LMFDB - Embedded newform 845.2.f.e.408.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(408,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 3]))

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

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

chi := DirichletCharacter("845.408");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			408.6
Root			$-0.274809i$ of defining polynomial
Character	$\chi$	$=$	845.408
Dual form			845.2.f.e.437.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.274809i q^{2} +(1.67095 + 1.67095i) q^{3} +1.92448 q^{4} +(1.45395 - 1.69883i) q^{5} +(0.459191 - 0.459191i) q^{6} +0.386104 q^{7} -1.07848i q^{8} +2.58414i q^{9} +O(q^{10})$	\(q-0.274809i q^{2} +(1.67095 + 1.67095i) q^{3} +1.92448 q^{4} +(1.45395 - 1.69883i) q^{5} +(0.459191 - 0.459191i) q^{6} +0.386104 q^{7} -1.07848i q^{8} +2.58414i q^{9} +(-0.466854 - 0.399558i) q^{10} +(-3.08375 - 3.08375i) q^{11} +(3.21571 + 3.21571i) q^{12} -0.106105i q^{14} +(5.26814 - 0.409188i) q^{15} +3.55258 q^{16} +(-1.39475 - 1.39475i) q^{17} +0.710144 q^{18} +(3.54274 + 3.54274i) q^{19} +(2.79810 - 3.26937i) q^{20} +(0.645159 + 0.645159i) q^{21} +(-0.847442 + 0.847442i) q^{22} +(-0.235896 + 0.235896i) q^{23} +(1.80209 - 1.80209i) q^{24} +(-0.772064 - 4.94003i) q^{25} +(0.694880 - 0.694880i) q^{27} +0.743049 q^{28} +8.16410i q^{29} +(-0.112448 - 1.44773i) q^{30} +(-2.54187 + 2.54187i) q^{31} -3.13324i q^{32} -10.3056i q^{33} +(-0.383290 + 0.383290i) q^{34} +(0.561375 - 0.655925i) q^{35} +4.97313i q^{36} +4.82502 q^{37} +(0.973575 - 0.973575i) q^{38} +(-1.83216 - 1.56806i) q^{40} +(-3.29253 + 3.29253i) q^{41} +(0.177295 - 0.177295i) q^{42} +(-4.82129 + 4.82129i) q^{43} +(-5.93462 - 5.93462i) q^{44} +(4.39002 + 3.75721i) q^{45} +(0.0648264 + 0.0648264i) q^{46} -9.83310 q^{47} +(5.93619 + 5.93619i) q^{48} -6.85092 q^{49} +(-1.35756 + 0.212170i) q^{50} -4.66112i q^{51} +(-7.17155 - 7.17155i) q^{53} +(-0.190959 - 0.190959i) q^{54} +(-9.72240 + 0.755161i) q^{55} -0.416405i q^{56} +11.8395i q^{57} +2.24356 q^{58} +(-1.71630 + 1.71630i) q^{59} +(10.1384 - 0.787474i) q^{60} +10.6468 q^{61} +(0.698529 + 0.698529i) q^{62} +0.997746i q^{63} +6.24413 q^{64} -2.83207 q^{66} +6.37591i q^{67} +(-2.68417 - 2.68417i) q^{68} -0.788342 q^{69} +(-0.180254 - 0.154271i) q^{70} +(-3.07858 + 3.07858i) q^{71} +2.78695 q^{72} +6.08593i q^{73} -1.32596i q^{74} +(6.96446 - 9.54462i) q^{75} +(6.81793 + 6.81793i) q^{76} +(-1.19065 - 1.19065i) q^{77} +3.34944i q^{79} +(5.16528 - 6.03525i) q^{80} +10.0746 q^{81} +(0.904815 + 0.904815i) q^{82} +5.18834 q^{83} +(1.24160 + 1.24160i) q^{84} +(-4.39735 + 0.341552i) q^{85} +(1.32493 + 1.32493i) q^{86} +(-13.6418 + 13.6418i) q^{87} +(-3.32577 + 3.32577i) q^{88} +(-3.53455 + 3.53455i) q^{89} +(1.03251 - 1.20642i) q^{90} +(-0.453978 + 0.453978i) q^{92} -8.49469 q^{93} +2.70222i q^{94} +(11.1695 - 0.867558i) q^{95} +(5.23549 - 5.23549i) q^{96} -14.7480i q^{97} +1.88269i q^{98} +(7.96886 - 7.96886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} - 12 q^{4} + 4 q^{6} + 4 q^{7}+O(q^{10}) $ 20 * q + 4 * q^3 - 12 * q^4 + 4 * q^6 + 4 * q^7	$ 20 q + 4 q^{3} - 12 q^{4} + 4 q^{6} + 4 q^{7} - 8 q^{10} + 8 q^{11} - 24 q^{12} + 28 q^{15} + 4 q^{16} - 14 q^{17} + 4 q^{19} - 12 q^{20} + 4 q^{21} - 32 q^{22} + 8 q^{23} - 4 q^{24} + 18 q^{25} + 4 q^{27} - 36 q^{28} + 40 q^{30} + 2 q^{34} - 20 q^{35} + 8 q^{37} - 8 q^{38} - 16 q^{40} - 38 q^{41} + 16 q^{42} - 32 q^{43} - 36 q^{44} - 6 q^{45} + 4 q^{46} - 40 q^{47} + 28 q^{48} - 36 q^{49} + 42 q^{50} - 10 q^{53} + 36 q^{54} - 16 q^{55} + 8 q^{59} + 28 q^{60} + 32 q^{61} + 4 q^{62} + 20 q^{64} - 32 q^{66} - 50 q^{68} + 32 q^{69} - 12 q^{70} - 40 q^{71} - 8 q^{72} + 4 q^{75} - 16 q^{76} - 28 q^{77} + 112 q^{80} + 28 q^{81} - 34 q^{82} + 48 q^{83} + 8 q^{84} - 2 q^{85} + 60 q^{86} - 28 q^{87} - 32 q^{88} + 12 q^{89} + 46 q^{90} - 8 q^{92} - 64 q^{93} + 40 q^{95} + 56 q^{96} + 60 q^{99}+O(q^{100}) $ 20 * q + 4 * q^3 - 12 * q^4 + 4 * q^6 + 4 * q^7 - 8 * q^10 + 8 * q^11 - 24 * q^12 + 28 * q^15 + 4 * q^16 - 14 * q^17 + 4 * q^19 - 12 * q^20 + 4 * q^21 - 32 * q^22 + 8 * q^23 - 4 * q^24 + 18 * q^25 + 4 * q^27 - 36 * q^28 + 40 * q^30 + 2 * q^34 - 20 * q^35 + 8 * q^37 - 8 * q^38 - 16 * q^40 - 38 * q^41 + 16 * q^42 - 32 * q^43 - 36 * q^44 - 6 * q^45 + 4 * q^46 - 40 * q^47 + 28 * q^48 - 36 * q^49 + 42 * q^50 - 10 * q^53 + 36 * q^54 - 16 * q^55 + 8 * q^59 + 28 * q^60 + 32 * q^61 + 4 * q^62 + 20 * q^64 - 32 * q^66 - 50 * q^68 + 32 * q^69 - 12 * q^70 - 40 * q^71 - 8 * q^72 + 4 * q^75 - 16 * q^76 - 28 * q^77 + 112 * q^80 + 28 * q^81 - 34 * q^82 + 48 * q^83 + 8 * q^84 - 2 * q^85 + 60 * q^86 - 28 * q^87 - 32 * q^88 + 12 * q^89 + 46 * q^90 - 8 * q^92 - 64 * q^93 + 40 * q^95 + 56 * q^96 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	0.274809i		−	0.194319i	−0.995269	−	0.0971595i	$-0.969024\pi$
$2$		−	0.274809i		−	0.194319i	0.995269	−	0.0971595i	$-0.0309757\pi$
$3$	1.67095	+	1.67095i	0.964723	+	0.964723i	0.999399	−	0.0346758i	$-0.0110399\pi$
$3$	1.67095	+	1.67095i	0.964723	+	0.964723i	−0.0346758	+	0.999399i	$0.511040\pi$
$4$	1.92448			0.962240
$5$	1.45395	−	1.69883i	0.650226	−	0.759741i
$5$	1.45395	−	1.69883i	0.650226	−	0.759741i
$6$	0.459191	−	0.459191i	0.187464	−	0.187464i
$7$	0.386104			0.145933			0.0729667	−	0.997334i	$-0.476753\pi$
$7$	0.386104			0.145933			0.0729667	+	0.997334i	$0.476753\pi$
$8$		−	1.07848i		−	0.381301i
$9$			2.58414i			0.861380i
$10$	−0.466854	−	0.399558i	−0.147632	−	0.126351i
$11$	−3.08375	−	3.08375i	−0.929787	−	0.929787i	0.0679048	−	0.997692i	$-0.478369\pi$
$11$	−3.08375	−	3.08375i	−0.929787	−	0.929787i	−0.997692	+	0.0679048i	$0.978369\pi$
$12$	3.21571	+	3.21571i	0.928295	+	0.928295i
$13$		0			0
$13$		0			0
$14$		−	0.106105i		−	0.0283576i
$15$	5.26814	−	0.409188i	1.36023	−	0.105652i
$16$	3.55258			0.888146
$17$	−1.39475	−	1.39475i	−0.338277	−	0.338277i	0.517442	−	0.855719i	$-0.326884\pi$
$17$	−1.39475	−	1.39475i	−0.338277	−	0.338277i	−0.855719	+	0.517442i	$0.826884\pi$
$18$	0.710144			0.167383
$19$	3.54274	+	3.54274i	0.812760	+	0.812760i	0.985047	−	0.172287i	$-0.0551157\pi$
$19$	3.54274	+	3.54274i	0.812760	+	0.812760i	−0.172287	+	0.985047i	$0.555116\pi$
$20$	2.79810	−	3.26937i	0.625673	−	0.731053i
$21$	0.645159	+	0.645159i	0.140785	+	0.140785i
$22$	−0.847442	+	0.847442i	−0.180675	+	0.180675i
$23$	−0.235896	+	0.235896i	−0.0491878	+	0.0491878i	−0.731273	−	0.682085i	$-0.761073\pi$
$23$	−0.235896	+	0.235896i	−0.0491878	+	0.0491878i	0.682085	+	0.731273i	$0.261073\pi$
$24$	1.80209	−	1.80209i	0.367849	−	0.367849i
$25$	−0.772064	−	4.94003i	−0.154413	−	0.988006i
$26$		0			0
$27$	0.694880	−	0.694880i	0.133730	−	0.133730i
$28$	0.743049			0.140423
$29$			8.16410i			1.51603i	0.652235	+	0.758017i	$0.273832\pi$
$29$			8.16410i			1.51603i	−0.652235	+	0.758017i	$0.726168\pi$
$30$	−0.112448	−	1.44773i	−0.0205302	−	0.264318i
$31$	−2.54187	+	2.54187i	−0.456534	+	0.456534i	−0.897516	−	0.440982i	$-0.854630\pi$
$31$	−2.54187	+	2.54187i	−0.456534	+	0.456534i	0.440982	+	0.897516i	$0.354630\pi$
$32$		−	3.13324i		−	0.553884i
$33$		−	10.3056i		−	1.79397i
$34$	−0.383290	+	0.383290i	−0.0657336	+	0.0657336i
$35$	0.561375	−	0.655925i	0.0948897	−	0.110872i
$36$			4.97313i			0.828855i
$37$	4.82502			0.793229			0.396614	−	0.917985i	$-0.370185\pi$
$37$	4.82502			0.793229			0.396614	+	0.917985i	$0.370185\pi$
$38$	0.973575	−	0.973575i	0.157935	−	0.157935i
$39$		0			0
$40$	−1.83216	−	1.56806i	−0.289690	−	0.247931i
$41$	−3.29253	+	3.29253i	−0.514207	+	0.514207i	−0.915813	−	0.401606i	$-0.868452\pi$
$41$	−3.29253	+	3.29253i	−0.514207	+	0.514207i	0.401606	+	0.915813i	$0.368452\pi$
$42$	0.177295	−	0.177295i	0.0273573	−	0.0273573i
$43$	−4.82129	+	4.82129i	−0.735240	+	0.735240i	−0.971653	−	0.236413i	$-0.924028\pi$
$43$	−4.82129	+	4.82129i	−0.735240	+	0.735240i	0.236413	+	0.971653i	$0.424028\pi$
$44$	−5.93462	−	5.93462i	−0.894678	−	0.894678i
$45$	4.39002	+	3.75721i	0.654426	+	0.560092i
$46$	0.0648264	+	0.0648264i	0.00955813	+	0.00955813i
$47$	−9.83310			−1.43430			−0.717152	−	0.696917i	$-0.754555\pi$
$47$	−9.83310			−1.43430			−0.717152	+	0.696917i	$0.754555\pi$
$48$	5.93619	+	5.93619i	0.856815	+	0.856815i
$49$	−6.85092			−0.978703
$50$	−1.35756	+	0.212170i	−0.191988	+	0.0300054i
$51$		−	4.66112i		−	0.652687i
$52$		0			0
$53$	−7.17155	−	7.17155i	−0.985088	−	0.985088i	0.0148021	−	0.999890i	$-0.495288\pi$
$53$	−7.17155	−	7.17155i	−0.985088	−	0.985088i	−0.999890	+	0.0148021i	$0.995288\pi$
$54$	−0.190959	−	0.190959i	−0.0259862	−	0.0259862i
$55$	−9.72240	+	0.755161i	−1.31097	+	0.101826i
$56$		−	0.416405i		−	0.0556445i
$57$			11.8395i			1.56818i
$58$	2.24356			0.294594
$59$	−1.71630	+	1.71630i	−0.223443	+	0.223443i	−0.809947	−	0.586504i	$-0.800504\pi$
$59$	−1.71630	+	1.71630i	−0.223443	+	0.223443i	0.586504	+	0.809947i	$0.300504\pi$
$60$	10.1384	−	0.787474i	1.30887	−	0.101662i
$61$	10.6468			1.36318			0.681589	−	0.731735i	$-0.261289\pi$
$61$	10.6468			1.36318			0.681589	+	0.731735i	$0.261289\pi$
$62$	0.698529	+	0.698529i	0.0887133	+	0.0887133i
$63$			0.997746i			0.125704i
$64$	6.24413			0.780516
$65$		0			0
$66$	−2.83207			−0.348603
$67$			6.37591i			0.778942i	0.921039	+	0.389471i	$0.127342\pi$
$67$			6.37591i			0.778942i	−0.921039	+	0.389471i	$0.872658\pi$
$68$	−2.68417	−	2.68417i	−0.325504	−	0.325504i
$69$	−0.788342			−0.0949052
$70$	−0.180254	−	0.154271i	−0.0215445	−	0.0184389i
$71$	−3.07858	+	3.07858i	−0.365360	+	0.365360i	−0.865782	−	0.500422i	$-0.833178\pi$
$71$	−3.07858	+	3.07858i	−0.365360	+	0.365360i	0.500422	+	0.865782i	$0.333178\pi$
$72$	2.78695			0.328445
$73$			6.08593i			0.712304i	0.934428	+	0.356152i	$0.115912\pi$
$73$			6.08593i			0.712304i	−0.934428	+	0.356152i	$0.884088\pi$
$74$		−	1.32596i		−	0.154139i
$75$	6.96446	−	9.54462i	0.804187	−	1.10212i
$76$	6.81793	+	6.81793i	0.782070	+	0.782070i
$77$	−1.19065	−	1.19065i	−0.135687	−	0.135687i
$78$		0			0
$79$			3.34944i			0.376842i	0.982088	+	0.188421i	$0.0603369\pi$
$79$			3.34944i			0.376842i	−0.982088	+	0.188421i	$0.939663\pi$
$80$	5.16528	−	6.03525i	0.577496	−	0.674761i
$81$	10.0746			1.11940
$82$	0.904815	+	0.904815i	0.0999202	+	0.0999202i
$83$	5.18834			0.569494			0.284747	−	0.958603i	$-0.408090\pi$
$83$	5.18834			0.569494			0.284747	+	0.958603i	$0.408090\pi$
$84$	1.24160	+	1.24160i	0.135469	+	0.135469i
$85$	−4.39735	+	0.341552i	−0.476959	+	0.0370465i
$86$	1.32493	+	1.32493i	0.142871	+	0.142871i
$87$	−13.6418	+	13.6418i	−1.46255	+	1.46255i
$88$	−3.32577	+	3.32577i	−0.354528	+	0.354528i
$89$	−3.53455	+	3.53455i	−0.374662	+	0.374662i	−0.869172	−	0.494510i	$-0.835348\pi$
$89$	−3.53455	+	3.53455i	−0.374662	+	0.374662i	0.494510	+	0.869172i	$0.335348\pi$
$90$	1.03251	−	1.20642i	0.108836	−	0.127167i
$91$		0			0
$92$	−0.453978	+	0.453978i	−0.0473305	+	0.0473305i
$93$	−8.49469			−0.880858
$94$			2.70222i			0.278713i
$95$	11.1695	−	0.867558i	1.14596	−	0.0890096i
$96$	5.23549	−	5.23549i	0.534345	−	0.534345i
$97$		−	14.7480i		−	1.49744i	−0.662889	−	0.748718i	$-0.730670\pi$
$97$		−	14.7480i		−	1.49744i	0.662889	−	0.748718i	$-0.269330\pi$
$98$			1.88269i			0.190181i
$99$	7.96886	−	7.96886i	0.800900	−	0.800900i
$100$	−1.48582	−	9.50699i	−0.148582	−	0.950699i
$101$			5.27950i			0.525329i	0.964887	+	0.262665i	$0.0846013\pi$
$101$			5.27950i			0.525329i	−0.964887	+	0.262665i	$0.915399\pi$
$102$	−1.28092			−0.126829
$103$	−1.21001	+	1.21001i	−0.119226	+	0.119226i	−0.764203	−	0.644976i	$-0.776867\pi$
$103$	−1.21001	+	1.21001i	−0.119226	+	0.119226i	0.644976	+	0.764203i	$0.276867\pi$
$104$		0			0
$105$	2.03405	−	0.157989i	0.198503	−	0.0154181i
$106$	−1.97080	+	1.97080i	−0.191421	+	0.191421i
$107$	2.86583	−	2.86583i	0.277050	−	0.277050i	−0.554880	−	0.831930i	$-0.687236\pi$
$107$	2.86583	−	2.86583i	0.277050	−	0.277050i	0.831930	+	0.554880i	$0.187236\pi$
$108$	1.33728	−	1.33728i	0.128680	−	0.128680i
$109$	−5.02898	−	5.02898i	−0.481689	−	0.481689i	0.423982	−	0.905671i	$-0.360632\pi$
$109$	−5.02898	−	5.02898i	−0.481689	−	0.481689i	−0.905671	+	0.423982i	$0.860632\pi$
$110$	0.207525	+	2.67180i	0.0197867	+	0.254746i
$111$	8.06237	+	8.06237i	0.765246	+	0.765246i
$112$	1.37167			0.129610
$113$	−2.81027	−	2.81027i	−0.264368	−	0.264368i	0.562458	−	0.826826i	$-0.309856\pi$
$113$	−2.81027	−	2.81027i	−0.264368	−	0.264368i	−0.826826	+	0.562458i	$0.809856\pi$
$114$	3.25359			0.304726
$115$	0.0577672	+	0.743730i	0.00538682	+	0.0693532i
$116$			15.7116i			1.45879i
$117$		0			0
$118$	0.471653	+	0.471653i	0.0434192	+	0.0434192i
$119$	−0.538519	−	0.538519i	−0.0493659	−	0.0493659i
$120$	−0.441301	−	5.68159i	−0.0402851	−	0.518655i
$121$			8.01908i			0.729008i
$122$		−	2.92582i		−	0.264892i
$123$	−11.0033			−0.992134
$124$	−4.89179	+	4.89179i	−0.439296	+	0.439296i
$125$	−9.51483	−	5.87095i	−0.851032	−	0.525113i
$126$	0.274189			0.0244267
$127$	−8.06380	−	8.06380i	−0.715547	−	0.715547i	0.252143	−	0.967690i	$-0.418865\pi$
$127$	−8.06380	−	8.06380i	−0.715547	−	0.715547i	−0.967690	+	0.252143i	$0.918865\pi$
$128$		−	7.98243i		−	0.705553i
$129$	−16.1123			−1.41860
$130$		0			0
$131$	20.8627			1.82279			0.911393	−	0.411536i	$-0.135008\pi$
$131$	20.8627			1.82279			0.911393	+	0.411536i	$0.135008\pi$
$132$		−	19.8329i		−	1.72623i
$133$	1.36786	+	1.36786i	0.118609	+	0.118609i
$134$	1.75216			0.151363
$135$	−0.170165	−	2.19080i	−0.0146454	−	0.188554i
$136$	−1.50421	+	1.50421i	−0.128985	+	0.128985i
$137$	−0.243949			−0.0208420			−0.0104210	−	0.999946i	$-0.503317\pi$
$137$	−0.243949			−0.0208420			−0.0104210	+	0.999946i	$0.503317\pi$
$138$			0.216643i			0.0184419i
$139$		−	11.6840i		−	0.991027i	−0.868600	−	0.495514i	$-0.834980\pi$
$139$		−	11.6840i		−	0.991027i	0.868600	−	0.495514i	$-0.165020\pi$
$140$	1.08036	−	1.26232i	0.0913067	−	0.106685i
$141$	−16.4306	−	16.4306i	−1.38371	−	1.38371i
$142$	0.846020	+	0.846020i	0.0709965	+	0.0709965i
$143$		0			0
$144$			9.18038i			0.765032i
$145$	13.8694	+	11.8702i	1.15179	+	0.985765i
$146$	1.67247			0.138414
$147$	−11.4475	−	11.4475i	−0.944178	−	0.944178i
$148$	9.28566			0.763277
$149$	1.79074	+	1.79074i	0.146703	+	0.146703i	0.776644	−	0.629940i	$-0.216921\pi$
$149$	1.79074	+	1.79074i	0.146703	+	0.146703i	−0.629940	+	0.776644i	$0.716921\pi$
$150$	−2.62294	−	1.91389i	−0.214162	−	0.156269i
$151$	2.58498	+	2.58498i	0.210362	+	0.210362i	0.804421	−	0.594059i	$-0.202475\pi$
$151$	2.58498	+	2.58498i	0.210362	+	0.210362i	−0.594059	+	0.804421i	$0.702475\pi$
$152$	3.82078	−	3.82078i	0.309906	−	0.309906i
$153$	3.60423	−	3.60423i	0.291385	−	0.291385i
$154$	−0.327201	+	0.327201i	−0.0263666	+	0.0263666i
$155$	0.622463	+	8.01398i	0.0499974	+	0.643698i
$156$		0			0
$157$	−2.21767	+	2.21767i	−0.176990	+	0.176990i	−0.790042	−	0.613053i	$-0.789941\pi$
$157$	−2.21767	+	2.21767i	−0.176990	+	0.176990i	0.613053	+	0.790042i	$0.289941\pi$
$158$	0.920455			0.0732275
$159$		−	23.9666i		−	1.90067i
$160$	−5.32285	−	4.55558i	−0.420809	−	0.360150i
$161$	−0.0910805	+	0.0910805i	−0.00717815	+	0.00717815i
$162$		−	2.76860i		−	0.217522i
$163$			14.8128i			1.16023i	0.814534	+	0.580116i	$0.196993\pi$
$163$			14.8128i			1.16023i	−0.814534	+	0.580116i	$0.803007\pi$
$164$	−6.33641	+	6.33641i	−0.494790	+	0.494790i
$165$	−17.5075	−	14.9838i	−1.36296	−	1.16649i
$166$		−	1.42580i		−	0.110664i
$167$	3.46812			0.268372			0.134186	−	0.990956i	$-0.457158\pi$
$167$	3.46812			0.268372			0.134186	+	0.990956i	$0.457158\pi$
$168$	0.695792	−	0.695792i	0.0536815	−	0.0536815i
$169$		0			0
$170$	0.0938613	+	1.20843i	0.00719883	+	0.0926823i
$171$	−9.15493	+	9.15493i	−0.700095	+	0.700095i
$172$	−9.27848	+	9.27848i	−0.707477	+	0.707477i
$173$	−2.76467	+	2.76467i	−0.210194	+	0.210194i	−0.804350	−	0.594156i	$-0.797486\pi$
$173$	−2.76467	+	2.76467i	−0.210194	+	0.210194i	0.594156	+	0.804350i	$0.297486\pi$
$174$	3.74888	+	3.74888i	0.284202	+	0.284202i
$175$	−0.298097	−	1.90736i	−0.0225340	−	0.144183i
$176$	−10.9553	−	10.9553i	−0.825787	−	0.825787i
$177$	−5.73569			−0.431121
$178$	0.971326	+	0.971326i	0.0728040	+	0.0728040i
$179$	6.49760			0.485653			0.242827	−	0.970070i	$-0.421925\pi$
$179$	6.49760			0.485653			0.242827	+	0.970070i	$0.421925\pi$
$180$	8.44851	+	7.23067i	0.629715	+	0.538943i
$181$		−	11.9845i		−	0.890802i	−0.895331	−	0.445401i	$-0.853061\pi$
$181$		−	11.9845i		−	0.890802i	0.895331	−	0.445401i	$-0.146939\pi$
$182$		0			0
$183$	17.7902	+	17.7902i	1.31509	+	1.31509i
$184$	0.254410	+	0.254410i	0.0187553	+	0.0187553i
$185$	7.01534	−	8.19691i	0.515778	−	0.602649i
$186$			2.33441i			0.171167i
$187$			8.60214i			0.629051i
$188$	−18.9236			−1.38015
$189$	0.268296	−	0.268296i	0.0195156	−	0.0195156i
$190$	−0.238412	−	3.06947i	−0.0172963	−	0.222683i
$191$	−5.19291			−0.375746			−0.187873	−	0.982193i	$-0.560159\pi$
$191$	−5.19291			−0.375746			−0.187873	+	0.982193i	$0.560159\pi$
$192$	10.4336	+	10.4336i	0.752981	+	0.752981i
$193$			6.67413i			0.480414i	0.970722	+	0.240207i	$0.0772153\pi$
$193$			6.67413i			0.480414i	−0.970722	+	0.240207i	$0.922785\pi$
$194$	−4.05289			−0.290980
$195$		0			0
$196$	−13.1845			−0.941748
$197$		−	19.5971i		−	1.39624i	−0.715982	−	0.698119i	$-0.754021\pi$
$197$		−	19.5971i		−	1.39624i	0.715982	−	0.698119i	$-0.245979\pi$
$198$	−2.18991	−	2.18991i	−0.155630	−	0.155630i
$199$	14.7060			1.04248			0.521242	−	0.853409i	$-0.325469\pi$
$199$	14.7060			1.04248			0.521242	+	0.853409i	$0.325469\pi$
$200$	−5.32773	+	0.832657i	−0.376727	+	0.0588777i
$201$	−10.6538	+	10.6538i	−0.751463	+	0.751463i
$202$	1.45085			0.102082
$203$			3.15219i			0.221240i
$204$		−	8.97023i		−	0.628042i
$205$	0.806286	+	10.3806i	0.0563135	+	0.725014i
$206$	0.332522	+	0.332522i	0.0231679	+	0.0231679i
$207$	−0.609590	−	0.609590i	−0.0423694	−	0.0423694i
$208$		0			0
$209$		−	21.8499i		−	1.51139i
$210$	−0.0434167	−	0.558974i	−0.00299604	−	0.0385728i
$211$	−21.4143			−1.47422			−0.737111	−	0.675771i	$-0.763811\pi$
$211$	−21.4143			−1.47422			−0.737111	+	0.675771i	$0.763811\pi$
$212$	−13.8015	−	13.8015i	−0.947892	−	0.947892i
$213$	−10.2883			−0.704943
$214$	−0.787555	−	0.787555i	−0.0538362	−	0.0538362i
$215$	1.18065	+	15.2005i	0.0805199	+	1.03666i
$216$	−0.749414	−	0.749414i	−0.0509912	−	0.0509912i
$217$	−0.981427	+	0.981427i	−0.0666236	+	0.0666236i
$218$	−1.38201	+	1.38201i	−0.0936014	+	0.0936014i
$219$	−10.1693	+	10.1693i	−0.687176	+	0.687176i
$220$	−18.7106	+	1.45329i	−1.26147	+	0.0979809i
$221$		0			0
$222$	2.21561	−	2.21561i	0.148702	−	0.148702i
$223$	−27.3356			−1.83053			−0.915264	−	0.402855i	$-0.868018\pi$
$223$	−27.3356			−1.83053			−0.915264	+	0.402855i	$0.868018\pi$
$224$		−	1.20976i		−	0.0808302i
$225$	12.7657	−	1.99512i	0.851049	−	0.133008i
$226$	−0.772287	+	0.772287i	−0.0513718	+	0.0513718i
$227$		−	6.92738i		−	0.459786i	−0.973216	−	0.229893i	$-0.926162\pi$
$227$		−	6.92738i		−	0.459786i	0.973216	−	0.229893i	$-0.0738376\pi$
$228$			22.7848i			1.50896i
$229$	4.56825	−	4.56825i	0.301879	−	0.301879i	−0.539870	−	0.841749i	$-0.681527\pi$
$229$	4.56825	−	4.56825i	0.301879	−	0.301879i	0.841749	+	0.539870i	$0.181527\pi$
$230$	0.204383	−	0.0158749i	0.0134766	−	0.00104676i
$231$		−	3.97903i		−	0.261801i
$232$	8.80482			0.578065
$233$	5.49074	−	5.49074i	0.359711	−	0.359711i	−0.503996	−	0.863706i	$-0.668137\pi$
$233$	5.49074	−	5.49074i	0.359711	−	0.359711i	0.863706	+	0.503996i	$0.168137\pi$
$234$		0			0
$235$	−14.2968	+	16.7048i	−0.932622	+	1.08970i
$236$	−3.30298	+	3.30298i	−0.215006	+	0.215006i
$237$	−5.59674	+	5.59674i	−0.363548	+	0.363548i
$238$	−0.147990	+	0.147990i	−0.00959274	+	0.00959274i
$239$	8.33949	+	8.33949i	0.539437	+	0.539437i	0.923363	−	0.383927i	$-0.125429\pi$
$239$	8.33949	+	8.33949i	0.539437	+	0.539437i	−0.383927	+	0.923363i	$0.625429\pi$
$240$	18.7155	−	1.45367i	1.20808	−	0.0938343i
$241$	1.03184	+	1.03184i	0.0664667	+	0.0664667i	0.739559	−	0.673092i	$-0.235034\pi$
$241$	1.03184	+	1.03184i	0.0664667	+	0.0664667i	−0.673092	+	0.739559i	$0.735034\pi$
$242$	2.20371			0.141660
$243$	14.7496	+	14.7496i	0.946185	+	0.946185i
$244$	20.4895			1.31171
$245$	−9.96089	+	11.6386i	−0.636378	+	0.743561i
$246$			3.02380i			0.192791i
$247$		0			0
$248$	2.74136	+	2.74136i	0.174077	+	0.174077i
$249$	8.66945	+	8.66945i	0.549404	+	0.549404i
$250$	−1.61339	+	2.61476i	−0.102040	+	0.165372i
$251$			13.0098i			0.821169i	0.911823	+	0.410585i	$0.134675\pi$
$251$			13.0098i			0.821169i	−0.911823	+	0.410585i	$0.865325\pi$
$252$			1.92014i			0.120958i
$253$	1.45489			0.0914684
$254$	−2.21600	+	2.21600i	−0.139044	+	0.139044i
$255$	−7.91846	−	6.77703i	−0.495873	−	0.424394i
$256$	10.2946			0.643413
$257$	−20.8324	−	20.8324i	−1.29949	−	1.29949i	−0.928729	−	0.370760i	$-0.879097\pi$
$257$	−20.8324	−	20.8324i	−1.29949	−	1.29949i	−0.370760	−	0.928729i	$-0.620903\pi$
$258$			4.42779i			0.275662i
$259$	1.86296			0.115759
$260$		0			0
$261$	−21.0972			−1.30588
$262$		−	5.73326i		−	0.354202i
$263$	−3.57265	−	3.57265i	−0.220299	−	0.220299i	0.588325	−	0.808624i	$-0.299788\pi$
$263$	−3.57265	−	3.57265i	−0.220299	−	0.220299i	−0.808624	+	0.588325i	$0.799788\pi$
$264$	−11.1144			−0.684043
$265$	−22.6103	+	1.75619i	−1.38894	+	0.107882i
$266$	0.375901	−	0.375901i	0.0230480	−	0.0230480i
$267$	−11.8121			−0.722890
$268$			12.2703i			0.749529i
$269$		−	8.64999i		−	0.527399i	−0.964605	−	0.263699i	$-0.915057\pi$
$269$		−	8.64999i		−	0.527399i	0.964605	−	0.263699i	$-0.0849427\pi$
$270$	−0.602052	+	0.0467627i	−0.0366397	+	0.00284589i
$271$	16.2843	+	16.2843i	0.989201	+	0.989201i	0.999942	−	0.0107409i	$-0.00341900\pi$
$271$	16.2843	+	16.2843i	0.989201	+	0.989201i	−0.0107409	+	0.999942i	$0.503419\pi$
$272$	−4.95497	−	4.95497i	−0.300439	−	0.300439i
$273$		0			0
$274$			0.0670394i			0.00405000i
$275$	−12.8530	+	17.6147i	−0.775064	+	1.06221i
$276$	−1.51715			−0.0913216
$277$	15.3026	+	15.3026i	0.919444	+	0.919444i	0.996989	−	0.0775451i	$-0.0247082\pi$
$277$	15.3026	+	15.3026i	0.919444	+	0.919444i	−0.0775451	+	0.996989i	$0.524708\pi$
$278$	−3.21087			−0.192575
$279$	−6.56856	−	6.56856i	−0.393250	−	0.393250i
$280$	−0.707403	−	0.605432i	−0.0422754	−	0.0361815i
$281$	8.17717	+	8.17717i	0.487809	+	0.487809i	0.907614	−	0.419805i	$-0.137902\pi$
$281$	8.17717	+	8.17717i	0.487809	+	0.487809i	−0.419805	+	0.907614i	$0.637902\pi$
$282$	−4.51527	+	4.51527i	−0.268880	+	0.268880i
$283$	3.18152	−	3.18152i	0.189122	−	0.189122i	−0.606195	−	0.795316i	$-0.707305\pi$
$283$	3.18152	−	3.18152i	0.189122	−	0.189122i	0.795316	+	0.606195i	$0.207305\pi$
$284$	−5.92467	+	5.92467i	−0.351564	+	0.351564i
$285$	20.1133	+	17.2140i	1.19141	+	1.01967i
$286$		0			0
$287$	−1.27126	+	1.27126i	−0.0750400	+	0.0750400i
$288$	8.09674			0.477105
$289$		−	13.1093i		−	0.771137i
$290$	3.26203	−	3.81144i	0.191553	−	0.223815i
$291$	24.6432	−	24.6432i	1.44461	−	1.44461i
$292$			11.7123i			0.685408i
$293$		−	13.1055i		−	0.765631i	−0.923825	−	0.382815i	$-0.874955\pi$
$293$		−	13.1055i		−	0.765631i	0.923825	−	0.382815i	$-0.125045\pi$
$294$	−3.14588	+	3.14588i	−0.183472	+	0.183472i
$295$	0.420293	+	5.41111i	0.0244704	+	0.315047i
$296$		−	5.20370i		−	0.302459i
$297$	−4.28568			−0.248680
$298$	0.492111	−	0.492111i	0.0285072	−	0.0285072i
$299$		0			0
$300$	13.4030	−	18.3684i	0.773821	−	1.06050i
$301$	−1.86152	+	1.86152i	−0.107296	+	0.107296i
$302$	0.710373	−	0.710373i	0.0408774	−	0.0408774i
$303$	−8.82177	+	8.82177i	−0.506797	+	0.506797i
$304$	12.5859	+	12.5859i	0.721849	+	0.721849i
$305$	15.4799	−	18.0871i	0.886374	−	1.03566i
$306$	−0.990475	−	0.990475i	−0.0566217	−	0.0566217i
$307$	7.75447			0.442571			0.221285	−	0.975209i	$-0.428975\pi$
$307$	7.75447			0.442571			0.221285	+	0.975209i	$0.428975\pi$
$308$	−2.29138	−	2.29138i	−0.130564	−	0.130564i
$309$	−4.04374			−0.230040
$310$	2.20231	−	0.171058i	0.125083	−	0.00971546i
$311$		−	11.6030i		−	0.657947i	−0.944339	−	0.328974i	$-0.893297\pi$
$311$		−	11.6030i		−	0.657947i	0.944339	−	0.328974i	$-0.106703\pi$
$312$		0			0
$313$	−10.1565	−	10.1565i	−0.574078	−	0.574078i	0.359188	−	0.933265i	$-0.383054\pi$
$313$	−10.1565	−	10.1565i	−0.574078	−	0.574078i	−0.933265	+	0.359188i	$0.883054\pi$
$314$	0.609436	+	0.609436i	0.0343924	+	0.0343924i
$315$	1.69500	+	1.45067i	0.0955026	+	0.0817361i
$316$			6.44593i			0.362612i
$317$		−	21.7686i		−	1.22265i	−0.791381	−	0.611323i	$-0.790638\pi$
$317$		−	21.7686i		−	1.22265i	0.791381	−	0.611323i	$-0.209362\pi$
$318$	−6.58623			−0.369337
$319$	25.1761	−	25.1761i	1.40959	−	1.40959i
$320$	9.07864	−	10.6077i	0.507512	−	0.592990i
$321$	9.57732			0.534554
$322$	0.0250297	+	0.0250297i	0.00139485	+	0.00139485i
$323$		−	9.88248i		−	0.549876i
$324$	19.3884			1.07714
$325$		0			0
$326$	4.07070			0.225455
$327$		−	16.8064i		−	0.929393i
$328$	3.55093	+	3.55093i	0.196067	+	0.196067i
$329$	−3.79659			−0.209313
$330$	−4.11768	+	4.81121i	−0.226671	+	0.264848i
$331$	−13.8731	+	13.8731i	−0.762536	+	0.762536i	−0.976780	−	0.214244i	$-0.931271\pi$
$331$	−13.8731	+	13.8731i	−0.762536	+	0.762536i	0.214244	+	0.976780i	$0.431271\pi$
$332$	9.98485			0.547990
$333$			12.4685i			0.683272i
$334$		−	0.953071i		−	0.0521497i
$335$	10.8316	+	9.27025i	0.591794	+	0.506488i
$336$	2.29198	+	2.29198i	0.125038	+	0.125038i
$337$	−9.35946	−	9.35946i	−0.509842	−	0.509842i	0.404636	−	0.914478i	$-0.367398\pi$
$337$	−9.35946	−	9.35946i	−0.509842	−	0.509842i	−0.914478	+	0.404636i	$0.867398\pi$
$338$		0			0
$339$		−	9.39165i		−	0.510084i
$340$	−8.46261	+	0.657309i	−0.458949	+	0.0356476i
$341$	15.6770			0.848959
$342$	2.51585	+	2.51585i	0.136042	+	0.136042i
$343$	−5.34789			−0.288759
$344$	5.19967	+	5.19967i	0.280347	+	0.280347i
$345$	−1.14621	+	1.33926i	−0.0617098	+	0.0721034i
$346$	0.759754	+	0.759754i	0.0408446	+	0.0408446i
$347$	−19.5532	+	19.5532i	−1.04967	+	1.04967i	−0.0509719	+	0.998700i	$0.516232\pi$
$347$	−19.5532	+	19.5532i	−1.04967	+	1.04967i	−0.998700	+	0.0509719i	$0.983768\pi$
$348$	−26.2533	+	26.2533i	−1.40733	+	1.40733i
$349$	20.8717	−	20.8717i	1.11724	−	1.11724i	0.125093	−	0.992145i	$-0.460077\pi$
$349$	20.8717	−	20.8717i	1.11724	−	1.11724i	0.992145	−	0.125093i	$-0.0399230\pi$
$350$	−0.524160	+	0.0819196i	−0.0280175	+	0.00437878i
$351$		0			0
$352$	−9.66215	+	9.66215i	−0.514994	+	0.514994i
$353$	15.6355			0.832195			0.416098	−	0.909320i	$-0.363397\pi$
$353$	15.6355			0.832195			0.416098	+	0.909320i	$0.363397\pi$
$354$			1.57622i			0.0837750i
$355$	0.753894	+	9.70609i	0.0400125	+	0.515146i
$356$	−6.80218	+	6.80218i	−0.360515	+	0.360515i
$357$		−	1.79967i		−	0.0952489i
$358$		−	1.78560i		−	0.0943716i
$359$	14.0592	−	14.0592i	0.742017	−	0.742017i	−0.230949	−	0.972966i	$-0.574183\pi$
$359$	14.0592	−	14.0592i	0.742017	−	0.742017i	0.972966	+	0.230949i	$0.0741830\pi$
$360$	4.05208	−	4.73456i	0.213563	−	0.249533i
$361$			6.10198i			0.321157i
$362$	−3.29345			−0.173100
$363$	−13.3995	+	13.3995i	−0.703290	+	0.703290i
$364$		0			0
$365$	10.3390	+	8.84863i	0.541167	+	0.463159i
$366$	4.88890	−	4.88890i	0.255547	−	0.255547i
$367$	−15.5741	+	15.5741i	−0.812963	+	0.812963i	−0.985077	−	0.172114i	$-0.944940\pi$
$367$	−15.5741	+	15.5741i	−0.812963	+	0.812963i	0.172114	+	0.985077i	$0.444940\pi$
$368$	−0.838042	+	0.838042i	−0.0436860	+	0.0436860i
$369$	−8.50836	−	8.50836i	−0.442928	−	0.442928i
$370$	−2.25258	−	1.92788i	−0.117106	−	0.100225i
$371$	−2.76896	−	2.76896i	−0.143757	−	0.143757i
$372$	−16.3479			−0.847597
$373$	−0.824171	−	0.824171i	−0.0426740	−	0.0426740i	0.685448	−	0.728122i	$-0.259606\pi$
$373$	−0.824171	−	0.824171i	−0.0426740	−	0.0426740i	−0.728122	+	0.685448i	$0.759606\pi$
$374$	2.36394			0.122237
$375$	−6.08874	−	25.7088i	−0.314421	−	1.32760i
$376$			10.6048i			0.546901i
$377$		0			0
$378$	−0.0737299	−	0.0737299i	−0.00379226	−	0.00379226i
$379$	18.6501	+	18.6501i	0.957990	+	0.957990i	0.999152	−	0.0411628i	$-0.0131062\pi$
$379$	18.6501	+	18.6501i	0.957990	+	0.957990i	−0.0411628	+	0.999152i	$0.513106\pi$
$380$	21.4954	−	1.66960i	1.10269	−	0.0856486i
$381$		−	26.9484i		−	1.38061i
$382$			1.42706i			0.0730146i
$383$	32.8001			1.67601			0.838004	−	0.545664i	$-0.183722\pi$
$383$	32.8001			1.67601			0.838004	+	0.545664i	$0.183722\pi$
$384$	13.3382	−	13.3382i	0.680663	−	0.680663i
$385$	−3.75386	+	0.291570i	−0.191314	+	0.0148598i
$386$	1.83411			0.0933536
$387$	−12.4589	−	12.4589i	−0.633321	−	0.633321i
$388$		−	28.3823i		−	1.44089i
$389$	9.36826			0.474989			0.237495	−	0.971389i	$-0.423674\pi$
$389$	9.36826			0.474989			0.237495	+	0.971389i	$0.423674\pi$
$390$		0			0
$391$	0.658034			0.0332782
$392$			7.38859i			0.373180i
$393$	34.8606	+	34.8606i	1.75848	+	1.75848i
$394$	−5.38546			−0.271316
$395$	5.69014	+	4.86992i	0.286302	+	0.245032i
$396$	15.3359	−	15.3359i	0.770658	−	0.770658i
$397$	−11.6520			−0.584797			−0.292399	−	0.956297i	$-0.594453\pi$
$397$	−11.6520			−0.584797			−0.292399	+	0.956297i	$0.594453\pi$
$398$		−	4.04135i		−	0.202574i
$399$			4.57126i			0.228849i
$400$	−2.74282	−	17.5499i	−0.137141	−	0.877494i
$401$	−14.5782	−	14.5782i	−0.728002	−	0.728002i	0.242220	−	0.970221i	$-0.422124\pi$
$401$	−14.5782	−	14.5782i	−0.728002	−	0.728002i	−0.970221	+	0.242220i	$0.922124\pi$
$402$	2.92776	+	2.92776i	0.146024	+	0.146024i
$403$		0			0
$404$			10.1603i			0.505493i
$405$	14.6480	−	17.1151i	0.727866	−	0.850457i
$406$	0.866248			0.0429912
$407$	−14.8792	−	14.8792i	−0.737534	−	0.737534i
$408$	−5.02693			−0.248870
$409$	−3.22285	−	3.22285i	−0.159360	−	0.159360i	0.622923	−	0.782283i	$-0.285945\pi$
$409$	−3.22285	−	3.22285i	−0.159360	−	0.159360i	−0.782283	+	0.622923i	$0.785945\pi$
$410$	2.85269	−	0.221574i	0.140884	−	0.0109428i
$411$	−0.407627	−	0.407627i	−0.0201067	−	0.0201067i
$412$	−2.32865	+	2.32865i	−0.114724	+	0.114724i
$413$	−0.662669	+	0.662669i	−0.0326078	+	0.0326078i
$414$	−0.167521	+	0.167521i	−0.00823318	+	0.00823318i
$415$	7.54358	−	8.81412i	0.370300	−	0.432668i
$416$		0			0
$417$	19.5234	−	19.5234i	0.956067	−	0.956067i
$418$	−6.00453			−0.293691
$419$			0.652044i			0.0318545i	0.999873	+	0.0159272i	$0.00507001\pi$
$419$			0.652044i			0.0318545i	−0.999873	+	0.0159272i	$0.994930\pi$
$420$	3.91448	−	0.304047i	0.191007	−	0.0148360i
$421$	−5.58095	+	5.58095i	−0.271999	+	0.271999i	−0.829904	−	0.557906i	$-0.811605\pi$
$421$	−5.58095	+	5.58095i	−0.271999	+	0.271999i	0.557906	+	0.829904i	$0.311605\pi$
$422$			5.88484i			0.286470i
$423$		−	25.4101i		−	1.23548i
$424$	−7.73438	+	7.73438i	−0.375615	+	0.375615i
$425$	−5.81328	+	7.96695i	−0.281985	+	0.386454i
$426$			2.82731i			0.136984i
$427$	4.11075			0.198933
$428$	5.51524	−	5.51524i	0.266589	−	0.266589i
$429$		0			0
$430$	4.17722	−	0.324454i	0.201443	−	0.0156466i
$431$	25.2795	−	25.2795i	1.21767	−	1.21767i	0.249227	−	0.968445i	$-0.419823\pi$
$431$	25.2795	−	25.2795i	1.21767	−	1.21767i	0.968445	−	0.249227i	$-0.0801767\pi$
$432$	2.46862	−	2.46862i	0.118771	−	0.118771i
$433$	18.6534	−	18.6534i	0.896424	−	0.896424i	−0.0986941	−	0.995118i	$-0.531467\pi$
$433$	18.6534	−	18.6534i	0.896424	−	0.896424i	0.995118	+	0.0986941i	$0.0314665\pi$
$434$	0.269705	+	0.269705i	0.0129462	+	0.0129462i
$435$	3.34065	+	43.0096i	0.160172	+	2.06215i
$436$	−9.67818	−	9.67818i	−0.463501	−	0.463501i
$437$	−1.67144			−0.0799558
$438$	2.79461	+	2.79461i	0.133531	+	0.133531i
$439$	1.72935			0.0825374			0.0412687	−	0.999148i	$-0.486860\pi$
$439$	1.72935			0.0825374			0.0412687	+	0.999148i	$0.486860\pi$
$440$	0.814426	+	10.4854i	0.0388263	+	0.499873i
$441$		−	17.7038i		−	0.843036i
$442$		0			0
$443$	2.86737	+	2.86737i	0.136233	+	0.136233i	0.771935	−	0.635702i	$-0.219289\pi$
$443$	2.86737	+	2.86737i	0.136233	+	0.136233i	−0.635702	+	0.771935i	$0.719289\pi$
$444$	15.5159	+	15.5159i	0.736350	+	0.736350i
$445$	0.865554	+	11.1437i	0.0410312	+	0.528261i
$446$			7.51206i			0.355706i
$447$			5.98448i			0.283056i
$448$	2.41088			0.113903
$449$	−14.2752	+	14.2752i	−0.673687	+	0.673687i	−0.958564	−	0.284877i	$-0.908047\pi$
$449$	−14.2752	+	14.2752i	−0.673687	+	0.673687i	0.284877	+	0.958564i	$0.408047\pi$
$450$	−0.548277	−	3.50813i	−0.0258460	−	0.165375i
$451$	20.3067			0.956205
$452$	−5.40832	−	5.40832i	−0.254386	−	0.254386i
$453$			8.63872i			0.405883i
$454$	−1.90370			−0.0893452
$455$		0			0
$456$	12.7686			0.597946
$457$			14.7816i			0.691454i	0.938335	+	0.345727i	$0.112368\pi$
$457$			14.7816i			0.691454i	−0.938335	+	0.345727i	$0.887632\pi$
$458$	−1.25540	−	1.25540i	−0.0586608	−	0.0586608i
$459$	−1.93837			−0.0904753
$460$	0.111172	+	1.43129i	0.00518341	+	0.0667344i
$461$	−4.29491	+	4.29491i	−0.200034	+	0.200034i	−0.800015	−	0.599981i	$-0.795175\pi$
$461$	−4.29491	+	4.29491i	−0.200034	+	0.200034i	0.599981	+	0.800015i	$0.295175\pi$
$462$	−1.09347			−0.0508729
$463$		−	36.0148i		−	1.67375i	−0.547396	−	0.836874i	$-0.684381\pi$
$463$		−	36.0148i		−	1.67375i	0.547396	−	0.836874i	$-0.315619\pi$
$464$			29.0036i			1.34646i
$465$	−12.3508	+	14.4310i	−0.572757	+	0.669224i
$466$	−1.50890	−	1.50890i	−0.0698986	−	0.0698986i
$467$	7.68952	+	7.68952i	0.355829	+	0.355829i	0.862273	−	0.506444i	$-0.169040\pi$
$467$	7.68952	+	7.68952i	0.355829	+	0.355829i	−0.506444	+	0.862273i	$0.669040\pi$
$468$		0			0
$469$			2.46176i			0.113674i
$470$	4.59062	+	3.92889i	0.211749	+	0.181226i
$471$	−7.41124			−0.341492
$472$	1.85099	+	1.85099i	0.0851989	+	0.0851989i
$473$	29.7353			1.36723
$474$	1.53803	+	1.53803i	0.0706442	+	0.0706442i
$475$	14.7660	−	20.2365i	0.677511	−	0.928512i
$476$	−1.03637	−	1.03637i	−0.0475019	−	0.0475019i
$477$	18.5323	−	18.5323i	0.848536	−	0.848536i
$478$	2.29176	−	2.29176i	0.104823	−	0.104823i
$479$	6.49399	−	6.49399i	0.296718	−	0.296718i	−0.543009	−	0.839727i	$-0.682715\pi$
$479$	6.49399	−	6.49399i	0.296718	−	0.296718i	0.839727	+	0.543009i	$0.182715\pi$
$480$	−1.28208	−	16.5064i	−0.0585189	−	0.753408i
$481$		0			0
$482$	0.283559	−	0.283559i	0.0129157	−	0.0129157i
$483$	−0.304382			−0.0138498
$484$			15.4326i			0.701480i
$485$	−25.0544	−	21.4429i	−1.13766	−	0.973672i
$486$	4.05331	−	4.05331i	0.183862	−	0.183862i
$487$		−	25.7313i		−	1.16600i	−0.812473	−	0.582998i	$-0.801879\pi$
$487$		−	25.7313i		−	1.16600i	0.812473	−	0.582998i	$-0.198121\pi$
$488$		−	11.4823i		−	0.519781i
$489$	−24.7515	+	24.7515i	−1.11930	+	1.11930i
$490$	3.19838	+	2.73734i	0.144488	+	0.123660i
$491$			13.1972i			0.595581i	0.954631	+	0.297790i	$0.0962497\pi$
$491$			13.1972i			0.595581i	−0.954631	+	0.297790i	$0.903750\pi$
$492$	−21.1756			−0.954671
$493$	11.3869	−	11.3869i	0.512839	−	0.512839i
$494$		0			0
$495$	−1.95144	−	25.1241i	−0.0877108	−	1.12924i
$496$	−9.03023	+	9.03023i	−0.405469	+	0.405469i
$497$	−1.18865	+	1.18865i	−0.0533183	+	0.0533183i
$498$	2.38244	−	2.38244i	0.106760	−	0.106760i
$499$	16.7683	+	16.7683i	0.750650	+	0.750650i	0.974601	−	0.223950i	$-0.0718954\pi$
$499$	16.7683	+	16.7683i	0.750650	+	0.750650i	−0.223950	+	0.974601i	$0.571895\pi$
$500$	−18.3111	−	11.2985i	−0.818897	−	0.505285i
$501$	5.79506	+	5.79506i	0.258904	+	0.258904i
$502$	3.57520			0.159569
$503$	5.33090	+	5.33090i	0.237693	+	0.237693i	0.815894	−	0.578201i	$-0.196245\pi$
$503$	5.33090	+	5.33090i	0.237693	+	0.237693i	−0.578201	+	0.815894i	$0.696245\pi$
$504$	1.07605			0.0479311
$505$	8.96898	+	7.67612i	0.399114	+	0.341583i
$506$		−	0.399817i		−	0.0177740i
$507$		0			0
$508$	−15.5186	−	15.5186i	−0.688528	−	0.688528i
$509$	−21.6741	−	21.6741i	−0.960687	−	0.960687i	0.0385690	−	0.999256i	$-0.487720\pi$
$509$	−21.6741	−	21.6741i	−0.960687	−	0.960687i	−0.999256	+	0.0385690i	$0.987720\pi$
$510$	−1.86239	+	2.17606i	−0.0824678	+	0.0963576i
$511$			2.34980i			0.103949i
$512$		−	18.7939i		−	0.830581i
$513$	4.92355			0.217380
$514$	−5.72492	+	5.72492i	−0.252515	+	0.252515i
$515$	0.296312	+	3.81491i	0.0130571	+	0.168105i
$516$	−31.0077			−1.36504
$517$	30.3229	+	30.3229i	1.33360	+	1.33360i
$518$		−	0.511957i		−	0.0224941i
$519$	−9.23923			−0.405557
$520$		0			0
$521$	−7.16076			−0.313719			−0.156859	−	0.987621i	$-0.550137\pi$
$521$	−7.16076			−0.313719			−0.156859	+	0.987621i	$0.550137\pi$
$522$			5.79768i			0.253758i
$523$	7.60576	+	7.60576i	0.332576	+	0.332576i	0.853564	−	0.520988i	$-0.174436\pi$
$523$	7.60576	+	7.60576i	0.332576	+	0.332576i	−0.520988	+	0.853564i	$0.674436\pi$
$524$	40.1499			1.75396
$525$	2.68900	−	3.68521i	0.117358	−	0.160836i
$526$	−0.981796	+	0.981796i	−0.0428083	+	0.0428083i
$527$	7.09057			0.308870
$528$		−	36.6115i		−	1.59331i
$529$			22.8887i			0.995161i
$530$	0.482617	+	6.21351i	0.0209636	+	0.269898i
$531$	−4.43516	−	4.43516i	−0.192469	−	0.192469i
$532$	2.63243	+	2.63243i	0.114130	+	0.114130i
$533$		0			0
$534$			3.24607i			0.140471i
$535$	−0.701795	−	9.03534i	−0.0303412	−	0.390632i
$536$	6.87630			0.297011
$537$	10.8572	+	10.8572i	0.468521	+	0.468521i
$538$	−2.37709			−0.102484
$539$	21.1266	+	21.1266i	0.909986	+	0.909986i
$540$	−0.327478	−	4.21616i	−0.0140924	−	0.181435i
$541$	11.1986	+	11.1986i	0.481464	+	0.481464i	0.905599	−	0.424135i	$-0.139422\pi$
$541$	11.1986	+	11.1986i	0.481464	+	0.481464i	−0.424135	+	0.905599i	$0.639422\pi$
$542$	4.47507	−	4.47507i	0.192221	−	0.192221i
$543$	20.0255	−	20.0255i	0.859377	−	0.859377i
$544$	−4.37009	+	4.37009i	−0.187366	+	0.187366i
$545$	−15.8553	+	1.23152i	−0.679166	+	0.0527523i
$546$		0			0
$547$	−23.6205	+	23.6205i	−1.00994	+	1.00994i	−0.00999077	+	0.999950i	$0.503180\pi$
$547$	−23.6205	+	23.6205i	−1.00994	+	1.00994i	−0.999950	+	0.00999077i	$0.996820\pi$
$548$	−0.469476			−0.0200550
$549$			27.5127i			1.17422i
$550$	4.84067	+	3.53211i	0.206407	+	0.150610i
$551$	−28.9232	+	28.9232i	−1.23217	+	1.23217i
$552$			0.850212i			0.0361874i
$553$			1.29323i			0.0549938i
$554$	4.20528	−	4.20528i	0.178665	−	0.178665i
$555$	25.4189	−	1.97434i	1.07897	−	0.0838061i
$556$		−	22.4857i		−	0.953606i
$557$	31.1464			1.31972			0.659859	−	0.751390i	$-0.270616\pi$
$557$	31.1464			1.31972			0.659859	+	0.751390i	$0.270616\pi$
$558$	−1.80510	+	1.80510i	−0.0764159	+	0.0764159i
$559$		0			0
$560$	1.99433	−	2.33023i	0.0842759	−	0.0984702i
$561$	−14.3737	+	14.3737i	−0.606860	+	0.606860i
$562$	2.24716	−	2.24716i	0.0947906	−	0.0947906i
$563$	−14.7397	+	14.7397i	−0.621203	+	0.621203i	−0.945839	−	0.324636i	$-0.894758\pi$
$563$	−14.7397	+	14.7397i	−0.621203	+	0.621203i	0.324636	+	0.945839i	$0.394758\pi$
$564$	−31.6204	−	31.6204i	−1.33146	−	1.33146i
$565$	−8.86018	+	0.688190i	−0.372751	+	0.0289524i
$566$	−0.874308	−	0.874308i	−0.0367499	−	0.0367499i
$567$	3.88985			0.163359
$568$	3.32019	+	3.32019i	0.139312	+	0.139312i
$569$	−41.7455			−1.75006			−0.875031	−	0.484066i	$-0.839159\pi$
$569$	−41.7455			−1.75006			−0.875031	+	0.484066i	$0.839159\pi$
$570$	4.73055	−	5.52730i	0.198141	−	0.231513i
$571$			19.2151i			0.804127i	0.915612	+	0.402064i	$0.131707\pi$
$571$			19.2151i			0.804127i	−0.915612	+	0.402064i	$0.868293\pi$
$572$		0			0
$573$	−8.67709	−	8.67709i	−0.362491	−	0.362491i
$574$	0.349353	+	0.349353i	0.0145817	+	0.0145817i
$575$	1.34746	+	0.983209i	0.0561931	+	0.0410027i
$576$			16.1357i			0.672321i
$577$			21.8168i			0.908243i	0.890940	+	0.454122i	$0.150047\pi$
$577$			21.8168i			0.908243i	−0.890940	+	0.454122i	$0.849953\pi$
$578$	−3.60256			−0.149847
$579$	−11.1521	+	11.1521i	−0.463466	+	0.463466i
$580$	26.6914	+	22.8439i	1.10830	+	0.948542i
$581$	2.00324			0.0831082
$582$	−6.77217	−	6.77217i	−0.280715	−	0.280715i
$583$			44.2306i			1.83184i
$584$	6.56356			0.271602
$585$		0			0
$586$	−3.60150			−0.148777
$587$			5.85530i			0.241674i	0.992672	+	0.120837i	$0.0385579\pi$
$587$			5.85530i			0.241674i	−0.992672	+	0.120837i	$0.961442\pi$
$588$	−22.0306	−	22.0306i	−0.908525	−	0.908525i
$589$	−18.0104			−0.742105
$590$	1.48702	−	0.115500i	0.0612197	−	0.00475507i
$591$	32.7458	−	32.7458i	1.34698	−	1.34698i
$592$	17.1413			0.704503
$593$			45.6277i			1.87370i	0.349727	+	0.936852i	$0.386274\pi$
$593$			45.6277i			1.87370i	−0.349727	+	0.936852i	$0.613726\pi$
$594$			1.17774i			0.0483233i
$595$	−1.69783	+	0.131874i	−0.0696043	+	0.00540632i
$596$	3.44625	+	3.44625i	0.141164	+	0.141164i
$597$	24.5730	+	24.5730i	1.00571	+	1.00571i
$598$		0			0
$599$			12.7240i			0.519888i	0.965624	+	0.259944i	$0.0837041\pi$
$599$			12.7240i			0.519888i	−0.965624	+	0.259944i	$0.916296\pi$
$600$	−10.2937	−	7.51104i	−0.420238	−	0.306637i
$601$	−24.7272			−1.00864			−0.504321	−	0.863516i	$-0.668257\pi$
$601$	−24.7272			−1.00864			−0.504321	+	0.863516i	$0.668257\pi$
$602$	0.511561	+	0.511561i	0.0208497	+	0.0208497i
$603$	−16.4763			−0.670965
$604$	4.97473	+	4.97473i	0.202419	+	0.202419i
$605$	13.6231	+	11.6593i	0.553857	+	0.474020i
$606$	2.42430	+	2.42430i	0.0984804	+	0.0984804i
$607$	3.11245	−	3.11245i	0.126331	−	0.126331i	−0.641115	−	0.767445i	$-0.721528\pi$
$607$	3.11245	−	3.11245i	0.126331	−	0.126331i	0.767445	+	0.641115i	$0.221528\pi$
$608$	11.1003	−	11.1003i	0.450175	−	0.450175i
$609$	−5.26714	+	5.26714i	−0.213435	+	0.213435i
$610$	−4.97048	−	4.25400i	−0.201249	−	0.172239i
$611$		0			0
$612$	6.93628	−	6.93628i	0.280382	−	0.280382i
$613$	1.16058			0.0468752			0.0234376	−	0.999725i	$-0.492539\pi$
$613$	1.16058			0.0468752			0.0234376	+	0.999725i	$0.492539\pi$
$614$		−	2.13099i		−	0.0859999i
$615$	−15.9982	+	18.6928i	−0.645111	+	0.753765i
$616$	−1.28409	+	1.28409i	−0.0517375	+	0.0517375i
$617$			38.4760i			1.54899i	0.632583	+	0.774493i	$0.281995\pi$
$617$			38.4760i			1.54899i	−0.632583	+	0.774493i	$0.718005\pi$
$618$			1.11126i			0.0447012i
$619$	24.7229	−	24.7229i	0.993698	−	0.993698i	−0.00628240	−	0.999980i	$-0.502000\pi$
$619$	24.7229	−	24.7229i	0.993698	−	0.993698i	0.999980	+	0.00628240i	$0.00199976\pi$
$620$	1.19792	+	15.4227i	0.0481096	+	0.619392i
$621$			0.327839i			0.0131557i
$622$	−3.18861			−0.127852
$623$	−1.36470	+	1.36470i	−0.0546757	+	0.0546757i
$624$		0			0
$625$	−23.8078	+	7.62804i	−0.952313	+	0.305122i
$626$	−2.79109	+	2.79109i	−0.111554	+	0.111554i
$627$	36.5100	−	36.5100i	1.45807	−	1.45807i
$628$	−4.26787	+	4.26787i	−0.170306	+	0.170306i
$629$	−6.72971	−	6.72971i	−0.268331	−	0.268331i
$630$	0.398657	−	0.465802i	0.0158829	−	0.0185580i
$631$	5.16604	+	5.16604i	0.205657	+	0.205657i	0.802419	−	0.596762i	$-0.203546\pi$
$631$	5.16604	+	5.16604i	0.205657	+	0.205657i	−0.596762	+	0.802419i	$0.703546\pi$
$632$	3.61231			0.143690
$633$	−35.7822	−	35.7822i	−1.42222	−	1.42222i
$634$	−5.98220			−0.237583
$635$	−25.4234	+	1.97469i	−1.00890	+	0.0783633i
$636$		−	46.1232i		−	1.82891i
$637$		0			0
$638$	−6.91860	−	6.91860i	−0.273910	−	0.273910i
$639$	−7.95548	−	7.95548i	−0.314714	−	0.314714i
$640$	−13.5608	−	11.6060i	−0.536038	−	0.458769i
$641$			8.31220i			0.328312i	0.986434	+	0.164156i	$0.0524901\pi$
$641$			8.31220i			0.328312i	−0.986434	+	0.164156i	$0.947510\pi$
$642$		−	2.63193i		−	0.103874i
$643$	11.1556			0.439933			0.219967	−	0.975507i	$-0.429405\pi$
$643$	11.1556			0.439933			0.219967	+	0.975507i	$0.429405\pi$
$644$	−0.175283	+	0.175283i	−0.00690710	+	0.00690710i
$645$	−23.4264	+	27.3720i	−0.922414	+	1.07777i
$646$	−2.71579			−0.106851
$647$	29.7686	+	29.7686i	1.17033	+	1.17033i	0.982132	+	0.188194i	$0.0602635\pi$
$647$	29.7686	+	29.7686i	1.17033	+	1.17033i	0.188194	+	0.982132i	$0.439736\pi$
$648$		−	10.8653i		−	0.426830i
$649$	10.5853			0.415509
$650$		0			0
$651$	−3.27983			−0.128547
$652$			28.5070i			1.11642i
$653$	−30.2101	−	30.2101i	−1.18221	−	1.18221i	−0.979169	−	0.203045i	$-0.934916\pi$
$653$	−30.2101	−	30.2101i	−1.18221	−	1.18221i	−0.203045	−	0.979169i	$-0.565084\pi$
$654$	−4.61853			−0.180599
$655$	30.3334	−	35.4423i	1.18522	−	1.38485i
$656$	−11.6970	+	11.6970i	−0.456691	+	0.456691i
$657$	−15.7269			−0.613565
$658$			1.04334i			0.0406735i
$659$		−	17.6082i		−	0.685916i	−0.939351	−	0.342958i	$-0.888571\pi$
$659$		−	17.6082i		−	0.685916i	0.939351	−	0.342958i	$-0.111429\pi$
$660$	−33.6928	−	28.8360i	−1.31149	−	1.12244i
$661$	19.7044	+	19.7044i	0.766413	+	0.766413i	0.977473	−	0.211060i	$-0.0676915\pi$
$661$	19.7044	+	19.7044i	0.766413	+	0.766413i	−0.211060	+	0.977473i	$0.567692\pi$
$662$	3.81246	+	3.81246i	0.148175	+	0.148175i
$663$		0			0
$664$		−	5.59552i		−	0.217148i
$665$	4.31258	−	0.334967i	0.167235	−	0.0129895i
$666$	3.42646			0.132773
$667$	−1.92588	−	1.92588i	−0.0745704	−	0.0745704i
$668$	6.67434			0.258238
$669$	−45.6764	−	45.6764i	−1.76595	−	1.76595i
$670$	2.54754	−	2.97662i	0.0984202	−	0.114997i
$671$	−32.8320	−	32.8320i	−1.26747	−	1.26747i
$672$	2.02144	−	2.02144i	0.0779788	−	0.0779788i
$673$	−5.16432	+	5.16432i	−0.199070	+	0.199070i	−0.799601	−	0.600531i	$-0.794956\pi$
$673$	−5.16432	+	5.16432i	−0.199070	+	0.199070i	0.600531	+	0.799601i	$0.294956\pi$
$674$	−2.57206	+	2.57206i	−0.0990721	+	0.0990721i
$675$	−3.96922	−	2.89624i	−0.152775	−	0.111476i
$676$		0			0
$677$	3.26988	−	3.26988i	0.125672	−	0.125672i	−0.641473	−	0.767145i	$-0.721677\pi$
$677$	3.26988	−	3.26988i	0.125672	−	0.125672i	0.767145	+	0.641473i	$0.221677\pi$
$678$	−2.58091			−0.0991191
$679$		−	5.69427i		−	0.218526i
$680$	0.368357	+	4.74245i	0.0141258	+	0.181865i
$681$	11.5753	−	11.5753i	0.443566	−	0.443566i
$682$		−	4.30818i		−	0.164969i
$683$		−	27.0952i		−	1.03677i	−0.855148	−	0.518384i	$-0.826534\pi$
$683$		−	27.0952i		−	1.03677i	0.855148	−	0.518384i	$-0.173466\pi$
$684$	−17.6185	+	17.6185i	−0.673660	+	0.673660i
$685$	−0.354690	+	0.414429i	−0.0135520	+	0.0158345i
$686$			1.46965i			0.0561114i
$687$	15.2666			0.582458
$688$	−17.1280	+	17.1280i	−0.653000	+	0.653000i
$689$		0			0
$690$	0.368040	+	0.314988i	0.0140111	+	0.0119914i
$691$	8.88521	−	8.88521i	0.338009	−	0.338009i	−0.517608	−	0.855618i	$-0.673178\pi$
$691$	8.88521	−	8.88521i	0.338009	−	0.338009i	0.855618	+	0.517608i	$0.173178\pi$
$692$	−5.32055	+	5.32055i	−0.202257	+	0.202257i
$693$	3.07680	−	3.07680i	0.116878	−	0.116878i
$694$	5.37339	+	5.37339i	0.203971	+	0.203971i
$695$	−19.8492	−	16.9880i	−0.752924	−	0.644392i
$696$	14.7124	+	14.7124i	0.557672	+	0.557672i
$697$	9.18452			0.347889
$698$	−5.73573	−	5.73573i	−0.217101	−	0.217101i
$699$	18.3495			0.694042
$700$	−0.573681	−	3.67068i	−0.0216831	−	0.138739i
$701$			39.3955i			1.48795i	0.668208	+	0.743974i	$0.267062\pi$
$701$			39.3955i			1.48795i	−0.668208	+	0.743974i	$0.732938\pi$
$702$		0			0
$703$	17.0938	+	17.0938i	0.644705	+	0.644705i
$704$	−19.2554	−	19.2554i	−0.725714	−	0.725714i
$705$	−51.8021	+	4.02358i	−1.95098	+	0.151537i
$706$		−	4.29678i		−	0.161711i
$707$			2.03843i			0.0766631i
$708$	−11.0382			−0.414842
$709$	−18.0945	+	18.0945i	−0.679552	+	0.679552i	−0.959899	−	0.280347i	$-0.909550\pi$
$709$	−18.0945	+	18.0945i	−0.679552	+	0.679552i	0.280347	+	0.959899i	$0.409550\pi$
$710$	2.66732	−	0.207176i	0.100103	−	0.00777519i
$711$	−8.65543			−0.324604
$712$	3.81195	+	3.81195i	0.142859	+	0.142859i
$713$		−	1.19924i		−	0.0449118i
$714$	−0.494566			−0.0185087
$715$		0			0
$716$	12.5045			0.467315
$717$			27.8697i			1.04081i
$718$	−3.86359	−	3.86359i	−0.144188	−	0.144188i
$719$	−8.68536			−0.323909			−0.161955	−	0.986798i	$-0.551780\pi$
$719$	−8.68536			−0.323909			−0.161955	+	0.986798i	$0.551780\pi$
$720$	15.5959	+	13.3478i	0.581226	+	0.497443i
$721$	−0.467191	+	0.467191i	−0.0173991	+	0.0173991i
$722$	1.67688			0.0624069
$723$			3.44830i			0.128244i
$724$		−	23.0640i		−	0.857166i
$725$	40.3309	−	6.30321i	1.49785	−	0.234095i
$726$	3.68229	+	3.68229i	0.136663	+	0.136663i
$727$	−17.4677	−	17.4677i	−0.647841	−	0.647841i	0.304630	−	0.952471i	$-0.401467\pi$
$727$	−17.4677	−	17.4677i	−0.647841	−	0.647841i	−0.952471	+	0.304630i	$0.901467\pi$
$728$		0			0
$729$			19.0676i			0.706209i
$730$	2.43168	−	2.84124i	0.0900005	−	0.105159i
$731$	13.4490			0.497429
$732$	34.2369	+	34.2369i	1.26543	+	1.26543i
$733$	−34.2413			−1.26473			−0.632365	−	0.774670i	$-0.717916\pi$
$733$	−34.2413			−1.26473			−0.632365	+	0.774670i	$0.717916\pi$
$734$	4.27990	+	4.27990i	0.157974	+	0.157974i
$735$	−36.0916	+	2.80331i	−1.33126	+	0.103402i
$736$	0.739121	+	0.739121i	0.0272444	+	0.0272444i
$737$	19.6617	−	19.6617i	0.724250	−	0.724250i
$738$	−2.33817	+	2.33817i	−0.0860692	+	0.0860692i
$739$	19.9754	−	19.9754i	0.734807	−	0.734807i	−0.236761	−	0.971568i	$-0.576086\pi$
$739$	19.9754	−	19.9754i	0.734807	−	0.734807i	0.971568	+	0.236761i	$0.0760859\pi$
$740$	13.5009	−	15.7748i	0.496302	−	0.579893i
$741$		0			0
$742$	−0.760935	+	0.760935i	−0.0279348	+	0.0279348i
$743$	31.6768			1.16211			0.581055	−	0.813864i	$-0.302640\pi$
$743$	31.6768			1.16211			0.581055	+	0.813864i	$0.302640\pi$
$744$			9.16136i			0.335872i
$745$	5.64582	−	0.438523i	0.206847	−	0.0160662i
$746$	−0.226489	+	0.226489i	−0.00829237	+	0.00829237i
$747$			13.4074i			0.490551i
$748$			16.5547i			0.605298i
$749$	1.10651	−	1.10651i	0.0404309	−	0.0404309i
$750$	−7.06501	+	1.67324i	−0.257978	+	0.0610980i
$751$			2.44047i			0.0890541i	0.999008	+	0.0445271i	$0.0141781\pi$
$751$			2.44047i			0.0890541i	−0.999008	+	0.0445271i	$0.985822\pi$
$752$	−34.9329			−1.27387
$753$	−21.7387	+	21.7387i	−0.792201	+	0.792201i
$754$		0			0
$755$	8.14986	−	0.633018i	0.296604	−	0.0230379i
$756$	0.516329	−	0.516329i	0.0187787	−	0.0187787i
$757$	30.1874	−	30.1874i	1.09718	−	1.09718i	0.102439	−	0.994739i	$-0.467335\pi$
$757$	30.1874	−	30.1874i	1.09718	−	1.09718i	0.994739	−	0.102439i	$-0.0326646\pi$
$758$	5.12520	−	5.12520i	0.186156	−	0.186156i
$759$	2.43105	+	2.43105i	0.0882416	+	0.0882416i
$760$	−0.935645	−	12.0461i	−0.0339394	−	0.436957i
$761$	28.2568	+	28.2568i	1.02431	+	1.02431i	0.999697	+	0.0246125i	$0.00783521\pi$
$761$	28.2568	+	28.2568i	1.02431	+	1.02431i	0.0246125	+	0.999697i	$0.492165\pi$
$762$	−7.40565			−0.268279
$763$	−1.94171	−	1.94171i	−0.0702946	−	0.0702946i
$764$	−9.99366			−0.361558
$765$	−0.882617	−	11.3634i	−0.0319111	−	0.410843i
$766$		−	9.01376i		−	0.325680i
$767$		0			0
$768$	17.2018	+	17.2018i	0.620716	+	0.620716i
$769$	−27.1011	−	27.1011i	−0.977291	−	0.977291i	0.0224570	−	0.999748i	$-0.492851\pi$
$769$	−27.1011	−	27.1011i	−0.977291	−	0.977291i	−0.999748	+	0.0224570i	$0.992851\pi$
$770$	0.0801260	+	1.03159i	0.00288754	+	0.0371760i
$771$		−	69.6197i		−	2.50729i
$772$			12.8442i			0.462274i
$773$	−14.5788			−0.524363			−0.262181	−	0.965019i	$-0.584442\pi$
$773$	−14.5788			−0.524363			−0.262181	+	0.965019i	$0.584442\pi$
$774$	−3.42381	+	3.42381i	−0.123066	+	0.123066i
$775$	14.5194	+	10.5945i	0.521553	+	0.380564i
$776$	−15.9055			−0.570973
$777$	3.11291	+	3.11291i	0.111675	+	0.111675i
$778$		−	2.57448i		−	0.0922995i
$779$	−23.3291			−0.835853
$780$		0			0
$781$	18.9872			0.679414
$782$		−	0.180833i		−	0.00646659i
$783$	5.67306	+	5.67306i	0.202739	+	0.202739i
$784$	−24.3385			−0.869232
$785$	0.543072	+	6.99184i	0.0193831	+	0.249549i
$786$	9.57999	−	9.57999i	0.341707	−	0.341707i
$787$	0.947805			0.0337856			0.0168928	−	0.999857i	$-0.494623\pi$
$787$	0.947805			0.0337856			0.0168928	+	0.999857i	$0.494623\pi$
$788$		−	37.7143i		−	1.34352i
$789$		−	11.9394i		−	0.425056i
$790$	1.33829	−	1.56370i	0.0476144	−	0.0556339i
$791$	−1.08506	−	1.08506i	−0.0385802	−	0.0385802i
$792$	−8.59426	−	8.59426i	−0.305384	−	0.305384i
$793$		0			0
$794$			3.20207i			0.113637i
$795$	−40.7152	−	34.8462i	−1.44402	−	1.23587i
$796$	28.3015			1.00312
$797$	3.30722	+	3.30722i	0.117148	+	0.117148i	0.763250	−	0.646103i	$-0.223602\pi$
$797$	3.30722	+	3.30722i	0.117148	+	0.117148i	−0.646103	+	0.763250i	$0.723602\pi$
$798$	1.25622			0.0444698
$799$	13.7147	+	13.7147i	0.485192	+	0.485192i
$800$	−15.4783	+	2.41906i	−0.547241	+	0.0855268i
$801$	−9.13379	−	9.13379i	−0.322726	−	0.322726i
$802$	−4.00622	+	4.00622i	−0.141465	+	0.141465i
$803$	18.7675	−	18.7675i	0.662291	−	0.662291i
$804$	−20.5031	+	20.5031i	−0.723088	+	0.723088i
$805$	0.0223041	+	0.287157i	0.000786117	+	0.0101210i
$806$		0			0
$807$	14.4537	−	14.4537i	0.508794	−	0.508794i
$808$	5.69384			0.200308
$809$			24.4365i			0.859143i	0.903033	+	0.429572i	$0.141335\pi$
$809$			24.4365i			0.859143i	−0.903033	+	0.429572i	$0.858665\pi$
$810$	−4.70338	−	4.02540i	−0.165260	−	0.141438i
$811$	−9.34795	+	9.34795i	−0.328251	+	0.328251i	−0.851921	−	0.523670i	$-0.824562\pi$
$811$	−9.34795	+	9.34795i	−0.328251	+	0.328251i	0.523670	+	0.851921i	$0.324562\pi$
$812$			6.06632i			0.212886i
$813$			54.4205i			1.90861i
$814$	−4.08893	+	4.08893i	−0.143317	+	0.143317i
$815$	25.1645	+	21.5371i	0.881475	+	0.754412i
$816$		−	16.5590i		−	0.579681i
$817$	−34.1611			−1.19515
$818$	−0.885667	+	0.885667i	−0.0309666	+	0.0309666i
$819$		0			0
$820$	1.55168	+	19.9773i	0.0541871	+	0.697638i
$821$	1.38999	−	1.38999i	0.0485110	−	0.0485110i	−0.682435	−	0.730946i	$-0.739079\pi$
$821$	1.38999	−	1.38999i	0.0485110	−	0.0485110i	0.730946	+	0.682435i	$0.239079\pi$
$822$	−0.112019	+	0.112019i	−0.00390712	+	0.00390712i
$823$	11.6284	−	11.6284i	0.405339	−	0.405339i	−0.474771	−	0.880110i	$-0.657469\pi$
$823$	11.6284	−	11.6284i	0.405339	−	0.405339i	0.880110	+	0.474771i	$0.157469\pi$
$824$	1.30498	+	1.30498i	0.0454610	+	0.0454610i
$825$	−50.9100	+	7.95658i	−1.77246	+	0.277013i
$826$	0.182107	+	0.182107i	0.00633632	+	0.00633632i
$827$	27.3262			0.950225			0.475113	−	0.879925i	$-0.342407\pi$
$827$	27.3262			0.950225			0.475113	+	0.879925i	$0.342407\pi$
$828$	−1.17314	−	1.17314i	−0.0407696	−	0.0407696i
$829$	−14.5553			−0.505526			−0.252763	−	0.967528i	$-0.581339\pi$
$829$	−14.5553			−0.505526			−0.252763	+	0.967528i	$0.581339\pi$
$830$	−2.42219	−	2.07304i	−0.0840756	−	0.0719563i
$831$			51.1397i			1.77402i
$832$		0			0
$833$	9.55534	+	9.55534i	0.331073	+	0.331073i
$834$	−5.36521	−	5.36521i	−0.185782	−	0.185782i
$835$	5.04248	−	5.89176i	0.174502	−	0.203893i
$836$		−	42.0496i		−	1.45432i
$837$			3.53259i			0.122104i
$838$	0.179187			0.00618993
$839$	−17.2947	+	17.2947i	−0.597079	+	0.597079i	−0.939534	−	0.342455i	$-0.888742\pi$
$839$	−17.2947	+	17.2947i	−0.597079	+	0.597079i	0.342455	+	0.939534i	$0.388742\pi$
$840$	−0.170388	−	2.19368i	−0.00587895	−	0.0756892i
$841$	−37.6525			−1.29836
$842$	1.53369	+	1.53369i	0.0528545	+	0.0528545i
$843$			27.3273i			0.941201i
$844$	−41.2114			−1.41856
$845$		0			0
$846$	−6.98292			−0.240078
$847$			3.09620i			0.106387i
$848$	−25.4775	−	25.4775i	−0.874902	−	0.874902i
$849$	10.6323			0.364900
$850$	2.18939	+	1.59754i	0.0750954	+	0.0547951i
$851$	−1.13821	+	1.13821i	−0.0390172	+	0.0390172i
$852$	−19.7996			−0.678324
$853$			2.94669i			0.100893i	0.998727	+	0.0504464i	$0.0160644\pi$
$853$			2.94669i			0.100893i	−0.998727	+	0.0504464i	$0.983936\pi$
$854$		−	1.12967i		−	0.0386565i
$855$	2.24189	+	28.8635i	0.0766711	+	0.987111i
$856$	−3.09075	−	3.09075i	−0.105640	−	0.105640i
$857$	−13.0632	−	13.0632i	−0.446229	−	0.446229i	0.447870	−	0.894099i	$-0.352183\pi$
$857$	−13.0632	−	13.0632i	−0.446229	−	0.446229i	−0.894099	+	0.447870i	$0.852183\pi$
$858$		0			0
$859$			3.08382i			0.105219i	0.998615	+	0.0526093i	$0.0167538\pi$
$859$			3.08382i			0.105219i	−0.998615	+	0.0526093i	$0.983246\pi$
$860$	2.27215	+	29.2530i	0.0774795	+	0.997519i
$861$	−4.24841			−0.144786
$862$	−6.94703	−	6.94703i	−0.236617	−	0.236617i
$863$	50.9818			1.73544			0.867720	−	0.497053i	$-0.165585\pi$
$863$	50.9818			1.73544			0.867720	+	0.497053i	$0.165585\pi$
$864$	−2.17723	−	2.17723i	−0.0740708	−	0.0740708i
$865$	0.677021	+	8.71639i	0.0230194	+	0.296366i
$866$	−5.12611	−	5.12611i	−0.174192	−	0.174192i
$867$	21.9050	−	21.9050i	0.743934	−	0.743934i
$868$	−1.88874	+	1.88874i	−0.0641079	+	0.0641079i
$869$	10.3289	−	10.3289i	0.350382	−	0.350382i
$870$	11.8194	−	0.918039i	0.400715	−	0.0311244i
$871$		0			0
$872$	−5.42366	+	5.42366i	−0.183668	+	0.183668i
$873$	38.1110			1.28986
$874$			0.459326i			0.0155369i
$875$	−3.67371	−	2.26679i	−0.124194	−	0.0766316i
$876$	−19.5706	+	19.5706i	−0.661228	+	0.661228i
$877$			26.7687i			0.903916i	0.892039	+	0.451958i	$0.149274\pi$
$877$			26.7687i			0.903916i	−0.892039	+	0.451958i	$0.850726\pi$
$878$		−	0.475240i		−	0.0160386i
$879$	21.8986	−	21.8986i	0.738621	−	0.738621i
$880$	−34.5397	+	2.68277i	−1.16433	+	0.0904362i
$881$			31.4805i			1.06061i	0.847808	+	0.530303i	$0.177922\pi$
$881$			31.4805i			1.06061i	−0.847808	+	0.530303i	$0.822078\pi$
$882$	−4.86514			−0.163818
$883$	27.3576	−	27.3576i	0.920657	−	0.920657i	−0.0764191	−	0.997076i	$-0.524349\pi$
$883$	27.3576	−	27.3576i	0.920657	−	0.920657i	0.997076	+	0.0764191i	$0.0243487\pi$
$884$		0			0
$885$	−8.33941	+	9.74398i	−0.280326	+	0.327540i
$886$	0.787978	−	0.787978i	0.0264726	−	0.0264726i
$887$	−0.971214	+	0.971214i	−0.0326102	+	0.0326102i	−0.723224	−	0.690614i	$-0.757341\pi$
$887$	−0.971214	+	0.971214i	−0.0326102	+	0.0326102i	0.690614	+	0.723224i	$0.257341\pi$
$888$	8.69511	−	8.69511i	0.291789	−	0.291789i
$889$	−3.11346	−	3.11346i	−0.104422	−	0.104422i
$890$	3.06238	−	0.237862i	0.102651	−	0.00797314i
$891$	−31.0677	−	31.0677i	−1.04081	−	1.04081i
$892$	−52.6068			−1.76141
$893$	−34.8361	−	34.8361i	−1.16575	−	1.16575i
$894$	1.64459			0.0550032
$895$	9.44717	−	11.0383i	0.315784	−	0.368971i
$896$		−	3.08204i		−	0.102964i
$897$		0			0
$898$	3.92294	+	3.92294i	0.130910	+	0.130910i
$899$	−20.7521	−	20.7521i	−0.692122	−	0.692122i
$900$	24.5674	−	3.83957i	0.818914	−	0.127986i
$901$			20.0051i			0.666465i
$902$		−	5.58046i		−	0.185809i
$903$	−6.22100			−0.207022
$904$	−3.03083	+	3.03083i	−0.100804	+	0.100804i
$905$	−20.3597	−	17.4249i	−0.676779	−	0.579223i
$906$	2.37400			0.0788707
$907$	−16.4640	−	16.4640i	−0.546679	−	0.546679i	0.378800	−	0.925479i	$-0.376337\pi$
$907$	−16.4640	−	16.4640i	−0.546679	−	0.546679i	−0.925479	+	0.378800i	$0.876337\pi$
$908$		−	13.3316i		−	0.442425i
$909$	−13.6430			−0.452508
$910$		0			0
$911$	2.89704			0.0959832			0.0479916	−	0.998848i	$-0.484718\pi$
$911$	2.89704			0.0959832			0.0479916	+	0.998848i	$0.484718\pi$
$912$			42.0607i			1.39277i
$913$	−15.9996	−	15.9996i	−0.529508	−	0.529508i
$914$	4.06211			0.134363
$915$	56.0886	−	4.35653i	1.85423	−	0.144022i
$916$	8.79151	−	8.79151i	0.290480	−	0.290480i
$917$	8.05518			0.266006
$918$			0.532680i			0.0175811i
$919$			16.6099i			0.547909i	0.961743	+	0.273955i	$0.0883318\pi$
$919$			16.6099i			0.547909i	−0.961743	+	0.273955i	$0.911668\pi$
$920$	0.802099	−	0.0623008i	0.0264444	−	0.00205400i
$921$	12.9573	+	12.9573i	0.426958	+	0.426958i
$922$	1.18028	+	1.18028i	0.0388704	+	0.0388704i
$923$		0			0
$924$		−	7.65756i		−	0.251915i
$925$	−3.72523	−	23.8358i	−0.122485	−	0.783715i
$926$	−9.89717			−0.325241
$927$	−3.12685	−	3.12685i	−0.102699	−	0.102699i
$928$	25.5801			0.839708
$929$	−30.2829	−	30.2829i	−0.993548	−	0.993548i	0.00643095	−	0.999979i	$-0.497953\pi$
$929$	−30.2829	−	30.2829i	−0.993548	−	0.993548i	−0.999979	+	0.00643095i	$0.997953\pi$
$930$	3.96578	+	3.39412i	0.130043	+	0.111297i
$931$	−24.2710	−	24.2710i	−0.795451	−	0.795451i
$932$	10.5668	−	10.5668i	0.346128	−	0.346128i
$933$	19.3881	−	19.3881i	0.634737	−	0.634737i
$934$	2.11315	−	2.11315i	0.0691443	−	0.0691443i
$935$	14.6136	+	12.5071i	0.477916	+	0.409025i
$936$		0			0
$937$	27.9881	−	27.9881i	0.914331	−	0.914331i	−0.0822783	−	0.996609i	$-0.526220\pi$
$937$	27.9881	−	27.9881i	0.914331	−	0.914331i	0.996609	+	0.0822783i	$0.0262196\pi$
$938$	0.676514			0.0220890
$939$		−	33.9419i		−	1.10765i
$940$	−27.5139	+	32.1480i	−0.897406	+	1.04855i
$941$	−4.15042	+	4.15042i	−0.135300	+	0.135300i	−0.771513	−	0.636213i	$-0.780500\pi$
$941$	−4.15042	+	4.15042i	−0.135300	+	0.135300i	0.636213	+	0.771513i	$0.280500\pi$
$942$			2.03667i			0.0663584i
$943$		−	1.55339i		−	0.0505854i
$944$	−6.09729	+	6.09729i	−0.198450	+	0.198450i
$945$	−0.0657011	−	0.845877i	−0.00213726	−	0.0275164i
$946$		−	8.17153i		−	0.265679i
$947$	−24.8598			−0.807836			−0.403918	−	0.914795i	$-0.632352\pi$
$947$	−24.8598			−0.807836			−0.403918	+	0.914795i	$0.632352\pi$
$948$	−10.7708	+	10.7708i	−0.349820	+	0.349820i
$949$		0			0
$950$	−5.56115	−	4.05783i	−0.180428	−	0.131653i
$951$	36.3742	−	36.3742i	1.17951	−	1.17951i
$952$	−0.580782	+	0.580782i	−0.0188233	+	0.0188233i
$953$	23.1258	−	23.1258i	0.749118	−	0.749118i	−0.225196	−	0.974314i	$-0.572302\pi$
$953$	23.1258	−	23.1258i	0.749118	−	0.749118i	0.974314	+	0.225196i	$0.0723022\pi$
$954$	−5.09284	−	5.09284i	−0.164887	−	0.164887i
$955$	−7.55023	+	8.82189i	−0.244320	+	0.285470i
$956$	16.0492	+	16.0492i	0.519068	+	0.519068i
$957$	84.1358			2.71973
$958$	−1.78460	−	1.78460i	−0.0576580	−	0.0576580i
$959$	−0.0941897			−0.00304154
$960$	32.8949	−	2.55502i	1.06168	−	0.0824629i
$961$			18.0777i			0.583153i
$962$		0			0
$963$	7.40571	+	7.40571i	0.238646	+	0.238646i
$964$	1.98576	+	1.98576i	0.0639569	+	0.0639569i
$965$	11.3382	+	9.70384i	0.364990	+	0.312378i
$966$			0.0836467i			0.00269129i
$967$		−	30.0090i		−	0.965023i	−0.875890	−	0.482512i	$-0.839725\pi$
$967$		−	30.0090i		−	0.965023i	0.875890	−	0.482512i	$-0.160275\pi$
$968$	8.64843			0.277971
$969$	16.5131	−	16.5131i	0.530478	−	0.530478i
$970$	−5.89269	+	6.88518i	−0.189203	+	0.221070i
$971$	−6.27318			−0.201316			−0.100658	−	0.994921i	$-0.532095\pi$
$971$	−6.27318			−0.201316			−0.100658	+	0.994921i	$0.532095\pi$
$972$	28.3853	+	28.3853i	0.910457	+	0.910457i
$973$		−	4.51125i		−	0.144624i
$974$	−7.07119			−0.226575
$975$		0			0
$976$	37.8235			1.21070
$977$			15.5621i			0.497876i	0.968519	+	0.248938i	$0.0800816\pi$
$977$			15.5621i			0.497876i	−0.968519	+	0.248938i	$0.919918\pi$
$978$	6.80193	+	6.80193i	0.217502	+	0.217502i
$979$	21.7994			0.696712
$980$	−19.1695	+	22.3982i	−0.612349	+	0.715484i
$981$	12.9956	−	12.9956i	0.414918	−	0.414918i
$982$	3.62670			0.115733
$983$			53.4558i			1.70498i	0.522746	+	0.852488i	$0.324907\pi$
$983$			53.4558i			1.70498i	−0.522746	+	0.852488i	$0.675093\pi$
$984$			11.8668i			0.378301i
$985$	−33.2923	−	28.4932i	−1.06078	−	0.907870i
$986$	−3.12921	−	3.12921i	−0.0996545	−	0.0996545i
$987$	−6.34391	−	6.34391i	−0.201929	−	0.201929i
$988$		0			0
$989$		−	2.27465i		−	0.0723297i
$990$	−6.90431	+	0.536273i	−0.219433	+	0.0170439i
$991$	−23.6397			−0.750940			−0.375470	−	0.926835i	$-0.622519\pi$
$991$	−23.6397			−0.750940			−0.375470	+	0.926835i	$0.622519\pi$
$992$	7.96431	+	7.96431i	0.252867	+	0.252867i
$993$	−46.3626			−1.47127
$994$	0.326652	+	0.326652i	0.0103608	+	0.0103608i
$995$	21.3818	−	24.9831i	0.677850	−	0.792018i
$996$	16.6842	+	16.6842i	0.528658	+	0.528658i
$997$	36.5771	−	36.5771i	1.15841	−	1.15841i	0.173591	−	0.984818i	$-0.444463\pi$
$997$	36.5771	−	36.5771i	1.15841	−	1.15841i	0.984818	−	0.173591i	$-0.0555370\pi$
$998$	4.60806	−	4.60806i	0.145866	−	0.145866i
$999$	3.35281	−	3.35281i	0.106078	−	0.106078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.f.e.408.6		20
5.2	odd	4		845.2.k.e.577.5		20
13.2	odd	12		845.2.o.g.488.2		20
13.3	even	3		845.2.t.f.188.2		20
13.4	even	6		845.2.t.g.418.2		20
13.5	odd	4		845.2.k.d.268.6		20
13.6	odd	12		845.2.o.f.258.2		20
13.7	odd	12		845.2.o.e.258.4		20
13.8	odd	4		845.2.k.e.268.5		20
13.9	even	3		65.2.t.a.28.4	yes	20
13.10	even	6		845.2.t.e.188.4		20
13.11	odd	12		65.2.o.a.33.4	yes	20
13.12	even	2		845.2.f.d.408.5		20
39.11	even	12		585.2.cf.a.163.2		20
39.35	odd	6		585.2.dp.a.28.2		20
65.2	even	12		845.2.t.g.657.2		20
65.7	even	12		845.2.t.f.427.2		20
65.9	even	6		325.2.x.b.93.2		20
65.12	odd	4		845.2.k.d.577.6		20
65.17	odd	12		845.2.o.g.587.2		20
65.22	odd	12		65.2.o.a.2.4	✓	20
65.24	odd	12		325.2.s.b.293.2		20
65.32	even	12		845.2.t.e.427.4		20
65.37	even	12		65.2.t.a.7.4	yes	20
65.42	odd	12		845.2.o.e.357.4		20
65.47	even	4	inner	845.2.f.e.437.5		20
65.48	odd	12		325.2.s.b.132.2		20
65.57	even	4		845.2.f.d.437.6		20
65.62	odd	12		845.2.o.f.357.2		20
65.63	even	12		325.2.x.b.7.2		20
195.152	even	12		585.2.cf.a.262.2		20
195.167	odd	12		585.2.dp.a.397.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.4	✓	20	65.22	odd	12
65.2.o.a.33.4	yes	20	13.11	odd	12
65.2.t.a.7.4	yes	20	65.37	even	12
65.2.t.a.28.4	yes	20	13.9	even	3
325.2.s.b.132.2		20	65.48	odd	12
325.2.s.b.293.2		20	65.24	odd	12
325.2.x.b.7.2		20	65.63	even	12
325.2.x.b.93.2		20	65.9	even	6
585.2.cf.a.163.2		20	39.11	even	12
585.2.cf.a.262.2		20	195.152	even	12
585.2.dp.a.28.2		20	39.35	odd	6
585.2.dp.a.397.2		20	195.167	odd	12
845.2.f.d.408.5		20	13.12	even	2
845.2.f.d.437.6		20	65.57	even	4
845.2.f.e.408.6		20	1.1	even	1	trivial
845.2.f.e.437.5		20	65.47	even	4	inner
845.2.k.d.268.6		20	13.5	odd	4
845.2.k.d.577.6		20	65.12	odd	4
845.2.k.e.268.5		20	13.8	odd	4
845.2.k.e.577.5		20	5.2	odd	4
845.2.o.e.258.4		20	13.7	odd	12
845.2.o.e.357.4		20	65.42	odd	12
845.2.o.f.258.2		20	13.6	odd	12
845.2.o.f.357.2		20	65.62	odd	12
845.2.o.g.488.2		20	13.2	odd	12
845.2.o.g.587.2		20	65.17	odd	12
845.2.t.e.188.4		20	13.10	even	6
845.2.t.e.427.4		20	65.32	even	12
845.2.t.f.188.2		20	13.3	even	3
845.2.t.f.427.2		20	65.7	even	12
845.2.t.g.418.2		20	13.4	even	6
845.2.t.g.657.2		20	65.2	even	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.274809i q^{2} +(1.67095 + 1.67095i) q^{3} +1.92448 q^{4} +(1.45395 - 1.69883i) q^{5} +(0.459191 - 0.459191i) q^{6} +0.386104 q^{7} -1.07848i q^{8} +2.58414i q^{9} +O(q^{10})\)	\(q-0.274809i q^{2} +(1.67095 + 1.67095i) q^{3} +1.92448 q^{4} +(1.45395 - 1.69883i) q^{5} +(0.459191 - 0.459191i) q^{6} +0.386104 q^{7} -1.07848i q^{8} +2.58414i q^{9} +(-0.466854 - 0.399558i) q^{10} +(-3.08375 - 3.08375i) q^{11} +(3.21571 + 3.21571i) q^{12} -0.106105i q^{14} +(5.26814 - 0.409188i) q^{15} +3.55258 q^{16} +(-1.39475 - 1.39475i) q^{17} +0.710144 q^{18} +(3.54274 + 3.54274i) q^{19} +(2.79810 - 3.26937i) q^{20} +(0.645159 + 0.645159i) q^{21} +(-0.847442 + 0.847442i) q^{22} +(-0.235896 + 0.235896i) q^{23} +(1.80209 - 1.80209i) q^{24} +(-0.772064 - 4.94003i) q^{25} +(0.694880 - 0.694880i) q^{27} +0.743049 q^{28} +8.16410i q^{29} +(-0.112448 - 1.44773i) q^{30} +(-2.54187 + 2.54187i) q^{31} -3.13324i q^{32} -10.3056i q^{33} +(-0.383290 + 0.383290i) q^{34} +(0.561375 - 0.655925i) q^{35} +4.97313i q^{36} +4.82502 q^{37} +(0.973575 - 0.973575i) q^{38} +(-1.83216 - 1.56806i) q^{40} +(-3.29253 + 3.29253i) q^{41} +(0.177295 - 0.177295i) q^{42} +(-4.82129 + 4.82129i) q^{43} +(-5.93462 - 5.93462i) q^{44} +(4.39002 + 3.75721i) q^{45} +(0.0648264 + 0.0648264i) q^{46} -9.83310 q^{47} +(5.93619 + 5.93619i) q^{48} -6.85092 q^{49} +(-1.35756 + 0.212170i) q^{50} -4.66112i q^{51} +(-7.17155 - 7.17155i) q^{53} +(-0.190959 - 0.190959i) q^{54} +(-9.72240 + 0.755161i) q^{55} -0.416405i q^{56} +11.8395i q^{57} +2.24356 q^{58} +(-1.71630 + 1.71630i) q^{59} +(10.1384 - 0.787474i) q^{60} +10.6468 q^{61} +(0.698529 + 0.698529i) q^{62} +0.997746i q^{63} +6.24413 q^{64} -2.83207 q^{66} +6.37591i q^{67} +(-2.68417 - 2.68417i) q^{68} -0.788342 q^{69} +(-0.180254 - 0.154271i) q^{70} +(-3.07858 + 3.07858i) q^{71} +2.78695 q^{72} +6.08593i q^{73} -1.32596i q^{74} +(6.96446 - 9.54462i) q^{75} +(6.81793 + 6.81793i) q^{76} +(-1.19065 - 1.19065i) q^{77} +3.34944i q^{79} +(5.16528 - 6.03525i) q^{80} +10.0746 q^{81} +(0.904815 + 0.904815i) q^{82} +5.18834 q^{83} +(1.24160 + 1.24160i) q^{84} +(-4.39735 + 0.341552i) q^{85} +(1.32493 + 1.32493i) q^{86} +(-13.6418 + 13.6418i) q^{87} +(-3.32577 + 3.32577i) q^{88} +(-3.53455 + 3.53455i) q^{89} +(1.03251 - 1.20642i) q^{90} +(-0.453978 + 0.453978i) q^{92} -8.49469 q^{93} +2.70222i q^{94} +(11.1695 - 0.867558i) q^{95} +(5.23549 - 5.23549i) q^{96} -14.7480i q^{97} +1.88269i q^{98} +(7.96886 - 7.96886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} - 12 q^{4} + 4 q^{6} + 4 q^{7}+O(q^{10}) \) 20 * q + 4 * q^3 - 12 * q^4 + 4 * q^6 + 4 * q^7	\( 20 q + 4 q^{3} - 12 q^{4} + 4 q^{6} + 4 q^{7} - 8 q^{10} + 8 q^{11} - 24 q^{12} + 28 q^{15} + 4 q^{16} - 14 q^{17} + 4 q^{19} - 12 q^{20} + 4 q^{21} - 32 q^{22} + 8 q^{23} - 4 q^{24} + 18 q^{25} + 4 q^{27} - 36 q^{28} + 40 q^{30} + 2 q^{34} - 20 q^{35} + 8 q^{37} - 8 q^{38} - 16 q^{40} - 38 q^{41} + 16 q^{42} - 32 q^{43} - 36 q^{44} - 6 q^{45} + 4 q^{46} - 40 q^{47} + 28 q^{48} - 36 q^{49} + 42 q^{50} - 10 q^{53} + 36 q^{54} - 16 q^{55} + 8 q^{59} + 28 q^{60} + 32 q^{61} + 4 q^{62} + 20 q^{64} - 32 q^{66} - 50 q^{68} + 32 q^{69} - 12 q^{70} - 40 q^{71} - 8 q^{72} + 4 q^{75} - 16 q^{76} - 28 q^{77} + 112 q^{80} + 28 q^{81} - 34 q^{82} + 48 q^{83} + 8 q^{84} - 2 q^{85} + 60 q^{86} - 28 q^{87} - 32 q^{88} + 12 q^{89} + 46 q^{90} - 8 q^{92} - 64 q^{93} + 40 q^{95} + 56 q^{96} + 60 q^{99}+O(q^{100}) \) 20 * q + 4 * q^3 - 12 * q^4 + 4 * q^6 + 4 * q^7 - 8 * q^10 + 8 * q^11 - 24 * q^12 + 28 * q^15 + 4 * q^16 - 14 * q^17 + 4 * q^19 - 12 * q^20 + 4 * q^21 - 32 * q^22 + 8 * q^23 - 4 * q^24 + 18 * q^25 + 4 * q^27 - 36 * q^28 + 40 * q^30 + 2 * q^34 - 20 * q^35 + 8 * q^37 - 8 * q^38 - 16 * q^40 - 38 * q^41 + 16 * q^42 - 32 * q^43 - 36 * q^44 - 6 * q^45 + 4 * q^46 - 40 * q^47 + 28 * q^48 - 36 * q^49 + 42 * q^50 - 10 * q^53 + 36 * q^54 - 16 * q^55 + 8 * q^59 + 28 * q^60 + 32 * q^61 + 4 * q^62 + 20 * q^64 - 32 * q^66 - 50 * q^68 + 32 * q^69 - 12 * q^70 - 40 * q^71 - 8 * q^72 + 4 * q^75 - 16 * q^76 - 28 * q^77 + 112 * q^80 + 28 * q^81 - 34 * q^82 + 48 * q^83 + 8 * q^84 - 2 * q^85 + 60 * q^86 - 28 * q^87 - 32 * q^88 + 12 * q^89 + 46 * q^90 - 8 * q^92 - 64 * q^93 + 40 * q^95 + 56 * q^96 + 60 * q^99

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