LMFDB - Embedded newform 108.3.k.a.5.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(5,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("108.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.k (of order $18$, 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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.6
Character	$\chi$	$=$	108.5
Dual form			108.3.k.a.65.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.99363 - 0.195330i) q^{3} +(-2.50118 - 6.87194i) q^{5} +(-1.62729 - 9.22884i) q^{7} +(8.92369 - 1.16949i) q^{9} +O(q^{10})$	\(q+(2.99363 - 0.195330i) q^{3} +(-2.50118 - 6.87194i) q^{5} +(-1.62729 - 9.22884i) q^{7} +(8.92369 - 1.16949i) q^{9} +(-4.02712 + 11.0644i) q^{11} +(17.4349 + 14.6296i) q^{13} +(-8.82992 - 20.0835i) q^{15} +(-13.5275 - 7.81011i) q^{17} +(9.08487 + 15.7354i) q^{19} +(-6.67419 - 27.3099i) q^{21} +(23.0574 + 4.06564i) q^{23} +(-21.8166 + 18.3063i) q^{25} +(26.4858 - 5.24410i) q^{27} +(-24.8898 - 29.6625i) q^{29} +(-4.47532 + 25.3808i) q^{31} +(-9.89451 + 33.9094i) q^{33} +(-59.3499 + 34.2657i) q^{35} +(1.45889 - 2.52687i) q^{37} +(55.0514 + 40.3903i) q^{39} +(-26.1577 + 31.1736i) q^{41} +(35.7017 + 12.9943i) q^{43} +(-30.3565 - 58.3980i) q^{45} +(-18.5209 + 3.26574i) q^{47} +(-36.4785 + 13.2771i) q^{49} +(-42.0220 - 20.7383i) q^{51} +12.3119i q^{53} +86.1066 q^{55} +(30.2704 + 45.3316i) q^{57} +(4.38973 + 12.0607i) q^{59} +(-15.6708 - 88.8733i) q^{61} +(-25.3145 - 80.4522i) q^{63} +(56.9261 - 156.403i) q^{65} +(-6.68767 - 5.61162i) q^{67} +(69.8195 + 7.66724i) q^{69} +(81.5508 + 47.0834i) q^{71} +(-25.3297 - 43.8724i) q^{73} +(-61.7350 + 59.0637i) q^{75} +(108.665 + 19.1606i) q^{77} +(-78.4939 + 65.8642i) q^{79} +(78.2646 - 20.8724i) q^{81} +(-12.1497 - 14.4795i) q^{83} +(-19.8359 + 112.495i) q^{85} +(-80.3049 - 83.9370i) q^{87} +(-52.8907 + 30.5364i) q^{89} +(106.643 - 184.711i) q^{91} +(-8.43984 + 76.8550i) q^{93} +(85.4102 - 101.788i) q^{95} +(-139.585 - 50.8047i) q^{97} +(-22.9970 + 103.445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q - 9 * q^5 + 6 * q^9	$ 36 q - 9 q^{5} + 6 q^{9} + 36 q^{11} + 45 q^{15} + 42 q^{21} - 18 q^{23} - 9 q^{25} - 18 q^{29} + 45 q^{31} - 153 q^{33} - 243 q^{35} - 123 q^{39} - 198 q^{41} + 90 q^{43} - 333 q^{45} - 243 q^{47} + 72 q^{49} - 99 q^{51} + 243 q^{57} + 252 q^{59} - 144 q^{61} + 381 q^{63} + 747 q^{65} + 108 q^{67} + 585 q^{69} + 324 q^{71} - 63 q^{73} + 597 q^{75} + 495 q^{77} + 36 q^{79} - 54 q^{81} - 27 q^{83} - 180 q^{85} - 441 q^{87} - 567 q^{89} + 99 q^{91} - 699 q^{93} - 1044 q^{95} - 216 q^{97} - 945 q^{99}+O(q^{100}) $ 36 * q - 9 * q^5 + 6 * q^9 + 36 * q^11 + 45 * q^15 + 42 * q^21 - 18 * q^23 - 9 * q^25 - 18 * q^29 + 45 * q^31 - 153 * q^33 - 243 * q^35 - 123 * q^39 - 198 * q^41 + 90 * q^43 - 333 * q^45 - 243 * q^47 + 72 * q^49 - 99 * q^51 + 243 * q^57 + 252 * q^59 - 144 * q^61 + 381 * q^63 + 747 * q^65 + 108 * q^67 + 585 * q^69 + 324 * q^71 - 63 * q^73 + 597 * q^75 + 495 * q^77 + 36 * q^79 - 54 * q^81 - 27 * q^83 - 180 * q^85 - 441 * q^87 - 567 * q^89 + 99 * q^91 - 699 * q^93 - 1044 * q^95 - 216 * q^97 - 945 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.99363	−	0.195330i	0.997878	−	0.0651100i
$3$	2.99363	−	0.195330i	0.997878	−	0.0651100i
$4$		0			0
$5$	−2.50118	−	6.87194i	−0.500236	−	1.37439i	−0.891044	−	0.453916i	$-0.850027\pi$
$5$	−2.50118	−	6.87194i	−0.500236	−	1.37439i	0.390808	−	0.920472i	$-0.372196\pi$
$6$		0			0
$7$	−1.62729	−	9.22884i	−0.232470	−	1.31841i	−0.847876	−	0.530195i	$-0.822119\pi$
$7$	−1.62729	−	9.22884i	−0.232470	−	1.31841i	0.615405	−	0.788211i	$-0.288992\pi$
$8$		0			0
$9$	8.92369	−	1.16949i	0.991521	−	0.129944i
$10$		0			0
$11$	−4.02712	+	11.0644i	−0.366102	+	1.00586i	0.610728	+	0.791840i	$0.290877\pi$
$11$	−4.02712	+	11.0644i	−0.366102	+	1.00586i	−0.976830	+	0.214016i	$0.931345\pi$
$12$		0			0
$13$	17.4349	+	14.6296i	1.34115	+	1.12536i	0.981329	+	0.192336i	$0.0616063\pi$
$13$	17.4349	+	14.6296i	1.34115	+	1.12536i	0.359820	+	0.933022i	$0.382838\pi$
$14$		0			0
$15$	−8.82992	−	20.0835i	−0.588661	−	1.33890i
$16$		0			0
$17$	−13.5275	−	7.81011i	−0.795736	−	0.459418i	0.0462422	−	0.998930i	$-0.485275\pi$
$17$	−13.5275	−	7.81011i	−0.795736	−	0.459418i	−0.841978	+	0.539512i	$0.818609\pi$
$18$		0			0
$19$	9.08487	+	15.7354i	0.478151	+	0.828182i	0.999686	−	0.0250481i	$-0.00797389\pi$
$19$	9.08487	+	15.7354i	0.478151	+	0.828182i	−0.521535	+	0.853230i	$0.674641\pi$
$20$		0			0
$21$	−6.67419	−	27.3099i	−0.317819	−	1.30047i
$22$		0			0
$23$	23.0574	+	4.06564i	1.00250	+	0.176767i	0.650720	−	0.759318i	$-0.274467\pi$
$23$	23.0574	+	4.06564i	1.00250	+	0.176767i	0.351775	+	0.936085i	$0.385578\pi$
$24$		0			0
$25$	−21.8166	+	18.3063i	−0.872662	+	0.732251i
$26$		0			0
$27$	26.4858	−	5.24410i	0.980957	−	0.194226i
$28$		0			0
$29$	−24.8898	−	29.6625i	−0.858269	−	1.02284i	−0.999460	−	0.0328626i	$-0.989538\pi$
$29$	−24.8898	−	29.6625i	−0.858269	−	1.02284i	0.141191	−	0.989982i	$-0.454907\pi$
$30$		0			0
$31$	−4.47532	+	25.3808i	−0.144365	+	0.818735i	0.823510	+	0.567302i	$0.192013\pi$
$31$	−4.47532	+	25.3808i	−0.144365	+	0.818735i	−0.967875	+	0.251433i	$0.919098\pi$
$32$		0			0
$33$	−9.89451	+	33.9094i	−0.299834	+	1.02756i
$34$		0			0
$35$	−59.3499	+	34.2657i	−1.69571	+	0.979019i
$36$		0			0
$37$	1.45889	−	2.52687i	0.0394294	−	0.0682937i	−0.845637	−	0.533758i	$-0.820779\pi$
$37$	1.45889	−	2.52687i	0.0394294	−	0.0682937i	0.885067	+	0.465464i	$0.154113\pi$
$38$		0			0
$39$	55.0514	+	40.3903i	1.41158	+	1.03565i
$40$		0			0
$41$	−26.1577	+	31.1736i	−0.637993	+	0.760331i	−0.984052	−	0.177882i	$-0.943075\pi$
$41$	−26.1577	+	31.1736i	−0.637993	+	0.760331i	0.346058	+	0.938213i	$0.387520\pi$
$42$		0			0
$43$	35.7017	+	12.9943i	0.830271	+	0.302194i	0.721970	−	0.691924i	$-0.243237\pi$
$43$	35.7017	+	12.9943i	0.830271	+	0.302194i	0.108301	+	0.994118i	$0.465459\pi$
$44$		0			0
$45$	−30.3565	−	58.3980i	−0.674588	−	1.29773i
$46$		0			0
$47$	−18.5209	+	3.26574i	−0.394063	+	0.0694839i	−0.367169	−	0.930154i	$-0.619673\pi$
$47$	−18.5209	+	3.26574i	−0.394063	+	0.0694839i	−0.0268941	+	0.999638i	$0.508562\pi$
$48$		0			0
$49$	−36.4785	+	13.2771i	−0.744458	+	0.270961i
$50$		0			0
$51$	−42.0220	−	20.7383i	−0.823960	−	0.406633i
$52$		0			0
$53$			12.3119i			0.232300i	0.993232	+	0.116150i	$0.0370554\pi$
$53$			12.3119i			0.232300i	−0.993232	+	0.116150i	$0.962945\pi$
$54$		0			0
$55$	86.1066			1.56557
$56$		0			0
$57$	30.2704	+	45.3316i	0.531059	+	0.795292i
$58$		0			0
$59$	4.38973	+	12.0607i	0.0744022	+	0.204418i	0.971319	−	0.237782i	$-0.0764203\pi$
$59$	4.38973	+	12.0607i	0.0744022	+	0.204418i	−0.896916	+	0.442200i	$0.854198\pi$
$60$		0			0
$61$	−15.6708	−	88.8733i	−0.256898	−	1.45694i	−0.791154	−	0.611617i	$-0.790520\pi$
$61$	−15.6708	−	88.8733i	−0.256898	−	1.45694i	0.534257	−	0.845322i	$-0.320592\pi$
$62$		0			0
$63$	−25.3145	−	80.4522i	−0.401818	−	1.27702i
$64$		0			0
$65$	56.9261	−	156.403i	0.875787	−	2.40620i
$66$		0			0
$67$	−6.68767	−	5.61162i	−0.0998159	−	0.0837555i	0.591514	−	0.806295i	$-0.298530\pi$
$67$	−6.68767	−	5.61162i	−0.0998159	−	0.0837555i	−0.691330	+	0.722539i	$0.742975\pi$
$68$		0			0
$69$	69.8195	+	7.66724i	1.01188	+	0.111119i
$70$		0			0
$71$	81.5508	+	47.0834i	1.14860	+	0.663146i	0.948546	−	0.316638i	$-0.102554\pi$
$71$	81.5508	+	47.0834i	1.14860	+	0.663146i	0.200057	+	0.979784i	$0.435887\pi$
$72$		0			0
$73$	−25.3297	−	43.8724i	−0.346983	−	0.600992i	0.638729	−	0.769432i	$-0.279460\pi$
$73$	−25.3297	−	43.8724i	−0.346983	−	0.600992i	−0.985712	+	0.168440i	$0.946127\pi$
$74$		0			0
$75$	−61.7350	+	59.0637i	−0.823134	+	0.787516i
$76$		0			0
$77$	108.665	+	19.1606i	1.41123	+	0.248839i
$78$		0			0
$79$	−78.4939	+	65.8642i	−0.993593	+	0.833724i	−0.986084	−	0.166248i	$-0.946835\pi$
$79$	−78.4939	+	65.8642i	−0.993593	+	0.833724i	−0.00750946	+	0.999972i	$0.502390\pi$
$80$		0			0
$81$	78.2646	−	20.8724i	0.966229	−	0.257684i
$82$		0			0
$83$	−12.1497	−	14.4795i	−0.146382	−	0.174451i	0.687871	−	0.725833i	$-0.258545\pi$
$83$	−12.1497	−	14.4795i	−0.146382	−	0.174451i	−0.834253	+	0.551381i	$0.814101\pi$
$84$		0			0
$85$	−19.8359	+	112.495i	−0.233363	+	1.32347i
$86$		0			0
$87$	−80.3049	−	83.9370i	−0.923045	−	0.964793i
$88$		0			0
$89$	−52.8907	+	30.5364i	−0.594277	+	0.343106i	−0.766787	−	0.641902i	$-0.778146\pi$
$89$	−52.8907	+	30.5364i	−0.594277	+	0.343106i	0.172510	+	0.985008i	$0.444812\pi$
$90$		0			0
$91$	106.643	−	184.711i	1.17190	−	2.02979i
$92$		0			0
$93$	−8.43984	+	76.8550i	−0.0907510	+	0.826398i
$94$		0			0
$95$	85.4102	−	101.788i	0.899055	−	1.07145i
$96$		0			0
$97$	−139.585	−	50.8047i	−1.43902	−	0.523760i	−0.499516	−	0.866305i	$-0.666489\pi$
$97$	−139.585	−	50.8047i	−1.43902	−	0.523760i	−0.939501	+	0.342545i	$0.888711\pi$
$98$		0			0
$99$	−22.9970	+	103.445i	−0.232293	+	1.04490i
$100$		0			0
$101$	3.22458	−	0.568581i	0.0319266	−	0.00562952i	−0.157662	−	0.987493i	$-0.550396\pi$
$101$	3.22458	−	0.568581i	0.0319266	−	0.00562952i	0.189589	+	0.981864i	$0.439285\pi$
$102$		0			0
$103$	18.2867	−	6.65582i	0.177541	−	0.0646196i	−0.251720	−	0.967800i	$-0.580996\pi$
$103$	18.2867	−	6.65582i	0.177541	−	0.0646196i	0.429261	+	0.903180i	$0.358774\pi$
$104$		0			0
$105$	−170.979	+	114.172i	−1.62837	+	1.08735i
$106$		0			0
$107$		−	24.7281i		−	0.231103i	−0.993301	−	0.115552i	$-0.963136\pi$
$107$		−	24.7281i		−	0.231103i	0.993301	−	0.115552i	$-0.0368636\pi$
$108$		0			0
$109$	1.01801			0.00933957			0.00466979	−	0.999989i	$-0.498514\pi$
$109$	1.01801			0.00933957			0.00466979	+	0.999989i	$0.498514\pi$
$110$		0			0
$111$	3.87380	−	7.84947i	0.0348991	−	0.0707160i
$112$		0			0
$113$	53.0907	+	145.865i	0.469829	+	1.29084i	0.917888	+	0.396840i	$0.129893\pi$
$113$	53.0907	+	145.865i	0.469829	+	1.29084i	−0.448059	+	0.894004i	$0.647884\pi$
$114$		0			0
$115$	−29.7319	−	168.618i	−0.258538	−	1.46624i
$116$		0			0
$117$	172.693	+	110.160i	1.47601	+	0.941542i
$118$		0			0
$119$	−50.0650	+	137.553i	−0.420714	+	1.15590i
$120$		0			0
$121$	−13.5123	−	11.3382i	−0.111672	−	0.0937041i
$122$		0			0
$123$	−72.2175	+	98.4316i	−0.587134	+	0.800257i
$124$		0			0
$125$	22.0364	+	12.7227i	0.176291	+	0.101782i
$126$		0			0
$127$	35.9061	+	62.1913i	0.282726	+	0.489695i	0.972055	−	0.234753i	$-0.0754281\pi$
$127$	35.9061	+	62.1913i	0.282726	+	0.489695i	−0.689330	+	0.724448i	$0.742095\pi$
$128$		0			0
$129$	109.416	+	31.9267i	0.848185	+	0.247494i
$130$		0			0
$131$	−17.2894	−	3.04859i	−0.131980	−	0.0232717i	0.107268	−	0.994230i	$-0.465790\pi$
$131$	−17.2894	−	3.04859i	−0.131980	−	0.0232717i	−0.239248	+	0.970958i	$0.576901\pi$
$132$		0			0
$133$	130.436	−	109.449i	0.980723	−	0.822924i
$134$		0			0
$135$	−102.283	−	168.893i	−0.757652	−	1.25106i
$136$		0			0
$137$	−13.3559	−	15.9169i	−0.0974881	−	0.116182i	0.715095	−	0.699028i	$-0.246384\pi$
$137$	−13.3559	−	15.9169i	−0.0974881	−	0.116182i	−0.812583	+	0.582846i	$0.801939\pi$
$138$		0			0
$139$	−1.08034	+	6.12690i	−0.00777221	+	0.0440784i	−0.988447	−	0.151565i	$-0.951569\pi$
$139$	−1.08034	+	6.12690i	−0.00777221	+	0.0440784i	0.980675	+	0.195644i	$0.0626797\pi$
$140$		0			0
$141$	−54.8070	+	13.3941i	−0.388702	+	0.0949938i
$142$		0			0
$143$	−232.081	+	133.992i	−1.62295	+	0.937008i
$144$		0			0
$145$	−141.585	+	245.233i	−0.976449	+	1.69126i
$146$		0			0
$147$	−106.610	+	46.8720i	−0.725236	+	0.318857i
$148$		0			0
$149$	144.811	−	172.579i	0.971888	−	1.15825i	−0.0154918	−	0.999880i	$-0.504931\pi$
$149$	144.811	−	172.579i	0.971888	−	1.15825i	0.987380	−	0.158371i	$-0.0506242\pi$
$150$		0			0
$151$	−221.794	−	80.7264i	−1.46883	−	0.534612i	−0.521051	−	0.853526i	$-0.674460\pi$
$151$	−221.794	−	80.7264i	−1.46883	−	0.534612i	−0.947784	+	0.318914i	$0.896682\pi$
$152$		0			0
$153$	−129.849	−	53.8747i	−0.848687	−	0.352122i
$154$		0			0
$155$	185.609	−	32.7279i	1.19748	−	0.211148i
$156$		0			0
$157$	−34.1578	+	12.4324i	−0.217566	+	0.0791874i	−0.448503	−	0.893781i	$-0.648043\pi$
$157$	−34.1578	+	12.4324i	−0.217566	+	0.0791874i	0.230938	+	0.972969i	$0.425821\pi$
$158$		0			0
$159$	2.40488	+	36.8573i	0.0151251	+	0.231807i
$160$		0			0
$161$		−	219.409i		−	1.36279i
$162$		0			0
$163$	−68.8785			−0.422568			−0.211284	−	0.977425i	$-0.567764\pi$
$163$	−68.8785			−0.422568			−0.211284	+	0.977425i	$0.567764\pi$
$164$		0			0
$165$	257.772	−	16.8192i	1.56225	−	0.101935i
$166$		0			0
$167$	38.6584	+	106.213i	0.231488	+	0.636007i	0.999993	−	0.00383681i	$-0.00122130\pi$
$167$	38.6584	+	106.213i	0.231488	+	0.636007i	−0.768505	+	0.639844i	$0.778999\pi$
$168$		0			0
$169$	60.6039	+	343.702i	0.358603	+	2.03374i
$170$		0			0
$171$	99.4730	+	129.794i	0.581714	+	0.759027i
$172$		0			0
$173$	46.9901	−	129.104i	0.271619	−	0.746267i	−0.726625	−	0.687034i	$-0.758912\pi$
$173$	46.9901	−	129.104i	0.271619	−	0.746267i	0.998244	−	0.0592329i	$-0.0188655\pi$
$174$		0			0
$175$	204.448	+	171.552i	1.16827	+	0.980296i
$176$		0			0
$177$	15.4971	+	35.2478i	0.0875540	+	0.199140i
$178$		0			0
$179$	166.758	+	96.2777i	0.931608	+	0.537864i	0.887320	−	0.461155i	$-0.152565\pi$
$179$	166.758	+	96.2777i	0.931608	+	0.537864i	0.0442884	+	0.999019i	$0.485898\pi$
$180$		0			0
$181$	−38.0528	−	65.9094i	−0.210237	−	0.364140i	0.741552	−	0.670895i	$-0.234090\pi$
$181$	−38.0528	−	65.9094i	−0.210237	−	0.364140i	−0.951788	+	0.306755i	$0.900757\pi$
$182$		0			0
$183$	−64.2721	−	262.993i	−0.351214	−	1.43712i
$184$		0			0
$185$	−21.0134	−	3.70523i	−0.113586	−	0.0200283i
$186$		0			0
$187$	140.891	−	118.222i	0.753429	−	0.632202i
$188$		0			0
$189$	−91.4971	−	235.900i	−0.484112	−	1.24815i
$190$		0			0
$191$	−132.171	−	157.515i	−0.691992	−	0.824684i	0.299603	−	0.954064i	$-0.403146\pi$
$191$	−132.171	−	157.515i	−0.691992	−	0.824684i	−0.991595	+	0.129380i	$0.958701\pi$
$192$		0			0
$193$	50.6060	−	287.001i	0.262207	−	1.48705i	−0.514665	−	0.857391i	$-0.672084\pi$
$193$	50.6060	−	287.001i	0.262207	−	1.48705i	0.776872	−	0.629659i	$-0.216805\pi$
$194$		0			0
$195$	139.866	−	479.334i	0.717261	−	2.45812i
$196$		0			0
$197$	−263.147	+	151.928i	−1.33577	+	0.771209i	−0.986178	−	0.165692i	$-0.947014\pi$
$197$	−263.147	+	151.928i	−1.33577	+	0.771209i	−0.349595	+	0.936901i	$0.613681\pi$
$198$		0			0
$199$	133.234	−	230.767i	0.669515	−	1.15963i	−0.308525	−	0.951216i	$-0.599835\pi$
$199$	133.234	−	230.767i	0.669515	−	1.15963i	0.978040	−	0.208418i	$-0.0668314\pi$
$200$		0			0
$201$	−21.1165	−	15.4928i	−0.105057	−	0.0770788i
$202$		0			0
$203$	−233.247	+	277.974i	−1.14900	+	1.36933i
$204$		0			0
$205$	279.648	+	101.784i	1.36414	+	0.496505i
$206$		0			0
$207$	210.512	+	9.31507i	1.01697	+	0.0450004i
$208$		0			0
$209$	−210.689	+	37.1502i	−1.00808	+	0.177752i
$210$		0			0
$211$	−83.5395	+	30.4059i	−0.395922	+	0.144104i	−0.532306	−	0.846552i	$-0.678674\pi$
$211$	−83.5395	+	30.4059i	−0.395922	+	0.144104i	0.136384	+	0.990656i	$0.456452\pi$
$212$		0			0
$213$	253.330	+	125.021i	1.18934	+	0.586954i
$214$		0			0
$215$		−	277.841i		−	1.29228i
$216$		0			0
$217$	241.518			1.11299
$218$		0			0
$219$	−84.3976	−	126.390i	−0.385377	−	0.577124i
$220$		0			0
$221$	−121.592	−	334.071i	−0.550190	−	1.51164i
$222$		0			0
$223$	50.4092	+	285.885i	0.226050	+	1.28199i	0.860667	+	0.509168i	$0.170047\pi$
$223$	50.4092	+	285.885i	0.226050	+	1.28199i	−0.634617	+	0.772827i	$0.718842\pi$
$224$		0			0
$225$	−173.275	+	188.874i	−0.770112	+	0.839439i
$226$		0			0
$227$	−63.1774	+	173.578i	−0.278315	+	0.764663i	0.719239	+	0.694762i	$0.244490\pi$
$227$	−63.1774	+	173.578i	−0.278315	+	0.764663i	−0.997554	+	0.0699006i	$0.977732\pi$
$228$		0			0
$229$	−261.099	−	219.088i	−1.14017	−	0.956715i	−0.140724	−	0.990049i	$-0.544943\pi$
$229$	−261.099	−	219.088i	−1.14017	−	0.956715i	−0.999444	+	0.0333342i	$0.989387\pi$
$230$		0			0
$231$	329.046	+	36.1342i	1.42444	+	0.156425i
$232$		0			0
$233$	262.837	+	151.749i	1.12806	+	0.651283i	0.943445	−	0.331528i	$-0.107564\pi$
$233$	262.837	+	151.749i	1.12806	+	0.651283i	0.184611	+	0.982812i	$0.440898\pi$
$234$		0			0
$235$	68.7662	+	119.107i	0.292622	+	0.506837i
$236$		0			0
$237$	−222.117	+	212.505i	−0.937201	+	0.896648i
$238$		0			0
$239$	−431.057	−	76.0070i	−1.80359	−	0.318021i	−0.832013	−	0.554756i	$-0.812812\pi$
$239$	−431.057	−	76.0070i	−1.80359	−	0.318021i	−0.971574	+	0.236735i	$0.923923\pi$
$240$		0			0
$241$	−124.647	+	104.591i	−0.517209	+	0.433990i	−0.863657	−	0.504079i	$-0.831832\pi$
$241$	−124.647	+	104.591i	−0.517209	+	0.433990i	0.346449	+	0.938069i	$0.387387\pi$
$242$		0			0
$243$	230.219	−	77.7717i	0.947401	−	0.320048i
$244$		0			0
$245$	182.479	+	217.469i	0.744810	+	0.887630i
$246$		0			0
$247$	−71.8100	+	407.255i	−0.290729	+	1.64881i
$248$		0			0
$249$	−39.2001	−	40.9730i	−0.157430	−	0.164550i
$250$		0			0
$251$	394.843	−	227.963i	1.57308	−	0.908219i	0.577292	−	0.816538i	$-0.304109\pi$
$251$	394.843	−	227.963i	1.57308	−	0.908219i	0.995788	−	0.0916811i	$-0.0292240\pi$
$252$		0			0
$253$	−137.839	+	238.744i	−0.544817	+	0.943652i
$254$		0			0
$255$	−37.4077	+	340.643i	−0.146697	+	1.33585i
$256$		0			0
$257$	−266.990	+	318.187i	−1.03887	+	1.23808i	−0.0682006	+	0.997672i	$0.521726\pi$
$257$	−266.990	+	318.187i	−1.03887	+	1.23808i	−0.970672	+	0.240408i	$0.922719\pi$
$258$		0			0
$259$	−25.6941	−	9.35188i	−0.0992049	−	0.0361076i
$260$		0			0
$261$	−256.799	−	235.591i	−0.983904	−	0.902646i
$262$		0			0
$263$	−420.070	+	74.0696i	−1.59722	+	0.281633i	−0.900220	−	0.435435i	$-0.856595\pi$
$263$	−420.070	+	74.0696i	−1.59722	+	0.281633i	−0.697003	+	0.717068i	$0.745483\pi$
$264$		0			0
$265$	84.6067	−	30.7943i	0.319271	−	0.116205i
$266$		0			0
$267$	−152.371	+	101.746i	−0.570676	+	0.381071i
$268$		0			0
$269$		−	229.784i		−	0.854215i	−0.904201	−	0.427108i	$-0.859533\pi$
$269$		−	229.784i		−	0.854215i	0.904201	−	0.427108i	$-0.140467\pi$
$270$		0			0
$271$	−247.394			−0.912892			−0.456446	−	0.889751i	$-0.650878\pi$
$271$	−247.394			−0.912892			−0.456446	+	0.889751i	$0.650878\pi$
$272$		0			0
$273$	283.170	−	573.788i	1.03725	−	2.10179i
$274$		0			0
$275$	−114.690	−	315.109i	−0.417056	−	1.14585i
$276$		0			0
$277$	25.5477	+	144.888i	0.0922299	+	0.523062i	0.995561	+	0.0941179i	$0.0300031\pi$
$277$	25.5477	+	144.888i	0.0922299	+	0.523062i	−0.903331	+	0.428944i	$0.858886\pi$
$278$		0			0
$279$	−10.2537	+	231.724i	−0.0367517	+	0.830553i
$280$		0			0
$281$	−15.8083	+	43.4331i	−0.0562575	+	0.154566i	−0.964638	−	0.263578i	$-0.915097\pi$
$281$	−15.8083	+	43.4331i	−0.0562575	+	0.154566i	0.908381	+	0.418145i	$0.137319\pi$
$282$		0			0
$283$	94.8323	+	79.5738i	0.335097	+	0.281179i	0.794773	−	0.606907i	$-0.207590\pi$
$283$	94.8323	+	79.5738i	0.335097	+	0.281179i	−0.459676	+	0.888087i	$0.652034\pi$
$284$		0			0
$285$	235.805	−	321.399i	0.827385	−	1.12772i
$286$		0			0
$287$	330.262	+	190.677i	1.15074	+	0.664379i
$288$		0			0
$289$	−22.5044	−	38.9787i	−0.0778698	−	0.134874i
$290$		0			0
$291$	−427.789	−	124.826i	−1.47007	−	0.428954i
$292$		0			0
$293$	134.669	+	23.7457i	0.459621	+	0.0810435i	0.398664	−	0.917097i	$-0.369474\pi$
$293$	134.669	+	23.7457i	0.459621	+	0.0810435i	0.0609563	+	0.998140i	$0.480585\pi$
$294$		0			0
$295$	71.9008	−	60.3319i	0.243731	−	0.204515i
$296$		0			0
$297$	−48.6387	+	314.169i	−0.163767	+	1.05781i
$298$		0			0
$299$	342.525	+	408.206i	1.14557	+	1.36524i
$300$		0			0
$301$	61.8256	−	350.630i	0.205401	−	1.16489i
$302$		0			0
$303$	9.54217	−	2.33198i	0.0314923	−	0.00769631i
$304$		0			0
$305$	−571.537	+	329.977i	−1.87389	+	1.08189i
$306$		0			0
$307$	−148.518	+	257.240i	−0.483771	+	0.837915i	−0.999826	−	0.0186398i	$-0.994066\pi$
$307$	−148.518	+	257.240i	−0.483771	+	0.837915i	0.516056	+	0.856555i	$0.327400\pi$
$308$		0			0
$309$	53.4436	−	23.4970i	0.172957	−	0.0760422i
$310$		0			0
$311$	237.230	−	282.720i	0.762797	−	0.909067i	−0.235224	−	0.971941i	$-0.575582\pi$
$311$	237.230	−	282.720i	0.762797	−	0.909067i	0.998021	+	0.0628746i	$0.0200268\pi$
$312$		0			0
$313$	322.695	+	117.451i	1.03097	+	0.375244i	0.801452	−	0.598059i	$-0.204061\pi$
$313$	322.695	+	117.451i	1.03097	+	0.375244i	0.229522	+	0.973303i	$0.426284\pi$
$314$		0			0
$315$	−489.547	+	375.186i	−1.55412	+	1.19107i
$316$		0			0
$317$	537.404	−	94.7588i	1.69528	−	0.298924i	0.759239	−	0.650812i	$-0.225572\pi$
$317$	537.404	−	94.7588i	1.69528	−	0.298924i	0.936042	+	0.351889i	$0.114460\pi$
$318$		0			0
$319$	428.433	−	155.937i	1.34305	−	0.488830i
$320$		0			0
$321$	−4.83013	−	74.0268i	−0.0150471	−	0.230613i
$322$		0			0
$323$		−	283.815i		−	0.878685i
$324$		0			0
$325$	−648.185			−1.99441
$326$		0			0
$327$	3.04756	−	0.198848i	0.00931975	−	0.000608099i
$328$		0			0
$329$	60.2780	+	165.612i	0.183216	+	0.503381i
$330$		0			0
$331$	−31.4888	−	178.582i	−0.0951322	−	0.539522i	−0.994707	−	0.102754i	$-0.967234\pi$
$331$	−31.4888	−	178.582i	−0.0951322	−	0.539522i	0.899575	−	0.436767i	$-0.143877\pi$
$332$		0			0
$333$	10.0635	−	24.2551i	0.0302207	−	0.0728382i
$334$		0			0
$335$	−21.8356	+	59.9929i	−0.0651810	+	0.179083i
$336$		0			0
$337$	−287.391	−	241.149i	−0.852791	−	0.715577i	0.107611	−	0.994193i	$-0.465680\pi$
$337$	−287.391	−	241.149i	−0.852791	−	0.715577i	−0.960403	+	0.278616i	$0.910124\pi$
$338$		0			0
$339$	187.426	+	426.298i	0.552879	+	1.25751i
$340$		0			0
$341$	−262.801	−	151.728i	−0.770678	−	0.444951i
$342$		0			0
$343$	−47.7015	−	82.6215i	−0.139072	−	0.240879i
$344$		0			0
$345$	−121.943	−	498.973i	−0.353457	−	1.44630i
$346$		0			0
$347$	167.538	+	29.5415i	0.482820	+	0.0851341i	0.409760	−	0.912193i	$-0.365613\pi$
$347$	167.538	+	29.5415i	0.482820	+	0.0851341i	0.0730598	+	0.997328i	$0.476724\pi$
$348$		0			0
$349$	126.546	−	106.185i	0.362596	−	0.304254i	−0.443229	−	0.896409i	$-0.646167\pi$
$349$	126.546	−	106.185i	0.362596	−	0.304254i	0.805824	+	0.592155i	$0.201723\pi$
$350$		0			0
$351$	538.498	+	296.048i	1.53418	+	0.843442i
$352$		0			0
$353$	−54.0593	−	64.4254i	−0.153143	−	0.182508i	0.684018	−	0.729465i	$-0.260231\pi$
$353$	−54.0593	−	64.4254i	−0.153143	−	0.182508i	−0.837161	+	0.546956i	$0.815786\pi$
$354$		0			0
$355$	119.581	−	678.177i	0.336847	−	1.91036i
$356$		0			0
$357$	−123.008	+	421.561i	−0.344561	+	1.18084i
$358$		0			0
$359$	289.723	−	167.271i	0.807027	−	0.465937i	−0.0388953	−	0.999243i	$-0.512384\pi$
$359$	289.723	−	167.271i	0.807027	−	0.465937i	0.845922	+	0.533306i	$0.179051\pi$
$360$		0			0
$361$	15.4304	−	26.7263i	0.0427436	−	0.0740340i
$362$		0			0
$363$	−42.6657	−	31.3031i	−0.117536	−	0.0862343i
$364$		0			0
$365$	−238.134	+	283.797i	−0.652423	+	0.777527i
$366$		0			0
$367$	149.979	+	54.5880i	0.408663	+	0.148741i	0.538168	−	0.842838i	$-0.319117\pi$
$367$	149.979	+	54.5880i	0.408663	+	0.148741i	−0.129505	+	0.991579i	$0.541339\pi$
$368$		0			0
$369$	−196.966	+	308.775i	−0.533784	+	0.836787i
$370$		0			0
$371$	113.625	−	20.0351i	0.306266	−	0.0540029i
$372$		0			0
$373$	307.437	−	111.898i	0.824227	−	0.299994i	0.104740	−	0.994500i	$-0.466599\pi$
$373$	307.437	−	111.898i	0.824227	−	0.299994i	0.719487	+	0.694506i	$0.244377\pi$
$374$		0			0
$375$	68.4541	+	33.7828i	0.182544	+	0.0900875i
$376$		0			0
$377$		−	881.293i		−	2.33765i
$378$		0			0
$379$	−244.316			−0.644634			−0.322317	−	0.946632i	$-0.604462\pi$
$379$	−244.316			−0.644634			−0.322317	+	0.946632i	$0.604462\pi$
$380$		0			0
$381$	119.638	+	179.164i	0.314010	+	0.470248i
$382$		0			0
$383$	−132.824	−	364.931i	−0.346799	−	0.952822i	−0.983372	−	0.181605i	$-0.941871\pi$
$383$	−132.824	−	364.931i	−0.346799	−	0.952822i	0.636573	−	0.771217i	$-0.280351\pi$
$384$		0			0
$385$	−140.121	−	794.664i	−0.363950	−	2.06406i
$386$		0			0
$387$	333.787	+	74.2047i	0.862500	+	0.191743i
$388$		0			0
$389$	−183.766	+	504.892i	−0.472406	+	1.29792i	0.443408	+	0.896320i	$0.353769\pi$
$389$	−183.766	+	504.892i	−0.472406	+	1.29792i	−0.915813	+	0.401604i	$0.868453\pi$
$390$		0			0
$391$	−280.156	−	235.079i	−0.716511	−	0.601224i
$392$		0			0
$393$	−52.3536	−	5.74922i	−0.133215	−	0.0146291i
$394$		0			0
$395$	648.942	+	374.667i	1.64289	+	0.948524i
$396$		0			0
$397$	−8.55286	−	14.8140i	−0.0215437	−	0.0373148i	0.855053	−	0.518541i	$-0.173525\pi$
$397$	−8.55286	−	14.8140i	−0.0215437	−	0.0373148i	−0.876596	+	0.481227i	$0.840191\pi$
$398$		0			0
$399$	369.100	−	353.128i	0.925062	−	0.885033i
$400$		0			0
$401$	534.855	+	94.3095i	1.33380	+	0.235186i	0.794674	−	0.607037i	$-0.207642\pi$
$401$	534.855	+	94.3095i	1.33380	+	0.235186i	0.539130	+	0.842222i	$0.318753\pi$
$402$		0			0
$403$	−449.339	+	377.040i	−1.11499	+	0.935584i
$404$		0			0
$405$	−339.188	−	485.624i	−0.837501	−	1.19907i
$406$		0			0
$407$	22.0832	+	26.3177i	0.0542585	+	0.0646627i
$408$		0			0
$409$	14.3282	−	81.2594i	0.0350323	−	0.198678i	−0.962269	−	0.272102i	$-0.912281\pi$
$409$	14.3282	−	81.2594i	0.0350323	−	0.198678i	0.997301	+	0.0734234i	$0.0233924\pi$
$410$		0			0
$411$	−43.0916	−	45.0406i	−0.104846	−	0.109588i
$412$		0			0
$413$	104.163	−	60.1384i	0.252210	−	0.145613i
$414$		0			0
$415$	−69.1134	+	119.708i	−0.166538	+	0.288453i
$416$		0			0
$417$	−2.03737	+	18.5527i	−0.00488578	+	0.0444909i
$418$		0			0
$419$	478.636	−	570.416i	1.14233	−	1.36137i	0.219755	−	0.975555i	$-0.429474\pi$
$419$	478.636	−	570.416i	1.14233	−	1.36137i	0.922574	−	0.385819i	$-0.126081\pi$
$420$		0			0
$421$	670.000	+	243.860i	1.59145	+	0.579240i	0.977653	−	0.210225i	$-0.0674196\pi$
$421$	670.000	+	243.860i	1.59145	+	0.579240i	0.613796	+	0.789465i	$0.289642\pi$
$422$		0			0
$423$	−161.456	+	50.8026i	−0.381693	+	0.120101i
$424$		0			0
$425$	438.098	−	77.2484i	1.03082	−	0.181761i
$426$		0			0
$427$	−794.696	+	289.246i	−1.86112	+	0.677391i
$428$		0			0
$429$	−668.593	+	446.456i	−1.55849	+	1.04069i
$430$		0			0
$431$			60.8696i			0.141229i	0.997504	+	0.0706144i	$0.0224960\pi$
$431$			60.8696i			0.141229i	−0.997504	+	0.0706144i	$0.977504\pi$
$432$		0			0
$433$	542.738			1.25344			0.626718	−	0.779246i	$-0.284398\pi$
$433$	542.738			1.25344			0.626718	+	0.779246i	$0.284398\pi$
$434$		0			0
$435$	−375.953	+	761.792i	−0.864259	+	1.75125i
$436$		0			0
$437$	145.499	+	399.754i	0.332949	+	0.914769i
$438$		0			0
$439$	−6.32635	−	35.8785i	−0.0144108	−	0.0817278i	0.976754	−	0.214363i	$-0.0687674\pi$
$439$	−6.32635	−	35.8785i	−0.0144108	−	0.0817278i	−0.991165	+	0.132635i	$0.957656\pi$
$440$		0			0
$441$	−309.995	+	161.142i	−0.702937	+	0.365401i
$442$		0			0
$443$	−102.451	+	281.481i	−0.231266	+	0.635398i	−0.999991	−	0.00418102i	$-0.998669\pi$
$443$	−102.451	+	281.481i	−0.231266	+	0.635398i	0.768725	+	0.639579i	$0.220891\pi$
$444$		0			0
$445$	342.134	+	287.084i	0.768840	+	0.645133i
$446$		0			0
$447$	399.802	−	544.926i	0.894412	−	1.21907i
$448$		0			0
$449$	569.528	+	328.817i	1.26844	+	0.732332i	0.974692	−	0.223551i	$-0.0717651\pi$
$449$	569.528	+	328.817i	1.26844	+	0.732332i	0.293745	+	0.955884i	$0.405098\pi$
$450$		0			0
$451$	−239.577	−	414.960i	−0.531213	−	0.920088i
$452$		0			0
$453$	−679.738	−	198.342i	−1.50053	−	0.437842i
$454$		0			0
$455$	−1536.06	−	270.848i	−3.37595	−	0.595271i
$456$		0			0
$457$	−191.262	+	160.488i	−0.418517	+	0.351177i	−0.827598	−	0.561321i	$-0.810293\pi$
$457$	−191.262	+	160.488i	−0.418517	+	0.351177i	0.409082	+	0.912498i	$0.365849\pi$
$458$		0			0
$459$	−399.244	−	135.918i	−0.869813	−	0.296117i
$460$		0			0
$461$	−100.503	−	119.775i	−0.218012	−	0.259816i	0.645943	−	0.763385i	$-0.276464\pi$
$461$	−100.503	−	119.775i	−0.218012	−	0.259816i	−0.863955	+	0.503569i	$0.832020\pi$
$462$		0			0
$463$	−112.206	+	636.349i	−0.242345	+	1.37440i	0.584235	+	0.811585i	$0.301395\pi$
$463$	−112.206	+	636.349i	−0.242345	+	1.37440i	−0.826580	+	0.562820i	$0.809716\pi$
$464$		0			0
$465$	549.253	−	134.230i	1.18119	−	0.288667i
$466$		0			0
$467$	−142.134	+	82.0612i	−0.304356	+	0.175720i	−0.644398	−	0.764690i	$-0.722892\pi$
$467$	−142.134	+	82.0612i	−0.304356	+	0.175720i	0.340042	+	0.940410i	$0.389559\pi$
$468$		0			0
$469$	−40.9059	+	70.8512i	−0.0872195	+	0.151069i
$470$		0			0
$471$	−99.8275	+	43.8902i	−0.211948	+	0.0931851i
$472$		0			0
$473$	−287.550	+	342.688i	−0.607927	+	0.724500i
$474$		0			0
$475$	−486.258	−	176.983i	−1.02370	−	0.372597i
$476$		0			0
$477$	14.3987	+	109.868i	0.0301859	+	0.230331i
$478$		0			0
$479$	−192.731	+	33.9838i	−0.402362	+	0.0709473i	−0.371167	−	0.928566i	$-0.621042\pi$
$479$	−192.731	+	33.9838i	−0.402362	+	0.0709473i	−0.0311949	+	0.999513i	$0.509931\pi$
$480$		0			0
$481$	62.4027	−	22.7127i	0.129735	−	0.0472198i
$482$		0			0
$483$	−42.8571	−	656.830i	−0.0887311	−	1.35990i
$484$		0			0
$485$			1086.29i			2.23977i
$486$		0			0
$487$	459.602			0.943741			0.471870	−	0.881668i	$-0.343579\pi$
$487$	459.602			0.943741			0.471870	+	0.881668i	$0.343579\pi$
$488$		0			0
$489$	−206.197	+	13.4540i	−0.421671	+	0.0275134i
$490$		0			0
$491$	157.868	+	433.740i	0.321524	+	0.883381i	0.990179	+	0.139807i	$0.0446483\pi$
$491$	157.868	+	433.740i	0.321524	+	0.883381i	−0.668654	+	0.743573i	$0.733129\pi$
$492$		0			0
$493$	105.029	+	595.652i	0.213042	+	1.20822i
$494$		0			0
$495$	768.389	−	100.701i	1.55230	−	0.203436i
$496$		0			0
$497$	301.818	−	829.238i	0.607279	−	1.66849i
$498$		0			0
$499$	−55.9965	−	46.9867i	−0.112218	−	0.0941617i	0.584952	−	0.811068i	$-0.301113\pi$
$499$	−55.9965	−	46.9867i	−0.112218	−	0.0941617i	−0.697170	+	0.716906i	$0.745558\pi$
$500$		0			0
$501$	136.476	+	310.412i	0.272407	+	0.619585i
$502$		0			0
$503$	−667.951	−	385.641i	−1.32793	−	0.766683i	−0.342954	−	0.939352i	$-0.611427\pi$
$503$	−667.951	−	385.641i	−1.32793	−	0.766683i	−0.984980	+	0.172670i	$0.944761\pi$
$504$		0			0
$505$	−11.9725	−	20.7370i	−0.0237080	−	0.0410634i
$506$		0			0
$507$	248.561	+	1017.08i	0.490258	+	2.00607i
$508$		0			0
$509$	−141.711	−	24.9874i	−0.278410	−	0.0490912i	0.0326996	−	0.999465i	$-0.489590\pi$
$509$	−141.711	−	24.9874i	−0.278410	−	0.0490912i	−0.311110	+	0.950374i	$0.600701\pi$
$510$		0			0
$511$	−363.672	+	305.157i	−0.711687	+	0.597177i
$512$		0			0
$513$	323.138	+	369.125i	0.629900	+	0.719541i
$514$		0			0
$515$	−91.4768	−	109.018i	−0.177625	−	0.211685i
$516$		0			0
$517$	38.4525	−	218.075i	0.0743762	−	0.421809i
$518$		0			0
$519$	115.453	−	395.669i	0.222453	−	0.762369i
$520$		0			0
$521$	19.8121	−	11.4385i	0.0380271	−	0.0219550i	−0.480866	−	0.876794i	$-0.659678\pi$
$521$	19.8121	−	11.4385i	0.0380271	−	0.0219550i	0.518893	+	0.854839i	$0.326344\pi$
$522$		0			0
$523$	504.779	−	874.303i	0.965160	−	1.67171i	0.255977	−	0.966683i	$-0.417603\pi$
$523$	504.779	−	874.303i	0.965160	−	1.67171i	0.709183	−	0.705024i	$-0.249064\pi$
$524$		0			0
$525$	645.550	+	473.629i	1.22962	+	0.902150i
$526$		0			0
$527$	258.767	−	308.386i	0.491018	−	0.585173i
$528$		0			0
$529$	18.0163	+	6.55741i	0.0340574	+	0.0123959i
$530$		0			0
$531$	53.2775	+	102.492i	0.100334	+	0.193017i
$532$		0			0
$533$	−912.117	+	160.831i	−1.71129	+	0.301746i
$534$		0			0
$535$	−169.930	+	61.8494i	−0.317626	+	0.115606i
$536$		0			0
$537$	518.018	+	255.647i	0.964652	+	0.476066i
$538$		0			0
$539$		−	457.081i		−	0.848017i
$540$		0			0
$541$	−593.097			−1.09630			−0.548149	−	0.836381i	$-0.684667\pi$
$541$	−593.097			−1.09630			−0.548149	+	0.836381i	$0.684667\pi$
$542$		0			0
$543$	−126.790	−	189.876i	−0.233500	−	0.349679i
$544$		0			0
$545$	−2.54624	−	6.99573i	−0.00467199	−	0.0128362i
$546$		0			0
$547$	−31.2102	−	177.002i	−0.0570570	−	0.323586i	0.942898	−	0.333082i	$-0.108089\pi$
$547$	−31.2102	−	177.002i	−0.0570570	−	0.323586i	−0.999955	+	0.00949559i	$0.996977\pi$
$548$		0			0
$549$	−243.778	−	774.751i	−0.444039	−	1.41120i
$550$		0			0
$551$	240.632	−	661.132i	0.436719	−	1.19988i
$552$		0			0
$553$	735.583	+	617.227i	1.33017	+	1.11614i
$554$		0			0
$555$	−63.6302	−	6.98756i	−0.114649	−	0.0125902i
$556$		0			0
$557$	−312.376	−	180.351i	−0.560819	−	0.323789i	0.192655	−	0.981267i	$-0.438290\pi$
$557$	−312.376	−	180.351i	−0.560819	−	0.323789i	−0.753474	+	0.657477i	$0.771624\pi$
$558$		0			0
$559$	432.353	+	748.858i	0.773441	+	1.33964i
$560$		0			0
$561$	398.685	−	381.433i	0.710668	−	0.679916i
$562$		0			0
$563$	571.890	+	100.840i	1.01579	+	0.179111i	0.656669	−	0.754179i	$-0.271965\pi$
$563$	571.890	+	100.840i	1.01579	+	0.179111i	0.359122	+	0.933291i	$0.383076\pi$
$564$		0			0
$565$	869.589	−	729.672i	1.53910	−	1.29145i
$566$		0			0
$567$	−319.987	−	688.326i	−0.564351	−	1.21398i
$568$		0			0
$569$	−356.121	−	424.408i	−0.625871	−	0.745884i	0.356197	−	0.934411i	$-0.384073\pi$
$569$	−356.121	−	424.408i	−0.625871	−	0.745884i	−0.982068	+	0.188527i	$0.939629\pi$
$570$		0			0
$571$	−41.9016	+	237.636i	−0.0733828	+	0.416175i	0.925881	+	0.377815i	$0.123324\pi$
$571$	−41.9016	+	237.636i	−0.0733828	+	0.416175i	−0.999264	+	0.0383598i	$0.987787\pi$
$572$		0			0
$573$	−426.438	−	445.725i	−0.744219	−	0.777879i
$574$		0			0
$575$	−577.460	+	333.396i	−1.00428	+	0.579820i
$576$		0			0
$577$	9.74580	−	16.8802i	0.0168905	−	0.0292552i	−0.857457	−	0.514556i	$-0.827957\pi$
$577$	9.74580	−	16.8802i	0.0168905	−	0.0292552i	0.874347	+	0.485301i	$0.161290\pi$
$578$		0			0
$579$	95.4359	−	869.060i	0.164829	−	1.50097i
$580$		0			0
$581$	−113.858	+	135.690i	−0.195968	+	0.233546i
$582$		0			0
$583$	−136.224	−	49.5815i	−0.233661	−	0.0850455i
$584$		0			0
$585$	325.079	−	1462.27i	0.555690	−	2.49961i
$586$		0			0
$587$	−489.063	+	86.2350i	−0.833156	+	0.146908i	−0.573926	−	0.818907i	$-0.694580\pi$
$587$	−489.063	+	86.2350i	−0.833156	+	0.146908i	−0.259231	+	0.965815i	$0.583469\pi$
$588$		0			0
$589$	−440.036	+	160.160i	−0.747090	+	0.271918i
$590$		0			0
$591$	−758.091	+	506.218i	−1.28273	+	0.856545i
$592$		0			0
$593$			629.836i			1.06212i	0.847335	+	0.531059i	$0.178206\pi$
$593$			629.836i			1.06212i	−0.847335	+	0.531059i	$0.821794\pi$
$594$		0			0
$595$	1070.47			1.79912
$596$		0			0
$597$	353.777	−	716.857i	0.592591	−	1.20077i
$598$		0			0
$599$	222.199	+	610.488i	0.370951	+	1.01918i	0.974995	+	0.222228i	$0.0713329\pi$
$599$	222.199	+	610.488i	0.370951	+	1.01918i	−0.604044	+	0.796951i	$0.706445\pi$
$600$		0			0
$601$	69.7993	+	395.852i	0.116139	+	0.658655i	0.986180	+	0.165677i	$0.0529808\pi$
$601$	69.7993	+	395.852i	0.116139	+	0.658655i	−0.870042	+	0.492978i	$0.835908\pi$
$602$		0			0
$603$	−66.2414	−	42.2552i	−0.109853	−	0.0700749i
$604$		0			0
$605$	−44.1186	+	121.215i	−0.0729233	+	0.200355i
$606$		0			0
$607$	−166.213	−	139.470i	−0.273828	−	0.229769i	0.495524	−	0.868594i	$-0.334976\pi$
$607$	−166.213	−	139.470i	−0.273828	−	0.229769i	−0.769352	+	0.638826i	$0.779421\pi$
$608$		0			0
$609$	−643.961	+	877.711i	−1.05741	+	1.44123i
$610$		0			0
$611$	−370.688	−	214.017i	−0.606691	−	0.350273i
$612$		0			0
$613$	469.156	+	812.602i	0.765344	+	1.32562i	0.940064	+	0.340997i	$0.110765\pi$
$613$	469.156	+	812.602i	0.765344	+	1.32562i	−0.174720	+	0.984618i	$0.555902\pi$
$614$		0			0
$615$	857.046	+	250.079i	1.39357	+	0.406633i
$616$		0			0
$617$	474.755	+	83.7120i	0.769456	+	0.135676i	0.544577	−	0.838711i	$-0.316690\pi$
$617$	474.755	+	83.7120i	0.769456	+	0.135676i	0.224879	+	0.974387i	$0.427801\pi$
$618$		0			0
$619$	71.9917	−	60.4082i	0.116303	−	0.0975900i	−0.582781	−	0.812629i	$-0.698036\pi$
$619$	71.9917	−	60.4082i	0.116303	−	0.0975900i	0.699084	+	0.715039i	$0.253591\pi$
$620$		0			0
$621$	632.015	−	13.2333i	1.01774	−	0.0213097i
$622$		0			0
$623$	367.885	+	438.428i	0.590505	+	0.703736i
$624$		0			0
$625$	−91.3226	+	517.916i	−0.146116	+	0.828666i
$626$		0			0
$627$	−623.471	+	152.368i	−0.994371	+	0.243011i
$628$		0			0
$629$	−39.4702	+	22.7881i	−0.0627507	+	0.0362291i
$630$		0			0
$631$	−266.288	+	461.224i	−0.422010	+	0.730942i	−0.996136	−	0.0878246i	$-0.972008\pi$
$631$	−266.288	+	461.224i	−0.422010	+	0.730942i	0.574126	+	0.818767i	$0.305342\pi$
$632$		0			0
$633$	−244.148	+	107.342i	−0.385699	+	0.169576i
$634$		0			0
$635$	337.567	−	402.297i	0.531601	−	0.633538i
$636$		0			0
$637$	−830.238	−	302.182i	−1.30336	−	0.474383i
$638$		0			0
$639$	782.798	+	324.785i	1.22504	+	0.508270i
$640$		0			0
$641$	811.167	−	143.031i	1.26547	−	0.223137i	0.499671	−	0.866215i	$-0.333454\pi$
$641$	811.167	−	143.031i	1.26547	−	0.223137i	0.765800	+	0.643079i	$0.222343\pi$
$642$		0			0
$643$	875.130	−	318.521i	1.36101	−	0.495367i	0.444644	−	0.895707i	$-0.353330\pi$
$643$	875.130	−	318.521i	1.36101	−	0.495367i	0.916367	+	0.400340i	$0.131108\pi$
$644$		0			0
$645$	−54.2706	−	831.754i	−0.0841405	−	1.28954i
$646$		0			0
$647$		−	255.455i		−	0.394830i	−0.980320	−	0.197415i	$-0.936745\pi$
$647$		−	255.455i		−	0.394830i	0.980320	−	0.197415i	$-0.0632546\pi$
$648$		0			0
$649$	−151.122			−0.232854
$650$		0			0
$651$	723.016	−	47.1757i	1.11062	−	0.0724665i
$652$		0			0
$653$	−277.404	−	762.162i	−0.424815	−	1.16717i	−0.948920	−	0.315516i	$-0.897822\pi$
$653$	−277.404	−	762.162i	−0.424815	−	1.16717i	0.524105	−	0.851653i	$-0.324400\pi$
$654$		0			0
$655$	22.2942	+	126.437i	0.0340370	+	0.193033i
$656$		0			0
$657$	−277.343	−	361.881i	−0.422136	−	0.550808i
$658$		0			0
$659$	118.588	−	325.819i	0.179952	−	0.494414i	−0.816617	−	0.577180i	$-0.804153\pi$
$659$	118.588	−	325.819i	0.179952	−	0.494414i	0.996569	+	0.0827659i	$0.0263754\pi$
$660$		0			0
$661$	−639.014	−	536.197i	−0.966739	−	0.811190i	0.0152975	−	0.999883i	$-0.495130\pi$
$661$	−639.014	−	536.197i	−0.966739	−	0.811190i	−0.982036	+	0.188693i	$0.939575\pi$
$662$		0			0
$663$	−429.256	−	976.337i	−0.647445	−	1.47261i
$664$		0			0
$665$	−1078.37	−	622.598i	−1.62161	−	0.936238i
$666$		0			0
$667$	−453.297	−	785.133i	−0.679605	−	1.17711i
$668$		0			0
$669$	206.749	+	845.988i	0.309041	+	1.26456i
$670$		0			0
$671$	1046.44	+	184.515i	1.55952	+	0.274986i
$672$		0			0
$673$	118.178	−	99.1631i	0.175599	−	0.147345i	−0.550752	−	0.834669i	$-0.685659\pi$
$673$	118.178	−	99.1631i	0.175599	−	0.147345i	0.726351	+	0.687324i	$0.241215\pi$
$674$		0			0
$675$	−481.830	+	599.265i	−0.713822	+	0.887800i
$676$		0			0
$677$	−576.975	−	687.612i	−0.852252	−	1.01567i	−0.999646	−	0.0265971i	$-0.991533\pi$
$677$	−576.975	−	687.612i	−0.852252	−	1.01567i	0.147394	−	0.989078i	$-0.452912\pi$
$678$		0			0
$679$	−241.723	+	1370.88i	−0.355998	+	2.01897i
$680$		0			0
$681$	−155.225	+	531.971i	−0.227937	+	0.781161i
$682$		0			0
$683$	−666.874	+	385.020i	−0.976390	+	0.563719i	−0.901178	−	0.433449i	$-0.857296\pi$
$683$	−666.874	+	385.020i	−0.976390	+	0.563719i	−0.0752113	+	0.997168i	$0.523963\pi$
$684$		0			0
$685$	−75.9746	+	131.592i	−0.110912	+	0.192105i
$686$		0			0
$687$	−824.428	−	604.868i	−1.20004	−	0.880448i
$688$		0			0
$689$	−180.119	+	214.657i	−0.261421	+	0.311549i
$690$		0			0
$691$	−831.656	−	302.698i	−1.20355	−	0.438058i	−0.339091	−	0.940754i	$-0.610119\pi$
$691$	−831.656	−	302.698i	−1.20355	−	0.438058i	−0.864463	+	0.502696i	$0.832342\pi$
$692$		0			0
$693$	992.102	+	43.9002i	1.43160	+	0.0633480i
$694$		0			0
$695$	44.8058	−	7.90048i	0.0644688	−	0.0113676i
$696$		0			0
$697$	597.318	−	217.406i	0.856984	−	0.311917i
$698$		0			0
$699$	816.479	+	402.941i	1.16807	+	0.576454i
$700$		0			0
$701$			924.832i			1.31930i	0.751571	+	0.659652i	$0.229296\pi$
$701$			924.832i			1.31930i	−0.751571	+	0.659652i	$0.770704\pi$
$702$		0			0
$703$	53.0151			0.0754127
$704$		0			0
$705$	229.126	+	343.130i	0.325002	+	0.486709i
$706$		0			0
$707$	−10.4947	−	28.8339i	−0.0148440	−	0.0407835i
$708$		0			0
$709$	−173.003	−	981.150i	−0.244010	−	1.38385i	−0.822780	−	0.568360i	$-0.807578\pi$
$709$	−173.003	−	981.150i	−0.244010	−	1.38385i	0.578770	−	0.815491i	$-0.303533\pi$
$710$		0			0
$711$	−623.428	+	679.550i	−0.876832	+	0.955766i
$712$		0			0
$713$	−206.378	+	567.020i	−0.289451	+	0.795259i
$714$		0			0
$715$	1501.26	+	1259.71i	2.09967	+	1.76183i
$716$		0			0
$717$	−1305.27	−	143.339i	−1.82047	−	0.199915i
$718$		0			0
$719$	−103.540	−	59.7791i	−0.144006	−	0.0831420i	0.426266	−	0.904598i	$-0.359829\pi$
$719$	−103.540	−	59.7791i	−0.144006	−	0.0831420i	−0.570272	+	0.821456i	$0.693162\pi$
$720$		0			0
$721$	−91.1833	−	157.934i	−0.126468	−	0.219049i
$722$		0			0
$723$	−352.719	+	337.456i	−0.487854	+	0.466744i
$724$		0			0
$725$	1086.02	+	191.495i	1.49796	+	0.264130i
$726$		0			0
$727$	391.062	−	328.140i	0.537911	−	0.451361i	−0.332912	−	0.942958i	$-0.608031\pi$
$727$	391.062	−	328.140i	0.537911	−	0.451361i	0.870823	+	0.491597i	$0.163587\pi$
$728$		0			0
$729$	673.999	−	277.789i	0.924553	−	0.381054i
$730$		0			0
$731$	−381.467	−	454.615i	−0.521843	−	0.621908i
$732$		0			0
$733$	−61.0496	+	346.229i	−0.0832872	+	0.472345i	0.914426	+	0.404754i	$0.132643\pi$
$733$	−61.0496	+	346.229i	−0.0832872	+	0.472345i	−0.997713	+	0.0675919i	$0.978468\pi$
$734$		0			0
$735$	588.752	+	615.380i	0.801023	+	0.837252i
$736$		0			0
$737$	89.0213	−	51.3965i	0.120789	−	0.0697374i
$738$		0			0
$739$	43.2066	−	74.8360i	0.0584663	−	0.101267i	−0.835311	−	0.549778i	$-0.814712\pi$
$739$	43.2066	−	74.8360i	0.0584663	−	0.101267i	0.893777	+	0.448511i	$0.148046\pi$
$740$		0			0
$741$	−135.424	+	1233.20i	−0.182758	+	1.66424i
$742$		0			0
$743$	−435.424	+	518.918i	−0.586035	+	0.698409i	−0.974839	−	0.222912i	$-0.928444\pi$
$743$	−435.424	+	518.918i	−0.586035	+	0.698409i	0.388804	+	0.921320i	$0.372888\pi$
$744$		0			0
$745$	−1548.15	−	563.482i	−2.07806	−	0.756352i
$746$		0			0
$747$	−125.354	−	115.001i	−0.167810	−	0.153951i
$748$		0			0
$749$	−228.211	+	40.2398i	−0.304688	+	0.0537247i
$750$		0			0
$751$	−378.743	+	137.851i	−0.504318	+	0.183557i	−0.581635	−	0.813450i	$-0.697587\pi$
$751$	−378.743	+	137.851i	−0.504318	+	0.183557i	0.0773173	+	0.997007i	$0.475365\pi$
$752$		0			0
$753$	1137.49	−	759.562i	1.51061	−	1.00871i
$754$		0			0
$755$			1726.07i			2.28618i
$756$		0			0
$757$	463.787			0.612665			0.306332	−	0.951925i	$-0.400898\pi$
$757$	463.787			0.612665			0.306332	+	0.951925i	$0.400898\pi$
$758$		0			0
$759$	−366.005	+	741.636i	−0.482220	+	0.977122i
$760$		0			0
$761$	−23.5534	−	64.7125i	−0.0309506	−	0.0850361i	0.923255	−	0.384188i	$-0.125519\pi$
$761$	−23.5534	−	64.7125i	−0.0309506	−	0.0850361i	−0.954206	+	0.299152i	$0.903296\pi$
$762$		0			0
$763$	−1.65661	−	9.39508i	−0.00217117	−	0.0123133i
$764$		0			0
$765$	−45.4473	+	1027.07i	−0.0594083	+	1.34257i
$766$		0			0
$767$	−99.9089	+	274.497i	−0.130259	+	0.357884i
$768$		0			0
$769$	−587.623	−	493.074i	−0.764139	−	0.641189i	0.175062	−	0.984557i	$-0.443988\pi$
$769$	−587.623	−	493.074i	−0.764139	−	0.641189i	−0.939201	+	0.343369i	$0.888432\pi$
$770$		0			0
$771$	−737.120	+	1004.69i	−0.956057	+	1.30309i
$772$		0			0
$773$	215.221	+	124.258i	0.278423	+	0.160747i	0.632709	−	0.774390i	$-0.281943\pi$
$773$	215.221	+	124.258i	0.278423	+	0.160747i	−0.354286	+	0.935137i	$0.615276\pi$
$774$		0			0
$775$	−366.992	−	635.648i	−0.473538	−	0.820191i
$776$		0			0
$777$	−78.7454	−	22.9773i	−0.101345	−	0.0295718i
$778$		0			0
$779$	−728.169	−	128.396i	−0.934749	−	0.164821i
$780$		0			0
$781$	−849.365	+	712.702i	−1.08754	+	0.912551i
$782$		0			0
$783$	−814.780	−	655.112i	−1.04059	−	0.836669i
$784$		0			0
$785$	170.870	+	203.635i	0.217668	+	0.259407i
$786$		0			0
$787$	226.645	−	1285.37i	0.287986	−	1.63325i	−0.406432	−	0.913681i	$-0.633227\pi$
$787$	226.645	−	1285.37i	0.287986	−	1.63325i	0.694419	−	0.719571i	$-0.255662\pi$
$788$		0			0
$789$	−1243.07	+	303.789i	−1.57550	+	0.385031i
$790$		0			0
$791$	1259.77	−	727.331i	1.59264	−	0.919508i
$792$		0			0
$793$	1026.97	−	1778.76i	1.29504	−	2.24307i
$794$		0			0
$795$	247.267	−	108.713i	0.311027	−	0.136746i
$796$		0			0
$797$	385.545	−	459.474i	0.483745	−	0.576505i	−0.467870	−	0.883797i	$-0.654979\pi$
$797$	385.545	−	459.474i	0.483745	−	0.576505i	0.951615	+	0.307292i	$0.0994230\pi$
$798$		0			0
$799$	276.048	+	100.473i	0.345492	+	0.125749i
$800$		0			0
$801$	−436.268	+	334.353i	−0.544654	+	0.417420i
$802$		0			0
$803$	587.428	−	103.579i	0.731542	−	0.128991i
$804$		0			0
$805$	−1507.77	+	548.782i	−1.87300	+	0.681716i
$806$		0			0
$807$	−44.8837	−	687.889i	−0.0556179	−	0.852402i
$808$		0			0
$809$		−	574.876i		−	0.710601i	−0.934752	−	0.355300i	$-0.884379\pi$
$809$		−	574.876i		−	0.710601i	0.934752	−	0.355300i	$-0.115621\pi$
$810$		0			0
$811$	942.729			1.16243			0.581214	−	0.813751i	$-0.302578\pi$
$811$	942.729			1.16243			0.581214	+	0.813751i	$0.302578\pi$
$812$		0			0
$813$	−740.607	+	48.3234i	−0.910955	+	0.0594384i
$814$		0			0
$815$	172.278	+	473.329i	0.211384	+	0.580772i
$816$		0			0
$817$	119.873	+	679.833i	0.146723	+	0.832109i
$818$		0			0
$819$	735.631	−	1773.02i	0.898206	−	2.16486i
$820$		0			0
$821$	267.373	−	734.600i	0.325667	−	0.894763i	−0.663527	−	0.748152i	$-0.730941\pi$
$821$	267.373	−	734.600i	0.325667	−	0.894763i	0.989194	−	0.146611i	$-0.0468364\pi$
$822$		0			0
$823$	−417.236	−	350.103i	−0.506970	−	0.425398i	0.353091	−	0.935589i	$-0.385130\pi$
$823$	−417.236	−	350.103i	−0.506970	−	0.425398i	−0.860061	+	0.510190i	$0.829575\pi$
$824$		0			0
$825$	−404.891	−	920.919i	−0.490777	−	1.11627i
$826$		0			0
$827$	813.492	+	469.670i	0.983666	+	0.567920i	0.903375	−	0.428851i	$-0.141082\pi$
$827$	813.492	+	469.670i	0.983666	+	0.567920i	0.0802912	+	0.996771i	$0.474415\pi$
$828$		0			0
$829$	340.470	+	589.711i	0.410699	+	0.711352i	0.994966	−	0.100209i	$-0.0319512\pi$
$829$	340.470	+	589.711i	0.410699	+	0.711352i	−0.584267	+	0.811562i	$0.698618\pi$
$830$		0			0
$831$	104.781	+	428.752i	0.126091	+	0.515947i
$832$		0			0
$833$	597.158	+	105.295i	0.716876	+	0.126405i
$834$		0			0
$835$	633.199	−	531.317i	0.758322	−	0.636308i
$836$		0			0
$837$	14.5668	+	695.701i	0.0174036	+	0.831183i
$838$		0			0
$839$	−24.0697	−	28.6852i	−0.0286886	−	0.0341897i	0.751509	−	0.659722i	$-0.229326\pi$
$839$	−24.0697	−	28.6852i	−0.0286886	−	0.0341897i	−0.780198	+	0.625533i	$0.784882\pi$
$840$		0			0
$841$	−114.324	+	648.364i	−0.135938	+	0.770944i
$842$		0			0
$843$	−38.8406	+	133.111i	−0.0460743	+	0.157901i
$844$		0			0
$845$	2210.32	−	1276.13i	2.61576	−	1.51021i
$846$		0			0
$847$	−82.6499	+	143.154i	−0.0975795	+	0.169013i
$848$		0			0
$849$	299.437	+	219.691i	0.352693	+	0.258765i
$850$		0			0
$851$	43.9114	−	52.3316i	0.0515998	−	0.0614943i
$852$		0			0
$853$	593.167	+	215.895i	0.695389	+	0.253101i	0.665441	−	0.746450i	$-0.268244\pi$
$853$	593.167	+	215.895i	0.695389	+	0.253101i	0.0299483	+	0.999551i	$0.490466\pi$
$854$		0			0
$855$	643.134	−	1008.21i	0.752204	−	1.17919i
$856$		0			0
$857$	1234.24	−	217.630i	1.44019	−	0.253944i	0.601638	−	0.798769i	$-0.294515\pi$
$857$	1234.24	−	217.630i	1.44019	−	0.253944i	0.838550	+	0.544825i	$0.183404\pi$
$858$		0			0
$859$	−753.601	+	274.288i	−0.877300	+	0.319311i	−0.741120	−	0.671373i	$-0.765705\pi$
$859$	−753.601	+	274.288i	−0.877300	+	0.319311i	−0.136180	+	0.990684i	$0.543483\pi$
$860$		0			0
$861$	1025.93	+	506.307i	1.19155	+	0.588045i
$862$		0			0
$863$			1108.04i			1.28394i	0.766731	+	0.641969i	$0.221882\pi$
$863$			1108.04i			1.28394i	−0.766731	+	0.641969i	$0.778118\pi$
$864$		0			0
$865$	−1004.73			−1.16153
$866$		0			0
$867$	−74.9836	−	112.292i	−0.0864862	−	0.129518i
$868$		0			0
$869$	−412.645	−	1133.73i	−0.474850	−	1.30464i
$870$		0			0
$871$	−34.5030	−	195.676i	−0.0396131	−	0.224657i
$872$		0			0
$873$	−1305.03	−	290.122i	−1.49488	−	0.332328i
$874$		0			0
$875$	81.5563	−	224.074i	0.0932072	−	0.256085i
$876$		0			0
$877$	−521.708	−	437.765i	−0.594878	−	0.499162i	0.294917	−	0.955523i	$-0.404708\pi$
$877$	−521.708	−	437.765i	−0.594878	−	0.499162i	−0.889795	+	0.456361i	$0.849152\pi$
$878$		0			0
$879$	407.787	+	44.7812i	0.463922	+	0.0509457i
$880$		0			0
$881$	−1449.13	−	836.658i	−1.64487	−	0.949669i	−0.979065	−	0.203547i	$-0.934753\pi$
$881$	−1449.13	−	836.658i	−1.64487	−	0.949669i	−0.665810	−	0.746122i	$-0.731914\pi$
$882$		0			0
$883$	−155.212	−	268.834i	−0.175778	−	0.304456i	0.764653	−	0.644443i	$-0.222911\pi$
$883$	−155.212	−	268.834i	−0.175778	−	0.304456i	−0.940430	+	0.339987i	$0.889577\pi$
$884$		0			0
$885$	203.460	−	194.656i	0.229898	−	0.219950i
$886$		0			0
$887$	−160.295	−	28.2644i	−0.180716	−	0.0318652i	0.0825576	−	0.996586i	$-0.473691\pi$
$887$	−160.295	−	28.2644i	−0.180716	−	0.0318652i	−0.263274	+	0.964721i	$0.584802\pi$
$888$		0			0
$889$	515.523	−	432.575i	0.579891	−	0.486587i
$890$		0			0
$891$	−84.2400	+	950.008i	−0.0945454	+	1.06623i
$892$		0			0
$893$	−219.648	−	261.767i	−0.245967	−	0.293132i
$894$		0			0
$895$	244.523	−	1386.76i	0.273210	−	1.54945i
$896$		0			0
$897$	1105.13	+	1155.11i	1.23203	+	1.28775i
$898$		0			0
$899$	864.248	−	498.974i	0.961343	−	0.555032i
$900$		0			0
$901$	96.1574	−	166.549i	0.106723	−	0.184850i
$902$		0			0
$903$	116.595	−	1061.74i	0.129119	−	1.17579i
$904$		0			0
$905$	−357.749	+	426.348i	−0.395302	+	0.471103i
$906$		0			0
$907$	797.885	+	290.406i	0.879697	+	0.320183i	0.742087	−	0.670303i	$-0.233836\pi$
$907$	797.885	+	290.406i	0.879697	+	0.320183i	0.137609	+	0.990487i	$0.456058\pi$
$908$		0			0
$909$	28.1103	−	8.84497i	0.0309244	−	0.00973044i
$910$		0			0
$911$	−2.80554	+	0.494692i	−0.00307962	+	0.000543021i	−0.175188	−	0.984535i	$-0.556053\pi$
$911$	−2.80554	+	0.494692i	−0.00307962	+	0.000543021i	0.172108	+	0.985078i	$0.444942\pi$
$912$		0			0
$913$	209.135	−	76.1191i	0.229064	−	0.0833725i
$914$		0			0
$915$	−1646.52	+	1099.47i	−1.79947	+	1.20160i
$916$		0			0
$917$			164.522i			0.179413i
$918$		0			0
$919$	−188.322			−0.204920			−0.102460	−	0.994737i	$-0.532671\pi$
$919$	−188.322			−0.204920			−0.102460	+	0.994737i	$0.532671\pi$
$920$		0			0
$921$	−394.361	+	799.092i	−0.428187	+	0.867636i
$922$		0			0
$923$	733.020	+	2013.96i	0.794171	+	2.18197i
$924$		0			0
$925$	14.4296	+	81.8343i	0.0155996	+	0.0884695i
$926$		0			0
$927$	155.401	−	80.7806i	0.167639	−	0.0871420i
$928$		0			0
$929$	270.413	−	742.955i	0.291080	−	0.799736i	−0.704829	−	0.709377i	$-0.748976\pi$
$929$	270.413	−	742.955i	0.291080	−	0.799736i	0.995909	−	0.0903589i	$-0.0288014\pi$
$930$		0			0
$931$	−540.322	−	453.384i	−0.580368	−	0.486986i
$932$		0			0
$933$	654.956	−	892.698i	0.701990	−	0.956803i
$934$		0			0
$935$	−1164.81	−	672.502i	−1.24578	−	0.719254i
$936$		0			0
$937$	−630.512	−	1092.08i	−0.672905	−	1.16551i	−0.977077	−	0.212888i	$-0.931713\pi$
$937$	−630.512	−	1092.08i	−0.672905	−	1.16551i	0.304172	−	0.952617i	$-0.401620\pi$
$938$		0			0
$939$	988.972	+	288.574i	1.05322	+	0.307321i
$940$		0			0
$941$	534.133	+	94.1821i	0.567623	+	0.100087i	0.450092	−	0.892982i	$-0.351391\pi$
$941$	534.133	+	94.1821i	0.567623	+	0.100087i	0.117531	+	0.993069i	$0.462502\pi$
$942$		0			0
$943$	−729.869	+	612.433i	−0.773987	+	0.649452i
$944$		0			0
$945$	−1392.24	+	1218.79i	−1.47327	+	1.28973i
$946$		0			0
$947$	−104.599	−	124.656i	−0.110453	−	0.131632i	0.707985	−	0.706227i	$-0.249604\pi$
$947$	−104.599	−	124.656i	−0.110453	−	0.131632i	−0.818438	+	0.574595i	$0.805160\pi$
$948$		0			0
$949$	200.215	−	1135.48i	0.210975	−	1.19650i
$950$		0			0
$951$	1590.28	−	388.644i	1.67222	−	0.408669i
$952$		0			0
$953$	−1529.94	+	883.311i	−1.60539	+	0.926874i	−0.615010	+	0.788519i	$0.710848\pi$
$953$	−1529.94	+	883.311i	−1.60539	+	0.926874i	−0.990383	+	0.138354i	$0.955819\pi$
$954$		0			0
$955$	−751.849	+	1302.24i	−0.787277	+	1.36360i
$956$		0			0
$957$	1252.11	−	550.503i	1.30837	−	0.575238i
$958$		0			0
$959$	−125.161	+	149.161i	−0.130512	+	0.155538i
$960$		0			0
$961$	278.888	+	101.507i	0.290206	+	0.105626i
$962$		0			0
$963$	−28.9193	−	220.666i	−0.0300304	−	0.229144i
$964$		0			0
$965$	−2098.83	+	370.080i	−2.17495	+	0.383502i
$966$		0			0
$967$	1526.43	−	555.575i	1.57852	−	0.574535i	0.603640	−	0.797257i	$-0.293717\pi$
$967$	1526.43	−	555.575i	1.57852	−	0.574535i	0.974882	+	0.222722i	$0.0714943\pi$
$968$		0			0
$969$	−55.4376	−	849.639i	−0.0572111	−	0.876820i
$970$		0			0
$971$			1343.18i			1.38330i	0.722235	+	0.691648i	$0.243115\pi$
$971$			1343.18i			1.38330i	−0.722235	+	0.691648i	$0.756885\pi$
$972$		0			0
$973$	58.3022			0.0599200
$974$		0			0
$975$	−1940.43	+	126.610i	−1.99018	+	0.129856i
$976$		0			0
$977$	−405.483	−	1114.06i	−0.415029	−	1.14028i	−0.954482	−	0.298268i	$-0.903591\pi$
$977$	−405.483	−	1114.06i	−0.415029	−	1.14028i	0.539453	−	0.842016i	$-0.318631\pi$
$978$		0			0
$979$	−124.871	−	708.178i	−0.127550	−	0.723369i
$980$		0			0
$981$	9.08444	−	1.19056i	0.00926038	−	0.00121362i
$982$		0			0
$983$	138.272	−	379.900i	0.140664	−	0.386470i	−0.849278	−	0.527946i	$-0.822962\pi$
$983$	138.272	−	379.900i	0.140664	−	0.386470i	0.989942	+	0.141475i	$0.0451846\pi$
$984$		0			0
$985$	1702.22	+	1428.33i	1.72814	+	1.45008i
$986$		0			0
$987$	212.799	+	484.009i	0.215602	+	0.490384i
$988$		0			0
$989$	770.357	+	444.766i	0.778925	+	0.449712i
$990$		0			0
$991$	500.942	+	867.656i	0.505491	+	0.875536i	0.999980	+	0.00635207i	$0.00202194\pi$
$991$	500.942	+	867.656i	0.505491	+	0.875536i	−0.494489	+	0.869184i	$0.664645\pi$
$992$		0			0
$993$	−129.148	−	528.458i	−0.130059	−	0.532183i
$994$		0			0
$995$	−1919.06	−	338.382i	−1.92870	−	0.340083i
$996$		0			0
$997$	−1154.65	+	968.864i	−1.15812	+	0.971779i	−0.999878	−	0.0156209i	$-0.995027\pi$
$997$	−1154.65	+	968.864i	−1.15812	+	0.971779i	−0.158243	+	0.987400i	$0.550583\pi$
$998$		0			0
$999$	25.3887	−	74.5767i	0.0254141	−	0.0746513i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.k.a.5.6	✓	36
3.2	odd	2		324.3.k.a.125.5		36
4.3	odd	2		432.3.bc.b.113.1		36
27.4	even	9		2916.3.c.b.1457.32		36
27.11	odd	18	inner	108.3.k.a.65.6	yes	36
27.16	even	9		324.3.k.a.197.5		36
27.23	odd	18		2916.3.c.b.1457.5		36
108.11	even	18		432.3.bc.b.65.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.5.6	✓	36	1.1	even	1	trivial
108.3.k.a.65.6	yes	36	27.11	odd	18	inner
324.3.k.a.125.5		36	3.2	odd	2
324.3.k.a.197.5		36	27.16	even	9
432.3.bc.b.65.1		36	108.11	even	18
432.3.bc.b.113.1		36	4.3	odd	2
2916.3.c.b.1457.5		36	27.23	odd	18
2916.3.c.b.1457.32		36	27.4	even	9

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.99363 - 0.195330i) q^{3} +(-2.50118 - 6.87194i) q^{5} +(-1.62729 - 9.22884i) q^{7} +(8.92369 - 1.16949i) q^{9} +O(q^{10})\)	\(q+(2.99363 - 0.195330i) q^{3} +(-2.50118 - 6.87194i) q^{5} +(-1.62729 - 9.22884i) q^{7} +(8.92369 - 1.16949i) q^{9} +(-4.02712 + 11.0644i) q^{11} +(17.4349 + 14.6296i) q^{13} +(-8.82992 - 20.0835i) q^{15} +(-13.5275 - 7.81011i) q^{17} +(9.08487 + 15.7354i) q^{19} +(-6.67419 - 27.3099i) q^{21} +(23.0574 + 4.06564i) q^{23} +(-21.8166 + 18.3063i) q^{25} +(26.4858 - 5.24410i) q^{27} +(-24.8898 - 29.6625i) q^{29} +(-4.47532 + 25.3808i) q^{31} +(-9.89451 + 33.9094i) q^{33} +(-59.3499 + 34.2657i) q^{35} +(1.45889 - 2.52687i) q^{37} +(55.0514 + 40.3903i) q^{39} +(-26.1577 + 31.1736i) q^{41} +(35.7017 + 12.9943i) q^{43} +(-30.3565 - 58.3980i) q^{45} +(-18.5209 + 3.26574i) q^{47} +(-36.4785 + 13.2771i) q^{49} +(-42.0220 - 20.7383i) q^{51} +12.3119i q^{53} +86.1066 q^{55} +(30.2704 + 45.3316i) q^{57} +(4.38973 + 12.0607i) q^{59} +(-15.6708 - 88.8733i) q^{61} +(-25.3145 - 80.4522i) q^{63} +(56.9261 - 156.403i) q^{65} +(-6.68767 - 5.61162i) q^{67} +(69.8195 + 7.66724i) q^{69} +(81.5508 + 47.0834i) q^{71} +(-25.3297 - 43.8724i) q^{73} +(-61.7350 + 59.0637i) q^{75} +(108.665 + 19.1606i) q^{77} +(-78.4939 + 65.8642i) q^{79} +(78.2646 - 20.8724i) q^{81} +(-12.1497 - 14.4795i) q^{83} +(-19.8359 + 112.495i) q^{85} +(-80.3049 - 83.9370i) q^{87} +(-52.8907 + 30.5364i) q^{89} +(106.643 - 184.711i) q^{91} +(-8.43984 + 76.8550i) q^{93} +(85.4102 - 101.788i) q^{95} +(-139.585 - 50.8047i) q^{97} +(-22.9970 + 103.445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q - 9 * q^5 + 6 * q^9	\( 36 q - 9 q^{5} + 6 q^{9} + 36 q^{11} + 45 q^{15} + 42 q^{21} - 18 q^{23} - 9 q^{25} - 18 q^{29} + 45 q^{31} - 153 q^{33} - 243 q^{35} - 123 q^{39} - 198 q^{41} + 90 q^{43} - 333 q^{45} - 243 q^{47} + 72 q^{49} - 99 q^{51} + 243 q^{57} + 252 q^{59} - 144 q^{61} + 381 q^{63} + 747 q^{65} + 108 q^{67} + 585 q^{69} + 324 q^{71} - 63 q^{73} + 597 q^{75} + 495 q^{77} + 36 q^{79} - 54 q^{81} - 27 q^{83} - 180 q^{85} - 441 q^{87} - 567 q^{89} + 99 q^{91} - 699 q^{93} - 1044 q^{95} - 216 q^{97} - 945 q^{99}+O(q^{100}) \) 36 * q - 9 * q^5 + 6 * q^9 + 36 * q^11 + 45 * q^15 + 42 * q^21 - 18 * q^23 - 9 * q^25 - 18 * q^29 + 45 * q^31 - 153 * q^33 - 243 * q^35 - 123 * q^39 - 198 * q^41 + 90 * q^43 - 333 * q^45 - 243 * q^47 + 72 * q^49 - 99 * q^51 + 243 * q^57 + 252 * q^59 - 144 * q^61 + 381 * q^63 + 747 * q^65 + 108 * q^67 + 585 * q^69 + 324 * q^71 - 63 * q^73 + 597 * q^75 + 495 * q^77 + 36 * q^79 - 54 * q^81 - 27 * q^83 - 180 * q^85 - 441 * q^87 - 567 * q^89 + 99 * q^91 - 699 * q^93 - 1044 * q^95 - 216 * q^97 - 945 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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