LMFDB - Embedded newform 572.2.n.b.157.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(53,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("572.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.n (of order $5$, degree $4$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.2
Character	$\chi$	$=$	572.157
Dual form			572.2.n.b.521.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.527342 - 1.62299i) q^{3} +(1.55733 + 1.13147i) q^{5} +(-0.0663952 + 0.204343i) q^{7} +(0.0710371 - 0.0516114i) q^{9} +O(q^{10})$	\(q+(-0.527342 - 1.62299i) q^{3} +(1.55733 + 1.13147i) q^{5} +(-0.0663952 + 0.204343i) q^{7} +(0.0710371 - 0.0516114i) q^{9} +(1.41985 + 2.99733i) q^{11} +(0.809017 - 0.587785i) q^{13} +(1.01511 - 3.12420i) q^{15} +(5.55513 + 4.03604i) q^{17} +(-1.19762 - 3.68590i) q^{19} +0.366661 q^{21} +3.40222 q^{23} +(-0.400026 - 1.23115i) q^{25} +(-4.26302 - 3.09727i) q^{27} +(-0.0803737 + 0.247365i) q^{29} +(1.10209 - 0.800713i) q^{31} +(4.11590 - 3.88503i) q^{33} +(-0.334607 + 0.243106i) q^{35} +(-0.532729 + 1.63957i) q^{37} +(-1.38060 - 1.00306i) q^{39} +(-0.417008 - 1.28342i) q^{41} +1.40814 q^{43} +0.169025 q^{45} +(-3.71349 - 11.4290i) q^{47} +(5.62577 + 4.08736i) q^{49} +(3.62101 - 11.1443i) q^{51} +(5.54245 - 4.02682i) q^{53} +(-1.18020 + 6.27435i) q^{55} +(-5.35063 + 3.88746i) q^{57} +(-1.14735 + 3.53119i) q^{59} +(8.20693 + 5.96268i) q^{61} +(0.00582994 + 0.0179427i) q^{63} +1.92496 q^{65} -8.18413 q^{67} +(-1.79413 - 5.52177i) q^{69} +(-7.53057 - 5.47128i) q^{71} +(1.76232 - 5.42386i) q^{73} +(-1.78720 + 1.29848i) q^{75} +(-0.706757 + 0.0911292i) q^{77} +(-2.80919 + 2.04100i) q^{79} +(-2.69737 + 8.30165i) q^{81} +(8.07251 + 5.86502i) q^{83} +(4.08453 + 12.5709i) q^{85} +0.443856 q^{87} -6.53627 q^{89} +(0.0663952 + 0.204343i) q^{91} +(-1.88073 - 1.36643i) q^{93} +(2.30538 - 7.09522i) q^{95} +(-10.9695 + 7.96978i) q^{97} +(0.255559 + 0.139641i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.527342	−	1.62299i	−0.304461	−	0.937035i	−0.979878	−	0.199599i	$-0.936036\pi$
$3$	−0.527342	−	1.62299i	−0.304461	−	0.937035i	0.675417	−	0.737436i	$-0.263964\pi$
$4$		0			0
$5$	1.55733	+	1.13147i	0.696459	+	0.506007i	0.878777	−	0.477233i	$-0.158360\pi$
$5$	1.55733	+	1.13147i	0.696459	+	0.506007i	−0.182318	+	0.983240i	$0.558360\pi$
$6$		0			0
$7$	−0.0663952	+	0.204343i	−0.0250950	+	0.0772345i	−0.962820	−	0.270145i	$-0.912928\pi$
$7$	−0.0663952	+	0.204343i	−0.0250950	+	0.0772345i	0.937725	+	0.347379i	$0.112928\pi$
$8$		0			0
$9$	0.0710371	−	0.0516114i	0.0236790	−	0.0172038i
$10$		0			0
$11$	1.41985	+	2.99733i	0.428102	+	0.903730i
$11$	1.41985	+	2.99733i	0.428102	+	0.903730i
$12$		0			0
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$		0			0
$15$	1.01511	−	3.12420i	0.262102	−	0.806666i
$16$		0			0
$17$	5.55513	+	4.03604i	1.34732	+	0.978883i	0.999140	+	0.0414546i	$0.0131992\pi$
$17$	5.55513	+	4.03604i	1.34732	+	0.978883i	0.348177	+	0.937429i	$0.386801\pi$
$18$		0			0
$19$	−1.19762	−	3.68590i	−0.274753	−	0.845603i	−0.989285	−	0.146000i	$-0.953360\pi$
$19$	−1.19762	−	3.68590i	−0.274753	−	0.845603i	0.714532	−	0.699603i	$-0.246640\pi$
$20$		0			0
$21$	0.366661			0.0800119
$22$		0			0
$23$	3.40222			0.709412			0.354706	−	0.934978i	$-0.384581\pi$
$23$	3.40222			0.709412			0.354706	+	0.934978i	$0.384581\pi$
$24$		0			0
$25$	−0.400026	−	1.23115i	−0.0800053	−	0.246231i
$26$		0			0
$27$	−4.26302	−	3.09727i	−0.820419	−	0.596070i
$28$		0			0
$29$	−0.0803737	+	0.247365i	−0.0149250	+	0.0459345i	−0.958242	−	0.285960i	$-0.907688\pi$
$29$	−0.0803737	+	0.247365i	−0.0149250	+	0.0459345i	0.943317	+	0.331894i	$0.107688\pi$
$30$		0			0
$31$	1.10209	−	0.800713i	0.197941	−	0.143812i	−0.484400	−	0.874847i	$-0.660962\pi$
$31$	1.10209	−	0.800713i	0.197941	−	0.143812i	0.682341	+	0.731034i	$0.260962\pi$
$32$		0			0
$33$	4.11590	−	3.88503i	0.716487	−	0.676297i
$34$		0			0
$35$	−0.334607	+	0.243106i	−0.0565588	+	0.0410924i
$36$		0			0
$37$	−0.532729	+	1.63957i	−0.0875802	+	0.269544i	−0.985249	−	0.171127i	$-0.945259\pi$
$37$	−0.532729	+	1.63957i	−0.0875802	+	0.269544i	0.897669	+	0.440671i	$0.145259\pi$
$38$		0			0
$39$	−1.38060	−	1.00306i	−0.221073	−	0.160619i
$40$		0			0
$41$	−0.417008	−	1.28342i	−0.0651257	−	0.200436i	0.913199	−	0.407515i	$-0.133604\pi$
$41$	−0.417008	−	1.28342i	−0.0651257	−	0.200436i	−0.978324	+	0.207078i	$0.933604\pi$
$42$		0			0
$43$	1.40814			0.214740			0.107370	−	0.994219i	$-0.465757\pi$
$43$	1.40814			0.214740			0.107370	+	0.994219i	$0.465757\pi$
$44$		0			0
$45$	0.169025			0.0251967
$46$		0			0
$47$	−3.71349	−	11.4290i	−0.541669	−	1.66709i	−0.728781	−	0.684747i	$-0.759913\pi$
$47$	−3.71349	−	11.4290i	−0.541669	−	1.66709i	0.187112	−	0.982339i	$-0.440087\pi$
$48$		0			0
$49$	5.62577	+	4.08736i	0.803682	+	0.583909i
$50$		0			0
$51$	3.62101	−	11.1443i	0.507042	−	1.56052i
$52$		0			0
$53$	5.54245	−	4.02682i	0.761314	−	0.553127i	−0.137999	−	0.990432i	$-0.544067\pi$
$53$	5.54245	−	4.02682i	0.761314	−	0.553127i	0.899313	+	0.437306i	$0.144067\pi$
$54$		0			0
$55$	−1.18020	+	6.27435i	−0.159138	+	0.846033i
$56$		0			0
$57$	−5.35063	+	3.88746i	−0.708708	+	0.514906i
$58$		0			0
$59$	−1.14735	+	3.53119i	−0.149373	+	0.459722i	−0.997547	−	0.0699949i	$-0.977702\pi$
$59$	−1.14735	+	3.53119i	−0.149373	+	0.459722i	0.848175	+	0.529717i	$0.177702\pi$
$60$		0			0
$61$	8.20693	+	5.96268i	1.05079	+	0.763443i	0.972362	−	0.233476i	$-0.0750102\pi$
$61$	8.20693	+	5.96268i	1.05079	+	0.763443i	0.0784272	+	0.996920i	$0.475010\pi$
$62$		0			0
$63$	0.00582994	+	0.0179427i	0.000734503	+	0.00226057i
$64$		0			0
$65$	1.92496			0.238762
$66$		0			0
$67$	−8.18413			−0.999851			−0.499926	−	0.866068i	$-0.666639\pi$
$67$	−8.18413			−0.999851			−0.499926	+	0.866068i	$0.666639\pi$
$68$		0			0
$69$	−1.79413	−	5.52177i	−0.215988	−	0.664744i
$70$		0			0
$71$	−7.53057	−	5.47128i	−0.893714	−	0.649321i	0.0431300	−	0.999069i	$-0.486267\pi$
$71$	−7.53057	−	5.47128i	−0.893714	−	0.649321i	−0.936844	+	0.349748i	$0.886267\pi$
$72$		0			0
$73$	1.76232	−	5.42386i	0.206264	−	0.634815i	−0.793395	−	0.608707i	$-0.791689\pi$
$73$	1.76232	−	5.42386i	0.206264	−	0.634815i	0.999659	−	0.0261079i	$-0.00831136\pi$
$74$		0			0
$75$	−1.78720	+	1.29848i	−0.206368	+	0.149935i
$76$		0			0
$77$	−0.706757	+	0.0911292i	−0.0805424	+	0.0103851i
$78$		0			0
$79$	−2.80919	+	2.04100i	−0.316059	+	0.229630i	−0.734492	−	0.678618i	$-0.762579\pi$
$79$	−2.80919	+	2.04100i	−0.316059	+	0.229630i	0.418433	+	0.908248i	$0.362579\pi$
$80$		0			0
$81$	−2.69737	+	8.30165i	−0.299708	+	0.922405i
$82$		0			0
$83$	8.07251	+	5.86502i	0.886073	+	0.643770i	0.934851	−	0.355040i	$-0.115533\pi$
$83$	8.07251	+	5.86502i	0.886073	+	0.643770i	−0.0487779	+	0.998810i	$0.515533\pi$
$84$		0			0
$85$	4.08453	+	12.5709i	0.443029	+	1.36350i
$86$		0			0
$87$	0.443856			0.0475863
$88$		0			0
$89$	−6.53627			−0.692843			−0.346422	−	0.938079i	$-0.612603\pi$
$89$	−6.53627			−0.692843			−0.346422	+	0.938079i	$0.612603\pi$
$90$		0			0
$91$	0.0663952	+	0.204343i	0.00696011	+	0.0214210i
$92$		0			0
$93$	−1.88073	−	1.36643i	−0.195022	−	0.141692i
$94$		0			0
$95$	2.30538	−	7.09522i	0.236527	−	0.727954i
$96$		0			0
$97$	−10.9695	+	7.96978i	−1.11378	+	0.809209i	−0.983255	−	0.182236i	$-0.941666\pi$
$97$	−10.9695	+	7.96978i	−1.11378	+	0.809209i	−0.130525	+	0.991445i	$0.541666\pi$
$98$		0			0
$99$	0.255559	+	0.139641i	0.0256846	+	0.0140345i
$100$		0			0
$101$	−9.65944	+	7.01799i	−0.961150	+	0.698317i	−0.953418	−	0.301654i	$-0.902461\pi$
$101$	−9.65944	+	7.01799i	−0.961150	+	0.698317i	−0.00773267	+	0.999970i	$0.502461\pi$
$102$		0			0
$103$	−0.985432	+	3.03285i	−0.0970975	+	0.298835i	−0.987795	−	0.155762i	$-0.950217\pi$
$103$	−0.985432	+	3.03285i	−0.0970975	+	0.298835i	0.890697	+	0.454597i	$0.150217\pi$
$104$		0			0
$105$	0.571011	+	0.414864i	0.0557250	+	0.0404866i
$106$		0			0
$107$	4.67637	+	14.3924i	0.452082	+	1.39137i	0.874527	+	0.484977i	$0.161172\pi$
$107$	4.67637	+	14.3924i	0.452082	+	1.39137i	−0.422445	+	0.906389i	$0.638828\pi$
$108$		0			0
$109$	−18.5976			−1.78133			−0.890663	−	0.454665i	$-0.849759\pi$
$109$	−18.5976			−1.78133			−0.890663	+	0.454665i	$0.849759\pi$
$110$		0			0
$111$	2.94194			0.279237
$112$		0			0
$113$	4.13269	+	12.7191i	0.388771	+	1.19651i	0.933708	+	0.358037i	$0.116554\pi$
$113$	4.13269	+	12.7191i	0.388771	+	1.19651i	−0.544937	+	0.838477i	$0.683446\pi$
$114$		0			0
$115$	5.29837	+	3.84949i	0.494076	+	0.358967i
$116$		0			0
$117$	0.0271337	−	0.0835091i	0.00250852	−	0.00772042i
$118$		0			0
$119$	−1.19357	+	0.867181i	−0.109415	+	0.0794943i
$120$		0			0
$121$	−6.96803	+	8.51156i	−0.633457	+	0.773778i
$122$		0			0
$123$	−1.86307	+	1.35360i	−0.167988	+	0.122050i
$124$		0			0
$125$	3.74427	−	11.5237i	0.334898	−	1.03071i
$126$		0			0
$127$	10.2308	+	7.43313i	0.907839	+	0.659584i	0.940467	−	0.339884i	$-0.110388\pi$
$127$	10.2308	+	7.43313i	0.907839	+	0.659584i	−0.0326285	+	0.999468i	$0.510388\pi$
$128$		0			0
$129$	−0.742573	−	2.28540i	−0.0653799	−	0.201219i
$130$		0			0
$131$	−13.8481			−1.20992			−0.604958	−	0.796257i	$-0.706810\pi$
$131$	−13.8481			−1.20992			−0.604958	+	0.796257i	$0.706810\pi$
$132$		0			0
$133$	0.832705			0.0722047
$134$		0			0
$135$	−3.13448	−	9.64693i	−0.269773	−	0.830276i
$136$		0			0
$137$	−1.05177	−	0.764158i	−0.0898591	−	0.0652865i	0.541949	−	0.840412i	$-0.317687\pi$
$137$	−1.05177	−	0.764158i	−0.0898591	−	0.0652865i	−0.631808	+	0.775125i	$0.717687\pi$
$138$		0			0
$139$	−1.95848	+	6.02759i	−0.166116	+	0.511254i	−0.999117	−	0.0420186i	$-0.986621\pi$
$139$	−1.95848	+	6.02759i	−0.166116	+	0.511254i	0.833000	+	0.553272i	$0.186621\pi$
$140$		0			0
$141$	−16.5908	+	12.0539i	−1.39720	+	1.01513i
$142$		0			0
$143$	2.91048	+	1.59033i	0.243386	+	0.132990i
$144$		0			0
$145$	−0.405053	+	0.294288i	−0.0336378	+	0.0244393i
$146$		0			0
$147$	3.66705	−	11.2860i	0.302453	−	0.930855i
$148$		0			0
$149$	−4.46495	−	3.24398i	−0.365783	−	0.265757i	0.389677	−	0.920952i	$-0.372587\pi$
$149$	−4.46495	−	3.24398i	−0.365783	−	0.265757i	−0.755460	+	0.655195i	$0.772587\pi$
$150$		0			0
$151$	−1.64384	−	5.05923i	−0.133774	−	0.411714i	0.861623	−	0.507548i	$-0.169448\pi$
$151$	−1.64384	−	5.05923i	−0.133774	−	0.411714i	−0.995397	+	0.0958341i	$0.969448\pi$
$152$		0			0
$153$	0.602926			0.0487437
$154$		0			0
$155$	2.62229			0.210627
$156$		0			0
$157$	−5.97024	−	18.3745i	−0.476477	−	1.46645i	−0.843955	−	0.536414i	$-0.819779\pi$
$157$	−5.97024	−	18.3745i	−0.476477	−	1.46645i	0.367478	−	0.930032i	$-0.380221\pi$
$158$		0			0
$159$	−9.45827	−	6.87183i	−0.750090	−	0.544972i
$160$		0			0
$161$	−0.225891	+	0.695221i	−0.0178027	+	0.0547911i
$162$		0			0
$163$	−6.41904	+	4.66370i	−0.502778	+	0.365289i	−0.810077	−	0.586324i	$-0.800575\pi$
$163$	−6.41904	+	4.66370i	−0.502778	+	0.365289i	0.307299	+	0.951613i	$0.400575\pi$
$164$		0			0
$165$	10.8056	−	1.39327i	0.841214	−	0.108466i
$166$		0			0
$167$	10.5596	−	7.67200i	0.817127	−	0.593678i	−0.0987611	−	0.995111i	$-0.531488\pi$
$167$	10.5596	−	7.67200i	0.817127	−	0.593678i	0.915888	+	0.401434i	$0.131488\pi$
$168$		0			0
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$		0			0
$171$	−0.275310	−	0.200024i	−0.0210535	−	0.0152962i
$172$		0			0
$173$	−0.830171	−	2.55500i	−0.0631167	−	0.194253i	0.914526	−	0.404528i	$-0.132564\pi$
$173$	−0.830171	−	2.55500i	−0.0631167	−	0.194253i	−0.977642	+	0.210275i	$0.932564\pi$
$174$		0			0
$175$	0.278138			0.0210253
$176$		0			0
$177$	6.33614			0.476253
$178$		0			0
$179$	−6.40650	−	19.7172i	−0.478844	−	1.47373i	−0.840702	−	0.541498i	$-0.817858\pi$
$179$	−6.40650	−	19.7172i	−0.478844	−	1.47373i	0.361858	−	0.932233i	$-0.382142\pi$
$180$		0			0
$181$	−2.30138	−	1.67205i	−0.171060	−	0.124283i	0.498961	−	0.866624i	$-0.333715\pi$
$181$	−2.30138	−	1.67205i	−0.171060	−	0.124283i	−0.670021	+	0.742342i	$0.733715\pi$
$182$		0			0
$183$	5.34953	−	16.4642i	0.395449	−	1.21707i
$184$		0			0
$185$	−2.68475	+	1.95059i	−0.197387	+	0.143410i
$186$		0			0
$187$	−4.20988	+	22.3812i	−0.307857	+	1.63667i
$188$		0			0
$189$	0.915951	−	0.665477i	0.0666256	−	0.0484063i
$190$		0			0
$191$	4.32477	−	13.3103i	0.312930	−	0.963098i	−0.663669	−	0.748027i	$-0.731002\pi$
$191$	4.32477	−	13.3103i	0.312930	−	0.963098i	0.976598	−	0.215072i	$-0.0689985\pi$
$192$		0			0
$193$	10.3730	+	7.53644i	0.746666	+	0.542485i	0.894792	−	0.446484i	$-0.147324\pi$
$193$	10.3730	+	7.53644i	0.746666	+	0.542485i	−0.148126	+	0.988969i	$0.547324\pi$
$194$		0			0
$195$	−1.01511	−	3.12420i	−0.0726939	−	0.223729i
$196$		0			0
$197$	−1.81806			−0.129531			−0.0647656	−	0.997901i	$-0.520630\pi$
$197$	−1.81806			−0.129531			−0.0647656	+	0.997901i	$0.520630\pi$
$198$		0			0
$199$	8.86903			0.628709			0.314355	−	0.949306i	$-0.398212\pi$
$199$	8.86903			0.628709			0.314355	+	0.949306i	$0.398212\pi$
$200$		0			0
$201$	4.31584	+	13.2828i	0.304416	+	0.936895i
$202$		0			0
$203$	−0.0452109	−	0.0328477i	−0.00317319	−	0.00230545i
$204$		0			0
$205$	0.802725	−	2.47053i	0.0560648	−	0.172550i
$206$		0			0
$207$	0.241684	−	0.175593i	0.0167982	−	0.0122046i
$208$		0			0
$209$	9.34742	−	8.82311i	0.646575	−	0.610307i
$210$		0			0
$211$	−21.8484	+	15.8738i	−1.50411	+	1.09280i	−0.535395	+	0.844601i	$0.679837\pi$
$211$	−21.8484	+	15.8738i	−1.50411	+	1.09280i	−0.968710	+	0.248195i	$0.920163\pi$
$212$		0			0
$213$	−4.90865	+	15.1073i	−0.336335	+	1.03513i
$214$		0			0
$215$	2.19294	+	1.59327i	0.149557	+	0.108660i
$216$		0			0
$217$	0.0904471	+	0.278367i	0.00613995	+	0.0188968i
$218$		0			0
$219$	−9.73222			−0.657643
$220$		0			0
$221$	6.86652			0.461892
$222$		0			0
$223$	−2.89064	−	8.89649i	−0.193572	−	0.595753i	−0.999990	−	0.00440747i	$-0.998597\pi$
$223$	−2.89064	−	8.89649i	−0.193572	−	0.595753i	0.806418	−	0.591345i	$-0.201403\pi$
$224$		0			0
$225$	−0.0919583	−	0.0668116i	−0.00613056	−	0.00445411i
$226$		0			0
$227$	−3.49376	+	10.7527i	−0.231889	+	0.713680i	0.765630	+	0.643281i	$0.222427\pi$
$227$	−3.49376	+	10.7527i	−0.231889	+	0.713680i	−0.997519	+	0.0703993i	$0.977573\pi$
$228$		0			0
$229$	−15.7564	+	11.4477i	−1.04121	+	0.756484i	−0.970522	−	0.241014i	$-0.922520\pi$
$229$	−15.7564	+	11.4477i	−1.04121	+	0.756484i	−0.0706898	+	0.997498i	$0.522520\pi$
$230$		0			0
$231$	0.520605	+	1.09900i	0.0342533	+	0.0723092i
$232$		0			0
$233$	17.0671	−	12.4000i	1.11811	−	0.812351i	0.134185	−	0.990956i	$-0.457158\pi$
$233$	17.0671	−	12.4000i	1.11811	−	0.812351i	0.983921	+	0.178605i	$0.0571584\pi$
$234$		0			0
$235$	7.14834	−	22.0003i	0.466307	−	1.43514i
$236$		0			0
$237$	4.79393	+	3.48299i	0.311399	+	0.226245i
$238$		0			0
$239$	1.76657	+	5.43694i	0.114270	+	0.351687i	0.991794	−	0.127846i	$-0.0408063\pi$
$239$	1.76657	+	5.43694i	0.114270	+	0.351687i	−0.877524	+	0.479532i	$0.840806\pi$
$240$		0			0
$241$	6.57563			0.423574			0.211787	−	0.977316i	$-0.432072\pi$
$241$	6.57563			0.423574			0.211787	+	0.977316i	$0.432072\pi$
$242$		0			0
$243$	−0.912217			−0.0585188
$244$		0			0
$245$	4.13647	+	12.7307i	0.264269	+	0.813337i
$246$		0			0
$247$	−3.13541	−	2.27801i	−0.199501	−	0.144946i
$248$		0			0
$249$	5.26191	−	16.1945i	0.333460	−	1.02628i
$250$		0			0
$251$	12.6237	−	9.17165i	0.796801	−	0.578910i	−0.113173	−	0.993575i	$-0.536101\pi$
$251$	12.6237	−	9.17165i	0.796801	−	0.578910i	0.909974	+	0.414666i	$0.136101\pi$
$252$		0			0
$253$	4.83065	+	10.1976i	0.303701	+	0.641117i
$254$		0			0
$255$	18.2485	−	13.2583i	1.14277	−	0.830268i
$256$		0			0
$257$	5.19089	−	15.9759i	0.323799	−	0.996551i	−0.648181	−	0.761486i	$-0.724470\pi$
$257$	5.19089	−	15.9759i	0.323799	−	0.996551i	0.971980	−	0.235064i	$-0.0755301\pi$
$258$		0			0
$259$	−0.299665	−	0.217719i	−0.0186203	−	0.0135284i
$260$		0			0
$261$	0.00705735	+	0.0217203i	0.000436839	+	0.00134445i
$262$		0			0
$263$	−5.90881			−0.364353			−0.182176	−	0.983266i	$-0.558314\pi$
$263$	−5.90881			−0.364353			−0.182176	+	0.983266i	$0.558314\pi$
$264$		0			0
$265$	13.1876			0.810109
$266$		0			0
$267$	3.44685	+	10.6083i	0.210944	+	0.649218i
$268$		0			0
$269$	−20.7555	−	15.0798i	−1.26549	−	0.919429i	−0.266472	−	0.963843i	$-0.585858\pi$
$269$	−20.7555	−	15.0798i	−1.26549	−	0.919429i	−0.999013	+	0.0444135i	$0.985858\pi$
$270$		0			0
$271$	−5.26880	+	16.2157i	−0.320057	+	0.985034i	0.653566	+	0.756870i	$0.273272\pi$
$271$	−5.26880	+	16.2157i	−0.320057	+	0.985034i	−0.973623	+	0.228164i	$0.926728\pi$
$272$		0			0
$273$	0.296635	−	0.215518i	0.0179531	−	0.0130437i
$274$		0			0
$275$	3.12220	−	2.94707i	0.188276	−	0.177715i
$276$		0			0
$277$	−3.07659	+	2.23528i	−0.184855	+	0.134305i	−0.676364	−	0.736568i	$-0.736445\pi$
$277$	−3.07659	+	2.23528i	−0.184855	+	0.134305i	0.491509	+	0.870872i	$0.336445\pi$
$278$		0			0
$279$	0.0369630	−	0.113761i	0.00221292	−	0.00681067i
$280$		0			0
$281$	−6.71726	−	4.88038i	−0.400718	−	0.291139i	0.369115	−	0.929384i	$-0.379661\pi$
$281$	−6.71726	−	4.88038i	−0.400718	−	0.291139i	−0.769833	+	0.638245i	$0.779661\pi$
$282$		0			0
$283$	7.10643	+	21.8713i	0.422434	+	1.30012i	0.905430	+	0.424495i	$0.139548\pi$
$283$	7.10643	+	21.8713i	0.422434	+	1.30012i	−0.482997	+	0.875622i	$0.660452\pi$
$284$		0			0
$285$	−12.7312			−0.754132
$286$		0			0
$287$	0.289945			0.0171149
$288$		0			0
$289$	9.31659	+	28.6735i	0.548034	+	1.68668i
$290$		0			0
$291$	18.7196	+	13.6006i	1.09736	+	0.797278i
$292$		0			0
$293$	5.68243	−	17.4887i	0.331971	−	1.02170i	−0.636224	−	0.771504i	$-0.719505\pi$
$293$	5.68243	−	17.4887i	0.331971	−	1.02170i	0.968195	−	0.250197i	$-0.0804954\pi$
$294$		0			0
$295$	−5.78222	+	4.20103i	−0.336654	+	0.244594i
$296$		0			0
$297$	3.23068	−	17.1754i	0.187463	−	0.996617i
$298$		0			0
$299$	2.75245	−	1.99977i	0.159178	−	0.115650i
$300$		0			0
$301$	−0.0934939	+	0.287745i	−0.00538890	+	0.0165853i
$302$		0			0
$303$	16.4840	+	11.9763i	0.946980	+	0.688021i
$304$		0			0
$305$	6.03432	+	18.5717i	0.345524	+	1.06341i
$306$		0			0
$307$	26.8988			1.53520			0.767598	−	0.640931i	$-0.221452\pi$
$307$	26.8988			1.53520			0.767598	+	0.640931i	$0.221452\pi$
$308$		0			0
$309$	5.44195			0.309582
$310$		0			0
$311$	0.670930	+	2.06491i	0.0380450	+	0.117090i	0.968275	−	0.249886i	$-0.0803931\pi$
$311$	0.670930	+	2.06491i	0.0380450	+	0.117090i	−0.930230	+	0.366976i	$0.880393\pi$
$312$		0			0
$313$	−8.72698	−	6.34053i	−0.493278	−	0.358388i	0.313165	−	0.949699i	$-0.398611\pi$
$313$	−8.72698	−	6.34053i	−0.493278	−	0.358388i	−0.806444	+	0.591311i	$0.798611\pi$
$314$		0			0
$315$	−0.0112224	+	0.0345391i	−0.000632312	+	0.00194606i
$316$		0			0
$317$	−24.7971	+	18.0161i	−1.39274	+	1.01189i	−0.397183	+	0.917739i	$0.630012\pi$
$317$	−24.7971	+	18.0161i	−1.39274	+	1.01189i	−0.995558	+	0.0941469i	$0.969988\pi$
$318$		0			0
$319$	−0.855554	+	0.110315i	−0.0479018	+	0.00617646i
$320$		0			0
$321$	20.8927	−	15.1794i	1.16612	−	0.847234i
$322$		0			0
$323$	8.22349	−	25.3093i	0.457567	−	1.40825i
$324$		0			0
$325$	−1.04728	−	0.760895i	−0.0580928	−	0.0422069i
$326$		0			0
$327$	9.80729	+	30.1837i	0.542344	+	1.66916i
$328$		0			0
$329$	2.58199			0.142350
$330$		0			0
$331$	−15.3315			−0.842696			−0.421348	−	0.906899i	$-0.638443\pi$
$331$	−15.3315			−0.842696			−0.421348	+	0.906899i	$0.638443\pi$
$332$		0			0
$333$	0.0467772	+	0.143965i	0.00256337	+	0.00788925i
$334$		0			0
$335$	−12.7454	−	9.26007i	−0.696355	−	0.505931i
$336$		0			0
$337$	6.60848	−	20.3388i	0.359987	−	1.10793i	−0.593074	−	0.805148i	$-0.702086\pi$
$337$	6.60848	−	20.3388i	0.359987	−	1.10793i	0.953061	−	0.302778i	$-0.0979140\pi$
$338$		0			0
$339$	18.4637	−	13.4147i	1.00281	−	0.728584i
$340$		0			0
$341$	3.96481	+	2.16643i	0.214706	+	0.117319i
$342$		0			0
$343$	−2.42552	+	1.76225i	−0.130966	+	0.0951523i
$344$		0			0
$345$	3.45364	−	10.6292i	0.185938	−	0.572258i
$346$		0			0
$347$	−20.0053	−	14.5347i	−1.07394	−	0.780262i	−0.0973222	−	0.995253i	$-0.531028\pi$
$347$	−20.0053	−	14.5347i	−1.07394	−	0.780262i	−0.976616	+	0.214991i	$0.931028\pi$
$348$		0			0
$349$	−9.13977	−	28.1293i	−0.489241	−	1.50573i	−0.825743	−	0.564046i	$-0.809244\pi$
$349$	−9.13977	−	28.1293i	−0.489241	−	1.50573i	0.336502	−	0.941683i	$-0.390756\pi$
$350$		0			0
$351$	−5.26939			−0.281259
$352$		0			0
$353$	37.0720			1.97314			0.986572	−	0.163330i	$-0.0522234\pi$
$353$	37.0720			1.97314			0.986572	+	0.163330i	$0.0522234\pi$
$354$		0			0
$355$	−5.53701	−	17.0412i	−0.293874	−	0.904450i
$356$		0			0
$357$	2.03685	+	1.47986i	0.107801	+	0.0783223i
$358$		0			0
$359$	5.50492	−	16.9424i	0.290538	−	0.894185i	−0.694145	−	0.719835i	$-0.744217\pi$
$359$	5.50492	−	16.9424i	0.290538	−	0.894185i	0.984684	−	0.174350i	$-0.0557825\pi$
$360$		0			0
$361$	3.21978	−	2.33930i	0.169462	−	0.123121i
$362$		0			0
$363$	17.4887	+	6.82055i	0.917920	+	0.357986i
$364$		0			0
$365$	8.88142	−	6.45273i	0.464875	−	0.337751i
$366$		0			0
$367$	−1.74281	+	5.36381i	−0.0909738	+	0.279989i	−0.986183	−	0.165657i	$-0.947026\pi$
$367$	−1.74281	+	5.36381i	−0.0909738	+	0.279989i	0.895210	+	0.445645i	$0.147026\pi$
$368$		0			0
$369$	−0.0958621	−	0.0696479i	−0.00499038	−	0.00362572i
$370$		0			0
$371$	0.454863	+	1.39992i	0.0236153	+	0.0726804i
$372$		0			0
$373$	−4.65851			−0.241208			−0.120604	−	0.992701i	$-0.538483\pi$
$373$	−4.65851			−0.241208			−0.120604	+	0.992701i	$0.538483\pi$
$374$		0			0
$375$	−20.6773			−1.06777
$376$		0			0
$377$	0.0803737	+	0.247365i	0.00413946	+	0.0127399i
$378$		0			0
$379$	−14.4899	−	10.5275i	−0.744296	−	0.540763i	0.149757	−	0.988723i	$-0.452151\pi$
$379$	−14.4899	−	10.5275i	−0.744296	−	0.540763i	−0.894054	+	0.447960i	$0.852151\pi$
$380$		0			0
$381$	6.66877	−	20.5244i	0.341651	−	1.05149i
$382$		0			0
$383$	−19.4938	+	14.1631i	−0.996085	+	0.723698i	−0.961245	−	0.275695i	$-0.911092\pi$
$383$	−19.4938	+	14.1631i	−0.996085	+	0.723698i	−0.0348399	+	0.999393i	$0.511092\pi$
$384$		0			0
$385$	−1.20376	−	0.657753i	−0.0613494	−	0.0335222i
$386$		0			0
$387$	0.100030	−	0.0726763i	0.00508483	−	0.00369434i
$388$		0			0
$389$	0.128390	−	0.395143i	0.00650962	−	0.0200346i	−0.947749	−	0.319017i	$-0.896647\pi$
$389$	0.128390	−	0.395143i	0.00650962	−	0.0200346i	0.954259	+	0.298983i	$0.0966472\pi$
$390$		0			0
$391$	18.8998	+	13.7315i	0.955803	+	0.694431i
$392$		0			0
$393$	7.30270	+	22.4754i	0.368372	+	1.13373i
$394$		0			0
$395$	−6.68415			−0.336316
$396$		0			0
$397$	−27.3398			−1.37214			−0.686072	−	0.727534i	$-0.740667\pi$
$397$	−27.3398			−1.37214			−0.686072	+	0.727534i	$0.740667\pi$
$398$		0			0
$399$	−0.439120	−	1.35147i	−0.0219835	−	0.0676583i
$400$		0			0
$401$	−4.59469	−	3.33823i	−0.229448	−	0.166703i	0.467122	−	0.884193i	$-0.345291\pi$
$401$	−4.59469	−	3.33823i	−0.229448	−	0.166703i	−0.696569	+	0.717490i	$0.745291\pi$
$402$		0			0
$403$	0.420960	−	1.29558i	0.0209695	−	0.0645374i
$404$		0			0
$405$	−13.5937	+	9.87642i	−0.675477	+	0.490763i
$406$		0			0
$407$	−5.67075	+	0.731186i	−0.281088	+	0.0362435i
$408$		0			0
$409$	13.8594	−	10.0694i	0.685303	−	0.497902i	−0.189810	−	0.981821i	$-0.560787\pi$
$409$	13.8594	−	10.0694i	0.685303	−	0.497902i	0.875113	+	0.483919i	$0.160787\pi$
$410$		0			0
$411$	−0.685578	+	2.10999i	−0.0338171	+	0.104078i
$412$		0			0
$413$	−0.645396	−	0.468908i	−0.0317579	−	0.0230734i
$414$		0			0
$415$	5.93548	+	18.2675i	0.291361	+	0.896718i
$416$		0			0
$417$	10.8155			0.529639
$418$		0			0
$419$	−8.30658			−0.405803			−0.202901	−	0.979199i	$-0.565037\pi$
$419$	−8.30658			−0.405803			−0.202901	+	0.979199i	$0.565037\pi$
$420$		0			0
$421$	1.25238	+	3.85443i	0.0610372	+	0.187853i	0.976926	−	0.213580i	$-0.0685123\pi$
$421$	1.25238	+	3.85443i	0.0610372	+	0.187853i	−0.915888	+	0.401433i	$0.868512\pi$
$422$		0			0
$423$	−0.853661	−	0.620221i	−0.0415064	−	0.0301562i
$424$		0			0
$425$	2.74679	−	8.45375i	0.133239	−	0.410067i
$426$		0			0
$427$	−1.76334	+	1.28114i	−0.0853338	+	0.0619986i
$428$		0			0
$429$	1.04627	−	5.56232i	0.0505144	−	0.268552i
$430$		0			0
$431$	−8.76179	+	6.36581i	−0.422041	+	0.306630i	−0.778458	−	0.627696i	$-0.783998\pi$
$431$	−8.76179	+	6.36581i	−0.422041	+	0.306630i	0.356418	+	0.934327i	$0.383998\pi$
$432$		0			0
$433$	3.13645	−	9.65299i	0.150728	−	0.463893i	−0.846975	−	0.531633i	$-0.821579\pi$
$433$	3.13645	−	9.65299i	0.150728	−	0.463893i	0.997703	+	0.0677397i	$0.0215787\pi$
$434$		0			0
$435$	0.691229	+	0.502207i	0.0331419	+	0.0240790i
$436$		0			0
$437$	−4.07457	−	12.5402i	−0.194913	−	0.599881i
$438$		0			0
$439$	−25.5044			−1.21726			−0.608630	−	0.793454i	$-0.708281\pi$
$439$	−25.5044			−1.21726			−0.608630	+	0.793454i	$0.708281\pi$
$440$		0			0
$441$	0.610593			0.0290759
$442$		0			0
$443$	9.62247	+	29.6149i	0.457177	+	1.40705i	0.868560	+	0.495584i	$0.165046\pi$
$443$	9.62247	+	29.6149i	0.457177	+	1.40705i	−0.411383	+	0.911463i	$0.634954\pi$
$444$		0			0
$445$	−10.1791	−	7.39556i	−0.482537	−	0.350583i
$446$		0			0
$447$	−2.91039	+	8.95727i	−0.137657	+	0.423664i
$448$		0			0
$449$	−17.9356	+	13.0310i	−0.846432	+	0.614969i	−0.924160	−	0.382006i	$-0.875234\pi$
$449$	−17.9356	+	13.0310i	−0.846432	+	0.614969i	0.0777277	+	0.996975i	$0.475234\pi$
$450$		0			0
$451$	3.25474	−	3.07218i	0.153260	−	0.144663i
$452$		0			0
$453$	−7.34422	+	5.33589i	−0.345062	+	0.250702i
$454$		0			0
$455$	−0.127808	+	0.393354i	−0.00599175	+	0.0184407i
$456$		0			0
$457$	−11.0175	−	8.00465i	−0.515375	−	0.374442i	0.299484	−	0.954101i	$-0.403186\pi$
$457$	−11.0175	−	8.00465i	−0.515375	−	0.374442i	−0.814859	+	0.579660i	$0.803186\pi$
$458$		0			0
$459$	−11.1810	−	34.4115i	−0.521883	−	1.60619i
$460$		0			0
$461$	21.3616			0.994910			0.497455	−	0.867490i	$-0.334268\pi$
$461$	21.3616			0.994910			0.497455	+	0.867490i	$0.334268\pi$
$462$		0			0
$463$	15.5264			0.721575			0.360787	−	0.932648i	$-0.382508\pi$
$463$	15.5264			0.721575			0.360787	+	0.932648i	$0.382508\pi$
$464$		0			0
$465$	−1.38284	−	4.25596i	−0.0641278	−	0.197365i
$466$		0			0
$467$	−3.05695	−	2.22100i	−0.141459	−	0.102776i	0.514805	−	0.857307i	$-0.327864\pi$
$467$	−3.05695	−	2.22100i	−0.141459	−	0.102776i	−0.656264	+	0.754531i	$0.727864\pi$
$468$		0			0
$469$	0.543387	−	1.67237i	0.0250913	−	0.0772230i
$470$		0			0
$471$	−26.6733	+	19.3793i	−1.22904	+	0.892951i
$472$		0			0
$473$	1.99936	+	4.22068i	0.0919305	+	0.194067i
$474$		0			0
$475$	−4.05883	+	2.94891i	−0.186232	+	0.135305i
$476$		0			0
$477$	0.185889	−	0.572107i	0.00851127	−	0.0261950i
$478$		0			0
$479$	27.5141	+	19.9902i	1.25715	+	0.913374i	0.998614	−	0.0526267i	$-0.0167593\pi$
$479$	27.5141	+	19.9902i	1.25715	+	0.913374i	0.258538	+	0.966001i	$0.416759\pi$
$480$		0			0
$481$	0.532729	+	1.63957i	0.0242904	+	0.0747581i
$482$		0			0
$483$	1.24746			0.0567614
$484$		0			0
$485$	−26.1006			−1.18517
$486$		0			0
$487$	−0.679753	−	2.09207i	−0.0308026	−	0.0948005i	0.934473	−	0.356033i	$-0.115871\pi$
$487$	−0.679753	−	2.09207i	−0.0308026	−	0.0948005i	−0.965276	+	0.261233i	$0.915871\pi$
$488$		0			0
$489$	10.9542	+	7.95868i	0.495365	+	0.359904i
$490$		0			0
$491$	−8.68614	+	26.7332i	−0.392000	+	1.20645i	0.539274	+	0.842131i	$0.318699\pi$
$491$	−8.68614	+	26.7332i	−0.392000	+	1.20645i	−0.931274	+	0.364321i	$0.881301\pi$
$492$		0			0
$493$	−1.44486	+	1.04975i	−0.0650733	+	0.0472785i
$494$		0			0
$495$	0.239990	+	0.506623i	0.0107868	+	0.0227710i
$496$		0			0
$497$	1.61801	−	1.17555i	0.0725778	−	0.0527308i
$498$		0			0
$499$	−9.22490	+	28.3913i	−0.412963	+	1.27097i	0.501097	+	0.865391i	$0.332930\pi$
$499$	−9.22490	+	28.3913i	−0.412963	+	1.27097i	−0.914060	+	0.405579i	$0.867070\pi$
$500$		0			0
$501$	−18.0201	−	13.0924i	−0.805080	−	0.584925i
$502$		0			0
$503$	−4.65069	−	14.3133i	−0.207364	−	0.638201i	−0.999608	−	0.0279963i	$-0.991087\pi$
$503$	−4.65069	−	14.3133i	−0.207364	−	0.638201i	0.792244	−	0.610204i	$-0.208913\pi$
$504$		0			0
$505$	−22.9835			−1.02275
$506$		0			0
$507$	−1.70651			−0.0757890
$508$		0			0
$509$	2.92114	+	8.99034i	0.129477	+	0.398490i	0.994690	−	0.102915i	$-0.0328168\pi$
$509$	2.92114	+	8.99034i	0.129477	+	0.398490i	−0.865213	+	0.501405i	$0.832817\pi$
$510$		0			0
$511$	0.991320	+	0.720236i	0.0438534	+	0.0318614i
$512$		0			0
$513$	−6.31073	+	19.4224i	−0.278625	+	0.857521i
$514$		0			0
$515$	−4.96620	+	3.60816i	−0.218837	+	0.158994i
$516$		0			0
$517$	28.9838	−	27.3580i	1.27471	−	1.20321i
$518$		0			0
$519$	−3.70897	+	2.69472i	−0.162806	+	0.118285i
$520$		0			0
$521$	6.24420	−	19.2177i	0.273563	−	0.841942i	−0.716032	−	0.698067i	$-0.754044\pi$
$521$	6.24420	−	19.2177i	0.273563	−	0.841942i	0.989596	−	0.143875i	$-0.0459562\pi$
$522$		0			0
$523$	10.9702	+	7.97028i	0.479691	+	0.348516i	0.801206	−	0.598388i	$-0.204192\pi$
$523$	10.9702	+	7.97028i	0.479691	+	0.348516i	−0.321515	+	0.946905i	$0.604192\pi$
$524$		0			0
$525$	−0.146674	−	0.451416i	−0.00640137	−	0.0197014i
$526$		0			0
$527$	9.35394			0.407464
$528$		0			0
$529$	−11.4249			−0.496735
$530$		0			0
$531$	0.100745	+	0.310062i	0.00437197	+	0.0134555i
$532$		0			0
$533$	−1.09174	−	0.793196i	−0.0472885	−	0.0343571i
$534$		0			0
$535$	−9.00185	+	27.7049i	−0.389184	+	1.19779i
$536$		0			0
$537$	−28.6224	+	20.7954i	−1.23515	+	0.897387i
$538$		0			0
$539$	−4.26342	+	22.6658i	−0.183638	+	0.976284i
$540$		0			0
$541$	0.563990	−	0.409763i	0.0242478	−	0.0176171i	−0.575595	−	0.817735i	$-0.695230\pi$
$541$	0.563990	−	0.409763i	0.0242478	−	0.0176171i	0.599843	+	0.800118i	$0.295230\pi$
$542$		0			0
$543$	−1.50011	+	4.61687i	−0.0643760	+	0.198129i
$544$		0			0
$545$	−28.9625	−	21.0425i	−1.24062	−	0.901363i
$546$		0			0
$547$	1.36338	+	4.19605i	0.0582939	+	0.179410i	0.975963	−	0.217934i	$-0.0699318\pi$
$547$	1.36338	+	4.19605i	0.0582939	+	0.179410i	−0.917670	+	0.397344i	$0.869932\pi$
$548$		0			0
$549$	0.890739			0.0380158
$550$		0			0
$551$	1.00802			0.0429430
$552$		0			0
$553$	−0.230547	−	0.709552i	−0.00980387	−	0.0301732i
$554$		0			0
$555$	4.58157	+	3.32871i	0.194477	+	0.141296i
$556$		0			0
$557$	−11.6344	+	35.8071i	−0.492967	+	1.51720i	0.327135	+	0.944978i	$0.393917\pi$
$557$	−11.6344	+	35.8071i	−0.492967	+	1.51720i	−0.820102	+	0.572218i	$0.806083\pi$
$558$		0			0
$559$	1.13921	−	0.827686i	0.0481835	−	0.0350074i
$560$		0			0
$561$	38.5445	−	4.96993i	1.62735	−	0.209831i
$562$		0			0
$563$	24.0688	−	17.4870i	1.01438	−	0.736989i	0.0492550	−	0.998786i	$-0.484315\pi$
$563$	24.0688	−	17.4870i	1.01438	−	0.736989i	0.965123	+	0.261798i	$0.0843153\pi$
$564$		0			0
$565$	−7.95529	+	24.4839i	−0.334681	+	1.03004i
$566$		0			0
$567$	−1.51729	−	1.10238i	−0.0637204	−	0.0462956i
$568$		0			0
$569$	−2.97869	−	9.16747i	−0.124873	−	0.384320i	0.869005	−	0.494804i	$-0.164760\pi$
$569$	−2.97869	−	9.16747i	−0.124873	−	0.384320i	−0.993878	+	0.110483i	$0.964760\pi$
$570$		0			0
$571$	27.7305			1.16048			0.580242	−	0.814444i	$-0.302958\pi$
$571$	27.7305			1.16048			0.580242	+	0.814444i	$0.302958\pi$
$572$		0			0
$573$	−23.8831			−0.997732
$574$		0			0
$575$	−1.36098	−	4.18866i	−0.0567567	−	0.174679i
$576$		0			0
$577$	−23.4686	−	17.0509i	−0.977010	−	0.709839i	−0.0199716	−	0.999801i	$-0.506358\pi$
$577$	−23.4686	−	17.0509i	−0.977010	−	0.709839i	−0.957038	+	0.289961i	$0.906358\pi$
$578$		0			0
$579$	6.76145	−	20.8096i	0.280996	−	0.864818i
$580$		0			0
$581$	−1.73445	+	1.26016i	−0.0719573	+	0.0522800i
$582$		0			0
$583$	19.9392	+	10.8951i	0.825797	+	0.451228i
$584$		0			0
$585$	0.136744	−	0.0993502i	0.00565366	−	0.00410763i
$586$		0			0
$587$	−4.68612	+	14.4224i	−0.193417	+	0.595276i	0.806574	+	0.591133i	$0.201319\pi$
$587$	−4.68612	+	14.4224i	−0.193417	+	0.595276i	−0.999991	+	0.00414373i	$0.998681\pi$
$588$		0			0
$589$	−4.27123	−	3.10323i	−0.175993	−	0.127866i
$590$		0			0
$591$	0.958738	+	2.95069i	0.0394372	+	0.121375i
$592$		0			0
$593$	8.08918			0.332183			0.166091	−	0.986110i	$-0.446885\pi$
$593$	8.08918			0.332183			0.166091	+	0.986110i	$0.446885\pi$
$594$		0			0
$595$	−2.83997			−0.116427
$596$		0			0
$597$	−4.67702	−	14.3944i	−0.191417	−	0.589122i
$598$		0			0
$599$	−13.3563	−	9.70394i	−0.545725	−	0.396492i	0.280482	−	0.959859i	$-0.409506\pi$
$599$	−13.3563	−	9.70394i	−0.545725	−	0.396492i	−0.826207	+	0.563367i	$0.809506\pi$
$600$		0			0
$601$	−2.58618	+	7.95944i	−0.105493	+	0.324673i	−0.989846	−	0.142146i	$-0.954600\pi$
$601$	−2.58618	+	7.95944i	−0.105493	+	0.324673i	0.884353	+	0.466818i	$0.154600\pi$
$602$		0			0
$603$	−0.581377	+	0.422395i	−0.0236755	+	0.0172013i
$604$		0			0
$605$	−20.4820	+	5.37121i	−0.832714	+	0.218371i
$606$		0			0
$607$	−22.0823	+	16.0438i	−0.896295	+	0.651196i	−0.937512	−	0.347954i	$-0.886877\pi$
$607$	−22.0823	+	16.0438i	−0.896295	+	0.651196i	0.0412169	+	0.999150i	$0.486877\pi$
$608$		0			0
$609$	−0.0294699	+	0.0906990i	−0.00119418	+	0.00367531i
$610$		0			0
$611$	−9.72205	−	7.06349i	−0.393312	−	0.285758i
$612$		0			0
$613$	−4.14114	−	12.7451i	−0.167259	−	0.514771i	0.831937	−	0.554871i	$-0.187232\pi$
$613$	−4.14114	−	12.7451i	−0.167259	−	0.514771i	−0.999196	+	0.0401002i	$0.987232\pi$
$614$		0			0
$615$	−4.43297			−0.178755
$616$		0			0
$617$	33.5887			1.35223			0.676114	−	0.736797i	$-0.263663\pi$
$617$	33.5887			1.35223			0.676114	+	0.736797i	$0.263663\pi$
$618$		0			0
$619$	−7.53838	−	23.2007i	−0.302993	−	0.932517i	−0.980418	−	0.196925i	$-0.936904\pi$
$619$	−7.53838	−	23.2007i	−0.302993	−	0.932517i	0.677425	−	0.735591i	$-0.263096\pi$
$620$		0			0
$621$	−14.5037	−	10.5376i	−0.582015	−	0.422859i
$622$		0			0
$623$	0.433977	−	1.33564i	0.0173869	−	0.0535114i
$624$		0			0
$625$	13.6333	−	9.90517i	0.545332	−	0.396207i
$626$		0			0
$627$	−19.2491	−	10.5180i	−0.768736	−	0.420048i
$628$		0			0
$629$	−9.57676	+	6.95792i	−0.381850	+	0.277431i
$630$		0			0
$631$	−4.23390	+	13.0306i	−0.168549	+	0.518740i	−0.999280	−	0.0379334i	$-0.987923\pi$
$631$	−4.23390	+	13.0306i	−0.168549	+	0.518740i	0.830731	+	0.556673i	$0.187923\pi$
$632$		0			0
$633$	37.2846	+	27.0889i	1.48193	+	1.07669i
$634$		0			0
$635$	7.52243	+	23.1517i	0.298518	+	0.918745i
$636$		0			0
$637$	6.95384			0.275521
$638$		0			0
$639$	−0.817330			−0.0323331
$640$		0			0
$641$	11.0395	+	33.9761i	0.436034	+	1.34198i	0.892023	+	0.451990i	$0.149286\pi$
$641$	11.0395	+	33.9761i	0.436034	+	1.34198i	−0.455989	+	0.889986i	$0.650714\pi$
$642$		0			0
$643$	19.6740	+	14.2940i	0.775868	+	0.563701i	0.903736	−	0.428090i	$-0.140813\pi$
$643$	19.6740	+	14.2940i	0.775868	+	0.563701i	−0.127868	+	0.991791i	$0.540813\pi$
$644$		0			0
$645$	1.42943	−	4.39932i	0.0562836	−	0.173223i
$646$		0			0
$647$	7.53128	−	5.47179i	0.296085	−	0.215118i	−0.429818	−	0.902916i	$-0.641422\pi$
$647$	7.53128	−	5.47179i	0.296085	−	0.215118i	0.725903	+	0.687797i	$0.241422\pi$
$648$		0			0
$649$	−12.2132	+	1.57477i	−0.479411	+	0.0618152i
$650$		0			0
$651$	0.404092	−	0.293590i	0.0158376	−	0.0115067i
$652$		0			0
$653$	−3.26877	+	10.0602i	−0.127917	+	0.393687i	−0.994421	−	0.105482i	$-0.966361\pi$
$653$	−3.26877	+	10.0602i	−0.127917	+	0.393687i	0.866504	+	0.499169i	$0.166361\pi$
$654$		0			0
$655$	−21.5661	−	15.6687i	−0.842656	−	0.612226i
$656$		0			0
$657$	−0.154743	−	0.476251i	−0.00603711	−	0.0185803i
$658$		0			0
$659$	−28.0463			−1.09253			−0.546264	−	0.837613i	$-0.683950\pi$
$659$	−28.0463			−1.09253			−0.546264	+	0.837613i	$0.683950\pi$
$660$		0			0
$661$	6.31657			0.245686			0.122843	−	0.992426i	$-0.460799\pi$
$661$	6.31657			0.245686			0.122843	+	0.992426i	$0.460799\pi$
$662$		0			0
$663$	−3.62101	−	11.1443i	−0.140628	−	0.432809i
$664$		0			0
$665$	1.29680	+	0.942177i	0.0502876	+	0.0365361i
$666$		0			0
$667$	−0.273449	+	0.841589i	−0.0105880	+	0.0325865i
$668$		0			0
$669$	−12.9146	+	9.38298i	−0.499306	+	0.362767i
$670$		0			0
$671$	−6.21951	+	33.0651i	−0.240102	+	1.27646i
$672$		0			0
$673$	−17.1227	+	12.4404i	−0.660032	+	0.479541i	−0.866674	−	0.498876i	$-0.833746\pi$
$673$	−17.1227	+	12.4404i	−0.660032	+	0.479541i	0.206642	+	0.978417i	$0.433746\pi$
$674$		0			0
$675$	−2.10789	+	6.48743i	−0.0811329	+	0.249701i
$676$		0			0
$677$	27.8418	+	20.2282i	1.07005	+	0.777434i	0.975921	−	0.218126i	$-0.0699945\pi$
$677$	27.8418	+	20.2282i	1.07005	+	0.777434i	0.0941254	+	0.995560i	$0.469995\pi$
$678$		0			0
$679$	−0.900252	−	2.77069i	−0.0345485	−	0.106329i
$680$		0			0
$681$	19.2939			0.739345
$682$		0			0
$683$	12.5189			0.479023			0.239511	−	0.970894i	$-0.423013\pi$
$683$	12.5189			0.479023			0.239511	+	0.970894i	$0.423013\pi$
$684$		0			0
$685$	−0.773339	−	2.38009i	−0.0295478	−	0.0909386i
$686$		0			0
$687$	26.8885	+	19.5356i	1.02586	+	0.745331i
$688$		0			0
$689$	2.11703	−	6.51554i	0.0806523	−	0.248222i
$690$		0			0
$691$	35.0642	−	25.4757i	1.33391	−	0.969140i	0.334262	−	0.942480i	$-0.391513\pi$
$691$	35.0642	−	25.4757i	1.33391	−	0.969140i	0.999645	−	0.0266595i	$-0.00848697\pi$
$692$		0			0
$693$	−0.0455026	+	0.0429503i	−0.00172850	+	0.00163155i
$694$		0			0
$695$	−9.87002	+	7.17099i	−0.374391	+	0.272011i
$696$		0			0
$697$	2.86339	−	8.81262i	0.108459	−	0.333802i
$698$		0			0
$699$	−29.1253	−	21.1608i	−1.10162	−	0.800375i
$700$		0			0
$701$	−9.78876	−	30.1267i	−0.369716	−	1.13787i	−0.946975	−	0.321309i	$-0.895877\pi$
$701$	−9.78876	−	30.1267i	−0.369716	−	1.13787i	0.577258	−	0.816562i	$-0.304123\pi$
$702$		0			0
$703$	6.68130			0.251990
$704$		0			0
$705$	−39.4760			−1.48675
$706$		0			0
$707$	−0.792740	−	2.43980i	−0.0298141	−	0.0917583i
$708$		0			0
$709$	−41.2015	−	29.9346i	−1.54736	−	1.12422i	−0.945504	−	0.325611i	$-0.894430\pi$
$709$	−41.2015	−	29.9346i	−1.54736	−	1.12422i	−0.601852	−	0.798608i	$-0.705570\pi$
$710$		0			0
$711$	−0.0942179	+	0.289973i	−0.00353345	+	0.0108748i
$712$		0			0
$713$	3.74954	−	2.72420i	0.140421	−	0.102022i
$714$		0			0
$715$	2.73317	+	5.76976i	0.102215	+	0.215777i
$716$		0			0
$717$	7.89253	−	5.73426i	0.294752	−	0.214150i
$718$		0			0
$719$	8.76108	−	26.9638i	0.326733	−	1.00558i	−0.643919	−	0.765093i	$-0.722693\pi$
$719$	8.76108	−	26.9638i	0.326733	−	1.00558i	0.970652	−	0.240487i	$-0.0773073\pi$
$720$		0			0
$721$	−0.554314	−	0.402733i	−0.0206437	−	0.0149986i
$722$		0			0
$723$	−3.46761	−	10.6722i	−0.128962	−	0.396904i
$724$		0			0
$725$	0.336696			0.0125046
$726$		0			0
$727$	40.5247			1.50298			0.751490	−	0.659745i	$-0.229336\pi$
$727$	40.5247			1.50298			0.751490	+	0.659745i	$0.229336\pi$
$728$		0			0
$729$	8.57316	+	26.3855i	0.317524	+	0.977240i
$730$		0			0
$731$	7.82242	+	5.68332i	0.289323	+	0.210205i
$732$		0			0
$733$	2.33790	−	7.19531i	0.0863522	−	0.265765i	−0.898551	−	0.438868i	$-0.855379\pi$
$733$	2.33790	−	7.19531i	0.0863522	−	0.265765i	0.984904	+	0.173103i	$0.0553795\pi$
$734$		0			0
$735$	18.4805	−	13.4269i	0.681665	−	0.495259i
$736$		0			0
$737$	−11.6203	−	24.5306i	−0.428038	−	0.903596i
$738$		0			0
$739$	−9.49391	+	6.89773i	−0.349239	+	0.253737i	−0.748550	−	0.663079i	$-0.769250\pi$
$739$	−9.49391	+	6.89773i	−0.349239	+	0.253737i	0.399311	+	0.916816i	$0.369250\pi$
$740$		0			0
$741$	−2.04376	+	6.29004i	−0.0750793	+	0.231070i
$742$		0			0
$743$	−5.26091	−	3.82227i	−0.193004	−	0.140226i	0.487087	−	0.873354i	$-0.338060\pi$
$743$	−5.26091	−	3.82227i	−0.193004	−	0.140226i	−0.680091	+	0.733128i	$0.738060\pi$
$744$		0			0
$745$	−3.28295	−	10.1039i	−0.120278	−	0.370178i
$746$		0			0
$747$	0.876150			0.0320567
$748$		0			0
$749$	−3.25148			−0.118807
$750$		0			0
$751$	−3.01950	−	9.29305i	−0.110183	−	0.339108i	0.880729	−	0.473621i	$-0.157053\pi$
$751$	−3.01950	−	9.29305i	−0.110183	−	0.339108i	−0.990912	+	0.134512i	$0.957053\pi$
$752$		0			0
$753$	−21.5425	−	15.6516i	−0.785053	−	0.570375i
$754$		0			0
$755$	3.16434	−	9.73884i	0.115162	−	0.354433i
$756$		0			0
$757$	42.5822	−	30.9378i	1.54768	−	1.12445i	0.602397	−	0.798197i	$-0.294212\pi$
$757$	42.5822	−	30.9378i	1.54768	−	1.12445i	0.945281	−	0.326257i	$-0.105788\pi$
$758$		0			0
$759$	14.0032	−	13.2177i	0.508284	−	0.479773i
$760$		0			0
$761$	14.8095	−	10.7597i	0.536843	−	0.390039i	−0.286068	−	0.958209i	$-0.592348\pi$
$761$	14.8095	−	10.7597i	0.536843	−	0.390039i	0.822911	+	0.568170i	$0.192348\pi$
$762$		0			0
$763$	1.23479	−	3.80029i	0.0447024	−	0.137580i
$764$		0			0
$765$	0.938954	+	0.682190i	0.0339480	+	0.0246646i
$766$		0			0
$767$	1.14735	+	3.53119i	0.0414285	+	0.127504i
$768$		0			0
$769$	−16.2335			−0.585394			−0.292697	−	0.956205i	$-0.594553\pi$
$769$	−16.2335			−0.585394			−0.292697	+	0.956205i	$0.594553\pi$
$770$		0			0
$771$	−28.6662			−1.03239
$772$		0			0
$773$	1.17798	+	3.62544i	0.0423689	+	0.130398i	0.970004	−	0.243091i	$-0.0781613\pi$
$773$	1.17798	+	3.62544i	0.0423689	+	0.130398i	−0.927635	+	0.373489i	$0.878161\pi$
$774$		0			0
$775$	−1.42666	−	1.03653i	−0.0512473	−	0.0372333i
$776$		0			0
$777$	−0.195331	+	0.601167i	−0.00700746	+	0.0215667i
$778$		0			0
$779$	−4.23113	+	3.07410i	−0.151596	+	0.110141i
$780$		0			0
$781$	5.70694	−	30.3400i	0.204210	−	1.08565i
$782$		0			0
$783$	1.10879	−	0.805584i	0.0396249	−	0.0287892i
$784$		0			0
$785$	11.4925	−	35.3703i	0.410185	−	1.26242i
$786$		0			0
$787$	41.0572	+	29.8298i	1.46353	+	1.06332i	0.982425	+	0.186657i	$0.0597653\pi$
$787$	41.0572	+	29.8298i	1.46353	+	1.06332i	0.481107	+	0.876662i	$0.340235\pi$
$788$		0			0
$789$	3.11596	+	9.58995i	0.110931	+	0.341411i
$790$		0			0
$791$	−2.87346			−0.102168
$792$		0			0
$793$	10.1443			0.360235
$794$		0			0
$795$	−6.95439	−	21.4034i	−0.246647	−	0.759101i
$796$		0			0
$797$	23.9868	+	17.4274i	0.849656	+	0.617311i	0.925051	−	0.379843i	$-0.124022\pi$
$797$	23.9868	+	17.4274i	0.849656	+	0.617311i	−0.0753955	+	0.997154i	$0.524022\pi$
$798$		0			0
$799$	25.4988	−	78.4772i	0.902082	−	2.77632i
$800$		0			0
$801$	−0.464317	+	0.337346i	−0.0164058	+	0.0119195i
$802$		0			0
$803$	18.7594	−	2.41883i	0.662003	−	0.0853586i
$804$		0			0
$805$	−1.13841	+	0.827100i	−0.0401235	+	0.0291514i
$806$		0			0
$807$	−13.5291	+	41.6382i	−0.476246	+	1.46573i
$808$		0			0
$809$	−14.5152	−	10.5459i	−0.510327	−	0.370774i	0.302621	−	0.953111i	$-0.402138\pi$
$809$	−14.5152	−	10.5459i	−0.510327	−	0.370774i	−0.812948	+	0.582337i	$0.802138\pi$
$810$		0			0
$811$	5.47993	+	16.8655i	0.192426	+	0.592228i	0.999997	+	0.00245663i	$0.000781971\pi$
$811$	5.47993	+	16.8655i	0.192426	+	0.592228i	−0.807571	+	0.589771i	$0.799218\pi$
$812$		0			0
$813$	29.0964			1.02046
$814$		0			0
$815$	−15.2734			−0.535003
$816$		0			0
$817$	−1.68642	−	5.19027i	−0.0590004	−	0.181585i
$818$		0			0
$819$	0.0152630	+	0.0110892i	0.000533332	+	0.000387488i
$820$		0			0
$821$	−9.10041	+	28.0082i	−0.317607	+	0.977493i	0.657062	+	0.753837i	$0.271799\pi$
$821$	−9.10041	+	28.0082i	−0.317607	+	0.977493i	−0.974668	+	0.223656i	$0.928201\pi$
$822$		0			0
$823$	−26.0701	+	18.9410i	−0.908745	+	0.660242i	−0.940697	−	0.339247i	$-0.889828\pi$
$823$	−26.0701	+	18.9410i	−0.908745	+	0.660242i	0.0319518	+	0.999489i	$0.489828\pi$
$824$		0			0
$825$	−6.42954	−	3.51319i	−0.223848	−	0.122314i
$826$		0			0
$827$	23.3348	−	16.9537i	0.811430	−	0.589538i	−0.102815	−	0.994701i	$-0.532785\pi$
$827$	23.3348	−	16.9537i	0.811430	−	0.589538i	0.914245	+	0.405162i	$0.132785\pi$
$828$		0			0
$829$	−8.43984	+	25.9751i	−0.293128	+	0.902154i	0.690716	+	0.723126i	$0.257295\pi$
$829$	−8.43984	+	25.9751i	−0.293128	+	0.902154i	−0.983844	+	0.179028i	$0.942705\pi$
$830$		0			0
$831$	5.25025	+	3.81453i	0.182129	+	0.132325i
$832$		0			0
$833$	14.7551	+	45.4117i	0.511236	+	1.57342i
$834$		0			0
$835$	25.1254			0.869500
$836$		0			0
$837$	−7.17824			−0.248116
$838$		0			0
$839$	6.71684	+	20.6723i	0.231891	+	0.713687i	0.997519	+	0.0704032i	$0.0224286\pi$
$839$	6.71684	+	20.6723i	0.231891	+	0.713687i	−0.765628	+	0.643284i	$0.777571\pi$
$840$		0			0
$841$	23.4068	+	17.0060i	0.807130	+	0.586414i
$842$		0			0
$843$	−4.37852	+	13.4757i	−0.150804	+	0.464127i
$844$		0			0
$845$	1.55733	−	1.13147i	0.0535737	−	0.0389236i
$846$		0			0
$847$	−1.27664	−	1.98900i	−0.0438657	−	0.0683427i
$848$		0			0
$849$	31.7495	−	23.0674i	1.08964	−	0.791670i
$850$		0			0
$851$	−1.81246	+	5.57818i	−0.0621304	+	0.191218i
$852$		0			0
$853$	−8.34929	−	6.06611i	−0.285874	−	0.207700i	0.435601	−	0.900140i	$-0.356536\pi$
$853$	−8.34929	−	6.06611i	−0.285874	−	0.207700i	−0.721476	+	0.692440i	$0.756536\pi$
$854$		0			0
$855$	−0.202427	−	0.623008i	−0.00692287	−	0.0213064i
$856$		0			0
$857$	24.7104			0.844090			0.422045	−	0.906575i	$-0.361312\pi$
$857$	24.7104			0.844090			0.422045	+	0.906575i	$0.361312\pi$
$858$		0			0
$859$	−22.4970			−0.767586			−0.383793	−	0.923419i	$-0.625382\pi$
$859$	−22.4970			−0.767586			−0.383793	+	0.923419i	$0.625382\pi$
$860$		0			0
$861$	−0.152900	−	0.470579i	−0.00521083	−	0.0160373i
$862$		0			0
$863$	−9.04083	−	6.56855i	−0.307753	−	0.223596i	0.423179	−	0.906046i	$-0.360914\pi$
$863$	−9.04083	−	6.56855i	−0.307753	−	0.223596i	−0.730932	+	0.682450i	$0.760914\pi$
$864$		0			0
$865$	1.59805	−	4.91829i	0.0543353	−	0.167227i
$866$		0			0
$867$	41.6238	−	30.2415i	1.41362	−	1.02705i
$868$		0			0
$869$	−10.1062	−	5.52217i	−0.342829	−	0.187327i
$870$		0			0
$871$	−6.62110	+	4.81051i	−0.224348	+	0.162998i
$872$		0			0
$873$	−0.367906	+	1.13230i	−0.0124517	+	0.0383225i
$874$		0			0
$875$	2.10619	+	1.53023i	0.0712021	+	0.0517313i
$876$		0			0
$877$	−12.3171	−	37.9082i	−0.415919	−	1.28007i	−0.911426	−	0.411464i	$-0.865018\pi$
$877$	−12.3171	−	37.9082i	−0.415919	−	1.28007i	0.495506	−	0.868604i	$-0.334982\pi$
$878$		0			0
$879$	−31.3806			−1.05844
$880$		0			0
$881$	59.0573			1.98969			0.994845	−	0.101405i	$-0.0323339\pi$
$881$	59.0573			1.98969			0.994845	+	0.101405i	$0.0323339\pi$
$882$		0			0
$883$	−9.04401	−	27.8346i	−0.304355	−	0.936709i	−0.979917	−	0.199406i	$-0.936099\pi$
$883$	−9.04401	−	27.8346i	−0.304355	−	0.936709i	0.675562	−	0.737303i	$-0.263901\pi$
$884$		0			0
$885$	9.86745	+	7.16912i	0.331691	+	0.240987i
$886$		0			0
$887$	16.2945	−	50.1495i	0.547117	−	1.68385i	−0.168785	−	0.985653i	$-0.553984\pi$
$887$	16.2945	−	50.1495i	0.547117	−	1.68385i	0.715902	−	0.698201i	$-0.246016\pi$
$888$		0			0
$889$	−2.19819	+	1.59708i	−0.0737249	+	0.0535642i
$890$		0			0
$891$	−28.7127	+	3.70221i	−0.961911	+	0.124029i
$892$		0			0
$893$	−37.6786	+	27.3751i	−1.26087	+	0.916073i
$894$		0			0
$895$	12.3323	−	37.9549i	0.412223	−	1.26869i
$896$		0			0
$897$	−4.69710	−	3.41264i	−0.156832	−	0.113945i
$898$		0			0
$899$	0.109489	+	0.336974i	0.00365168	+	0.0112387i
$900$		0			0
$901$	47.0414			1.56718
$902$		0			0
$903$	0.516311			0.0171817
$904$		0			0
$905$	−1.69214	−	5.20787i	−0.0562486	−	0.173115i
$906$		0			0
$907$	19.1081	+	13.8828i	0.634474	+	0.460972i	0.857947	−	0.513738i	$-0.171740\pi$
$907$	19.1081	+	13.8828i	0.634474	+	0.460972i	−0.223473	+	0.974710i	$0.571740\pi$
$908$		0			0
$909$	−0.323969	+	0.997075i	−0.0107454	+	0.0330709i
$910$		0			0
$911$	16.4368	−	11.9421i	0.544576	−	0.395658i	−0.281205	−	0.959648i	$-0.590734\pi$
$911$	16.4368	−	11.9421i	0.544576	−	0.395658i	0.825782	+	0.563990i	$0.190734\pi$
$912$		0			0
$913$	−6.11765	+	32.5235i	−0.202465	+	1.07637i
$914$		0			0
$915$	26.9596	−	19.5873i	0.891257	−	0.647536i
$916$		0			0
$917$	0.919449	−	2.82977i	0.0303629	−	0.0934473i
$918$		0			0
$919$	32.3361	+	23.4935i	1.06667	+	0.774980i	0.975310	−	0.220838i	$-0.0708792\pi$
$919$	32.3361	+	23.4935i	1.06667	+	0.774980i	0.0913580	+	0.995818i	$0.470879\pi$
$920$		0			0
$921$	−14.1849	−	43.6566i	−0.467408	−	1.43853i
$922$		0			0
$923$	−9.30829			−0.306386
$924$		0			0
$925$	2.23167			0.0733769
$926$		0			0
$927$	0.0865275	+	0.266304i	0.00284193	+	0.00874657i
$928$		0			0
$929$	19.1173	+	13.8896i	0.627219	+	0.455702i	0.855436	−	0.517909i	$-0.173289\pi$
$929$	19.1173	+	13.8896i	0.627219	+	0.455702i	−0.228216	+	0.973610i	$0.573289\pi$
$930$		0			0
$931$	8.32806	−	25.6311i	0.272941	−	0.840026i
$932$		0			0
$933$	2.99752	−	2.17783i	0.0981345	−	0.0712989i
$934$		0			0
$935$	−31.8797	+	30.0915i	−1.04258	+	0.984098i
$936$		0			0
$937$	−16.1217	+	11.7131i	−0.526675	+	0.382651i	−0.819112	−	0.573633i	$-0.805534\pi$
$937$	−16.1217	+	11.7131i	−0.526675	+	0.382651i	0.292438	+	0.956285i	$0.405534\pi$
$938$		0			0
$939$	−5.68852	+	17.5075i	−0.185638	+	0.571334i
$940$		0			0
$941$	−28.9813	−	21.0562i	−0.944764	−	0.686411i	0.00479897	−	0.999988i	$-0.498472\pi$
$941$	−28.9813	−	21.0562i	−0.944764	−	0.686411i	−0.949563	+	0.313578i	$0.898472\pi$
$942$		0			0
$943$	−1.41875	−	4.36647i	−0.0462009	−	0.142192i
$944$		0			0
$945$	2.17940			0.0708959
$946$		0			0
$947$	−3.44203			−0.111851			−0.0559254	−	0.998435i	$-0.517811\pi$
$947$	−3.44203			−0.111851			−0.0559254	+	0.998435i	$0.517811\pi$
$948$		0			0
$949$	−1.76232	−	5.42386i	−0.0572073	−	0.176066i
$950$		0			0
$951$	42.3166	+	30.7448i	1.37221	+	0.996968i
$952$		0			0
$953$	−8.95654	+	27.5654i	−0.290131	+	0.892931i	0.694683	+	0.719316i	$0.255545\pi$
$953$	−8.95654	+	27.5654i	−0.290131	+	0.892931i	−0.984814	+	0.173615i	$0.944455\pi$
$954$		0			0
$955$	21.7952	−	15.8352i	0.705277	−	0.512414i
$956$		0			0
$957$	0.630210	+	1.33038i	0.0203718	+	0.0430052i
$958$		0			0
$959$	0.225983	−	0.164187i	0.00729738	−	0.00530186i
$960$		0			0
$961$	−9.00607	+	27.7178i	−0.290518	+	0.894124i
$962$		0			0
$963$	1.07501	+	0.781039i	0.0346417	+	0.0251686i
$964$		0			0
$965$	7.62698	+	23.4734i	0.245521	+	0.755636i
$966$		0			0
$967$	27.2460			0.876171			0.438085	−	0.898933i	$-0.355657\pi$
$967$	27.2460			0.876171			0.438085	+	0.898933i	$0.355657\pi$
$968$		0			0
$969$	−45.4134			−1.45889
$970$		0			0
$971$	−10.4284	−	32.0953i	−0.334663	−	1.02999i	−0.966888	−	0.255202i	$-0.917858\pi$
$971$	−10.4284	−	32.0953i	−0.334663	−	1.02999i	0.632224	−	0.774785i	$-0.282142\pi$
$972$		0			0
$973$	−1.10166	−	0.800406i	−0.0353178	−	0.0256598i
$974$		0			0
$975$	−0.682651	+	2.10098i	−0.0218623	+	0.0672853i
$976$		0			0
$977$	6.37948	−	4.63496i	0.204098	−	0.148286i	−0.481042	−	0.876698i	$-0.659741\pi$
$977$	6.37948	−	4.63496i	0.204098	−	0.148286i	0.685139	+	0.728412i	$0.259741\pi$
$978$		0			0
$979$	−9.28055	−	19.5914i	−0.296608	−	0.626143i
$980$		0			0
$981$	−1.32112	+	0.959848i	−0.0421800	+	0.0306456i
$982$		0			0
$983$	−13.6581	+	42.0353i	−0.435625	+	1.34072i	0.456819	+	0.889559i	$0.348989\pi$
$983$	−13.6581	+	42.0353i	−0.435625	+	1.34072i	−0.892445	+	0.451157i	$0.851011\pi$
$984$		0			0
$985$	−2.83131	−	2.05707i	−0.0902131	−	0.0655437i
$986$		0			0
$987$	−1.36159	−	4.19055i	−0.0433400	−	0.133387i
$988$		0			0
$989$	4.79081			0.152339
$990$		0			0
$991$	25.9823			0.825354			0.412677	−	0.910877i	$-0.364594\pi$
$991$	25.9823			0.825354			0.412677	+	0.910877i	$0.364594\pi$
$992$		0			0
$993$	8.08495	+	24.8829i	0.256568	+	0.789636i
$994$		0			0
$995$	13.8120	+	10.0350i	0.437870	+	0.318131i
$996$		0			0
$997$	−14.4608	+	44.5057i	−0.457978	+	1.40951i	0.409625	+	0.912254i	$0.365659\pi$
$997$	−14.4608	+	44.5057i	−0.457978	+	1.40951i	−0.867603	+	0.497257i	$0.834341\pi$
$998$		0			0
$999$	7.34924	−	5.33953i	0.232520	−	0.168935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.n.b.157.2	✓	28
11.2	odd	10		6292.2.a.y.1.4		14
11.4	even	5	inner	572.2.n.b.521.2	yes	28
11.9	even	5		6292.2.a.z.1.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.n.b.157.2	✓	28	1.1	even	1	trivial
572.2.n.b.521.2	yes	28	11.4	even	5	inner
6292.2.a.y.1.4		14	11.2	odd	10
6292.2.a.z.1.4		14	11.9	even	5

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.527342 - 1.62299i) q^{3} +(1.55733 + 1.13147i) q^{5} +(-0.0663952 + 0.204343i) q^{7} +(0.0710371 - 0.0516114i) q^{9} +O(q^{10})\)	\(q+(-0.527342 - 1.62299i) q^{3} +(1.55733 + 1.13147i) q^{5} +(-0.0663952 + 0.204343i) q^{7} +(0.0710371 - 0.0516114i) q^{9} +(1.41985 + 2.99733i) q^{11} +(0.809017 - 0.587785i) q^{13} +(1.01511 - 3.12420i) q^{15} +(5.55513 + 4.03604i) q^{17} +(-1.19762 - 3.68590i) q^{19} +0.366661 q^{21} +3.40222 q^{23} +(-0.400026 - 1.23115i) q^{25} +(-4.26302 - 3.09727i) q^{27} +(-0.0803737 + 0.247365i) q^{29} +(1.10209 - 0.800713i) q^{31} +(4.11590 - 3.88503i) q^{33} +(-0.334607 + 0.243106i) q^{35} +(-0.532729 + 1.63957i) q^{37} +(-1.38060 - 1.00306i) q^{39} +(-0.417008 - 1.28342i) q^{41} +1.40814 q^{43} +0.169025 q^{45} +(-3.71349 - 11.4290i) q^{47} +(5.62577 + 4.08736i) q^{49} +(3.62101 - 11.1443i) q^{51} +(5.54245 - 4.02682i) q^{53} +(-1.18020 + 6.27435i) q^{55} +(-5.35063 + 3.88746i) q^{57} +(-1.14735 + 3.53119i) q^{59} +(8.20693 + 5.96268i) q^{61} +(0.00582994 + 0.0179427i) q^{63} +1.92496 q^{65} -8.18413 q^{67} +(-1.79413 - 5.52177i) q^{69} +(-7.53057 - 5.47128i) q^{71} +(1.76232 - 5.42386i) q^{73} +(-1.78720 + 1.29848i) q^{75} +(-0.706757 + 0.0911292i) q^{77} +(-2.80919 + 2.04100i) q^{79} +(-2.69737 + 8.30165i) q^{81} +(8.07251 + 5.86502i) q^{83} +(4.08453 + 12.5709i) q^{85} +0.443856 q^{87} -6.53627 q^{89} +(0.0663952 + 0.204343i) q^{91} +(-1.88073 - 1.36643i) q^{93} +(2.30538 - 7.09522i) q^{95} +(-10.9695 + 7.96978i) q^{97} +(0.255559 + 0.139641i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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