LMFDB - Embedded newform 140.2.u.a.117.4

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			117.4
Root			$0.500000 + 1.27536i$ of defining polynomial
Character	$\chi$	$=$	140.117
Dual form			140.2.u.a.73.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.649827 - 2.42519i) q^{3} +(-0.746366 - 2.10783i) q^{5} +(-0.513853 + 2.59537i) q^{7} +(-2.86119 - 1.65191i) q^{9} +O(q^{10})$	\(q+(0.649827 - 2.42519i) q^{3} +(-0.746366 - 2.10783i) q^{5} +(-0.513853 + 2.59537i) q^{7} +(-2.86119 - 1.65191i) q^{9} +(-1.86346 - 3.22761i) q^{11} +(2.90450 + 2.90450i) q^{13} +(-5.59689 + 0.440354i) q^{15} +(6.67247 + 1.78788i) q^{17} +(1.65698 - 2.86997i) q^{19} +(5.96035 + 2.93273i) q^{21} +(0.493436 + 1.84153i) q^{23} +(-3.88588 + 3.14642i) q^{25} +(-0.539383 + 0.539383i) q^{27} +0.563886i q^{29} +(-3.20505 + 1.85044i) q^{31} +(-9.03849 + 2.42186i) q^{33} +(5.85412 - 0.853984i) q^{35} +(1.00188 - 0.268453i) q^{37} +(8.93138 - 5.15654i) q^{39} +7.88697i q^{41} +(-7.53537 + 7.53537i) q^{43} +(-1.34644 + 7.26382i) q^{45} +(-0.145747 - 0.543934i) q^{47} +(-6.47191 - 2.66728i) q^{49} +(8.67191 - 15.0202i) q^{51} +(-1.78993 - 0.479610i) q^{53} +(-5.41242 + 6.33684i) q^{55} +(-5.88346 - 5.88346i) q^{57} +(-6.38015 - 11.0507i) q^{59} +(8.00463 + 4.62147i) q^{61} +(5.75754 - 6.57701i) q^{63} +(3.95436 - 8.29000i) q^{65} +(-1.49156 + 5.56658i) q^{67} +4.78670 q^{69} +0.683178 q^{71} +(3.11079 - 11.6096i) q^{73} +(5.10552 + 11.4686i) q^{75} +(9.33440 - 3.17786i) q^{77} +(2.76589 + 1.59689i) q^{79} +(-3.99812 - 6.92495i) q^{81} +(-1.44070 - 1.44070i) q^{83} +(-1.21155 - 15.3988i) q^{85} +(1.36753 + 0.366428i) q^{87} +(1.26421 - 2.18968i) q^{89} +(-9.03074 + 6.04577i) q^{91} +(2.40493 + 8.97532i) q^{93} +(-7.28610 - 1.35057i) q^{95} +(-3.99033 + 3.99033i) q^{97} +12.3131i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

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

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
$3$	0.649827	−	2.42519i	0.375178	−	1.40018i	−0.477907	−	0.878411i	$-0.658604\pi$
$3$	0.649827	−	2.42519i	0.375178	−	1.40018i	0.853085	−	0.521773i	$-0.174729\pi$
$4$		0			0
$5$	−0.746366	−	2.10783i	−0.333785	−	0.942649i
$5$	−0.746366	−	2.10783i	−0.333785	−	0.942649i
$6$		0			0
$7$	−0.513853	+	2.59537i	−0.194218	+	0.980958i
$7$	−0.513853	+	2.59537i	−0.194218	+	0.980958i
$8$		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	$-0.0570907\pi$
$13$	2.90450	+	2.90450i	0.805563	+	0.805563i	−0.178396	+	0.983959i	$0.557091\pi$
$14$		0			0
$15$	−5.59689	+	0.440354i	−1.44511	+	0.113699i
$16$		0			0
$17$	6.67247	+	1.78788i	1.61831	+	0.433625i	0.950505	−	0.310710i	$-0.100567\pi$
$17$	6.67247	+	1.78788i	1.61831	+	0.433625i	0.667806	+	0.744335i	$0.267233\pi$
$18$		0			0
$19$	1.65698	−	2.86997i	0.380136	−	0.658415i	−0.610945	−	0.791673i	$-0.709210\pi$
$19$	1.65698	−	2.86997i	0.380136	−	0.658415i	0.991081	+	0.133258i	$0.0425438\pi$
$20$		0			0
$21$	5.96035	+	2.93273i	1.30066	+	0.639975i
$22$		0			0
$23$	0.493436	+	1.84153i	0.102889	+	0.383985i	0.998097	−	0.0616623i	$-0.0196402\pi$
$23$	0.493436	+	1.84153i	0.102889	+	0.383985i	−0.895209	+	0.445647i	$0.852974\pi$
$24$		0			0
$25$	−3.88588	+	3.14642i	−0.777175	+	0.629284i
$26$		0			0
$27$	−0.539383	+	0.539383i	−0.103804	+	0.103804i
$28$		0			0
$29$			0.563886i			0.104711i	0.998629	+	0.0523555i	$0.0166729\pi$
$29$			0.563886i			0.104711i	−0.998629	+	0.0523555i	$0.983327\pi$
$30$		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
$33$	−9.03849	+	2.42186i	−1.57340	+	0.421591i
$34$		0			0
$35$	5.85412	−	0.853984i	0.989527	−	0.144350i
$36$		0			0
$37$	1.00188	−	0.268453i	0.164708	−	0.0441334i	−0.175523	−	0.984475i	$-0.556162\pi$
$37$	1.00188	−	0.268453i	0.164708	−	0.0441334i	0.340231	+	0.940342i	$0.389495\pi$
$38$		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	−0.162409	+	0.986723i	$0.551926\pi$
$43$	−7.53537	+	7.53537i	−1.14913	+	1.14913i	−0.986723	+	0.162409i	$0.948074\pi$
$44$		0			0
$45$	−1.34644	+	7.26382i	−0.200716	+	1.08283i
$46$		0			0
$47$	−0.145747	−	0.543934i	−0.0212593	−	0.0793410i	0.954481	−	0.298271i	$-0.0964100\pi$
$47$	−0.145747	−	0.543934i	−0.0212593	−	0.0793410i	−0.975741	+	0.218930i	$0.929743\pi$
$48$		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
$53$	−1.78993	−	0.479610i	−0.245866	−	0.0658795i	0.133782	−	0.991011i	$-0.457288\pi$
$53$	−1.78993	−	0.479610i	−0.245866	−	0.0658795i	−0.379647	+	0.925131i	$0.623955\pi$
$54$		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	$-0.854650\pi$
$59$	−6.38015	−	11.0507i	−0.830624	−	1.43868i	0.0669197	−	0.997758i	$-0.478683\pi$
$60$		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
$63$	5.75754	−	6.57701i	0.725382	−	0.828625i
$64$		0			0
$65$	3.95436	−	8.29000i	0.490479	−	1.02825i
$66$		0			0
$67$	−1.49156	+	5.56658i	−0.182223	+	0.680065i	0.812985	+	0.582285i	$0.197841\pi$
$67$	−1.49156	+	5.56658i	−0.182223	+	0.680065i	−0.995208	+	0.0977808i	$0.968826\pi$
$68$		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
$73$	3.11079	−	11.6096i	0.364091	−	1.35880i	−0.504559	−	0.863377i	$-0.668345\pi$
$73$	3.11079	−	11.6096i	0.364091	−	1.35880i	0.868649	−	0.495427i	$-0.164988\pi$
$74$		0			0
$75$	5.10552	+	11.4686i	0.589534	+	1.32428i
$76$		0			0
$77$	9.33440	−	3.17786i	1.06375	−	0.362151i
$78$		0			0
$79$	2.76589	+	1.59689i	0.311187	+	0.179664i	0.647458	−	0.762101i	$-0.275832\pi$
$79$	2.76589	+	1.59689i	0.311187	+	0.179664i	−0.336270	+	0.941765i	$0.609166\pi$
$80$		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	$-0.285668\pi$
$83$	−1.44070	−	1.44070i	−0.158138	−	0.158138i	−0.781741	+	0.623603i	$0.785668\pi$
$84$		0			0
$85$	−1.21155	−	15.3988i	−0.131411	−	1.67024i
$86$		0			0
$87$	1.36753	+	0.366428i	0.146614	+	0.0392852i
$88$		0			0
$89$	1.26421	−	2.18968i	0.134006	−	0.232106i	−0.791211	−	0.611543i	$-0.790549\pi$
$89$	1.26421	−	2.18968i	0.134006	−	0.232106i	0.925217	+	0.379437i	$0.123882\pi$
$90$		0			0
$91$	−9.03074	+	6.04577i	−0.946679	+	0.633769i
$92$		0			0
$93$	2.40493	+	8.97532i	0.249380	+	0.930697i
$94$		0			0
$95$	−7.28610	−	1.35057i	−0.747538	−	0.138566i
$96$		0			0
$97$	−3.99033	+	3.99033i	−0.405156	+	0.405156i	−0.880046	−	0.474889i	$-0.842488\pi$
$97$	−3.99033	+	3.99033i	−0.405156	+	0.405156i	0.474889	+	0.880046i	$0.342488\pi$
$98$		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
$103$	−0.910379	+	0.243935i	−0.0897023	+	0.0240357i	−0.303391	−	0.952866i	$-0.598119\pi$
$103$	−0.910379	+	0.243935i	−0.0897023	+	0.0240357i	0.213689	+	0.976902i	$0.431452\pi$
$104$		0			0
$105$	1.73309	−	14.7523i	0.169133	−	1.43968i
$106$		0			0
$107$	−7.72065	+	2.06874i	−0.746383	+	0.199993i	−0.611913	−	0.790925i	$-0.709600\pi$
$107$	−7.72065	+	2.06874i	−0.746383	+	0.199993i	−0.134470	+	0.990918i	$0.542933\pi$
$108$		0			0
$109$	−12.1969	+	7.04187i	−1.16825	+	0.674489i	−0.953267	−	0.302129i	$-0.902303\pi$
$109$	−12.1969	+	7.04187i	−1.16825	+	0.674489i	−0.214982	+	0.976618i	$0.568969\pi$
$110$		0			0
$111$		−	2.60420i		−	0.247179i
$112$		0			0
$113$	3.16304	−	3.16304i	0.297554	−	0.297554i	−0.542501	−	0.840055i	$-0.682523\pi$
$113$	3.16304	−	3.16304i	0.297554	−	0.297554i	0.840055	+	0.542501i	$0.182523\pi$
$114$		0			0
$115$	3.51334	−	2.41453i	0.327621	−	0.225156i
$116$		0			0
$117$	−3.51235	−	13.1083i	−0.324717	−	1.21186i
$118$		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
$123$	19.1274	+	5.12517i	1.72466	+	0.462121i
$124$		0			0
$125$	9.53240	+	5.84238i	0.852604	+	0.522558i
$126$		0			0
$127$	7.75766	+	7.75766i	0.688381	+	0.688381i	0.961874	−	0.273493i	$-0.0881789\pi$
$127$	7.75766	+	7.75766i	0.688381	+	0.688381i	−0.273493	+	0.961874i	$0.588179\pi$
$128$		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
$133$	6.59719	+	5.77521i	0.572049	+	0.500774i
$134$		0			0
$135$	1.53950	+	0.734349i	0.132499	+	0.0632027i
$136$		0			0
$137$	1.83251	−	6.83901i	0.156562	−	0.584296i	−0.842405	−	0.538845i	$-0.818861\pi$
$137$	1.83251	−	6.83901i	0.156562	−	0.584296i	0.998967	−	0.0454510i	$-0.0144725\pi$
$138$		0			0
$139$	9.68255			0.821263			0.410632	−	0.911801i	$-0.365308\pi$
$139$	9.68255			0.821263			0.410632	+	0.911801i	$0.365308\pi$
$140$		0			0
$141$	−1.41385			−0.119068
$142$		0			0
$143$	3.96217	−	14.7870i	0.331333	−	1.23655i
$144$		0			0
$145$	1.18857	−	0.420865i	0.0987057	−	0.0349509i
$146$		0			0
$147$	−10.6743	+	13.9623i	−0.880400	+	1.15159i
$148$		0			0
$149$	−6.21464	−	3.58802i	−0.509123	−	0.293942i	0.223350	−	0.974738i	$-0.428301\pi$
$149$	−6.21464	−	3.58802i	−0.509123	−	0.293942i	−0.732473	+	0.680796i	$0.761634\pi$
$150$		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
$157$	−0.338824	−	0.0907875i	−0.0270411	−	0.00724563i	0.245273	−	0.969454i	$-0.421122\pi$
$157$	−0.338824	−	0.0907875i	−0.0270411	−	0.00724563i	−0.272314	+	0.962208i	$0.587789\pi$
$158$		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
$163$	6.12825	+	22.8709i	0.480001	+	1.79139i	0.601586	+	0.798808i	$0.294536\pi$
$163$	6.12825	+	22.8709i	0.480001	+	1.79139i	−0.121584	+	0.992581i	$0.538797\pi$
$164$		0			0
$165$	11.8509	+	17.2440i	0.922590	+	1.34244i
$166$		0			0
$167$	12.2886	−	12.2886i	0.950924	−	0.950924i	−0.0479272	−	0.998851i	$-0.515262\pi$
$167$	12.2886	−	12.2886i	0.950924	−	0.950924i	0.998851	+	0.0479272i	$0.0152615\pi$
$168$		0			0
$169$			3.87223i			0.297864i
$170$		0			0
$171$	−9.48184	+	5.47434i	−0.725094	+	0.418633i
$172$		0			0
$173$	−12.4924	+	3.34733i	−0.949779	+	0.254492i	−0.700268	−	0.713880i	$-0.746936\pi$
$173$	−12.4924	+	3.34733i	−0.949779	+	0.254492i	−0.249510	+	0.968372i	$0.580270\pi$
$174$		0			0
$175$	−6.16937	−	11.7021i	−0.466360	−	0.884595i
$176$		0			0
$177$	−30.9461	+	8.29199i	−2.32605	+	0.623264i
$178$		0			0
$179$	15.5351	−	8.96922i	1.16115	−	0.670391i	0.209571	−	0.977793i	$-0.432793\pi$
$179$	15.5351	−	8.96922i	1.16115	−	0.670391i	0.951580	+	0.307403i	$0.0994598\pi$
$180$		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
$185$	−1.31362	−	1.91143i	−0.0965794	−	0.140531i
$186$		0			0
$187$	−6.66330	−	24.8678i	−0.487269	−	1.81851i
$188$		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
$193$	−14.0968	−	3.77723i	−1.01471	−	0.271891i	−0.287114	−	0.957896i	$-0.592696\pi$
$193$	−14.0968	−	3.77723i	−1.01471	−	0.271891i	−0.727596	+	0.686006i	$0.759362\pi$
$194$		0			0
$195$	−17.5352	−	14.9772i	−1.25572	−	1.07254i
$196$		0			0
$197$	4.55541	+	4.55541i	0.324559	+	0.324559i	0.850513	−	0.525954i	$-0.176292\pi$
$197$	4.55541	+	4.55541i	0.324559	+	0.324559i	−0.525954	+	0.850513i	$0.676292\pi$
$198$		0			0
$199$	6.64840	+	11.5154i	0.471293	+	0.816303i	0.999461	−	0.0328370i	$-0.0104542\pi$
$199$	6.64840	+	11.5154i	0.471293	+	0.816303i	−0.528168	+	0.849140i	$0.677121\pi$
$200$		0			0
$201$	12.5307	+	7.23463i	0.883850	+	0.510291i
$202$		0			0
$203$	−1.46349	−	0.289754i	−0.102717	−	0.0203368i
$204$		0			0
$205$	16.6244	−	5.88656i	1.16110	−	0.411136i
$206$		0			0
$207$	1.63022	−	6.08407i	0.113308	−	0.422872i
$208$		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
$213$	0.443948	−	1.65684i	0.0304188	−	0.113524i
$214$		0			0
$215$	21.5074	+	10.2591i	1.46679	+	0.699666i
$216$		0			0
$217$	−3.15565	−	9.26915i	−0.214219	−	0.629231i
$218$		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	$-0.217667\pi$
$223$	2.14150	+	2.14150i	0.143406	+	0.143406i	−0.631759	+	0.775165i	$0.717667\pi$
$224$		0			0
$225$	16.3158	−	2.58339i	1.08772	−	0.172226i
$226$		0			0
$227$	9.00695	+	2.41341i	0.597812	+	0.160183i	0.545021	−	0.838422i	$-0.316522\pi$
$227$	9.00695	+	2.41341i	0.597812	+	0.160183i	0.0527911	+	0.998606i	$0.483188\pi$
$228$		0			0
$229$	13.6863	−	23.7054i	0.904417	−	1.56650i	0.0827198	−	0.996573i	$-0.473639\pi$
$229$	13.6863	−	23.7054i	0.904417	−	1.56650i	0.821698	−	0.569924i	$-0.193027\pi$
$230$		0			0
$231$	−1.64117	−	24.7027i	−0.107981	−	1.62532i
$232$		0			0
$233$	−1.21505	−	4.53462i	−0.0796005	−	0.297073i	0.914637	−	0.404277i	$-0.132477\pi$
$233$	−1.21505	−	4.53462i	−0.0796005	−	0.297073i	−0.994237	+	0.107204i	$0.965810\pi$
$234$		0			0
$235$	−1.03774	+	0.713183i	−0.0676947	+	0.0465229i
$236$		0			0
$237$	5.67011	−	5.67011i	0.368313	−	0.368313i
$238$		0			0
$239$		−	10.3001i		−	0.666256i	−0.942882	−	0.333128i	$-0.891896\pi$
$239$		−	10.3001i		−	0.666256i	0.942882	−	0.333128i	$-0.108104\pi$
$240$		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
$243$	−21.6028	+	5.78846i	−1.38582	+	0.371330i
$244$		0			0
$245$	−0.791749	+	15.6324i	−0.0505830	+	0.998720i
$246$		0			0
$247$	13.1485	−	3.52313i	0.836619	−	0.224171i
$248$		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
$255$	−38.1324	−	7.06833i	−2.38794	−	0.442636i
$256$		0			0
$257$	5.19052	+	19.3713i	0.323776	+	1.20835i	0.915537	+	0.402235i	$0.131766\pi$
$257$	5.19052	+	19.3713i	0.323776	+	1.20835i	−0.591761	+	0.806114i	$0.701567\pi$
$258$		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
$263$	−20.6171	−	5.52433i	−1.27130	−	0.340645i	−0.440773	−	0.897618i	$-0.645296\pi$
$263$	−20.6171	−	5.52433i	−1.27130	−	0.340645i	−0.830530	+	0.556974i	$0.811962\pi$
$264$		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	0.812824	−	0.582510i	$-0.197929\pi$
$269$	−1.60824	−	2.78555i	−0.0980561	−	0.169838i	−0.910880	+	0.412671i	$0.864596\pi$
$270$		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
$273$	8.79371	+	25.8300i	0.532220	+	1.56330i
$274$		0			0
$275$	17.3966	+	6.67886i	1.04905	+	0.402750i
$276$		0			0
$277$	−2.59182	+	9.67281i	−0.155727	+	0.581183i	0.843314	+	0.537420i	$0.180601\pi$
$277$	−2.59182	+	9.67281i	−0.155727	+	0.581183i	−0.999042	+	0.0437625i	$0.986066\pi$
$278$		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
$283$	−2.45356	+	9.15682i	−0.145849	+	0.544316i	0.853867	+	0.520491i	$0.174251\pi$
$283$	−2.45356	+	9.15682i	−0.145849	+	0.544316i	−0.999716	+	0.0238252i	$0.992415\pi$
$284$		0			0
$285$	−8.01011	+	16.7925i	−0.474478	+	0.994704i
$286$		0			0
$287$	−20.4696	−	4.05274i	−1.20828	−	0.239226i
$288$		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	$-0.345957\pi$
$293$	−7.18750	−	7.18750i	−0.419898	−	0.419898i	−0.885169	+	0.465270i	$0.845957\pi$
$294$		0			0
$295$	−18.5311	+	21.6961i	−1.07892	+	1.26320i
$296$		0			0
$297$	2.74604	+	0.735799i	0.159341	+	0.0426954i
$298$		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
$303$	8.63604	+	32.2301i	0.496127	+	1.85157i
$304$		0			0
$305$	3.76689	−	20.3217i	0.215692	−	1.16362i
$306$		0			0
$307$	5.61456	−	5.61456i	0.320440	−	0.320440i	−0.528496	−	0.848936i	$-0.677244\pi$
$307$	5.61456	−	5.61456i	0.320440	−	0.320440i	0.848936	+	0.528496i	$0.177244\pi$
$308$		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
$313$	20.9317	−	5.60863i	1.18313	−	0.317019i	0.386963	−	0.922095i	$-0.373524\pi$
$313$	20.9317	−	5.60863i	1.18313	−	0.317019i	0.796167	+	0.605077i	$0.206858\pi$
$314$		0			0
$315$	−18.1604	−	7.22706i	−1.02322	−	0.407199i
$316$		0			0
$317$	−7.38145	+	1.97785i	−0.414584	+	0.111087i	−0.460081	−	0.887877i	$-0.652180\pi$
$317$	−7.38145	+	1.97785i	−0.414584	+	0.111087i	0.0454970	+	0.998964i	$0.485513\pi$
$318$		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
$325$	−20.4253	−	2.14775i	−1.13299	−	0.119135i
$326$		0			0
$327$	9.15200	+	34.1557i	0.506107	+	1.88882i
$328$		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
$333$	−3.31003	−	0.886919i	−0.181388	−	0.0486029i
$334$		0			0
$335$	12.8466	−	1.01075i	0.701886	−	0.0552233i
$336$		0			0
$337$	17.3001	+	17.3001i	0.942395	+	0.942395i	0.998429	−	0.0560343i	$-0.0178456\pi$
$337$	17.3001	+	17.3001i	0.942395	+	0.942395i	−0.0560343	+	0.998429i	$0.517846\pi$
$338$		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
$343$	10.2482	−	15.4264i	0.553350	−	0.832949i
$344$		0			0
$345$	−3.57263	−	10.0895i	−0.192344	−	0.543203i
$346$		0			0
$347$	0.135275	−	0.504852i	0.00726192	−	0.0271019i	−0.962200	−	0.272345i	$-0.912201\pi$
$347$	0.135275	−	0.504852i	0.00726192	−	0.0271019i	0.969462	+	0.245243i	$0.0788676\pi$
$348$		0			0
$349$	−20.3880			−1.09134			−0.545671	−	0.837999i	$-0.683725\pi$
$349$	−20.3880			−1.09134			−0.545671	+	0.837999i	$0.683725\pi$
$350$		0			0
$351$	−3.13327			−0.167242
$352$		0			0
$353$	−3.39007	+	12.6519i	−0.180435	+	0.673393i	0.815127	+	0.579283i	$0.196667\pi$
$353$	−3.39007	+	12.6519i	−0.180435	+	0.673393i	−0.995562	+	0.0941102i	$0.969999\pi$
$354$		0			0
$355$	−0.509901	−	1.44002i	−0.0270627	−	0.0764284i
$356$		0			0
$357$	34.5269	+	30.2250i	1.82736	+	1.59968i
$358$		0			0
$359$	−24.9508	−	14.4053i	−1.31685	−	0.760284i	−0.333630	−	0.942704i	$-0.608274\pi$
$359$	−24.9508	−	14.4053i	−1.31685	−	0.760284i	−0.983221	+	0.182420i	$0.941607\pi$
$360$		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
$367$	−10.6839	−	2.86273i	−0.557693	−	0.149433i	−0.0310469	−	0.999518i	$-0.509884\pi$
$367$	−10.6839	−	2.86273i	−0.557693	−	0.149433i	−0.526646	+	0.850084i	$0.676551\pi$
$368$		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
$373$	−1.08617	−	4.05366i	−0.0562400	−	0.209891i	0.932088	−	0.362232i	$-0.117985\pi$
$373$	−1.08617	−	4.05366i	−0.0562400	−	0.209891i	−0.988328	+	0.152342i	$0.951319\pi$
$374$		0			0
$375$	20.3633	−	19.3213i	1.05156	−	0.997749i
$376$		0			0
$377$	−1.63781	+	1.63781i	−0.0843513	+	0.0843513i
$378$		0			0
$379$		−	13.8555i		−	0.711708i	−0.934542	−	0.355854i	$-0.884190\pi$
$379$		−	13.8555i		−	0.711708i	0.934542	−	0.355854i	$-0.115810\pi$
$380$		0			0
$381$	23.8549	−	13.7727i	1.22213	−	0.705595i
$382$		0			0
$383$	−12.2435	+	3.28064i	−0.625614	+	0.167633i	−0.557678	−	0.830057i	$-0.688308\pi$
$383$	−12.2435	+	3.28064i	−0.625614	+	0.167633i	−0.0679352	+	0.997690i	$0.521641\pi$
$384$		0			0
$385$	−13.6653	−	17.3035i	−0.696446	−	0.881866i
$386$		0			0
$387$	34.0078	−	9.11237i	1.72872	−	0.463208i
$388$		0			0
$389$	−27.9033	+	16.1100i	−1.41476	+	0.816809i	−0.995831	−	0.0912123i	$-0.970926\pi$
$389$	−27.9033	+	16.1100i	−1.41476	+	0.816809i	−0.418924	+	0.908022i	$0.637592\pi$
$390$		0			0
$391$			13.1697i			0.666023i
$392$		0			0
$393$	−7.79866	+	7.79866i	−0.393390	+	0.393390i
$394$		0			0
$395$	1.30160	−	7.02189i	0.0654906	−	0.353310i
$396$		0			0
$397$	−6.93413	−	25.8785i	−0.348014	−	1.29881i	−0.889052	−	0.457807i	$-0.848635\pi$
$397$	−6.93413	−	25.8785i	−0.348014	−	1.29881i	0.541038	−	0.840998i	$-0.318032\pi$
$398$		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
$403$	−14.6837	−	3.93447i	−0.731445	−	0.195990i
$404$		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	$0.0320431\pi$
$409$	11.8208	+	20.4742i	0.584501	+	1.01239i	−0.410436	+	0.911889i	$0.634624\pi$
$410$		0			0
$411$	−15.3951	−	8.88835i	−0.759383	−	0.438430i
$412$		0			0
$413$	31.9592	−	10.8804i	1.57261	−	0.535390i
$414$		0			0
$415$	−1.96146	+	4.11205i	−0.0962845	+	0.201853i
$416$		0			0
$417$	6.29199	−	23.4820i	0.308120	−	1.14992i
$418$		0			0
$419$	1.35275			0.0660862			0.0330431	−	0.999454i	$-0.489480\pi$
$419$	1.35275			0.0660862			0.0330431	+	0.999454i	$0.489480\pi$
$420$		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
$423$	−0.481520	+	1.79706i	−0.0234123	+	0.0873760i
$424$		0			0
$425$	−31.5538	+	14.0469i	−1.53058	+	0.681375i
$426$		0			0
$427$	−16.1076	+	18.4002i	−0.779503	+	0.890449i
$428$		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	$-0.346063\pi$
$433$	−8.74688	−	8.74688i	−0.420348	−	0.420348i	−0.885324	+	0.464976i	$0.846063\pi$
$434$		0			0
$435$	−0.248309	−	3.15601i	−0.0119055	−	0.151319i
$436$		0			0
$437$	6.10273	+	1.63522i	0.291933	+	0.0782233i
$438$		0			0
$439$	10.5117	−	18.2067i	0.501695	−	0.868960i	−0.498304	−	0.867003i	$-0.666043\pi$
$439$	10.5117	−	18.2067i	0.501695	−	0.868960i	0.999998	−	0.00195777i	$-0.000623177\pi$
$440$		0			0
$441$	14.1113	+	18.3226i	0.671965	+	0.872504i
$442$		0			0
$443$	−10.1792	−	37.9894i	−0.483629	−	1.80493i	−0.586156	−	0.810198i	$-0.699359\pi$
$443$	−10.1792	−	37.9894i	−0.483629	−	1.80493i	0.102527	−	0.994730i	$-0.467307\pi$
$444$		0			0
$445$	−5.55904	−	1.03044i	−0.263524	−	0.0488475i
$446$		0			0
$447$	−12.7401	+	12.7401i	−0.602585	+	0.602585i
$448$		0			0
$449$		−	40.8069i		−	1.92580i	−0.269863	−	0.962899i	$-0.586979\pi$
$449$		−	40.8069i		−	1.92580i	0.269863	−	0.962899i	$-0.413021\pi$
$450$		0			0
$451$	25.4561	−	14.6971i	1.19868	−	0.692058i
$452$		0			0
$453$	−17.0824	+	4.57722i	−0.802602	+	0.215057i
$454$		0			0
$455$	19.4837	+	14.5229i	0.913409	+	0.680843i
$456$		0			0
$457$	−16.7691	+	4.49326i	−0.784425	+	0.210186i	−0.628735	−	0.777620i	$-0.716427\pi$
$457$	−16.7691	+	4.49326i	−0.784425	+	0.210186i	−0.155690	+	0.987806i	$0.549760\pi$
$458$		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	−0.998904	−	0.0468014i	$-0.985097\pi$
$463$	−20.4868	+	20.4868i	−0.952103	+	0.952103i	0.0468014	+	0.998904i	$0.485097\pi$
$464$		0			0
$465$	17.1235	−	11.7680i	0.794082	−	0.545730i
$466$		0			0
$467$	−2.95367	−	11.0233i	−0.136680	−	0.510095i	−0.999985	−	0.00541398i	$-0.998277\pi$
$467$	−2.95367	−	11.0233i	−0.136680	−	0.510095i	0.863306	−	0.504681i	$-0.168390\pi$
$468$		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
$473$	38.3631	+	10.2794i	1.76394	+	0.472646i
$474$		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	0.998987	−	0.0449948i	$-0.0143271\pi$
$479$	10.0791	+	17.4576i	0.460527	+	0.797656i	−0.538460	+	0.842651i	$0.680994\pi$
$480$		0			0
$481$	3.68968	+	2.13024i	0.168235	+	0.0971305i
$482$		0			0
$483$	−2.45966	+	12.4233i	−0.111918	+	0.565278i
$484$		0			0
$485$	11.3892	+	5.43268i	0.517155	+	0.246685i
$486$		0			0
$487$	−2.02938	+	7.57376i	−0.0919601	+	0.343200i	−0.996541	−	0.0831022i	$-0.973517\pi$
$487$	−2.02938	+	7.57376i	−0.0919601	+	0.343200i	0.904581	+	0.426302i	$0.140184\pi$
$488$		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
$493$	−1.00816	+	3.76251i	−0.0454053	+	0.169455i
$494$		0			0
$495$	25.9538	−	9.19006i	1.16654	−	0.413062i
$496$		0			0
$497$	−0.351053	+	1.77310i	−0.0157469	+	0.0795344i
$498$		0			0
$499$	13.6472	+	7.87922i	0.610933	+	0.352722i	0.773331	−	0.634003i	$-0.218589\pi$
$499$	13.6472	+	7.87922i	0.610933	+	0.352722i	−0.162398	+	0.986725i	$0.551923\pi$
$500$		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	$-0.278227\pi$
$503$	−2.80892	−	2.80892i	−0.125244	−	0.125244i	−0.766950	+	0.641707i	$0.778227\pi$
$504$		0			0
$505$	22.5964	+	19.3000i	1.00552	+	0.858840i
$506$		0			0
$507$	9.39089	+	2.51628i	0.417064	+	0.111752i
$508$		0			0
$509$	−1.79044	+	3.10113i	−0.0793597	+	0.137455i	−0.902974	−	0.429695i	$-0.858621\pi$
$509$	−1.79044	+	3.10113i	−0.0793597	+	0.137455i	0.823614	+	0.567151i	$0.191954\pi$
$510$		0			0
$511$	28.5328	+	14.0393i	1.26222	+	0.621062i
$512$		0			0
$513$	0.654266	+	2.44175i	0.0288866	+	0.107806i
$514$		0			0
$515$	1.19365	+	1.73686i	0.0525985	+	0.0765350i
$516$		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
$523$	−5.15843	+	1.38220i	−0.225562	+	0.0604392i	−0.369830	−	0.929099i	$-0.620584\pi$
$523$	−5.15843	+	1.38220i	−0.225562	+	0.0604392i	0.144268	+	0.989539i	$0.453917\pi$
$524$		0			0
$525$	−32.3888	+	7.35754i	−1.41356	+	0.321109i
$526$		0			0
$527$	−24.6940	+	6.61673i	−1.07569	+	0.288229i
$528$		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
$535$	10.1230	+	14.7298i	0.437655	+	0.636823i
$536$		0			0
$537$	−11.6569	−	43.5041i	−0.503032	−	1.87734i
$538$		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
$543$	−60.2519	−	16.1444i	−2.58566	−	0.692824i
$544$		0			0
$545$	23.9464	+	20.4531i	1.02575	+	0.876115i
$546$		0			0
$547$	−7.51763	−	7.51763i	−0.321431	−	0.321431i	0.527885	−	0.849316i	$-0.322985\pi$
$547$	−7.51763	−	7.51763i	−0.321431	−	0.321431i	−0.849316	+	0.527885i	$0.822985\pi$
$548$		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
$553$	−5.56578	+	6.35796i	−0.236681	+	0.270368i
$554$		0			0
$555$	−5.48920	+	1.94368i	−0.233003	+	0.0825048i
$556$		0			0
$557$	9.75133	−	36.3925i	0.413177	−	1.54200i	−0.375282	−	0.926911i	$-0.622454\pi$
$557$	9.75133	−	36.3925i	0.413177	−	1.54200i	0.788459	−	0.615087i	$-0.210879\pi$
$558$		0			0
$559$	−43.7729			−1.85140
$560$		0			0
$561$	−64.6391			−2.72906
$562$		0			0
$563$	1.70918	−	6.37876i	0.0720334	−	0.268832i	−0.920511	−	0.390717i	$-0.872227\pi$
$563$	1.70918	−	6.37876i	0.0720334	−	0.268832i	0.992544	+	0.121885i	$0.0388938\pi$
$564$		0			0
$565$	−9.02792	−	4.30636i	−0.379808	−	0.181170i
$566$		0			0
$567$	20.0273	−	6.81821i	0.841067	−	0.286338i
$568$		0			0
$569$	25.6304	+	14.7977i	1.07448	+	0.620352i	0.929402	−	0.369068i	$-0.120323\pi$
$569$	25.6304	+	14.7977i	1.07448	+	0.620352i	0.145079	+	0.989420i	$0.453656\pi$
$570$		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
$577$	−27.3514	−	7.32878i	−1.13865	−	0.305101i	−0.360243	−	0.932858i	$-0.617306\pi$
$577$	−27.3514	−	7.32878i	−1.13865	−	0.305101i	−0.778409	+	0.627757i	$0.783973\pi$
$578$		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
$583$	1.78747	+	6.67093i	0.0740294	+	0.276282i
$584$		0			0
$585$	−25.0085	+	17.1870i	−1.03397	+	0.710596i
$586$		0			0
$587$	−0.913148	+	0.913148i	−0.0376897	+	0.0376897i	−0.725700	−	0.688011i	$-0.758484\pi$
$587$	−0.913148	+	0.913148i	−0.0376897	+	0.0376897i	0.688011	+	0.725700i	$0.258484\pi$
$588$		0			0
$589$			12.2645i			0.505350i
$590$		0			0
$591$	14.0079	−	8.08749i	0.576210	−	0.332675i
$592$		0			0
$593$	2.39623	−	0.642069i	0.0984015	−	0.0263666i	−0.209282	−	0.977855i	$-0.567113\pi$
$593$	2.39623	−	0.642069i	0.0984015	−	0.0263666i	0.307684	+	0.951489i	$0.400446\pi$
$594$		0			0
$595$	40.5882	+	4.76830i	1.66396	+	0.195481i
$596$		0			0
$597$	32.2473	−	8.64063i	1.31979	−	0.353637i
$598$		0			0
$599$	7.27210	−	4.19855i	0.297130	−	0.171548i	−0.344023	−	0.938961i	$-0.611790\pi$
$599$	7.27210	−	4.19855i	0.297130	−	0.171548i	0.641153	+	0.767413i	$0.278456\pi$
$600$		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
$605$	6.35392	+	1.17778i	0.258323	+	0.0478836i
$606$		0			0
$607$	3.62709	+	13.5365i	0.147219	+	0.549429i	0.999647	+	0.0265835i	$0.00846278\pi$
$607$	3.62709	+	13.5365i	0.147219	+	0.549429i	−0.852428	+	0.522845i	$0.824871\pi$
$608$		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
$613$	10.0636	+	2.69654i	0.406465	+	0.108912i	0.456258	−	0.889848i	$-0.349189\pi$
$613$	10.0636	+	2.69654i	0.406465	+	0.108912i	−0.0497928	+	0.998760i	$0.515856\pi$
$614$		0			0
$615$	−3.47306	−	44.1425i	−0.140047	−	1.78000i
$616$		0			0
$617$	3.40085	+	3.40085i	0.136913	+	0.136913i	0.772242	−	0.635329i	$-0.219135\pi$
$617$	3.40085	+	3.40085i	0.136913	+	0.136913i	−0.635329	+	0.772242i	$0.719135\pi$
$618$		0			0
$619$	4.43441	+	7.68063i	0.178234	+	0.308711i	0.941276	−	0.337639i	$-0.109628\pi$
$619$	4.43441	+	7.68063i	0.178234	+	0.308711i	−0.763042	+	0.646349i	$0.776295\pi$
$620$		0			0
$621$	−1.25944	−	0.727138i	−0.0505396	−	0.0291790i
$622$		0			0
$623$	5.03342	+	4.40628i	0.201660	+	0.176534i
$624$		0			0
$625$	5.20007	−	24.4532i	0.208003	−	0.978128i
$626$		0			0
$627$	−8.02591	+	29.9531i	−0.320524	+	1.19621i
$628$		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
$633$	9.24348	−	34.4971i	0.367395	−	1.37114i
$634$		0			0
$635$	10.5618	−	22.1419i	0.419131	−	0.878673i
$636$		0			0
$637$	−11.0506	−	26.5448i	−0.437839	−	1.05174i
$638$		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	$-0.217230\pi$
$643$	3.68541	+	3.68541i	0.145338	+	0.145338i	−0.630694	+	0.776032i	$0.717230\pi$
$644$		0			0
$645$	38.8564	−	45.4928i	1.52997	−	1.79128i
$646$		0			0
$647$	22.7647	+	6.09978i	0.894973	+	0.239807i	0.676856	−	0.736116i	$-0.263342\pi$
$647$	22.7647	+	6.09978i	0.894973	+	0.239807i	0.218117	+	0.975923i	$0.430009\pi$
$648$		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
$653$	−9.82740	−	36.6764i	−0.384576	−	1.43526i	−0.838834	−	0.544387i	$-0.816762\pi$
$653$	−9.82740	−	36.6764i	−0.384576	−	1.43526i	0.454258	−	0.890870i	$-0.349904\pi$
$654$		0			0
$655$	−1.79022	+	9.65789i	−0.0699496	+	0.377365i
$656$		0			0
$657$	−28.0786	+	28.0786i	−1.09545	+	1.09545i
$658$		0			0
$659$			23.0353i			0.897327i	0.893701	+	0.448663i	$0.148100\pi$
$659$			23.0353i			0.897327i	−0.893701	+	0.448663i	$0.851900\pi$
$660$		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
$663$	68.8136	−	18.4386i	2.67250	−	0.716094i
$664$		0			0
$665$	7.24923	−	18.2161i	0.281113	−	0.706392i
$666$		0			0
$667$	−1.03841	+	0.278241i	−0.0402074	+	0.0107736i
$668$		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	0.0483701	−	0.998829i	$-0.484597\pi$
$673$	27.1667	−	27.1667i	1.04720	−	1.04720i	0.998829	−	0.0483701i	$-0.0154027\pi$
$674$		0			0
$675$	0.398849	−	3.79310i	0.0153517	−	0.145997i
$676$		0			0
$677$	12.2786	+	45.8245i	0.471907	+	1.76118i	0.632910	+	0.774226i	$0.281860\pi$
$677$	12.2786	+	45.8245i	0.471907	+	1.76118i	−0.161003	+	0.986954i	$0.551473\pi$
$678$		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
$683$	35.2881	+	9.45542i	1.35026	+	0.361801i	0.860231	−	0.509904i	$-0.170319\pi$
$683$	35.2881	+	9.45542i	1.35026	+	0.361801i	0.490030	+	0.871705i	$0.336986\pi$
$684$		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
$693$	−31.9570	−	6.32710i	−1.21395	−	0.240347i
$694$		0			0
$695$	−7.22673	−	20.4091i	−0.274125	−	0.774163i
$696$		0			0
$697$	−14.1010	+	52.6256i	−0.534113	+	1.99334i
$698$		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
$703$	0.889640	−	3.32018i	0.0335534	−	0.125223i
$704$		0			0
$705$	1.05525	+	2.98016i	0.0397431	+	0.112239i
$706$		0			0
$707$	−11.3319	−	33.2853i	−0.426178	−	1.25182i
$708$		0			0
$709$	28.2236	+	16.2949i	1.05996	+	0.611968i	0.925421	−	0.378940i	$-0.123711\pi$
$709$	28.2236	+	16.2949i	1.05996	+	0.611968i	0.134539	+	0.990908i	$0.457045\pi$
$710$		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
$717$	−24.9796	−	6.69326i	−0.932880	−	0.249965i
$718$		0			0
$719$	0.555682	−	0.962469i	0.0207234	−	0.0358940i	−0.855478	−	0.517840i	$-0.826736\pi$
$719$	0.555682	−	0.962469i	0.0207234	−	0.0358940i	0.876201	+	0.481946i	$0.160070\pi$
$720$		0			0
$721$	−0.165302	−	2.48812i	−0.00615617	−	0.0926624i
$722$		0			0
$723$	−8.43084	−	31.4643i	−0.313546	−	1.17017i
$724$		0			0
$725$	−1.77422	−	2.19119i	−0.0658929	−	0.0813787i
$726$		0			0
$727$	17.4058	−	17.4058i	0.645545	−	0.645545i	−0.306368	−	0.951913i	$-0.599114\pi$
$727$	17.4058	−	17.4058i	0.645545	−	0.645545i	0.951913	+	0.306368i	$0.0991138\pi$
$728$		0			0
$729$			32.1637i			1.19125i
$730$		0			0
$731$	−63.7519	+	36.8071i	−2.35795	+	1.36136i
$732$		0			0
$733$	20.7406	−	5.55744i	0.766073	−	0.205269i	0.145437	−	0.989367i	$-0.453541\pi$
$733$	20.7406	−	5.55744i	0.766073	−	0.205269i	0.620636	+	0.784099i	$0.286874\pi$
$734$		0			0
$735$	37.3971	+	12.0785i	1.37941	+	0.445523i
$736$		0			0
$737$	20.7462	−	5.55893i	0.764196	−	0.204766i
$738$		0			0
$739$	−19.1855	+	11.0767i	−0.705750	+	0.407465i	−0.809485	−	0.587140i	$-0.800254\pi$
$739$	−19.1855	+	11.0767i	−0.705750	+	0.407465i	0.103736	+	0.994605i	$0.466920\pi$
$740$		0			0
$741$		−	34.1770i		−	1.25552i
$742$		0			0
$743$	−15.3901	+	15.3901i	−0.564607	+	0.564607i	−0.930613	−	0.366006i	$-0.880725\pi$
$743$	−15.3901	+	15.3901i	−0.564607	+	0.564607i	0.366006	+	0.930613i	$0.380725\pi$
$744$		0			0
$745$	−2.92454	+	15.7774i	−0.107147	+	0.578038i
$746$		0			0
$747$	1.74222	+	6.50204i	0.0637443	+	0.237897i
$748$		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
$753$	30.4700	+	8.16440i	1.11039	+	0.297527i
$754$		0			0
$755$	−10.2293	+	11.9764i	−0.372281	+	0.435865i
$756$		0			0
$757$	−4.00848	−	4.00848i	−0.145691	−	0.145691i	0.630499	−	0.776190i	$-0.282850\pi$
$757$	−4.00848	−	4.00848i	−0.145691	−	0.145691i	−0.776190	+	0.630499i	$0.782850\pi$
$758$		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
$763$	−12.0089	−	35.2739i	−0.434750	−	1.27700i
$764$		0			0
$765$	−21.9710	+	46.0603i	−0.794362	+	1.66531i
$766$		0			0
$767$	13.5657	−	50.6280i	0.489830	−	1.82807i
$768$		0			0
$769$	−17.2755			−0.622969			−0.311484	−	0.950251i	$-0.600826\pi$
$769$	−17.2755			−0.622969			−0.311484	+	0.950251i	$0.600826\pi$
$770$		0			0
$771$	50.3520			1.81338
$772$		0			0
$773$	−2.04746	+	7.64124i	−0.0736422	+	0.274836i	−0.992922	−	0.118768i	$-0.962105\pi$
$773$	−2.04746	+	7.64124i	−0.0736422	+	0.274836i	0.919280	+	0.393605i	$0.128772\pi$
$774$		0			0
$775$	6.63218	−	17.2750i	0.238235	−	0.620537i
$776$		0			0
$777$	6.75886	+	1.33817i	0.242473	+	0.0480067i
$778$		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
$787$	15.8744	+	4.25353i	0.565861	+	0.151622i	0.530398	−	0.847749i	$-0.322043\pi$
$787$	15.8744	+	4.25353i	0.565861	+	0.151622i	0.0354635	+	0.999371i	$0.488709\pi$
$788$		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
$793$	9.82637	+	36.6725i	0.348944	+	1.30228i
$794$		0			0
$795$	10.2292	+	1.89612i	0.362793	+	0.0672485i
$796$		0			0
$797$	−32.0830	+	32.0830i	−1.13644	+	1.13644i	−0.147354	+	0.989084i	$0.547076\pi$
$797$	−32.0830	+	32.0830i	−1.13644	+	1.13644i	−0.989084	+	0.147354i	$0.952924\pi$
$798$		0			0
$799$		−	3.88996i		−	0.137617i
$800$		0			0
$801$	−7.23430	+	4.17673i	−0.255612	+	0.147577i
$802$		0			0
$803$	−43.2682	+	11.5937i	−1.52690	+	0.409132i
$804$		0			0
$805$	4.46127	+	10.3591i	0.157239	+	0.365112i
$806$		0			0
$807$	−7.80057	+	2.09016i	−0.274593	+	0.0735770i
$808$		0			0
$809$	25.4551	−	14.6965i	0.894955	−	0.516702i	0.0193950	−	0.999812i	$-0.493826\pi$
$809$	25.4551	−	14.6965i	0.894955	−	0.516702i	0.875560	+	0.483109i	$0.160493\pi$
$810$		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
$815$	43.6341	−	29.9874i	1.52843	−	1.05041i
$816$		0			0
$817$	9.14032	+	34.1122i	0.319779	+	1.19343i
$818$		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
$823$	13.7576	+	3.68634i	0.479560	+	0.128498i	0.490498	−	0.871442i	$-0.336815\pi$
$823$	13.7576	+	3.68634i	0.479560	+	0.128498i	−0.0109378	+	0.999940i	$0.503482\pi$
$824$		0			0
$825$	27.5023	−	37.8499i	0.957507	−	1.31777i
$826$		0			0
$827$	13.3153	+	13.3153i	0.463018	+	0.463018i	0.899643	−	0.436625i	$-0.143826\pi$
$827$	13.3153	+	13.3153i	0.463018	+	0.463018i	−0.436625	+	0.899643i	$0.643826\pi$
$828$		0			0
$829$	−5.93159	−	10.2738i	−0.206013	−	0.356824i	0.744442	−	0.667687i	$-0.232715\pi$
$829$	−5.93159	−	10.2738i	−0.206013	−	0.356824i	−0.950455	+	0.310863i	$0.899382\pi$
$830$		0			0
$831$	21.7742	+	12.5713i	0.755337	+	0.436094i
$832$		0			0
$833$	−38.4148	−	29.3683i	−1.33100	−	1.01755i
$834$		0			0
$835$	−35.0742	−	16.7305i	−1.21379	−	0.578983i
$836$		0			0
$837$	0.730656	−	2.72684i	0.0252552	−	0.0942535i
$838$		0			0
$839$	−25.5847			−0.883281			−0.441641	−	0.897192i	$-0.645603\pi$
$839$	−25.5847			−0.883281			−0.441641	+	0.897192i	$0.645603\pi$
$840$		0			0
$841$	28.6820			0.989036
$842$		0			0
$843$	−10.1974	+	38.0571i	−0.351216	+	1.31076i
$844$		0			0
$845$	8.16199	−	2.89010i	0.280781	−	0.0994224i
$846$		0			0
$847$	−5.75314	−	5.03632i	−0.197680	−	0.173050i
$848$		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	$-0.236307\pi$
$853$	1.77628	+	1.77628i	0.0608187	+	0.0608187i	−0.676043	+	0.736862i	$0.736307\pi$
$854$		0			0
$855$	18.6159	+	15.9002i	0.636650	+	0.543776i
$856$		0			0
$857$	−31.2645	−	8.37730i	−1.06798	−	0.286163i	−0.318314	−	0.947985i	$-0.603117\pi$
$857$	−31.2645	−	8.37730i	−1.06798	−	0.286163i	−0.749661	+	0.661822i	$0.769783\pi$
$858$		0			0
$859$	28.2878	−	48.9959i	0.965168	−	1.67172i	0.256003	−	0.966676i	$-0.417594\pi$
$859$	28.2878	−	48.9959i	0.965168	−	1.67172i	0.709164	−	0.705043i	$-0.249072\pi$
$860$		0			0
$861$	−23.1304	+	47.0091i	−0.788281	+	1.60207i
$862$		0			0
$863$	13.4786	+	50.3027i	0.458816	+	1.71232i	0.676622	+	0.736331i	$0.263443\pi$
$863$	13.4786	+	50.3027i	0.458816	+	1.71232i	−0.217806	+	0.975992i	$0.569890\pi$
$864$		0			0
$865$	16.3795	+	23.8335i	0.556919	+	0.810362i
$866$		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
$873$	18.0087	−	4.82542i	0.609503	−	0.163316i
$874$		0			0
$875$	−20.0614	+	21.7380i	−0.678199	+	0.734879i
$876$		0			0
$877$	3.83607	−	1.02787i	0.129535	−	0.0347088i	−0.193469	−	0.981106i	$-0.561974\pi$
$877$	3.83607	−	1.02787i	0.129535	−	0.0347088i	0.323004	+	0.946398i	$0.395307\pi$
$878$		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	−0.766560	−	0.642173i	$-0.778033\pi$
$883$	−3.69618	+	3.69618i	−0.124387	+	0.124387i	0.642173	+	0.766560i	$0.278033\pi$
$884$		0			0
$885$	40.5752	+	59.0402i	1.36392	+	1.98462i
$886$		0			0
$887$	−5.02913	−	18.7690i	−0.168862	−	0.630200i	−0.997516	−	0.0704398i	$-0.977560\pi$
$887$	−5.02913	−	18.7690i	−0.168862	−	0.630200i	0.828654	−	0.559761i	$-0.189107\pi$
$888$		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
$893$	−1.80257	−	0.482997i	−0.0603207	−	0.0161629i
$894$		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
$903$	−67.0127	+	22.8142i	−2.23004	+	0.759209i
$904$		0			0
$905$	−52.3673	+	18.5429i	−1.74075	+	0.616386i
$906$		0			0
$907$	−12.0980	+	45.1505i	−0.401709	+	1.49920i	0.408337	+	0.912831i	$0.366109\pi$
$907$	−12.0980	+	45.1505i	−0.401709	+	1.49920i	−0.810046	+	0.586367i	$0.800558\pi$
$908$		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
$913$	−1.96533	+	7.33473i	−0.0650431	+	0.242744i
$914$		0			0
$915$	−46.8361	−	22.3410i	−1.54835	−	0.738571i
$916$		0			0
$917$	7.65517	−	8.74472i	0.252796	−	0.288776i
$918$		0			0
$919$	−6.80127	−	3.92672i	−0.224353	−	0.129530i	0.383611	−	0.923495i	$-0.374680\pi$
$919$	−6.80127	−	3.92672i	−0.224353	−	0.129530i	−0.607964	+	0.793964i	$0.708014\pi$
$920$		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
$927$	3.00772	+	0.805917i	0.0987866	+	0.0264698i
$928$		0			0
$929$	13.2493	−	22.9485i	0.434696	−	0.752916i	−0.562575	−	0.826747i	$-0.690189\pi$
$929$	13.2493	−	22.9485i	0.434696	−	0.752916i	0.997271	+	0.0738305i	$0.0235224\pi$
$930$		0			0
$931$	−18.3788	+	14.1545i	−0.602341	+	0.463896i
$932$		0			0
$933$	−0.000366053	−	0.00136613i	−1.19841e−5	−	4.47251e-5i
$934$		0			0
$935$	−47.4437	+	32.6056i	−1.55158	+	1.06632i
$936$		0			0
$937$	37.0373	−	37.0373i	1.20995	−	1.20995i	0.238914	−	0.971041i	$-0.423208\pi$
$937$	37.0373	−	37.0373i	1.20995	−	1.20995i	0.971041	−	0.238914i	$-0.0767915\pi$
$938$		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
$943$	−14.5241	+	3.89171i	−0.472969	+	0.126732i
$944$		0			0
$945$	−2.69699	+	3.61824i	−0.0877330	+	0.117701i
$946$		0			0
$947$	−22.6564	+	6.07076i	−0.736233	+	0.197273i	−0.607403	−	0.794394i	$-0.707789\pi$
$947$	−22.6564	+	6.07076i	−0.736233	+	0.197273i	−0.128830	+	0.991667i	$0.541122\pi$
$948$		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	−0.916227	−	0.400658i	$-0.868781\pi$
$953$	−15.9160	+	15.9160i	−0.515569	+	0.515569i	0.400658	+	0.916227i	$0.368781\pi$
$954$		0			0
$955$	45.5600	+	8.44513i	1.47429	+	0.273278i
$956$		0			0
$957$	−1.36565	−	5.09668i	−0.0441452	−	0.164752i
$958$		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
$963$	25.5076	+	6.83474i	0.821971	+	0.220246i
$964$		0			0
$965$	2.55963	+	32.5328i	0.0823973	+	1.04727i
$966$		0			0
$967$	−20.3556	−	20.3556i	−0.654591	−	0.654591i	0.299504	−	0.954095i	$-0.403179\pi$
$967$	−20.3556	−	20.3556i	−0.654591	−	0.654591i	−0.954095	+	0.299504i	$0.903179\pi$
$968$		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
$973$	−4.97541	+	25.1298i	−0.159504	+	0.805625i
$974$		0			0
$975$	−18.4816	+	48.1395i	−0.591885	+	1.54170i
$976$		0			0
$977$	−4.58835	+	17.1240i	−0.146794	+	0.547844i	0.852875	+	0.522116i	$0.174857\pi$
$977$	−4.58835	+	17.1240i	−0.146794	+	0.547844i	−0.999669	+	0.0257283i	$0.991810\pi$
$978$		0			0
$979$	−9.42325			−0.301168
$980$		0			0
$981$	46.5301			1.48559
$982$		0			0
$983$	−10.5466	+	39.3603i	−0.336383	+	1.25540i	0.565979	+	0.824420i	$0.308498\pi$
$983$	−10.5466	+	39.3603i	−0.336383	+	1.25540i	−0.902362	+	0.430979i	$0.858168\pi$
$984$		0			0
$985$	6.20201	−	13.0020i	0.197613	−	0.414279i
$986$		0			0
$987$	0.726512	−	3.66948i	0.0231251	−	0.116801i
$988$		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
$997$	23.8526	+	6.39130i	0.755421	+	0.202414i	0.615921	−	0.787808i	$-0.288784\pi$
$997$	23.8526	+	6.39130i	0.755421	+	0.202414i	0.139500	+	0.990222i	$0.455451\pi$
$998$		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.117.4	yes	16
3.2	odd	2		1260.2.dq.a.397.3		16
4.3	odd	2		560.2.ci.d.257.1		16
5.2	odd	4		700.2.bc.b.593.1		16
5.3	odd	4	inner	140.2.u.a.33.4	yes	16
5.4	even	2		700.2.bc.b.257.1		16
7.2	even	3		980.2.m.a.97.7		16
7.3	odd	6	inner	140.2.u.a.17.4	✓	16
7.4	even	3		980.2.v.a.717.1		16
7.5	odd	6		980.2.m.a.97.2		16
7.6	odd	2		980.2.v.a.117.1		16
15.8	even	4		1260.2.dq.a.1153.4		16
20.3	even	4		560.2.ci.d.33.1		16
21.17	even	6		1260.2.dq.a.577.4		16
28.3	even	6		560.2.ci.d.17.1		16
35.3	even	12	inner	140.2.u.a.73.4	yes	16
35.13	even	4		980.2.v.a.313.1		16
35.17	even	12		700.2.bc.b.493.1		16
35.18	odd	12		980.2.v.a.913.1		16
35.23	odd	12		980.2.m.a.293.2		16
35.24	odd	6		700.2.bc.b.157.1		16
35.33	even	12		980.2.m.a.293.7		16
105.38	odd	12		1260.2.dq.a.73.3		16
140.3	odd	12		560.2.ci.d.353.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.u.a.17.4	✓	16	7.3	odd	6	inner
140.2.u.a.33.4	yes	16	5.3	odd	4	inner
140.2.u.a.73.4	yes	16	35.3	even	12	inner
140.2.u.a.117.4	yes	16	1.1	even	1	trivial
560.2.ci.d.17.1		16	28.3	even	6
560.2.ci.d.33.1		16	20.3	even	4
560.2.ci.d.257.1		16	4.3	odd	2
560.2.ci.d.353.1		16	140.3	odd	12
700.2.bc.b.157.1		16	35.24	odd	6
700.2.bc.b.257.1		16	5.4	even	2
700.2.bc.b.493.1		16	35.17	even	12
700.2.bc.b.593.1		16	5.2	odd	4
980.2.m.a.97.2		16	7.5	odd	6
980.2.m.a.97.7		16	7.2	even	3
980.2.m.a.293.2		16	35.23	odd	12
980.2.m.a.293.7		16	35.33	even	12
980.2.v.a.117.1		16	7.6	odd	2
980.2.v.a.313.1		16	35.13	even	4
980.2.v.a.717.1		16	7.4	even	3
980.2.v.a.913.1		16	35.18	odd	12
1260.2.dq.a.73.3		16	105.38	odd	12
1260.2.dq.a.397.3		16	3.2	odd	2
1260.2.dq.a.577.4		16	21.17	even	6
1260.2.dq.a.1153.4		16	15.8	even	4

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)

\(f(q)\)	\(=\)	\(q+(0.649827 - 2.42519i) q^{3} +(-0.746366 - 2.10783i) q^{5} +(-0.513853 + 2.59537i) q^{7} +(-2.86119 - 1.65191i) q^{9} +O(q^{10})\)	\(q+(0.649827 - 2.42519i) q^{3} +(-0.746366 - 2.10783i) q^{5} +(-0.513853 + 2.59537i) q^{7} +(-2.86119 - 1.65191i) q^{9} +(-1.86346 - 3.22761i) q^{11} +(2.90450 + 2.90450i) q^{13} +(-5.59689 + 0.440354i) q^{15} +(6.67247 + 1.78788i) q^{17} +(1.65698 - 2.86997i) q^{19} +(5.96035 + 2.93273i) q^{21} +(0.493436 + 1.84153i) q^{23} +(-3.88588 + 3.14642i) q^{25} +(-0.539383 + 0.539383i) q^{27} +0.563886i q^{29} +(-3.20505 + 1.85044i) q^{31} +(-9.03849 + 2.42186i) q^{33} +(5.85412 - 0.853984i) q^{35} +(1.00188 - 0.268453i) q^{37} +(8.93138 - 5.15654i) q^{39} +7.88697i q^{41} +(-7.53537 + 7.53537i) q^{43} +(-1.34644 + 7.26382i) q^{45} +(-0.145747 - 0.543934i) q^{47} +(-6.47191 - 2.66728i) q^{49} +(8.67191 - 15.0202i) q^{51} +(-1.78993 - 0.479610i) q^{53} +(-5.41242 + 6.33684i) q^{55} +(-5.88346 - 5.88346i) q^{57} +(-6.38015 - 11.0507i) q^{59} +(8.00463 + 4.62147i) q^{61} +(5.75754 - 6.57701i) q^{63} +(3.95436 - 8.29000i) q^{65} +(-1.49156 + 5.56658i) q^{67} +4.78670 q^{69} +0.683178 q^{71} +(3.11079 - 11.6096i) q^{73} +(5.10552 + 11.4686i) q^{75} +(9.33440 - 3.17786i) q^{77} +(2.76589 + 1.59689i) q^{79} +(-3.99812 - 6.92495i) q^{81} +(-1.44070 - 1.44070i) q^{83} +(-1.21155 - 15.3988i) q^{85} +(1.36753 + 0.366428i) q^{87} +(1.26421 - 2.18968i) q^{89} +(-9.03074 + 6.04577i) q^{91} +(2.40493 + 8.97532i) q^{93} +(-7.28610 - 1.35057i) q^{95} +(-3.99033 + 3.99033i) q^{97} +12.3131i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5} + 2 q^{7}+O(q^{10}) \) 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

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