LMFDB - Embedded newform 1638.2.dt.c.1369.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1638,2,Mod(1297,1638)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1638, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1638.1297"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.dt (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,-20,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
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} + 46 x^{18} + 895 x^{16} + 9634 x^{14} + 62977 x^{12} + 257850 x^{10} + 656102 x^{8} + \cdots + 32041 $ x^20 + 46x^18 + 895x^16 + 9634x^14 + 62977x^12 + 257850x^10 + 656102x^8 + 989866x^6 + 795896x^4 + 273668*x^2 + 32041
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1369.10
Root			$-2.35757i$ of defining polynomial
Character	$\chi$	$=$	1638.1369
Dual form			1638.2.dt.c.1297.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -1.00000 q^{4} +(2.89612 - 1.67208i) q^{5} +(0.268506 + 2.63209i) q^{7} -1.00000i q^{8} +(1.67208 + 2.89612i) q^{10} +(-4.36176 + 2.51826i) q^{11} +(-1.92804 + 3.04674i) q^{13} +(-2.63209 + 0.268506i) q^{14} +1.00000 q^{16} -3.73270 q^{17} +(-5.08703 - 2.93700i) q^{19} +(-2.89612 + 1.67208i) q^{20} +(-2.51826 - 4.36176i) q^{22} -3.78370 q^{23} +(3.09168 - 5.35494i) q^{25} +(-3.04674 - 1.92804i) q^{26} +(-0.268506 - 2.63209i) q^{28} +(-3.36143 + 5.82216i) q^{29} +(0.884906 + 0.510901i) q^{31} +1.00000i q^{32} -3.73270i q^{34} +(5.17868 + 7.17389i) q^{35} -0.428222i q^{37} +(2.93700 - 5.08703i) q^{38} +(-1.67208 - 2.89612i) q^{40} +(-0.917963 - 0.529986i) q^{41} +(1.65120 + 2.85996i) q^{43} +(4.36176 - 2.51826i) q^{44} -3.78370i q^{46} +(4.60157 - 2.65672i) q^{47} +(-6.85581 + 1.41346i) q^{49} +(5.35494 + 3.09168i) q^{50} +(1.92804 - 3.04674i) q^{52} +(1.15836 - 2.00634i) q^{53} +(-8.42146 + 14.5864i) q^{55} +(2.63209 - 0.268506i) q^{56} +(-5.82216 - 3.36143i) q^{58} +8.08665i q^{59} +(5.05050 - 8.74773i) q^{61} +(-0.510901 + 0.884906i) q^{62} -1.00000 q^{64} +(-0.489457 + 12.0476i) q^{65} +(-11.5166 + 6.64910i) q^{67} +3.73270 q^{68} +(-7.17389 + 5.17868i) q^{70} +(-2.35754 + 1.36113i) q^{71} +(6.88886 + 3.97728i) q^{73} +0.428222 q^{74} +(5.08703 + 2.93700i) q^{76} +(-7.79946 - 10.8044i) q^{77} +(7.07112 + 12.2475i) q^{79} +(2.89612 - 1.67208i) q^{80} +(0.529986 - 0.917963i) q^{82} +9.17859i q^{83} +(-10.8104 + 6.24136i) q^{85} +(-2.85996 + 1.65120i) q^{86} +(2.51826 + 4.36176i) q^{88} -5.41291i q^{89} +(-8.53700 - 4.25672i) q^{91} +3.78370 q^{92} +(2.65672 + 4.60157i) q^{94} -19.6435 q^{95} +(14.8742 - 8.58763i) q^{97} +(-1.41346 - 6.85581i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{4} + 2 q^{7} - 4 q^{10} + 6 q^{11} + 6 q^{13} + 4 q^{14} + 20 q^{16} - 20 q^{17} - 24 q^{19} + 2 q^{22} + 18 q^{25} - 6 q^{26} - 2 q^{28} - 2 q^{29} - 6 q^{31} + 14 q^{38} + 4 q^{40} - 18 q^{41}+ \cdots - 24 q^{98}+O(q^{100}) $ 20 * q - 20 * q^4 + 2 * q^7 - 4 * q^10 + 6 * q^11 + 6 * q^13 + 4 * q^14 + 20 * q^16 - 20 * q^17 - 24 * q^19 + 2 * q^22 + 18 * q^25 - 6 * q^26 - 2 * q^28 - 2 * q^29 - 6 * q^31 + 14 * q^38 + 4 * q^40 - 18 * q^41 + 8 * q^43 - 6 * q^44 - 18 * q^47 - 6 * q^49 + 12 * q^50 - 6 * q^52 + 4 * q^53 + 2 * q^55 - 4 * q^56 - 24 * q^58 - 4 * q^61 + 24 * q^62 - 20 * q^64 + 6 * q^65 - 60 * q^67 + 20 * q^68 - 48 * q^70 + 18 * q^71 - 72 * q^73 + 24 * q^74 + 24 * q^76 - 42 * q^77 + 42 * q^79 - 16 * q^82 - 12 * q^85 - 42 * q^86 - 2 * q^88 + 14 * q^91 + 16 * q^94 - 24 * q^95 + 78 * q^97 - 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	2.89612	−	1.67208i	1.29518	−	0.747775i	0.315616	−	0.948887i	$-0.397789\pi$
$5$	2.89612	−	1.67208i	1.29518	−	0.747775i	0.979568	+	0.201112i	$0.0644554\pi$
$6$		0			0
$7$	0.268506	+	2.63209i	0.101486	+	0.994837i
$7$	0.268506	+	2.63209i	0.101486	+	0.994837i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.67208	+	2.89612i	0.528757	+	0.915834i
$11$	−4.36176	+	2.51826i	−1.31512	+	0.759285i	−0.982939	−	0.183930i	$-0.941118\pi$
$11$	−4.36176	+	2.51826i	−1.31512	+	0.759285i	−0.332182	+	0.943215i	$0.607785\pi$
$12$		0			0
$13$	−1.92804	+	3.04674i	−0.534743	+	0.845015i
$13$	−1.92804	+	3.04674i	−0.534743	+	0.845015i
$14$	−2.63209	+	0.268506i	−0.703456	+	0.0717612i
$15$		0			0
$16$	1.00000			0.250000
$17$	−3.73270			−0.905313			−0.452657	−	0.891685i	$-0.649524\pi$
$17$	−3.73270			−0.905313			−0.452657	+	0.891685i	$0.649524\pi$
$18$		0			0
$19$	−5.08703	−	2.93700i	−1.16705	−	0.673794i	−0.214063	−	0.976820i	$-0.568670\pi$
$19$	−5.08703	−	2.93700i	−1.16705	−	0.673794i	−0.952982	+	0.303026i	$0.902003\pi$
$20$	−2.89612	+	1.67208i	−0.647592	+	0.373888i
$21$		0			0
$22$	−2.51826	−	4.36176i	−0.536896	−	0.929931i
$23$	−3.78370			−0.788957			−0.394478	−	0.918905i	$-0.629075\pi$
$23$	−3.78370			−0.788957			−0.394478	+	0.918905i	$0.629075\pi$
$24$		0			0
$25$	3.09168	−	5.35494i	0.618336	−	1.07099i
$26$	−3.04674	−	1.92804i	−0.597516	−	0.378120i
$27$		0			0
$28$	−0.268506	−	2.63209i	−0.0507428	−	0.497419i
$29$	−3.36143	+	5.82216i	−0.624201	+	1.08115i	0.364494	+	0.931206i	$0.381242\pi$
$29$	−3.36143	+	5.82216i	−0.624201	+	1.08115i	−0.988695	+	0.149942i	$0.952091\pi$
$30$		0			0
$31$	0.884906	+	0.510901i	0.158934	+	0.0917605i	0.577357	−	0.816491i	$-0.304084\pi$
$31$	0.884906	+	0.510901i	0.158934	+	0.0917605i	−0.418424	+	0.908252i	$0.637417\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$		−	3.73270i		−	0.640153i
$35$	5.17868	+	7.17389i	0.875357	+	1.21261i
$36$		0			0
$37$		−	0.428222i		−	0.0703993i	−0.999380	−	0.0351997i	$-0.988793\pi$
$37$		−	0.428222i		−	0.0703993i	0.999380	−	0.0351997i	$-0.0112067\pi$
$38$	2.93700	−	5.08703i	0.476444	−	0.825226i
$39$		0			0
$40$	−1.67208	−	2.89612i	−0.264378	−	0.457917i
$41$	−0.917963	−	0.529986i	−0.143362	−	0.0827699i	0.426603	−	0.904439i	$-0.359710\pi$
$41$	−0.917963	−	0.529986i	−0.143362	−	0.0827699i	−0.569965	+	0.821669i	$0.693043\pi$
$42$		0			0
$43$	1.65120	+	2.85996i	0.251805	+	0.436140i	0.964023	−	0.265819i	$-0.0856423\pi$
$43$	1.65120	+	2.85996i	0.251805	+	0.436140i	−0.712217	+	0.701959i	$0.752309\pi$
$44$	4.36176	−	2.51826i	0.657560	−	0.379643i
$45$		0			0
$46$		−	3.78370i		−	0.557877i
$47$	4.60157	−	2.65672i	0.671207	−	0.387522i	−0.125327	−	0.992116i	$-0.539998\pi$
$47$	4.60157	−	2.65672i	0.671207	−	0.387522i	0.796534	+	0.604594i	$0.206665\pi$
$48$		0			0
$49$	−6.85581	+	1.41346i	−0.979401	+	0.201923i
$50$	5.35494	+	3.09168i	0.757303	+	0.437229i
$51$		0			0
$52$	1.92804	−	3.04674i	0.267371	−	0.422507i
$53$	1.15836	−	2.00634i	0.159113	−	0.275592i	−0.775436	−	0.631426i	$-0.782470\pi$
$53$	1.15836	−	2.00634i	0.159113	−	0.275592i	0.934549	+	0.355834i	$0.115803\pi$
$54$		0			0
$55$	−8.42146	+	14.5864i	−1.13555	+	1.96683i
$56$	2.63209	−	0.268506i	0.351728	−	0.0358806i
$57$		0			0
$58$	−5.82216	−	3.36143i	−0.764487	−	0.441377i
$59$			8.08665i			1.05279i	0.850240	+	0.526396i	$0.176457\pi$
$59$			8.08665i			1.05279i	−0.850240	+	0.526396i	$0.823543\pi$
$60$		0			0
$61$	5.05050	−	8.74773i	0.646651	−	1.12003i	−0.337267	−	0.941409i	$-0.609502\pi$
$61$	5.05050	−	8.74773i	0.646651	−	1.12003i	0.983918	−	0.178623i	$-0.0571643\pi$
$62$	−0.510901	+	0.884906i	−0.0648845	+	0.112383i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.489457	+	12.0476i	−0.0607096	+	1.49432i
$66$		0			0
$67$	−11.5166	+	6.64910i	−1.40697	+	0.812317i	−0.995095	−	0.0989215i	$-0.968461\pi$
$67$	−11.5166	+	6.64910i	−1.40697	+	0.812317i	−0.411879	+	0.911239i	$0.635127\pi$
$68$	3.73270			0.452657
$69$		0			0
$70$	−7.17389	+	5.17868i	−0.857444	+	0.618971i
$71$	−2.35754	+	1.36113i	−0.279788	+	0.161536i	−0.633328	−	0.773884i	$-0.718311\pi$
$71$	−2.35754	+	1.36113i	−0.279788	+	0.161536i	0.353539	+	0.935420i	$0.384978\pi$
$72$		0			0
$73$	6.88886	+	3.97728i	0.806280	+	0.465506i	0.845662	−	0.533718i	$-0.179206\pi$
$73$	6.88886	+	3.97728i	0.806280	+	0.465506i	−0.0393824	+	0.999224i	$0.512539\pi$
$74$	0.428222			0.0497798
$75$		0			0
$76$	5.08703	+	2.93700i	0.583523	+	0.336897i
$77$	−7.79946	−	10.8044i	−0.888831	−	1.23127i
$78$		0			0
$79$	7.07112	+	12.2475i	0.795563	+	1.37796i	0.922481	+	0.386043i	$0.126158\pi$
$79$	7.07112	+	12.2475i	0.795563	+	1.37796i	−0.126918	+	0.991913i	$0.540508\pi$
$80$	2.89612	−	1.67208i	0.323796	−	0.186944i
$81$		0			0
$82$	0.529986	−	0.917963i	0.0585272	−	0.101372i
$83$			9.17859i			1.00748i	0.863855	+	0.503741i	$0.168043\pi$
$83$			9.17859i			1.00748i	−0.863855	+	0.503741i	$0.831957\pi$
$84$		0			0
$85$	−10.8104	+	6.24136i	−1.17255	+	0.676971i
$86$	−2.85996	+	1.65120i	−0.308397	+	0.178053i
$87$		0			0
$88$	2.51826	+	4.36176i	0.268448	+	0.464965i
$89$		−	5.41291i		−	0.573767i	−0.957965	−	0.286884i	$-0.907381\pi$
$89$		−	5.41291i		−	0.573767i	0.957965	−	0.286884i	$-0.0926193\pi$
$90$		0			0
$91$	−8.53700	−	4.25672i	−0.894921	−	0.446225i
$92$	3.78370			0.394478
$93$		0			0
$94$	2.65672	+	4.60157i	0.274019	+	0.474615i
$95$	−19.6435			−2.01539
$96$		0			0
$97$	14.8742	−	8.58763i	1.51025	−	0.871941i	0.510318	−	0.859986i	$-0.329528\pi$
$97$	14.8742	−	8.58763i	1.51025	−	0.871941i	0.999929	−	0.0119557i	$-0.00380571\pi$
$98$	−1.41346	−	6.85581i	−0.142781	−	0.692541i
$99$		0			0
$100$	−3.09168	+	5.35494i	−0.309168	+	0.535494i
$101$	1.22413	+	2.12026i	0.121806	+	0.210973i	0.920480	−	0.390790i	$-0.127798\pi$
$101$	1.22413	+	2.12026i	0.121806	+	0.210973i	−0.798674	+	0.601764i	$0.794465\pi$
$102$		0			0
$103$	−8.96428	−	15.5266i	−0.883277	−	1.52988i	−0.847676	−	0.530514i	$-0.821999\pi$
$103$	−8.96428	−	15.5266i	−0.883277	−	1.52988i	−0.0356010	−	0.999366i	$-0.511335\pi$
$104$	3.04674	+	1.92804i	0.298758	+	0.189060i
$105$		0			0
$106$	2.00634	+	1.15836i	0.194873	+	0.112510i
$107$	9.90239			0.957300			0.478650	−	0.878006i	$-0.341126\pi$
$107$	9.90239			0.957300			0.478650	+	0.878006i	$0.341126\pi$
$108$		0			0
$109$	−3.08121	−	1.77894i	−0.295127	−	0.170391i	0.345125	−	0.938557i	$-0.387837\pi$
$109$	−3.08121	−	1.77894i	−0.295127	−	0.170391i	−0.640252	+	0.768165i	$0.721170\pi$
$110$	−14.5864	−	8.42146i	−1.39076	−	0.802955i
$111$		0			0
$112$	0.268506	+	2.63209i	0.0253714	+	0.248709i
$113$	−2.44458	−	4.23414i	−0.229967	−	0.398314i	0.727831	−	0.685756i	$-0.240528\pi$
$113$	−2.44458	−	4.23414i	−0.229967	−	0.398314i	−0.957798	+	0.287442i	$0.907195\pi$
$114$		0			0
$115$	−10.9581	+	6.32664i	−1.02184	+	0.589962i
$116$	3.36143	−	5.82216i	0.312101	−	0.540574i
$117$		0			0
$118$	−8.08665			−0.744436
$119$	−1.00225	−	9.82481i	−0.0918762	−	0.900639i
$120$		0			0
$121$	7.18332	−	12.4419i	0.653029	−	1.13108i
$122$	8.74773	+	5.05050i	0.791982	+	0.457251i
$123$		0			0
$124$	−0.884906	−	0.510901i	−0.0794669	−	0.0458803i
$125$		−	3.95733i		−	0.353954i
$126$		0			0
$127$	−4.14641	+	7.18180i	−0.367935	+	0.637281i	−0.989242	−	0.146285i	$-0.953268\pi$
$127$	−4.14641	+	7.18180i	−0.367935	+	0.637281i	0.621308	+	0.783567i	$0.286602\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−12.0476	−	0.489457i	−1.05664	−	0.0429282i
$131$	3.08084	+	5.33618i	0.269174	+	0.466224i	0.968649	−	0.248434i	$-0.0799158\pi$
$131$	3.08084	+	5.33618i	0.269174	+	0.466224i	−0.699474	+	0.714658i	$0.746583\pi$
$132$		0			0
$133$	6.36455	−	14.1781i	0.551877	−	1.22940i
$134$	−6.64910	−	11.5166i	−0.574395	−	0.994881i
$135$		0			0
$136$			3.73270i			0.320076i
$137$			7.43816i			0.635485i	0.948177	+	0.317742i	$0.102925\pi$
$137$			7.43816i			0.635485i	−0.948177	+	0.317742i	$0.897075\pi$
$138$		0			0
$139$	2.44199	+	4.22965i	0.207127	+	0.358754i	0.950808	−	0.309780i	$-0.100255\pi$
$139$	2.44199	+	4.22965i	0.207127	+	0.358754i	−0.743682	+	0.668534i	$0.766922\pi$
$140$	−5.17868	−	7.17389i	−0.437679	−	0.606305i
$141$		0			0
$142$	−1.36113	−	2.35754i	−0.114223	−	0.197840i
$143$	0.737156	−	18.1445i	0.0616441	−	1.51732i
$144$		0			0
$145$			22.4822i			1.86705i
$146$	−3.97728	+	6.88886i	−0.329162	+	0.570126i
$147$		0			0
$148$			0.428222i			0.0351997i
$149$	4.86592	+	2.80934i	0.398632	+	0.230150i	0.685894	−	0.727702i	$-0.259412\pi$
$149$	4.86592	+	2.80934i	0.398632	+	0.230150i	−0.287262	+	0.957852i	$0.592745\pi$
$150$		0			0
$151$	−7.19648	−	4.15489i	−0.585641	−	0.338120i	0.177731	−	0.984079i	$-0.443124\pi$
$151$	−7.19648	−	4.15489i	−0.585641	−	0.338120i	−0.763372	+	0.645959i	$0.776458\pi$
$152$	−2.93700	+	5.08703i	−0.238222	+	0.412613i
$153$		0			0
$154$	10.8044	−	7.79946i	0.870643	−	0.628498i
$155$	3.41706			0.274465
$156$		0			0
$157$	−2.60751	+	4.51635i	−0.208102	+	0.360444i	−0.951117	−	0.308832i	$-0.900062\pi$
$157$	−2.60751	+	4.51635i	−0.208102	+	0.360444i	0.743014	+	0.669275i	$0.233395\pi$
$158$	−12.2475	+	7.07112i	−0.974362	+	0.562548i
$159$		0			0
$160$	1.67208	+	2.89612i	0.132189	+	0.228958i
$161$	−1.01595	−	9.95905i	−0.0800678	−	0.784883i
$162$		0			0
$163$	−10.8077	−	6.23982i	−0.846524	−	0.488741i	0.0129528	−	0.999916i	$-0.495877\pi$
$163$	−10.8077	−	6.23982i	−0.846524	−	0.488741i	−0.859476	+	0.511176i	$0.829210\pi$
$164$	0.917963	+	0.529986i	0.0716809	+	0.0413850i
$165$		0			0
$166$	−9.17859			−0.712397
$167$	0.409946	+	0.236682i	0.0317226	+	0.0183150i	0.515777	−	0.856723i	$-0.327503\pi$
$167$	0.409946	+	0.236682i	0.0317226	+	0.0183150i	−0.484055	+	0.875038i	$0.660836\pi$
$168$		0			0
$169$	−5.56530	−	11.7485i	−0.428100	−	0.903731i
$170$	−6.24136	−	10.8104i	−0.478691	−	0.829116i
$171$		0			0
$172$	−1.65120	−	2.85996i	−0.125903	−	0.218070i
$173$	5.06601	−	8.77459i	0.385162	−	0.667120i	−0.606630	−	0.794984i	$-0.707479\pi$
$173$	5.06601	−	8.77459i	0.385162	−	0.667120i	0.991792	+	0.127865i	$0.0408123\pi$
$174$		0			0
$175$	14.9248	+	6.69975i	1.12821	+	0.506453i
$176$	−4.36176	+	2.51826i	−0.328780	+	0.189821i
$177$		0			0
$178$	5.41291			0.405715
$179$	5.35710	+	9.27876i	0.400408	+	0.693527i	0.993775	−	0.111405i	$-0.0355350\pi$
$179$	5.35710	+	9.27876i	0.400408	+	0.693527i	−0.593367	+	0.804932i	$0.702202\pi$
$180$		0			0
$181$	1.56347			0.116212			0.0581058	−	0.998310i	$-0.481494\pi$
$181$	1.56347			0.116212			0.0581058	+	0.998310i	$0.481494\pi$
$182$	4.25672	−	8.53700i	0.315529	−	0.632805i
$183$		0			0
$184$			3.78370i			0.278938i
$185$	−0.716021	−	1.24018i	−0.0526429	−	0.0911801i
$186$		0			0
$187$	16.2812	−	9.39993i	1.19060	−	0.687391i
$188$	−4.60157	+	2.65672i	−0.335604	+	0.193761i
$189$		0			0
$190$		−	19.6435i		−	1.42509i
$191$	−4.69659	+	8.13473i	−0.339833	+	0.588608i	−0.984401	−	0.175939i	$-0.943704\pi$
$191$	−4.69659	+	8.13473i	−0.339833	+	0.588608i	0.644568	+	0.764547i	$0.277037\pi$
$192$		0			0
$193$	7.93269	−	4.57994i	0.571008	−	0.329672i	−0.186544	−	0.982447i	$-0.559729\pi$
$193$	7.93269	−	4.57994i	0.571008	−	0.329672i	0.757552	+	0.652775i	$0.226395\pi$
$194$	8.58763	+	14.8742i	0.616556	+	1.06791i
$195$		0			0
$196$	6.85581	−	1.41346i	0.489701	−	0.100962i
$197$	−13.4152	−	7.74526i	−0.955793	−	0.551827i	−0.0609170	−	0.998143i	$-0.519402\pi$
$197$	−13.4152	−	7.74526i	−0.955793	−	0.551827i	−0.894876	+	0.446316i	$0.852736\pi$
$198$		0			0
$199$	−5.48387			−0.388741			−0.194371	−	0.980928i	$-0.562266\pi$
$199$	−5.48387			−0.388741			−0.194371	+	0.980928i	$0.562266\pi$
$200$	−5.35494	−	3.09168i	−0.378652	−	0.218615i
$201$		0			0
$202$	−2.12026	+	1.22413i	−0.149181	+	0.0861295i
$203$	−16.2270	−	7.28430i	−1.13891	−	0.511257i
$204$		0			0
$205$	−3.54471			−0.247573
$206$	15.5266	−	8.96428i	1.08179	−	0.624571i
$207$		0			0
$208$	−1.92804	+	3.04674i	−0.133686	+	0.211254i
$209$	29.5846			2.04641
$210$		0			0
$211$	−2.54733	+	4.41210i	−0.175365	+	0.303741i	−0.940288	−	0.340381i	$-0.889444\pi$
$211$	−2.54733	+	4.41210i	−0.175365	+	0.303741i	0.764922	+	0.644122i	$0.222777\pi$
$212$	−1.15836	+	2.00634i	−0.0795567	+	0.137796i
$213$		0			0
$214$			9.90239i			0.676913i
$215$	9.56414	+	5.52186i	0.652269	+	0.376588i
$216$		0			0
$217$	−1.10714	+	2.46633i	−0.0751573	+	0.167426i
$218$	1.77894	−	3.08121i	0.120485	−	0.208686i
$219$		0			0
$220$	8.42146	−	14.5864i	0.567775	−	0.983415i
$221$	7.19681	−	11.3726i	0.484110	−	0.765003i
$222$		0			0
$223$	−8.65366	−	4.99619i	−0.579492	−	0.334570i	0.181440	−	0.983402i	$-0.441924\pi$
$223$	−8.65366	−	4.99619i	−0.579492	−	0.334570i	−0.760931	+	0.648832i	$0.775258\pi$
$224$	−2.63209	+	0.268506i	−0.175864	+	0.0179403i
$225$		0			0
$226$	4.23414	−	2.44458i	0.281651	−	0.162611i
$227$			13.2146i			0.877082i	0.898711	+	0.438541i	$0.144505\pi$
$227$			13.2146i			0.877082i	−0.898711	+	0.438541i	$0.855495\pi$
$228$		0			0
$229$	−8.62549	+	4.97993i	−0.569989	+	0.329083i	−0.757145	−	0.653247i	$-0.773406\pi$
$229$	−8.62549	+	4.97993i	−0.569989	+	0.329083i	0.187156	+	0.982330i	$0.440073\pi$
$230$	−6.32664	−	10.9581i	−0.417166	−	0.722553i
$231$		0			0
$232$	5.82216	+	3.36143i	0.382244	+	0.220688i
$233$	4.29233	+	7.43454i	0.281200	+	0.487053i	0.971681	−	0.236298i	$-0.0759342\pi$
$233$	4.29233	+	7.43454i	0.281200	+	0.487053i	−0.690480	+	0.723351i	$0.742601\pi$
$234$		0			0
$235$	8.88446	−	15.3883i	0.579558	−	1.00382i
$236$		−	8.08665i		−	0.526396i
$237$		0			0
$238$	9.82481	−	1.00225i	0.636848	−	0.0649663i
$239$		−	1.17300i		−	0.0758748i	−0.999280	−	0.0379374i	$-0.987921\pi$
$239$		−	1.17300i		−	0.0758748i	0.999280	−	0.0379374i	$-0.0120787\pi$
$240$		0			0
$241$			24.3882i			1.57098i	0.618874	+	0.785490i	$0.287589\pi$
$241$			24.3882i			1.57098i	−0.618874	+	0.785490i	$0.712411\pi$
$242$	12.4419	+	7.18332i	0.799794	+	0.461761i
$243$		0			0
$244$	−5.05050	+	8.74773i	−0.323325	+	0.560016i
$245$	−17.4918	+	15.5570i	−1.11751	+	0.993900i
$246$		0			0
$247$	18.7563	−	9.83622i	1.19343	−	0.625864i
$248$	0.510901	−	0.884906i	0.0324422	−	0.0561916i
$249$		0			0
$250$	3.95733			0.250283
$251$	10.6649	+	18.4721i	0.673162	+	1.16595i	0.977002	+	0.213228i	$0.0683978\pi$
$251$	10.6649	+	18.4721i	0.673162	+	1.16595i	−0.303840	+	0.952723i	$0.598269\pi$
$252$		0			0
$253$	16.5036	−	9.52837i	1.03757	−	0.599043i
$254$	−7.18180	−	4.14641i	−0.450626	−	0.260169i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−12.8591			−0.802129			−0.401065	−	0.916050i	$-0.631360\pi$
$257$	−12.8591			−0.802129			−0.401065	+	0.916050i	$0.631360\pi$
$258$		0			0
$259$	1.12712	−	0.114980i	0.0700359	−	0.00714452i
$260$	0.489457	−	12.0476i	0.0303548	−	0.747159i
$261$		0			0
$262$	−5.33618	+	3.08084i	−0.329670	+	0.190335i
$263$	12.4300	+	21.5295i	0.766470	+	1.32756i	0.939466	+	0.342642i	$0.111322\pi$
$263$	12.4300	+	21.5295i	0.766470	+	1.32756i	−0.172997	+	0.984922i	$0.555345\pi$
$264$		0			0
$265$		−	7.74748i		−	0.475924i
$266$	14.1781	+	6.36455i	0.869317	+	0.390236i
$267$		0			0
$268$	11.5166	−	6.64910i	0.703487	−	0.406158i
$269$	20.6024			1.25615			0.628074	−	0.778154i	$-0.283844\pi$
$269$	20.6024			1.25615			0.628074	+	0.778154i	$0.283844\pi$
$270$		0			0
$271$		−	5.28145i		−	0.320825i	−0.987050	−	0.160413i	$-0.948718\pi$
$271$		−	5.28145i		−	0.320825i	0.987050	−	0.160413i	$-0.0512825\pi$
$272$	−3.73270			−0.226328
$273$		0			0
$274$	−7.43816			−0.449355
$275$			31.1427i			1.87797i
$276$		0			0
$277$	5.25013			0.315450			0.157725	−	0.987483i	$-0.449584\pi$
$277$	5.25013			0.315450			0.157725	+	0.987483i	$0.449584\pi$
$278$	−4.22965	+	2.44199i	−0.253677	+	0.146461i
$279$		0			0
$280$	7.17389	−	5.17868i	0.428722	−	0.309485i
$281$		−	31.3151i		−	1.86810i	−0.357141	−	0.934051i	$-0.616248\pi$
$281$		−	31.3151i		−	1.86810i	0.357141	−	0.934051i	$-0.383752\pi$
$282$		0			0
$283$	−3.86020	−	6.68606i	−0.229465	−	0.397445i	0.728185	−	0.685381i	$-0.240364\pi$
$283$	−3.86020	−	6.68606i	−0.229465	−	0.397445i	−0.957650	+	0.287936i	$0.907031\pi$
$284$	2.35754	−	1.36113i	0.139894	−	0.0807679i
$285$		0			0
$286$	18.1445	+	0.737156i	1.07291	+	0.0435890i
$287$	1.14849	−	2.55847i	0.0677934	−	0.151022i
$288$		0			0
$289$	−3.06694			−0.180408
$290$	−22.4822			−1.32020
$291$		0			0
$292$	−6.88886	−	3.97728i	−0.403140	−	0.232753i
$293$	−18.3856	+	10.6150i	−1.07410	+	0.620133i	−0.929299	−	0.369328i	$-0.879588\pi$
$293$	−18.3856	+	10.6150i	−1.07410	+	0.620133i	−0.144802	+	0.989461i	$0.546255\pi$
$294$		0			0
$295$	13.5215	+	23.4199i	0.787252	+	1.36356i
$296$	−0.428222			−0.0248899
$297$		0			0
$298$	−2.80934	+	4.86592i	−0.162741	+	0.281875i
$299$	7.29514	−	11.5280i	0.421889	−	0.666680i
$300$		0			0
$301$	−7.08432	+	5.11402i	−0.408333	+	0.294767i
$302$	4.15489	−	7.19648i	0.239087	−	0.414111i
$303$		0			0
$304$	−5.08703	−	2.93700i	−0.291761	−	0.168448i
$305$		−	33.7793i		−	1.93420i
$306$		0			0
$307$			33.9938i			1.94013i	0.242850	+	0.970064i	$0.421918\pi$
$307$			33.9938i			1.94013i	−0.242850	+	0.970064i	$0.578082\pi$
$308$	7.79946	+	10.8044i	0.444416	+	0.615637i
$309$		0			0
$310$			3.41706i			0.194076i
$311$	0.365883	−	0.633728i	0.0207473	−	0.0359354i	−0.855465	−	0.517860i	$-0.826729\pi$
$311$	0.365883	−	0.633728i	0.0207473	−	0.0359354i	0.876213	+	0.481925i	$0.160062\pi$
$312$		0			0
$313$	3.68359	+	6.38016i	0.208209	+	0.360628i	0.951150	−	0.308728i	$-0.0999034\pi$
$313$	3.68359	+	6.38016i	0.208209	+	0.360628i	−0.742942	+	0.669356i	$0.766570\pi$
$314$	−4.51635	−	2.60751i	−0.254872	−	0.147150i
$315$		0			0
$316$	−7.07112	−	12.2475i	−0.397782	−	0.688978i
$317$	24.6012	−	14.2035i	1.38174	−	0.797748i	0.389375	−	0.921079i	$-0.372691\pi$
$317$	24.6012	−	14.2035i	1.38174	−	0.797748i	0.992366	+	0.123331i	$0.0393577\pi$
$318$		0			0
$319$		−	33.8598i		−	1.89579i
$320$	−2.89612	+	1.67208i	−0.161898	+	0.0934719i
$321$		0			0
$322$	9.95905	−	1.01595i	0.554996	−	0.0566165i
$323$	18.9884	+	10.9629i	1.05654	+	0.609994i
$324$		0			0
$325$	10.3543	+	19.7441i	0.574351	+	1.09521i
$326$	6.23982	−	10.8077i	0.345592	−	0.598583i
$327$		0			0
$328$	−0.529986	+	0.917963i	−0.0292636	+	0.0506860i
$329$	8.22826	+	11.3984i	0.453639	+	0.628414i
$330$		0			0
$331$	17.5783	+	10.1489i	0.966193	+	0.557832i	0.898073	−	0.439846i	$-0.144967\pi$
$331$	17.5783	+	10.1489i	0.966193	+	0.557832i	0.0681192	+	0.997677i	$0.478300\pi$
$332$		−	9.17859i		−	0.503741i
$333$		0			0
$334$	−0.236682	+	0.409946i	−0.0129507	+	0.0224312i
$335$	−22.2356	+	38.5132i	−1.21486	+	2.10420i
$336$		0			0
$337$	−8.85616			−0.482426			−0.241213	−	0.970472i	$-0.577545\pi$
$337$	−8.85616			−0.482426			−0.241213	+	0.970472i	$0.577545\pi$
$338$	11.7485	−	5.56530i	0.639035	−	0.302712i
$339$		0			0
$340$	10.8104	−	6.24136i	0.586274	−	0.338485i
$341$	−5.14634			−0.278690
$342$		0			0
$343$	−5.56119	−	17.6656i	−0.300276	−	0.953852i
$344$	2.85996	−	1.65120i	0.154199	−	0.0890267i
$345$		0			0
$346$	8.77459	+	5.06601i	0.471725	+	0.272350i
$347$	−6.89722			−0.370262			−0.185131	−	0.982714i	$-0.559271\pi$
$347$	−6.89722			−0.370262			−0.185131	+	0.982714i	$0.559271\pi$
$348$		0			0
$349$	−3.63303	−	2.09753i	−0.194472	−	0.112278i	0.399602	−	0.916689i	$-0.369148\pi$
$349$	−3.63303	−	2.09753i	−0.194472	−	0.112278i	−0.594074	+	0.804410i	$0.702482\pi$
$350$	−6.69975	+	14.9248i	−0.358117	+	0.797766i
$351$		0			0
$352$	−2.51826	−	4.36176i	−0.134224	−	0.232483i
$353$	−21.7100	+	12.5343i	−1.15551	+	0.667132i	−0.950223	−	0.311570i	$-0.899145\pi$
$353$	−21.7100	+	12.5343i	−1.15551	+	0.667132i	−0.205284	+	0.978702i	$0.565812\pi$
$354$		0			0
$355$	−4.55181	+	7.88397i	−0.241585	+	0.418438i
$356$			5.41291i			0.286884i
$357$		0			0
$358$	−9.27876	+	5.35710i	−0.490398	+	0.283131i
$359$	−17.2117	+	9.93716i	−0.908397	+	0.524463i	−0.879915	−	0.475131i	$-0.842401\pi$
$359$	−17.2117	+	9.93716i	−0.908397	+	0.524463i	−0.0284821	+	0.999594i	$0.509067\pi$
$360$		0			0
$361$	7.75193	+	13.4267i	0.407996	+	0.706670i
$362$			1.56347i			0.0821740i
$363$		0			0
$364$	8.53700	+	4.25672i	0.447460	+	0.223113i
$365$	26.6013			1.39238
$366$		0			0
$367$	−7.10630	−	12.3085i	−0.370946	−	0.642497i	0.618765	−	0.785576i	$-0.287633\pi$
$367$	−7.10630	−	12.3085i	−0.370946	−	0.642497i	−0.989711	+	0.143079i	$0.954300\pi$
$368$	−3.78370			−0.197239
$369$		0			0
$370$	1.24018	−	0.716021i	0.0644741	−	0.0372241i
$371$	5.59190	+	2.51020i	0.290317	+	0.130323i
$372$		0			0
$373$	15.6299	−	27.0718i	0.809288	−	1.40173i	−0.104070	−	0.994570i	$-0.533187\pi$
$373$	15.6299	−	27.0718i	0.809288	−	1.40173i	0.913358	−	0.407157i	$-0.133480\pi$
$374$	9.39993	+	16.2812i	0.486059	+	0.841879i
$375$		0			0
$376$	−2.65672	−	4.60157i	−0.137010	−	0.237308i
$377$	−11.2577	−	21.4668i	−0.579799	−	1.10560i
$378$		0			0
$379$	19.0369	+	10.9909i	0.977858	+	0.564567i	0.901623	−	0.432523i	$-0.142377\pi$
$379$	19.0369	+	10.9909i	0.977858	+	0.564567i	0.0762355	+	0.997090i	$0.475710\pi$
$380$	19.6435			1.00769
$381$		0			0
$382$	−8.13473	−	4.69659i	−0.416209	−	0.240298i
$383$	4.21349	+	2.43266i	0.215299	+	0.124303i	0.603772	−	0.797157i	$-0.293664\pi$
$383$	4.21349	+	2.43266i	0.215299	+	0.124303i	−0.388472	+	0.921460i	$0.626997\pi$
$384$		0			0
$385$	−40.6539	−	18.2495i	−2.07192	−	0.930082i
$386$	4.57994	+	7.93269i	0.233113	+	0.403764i
$387$		0			0
$388$	−14.8742	+	8.58763i	−0.755123	+	0.435971i
$389$	−6.43897	+	11.1526i	−0.326469	+	0.565460i	−0.981809	−	0.189874i	$-0.939192\pi$
$389$	−6.43897	+	11.1526i	−0.326469	+	0.565460i	0.655340	+	0.755334i	$0.272525\pi$
$390$		0			0
$391$	14.1234			0.714253
$392$	1.41346	+	6.85581i	0.0713907	+	0.346271i
$393$		0			0
$394$	7.74526	−	13.4152i	0.390201	−	0.675847i
$395$	40.9576	+	23.6469i	2.06080	+	1.18980i
$396$		0			0
$397$	25.8091	+	14.9009i	1.29532	+	0.747855i	0.979593	−	0.200993i	$-0.0644170\pi$
$397$	25.8091	+	14.9009i	1.29532	+	0.747855i	0.315731	+	0.948849i	$0.397750\pi$
$398$		−	5.48387i		−	0.274882i
$399$		0			0
$400$	3.09168	−	5.35494i	0.154584	−	0.267747i
$401$			9.85564i			0.492167i	0.969249	+	0.246084i	$0.0791438\pi$
$401$			9.85564i			0.492167i	−0.969249	+	0.246084i	$0.920856\pi$
$402$		0			0
$403$	−3.26272	+	1.71104i	−0.162528	+	0.0852332i
$404$	−1.22413	−	2.12026i	−0.0609028	−	0.105487i
$405$		0			0
$406$	7.28430	−	16.2270i	0.361514	−	0.805334i
$407$	1.07838	+	1.86780i	0.0534532	+	0.0925836i
$408$		0			0
$409$			25.4173i			1.25681i	0.777888	+	0.628403i	$0.216291\pi$
$409$			25.4173i			1.25681i	−0.777888	+	0.628403i	$0.783709\pi$
$410$		−	3.54471i		−	0.175061i
$411$		0			0
$412$	8.96428	+	15.5266i	0.441638	+	0.764940i
$413$	−21.2848	+	2.17131i	−1.04736	+	0.106843i
$414$		0			0
$415$	15.3473	+	26.5823i	0.753370	+	1.30487i
$416$	−3.04674	−	1.92804i	−0.149379	−	0.0945301i
$417$		0			0
$418$			29.5846i			1.44703i
$419$	15.5587	−	26.9484i	0.760091	−	1.31652i	−0.182712	−	0.983167i	$-0.558488\pi$
$419$	15.5587	−	26.9484i	0.760091	−	1.31652i	0.942803	−	0.333350i	$-0.108179\pi$
$420$		0			0
$421$			13.8090i			0.673009i	0.941682	+	0.336505i	$0.109245\pi$
$421$			13.8090i			0.673009i	−0.941682	+	0.336505i	$0.890755\pi$
$422$	−4.41210	−	2.54733i	−0.214778	−	0.124002i
$423$		0			0
$424$	−2.00634	−	1.15836i	−0.0974366	−	0.0562551i
$425$	−11.5403	+	19.9884i	−0.559787	+	0.969580i
$426$		0			0
$427$	24.3809	+	10.9446i	1.17988	+	0.529645i
$428$	−9.90239			−0.478650
$429$		0			0
$430$	−5.52186	+	9.56414i	−0.266288	+	0.461224i
$431$	27.4347	−	15.8394i	1.32148	−	0.762958i	0.337516	−	0.941320i	$-0.390413\pi$
$431$	27.4347	−	15.8394i	1.32148	−	0.762958i	0.983965	+	0.178362i	$0.0570798\pi$
$432$		0			0
$433$	−13.7233	−	23.7695i	−0.659500	−	1.14229i	−0.980745	−	0.195292i	$-0.937435\pi$
$433$	−13.7233	−	23.7695i	−0.659500	−	1.14229i	0.321245	−	0.946996i	$-0.395899\pi$
$434$	−2.46633	−	1.10714i	−0.118388	−	0.0531442i
$435$		0			0
$436$	3.08121	+	1.77894i	0.147563	+	0.0851957i
$437$	19.2478	+	11.1127i	0.920748	+	0.531594i
$438$		0			0
$439$	12.1823			0.581431			0.290715	−	0.956810i	$-0.406107\pi$
$439$	12.1823			0.581431			0.290715	+	0.956810i	$0.406107\pi$
$440$	14.5864	+	8.42146i	0.695379	+	0.401477i
$441$		0			0
$442$	11.3726	+	7.19681i	0.540939	+	0.342317i
$443$	−14.9531	−	25.8996i	−0.710445	−	1.23053i	−0.964690	−	0.263387i	$-0.915160\pi$
$443$	−14.9531	−	25.8996i	−0.710445	−	1.23053i	0.254245	−	0.967140i	$-0.418173\pi$
$444$		0			0
$445$	−9.05080	−	15.6764i	−0.429049	−	0.743135i
$446$	4.99619	−	8.65366i	0.236577	−	0.409763i
$447$		0			0
$448$	−0.268506	−	2.63209i	−0.0126857	−	0.124355i
$449$	−30.6709	+	17.7079i	−1.44745	+	0.835685i	−0.998329	−	0.0577858i	$-0.981596\pi$
$449$	−30.6709	+	17.7079i	−1.44745	+	0.835685i	−0.449121	+	0.893471i	$0.648263\pi$
$450$		0			0
$451$	5.33858			0.251384
$452$	2.44458	+	4.23414i	0.114983	+	0.199157i
$453$		0			0
$454$	−13.2146			−0.620191
$455$	−31.8417	+	1.94655i	−1.49276	+	0.0912556i
$456$		0			0
$457$			20.5116i			0.959490i	0.877408	+	0.479745i	$0.159271\pi$
$457$			20.5116i			0.959490i	−0.877408	+	0.479745i	$0.840729\pi$
$458$	−4.97993	−	8.62549i	−0.232697	−	0.403043i
$459$		0			0
$460$	10.9581	−	6.32664i	0.510922	−	0.294981i
$461$	2.94204	−	1.69858i	0.137024	−	0.0791110i	−0.429921	−	0.902867i	$-0.641459\pi$
$461$	2.94204	−	1.69858i	0.137024	−	0.0791110i	0.566945	+	0.823756i	$0.308125\pi$
$462$		0			0
$463$		−	39.3586i		−	1.82915i	−0.404417	−	0.914575i	$-0.632526\pi$
$463$		−	39.3586i		−	1.82915i	0.404417	−	0.914575i	$-0.367474\pi$
$464$	−3.36143	+	5.82216i	−0.156050	+	0.270287i
$465$		0			0
$466$	−7.43454	+	4.29233i	−0.344399	+	0.198839i
$467$	−2.99442	−	5.18650i	−0.138565	−	0.240002i	0.788388	−	0.615178i	$-0.210916\pi$
$467$	−2.99442	−	5.18650i	−0.138565	−	0.240002i	−0.926954	+	0.375175i	$0.877582\pi$
$468$		0			0
$469$	−20.5933	−	28.5274i	−0.950911	−	1.31727i
$470$	15.3883	+	8.88446i	0.709811	+	0.409810i
$471$		0			0
$472$	8.08665			0.372218
$473$	−14.4043	−	8.31631i	−0.662309	−	0.382384i
$474$		0			0
$475$	−31.4549	+	18.1605i	−1.44325	+	0.833262i
$476$	1.00225	+	9.82481i	0.0459381	+	0.450319i
$477$		0			0
$478$	1.17300			0.0536516
$479$	−11.8476	+	6.84021i	−0.541330	+	0.312537i	−0.745618	−	0.666374i	$-0.767846\pi$
$479$	−11.8476	+	6.84021i	−0.541330	+	0.312537i	0.204288	+	0.978911i	$0.434512\pi$
$480$		0			0
$481$	1.30468	+	0.825631i	0.0594885	+	0.0376455i
$482$	−24.3882			−1.11085
$483$		0			0
$484$	−7.18332	+	12.4419i	−0.326514	+	0.565539i
$485$	28.7183	−	49.7416i	1.30403	−	2.25865i
$486$		0			0
$487$		−	1.05079i		−	0.0476156i	−0.999717	−	0.0238078i	$-0.992421\pi$
$487$		−	1.05079i		−	0.0476156i	0.999717	−	0.0238078i	$-0.00757898\pi$
$488$	−8.74773	−	5.05050i	−0.395991	−	0.228626i
$489$		0			0
$490$	−15.5570	−	17.4918i	−0.702793	−	0.790201i
$491$	13.7757	−	23.8602i	0.621688	−	1.07679i	−0.367484	−	0.930030i	$-0.619781\pi$
$491$	13.7757	−	23.8602i	0.621688	−	1.07679i	0.989171	−	0.146765i	$-0.0468861\pi$
$492$		0			0
$493$	12.5472	−	21.7324i	0.565097	−	0.978778i
$494$	9.83622	+	18.7563i	0.442553	+	0.843886i
$495$		0			0
$496$	0.884906	+	0.510901i	0.0397335	+	0.0229401i
$497$	−4.21562	−	5.83979i	−0.189096	−	0.261950i
$498$		0			0
$499$	−1.82233	+	1.05212i	−0.0815788	+	0.0470995i	−0.540235	−	0.841515i	$-0.681664\pi$
$499$	−1.82233	+	1.05212i	−0.0815788	+	0.0470995i	0.458656	+	0.888614i	$0.348331\pi$
$500$			3.95733i			0.176977i
$501$		0			0
$502$	−18.4721	+	10.6649i	−0.824452	+	0.475998i
$503$	−19.3301	−	33.4807i	−0.861886	−	1.49283i	−0.870106	−	0.492864i	$-0.835950\pi$
$503$	−19.3301	−	33.4807i	−0.861886	−	1.49283i	0.00822020	−	0.999966i	$-0.497383\pi$
$504$		0			0
$505$	7.09046	+	4.09368i	0.315521	+	0.182166i
$506$	9.52837	+	16.5036i	0.423588	+	0.733675i
$507$		0			0
$508$	4.14641	−	7.18180i	0.183967	−	0.318641i
$509$			25.4411i			1.12766i	0.825892	+	0.563828i	$0.190672\pi$
$509$			25.4411i			1.12766i	−0.825892	+	0.563828i	$0.809328\pi$
$510$		0			0
$511$	−8.61888	+	19.2000i	−0.381277	+	0.849359i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$		−	12.8591i		−	0.567191i
$515$	−51.9233	−	29.9779i	−2.28801	−	1.32099i
$516$		0			0
$517$	−13.3806	+	23.1759i	−0.588479	+	1.01928i
$518$	0.114980	+	1.12712i	0.00505194	+	0.0495228i
$519$		0			0
$520$	12.0476	+	0.489457i	0.528321	+	0.0214641i
$521$	−7.99393	+	13.8459i	−0.350221	+	0.606600i	−0.986288	−	0.165034i	$-0.947227\pi$
$521$	−7.99393	+	13.8459i	−0.350221	+	0.606600i	0.636067	+	0.771634i	$0.280560\pi$
$522$		0			0
$523$	18.2292			0.797107			0.398553	−	0.917145i	$-0.369512\pi$
$523$	18.2292			0.797107			0.398553	+	0.917145i	$0.369512\pi$
$524$	−3.08084	−	5.33618i	−0.134587	−	0.233112i
$525$		0			0
$526$	−21.5295	+	12.4300i	−0.938730	+	0.541976i
$527$	−3.30309	−	1.90704i	−0.143885	−	0.0830720i
$528$		0			0
$529$	−8.68359			−0.377547
$530$	7.74748			0.336529
$531$		0			0
$532$	−6.36455	+	14.1781i	−0.275938	+	0.614700i
$533$	3.38460	−	1.77496i	0.146603	−	0.0768822i
$534$		0			0
$535$	28.6785	−	16.5575i	1.23988	−	0.715845i
$536$	6.64910	+	11.5166i	0.287197	+	0.497441i
$537$		0			0
$538$			20.6024i			0.888231i
$539$	26.3439	−	23.4299i	1.13471	−	1.00920i
$540$		0			0
$541$	16.6334	−	9.60332i	0.715128	−	0.412879i	−0.0978290	−	0.995203i	$-0.531190\pi$
$541$	16.6334	−	9.60332i	0.715128	−	0.412879i	0.812957	+	0.582324i	$0.197857\pi$
$542$	5.28145			0.226858
$543$		0			0
$544$		−	3.73270i		−	0.160038i
$545$	−11.8981			−0.509658
$546$		0			0
$547$	−12.3643			−0.528659			−0.264329	−	0.964432i	$-0.585151\pi$
$547$	−12.3643			−0.528659			−0.264329	+	0.964432i	$0.585151\pi$
$548$		−	7.43816i		−	0.317742i
$549$		0			0
$550$	−31.1427			−1.32793
$551$	34.1994	−	19.7450i	1.45694	−	0.841166i
$552$		0			0
$553$	−30.3380	+	21.9004i	−1.29010	+	0.931298i
$554$			5.25013i			0.223057i
$555$		0			0
$556$	−2.44199	−	4.22965i	−0.103563	−	0.179377i
$557$	25.5877	−	14.7731i	1.08419	−	0.625956i	0.152165	−	0.988355i	$-0.451376\pi$
$557$	25.5877	−	14.7731i	1.08419	−	0.625956i	0.932023	+	0.362399i	$0.118042\pi$
$558$		0			0
$559$	−11.8972	−	0.483345i	−0.503196	−	0.0204433i
$560$	5.17868	+	7.17389i	0.218839	+	0.303152i
$561$		0			0
$562$	31.3151			1.32095
$563$	2.52309			0.106336			0.0531678	−	0.998586i	$-0.483068\pi$
$563$	2.52309			0.106336			0.0531678	+	0.998586i	$0.483068\pi$
$564$		0			0
$565$	−14.1596	−	8.17505i	−0.595699	−	0.343927i
$566$	6.68606	−	3.86020i	0.281036	−	0.162256i
$567$		0			0
$568$	1.36113	+	2.35754i	0.0571115	+	0.0989201i
$569$	−10.4325			−0.437352			−0.218676	−	0.975798i	$-0.570174\pi$
$569$	−10.4325			−0.437352			−0.218676	+	0.975798i	$0.570174\pi$
$570$		0			0
$571$	0.0728934	−	0.126255i	0.00305049	−	0.00528361i	−0.864496	−	0.502639i	$-0.832362\pi$
$571$	0.0728934	−	0.126255i	0.00305049	−	0.00528361i	0.867547	+	0.497356i	$0.165696\pi$
$572$	−0.737156	+	18.1445i	−0.0308221	+	0.758660i
$573$		0			0
$574$	2.55847	+	1.14849i	0.106788	+	0.0479372i
$575$	−11.6980	+	20.2615i	−0.487840	+	0.844964i
$576$		0			0
$577$	19.4377	+	11.2223i	0.809201	+	0.467192i	0.846678	−	0.532105i	$-0.178599\pi$
$577$	19.4377	+	11.2223i	0.809201	+	0.467192i	−0.0374775	+	0.999297i	$0.511932\pi$
$578$		−	3.06694i		−	0.127568i
$579$		0			0
$580$		−	22.4822i		−	0.933524i
$581$	−24.1589	+	2.46450i	−1.00228	+	0.102245i
$582$		0			0
$583$			11.6683i			0.483250i
$584$	3.97728	−	6.88886i	0.164581	−	0.285063i
$585$		0			0
$586$	−10.6150	−	18.3856i	−0.438500	−	0.759504i
$587$	18.2824	+	10.5554i	0.754596	+	0.435666i	0.827352	−	0.561684i	$-0.189846\pi$
$587$	18.2824	+	10.5554i	0.754596	+	0.435666i	−0.0727563	+	0.997350i	$0.523180\pi$
$588$		0			0
$589$	−3.00103	−	5.19794i	−0.123655	−	0.214177i
$590$	−23.4199	+	13.5215i	−0.964183	+	0.556671i
$591$		0			0
$592$		−	0.428222i		−	0.0175998i
$593$	25.8339	−	14.9152i	1.06087	−	0.612494i	0.135198	−	0.990819i	$-0.456833\pi$
$593$	25.8339	−	14.9152i	1.06087	−	0.612494i	0.925673	+	0.378324i	$0.123500\pi$
$594$		0			0
$595$	−19.3305	−	26.7780i	−0.792472	−	1.09779i
$596$	−4.86592	−	2.80934i	−0.199316	−	0.115075i
$597$		0			0
$598$	11.5280	+	7.29514i	0.471414	+	0.298321i
$599$	16.7520	−	29.0153i	0.684469	−	1.18553i	−0.289135	−	0.957288i	$-0.593368\pi$
$599$	16.7520	−	29.0153i	0.684469	−	1.18553i	0.973603	−	0.228246i	$-0.0732990\pi$
$600$		0			0
$601$	18.9681	−	32.8537i	0.773724	−	1.34013i	−0.161785	−	0.986826i	$-0.551725\pi$
$601$	18.9681	−	32.8537i	0.773724	−	1.34013i	0.935509	−	0.353303i	$-0.114942\pi$
$602$	−5.11402	−	7.08432i	−0.208432	−	0.288735i
$603$		0			0
$604$	7.19648	+	4.15489i	0.292821	+	0.169060i
$605$		−	48.0442i		−	1.95327i
$606$		0			0
$607$	−17.9335	+	31.0618i	−0.727900	+	1.26076i	0.229870	+	0.973221i	$0.426170\pi$
$607$	−17.9335	+	31.0618i	−0.727900	+	1.26076i	−0.957769	+	0.287538i	$0.907163\pi$
$608$	2.93700	−	5.08703i	0.119111	−	0.206306i
$609$		0			0
$610$	33.7793			1.36768
$611$	−0.777684	+	19.1421i	−0.0314617	+	0.774405i
$612$		0			0
$613$	10.9563	−	6.32562i	0.442521	−	0.255489i	−0.262146	−	0.965028i	$-0.584430\pi$
$613$	10.9563	−	6.32562i	0.442521	−	0.255489i	0.704666	+	0.709539i	$0.251097\pi$
$614$	−33.9938			−1.37188
$615$		0			0
$616$	−10.8044	+	7.79946i	−0.435321	+	0.314249i
$617$	−34.6231	+	19.9896i	−1.39387	+	0.804753i	−0.993741	−	0.111705i	$-0.964369\pi$
$617$	−34.6231	+	19.9896i	−1.39387	+	0.804753i	−0.400131	+	0.916458i	$0.631035\pi$
$618$		0			0
$619$	−8.58564	−	4.95692i	−0.345086	−	0.199235i	0.317433	−	0.948281i	$-0.397179\pi$
$619$	−8.58564	−	4.95692i	−0.345086	−	0.199235i	−0.662519	+	0.749045i	$0.730513\pi$
$620$	−3.41706			−0.137232
$621$		0			0
$622$	0.633728	+	0.365883i	0.0254102	+	0.0146706i
$623$	14.2473	−	1.45340i	0.570805	−	0.0582291i
$624$		0			0
$625$	8.84144	+	15.3138i	0.353658	+	0.612553i
$626$	−6.38016	+	3.68359i	−0.255002	+	0.147226i
$627$		0			0
$628$	2.60751	−	4.51635i	0.104051	−	0.180222i
$629$			1.59843i			0.0637334i
$630$		0			0
$631$	21.7056	−	12.5318i	0.864088	−	0.498881i	−0.00129129	−	0.999999i	$-0.500411\pi$
$631$	21.7056	−	12.5318i	0.864088	−	0.498881i	0.865379	+	0.501118i	$0.167078\pi$
$632$	12.2475	−	7.07112i	0.487181	−	0.281274i
$633$		0			0
$634$	14.2035	+	24.6012i	0.564093	+	0.977038i
$635$			27.7325i			1.10053i
$636$		0			0
$637$	8.91183	−	23.6131i	0.353100	−	0.935586i
$638$	33.8598			1.34052
$639$		0			0
$640$	−1.67208	−	2.89612i	−0.0660946	−	0.114479i
$641$	8.03012			0.317171			0.158585	−	0.987345i	$-0.449307\pi$
$641$	8.03012			0.317171			0.158585	+	0.987345i	$0.449307\pi$
$642$		0			0
$643$	−13.3951	+	7.73367i	−0.528251	+	0.304986i	−0.740304	−	0.672272i	$-0.765318\pi$
$643$	−13.3951	+	7.73367i	−0.528251	+	0.304986i	0.212053	+	0.977258i	$0.431985\pi$
$644$	1.01595	+	9.95905i	0.0400339	+	0.392442i
$645$		0			0
$646$	−10.9629	+	18.9884i	−0.431331	+	0.747087i
$647$	3.34618	+	5.79575i	0.131552	+	0.227854i	0.924275	−	0.381727i	$-0.124671\pi$
$647$	3.34618	+	5.79575i	0.131552	+	0.227854i	−0.792723	+	0.609582i	$0.791337\pi$
$648$		0			0
$649$	−20.3643	−	35.2720i	−0.799370	−	1.38455i
$650$	−19.7441	+	10.3543i	−0.774428	+	0.406127i
$651$		0			0
$652$	10.8077	+	6.23982i	0.423262	+	0.244370i
$653$	24.1607			0.945482			0.472741	−	0.881201i	$-0.343265\pi$
$653$	24.1607			0.945482			0.472741	+	0.881201i	$0.343265\pi$
$654$		0			0
$655$	17.8450	+	10.3028i	0.697261	+	0.402564i
$656$	−0.917963	−	0.529986i	−0.0358404	−	0.0206925i
$657$		0			0
$658$	−11.3984	+	8.22826i	−0.444356	+	0.320771i
$659$	6.47769	+	11.2197i	0.252335	+	0.437057i	0.964168	−	0.265291i	$-0.0854681\pi$
$659$	6.47769	+	11.2197i	0.252335	+	0.437057i	−0.711833	+	0.702349i	$0.752135\pi$
$660$		0			0
$661$	16.7049	−	9.64460i	0.649747	−	0.375132i	−0.138612	−	0.990347i	$-0.544264\pi$
$661$	16.7049	−	9.64460i	0.649747	−	0.375132i	0.788359	+	0.615215i	$0.210931\pi$
$662$	−10.1489	+	17.5783i	−0.394446	+	0.683201i
$663$		0			0
$664$	9.17859			0.356198
$665$	−5.27440	−	51.7036i	−0.204533	−	2.00498i
$666$		0			0
$667$	12.7186	−	22.0293i	0.492468	−	0.852979i
$668$	−0.409946	−	0.236682i	−0.0158613	−	0.00915752i
$669$		0			0
$670$	−38.5132	−	22.2356i	−1.48789	−	0.859037i
$671$			50.8740i			1.96397i
$672$		0			0
$673$	−14.7943	+	25.6245i	−0.570279	+	0.987752i	0.426258	+	0.904602i	$0.359832\pi$
$673$	−14.7943	+	25.6245i	−0.570279	+	0.987752i	−0.996537	+	0.0831505i	$0.973502\pi$
$674$		−	8.85616i		−	0.341127i
$675$		0			0
$676$	5.56530	+	11.7485i	0.214050	+	0.451866i
$677$	−6.92108	−	11.9877i	−0.265999	−	0.460723i	0.701826	−	0.712348i	$-0.252368\pi$
$677$	−6.92108	−	11.9877i	−0.265999	−	0.460723i	−0.967825	+	0.251625i	$0.919035\pi$
$678$		0			0
$679$	26.5972	+	36.8444i	1.02071	+	1.41396i
$680$	6.24136	+	10.8104i	0.239345	+	0.414558i
$681$		0			0
$682$		−	5.14634i		−	0.197063i
$683$		−	35.7175i		−	1.36669i	−0.730094	−	0.683347i	$-0.760524\pi$
$683$		−	35.7175i		−	1.36669i	0.730094	−	0.683347i	$-0.239476\pi$
$684$		0			0
$685$	12.4372	+	21.5418i	0.475200	+	0.823070i
$686$	17.6656	−	5.56119i	0.674475	−	0.212327i
$687$		0			0
$688$	1.65120	+	2.85996i	0.0629514	+	0.109035i
$689$	3.87944	+	7.39755i	0.147795	+	0.281824i
$690$		0			0
$691$			26.0063i			0.989326i	0.869085	+	0.494663i	$0.164709\pi$
$691$			26.0063i			0.989326i	−0.869085	+	0.494663i	$0.835291\pi$
$692$	−5.06601	+	8.77459i	−0.192581	+	0.333560i
$693$		0			0
$694$		−	6.89722i		−	0.261815i
$695$	14.1446	+	8.16638i	0.536535	+	0.309768i
$696$		0			0
$697$	3.42648	+	1.97828i	0.129787	+	0.0749327i
$698$	2.09753	−	3.63303i	0.0793928	−	0.137512i
$699$		0			0
$700$	−14.9248	−	6.69975i	−0.564106	−	0.253227i
$701$	−24.7068			−0.933164			−0.466582	−	0.884478i	$-0.654515\pi$
$701$	−24.7068			−0.933164			−0.466582	+	0.884478i	$0.654515\pi$
$702$		0			0
$703$	−1.25769	+	2.17838i	−0.0474346	+	0.0821592i
$704$	4.36176	−	2.51826i	0.164390	−	0.0949107i
$705$		0			0
$706$	−12.5343	−	21.7100i	−0.471734	−	0.817067i
$707$	−5.25202	+	3.79132i	−0.197523	+	0.142587i
$708$		0			0
$709$	−19.3947	−	11.1975i	−0.728383	−	0.420532i	0.0894476	−	0.995992i	$-0.471490\pi$
$709$	−19.3947	−	11.1975i	−0.728383	−	0.420532i	−0.817830	+	0.575460i	$0.804823\pi$
$710$	−7.88397	−	4.55181i	−0.295880	−	0.170826i
$711$		0			0
$712$	−5.41291			−0.202857
$713$	−3.34822	−	1.93310i	−0.125392	−	0.0723951i
$714$		0			0
$715$	−28.2041	−	53.7812i	−1.05477	−	2.01130i
$716$	−5.35710	−	9.27876i	−0.200204	−	0.346764i
$717$		0			0
$718$	−9.93716	−	17.2117i	−0.370852	−	0.642334i
$719$	−12.6421	+	21.8968i	−0.471472	+	0.816613i	−0.999467	−	0.0326342i	$-0.989610\pi$
$719$	−12.6421	+	21.8968i	−0.471472	+	0.816613i	0.527996	+	0.849247i	$0.322944\pi$
$720$		0			0
$721$	38.4604	−	27.7638i	1.43234	−	1.03398i
$722$	−13.4267	+	7.75193i	−0.499691	+	0.288497i
$723$		0			0
$724$	−1.56347			−0.0581058
$725$	20.7849	+	36.0005i	0.771932	+	1.33702i
$726$		0			0
$727$	−39.9649			−1.48221			−0.741107	−	0.671386i	$-0.765699\pi$
$727$	−39.9649			−1.48221			−0.741107	+	0.671386i	$0.765699\pi$
$728$	−4.25672	+	8.53700i	−0.157764	+	0.316402i
$729$		0			0
$730$			26.6013i			0.984558i
$731$	−6.16343	−	10.6754i	−0.227963	−	0.394843i
$732$		0			0
$733$	−20.8858	+	12.0584i	−0.771433	+	0.445387i	−0.833386	−	0.552692i	$-0.813601\pi$
$733$	−20.8858	+	12.0584i	−0.771433	+	0.445387i	0.0619525	+	0.998079i	$0.480267\pi$
$734$	12.3085	−	7.10630i	0.454314	−	0.262298i
$735$		0			0
$736$		−	3.78370i		−	0.139469i
$737$	33.4884	−	58.0036i	1.23356	−	2.13659i
$738$		0			0
$739$	24.7187	−	14.2714i	0.909292	−	0.524980i	0.0290890	−	0.999577i	$-0.490739\pi$
$739$	24.7187	−	14.2714i	0.909292	−	0.524980i	0.880203	+	0.474597i	$0.157406\pi$
$740$	0.716021	+	1.24018i	0.0263214	+	0.0455901i
$741$		0			0
$742$	−2.51020	+	5.59190i	−0.0921524	+	0.205285i
$743$	37.9322	+	21.9001i	1.39160	+	0.803438i	0.993492	−	0.113902i	$-0.0363350\pi$
$743$	37.9322	+	21.9001i	1.39160	+	0.803438i	0.398104	+	0.917340i	$0.369668\pi$
$744$		0			0
$745$	18.7897			0.688403
$746$	27.0718	+	15.6299i	0.991171	+	0.572253i
$747$		0			0
$748$	−16.2812	+	9.39993i	−0.595298	+	0.343696i
$749$	2.65885	+	26.0640i	0.0971522	+	0.952357i
$750$		0			0
$751$	−40.4674			−1.47668			−0.738338	−	0.674431i	$-0.764389\pi$
$751$	−40.4674			−1.47668			−0.738338	+	0.674431i	$0.764389\pi$
$752$	4.60157	−	2.65672i	0.167802	−	0.0968804i
$753$		0			0
$754$	21.4668	−	11.2577i	0.781774	−	0.409980i
$755$	−27.7892			−1.01135
$756$		0			0
$757$	−6.36103	+	11.0176i	−0.231196	+	0.400442i	−0.958160	−	0.286232i	$-0.907597\pi$
$757$	−6.36103	+	11.0176i	−0.231196	+	0.400442i	0.726965	+	0.686675i	$0.240930\pi$
$758$	−10.9909	+	19.0369i	−0.399209	+	0.691450i
$759$		0			0
$760$			19.6435i			0.712546i
$761$	26.6191	+	15.3686i	0.964943	+	0.557110i	0.897691	−	0.440626i	$-0.145244\pi$
$761$	26.6191	+	15.3686i	0.964943	+	0.557110i	0.0672521	+	0.997736i	$0.478577\pi$
$762$		0			0
$763$	3.85501	−	8.58769i	0.139561	−	0.310895i
$764$	4.69659	−	8.13473i	0.169917	−	0.294304i
$765$		0			0
$766$	−2.43266	+	4.21349i	−0.0878956	+	0.152240i
$767$	−24.6380	−	15.5914i	−0.889625	−	0.562973i
$768$		0			0
$769$	−10.0887	−	5.82469i	−0.363806	−	0.210044i	0.306943	−	0.951728i	$-0.400694\pi$
$769$	−10.0887	−	5.82469i	−0.363806	−	0.210044i	−0.670749	+	0.741684i	$0.734027\pi$
$770$	18.2495	−	40.6539i	0.657667	−	1.46507i
$771$		0			0
$772$	−7.93269	+	4.57994i	−0.285504	+	0.164836i
$773$			28.3529i			1.01978i	0.860238	+	0.509892i	$0.170315\pi$
$773$			28.3529i			1.01978i	−0.860238	+	0.509892i	$0.829685\pi$
$774$		0			0
$775$	5.47169	−	3.15908i	0.196549	−	0.113478i
$776$	−8.58763	−	14.8742i	−0.308278	−	0.533953i
$777$		0			0
$778$	−11.1526	−	6.43897i	−0.399841	−	0.230848i
$779$	3.11314	+	5.39211i	0.111540	+	0.193193i
$780$		0			0
$781$	6.85535	−	11.8738i	0.245304	−	0.424878i
$782$			14.1234i			0.505053i
$783$		0			0
$784$	−6.85581	+	1.41346i	−0.244850	+	0.0504808i
$785$			17.4398i			0.622455i
$786$		0			0
$787$			2.13734i			0.0761881i	0.999274	+	0.0380940i	$0.0121286\pi$
$787$			2.13734i			0.0761881i	−0.999274	+	0.0380940i	$0.987871\pi$
$788$	13.4152	+	7.74526i	0.477896	+	0.275914i
$789$		0			0
$790$	−23.6469	+	40.9576i	−0.841319	+	1.45721i
$791$	10.4883	−	7.57125i	0.372919	−	0.269203i
$792$		0			0
$793$	16.9145	+	32.2536i	0.600652	+	1.14536i
$794$	−14.9009	+	25.8091i	−0.528814	+	0.915932i
$795$		0			0
$796$	5.48387			0.194371
$797$	13.9817	+	24.2170i	0.495257	+	0.857810i	0.999985	−	0.00546806i	$-0.00174055\pi$
$797$	13.9817	+	24.2170i	0.495257	+	0.857810i	−0.504728	+	0.863278i	$0.668407\pi$
$798$		0			0
$799$	−17.1763	+	9.91672i	−0.607653	+	0.350829i
$800$	5.35494	+	3.09168i	0.189326	+	0.109307i
$801$		0			0
$802$	−9.85564			−0.348015
$803$	−40.0634			−1.41381
$804$		0			0
$805$	−19.5946	−	27.1439i	−0.690619	−	0.956696i
$806$	−1.71104	−	3.26272i	−0.0602690	−	0.114924i
$807$		0			0
$808$	2.12026	−	1.22413i	0.0745903	−	0.0430648i
$809$	−24.3621	−	42.1965i	−0.856527	−	1.48355i	−0.875221	−	0.483724i	$-0.839284\pi$
$809$	−24.3621	−	42.1965i	−0.856527	−	1.48355i	0.0186933	−	0.999825i	$-0.494049\pi$
$810$		0			0
$811$		−	31.9965i		−	1.12355i	−0.827290	−	0.561774i	$-0.810119\pi$
$811$		−	31.9965i		−	1.12355i	0.827290	−	0.561774i	$-0.189881\pi$
$812$	16.2270	+	7.28430i	0.569457	+	0.255629i
$813$		0			0
$814$	−1.86780	+	1.07838i	−0.0654665	+	0.0377971i
$815$	−41.7338			−1.46187
$816$		0			0
$817$		−	19.3983i		−	0.678660i
$818$	−25.4173			−0.888696
$819$		0			0
$820$	3.54471			0.123787
$821$		−	12.4740i		−	0.435347i	−0.976022	−	0.217673i	$-0.930153\pi$
$821$		−	12.4740i		−	0.435347i	0.976022	−	0.217673i	$-0.0698467\pi$
$822$		0			0
$823$	−16.0260			−0.558631			−0.279316	−	0.960199i	$-0.590108\pi$
$823$	−16.0260			−0.558631			−0.279316	+	0.960199i	$0.590108\pi$
$824$	−15.5266	+	8.96428i	−0.540894	+	0.312286i
$825$		0			0
$826$	−2.17131	−	21.2848i	−0.0755496	−	0.740593i
$827$		−	6.94225i		−	0.241406i	−0.992689	−	0.120703i	$-0.961485\pi$
$827$		−	6.94225i		−	0.241406i	0.992689	−	0.120703i	$-0.0385148\pi$
$828$		0			0
$829$	4.54445	+	7.87122i	0.157835	+	0.273379i	0.934088	−	0.357043i	$-0.116215\pi$
$829$	4.54445	+	7.87122i	0.157835	+	0.273379i	−0.776252	+	0.630422i	$0.782882\pi$
$830$	−26.5823	+	15.3473i	−0.922686	+	0.532713i
$831$		0			0
$832$	1.92804	−	3.04674i	0.0668429	−	0.105627i
$833$	25.5907	−	5.27604i	0.886665	−	0.182804i
$834$		0			0
$835$	1.58300			0.0547821
$836$	−29.5846			−1.02320
$837$		0			0
$838$	26.9484	+	15.5587i	0.930918	+	0.537466i
$839$	15.8840	−	9.17062i	0.548376	−	0.316605i	−0.200091	−	0.979777i	$-0.564124\pi$
$839$	15.8840	−	9.17062i	0.548376	−	0.316605i	0.748467	+	0.663173i	$0.230790\pi$
$840$		0			0
$841$	−8.09837	−	14.0268i	−0.279254	−	0.483683i
$842$	−13.8090			−0.475889
$843$		0			0
$844$	2.54733	−	4.41210i	0.0876826	−	0.151871i
$845$	−35.7622	−	24.7195i	−1.23026	−	0.850376i
$846$		0			0
$847$	34.6769	+	15.5664i	1.19151	+	0.534869i
$848$	1.15836	−	2.00634i	0.0397783	−	0.0688981i
$849$		0			0
$850$	−19.9884	−	11.5403i	−0.685597	−	0.395829i
$851$			1.62027i			0.0555420i
$852$		0			0
$853$			53.7617i			1.84077i	0.391018	+	0.920383i	$0.372123\pi$
$853$			53.7617i			1.84077i	−0.391018	+	0.920383i	$0.627877\pi$
$854$	−10.9446	+	24.3809i	−0.374516	+	0.834298i
$855$		0			0
$856$		−	9.90239i		−	0.338457i
$857$	19.1290	−	33.1324i	0.653434	−	1.13178i	−0.328850	−	0.944382i	$-0.606661\pi$
$857$	19.1290	−	33.1324i	0.653434	−	1.13178i	0.982284	−	0.187399i	$-0.0600056\pi$
$858$		0			0
$859$	7.89494	+	13.6744i	0.269372	+	0.466566i	0.968700	−	0.248235i	$-0.0798506\pi$
$859$	7.89494	+	13.6744i	0.269372	+	0.466566i	−0.699328	+	0.714801i	$0.746517\pi$
$860$	−9.56414	−	5.52186i	−0.326135	−	0.188294i
$861$		0			0
$862$	15.8394	+	27.4347i	0.539492	+	0.934428i
$863$	−38.6063	+	22.2894i	−1.31417	+	0.758739i	−0.982785	−	0.184755i	$-0.940851\pi$
$863$	−38.6063	+	22.2894i	−1.31417	+	0.758739i	−0.331390	+	0.943494i	$0.607518\pi$
$864$		0			0
$865$		−	33.8830i		−	1.15206i
$866$	23.7695	−	13.7233i	0.807720	−	0.466337i
$867$		0			0
$868$	1.10714	−	2.46633i	0.0375786	−	0.0837128i
$869$	−61.6851	−	35.6139i	−2.09252	−	1.20812i
$870$		0			0
$871$	1.94635	−	47.9078i	0.0659496	−	1.62329i
$872$	−1.77894	+	3.08121i	−0.0602425	+	0.104343i
$873$		0			0
$874$	−11.1127	+	19.2478i	−0.375894	+	0.651067i
$875$	10.4160	−	1.06256i	0.352127	−	0.0359212i
$876$		0			0
$877$	0.121237	+	0.0699963i	0.00409389	+	0.00236361i	0.502046	−	0.864841i	$-0.332581\pi$
$877$	0.121237	+	0.0699963i	0.00409389	+	0.00236361i	−0.497952	+	0.867205i	$0.665914\pi$
$878$			12.1823i			0.411134i
$879$		0			0
$880$	−8.42146	+	14.5864i	−0.283887	+	0.491707i
$881$	22.6522	−	39.2347i	0.763172	−	1.32185i	−0.178036	−	0.984024i	$-0.556974\pi$
$881$	22.6522	−	39.2347i	0.763172	−	1.32185i	0.941208	−	0.337828i	$-0.109692\pi$
$882$		0			0
$883$	−46.5419			−1.56626			−0.783130	−	0.621858i	$-0.786378\pi$
$883$	−46.5419			−1.56626			−0.783130	+	0.621858i	$0.786378\pi$
$884$	−7.19681	+	11.3726i	−0.242055	+	0.382501i
$885$		0			0
$886$	25.8996	−	14.9531i	0.870114	−	0.502360i
$887$	−48.9299			−1.64291			−0.821453	−	0.570276i	$-0.806836\pi$
$887$	−48.9299			−1.64291			−0.821453	+	0.570276i	$0.806836\pi$
$888$		0			0
$889$	−20.0165	−	8.98538i	−0.671331	−	0.301360i
$890$	15.6764	−	9.05080i	0.525476	−	0.303383i
$891$		0			0
$892$	8.65366	+	4.99619i	0.289746	+	0.167285i
$893$	−31.2111			−1.04444
$894$		0			0
$895$	31.0296	+	17.9149i	1.03721	+	0.598831i
$896$	2.63209	−	0.268506i	0.0879320	−	0.00897015i
$897$		0			0
$898$	−17.7079	−	30.6709i	−0.590919	−	1.02350i
$899$	−5.94910	+	3.43471i	−0.198413	+	0.114554i
$900$		0			0
$901$	−4.32382	+	7.48908i	−0.144047	+	0.249497i
$902$			5.33858i			0.177755i
$903$		0			0
$904$	−4.23414	+	2.44458i	−0.140825	+	0.0813056i
$905$	4.52799	−	2.61424i	0.150515	−	0.0869001i
$906$		0			0
$907$	−24.9923	−	43.2879i	−0.829856	−	1.43735i	−0.898151	−	0.439687i	$-0.855089\pi$
$907$	−24.9923	−	43.2879i	−0.829856	−	1.43735i	0.0682950	−	0.997665i	$-0.478244\pi$
$908$		−	13.2146i		−	0.438541i
$909$		0			0
$910$	−1.94655	−	31.8417i	−0.0645274	−	1.05554i
$911$	−17.2655			−0.572033			−0.286016	−	0.958225i	$-0.592331\pi$
$911$	−17.2655			−0.572033			−0.286016	+	0.958225i	$0.592331\pi$
$912$		0			0
$913$	−23.1141	−	40.0348i	−0.764966	−	1.32496i
$914$	−20.5116			−0.678462
$915$		0			0
$916$	8.62549	−	4.97993i	0.284994	−	0.164542i
$917$	−13.2181	+	9.54185i	−0.436499	+	0.315100i
$918$		0			0
$919$	−7.95486	+	13.7782i	−0.262407	+	0.454502i	−0.966881	−	0.255228i	$-0.917849\pi$
$919$	−7.95486	+	13.7782i	−0.262407	+	0.454502i	0.704474	+	0.709729i	$0.251183\pi$
$920$	6.32664	+	10.9581i	0.208583	+	0.361277i
$921$		0			0
$922$	1.69858	+	2.94204i	0.0559399	+	0.0968908i
$923$	0.398434	−	9.80712i	0.0131146	−	0.322805i
$924$		0			0
$925$	−2.29311	−	1.32393i	−0.0753969	−	0.0435304i
$926$	39.3586			1.29340
$927$		0			0
$928$	−5.82216	−	3.36143i	−0.191122	−	0.110344i
$929$	19.6257	+	11.3309i	0.643900	+	0.371756i	0.786115	−	0.618080i	$-0.212089\pi$
$929$	19.6257	+	11.3309i	0.643900	+	0.371756i	−0.142215	+	0.989836i	$0.545423\pi$
$930$		0			0
$931$	39.0271	+	12.9452i	1.27906	+	0.424261i
$932$	−4.29233	−	7.43454i	−0.140600	−	0.243527i
$933$		0			0
$934$	5.18650	−	2.99442i	0.169707	−	0.0979806i
$935$	31.4348	−	54.4467i	1.02803	−	1.78060i
$936$		0			0
$937$	−22.3601			−0.730473			−0.365237	−	0.930915i	$-0.619012\pi$
$937$	−22.3601			−0.730473			−0.365237	+	0.930915i	$0.619012\pi$
$938$	28.5274	−	20.5933i	0.931452	−	0.672395i
$939$		0			0
$940$	−8.88446	+	15.3883i	−0.289779	+	0.501912i
$941$	−24.4378	−	14.1092i	−0.796650	−	0.459946i	0.0456486	−	0.998958i	$-0.485465\pi$
$941$	−24.4378	−	14.1092i	−0.796650	−	0.459946i	−0.842298	+	0.539012i	$0.818798\pi$
$942$		0			0
$943$	3.47330	+	2.00531i	0.113106	+	0.0653019i
$944$			8.08665i			0.263198i
$945$		0			0
$946$	8.31631	−	14.4043i	0.270387	−	0.468323i
$947$		−	6.36679i		−	0.206893i	−0.994635	−	0.103446i	$-0.967013\pi$
$947$		−	6.36679i		−	0.206893i	0.994635	−	0.103446i	$-0.0329870\pi$
$948$		0			0
$949$	−25.3998	+	13.3202i	−0.824512	+	0.432392i
$950$	−18.1605	−	31.4549i	−0.589205	−	1.02053i
$951$		0			0
$952$	−9.82481	+	1.00225i	−0.318424	+	0.0324832i
$953$	−1.16258	−	2.01365i	−0.0376597	−	0.0652285i	0.846581	−	0.532260i	$-0.178657\pi$
$953$	−1.16258	−	2.01365i	−0.0376597	−	0.0652285i	−0.884241	+	0.467031i	$0.845324\pi$
$954$		0			0
$955$			31.4122i			1.01648i
$956$			1.17300i			0.0379374i
$957$		0			0
$958$	−6.84021	−	11.8476i	−0.220997	−	0.382778i
$959$	−19.5779	+	1.99719i	−0.632204	+	0.0644925i
$960$		0			0
$961$	−14.9780	−	25.9426i	−0.483160	−	0.836858i
$962$	−0.825631	+	1.30468i	−0.0266194	+	0.0420647i
$963$		0			0
$964$		−	24.3882i		−	0.785490i
$965$	15.3160	−	26.5281i	0.493040	−	0.853971i
$966$		0			0
$967$			58.7262i			1.88851i	0.329219	+	0.944254i	$0.393215\pi$
$967$			58.7262i			1.88851i	−0.329219	+	0.944254i	$0.606785\pi$
$968$	−12.4419	−	7.18332i	−0.399897	−	0.230881i
$969$		0			0
$970$	49.7416	+	28.7183i	1.59711	+	0.922090i
$971$	−5.03497	+	8.72083i	−0.161580	+	0.279865i	−0.935436	−	0.353497i	$-0.884992\pi$
$971$	−5.03497	+	8.72083i	−0.161580	+	0.279865i	0.773855	+	0.633362i	$0.218326\pi$
$972$		0			0
$973$	−10.4771	+	7.56322i	−0.335881	+	0.242466i
$974$	1.05079			0.0336693
$975$		0			0
$976$	5.05050	−	8.74773i	0.161663	−	0.280008i
$977$	−42.2830	+	24.4121i	−1.35275	+	0.781012i	−0.988634	−	0.150341i	$-0.951963\pi$
$977$	−42.2830	+	24.4121i	−1.35275	+	0.781012i	−0.364118	+	0.931353i	$0.618629\pi$
$978$		0			0
$979$	13.6311	+	23.6098i	0.435653	+	0.754573i
$980$	17.4918	−	15.5570i	0.558756	−	0.496950i
$981$		0			0
$982$	23.8602	+	13.7757i	0.761409	+	0.439600i
$983$	5.74087	+	3.31449i	0.183105	+	0.105716i	0.588751	−	0.808315i	$-0.299620\pi$
$983$	5.74087	+	3.31449i	0.183105	+	0.105716i	−0.405646	+	0.914030i	$0.632953\pi$
$984$		0			0
$985$	−51.8027			−1.65057
$986$	21.7324	+	12.5472i	0.692100	+	0.399584i
$987$		0			0
$988$	−18.7563	+	9.83622i	−0.596717	+	0.312932i
$989$	−6.24765	−	10.8212i	−0.198664	−	0.344096i
$990$		0			0
$991$	−12.4847	−	21.6241i	−0.396589	−	0.686911i	0.596714	−	0.802454i	$-0.296473\pi$
$991$	−12.4847	−	21.6241i	−0.396589	−	0.686911i	−0.993303	+	0.115543i	$0.963139\pi$
$992$	−0.510901	+	0.884906i	−0.0162211	+	0.0280958i
$993$		0			0
$994$	5.83979	−	4.21562i	0.185227	−	0.133711i
$995$	−15.8820	+	9.16945i	−0.503492	+	0.290691i
$996$		0			0
$997$	−39.5168			−1.25151			−0.625754	−	0.780020i	$-0.715209\pi$
$997$	−39.5168			−1.25151			−0.625754	+	0.780020i	$0.715209\pi$
$998$	−1.05212	−	1.82233i	−0.0333044	−	0.0576849i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.dt.c.1369.10		20
3.2	odd	2		182.2.o.a.95.4	yes	20
7.2	even	3		1638.2.cr.c.667.6		20
13.10	even	6		1638.2.cr.c.361.6		20
21.2	odd	6		182.2.v.a.121.2	yes	20
21.5	even	6		1274.2.v.h.667.4		20
21.11	odd	6		1274.2.m.g.589.9		20
21.17	even	6		1274.2.m.f.589.7		20
21.20	even	2		1274.2.o.h.459.2		20
39.23	odd	6		182.2.v.a.179.2	yes	20
91.23	even	6	inner	1638.2.dt.c.1297.5		20
273.23	odd	6		182.2.o.a.23.9	✓	20
273.62	even	6		1274.2.v.h.361.4		20
273.101	even	6		1274.2.m.f.491.7		20
273.179	odd	6		1274.2.m.g.491.9		20
273.257	even	6		1274.2.o.h.569.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.o.a.23.9	✓	20	273.23	odd	6
182.2.o.a.95.4	yes	20	3.2	odd	2
182.2.v.a.121.2	yes	20	21.2	odd	6
182.2.v.a.179.2	yes	20	39.23	odd	6
1274.2.m.f.491.7		20	273.101	even	6
1274.2.m.f.589.7		20	21.17	even	6
1274.2.m.g.491.9		20	273.179	odd	6
1274.2.m.g.589.9		20	21.11	odd	6
1274.2.o.h.459.2		20	21.20	even	2
1274.2.o.h.569.7		20	273.257	even	6
1274.2.v.h.361.4		20	273.62	even	6
1274.2.v.h.667.4		20	21.5	even	6
1638.2.cr.c.361.6		20	13.10	even	6
1638.2.cr.c.667.6		20	7.2	even	3
1638.2.dt.c.1297.5		20	91.23	even	6	inner
1638.2.dt.c.1369.10		20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.dt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(2.89612 - 1.67208i) q^{5} +(0.268506 + 2.63209i) q^{7} -1.00000i q^{8} +(1.67208 + 2.89612i) q^{10} +(-4.36176 + 2.51826i) q^{11} +(-1.92804 + 3.04674i) q^{13} +(-2.63209 + 0.268506i) q^{14} +1.00000 q^{16} -3.73270 q^{17} +(-5.08703 - 2.93700i) q^{19} +(-2.89612 + 1.67208i) q^{20} +(-2.51826 - 4.36176i) q^{22} -3.78370 q^{23} +(3.09168 - 5.35494i) q^{25} +(-3.04674 - 1.92804i) q^{26} +(-0.268506 - 2.63209i) q^{28} +(-3.36143 + 5.82216i) q^{29} +(0.884906 + 0.510901i) q^{31} +1.00000i q^{32} -3.73270i q^{34} +(5.17868 + 7.17389i) q^{35} -0.428222i q^{37} +(2.93700 - 5.08703i) q^{38} +(-1.67208 - 2.89612i) q^{40} +(-0.917963 - 0.529986i) q^{41} +(1.65120 + 2.85996i) q^{43} +(4.36176 - 2.51826i) q^{44} -3.78370i q^{46} +(4.60157 - 2.65672i) q^{47} +(-6.85581 + 1.41346i) q^{49} +(5.35494 + 3.09168i) q^{50} +(1.92804 - 3.04674i) q^{52} +(1.15836 - 2.00634i) q^{53} +(-8.42146 + 14.5864i) q^{55} +(2.63209 - 0.268506i) q^{56} +(-5.82216 - 3.36143i) q^{58} +8.08665i q^{59} +(5.05050 - 8.74773i) q^{61} +(-0.510901 + 0.884906i) q^{62} -1.00000 q^{64} +(-0.489457 + 12.0476i) q^{65} +(-11.5166 + 6.64910i) q^{67} +3.73270 q^{68} +(-7.17389 + 5.17868i) q^{70} +(-2.35754 + 1.36113i) q^{71} +(6.88886 + 3.97728i) q^{73} +0.428222 q^{74} +(5.08703 + 2.93700i) q^{76} +(-7.79946 - 10.8044i) q^{77} +(7.07112 + 12.2475i) q^{79} +(2.89612 - 1.67208i) q^{80} +(0.529986 - 0.917963i) q^{82} +9.17859i q^{83} +(-10.8104 + 6.24136i) q^{85} +(-2.85996 + 1.65120i) q^{86} +(2.51826 + 4.36176i) q^{88} -5.41291i q^{89} +(-8.53700 - 4.25672i) q^{91} +3.78370 q^{92} +(2.65672 + 4.60157i) q^{94} -19.6435 q^{95} +(14.8742 - 8.58763i) q^{97} +(-1.41346 - 6.85581i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{4} + 2 q^{7} - 4 q^{10} + 6 q^{11} + 6 q^{13} + 4 q^{14} + 20 q^{16} - 20 q^{17} - 24 q^{19} + 2 q^{22} + 18 q^{25} - 6 q^{26} - 2 q^{28} - 2 q^{29} - 6 q^{31} + 14 q^{38} + 4 q^{40} - 18 q^{41}+ \cdots - 24 q^{98}+O(q^{100}) \) 20 * q - 20 * q^4 + 2 * q^7 - 4 * q^10 + 6 * q^11 + 6 * q^13 + 4 * q^14 + 20 * q^16 - 20 * q^17 - 24 * q^19 + 2 * q^22 + 18 * q^25 - 6 * q^26 - 2 * q^28 - 2 * q^29 - 6 * q^31 + 14 * q^38 + 4 * q^40 - 18 * q^41 + 8 * q^43 - 6 * q^44 - 18 * q^47 - 6 * q^49 + 12 * q^50 - 6 * q^52 + 4 * q^53 + 2 * q^55 - 4 * q^56 - 24 * q^58 - 4 * q^61 + 24 * q^62 - 20 * q^64 + 6 * q^65 - 60 * q^67 + 20 * q^68 - 48 * q^70 + 18 * q^71 - 72 * q^73 + 24 * q^74 + 24 * q^76 - 42 * q^77 + 42 * q^79 - 16 * q^82 - 12 * q^85 - 42 * q^86 - 2 * q^88 + 14 * q^91 + 16 * q^94 - 24 * q^95 + 78 * q^97 - 24 * q^98

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