LMFDB - Embedded newform 675.2.l.g.76.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(76,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 0]))

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

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

chi := DirichletCharacter("675.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			76.5
Character	$\chi$	$=$	675.76
Dual form			675.2.l.g.151.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.211903 + 0.177808i) q^{2} +(0.483303 + 1.66326i) q^{3} +(-0.334009 + 1.89426i) q^{4} +(-0.398153 - 0.266514i) q^{6} +(-0.293371 - 1.66379i) q^{7} +(-0.542656 - 0.939908i) q^{8} +(-2.53284 + 1.60771i) q^{9} +(-4.65944 - 1.69590i) q^{11} +(-3.31206 + 0.359958i) q^{12} +(2.87084 + 2.40892i) q^{13} +(0.358001 + 0.300398i) q^{14} +(-3.33285 - 1.21306i) q^{16} +(-3.15798 + 5.46979i) q^{17} +(0.250852 - 0.791037i) q^{18} +(-3.42671 - 5.93524i) q^{19} +(2.62552 - 1.29206i) q^{21} +(1.28889 - 0.469119i) q^{22} +(-1.12343 + 6.37131i) q^{23} +(1.30104 - 1.35684i) q^{24} -1.03667 q^{26} +(-3.89816 - 3.43574i) q^{27} +3.24964 q^{28} +(-0.115261 + 0.0967151i) q^{29} +(-1.06440 + 6.03653i) q^{31} +(2.96165 - 1.07795i) q^{32} +(0.568791 - 8.56948i) q^{33} +(-0.303384 - 1.72058i) q^{34} +(-2.19943 - 5.33484i) q^{36} +(1.23541 - 2.13979i) q^{37} +(1.78146 + 0.648400i) q^{38} +(-2.61917 + 5.93918i) q^{39} +(-3.02499 - 2.53826i) q^{41} +(-0.326617 + 0.740630i) q^{42} +(6.57849 + 2.39437i) q^{43} +(4.76877 - 8.25975i) q^{44} +(-0.894809 - 1.54985i) q^{46} +(-1.07632 - 6.10414i) q^{47} +(0.406850 - 6.12965i) q^{48} +(3.89572 - 1.41793i) q^{49} +(-10.6239 - 2.60897i) q^{51} +(-5.52201 + 4.63352i) q^{52} +0.373453 q^{53} +(1.43693 + 0.0349210i) q^{54} +(-1.40461 + 1.17861i) q^{56} +(8.21568 - 8.56802i) q^{57} +(0.00722737 - 0.0409885i) q^{58} +(0.342887 - 0.124801i) q^{59} +(1.07271 + 6.08365i) q^{61} +(-0.847791 - 1.46842i) q^{62} +(3.41795 + 3.74245i) q^{63} +(3.11083 - 5.38811i) q^{64} +(1.40319 + 1.91703i) q^{66} +(-0.475424 - 0.398928i) q^{67} +(-9.30640 - 7.80900i) q^{68} +(-11.1401 + 1.21071i) q^{69} +(-3.39814 + 5.88576i) q^{71} +(2.88556 + 1.50820i) q^{72} +(2.27683 + 3.94359i) q^{73} +(0.118685 + 0.673094i) q^{74} +(12.3874 - 4.50866i) q^{76} +(-1.45467 + 8.24986i) q^{77} +(-0.501023 - 1.72424i) q^{78} +(-12.4889 + 10.4794i) q^{79} +(3.83053 - 8.14414i) q^{81} +1.09233 q^{82} +(-8.56544 + 7.18726i) q^{83} +(1.57056 + 5.40498i) q^{84} +(-1.81974 + 0.662331i) q^{86} +(-0.216568 - 0.144965i) q^{87} +(0.934487 + 5.29974i) q^{88} +(4.58274 + 7.93753i) q^{89} +(3.16572 - 5.48319i) q^{91} +(-11.6937 - 4.25615i) q^{92} +(-10.5547 + 1.14710i) q^{93} +(1.31344 + 1.10211i) q^{94} +(3.22429 + 4.40501i) q^{96} +(12.9391 + 4.70945i) q^{97} +(-0.573397 + 0.993152i) q^{98} +(14.5281 - 3.19561i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 6 q^{2} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 6 q^{9} + 15 q^{11} + 18 q^{12} + 15 q^{14} + 18 q^{16} + 30 q^{17} - 12 q^{18} + 12 q^{19} + 12 q^{21} - 45 q^{22} + 36 q^{23} - 39 q^{24} + 6 q^{26} + 51 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) $ 66 * q + 6 * q^2 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 6 * q^9 + 15 * q^11 + 18 * q^12 + 15 * q^14 + 18 * q^16 + 30 * q^17 - 12 * q^18 + 12 * q^19 + 12 * q^21 - 45 * q^22 + 36 * q^23 - 39 * q^24 + 6 * q^26 + 51 * q^27 - 36 * q^28 - 15 * q^29 + 3 * q^31 + 27 * q^32 - 3 * q^33 + 30 * q^36 + 6 * q^37 - 12 * q^38 - 15 * q^39 + 39 * q^41 + 48 * q^42 + 12 * q^43 + 51 * q^44 + 9 * q^46 + 30 * q^47 - 132 * q^48 - 6 * q^49 + 9 * q^52 - 24 * q^53 + 75 * q^54 + 144 * q^56 + 33 * q^57 + 27 * q^58 + 45 * q^59 - 54 * q^61 + 66 * q^62 - 120 * q^63 - 24 * q^64 + 48 * q^66 + 9 * q^67 - 69 * q^68 + 51 * q^69 - 15 * q^71 + 9 * q^72 - 15 * q^73 + 96 * q^74 - 48 * q^76 - 36 * q^77 - 18 * q^78 + 48 * q^79 - 54 * q^81 - 36 * q^82 + 30 * q^83 + 57 * q^84 - 111 * q^86 - 33 * q^87 + 36 * q^88 - 12 * q^89 + 9 * q^91 - 219 * q^92 + 63 * q^93 + 36 * q^94 - 249 * q^96 + 57 * q^97 + 75 * q^98 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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 $

$2$	−0.211903	+	0.177808i	−0.149838	+	0.125729i	−0.714625	−	0.699508i	$-0.753403\pi$
$2$	−0.211903	+	0.177808i	−0.149838	+	0.125729i	0.564787	+	0.825237i	$0.308958\pi$
$3$	0.483303	+	1.66326i	0.279035	+	0.960281i
$3$	0.483303	+	1.66326i	0.279035	+	0.960281i
$4$	−0.334009	+	1.89426i	−0.167005	+	0.947130i
$5$		0			0
$5$		0			0
$6$	−0.398153	−	0.266514i	−0.162545	−	0.108804i
$7$	−0.293371	−	1.66379i	−0.110884	−	0.628853i	−0.988706	−	0.149867i	$-0.952115\pi$
$7$	−0.293371	−	1.66379i	−0.110884	−	0.628853i	0.877822	−	0.478986i	$-0.158996\pi$
$8$	−0.542656	−	0.939908i	−0.191858	−	0.332308i
$9$	−2.53284	+	1.60771i	−0.844279	+	0.535904i
$10$		0			0
$11$	−4.65944	−	1.69590i	−1.40488	−	0.511333i	−0.475254	−	0.879849i	$-0.657644\pi$
$11$	−4.65944	−	1.69590i	−1.40488	−	0.511333i	−0.929621	+	0.368516i	$0.879866\pi$
$12$	−3.31206	+	0.359958i	−0.956111	+	0.103911i
$13$	2.87084	+	2.40892i	0.796229	+	0.668115i	0.947279	−	0.320411i	$-0.103821\pi$
$13$	2.87084	+	2.40892i	0.796229	+	0.668115i	−0.151050	+	0.988526i	$0.548265\pi$
$14$	0.358001	+	0.300398i	0.0956798	+	0.0802849i
$15$		0			0
$16$	−3.33285	−	1.21306i	−0.833212	−	0.303264i
$17$	−3.15798	+	5.46979i	−0.765923	+	1.32662i	0.173834	+	0.984775i	$0.444385\pi$
$17$	−3.15798	+	5.46979i	−0.765923	+	1.32662i	−0.939757	+	0.341843i	$0.888949\pi$
$18$	0.250852	−	0.791037i	0.0591265	−	0.186449i
$19$	−3.42671	−	5.93524i	−0.786142	−	1.36164i	−0.928314	−	0.371796i	$-0.878742\pi$
$19$	−3.42671	−	5.93524i	−0.786142	−	1.36164i	0.142172	−	0.989842i	$-0.454591\pi$
$20$		0			0
$21$	2.62552	−	1.29206i	0.572935	−	0.281952i
$22$	1.28889	−	0.469119i	0.274793	−	0.100017i
$23$	−1.12343	+	6.37131i	−0.234252	+	1.32851i	0.609931	+	0.792454i	$0.291197\pi$
$23$	−1.12343	+	6.37131i	−0.234252	+	1.32851i	−0.844183	+	0.536055i	$0.819914\pi$
$24$	1.30104	−	1.35684i	0.265574	−	0.276963i
$25$		0			0
$26$	−1.03667			−0.203307
$27$	−3.89816	−	3.43574i	−0.750202	−	0.661209i
$28$	3.24964			0.614124
$29$	−0.115261	+	0.0967151i	−0.0214034	+	0.0179596i	−0.653427	−	0.756990i	$-0.726669\pi$
$29$	−0.115261	+	0.0967151i	−0.0214034	+	0.0179596i	0.632023	+	0.774949i	$0.282225\pi$
$30$		0			0
$31$	−1.06440	+	6.03653i	−0.191172	+	1.08419i	0.726593	+	0.687068i	$0.241103\pi$
$31$	−1.06440	+	6.03653i	−0.191172	+	1.08419i	−0.917765	+	0.397124i	$0.870008\pi$
$32$	2.96165	−	1.07795i	0.523551	−	0.190557i
$33$	0.568791	−	8.56948i	0.0990138	−	1.49175i
$34$	−0.303384	−	1.72058i	−0.0520300	−	0.295077i
$35$		0			0
$36$	−2.19943	−	5.33484i	−0.366572	−	0.889140i
$37$	1.23541	−	2.13979i	0.203100	−	0.351780i	−0.746426	−	0.665469i	$-0.768232\pi$
$37$	1.23541	−	2.13979i	0.203100	−	0.351780i	0.949526	+	0.313689i	$0.101565\pi$
$38$	1.78146	+	0.648400i	0.288992	+	0.105184i
$39$	−2.61917	+	5.93918i	−0.419403	+	0.951031i
$40$		0			0
$41$	−3.02499	−	2.53826i	−0.472423	−	0.396410i	0.375254	−	0.926922i	$-0.377555\pi$
$41$	−3.02499	−	2.53826i	−0.472423	−	0.396410i	−0.847678	+	0.530512i	$0.822000\pi$
$42$	−0.326617	+	0.740630i	−0.0503980	+	0.114282i
$43$	6.57849	+	2.39437i	1.00321	+	0.365139i	0.790822	−	0.612047i	$-0.209654\pi$
$43$	6.57849	+	2.39437i	1.00321	+	0.365139i	0.212388	+	0.977185i	$0.431876\pi$
$44$	4.76877	−	8.25975i	0.718919	−	1.24520i
$45$		0			0
$46$	−0.894809	−	1.54985i	−0.131932	−	0.228514i
$47$	−1.07632	−	6.10414i	−0.156998	−	0.890380i	−0.956936	−	0.290298i	$-0.906246\pi$
$47$	−1.07632	−	6.10414i	−0.156998	−	0.890380i	0.799938	−	0.600082i	$-0.204865\pi$
$48$	0.406850	−	6.12965i	0.0587238	−	0.884739i
$49$	3.89572	−	1.41793i	0.556531	−	0.202561i
$50$		0			0
$51$	−10.6239	−	2.60897i	−1.48765	−	0.365329i
$52$	−5.52201	+	4.63352i	−0.765766	+	0.642554i
$53$	0.373453			0.0512977			0.0256488	−	0.999671i	$-0.491835\pi$
$53$	0.373453			0.0512977			0.0256488	+	0.999671i	$0.491835\pi$
$54$	1.43693	+	0.0349210i	0.195542	+	0.00475215i
$55$		0			0
$56$	−1.40461	+	1.17861i	−0.187699	+	0.157498i
$57$	8.21568	−	8.56802i	1.08819	−	1.13486i
$58$	0.00722737	−	0.0409885i	0.000949001	−	0.00538205i
$59$	0.342887	−	0.124801i	0.0446401	−	0.0162477i	−0.319604	−	0.947551i	$-0.603550\pi$
$59$	0.342887	−	0.124801i	0.0446401	−	0.0162477i	0.364244	+	0.931304i	$0.381328\pi$
$60$		0			0
$61$	1.07271	+	6.08365i	0.137347	+	0.778931i	0.973197	+	0.229974i	$0.0738640\pi$
$61$	1.07271	+	6.08365i	0.137347	+	0.778931i	−0.835850	+	0.548958i	$0.815025\pi$
$62$	−0.847791	−	1.46842i	−0.107670	−	0.186489i
$63$	3.41795	+	3.74245i	0.430622	+	0.471505i
$64$	3.11083	−	5.38811i	0.388854	−	0.673514i
$65$		0			0
$66$	1.40319	+	1.91703i	0.172721	+	0.235971i
$67$	−0.475424	−	0.398928i	−0.0580823	−	0.0487369i	0.613284	−	0.789862i	$-0.289848\pi$
$67$	−0.475424	−	0.398928i	−0.0580823	−	0.0487369i	−0.671367	+	0.741125i	$0.734292\pi$
$68$	−9.30640	−	7.80900i	−1.12857	−	0.946980i
$69$	−11.1401	+	1.21071i	−1.34111	+	0.145753i
$70$		0			0
$71$	−3.39814	+	5.88576i	−0.403285	+	0.698511i	−0.994120	−	0.108282i	$-0.965465\pi$
$71$	−3.39814	+	5.88576i	−0.403285	+	0.698511i	0.590835	+	0.806793i	$0.298799\pi$
$72$	2.88556	+	1.50820i	0.340067	+	0.177743i
$73$	2.27683	+	3.94359i	0.266483	+	0.461563i	0.967951	−	0.251138i	$-0.0808049\pi$
$73$	2.27683	+	3.94359i	0.266483	+	0.461563i	−0.701468	+	0.712701i	$0.747472\pi$
$74$	0.118685	+	0.673094i	0.0137968	+	0.0782456i
$75$		0			0
$76$	12.3874	−	4.50866i	1.42094	−	0.517179i
$77$	−1.45467	+	8.24986i	−0.165775	+	0.940159i
$78$	−0.501023	−	1.72424i	−0.0567297	−	0.195232i
$79$	−12.4889	+	10.4794i	−1.40511	+	1.17903i	−0.446338	+	0.894864i	$0.647272\pi$
$79$	−12.4889	+	10.4794i	−1.40511	+	1.17903i	−0.958775	+	0.284166i	$0.908283\pi$
$80$		0			0
$81$	3.83053	−	8.14414i	0.425614	−	0.904905i
$82$	1.09233			0.120627
$83$	−8.56544	+	7.18726i	−0.940179	+	0.788904i	−0.977616	−	0.210395i	$-0.932525\pi$
$83$	−8.56544	+	7.18726i	−0.940179	+	0.788904i	0.0374374	+	0.999299i	$0.488081\pi$
$84$	1.57056	+	5.40498i	0.171362	+	0.589731i
$85$		0			0
$86$	−1.81974	+	0.662331i	−0.196228	+	0.0714210i
$87$	−0.216568	−	0.144965i	−0.0232185	−	0.0155419i
$88$	0.934487	+	5.29974i	0.0996167	+	0.564954i
$89$	4.58274	+	7.93753i	0.485769	+	0.841377i	0.999866	−	0.0163553i	$-0.00520627\pi$
$89$	4.58274	+	7.93753i	0.485769	+	0.841377i	−0.514097	+	0.857732i	$0.671873\pi$
$90$		0			0
$91$	3.16572	−	5.48319i	0.331858	−	0.574794i
$92$	−11.6937	−	4.25615i	−1.21915	−	0.443734i
$93$	−10.5547	+	1.14710i	−1.09447	+	0.118948i
$94$	1.31344	+	1.10211i	0.135471	+	0.113674i
$95$		0			0
$96$	3.22429	+	4.40501i	0.329077	+	0.449584i
$97$	12.9391	+	4.70945i	1.31377	+	0.478172i	0.901456	−	0.432871i	$-0.142499\pi$
$97$	12.9391	+	4.70945i	1.31377	+	0.478172i	0.412312	+	0.911043i	$0.364721\pi$
$98$	−0.573397	+	0.993152i	−0.0579218	+	0.100324i
$99$	14.5281	−	3.19561i	1.46013	−	0.321171i
$100$		0			0
$101$	1.98385	+	11.2510i	0.197400	+	1.11951i	0.908959	+	0.416886i	$0.136879\pi$
$101$	1.98385	+	11.2510i	0.197400	+	1.11951i	−0.711558	+	0.702627i	$0.752010\pi$
$102$	2.71514	−	1.33617i	0.268838	−	0.132300i
$103$	8.62703	−	3.13998i	0.850046	−	0.309392i	0.119987	−	0.992775i	$-0.461715\pi$
$103$	8.62703	−	3.13998i	0.850046	−	0.309392i	0.730059	+	0.683384i	$0.239492\pi$
$104$	0.706286	−	4.00555i	0.0692571	−	0.392776i
$105$		0			0
$106$	−0.0791358	+	0.0664028i	−0.00768635	+	0.00644961i
$107$	1.09015			0.105389			0.0526946	−	0.998611i	$-0.483219\pi$
$107$	1.09015			0.105389			0.0526946	+	0.998611i	$0.483219\pi$
$108$	7.81021	−	6.23656i	0.751538	−	0.600113i
$109$	−0.574982			−0.0550733			−0.0275366	−	0.999621i	$-0.508766\pi$
$109$	−0.574982			−0.0550733			−0.0275366	+	0.999621i	$0.508766\pi$
$110$		0			0
$111$	4.15610	+	1.02063i	0.394480	+	0.0968744i
$112$	−1.04051	+	5.90104i	−0.0983191	+	0.557595i
$113$	−16.5549	+	6.02550i	−1.55736	+	0.566832i	−0.970129	−	0.242590i	$-0.922003\pi$
$113$	−16.5549	+	6.02550i	−1.55736	+	0.566832i	−0.587228	+	0.809421i	$0.699781\pi$
$114$	−0.217468	+	3.27640i	−0.0203678	+	0.306863i
$115$		0			0
$116$	−0.144705	−	0.250637i	−0.0134356	−	0.0232711i
$117$	−11.1442	−	1.48592i	−1.03028	−	0.137374i
$118$	−0.0504683	+	0.0874136i	−0.00464598	+	0.00804708i
$119$	10.0270	+	3.64954i	0.919177	+	0.334553i
$120$		0			0
$121$	10.4079	+	8.73323i	0.946169	+	0.793930i
$122$	−1.30903	−	1.09841i	−0.118514	−	0.0994451i
$123$	2.75980	−	6.25807i	0.248843	−	0.564272i
$124$	−11.0792	−	4.03251i	−0.994944	−	0.362130i
$125$		0			0
$126$	−1.38971	−	0.185298i	−0.123805	−	0.0165077i
$127$	3.97850	+	6.89096i	0.353035	+	0.611474i	0.986780	−	0.162068i	$-0.0518164\pi$
$127$	3.97850	+	6.89096i	0.353035	+	0.611474i	−0.633745	+	0.773542i	$0.718483\pi$
$128$	1.39344	+	7.90257i	0.123164	+	0.698496i
$129$	−0.803054	+	12.0989i	−0.0707050	+	1.06525i
$130$		0			0
$131$	1.46844	−	8.32796i	0.128298	−	0.727617i	−0.850995	−	0.525173i	$-0.824001\pi$
$131$	1.46844	−	8.32796i	0.128298	−	0.727617i	0.979294	−	0.202444i	$-0.0648883\pi$
$132$	16.0428	+	3.93972i	1.39635	+	0.342909i
$133$	−8.86970	+	7.44256i	−0.769100	+	0.645352i
$134$	0.171676			0.0148306
$135$		0			0
$136$	6.85480			0.587794
$137$	−0.303815	+	0.254931i	−0.0259567	+	0.0217802i	−0.655674	−	0.755044i	$-0.727615\pi$
$137$	−0.303815	+	0.254931i	−0.0259567	+	0.0217802i	0.629717	+	0.776825i	$0.283171\pi$
$138$	2.14534	−	2.23734i	0.182624	−	0.190455i
$139$	−0.813377	+	4.61289i	−0.0689897	+	0.391260i	0.930687	+	0.365818i	$0.119211\pi$
$139$	−0.813377	+	4.61289i	−0.0689897	+	0.391260i	−0.999676	+	0.0254426i	$0.991901\pi$
$140$		0			0
$141$	9.63255	−	4.74035i	0.811207	−	0.399209i
$142$	−0.326456	−	1.85143i	−0.0273956	−	0.155368i
$143$	−9.29124	−	16.0929i	−0.776973	−	1.34576i
$144$	10.3918	−	2.28578i	0.865984	−	0.190482i
$145$		0			0
$146$	−1.18367	−	0.430821i	−0.0979612	−	0.0356550i
$147$	4.24118	+	5.79429i	0.349807	+	0.477905i
$148$	3.64069	+	3.05490i	0.299263	+	0.251111i
$149$	−17.6585	−	14.8172i	−1.44664	−	1.21387i	−0.934987	−	0.354682i	$-0.884589\pi$
$149$	−17.6585	−	14.8172i	−1.44664	−	1.21387i	−0.511653	−	0.859192i	$-0.670967\pi$
$150$		0			0
$151$	−4.86203	−	1.76963i	−0.395666	−	0.144011i	0.136522	−	0.990637i	$-0.456408\pi$
$151$	−4.86203	−	1.76963i	−0.395666	−	0.144011i	−0.532188	+	0.846626i	$0.678630\pi$
$152$	−3.71906	+	6.44159i	−0.301655	+	0.522482i
$153$	−0.795184	−	18.9312i	−0.0642868	−	1.53050i
$154$	−1.15864	−	2.00682i	−0.0933659	−	0.161714i
$155$		0			0
$156$	−10.3755	−	6.94513i	−0.830707	−	0.556055i
$157$	−13.0179	+	4.73812i	−1.03894	+	0.378143i	−0.804478	−	0.593982i	$-0.797555\pi$
$157$	−13.0179	+	4.73812i	−1.03894	+	0.378143i	−0.234462	+	0.972125i	$0.575333\pi$
$158$	0.783113	−	4.44125i	0.0623011	−	0.353327i
$159$	0.180491	+	0.621147i	0.0143138	+	0.0492602i
$160$		0			0
$161$	10.9301			0.861412
$162$	0.636392	+	2.40687i	0.0499997	+	0.189101i
$163$	−2.98083			−0.233477			−0.116738	−	0.993163i	$-0.537244\pi$
$163$	−2.98083			−0.233477			−0.116738	+	0.993163i	$0.537244\pi$
$164$	5.81850	−	4.88231i	0.454349	−	0.381244i
$165$		0			0
$166$	0.537093	−	3.04600i	0.0416865	−	0.236416i
$167$	17.6335	−	6.41805i	1.36452	−	0.496644i	0.447070	−	0.894499i	$-0.352468\pi$
$167$	17.6335	−	6.41805i	1.36452	−	0.496644i	0.917448	+	0.397855i	$0.130245\pi$
$168$	−2.63918	−	1.76660i	−0.203617	−	0.136296i
$169$	0.181402	+	1.02878i	0.0139540	+	0.0791371i
$170$		0			0
$171$	18.2215	+	9.52383i	1.39343	+	0.728306i
$172$	−6.73284	+	11.6616i	−0.513374	+	0.889190i
$173$	7.89065	+	2.87196i	0.599915	+	0.218351i	0.624085	−	0.781357i	$-0.285472\pi$
$173$	7.89065	+	2.87196i	0.599915	+	0.218351i	−0.0241697	+	0.999708i	$0.507694\pi$
$174$	0.0716673	−	0.00778887i	0.00543308	−	0.000590473i
$175$		0			0
$176$	13.4720	+	11.3043i	1.01549	+	0.852097i
$177$	0.373294	+	0.509992i	0.0280585	+	0.0383334i
$178$	−2.38245	−	0.867141i	−0.178572	−	0.0649950i
$179$	11.7123	−	20.2863i	0.875420	−	1.51627i	0.0191052	−	0.999817i	$-0.493918\pi$
$179$	11.7123	−	20.2863i	0.875420	−	1.51627i	0.856315	−	0.516454i	$-0.172748\pi$
$180$		0			0
$181$	4.02049	+	6.96369i	0.298841	+	0.517607i	0.975871	−	0.218348i	$-0.0700667\pi$
$181$	4.02049	+	6.96369i	0.298841	+	0.517607i	−0.677030	+	0.735955i	$0.736733\pi$
$182$	0.304128	+	1.72479i	0.0225434	+	0.127850i
$183$	−9.60022	+	4.72444i	−0.709668	+	0.349240i
$184$	6.59808	−	2.40151i	0.486417	−	0.177041i
$185$		0			0
$186$	2.03261	−	2.11978i	0.149038	−	0.155430i
$187$	23.9906	−	20.1305i	1.75437	−	1.47209i
$188$	11.9223			0.869525
$189$	−4.57275	+	7.49367i	−0.332618	+	0.545084i
$190$		0			0
$191$	2.02875	−	1.70232i	0.146795	−	0.123176i	−0.566433	−	0.824108i	$-0.691677\pi$
$191$	2.02875	−	1.70232i	0.146795	−	0.123176i	0.713228	+	0.700932i	$0.247232\pi$
$192$	10.4653	+	2.57001i	0.755267	+	0.185475i
$193$	−2.39096	+	13.5598i	−0.172105	+	0.976055i	0.769328	+	0.638854i	$0.220591\pi$
$193$	−2.39096	+	13.5598i	−0.172105	+	0.976055i	−0.941433	+	0.337201i	$0.890520\pi$
$194$	−3.57921	+	1.30273i	−0.256973	+	0.0935304i
$195$		0			0
$196$	1.38471	+	7.85310i	0.0989081	+	0.560936i
$197$	5.44000	+	9.42236i	0.387584	+	0.671315i	0.992124	−	0.125260i	$-0.0399764\pi$
$197$	5.44000	+	9.42236i	0.387584	+	0.671315i	−0.604540	+	0.796575i	$0.706643\pi$
$198$	−2.51035	+	3.26037i	−0.178403	+	0.231705i
$199$	9.58456	−	16.6009i	0.679431	−	1.17681i	−0.295721	−	0.955274i	$-0.595560\pi$
$199$	9.58456	−	16.6009i	0.679431	−	1.17681i	0.975152	−	0.221535i	$-0.0711068\pi$
$200$		0			0
$201$	0.433746	−	0.983555i	0.0305941	−	0.0693747i
$202$	−2.42089	−	2.03137i	−0.170334	−	0.142927i
$203$	0.194728	+	0.163396i	0.0136672	+	0.0114682i
$204$	8.49055	−	19.2530i	0.594457	−	1.34798i
$205$		0			0
$206$	−1.26978	+	2.19932i	−0.0884698	+	0.153234i
$207$	−7.39775	−	17.9436i	−0.514179	−	1.24717i
$208$	−6.64592	−	11.5111i	−0.460812	−	0.798150i
$209$	5.90101	+	33.4663i	0.408181	+	2.31491i
$210$		0			0
$211$	−14.2097	+	5.17190i	−0.978235	+	0.356048i	−0.781154	−	0.624339i	$-0.785369\pi$
$211$	−14.2097	+	5.17190i	−0.978235	+	0.356048i	−0.197081	+	0.980387i	$0.563146\pi$
$212$	−0.124737	+	0.707417i	−0.00856695	+	0.0485856i
$213$	−11.4319	−	2.80738i	−0.783297	−	0.192358i
$214$	−0.231007	+	0.193838i	−0.0157913	+	0.0132505i
$215$		0			0
$216$	−1.11392	+	5.52834i	−0.0757928	+	0.376156i
$217$	10.3558			0.702996
$218$	0.121840	−	0.102236i	0.00825207	−	0.00692431i
$219$	−5.45880	+	5.69291i	−0.368872	+	0.384691i
$220$		0			0
$221$	−22.2424	+	8.09556i	−1.49618	+	0.544566i
$222$	−1.06217	+	0.522711i	−0.0712880	+	0.0350821i
$223$	−0.809497	−	4.59088i	−0.0542079	−	0.307428i	0.945634	−	0.325234i	$-0.105443\pi$
$223$	−0.809497	−	4.59088i	−0.0542079	−	0.307428i	−0.999841	+	0.0178057i	$0.994332\pi$
$224$	−2.66235	−	4.61133i	−0.177886	−	0.308107i
$225$		0			0
$226$	2.43666	−	4.22042i	0.162084	−	0.280738i
$227$	−0.187481	−	0.0682374i	−0.0124435	−	0.00452908i	0.335791	−	0.941937i	$-0.390996\pi$
$227$	−0.187481	−	0.0682374i	−0.0124435	−	0.00452908i	−0.348234	+	0.937407i	$0.613219\pi$
$228$	13.4859	+	18.4244i	0.893128	+	1.22019i
$229$	13.3044	+	11.1637i	0.879179	+	0.737719i	0.966010	−	0.258504i	$-0.0832296\pi$
$229$	13.3044	+	11.1637i	0.879179	+	0.737719i	−0.0868311	+	0.996223i	$0.527674\pi$
$230$		0			0
$231$	−14.4247	+	1.56769i	−0.949074	+	0.103146i
$232$	0.153450	+	0.0558513i	0.0100745	+	0.00366682i
$233$	−7.90504	+	13.6919i	−0.517876	+	0.896988i	0.481908	+	0.876222i	$0.339944\pi$
$233$	−7.90504	+	13.6919i	−0.517876	+	0.896988i	−0.999784	+	0.0207662i	$0.993389\pi$
$234$	2.62571	−	1.66666i	0.171648	−	0.108953i
$235$		0			0
$236$	0.121877	+	0.691202i	0.00793355	+	0.0449934i
$237$	−23.4659	−	15.7075i	−1.52428	−	1.02031i
$238$	−2.77368	+	1.00954i	−0.179791	+	0.0654385i
$239$	−5.21235	+	29.5607i	−0.337159	+	1.91212i	0.0676249	+	0.997711i	$0.478458\pi$
$239$	−5.21235	+	29.5607i	−0.337159	+	1.91212i	−0.404784	+	0.914412i	$0.632653\pi$
$240$		0			0
$241$	−2.74958	+	2.30717i	−0.177116	+	0.148618i	−0.727036	−	0.686600i	$-0.759103\pi$
$241$	−2.74958	+	2.30717i	−0.177116	+	0.148618i	0.549920	+	0.835217i	$0.314658\pi$
$242$	−3.75829			−0.241592
$243$	15.3971	+	2.43506i	0.987724	+	0.156209i
$244$	−11.8823			−0.760686
$245$		0			0
$246$	0.527925	+	1.81682i	0.0336592	+	0.115836i
$247$	4.45999	−	25.2938i	0.283782	−	1.60941i
$248$	6.25139	−	2.27532i	0.396964	−	0.144483i
$249$	−16.0939	−	10.7729i	−1.01991	−	0.682704i
$250$		0			0
$251$	−12.8233	−	22.2107i	−0.809401	−	1.40192i	−0.913279	−	0.407334i	$-0.866458\pi$
$251$	−12.8233	−	22.2107i	−0.809401	−	1.40192i	0.103878	−	0.994590i	$-0.466875\pi$
$252$	−8.23080	+	5.22448i	−0.518492	+	0.329111i
$253$	16.0397	−	27.7815i	1.00841	−	1.74661i
$254$	−2.06832	−	0.752808i	−0.129778	−	0.0472354i
$255$		0			0
$256$	7.83172	+	6.57159i	0.489483	+	0.410725i
$257$	−6.42079	−	5.38768i	−0.400518	−	0.336075i	0.420176	−	0.907443i	$-0.361968\pi$
$257$	−6.42079	−	5.38768i	−0.400518	−	0.336075i	−0.820694	+	0.571368i	$0.806413\pi$
$258$	−1.98111	−	2.70659i	−0.123339	−	0.168505i
$259$	−3.92260	−	1.42771i	−0.243738	−	0.0887135i
$260$		0			0
$261$	0.136446	−	0.430270i	0.00844581	−	0.0266330i
$262$	1.16961	+	2.02582i	0.0722586	+	0.125156i
$263$	0.883720	+	5.01183i	0.0544925	+	0.309043i	0.999856	−	0.0169761i	$-0.00540391\pi$
$263$	0.883720	+	5.01183i	0.0544925	+	0.309043i	−0.945363	+	0.326019i	$0.894293\pi$
$264$	−8.36318	+	4.11567i	−0.514718	+	0.253302i
$265$		0			0
$266$	0.556171	−	3.15420i	0.0341010	−	0.193397i
$267$	−10.9873	+	11.4585i	−0.672411	+	0.701248i
$268$	0.914470	−	0.767331i	0.0558601	−	0.0468722i
$269$	28.2625			1.72320			0.861599	−	0.507590i	$-0.169464\pi$
$269$	28.2625			1.72320			0.861599	+	0.507590i	$0.169464\pi$
$270$		0			0
$271$	−17.2893			−1.05025			−0.525125	−	0.851025i	$-0.675982\pi$
$271$	−17.2893			−1.05025			−0.525125	+	0.851025i	$0.675982\pi$
$272$	17.1602	−	14.3992i	1.04049	−	0.873077i
$273$	10.6499	+	2.61536i	0.644564	+	0.158289i
$274$	0.0190506	−	0.108041i	0.00115089	−	0.00652702i
$275$		0			0
$276$	1.42748	−	21.5066i	0.0859241	−	1.29454i
$277$	0.718943	+	4.07733i	0.0431971	+	0.244983i	0.998759	−	0.0498083i	$-0.0158610\pi$
$277$	0.718943	+	4.07733i	0.0431971	+	0.244983i	−0.955562	+	0.294791i	$0.904750\pi$
$278$	−0.647851	−	1.12211i	−0.0388555	−	0.0672997i
$279$	−7.00904	−	17.0008i	−0.419620	−	1.01781i
$280$		0			0
$281$	18.0380	+	6.56528i	1.07605	+	0.391652i	0.818438	−	0.574595i	$-0.194840\pi$
$281$	18.0380	+	6.56528i	1.07605	+	0.391652i	0.257617	+	0.966247i	$0.417063\pi$
$282$	−1.19830	+	2.71724i	−0.0713575	+	0.161809i
$283$	7.31199	+	6.13548i	0.434652	+	0.364717i	0.833704	−	0.552212i	$-0.186216\pi$
$283$	7.31199	+	6.13548i	0.434652	+	0.364717i	−0.399051	+	0.916929i	$0.630661\pi$
$284$	−10.0141	−	8.40286i	−0.594230	−	0.498618i
$285$		0			0
$286$	4.83029	+	1.75808i	0.285621	+	0.103957i
$287$	−3.33570	+	5.77759i	−0.196900	+	0.341041i
$288$	−5.76835	+	7.49176i	−0.339903	+	0.441456i
$289$	−11.4457	−	19.8246i	−0.673277	−	1.16615i
$290$		0			0
$291$	−1.57951	+	23.7971i	−0.0925927	+	1.39501i
$292$	−8.23067	+	2.99572i	−0.481664	+	0.175311i
$293$	−1.10363	+	6.25900i	−0.0644748	+	0.365655i	0.935451	+	0.353457i	$0.114994\pi$
$293$	−1.10363	+	6.25900i	−0.0644748	+	0.365655i	−0.999926	+	0.0121977i	$0.996117\pi$
$294$	−1.92899	−	0.473712i	−0.112501	−	0.0276274i
$295$		0			0
$296$	−2.68161			−0.155866
$297$	12.3366	+	22.6195i	0.715842	+	1.31252i
$298$	6.37651			0.369381
$299$	−18.5732	+	15.5848i	−1.07412	+	0.901290i
$300$		0			0
$301$	2.05380	−	11.6477i	0.118379	−	0.671360i
$302$	1.34493	−	0.489516i	0.0773922	−	0.0281685i
$303$	−17.7544	+	8.73727i	−1.01997	+	0.501943i
$304$	4.22093	+	23.9381i	0.242087	+	1.37294i
$305$		0			0
$306$	3.53462	+	3.87019i	0.202061	+	0.221244i
$307$	−4.29280	+	7.43535i	−0.245003	+	0.424358i	−0.962133	−	0.272582i	$-0.912122\pi$
$307$	−4.29280	+	7.43535i	−0.245003	+	0.424358i	0.717129	+	0.696940i	$0.245456\pi$
$308$	−15.1415	−	5.51106i	−0.862767	−	0.314022i
$309$	9.39206	+	12.8314i	0.534295	+	0.729952i
$310$		0			0
$311$	−8.78608	−	7.37239i	−0.498213	−	0.418050i	0.358746	−	0.933435i	$-0.383204\pi$
$311$	−8.78608	−	7.37239i	−0.498213	−	0.418050i	−0.856959	+	0.515385i	$0.827649\pi$
$312$	7.00360	−	0.761158i	0.396501	−	0.0430921i
$313$	−23.4476	−	8.53424i	−1.32534	−	0.482384i	−0.420173	−	0.907444i	$-0.638031\pi$
$313$	−23.4476	−	8.53424i	−1.32534	−	0.482384i	−0.905165	+	0.425060i	$0.860253\pi$
$314$	1.91605	−	3.31870i	0.108129	−	0.187285i
$315$		0			0
$316$	−15.6794	−	27.1575i	−0.882034	−	1.52773i
$317$	−0.110144	−	0.624658i	−0.00618630	−	0.0350843i	0.981558	−	0.191163i	$-0.0612258\pi$
$317$	−0.110144	−	0.624658i	−0.00618630	−	0.0350843i	−0.987745	+	0.156078i	$0.950115\pi$
$318$	−0.148691	−	0.0995304i	−0.00833820	−	0.00558139i
$319$	0.701069	−	0.255168i	0.0392524	−	0.0142867i
$320$		0			0
$321$	0.526875	+	1.81321i	0.0294073	+	0.101203i
$322$	−2.31612	+	1.94346i	−0.129072	+	0.108305i
$323$	43.2860			2.40850
$324$	14.1477	+	9.97623i	0.785983	+	0.554235i
$325$		0			0
$326$	0.631648	−	0.530015i	0.0349837	−	0.0293548i
$327$	−0.277890	−	0.956342i	−0.0153674	−	0.0528858i
$328$	−0.744208	+	4.22062i	−0.0410920	+	0.233045i
$329$	−9.84024	+	3.58155i	−0.542510	+	0.197457i
$330$		0			0
$331$	−3.50296	−	19.8662i	−0.192540	−	1.09195i	−0.915879	−	0.401455i	$-0.868505\pi$
$331$	−3.50296	−	19.8662i	−0.192540	−	1.09195i	0.723339	−	0.690493i	$-0.242606\pi$
$332$	−10.7536	−	18.6258i	−0.590180	−	1.02222i
$333$	0.311078	+	7.40593i	0.0170470	+	0.405843i
$334$	−2.59540	+	4.49537i	−0.142014	+	0.245976i
$335$		0			0
$336$	−10.3178	+	1.12135i	−0.562883	+	0.0611746i
$337$	−23.2996	−	19.5507i	−1.26921	−	1.06499i	−0.994637	−	0.103428i	$-0.967019\pi$
$337$	−23.2996	−	19.5507i	−1.26921	−	1.06499i	−0.274574	−	0.961566i	$-0.588537\pi$
$338$	−0.221365	−	0.185747i	−0.0120407	−	0.0101033i
$339$	−18.0230	−	24.6229i	−0.978875	−	1.33733i
$340$		0			0
$341$	15.1969	−	26.3217i	0.822956	−	1.42540i
$342$	−5.55460	+	1.22179i	−0.300358	+	0.0660668i
$343$	−9.41512	−	16.3075i	−0.508369	−	0.880520i
$344$	−1.31937	−	7.48250i	−0.0711355	−	0.403429i
$345$		0			0
$346$	−2.18271	+	0.794442i	−0.117343	+	0.0427094i
$347$	−6.41781	+	36.3972i	−0.344526	+	1.95391i	−0.0481276	+	0.998841i	$0.515325\pi$
$347$	−6.41781	+	36.3972i	−0.344526	+	1.95391i	−0.296399	+	0.955064i	$0.595786\pi$
$348$	0.346937	−	0.361816i	0.0185978	−	0.0193954i
$349$	5.58600	−	4.68721i	0.299012	−	0.250901i	−0.480921	−	0.876764i	$-0.659698\pi$
$349$	5.58600	−	4.68721i	0.299012	−	0.250901i	0.779933	+	0.625863i	$0.215253\pi$
$350$		0			0
$351$	−2.91457	−	19.2539i	−0.155568	−	1.02769i
$352$	−15.6278			−0.832962
$353$	8.72291	−	7.31939i	0.464273	−	0.389572i	−0.380427	−	0.924811i	$-0.624223\pi$
$353$	8.72291	−	7.31939i	0.464273	−	0.389572i	0.844700	+	0.535239i	$0.179779\pi$
$354$	−0.169783	−	0.0416944i	−0.00902385	−	0.00221603i
$355$		0			0
$356$	−16.5664	+	6.02968i	−0.878018	+	0.319573i
$357$	−1.22403	+	18.4414i	−0.0647824	+	0.976020i
$358$	1.12519	+	6.38128i	0.0594682	+	0.337261i
$359$	−12.4562	−	21.5748i	−0.657414	−	1.13867i	−0.981283	−	0.192573i	$-0.938317\pi$
$359$	−12.4562	−	21.5748i	−0.657414	−	1.13867i	0.323869	−	0.946102i	$-0.395016\pi$
$360$		0			0
$361$	−13.9847	+	24.2223i	−0.736039	+	1.27486i
$362$	−2.09015	−	0.760754i	−0.109856	−	0.0399843i
$363$	−9.49544	+	21.5317i	−0.498381	+	1.13012i
$364$	9.32920	+	7.82813i	0.488983	+	0.410305i
$365$		0			0
$366$	1.19427	−	2.70812i	0.0624257	−	0.141555i
$367$	−27.0081	−	9.83014i	−1.40981	−	0.513129i	−0.478736	−	0.877959i	$-0.658905\pi$
$367$	−27.0081	−	9.83014i	−1.40981	−	0.513129i	−0.931074	+	0.364830i	$0.881127\pi$
$368$	11.4730	−	19.8718i	0.598071	−	1.03589i
$369$	11.7426	+	1.56571i	0.611295	+	0.0815074i
$370$		0			0
$371$	−0.109560	−	0.621347i	−0.00568808	−	0.0322587i
$372$	1.35247	−	20.3765i	0.0701224	−	1.05647i
$373$	17.4252	−	6.34227i	0.902245	−	0.328390i	0.151093	−	0.988520i	$-0.451721\pi$
$373$	17.4252	−	6.34227i	0.902245	−	0.328390i	0.751152	+	0.660129i	$0.229499\pi$
$374$	−1.50432	+	8.53145i	−0.0777868	+	0.441151i
$375$		0			0
$376$	−5.15326	+	4.32410i	−0.265759	+	0.222998i
$377$	−0.563875			−0.0290410
$378$	−0.363454	−	2.40100i	−0.0186940	−	0.123494i
$379$	23.8701			1.22613			0.613063	−	0.790034i	$-0.289937\pi$
$379$	23.8701			1.22613			0.613063	+	0.790034i	$0.289937\pi$
$380$		0			0
$381$	−9.53861	+	9.94768i	−0.488678	+	0.509635i
$382$	−0.127212	+	0.721455i	−0.00650873	+	0.0369129i
$383$	28.7180	−	10.4525i	1.46742	−	0.534097i	0.520021	−	0.854154i	$-0.325924\pi$
$383$	28.7180	−	10.4525i	1.46742	−	0.534097i	0.947398	+	0.320057i	$0.103702\pi$
$384$	−12.4705	+	6.13698i	−0.636385	+	0.313176i
$385$		0			0
$386$	−1.90439	−	3.29849i	−0.0969307	−	0.167889i
$387$	−20.5117	+	4.51175i	−1.04267	+	0.229345i
$388$	−13.2427	+	22.9370i	−0.672296	+	1.16445i
$389$	7.60180	+	2.76683i	0.385427	+	0.140284i	0.527464	−	0.849578i	$-0.323143\pi$
$389$	7.60180	+	2.76683i	0.385427	+	0.140284i	−0.142037	+	0.989861i	$0.545365\pi$
$390$		0			0
$391$	−31.3019	−	26.2654i	−1.58301	−	1.32830i
$392$	−3.44676	−	2.89217i	−0.174088	−	0.146077i
$393$	14.5612	−	1.58253i	0.734516	−	0.0798279i
$394$	−2.82812	−	1.02935i	−0.142479	−	0.0518580i
$395$		0			0
$396$	1.20078	+	28.5874i	0.0603416	+	1.43657i
$397$	9.75843	+	16.9021i	0.489762	+	0.848292i	0.999931	−	0.0117821i	$-0.00375045\pi$
$397$	9.75843	+	16.9021i	0.489762	+	0.848292i	−0.510169	+	0.860074i	$0.670417\pi$
$398$	0.920780	+	5.22200i	0.0461545	+	0.261755i
$399$	−16.6656	−	11.1556i	−0.834325	−	0.558477i
$400$		0			0
$401$	2.44572	−	13.8704i	0.122134	−	0.692654i	−0.860835	−	0.508883i	$-0.830058\pi$
$401$	2.44572	−	13.8704i	0.122134	−	0.692654i	0.982969	−	0.183771i	$-0.0588305\pi$
$402$	0.0829717	+	0.285542i	0.00413825	+	0.0142415i
$403$	−17.5973	+	14.7659i	−0.876582	+	0.735540i
$404$	−21.9749			−1.09329
$405$		0			0
$406$	−0.0703165			−0.00348975
$407$	−9.38520	+	7.87512i	−0.465207	+	0.390355i
$408$	3.31294	+	11.4013i	0.164015	+	0.564448i
$409$	0.282399	−	1.60156i	0.0139637	−	0.0791923i	−0.977030	−	0.213104i	$-0.931643\pi$
$409$	0.282399	−	1.60156i	0.0139637	−	0.0791923i	0.990993	+	0.133912i	$0.0427538\pi$
$410$		0			0
$411$	−0.570850	−	0.382113i	−0.0281580	−	0.0188482i
$412$	3.06643	+	17.3906i	0.151072	+	0.856774i
$413$	−0.308235	−	0.533879i	−0.0151673	−	0.0262705i
$414$	4.75812	+	2.48693i	0.233849	+	0.122226i
$415$		0			0
$416$	11.0991	+	4.03976i	0.544181	+	0.198066i
$417$	−8.06552	+	0.876569i	−0.394970	+	0.0429257i
$418$	−7.20101	−	6.04236i	−0.352213	−	0.295542i
$419$	−24.5436	−	20.5945i	−1.19903	−	1.00611i	−0.999657	−	0.0261853i	$-0.991664\pi$
$419$	−24.5436	−	20.5945i	−1.19903	−	1.00611i	−0.199376	−	0.979923i	$-0.563892\pi$
$420$		0			0
$421$	−3.21532	−	1.17028i	−0.156705	−	0.0570360i	0.262477	−	0.964938i	$-0.415461\pi$
$421$	−3.21532	−	1.17028i	−0.156705	−	0.0570360i	−0.419182	+	0.907902i	$0.637683\pi$
$422$	2.09147	−	3.62254i	0.101811	−	0.176342i
$423$	12.5398	+	13.7304i	0.609708	+	0.667593i
$424$	−0.202657	−	0.351011i	−0.00984187	−	0.0170466i
$425$		0			0
$426$	2.92162	−	1.43778i	0.141553	−	0.0696607i
$427$	9.80721	−	3.56953i	0.474604	−	0.172742i
$428$	−0.364121	+	2.06504i	−0.0176005	+	0.0998173i
$429$	22.2761	−	23.2315i	1.07550	−	1.12163i
$430$		0			0
$431$	33.8955			1.63269			0.816344	−	0.577565i	$-0.195997\pi$
$431$	33.8955			1.63269			0.816344	+	0.577565i	$0.195997\pi$
$432$	8.82423	+	16.1795i	0.424556	+	0.778437i
$433$	−17.6676			−0.849049			−0.424524	−	0.905417i	$-0.639559\pi$
$433$	−17.6676			−0.849049			−0.424524	+	0.905417i	$0.639559\pi$
$434$	−2.19442	+	1.84134i	−0.105336	+	0.0883870i
$435$		0			0
$436$	0.192049	−	1.08916i	0.00919748	−	0.0521615i
$437$	41.6649	−	15.1648i	1.99310	−	0.725430i
$438$	0.144494	−	2.17696i	0.00690418	−	0.104019i
$439$	1.25144	+	7.09728i	0.0597281	+	0.338735i	0.999999	−	0.00169354i	$-0.000539072\pi$
$439$	1.25144	+	7.09728i	0.0597281	+	0.338735i	−0.940270	+	0.340428i	$0.889428\pi$
$440$		0			0
$441$	−7.58761	+	9.85457i	−0.361315	+	0.469265i
$442$	3.27377	−	5.67034i	0.155718	−	0.269711i
$443$	32.5861	+	11.8604i	1.54821	+	0.563504i	0.967998	−	0.250959i	$-0.0807461\pi$
$443$	32.5861	+	11.8604i	1.54821	+	0.563504i	0.580216	+	0.814463i	$0.302968\pi$
$444$	−3.32152	+	7.53183i	−0.157632	+	0.357445i
$445$		0			0
$446$	0.987830	+	0.828888i	0.0467751	+	0.0392490i
$447$	16.1104	−	36.5318i	0.761998	−	1.72789i
$448$	−9.87731	−	3.59505i	−0.466659	−	0.169850i
$449$	−4.87046	+	8.43589i	−0.229851	+	0.398114i	−0.957764	−	0.287556i	$-0.907157\pi$
$449$	−4.87046	+	8.43589i	−0.229851	+	0.398114i	0.727913	+	0.685670i	$0.240491\pi$
$450$		0			0
$451$	9.79011	+	16.9570i	0.460998	+	0.798473i
$452$	−5.88437	−	33.3719i	−0.276777	−	1.56968i
$453$	0.593521	−	8.94206i	0.0278861	−	0.420135i
$454$	0.0518609	−	0.0188758i	0.00243395	−	0.000885886i
$455$		0			0
$456$	−12.5114	−	3.07250i	−0.585902	−	0.143883i
$457$	24.2137	−	20.3177i	1.13267	−	0.950421i	0.133493	−	0.991050i	$-0.457381\pi$
$457$	24.2137	−	20.3177i	1.13267	−	0.950421i	0.999174	+	0.0406289i	$0.0129361\pi$
$458$	−4.80424			−0.224487
$459$	31.1031	−	10.4721i	1.45177	−	0.488796i
$460$		0			0
$461$	−13.9469	+	11.7028i	−0.649572	+	0.545056i	−0.906941	−	0.421258i	$-0.861589\pi$
$461$	−13.9469	+	11.7028i	−0.649572	+	0.545056i	0.257369	+	0.966313i	$0.417144\pi$
$462$	2.77789	−	2.89702i	0.129239	−	0.134781i
$463$	4.90983	−	27.8450i	0.228179	−	1.29407i	−0.628334	−	0.777943i	$-0.716263\pi$
$463$	4.90983	−	27.8450i	0.228179	−	1.29407i	0.856513	−	0.516125i	$-0.172626\pi$
$464$	0.501467	−	0.182519i	0.0232800	−	0.00847324i
$465$		0			0
$466$	−0.759430	−	4.30694i	−0.0351799	−	0.199515i
$467$	7.02539	+	12.1683i	0.325096	+	0.563083i	0.981532	−	0.191299i	$-0.0612699\pi$
$467$	7.02539	+	12.1683i	0.325096	+	0.563083i	−0.656435	+	0.754382i	$0.727937\pi$
$468$	6.53700	−	20.6138i	0.302173	−	0.952871i
$469$	−0.524257	+	0.908040i	−0.0242080	+	0.0419294i
$470$		0			0
$471$	−14.1723	−	19.3621i	−0.653024	−	0.892159i
$472$	−0.303371	−	0.254559i	−0.0139638	−	0.0117170i
$473$	−26.5915	−	22.3129i	−1.22268	−	1.02595i
$474$	7.76542	−	0.843953i	0.356678	−	0.0387641i
$475$		0			0
$476$	−10.2623	+	17.7748i	−0.470372	+	0.814708i
$477$	−0.945895	+	0.600404i	−0.0433096	+	0.0274906i
$478$	−4.15161	−	7.19080i	−0.189890	−	0.328900i
$479$	1.21657	+	6.89953i	0.0555867	+	0.315248i	0.999905	−	0.0137857i	$-0.00438826\pi$
$479$	1.21657	+	6.89953i	0.0555867	+	0.315248i	−0.944318	+	0.329033i	$0.893277\pi$
$480$		0			0
$481$	8.70127	−	3.16700i	0.396744	−	0.144403i
$482$	0.172411	−	0.977792i	0.00785311	−	0.0445372i
$483$	5.28254	+	18.1795i	0.240364	+	0.827198i
$484$	−20.0193	+	16.7982i	−0.909969	+	0.763555i
$485$		0			0
$486$	−3.69566	+	2.22173i	−0.167639	+	0.100780i
$487$	−20.2826			−0.919093			−0.459547	−	0.888154i	$-0.651988\pi$
$487$	−20.2826			−0.919093			−0.459547	+	0.888154i	$0.651988\pi$
$488$	5.13596	−	4.30958i	0.232494	−	0.195086i
$489$	−1.44064	−	4.95789i	−0.0651482	−	0.224203i
$490$		0			0
$491$	4.72637	−	1.72026i	0.213298	−	0.0776342i	−0.233161	−	0.972438i	$-0.574907\pi$
$491$	4.72637	−	1.72026i	0.213298	−	0.0776342i	0.446459	+	0.894804i	$0.352685\pi$
$492$	10.9326	+	7.31803i	0.492881	+	0.329922i
$493$	−0.165020	−	0.935876i	−0.00743213	−	0.0421497i
$494$	3.55236	+	6.15286i	0.159828	+	0.276830i
$495$		0			0
$496$	10.8701	−	18.8277i	0.488084	−	0.845387i
$497$	10.7896	+	3.92709i	0.483979	+	0.176154i
$498$	5.32586	−	0.578820i	0.238658	−	0.0259375i
$499$	18.3084	+	15.3625i	0.819595	+	0.687722i	0.952877	−	0.303356i	$-0.0981072\pi$
$499$	18.3084	+	15.3625i	0.819595	+	0.687722i	−0.133282	+	0.991078i	$0.542552\pi$
$500$		0			0
$501$	19.1972	+	26.2271i	0.857666	+	1.17174i
$502$	6.66653	+	2.42642i	0.297542	+	0.108296i
$503$	4.04017	−	6.99778i	0.180142	−	0.312015i	−0.761787	−	0.647828i	$-0.775678\pi$
$503$	4.04017	−	6.99778i	0.180142	−	0.312015i	0.941929	+	0.335813i	$0.109011\pi$
$504$	1.66279	−	5.24343i	0.0740664	−	0.233561i
$505$		0			0
$506$	1.54092	+	8.73897i	0.0685020	+	0.388494i
$507$	−1.62346	+	0.798931i	−0.0721002	+	0.0354818i
$508$	−14.3821	+	5.23467i	−0.638104	+	0.232251i
$509$	2.73491	−	15.5104i	0.121223	−	0.687487i	−0.862257	−	0.506470i	$-0.830950\pi$
$509$	2.73491	−	15.5104i	0.121223	−	0.687487i	0.983480	−	0.181017i	$-0.0579389\pi$
$510$		0			0
$511$	5.89335	−	4.94511i	0.260707	−	0.218759i
$512$	−18.8770			−0.834254
$513$	−7.03408	+	34.9098i	−0.310562	+	1.54131i
$514$	2.31856			0.102267
$515$		0			0
$516$	−22.6503	−	5.56234i	−0.997122	−	0.244868i
$517$	−5.33693	+	30.2672i	−0.234718	+	1.33115i
$518$	1.08507	−	0.394933i	0.0476752	−	0.0173523i
$519$	−0.963233	+	14.5122i	−0.0422813	+	0.637015i
$520$		0			0
$521$	6.71663	+	11.6335i	0.294261	+	0.509675i	0.974813	−	0.223025i	$-0.0715932\pi$
$521$	6.71663	+	11.6335i	0.294261	+	0.509675i	−0.680552	+	0.732700i	$0.738260\pi$
$522$	0.0475919	+	0.115437i	0.00208304	+	0.00505253i
$523$	9.04762	−	15.6709i	0.395625	−	0.685242i	−0.597556	−	0.801827i	$-0.703861\pi$
$523$	9.04762	−	15.6709i	0.395625	−	0.685242i	0.993181	+	0.116585i	$0.0371948\pi$
$524$	15.2848	+	5.56323i	0.667721	+	0.243031i
$525$		0			0
$526$	−1.07841	−	0.904889i	−0.0470207	−	0.0394551i
$527$	−29.6572	−	24.8853i	−1.29189	−	1.08402i
$528$	−12.2910	+	27.8708i	−0.534896	+	1.21292i
$529$	−17.7185	−	6.44901i	−0.770370	−	0.280392i
$530$		0			0
$531$	−0.667833	+	0.867363i	−0.0289815	+	0.0376404i
$532$	−11.1356	−	19.2874i	−0.482789	−	0.836214i
$533$	−2.56978	−	14.5739i	−0.111309	−	0.631267i
$534$	0.290832	−	4.38172i	0.0125855	−	0.189615i
$535$		0			0
$536$	−0.116964	+	0.663337i	−0.00505208	+	0.0286518i
$537$	39.4020	+	9.67614i	1.70032	+	0.417556i
$538$	−5.98892	+	5.02530i	−0.258201	+	0.216656i
$539$	−20.5565			−0.885433
$540$		0			0
$541$	10.6112			0.456211			0.228106	−	0.973636i	$-0.426747\pi$
$541$	10.6112			0.456211			0.228106	+	0.973636i	$0.426747\pi$
$542$	3.66366	−	3.07417i	0.157368	−	0.132047i
$543$	−9.63929	+	10.0527i	−0.413661	+	0.431402i
$544$	−3.45667	+	19.6038i	−0.148204	+	0.840505i
$545$		0			0
$546$	−2.72179	+	1.33944i	−0.116482	+	0.0573227i
$547$	−2.92380	−	16.5817i	−0.125013	−	0.708983i	−0.981300	−	0.192483i	$-0.938346\pi$
$547$	−2.92380	−	16.5817i	−0.125013	−	0.708983i	0.856287	−	0.516500i	$-0.172765\pi$
$548$	−0.381429	−	0.660654i	−0.0162938	−	0.0282217i
$549$	−12.4978	−	13.6843i	−0.533391	−	0.584031i
$550$		0			0
$551$	0.968993	+	0.352685i	0.0412805	+	0.0150249i
$552$	7.18319	+	9.81364i	0.305737	+	0.417696i
$553$	21.0995	+	17.7046i	0.897241	+	0.752875i
$554$	−0.877326	−	0.736164i	−0.0372740	−	0.0312766i
$555$		0			0
$556$	−8.46634	−	3.08149i	−0.359053	−	0.130684i
$557$	2.30112	−	3.98565i	0.0975015	−	0.168877i	−0.813148	−	0.582056i	$-0.802248\pi$
$557$	2.30112	−	3.98565i	0.0975015	−	0.168877i	0.910650	+	0.413179i	$0.135582\pi$
$558$	4.50811	+	2.35626i	0.190844	+	0.0997484i
$559$	13.1179	+	22.7209i	0.554830	+	0.960994i
$560$		0			0
$561$	45.0770	+	30.1734i	1.90315	+	1.27392i
$562$	−4.98966	+	1.81609i	−0.210476	+	0.0766070i
$563$	−1.86442	+	10.5736i	−0.0785758	+	0.445626i	0.919983	+	0.391958i	$0.128202\pi$
$563$	−1.86442	+	10.5736i	−0.0785758	+	0.445626i	−0.998559	+	0.0536674i	$0.982909\pi$
$564$	5.76209	+	19.8299i	0.242628	+	0.834988i
$565$		0			0
$566$	−2.64037			−0.110983
$567$	−14.6739	−	3.98393i	−0.616246	−	0.167310i
$568$	7.37610			0.309494
$569$	10.4618	−	8.77850i	0.438582	−	0.368014i	−0.396597	−	0.917993i	$-0.629809\pi$
$569$	10.4618	−	8.77850i	0.438582	−	0.368014i	0.835178	+	0.549979i	$0.185364\pi$
$570$		0			0
$571$	−2.92720	+	16.6010i	−0.122499	+	0.694729i	0.860262	+	0.509852i	$0.170300\pi$
$571$	−2.92720	+	16.6010i	−0.122499	+	0.694729i	−0.982762	+	0.184877i	$0.940811\pi$
$572$	33.5875	−	12.2248i	1.40436	−	0.511147i
$573$	3.81190	+	2.55159i	0.159244	+	0.106594i
$574$	−0.320457	−	1.81740i	−0.0133756	−	0.0758569i
$575$		0			0
$576$	0.783310	+	18.6485i	0.0326379	+	0.777022i
$577$	−7.71289	+	13.3591i	−0.321092	+	0.556147i	−0.980714	−	0.195450i	$-0.937383\pi$
$577$	−7.71289	+	13.3591i	−0.321092	+	0.556147i	0.659622	+	0.751598i	$0.270716\pi$
$578$	5.95034	+	2.16575i	0.247502	+	0.0900832i
$579$	−23.7090	+	2.57671i	−0.985311	+	0.107085i
$580$		0			0
$581$	14.4709	+	12.1426i	0.600355	+	0.503758i
$582$	−3.89661	−	5.32354i	−0.161520	−	0.220668i
$583$	−1.74008	−	0.633338i	−0.0720668	−	0.0262302i
$584$	2.47108	−	4.28003i	0.102254	−	0.177109i
$585$		0			0
$586$	−0.879036	−	1.52254i	−0.0363126	−	0.0628953i
$587$	2.05906	+	11.6775i	0.0849866	+	0.481983i	0.997359	+	0.0726229i	$0.0231369\pi$
$587$	2.05906	+	11.6775i	0.0849866	+	0.481983i	−0.912373	+	0.409360i	$0.865752\pi$
$588$	−12.3925	+	6.09856i	−0.511057	+	0.251500i
$589$	39.4757	−	14.3680i	1.62657	−	0.592022i
$590$		0			0
$591$	−13.0426	+	13.6020i	−0.536502	+	0.559510i
$592$	−6.71313	+	5.63298i	−0.275908	+	0.231514i
$593$	−34.8582			−1.43146			−0.715728	−	0.698379i	$-0.753905\pi$
$593$	−34.8582			−1.43146			−0.715728	+	0.698379i	$0.753905\pi$
$594$	−6.63609	−	2.59961i	−0.272282	−	0.106663i
$595$		0			0
$596$	33.9658	−	28.5007i	1.39129	−	1.16743i
$597$	32.2439	+	7.91829i	1.31965	+	0.324074i
$598$	1.16462	−	6.60492i	0.0476251	−	0.270095i
$599$	11.2279	−	4.08662i	0.458759	−	0.166975i	−0.102294	−	0.994754i	$-0.532618\pi$
$599$	11.2279	−	4.08662i	0.458759	−	0.166975i	0.561054	+	0.827779i	$0.310396\pi$
$600$		0			0
$601$	3.39336	+	19.2447i	0.138418	+	0.785007i	0.972418	+	0.233243i	$0.0749338\pi$
$601$	3.39336	+	19.2447i	0.138418	+	0.785007i	−0.834001	+	0.551764i	$0.813955\pi$
$602$	1.63584	+	2.83336i	0.0666718	+	0.115479i
$603$	1.84553	+	0.246075i	0.0751560	+	0.0100210i
$604$	4.97611	−	8.61887i	0.202475	−	0.350697i
$605$		0			0
$606$	2.20867	−	5.00833i	0.0897209	−	0.203450i
$607$	7.81863	+	6.56061i	0.317348	+	0.266287i	0.787521	−	0.616287i	$-0.211364\pi$
$607$	7.81863	+	6.56061i	0.317348	+	0.266287i	−0.470173	+	0.882574i	$0.655808\pi$
$608$	−16.5467	−	13.8843i	−0.671055	−	0.563082i
$609$	−0.177657	+	0.402852i	−0.00719902	+	0.0163244i
$610$		0			0
$611$	11.6144	−	20.1168i	0.469870	−	0.813839i
$612$	36.1262	+	4.81691i	1.46032	+	0.194712i
$613$	−7.38192	−	12.7859i	−0.298153	−	0.516416i	0.677560	−	0.735467i	$-0.263037\pi$
$613$	−7.38192	−	12.7859i	−0.298153	−	0.516416i	−0.975713	+	0.219051i	$0.929704\pi$
$614$	−0.412406	−	2.33887i	−0.0166433	−	0.0943890i
$615$		0			0
$616$	8.54350	−	3.10958i	0.344228	−	0.125289i
$617$	−5.66996	+	32.1559i	−0.228264	+	1.29455i	0.628082	+	0.778147i	$0.283840\pi$
$617$	−5.66996	+	32.1559i	−0.228264	+	1.29455i	−0.856346	+	0.516402i	$0.827271\pi$
$618$	−4.27173	−	1.04903i	−0.171834	−	0.0421982i
$619$	11.2792	−	9.46438i	0.453350	−	0.380406i	−0.387327	−	0.921942i	$-0.626602\pi$
$619$	11.2792	−	9.46438i	0.453350	−	0.380406i	0.840677	+	0.541537i	$0.182157\pi$
$620$		0			0
$621$	26.2695	−	20.9766i	1.05416	−	0.841760i
$622$	3.17267			0.127212
$623$	11.8619	−	9.95335i	0.475239	−	0.398773i
$624$	15.9339	−	16.6172i	0.637865	−	0.665220i
$625$		0			0
$626$	6.48608	−	2.36074i	0.259236	−	0.0943541i
$627$	−52.8110	+	25.9892i	−2.10907	+	1.03791i
$628$	−4.62714	−	26.2418i	−0.184643	−	1.04716i
$629$	7.80281	+	13.5149i	0.311118	+	0.538873i
$630$		0			0
$631$	12.9621	−	22.4511i	0.516014	−	0.893762i	−0.483813	−	0.875171i	$-0.660749\pi$
$631$	12.9621	−	22.4511i	0.516014	−	0.893762i	0.999827	−	0.0185911i	$-0.00591806\pi$
$632$	16.6269	+	6.05170i	0.661383	+	0.240724i
$633$	−15.4698	−	21.1347i	−0.614868	−	0.840031i
$634$	0.134409	+	0.112782i	0.00533806	+	0.00447916i
$635$		0			0
$636$	−1.23690	+	0.134427i	−0.0490463	+	0.00533040i
$637$	14.5997	+	5.31385i	0.578460	+	0.210542i
$638$	−0.103188	+	0.178727i	−0.00408525	+	0.00707585i
$639$	−0.855657	−	20.3709i	−0.0338493	−	0.805860i
$640$		0			0
$641$	−3.45147	−	19.5742i	−0.136325	−	0.773136i	−0.973928	−	0.226857i	$-0.927155\pi$
$641$	−3.45147	−	19.5742i	−0.136325	−	0.773136i	0.837603	−	0.546279i	$-0.183956\pi$
$642$	−0.434048	−	0.290541i	−0.0171305	−	0.0114668i
$643$	−31.1702	+	11.3450i	−1.22923	+	0.447404i	−0.873334	−	0.487121i	$-0.838047\pi$
$643$	−31.1702	+	11.3450i	−1.22923	+	0.447404i	−0.355897	+	0.934525i	$0.615825\pi$
$644$	−3.65075	+	20.7044i	−0.143860	+	0.815869i
$645$		0			0
$646$	−9.17244	+	7.69659i	−0.360885	+	0.302818i
$647$	18.8740			0.742014			0.371007	−	0.928630i	$-0.379013\pi$
$647$	18.8740			0.742014			0.371007	+	0.928630i	$0.379013\pi$
$648$	−9.73341	+	0.819127i	−0.382364	+	0.0321783i
$649$	−1.80931			−0.0710217
$650$		0			0
$651$	5.00497	+	17.2243i	0.196160	+	0.675074i
$652$	0.995625	−	5.64647i	0.0389917	−	0.221133i
$653$	25.7663	−	9.37817i	1.00831	−	0.366996i	0.215528	−	0.976498i	$-0.430853\pi$
$653$	25.7663	−	9.37817i	1.00831	−	0.366996i	0.792785	+	0.609502i	$0.208630\pi$
$654$	0.228931	+	0.153241i	0.00895190	+	0.00599218i
$655$		0			0
$656$	7.00276	+	12.1291i	0.273412	+	0.473563i
$657$	−12.1070	−	6.32798i	−0.472339	−	0.246878i
$658$	1.44835	−	2.50861i	0.0564625	−	0.0977959i
$659$	−4.90832	−	1.78648i	−0.191201	−	0.0695915i	0.244645	−	0.969613i	$-0.421329\pi$
$659$	−4.90832	−	1.78648i	−0.191201	−	0.0695915i	−0.435846	+	0.900021i	$0.643551\pi$
$660$		0			0
$661$	17.4652	+	14.6551i	0.679319	+	0.570017i	0.915807	−	0.401618i	$-0.131552\pi$
$661$	17.4652	+	14.6551i	0.679319	+	0.570017i	−0.236488	+	0.971634i	$0.575996\pi$
$662$	4.27466	+	3.58687i	0.166139	+	0.139408i
$663$	−24.2148	−	33.0821i	−0.940424	−	1.28480i
$664$	11.4035	+	4.15052i	0.442540	+	0.161071i
$665$		0			0
$666$	−1.38275	−	1.51403i	−0.0535805	−	0.0586674i
$667$	−0.486714	−	0.843014i	−0.0188456	−	0.0326416i
$668$	6.26772	+	35.5460i	0.242505	+	1.37532i
$669$	7.24458	−	3.56519i	0.280092	−	0.137838i
$670$		0			0
$671$	5.31901	−	30.1656i	0.205338	−	1.16453i
$672$	6.38309	−	6.65684i	0.246233	−	0.256793i
$673$	13.3460	−	11.1986i	0.514450	−	0.431675i	−0.348242	−	0.937405i	$-0.613221\pi$
$673$	13.3460	−	11.1986i	0.514450	−	0.431675i	0.862692	+	0.505730i	$0.168777\pi$
$674$	8.41353			0.324077
$675$		0			0
$676$	−2.00937			−0.0772835
$677$	−24.5750	+	20.6209i	−0.944495	+	0.792526i	−0.978362	−	0.206901i	$-0.933662\pi$
$677$	−24.5750	+	20.6209i	−0.944495	+	0.792526i	0.0338665	+	0.999426i	$0.489218\pi$
$678$	8.19728	+	2.01305i	0.314815	+	0.0773107i
$679$	4.03958	−	22.9096i	0.155025	−	0.879189i
$680$		0			0
$681$	0.0228863	−	0.344808i	0.000877005	−	0.0132131i
$682$	1.45995	+	8.27978i	0.0559043	+	0.317049i
$683$	10.6001	+	18.3599i	0.405600	+	0.702520i	0.994391	−	0.105765i	$-0.0337292\pi$
$683$	10.6001	+	18.3599i	0.405600	+	0.702520i	−0.588791	+	0.808285i	$0.700396\pi$
$684$	−24.1267	+	31.3351i	−0.922509	+	1.19813i
$685$		0			0
$686$	4.89469	+	1.78152i	0.186880	+	0.0680188i
$687$	−12.1381	+	27.5241i	−0.463096	+	1.05011i
$688$	−19.0206	−	15.9602i	−0.725153	−	0.608476i
$689$	1.07212	+	0.899619i	0.0408447	+	0.0342728i
$690$		0			0
$691$	−10.2500	−	3.73069i	−0.389928	−	0.141922i	0.139614	−	0.990206i	$-0.455414\pi$
$691$	−10.2500	−	3.73069i	−0.389928	−	0.141922i	−0.529542	+	0.848284i	$0.677636\pi$
$692$	−8.07579	+	13.9877i	−0.306995	+	0.531732i
$693$	−9.57895	−	23.2342i	−0.363874	−	0.882596i
$694$	−5.11176	−	8.85382i	−0.194040	−	0.336086i
$695$		0			0
$696$	−0.0187321	+	0.282220i	−0.000710038	+	0.0106975i
$697$	23.4366	−	8.53023i	0.887725	−	0.323106i
$698$	−0.350268	+	1.98647i	−0.0132578	+	0.0751889i
$699$	−26.5937	−	6.53075i	−1.00587	−	0.247016i
$700$		0			0
$701$	−16.5817			−0.626282			−0.313141	−	0.949707i	$-0.601381\pi$
$701$	−16.5817			−0.626282			−0.313141	+	0.949707i	$0.601381\pi$
$702$	4.04109	+	3.56172i	0.152521	+	0.134428i
$703$	−16.9336			−0.638662
$704$	−23.6324	+	19.8300i	−0.890681	+	0.747370i
$705$		0			0
$706$	−0.546967	+	3.10200i	−0.0205854	+	0.116745i
$707$	18.1372	−	6.60142i	0.682121	−	0.248272i
$708$	−1.09074	+	0.536773i	−0.0409926	+	0.0201732i
$709$	−0.653972	−	3.70886i	−0.0245604	−	0.139289i	0.970062	−	0.242858i	$-0.0780849\pi$
$709$	−0.653972	−	3.70886i	−0.0245604	−	0.139289i	−0.994622	+	0.103569i	$0.966974\pi$
$710$		0			0
$711$	14.7845	−	46.6213i	0.554461	−	1.74844i
$712$	4.97370	−	8.61470i	0.186397	−	0.322850i
$713$	−37.2648	−	13.5633i	−1.39558	−	0.507948i
$714$	−3.01964	−	4.12542i	−0.113007	−	0.154390i
$715$		0			0
$716$	34.5156	+	28.9620i	1.28991	+	1.08236i
$717$	−51.6861	+	5.61730i	−1.93025	+	0.209782i
$718$	6.47568	+	2.35695i	0.241670	+	0.0879608i
$719$	0.0341167	−	0.0590919i	0.00127234	−	0.00220375i	−0.865389	−	0.501101i	$-0.832928\pi$
$719$	0.0341167	−	0.0590919i	0.00127234	−	0.00220375i	0.866661	+	0.498898i	$0.166262\pi$
$720$		0			0
$721$	−7.75519	−	13.4324i	−0.288818	−	0.500248i
$722$	−1.34350	−	7.61937i	−0.0499999	−	0.283564i
$723$	−5.16629	−	3.45819i	−0.192136	−	0.128611i
$724$	−14.5339	+	5.28992i	−0.540149	+	0.196598i
$725$		0			0
$726$	−1.81639	−	6.25100i	−0.0674127	−	0.231996i
$727$	−33.5717	+	28.1700i	−1.24511	+	1.04477i	−0.247998	+	0.968760i	$0.579773\pi$
$727$	−33.5717	+	28.1700i	−1.24511	+	1.04477i	−0.997107	+	0.0760072i	$0.975783\pi$
$728$	−6.87159			−0.254678
$729$	3.39133	+	26.7862i	0.125605	+	0.992080i
$730$		0			0
$731$	−33.8715	+	28.4215i	−1.25278	+	1.05121i
$732$	−5.74275	−	19.7633i	−0.212258	−	0.730473i
$733$	−0.894591	+	5.07348i	−0.0330425	+	0.187393i	−0.996862	−	0.0791639i	$-0.974775\pi$
$733$	−0.894591	+	5.07348i	−0.0330425	+	0.187393i	0.963819	+	0.266557i	$0.0858861\pi$
$734$	7.47097	−	2.71921i	0.275759	−	0.100368i
$735$		0			0
$736$	3.54075	+	20.0806i	0.130514	+	0.740181i
$737$	1.53867	+	2.66506i	0.0566777	+	0.0981686i
$738$	−2.76669	+	1.75615i	−0.101843	+	0.0646447i
$739$	−0.515367	+	0.892642i	−0.0189581	+	0.0328364i	−0.875349	−	0.483492i	$-0.839368\pi$
$739$	−0.515367	+	0.892642i	−0.0189581	+	0.0328364i	0.856391	+	0.516328i	$0.172702\pi$
$740$		0			0
$741$	44.2256	−	4.80648i	1.62467	−	0.176571i
$742$	0.133696	+	0.112185i	0.00490815	+	0.00411843i
$743$	32.5316	+	27.2972i	1.19347	+	1.00144i	0.999792	+	0.0203733i	$0.00648548\pi$
$743$	32.5316	+	27.2972i	1.19347	+	1.00144i	0.193676	+	0.981066i	$0.437959\pi$
$744$	6.80575	+	9.29799i	0.249511	+	0.340881i
$745$		0			0
$746$	−2.56476	+	4.44229i	−0.0939025	+	0.162644i
$747$	10.1398	−	31.9749i	0.370997	−	1.16990i
$748$	30.1194	+	52.1683i	1.10127	+	1.90746i
$749$	−0.319820	−	1.81379i	−0.0116860	−	0.0662744i
$750$		0			0
$751$	2.32349	−	0.845681i	0.0847853	−	0.0308593i	−0.299279	−	0.954166i	$-0.596746\pi$
$751$	2.32349	−	0.845681i	0.0847853	−	0.0308593i	0.384065	+	0.923306i	$0.374524\pi$
$752$	−3.81745	+	21.6498i	−0.139208	+	0.789487i
$753$	30.7444	−	32.0629i	1.12039	−	1.16844i
$754$	0.119487	−	0.100261i	0.00435145	−	0.00365130i
$755$		0			0
$756$	−12.6676	−	11.1649i	−0.460717	−	0.406064i
$757$	52.6699			1.91432			0.957160	−	0.289559i	$-0.0935087\pi$
$757$	52.6699			1.91432			0.957160	+	0.289559i	$0.0935087\pi$
$758$	−5.05816	+	4.24430i	−0.183721	+	0.154160i
$759$	53.9598	+	13.2512i	1.95862	+	0.480987i
$760$		0			0
$761$	−28.1597	+	10.2493i	−1.02079	+	0.371537i	−0.797567	−	0.603231i	$-0.793880\pi$
$761$	−28.1597	+	10.2493i	−1.02079	+	0.371537i	−0.223222	+	0.974768i	$0.571658\pi$
$762$	0.252486	−	3.80398i	0.00914660	−	0.137804i
$763$	0.168683	+	0.956649i	0.00610673	+	0.0346330i
$764$	2.54702	+	4.41157i	0.0921480	+	0.159605i
$765$		0			0
$766$	−4.22689	+	7.32119i	−0.152724	+	0.264525i
$767$	1.28501	+	0.467705i	0.0463990	+	0.0168879i
$768$	−7.14515	+	16.2022i	−0.257828	+	0.584647i
$769$	−33.0529	−	27.7347i	−1.19192	−	1.00014i	−0.999824	−	0.0187613i	$-0.994028\pi$
$769$	−33.0529	−	27.7347i	−1.19192	−	1.00014i	−0.192094	−	0.981377i	$-0.561528\pi$
$770$		0			0
$771$	5.85791	−	13.2833i	0.210967	−	0.478386i
$772$	−24.8872	−	9.05819i	−0.895709	−	0.326011i
$773$	19.4784	−	33.7376i	0.700590	−	1.21346i	−0.267669	−	0.963511i	$-0.586254\pi$
$773$	19.4784	−	33.7376i	0.700590	−	1.21346i	0.968260	−	0.249947i	$-0.0804132\pi$
$774$	3.54427	−	4.60319i	0.127396	−	0.165458i
$775$		0			0
$776$	−2.59504	−	14.7172i	−0.0931565	−	0.528316i
$777$	0.478843	−	7.21430i	0.0171784	−	0.258812i
$778$	−2.10281	+	0.765360i	−0.0753894	+	0.0274395i
$779$	−4.69945	+	26.6519i	−0.168375	+	0.954905i
$780$		0			0
$781$	25.8151	−	21.6614i	0.923737	−	0.775108i
$782$	11.3032			0.404200
$783$	0.781593	+	0.0189946i	0.0279319	+	0.000678813i
$784$	−14.7039			−0.525138
$785$		0			0
$786$	−2.80418	+	2.92444i	−0.100022	+	0.104311i
$787$	1.82048	−	10.3244i	0.0648930	−	0.368027i	−0.935017	−	0.354603i	$-0.884616\pi$
$787$	1.82048	−	10.3244i	0.0648930	−	0.368027i	0.999910	−	0.0134234i	$-0.00427292\pi$
$788$	−19.6654	+	7.15762i	−0.700551	+	0.254980i
$789$	−7.90884	+	3.89208i	−0.281562	+	0.138562i
$790$		0			0
$791$	14.8819	+	25.7762i	0.529140	+	0.916497i
$792$	−10.8874	−	11.9210i	−0.386865	−	0.423594i
$793$	−11.5755	+	20.0493i	−0.411056	+	0.711971i
$794$	−5.07317	−	1.84648i	−0.180040	−	0.0655292i
$795$		0			0
$796$	28.2452	+	23.7005i	1.00112	+	0.840042i
$797$	−22.2746	−	18.6906i	−0.789007	−	0.662055i	0.156493	−	0.987679i	$-0.449981\pi$
$797$	−22.2746	−	18.6906i	−0.789007	−	0.662055i	−0.945499	+	0.325624i	$0.894426\pi$
$798$	5.51504	−	0.599380i	0.195230	−	0.0212178i
$799$	36.7873	+	13.3895i	1.30144	+	0.473686i
$800$		0			0
$801$	−24.3686	−	12.7368i	−0.861022	−	0.450031i
$802$	1.94801	+	3.37405i	0.0687865	+	0.119142i
$803$	−3.92085	−	22.2362i	−0.138364	−	0.784699i
$804$	1.71823	+	1.15014i	0.0605974	+	0.0405624i
$805$		0			0
$806$	1.10343	−	6.25786i	0.0388667	−	0.220424i
$807$	13.6594	+	47.0078i	0.480832	+	1.65475i
$808$	9.49834	−	7.97005i	0.334150	−	0.280385i
$809$	37.5077			1.31870			0.659350	−	0.751836i	$-0.270831\pi$
$809$	37.5077			1.31870			0.659350	+	0.751836i	$0.270831\pi$
$810$		0			0
$811$	−9.23252			−0.324198			−0.162099	−	0.986775i	$-0.551826\pi$
$811$	−9.23252			−0.324198			−0.162099	+	0.986775i	$0.551826\pi$
$812$	−0.374555	+	0.314289i	−0.0131443	+	0.0110294i
$813$	−8.35597	−	28.7565i	−0.293057	−	1.00854i
$814$	0.588495	−	3.33752i	0.0206268	−	0.116980i
$815$		0			0
$816$	32.2431	+	21.5827i	1.12873	+	0.755546i
$817$	−8.33141	−	47.2498i	−0.291479	−	1.65306i
$818$	0.224929	+	0.389589i	0.00786447	+	0.0136217i
$819$	0.797132	+	18.9776i	0.0278540	+	0.663130i
$820$		0			0
$821$	−26.4820	−	9.63866i	−0.924228	−	0.336392i	−0.164309	−	0.986409i	$-0.552539\pi$
$821$	−26.4820	−	9.63866i	−0.924228	−	0.336392i	−0.759919	+	0.650017i	$0.774762\pi$
$822$	0.188908	−	0.0205307i	0.00658891	−	0.000716089i
$823$	−16.8538	−	14.1420i	−0.587485	−	0.492959i	0.299910	−	0.953967i	$-0.403043\pi$
$823$	−16.8538	−	14.1420i	−0.587485	−	0.492959i	−0.887396	+	0.461009i	$0.847488\pi$
$824$	−7.63281	−	6.40468i	−0.265901	−	0.223118i
$825$		0			0
$826$	0.160244	+	0.0583240i	0.00557560	+	0.00202935i
$827$	4.11260	−	7.12323i	0.143009	−	0.247699i	−0.785619	−	0.618710i	$-0.787656\pi$
$827$	4.11260	−	7.12323i	0.143009	−	0.247699i	0.928628	+	0.371011i	$0.120989\pi$
$828$	36.4608	−	8.01992i	1.26710	−	0.278712i
$829$	5.60468	+	9.70759i	0.194659	+	0.337159i	0.946789	−	0.321856i	$-0.104307\pi$
$829$	5.60468	+	9.70759i	0.194659	+	0.337159i	−0.752130	+	0.659015i	$0.770973\pi$
$830$		0			0
$831$	−6.43417	+	3.16637i	−0.223199	+	0.109840i
$832$	21.9103	−	7.97468i	0.759601	−	0.276472i
$833$	−4.54686	+	25.7865i	−0.157539	+	0.893451i
$834$	1.55325	−	1.61986i	0.0537846	−	0.0560912i
$835$		0			0
$836$	−65.3648			−2.26069
$837$	24.8892	−	19.8743i	0.860296	−	0.686958i
$838$	8.86273			0.306158
$839$	6.85960	−	5.75589i	0.236820	−	0.198715i	−0.516652	−	0.856195i	$-0.672822\pi$
$839$	6.85960	−	5.75589i	0.236820	−	0.198715i	0.753472	+	0.657480i	$0.228378\pi$
$840$		0			0
$841$	−5.03187	+	28.5371i	−0.173513	+	0.984039i
$842$	0.889421	−	0.323723i	0.0306515	−	0.0111562i
$843$	−2.20194	+	33.1748i	−0.0758390	+	1.14260i
$844$	−5.05076	−	28.6443i	−0.173854	−	0.985977i
$845$		0			0
$846$	−5.09860	−	0.679825i	−0.175293	−	0.0233729i
$847$	11.4769	−	19.8786i	0.394351	−	0.683035i
$848$	−1.24466	−	0.453020i	−0.0427419	−	0.0155568i
$849$	−6.67097	+	15.1270i	−0.228947	+	0.519157i
$850$		0			0
$851$	12.2454	+	10.2751i	0.419766	+	0.352226i
$852$	9.13624	−	20.7172i	0.313003	−	0.709760i
$853$	47.5581	+	17.3097i	1.62836	+	0.592674i	0.984949	−	0.172847i	$-0.0552968\pi$
$853$	47.5581	+	17.3097i	1.62836	+	0.592674i	0.643410	+	0.765522i	$0.277519\pi$
$854$	−1.44349	+	2.50019i	−0.0493951	+	0.0855548i
$855$		0			0
$856$	−0.591579	−	1.02465i	−0.0202198	−	0.0350217i
$857$	4.66987	+	26.4841i	0.159520	+	0.904681i	0.954537	+	0.298094i	$0.0963508\pi$
$857$	4.66987	+	26.4841i	0.159520	+	0.904681i	−0.795017	+	0.606587i	$0.792538\pi$
$858$	−0.589646	+	8.88369i	−0.0201302	+	0.303284i
$859$	−51.3051	+	18.6735i	−1.75051	+	0.637133i	−0.999726	−	0.0234172i	$-0.992545\pi$
$859$	−51.3051	+	18.6735i	−1.75051	+	0.637133i	−0.750782	+	0.660550i	$0.770323\pi$
$860$		0			0
$861$	−11.2218	−	2.75579i	−0.382437	−	0.0939170i
$862$	−7.18256	+	6.02689i	−0.244639	+	0.205277i
$863$	−36.0299			−1.22647			−0.613235	−	0.789900i	$-0.710132\pi$
$863$	−36.0299			−1.22647			−0.613235	+	0.789900i	$0.710132\pi$
$864$	−15.2486	−	5.97344i	−0.518767	−	0.203221i
$865$		0			0
$866$	3.74381	−	3.14143i	0.127220	−	0.106750i
$867$	27.4416	−	28.6184i	0.931964	−	0.971932i
$868$	−3.45892	+	19.6165i	−0.117403	+	0.665828i
$869$	75.9635	−	27.6485i	2.57689	−	0.937910i
$870$		0			0
$871$	−0.403881	−	2.29052i	−0.0136850	−	0.0776114i
$872$	0.312018	+	0.540430i	0.0105662	+	0.0183013i
$873$	−40.3441	+	8.87409i	−1.36544	+	0.300342i
$874$	−6.13251	+	10.6218i	−0.207435	+	0.359288i
$875$		0			0
$876$	−8.96055	−	12.2419i	−0.302749	−	0.413614i
$877$	5.90106	+	4.95158i	0.199265	+	0.167203i	0.736960	−	0.675936i	$-0.236261\pi$
$877$	5.90106	+	4.95158i	0.199265	+	0.167203i	−0.537695	+	0.843139i	$0.680705\pi$
$878$	−1.52714	−	1.28142i	−0.0515384	−	0.0432458i
$879$	−10.9437	+	1.18937i	−0.369122	+	0.0401165i
$880$		0			0
$881$	−8.21595	+	14.2305i	−0.276803	+	0.479436i	−0.970588	−	0.240745i	$-0.922608\pi$
$881$	−8.21595	+	14.2305i	−0.276803	+	0.479436i	0.693786	+	0.720181i	$0.255941\pi$
$882$	−0.144382	−	3.43735i	−0.00486159	−	0.115742i
$883$	−0.908772	−	1.57404i	−0.0305826	−	0.0529706i	0.850329	−	0.526251i	$-0.176403\pi$
$883$	−0.908772	−	1.57404i	−0.0305826	−	0.0529706i	−0.880912	+	0.473281i	$0.843070\pi$
$884$	−7.90594	−	44.8368i	−0.265906	−	1.50803i
$885$		0			0
$886$	−9.01397	+	3.28082i	−0.302830	+	0.110221i
$887$	3.37292	−	19.1288i	0.113251	−	0.642281i	−0.874350	−	0.485297i	$-0.838712\pi$
$887$	3.37292	−	19.1288i	0.113251	−	0.642281i	0.987601	−	0.156985i	$-0.0501773\pi$
$888$	−1.29603	−	4.46021i	−0.0434919	−	0.149675i
$889$	10.2979	−	8.64099i	0.345382	−	0.289810i
$890$		0			0
$891$	−31.6598	+	31.4510i	−1.06064	+	1.05365i
$892$	8.96671			0.300228
$893$	−32.5413	+	27.3054i	−1.08895	+	0.913740i
$894$	3.08178	+	10.6058i	0.103070	+	0.354710i
$895$		0			0
$896$	12.7394	−	4.63677i	0.425594	−	0.154904i
$897$	−34.8979	−	23.3598i	−1.16521	−	0.779961i
$898$	−0.467901	−	2.65360i	−0.0156140	−	0.0885516i
$899$	−0.461140	−	0.798718i	−0.0153799	−	0.0266387i
$900$		0			0
$901$	−1.17936	+	2.04271i	−0.0392901	+	0.0680524i
$902$	−5.08964	−	1.85248i	−0.169466	−	0.0616807i
$903$	20.3656	−	2.21336i	0.677726	−	0.0736559i
$904$	14.6471	+	12.2903i	0.487154	+	0.408771i
$905$		0			0
$906$	1.46420	+	2.00038i	0.0486448	+	0.0664583i
$907$	32.5455	+	11.8456i	1.08066	+	0.393327i	0.820152	−	0.572146i	$-0.193889\pi$
$907$	32.5455	+	11.8456i	1.08066	+	0.393327i	0.260505	+	0.965473i	$0.416111\pi$
$908$	0.191880	−	0.332345i	0.00636775	−	0.0110293i
$909$	−23.1131	−	25.3074i	−0.766613	−	0.839394i
$910$		0			0
$911$	−3.90409	−	22.1412i	−0.129348	−	0.733570i	−0.978630	−	0.205630i	$-0.934076\pi$
$911$	−3.90409	−	22.1412i	−0.129348	−	0.733570i	0.849282	−	0.527940i	$-0.177035\pi$
$912$	−37.7751	+	18.5898i	−1.25086	+	0.615570i
$913$	52.0990	−	18.9625i	1.72423	−	0.627567i
$914$	−1.51831	+	8.61076i	−0.0502212	+	0.284819i
$915$		0			0
$916$	−25.5908	+	21.4732i	−0.845542	+	0.709494i
$917$	−14.2868			−0.471791
$918$	−4.72883	+	7.74945i	−0.156075	+	0.255770i
$919$	−21.3527			−0.704360			−0.352180	−	0.935932i	$-0.614560\pi$
$919$	−21.3527			−0.704360			−0.352180	+	0.935932i	$0.614560\pi$
$920$		0			0
$921$	−14.4416	−	3.54650i	−0.475867	−	0.116861i
$922$	0.874535	−	4.95974i	0.0288013	−	0.163340i
$923$	−23.9339	+	8.71122i	−0.787793	+	0.286733i
$924$	1.84837	−	27.8477i	0.0608068	−	0.916122i
$925$		0			0
$926$	3.91066	+	6.77345i	0.128512	+	0.222589i
$927$	−16.8027	+	21.8228i	−0.551872	+	0.716756i
$928$	−0.237108	+	0.410682i	−0.00778344	+	0.0134813i
$929$	−41.3431	−	15.0476i	−1.35642	−	0.493697i	−0.441476	−	0.897273i	$-0.645545\pi$
$929$	−41.3431	−	15.0476i	−1.35642	−	0.493697i	−0.914946	+	0.403576i	$0.867767\pi$
$930$		0			0
$931$	−21.7652	−	18.2632i	−0.713327	−	0.598553i
$932$	−23.2957	−	19.5474i	−0.763076	−	0.640297i
$933$	8.01584	−	18.1766i	0.262427	−	0.595075i
$934$	−3.65233	−	1.32934i	−0.119508	−	0.0434973i
$935$		0			0
$936$	4.65086	+	11.2809i	0.152018	+	0.368728i
$937$	−1.06136	−	1.83833i	−0.0346731	−	0.0600555i	0.848168	−	0.529727i	$-0.177706\pi$
$937$	−1.06136	−	1.83833i	−0.0346731	−	0.0600555i	−0.882841	+	0.469672i	$0.844372\pi$
$938$	−0.0503649	−	0.285634i	−0.00164447	−	0.00932627i
$939$	2.86232	−	43.1240i	0.0934082	−	1.40730i
$940$		0			0
$941$	9.63291	−	54.6309i	0.314024	−	1.78092i	−0.263617	−	0.964627i	$-0.584916\pi$
$941$	9.63291	−	54.6309i	0.314024	−	1.78092i	0.577641	−	0.816291i	$-0.303973\pi$
$942$	6.44589	+	1.58295i	0.210018	+	0.0515753i
$943$	19.5704	−	16.4215i	0.637301	−	0.534759i
$944$	−1.29418			−0.0421220
$945$		0			0
$946$	9.60222			0.312195
$947$	6.92360	−	5.80959i	0.224987	−	0.188786i	−0.523326	−	0.852133i	$-0.675309\pi$
$947$	6.92360	−	5.80959i	0.224987	−	0.188786i	0.748312	+	0.663346i	$0.230864\pi$
$948$	37.5919	−	39.2041i	1.22093	−	1.27329i
$949$	−2.96338	+	16.8062i	−0.0961953	+	0.545551i
$950$		0			0
$951$	0.985732	−	0.485096i	0.0319646	−	0.0157303i
$952$	−2.01100	−	11.4049i	−0.0651769	−	0.369636i
$953$	8.14599	+	14.1093i	0.263874	+	0.457044i	0.967268	−	0.253757i	$-0.0816662\pi$
$953$	8.14599	+	14.1093i	0.263874	+	0.457044i	−0.703394	+	0.710801i	$0.748333\pi$
$954$	0.0936815	−	0.295415i	0.00303305	−	0.00956442i
$955$		0			0
$956$	−54.2547	−	19.7471i	−1.75472	−	0.638666i
$957$	0.763239	+	1.04273i	0.0246720	+	0.0337068i
$958$	−1.48459	−	1.24572i	−0.0479648	−	0.0402472i
$959$	0.513282	+	0.430695i	0.0165747	+	0.0139079i
$960$		0			0
$961$	−6.17624	−	2.24797i	−0.199233	−	0.0725150i
$962$	−1.28071	+	2.21825i	−0.0412917	+	0.0715193i
$963$	−2.76118	+	1.75265i	−0.0889779	+	0.0564785i
$964$	−3.45199	−	5.97902i	−0.111181	−	0.192571i
$965$		0			0
$966$	−4.35185	−	2.91302i	−0.140019	−	0.0937250i
$967$	−44.9743	+	16.3693i	−1.44628	+	0.526402i	−0.941549	−	0.336877i	$-0.890629\pi$
$967$	−44.9743	+	16.3693i	−1.44628	+	0.526402i	−0.504728	+	0.863279i	$0.668407\pi$
$968$	2.56054	−	14.5216i	0.0822990	−	0.466741i
$969$	20.9202	+	71.9957i	0.672055	+	2.31284i
$970$		0			0
$971$	17.2383			0.553202			0.276601	−	0.960985i	$-0.410792\pi$
$971$	17.2383			0.553202			0.276601	+	0.960985i	$0.410792\pi$
$972$	−9.75540	+	28.3528i	−0.312905	+	0.909415i
$973$	7.91350			0.253695
$974$	4.29795	−	3.60641i	0.137715	−	0.115557i
$975$		0			0
$976$	3.80463	−	21.5771i	0.121783	−	0.690667i
$977$	−13.1424	+	4.78345i	−0.420463	+	0.153036i	−0.543582	−	0.839356i	$-0.682932\pi$
$977$	−13.1424	+	4.78345i	−0.420463	+	0.153036i	0.123119	+	0.992392i	$0.460710\pi$
$978$	1.18683	+	0.794434i	0.0379506	+	0.0254032i
$979$	−7.89175	−	44.7563i	−0.252221	−	1.43042i
$980$		0			0
$981$	1.45634	−	0.924405i	0.0464972	−	0.0295140i
$982$	−0.695657	+	1.20491i	−0.0221993	+	0.0384503i
$983$	18.1844	+	6.61856i	0.579991	+	0.211099i	0.615322	−	0.788276i	$-0.289026\pi$
$983$	18.1844	+	6.61856i	0.579991	+	0.211099i	−0.0353306	+	0.999376i	$0.511248\pi$
$984$	−7.37964	+	0.802026i	−0.235254	+	0.0255677i
$985$		0			0
$986$	0.201374	+	0.168973i	0.00641306	+	0.00538120i
$987$	−10.7129	−	14.6359i	−0.340994	−	0.465864i
$988$	46.4234	+	16.8967i	1.47693	+	0.537557i
$989$	−22.6458	+	39.2236i	−0.720094	+	1.24724i
$990$		0			0
$991$	8.67263	+	15.0214i	0.275495	+	0.477172i	0.970260	−	0.242065i	$-0.0778249\pi$
$991$	8.67263	+	15.0214i	0.275495	+	0.477172i	−0.694765	+	0.719237i	$0.744492\pi$
$992$	3.35470	+	19.0255i	0.106512	+	0.604059i
$993$	31.3497	−	15.4277i	0.994851	−	0.489584i
$994$	−2.98461	+	1.08631i	−0.0946661	+	0.0344557i
$995$		0			0
$996$	25.7822	−	26.8879i	0.816939	−	0.851974i
$997$	−13.7671	+	11.5520i	−0.436009	+	0.365855i	−0.834214	−	0.551442i	$-0.814078\pi$
$997$	−13.7671	+	11.5520i	−0.436009	+	0.365855i	0.398204	+	0.917297i	$0.369634\pi$
$998$	−6.61118			−0.209273
$999$	−12.1676	+	4.09671i	−0.384966	+	0.129614i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.l.g.76.5	yes	66
5.2	odd	4		675.2.u.e.49.10		132
5.3	odd	4		675.2.u.e.49.13		132
5.4	even	2		675.2.l.f.76.7	✓	66
27.16	even	9	inner	675.2.l.g.151.5	yes	66
135.43	odd	36		675.2.u.e.124.10		132
135.97	odd	36		675.2.u.e.124.13		132
135.124	even	18		675.2.l.f.151.7	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.f.76.7	✓	66	5.4	even	2
675.2.l.f.151.7	yes	66	135.124	even	18
675.2.l.g.76.5	yes	66	1.1	even	1	trivial
675.2.l.g.151.5	yes	66	27.16	even	9	inner
675.2.u.e.49.10		132	5.2	odd	4
675.2.u.e.49.13		132	5.3	odd	4
675.2.u.e.124.10		132	135.43	odd	36
675.2.u.e.124.13		132	135.97	odd	36

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.211903 + 0.177808i) q^{2} +(0.483303 + 1.66326i) q^{3} +(-0.334009 + 1.89426i) q^{4} +(-0.398153 - 0.266514i) q^{6} +(-0.293371 - 1.66379i) q^{7} +(-0.542656 - 0.939908i) q^{8} +(-2.53284 + 1.60771i) q^{9} +(-4.65944 - 1.69590i) q^{11} +(-3.31206 + 0.359958i) q^{12} +(2.87084 + 2.40892i) q^{13} +(0.358001 + 0.300398i) q^{14} +(-3.33285 - 1.21306i) q^{16} +(-3.15798 + 5.46979i) q^{17} +(0.250852 - 0.791037i) q^{18} +(-3.42671 - 5.93524i) q^{19} +(2.62552 - 1.29206i) q^{21} +(1.28889 - 0.469119i) q^{22} +(-1.12343 + 6.37131i) q^{23} +(1.30104 - 1.35684i) q^{24} -1.03667 q^{26} +(-3.89816 - 3.43574i) q^{27} +3.24964 q^{28} +(-0.115261 + 0.0967151i) q^{29} +(-1.06440 + 6.03653i) q^{31} +(2.96165 - 1.07795i) q^{32} +(0.568791 - 8.56948i) q^{33} +(-0.303384 - 1.72058i) q^{34} +(-2.19943 - 5.33484i) q^{36} +(1.23541 - 2.13979i) q^{37} +(1.78146 + 0.648400i) q^{38} +(-2.61917 + 5.93918i) q^{39} +(-3.02499 - 2.53826i) q^{41} +(-0.326617 + 0.740630i) q^{42} +(6.57849 + 2.39437i) q^{43} +(4.76877 - 8.25975i) q^{44} +(-0.894809 - 1.54985i) q^{46} +(-1.07632 - 6.10414i) q^{47} +(0.406850 - 6.12965i) q^{48} +(3.89572 - 1.41793i) q^{49} +(-10.6239 - 2.60897i) q^{51} +(-5.52201 + 4.63352i) q^{52} +0.373453 q^{53} +(1.43693 + 0.0349210i) q^{54} +(-1.40461 + 1.17861i) q^{56} +(8.21568 - 8.56802i) q^{57} +(0.00722737 - 0.0409885i) q^{58} +(0.342887 - 0.124801i) q^{59} +(1.07271 + 6.08365i) q^{61} +(-0.847791 - 1.46842i) q^{62} +(3.41795 + 3.74245i) q^{63} +(3.11083 - 5.38811i) q^{64} +(1.40319 + 1.91703i) q^{66} +(-0.475424 - 0.398928i) q^{67} +(-9.30640 - 7.80900i) q^{68} +(-11.1401 + 1.21071i) q^{69} +(-3.39814 + 5.88576i) q^{71} +(2.88556 + 1.50820i) q^{72} +(2.27683 + 3.94359i) q^{73} +(0.118685 + 0.673094i) q^{74} +(12.3874 - 4.50866i) q^{76} +(-1.45467 + 8.24986i) q^{77} +(-0.501023 - 1.72424i) q^{78} +(-12.4889 + 10.4794i) q^{79} +(3.83053 - 8.14414i) q^{81} +1.09233 q^{82} +(-8.56544 + 7.18726i) q^{83} +(1.57056 + 5.40498i) q^{84} +(-1.81974 + 0.662331i) q^{86} +(-0.216568 - 0.144965i) q^{87} +(0.934487 + 5.29974i) q^{88} +(4.58274 + 7.93753i) q^{89} +(3.16572 - 5.48319i) q^{91} +(-11.6937 - 4.25615i) q^{92} +(-10.5547 + 1.14710i) q^{93} +(1.31344 + 1.10211i) q^{94} +(3.22429 + 4.40501i) q^{96} +(12.9391 + 4.70945i) q^{97} +(-0.573397 + 0.993152i) q^{98} +(14.5281 - 3.19561i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 6 q^{9} + 15 q^{11} + 18 q^{12} + 15 q^{14} + 18 q^{16} + 30 q^{17} - 12 q^{18} + 12 q^{19} + 12 q^{21} - 45 q^{22} + 36 q^{23} - 39 q^{24} + 6 q^{26} + 51 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) \) 66 * q + 6 * q^2 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 6 * q^9 + 15 * q^11 + 18 * q^12 + 15 * q^14 + 18 * q^16 + 30 * q^17 - 12 * q^18 + 12 * q^19 + 12 * q^21 - 45 * q^22 + 36 * q^23 - 39 * q^24 + 6 * q^26 + 51 * q^27 - 36 * q^28 - 15 * q^29 + 3 * q^31 + 27 * q^32 - 3 * q^33 + 30 * q^36 + 6 * q^37 - 12 * q^38 - 15 * q^39 + 39 * q^41 + 48 * q^42 + 12 * q^43 + 51 * q^44 + 9 * q^46 + 30 * q^47 - 132 * q^48 - 6 * q^49 + 9 * q^52 - 24 * q^53 + 75 * q^54 + 144 * q^56 + 33 * q^57 + 27 * q^58 + 45 * q^59 - 54 * q^61 + 66 * q^62 - 120 * q^63 - 24 * q^64 + 48 * q^66 + 9 * q^67 - 69 * q^68 + 51 * q^69 - 15 * q^71 + 9 * q^72 - 15 * q^73 + 96 * q^74 - 48 * q^76 - 36 * q^77 - 18 * q^78 + 48 * q^79 - 54 * q^81 - 36 * q^82 + 30 * q^83 + 57 * q^84 - 111 * q^86 - 33 * q^87 + 36 * q^88 - 12 * q^89 + 9 * q^91 - 219 * q^92 + 63 * q^93 + 36 * q^94 - 249 * q^96 + 57 * q^97 + 75 * q^98 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more