi$
$758$	4.55246	−	7.88509i	0.165353	−	0.286399i
$759$		0			0
$760$	−0.674460	−	1.16820i	−0.0244652	−	0.0423750i
$761$	28.7562	+	6.11232i	1.04241	+	0.221571i	0.697143	−	0.716933i	$-0.254454\pi$
$761$	28.7562	+	6.11232i	1.04241	+	0.221571i	0.345269	+	0.938504i	$0.387788\pi$
$762$		0			0
$763$	12.4511	+	11.2141i	0.450760	+	0.405978i
$764$	4.11007	−	12.6495i	0.148697	−	0.457643i
$765$		0			0
$766$	−0.308592	−	0.137394i	−0.0111499	−	0.00496425i
$767$	0.0145343	−	0.138285i	0.000524804	−	0.00499317i
$768$		0			0
$769$	−1.47798			−0.0532972			−0.0266486	−	0.999645i	$-0.508484\pi$
$769$	−1.47798			−0.0532972			−0.0266486	+	0.999645i	$0.508484\pi$
$770$	1.85117	+	9.81629i	0.0667117	+	0.353755i
$771$		0			0
$772$	0.386366	+	0.0821247i	0.0139056	+	0.00295573i
$773$	1.96111	−	18.6587i	0.0705363	−	0.671108i	−0.900936	−	0.433953i	$-0.857118\pi$
$773$	1.96111	−	18.6587i	0.0705363	−	0.671108i	0.971472	−	0.237155i	$-0.0762149\pi$
$774$		0			0
$775$	10.9884	+	12.2039i	0.394717	+	0.438377i
$776$	2.44306	−	7.51895i	0.0877006	−	0.269915i
$777$		0			0
$778$	−10.1997	−	7.41054i	−0.365678	−	0.265681i
$779$	−3.54145	−	0.752758i	−0.126885	−	0.0269703i
$780$		0			0
$781$	−25.7204	+	17.8012i	−0.920347	+	0.636978i
$782$	3.66802	−	6.35320i	0.131168	−	0.227190i
$783$		0			0
$784$	10.1396	+	2.15814i	0.362128	+	0.0770763i
$785$	9.31782	−	6.76979i	0.332567	−	0.241624i
$786$		0			0
$787$	18.5419	−	3.94120i	0.660946	−	0.140488i	0.134787	−	0.990875i	$-0.456965\pi$
$787$	18.5419	−	3.94120i	0.660946	−	0.140488i	0.526159	+	0.850386i	$0.323632\pi$
$788$	−13.7907	−	6.14002i	−0.491274	−	0.218729i
$789$		0			0
$790$	5.00790	+	15.4127i	0.178173	+	0.548360i
$791$	−38.2854	−	12.4455i	−1.36127	−	0.442510i
$792$		0			0
$793$	−8.16096	+	14.1352i	−0.289804	+	0.501956i
$794$	2.12887	−	2.36435i	0.0755509	−	0.0839077i
$795$		0			0
$796$	−0.0571961	−	0.544184i	−0.00202726	−	0.0192881i
$797$	12.2905	−	37.8263i	0.435352	−	1.33988i	−0.457373	−	0.889275i	$-0.651210\pi$
$797$	12.2905	−	37.8263i	0.435352	−	1.33988i	0.892725	−	0.450601i	$-0.148790\pi$
$798$		0			0
$799$	−4.91323	+	3.56967i	−0.173818	+	0.126286i
$800$	−11.3318	+	5.04525i	−0.400640	+	0.178376i
$801$		0			0
$802$	5.69757	+	9.86849i	0.201188	+	0.348468i
$803$	−0.477178	−	0.872039i	−0.0168392	−	0.0307736i
$804$		0			0
$805$	−16.4000	+	9.46554i	−0.578024	+	0.333617i
$806$	−16.5731	−	12.0410i	−0.583762	−	0.424128i
$807$		0			0
$808$	−21.5320	+	4.57677i	−0.757494	+	0.161010i
$809$	54.8176	−	11.6518i	1.92728	−	0.409657i	0.927968	−	0.372661i	$-0.121555\pi$
$809$	54.8176	−	11.6518i	1.92728	−	0.409657i	0.999315	−	0.0369956i	$-0.0117788\pi$
$810$		0			0
$811$	16.9878	+	12.3423i	0.596521	+	0.433398i	0.844642	−	0.535331i	$-0.179813\pi$
$811$	16.9878	+	12.3423i	0.596521	+	0.433398i	−0.248121	+	0.968729i	$0.579813\pi$
$812$	−11.0255	+	6.36355i	−0.386919	+	0.223317i
$813$		0			0
$814$	−15.5512	+	16.4952i	−0.545068	+	0.578157i
$815$	−11.5867	−	20.0687i	−0.405863	−	0.702976i
$816$		0			0
$817$	−1.91356	+	0.851972i	−0.0669470	+	0.0298067i
$818$	13.9004	−	10.0993i	0.486017	−	0.353112i
$819$		0			0
$820$	8.74123	−	26.9027i	0.305257	−	0.939485i
$821$	3.38979	+	32.2517i	0.118304	+	1.12559i	0.879112	+	0.476615i	$0.158136\pi$
$821$	3.38979	+	32.2517i	0.118304	+	1.12559i	−0.760808	+	0.648977i	$0.775197\pi$
$822$		0			0
$823$	1.17404	−	1.30391i	0.0409246	−	0.0454514i	−0.722335	−	0.691543i	$-0.756931\pi$
$823$	1.17404	−	1.30391i	0.0409246	−	0.0454514i	0.763260	+	0.646092i	$0.223598\pi$
$824$	−19.9300	+	34.5197i	−0.694294	+	1.20255i
$825$		0			0
$826$	−0.0593368	−	0.0192887i	−0.00206459	−	0.000671139i
$827$	−3.60014	−	11.0801i	−0.125189	−	0.385293i	0.868746	−	0.495257i	$-0.164926\pi$
$827$	−3.60014	−	11.0801i	−0.125189	−	0.385293i	−0.993935	+	0.109965i	$0.964926\pi$
$828$		0			0
$829$	17.9410	+	7.98784i	0.623116	+	0.277429i	0.693910	−	0.720062i	$-0.255887\pi$
$829$	17.9410	+	7.98784i	0.623116	+	0.277429i	−0.0707938	+	0.997491i	$0.522553\pi$
$830$	5.17143	−	1.09922i	0.179503	−	0.0381545i
$831$		0			0
$832$	2.99612	−	2.17681i	0.103872	−	0.0754673i
$833$	−12.0362	+	13.3602i	−0.417030	+	0.462904i
$834$		0			0
$835$	16.5185	−	28.6108i	0.571645	−	0.990119i
$836$	−1.36264	−	1.03853i	−0.0471277	−	0.0359181i
$837$		0			0
$838$	−14.9399	−	3.17557i	−0.516089	−	0.109698i
$839$	−35.8478	−	26.0450i	−1.23760	−	0.899173i	−0.240168	−	0.970731i	$-0.577203\pi$
$839$	−35.8478	−	26.0450i	−1.23760	−	0.899173i	−0.997436	+	0.0715587i	$0.977203\pi$
$840$		0			0
$841$	−5.96745	+	18.3659i	−0.205774	+	0.633307i
$842$	−8.47261	−	9.40978i	−0.291985	−	0.324283i
$843$		0			0
$844$	2.40855	−	22.9158i	0.0829056	−	0.788794i
$845$	4.61168	+	0.980242i	0.158646	+	0.0337213i
$846$		0			0
$847$	16.0067	+	24.3061i	0.549998	+	0.835166i
$848$	6.49678			0.223100
$849$		0			0
$850$	0.388549	−	3.69679i	0.0133271	−	0.126799i
$851$	−39.2578	−	17.4787i	−1.34574	−	0.599162i
$852$		0			0
$853$	6.10569	−	18.7914i	0.209055	−	0.643405i	−0.790468	−	0.612504i	$-0.790162\pi$
$853$	6.10569	−	18.7914i	0.209055	−	0.643405i	0.999522	−	0.0309007i	$-0.00983757\pi$
$854$	5.44213	+	4.90146i	0.186226	+	0.167725i
$855$		0			0
$856$	−3.13326	−	0.665996i	−0.107093	−	0.0227633i
$857$	−1.69370	−	2.93357i	−0.0578556	−	0.100209i	0.835647	−	0.549267i	$-0.185093\pi$
$857$	−1.69370	−	2.93357i	−0.0578556	−	0.100209i	−0.893503	+	0.449058i	$0.851760\pi$
$858$		0			0
$859$	−8.04855	+	13.9405i	−0.274613	+	0.475643i	−0.970037	−	0.242956i	$-0.921883\pi$
$859$	−8.04855	+	13.9405i	−0.274613	+	0.475643i	0.695425	+	0.718599i	$0.255216\pi$
$860$	−5.05718	−	15.5644i	−0.172448	−	0.530742i
$861$		0			0
$862$	18.6997	−	13.5861i	0.636915	−	0.462746i
$863$	30.1671	+	33.5040i	1.02690	+	1.14049i	0.989985	+	0.141170i	$0.0450866\pi$
$863$	30.1671	+	33.5040i	1.02690	+	1.14049i	0.0369155	+	0.999318i	$0.488247\pi$
$864$		0			0
$865$	5.67764	+	2.52785i	0.193046	+	0.0859495i
$866$	1.96199	−	0.873535i	0.0666712	−	0.0296839i
$867$		0			0
$868$	23.2499	−	20.9286i	0.789154	−	0.710362i
$869$	30.7809	+	35.8020i	1.04417	+	1.21450i
$870$		0			0
$871$	−14.5172	+	16.1229i	−0.491895	+	0.546305i
$872$	−1.58205	+	15.0522i	−0.0535751	+	0.509733i
$873$		0			0
$874$	−0.294904	+	0.907620i	−0.00997527	+	0.0307007i
$875$	−18.7769	+	25.8368i	−0.634776	+	0.873443i
$876$		0			0
$877$	−51.2988	+	22.8397i	−1.73224	+	0.771241i	−0.736769	+	0.676145i	$0.763649\pi$
$877$	−51.2988	+	22.8397i	−1.73224	+	0.771241i	−0.995468	+	0.0950966i	$0.969684\pi$
$878$	5.57750	−	6.19444i	0.188232	−	0.209052i
$879$		0			0
$880$	5.69119	−	6.03668i	0.191850	−	0.203496i
$881$	−20.4943			−0.690469			−0.345235	−	0.938516i	$-0.612201\pi$
$881$	−20.4943			−0.690469			−0.345235	+	0.938516i	$0.612201\pi$
$882$		0			0
$883$	−14.6613	−	10.6521i	−0.493393	−	0.358471i	0.313095	−	0.949722i	$-0.398634\pi$
$883$	−14.6613	−	10.6521i	−0.493393	−	0.358471i	−0.806488	+	0.591251i	$0.798634\pi$
$884$	−1.64945	−	15.6934i	−0.0554768	−	0.527827i
$885$		0			0
$886$	−3.36407	+	0.715056i	−0.113018	+	0.0240228i
$887$	−1.57543	−	14.9892i	−0.0528977	−	0.503288i	−0.988607	−	0.150517i	$-0.951906\pi$
$887$	−1.57543	−	14.9892i	−0.0528977	−	0.503288i	0.935710	−	0.352771i	$-0.114761\pi$
$888$		0			0
$889$	0.00198040	−	14.4619i	6.64204e−5	−	0.485035i
$890$	15.9349			0.534140
$891$		0			0
$892$	22.1465	+	38.3588i	0.741518	+	1.28435i
$893$	0.528635	−	0.587109i	0.0176901	−	0.0196469i
$894$		0			0
$895$	−26.9688	+	19.5940i	−0.901468	+	0.654955i
$896$	11.7552	+	26.4124i	0.392714	+	0.882375i
$897$		0			0
$898$	−0.0861799	−	0.819947i	−0.00287586	−	0.0273620i
$899$	−2.48870	+	23.6784i	−0.0830029	+	0.789720i
$900$		0			0
$901$	−5.63475	+	9.75967i	−0.187721	+	0.325142i
$902$	1.97900	+	24.1362i	0.0658936	+	0.803648i
$903$		0			0
$904$	−11.2364	−	34.5821i	−0.373717	−	1.15018i
$905$	3.41393	−	1.51998i	0.113483	−	0.0505258i
$906$		0			0
$907$	−15.9214	+	3.38419i	−0.528661	+	0.112370i	−0.464507	−	0.885570i	$-0.653768\pi$
$907$	−15.9214	+	3.38419i	−0.528661	+	0.112370i	−0.0641543	+	0.997940i	$0.520435\pi$
$908$	−21.7889	−	24.1991i	−0.723091	−	0.803074i
$909$		0			0
$910$	4.86961	−	10.9333i	0.161426	−	0.362436i
$911$	2.55183	+	7.85372i	0.0845459	+	0.260206i	0.984389	−	0.176009i	$-0.0563188\pi$
$911$	2.55183	+	7.85372i	0.0845459	+	0.260206i	−0.899843	+	0.436215i	$0.856319\pi$
$912$		0			0
$913$	12.6656	−	8.76596i	0.419171	−	0.290111i
$914$	−1.73006	−	2.99655i	−0.0572253	−	0.0991172i
$915$		0			0
$916$	−9.02618	−	6.55791i	−0.298233	−	0.216679i
$917$	2.71716	−	12.7746i	0.0897286	−	0.421856i
$918$		0			0
$919$	−25.0498	−	27.8206i	−0.826316	−	0.917717i	0.171405	−	0.985201i	$-0.445169\pi$
$919$	−25.0498	−	27.8206i	−0.826316	−	0.917717i	−0.997720	+	0.0674841i	$0.978503\pi$
$920$	−15.6245	−	6.95649i	−0.515126	−	0.229349i
$921$		0			0
$922$	15.0146	+	3.19145i	0.494479	+	0.105105i
$923$	37.4779			1.23360
$924$		0			0
$925$	−21.7743			−0.715935
$926$	−19.6746	−	4.18196i	−0.646547	−	0.137428i
$927$		0			0
$928$	−16.4291	−	7.31469i	−0.539310	−	0.240116i
$929$	−36.2760	−	40.2886i	−1.19018	−	1.32183i	−0.934880	−	0.354965i	$-0.884493\pi$
$929$	−36.2760	−	40.2886i	−1.19018	−	1.32183i	−0.255299	−	0.966862i	$-0.582174\pi$
$930$		0			0
$931$	1.17020	−	2.02556i	0.0383517	−	0.0663850i
$932$	−32.1193	−	23.3361i	−1.05210	−	0.764398i
$933$		0			0
$934$	0.522321	+	0.904686i	0.0170909	+	0.0296022i
$935$	4.13244	+	13.7852i	0.135145	+	0.450824i
$936$		0			0
$937$	7.25100	+	22.3163i	0.236880	+	0.729042i	0.996866	+	0.0791027i	$0.0252055\pi$
$937$	7.25100	+	22.3163i	0.236880	+	0.729042i	−0.759987	+	0.649939i	$0.774794\pi$
$938$	5.72117	+	7.87678i	0.186803	+	0.257186i
$939$		0			0
$940$	4.13019	+	4.58704i	0.134712	+	0.149613i
$941$	41.9748	−	8.92202i	1.36834	−	0.290850i	0.535580	−	0.844484i	$-0.320093\pi$
$941$	41.9748	−	8.92202i	1.36834	−	0.290850i	0.832760	+	0.553635i	$0.186760\pi$
$942$		0			0
$943$	−41.9370	+	18.6716i	−1.36566	+	0.608029i
$944$	0.0160131	+	0.0492834i	0.000521183	+	0.00160404i
$945$		0			0
$946$	9.13402	+	10.6240i	0.296973	+	0.345417i
$947$	26.8719	−	46.5435i	0.873219	−	1.51246i	0.0145710	−	0.999894i	$-0.495362\pi$
$947$	26.8719	−	46.5435i	0.873219	−	1.51246i	0.858648	−	0.512566i	$-0.171305\pi$
$948$		0			0
$949$	−0.124497	+	1.18451i	−0.00404134	+	0.0384508i
$950$	0.0505454	+	0.480907i	0.00163991	+	0.0156027i
$951$		0			0
$952$	−16.1530	−	1.69999i	−0.523523	−	0.0550969i
$953$	7.73653	−	5.62092i	0.250611	−	0.182079i	−0.455387	−	0.890294i	$-0.650499\pi$
$953$	7.73653	−	5.62092i	0.250611	−	0.182079i	0.705998	+	0.708214i	$0.250499\pi$
$954$		0			0
$955$	9.72492	−	10.8006i	0.314691	−	0.349500i
$956$	6.70500	+	11.6134i	0.216855	+	0.375604i
$957$		0			0
$958$	7.91603			0.255755
$959$	3.74733	−	2.16284i	0.121007	−	0.0698416i
$960$		0			0
$961$	−2.87516	−	27.3554i	−0.0927472	−	0.882431i
$962$	26.5686	−	5.64734i	0.856607	−	0.182077i
$963$		0			0
$964$	−3.56619	−	33.9300i	−0.114859	−	1.09281i
$965$	0.349189	+	0.253701i	0.0112408	+	0.00816692i
$966$		0			0
$967$	34.7245			1.11666			0.558332	−	0.829618i	$-0.311442\pi$
$967$	34.7245			1.11666			0.558332	+	0.829618i	$0.311442\pi$
$968$	−9.25969	+	24.6021i	−0.297618	+	0.790741i
$969$		0			0
$970$	2.52002	−	2.79877i	0.0809131	−	0.0898631i
$971$	7.48903	−	3.33433i	0.240334	−	0.107004i	−0.283035	−	0.959110i	$-0.591341\pi$
$971$	7.48903	−	3.33433i	0.240334	−	0.107004i	0.523370	+	0.852106i	$0.324675\pi$
$972$		0			0
$973$	13.7757	−	18.9551i	0.441628	−	0.607674i
$974$	1.52949	−	4.70729i	0.0490080	−	0.150831i
$975$		0			0
$976$	0.635829	−	6.04951i	0.0203524	−	0.193640i
$977$	−1.26495	+	1.40487i	−0.0404694	+	0.0449458i	−0.763040	−	0.646352i	$-0.776294\pi$
$977$	−1.26495	+	1.40487i	−0.0404694	+	0.0449458i	0.722570	+	0.691297i	$0.242961\pi$
$978$		0			0
$979$	42.8332	−	17.9064i	1.36896	−	0.572292i
$980$	14.7832	+	10.7468i	0.472232	+	0.343294i
$981$		0			0
$982$	7.98022	−	3.55302i	0.254659	−	0.113382i
$983$	36.7543	+	16.3641i	1.17228	+	0.521933i	0.898119	−	0.439752i	$-0.144933\pi$
$983$	36.7543	+	16.3641i	1.17228	+	0.521933i	0.274160	+	0.961684i	$0.411600\pi$
$984$		0			0
$985$	−11.0376	−	12.2585i	−0.351688	−	0.390589i
$986$	4.35995	−	3.16769i	0.138849	−	0.100880i
$987$		0			0
$988$	0.634339	+	1.95230i	0.0201810	+	0.0621108i
$989$	−13.2792	+	23.0003i	−0.422255	+	0.731367i
$990$		0			0
$991$	−12.7333	−	22.0548i	−0.404487	−	0.700592i	0.589774	−	0.807568i	$-0.299217\pi$
$991$	−12.7333	−	22.0548i	−0.404487	−	0.700592i	−0.994262	+	0.106976i	$0.965883\pi$
$992$	43.2264	+	9.18805i	1.37244	+	0.291721i
$993$		0			0
$994$	3.49873	−	16.4492i	0.110973	−	0.521736i
$995$	0.184766	−	0.568651i	0.00585748	−	0.0180275i
$996$		0			0
$997$	−15.0671	−	6.70832i	−0.477181	−	0.212455i	0.154030	−	0.988066i	$-0.450775\pi$
$997$	−15.0671	−	6.70832i	−0.477181	−	0.212455i	−0.631210	+	0.775612i	$0.717442\pi$
$998$	−0.308109	+	2.93146i	−0.00975302	+	0.0927938i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.by.b.478.2		40
3.2	odd	2		77.2.m.b.16.4	yes	40
7.4	even	3	inner	693.2.by.b.676.4		40
11.9	even	5	inner	693.2.by.b.163.4		40
21.2	odd	6		539.2.f.h.148.2		20
21.5	even	6		539.2.f.g.148.2		20
21.11	odd	6		77.2.m.b.60.2	yes	40
21.17	even	6		539.2.q.h.214.2		40
21.20	even	2		539.2.q.h.324.4		40
33.2	even	10		847.2.n.j.9.4		40
33.5	odd	10		847.2.n.i.807.2		40
33.8	even	10		847.2.e.h.485.4		20
33.14	odd	10		847.2.e.i.485.7		20
33.17	even	10		847.2.n.h.807.4		40
33.20	odd	10		77.2.m.b.9.2	✓	40
33.26	odd	10		847.2.n.i.366.4		40
33.29	even	10		847.2.n.h.366.2		40
33.32	even	2		847.2.n.j.632.2		40
77.53	even	15	inner	693.2.by.b.361.2		40
231.20	even	10		539.2.q.h.471.2		40
231.32	even	6		847.2.n.j.753.4		40
231.47	even	30		5929.2.a.bx.1.4		10
231.53	odd	30		77.2.m.b.53.4	yes	40
231.74	even	30		847.2.e.h.606.4		20
231.86	odd	30		539.2.f.h.295.2		20
231.95	even	30		847.2.n.h.487.4		40
231.107	even	30		5929.2.a.by.1.7		10
231.116	even	30		847.2.n.h.81.2		40
231.137	odd	30		847.2.n.i.81.4		40
231.152	even	30		539.2.f.g.295.2		20
231.158	odd	30		847.2.n.i.487.2		40
231.173	odd	30		5929.2.a.bz.1.7		10
231.179	odd	30		847.2.e.i.606.7		20
231.185	even	30		539.2.q.h.361.4		40
231.200	even	30		847.2.n.j.130.2		40
231.212	odd	30		5929.2.a.bw.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.b.9.2	✓	40	33.20	odd	10
77.2.m.b.16.4	yes	40	3.2	odd	2
77.2.m.b.53.4	yes	40	231.53	odd	30
77.2.m.b.60.2	yes	40	21.11	odd	6
539.2.f.g.148.2		20	21.5	even	6
539.2.f.g.295.2		20	231.152	even	30
539.2.f.h.148.2		20	21.2	odd	6
539.2.f.h.295.2		20	231.86	odd	30
539.2.q.h.214.2		40	21.17	even	6
539.2.q.h.324.4		40	21.20	even	2
539.2.q.h.361.4		40	231.185	even	30
539.2.q.h.471.2		40	231.20	even	10
693.2.by.b.163.4		40	11.9	even	5	inner
693.2.by.b.361.2		40	77.53	even	15	inner
693.2.by.b.478.2		40	1.1	even	1	trivial
693.2.by.b.676.4		40	7.4	even	3	inner
847.2.e.h.485.4		20	33.8	even	10
847.2.e.h.606.4		20	231.74	even	30
847.2.e.i.485.7		20	33.14	odd	10
847.2.e.i.606.7		20	231.179	odd	30
847.2.n.h.81.2		40	231.116	even	30
847.2.n.h.366.2		40	33.29	even	10
847.2.n.h.487.4		40	231.95	even	30
847.2.n.h.807.4		40	33.17	even	10
847.2.n.i.81.4		40	231.137	odd	30
847.2.n.i.366.4		40	33.26	odd	10
847.2.n.i.487.2		40	231.158	odd	30
847.2.n.i.807.2		40	33.5	odd	10
847.2.n.j.9.4		40	33.2	even	10
847.2.n.j.130.2		40	231.200	even	30
847.2.n.j.632.2		40	33.32	even	2
847.2.n.j.753.4		40	231.32	even	6
5929.2.a.bw.1.4		10	231.212	odd	30
5929.2.a.bx.1.4		10	231.47	even	30
5929.2.a.by.1.7		10	231.107	even	30
5929.2.a.bz.1.7		10	231.173	odd	30

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.by (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.659236 - 0.140125i) q^{2} +(-1.41213 - 0.628722i) q^{4} +(-1.13022 - 1.25524i) q^{5} +(2.51637 - 0.817238i) q^{7} +(1.93333 + 1.40464i) q^{8} +O(q^{10})\)	\(q+(-0.659236 - 0.140125i) q^{2} +(-1.41213 - 0.628722i) q^{4} +(-1.13022 - 1.25524i) q^{5} +(2.51637 - 0.817238i) q^{7} +(1.93333 + 1.40464i) q^{8} +(0.569194 + 0.985873i) q^{10} +(2.63784 + 2.01042i) q^{11} +(-1.22798 - 3.77933i) q^{13} +(-1.77340 + 0.186146i) q^{14} +(0.990954 + 1.10057i) q^{16} +(-2.51278 + 0.534107i) q^{17} +(0.305292 - 0.135925i) q^{19} +(0.806829 + 2.48316i) q^{20} +(-1.45725 - 1.69497i) q^{22} +(2.11859 - 3.66950i) q^{23} +(0.224419 - 2.13520i) q^{25} +(0.279950 + 2.66354i) q^{26} +(-4.06727 - 0.428050i) q^{28} +(2.51823 - 1.82960i) q^{29} +(-5.11813 + 5.68426i) q^{31} +(-2.88878 - 5.00351i) q^{32} +1.73135 q^{34} +(-3.86989 - 2.23499i) q^{35} +(-1.06012 - 10.0863i) q^{37} +(-0.220306 + 0.0468275i) q^{38} +(-0.421925 - 4.01435i) q^{40} +(-8.76494 - 6.36810i) q^{41} -6.26797 q^{43} +(-2.46099 - 4.49745i) q^{44} +(-1.91084 + 2.12220i) q^{46} +(2.15968 - 0.961554i) q^{47} +(5.66425 - 4.11295i) q^{49} +(-0.447141 + 1.37616i) q^{50} +(-0.642079 + 6.10898i) q^{52} +(2.93539 - 3.26008i) q^{53} +(-0.457796 - 5.58335i) q^{55} +(6.01289 + 1.95462i) q^{56} +(-1.91648 + 0.853273i) q^{58} +(0.0319655 + 0.0142320i) q^{59} +(-2.74836 - 3.05237i) q^{61} +(4.17056 - 3.03009i) q^{62} +(0.287989 + 0.886339i) q^{64} +(-3.35608 + 5.81290i) q^{65} +(-2.72981 - 4.72817i) q^{67} +(3.88418 + 0.825608i) q^{68} +(2.23800 + 2.01566i) q^{70} +(-2.91440 + 8.96959i) q^{71} +(-0.273807 - 0.121907i) q^{73} +(-0.714481 + 6.79783i) q^{74} -0.516572 q^{76} +(8.28078 + 2.90321i) q^{77} +(13.9247 + 2.95979i) q^{79} +(0.261475 - 2.48777i) q^{80} +(4.88583 + 5.42627i) q^{82} +(1.43515 - 4.41695i) q^{83} +(3.51043 + 2.55048i) q^{85} +(4.13208 + 0.878300i) q^{86} +(2.27589 + 7.59203i) q^{88} +(6.99890 - 12.1225i) q^{89} +(-6.17866 - 8.50664i) q^{91} +(-5.29882 + 3.84982i) q^{92} +(-1.55848 + 0.331265i) q^{94} +(-0.515666 - 0.229589i) q^{95} +(-1.02232 - 3.14637i) q^{97} +(-4.31040 + 1.91770i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 3 q^{2} - 3 q^{4} - 4 q^{5} - 2 q^{7} + 38 q^{8}+O(q^{10}) \) 40 * q + 3 * q^2 - 3 * q^4 - 4 * q^5 - 2 * q^7 + 38 * q^8	\( 40 q + 3 q^{2} - 3 q^{4} - 4 q^{5} - 2 q^{7} + 38 q^{8} + 14 q^{10} + 9 q^{11} + 6 q^{13} + 3 q^{14} - 5 q^{16} + 7 q^{17} - 4 q^{19} + 30 q^{20} + 44 q^{22} + 14 q^{23} + 21 q^{25} + 16 q^{28} - 17 q^{31} + 30 q^{32} + 48 q^{34} + 14 q^{35} + 24 q^{37} - 12 q^{38} + 10 q^{40} - 60 q^{41} - 72 q^{43} - 18 q^{44} + 8 q^{46} - 13 q^{47} - 10 q^{49} - 6 q^{50} + 2 q^{52} - 33 q^{53} - 6 q^{55} - 24 q^{56} - 17 q^{58} - 21 q^{59} + 52 q^{62} + 94 q^{64} + 40 q^{65} - 38 q^{67} + 23 q^{68} - 3 q^{70} - 20 q^{71} + 11 q^{73} + 41 q^{74} - 96 q^{76} - 36 q^{77} + 21 q^{79} - 12 q^{80} + 6 q^{82} + 46 q^{83} - 78 q^{85} - 7 q^{86} + 32 q^{88} + 10 q^{89} - 14 q^{91} + 110 q^{92} + 37 q^{94} - 7 q^{95} - 54 q^{97} - 116 q^{98}+O(q^{100}) \) 40 * q + 3 * q^2 - 3 * q^4 - 4 * q^5 - 2 * q^7 + 38 * q^8 + 14 * q^10 + 9 * q^11 + 6 * q^13 + 3 * q^14 - 5 * q^16 + 7 * q^17 - 4 * q^19 + 30 * q^20 + 44 * q^22 + 14 * q^23 + 21 * q^25 + 16 * q^28 - 17 * q^31 + 30 * q^32 + 48 * q^34 + 14 * q^35 + 24 * q^37 - 12 * q^38 + 10 * q^40 - 60 * q^41 - 72 * q^43 - 18 * q^44 + 8 * q^46 - 13 * q^47 - 10 * q^49 - 6 * q^50 + 2 * q^52 - 33 * q^53 - 6 * q^55 - 24 * q^56 - 17 * q^58 - 21 * q^59 + 52 * q^62 + 94 * q^64 + 40 * q^65 - 38 * q^67 + 23 * q^68 - 3 * q^70 - 20 * q^71 + 11 * q^73 + 41 * q^74 - 96 * q^76 - 36 * q^77 + 21 * q^79 - 12 * q^80 + 6 * q^82 + 46 * q^83 - 78 * q^85 - 7 * q^86 + 32 * q^88 + 10 * q^89 - 14 * q^91 + 110 * q^92 + 37 * q^94 - 7 * q^95 - 54 * q^97 - 116 * q^98

Introduction

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