LMFDB - Embedded newform 140.2.u.a.33.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(17,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("140.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.u (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 802 x^{12} - 2264 x^{11} + 5402 x^{10} - 10642 x^{9} + \cdots + 196 $ x^16 - 8x^15 + 52x^14 - 224x^13 + 802x^12 - 2264x^11 + 5402x^10 - 10642x^9 + 17766x^8 - 24680x^7 + 28682x^6 - 27248x^5 + 20861x^4 - 12338x^3 + 5322x^2 - 1484*x + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			33.4
Root			$0.500000 + 2.27536i$ of defining polynomial
Character	$\chi$	$=$	140.33
Dual form			140.2.u.a.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.42519 + 0.649827i) q^{3} +(-2.19862 + 0.407542i) q^{5} +(2.59537 + 0.513853i) q^{7} +(2.86119 + 1.65191i) q^{9} +O(q^{10})$	\(q+(2.42519 + 0.649827i) q^{3} +(-2.19862 + 0.407542i) q^{5} +(2.59537 + 0.513853i) q^{7} +(2.86119 + 1.65191i) q^{9} +(-1.86346 - 3.22761i) q^{11} +(-2.90450 + 2.90450i) q^{13} +(-5.59689 - 0.440354i) q^{15} +(1.78788 - 6.67247i) q^{17} +(-1.65698 + 2.86997i) q^{19} +(5.96035 + 2.93273i) q^{21} +(-1.84153 + 0.493436i) q^{23} +(4.66782 - 1.79206i) q^{25} +(0.539383 + 0.539383i) q^{27} -0.563886i q^{29} +(-3.20505 + 1.85044i) q^{31} +(-2.42186 - 9.03849i) q^{33} +(-5.91564 - 0.0720411i) q^{35} +(-0.268453 - 1.00188i) q^{37} +(-8.93138 + 5.15654i) q^{39} +7.88697i q^{41} +(-7.53537 - 7.53537i) q^{43} +(-6.96387 - 2.46586i) q^{45} +(-0.543934 + 0.145747i) q^{47} +(6.47191 + 2.66728i) q^{49} +(8.67191 - 15.0202i) q^{51} +(0.479610 - 1.78993i) q^{53} +(5.41242 + 6.33684i) q^{55} +(-5.88346 + 5.88346i) q^{57} +(6.38015 + 11.0507i) q^{59} +(8.00463 + 4.62147i) q^{61} +(6.57701 + 5.75754i) q^{63} +(5.20217 - 7.56958i) q^{65} +(5.56658 + 1.49156i) q^{67} -4.78670 q^{69} +0.683178 q^{71} +(11.6096 + 3.11079i) q^{73} +(12.4849 - 1.31280i) q^{75} +(-3.17786 - 9.33440i) q^{77} +(-2.76589 - 1.59689i) q^{79} +(-3.99812 - 6.92495i) q^{81} +(1.44070 - 1.44070i) q^{83} +(-1.21155 + 15.3988i) q^{85} +(0.366428 - 1.36753i) q^{87} +(-1.26421 + 2.18968i) q^{89} +(-9.03074 + 6.04577i) q^{91} +(-8.97532 + 2.40493i) q^{93} +(2.47342 - 6.98524i) q^{95} +(3.99033 + 3.99033i) q^{97} -12.3131i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{5} + 2 q^{7}+O(q^{10}) $ 16 * q + 6 * q^5 + 2 * q^7	$ 16 q + 6 q^{5} + 2 q^{7} - 20 q^{15} + 18 q^{17} - 4 q^{21} - 16 q^{23} + 6 q^{25} - 12 q^{31} - 42 q^{33} - 40 q^{35} - 14 q^{37} + 28 q^{43} - 66 q^{45} - 6 q^{47} + 20 q^{51} - 10 q^{53} + 44 q^{57} + 60 q^{61} + 48 q^{63} + 34 q^{65} + 8 q^{67} - 8 q^{71} + 78 q^{73} + 96 q^{75} + 10 q^{77} + 24 q^{81} + 30 q^{87} - 64 q^{91} - 62 q^{93} + 2 q^{95}+O(q^{100}) $ 16 * q + 6 * q^5 + 2 * q^7 - 20 * q^15 + 18 * q^17 - 4 * q^21 - 16 * q^23 + 6 * q^25 - 12 * q^31 - 42 * q^33 - 40 * q^35 - 14 * q^37 + 28 * q^43 - 66 * q^45 - 6 * q^47 + 20 * q^51 - 10 * q^53 + 44 * q^57 + 60 * q^61 + 48 * q^63 + 34 * q^65 + 8 * q^67 - 8 * q^71 + 78 * q^73 + 96 * q^75 + 10 * q^77 + 24 * q^81 + 30 * q^87 - 64 * q^91 - 62 * q^93 + 2 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.42519	+	0.649827i	1.40018	+	0.375178i	0.878411	−	0.477907i	$-0.158604\pi$
$3$	2.42519	+	0.649827i	1.40018	+	0.375178i	0.521773	+	0.853085i	$0.325271\pi$
$4$		0			0
$5$	−2.19862	+	0.407542i	−0.983251	+	0.182258i
$5$	−2.19862	+	0.407542i	−0.983251	+	0.182258i
$6$		0			0
$7$	2.59537	+	0.513853i	0.980958	+	0.194218i
$7$	2.59537	+	0.513853i	0.980958	+	0.194218i
$8$		0			0
$9$	2.86119	+	1.65191i	0.953729	+	0.550636i
$10$		0			0
$11$	−1.86346	−	3.22761i	−0.561855	−	0.973161i	−0.997335	−	0.0729628i	$-0.976755\pi$
$11$	−1.86346	−	3.22761i	−0.561855	−	0.973161i	0.435480	−	0.900199i	$-0.356579\pi$
$12$		0			0
$13$	−2.90450	+	2.90450i	−0.805563	+	0.805563i	−0.983959	−	0.178396i	$-0.942909\pi$
$13$	−2.90450	+	2.90450i	−0.805563	+	0.805563i	0.178396	+	0.983959i	$0.442909\pi$
$14$		0			0
$15$	−5.59689	−	0.440354i	−1.44511	−	0.113699i
$16$		0			0
$17$	1.78788	−	6.67247i	0.433625	−	1.61831i	−0.310710	−	0.950505i	$-0.600567\pi$
$17$	1.78788	−	6.67247i	0.433625	−	1.61831i	0.744335	−	0.667806i	$-0.232767\pi$
$18$		0			0
$19$	−1.65698	+	2.86997i	−0.380136	+	0.658415i	−0.991081	−	0.133258i	$-0.957456\pi$
$19$	−1.65698	+	2.86997i	−0.380136	+	0.658415i	0.610945	+	0.791673i	$0.290790\pi$
$20$		0			0
$21$	5.96035	+	2.93273i	1.30066	+	0.639975i
$22$		0			0
$23$	−1.84153	+	0.493436i	−0.383985	+	0.102889i	−0.445647	−	0.895209i	$-0.647026\pi$
$23$	−1.84153	+	0.493436i	−0.383985	+	0.102889i	0.0616623	+	0.998097i	$0.480360\pi$
$24$		0			0
$25$	4.66782	−	1.79206i	0.933564	−	0.358411i
$26$		0			0
$27$	0.539383	+	0.539383i	0.103804	+	0.103804i
$28$		0			0
$29$		−	0.563886i		−	0.104711i	−0.998629	−	0.0523555i	$-0.983327\pi$
$29$		−	0.563886i		−	0.104711i	0.998629	−	0.0523555i	$-0.0166729\pi$
$30$		0			0
$31$	−3.20505	+	1.85044i	−0.575644	+	0.332348i	−0.759400	−	0.650624i	$-0.774508\pi$
$31$	−3.20505	+	1.85044i	−0.575644	+	0.332348i	0.183756	+	0.982972i	$0.441174\pi$
$32$		0			0
$33$	−2.42186	−	9.03849i	−0.421591	−	1.57340i
$34$		0			0
$35$	−5.91564	−	0.0720411i	−0.999926	−	0.0121772i
$36$		0			0
$37$	−0.268453	−	1.00188i	−0.0441334	−	0.164708i	0.940342	−	0.340231i	$-0.110505\pi$
$37$	−0.268453	−	1.00188i	−0.0441334	−	0.164708i	−0.984475	+	0.175523i	$0.943838\pi$
$38$		0			0
$39$	−8.93138	+	5.15654i	−1.43017	+	0.825706i
$40$		0			0
$41$			7.88697i			1.23174i	0.787849	+	0.615869i	$0.211195\pi$
$41$			7.88697i			1.23174i	−0.787849	+	0.615869i	$0.788805\pi$
$42$		0			0
$43$	−7.53537	−	7.53537i	−1.14913	−	1.14913i	−0.986723	−	0.162409i	$-0.948074\pi$
$43$	−7.53537	−	7.53537i	−1.14913	−	1.14913i	−0.162409	−	0.986723i	$-0.551926\pi$
$44$		0			0
$45$	−6.96387	−	2.46586i	−1.03811	−	0.367588i
$46$		0			0
$47$	−0.543934	+	0.145747i	−0.0793410	+	0.0212593i	−0.298271	−	0.954481i	$-0.596410\pi$
$47$	−0.543934	+	0.145747i	−0.0793410	+	0.0212593i	0.218930	+	0.975741i	$0.429743\pi$
$48$		0			0
$49$	6.47191	+	2.66728i	0.924559	+	0.381040i
$50$		0			0
$51$	8.67191	−	15.0202i	1.21431	−	2.10325i
$52$		0			0
$53$	0.479610	−	1.78993i	0.0658795	−	0.245866i	−0.925131	−	0.379647i	$-0.876045\pi$
$53$	0.479610	−	1.78993i	0.0658795	−	0.245866i	0.991011	+	0.133782i	$0.0427120\pi$
$54$		0			0
$55$	5.41242	+	6.33684i	0.729811	+	0.854459i
$56$		0			0
$57$	−5.88346	+	5.88346i	−0.779283	+	0.779283i
$58$		0			0
$59$	6.38015	+	11.0507i	0.830624	+	1.43868i	0.897544	+	0.440925i	$0.145350\pi$
$59$	6.38015	+	11.0507i	0.830624	+	1.43868i	−0.0669197	+	0.997758i	$0.521317\pi$
$60$		0			0
$61$	8.00463	+	4.62147i	1.02489	+	0.591719i	0.915516	−	0.402282i	$-0.131783\pi$
$61$	8.00463	+	4.62147i	1.02489	+	0.591719i	0.109372	+	0.994001i	$0.465116\pi$
$62$		0			0
$63$	6.57701	+	5.75754i	0.828625	+	0.725382i
$64$		0			0
$65$	5.20217	−	7.56958i	0.645250	−	0.938891i
$66$		0			0
$67$	5.56658	+	1.49156i	0.680065	+	0.182223i	0.582285	−	0.812985i	$-0.302159\pi$
$67$	5.56658	+	1.49156i	0.680065	+	0.182223i	0.0977808	+	0.995208i	$0.468826\pi$
$68$		0			0
$69$	−4.78670			−0.576251
$70$		0			0
$71$	0.683178			0.0810783			0.0405391	−	0.999178i	$-0.487092\pi$
$71$	0.683178			0.0810783			0.0405391	+	0.999178i	$0.487092\pi$
$72$		0			0
$73$	11.6096	+	3.11079i	1.35880	+	0.364091i	0.863377	−	0.504559i	$-0.168345\pi$
$73$	11.6096	+	3.11079i	1.35880	+	0.364091i	0.495427	+	0.868649i	$0.335012\pi$
$74$		0			0
$75$	12.4849	−	1.31280i	1.44163	−	0.151589i
$76$		0			0
$77$	−3.17786	−	9.33440i	−0.362151	−	1.06375i
$78$		0			0
$79$	−2.76589	−	1.59689i	−0.311187	−	0.179664i	0.336270	−	0.941765i	$-0.390834\pi$
$79$	−2.76589	−	1.59689i	−0.311187	−	0.179664i	−0.647458	+	0.762101i	$0.724168\pi$
$80$		0			0
$81$	−3.99812	−	6.92495i	−0.444236	−	0.769439i
$82$		0			0
$83$	1.44070	−	1.44070i	0.158138	−	0.158138i	−0.623603	−	0.781741i	$-0.714332\pi$
$83$	1.44070	−	1.44070i	0.158138	−	0.158138i	0.781741	+	0.623603i	$0.214332\pi$
$84$		0			0
$85$	−1.21155	+	15.3988i	−0.131411	+	1.67024i
$86$		0			0
$87$	0.366428	−	1.36753i	0.0392852	−	0.146614i
$88$		0			0
$89$	−1.26421	+	2.18968i	−0.134006	+	0.232106i	−0.925217	−	0.379437i	$-0.876118\pi$
$89$	−1.26421	+	2.18968i	−0.134006	+	0.232106i	0.791211	+	0.611543i	$0.209451\pi$
$90$		0			0
$91$	−9.03074	+	6.04577i	−0.946679	+	0.633769i
$92$		0			0
$93$	−8.97532	+	2.40493i	−0.930697	+	0.249380i
$94$		0			0
$95$	2.47342	−	6.98524i	0.253767	−	0.716670i
$96$		0			0
$97$	3.99033	+	3.99033i	0.405156	+	0.405156i	0.880046	−	0.474889i	$-0.157512\pi$
$97$	3.99033	+	3.99033i	0.405156	+	0.405156i	−0.474889	+	0.880046i	$0.657512\pi$
$98$		0			0
$99$		−	12.3131i		−	1.23751i
$100$		0			0
$101$	−11.5093	+	6.64487i	−1.14521	+	0.661189i	−0.947716	−	0.319114i	$-0.896615\pi$
$101$	−11.5093	+	6.64487i	−1.14521	+	0.661189i	−0.197497	+	0.980303i	$0.563281\pi$
$102$		0			0
$103$	−0.243935	−	0.910379i	−0.0240357	−	0.0897023i	0.952866	−	0.303391i	$-0.0981188\pi$
$103$	−0.243935	−	0.910379i	−0.0240357	−	0.0897023i	−0.976902	+	0.213689i	$0.931452\pi$
$104$		0			0
$105$	−14.2997	−	4.01886i	−1.39551	−	0.392200i
$106$		0			0
$107$	2.06874	+	7.72065i	0.199993	+	0.746383i	0.990918	+	0.134470i	$0.0429332\pi$
$107$	2.06874	+	7.72065i	0.199993	+	0.746383i	−0.790925	+	0.611913i	$0.790400\pi$
$108$		0			0
$109$	12.1969	−	7.04187i	1.16825	−	0.674489i	0.214982	−	0.976618i	$-0.431031\pi$
$109$	12.1969	−	7.04187i	1.16825	−	0.674489i	0.953267	+	0.302129i	$0.0976974\pi$
$110$		0			0
$111$		−	2.60420i		−	0.247179i
$112$		0			0
$113$	3.16304	+	3.16304i	0.297554	+	0.297554i	0.840055	−	0.542501i	$-0.182523\pi$
$113$	3.16304	+	3.16304i	0.297554	+	0.297554i	−0.542501	+	0.840055i	$0.682523\pi$
$114$		0			0
$115$	3.84772	−	1.83538i	0.358801	−	0.171150i
$116$		0			0
$117$	−13.1083	+	3.51235i	−1.21186	+	0.324717i
$118$		0			0
$119$	8.06889	−	16.3988i	0.739674	−	1.50328i
$120$		0			0
$121$	−1.44498	+	2.50278i	−0.131362	+	0.227526i
$122$		0			0
$123$	−5.12517	+	19.1274i	−0.462121	+	1.72466i
$124$		0			0
$125$	−9.53240	+	5.84238i	−0.852604	+	0.522558i
$126$		0			0
$127$	7.75766	−	7.75766i	0.688381	−	0.688381i	−0.273493	−	0.961874i	$-0.588179\pi$
$127$	7.75766	−	7.75766i	0.688381	−	0.688381i	0.961874	+	0.273493i	$0.0881789\pi$
$128$		0			0
$129$	−13.3780	−	23.1714i	−1.17787	−	2.04013i
$130$		0			0
$131$	−3.80420	−	2.19636i	−0.332375	−	0.191897i	0.324520	−	0.945879i	$-0.394797\pi$
$131$	−3.80420	−	2.19636i	−0.332375	−	0.191897i	−0.656895	+	0.753982i	$0.728131\pi$
$132$		0			0
$133$	−5.77521	+	6.59719i	−0.500774	+	0.572049i
$134$		0			0
$135$	−1.40572	−	0.966074i	−0.120985	−	0.0831464i
$136$		0			0
$137$	−6.83901	−	1.83251i	−0.584296	−	0.156562i	−0.0454510	−	0.998967i	$-0.514473\pi$
$137$	−6.83901	−	1.83251i	−0.584296	−	0.156562i	−0.538845	+	0.842405i	$0.681139\pi$
$138$		0			0
$139$	−9.68255			−0.821263			−0.410632	−	0.911801i	$-0.634692\pi$
$139$	−9.68255			−0.821263			−0.410632	+	0.911801i	$0.634692\pi$
$140$		0			0
$141$	−1.41385			−0.119068
$142$		0			0
$143$	14.7870	+	3.96217i	1.23655	+	0.331333i
$144$		0			0
$145$	0.229807	+	1.23977i	0.0190844	+	0.102957i
$146$		0			0
$147$	13.9623	+	10.6743i	1.15159	+	0.880400i
$148$		0			0
$149$	6.21464	+	3.58802i	0.509123	+	0.293942i	0.732473	−	0.680796i	$-0.238366\pi$
$149$	6.21464	+	3.58802i	0.509123	+	0.293942i	−0.223350	+	0.974738i	$0.571699\pi$
$150$		0			0
$151$	−3.52187	−	6.10006i	−0.286606	−	0.496416i	0.686391	−	0.727232i	$-0.259194\pi$
$151$	−3.52187	−	6.10006i	−0.286606	−	0.496416i	−0.972997	+	0.230816i	$0.925860\pi$
$152$		0			0
$153$	16.1378	−	16.1378i	1.30466	−	1.30466i
$154$		0			0
$155$	6.29254	−	5.37459i	0.505429	−	0.431698i
$156$		0			0
$157$	−0.0907875	+	0.338824i	−0.00724563	+	0.0270411i	−0.969454	−	0.245273i	$-0.921122\pi$
$157$	−0.0907875	+	0.338824i	−0.00724563	+	0.0270411i	0.962208	+	0.272314i	$0.0877890\pi$
$158$		0			0
$159$	2.32629	−	4.02925i	0.184487	−	0.319540i
$160$		0			0
$161$	−5.03300	+	0.334376i	−0.396656	+	0.0263525i
$162$		0			0
$163$	−22.8709	+	6.12825i	−1.79139	+	0.480001i	−0.992581	−	0.121584i	$-0.961203\pi$
$163$	−22.8709	+	6.12825i	−1.79139	+	0.480001i	−0.798808	+	0.601586i	$0.794536\pi$
$164$		0			0
$165$	9.00830	+	18.8852i	0.701295	+	1.47021i
$166$		0			0
$167$	−12.2886	−	12.2886i	−0.950924	−	0.950924i	0.0479272	−	0.998851i	$-0.484738\pi$
$167$	−12.2886	−	12.2886i	−0.950924	−	0.950924i	−0.998851	+	0.0479272i	$0.984738\pi$
$168$		0			0
$169$		−	3.87223i		−	0.297864i
$170$		0			0
$171$	−9.48184	+	5.47434i	−0.725094	+	0.418633i
$172$		0			0
$173$	−3.34733	−	12.4924i	−0.254492	−	0.949779i	−0.968372	−	0.249510i	$-0.919730\pi$
$173$	−3.34733	−	12.4924i	−0.254492	−	0.949779i	0.713880	−	0.700268i	$-0.246936\pi$
$174$		0			0
$175$	13.0356	−	2.25248i	0.985397	−	0.170272i
$176$		0			0
$177$	8.29199	+	30.9461i	0.623264	+	2.32605i
$178$		0			0
$179$	−15.5351	+	8.96922i	−1.16115	+	0.670391i	−0.951580	−	0.307403i	$-0.900540\pi$
$179$	−15.5351	+	8.96922i	−1.16115	+	0.670391i	−0.209571	+	0.977793i	$0.567207\pi$
$180$		0			0
$181$		−	24.8442i		−	1.84666i	−0.384013	−	0.923328i	$-0.625458\pi$
$181$		−	24.8442i		−	1.84666i	0.384013	−	0.923328i	$-0.374542\pi$
$182$		0			0
$183$	16.4096	+	16.4096i	1.21303	+	1.21303i
$184$		0			0
$185$	0.998533	+	2.09334i	0.0734136	+	0.153906i
$186$		0			0
$187$	−24.8678	+	6.66330i	−1.81851	+	0.487269i
$188$		0			0
$189$	1.12274	+	1.67706i	0.0816670	+	0.121988i
$190$		0			0
$191$	−10.3611	+	17.9459i	−0.749700	+	1.29852i	0.198267	+	0.980148i	$0.436469\pi$
$191$	−10.3611	+	17.9459i	−0.749700	+	1.29852i	−0.947967	+	0.318370i	$0.896865\pi$
$192$		0			0
$193$	3.77723	−	14.0968i	0.271891	−	1.01471i	−0.686006	−	0.727596i	$-0.740638\pi$
$193$	3.77723	−	14.0968i	0.271891	−	1.01471i	0.957896	−	0.287114i	$-0.0926958\pi$
$194$		0			0
$195$	17.5352	−	14.9772i	1.25572	−	1.07254i
$196$		0			0
$197$	4.55541	−	4.55541i	0.324559	−	0.324559i	−0.525954	−	0.850513i	$-0.676292\pi$
$197$	4.55541	−	4.55541i	0.324559	−	0.324559i	0.850513	+	0.525954i	$0.176292\pi$
$198$		0			0
$199$	−6.64840	−	11.5154i	−0.471293	−	0.816303i	0.528168	−	0.849140i	$-0.322879\pi$
$199$	−6.64840	−	11.5154i	−0.471293	−	0.816303i	−0.999461	+	0.0328370i	$0.989546\pi$
$200$		0			0
$201$	12.5307	+	7.23463i	0.883850	+	0.510291i
$202$		0			0
$203$	0.289754	−	1.46349i	0.0203368	−	0.102717i
$204$		0			0
$205$	−3.21427	−	17.3404i	−0.224495	−	1.21111i
$206$		0			0
$207$	−6.08407	−	1.63022i	−0.422872	−	0.113308i
$208$		0			0
$209$	12.3508			0.854326
$210$		0			0
$211$	14.2245			0.979256			0.489628	−	0.871931i	$-0.337133\pi$
$211$	14.2245			0.979256			0.489628	+	0.871931i	$0.337133\pi$
$212$		0			0
$213$	1.65684	+	0.443948i	0.113524	+	0.0304188i
$214$		0			0
$215$	19.6384	+	13.4964i	1.33932	+	0.920446i
$216$		0			0
$217$	−9.26915	+	3.15565i	−0.629231	+	0.214219i
$218$		0			0
$219$	26.1341	+	15.0885i	1.76598	+	1.01959i
$220$		0			0
$221$	14.1873	+	24.5731i	0.954339	+	1.65296i
$222$		0			0
$223$	−2.14150	+	2.14150i	−0.143406	+	0.143406i	−0.775165	−	0.631759i	$-0.782333\pi$
$223$	−2.14150	+	2.14150i	−0.143406	+	0.143406i	0.631759	+	0.775165i	$0.282333\pi$
$224$		0			0
$225$	16.3158	+	2.58339i	1.08772	+	0.172226i
$226$		0			0
$227$	2.41341	−	9.00695i	0.160183	−	0.597812i	−0.838422	−	0.545021i	$-0.816522\pi$
$227$	2.41341	−	9.00695i	0.160183	−	0.597812i	0.998606	−	0.0527911i	$-0.0168117\pi$
$228$		0			0
$229$	−13.6863	+	23.7054i	−0.904417	+	1.56650i	−0.0827198	+	0.996573i	$0.526361\pi$
$229$	−13.6863	+	23.7054i	−0.904417	+	1.56650i	−0.821698	+	0.569924i	$0.806973\pi$
$230$		0			0
$231$	−1.64117	−	24.7027i	−0.107981	−	1.62532i
$232$		0			0
$233$	4.53462	−	1.21505i	0.297073	−	0.0796005i	−0.107204	−	0.994237i	$-0.534190\pi$
$233$	4.53462	−	1.21505i	0.297073	−	0.0796005i	0.404277	+	0.914637i	$0.367523\pi$
$234$		0			0
$235$	1.13650	−	0.542117i	0.0741374	−	0.0353638i
$236$		0			0
$237$	−5.67011	−	5.67011i	−0.368313	−	0.368313i
$238$		0			0
$239$			10.3001i			0.666256i	0.942882	+	0.333128i	$0.108104\pi$
$239$			10.3001i			0.666256i	−0.942882	+	0.333128i	$0.891896\pi$
$240$		0			0
$241$	11.2358	−	6.48699i	0.723761	−	0.417864i	−0.0923744	−	0.995724i	$-0.529446\pi$
$241$	11.2358	−	6.48699i	0.723761	−	0.417864i	0.816135	+	0.577861i	$0.196112\pi$
$242$		0			0
$243$	−5.78846	−	21.6028i	−0.371330	−	1.38582i
$244$		0			0
$245$	−15.3163	−	3.22674i	−0.978521	−	0.206149i
$246$		0			0
$247$	−3.52313	−	13.1485i	−0.224171	−	0.836619i
$248$		0			0
$249$	4.43019	−	2.55777i	0.280752	−	0.162092i
$250$		0			0
$251$			12.5640i			0.793030i	0.918028	+	0.396515i	$0.129781\pi$
$251$			12.5640i			0.793030i	−0.918028	+	0.396515i	$0.870219\pi$
$252$		0			0
$253$	5.02424	+	5.02424i	0.315871	+	0.315871i
$254$		0			0
$255$	−12.9448	+	36.5578i	−0.810637	+	2.28934i
$256$		0			0
$257$	19.3713	−	5.19052i	1.20835	−	0.323776i	0.402235	−	0.915537i	$-0.368234\pi$
$257$	19.3713	−	5.19052i	1.20835	−	0.323776i	0.806114	+	0.591761i	$0.201567\pi$
$258$		0			0
$259$	−0.181916	−	2.73820i	−0.0113037	−	0.170143i
$260$		0			0
$261$	0.931487	−	1.61338i	0.0576576	−	0.0998659i
$262$		0			0
$263$	5.52433	−	20.6171i	0.340645	−	1.27130i	−0.556974	−	0.830530i	$-0.688038\pi$
$263$	5.52433	−	20.6171i	0.340645	−	1.27130i	0.897618	−	0.440773i	$-0.145296\pi$
$264$		0			0
$265$	−0.325007	+	4.13083i	−0.0199650	+	0.253755i
$266$		0			0
$267$	−4.48887	+	4.48887i	−0.274714	+	0.274714i
$268$		0			0
$269$	1.60824	+	2.78555i	0.0980561	+	0.169838i	0.910880	−	0.412671i	$-0.135404\pi$
$269$	1.60824	+	2.78555i	0.0980561	+	0.169838i	−0.812824	+	0.582510i	$0.802071\pi$
$270$		0			0
$271$	−6.87194	−	3.96752i	−0.417441	−	0.241009i	0.276541	−	0.961002i	$-0.410812\pi$
$271$	−6.87194	−	3.96752i	−0.417441	−	0.241009i	−0.693982	+	0.719993i	$0.744145\pi$
$272$		0			0
$273$	−25.8300	+	8.79371i	−1.56330	+	0.532220i
$274$		0			0
$275$	−14.4824	−	11.7265i	−0.873319	−	0.707133i
$276$		0			0
$277$	9.67281	+	2.59182i	0.581183	+	0.155727i	0.537420	−	0.843314i	$-0.319399\pi$
$277$	9.67281	+	2.59182i	0.581183	+	0.155727i	0.0437625	+	0.999042i	$0.486066\pi$
$278$		0			0
$279$	−12.2270			−0.732012
$280$		0			0
$281$	−15.6924			−0.936132			−0.468066	−	0.883693i	$-0.655049\pi$
$281$	−15.6924			−0.936132			−0.468066	+	0.883693i	$0.655049\pi$
$282$		0			0
$283$	−9.15682	−	2.45356i	−0.544316	−	0.145849i	−0.0238252	−	0.999716i	$-0.507585\pi$
$283$	−9.15682	−	2.45356i	−0.544316	−	0.145849i	−0.520491	+	0.853867i	$0.674251\pi$
$284$		0			0
$285$	10.5377	−	15.3332i	0.624200	−	0.908262i
$286$		0			0
$287$	−4.05274	+	20.4696i	−0.239226	+	1.20828i
$288$		0			0
$289$	−26.6029	−	15.3592i	−1.56488	−	0.903481i
$290$		0			0
$291$	7.08427	+	12.2703i	0.415287	+	0.719299i
$292$		0			0
$293$	7.18750	−	7.18750i	0.419898	−	0.419898i	−0.465270	−	0.885169i	$-0.654043\pi$
$293$	7.18750	−	7.18750i	0.419898	−	0.419898i	0.885169	+	0.465270i	$0.154043\pi$
$294$		0			0
$295$	−18.5311	−	21.6961i	−1.07892	−	1.26320i
$296$		0			0
$297$	0.735799	−	2.74604i	0.0426954	−	0.159341i
$298$		0			0
$299$	3.91553	−	6.78190i	0.226441	−	0.392207i
$300$		0			0
$301$	−15.6850	−	23.4291i	−0.904069	−	1.35043i
$302$		0			0
$303$	−32.2301	+	8.63604i	−1.85157	+	0.496127i
$304$		0			0
$305$	−19.4825	−	6.89862i	−1.11557	−	0.395014i
$306$		0			0
$307$	−5.61456	−	5.61456i	−0.320440	−	0.320440i	0.528496	−	0.848936i	$-0.322756\pi$
$307$	−5.61456	−	5.61456i	−0.320440	−	0.320440i	−0.848936	+	0.528496i	$0.822756\pi$
$308$		0			0
$309$		−	2.36636i		−	0.134617i
$310$		0			0
$311$	0.000487840	0	0.000281654i	2.76628e−5	0	1.59712e-5i	−0.499986	−	0.866033i	$-0.666662\pi$
$311$	0.000487840	0	0.000281654i	2.76628e−5	0	1.59712e-5i	0.500014	+	0.866017i	$0.333328\pi$
$312$		0			0
$313$	5.60863	+	20.9317i	0.317019	+	1.18313i	0.922095	+	0.386963i	$0.126476\pi$
$313$	5.60863	+	20.9317i	0.317019	+	1.18313i	−0.605077	+	0.796167i	$0.706858\pi$
$314$		0			0
$315$	−16.8068	−	9.97822i	−0.946954	−	0.562209i
$316$		0			0
$317$	1.97785	+	7.38145i	0.111087	+	0.414584i	0.998964	−	0.0454970i	$-0.0144871\pi$
$317$	1.97785	+	7.38145i	0.111087	+	0.414584i	−0.887877	+	0.460081i	$0.847820\pi$
$318$		0			0
$319$	−1.82000	+	1.05078i	−0.101901	+	0.0588323i
$320$		0			0
$321$			20.0684i			1.12011i
$322$		0			0
$323$	16.1873	+	16.1873i	0.900684	+	0.900684i
$324$		0			0
$325$	−8.35265	+	18.7627i	−0.463322	+	1.04077i
$326$		0			0
$327$	34.1557	−	9.15200i	1.88882	−	0.506107i
$328$		0			0
$329$	−1.48660	+	0.0987649i	−0.0819591	+	0.00544509i
$330$		0			0
$331$	13.5834	−	23.5271i	0.746609	−	1.29316i	−0.202831	−	0.979214i	$-0.565014\pi$
$331$	13.5834	−	23.5271i	0.746609	−	1.29316i	0.949439	−	0.313950i	$-0.101653\pi$
$332$		0			0
$333$	0.886919	−	3.31003i	0.0486029	−	0.181388i
$334$		0			0
$335$	−12.8466	−	1.01075i	−0.701886	−	0.0552233i
$336$		0			0
$337$	17.3001	−	17.3001i	0.942395	−	0.942395i	−0.0560343	−	0.998429i	$-0.517846\pi$
$337$	17.3001	−	17.3001i	0.942395	−	0.942395i	0.998429	+	0.0560343i	$0.0178456\pi$
$338$		0			0
$339$	5.61554	+	9.72639i	0.304994	+	0.528265i
$340$		0			0
$341$	11.9450	+	6.89644i	0.646857	+	0.373463i
$342$		0			0
$343$	15.4264	+	10.2482i	0.832949	+	0.553350i
$344$		0			0
$345$	10.5241	−	1.95078i	0.566599	−	0.105027i
$346$		0			0
$347$	−0.504852	−	0.135275i	−0.0271019	−	0.00726192i	0.245243	−	0.969462i	$-0.421132\pi$
$347$	−0.504852	−	0.135275i	−0.0271019	−	0.00726192i	−0.272345	+	0.962200i	$0.587799\pi$
$348$		0			0
$349$	20.3880			1.09134			0.545671	−	0.837999i	$-0.316275\pi$
$349$	20.3880			1.09134			0.545671	+	0.837999i	$0.316275\pi$
$350$		0			0
$351$	−3.13327			−0.167242
$352$		0			0
$353$	−12.6519	−	3.39007i	−0.673393	−	0.180435i	−0.0941102	−	0.995562i	$-0.530001\pi$
$353$	−12.6519	−	3.39007i	−0.673393	−	0.180435i	−0.579283	+	0.815127i	$0.696667\pi$
$354$		0			0
$355$	−1.50205	+	0.278424i	−0.0797203	+	0.0147772i
$356$		0			0
$357$	30.2250	−	34.5269i	1.59968	−	1.82736i
$358$		0			0
$359$	24.9508	+	14.4053i	1.31685	+	0.760284i	0.983221	−	0.182420i	$-0.0583929\pi$
$359$	24.9508	+	14.4053i	1.31685	+	0.760284i	0.333630	+	0.942704i	$0.391726\pi$
$360$		0			0
$361$	4.00887	+	6.94356i	0.210993	+	0.365451i
$362$		0			0
$363$	−5.13073	+	5.13073i	−0.269293	+	0.269293i
$364$		0			0
$365$	−26.7929	−	2.10802i	−1.40240	−	0.110339i
$366$		0			0
$367$	−2.86273	+	10.6839i	−0.149433	+	0.557693i	0.850084	+	0.526646i	$0.176551\pi$
$367$	−2.86273	+	10.6839i	−0.149433	+	0.557693i	−0.999518	+	0.0310469i	$0.990116\pi$
$368$		0			0
$369$	−13.0285	+	22.5661i	−0.678239	+	1.17474i
$370$		0			0
$371$	2.16453	−	4.39908i	0.112377	−	0.228389i
$372$		0			0
$373$	4.05366	−	1.08617i	0.209891	−	0.0562400i	−0.152342	−	0.988328i	$-0.548681\pi$
$373$	4.05366	−	1.08617i	0.209891	−	0.0562400i	0.362232	+	0.932088i	$0.382015\pi$
$374$		0			0
$375$	−26.9144	+	7.97445i	−1.38985	+	0.411799i
$376$		0			0
$377$	1.63781	+	1.63781i	0.0843513	+	0.0843513i
$378$		0			0
$379$			13.8555i			0.711708i	0.934542	+	0.355854i	$0.115810\pi$
$379$			13.8555i			0.711708i	−0.934542	+	0.355854i	$0.884190\pi$
$380$		0			0
$381$	23.8549	−	13.7727i	1.22213	−	0.705595i
$382$		0			0
$383$	−3.28064	−	12.2435i	−0.167633	−	0.625614i	−0.997690	−	0.0679352i	$-0.978359\pi$
$383$	−3.28064	−	12.2435i	−0.167633	−	0.625614i	0.830057	−	0.557678i	$-0.188308\pi$
$384$		0			0
$385$	10.7911	+	19.2276i	0.549963	+	0.979931i
$386$		0			0
$387$	−9.11237	−	34.0078i	−0.463208	−	1.72872i
$388$		0			0
$389$	27.9033	−	16.1100i	1.41476	−	0.816809i	0.418924	−	0.908022i	$-0.362408\pi$
$389$	27.9033	−	16.1100i	1.41476	−	0.816809i	0.995831	+	0.0912123i	$0.0290742\pi$
$390$		0			0
$391$			13.1697i			0.666023i
$392$		0			0
$393$	−7.79866	−	7.79866i	−0.393390	−	0.393390i
$394$		0			0
$395$	6.73193	+	2.38373i	0.338720	+	0.119938i
$396$		0			0
$397$	−25.8785	+	6.93413i	−1.29881	+	0.348014i	−0.840998	−	0.541038i	$-0.818032\pi$
$397$	−25.8785	+	6.93413i	−1.29881	+	0.348014i	−0.457807	+	0.889052i	$0.651365\pi$
$398$		0			0
$399$	−18.2930	+	12.2465i	−0.915795	+	0.613094i
$400$		0			0
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	−0.901046	−	0.433724i	$-0.857199\pi$
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	0.826139	+	0.563466i	$0.190532\pi$
$402$		0			0
$403$	3.93447	−	14.6837i	0.195990	−	0.731445i
$404$		0			0
$405$	11.6125	+	13.5959i	0.577032	+	0.675586i
$406$		0			0
$407$	−2.73343	+	2.73343i	−0.135491	+	0.135491i
$408$		0			0
$409$	−11.8208	−	20.4742i	−0.584501	−	1.01239i	−0.994937	−	0.100496i	$-0.967957\pi$
$409$	−11.8208	−	20.4742i	−0.584501	−	1.01239i	0.410436	−	0.911889i	$-0.365376\pi$
$410$		0			0
$411$	−15.3951	−	8.88835i	−0.759383	−	0.438430i
$412$		0			0
$413$	10.8804	+	31.9592i	0.535390	+	1.57261i
$414$		0			0
$415$	−2.58041	+	3.75470i	−0.126667	+	0.184311i
$416$		0			0
$417$	−23.4820	−	6.29199i	−1.14992	−	0.308120i
$418$		0			0
$419$	−1.35275			−0.0660862			−0.0330431	−	0.999454i	$-0.510520\pi$
$419$	−1.35275			−0.0660862			−0.0330431	+	0.999454i	$0.510520\pi$
$420$		0			0
$421$	−11.3346			−0.552412			−0.276206	−	0.961098i	$-0.589077\pi$
$421$	−11.3346			−0.552412			−0.276206	+	0.961098i	$0.589077\pi$
$422$		0			0
$423$	−1.79706	−	0.481520i	−0.0873760	−	0.0234123i
$424$		0			0
$425$	−3.61193	−	34.3499i	−0.175204	−	1.66621i
$426$		0			0
$427$	18.4002	+	16.1076i	0.890449	+	0.779503i
$428$		0			0
$429$	33.2866	+	19.2180i	1.60709	+	0.927855i
$430$		0			0
$431$	10.8635	+	18.8161i	0.523275	+	0.906338i	0.999633	+	0.0270870i	$0.00862311\pi$
$431$	10.8635	+	18.8161i	0.523275	+	0.906338i	−0.476359	+	0.879251i	$0.658044\pi$
$432$		0			0
$433$	8.74688	−	8.74688i	0.420348	−	0.420348i	−0.464976	−	0.885324i	$-0.653937\pi$
$433$	8.74688	−	8.74688i	0.420348	−	0.420348i	0.885324	+	0.464976i	$0.153937\pi$
$434$		0			0
$435$	−0.248309	+	3.15601i	−0.0119055	+	0.151319i
$436$		0			0
$437$	1.63522	−	6.10273i	0.0782233	−	0.291933i
$438$		0			0
$439$	−10.5117	+	18.2067i	−0.501695	+	0.868960i	0.498304	+	0.867003i	$0.333957\pi$
$439$	−10.5117	+	18.2067i	−0.501695	+	0.868960i	−0.999998	+	0.00195777i	$0.999377\pi$
$440$		0			0
$441$	14.1113	+	18.3226i	0.671965	+	0.872504i
$442$		0			0
$443$	37.9894	−	10.1792i	1.80493	−	0.483629i	0.810198	−	0.586156i	$-0.199359\pi$
$443$	37.9894	−	10.1792i	1.80493	−	0.483629i	0.994730	+	0.102527i	$0.0326927\pi$
$444$		0			0
$445$	1.88713	−	5.32949i	0.0894586	−	0.252642i
$446$		0			0
$447$	12.7401	+	12.7401i	0.602585	+	0.602585i
$448$		0			0
$449$			40.8069i			1.92580i	0.269863	+	0.962899i	$0.413021\pi$
$449$			40.8069i			1.92580i	−0.269863	+	0.962899i	$0.586979\pi$
$450$		0			0
$451$	25.4561	−	14.6971i	1.19868	−	0.692058i
$452$		0			0
$453$	−4.57722	−	17.0824i	−0.215057	−	0.802602i
$454$		0			0
$455$	17.3912	−	16.9727i	0.815313	−	0.795694i
$456$		0			0
$457$	4.49326	+	16.7691i	0.210186	+	0.784425i	0.987806	+	0.155690i	$0.0497602\pi$
$457$	4.49326	+	16.7691i	0.210186	+	0.784425i	−0.777620	+	0.628735i	$0.783573\pi$
$458$		0			0
$459$	4.56337	−	2.63466i	0.213000	−	0.122976i
$460$		0			0
$461$		−	31.6505i		−	1.47411i	−0.675833	−	0.737054i	$-0.736216\pi$
$461$		−	31.6505i		−	1.47411i	0.675833	−	0.737054i	$-0.263784\pi$
$462$		0			0
$463$	−20.4868	−	20.4868i	−0.952103	−	0.952103i	0.0468014	−	0.998904i	$-0.485097\pi$
$463$	−20.4868	−	20.4868i	−0.952103	−	0.952103i	−0.998904	+	0.0468014i	$0.985097\pi$
$464$		0			0
$465$	18.7532	−	8.94533i	0.869657	−	0.414830i
$466$		0			0
$467$	−11.0233	+	2.95367i	−0.510095	+	0.136680i	−0.504681	−	0.863306i	$-0.668390\pi$
$467$	−11.0233	+	2.95367i	−0.510095	+	0.136680i	−0.00541398	+	0.999985i	$0.501723\pi$
$468$		0			0
$469$	13.6809	+	6.73155i	0.631725	+	0.310834i
$470$		0			0
$471$	−0.440354	+	0.762715i	−0.0202904	+	0.0351441i
$472$		0			0
$473$	−10.2794	+	38.3631i	−0.472646	+	1.76394i
$474$		0			0
$475$	−2.59132	+	16.3659i	−0.118898	+	0.750918i
$476$		0			0
$477$	4.32905	−	4.32905i	0.198214	−	0.198214i
$478$		0			0
$479$	−10.0791	−	17.4576i	−0.460527	−	0.797656i	0.538460	−	0.842651i	$-0.319006\pi$
$479$	−10.0791	−	17.4576i	−0.460527	−	0.797656i	−0.998987	+	0.0449948i	$0.985673\pi$
$480$		0			0
$481$	3.68968	+	2.13024i	0.168235	+	0.0971305i
$482$		0			0
$483$	−12.4233	−	2.45966i	−0.565278	−	0.111918i
$484$		0			0
$485$	−10.3994	−	7.14697i	−0.472213	−	0.324527i
$486$		0			0
$487$	7.57376	+	2.02938i	0.343200	+	0.0919601i	0.426302	−	0.904581i	$-0.359816\pi$
$487$	7.57376	+	2.02938i	0.343200	+	0.0919601i	−0.0831022	+	0.996541i	$0.526483\pi$
$488$		0			0
$489$	−59.4486			−2.68836
$490$		0			0
$491$	−4.08749			−0.184466			−0.0922330	−	0.995737i	$-0.529400\pi$
$491$	−4.08749			−0.184466			−0.0922330	+	0.995737i	$0.529400\pi$
$492$		0			0
$493$	−3.76251	−	1.00816i	−0.169455	−	0.0454053i
$494$		0			0
$495$	5.01809	+	27.0717i	0.225547	+	1.21678i
$496$		0			0
$497$	1.77310	+	0.351053i	0.0795344	+	0.0157469i
$498$		0			0
$499$	−13.6472	−	7.87922i	−0.610933	−	0.352722i	0.162398	−	0.986725i	$-0.448077\pi$
$499$	−13.6472	−	7.87922i	−0.610933	−	0.352722i	−0.773331	+	0.634003i	$0.781411\pi$
$500$		0			0
$501$	−21.8168	−	37.7878i	−0.974702	−	1.68823i
$502$		0			0
$503$	2.80892	−	2.80892i	0.125244	−	0.125244i	−0.641707	−	0.766950i	$-0.721773\pi$
$503$	2.80892	−	2.80892i	0.125244	−	0.125244i	0.766950	+	0.641707i	$0.221773\pi$
$504$		0			0
$505$	22.5964	−	19.3000i	1.00552	−	0.858840i
$506$		0			0
$507$	2.51628	−	9.39089i	0.111752	−	0.417064i
$508$		0			0
$509$	1.79044	−	3.10113i	0.0793597	−	0.137455i	−0.823614	−	0.567151i	$-0.808046\pi$
$509$	1.79044	−	3.10113i	0.0793597	−	0.137455i	0.902974	+	0.429695i	$0.141379\pi$
$510$		0			0
$511$	28.5328	+	14.0393i	1.26222	+	0.621062i
$512$		0			0
$513$	−2.44175	+	0.654266i	−0.107806	+	0.0288866i
$514$		0			0
$515$	0.907337	+	1.90216i	0.0399821	+	0.0838191i
$516$		0			0
$517$	1.48401	+	1.48401i	0.0652669	+	0.0652669i
$518$		0			0
$519$		−	32.4716i		−	1.42534i
$520$		0			0
$521$	−12.7064	+	7.33604i	−0.556677	+	0.321398i	−0.751811	−	0.659379i	$-0.770819\pi$
$521$	−12.7064	+	7.33604i	−0.556677	+	0.321398i	0.195133	+	0.980777i	$0.437486\pi$
$522$		0			0
$523$	−1.38220	−	5.15843i	−0.0604392	−	0.225562i	0.929099	−	0.369830i	$-0.120584\pi$
$523$	−1.38220	−	5.15843i	−0.0604392	−	0.225562i	−0.989539	+	0.144268i	$0.953917\pi$
$524$		0			0
$525$	33.0775	+	3.00818i	1.44362	+	0.131288i
$526$		0			0
$527$	6.61673	+	24.6940i	0.288229	+	1.07569i
$528$		0			0
$529$	−16.7708	+	9.68265i	−0.729167	+	0.420985i
$530$		0			0
$531$			42.1577i			1.82949i
$532$		0			0
$533$	−22.9077	−	22.9077i	−0.992242	−	0.992242i
$534$		0			0
$535$	−7.69486	−	16.1316i	−0.332678	−	0.697432i
$536$		0			0
$537$	−43.5041	+	11.6569i	−1.87734	+	0.503032i
$538$		0			0
$539$	−3.45122	−	25.8592i	−0.148655	−	1.11383i
$540$		0			0
$541$	−4.91010	+	8.50455i	−0.211102	+	0.365639i	−0.952060	−	0.305913i	$-0.901038\pi$
$541$	−4.91010	+	8.50455i	−0.211102	+	0.365639i	0.740958	+	0.671552i	$0.234372\pi$
$542$		0			0
$543$	16.1444	−	60.2519i	0.692824	−	2.58566i
$544$		0			0
$545$	−23.9464	+	20.4531i	−1.02575	+	0.876115i
$546$		0			0
$547$	−7.51763	+	7.51763i	−0.321431	+	0.321431i	−0.849316	−	0.527885i	$-0.822985\pi$
$547$	−7.51763	+	7.51763i	−0.321431	+	0.321431i	0.527885	+	0.849316i	$0.322985\pi$
$548$		0			0
$549$	15.2685	+	26.4458i	0.651644	+	1.12868i
$550$		0			0
$551$	1.61833	+	0.934344i	0.0689433	+	0.0398044i
$552$		0			0
$553$	−6.35796	−	5.56578i	−0.270368	−	0.236681i
$554$		0			0
$555$	1.06132	+	5.72563i	0.0450505	+	0.243039i
$556$		0			0
$557$	−36.3925	−	9.75133i	−1.54200	−	0.413177i	−0.615087	−	0.788459i	$-0.710879\pi$
$557$	−36.3925	−	9.75133i	−1.54200	−	0.413177i	−0.926911	+	0.375282i	$0.877546\pi$
$558$		0			0
$559$	43.7729			1.85140
$560$		0			0
$561$	−64.6391			−2.72906
$562$		0			0
$563$	6.37876	+	1.70918i	0.268832	+	0.0720334i	0.390717	−	0.920511i	$-0.372227\pi$
$563$	6.37876	+	1.70918i	0.268832	+	0.0720334i	−0.121885	+	0.992544i	$0.538894\pi$
$564$		0			0
$565$	−8.24338	−	5.66523i	−0.346801	−	0.238338i
$566$		0			0
$567$	−6.81821	−	20.0273i	−0.286338	−	0.841067i
$568$		0			0
$569$	−25.6304	−	14.7977i	−1.07448	−	0.620352i	−0.145079	−	0.989420i	$-0.546344\pi$
$569$	−25.6304	−	14.7977i	−1.07448	−	0.620352i	−0.929402	+	0.369068i	$0.879677\pi$
$570$		0			0
$571$	3.35180	+	5.80549i	0.140269	+	0.242952i	0.927598	−	0.373581i	$-0.121870\pi$
$571$	3.35180	+	5.80549i	0.140269	+	0.242952i	−0.787329	+	0.616533i	$0.788537\pi$
$572$		0			0
$573$	−36.7892	+	36.7892i	−1.53689	+	1.53689i
$574$		0			0
$575$	−7.71165	+	5.60339i	−0.321598	+	0.233678i
$576$		0			0
$577$	−7.32878	+	27.3514i	−0.305101	+	1.13865i	0.627757	+	0.778409i	$0.283973\pi$
$577$	−7.32878	+	27.3514i	−0.305101	+	1.13865i	−0.932858	+	0.360243i	$0.882694\pi$
$578$		0			0
$579$	18.3210	−	31.7329i	0.761394	−	1.31877i
$580$		0			0
$581$	4.47947	−	2.99885i	0.185840	−	0.124413i
$582$		0			0
$583$	−6.67093	+	1.78747i	−0.276282	+	0.0740294i
$584$		0			0
$585$	27.3886	−	13.0645i	1.13238	−	0.540150i
$586$		0			0
$587$	0.913148	+	0.913148i	0.0376897	+	0.0376897i	0.725700	−	0.688011i	$-0.241516\pi$
$587$	0.913148	+	0.913148i	0.0376897	+	0.0376897i	−0.688011	+	0.725700i	$0.741516\pi$
$588$		0			0
$589$		−	12.2645i		−	0.505350i
$590$		0			0
$591$	14.0079	−	8.08749i	0.576210	−	0.332675i
$592$		0			0
$593$	0.642069	+	2.39623i	0.0263666	+	0.0984015i	0.977855	−	0.209282i	$-0.0671128\pi$
$593$	0.642069	+	2.39623i	0.0263666	+	0.0984015i	−0.951489	+	0.307684i	$0.900446\pi$
$594$		0			0
$595$	−11.0572	+	39.3431i	−0.453300	+	1.61291i
$596$		0			0
$597$	−8.64063	−	32.2473i	−0.353637	−	1.31979i
$598$		0			0
$599$	−7.27210	+	4.19855i	−0.297130	+	0.171548i	−0.641153	−	0.767413i	$-0.721544\pi$
$599$	−7.27210	+	4.19855i	−0.297130	+	0.171548i	0.344023	+	0.938961i	$0.388210\pi$
$600$		0			0
$601$			24.6555i			1.00572i	0.864368	+	0.502859i	$0.167719\pi$
$601$			24.6555i			1.00572i	−0.864368	+	0.502859i	$0.832281\pi$
$602$		0			0
$603$	13.4631	+	13.4631i	0.548260	+	0.548260i
$604$		0			0
$605$	2.15697	−	6.09154i	0.0876933	−	0.247656i
$606$		0			0
$607$	13.5365	−	3.62709i	0.549429	−	0.147219i	0.0265835	−	0.999647i	$-0.491537\pi$
$607$	13.5365	−	3.62709i	0.549429	−	0.147219i	0.522845	+	0.852428i	$0.324871\pi$
$608$		0			0
$609$	1.65373	−	3.36096i	0.0670124	−	0.136193i
$610$		0			0
$611$	1.15654	−	2.00318i	0.0467884	−	0.0810399i
$612$		0			0
$613$	−2.69654	+	10.0636i	−0.108912	+	0.406465i	−0.998760	−	0.0497928i	$-0.984144\pi$
$613$	−2.69654	+	10.0636i	−0.108912	+	0.406465i	0.889848	+	0.456258i	$0.150811\pi$
$614$		0			0
$615$	3.47306	−	44.1425i	0.140047	−	1.78000i
$616$		0			0
$617$	3.40085	−	3.40085i	0.136913	−	0.136913i	−0.635329	−	0.772242i	$-0.719135\pi$
$617$	3.40085	−	3.40085i	0.136913	−	0.136913i	0.772242	+	0.635329i	$0.219135\pi$
$618$		0			0
$619$	−4.43441	−	7.68063i	−0.178234	−	0.308711i	0.763042	−	0.646349i	$-0.223705\pi$
$619$	−4.43441	−	7.68063i	−0.178234	−	0.308711i	−0.941276	+	0.337639i	$0.890372\pi$
$620$		0			0
$621$	−1.25944	−	0.727138i	−0.0505396	−	0.0291790i
$622$		0			0
$623$	−4.40628	+	5.03342i	−0.176534	+	0.201660i
$624$		0			0
$625$	18.5771	−	16.7300i	0.743083	−	0.669200i
$626$		0			0
$627$	29.9531	+	8.02591i	1.19621	+	0.320524i
$628$		0			0
$629$	−7.16498			−0.285686
$630$		0			0
$631$	−0.858162			−0.0341629			−0.0170815	−	0.999854i	$-0.505437\pi$
$631$	−0.858162			−0.0341629			−0.0170815	+	0.999854i	$0.505437\pi$
$632$		0			0
$633$	34.4971	+	9.24348i	1.37114	+	0.367395i
$634$		0			0
$635$	−13.8945	+	20.2177i	−0.551388	+	0.802315i
$636$		0			0
$637$	−26.5448	+	11.0506i	−1.05174	+	0.437839i
$638$		0			0
$639$	1.95470	+	1.12855i	0.0773268	+	0.0446446i
$640$		0			0
$641$	−10.0661	−	17.4350i	−0.397587	−	0.688641i	0.595840	−	0.803103i	$-0.296819\pi$
$641$	−10.0661	−	17.4350i	−0.397587	−	0.688641i	−0.993428	+	0.114461i	$0.963486\pi$
$642$		0			0
$643$	−3.68541	+	3.68541i	−0.145338	+	0.145338i	−0.776032	−	0.630694i	$-0.782770\pi$
$643$	−3.68541	+	3.68541i	−0.145338	+	0.145338i	0.630694	+	0.776032i	$0.282770\pi$
$644$		0			0
$645$	38.8564	+	45.4928i	1.52997	+	1.79128i
$646$		0			0
$647$	6.09978	−	22.7647i	0.239807	−	0.894973i	−0.736116	−	0.676856i	$-0.763342\pi$
$647$	6.09978	−	22.7647i	0.239807	−	0.894973i	0.975923	−	0.218117i	$-0.0699913\pi$
$648$		0			0
$649$	23.7783	−	41.1853i	0.933381	−	1.61666i
$650$		0			0
$651$	−24.5301	+	1.62969i	−0.961409	+	0.0638727i
$652$		0			0
$653$	36.6764	−	9.82740i	1.43526	−	0.384576i	0.544387	−	0.838834i	$-0.316762\pi$
$653$	36.6764	−	9.82740i	1.43526	−	0.384576i	0.890870	+	0.454258i	$0.150096\pi$
$654$		0			0
$655$	9.25909	+	3.27857i	0.361783	+	0.128104i
$656$		0			0
$657$	28.0786	+	28.0786i	1.09545	+	1.09545i
$658$		0			0
$659$		−	23.0353i		−	0.897327i	−0.893701	−	0.448663i	$-0.851900\pi$
$659$		−	23.0353i		−	0.897327i	0.893701	−	0.448663i	$-0.148100\pi$
$660$		0			0
$661$	−22.5377	+	13.0121i	−0.876614	+	0.506114i	−0.869541	−	0.493861i	$-0.835585\pi$
$661$	−22.5377	+	13.0121i	−0.876614	+	0.506114i	−0.00707383	+	0.999975i	$0.502252\pi$
$662$		0			0
$663$	18.4386	+	68.8136i	0.716094	+	2.67250i
$664$		0			0
$665$	10.0088	−	16.8583i	0.388126	−	0.653737i
$666$		0			0
$667$	0.278241	+	1.03841i	0.0107736	+	0.0402074i
$668$		0			0
$669$	−6.58515	+	3.80194i	−0.254597	+	0.146991i
$670$		0			0
$671$		−	34.4478i		−	1.32984i
$672$		0			0
$673$	27.1667	+	27.1667i	1.04720	+	1.04720i	0.998829	+	0.0483701i	$0.0154027\pi$
$673$	27.1667	+	27.1667i	1.04720	+	1.04720i	0.0483701	+	0.998829i	$0.484597\pi$
$674$		0			0
$675$	3.48435	+	1.55114i	0.134113	+	0.0597033i
$676$		0			0
$677$	45.8245	−	12.2786i	1.76118	−	0.471907i	0.774226	−	0.632910i	$-0.218140\pi$
$677$	45.8245	−	12.2786i	1.76118	−	0.471907i	0.986954	+	0.161003i	$0.0514729\pi$
$678$		0			0
$679$	8.30594	+	12.4068i	0.318753	+	0.476130i
$680$		0			0
$681$	11.7059	−	20.2753i	0.448572	−	0.776950i
$682$		0			0
$683$	−9.45542	+	35.2881i	−0.361801	+	1.35026i	0.509904	+	0.860231i	$0.329681\pi$
$683$	−9.45542	+	35.2881i	−0.361801	+	1.35026i	−0.871705	+	0.490030i	$0.836986\pi$
$684$		0			0
$685$	15.7832	+	1.24179i	0.603044	+	0.0474465i
$686$		0			0
$687$	−48.5963	+	48.5963i	−1.85407	+	1.85407i
$688$		0			0
$689$	3.80582	+	6.59187i	0.144990	+	0.251130i
$690$		0			0
$691$	−12.6519	−	7.30456i	−0.481300	−	0.277878i	0.239658	−	0.970857i	$-0.422965\pi$
$691$	−12.6519	−	7.30456i	−0.481300	−	0.277878i	−0.720958	+	0.692979i	$0.756298\pi$
$692$		0			0
$693$	6.32710	−	31.9570i	0.240347	−	1.21395i
$694$		0			0
$695$	21.2882	−	3.94605i	0.807508	−	0.149682i
$696$		0			0
$697$	52.6256	+	14.1010i	1.99334	+	0.534113i
$698$		0			0
$699$	11.7869			0.445821
$700$		0			0
$701$	41.3885			1.56322			0.781612	−	0.623765i	$-0.214398\pi$
$701$	41.3885			1.56322			0.781612	+	0.623765i	$0.214398\pi$
$702$		0			0
$703$	3.32018	+	0.889640i	0.125223	+	0.0335534i
$704$		0			0
$705$	3.10852	−	0.576205i	0.117074	−	0.0217011i
$706$		0			0
$707$	−33.2853	+	11.3319i	−1.25182	+	0.426178i
$708$		0			0
$709$	−28.2236	−	16.2949i	−1.05996	−	0.611968i	−0.134539	−	0.990908i	$-0.542955\pi$
$709$	−28.2236	−	16.2949i	−1.05996	−	0.611968i	−0.925421	+	0.378940i	$0.876289\pi$
$710$		0			0
$711$	−5.27583	−	9.13800i	−0.197859	−	0.342702i
$712$		0			0
$713$	4.98912	−	4.98912i	0.186844	−	0.186844i
$714$		0			0
$715$	−34.1257	−	2.68495i	−1.27623	−	0.100412i
$716$		0			0
$717$	−6.69326	+	24.9796i	−0.249965	+	0.932880i
$718$		0			0
$719$	−0.555682	+	0.962469i	−0.0207234	+	0.0358940i	−0.876201	−	0.481946i	$-0.839930\pi$
$719$	−0.555682	+	0.962469i	−0.0207234	+	0.0358940i	0.855478	+	0.517840i	$0.173264\pi$
$720$		0			0
$721$	−0.165302	−	2.48812i	−0.00615617	−	0.0926624i
$722$		0			0
$723$	31.4643	−	8.43084i	1.17017	−	0.313546i
$724$		0			0
$725$	−1.01051	−	2.63212i	−0.0375296	−	0.0977543i
$726$		0			0
$727$	−17.4058	−	17.4058i	−0.645545	−	0.645545i	0.306368	−	0.951913i	$-0.400886\pi$
$727$	−17.4058	−	17.4058i	−0.645545	−	0.645545i	−0.951913	+	0.306368i	$0.900886\pi$
$728$		0			0
$729$		−	32.1637i		−	1.19125i
$730$		0			0
$731$	−63.7519	+	36.8071i	−2.35795	+	1.36136i
$732$		0			0
$733$	5.55744	+	20.7406i	0.205269	+	0.766073i	0.989367	+	0.145437i	$0.0464589\pi$
$733$	5.55744	+	20.7406i	0.205269	+	0.766073i	−0.784099	+	0.620636i	$0.786874\pi$
$734$		0			0
$735$	−35.0480	−	17.7784i	−1.29277	−	0.655766i
$736$		0			0
$737$	−5.55893	−	20.7462i	−0.204766	−	0.764196i
$738$		0			0
$739$	19.1855	−	11.0767i	0.705750	−	0.407465i	−0.103736	−	0.994605i	$-0.533080\pi$
$739$	19.1855	−	11.0767i	0.705750	−	0.407465i	0.809485	+	0.587140i	$0.199746\pi$
$740$		0			0
$741$		−	34.1770i		−	1.25552i
$742$		0			0
$743$	−15.3901	−	15.3901i	−0.564607	−	0.564607i	0.366006	−	0.930613i	$-0.380725\pi$
$743$	−15.3901	−	15.3901i	−0.564607	−	0.564607i	−0.930613	+	0.366006i	$0.880725\pi$
$744$		0			0
$745$	−15.1259	−	5.35595i	−0.554169	−	0.196227i
$746$		0			0
$747$	6.50204	−	1.74222i	0.237897	−	0.0637443i
$748$		0			0
$749$	1.40188	+	21.1010i	0.0512235	+	0.771013i
$750$		0			0
$751$	−8.68491	+	15.0427i	−0.316917	+	0.548916i	−0.979843	−	0.199769i	$-0.935981\pi$
$751$	−8.68491	+	15.0427i	−0.316917	+	0.548916i	0.662926	+	0.748685i	$0.269314\pi$
$752$		0			0
$753$	−8.16440	+	30.4700i	−0.297527	+	1.11039i
$754$		0			0
$755$	10.2293	+	11.9764i	0.372281	+	0.435865i
$756$		0			0
$757$	−4.00848	+	4.00848i	−0.145691	+	0.145691i	−0.776190	−	0.630499i	$-0.782850\pi$
$757$	−4.00848	+	4.00848i	−0.145691	+	0.145691i	0.630499	+	0.776190i	$0.282850\pi$
$758$		0			0
$759$	8.91984	+	15.4496i	0.323770	+	0.560785i
$760$		0			0
$761$	−14.8872	−	8.59511i	−0.539659	−	0.311573i	0.205281	−	0.978703i	$-0.434189\pi$
$761$	−14.8872	−	8.59511i	−0.539659	−	0.311573i	−0.744941	+	0.667130i	$0.767522\pi$
$762$		0			0
$763$	35.2739	−	12.0089i	1.27700	−	0.434750i
$764$		0			0
$765$	−28.9039	+	42.0576i	−1.04502	+	1.52059i
$766$		0			0
$767$	−50.6280	−	13.5657i	−1.82807	−	0.489830i
$768$		0			0
$769$	17.2755			0.622969			0.311484	−	0.950251i	$-0.399174\pi$
$769$	17.2755			0.622969			0.311484	+	0.950251i	$0.399174\pi$
$770$		0			0
$771$	50.3520			1.81338
$772$		0			0
$773$	−7.64124	−	2.04746i	−0.274836	−	0.0736422i	0.118768	−	0.992922i	$-0.462105\pi$
$773$	−7.64124	−	2.04746i	−0.274836	−	0.0736422i	−0.393605	+	0.919280i	$0.628772\pi$
$774$		0			0
$775$	−11.6445	+	14.3811i	−0.418283	+	0.516586i
$776$		0			0
$777$	1.33817	−	6.75886i	0.0480067	−	0.242473i
$778$		0			0
$779$	−22.6353	−	13.0685i	−0.810995	−	0.468228i
$780$		0			0
$781$	−1.27308	−	2.20503i	−0.0455542	−	0.0789023i
$782$		0			0
$783$	0.304150	−	0.304150i	0.0108694	−	0.0108694i
$784$		0			0
$785$	0.0615219	−	0.781943i	0.00219581	−	0.0279087i
$786$		0			0
$787$	4.25353	−	15.8744i	0.151622	−	0.565861i	−0.847749	−	0.530398i	$-0.822043\pi$
$787$	4.25353	−	15.8744i	0.151622	−	0.565861i	0.999371	−	0.0354635i	$-0.0112907\pi$
$788$		0			0
$789$	26.7951	−	46.4104i	0.953930	−	1.65226i
$790$		0			0
$791$	6.58393	+	9.83460i	0.234097	+	0.349678i
$792$		0			0
$793$	−36.6725	+	9.82637i	−1.30228	+	0.348944i
$794$		0			0
$795$	−3.47253	+	9.80684i	−0.123158	+	0.347813i
$796$		0			0
$797$	32.0830	+	32.0830i	1.13644	+	1.13644i	0.989084	+	0.147354i	$0.0470758\pi$
$797$	32.0830	+	32.0830i	1.13644	+	1.13644i	0.147354	+	0.989084i	$0.452924\pi$
$798$		0			0
$799$			3.88996i			0.137617i
$800$		0			0
$801$	−7.23430	+	4.17673i	−0.255612	+	0.147577i
$802$		0			0
$803$	−11.5937	−	43.2682i	−0.409132	−	1.52690i
$804$		0			0
$805$	10.9294	−	2.78632i	0.385210	−	0.0982050i
$806$		0			0
$807$	2.09016	+	7.80057i	0.0735770	+	0.274593i
$808$		0			0
$809$	−25.4551	+	14.6965i	−0.894955	+	0.516702i	−0.875560	−	0.483109i	$-0.839507\pi$
$809$	−25.4551	+	14.6965i	−0.894955	+	0.516702i	−0.0193950	+	0.999812i	$0.506174\pi$
$810$		0			0
$811$			5.63576i			0.197898i	0.995092	+	0.0989491i	$0.0315481\pi$
$811$			5.63576i			0.197898i	−0.995092	+	0.0989491i	$0.968452\pi$
$812$		0			0
$813$	−14.0876	−	14.0876i	−0.494072	−	0.494072i
$814$		0			0
$815$	47.7869	−	22.7945i	1.67390	−	0.798457i
$816$		0			0
$817$	34.1122	−	9.14032i	1.19343	−	0.319779i
$818$		0			0
$819$	−35.8257	+	2.38014i	−1.25185	+	0.0831687i
$820$		0			0
$821$	4.70640	−	8.15172i	0.164254	−	0.284497i	−0.772136	−	0.635457i	$-0.780812\pi$
$821$	4.70640	−	8.15172i	0.164254	−	0.284497i	0.936390	+	0.350961i	$0.114145\pi$
$822$		0			0
$823$	−3.68634	+	13.7576i	−0.128498	+	0.479560i	−0.999940	−	0.0109378i	$-0.996518\pi$
$823$	−3.68634	+	13.7576i	−0.128498	+	0.479560i	0.871442	+	0.490498i	$0.163185\pi$
$824$		0			0
$825$	−27.5023	−	37.8499i	−0.957507	−	1.31777i
$826$		0			0
$827$	13.3153	−	13.3153i	0.463018	−	0.463018i	−0.436625	−	0.899643i	$-0.643826\pi$
$827$	13.3153	−	13.3153i	0.463018	−	0.463018i	0.899643	+	0.436625i	$0.143826\pi$
$828$		0			0
$829$	5.93159	+	10.2738i	0.206013	+	0.356824i	0.950455	−	0.310863i	$-0.100618\pi$
$829$	5.93159	+	10.2738i	0.206013	+	0.356824i	−0.744442	+	0.667687i	$0.767285\pi$
$830$		0			0
$831$	21.7742	+	12.5713i	0.755337	+	0.436094i
$832$		0			0
$833$	29.3683	−	38.4148i	1.01755	−	1.33100i
$834$		0			0
$835$	32.0261	+	22.0099i	1.10831	+	0.761683i
$836$		0			0
$837$	−2.72684	−	0.730656i	−0.0942535	−	0.0252552i
$838$		0			0
$839$	25.5847			0.883281			0.441641	−	0.897192i	$-0.354397\pi$
$839$	25.5847			0.883281			0.441641	+	0.897192i	$0.354397\pi$
$840$		0			0
$841$	28.6820			0.989036
$842$		0			0
$843$	−38.0571	−	10.1974i	−1.31076	−	0.351216i
$844$		0			0
$845$	1.57810	+	8.51354i	0.0542882	+	0.292875i
$846$		0			0
$847$	−5.03632	+	5.75314i	−0.173050	+	0.197680i
$848$		0			0
$849$	−20.6126	−	11.9007i	−0.707423	−	0.408431i
$850$		0			0
$851$	0.988727	+	1.71253i	0.0338931	+	0.0587046i
$852$		0			0
$853$	−1.77628	+	1.77628i	−0.0608187	+	0.0608187i	−0.736862	−	0.676043i	$-0.763693\pi$
$853$	−1.77628	+	1.77628i	−0.0608187	+	0.0608187i	0.676043	+	0.736862i	$0.263693\pi$
$854$		0			0
$855$	18.6159	−	15.9002i	0.636650	−	0.543776i
$856$		0			0
$857$	−8.37730	+	31.2645i	−0.286163	+	1.06798i	0.661822	+	0.749661i	$0.269783\pi$
$857$	−8.37730	+	31.2645i	−0.286163	+	1.06798i	−0.947985	+	0.318314i	$0.896883\pi$
$858$		0			0
$859$	−28.2878	+	48.9959i	−0.965168	+	1.67172i	−0.256003	+	0.966676i	$0.582406\pi$
$859$	−28.2878	+	48.9959i	−0.965168	+	1.67172i	−0.709164	+	0.705043i	$0.750928\pi$
$860$		0			0
$861$	−23.1304	+	47.0091i	−0.788281	+	1.60207i
$862$		0			0
$863$	−50.3027	+	13.4786i	−1.71232	+	0.458816i	−0.975992	−	0.217806i	$-0.930110\pi$
$863$	−50.3027	+	13.4786i	−1.71232	+	0.458816i	−0.736331	+	0.676622i	$0.763443\pi$
$864$		0			0
$865$	12.4507	+	26.1018i	0.423335	+	0.887487i
$866$		0			0
$867$	−54.5362	−	54.5362i	−1.85215	−	1.85215i
$868$		0			0
$869$			11.9030i			0.403781i
$870$		0			0
$871$	−20.5003	+	11.8359i	−0.694628	+	0.401043i
$872$		0			0
$873$	4.82542	+	18.0087i	0.163316	+	0.609503i
$874$		0			0
$875$	−27.7422	+	10.2649i	−0.937859	+	0.347017i
$876$		0			0
$877$	−1.02787	−	3.83607i	−0.0347088	−	0.129535i	0.946398	−	0.323004i	$-0.104693\pi$
$877$	−1.02787	−	3.83607i	−0.0347088	−	0.129535i	−0.981106	+	0.193469i	$0.938026\pi$
$878$		0			0
$879$	22.1017	−	12.7604i	0.745471	−	0.430398i
$880$		0			0
$881$		−	24.7339i		−	0.833307i	−0.909065	−	0.416654i	$-0.863203\pi$
$881$		−	24.7339i		−	0.833307i	0.909065	−	0.416654i	$-0.136797\pi$
$882$		0			0
$883$	−3.69618	−	3.69618i	−0.124387	−	0.124387i	0.642173	−	0.766560i	$-0.278033\pi$
$883$	−3.69618	−	3.69618i	−0.124387	−	0.124387i	−0.766560	+	0.642173i	$0.778033\pi$
$884$		0			0
$885$	−30.8427	−	64.6593i	−1.03677	−	2.17350i
$886$		0			0
$887$	−18.7690	+	5.02913i	−0.630200	+	0.168862i	−0.559761	−	0.828654i	$-0.689107\pi$
$887$	−18.7690	+	5.02913i	−0.630200	+	0.168862i	−0.0704398	+	0.997516i	$0.522440\pi$
$888$		0			0
$889$	24.1203	−	16.1477i	0.808970	−	0.541577i
$890$		0			0
$891$	−14.9007	+	25.8088i	−0.499192	+	0.864627i
$892$		0			0
$893$	0.482997	−	1.80257i	0.0161629	−	0.0603207i
$894$		0			0
$895$	30.5005	−	26.0511i	1.01952	−	0.870792i
$896$		0			0
$897$	13.9030	−	13.9030i	0.464207	−	0.464207i
$898$		0			0
$899$	1.04343	+	1.80728i	0.0348005	+	0.0602762i
$900$		0			0
$901$	−11.0858	−	6.40037i	−0.369320	−	0.213227i
$902$		0			0
$903$	−22.8142	−	67.0127i	−0.759209	−	2.23004i
$904$		0			0
$905$	10.1251	+	54.6229i	0.336568	+	1.81573i
$906$		0			0
$907$	45.1505	+	12.0980i	1.49920	+	0.401709i	0.912831	−	0.408337i	$-0.133891\pi$
$907$	45.1505	+	12.0980i	1.49920	+	0.401709i	0.586367	+	0.810046i	$0.300558\pi$
$908$		0			0
$909$	−43.9069			−1.45630
$910$		0			0
$911$	43.4768			1.44045			0.720225	−	0.693740i	$-0.244038\pi$
$911$	43.4768			1.44045			0.720225	+	0.693740i	$0.244038\pi$
$912$		0			0
$913$	−7.33473	−	1.96533i	−0.242744	−	0.0650431i
$914$		0			0
$915$	−42.7659	−	29.3907i	−1.41380	−	0.971628i
$916$		0			0
$917$	−8.74472	−	7.65517i	−0.288776	−	0.252796i
$918$		0			0
$919$	6.80127	+	3.92672i	0.224353	+	0.129530i	0.607964	−	0.793964i	$-0.291986\pi$
$919$	6.80127	+	3.92672i	0.224353	+	0.129530i	−0.383611	+	0.923495i	$0.625320\pi$
$920$		0			0
$921$	−9.96787	−	17.2649i	−0.328453	−	0.568897i
$922$		0			0
$923$	−1.98429	+	1.98429i	−0.0653137	+	0.0653137i
$924$		0			0
$925$	−3.04852	−	4.19551i	−0.100235	−	0.137948i
$926$		0			0
$927$	0.805917	−	3.00772i	0.0264698	−	0.0987866i
$928$		0			0
$929$	−13.2493	+	22.9485i	−0.434696	+	0.752916i	−0.997271	−	0.0738305i	$-0.976478\pi$
$929$	−13.2493	+	22.9485i	−0.434696	+	0.752916i	0.562575	+	0.826747i	$0.309811\pi$
$930$		0			0
$931$	−18.3788	+	14.1545i	−0.602341	+	0.463896i
$932$		0			0
$933$	0.00136613		0.000366053i	4.47251e−5		1.19841e-5i
$934$		0			0
$935$	51.9591	−	24.7847i	1.69924	−	0.810547i
$936$		0			0
$937$	−37.0373	−	37.0373i	−1.20995	−	1.20995i	−0.971041	−	0.238914i	$-0.923208\pi$
$937$	−37.0373	−	37.0373i	−1.20995	−	1.20995i	−0.238914	−	0.971041i	$-0.576792\pi$
$938$		0			0
$939$			54.4080i			1.77554i
$940$		0			0
$941$	38.0947	−	21.9940i	1.24185	−	0.716984i	0.272382	−	0.962189i	$-0.412189\pi$
$941$	38.0947	−	21.9940i	1.24185	−	0.716984i	0.969471	+	0.245205i	$0.0788554\pi$
$942$		0			0
$943$	−3.89171	−	14.5241i	−0.126732	−	0.472969i
$944$		0			0
$945$	−3.15194	−	3.22965i	−0.102533	−	0.105061i
$946$		0			0
$947$	6.07076	+	22.6564i	0.197273	+	0.736233i	0.991667	+	0.128830i	$0.0411221\pi$
$947$	6.07076	+	22.6564i	0.197273	+	0.736233i	−0.794394	+	0.607403i	$0.792211\pi$
$948$		0			0
$949$	−42.7554	+	24.6849i	−1.38790	+	0.801305i
$950$		0			0
$951$			19.1867i			0.622171i
$952$		0			0
$953$	−15.9160	−	15.9160i	−0.515569	−	0.515569i	0.400658	−	0.916227i	$-0.368781\pi$
$953$	−15.9160	−	15.9160i	−0.515569	−	0.515569i	−0.916227	+	0.400658i	$0.868781\pi$
$954$		0			0
$955$	15.4663	−	43.6786i	0.500477	−	1.41341i
$956$		0			0
$957$	−5.09668	+	1.36565i	−0.164752	+	0.0441452i
$958$		0			0
$959$	−16.8081	−	8.27028i	−0.542763	−	0.267061i
$960$		0			0
$961$	−8.65177	+	14.9853i	−0.279089	+	0.483397i
$962$		0			0
$963$	−6.83474	+	25.5076i	−0.220246	+	0.821971i
$964$		0			0
$965$	−2.55963	+	32.5328i	−0.0823973	+	1.04727i
$966$		0			0
$967$	−20.3556	+	20.3556i	−0.654591	+	0.654591i	−0.954095	−	0.299504i	$-0.903179\pi$
$967$	−20.3556	+	20.3556i	−0.654591	+	0.654591i	0.299504	+	0.954095i	$0.403179\pi$
$968$		0			0
$969$	28.7383	+	49.7761i	0.923206	+	1.59904i
$970$		0			0
$971$	−11.3848	−	6.57304i	−0.365357	−	0.210939i	0.306071	−	0.952009i	$-0.400985\pi$
$971$	−11.3848	−	6.57304i	−0.365357	−	0.210939i	−0.671428	+	0.741070i	$0.734319\pi$
$972$		0			0
$973$	−25.1298	−	4.97541i	−0.805625	−	0.159504i
$974$		0			0
$975$	−32.4493	+	40.0753i	−1.03921	+	1.28344i
$976$		0			0
$977$	17.1240	+	4.58835i	0.547844	+	0.146794i	0.522116	−	0.852875i	$-0.325143\pi$
$977$	17.1240	+	4.58835i	0.547844	+	0.146794i	0.0257283	+	0.999669i	$0.491810\pi$
$978$		0			0
$979$	9.42325			0.301168
$980$		0			0
$981$	46.5301			1.48559
$982$		0			0
$983$	−39.3603	−	10.5466i	−1.25540	−	0.336383i	−0.430979	−	0.902362i	$-0.641832\pi$
$983$	−39.3603	−	10.5466i	−1.25540	−	0.336383i	−0.824420	+	0.565979i	$0.808498\pi$
$984$		0			0
$985$	−8.15907	+	11.8721i	−0.259969	+	0.378277i
$986$		0			0
$987$	−3.66948	−	0.726512i	−0.116801	−	0.0231251i
$988$		0			0
$989$	17.5948	+	10.1584i	0.559482	+	0.323017i
$990$		0			0
$991$	−29.8834	−	51.7596i	−0.949278	−	1.64420i	−0.746950	−	0.664880i	$-0.768483\pi$
$991$	−29.8834	−	51.7596i	−0.949278	−	1.64420i	−0.202328	−	0.979318i	$-0.564851\pi$
$992$		0			0
$993$	48.2307	−	48.2307i	1.53056	−	1.53056i
$994$		0			0
$995$	19.3103	+	22.6084i	0.612177	+	0.716733i
$996$		0			0
$997$	6.39130	−	23.8526i	0.202414	−	0.755421i	−0.787808	−	0.615921i	$-0.788784\pi$
$997$	6.39130	−	23.8526i	0.202414	−	0.755421i	0.990222	−	0.139500i	$-0.0445494\pi$
$998$		0			0
$999$	0.395598	−	0.685196i	0.0125162	−	0.0216786i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.u.a.33.4	yes	16
3.2	odd	2		1260.2.dq.a.1153.4		16
4.3	odd	2		560.2.ci.d.33.1		16
5.2	odd	4	inner	140.2.u.a.117.4	yes	16
5.3	odd	4		700.2.bc.b.257.1		16
5.4	even	2		700.2.bc.b.593.1		16
7.2	even	3		980.2.m.a.293.2		16
7.3	odd	6	inner	140.2.u.a.73.4	yes	16
7.4	even	3		980.2.v.a.913.1		16
7.5	odd	6		980.2.m.a.293.7		16
7.6	odd	2		980.2.v.a.313.1		16
15.2	even	4		1260.2.dq.a.397.3		16
20.7	even	4		560.2.ci.d.257.1		16
21.17	even	6		1260.2.dq.a.73.3		16
28.3	even	6		560.2.ci.d.353.1		16
35.2	odd	12		980.2.m.a.97.7		16
35.3	even	12		700.2.bc.b.157.1		16
35.12	even	12		980.2.m.a.97.2		16
35.17	even	12	inner	140.2.u.a.17.4	✓	16
35.24	odd	6		700.2.bc.b.493.1		16
35.27	even	4		980.2.v.a.117.1		16
35.32	odd	12		980.2.v.a.717.1		16
105.17	odd	12		1260.2.dq.a.577.4		16
140.87	odd	12		560.2.ci.d.17.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.u.a.17.4	✓	16	35.17	even	12	inner
140.2.u.a.33.4	yes	16	1.1	even	1	trivial
140.2.u.a.73.4	yes	16	7.3	odd	6	inner
140.2.u.a.117.4	yes	16	5.2	odd	4	inner
560.2.ci.d.17.1		16	140.87	odd	12
560.2.ci.d.33.1		16	4.3	odd	2
560.2.ci.d.257.1		16	20.7	even	4
560.2.ci.d.353.1		16	28.3	even	6
700.2.bc.b.157.1		16	35.3	even	12
700.2.bc.b.257.1		16	5.3	odd	4
700.2.bc.b.493.1		16	35.24	odd	6
700.2.bc.b.593.1		16	5.4	even	2
980.2.m.a.97.2		16	35.12	even	12
980.2.m.a.97.7		16	35.2	odd	12
980.2.m.a.293.2		16	7.2	even	3
980.2.m.a.293.7		16	7.5	odd	6
980.2.v.a.117.1		16	35.27	even	4
980.2.v.a.313.1		16	7.6	odd	2
980.2.v.a.717.1		16	35.32	odd	12
980.2.v.a.913.1		16	7.4	even	3
1260.2.dq.a.73.3		16	21.17	even	6
1260.2.dq.a.397.3		16	15.2	even	4
1260.2.dq.a.577.4		16	105.17	odd	12
1260.2.dq.a.1153.4		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.42519 + 0.649827i) q^{3} +(-2.19862 + 0.407542i) q^{5} +(2.59537 + 0.513853i) q^{7} +(2.86119 + 1.65191i) q^{9} +O(q^{10})\)	\(q+(2.42519 + 0.649827i) q^{3} +(-2.19862 + 0.407542i) q^{5} +(2.59537 + 0.513853i) q^{7} +(2.86119 + 1.65191i) q^{9} +(-1.86346 - 3.22761i) q^{11} +(-2.90450 + 2.90450i) q^{13} +(-5.59689 - 0.440354i) q^{15} +(1.78788 - 6.67247i) q^{17} +(-1.65698 + 2.86997i) q^{19} +(5.96035 + 2.93273i) q^{21} +(-1.84153 + 0.493436i) q^{23} +(4.66782 - 1.79206i) q^{25} +(0.539383 + 0.539383i) q^{27} -0.563886i q^{29} +(-3.20505 + 1.85044i) q^{31} +(-2.42186 - 9.03849i) q^{33} +(-5.91564 - 0.0720411i) q^{35} +(-0.268453 - 1.00188i) q^{37} +(-8.93138 + 5.15654i) q^{39} +7.88697i q^{41} +(-7.53537 - 7.53537i) q^{43} +(-6.96387 - 2.46586i) q^{45} +(-0.543934 + 0.145747i) q^{47} +(6.47191 + 2.66728i) q^{49} +(8.67191 - 15.0202i) q^{51} +(0.479610 - 1.78993i) q^{53} +(5.41242 + 6.33684i) q^{55} +(-5.88346 + 5.88346i) q^{57} +(6.38015 + 11.0507i) q^{59} +(8.00463 + 4.62147i) q^{61} +(6.57701 + 5.75754i) q^{63} +(5.20217 - 7.56958i) q^{65} +(5.56658 + 1.49156i) q^{67} -4.78670 q^{69} +0.683178 q^{71} +(11.6096 + 3.11079i) q^{73} +(12.4849 - 1.31280i) q^{75} +(-3.17786 - 9.33440i) q^{77} +(-2.76589 - 1.59689i) q^{79} +(-3.99812 - 6.92495i) q^{81} +(1.44070 - 1.44070i) q^{83} +(-1.21155 + 15.3988i) q^{85} +(0.366428 - 1.36753i) q^{87} +(-1.26421 + 2.18968i) q^{89} +(-9.03074 + 6.04577i) q^{91} +(-8.97532 + 2.40493i) q^{93} +(2.47342 - 6.98524i) q^{95} +(3.99033 + 3.99033i) q^{97} -12.3131i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5} + 2 q^{7}+O(q^{10}) \) 16 * q + 6 * q^5 + 2 * q^7	\( 16 q + 6 q^{5} + 2 q^{7} - 20 q^{15} + 18 q^{17} - 4 q^{21} - 16 q^{23} + 6 q^{25} - 12 q^{31} - 42 q^{33} - 40 q^{35} - 14 q^{37} + 28 q^{43} - 66 q^{45} - 6 q^{47} + 20 q^{51} - 10 q^{53} + 44 q^{57} + 60 q^{61} + 48 q^{63} + 34 q^{65} + 8 q^{67} - 8 q^{71} + 78 q^{73} + 96 q^{75} + 10 q^{77} + 24 q^{81} + 30 q^{87} - 64 q^{91} - 62 q^{93} + 2 q^{95}+O(q^{100}) \) 16 * q + 6 * q^5 + 2 * q^7 - 20 * q^15 + 18 * q^17 - 4 * q^21 - 16 * q^23 + 6 * q^25 - 12 * q^31 - 42 * q^33 - 40 * q^35 - 14 * q^37 + 28 * q^43 - 66 * q^45 - 6 * q^47 + 20 * q^51 - 10 * q^53 + 44 * q^57 + 60 * q^61 + 48 * q^63 + 34 * q^65 + 8 * q^67 - 8 * q^71 + 78 * q^73 + 96 * q^75 + 10 * q^77 + 24 * q^81 + 30 * q^87 - 64 * q^91 - 62 * q^93 + 2 * q^95

Introduction

L-functions

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