LMFDB - Embedded newform 512.2.i.b.33.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(33,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15]))

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

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

chi := DirichletCharacter("512.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.i (of order $16$, degree $8$, not 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			33.4
Character	$\chi$	$=$	512.33
Dual form			512.2.i.b.481.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0799701 + 0.0534343i) q^{3} +(3.47403 - 0.691028i) q^{5} +(1.22800 + 2.96465i) q^{7} +(-1.14451 + 2.76309i) q^{9} +O(q^{10})$	\(q+(-0.0799701 + 0.0534343i) q^{3} +(3.47403 - 0.691028i) q^{5} +(1.22800 + 2.96465i) q^{7} +(-1.14451 + 2.76309i) q^{9} +(-2.79833 + 4.18799i) q^{11} +(1.09820 + 0.218446i) q^{13} +(-0.240894 + 0.240894i) q^{15} +(-2.65418 - 2.65418i) q^{17} +(0.382328 - 1.92209i) q^{19} +(-0.256617 - 0.171466i) q^{21} +(1.03743 + 0.429717i) q^{23} +(6.97198 - 2.88789i) q^{25} +(-0.112408 - 0.565114i) q^{27} +(0.389126 + 0.582369i) q^{29} -3.88281i q^{31} -0.484441i q^{33} +(6.31476 + 9.45071i) q^{35} +(-0.183408 - 0.922056i) q^{37} +(-0.0994958 + 0.0412125i) q^{39} +(7.08379 + 2.93420i) q^{41} +(-5.66688 - 3.78649i) q^{43} +(-2.06669 + 10.3900i) q^{45} +(2.32284 + 2.32284i) q^{47} +(-2.33143 + 2.33143i) q^{49} +(0.354079 + 0.0704307i) q^{51} +(5.11546 - 7.65583i) q^{53} +(-6.82746 + 16.4829i) q^{55} +(0.0721309 + 0.174139i) q^{57} +(3.76937 - 0.749773i) q^{59} +(2.78586 - 1.86145i) q^{61} -9.59706 q^{63} +3.96614 q^{65} +(5.52163 - 3.68943i) q^{67} +(-0.105925 + 0.0210698i) q^{69} +(-3.72629 - 8.99606i) q^{71} +(-0.610714 + 1.47439i) q^{73} +(-0.403237 + 0.603488i) q^{75} +(-15.8523 - 3.15321i) q^{77} +(8.22980 - 8.22980i) q^{79} +(-6.30515 - 6.30515i) q^{81} +(1.83962 - 9.24837i) q^{83} +(-11.0548 - 7.38658i) q^{85} +(-0.0622370 - 0.0257794i) q^{87} +(-12.0003 + 4.97070i) q^{89} +(0.700974 + 3.52403i) q^{91} +(0.207475 + 0.310509i) q^{93} -6.94161i q^{95} -5.29500i q^{97} +(-8.36909 - 12.5252i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9	$ 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{17} + 8 q^{19} + 8 q^{21} - 8 q^{23} - 8 q^{25} + 8 q^{27} + 8 q^{29} + 8 q^{35} + 8 q^{37} - 8 q^{39} - 8 q^{41} + 8 q^{43} + 8 q^{45} - 8 q^{47} - 8 q^{49} - 24 q^{51} + 8 q^{53} + 56 q^{55} - 8 q^{57} - 56 q^{59} + 8 q^{61} + 64 q^{63} - 16 q^{65} - 72 q^{67} + 8 q^{69} + 56 q^{71} - 8 q^{73} - 56 q^{75} + 8 q^{77} + 24 q^{79} - 8 q^{81} + 8 q^{83} + 8 q^{85} - 8 q^{87} - 8 q^{89} + 8 q^{91} - 16 q^{93} - 16 q^{99}+O(q^{100}) $ 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9 + 8 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^17 + 8 * q^19 + 8 * q^21 - 8 * q^23 - 8 * q^25 + 8 * q^27 + 8 * q^29 + 8 * q^35 + 8 * q^37 - 8 * q^39 - 8 * q^41 + 8 * q^43 + 8 * q^45 - 8 * q^47 - 8 * q^49 - 24 * q^51 + 8 * q^53 + 56 * q^55 - 8 * q^57 - 56 * q^59 + 8 * q^61 + 64 * q^63 - 16 * q^65 - 72 * q^67 + 8 * q^69 + 56 * q^71 - 8 * q^73 - 56 * q^75 + 8 * q^77 + 24 * q^79 - 8 * q^81 + 8 * q^83 + 8 * q^85 - 8 * q^87 - 8 * q^89 + 8 * q^91 - 16 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{15}{16}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.0799701	+	0.0534343i	−0.0461708	+	0.0308503i	−0.578441	−	0.815724i	$-0.696339\pi$
$3$	−0.0799701	+	0.0534343i	−0.0461708	+	0.0308503i	0.532271	+	0.846574i	$0.321339\pi$
$4$		0			0
$5$	3.47403	−	0.691028i	1.55363	−	0.309037i	0.657719	−	0.753263i	$-0.271521\pi$
$5$	3.47403	−	0.691028i	1.55363	−	0.309037i	0.895915	+	0.444226i	$0.146521\pi$
$6$		0			0
$7$	1.22800	+	2.96465i	0.464140	+	1.12053i	0.966682	+	0.255980i	$0.0823981\pi$
$7$	1.22800	+	2.96465i	0.464140	+	1.12053i	−0.502542	+	0.864553i	$0.667602\pi$
$8$		0			0
$9$	−1.14451	+	2.76309i	−0.381503	+	0.921031i
$10$		0			0
$11$	−2.79833	+	4.18799i	−0.843727	+	1.26273i	0.119174	+	0.992873i	$0.461975\pi$
$11$	−2.79833	+	4.18799i	−0.843727	+	1.26273i	−0.962901	+	0.269854i	$0.913025\pi$
$12$		0			0
$13$	1.09820	+	0.218446i	0.304586	+	0.0605860i	0.345017	−	0.938596i	$-0.387873\pi$
$13$	1.09820	+	0.218446i	0.304586	+	0.0605860i	−0.0404309	+	0.999182i	$0.512873\pi$
$14$		0			0
$15$	−0.240894	+	0.240894i	−0.0621986	+	0.0621986i
$16$		0			0
$17$	−2.65418	−	2.65418i	−0.643732	−	0.643732i	0.307739	−	0.951471i	$-0.400428\pi$
$17$	−2.65418	−	2.65418i	−0.643732	−	0.643732i	−0.951471	+	0.307739i	$0.900428\pi$
$18$		0			0
$19$	0.382328	−	1.92209i	0.0877120	−	0.440958i	−0.911826	−	0.410576i	$-0.865328\pi$
$19$	0.382328	−	1.92209i	0.0877120	−	0.440958i	0.999538	−	0.0303820i	$-0.00967237\pi$
$20$		0			0
$21$	−0.256617	−	0.171466i	−0.0559985	−	0.0374170i
$22$		0			0
$23$	1.03743	+	0.429717i	0.216319	+	0.0896023i	0.488211	−	0.872725i	$-0.337649\pi$
$23$	1.03743	+	0.429717i	0.216319	+	0.0896023i	−0.271892	+	0.962328i	$0.587649\pi$
$24$		0			0
$25$	6.97198	−	2.88789i	1.39440	−	0.577578i
$26$		0			0
$27$	−0.112408	−	0.565114i	−0.0216330	−	0.108756i
$28$		0			0
$29$	0.389126	+	0.582369i	0.0722590	+	0.108143i	0.865839	−	0.500323i	$-0.166785\pi$
$29$	0.389126	+	0.582369i	0.0722590	+	0.108143i	−0.793580	+	0.608466i	$0.791785\pi$
$30$		0			0
$31$		−	3.88281i		−	0.697373i	−0.937239	−	0.348687i	$-0.886628\pi$
$31$		−	3.88281i		−	0.697373i	0.937239	−	0.348687i	$-0.113372\pi$
$32$		0			0
$33$		−	0.484441i		−	0.0843303i
$34$		0			0
$35$	6.31476	+	9.45071i	1.06739	+	1.59746i
$36$		0			0
$37$	−0.183408	−	0.922056i	−0.0301522	−	0.151585i	0.962776	−	0.270299i	$-0.0871227\pi$
$37$	−0.183408	−	0.922056i	−0.0301522	−	0.151585i	−0.992928	+	0.118714i	$0.962123\pi$
$38$		0			0
$39$	−0.0994958	+	0.0412125i	−0.0159321	+	0.00659928i
$40$		0			0
$41$	7.08379	+	2.93420i	1.10630	+	0.458245i	0.859663	−	0.510862i	$-0.170674\pi$
$41$	7.08379	+	2.93420i	1.10630	+	0.458245i	0.246640	+	0.969107i	$0.420674\pi$
$42$		0			0
$43$	−5.66688	−	3.78649i	−0.864191	−	0.577434i	0.0425633	−	0.999094i	$-0.486448\pi$
$43$	−5.66688	−	3.78649i	−0.864191	−	0.577434i	−0.906754	+	0.421660i	$0.861448\pi$
$44$		0			0
$45$	−2.06669	+	10.3900i	−0.308084	+	1.54884i
$46$		0			0
$47$	2.32284	+	2.32284i	0.338820	+	0.338820i	0.855923	−	0.517103i	$-0.172990\pi$
$47$	2.32284	+	2.32284i	0.338820	+	0.338820i	−0.517103	+	0.855923i	$0.672990\pi$
$48$		0			0
$49$	−2.33143	+	2.33143i	−0.333061	+	0.333061i
$50$		0			0
$51$	0.354079	+	0.0704307i	0.0495810	+	0.00986226i
$52$		0			0
$53$	5.11546	−	7.65583i	0.702662	−	1.05161i	−0.292774	−	0.956182i	$-0.594578\pi$
$53$	5.11546	−	7.65583i	0.702662	−	1.05161i	0.995436	−	0.0954269i	$-0.0304216\pi$
$54$		0			0
$55$	−6.82746	+	16.4829i	−0.920614	+	2.22256i
$56$		0			0
$57$	0.0721309	+	0.174139i	0.00955396	+	0.0230653i
$58$		0			0
$59$	3.76937	−	0.749773i	0.490730	−	0.0976122i	0.0564780	−	0.998404i	$-0.482013\pi$
$59$	3.76937	−	0.749773i	0.490730	−	0.0976122i	0.434252	+	0.900792i	$0.357013\pi$
$60$		0			0
$61$	2.78586	−	1.86145i	0.356692	−	0.238334i	−0.364293	−	0.931284i	$-0.618689\pi$
$61$	2.78586	−	1.86145i	0.356692	−	0.238334i	0.720986	+	0.692950i	$0.243689\pi$
$62$		0			0
$63$	−9.59706			−1.20912
$64$		0			0
$65$	3.96614			0.491939
$66$		0			0
$67$	5.52163	−	3.68943i	0.674574	−	0.450736i	−0.170519	−	0.985354i	$-0.554545\pi$
$67$	5.52163	−	3.68943i	0.674574	−	0.450736i	0.845094	+	0.534618i	$0.179545\pi$
$68$		0			0
$69$	−0.105925	+	0.0210698i	−0.0127519	+	0.00253650i
$70$		0			0
$71$	−3.72629	−	8.99606i	−0.442229	−	1.06764i	−0.975165	−	0.221480i	$-0.928911\pi$
$71$	−3.72629	−	8.99606i	−0.442229	−	1.06764i	0.532936	−	0.846156i	$-0.321089\pi$
$72$		0			0
$73$	−0.610714	+	1.47439i	−0.0714786	+	0.172565i	−0.955581	−	0.294729i	$-0.904771\pi$
$73$	−0.610714	+	1.47439i	−0.0714786	+	0.172565i	0.884102	+	0.467293i	$0.154771\pi$
$74$		0			0
$75$	−0.403237	+	0.603488i	−0.0465619	+	0.0696847i
$76$		0			0
$77$	−15.8523	−	3.15321i	−1.80653	−	0.359342i
$78$		0			0
$79$	8.22980	−	8.22980i	0.925925	−	0.925925i	−0.0715143	−	0.997440i	$-0.522783\pi$
$79$	8.22980	−	8.22980i	0.925925	−	0.925925i	0.997440	+	0.0715143i	$0.0227832\pi$
$80$		0			0
$81$	−6.30515	−	6.30515i	−0.700572	−	0.700572i
$82$		0			0
$83$	1.83962	−	9.24837i	0.201924	−	1.01514i	−0.738271	−	0.674504i	$-0.764357\pi$
$83$	1.83962	−	9.24837i	0.201924	−	1.01514i	0.940195	−	0.340636i	$-0.110643\pi$
$84$		0			0
$85$	−11.0548	−	7.38658i	−1.19906	−	0.801187i
$86$		0			0
$87$	−0.0622370	−	0.0257794i	−0.00667250	−	0.00276384i
$88$		0			0
$89$	−12.0003	+	4.97070i	−1.27203	+	0.526893i	−0.913582	−	0.406655i	$-0.866695\pi$
$89$	−12.0003	+	4.97070i	−1.27203	+	0.526893i	−0.358451	+	0.933548i	$0.616695\pi$
$90$		0			0
$91$	0.700974	+	3.52403i	0.0734821	+	0.369419i
$92$		0			0
$93$	0.207475	+	0.310509i	0.0215142	+	0.0321983i
$94$		0			0
$95$		−	6.94161i		−	0.712194i
$96$		0			0
$97$		−	5.29500i		−	0.537626i	−0.963192	−	0.268813i	$-0.913369\pi$
$97$		−	5.29500i		−	0.537626i	0.963192	−	0.268813i	$-0.0866314\pi$
$98$		0			0
$99$	−8.36909	−	12.5252i	−0.841126	−	1.25883i
$100$		0			0
$101$	3.13084	+	15.7398i	0.311530	+	1.56617i	0.746290	+	0.665621i	$0.231833\pi$
$101$	3.13084	+	15.7398i	0.311530	+	1.56617i	−0.434760	+	0.900547i	$0.643167\pi$
$102$		0			0
$103$	17.4336	−	7.22122i	1.71778	−	0.711528i	0.717900	−	0.696147i	$-0.245104\pi$
$103$	17.4336	−	7.22122i	1.71778	−	0.711528i	0.999882	−	0.0153816i	$-0.00489631\pi$
$104$		0			0
$105$	−1.00998	−	0.418349i	−0.0985644	−	0.0408267i
$106$		0			0
$107$	−4.11276	−	2.74806i	−0.397596	−	0.265665i	0.340659	−	0.940187i	$-0.389350\pi$
$107$	−4.11276	−	2.74806i	−0.397596	−	0.265665i	−0.738255	+	0.674522i	$0.764350\pi$
$108$		0			0
$109$	−0.0475309	+	0.238954i	−0.00455264	+	0.0228876i	−0.982995	−	0.183633i	$-0.941214\pi$
$109$	−0.0475309	+	0.238954i	−0.00455264	+	0.0228876i	0.978442	+	0.206521i	$0.0662141\pi$
$110$		0			0
$111$	0.0639366	+	0.0639366i	0.00606860	+	0.00606860i
$112$		0			0
$113$	−6.95720	+	6.95720i	−0.654478	+	0.654478i	−0.954068	−	0.299590i	$-0.903150\pi$
$113$	−6.95720	+	6.95720i	−0.654478	+	0.654478i	0.299590	+	0.954068i	$0.403150\pi$
$114$		0			0
$115$	3.90101	+	0.775959i	0.363771	+	0.0723586i
$116$		0			0
$117$	−1.86049	+	2.78442i	−0.172002	+	0.257420i
$118$		0			0
$119$	4.60938	−	11.1280i	0.422541	−	1.02010i
$120$		0			0
$121$	−5.49912	−	13.2761i	−0.499920	−	1.20691i
$122$		0			0
$123$	−0.723279	+	0.143869i	−0.0652158	+	0.0129722i
$124$		0			0
$125$	7.49955	−	5.01104i	0.670780	−	0.448201i
$126$		0			0
$127$	−7.76241			−0.688803			−0.344401	−	0.938823i	$-0.611918\pi$
$127$	−7.76241			−0.688803			−0.344401	+	0.938823i	$0.611918\pi$
$128$		0			0
$129$	0.655509			0.0577144
$130$		0			0
$131$	−12.3086	+	8.22432i	−1.07540	+	0.718562i	−0.961465	−	0.274926i	$-0.911347\pi$
$131$	−12.3086	+	8.22432i	−1.07540	+	0.718562i	−0.113939	+	0.993488i	$0.536347\pi$
$132$		0			0
$133$	6.16783	−	1.22686i	0.534819	−	0.106382i
$134$		0			0
$135$	−0.781020	−	1.88555i	−0.0672195	−	0.162282i
$136$		0			0
$137$	−5.36370	+	12.9491i	−0.458252	+	1.10632i	0.510853	+	0.859668i	$0.329330\pi$
$137$	−5.36370	+	12.9491i	−0.458252	+	1.10632i	−0.969105	+	0.246650i	$0.920670\pi$
$138$		0			0
$139$	−0.749892	+	1.12229i	−0.0636050	+	0.0951917i	−0.861909	−	0.507063i	$-0.830731\pi$
$139$	−0.749892	+	1.12229i	−0.0636050	+	0.0951917i	0.798304	+	0.602255i	$0.205731\pi$
$140$		0			0
$141$	−0.309877	−	0.0616383i	−0.0260963	−	0.00519088i
$142$		0			0
$143$	−3.98798	+	3.98798i	−0.333491	+	0.333491i
$144$		0			0
$145$	1.75427	+	1.75427i	0.145684	+	0.145684i
$146$		0			0
$147$	0.0618662	−	0.311022i	0.00510264	−	0.0256527i
$148$		0			0
$149$	−1.76585	−	1.17991i	−0.144664	−	0.0966617i	0.481132	−	0.876648i	$-0.340226\pi$
$149$	−1.76585	−	1.17991i	−0.144664	−	0.0966617i	−0.625796	+	0.779987i	$0.715226\pi$
$150$		0			0
$151$	4.00592	+	1.65931i	0.325997	+	0.135033i	0.539679	−	0.841871i	$-0.318546\pi$
$151$	4.00592	+	1.65931i	0.325997	+	0.135033i	−0.213682	+	0.976903i	$0.568546\pi$
$152$		0			0
$153$	10.3715	−	4.29600i	0.838483	−	0.347311i
$154$		0			0
$155$	−2.68313	−	13.4890i	−0.215514	−	1.08346i
$156$		0			0
$157$	−2.07839	−	3.11052i	−0.165873	−	0.248247i	0.739216	−	0.673468i	$-0.235196\pi$
$157$	−2.07839	−	3.11052i	−0.165873	−	0.248247i	−0.905089	+	0.425221i	$0.860196\pi$
$158$		0			0
$159$			0.885578i			0.0702309i
$160$		0			0
$161$			3.60331i			0.283980i
$162$		0			0
$163$	13.3708	+	20.0108i	1.04728	+	1.56736i	0.801460	+	0.598049i	$0.204057\pi$
$163$	13.3708	+	20.0108i	1.04728	+	1.56736i	0.245820	+	0.969316i	$0.420943\pi$
$164$		0			0
$165$	−0.334762	−	1.68296i	−0.0260612	−	0.131018i
$166$		0			0
$167$	−15.6357	+	6.47650i	−1.20992	+	0.501167i	−0.894193	−	0.447682i	$-0.852250\pi$
$167$	−15.6357	+	6.47650i	−1.20992	+	0.501167i	−0.315730	+	0.948849i	$0.602250\pi$
$168$		0			0
$169$	−10.8521	−	4.49509i	−0.834777	−	0.345776i
$170$		0			0
$171$	4.87334	+	3.25626i	0.372673	+	0.249012i
$172$		0			0
$173$	1.28256	−	6.44786i	0.0975112	−	0.490222i	−0.900908	−	0.434011i	$-0.857098\pi$
$173$	1.28256	−	6.44786i	0.0975112	−	0.490222i	0.998419	−	0.0562112i	$-0.0179020\pi$
$174$		0			0
$175$	17.1232	+	17.1232i	1.29439	+	1.29439i
$176$		0			0
$177$	−0.261373	+	0.261373i	−0.0196460	+	0.0196460i
$178$		0			0
$179$	−23.4172	−	4.65797i	−1.75028	−	0.348153i	−0.787064	−	0.616872i	$-0.788400\pi$
$179$	−23.4172	−	4.65797i	−1.75028	−	0.348153i	−0.963219	+	0.268719i	$0.913400\pi$
$180$		0			0
$181$	−4.98506	+	7.46067i	−0.370537	+	0.554547i	−0.969144	−	0.246495i	$-0.920721\pi$
$181$	−4.98506	+	7.46067i	−0.370537	+	0.554547i	0.598607	+	0.801043i	$0.295721\pi$
$182$		0			0
$183$	−0.123320	+	0.297721i	−0.00911607	+	0.0220081i
$184$		0			0
$185$	−1.27433	−	3.07651i	−0.0936908	−	0.226190i
$186$		0			0
$187$	18.5429	−	3.68842i	1.35599	−	0.269724i
$188$		0			0
$189$	1.53733	−	1.02721i	0.111824	−	0.0747186i
$190$		0			0
$191$	15.9816			1.15639			0.578195	−	0.815899i	$-0.303757\pi$
$191$	15.9816			1.15639			0.578195	+	0.815899i	$0.303757\pi$
$192$		0			0
$193$	3.68140			0.264993			0.132496	−	0.991183i	$-0.457701\pi$
$193$	3.68140			0.264993			0.132496	+	0.991183i	$0.457701\pi$
$194$		0			0
$195$	−0.317173	+	0.211928i	−0.0227132	+	0.0151765i
$196$		0			0
$197$	−11.0892	+	2.20577i	−0.790070	+	0.157155i	−0.573601	−	0.819135i	$-0.694454\pi$
$197$	−11.0892	+	2.20577i	−0.790070	+	0.157155i	−0.216469	+	0.976290i	$0.569454\pi$
$198$		0			0
$199$	−3.41515	−	8.24489i	−0.242093	−	0.584465i	0.755397	−	0.655267i	$-0.227444\pi$
$199$	−3.41515	−	8.24489i	−0.242093	−	0.584465i	−0.997490	+	0.0708023i	$0.977444\pi$
$200$		0			0
$201$	−0.244423	+	0.590089i	−0.0172403	+	0.0416217i
$202$		0			0
$203$	−1.24867	+	1.86877i	−0.0876397	+	0.131162i
$204$		0			0
$205$	26.6369	+	5.29842i	1.86040	+	0.370057i
$206$		0			0
$207$	−2.37470	+	2.37470i	−0.165053	+	0.165053i
$208$		0			0
$209$	6.97982	+	6.97982i	0.482805	+	0.482805i
$210$		0			0
$211$	1.91737	−	9.63929i	0.131997	−	0.663596i	−0.856958	−	0.515386i	$-0.827649\pi$
$211$	1.91737	−	9.63929i	0.131997	−	0.663596i	0.988956	−	0.148210i	$-0.0473513\pi$
$212$		0			0
$213$	0.778690	+	0.520304i	0.0533549	+	0.0356506i
$214$		0			0
$215$	−22.3035	−	9.23840i	−1.52108	−	0.630054i
$216$		0			0
$217$	11.5112	−	4.76809i	0.781430	−	0.323679i
$218$		0			0
$219$	−0.0299444	−	0.150540i	−0.00202345	−	0.0101726i
$220$		0			0
$221$	−2.33503	−	3.49461i	−0.157071	−	0.235073i
$222$		0			0
$223$			11.7193i			0.784782i	0.919798	+	0.392391i	$0.128352\pi$
$223$			11.7193i			0.784782i	−0.919798	+	0.392391i	$0.871648\pi$
$224$		0			0
$225$			22.5694i			1.50463i
$226$		0			0
$227$	−4.43507	−	6.63755i	−0.294366	−	0.440549i	0.654578	−	0.755994i	$-0.272846\pi$
$227$	−4.43507	−	6.63755i	−0.294366	−	0.440549i	−0.948944	+	0.315445i	$0.897846\pi$
$228$		0			0
$229$	−3.07163	−	15.4421i	−0.202979	−	1.02045i	−0.939113	−	0.343609i	$-0.888350\pi$
$229$	−3.07163	−	15.4421i	−0.202979	−	1.02045i	0.736133	−	0.676836i	$-0.236650\pi$
$230$		0			0
$231$	1.43620	−	0.594893i	0.0944949	−	0.0391411i
$232$		0			0
$233$	−2.37521	−	0.983843i	−0.155605	−	0.0644537i	0.303522	−	0.952825i	$-0.401838\pi$
$233$	−2.37521	−	0.983843i	−0.155605	−	0.0644537i	−0.459127	+	0.888371i	$0.651838\pi$
$234$		0			0
$235$	9.67475	+	6.46446i	0.631111	+	0.421695i
$236$		0			0
$237$	−0.218384	+	1.09789i	−0.0141856	+	0.0713158i
$238$		0			0
$239$	−14.4718	−	14.4718i	−0.936102	−	0.936102i	0.0619760	−	0.998078i	$-0.480260\pi$
$239$	−14.4718	−	14.4718i	−0.936102	−	0.936102i	−0.998078	+	0.0619760i	$0.980260\pi$
$240$		0			0
$241$	13.8159	−	13.8159i	0.889960	−	0.889960i	−0.104558	−	0.994519i	$-0.533343\pi$
$241$	13.8159	−	13.8159i	0.889960	−	0.889960i	0.994519	+	0.104558i	$0.0333429\pi$
$242$		0			0
$243$	2.53648	+	0.504537i	0.162715	+	0.0323661i
$244$		0			0
$245$	−6.48837	+	9.71053i	−0.414526	+	0.620383i
$246$		0			0
$247$	0.839746	−	2.02733i	0.0534317	−	0.128996i
$248$		0			0
$249$	0.347066	+	0.837892i	0.0219944	+	0.0530992i
$250$		0			0
$251$	14.6959	−	2.92320i	0.927599	−	0.184511i	0.291901	−	0.956449i	$-0.405712\pi$
$251$	14.6959	−	2.92320i	0.927599	−	0.184511i	0.635698	+	0.771938i	$0.280712\pi$
$252$		0			0
$253$	−4.70272	+	3.14226i	−0.295657	+	0.197552i
$254$		0			0
$255$	1.27875			0.0800785
$256$		0			0
$257$	24.4316			1.52400			0.762001	−	0.647576i	$-0.224217\pi$
$257$	24.4316			1.52400			0.762001	+	0.647576i	$0.224217\pi$
$258$		0			0
$259$	2.50835	−	1.67603i	0.155861	−	0.104143i
$260$		0			0
$261$	−2.05450	+	0.408665i	−0.127170	+	0.0252957i
$262$		0			0
$263$	6.31226	+	15.2391i	0.389231	+	0.939686i	0.990103	+	0.140341i	$0.0448199\pi$
$263$	6.31226	+	15.2391i	0.389231	+	0.939686i	−0.600873	+	0.799345i	$0.705180\pi$
$264$		0			0
$265$	12.4809	−	30.1315i	0.766694	−	1.85096i
$266$		0			0
$267$	0.694062	−	1.03874i	0.0424759	−	0.0635697i
$268$		0			0
$269$	−6.17863	−	1.22901i	−0.376718	−	0.0749338i	0.00309991	−	0.999995i	$-0.499013\pi$
$269$	−6.17863	−	1.22901i	−0.376718	−	0.0749338i	−0.379818	+	0.925061i	$0.624013\pi$
$270$		0			0
$271$	−22.0018	+	22.0018i	−1.33651	+	1.33651i	−0.437100	+	0.899413i	$0.643995\pi$
$271$	−22.0018	+	22.0018i	−1.33651	+	1.33651i	−0.899413	+	0.437100i	$0.856005\pi$
$272$		0			0
$273$	−0.244361	−	0.244361i	−0.0147894	−	0.0147894i
$274$		0			0
$275$	−7.41542	+	37.2798i	−0.447167	+	2.24806i
$276$		0			0
$277$	16.8544	+	11.2618i	1.01269	+	0.676655i	0.947016	−	0.321187i	$-0.104082\pi$
$277$	16.8544	+	11.2618i	1.01269	+	0.676655i	0.0656692	+	0.997841i	$0.479082\pi$
$278$		0			0
$279$	10.7286	+	4.44392i	0.642302	+	0.266050i
$280$		0			0
$281$	−21.0372	+	8.71391i	−1.25498	+	0.519828i	−0.908364	−	0.418180i	$-0.862668\pi$
$281$	−21.0372	+	8.71391i	−1.25498	+	0.519828i	−0.346613	+	0.938008i	$0.612668\pi$
$282$		0			0
$283$	5.85317	+	29.4259i	0.347935	+	1.74919i	0.617844	+	0.786301i	$0.288006\pi$
$283$	5.85317	+	29.4259i	0.347935	+	1.74919i	−0.269909	+	0.962886i	$0.586994\pi$
$284$		0			0
$285$	0.370920	+	0.555121i	0.0219714	+	0.0328825i
$286$		0			0
$287$			24.6042i			1.45234i
$288$		0			0
$289$		−	2.91070i		−	0.171218i
$290$		0			0
$291$	0.282935	+	0.423442i	0.0165859	+	0.0248226i
$292$		0			0
$293$	3.59311	+	18.0638i	0.209912	+	1.05530i	0.931713	+	0.363196i	$0.118315\pi$
$293$	3.59311	+	18.0638i	0.209912	+	1.05530i	−0.721801	+	0.692100i	$0.756685\pi$
$294$		0			0
$295$	12.5768	−	5.20947i	0.732248	−	0.303307i
$296$		0			0
$297$	2.68125	+	1.11061i	0.155582	+	0.0644441i
$298$		0			0
$299$	1.04544	+	0.698538i	0.0604592	+	0.0403975i
$300$		0			0
$301$	4.26669	−	21.4501i	0.245928	−	1.23636i
$302$		0			0
$303$	−1.09142	−	1.09142i	−0.0627004	−	0.0627004i
$304$		0			0
$305$	8.39184	−	8.39184i	0.480515	−	0.480515i
$306$		0			0
$307$	−0.624761	−	0.124273i	−0.0356570	−	0.00709262i	0.177230	−	0.984170i	$-0.443286\pi$
$307$	−0.624761	−	0.124273i	−0.0356570	−	0.00709262i	−0.212887	+	0.977077i	$0.568286\pi$
$308$		0			0
$309$	−1.00830	+	1.50903i	−0.0573604	+	0.0858459i
$310$		0			0
$311$	3.87831	−	9.36307i	0.219919	−	0.530931i	−0.774959	−	0.632011i	$-0.782230\pi$
$311$	3.87831	−	9.36307i	0.219919	−	0.530931i	0.994878	+	0.101080i	$0.0322298\pi$
$312$		0			0
$313$	7.60854	+	18.3686i	0.430060	+	1.03826i	0.979268	+	0.202571i	$0.0649297\pi$
$313$	7.60854	+	18.3686i	0.430060	+	1.03826i	−0.549207	+	0.835686i	$0.685070\pi$
$314$		0			0
$315$	−33.3405	+	6.63184i	−1.87852	+	0.373662i
$316$		0			0
$317$	9.31093	−	6.22136i	0.522954	−	0.349427i	−0.265907	−	0.963999i	$-0.585671\pi$
$317$	9.31093	−	6.22136i	0.522954	−	0.349427i	0.788861	+	0.614572i	$0.210671\pi$
$318$		0			0
$319$	−3.52786			−0.197522
$320$		0			0
$321$	0.475738			0.0265531
$322$		0			0
$323$	−6.11633	+	4.08680i	−0.340322	+	0.227396i
$324$		0			0
$325$	8.28748	−	1.64848i	0.459707	−	0.0914414i
$326$		0			0
$327$	−0.00896729	−	0.0216490i	−0.000495892	−	0.00119719i
$328$		0			0
$329$	−4.03396	+	9.73883i	−0.222399	+	0.536919i
$330$		0			0
$331$	2.60514	−	3.89887i	0.143192	−	0.214301i	−0.752941	−	0.658088i	$-0.771365\pi$
$331$	2.60514	−	3.89887i	0.143192	−	0.214301i	0.896132	+	0.443787i	$0.146365\pi$
$332$		0			0
$333$	2.75764	+	0.548529i	0.151118	+	0.0300592i
$334$		0			0
$335$	16.6328	−	16.6328i	0.908747	−	0.908747i
$336$		0			0
$337$	7.15691	+	7.15691i	0.389862	+	0.389862i	0.874638	−	0.484777i	$-0.161099\pi$
$337$	7.15691	+	7.15691i	0.389862	+	0.389862i	−0.484777	+	0.874638i	$0.661099\pi$
$338$		0			0
$339$	0.184615	−	0.928121i	0.0100269	−	0.0504086i
$340$		0			0
$341$	16.2612	+	10.8654i	0.880592	+	0.588393i
$342$		0			0
$343$	10.9777	+	4.54711i	0.592740	+	0.245521i
$344$		0			0
$345$	−0.353427	+	0.146394i	−0.0190279	+	0.00788160i
$346$		0			0
$347$	−1.83440	−	9.22214i	−0.0984756	−	0.495070i	−0.998272	−	0.0587604i	$-0.981285\pi$
$347$	−1.83440	−	9.22214i	−0.0984756	−	0.495070i	0.899797	−	0.436310i	$-0.143715\pi$
$348$		0			0
$349$	0.202878	+	0.303629i	0.0108598	+	0.0162529i	0.836860	−	0.547417i	$-0.184389\pi$
$349$	0.202878	+	0.303629i	0.0108598	+	0.0162529i	−0.826000	+	0.563670i	$0.809389\pi$
$350$		0			0
$351$		−	0.645165i		−	0.0344363i
$352$		0			0
$353$		−	28.2164i		−	1.50181i	−0.660411	−	0.750904i	$-0.729618\pi$
$353$		−	28.2164i		−	1.50181i	0.660411	−	0.750904i	$-0.270382\pi$
$354$		0			0
$355$	−19.1618	−	28.6776i	−1.01700	−	1.52205i
$356$		0			0
$357$	0.226006	+	1.13621i	0.0119615	+	0.0601345i
$358$		0			0
$359$	−21.6280	+	8.95860i	−1.14148	+	0.472817i	−0.871668	−	0.490096i	$-0.836962\pi$
$359$	−21.6280	+	8.95860i	−1.14148	+	0.472817i	−0.269812	+	0.962913i	$0.586962\pi$
$360$		0			0
$361$	14.0054	+	5.80125i	0.737129	+	0.305329i
$362$		0			0
$363$	1.14916	+	0.767846i	0.0603154	+	0.0403015i
$364$		0			0
$365$	−1.10279	+	5.54411i	−0.0577228	+	0.290192i
$366$		0			0
$367$	−7.75795	−	7.75795i	−0.404962	−	0.404962i	0.475016	−	0.879977i	$-0.342442\pi$
$367$	−7.75795	−	7.75795i	−0.404962	−	0.404962i	−0.879977	+	0.475016i	$0.842442\pi$
$368$		0			0
$369$	−16.2149	+	16.2149i	−0.844116	+	0.844116i
$370$		0			0
$371$	28.9786	+	5.76421i	1.50450	+	0.299263i
$372$		0			0
$373$	13.4903	−	20.1897i	0.698502	−	1.04538i	−0.297384	−	0.954758i	$-0.596114\pi$
$373$	13.4903	−	20.1897i	0.698502	−	1.04538i	0.995885	−	0.0906234i	$-0.0288860\pi$
$374$		0			0
$375$	−0.331978	+	0.801467i	−0.0171433	+	0.0413876i
$376$		0			0
$377$	0.300123	+	0.724561i	0.0154571	+	0.0373168i
$378$		0			0
$379$	−17.2347	+	3.42819i	−0.885286	+	0.176094i	−0.616735	−	0.787171i	$-0.711545\pi$
$379$	−17.2347	+	3.42819i	−0.885286	+	0.176094i	−0.268551	+	0.963265i	$0.586545\pi$
$380$		0			0
$381$	0.620761	−	0.414779i	0.0318025	−	0.0212498i
$382$		0			0
$383$	16.8809			0.862575			0.431287	−	0.902215i	$-0.358060\pi$
$383$	16.8809			0.862575			0.431287	+	0.902215i	$0.358060\pi$
$384$		0			0
$385$	−57.2502			−2.91774
$386$		0			0
$387$	16.9482	−	11.3244i	0.861526	−	0.575653i
$388$		0			0
$389$	−16.6486	+	3.31162i	−0.844119	+	0.167906i	−0.598162	−	0.801375i	$-0.704102\pi$
$389$	−16.6486	+	3.31162i	−0.844119	+	0.167906i	−0.245957	+	0.969281i	$0.579102\pi$
$390$		0			0
$391$	−1.61298	−	3.89407i	−0.0815717	−	0.196931i
$392$		0			0
$393$	0.544856	−	1.31540i	0.0274844	−	0.0663531i
$394$		0			0
$395$	22.9036	−	34.2776i	1.15240	−	1.72469i
$396$		0			0
$397$	−3.99127	−	0.793913i	−0.200316	−	0.0398454i	0.0939123	−	0.995580i	$-0.470063\pi$
$397$	−3.99127	−	0.793913i	−0.200316	−	0.0398454i	−0.294228	+	0.955735i	$0.595063\pi$
$398$		0			0
$399$	−0.427686	+	0.427686i	−0.0214111	+	0.0214111i
$400$		0			0
$401$	17.0281	+	17.0281i	0.850344	+	0.850344i	0.990175	−	0.139832i	$-0.0446561\pi$
$401$	17.0281	+	17.0281i	0.850344	+	0.850344i	−0.139832	+	0.990175i	$0.544656\pi$
$402$		0			0
$403$	0.848184	−	4.26411i	0.0422510	−	0.212410i
$404$		0			0
$405$	−26.2613	−	17.5473i	−1.30494	−	0.871930i
$406$		0			0
$407$	4.37480	+	1.81210i	0.216851	+	0.0898225i
$408$		0			0
$409$	−26.8028	+	11.1021i	−1.32531	+	0.548963i	−0.929315	−	0.369288i	$-0.879602\pi$
$409$	−26.8028	+	11.1021i	−1.32531	+	0.548963i	−0.395999	+	0.918251i	$0.629602\pi$
$410$		0			0
$411$	−0.262992	−	1.32215i	−0.0129724	−	0.0652168i
$412$		0			0
$413$	6.85159	+	10.2541i	0.337145	+	0.504573i
$414$		0			0
$415$		−	33.4004i		−	1.63956i
$416$		0			0
$417$		−	0.129820i		−	0.00635731i
$418$		0			0
$419$	−5.32427	−	7.96834i	−0.260108	−	0.389279i	0.678313	−	0.734773i	$-0.262711\pi$
$419$	−5.32427	−	7.96834i	−0.260108	−	0.389279i	−0.938421	+	0.345494i	$0.887711\pi$
$420$		0			0
$421$	−6.67598	−	33.5624i	−0.325367	−	1.63573i	−0.704011	−	0.710189i	$-0.748609\pi$
$421$	−6.67598	−	33.5624i	−0.325367	−	1.63573i	0.378644	−	0.925542i	$-0.376391\pi$
$422$		0			0
$423$	−9.07672	+	3.75970i	−0.441325	+	0.182803i
$424$		0			0
$425$	−26.1698	−	10.8399i	−1.26942	−	0.525812i
$426$		0			0
$427$	8.93957	+	5.97323i	0.432616	+	0.289065i
$428$		0			0
$429$	0.105824	−	0.532014i	0.00510923	−	0.0256859i
$430$		0			0
$431$	15.6106	+	15.6106i	0.751934	+	0.751934i	0.974840	−	0.222906i	$-0.0715543\pi$
$431$	15.6106	+	15.6106i	0.751934	+	0.751934i	−0.222906	+	0.974840i	$0.571554\pi$
$432$		0			0
$433$	−2.26932	+	2.26932i	−0.109057	+	0.109057i	−0.759529	−	0.650473i	$-0.774571\pi$
$433$	−2.26932	+	2.26932i	−0.109057	+	0.109057i	0.650473	+	0.759529i	$0.274571\pi$
$434$		0			0
$435$	−0.234027	−	0.0465509i	−0.0112208	−	0.00223195i
$436$		0			0
$437$	1.22259	−	1.82974i	0.0584846	−	0.0875284i
$438$		0			0
$439$	9.28224	−	22.4093i	0.443017	−	1.06954i	−0.531867	−	0.846828i	$-0.678510\pi$
$439$	9.28224	−	22.4093i	0.443017	−	1.06954i	0.974885	−	0.222710i	$-0.0714905\pi$
$440$		0			0
$441$	−3.77360	−	9.11028i	−0.179695	−	0.433823i
$442$		0			0
$443$	−27.8229	+	5.53431i	−1.32190	+	0.262943i	−0.805089	−	0.593154i	$-0.797883\pi$
$443$	−27.8229	+	5.53431i	−1.32190	+	0.262943i	−0.516815	+	0.856097i	$0.672883\pi$
$444$		0			0
$445$	−38.2546	+	25.5609i	−1.81344	+	1.21170i
$446$		0			0
$447$	0.204263			0.00966131
$448$		0			0
$449$	−30.2350			−1.42688			−0.713439	−	0.700717i	$-0.752864\pi$
$449$	−30.2350			−1.42688			−0.713439	+	0.700717i	$0.752864\pi$
$450$		0			0
$451$	−32.1112	+	21.4560i	−1.51206	+	1.01032i
$452$		0			0
$453$	−0.409018	+	0.0813588i	−0.0192174	+	0.00382257i
$454$		0			0
$455$	4.87041	+	11.7582i	0.228328	+	0.551234i
$456$		0			0
$457$	10.5302	−	25.4220i	0.492580	−	1.18919i	−0.460823	−	0.887492i	$-0.652446\pi$
$457$	10.5302	−	25.4220i	0.492580	−	1.18919i	0.953403	−	0.301701i	$-0.0975544\pi$
$458$		0			0
$459$	−1.20156	+	1.79826i	−0.0560841	+	0.0839358i
$460$		0			0
$461$	0.814259	+	0.161966i	0.0379238	+	0.00754352i	0.214016	−	0.976830i	$-0.431346\pi$
$461$	0.814259	+	0.161966i	0.0379238	+	0.00754352i	−0.176092	+	0.984374i	$0.556346\pi$
$462$		0			0
$463$	21.5717	−	21.5717i	1.00252	−	1.00252i	0.00252293	−	0.999997i	$-0.499197\pi$
$463$	21.5717	−	21.5717i	1.00252	−	1.00252i	0.999997	−	0.00252293i	$-0.000803073\pi$
$464$		0			0
$465$	0.935346	+	0.935346i	0.0433756	+	0.0433756i
$466$		0			0
$467$	−1.39757	+	7.02605i	−0.0646717	+	0.325127i	−0.999555	−	0.0298285i	$-0.990504\pi$
$467$	−1.39757	+	7.02605i	−0.0646717	+	0.325127i	0.934883	+	0.354955i	$0.115504\pi$
$468$		0			0
$469$	17.7184	+	11.8391i	0.818161	+	0.546678i
$470$		0			0
$471$	0.332417	+	0.137692i	0.0153170	+	0.00634450i
$472$		0			0
$473$	31.7155	−	13.1370i	1.45828	−	0.604040i
$474$		0			0
$475$	−2.88520	−	14.5049i	−0.132382	−	0.665530i
$476$		0			0
$477$	15.2991	+	22.8967i	0.700496	+	1.04837i
$478$		0			0
$479$			2.21732i			0.101312i	0.998716	+	0.0506560i	$0.0161312\pi$
$479$			2.21732i			0.101312i	−0.998716	+	0.0506560i	$0.983869\pi$
$480$		0			0
$481$		−	1.05267i		−	0.0479975i
$482$		0			0
$483$	−0.192540	−	0.288157i	−0.00876089	−	0.0131116i
$484$		0			0
$485$	−3.65900	−	18.3950i	−0.166146	−	0.835274i
$486$		0			0
$487$	−9.10197	+	3.77016i	−0.412450	+	0.170842i	−0.579253	−	0.815148i	$-0.696656\pi$
$487$	−9.10197	+	3.77016i	−0.412450	+	0.170842i	0.166803	+	0.985990i	$0.446656\pi$
$488$		0			0
$489$	−2.13852	−	0.885805i	−0.0967074	−	0.0400575i
$490$		0			0
$491$	−9.57984	−	6.40104i	−0.432332	−	0.288875i	0.320300	−	0.947316i	$-0.396216\pi$
$491$	−9.57984	−	6.40104i	−0.432332	−	0.288875i	−0.752632	+	0.658441i	$0.771216\pi$
$492$		0			0
$493$	0.512899	−	2.57852i	0.0230998	−	0.116131i
$494$		0			0
$495$	−37.7298	−	37.7298i	−1.69583	−	1.69583i
$496$		0			0
$497$	22.0943	−	22.0943i	0.991064	−	0.991064i
$498$		0			0
$499$	19.6134	+	3.90135i	0.878017	+	0.174649i	0.613464	−	0.789723i	$-0.289776\pi$
$499$	19.6134	+	3.90135i	0.878017	+	0.174649i	0.264553	+	0.964371i	$0.414776\pi$
$500$		0			0
$501$	0.904317	−	1.35341i	0.0404019	−	0.0604658i
$502$		0			0
$503$	−7.62487	+	18.4081i	−0.339976	+	0.820775i	0.657741	+	0.753244i	$0.271512\pi$
$503$	−7.62487	+	18.4081i	−0.339976	+	0.820775i	−0.997717	+	0.0675306i	$0.978488\pi$
$504$		0			0
$505$	21.7533	+	52.5170i	0.968008	+	2.33698i
$506$		0			0
$507$	1.10804	−	0.220402i	0.0492096	−	0.00978840i
$508$		0			0
$509$	−30.1072	+	20.1170i	−1.33448	+	0.891671i	−0.998735	−	0.0502826i	$-0.983988\pi$
$509$	−30.1072	+	20.1170i	−1.33448	+	0.891671i	−0.335744	+	0.941953i	$0.608988\pi$
$510$		0			0
$511$	−5.12102			−0.226540
$512$		0			0
$513$	−1.12918			−0.0498544
$514$		0			0
$515$	55.5747	−	37.1338i	2.44891	−	1.63631i
$516$		0			0
$517$	−16.2281	+	3.22796i	−0.713710	+	0.141966i
$518$		0			0
$519$	0.241971	+	0.584169i	0.0106213	+	0.0256422i
$520$		0			0
$521$	1.49640	−	3.61262i	0.0655583	−	0.158272i	−0.887705	−	0.460413i	$-0.847701\pi$
$521$	1.49640	−	3.61262i	0.0655583	−	0.158272i	0.953263	+	0.302141i	$0.0977014\pi$
$522$		0			0
$523$	−17.6817	+	26.4626i	−0.773168	+	1.15713i	0.210581	+	0.977576i	$0.432465\pi$
$523$	−17.6817	+	26.4626i	−0.773168	+	1.15713i	−0.983749	+	0.179551i	$0.942535\pi$
$524$		0			0
$525$	−2.28430	−	0.454376i	−0.0996952	−	0.0198306i
$526$		0			0
$527$	−10.3057	+	10.3057i	−0.448922	+	0.448922i
$528$		0			0
$529$	−15.3719	−	15.3719i	−0.668341	−	0.668341i
$530$		0			0
$531$	−2.24238	+	11.2732i	−0.0973112	+	0.489216i
$532$		0			0
$533$	7.13847	+	4.76977i	0.309201	+	0.206602i
$534$		0			0
$535$	−16.1868	−	6.70481i	−0.699818	−	0.289874i
$536$		0			0
$537$	2.12157	−	0.878783i	0.0915525	−	0.0379223i
$538$		0			0
$539$	−3.23990	−	16.2881i	−0.139552	−	0.701577i
$540$		0			0
$541$	−8.23111	−	12.3187i	−0.353883	−	0.529623i	0.611231	−	0.791452i	$-0.290674\pi$
$541$	−8.23111	−	12.3187i	−0.353883	−	0.529623i	−0.965114	+	0.261829i	$0.915674\pi$
$542$		0			0
$543$		−	0.863004i		−	0.0370350i
$544$		0			0
$545$			0.862979i			0.0369660i
$546$		0			0
$547$	4.06786	+	6.08798i	0.173929	+	0.260303i	0.908185	−	0.418570i	$-0.137469\pi$
$547$	4.06786	+	6.08798i	0.173929	+	0.260303i	−0.734255	+	0.678873i	$0.762469\pi$
$548$		0			0
$549$	1.95492	+	9.82802i	0.0834338	+	0.419450i
$550$		0			0
$551$	1.26814	−	0.525281i	0.0540246	−	0.0223777i
$552$		0			0
$553$	34.5047	+	14.2923i	1.46729	+	0.607771i
$554$		0			0
$555$	0.266300	+	0.177936i	0.0113038	+	0.00755296i
$556$		0			0
$557$	1.69218	−	8.50718i	0.0717001	−	0.360461i	−0.928233	−	0.371999i	$-0.878673\pi$
$557$	1.69218	−	8.50718i	0.0717001	−	0.360461i	0.999933	+	0.0115376i	$0.00367262\pi$
$558$		0			0
$559$	−5.39623	−	5.39623i	−0.228236	−	0.228236i
$560$		0			0
$561$	−1.28579	+	1.28579i	−0.0542861	+	0.0542861i
$562$		0			0
$563$	4.00239	+	0.796125i	0.168681	+	0.0335527i	0.278708	−	0.960376i	$-0.410094\pi$
$563$	4.00239	+	0.796125i	0.168681	+	0.0335527i	−0.110027	+	0.993929i	$0.535094\pi$
$564$		0			0
$565$	−19.3619	+	28.9771i	−0.814561	+	1.21908i
$566$		0			0
$567$	10.9499	−	26.4353i	0.459851	−	1.11018i
$568$		0			0
$569$	−0.0703648	−	0.169876i	−0.00294984	−	0.00712155i	0.922398	−	0.386241i	$-0.126227\pi$
$569$	−0.0703648	−	0.169876i	−0.00294984	−	0.00712155i	−0.925348	+	0.379120i	$0.876227\pi$
$570$		0			0
$571$	25.5865	−	5.08948i	1.07076	−	0.212988i	0.371921	−	0.928264i	$-0.378699\pi$
$571$	25.5865	−	5.08948i	1.07076	−	0.212988i	0.698842	+	0.715276i	$0.253699\pi$
$572$		0			0
$573$	−1.27805	+	0.853967i	−0.0533914	+	0.0356750i
$574$		0			0
$575$	8.47391			0.353387
$576$		0			0
$577$	3.89521			0.162160			0.0810800	−	0.996708i	$-0.474163\pi$
$577$	3.89521			0.162160			0.0810800	+	0.996708i	$0.474163\pi$
$578$		0			0
$579$	−0.294402	+	0.196713i	−0.0122349	+	0.00817512i
$580$		0			0
$581$	29.6772	−	5.90317i	1.23122	−	0.244905i
$582$		0			0
$583$	17.7478	+	42.8470i	0.735039	+	1.77454i
$584$		0			0
$585$	−4.53929	+	10.9588i	−0.187676	+	0.453091i
$586$		0			0
$587$	5.18453	−	7.75920i	0.213989	−	0.320257i	−0.708910	−	0.705298i	$-0.750813\pi$
$587$	5.18453	−	7.75920i	0.213989	−	0.320257i	0.922899	+	0.385042i	$0.125813\pi$
$588$		0			0
$589$	−7.46312	−	1.48451i	−0.307512	−	0.0611680i
$590$		0			0
$591$	0.768937	−	0.768937i	0.0316299	−	0.0316299i
$592$		0			0
$593$	−32.7658	−	32.7658i	−1.34553	−	1.34553i	−0.890449	−	0.455082i	$-0.849610\pi$
$593$	−32.7658	−	32.7658i	−1.34553	−	1.34553i	−0.455082	−	0.890449i	$-0.650390\pi$
$594$		0			0
$595$	8.32336	−	41.8443i	0.341224	−	1.71545i
$596$		0			0
$597$	0.713670	+	0.476859i	0.0292086	+	0.0195165i
$598$		0			0
$599$	9.21102	+	3.81533i	0.376352	+	0.155890i	0.562837	−	0.826568i	$-0.309710\pi$
$599$	9.21102	+	3.81533i	0.376352	+	0.155890i	−0.186485	+	0.982458i	$0.559710\pi$
$600$		0			0
$601$	−30.1614	+	12.4933i	−1.23031	+	0.509611i	−0.900673	−	0.434497i	$-0.856926\pi$
$601$	−30.1614	+	12.4933i	−1.23031	+	0.509611i	−0.329637	+	0.944108i	$0.606926\pi$
$602$		0			0
$603$	3.87469	+	19.4794i	0.157789	+	0.793261i
$604$		0			0
$605$	−28.2783	−	42.3214i	−1.14967	−	1.72061i
$606$		0			0
$607$		−	5.63753i		−	0.228820i	−0.993434	−	0.114410i	$-0.963502\pi$
$607$		−	5.63753i		−	0.228820i	0.993434	−	0.114410i	$-0.0364978\pi$
$608$		0			0
$609$		−	0.216168i		−	0.00875956i
$610$		0			0
$611$	2.04353	+	3.05836i	0.0826723	+	0.123728i
$612$		0			0
$613$	−7.19644	−	36.1790i	−0.290662	−	1.46125i	−0.799642	−	0.600476i	$-0.794978\pi$
$613$	−7.19644	−	36.1790i	−0.290662	−	1.46125i	0.508981	−	0.860778i	$-0.330022\pi$
$614$		0			0
$615$	−2.41328	+	0.999611i	−0.0973127	+	0.0403082i
$616$		0			0
$617$	−13.8368	−	5.73141i	−0.557050	−	0.230738i	0.0863538	−	0.996265i	$-0.472478\pi$
$617$	−13.8368	−	5.73141i	−0.557050	−	0.230738i	−0.643404	+	0.765527i	$0.722478\pi$
$618$		0			0
$619$	−21.0023	−	14.0333i	−0.844152	−	0.564044i	0.0565907	−	0.998397i	$-0.481977\pi$
$619$	−21.0023	−	14.0333i	−0.844152	−	0.564044i	−0.900743	+	0.434353i	$0.856977\pi$
$620$		0			0
$621$	0.126224	−	0.634570i	0.00506519	−	0.0254644i
$622$		0			0
$623$	−29.4728	−	29.4728i	−1.18080	−	1.18080i
$624$		0			0
$625$	−4.08970	+	4.08970i	−0.163588	+	0.163588i
$626$		0			0
$627$	−0.931139	−	0.185215i	−0.0371861	−	0.00739678i
$628$		0			0
$629$	−1.96050	+	2.93410i	−0.0781703	+	0.116990i
$630$		0			0
$631$	−5.59874	+	13.5166i	−0.222882	+	0.538086i	−0.995279	−	0.0970548i	$-0.969058\pi$
$631$	−5.59874	+	13.5166i	−0.222882	+	0.538086i	0.772397	+	0.635140i	$0.219058\pi$
$632$		0			0
$633$	0.361736	+	0.873308i	0.0143777	+	0.0347109i
$634$		0			0
$635$	−26.9669	+	5.36404i	−1.07015	+	0.212866i
$636$		0			0
$637$	−3.06967	+	2.05108i	−0.121625	+	0.0812669i
$638$		0			0
$639$	29.1217			1.15204
$640$		0			0
$641$	28.7316			1.13483			0.567414	−	0.823432i	$-0.307944\pi$
$641$	28.7316			1.13483			0.567414	+	0.823432i	$0.307944\pi$
$642$		0			0
$643$	29.2315	−	19.5318i	1.15278	−	0.770261i	0.175973	−	0.984395i	$-0.443693\pi$
$643$	29.2315	−	19.5318i	1.15278	−	0.770261i	0.976804	+	0.214134i	$0.0686929\pi$
$644$		0			0
$645$	2.27726	−	0.452975i	0.0896670	−	0.0178359i
$646$		0			0
$647$	−7.41448	−	17.9001i	−0.291493	−	0.703727i	0.708505	−	0.705706i	$-0.249370\pi$
$647$	−7.41448	−	17.9001i	−0.291493	−	0.703727i	−0.999998	+	0.00197916i	$0.999370\pi$
$648$		0			0
$649$	−7.40787	+	17.8842i	−0.290784	+	0.702015i
$650$		0			0
$651$	−0.665771	+	0.996396i	−0.0260936	+	0.0390518i
$652$		0			0
$653$	20.9556	+	4.16833i	0.820057	+	0.163119i	0.587252	−	0.809404i	$-0.300210\pi$
$653$	20.9556	+	4.16833i	0.820057	+	0.163119i	0.232805	+	0.972523i	$0.425210\pi$
$654$		0			0
$655$	−37.0771	+	37.0771i	−1.44872	+	1.44872i
$656$		0			0
$657$	−3.37492	−	3.37492i	−0.131668	−	0.131668i
$658$		0			0
$659$	−4.81340	+	24.1986i	−0.187503	+	0.942643i	0.766362	+	0.642409i	$0.222065\pi$
$659$	−4.81340	+	24.1986i	−0.187503	+	0.942643i	−0.953866	+	0.300234i	$0.902935\pi$
$660$		0			0
$661$	13.2970	+	8.88474i	0.517192	+	0.345576i	0.786613	−	0.617446i	$-0.211833\pi$
$661$	13.2970	+	8.88474i	0.517192	+	0.345576i	−0.269422	+	0.963022i	$0.586833\pi$
$662$		0			0
$663$	0.373465	+	0.154694i	0.0145042	+	0.00600782i
$664$		0			0
$665$	20.5794	−	8.52428i	0.798036	−	0.330557i
$666$		0			0
$667$	0.153437	+	0.771381i	0.00594111	+	0.0298680i
$668$		0			0
$669$	−0.626213	−	0.937193i	−0.0242108	−	0.0362340i
$670$		0			0
$671$			16.8761i			0.651494i
$672$		0			0
$673$			8.00824i			0.308695i	0.988017	+	0.154348i	$0.0493275\pi$
$673$			8.00824i			0.308695i	−0.988017	+	0.154348i	$0.950672\pi$
$674$		0			0
$675$	−2.41569	−	3.61534i	−0.0929801	−	0.139155i
$676$		0			0
$677$	3.48992	+	17.5450i	0.134129	+	0.674310i	0.988078	+	0.153954i	$0.0492008\pi$
$677$	3.48992	+	17.5450i	0.134129	+	0.674310i	−0.853949	+	0.520356i	$0.825799\pi$
$678$		0			0
$679$	15.6978	−	6.50226i	0.602428	−	0.249534i
$680$		0			0
$681$	0.709346	+	0.293821i	0.0271822	+	0.0112592i
$682$		0			0
$683$	19.1391	+	12.7883i	0.732336	+	0.489331i	0.864964	−	0.501835i	$-0.167341\pi$
$683$	19.1391	+	12.7883i	0.732336	+	0.489331i	−0.132628	+	0.991166i	$0.542341\pi$
$684$		0			0
$685$	−9.68546	+	48.6921i	−0.370063	+	1.86043i
$686$		0			0
$687$	1.07078	+	1.07078i	0.0408528	+	0.0408528i
$688$		0			0
$689$	7.29019	−	7.29019i	0.277734	−	0.277734i
$690$		0			0
$691$	−38.0071	−	7.56007i	−1.44586	−	0.287599i	−0.591088	−	0.806607i	$-0.701301\pi$
$691$	−38.0071	−	7.56007i	−1.44586	−	0.287599i	−0.854769	+	0.519008i	$0.826301\pi$
$692$		0			0
$693$	26.8557	−	40.1924i	1.02016	−	1.52678i
$694$		0			0
$695$	−1.82961	+	4.41708i	−0.0694012	+	0.167549i
$696$		0			0
$697$	−11.0137	−	26.5895i	−0.417175	−	1.00715i
$698$		0			0
$699$	0.242517	−	0.0482395i	0.00917282	−	0.00182459i
$700$		0			0
$701$	11.1321	−	7.43826i	0.420455	−	0.280939i	−0.327291	−	0.944923i	$-0.606136\pi$
$701$	11.1321	−	7.43826i	0.420455	−	0.280939i	0.747747	+	0.663984i	$0.231136\pi$
$702$		0			0
$703$	−1.84240			−0.0694874
$704$		0			0
$705$	−1.11911			−0.0421483
$706$		0			0
$707$	−42.8183	+	28.6103i	−1.61035	+	1.07600i
$708$		0			0
$709$	−20.5812	+	4.09386i	−0.772944	+	0.153748i	−0.565778	−	0.824558i	$-0.691424\pi$
$709$	−20.5812	+	4.09386i	−0.772944	+	0.153748i	−0.207166	+	0.978306i	$0.566424\pi$
$710$		0			0
$711$	13.3206	+	32.1588i	0.499562	+	1.20605i
$712$		0			0
$713$	1.66851	−	4.02814i	0.0624862	−	0.150855i
$714$		0			0
$715$	−11.0986	+	16.6102i	−0.415062	+	0.621185i
$716$		0			0
$717$	1.93060	+	0.384020i	0.0720996	+	0.0143415i
$718$		0			0
$719$	14.9402	−	14.9402i	0.557174	−	0.557174i	−0.371328	−	0.928502i	$-0.621097\pi$
$719$	14.9402	−	14.9402i	0.557174	−	0.557174i	0.928502	+	0.371328i	$0.121097\pi$
$720$		0			0
$721$	42.8168	+	42.8168i	1.59458	+	1.59458i
$722$		0			0
$723$	−0.366616	+	1.84310i	−0.0136346	+	0.0685457i
$724$		0			0
$725$	4.39480	+	2.93651i	0.163219	+	0.109059i
$726$		0			0
$727$	25.4837	+	10.5557i	0.945139	+	0.391489i	0.801402	−	0.598127i	$-0.204088\pi$
$727$	25.4837	+	10.5557i	0.945139	+	0.391489i	0.143737	+	0.989616i	$0.454088\pi$
$728$		0			0
$729$	24.4844	−	10.1418i	0.906831	−	0.375622i
$730$		0			0
$731$	4.99089	+	25.0909i	0.184595	+	0.928020i
$732$		0			0
$733$	22.0843	+	33.0515i	0.815702	+	1.22078i	0.972442	+	0.233145i	$0.0749017\pi$
$733$	22.0843	+	33.0515i	0.815702	+	1.22078i	−0.156740	+	0.987640i	$0.550098\pi$
$734$		0			0
$735$		−	1.12325i		−	0.0414318i
$736$		0			0
$737$			33.4488i			1.23210i
$738$		0			0
$739$	19.4284	+	29.0766i	0.714685	+	1.06960i	0.993998	+	0.109402i	$0.0348934\pi$
$739$	19.4284	+	29.0766i	0.714685	+	1.06960i	−0.279313	+	0.960200i	$0.590107\pi$
$740$		0			0
$741$	0.0411742	+	0.206997i	0.00151257	+	0.00760421i
$742$		0			0
$743$	−21.9574	+	9.09505i	−0.805539	+	0.333665i	−0.747172	−	0.664630i	$-0.768589\pi$
$743$	−21.9574	+	9.09505i	−0.805539	+	0.333665i	−0.0583662	+	0.998295i	$0.518589\pi$
$744$		0			0
$745$	−6.94998	−	2.87878i	−0.254628	−	0.105470i
$746$		0			0
$747$	23.4486	+	15.6679i	0.857941	+	0.573258i
$748$		0			0
$749$	3.09657	−	15.5675i	0.113146	−	0.568824i
$750$		0			0
$751$	29.0783	+	29.0783i	1.06108	+	1.06108i	0.998009	+	0.0630715i	$0.0200896\pi$
$751$	29.0783	+	29.0783i	1.06108	+	1.06108i	0.0630715	+	0.998009i	$0.479910\pi$
$752$		0			0
$753$	−1.01904	+	1.01904i	−0.0371357	+	0.0371357i
$754$		0			0
$755$	15.0633	+	2.99628i	0.548211	+	0.109046i
$756$		0			0
$757$	8.14810	−	12.1945i	0.296148	−	0.443216i	−0.653320	−	0.757082i	$-0.726624\pi$
$757$	8.14810	−	12.1945i	0.296148	−	0.443216i	0.949467	+	0.313866i	$0.101624\pi$
$758$		0			0
$759$	0.208173	−	0.502573i	0.00755619	−	0.0182422i
$760$		0			0
$761$	1.19079	+	2.87483i	0.0431662	+	0.104212i	0.943992	−	0.329968i	$-0.107038\pi$
$761$	1.19079	+	2.87483i	0.0431662	+	0.104212i	−0.900826	+	0.434181i	$0.857038\pi$
$762$		0			0
$763$	−0.766783	+	0.152523i	−0.0277594	+	0.00552169i
$764$		0			0
$765$	33.0621	−	22.0914i	1.19536	−	0.798717i
$766$		0			0
$767$	4.30331			0.155383
$768$		0			0
$769$	−1.71536			−0.0618576			−0.0309288	−	0.999522i	$-0.509847\pi$
$769$	−1.71536			−0.0618576			−0.0309288	+	0.999522i	$0.509847\pi$
$770$		0			0
$771$	−1.95380	+	1.30549i	−0.0703643	+	0.0470159i
$772$		0			0
$773$	42.9791	−	8.54907i	1.54585	−	0.307489i	0.652830	−	0.757505i	$-0.273582\pi$
$773$	42.9791	−	8.54907i	1.54585	−	0.307489i	0.893020	+	0.450016i	$0.148582\pi$
$774$		0			0
$775$	−11.2131	−	27.0709i	−0.402787	−	0.972414i
$776$		0			0
$777$	−0.111036	+	0.268064i	−0.00398338	+	0.00961674i
$778$		0			0
$779$	8.34814	−	12.4939i	0.299103	−	0.447639i
$780$		0			0
$781$	48.1028	+	9.56824i	1.72125	+	0.342378i
$782$		0			0
$783$	0.285364	−	0.285364i	0.0101981	−	0.0101981i
$784$		0			0
$785$	−9.36983	−	9.36983i	−0.334424	−	0.334424i
$786$		0			0
$787$	−4.53406	+	22.7942i	−0.161622	+	0.812527i	0.811876	+	0.583830i	$0.198446\pi$
$787$	−4.53406	+	22.7942i	−0.161622	+	0.812527i	−0.973498	+	0.228697i	$0.926554\pi$
$788$		0			0
$789$	−1.31909	−	0.881385i	−0.0469607	−	0.0313781i
$790$		0			0
$791$	−29.1691	−	12.0822i	−1.03713	−	0.429595i
$792$		0			0
$793$	3.46606	−	1.43569i	0.123083	−	0.0509828i
$794$		0			0
$795$	0.611959	+	3.07653i	0.0217040	+	0.109113i
$796$		0			0
$797$	13.4092	+	20.0683i	0.474979	+	0.710856i	0.989163	−	0.146824i	$-0.0469050\pi$
$797$	13.4092	+	20.0683i	0.474979	+	0.710856i	−0.514184	+	0.857680i	$0.671905\pi$
$798$		0			0
$799$		−	12.3304i		−	0.436219i
$800$		0			0
$801$		−	38.8470i		−	1.37259i
$802$		0			0
$803$	−4.46577	−	6.68350i	−0.157594	−	0.235856i
$804$		0			0
$805$	2.48999	+	12.5180i	0.0877605	+	0.441202i
$806$		0			0
$807$	0.559777	−	0.231867i	0.0197051	−	0.00816211i
$808$		0			0
$809$	13.0913	+	5.42259i	0.460266	+	0.190648i	0.600754	−	0.799434i	$-0.294867\pi$
$809$	13.0913	+	5.42259i	0.460266	+	0.190648i	−0.140488	+	0.990082i	$0.544867\pi$
$810$		0			0
$811$	−40.1862	−	26.8515i	−1.41113	−	0.942885i	−0.999503	−	0.0315313i	$-0.989962\pi$
$811$	−40.1862	−	26.8515i	−1.41113	−	0.942885i	−0.411624	−	0.911354i	$-0.635038\pi$
$812$		0			0
$813$	0.583835	−	2.93513i	0.0204760	−	0.102940i
$814$		0			0
$815$	60.2785	+	60.2785i	2.11146	+	2.11146i
$816$		0			0
$817$	−9.44458	+	9.44458i	−0.330424	+	0.330424i
$818$		0			0
$819$	−10.5395	−	2.09644i	−0.368280	−	0.0732555i
$820$		0			0
$821$	−19.0683	+	28.5378i	−0.665489	+	0.995975i	0.333101	+	0.942891i	$0.391905\pi$
$821$	−19.0683	+	28.5378i	−0.665489	+	0.995975i	−0.998590	+	0.0530841i	$0.983095\pi$
$822$		0			0
$823$	−10.9732	+	26.4916i	−0.382500	+	0.923437i	0.608981	+	0.793185i	$0.291579\pi$
$823$	−10.9732	+	26.4916i	−0.382500	+	0.923437i	−0.991481	+	0.130252i	$0.958421\pi$
$824$		0			0
$825$	−1.39901	−	3.37751i	−0.0487073	−	0.117590i
$826$		0			0
$827$	−5.52679	+	1.09935i	−0.192185	+	0.0382280i	−0.290244	−	0.956953i	$-0.593737\pi$
$827$	−5.52679	+	1.09935i	−0.192185	+	0.0382280i	0.0980591	+	0.995181i	$0.468737\pi$
$828$		0			0
$829$	25.3564	−	16.9426i	0.880663	−	0.588440i	−0.0309356	−	0.999521i	$-0.509849\pi$
$829$	25.3564	−	16.9426i	0.880663	−	0.588440i	0.911599	+	0.411081i	$0.134849\pi$
$830$		0			0
$831$	−1.94962			−0.0676314
$832$		0			0
$833$	12.3760			0.428804
$834$		0			0
$835$	−49.8433	+	33.3042i	−1.72490	+	1.15254i
$836$		0			0
$837$	−2.19423	+	0.436460i	−0.0758438	+	0.0150863i
$838$		0			0
$839$	−18.4654	−	44.5794i	−0.637496	−	1.53905i	−0.830004	−	0.557757i	$-0.811662\pi$
$839$	−18.4654	−	44.5794i	−0.637496	−	1.53905i	0.192508	−	0.981295i	$-0.438338\pi$
$840$		0			0
$841$	10.9101	−	26.3393i	0.376210	−	0.908251i
$842$		0			0
$843$	1.21673	−	1.82096i	0.0419064	−	0.0627173i
$844$		0			0
$845$	−40.8068	−	8.11698i	−1.40380	−	0.279232i
$846$		0			0
$847$	32.6060	−	32.6060i	1.12035	−	1.12035i
$848$		0			0
$849$	−2.04043	−	2.04043i	−0.0700274	−	0.0700274i
$850$		0			0
$851$	0.205950	−	1.03538i	0.00705989	−	0.0354924i
$852$		0			0
$853$	−27.7758	−	18.5592i	−0.951025	−	0.635455i	−0.0197631	−	0.999805i	$-0.506291\pi$
$853$	−27.7758	−	18.5592i	−0.951025	−	0.635455i	−0.931262	+	0.364350i	$0.881291\pi$
$854$		0			0
$855$	19.1803	+	7.94474i	0.655952	+	0.271704i
$856$		0			0
$857$	−18.0760	+	7.48732i	−0.617464	+	0.255762i	−0.669416	−	0.742888i	$-0.733456\pi$
$857$	−18.0760	+	7.48732i	−0.617464	+	0.255762i	0.0519523	+	0.998650i	$0.483456\pi$
$858$		0			0
$859$	−5.83867	−	29.3530i	−0.199213	−	1.00151i	−0.942924	−	0.333009i	$-0.891936\pi$
$859$	−5.83867	−	29.3530i	−0.199213	−	1.00151i	0.743711	−	0.668501i	$-0.233064\pi$
$860$		0			0
$861$	−1.31471	−	1.96760i	−0.0448051	−	0.0670555i
$862$		0			0
$863$			6.59334i			0.224440i	0.993683	+	0.112220i	$0.0357961\pi$
$863$			6.59334i			0.224440i	−0.993683	+	0.112220i	$0.964204\pi$
$864$		0			0
$865$		−	23.2864i		−	0.791760i
$866$		0			0
$867$	0.155531	+	0.232769i	0.00528212	+	0.00790525i
$868$		0			0
$869$	11.4367	+	57.4960i	0.387962	+	1.95042i
$870$		0			0
$871$	6.86980	−	2.84556i	0.232774	−	0.0964183i
$872$		0			0
$873$	14.6306	+	6.06019i	0.495170	+	0.205106i
$874$		0			0
$875$	24.0654	+	16.0800i	0.813560	+	0.543603i
$876$		0			0
$877$	8.27377	−	41.5950i	0.279385	−	1.40456i	−0.544953	−	0.838467i	$-0.683452\pi$
$877$	8.27377	−	41.5950i	0.279385	−	1.40456i	0.824338	−	0.566098i	$-0.191548\pi$
$878$		0			0
$879$	−1.25257	−	1.25257i	−0.0422480	−	0.0422480i
$880$		0			0
$881$	−16.3212	+	16.3212i	−0.549874	+	0.549874i	−0.926404	−	0.376530i	$-0.877117\pi$
$881$	−16.3212	+	16.3212i	−0.549874	+	0.549874i	0.376530	+	0.926404i	$0.377117\pi$
$882$		0			0
$883$	26.8219	+	5.33522i	0.902630	+	0.179544i	0.624524	−	0.781006i	$-0.285293\pi$
$883$	26.8219	+	5.33522i	0.902630	+	0.179544i	0.278107	+	0.960550i	$0.410293\pi$
$884$		0			0
$885$	−0.727402	+	1.08863i	−0.0244513	+	0.0365940i
$886$		0			0
$887$	−2.57395	+	6.21406i	−0.0864248	+	0.208648i	−0.961183	−	0.275912i	$-0.911020\pi$
$887$	−2.57395	+	6.21406i	−0.0864248	+	0.208648i	0.874758	+	0.484560i	$0.161020\pi$
$888$		0			0
$889$	−9.53223	−	23.0128i	−0.319701	−	0.771826i
$890$		0			0
$891$	44.0498	−	8.76205i	1.47572	−	0.293540i
$892$		0			0
$893$	5.35279	−	3.57662i	0.179124	−	0.119687i
$894$		0			0
$895$	−84.5708			−2.82689
$896$		0			0
$897$	−0.120930			−0.00403772
$898$		0			0
$899$	2.26123	−	1.51090i	0.0754162	−	0.0503915i
$900$		0			0
$901$	−33.8972	+	6.74258i	−1.12928	+	0.224628i
$902$		0			0
$903$	0.804964	+	1.94336i	0.0267875	+	0.0646708i
$904$		0			0
$905$	−12.1627	+	29.3634i	−0.404303	+	0.976073i
$906$		0			0
$907$	−17.8600	+	26.7294i	−0.593033	+	0.887537i	−0.999660	−	0.0260574i	$-0.991705\pi$
$907$	−17.8600	+	26.7294i	−0.593033	+	0.887537i	0.406627	+	0.913594i	$0.366705\pi$
$908$		0			0
$909$	−47.0738	−	9.36356i	−1.56134	−	0.310570i
$910$		0			0
$911$	−7.66743	+	7.66743i	−0.254033	+	0.254033i	−0.822622	−	0.568589i	$-0.807490\pi$
$911$	−7.66743	+	7.66743i	−0.254033	+	0.254033i	0.568589	+	0.822622i	$0.307490\pi$
$912$		0			0
$913$	33.5843	+	33.5843i	1.11148	+	1.11148i
$914$		0			0
$915$	−0.222684	+	1.11951i	−0.00736171	+	0.0370098i
$916$		0			0
$917$	−39.4971	−	26.3911i	−1.30431	−	0.871512i
$918$		0			0
$919$	−45.2071	−	18.7254i	−1.49124	−	0.617693i	−0.519656	−	0.854376i	$-0.673940\pi$
$919$	−45.2071	−	18.7254i	−1.49124	−	0.617693i	−0.971587	+	0.236682i	$0.923940\pi$
$920$		0			0
$921$	0.0566026	−	0.0234456i	0.00186512	−	0.000772558i
$922$		0			0
$923$	−2.12706	−	10.6935i	−0.0700132	−	0.351980i
$924$		0			0
$925$	−3.94151	−	5.89889i	−0.129596	−	0.193954i
$926$		0			0
$927$			56.4353i			1.85358i
$928$		0			0
$929$			31.1191i			1.02098i	0.859883	+	0.510492i	$0.170537\pi$
$929$			31.1191i			1.02098i	−0.859883	+	0.510492i	$0.829463\pi$
$930$		0			0
$931$	3.58984	+	5.37258i	0.117652	+	0.176079i
$932$		0			0
$933$	0.190160	+	0.956001i	0.00622557	+	0.0312981i
$934$		0			0
$935$	61.8699	−	25.6273i	2.02336	−	0.838104i
$936$		0			0
$937$	−17.7192	−	7.33952i	−0.578860	−	0.239772i	0.0739899	−	0.997259i	$-0.476427\pi$
$937$	−17.7192	−	7.33952i	−0.578860	−	0.239772i	−0.652850	+	0.757487i	$0.726427\pi$
$938$		0			0
$939$	−1.58997	−	1.06239i	−0.0518868	−	0.0346696i
$940$		0			0
$941$	0.147266	−	0.740357i	0.00480074	−	0.0241350i	−0.978311	−	0.207143i	$-0.933583\pi$
$941$	0.147266	−	0.740357i	0.00480074	−	0.0241350i	0.983111	+	0.183008i	$0.0585835\pi$
$942$		0			0
$943$	6.08806	+	6.08806i	0.198254	+	0.198254i
$944$		0			0
$945$	4.63090	−	4.63090i	0.150643	−	0.150643i
$946$		0			0
$947$	−20.3435	−	4.04657i	−0.661074	−	0.131496i	−0.146860	−	0.989157i	$-0.546917\pi$
$947$	−20.3435	−	4.04657i	−0.661074	−	0.131496i	−0.514215	+	0.857662i	$0.671917\pi$
$948$		0			0
$949$	−0.992762	+	1.48577i	−0.0322264	+	0.0482302i
$950$		0			0
$951$	−0.412162	+	0.995046i	−0.0133653	+	0.0322666i
$952$		0			0
$953$	−3.75053	−	9.05459i	−0.121492	−	0.293307i	0.851420	−	0.524485i	$-0.175742\pi$
$953$	−3.75053	−	9.05459i	−0.121492	−	0.293307i	−0.972911	+	0.231178i	$0.925742\pi$
$954$		0			0
$955$	55.5206	−	11.0437i	1.79661	−	0.357367i
$956$		0			0
$957$	0.282123	−	0.188509i	0.00911975	−	0.00609362i
$958$		0			0
$959$	−44.9762			−1.45236
$960$		0			0
$961$	15.9238			0.513670
$962$		0			0
$963$	12.3002	−	8.21875i	0.396370	−	0.264846i
$964$		0			0
$965$	12.7893	−	2.54395i	0.411702	−	0.0818926i
$966$		0			0
$967$	−14.0556	−	33.9332i	−0.451997	−	1.09122i	−0.971562	−	0.236787i	$-0.923906\pi$
$967$	−14.0556	−	33.9332i	−0.451997	−	1.09122i	0.519564	−	0.854431i	$-0.326094\pi$
$968$		0			0
$969$	0.270748	−	0.653644i	0.00869769	−	0.0209981i
$970$		0			0
$971$	19.9404	−	29.8428i	0.639916	−	0.957702i	−0.359779	−	0.933037i	$-0.617148\pi$
$971$	19.9404	−	29.8428i	0.639916	−	0.957702i	0.999696	−	0.0246651i	$-0.00785194\pi$
$972$		0			0
$973$	−4.24807	−	0.844994i	−0.136187	−	0.0270893i
$974$		0			0
$975$	−0.574665	+	0.574665i	−0.0184040	+	0.0184040i
$976$		0			0
$977$	−17.1968	−	17.1968i	−0.550174	−	0.550174i	0.376317	−	0.926491i	$-0.377190\pi$
$977$	−17.1968	−	17.1968i	−0.550174	−	0.550174i	−0.926491	+	0.376317i	$0.877190\pi$
$978$		0			0
$979$	12.7636	−	64.1669i	0.407926	−	2.05078i
$980$		0			0
$981$	−0.605852	−	0.404818i	−0.0193434	−	0.0129248i
$982$		0			0
$983$	45.7275	+	18.9410i	1.45848	+	0.604123i	0.964199	−	0.265178i	$-0.0854309\pi$
$983$	45.7275	+	18.9410i	1.45848	+	0.604123i	0.494282	+	0.869301i	$0.335431\pi$
$984$		0			0
$985$	−36.9998	+	15.3258i	−1.17891	+	0.488322i
$986$		0			0
$987$	−0.197792	−	0.994367i	−0.00629579	−	0.0316511i
$988$		0			0
$989$	−4.25187	−	6.36337i	−0.135201	−	0.202343i
$990$		0			0
$991$		−	19.1024i		−	0.606808i	−0.952862	−	0.303404i	$-0.901877\pi$
$991$		−	19.1024i		−	0.606808i	0.952862	−	0.303404i	$-0.0981232\pi$
$992$		0			0
$993$			0.450997i			0.0143120i
$994$		0			0
$995$	−17.5618	−	26.2831i	−0.556746	−	0.833229i
$996$		0			0
$997$	9.04071	+	45.4507i	0.286322	+	1.43944i	0.809452	+	0.587186i	$0.199764\pi$
$997$	9.04071	+	45.4507i	0.286322	+	1.43944i	−0.523130	+	0.852253i	$0.675236\pi$
$998$		0			0
$999$	−0.500451	+	0.207293i	−0.0158336	+	0.00655847i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.i.b.33.4		56
4.3	odd	2		512.2.i.a.33.4		56
8.3	odd	2		256.2.i.a.145.4		56
8.5	even	2		64.2.i.a.13.6	yes	56
24.5	odd	2		576.2.bd.a.397.2		56
64.5	even	16	inner	512.2.i.b.481.4		56
64.27	odd	16		256.2.i.a.113.4		56
64.37	even	16		64.2.i.a.5.6	✓	56
64.59	odd	16		512.2.i.a.481.4		56
192.101	odd	16		576.2.bd.a.325.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.5.6	✓	56	64.37	even	16
64.2.i.a.13.6	yes	56	8.5	even	2
256.2.i.a.113.4		56	64.27	odd	16
256.2.i.a.145.4		56	8.3	odd	2
512.2.i.a.33.4		56	4.3	odd	2
512.2.i.a.481.4		56	64.59	odd	16
512.2.i.b.33.4		56	1.1	even	1	trivial
512.2.i.b.481.4		56	64.5	even	16	inner
576.2.bd.a.325.2		56	192.101	odd	16
576.2.bd.a.397.2		56	24.5	odd	2

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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0799701 + 0.0534343i) q^{3} +(3.47403 - 0.691028i) q^{5} +(1.22800 + 2.96465i) q^{7} +(-1.14451 + 2.76309i) q^{9} +O(q^{10})\)	\(q+(-0.0799701 + 0.0534343i) q^{3} +(3.47403 - 0.691028i) q^{5} +(1.22800 + 2.96465i) q^{7} +(-1.14451 + 2.76309i) q^{9} +(-2.79833 + 4.18799i) q^{11} +(1.09820 + 0.218446i) q^{13} +(-0.240894 + 0.240894i) q^{15} +(-2.65418 - 2.65418i) q^{17} +(0.382328 - 1.92209i) q^{19} +(-0.256617 - 0.171466i) q^{21} +(1.03743 + 0.429717i) q^{23} +(6.97198 - 2.88789i) q^{25} +(-0.112408 - 0.565114i) q^{27} +(0.389126 + 0.582369i) q^{29} -3.88281i q^{31} -0.484441i q^{33} +(6.31476 + 9.45071i) q^{35} +(-0.183408 - 0.922056i) q^{37} +(-0.0994958 + 0.0412125i) q^{39} +(7.08379 + 2.93420i) q^{41} +(-5.66688 - 3.78649i) q^{43} +(-2.06669 + 10.3900i) q^{45} +(2.32284 + 2.32284i) q^{47} +(-2.33143 + 2.33143i) q^{49} +(0.354079 + 0.0704307i) q^{51} +(5.11546 - 7.65583i) q^{53} +(-6.82746 + 16.4829i) q^{55} +(0.0721309 + 0.174139i) q^{57} +(3.76937 - 0.749773i) q^{59} +(2.78586 - 1.86145i) q^{61} -9.59706 q^{63} +3.96614 q^{65} +(5.52163 - 3.68943i) q^{67} +(-0.105925 + 0.0210698i) q^{69} +(-3.72629 - 8.99606i) q^{71} +(-0.610714 + 1.47439i) q^{73} +(-0.403237 + 0.603488i) q^{75} +(-15.8523 - 3.15321i) q^{77} +(8.22980 - 8.22980i) q^{79} +(-6.30515 - 6.30515i) q^{81} +(1.83962 - 9.24837i) q^{83} +(-11.0548 - 7.38658i) q^{85} +(-0.0622370 - 0.0257794i) q^{87} +(-12.0003 + 4.97070i) q^{89} +(0.700974 + 3.52403i) q^{91} +(0.207475 + 0.310509i) q^{93} -6.94161i q^{95} -5.29500i q^{97} +(-8.36909 - 12.5252i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9	\( 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{17} + 8 q^{19} + 8 q^{21} - 8 q^{23} - 8 q^{25} + 8 q^{27} + 8 q^{29} + 8 q^{35} + 8 q^{37} - 8 q^{39} - 8 q^{41} + 8 q^{43} + 8 q^{45} - 8 q^{47} - 8 q^{49} - 24 q^{51} + 8 q^{53} + 56 q^{55} - 8 q^{57} - 56 q^{59} + 8 q^{61} + 64 q^{63} - 16 q^{65} - 72 q^{67} + 8 q^{69} + 56 q^{71} - 8 q^{73} - 56 q^{75} + 8 q^{77} + 24 q^{79} - 8 q^{81} + 8 q^{83} + 8 q^{85} - 8 q^{87} - 8 q^{89} + 8 q^{91} - 16 q^{93} - 16 q^{99}+O(q^{100}) \) 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9 + 8 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^17 + 8 * q^19 + 8 * q^21 - 8 * q^23 - 8 * q^25 + 8 * q^27 + 8 * q^29 + 8 * q^35 + 8 * q^37 - 8 * q^39 - 8 * q^41 + 8 * q^43 + 8 * q^45 - 8 * q^47 - 8 * q^49 - 24 * q^51 + 8 * q^53 + 56 * q^55 - 8 * q^57 - 56 * q^59 + 8 * q^61 + 64 * q^63 - 16 * q^65 - 72 * q^67 + 8 * q^69 + 56 * q^71 - 8 * q^73 - 56 * q^75 + 8 * q^77 + 24 * q^79 - 8 * q^81 + 8 * q^83 + 8 * q^85 - 8 * q^87 - 8 * q^89 + 8 * q^91 - 16 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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