LMFDB - Embedded newform 700.2.p.d.451.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(451,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("700.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.4
Character	$\chi$	$=$	700.451
Dual form			700.2.p.d.551.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07322 + 0.920983i) q^{2} +(1.28534 - 2.22627i) q^{3} +(0.303582 - 1.97683i) q^{4} +(0.670911 + 3.57303i) q^{6} +(-0.304602 + 2.62816i) q^{7} +(1.49481 + 2.40115i) q^{8} +(-1.80417 - 3.12492i) q^{9} +O(q^{10})$	\(q+(-1.07322 + 0.920983i) q^{2} +(1.28534 - 2.22627i) q^{3} +(0.303582 - 1.97683i) q^{4} +(0.670911 + 3.57303i) q^{6} +(-0.304602 + 2.62816i) q^{7} +(1.49481 + 2.40115i) q^{8} +(-1.80417 - 3.12492i) q^{9} +(-5.44112 - 3.14143i) q^{11} +(-4.01073 - 3.21674i) q^{12} -3.00876i q^{13} +(-2.09358 - 3.10111i) q^{14} +(-3.81568 - 1.20026i) q^{16} +(-0.935120 - 0.539892i) q^{17} +(4.81426 + 1.69210i) q^{18} +(-3.18341 - 5.51382i) q^{19} +(5.45946 + 4.05619i) q^{21} +(8.73269 - 1.63974i) q^{22} +(-2.77450 + 1.60186i) q^{23} +(7.26694 - 0.241563i) q^{24} +(2.77101 + 3.22904i) q^{26} -1.56386 q^{27} +(5.10294 + 1.40001i) q^{28} +0.512747 q^{29} +(2.55123 - 4.41886i) q^{31} +(5.20046 - 2.22604i) q^{32} +(-13.9873 + 8.07558i) q^{33} +(1.50082 - 0.281809i) q^{34} +(-6.72514 + 2.61787i) q^{36} +(2.63332 + 4.56104i) q^{37} +(8.49461 + 2.98566i) q^{38} +(-6.69829 - 3.86726i) q^{39} -7.61555i q^{41} +(-9.59486 + 0.674906i) q^{42} +0.683409i q^{43} +(-7.86189 + 9.80246i) q^{44} +(1.50235 - 4.27441i) q^{46} +(-5.61176 - 9.71985i) q^{47} +(-7.57652 + 6.95197i) q^{48} +(-6.81444 - 1.60109i) q^{49} +(-2.40388 + 1.38788i) q^{51} +(-5.94778 - 0.913405i) q^{52} +(-1.11837 + 1.93707i) q^{53} +(1.67836 - 1.44029i) q^{54} +(-6.76593 + 3.19721i) q^{56} -16.3670 q^{57} +(-0.550288 + 0.472231i) q^{58} +(-1.62035 + 2.80652i) q^{59} +(2.28536 - 1.31945i) q^{61} +(1.33167 + 7.09203i) q^{62} +(8.76234 - 3.78980i) q^{63} +(-3.53107 + 7.17855i) q^{64} +(7.57394 - 21.5489i) q^{66} +(6.55453 + 3.78426i) q^{67} +(-1.35116 + 1.68467i) q^{68} +8.23571i q^{69} +13.2136i q^{71} +(4.80651 - 9.00327i) q^{72} +(-2.18683 - 1.26257i) q^{73} +(-7.02675 - 2.46974i) q^{74} +(-11.8663 + 4.61914i) q^{76} +(9.91356 - 13.3432i) q^{77} +(10.7504 - 2.01861i) q^{78} +(9.18163 - 5.30102i) q^{79} +(3.40244 - 5.89319i) q^{81} +(7.01379 + 8.17313i) q^{82} +1.37443 q^{83} +(9.67578 - 9.56102i) q^{84} +(-0.629408 - 0.733445i) q^{86} +(0.659051 - 1.14151i) q^{87} +(-0.590394 - 17.7608i) q^{88} +(-7.79161 + 4.49849i) q^{89} +(7.90749 + 0.916474i) q^{91} +(2.32431 + 5.97101i) q^{92} +(-6.55838 - 11.3594i) q^{93} +(14.9744 + 5.26316i) q^{94} +(1.72859 - 14.4388i) q^{96} -7.56469i q^{97} +(8.78793 - 4.55767i) q^{98} +22.6707i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} + q^{4} - 4 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q - q^2 + q^4 - 4 * q^8 - 16 * q^9	$ 32 q - q^{2} + q^{4} - 4 q^{8} - 16 q^{9} + 15 q^{12} - 13 q^{14} + q^{16} - 15 q^{18} + 12 q^{21} + 34 q^{22} - 18 q^{24} - 15 q^{26} + 17 q^{28} + 8 q^{29} + 14 q^{32} - 30 q^{36} - 16 q^{37} + 30 q^{38} + q^{42} + 12 q^{44} + 2 q^{46} + 20 q^{49} + 18 q^{52} - 20 q^{53} + 57 q^{54} - 31 q^{56} - 24 q^{57} - 4 q^{58} - 12 q^{61} + 40 q^{64} - 66 q^{66} + 15 q^{68} + 13 q^{72} - 72 q^{73} - q^{74} + 8 q^{77} + 60 q^{78} - 36 q^{81} - 66 q^{82} + 67 q^{84} + 4 q^{86} + 34 q^{88} - 60 q^{89} - 148 q^{92} - 20 q^{93} + 45 q^{94} + 93 q^{96}+O(q^{100}) $ 32 * q - q^2 + q^4 - 4 * q^8 - 16 * q^9 + 15 * q^12 - 13 * q^14 + q^16 - 15 * q^18 + 12 * q^21 + 34 * q^22 - 18 * q^24 - 15 * q^26 + 17 * q^28 + 8 * q^29 + 14 * q^32 - 30 * q^36 - 16 * q^37 + 30 * q^38 + q^42 + 12 * q^44 + 2 * q^46 + 20 * q^49 + 18 * q^52 - 20 * q^53 + 57 * q^54 - 31 * q^56 - 24 * q^57 - 4 * q^58 - 12 * q^61 + 40 * q^64 - 66 * q^66 + 15 * q^68 + 13 * q^72 - 72 * q^73 - q^74 + 8 * q^77 + 60 * q^78 - 36 * q^81 - 66 * q^82 + 67 * q^84 + 4 * q^86 + 34 * q^88 - 60 * q^89 - 148 * q^92 - 20 * q^93 + 45 * q^94 + 93 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.07322	+	0.920983i	−0.758878	+	0.651233i
$2$	−1.07322	+	0.920983i	−0.758878	+	0.651233i
$3$	1.28534	−	2.22627i	0.742089	−	1.28534i	−0.209454	−	0.977819i	$-0.567169\pi$
$3$	1.28534	−	2.22627i	0.742089	−	1.28534i	0.951543	−	0.307517i	$-0.0994980\pi$
$4$	0.303582	−	1.97683i	0.151791	−	0.988413i
$5$		0			0
$5$		0			0
$6$	0.670911	+	3.57303i	0.273898	+	1.45869i
$7$	−0.304602	+	2.62816i	−0.115129	+	0.993351i
$7$	−0.304602	+	2.62816i	−0.115129	+	0.993351i
$8$	1.49481	+	2.40115i	0.528496	+	0.848936i
$9$	−1.80417	−	3.12492i	−0.601391	−	1.04164i
$10$		0			0
$11$	−5.44112	−	3.14143i	−1.64056	−	0.947177i	−0.980635	−	0.195845i	$-0.937255\pi$
$11$	−5.44112	−	3.14143i	−1.64056	−	0.947177i	−0.659924	−	0.751332i	$-0.729412\pi$
$12$	−4.01073	−	3.21674i	−1.15780	−	0.928592i
$13$		−	3.00876i		−	0.834479i	−0.908797	−	0.417239i	$-0.862998\pi$
$13$		−	3.00876i		−	0.834479i	0.908797	−	0.417239i	$-0.137002\pi$
$14$	−2.09358	−	3.10111i	−0.559534	−	0.828807i
$15$		0			0
$16$	−3.81568	−	1.20026i	−0.953919	−	0.300065i
$17$	−0.935120	−	0.539892i	−0.226800	−	0.130943i	0.382295	−	0.924040i	$-0.375134\pi$
$17$	−0.935120	−	0.539892i	−0.226800	−	0.130943i	−0.609095	+	0.793097i	$0.708467\pi$
$18$	4.81426	+	1.69210i	1.13473	+	0.398832i
$19$	−3.18341	−	5.51382i	−0.730324	−	1.26496i	−0.956745	−	0.290928i	$-0.906036\pi$
$19$	−3.18341	−	5.51382i	−0.730324	−	1.26496i	0.226421	−	0.974029i	$-0.427297\pi$
$20$		0			0
$21$	5.45946	+	4.05619i	1.19135	+	0.885133i
$22$	8.73269	−	1.63974i	1.86182	−	0.349594i
$23$	−2.77450	+	1.60186i	−0.578524	+	0.334011i	−0.760547	−	0.649283i	$-0.775069\pi$
$23$	−2.77450	+	1.60186i	−0.578524	+	0.334011i	0.182023	+	0.983294i	$0.441736\pi$
$24$	7.26694	−	0.241563i	1.48336	−	0.0493089i
$25$		0			0
$26$	2.77101	+	3.22904i	0.543440	+	0.633267i
$27$	−1.56386			−0.300965
$28$	5.10294	+	1.40001i	0.964365	+	0.264577i
$29$	0.512747			0.0952147			0.0476073	−	0.998866i	$-0.484840\pi$
$29$	0.512747			0.0952147			0.0476073	+	0.998866i	$0.484840\pi$
$30$		0			0
$31$	2.55123	−	4.41886i	0.458215	−	0.793651i	−0.540652	−	0.841246i	$-0.681822\pi$
$31$	2.55123	−	4.41886i	0.458215	−	0.793651i	0.998867	+	0.0475952i	$0.0151557\pi$
$32$	5.20046	−	2.22604i	0.919320	−	0.393511i
$33$	−13.9873	+	8.07558i	−2.43488	+	1.40578i
$34$	1.50082	−	0.281809i	0.257388	−	0.0483298i
$35$		0			0
$36$	−6.72514	+	2.61787i	−1.12086	+	0.436311i
$37$	2.63332	+	4.56104i	0.432915	+	0.749830i	0.997123	−	0.0758023i	$-0.0241518\pi$
$37$	2.63332	+	4.56104i	0.432915	+	0.749830i	−0.564208	+	0.825633i	$0.690818\pi$
$38$	8.49461	+	2.98566i	1.37801	+	0.484337i
$39$	−6.69829	−	3.86726i	−1.07259	−	0.619257i
$40$		0			0
$41$		−	7.61555i		−	1.18935i	−0.803966	−	0.594675i	$-0.797281\pi$
$41$		−	7.61555i		−	1.18935i	0.803966	−	0.594675i	$-0.202719\pi$
$42$	−9.59486	+	0.674906i	−1.48052	+	0.104140i
$43$			0.683409i			0.104219i	0.998641	+	0.0521095i	$0.0165945\pi$
$43$			0.683409i			0.104219i	−0.998641	+	0.0521095i	$0.983406\pi$
$44$	−7.86189	+	9.80246i	−1.18522	+	1.47778i
$45$		0			0
$46$	1.50235	−	4.27441i	0.221510	−	0.630227i
$47$	−5.61176	−	9.71985i	−0.818559	−	1.41779i	−0.906744	−	0.421682i	$-0.861440\pi$
$47$	−5.61176	−	9.71985i	−0.818559	−	1.41779i	0.0881845	−	0.996104i	$-0.471893\pi$
$48$	−7.57652	+	6.95197i	−1.09358	+	1.00343i
$49$	−6.81444	−	1.60109i	−0.973491	−	0.228726i
$50$		0			0
$51$	−2.40388	+	1.38788i	−0.336611	+	0.194343i
$52$	−5.94778	−	0.913405i	−0.824809	−	0.126666i
$53$	−1.11837	+	1.93707i	−0.153619	+	0.266076i	−0.932555	−	0.361027i	$-0.882426\pi$
$53$	−1.11837	+	1.93707i	−0.153619	+	0.266076i	0.778936	+	0.627103i	$0.215760\pi$
$54$	1.67836	−	1.44029i	0.228396	−	0.195998i
$55$		0			0
$56$	−6.76593	+	3.19721i	−0.904136	+	0.427245i
$57$	−16.3670			−2.16786
$58$	−0.550288	+	0.472231i	−0.0722563	+	0.0620069i
$59$	−1.62035	+	2.80652i	−0.210951	+	0.365378i	−0.952012	−	0.306059i	$-0.900989\pi$
$59$	−1.62035	+	2.80652i	−0.210951	+	0.365378i	0.741061	+	0.671437i	$0.234323\pi$
$60$		0			0
$61$	2.28536	−	1.31945i	0.292611	−	0.168939i	−0.346508	−	0.938047i	$-0.612633\pi$
$61$	2.28536	−	1.31945i	0.292611	−	0.168939i	0.639119	+	0.769108i	$0.279299\pi$
$62$	1.33167	+	7.09203i	0.169123	+	0.900689i
$63$	8.76234	−	3.78980i	1.10395	−	0.477470i
$64$	−3.53107	+	7.17855i	−0.441384	+	0.897318i
$65$		0			0
$66$	7.57394	−	21.5489i	0.932287	−	2.65249i
$67$	6.55453	+	3.78426i	0.800763	+	0.462321i	0.843738	−	0.536755i	$-0.180350\pi$
$67$	6.55453	+	3.78426i	0.800763	+	0.462321i	−0.0429749	+	0.999076i	$0.513684\pi$
$68$	−1.35116	+	1.68467i	−0.163852	+	0.204296i
$69$			8.23571i			0.991463i
$70$		0			0
$71$			13.2136i			1.56817i	0.620656	+	0.784083i	$0.286866\pi$
$71$			13.2136i			1.56817i	−0.620656	+	0.784083i	$0.713134\pi$
$72$	4.80651	−	9.00327i	0.566453	−	1.06105i
$73$	−2.18683	−	1.26257i	−0.255949	−	0.147772i	0.366536	−	0.930404i	$-0.380544\pi$
$73$	−2.18683	−	1.26257i	−0.255949	−	0.147772i	−0.622485	+	0.782632i	$0.713877\pi$
$74$	−7.02675	−	2.46974i	−0.816844	−	0.287101i
$75$		0			0
$76$	−11.8663	+	4.61914i	−1.36116	+	0.529852i
$77$	9.91356	−	13.3432i	1.12975	−	1.52060i
$78$	10.7504	−	2.01861i	1.21724	−	0.228562i
$79$	9.18163	−	5.30102i	1.03301	−	0.596411i	0.115168	−	0.993346i	$-0.463259\pi$
$79$	9.18163	−	5.30102i	1.03301	−	0.596411i	0.917847	+	0.396935i	$0.129926\pi$
$80$		0			0
$81$	3.40244	−	5.89319i	0.378049	−	0.654799i
$82$	7.01379	+	8.17313i	0.774544	+	0.902571i
$83$	1.37443			0.150863			0.0754315	−	0.997151i	$-0.475967\pi$
$83$	1.37443			0.150863			0.0754315	+	0.997151i	$0.475967\pi$
$84$	9.67578	−	9.56102i	1.05571	−	1.04319i
$85$		0			0
$86$	−0.629408	−	0.733445i	−0.0678708	−	0.0790894i
$87$	0.659051	−	1.14151i	0.0706577	−	0.122383i
$88$	−0.590394	−	17.7608i	−0.0629362	−	1.89331i
$89$	−7.79161	+	4.49849i	−0.825909	+	0.476839i	−0.852450	−	0.522809i	$-0.824884\pi$
$89$	−7.79161	+	4.49849i	−0.825909	+	0.476839i	0.0265409	+	0.999648i	$0.491551\pi$
$90$		0			0
$91$	7.90749	+	0.916474i	0.828930	+	0.0960725i
$92$	2.32431	+	5.97101i	0.242326	+	0.622520i
$93$	−6.55838	−	11.3594i	−0.680072	−	1.17792i
$94$	14.9744	+	5.26316i	1.54450	+	0.542854i
$95$		0			0
$96$	1.72859	−	14.4388i	0.176423	−	1.47365i
$97$		−	7.56469i		−	0.768078i	−0.923317	−	0.384039i	$-0.874533\pi$
$97$		−	7.56469i		−	0.768078i	0.923317	−	0.384039i	$-0.125467\pi$
$98$	8.78793	−	4.55767i	0.887715	−	0.460394i
$99$			22.6707i			2.27850i
$100$		0			0
$101$	3.08052	+	1.77854i	0.306523	+	0.176971i	0.645370	−	0.763871i	$-0.276703\pi$
$101$	3.08052	+	1.77854i	0.306523	+	0.176971i	−0.338846	+	0.940842i	$0.610037\pi$
$102$	1.30167	−	3.70343i	0.128884	−	0.366695i
$103$	4.07092	+	7.05104i	0.401120	+	0.694760i	0.993861	−	0.110633i	$-0.0352878\pi$
$103$	4.07092	+	7.05104i	0.401120	+	0.694760i	−0.592742	+	0.805393i	$0.701954\pi$
$104$	7.22448	−	4.49753i	0.708419	−	0.441019i
$105$		0			0
$106$	−0.583757	−	3.10888i	−0.0566995	−	0.301962i
$107$	3.96330	−	2.28821i	0.383147	−	0.221210i	−0.296040	−	0.955176i	$-0.595666\pi$
$107$	3.96330	−	2.28821i	0.383147	−	0.221210i	0.679187	+	0.733966i	$0.262333\pi$
$108$	−0.474760	+	3.09148i	−0.0456838	+	0.297478i
$109$	2.12763	−	3.68517i	0.203790	−	0.352975i	−0.745956	−	0.665995i	$-0.768007\pi$
$109$	2.12763	−	3.68517i	0.203790	−	0.352975i	0.949747	+	0.313020i	$0.101341\pi$
$110$		0			0
$111$	13.5388			1.28504
$112$	4.31673	−	9.66260i	0.407893	−	0.913030i
$113$	−13.3019			−1.25134			−0.625669	−	0.780088i	$-0.715174\pi$
$113$	−13.3019			−1.25134			−0.625669	+	0.780088i	$0.715174\pi$
$114$	17.5653	−	15.0737i	1.64514	−	1.41178i
$115$		0			0
$116$	0.155661	−	1.01361i	0.0144527	−	0.0941114i
$117$	−9.40212	+	5.42832i	−0.869227	+	0.501848i
$118$	−0.845777	−	4.50431i	−0.0778601	−	0.414655i
$119$	1.70376	−	2.29319i	0.156183	−	0.210216i
$120$		0			0
$121$	14.2372	+	24.6595i	1.29429	+	2.24177i
$122$	−1.23749	+	3.52084i	−0.112037	+	0.318762i
$123$	−16.9542	−	9.78854i	−1.52871	−	0.882603i
$124$	−7.96081	−	6.38483i	−0.714902	−	0.573374i
$125$		0			0
$126$	−5.91354	+	12.1372i	−0.526820	+	1.08127i
$127$		−	8.93473i		−	0.792829i	−0.918072	−	0.396415i	$-0.870254\pi$
$127$		−	8.93473i		−	0.792829i	0.918072	−	0.396415i	$-0.129746\pi$
$128$	−2.82172	−	10.9562i	−0.249407	−	0.968399i
$129$	1.52145	+	0.878410i	0.133956	+	0.0773397i
$130$		0			0
$131$	6.48963	+	11.2404i	0.567002	+	0.982076i	0.996860	+	0.0791798i	$0.0252301\pi$
$131$	6.48963	+	11.2404i	0.567002	+	0.982076i	−0.429858	+	0.902896i	$0.641437\pi$
$132$	11.7177	+	30.1021i	1.01990	+	2.62005i
$133$	15.4609	−	6.68698i	1.34063	−	0.579834i
$134$	−10.5197	+	1.97528i	−0.908760	+	0.170638i
$135$		0			0
$136$	−0.101466	−	3.05240i	−0.00870064	−	0.261741i
$137$	−7.16118	+	12.4035i	−0.611821	+	1.05971i	0.379112	+	0.925351i	$0.376229\pi$
$137$	−7.16118	+	12.4035i	−0.611821	+	1.05971i	−0.990933	+	0.134354i	$0.957104\pi$
$138$	−7.58495	−	8.83869i	−0.645673	−	0.752399i
$139$	18.1087			1.53596			0.767981	−	0.640472i	$-0.221261\pi$
$139$	18.1087			1.53596			0.767981	+	0.640472i	$0.221261\pi$
$140$		0			0
$141$	−28.8520			−2.42977
$142$	−12.1695	−	14.1810i	−1.02124	−	1.19005i
$143$	−9.45180	+	16.3710i	−0.790399	+	1.36901i
$144$	3.13343	+	14.0892i	0.261119	+	1.17410i
$145$		0			0
$146$	3.50974	−	0.659026i	0.290468	−	0.0545414i
$147$	−12.3233	+	13.1128i	−1.01641	+	1.08153i
$148$	9.81581	−	3.82096i	0.806854	−	0.314081i
$149$	−9.34209	−	16.1810i	−0.765334	−	1.32560i	−0.940070	−	0.340982i	$-0.889241\pi$
$149$	−9.34209	−	16.1810i	−0.765334	−	1.32560i	0.174736	−	0.984615i	$-0.444093\pi$
$150$		0			0
$151$	−13.2121	−	7.62802i	−1.07519	−	0.620760i	−0.145593	−	0.989345i	$-0.546509\pi$
$151$	−13.2121	−	7.62802i	−1.07519	−	0.620760i	−0.929594	+	0.368585i	$0.879842\pi$
$152$	8.48093	−	15.8860i	0.687895	−	1.28852i
$153$			3.89623i			0.314992i
$154$	1.64951	+	23.4504i	0.132921	+	1.88969i
$155$		0			0
$156$	−9.67838	+	12.0673i	−0.774891	+	0.966159i
$157$	14.8754	+	8.58829i	1.18718	+	0.685420i	0.957665	−	0.287884i	$-0.0929519\pi$
$157$	14.8754	+	8.58829i	1.18718	+	0.685420i	0.229517	+	0.973305i	$0.426285\pi$
$158$	−4.97172	+	14.1453i	−0.395529	+	1.12534i
$159$	2.87495	+	4.97956i	0.227998	+	0.394905i
$160$		0			0
$161$	−3.36482	−	7.77977i	−0.265185	−	0.613131i
$162$	1.77598	+	9.45825i	0.139534	+	0.743110i
$163$	15.1705	−	8.75871i	1.18825	−	0.686035i	0.230340	−	0.973110i	$-0.426016\pi$
$163$	15.1705	−	8.75871i	1.18825	−	0.686035i	0.957908	+	0.287075i	$0.0926830\pi$
$164$	−15.0546	−	2.31195i	−1.17557	−	0.180533i
$165$		0			0
$166$	−1.47506	+	1.26582i	−0.114487	+	0.0982470i
$167$	8.80963			0.681710			0.340855	−	0.940116i	$-0.389284\pi$
$167$	8.80963			0.681710			0.340855	+	0.940116i	$0.389284\pi$
$168$	−1.57866	+	19.1723i	−0.121796	+	1.47917i
$169$	3.94739			0.303645
$170$		0			0
$171$	−11.4868	+	19.8958i	−0.878420	+	1.52147i
$172$	1.35098	+	0.207471i	0.103011	+	0.0158195i
$173$	4.13719	−	2.38861i	0.314545	−	0.181602i	−0.334414	−	0.942426i	$-0.608538\pi$
$173$	4.13719	−	2.38861i	0.314545	−	0.181602i	0.648958	+	0.760824i	$0.275205\pi$
$174$	0.344007	+	1.83206i	0.0260791	+	0.138888i
$175$		0			0
$176$	16.9910	+	18.5174i	1.28075	+	1.39580i
$177$	4.16537	+	7.21464i	0.313089	+	0.542286i
$178$	4.21905	−	12.0038i	0.316231	−	0.899722i
$179$	−0.824706	−	0.476144i	−0.0616414	−	0.0355887i	0.468863	−	0.883271i	$-0.344664\pi$
$179$	−0.824706	−	0.476144i	−0.0616414	−	0.0355887i	−0.530504	+	0.847682i	$0.677997\pi$
$180$		0			0
$181$			1.68056i			0.124915i	0.998048	+	0.0624575i	$0.0198938\pi$
$181$			1.68056i			0.124915i	−0.998048	+	0.0624575i	$0.980106\pi$
$182$	−9.33049	+	6.29909i	−0.691622	+	0.466919i
$183$		−	6.78377i		−	0.501470i
$184$	−7.99367	−	4.26753i	−0.589301	−	0.314606i
$185$		0			0
$186$	17.5004	+	6.15098i	1.28319	+	0.451011i
$187$	3.39206	+	5.87523i	0.248052	+	0.429639i
$188$	−20.9181	+	8.14269i	−1.52561	+	0.593867i
$189$	0.476355	−	4.11007i	0.0346497	−	0.298964i
$190$		0			0
$191$	1.65424	−	0.955079i	0.119697	−	0.0691071i	−0.438956	−	0.898508i	$-0.644652\pi$
$191$	1.65424	−	0.955079i	0.119697	−	0.0691071i	0.558653	+	0.829401i	$0.311318\pi$
$192$	11.4427	+	17.0879i	0.825809	+	1.23322i
$193$	−5.30421	+	9.18716i	−0.381805	+	0.661306i	−0.991320	−	0.131468i	$-0.958031\pi$
$193$	−5.30421	+	9.18716i	−0.381805	+	0.661306i	0.609515	+	0.792774i	$0.291364\pi$
$194$	6.96695	+	8.11854i	0.500198	+	0.582877i
$195$		0			0
$196$	−5.23381	+	12.9849i	−0.373843	+	0.927492i
$197$	−0.656625			−0.0467826			−0.0233913	−	0.999726i	$-0.507446\pi$
$197$	−0.656625			−0.0467826			−0.0233913	+	0.999726i	$0.507446\pi$
$198$	−20.8794	−	24.3306i	−1.48383	−	1.72910i
$199$	5.43689	−	9.41698i	0.385411	−	0.667552i	−0.606415	−	0.795148i	$-0.707393\pi$
$199$	5.43689	−	9.41698i	0.385411	−	0.667552i	0.991826	+	0.127597i	$0.0407263\pi$
$200$		0			0
$201$	16.8495	−	9.72808i	1.18847	−	0.686166i
$202$	−4.94406	+	0.928349i	−0.347863	+	0.0653184i
$203$	−0.156184	+	1.34758i	−0.0109619	+	0.0945815i
$204$	2.01383	+	5.17340i	0.140996	+	0.362210i
$205$		0			0
$206$	−10.8629	−	3.81804i	−0.756852	−	0.266015i
$207$	10.0114	+	5.78007i	0.695838	+	0.401743i
$208$	−3.61128	+	11.4804i	−0.250398	+	0.796025i
$209$			40.0018i			2.76698i
$210$		0			0
$211$		−	20.1099i		−	1.38442i	−0.721695	−	0.692211i	$-0.756637\pi$
$211$		−	20.1099i		−	1.38442i	0.721695	−	0.692211i	$-0.243363\pi$
$212$	3.48972	+	2.79887i	0.239675	+	0.192227i
$213$	29.4170	+	16.9839i	2.01562	+	1.16372i
$214$	−2.14607	+	6.10588i	−0.146703	+	0.417389i
$215$		0			0
$216$	−2.33768	−	3.75507i	−0.159059	−	0.255500i
$217$	10.8364	+	8.05104i	0.735620	+	0.546540i
$218$	1.11057	+	5.91449i	0.0752171	+	0.400580i
$219$	−5.62162	+	3.24564i	−0.379874	+	0.219320i
$220$		0			0
$221$	−1.62440	+	2.81355i	−0.109269	+	0.189260i
$222$	−14.5300	+	12.4690i	−0.975192	+	0.836863i
$223$	−16.8755			−1.13007			−0.565035	−	0.825067i	$-0.691137\pi$
$223$	−16.8755			−1.13007			−0.565035	+	0.825067i	$0.691137\pi$
$224$	4.26630	+	14.3457i	0.285054	+	0.958511i
$225$		0			0
$226$	14.2758	−	12.2508i	0.949613	−	0.814913i
$227$	5.39331	−	9.34148i	0.357966	−	0.620016i	−0.629655	−	0.776875i	$-0.716804\pi$
$227$	5.39331	−	9.34148i	0.357966	−	0.620016i	0.987621	+	0.156859i	$0.0501369\pi$
$228$	−4.96872	+	32.3547i	−0.329062	+	2.14274i
$229$	16.8003	−	9.69964i	1.11019	−	0.640970i	0.171314	−	0.985217i	$-0.445199\pi$
$229$	16.8003	−	9.69964i	1.11019	−	0.640970i	0.938879	+	0.344246i	$0.111865\pi$
$230$		0			0
$231$	−16.9633	−	39.2207i	−1.11611	−	2.58054i
$232$	0.766460	+	1.23118i	0.0503206	+	0.0808311i
$233$	0.194869	+	0.337524i	0.0127663	+	0.0221119i	0.872338	−	0.488903i	$-0.162603\pi$
$233$	0.194869	+	0.337524i	0.0127663	+	0.0221119i	−0.859572	+	0.511015i	$0.829270\pi$
$234$	5.09112	−	14.4849i	0.332817	−	0.946910i
$235$		0			0
$236$	5.05609	+	4.05515i	0.329124	+	0.263968i
$237$		−	27.2543i		−	1.77036i
$238$	0.283487	+	4.03022i	0.0183757	+	0.261240i
$239$		−	23.8384i		−	1.54198i	−0.636850	−	0.770988i	$-0.719763\pi$
$239$		−	23.8384i		−	1.54198i	0.636850	−	0.770988i	$-0.280237\pi$
$240$		0			0
$241$	−13.2723	−	7.66275i	−0.854942	−	0.493601i	0.00737296	−	0.999973i	$-0.497653\pi$
$241$	−13.2723	−	7.66275i	−0.854942	−	0.493601i	−0.862315	+	0.506372i	$0.830986\pi$
$242$	−37.9905	−	13.3528i	−2.44212	−	0.858349i
$243$	−11.0923	−	19.2125i	−0.711573	−	1.23248i
$244$	−1.91454	−	4.91833i	−0.122566	−	0.314864i
$245$		0			0
$246$	27.2106	−	5.10935i	1.73489	−	0.325761i
$247$	−16.5897	+	9.57809i	−1.05558	+	0.609439i
$248$	14.4240	−	0.479473i	0.915924	−	0.0304466i
$249$	1.76660	−	3.05984i	0.111954	−	0.193910i
$250$		0			0
$251$	28.9335			1.82626			0.913132	−	0.407664i	$-0.133657\pi$
$251$	28.9335			1.82626			0.913132	+	0.407664i	$0.133657\pi$
$252$	−4.83167	−	18.4721i	−0.304367	−	1.16363i
$253$	20.1285			1.26547
$254$	8.22873	+	9.58889i	0.516317	+	0.601661i
$255$		0			0
$256$	13.1188	+	9.15959i	0.819923	+	0.572474i
$257$	4.80055	−	2.77160i	0.299450	−	0.172888i	−0.342746	−	0.939428i	$-0.611357\pi$
$257$	4.80055	−	2.77160i	0.299450	−	0.172888i	0.642196	+	0.766541i	$0.278024\pi$
$258$	−2.44184	+	0.458506i	−0.152023	+	0.0285454i
$259$	−12.7892	+	5.53147i	−0.794685	+	0.343709i
$260$		0			0
$261$	−0.925084	−	1.60229i	−0.0572613	−	0.0991794i
$262$	−17.3170	−	6.08650i	−1.06985	−	0.376025i
$263$	3.91684	+	2.26139i	0.241523	+	0.139443i	0.615876	−	0.787843i	$-0.288802\pi$
$263$	3.91684	+	2.26139i	0.241523	+	0.139443i	−0.374354	+	0.927286i	$0.622135\pi$
$264$	−40.2991	−	21.5142i	−2.48024	−	1.32411i
$265$		0			0
$266$	−10.4343	+	21.4158i	−0.639765	+	1.31308i
$267$			23.1283i			1.41543i
$268$	9.47065	−	11.8083i	0.578512	−	0.721308i
$269$	14.1145	+	8.14903i	0.860579	+	0.496855i	0.864206	−	0.503138i	$-0.167821\pi$
$269$	14.1145	+	8.14903i	0.860579	+	0.496855i	−0.00362727	+	0.999993i	$0.501155\pi$
$270$		0			0
$271$	−2.37107	−	4.10681i	−0.144032	−	0.249471i	0.784979	−	0.619522i	$-0.212674\pi$
$271$	−2.37107	−	4.10681i	−0.144032	−	0.249471i	−0.929011	+	0.370051i	$0.879340\pi$
$272$	2.92010	+	3.18244i	0.177057	+	0.192964i
$273$	12.2041	−	16.4262i	0.738625	−	0.994159i
$274$	−3.73794	−	19.9070i	−0.225818	−	1.20262i
$275$		0			0
$276$	16.2806	+	2.50022i	0.979975	+	0.150495i
$277$	−9.73350	+	16.8589i	−0.584829	+	1.01295i	0.410067	+	0.912055i	$0.365505\pi$
$277$	−9.73350	+	16.8589i	−0.584829	+	1.01295i	−0.994897	+	0.100899i	$0.967828\pi$
$278$	−19.4346	+	16.6778i	−1.16561	+	1.00027i
$279$	−18.4115			−1.10227
$280$		0			0
$281$	−3.41581			−0.203770			−0.101885	−	0.994796i	$-0.532487\pi$
$281$	−3.41581			−0.203770			−0.101885	+	0.994796i	$0.532487\pi$
$282$	30.9644	−	26.5722i	1.84390	−	1.58235i
$283$	−11.2824	+	19.5417i	−0.670670	+	1.16163i	0.307044	+	0.951695i	$0.400660\pi$
$283$	−11.2824	+	19.5417i	−0.670670	+	1.16163i	−0.977714	+	0.209939i	$0.932673\pi$
$284$	26.1210	+	4.01141i	1.54999	+	0.238034i
$285$		0			0
$286$	−4.93359	−	26.2745i	−0.291729	−	1.55365i
$287$	20.0149	+	2.31971i	1.18144	+	0.136928i
$288$	−16.3387	−	12.2349i	−0.962768	−	0.720946i
$289$	−7.91703	−	13.7127i	−0.465708	−	0.806630i
$290$		0			0
$291$	−16.8410	−	9.72316i	−0.987237	−	0.569982i
$292$	−3.15976	+	3.93969i	−0.184911	+	0.230553i
$293$			1.49614i			0.0874057i	0.999045	+	0.0437028i	$0.0139155\pi$
$293$			1.49614i			0.0874057i	−0.999045	+	0.0437028i	$0.986085\pi$
$294$	1.14886	−	25.4224i	0.0670026	−	1.48266i
$295$		0			0
$296$	−7.01544	+	13.1409i	−0.407764	+	0.763799i
$297$	8.50915	+	4.91276i	0.493751	+	0.285067i
$298$	24.9285	+	8.76177i	1.44407	+	0.507556i
$299$	4.81961	+	8.34780i	0.278725	+	0.482766i
$300$		0			0
$301$	−1.79611	−	0.208168i	−0.103526	−	0.0119986i
$302$	21.2047	−	3.98162i	1.22020	−	0.229117i
$303$	7.91900	−	4.57204i	0.454935	−	0.262657i
$304$	5.52884	+	24.8599i	0.317101	+	1.42581i
$305$		0			0
$306$	−3.58836	−	4.18150i	−0.205133	−	0.239040i
$307$	−13.0912			−0.747153			−0.373577	−	0.927599i	$-0.621869\pi$
$307$	−13.0912			−0.747153			−0.373577	+	0.927599i	$0.621869\pi$
$308$	−23.3677	−	23.6481i	−1.33150	−	1.34748i
$309$	20.9300			1.19067
$310$		0			0
$311$	−9.84999	+	17.0607i	−0.558542	+	0.967423i	0.439077	+	0.898450i	$0.355306\pi$
$311$	−9.84999	+	17.0607i	−0.558542	+	0.967423i	−0.997619	+	0.0689731i	$0.978028\pi$
$312$	−0.726805	−	21.8645i	−0.0411472	−	1.23783i
$313$	−2.96061	+	1.70931i	−0.167344	+	0.0966160i	−0.581333	−	0.813666i	$-0.697469\pi$
$313$	−2.96061	+	1.70931i	−0.167344	+	0.0966160i	0.413989	+	0.910282i	$0.364135\pi$
$314$	−23.8741	+	4.48286i	−1.34729	+	0.252982i
$315$		0			0
$316$	−7.69180	−	19.7598i	−0.432698	−	1.11157i
$317$	−12.2769	−	21.2642i	−0.689539	−	1.19432i	−0.971987	−	0.235035i	$-0.924480\pi$
$317$	−12.2769	−	21.2642i	−0.689539	−	1.19432i	0.282448	−	0.959283i	$-0.408854\pi$
$318$	−7.67153	−	2.69636i	−0.430198	−	0.151204i
$319$	−2.78992	−	1.61076i	−0.156205	−	0.0901852i
$320$		0			0
$321$		−	11.7645i		−	0.656630i
$322$	10.7762	+	5.25042i	0.600535	+	0.292594i
$323$			6.87478i			0.382523i
$324$	−10.6169	−	8.51509i	−0.589827	−	0.473061i
$325$		0			0
$326$	−8.21463	+	23.3718i	−0.454966	+	1.29444i
$327$	−5.46944	−	9.47335i	−0.302461	−	0.523878i
$328$	18.2861	−	11.3838i	1.00968	−	0.628566i
$329$	27.2547	−	11.7879i	1.50260	−	0.649888i
$330$		0			0
$331$	0.854261	−	0.493208i	0.0469544	−	0.0271092i	−0.476339	−	0.879262i	$-0.658036\pi$
$331$	0.854261	−	0.493208i	0.0469544	−	0.0271092i	0.523293	+	0.852153i	$0.324703\pi$
$332$	0.417252	−	2.71700i	0.0228997	−	0.149115i
$333$	9.50192	−	16.4578i	0.520702	−	0.901883i
$334$	−9.45463	+	8.11351i	−0.517334	+	0.443952i
$335$		0			0
$336$	−15.9631	−	22.0299i	−0.870857	−	1.20183i
$337$	8.57714			0.467226			0.233613	−	0.972330i	$-0.424945\pi$
$337$	8.57714			0.467226			0.233613	+	0.972330i	$0.424945\pi$
$338$	−4.23640	+	3.63547i	−0.230430	+	0.197744i
$339$	−17.0974	+	29.6136i	−0.928604	+	1.60839i
$340$		0			0
$341$	−27.7631	+	16.0290i	−1.50346	+	0.868021i
$342$	−5.99582	−	31.9316i	−0.324217	−	1.72666i
$343$	6.28360	−	17.4217i	0.339282	−	0.940685i
$344$	−1.64097	+	1.02157i	−0.0884752	+	0.0550793i
$345$		0			0
$346$	−2.24023	+	6.37377i	−0.120435	+	0.342656i
$347$	−14.4710	−	8.35484i	−0.776844	−	0.448511i	0.0584664	−	0.998289i	$-0.481379\pi$
$347$	−14.4710	−	8.35484i	−0.776844	−	0.448511i	−0.835311	+	0.549778i	$0.814712\pi$
$348$	−2.05649	−	1.64937i	−0.110239	−	0.0884156i
$349$		−	25.6808i		−	1.37466i	−0.726345	−	0.687330i	$-0.758783\pi$
$349$		−	25.6808i		−	1.37466i	0.726345	−	0.687330i	$-0.241217\pi$
$350$		0			0
$351$			4.70527i			0.251149i
$352$	−35.2892	−	4.22476i	−1.88092	−	0.225181i
$353$	−3.24282	−	1.87224i	−0.172598	−	0.0996493i	0.411212	−	0.911540i	$-0.365105\pi$
$353$	−3.24282	−	1.87224i	−0.172598	−	0.0996493i	−0.583810	+	0.811890i	$0.698439\pi$
$354$	−11.1149	−	3.90663i	−0.590750	−	0.207635i
$355$		0			0
$356$	6.52733	+	16.7683i	0.345948	+	0.888719i
$357$	−2.91535	−	6.74054i	−0.154297	−	0.356747i
$358$	1.32361	−	0.248535i	0.0699549	−	0.0131355i
$359$	2.42733	−	1.40142i	0.128109	−	0.0739640i	−0.434576	−	0.900635i	$-0.643102\pi$
$359$	2.42733	−	1.40142i	0.128109	−	0.0739640i	0.562685	+	0.826671i	$0.309768\pi$
$360$		0			0
$361$	−10.7682	+	18.6510i	−0.566745	+	0.981631i
$362$	−1.54777	−	1.80360i	−0.0813488	−	0.0947952i
$363$	73.1982			3.84191
$364$	4.21228	−	15.3535i	0.220784	−	0.804742i
$365$		0			0
$366$	6.24773	+	7.28044i	0.326574	+	0.380555i
$367$	13.8665	−	24.0174i	0.723823	−	1.25370i	−0.235634	−	0.971842i	$-0.575717\pi$
$367$	13.8665	−	24.0174i	0.723823	−	1.25370i	0.959457	−	0.281856i	$-0.0909502\pi$
$368$	12.5093	−	2.78206i	0.652090	−	0.145025i
$369$	−23.7980	+	13.7398i	−1.23887	+	0.715264i
$370$		0			0
$371$	−4.75026	−	3.52928i	−0.246621	−	0.183231i
$372$	−24.4466	+	9.51624i	−1.26750	+	0.493394i
$373$	−0.167314	−	0.289797i	−0.00866321	−	0.0150051i	0.861661	−	0.507484i	$-0.169424\pi$
$373$	−0.167314	−	0.289797i	−0.00866321	−	0.0150051i	−0.870325	+	0.492479i	$0.836091\pi$
$374$	−9.05140	−	3.18135i	−0.468037	−	0.164504i
$375$		0			0
$376$	14.9503	−	28.0040i	0.771004	−	1.44420i
$377$		−	1.54273i		−	0.0794546i
$378$	3.27407	+	4.84971i	0.168400	+	0.249442i
$379$			5.62231i			0.288799i	0.989519	+	0.144399i	$0.0461250\pi$
$379$			5.62231i			0.288799i	−0.989519	+	0.144399i	$0.953875\pi$
$380$		0			0
$381$	−19.8911	−	11.4841i	−1.01905	−	0.588350i
$382$	−0.895750	+	2.54854i	−0.0458306	+	0.130394i
$383$	17.2412	+	29.8627i	0.880986	+	1.52591i	0.850246	+	0.526385i	$0.176453\pi$
$383$	17.2412	+	29.8627i	0.880986	+	1.52591i	0.0307396	+	0.999527i	$0.490214\pi$
$384$	−28.0182	−	7.80048i	−1.42980	−	0.398066i
$385$		0			0
$386$	−2.76865	−	14.7449i	−0.140921	−	0.750495i
$387$	2.13560	−	1.23299i	0.108559	−	0.0626763i
$388$	−14.9541	−	2.29651i	−0.759178	−	0.116587i
$389$	5.10332	−	8.83921i	0.258749	−	0.448166i	−0.707158	−	0.707055i	$-0.750023\pi$
$389$	5.10332	−	8.83921i	0.258749	−	0.448166i	0.965907	+	0.258889i	$0.0833565\pi$
$390$		0			0
$391$	3.45932			0.174946
$392$	−6.34185	−	18.7558i	−0.320312	−	0.947312i
$393$	33.3654			1.68306
$394$	0.704700	−	0.604740i	0.0355023	−	0.0304664i
$395$		0			0
$396$	44.8161	+	6.88244i	2.25209	+	0.345855i
$397$	0.198633	−	0.114681i	0.00996909	−	0.00575566i	−0.495007	−	0.868889i	$-0.664835\pi$
$397$	0.198633	−	0.114681i	0.00996909	−	0.00575566i	0.504976	+	0.863133i	$0.331501\pi$
$398$	2.83791	+	15.1137i	0.142252	+	0.757583i
$399$	4.98542	−	43.0150i	0.249583	−	2.15344i
$400$		0			0
$401$	−9.43363	−	16.3395i	−0.471093	−	0.815957i	0.528360	−	0.849020i	$-0.322807\pi$
$401$	−9.43363	−	16.3395i	−0.471093	−	0.815957i	−0.999453	+	0.0330632i	$0.989474\pi$
$402$	−9.12378	+	25.9584i	−0.455053	+	1.29469i
$403$	−13.2953	−	7.67603i	−0.662285	−	0.382370i
$404$	4.45105	−	5.54971i	0.221448	−	0.276109i
$405$		0			0
$406$	−1.07348	−	1.59009i	−0.0532758	−	0.0789146i
$407$		−	33.0895i		−	1.64019i
$408$	−6.92588	−	3.69747i	−0.342882	−	0.183052i
$409$	−11.1260	−	6.42359i	−0.550144	−	0.317626i	0.199036	−	0.979992i	$-0.436219\pi$
$409$	−11.1260	−	6.42359i	−0.550144	−	0.317626i	−0.749180	+	0.662366i	$0.769552\pi$
$410$		0			0
$411$	18.4090	+	31.8854i	0.908051	+	1.57279i
$412$	15.1745	−	5.90693i	0.747596	−	0.291013i
$413$	−6.88242	−	5.11340i	−0.338662	−	0.251614i
$414$	−16.0677	+	3.01704i	−0.789684	+	0.148279i
$415$		0			0
$416$	−6.69760	−	15.6469i	−0.328377	−	0.767153i
$417$	23.2758	−	40.3148i	1.13982	−	1.97423i
$418$	−36.8410	−	42.9306i	−1.80195	−	2.09980i
$419$	8.03925			0.392743			0.196372	−	0.980530i	$-0.437084\pi$
$419$	8.03925			0.392743			0.196372	+	0.980530i	$0.437084\pi$
$420$		0			0
$421$	27.5206			1.34127			0.670636	−	0.741787i	$-0.266021\pi$
$421$	27.5206			1.34127			0.670636	+	0.741787i	$0.266021\pi$
$422$	18.5209	+	21.5822i	0.901581	+	1.05061i
$423$	−20.2492	+	35.0726i	−0.984549	+	1.70529i
$424$	−6.32294	+	0.210183i	−0.307069	+	0.0102074i
$425$		0			0
$426$	−47.2126	+	8.86514i	−2.28746	+	0.429518i
$427$	2.77161	+	6.40820i	0.134128	+	0.310115i
$428$	−3.32021	−	8.52942i	−0.160488	−	0.412285i
$429$	24.2975	+	42.0844i	1.17309	+	2.03186i
$430$		0			0
$431$	3.18583	+	1.83934i	0.153456	+	0.0885980i	0.574762	−	0.818321i	$-0.305095\pi$
$431$	3.18583	+	1.83934i	0.153456	+	0.0885980i	−0.421306	+	0.906919i	$0.638428\pi$
$432$	5.96718	+	1.87704i	0.287096	+	0.0903089i
$433$			18.5390i			0.890928i	0.895300	+	0.445464i	$0.146961\pi$
$433$			18.5390i			0.890928i	−0.895300	+	0.445464i	$0.853039\pi$
$434$	−19.0446	+	1.33960i	−0.914171	+	0.0643031i
$435$		0			0
$436$	−6.63902	−	5.32471i	−0.317951	−	0.255007i
$437$	17.6647	+	10.1987i	0.845019	+	0.487872i
$438$	3.04403	−	8.66069i	0.145449	−	0.413824i
$439$	−11.4811	−	19.8859i	−0.547963	−	0.949100i	−0.998414	−	0.0562989i	$-0.982070\pi$
$439$	−11.4811	−	19.8859i	−0.547963	−	0.949100i	0.450451	−	0.892801i	$-0.351263\pi$
$440$		0			0
$441$	7.29116	+	24.1832i	0.347198	+	1.15158i
$442$	−0.847894	−	4.51559i	−0.0403302	−	0.214785i
$443$	−2.67900	+	1.54672i	−0.127283	+	0.0734868i	−0.562290	−	0.826940i	$-0.690079\pi$
$443$	−2.67900	+	1.54672i	−0.127283	+	0.0734868i	0.435007	+	0.900427i	$0.356746\pi$
$444$	4.11013	−	26.7638i	0.195058	−	1.27015i
$445$		0			0
$446$	18.1111	−	15.5421i	0.857585	−	0.735939i
$447$	−48.0309			−2.27178
$448$	−17.7908	−	11.4668i	−0.840536	−	0.541756i
$449$	17.1346			0.808630			0.404315	−	0.914620i	$-0.367510\pi$
$449$	17.1346			0.808630			0.404315	+	0.914620i	$0.367510\pi$
$450$		0			0
$451$	−23.9237	+	41.4371i	−1.12652	+	1.95120i
$452$	−4.03823	+	26.2956i	−0.189942	+	1.23684i
$453$	−33.9640	+	19.6091i	−1.59577	+	0.921317i
$454$	2.81516	+	14.9926i	0.132122	+	0.703636i
$455$		0			0
$456$	−24.4656	−	39.2996i	−1.14570	−	1.84037i
$457$	10.4704	+	18.1352i	0.489783	+	0.848328i	0.999931	−	0.0117581i	$-0.00374281\pi$
$457$	10.4704	+	18.1352i	0.489783	+	0.848328i	−0.510148	+	0.860086i	$0.670409\pi$
$458$	−9.09711	+	25.8826i	−0.425080	+	1.20941i
$459$	1.46240	+	0.844315i	0.0682588	+	0.0394092i
$460$		0			0
$461$		−	3.96999i		−	0.184901i	−0.995717	−	0.0924504i	$-0.970530\pi$
$461$		−	3.96999i		−	0.184901i	0.995717	−	0.0924504i	$-0.0294699\pi$
$462$	54.3269	+	26.4694i	2.52752	+	1.23147i
$463$			35.7908i			1.66334i	0.555272	+	0.831669i	$0.312614\pi$
$463$			35.7908i			1.66334i	−0.555272	+	0.831669i	$0.687386\pi$
$464$	−1.95648	−	0.615428i	−0.0908271	−	0.0285705i
$465$		0			0
$466$	−0.519990	−	0.182764i	−0.0240881	−	0.00846639i
$467$	1.03754	+	1.79708i	0.0480117	+	0.0831588i	0.889033	−	0.457844i	$-0.151378\pi$
$467$	1.03754	+	1.79708i	0.0480117	+	0.0831588i	−0.841021	+	0.541003i	$0.818045\pi$
$468$	7.87652	+	20.2343i	0.364092	+	0.935331i
$469$	−11.9422	+	16.0736i	−0.551437	+	0.742212i
$470$		0			0
$471$	38.2396	−	22.0777i	1.76199	−	1.01729i
$472$	−9.16100	+	0.304524i	−0.421669	+	0.0140169i
$473$	2.14688	−	3.71851i	0.0987138	−	0.170977i
$474$	25.1008	+	29.2498i	1.15292	+	1.34349i
$475$		0			0
$476$	−4.01601	−	4.06421i	−0.184073	−	0.186283i
$477$	8.07090			0.369541
$478$	21.9547	+	25.5837i	1.00419	+	1.17017i
$479$	−14.4805	+	25.0810i	−0.661633	+	1.14598i	0.318553	+	0.947905i	$0.396803\pi$
$479$	−14.4805	+	25.0810i	−0.661633	+	1.14598i	−0.980186	+	0.198077i	$0.936530\pi$
$480$		0			0
$481$	13.7231	−	7.92301i	0.625718	−	0.361258i
$482$	21.3013	−	3.99975i	0.970246	−	0.182184i
$483$	−21.6448	−	2.50862i	−0.984870	−	0.114146i
$484$	53.0697	−	20.6582i	2.41226	−	0.939010i
$485$		0			0
$486$	29.5988	+	10.4033i	1.34263	+	0.471903i
$487$	−2.15488	−	1.24412i	−0.0976468	−	0.0563764i	0.450381	−	0.892836i	$-0.351288\pi$
$487$	−2.15488	−	1.24412i	−0.0976468	−	0.0563764i	−0.548028	+	0.836460i	$0.684621\pi$
$488$	6.58440	+	3.51517i	0.298062	+	0.159124i
$489$		−	45.0315i		−	2.03640i
$490$		0			0
$491$		−	11.5030i		−	0.519125i	−0.965726	−	0.259562i	$-0.916422\pi$
$491$		−	11.5030i		−	0.519125i	0.965726	−	0.259562i	$-0.0835783\pi$
$492$	−24.4972	+	30.5440i	−1.10442	+	1.37703i
$493$	−0.479479	−	0.276828i	−0.0215947	−	0.0124677i
$494$	8.98311	−	25.5582i	0.404169	−	1.14992i
$495$		0			0
$496$	−15.0384	+	13.7988i	−0.675246	+	0.619585i
$497$	−34.7274	−	4.02489i	−1.55774	−	0.180541i
$498$	0.922118	+	4.91088i	0.0413211	+	0.220062i
$499$	0.404414	−	0.233489i	0.0181041	−	0.0104524i	−0.490921	−	0.871204i	$-0.663340\pi$
$499$	0.404414	−	0.233489i	0.0181041	−	0.0104524i	0.509025	+	0.860752i	$0.330006\pi$
$500$		0			0
$501$	11.3233	−	19.6126i	0.505889	−	0.876225i
$502$	−31.0518	+	26.6472i	−1.38591	+	1.18932i
$503$	−16.4547			−0.733679			−0.366840	−	0.930284i	$-0.619560\pi$
$503$	−16.4547			−0.733679			−0.366840	+	0.930284i	$0.619560\pi$
$504$	22.1979	+	15.3747i	0.988775	+	0.684843i
$505$		0			0
$506$	−21.6023	+	18.5380i	−0.960337	+	0.824116i
$507$	5.07371	−	8.78793i	0.225332	−	0.390286i
$508$	−17.6624	−	2.71243i	−0.783642	−	0.120344i
$509$	−25.2083	+	14.5540i	−1.11734	+	0.645095i	−0.940720	−	0.339185i	$-0.889849\pi$
$509$	−25.2083	+	14.5540i	−1.11734	+	0.645095i	−0.176617	+	0.984280i	$0.556515\pi$
$510$		0			0
$511$	3.98434	−	5.36276i	0.176257	−	0.237234i
$512$	−22.5151	+	2.25193i	−0.995035	+	0.0995224i
$513$	4.97840	+	8.62284i	0.219802	+	0.380708i
$514$	−2.59943	+	7.39575i	−0.114656	+	0.326213i
$515$		0			0
$516$	2.19835	−	2.74097i	0.0967769	−	0.120665i
$517$			70.5158i			3.10128i
$518$	8.63123	−	17.7151i	0.379234	−	0.778358i
$519$		−	12.2806i		−	0.539060i
$520$		0			0
$521$	−15.2705	−	8.81643i	−0.669013	−	0.386255i	0.126690	−	0.991942i	$-0.459565\pi$
$521$	−15.2705	−	8.81643i	−0.669013	−	0.386255i	−0.795702	+	0.605688i	$0.792898\pi$
$522$	2.46850	+	0.867619i	0.108043	+	0.0379746i
$523$	−14.9732	−	25.9343i	−0.654732	−	1.13403i	−0.981961	−	0.189084i	$-0.939448\pi$
$523$	−14.9732	−	25.9343i	−0.654732	−	1.13403i	0.327229	−	0.944945i	$-0.393885\pi$
$524$	24.1904	−	9.41649i	1.05676	−	0.411361i
$525$		0			0
$526$	−6.28631	+	1.18038i	−0.274096	+	0.0514672i
$527$	−4.77141	+	2.75478i	−0.207846	+	0.120000i
$528$	63.0639	−	14.0254i	2.74450	−	0.610378i
$529$	−6.36809	+	11.0298i	−0.276873	+	0.479559i
$530$		0			0
$531$	11.6935			0.507456
$532$	−8.52533	−	32.5935i	−0.369620	−	1.41311i
$533$	−22.9133			−0.992487
$534$	−21.3007	−	24.8216i	−0.921773	−	1.07414i
$535$		0			0
$536$	0.711205	+	21.3952i	0.0307194	+	0.924131i
$537$	−2.12005	+	1.22401i	−0.0914868	+	0.0528199i
$538$	−22.6531	+	4.25358i	−0.976643	+	0.183385i
$539$	32.0484	+	30.1188i	1.38042	+	1.29731i
$540$		0			0
$541$	9.92543	+	17.1913i	0.426727	+	0.739114i	0.996580	−	0.0826334i	$-0.0263330\pi$
$541$	9.92543	+	17.1913i	0.426727	+	0.739114i	−0.569853	+	0.821747i	$0.693000\pi$
$542$	6.32697	+	2.22378i	0.271767	+	0.0955195i
$543$	3.74137	+	2.16008i	0.160558	+	0.0926980i
$544$	−6.06487	−	0.726074i	−0.260029	−	0.0311302i
$545$		0			0
$546$	2.03063	+	28.8686i	0.0869028	+	1.23546i
$547$			31.0237i			1.32648i	0.748409	+	0.663238i	$0.230818\pi$
$547$			31.0237i			1.32648i	−0.748409	+	0.663238i	$0.769182\pi$
$548$	22.3456	+	17.9219i	0.954557	+	0.765585i
$549$	−8.24638	−	4.76105i	−0.351947	−	0.203197i
$550$		0			0
$551$	−1.63228	−	2.82719i	−0.0695375	−	0.120443i
$552$	−19.7752	+	12.3108i	−0.841689	+	0.523984i
$553$	11.1352	+	25.7455i	0.473516	+	1.09481i
$554$	−5.08063	−	27.0576i	−0.215855	−	1.14957i
$555$		0			0
$556$	5.49749	−	35.7978i	0.233145	−	1.51816i
$557$	−1.56367	+	2.70836i	−0.0662549	+	0.114757i	−0.897250	−	0.441523i	$-0.854438\pi$
$557$	−1.56367	+	2.70836i	−0.0662549	+	0.114757i	0.830995	+	0.556280i	$0.187772\pi$
$558$	19.7595	−	16.9566i	0.836485	−	0.717831i
$559$	2.05621			0.0869685
$560$		0			0
$561$	17.4398			0.736307
$562$	3.66590	−	3.14590i	0.154637	−	0.132702i
$563$	18.2136	−	31.5469i	0.767612	−	1.32954i	−0.171242	−	0.985229i	$-0.554778\pi$
$563$	18.2136	−	31.5469i	0.767612	−	1.32954i	0.938854	−	0.344315i	$-0.111889\pi$
$564$	−8.75895	+	57.0353i	−0.368818	+	2.40162i
$565$		0			0
$566$	−5.88912	−	31.3634i	−0.247538	−	1.31830i
$567$	14.4519	+	10.7372i	0.606921	+	0.450921i
$568$	−31.7279	+	19.7518i	−1.33127	+	0.828769i
$569$	−6.12584	−	10.6103i	−0.256809	−	0.444806i	0.708577	−	0.705634i	$-0.249338\pi$
$569$	−6.12584	−	10.6103i	−0.256809	−	0.444806i	−0.965385	+	0.260828i	$0.916004\pi$
$570$		0			0
$571$	−15.7382	−	9.08645i	−0.658623	−	0.380256i	0.133129	−	0.991099i	$-0.457498\pi$
$571$	−15.7382	−	9.08645i	−0.658623	−	0.380256i	−0.791752	+	0.610842i	$0.790831\pi$
$572$	29.4932	+	23.6545i	1.23317	+	0.989044i
$573$		−	4.91039i		−	0.205134i
$574$	−23.6167	+	15.9438i	−0.985742	+	0.665481i
$575$		0			0
$576$	28.8031	−	1.91702i	1.20013	−	0.0798760i
$577$	−27.1323	−	15.6648i	−1.12953	−	0.652135i	−0.185714	−	0.982604i	$-0.559460\pi$
$577$	−27.1323	−	15.6648i	−1.12953	−	0.652135i	−0.943817	+	0.330468i	$0.892793\pi$
$578$	21.1258	+	7.42524i	0.878719	+	0.308849i
$579$	13.6354	+	23.6172i	0.566667	+	0.981496i
$580$		0			0
$581$	−0.418653	+	3.61221i	−0.0173687	+	0.149860i
$582$	27.0289	−	5.07523i	1.12038	−	0.210375i
$583$	12.1703	−	7.02654i	0.504043	−	0.291009i
$584$	−0.237284	−	7.13821i	−0.00981889	−	0.295381i
$585$		0			0
$586$	−1.37792	−	1.60569i	−0.0569215	−	0.0663302i
$587$	−25.7715			−1.06370			−0.531851	−	0.846838i	$-0.678504\pi$
$587$	−25.7715			−1.06370			−0.531851	+	0.846838i	$0.678504\pi$
$588$	22.1806	+	28.3418i	0.914713	+	1.16880i
$589$	−32.4864			−1.33858
$590$		0			0
$591$	−0.843983	+	1.46182i	−0.0347168	+	0.0601313i
$592$	−4.57346	−	20.5641i	−0.187968	−	0.845180i
$593$	42.0778	−	24.2936i	1.72793	−	0.997620i	0.829491	−	0.558520i	$-0.188631\pi$
$593$	42.0778	−	24.2936i	1.72793	−	0.997620i	0.898438	−	0.439100i	$-0.144703\pi$
$594$	−13.6567	+	2.56433i	−0.560342	+	0.105216i
$595$		0			0
$596$	−34.8231	+	13.5554i	−1.42641	+	0.555252i
$597$	−13.9765	−	24.2079i	−0.572018	−	0.990765i
$598$	−12.8607	−	4.52022i	−0.525911	−	0.184845i
$599$	−8.04858	−	4.64685i	−0.328856	−	0.189865i	0.326477	−	0.945205i	$-0.394138\pi$
$599$	−8.04858	−	4.64685i	−0.328856	−	0.189865i	−0.655333	+	0.755340i	$0.727472\pi$
$600$		0			0
$601$			34.0570i			1.38922i	0.719388	+	0.694608i	$0.244422\pi$
$601$			34.0570i			1.38922i	−0.719388	+	0.694608i	$0.755578\pi$
$602$	2.11933	−	1.43077i	0.0863774	−	0.0583140i
$603$		−	27.3098i		−	1.11214i
$604$	−19.0902	+	23.8023i	−0.776771	+	0.968503i
$605$		0			0
$606$	−4.28802	+	12.2000i	−0.174189	+	0.495593i
$607$	−3.31994	−	5.75030i	−0.134752	−	0.233397i	0.790751	−	0.612138i	$-0.209690\pi$
$607$	−3.31994	−	5.75030i	−0.134752	−	0.233397i	−0.925503	+	0.378741i	$0.876357\pi$
$608$	−28.8291	−	21.5880i	−1.16918	−	0.875510i
$609$	2.79932	+	2.07980i	0.113434	+	0.0842777i
$610$		0			0
$611$	−29.2447	+	16.8844i	−1.18311	+	0.683070i
$612$	7.70217	+	1.18283i	0.311342	+	0.0478129i
$613$	−13.6422	+	23.6290i	−0.551003	+	0.954366i	0.447199	+	0.894434i	$0.352422\pi$
$613$	−13.6422	+	23.6290i	−0.551003	+	0.954366i	−0.998202	+	0.0599315i	$0.980912\pi$
$614$	14.0497	−	12.0568i	0.566998	−	0.486571i
$615$		0			0
$616$	46.8581	+	3.85833i	1.88796	+	0.155457i
$617$	19.4392			0.782591			0.391296	−	0.920265i	$-0.372027\pi$
$617$	19.4392			0.782591			0.391296	+	0.920265i	$0.372027\pi$
$618$	−22.4624	+	19.2762i	−0.903570	+	0.775401i
$619$	−9.21113	+	15.9541i	−0.370226	+	0.641251i	−0.989600	−	0.143845i	$-0.954053\pi$
$619$	−9.21113	+	15.9541i	−0.370226	+	0.641251i	0.619374	+	0.785096i	$0.287387\pi$
$620$		0			0
$621$	4.33893	−	2.50508i	0.174115	−	0.100526i
$622$	−5.14143	−	27.3815i	−0.206153	−	1.09790i
$623$	−9.44940	−	21.8478i	−0.378582	−	0.875315i
$624$	20.9168	+	22.7959i	0.837342	+	0.912566i
$625$		0			0
$626$	1.60313	−	4.56113i	0.0640740	−	0.182300i
$627$	89.0547	+	51.4157i	3.55650	+	2.05335i
$628$	21.4934	−	26.7987i	0.857682	−	1.06939i
$629$		−	5.68682i		−	0.226748i
$630$		0			0
$631$			36.2378i			1.44260i	0.692621	+	0.721301i	$0.256456\pi$
$631$			36.2378i			1.44260i	−0.692621	+	0.721301i	$0.743544\pi$
$632$	26.4534	+	14.1225i	1.05226	+	0.561762i
$633$	−44.7700	−	25.8480i	−1.77945	−	1.02736i
$634$	32.7597	+	11.5143i	1.30106	+	0.457290i
$635$		0			0
$636$	10.7165	−	4.17157i	0.424937	−	0.165413i
$637$	−4.81728	+	20.5030i	−0.190867	+	0.812357i
$638$	4.47766	−	0.840773i	0.177272	−	0.0332865i
$639$	41.2914	−	23.8396i	1.63346	−	0.943081i
$640$		0			0
$641$	4.11480	−	7.12704i	0.162525	−	0.281501i	−0.773249	−	0.634103i	$-0.781370\pi$
$641$	4.11480	−	7.12704i	0.162525	−	0.281501i	0.935774	+	0.352602i	$0.114703\pi$
$642$	10.8349	+	12.6258i	0.427619	+	0.498302i
$643$	−11.2586			−0.443997			−0.221999	−	0.975047i	$-0.571258\pi$
$643$	−11.2586			−0.443997			−0.221999	+	0.975047i	$0.571258\pi$
$644$	−16.4007	+	4.28987i	−0.646280	+	0.169045i
$645$		0			0
$646$	−6.33155	−	7.37812i	−0.249111	−	0.290288i
$647$	−6.66075	+	11.5368i	−0.261861	+	0.453557i	−0.966737	−	0.255774i	$-0.917670\pi$
$647$	−6.66075	+	11.5368i	−0.261861	+	0.453557i	0.704875	+	0.709331i	$0.251003\pi$
$648$	19.2365	−	0.639447i	0.755680	−	0.0251198i
$649$	17.6330	−	10.1804i	0.692155	−	0.399616i
$650$		0			0
$651$	31.8521	−	13.7763i	1.24838	−	0.539937i
$652$	−12.7089	−	32.6485i	−0.497720	−	1.27861i
$653$	−15.8695	−	27.4868i	−0.621022	−	1.07564i	−0.989296	−	0.145925i	$-0.953384\pi$
$653$	−15.8695	−	27.4868i	−0.621022	−	1.07564i	0.368273	−	0.929718i	$-0.379949\pi$
$654$	14.5947	+	5.12969i	0.570697	+	0.200587i
$655$		0			0
$656$	−9.14063	+	29.0585i	−0.356882	+	1.13454i
$657$			9.11156i			0.355476i
$658$	−18.3937	+	37.7520i	−0.717060	+	1.47173i
$659$		−	14.2935i		−	0.556794i	−0.960466	−	0.278397i	$-0.910197\pi$
$659$		−	14.2935i		−	0.556794i	0.960466	−	0.278397i	$-0.0898031\pi$
$660$		0			0
$661$	9.88604	+	5.70771i	0.384522	+	0.222004i	0.679784	−	0.733412i	$-0.262074\pi$
$661$	9.88604	+	5.70771i	0.384522	+	0.222004i	−0.295262	+	0.955416i	$0.595407\pi$
$662$	−0.462570	+	1.31608i	−0.0179783	+	0.0511508i
$663$	4.17580	+	7.23270i	0.162175	+	0.280895i
$664$	2.05451	+	3.30021i	0.0797305	+	0.128073i
$665$		0			0
$666$	4.95975	+	26.4139i	0.192186	+	1.02352i
$667$	−1.42262	+	0.821349i	−0.0550840	+	0.0318027i
$668$	2.67445	−	17.4151i	0.103477	−	0.673810i
$669$	−21.6907	+	37.5694i	−0.838612	+	1.45252i
$670$		0			0
$671$	−16.5799			−0.640060
$672$	37.4209	+	8.94109i	1.44354	+	0.344910i
$673$	−37.1970			−1.43384			−0.716920	−	0.697155i	$-0.754449\pi$
$673$	−37.1970			−1.43384			−0.716920	+	0.697155i	$0.754449\pi$
$674$	−9.20511	+	7.89939i	−0.354568	+	0.304273i
$675$		0			0
$676$	1.19836	−	7.80329i	0.0460906	−	0.300127i
$677$	3.84578	−	2.22036i	0.147805	−	0.0853354i	−0.424274	−	0.905534i	$-0.639471\pi$
$677$	3.84578	−	2.22036i	0.147805	−	0.0853354i	0.572079	+	0.820199i	$0.306137\pi$
$678$	−8.92440	−	47.5282i	−0.342739	−	1.82531i
$679$	19.8812	+	2.30422i	0.762970	+	0.0884278i
$680$		0			0
$681$	−13.8644	−	24.0139i	−0.531286	−	0.920214i
$682$	15.0333	−	42.7719i	0.575656	−	1.63782i
$683$	−30.3854	−	17.5430i	−1.16267	−	0.671265i	−0.210724	−	0.977546i	$-0.567582\pi$
$683$	−30.3854	−	17.5430i	−1.16267	−	0.671265i	−0.951941	+	0.306280i	$0.900916\pi$
$684$	35.8433	+	28.7475i	1.37050	+	1.09919i
$685$		0			0
$686$	9.30145	+	24.4843i	0.355131	+	0.934817i
$687$		−	49.8692i		−	1.90263i
$688$	0.820267	−	2.60767i	0.0312724	−	0.0994164i
$689$	5.82816	+	3.36489i	0.222035	+	0.128192i
$690$		0			0
$691$	−19.1235	−	33.1229i	−0.727493	−	1.26005i	−0.957940	−	0.286969i	$-0.907352\pi$
$691$	−19.1235	−	33.1229i	−0.727493	−	1.26005i	0.230447	−	0.973085i	$-0.425981\pi$
$692$	−3.46588	−	8.90364i	−0.131753	−	0.338466i
$693$	−59.5823	−	6.90556i	−2.26335	−	0.262320i
$694$	23.2252	−	4.36100i	0.881615	−	0.165541i
$695$		0			0
$696$	3.72610	−	0.123861i	0.141237	−	0.00469493i
$697$	−4.11157	+	7.12145i	−0.155737	+	0.269744i
$698$	23.6515	+	27.5610i	0.895224	+	1.04320i
$699$	1.00189			0.0378950
$700$		0			0
$701$	43.0543			1.62614			0.813070	−	0.582166i	$-0.197795\pi$
$701$	43.0543			1.62614			0.813070	+	0.582166i	$0.197795\pi$
$702$	−4.33347	−	5.04977i	−0.163556	−	0.190591i
$703$	16.7658	−	29.0393i	0.632336	−	1.09524i
$704$	41.7639	−	27.9667i	1.57404	−	1.05403i
$705$		0			0
$706$	5.20454	−	0.977260i	0.195875	−	0.0367796i
$707$	−5.61261	+	7.55434i	−0.211084	+	0.284110i
$708$	15.5266	−	6.04398i	0.583526	−	0.227147i
$709$	−8.81431	−	15.2668i	−0.331028	−	0.573358i	0.651685	−	0.758489i	$-0.274062\pi$
$709$	−8.81431	−	15.2668i	−0.331028	−	0.573358i	−0.982714	+	0.185131i	$0.940729\pi$
$710$		0			0
$711$	−33.1305	−	19.1279i	−1.24249	−	0.717353i
$712$	−22.4486	−	11.9845i	−0.841295	−	0.449136i
$713$			16.3469i			0.612195i
$714$	9.33672	+	4.54907i	0.349418	+	0.170245i
$715$		0			0
$716$	−1.19162	+	1.48575i	−0.0445329	+	0.0555251i
$717$	−53.0706	−	30.6403i	−1.98196	−	1.14428i
$718$	−1.31436	+	3.73955i	−0.0490516	+	0.139559i
$719$	8.62714	+	14.9426i	0.321738	+	0.557266i	0.980847	−	0.194781i	$-0.0623997\pi$
$719$	8.62714	+	14.9426i	0.321738	+	0.557266i	−0.659109	+	0.752048i	$0.729066\pi$
$720$		0			0
$721$	−19.7713	+	8.55126i	−0.736321	+	0.318466i
$722$	−5.62069	−	29.9338i	−0.209180	−	1.11402i
$723$	−34.1186	+	19.6984i	−1.26889	+	0.732592i
$724$	3.32217	+	0.510188i	0.123468	+	0.0189610i
$725$		0			0
$726$	−78.5574	+	67.4143i	−2.91554	+	2.50198i
$727$	45.1263			1.67364			0.836822	−	0.547476i	$-0.184411\pi$
$727$	45.1263			1.67364			0.836822	+	0.547476i	$0.184411\pi$
$728$	9.61962	+	20.3570i	0.356527	+	0.754482i
$729$	−36.6148			−1.35611
$730$		0			0
$731$	0.368967	−	0.639069i	0.0136467	−	0.0236368i
$732$	−13.4103	−	2.05943i	−0.495660	−	0.0761188i
$733$	10.0484	−	5.80146i	0.371147	−	0.214282i	−0.302813	−	0.953050i	$-0.597926\pi$
$733$	10.0484	−	5.80146i	0.371147	−	0.214282i	0.673959	+	0.738768i	$0.264592\pi$
$734$	7.23792	+	38.5466i	0.267156	+	1.42278i
$735$		0			0
$736$	−10.8629	+	14.5066i	−0.400412	+	0.534719i
$737$	−23.7760	−	41.1812i	−0.875799	−	1.51693i
$738$	12.8863	−	36.6633i	0.474350	−	1.34959i
$739$	−28.9910	−	16.7380i	−1.06645	−	0.615716i	−0.139241	−	0.990258i	$-0.544466\pi$
$739$	−28.9910	−	16.7380i	−1.06645	−	0.615716i	−0.927210	+	0.374543i	$0.877800\pi$
$740$		0			0
$741$			49.2442i			1.80903i
$742$	8.34845	−	0.587233i	0.306481	−	0.0215580i
$743$			9.16966i			0.336402i	0.985753	+	0.168201i	$0.0537958\pi$
$743$			9.16966i			0.336402i	−0.985753	+	0.168201i	$0.946204\pi$
$744$	17.4722	−	32.7279i	0.640562	−	1.19986i
$745$		0			0
$746$	0.446463	+	0.156921i	0.0163462	+	0.00574529i
$747$	−2.47971	−	4.29498i	−0.0907277	−	0.157145i
$748$	12.6441	−	4.92190i	0.462313	−	0.179963i
$749$	4.80656	+	11.1132i	0.175628	+	0.406067i
$750$		0			0
$751$	34.9750	−	20.1928i	1.27626	−	0.736847i	0.300098	−	0.953908i	$-0.402980\pi$
$751$	34.9750	−	20.1928i	1.27626	−	0.736847i	0.976158	+	0.217061i	$0.0696472\pi$
$752$	9.74632	+	43.8234i	0.355412	+	1.59807i
$753$	37.1892	−	64.4136i	1.35525	−	2.34736i
$754$	1.42083	+	1.65568i	0.0517435	+	0.0602964i
$755$		0			0
$756$	−7.98028	−	2.18942i	−0.290240	−	0.0796283i
$757$	38.3251			1.39295			0.696475	−	0.717581i	$-0.254751\pi$
$757$	38.3251			1.39295			0.696475	+	0.717581i	$0.254751\pi$
$758$	−5.17805	−	6.03395i	−0.188075	−	0.219163i
$759$	25.8719	−	44.8115i	0.939091	−	1.62655i
$760$		0			0
$761$	−7.85793	+	4.53678i	−0.284850	+	0.164458i	−0.635617	−	0.772005i	$-0.719254\pi$
$761$	−7.85793	+	4.53678i	−0.284850	+	0.164458i	0.350767	+	0.936463i	$0.385921\pi$
$762$	31.9241	−	5.99441i	1.15649	−	0.217154i
$763$	9.03712	+	6.71427i	0.327166	+	0.243073i
$764$	−1.38582	−	3.56010i	−0.0501374	−	0.128800i
$765$		0			0
$766$	−46.0066	−	16.1702i	−1.66229	−	0.584254i
$767$	8.44414	+	4.87522i	0.304900	+	0.176034i
$768$	37.2537	−	17.4327i	1.34428	−	0.629049i
$769$		−	0.838217i		−	0.0302269i	−0.999886	−	0.0151134i	$-0.995189\pi$
$769$		−	0.838217i		−	0.0302269i	0.999886	−	0.0151134i	$-0.00481094\pi$
$770$		0			0
$771$		−	14.2497i		−	0.513192i
$772$	16.5511	+	13.2746i	0.595689	+	0.477762i
$773$	−10.7431	−	6.20254i	−0.386403	−	0.223090i	0.294198	−	0.955745i	$-0.404948\pi$
$773$	−10.7431	−	6.20254i	−0.386403	−	0.223090i	−0.680600	+	0.732655i	$0.738281\pi$
$774$	−1.15640	+	3.29011i	−0.0415658	+	0.118261i
$775$		0			0
$776$	18.1640	−	11.3078i	0.652049	−	0.405926i
$777$	−4.12394	+	35.5821i	−0.147946	+	1.27650i
$778$	2.66380	+	14.1864i	0.0955018	+	0.508609i
$779$	−41.9908	+	24.2434i	−1.50448	+	0.868610i
$780$		0			0
$781$	41.5096	−	71.8968i	1.48533	−	2.57267i
$782$	−3.71260	+	3.18598i	−0.132762	+	0.113930i
$783$	−0.801864			−0.0286563
$784$	24.0800	+	14.2883i	0.859998	+	0.510297i
$785$		0			0
$786$	−35.8083	+	30.7290i	−1.27724	+	1.09607i
$787$	1.01322	−	1.75496i	0.0361176	−	0.0625574i	−0.847402	−	0.530952i	$-0.821834\pi$
$787$	1.01322	−	1.75496i	0.0361176	−	0.0625574i	0.883519	+	0.468395i	$0.155168\pi$
$788$	−0.199340	+	1.29803i	−0.00710118	+	0.0462405i
$789$	10.0689	−	5.81328i	0.358462	−	0.206958i
$790$		0			0
$791$	4.05179	−	34.9595i	0.144065	−	1.24302i
$792$	−54.4359	+	33.8885i	−1.93430	+	1.20418i
$793$	−3.96992	−	6.87610i	−0.140976	−	0.244177i
$794$	−0.107557	+	0.306014i	−0.00381705	+	0.0108600i
$795$		0			0
$796$	−16.9652	−	13.6066i	−0.601314	−	0.482274i
$797$		−	32.6986i		−	1.15824i	−0.815241	−	0.579122i	$-0.803395\pi$
$797$		−	32.6986i		−	1.15824i	0.815241	−	0.579122i	$-0.196605\pi$
$798$	34.2657	+	50.7559i	1.21299	+	1.79674i
$799$			12.1190i			0.428738i
$800$		0			0
$801$	28.1148	+	16.2321i	0.993389	+	0.573533i
$802$	25.1727	+	8.84762i	0.888880	+	0.312420i
$803$	7.93253	+	13.7396i	0.279933	+	0.484858i
$804$	−14.1155	−	36.2618i	−0.497815	−	1.27886i
$805$		0			0
$806$	21.3382	−	4.00668i	0.751606	−	0.141129i
$807$	36.2838	−	20.9485i	1.27725	−	0.737422i
$808$	0.334255	+	10.0554i	0.0117590	+	0.353747i
$809$	1.19697	−	2.07322i	0.0420833	−	0.0728904i	−0.844217	−	0.536002i	$-0.819934\pi$
$809$	1.19697	−	2.07322i	0.0420833	−	0.0728904i	0.886300	+	0.463112i	$0.153267\pi$
$810$		0			0
$811$	32.2577			1.13272			0.566360	−	0.824158i	$-0.308351\pi$
$811$	32.2577			1.13272			0.566360	+	0.824158i	$0.308351\pi$
$812$	2.61651	+	0.717849i	0.0918217	+	0.0251916i
$813$	−12.1905			−0.427538
$814$	30.4749	+	35.5122i	1.06814	+	1.24470i
$815$		0			0
$816$	10.8383	−	2.41043i	0.379415	−	0.0843819i
$817$	3.76820	−	2.17557i	0.131832	−	0.0761135i
$818$	17.8566	−	3.35294i	0.624341	−	0.117233i
$819$	−11.4026	−	26.3637i	−0.398438	−	0.921224i
$820$		0			0
$821$	−10.5830	−	18.3303i	−0.369350	−	0.639734i	0.620114	−	0.784512i	$-0.287086\pi$
$821$	−10.5830	−	18.3303i	−0.369350	−	0.639734i	−0.989464	+	0.144778i	$0.953753\pi$
$822$	−49.1227	−	17.2655i	−1.71335	−	0.602203i
$823$	−18.6709	−	10.7796i	−0.650825	−	0.375754i	0.137947	−	0.990440i	$-0.455950\pi$
$823$	−18.6709	−	10.7796i	−0.650825	−	0.375754i	−0.788772	+	0.614685i	$0.789283\pi$
$824$	−10.8454	+	20.3149i	−0.377816	+	0.707703i
$825$		0			0
$826$	12.0957	−	0.850813i	0.420862	−	0.0296036i
$827$			11.5943i			0.403175i	0.979471	+	0.201587i	$0.0646100\pi$
$827$			11.5943i			0.403175i	−0.979471	+	0.201587i	$0.935390\pi$
$828$	14.4655	−	18.0360i	0.502709	−	0.626795i
$829$	−18.6146	−	10.7471i	−0.646510	−	0.373263i	0.140608	−	0.990065i	$-0.455094\pi$
$829$	−18.6146	−	10.7471i	−0.646510	−	0.373263i	−0.787118	+	0.616802i	$0.788428\pi$
$830$		0			0
$831$	25.0216	+	43.3387i	0.867990	+	1.50340i
$832$	21.5985	+	10.6241i	0.748793	+	0.368326i
$833$	5.50790	+	5.17626i	0.190837	+	0.179347i
$834$	12.1493	+	64.7031i	0.420697	+	2.24049i
$835$		0			0
$836$	79.0766	+	12.1438i	2.73492	+	0.420004i
$837$	−3.98977	+	6.91048i	−0.137907	+	0.238861i
$838$	−8.62785	+	7.40401i	−0.298044	+	0.255767i
$839$	−15.9350			−0.550138			−0.275069	−	0.961425i	$-0.588701\pi$
$839$	−15.9350			−0.550138			−0.275069	+	0.961425i	$0.588701\pi$
$840$		0			0
$841$	−28.7371			−0.990934
$842$	−29.5355	+	25.3460i	−1.01786	+	0.873480i
$843$	−4.39047	+	7.60451i	−0.151216	+	0.261913i
$844$	−39.7537	−	6.10501i	−1.36838	−	0.210143i
$845$		0			0
$846$	−10.5695	−	56.2896i	−0.363388	−	1.93528i
$847$	−69.1458	+	29.9062i	−2.37588	+	1.02759i
$848$	6.59230	−	6.04889i	0.226380	−	0.207720i
$849$	29.0034	+	50.2353i	0.995393	+	1.72407i
$850$		0			0
$851$	−14.6123	−	8.43641i	−0.500903	−	0.289197i
$852$	42.5047	−	52.9962i	1.45619	−	1.81562i
$853$			22.1234i			0.757492i	0.925501	+	0.378746i	$0.123645\pi$
$853$			22.1234i			0.757492i	−0.925501	+	0.378746i	$0.876355\pi$
$854$	−8.87638	−	4.32478i	−0.303743	−	0.147991i
$855$		0			0
$856$	11.4187	+	6.09605i	0.390285	+	0.208359i
$857$	−21.8630	−	12.6226i	−0.746825	−	0.431180i	0.0777204	−	0.996975i	$-0.475236\pi$
$857$	−21.8630	−	12.6226i	−0.746825	−	0.431180i	−0.824546	+	0.565795i	$0.808569\pi$
$858$	−64.8354	−	22.7881i	−2.21345	−	0.777974i
$859$	10.7089	+	18.5483i	0.365382	+	0.632860i	0.988837	−	0.148999i	$-0.0476051\pi$
$859$	10.7089	+	18.5483i	0.365382	+	0.632860i	−0.623456	+	0.781859i	$0.714272\pi$
$860$		0			0
$861$	30.8901	−	41.5768i	1.05273	−	1.41693i
$862$	−5.11309	+	0.960087i	−0.174152	+	0.0327007i
$863$	23.6694	−	13.6655i	0.805715	−	0.465180i	−0.0397506	−	0.999210i	$-0.512656\pi$
$863$	23.6694	−	13.6655i	0.805715	−	0.465180i	0.845466	+	0.534030i	$0.179323\pi$
$864$	−8.13279	+	3.48121i	−0.276683	+	0.118433i
$865$		0			0
$866$	−17.0741	−	19.8963i	−0.580202	−	0.676105i
$867$	−40.7042			−1.38239
$868$	19.2052	−	18.9774i	0.651868	−	0.644136i
$869$	−66.6111			−2.25963
$870$		0			0
$871$	11.3859	−	19.7210i	0.385797	−	0.668220i
$872$	12.0291	−	0.399863i	0.407355	−	0.0135411i
$873$	−23.6390	+	13.6480i	−0.800060	+	0.461915i
$874$	−28.3509	+	5.32347i	−0.958985	+	0.180069i
$875$		0			0
$876$	4.70945	+	12.0983i	0.159117	+	0.408763i
$877$	−2.88404	−	4.99531i	−0.0973872	−	0.168680i	0.813215	−	0.581963i	$-0.197715\pi$
$877$	−2.88404	−	4.99531i	−0.0973872	−	0.168680i	−0.910602	+	0.413283i	$0.864382\pi$
$878$	30.6362	+	10.7679i	1.03392	+	0.363399i
$879$	3.33082	+	1.92305i	0.112346	+	0.0648628i
$880$		0			0
$881$		−	5.17545i		−	0.174365i	−0.996192	−	0.0871827i	$-0.972214\pi$
$881$		−	5.17545i		−	0.174365i	0.996192	−	0.0871827i	$-0.0277864\pi$
$882$	−30.0973	−	19.2388i	−1.01343	−	0.647802i
$883$		−	29.4077i		−	0.989646i	−0.868994	−	0.494823i	$-0.835233\pi$
$883$		−	29.4077i		−	0.989646i	0.868994	−	0.494823i	$-0.164767\pi$
$884$	5.06875	+	4.06530i	0.170481	+	0.136731i
$885$		0			0
$886$	1.45064	−	4.12727i	0.0487351	−	0.138658i
$887$	14.0304	+	24.3014i	0.471095	+	0.815960i	0.999453	−	0.0330611i	$-0.0105256\pi$
$887$	14.0304	+	24.3014i	0.471095	+	0.815960i	−0.528358	+	0.849021i	$0.677192\pi$
$888$	20.2379	+	32.5087i	0.679141	+	1.09092i
$889$	23.4819	+	2.72154i	0.787557	+	0.0912775i
$890$		0			0
$891$	−37.0261	+	21.3770i	−1.24042	+	0.716158i
$892$	−5.12312	+	33.3600i	−0.171535	+	1.11698i
$893$	−35.7290	+	61.8845i	−1.19563	+	2.07089i
$894$	51.5475	−	44.2356i	1.72401	−	1.47946i
$895$		0			0
$896$	29.6541	−	4.07864i	0.990673	−	0.136258i
$897$	24.7792			0.827355
$898$	−18.3891	+	15.7806i	−0.613652	+	0.526607i
$899$	1.30814	−	2.26576i	0.0436288	−	0.0755672i
$900$		0			0
$901$	2.09161	−	1.20759i	0.0696817	−	0.0402307i
$902$	−12.4875	−	66.5043i	−0.415790	−	2.21435i
$903$	−2.77204	+	3.73105i	−0.0922476	+	0.124161i
$904$	−19.8839	−	31.9399i	−0.661328	−	1.06231i
$905$		0			0
$906$	18.3910	−	52.3251i	0.611001	−	1.73838i
$907$	−26.3877	−	15.2350i	−0.876191	−	0.505869i	−0.00679011	−	0.999977i	$-0.502161\pi$
$907$	−26.3877	−	15.2350i	−0.876191	−	0.505869i	−0.869400	+	0.494108i	$0.835495\pi$
$908$	−16.8292	−	13.4975i	−0.558495	−	0.447931i
$909$		−	12.8352i		−	0.425716i
$910$		0			0
$911$			31.0431i			1.02850i	0.857639	+	0.514252i	$0.171930\pi$
$911$			31.0431i			1.02850i	−0.857639	+	0.514252i	$0.828070\pi$
$912$	62.4511	+	19.6446i	2.06796	+	0.650498i
$913$	−7.47842	−	4.31767i	−0.247500	−	0.142894i
$914$	−27.9391	−	9.81995i	−0.924145	−	0.324815i
$915$		0			0
$916$	−14.0742	−	36.1558i	−0.465026	−	1.19462i
$917$	−31.5182	+	13.6319i	−1.04082	+	0.450166i
$918$	−2.34706	+	0.440710i	−0.0774647	+	0.0145456i
$919$	−22.3900	+	12.9268i	−0.738577	+	0.426417i	−0.821552	−	0.570134i	$-0.806891\pi$
$919$	−22.3900	+	12.9268i	−0.738577	+	0.426417i	0.0829750	+	0.996552i	$0.473558\pi$
$920$		0			0
$921$	−16.8266	+	29.1445i	−0.554454	+	0.960342i
$922$	3.65629	+	4.26065i	0.120413	+	0.140317i
$923$	39.7565			1.30860
$924$	−82.6823	+	21.6269i	−2.72005	+	0.711471i
$925$		0			0
$926$	−32.9627	−	38.4112i	−1.08322	−	1.26227i
$927$	14.6893	−	25.4426i	0.482460	−	0.835645i
$928$	2.66652	−	1.14139i	0.0875327	−	0.0374680i
$929$	31.8338	−	18.3793i	1.04443	−	0.603005i	0.123349	−	0.992363i	$-0.460637\pi$
$929$	31.8338	−	18.3793i	1.04443	−	0.603005i	0.921086	+	0.389359i	$0.127303\pi$
$930$		0			0
$931$	12.8650	+	42.6705i	0.421634	+	1.39847i
$932$	0.726384	−	0.282757i	0.0237935	−	0.00926200i
$933$	25.3211	+	43.8574i	0.828975	+	1.43583i
$934$	−2.76858	−	0.973091i	−0.0905908	−	0.0318405i
$935$		0			0
$936$	−27.0886	−	14.4616i	−0.885420	−	0.472693i
$937$			33.9818i			1.11014i	0.831804	+	0.555069i	$0.187308\pi$
$937$			33.9818i			1.11014i	−0.831804	+	0.555069i	$0.812692\pi$
$938$	−1.98704	−	28.2490i	−0.0648793	−	0.922362i
$939$			8.78816i			0.286791i
$940$		0			0
$941$	39.2248	+	22.6464i	1.27869	+	0.738253i	0.976608	−	0.215029i	$-0.0689846\pi$
$941$	39.2248	+	22.6464i	1.27869	+	0.738253i	0.302083	+	0.953282i	$0.402318\pi$
$942$	−20.7062	+	58.9121i	−0.674645	+	1.91946i
$943$	12.1991	+	21.1294i	0.397256	+	0.688067i
$944$	9.55126	−	8.76394i	0.310867	−	0.285242i
$945$		0			0
$946$	1.12062	+	5.96800i	0.0364343	+	0.194037i
$947$	1.46745	−	0.847235i	0.0476858	−	0.0275314i	−0.475968	−	0.879463i	$-0.657902\pi$
$947$	1.46745	−	0.847235i	0.0476858	−	0.0275314i	0.523653	+	0.851931i	$0.324569\pi$
$948$	−53.8771	−	8.27394i	−1.74985	−	0.268725i
$949$	−3.79876	+	6.57964i	−0.123313	+	0.213584i
$950$		0			0
$951$	−63.1197			−2.04680
$952$	8.05310	+	0.663099i	0.261003	+	0.0214912i
$953$	−1.16457			−0.0377243			−0.0188621	−	0.999822i	$-0.506004\pi$
$953$	−1.16457			−0.0377243			−0.0188621	+	0.999822i	$0.506004\pi$
$954$	−8.66182	+	7.43316i	−0.280437	+	0.240657i
$955$		0			0
$956$	−47.1243	−	7.23691i	−1.52411	−	0.234058i
$957$	−7.17195	+	4.14073i	−0.231836	+	0.133851i
$958$	−7.55846	−	40.2537i	−0.244203	−	1.30054i
$959$	−30.4171	−	22.5989i	−0.982220	−	0.729755i
$960$		0			0
$961$	2.48244	+	4.29970i	0.0800786	+	0.138700i
$962$	−7.43084	+	21.1418i	−0.239580	+	0.681639i
$963$	−14.3010	−	8.25667i	−0.460842	−	0.266068i
$964$	−19.1771	+	23.9107i	−0.617654	+	0.770112i
$965$		0			0
$966$	25.5399	−	17.2422i	0.821732	−	0.554757i
$967$			4.42142i			0.142183i	0.997470	+	0.0710916i	$0.0226483\pi$
$967$			4.42142i			0.142183i	−0.997470	+	0.0710916i	$0.977352\pi$
$968$	−37.9294	+	71.0470i	−1.21910	+	2.28354i
$969$	15.3051	+	8.83639i	0.491670	+	0.283866i
$970$		0			0
$971$	14.4037	+	24.9479i	0.462235	+	0.800615i	0.999072	−	0.0430713i	$-0.0137142\pi$
$971$	14.4037	+	24.9479i	0.462235	+	0.800615i	−0.536837	+	0.843686i	$0.680381\pi$
$972$	−41.3472	+	16.0950i	−1.32621	+	0.516248i
$973$	−5.51596	+	47.5926i	−0.176833	+	1.52575i
$974$	3.45846	−	0.649397i	0.110816	−	0.0208080i
$975$		0			0
$976$	−10.3039	+	2.29159i	−0.329819	+	0.0733519i
$977$	−5.47035	+	9.47493i	−0.175012	+	0.303130i	−0.940165	−	0.340718i	$-0.889330\pi$
$977$	−5.47035	+	9.47493i	−0.175012	+	0.303130i	0.765153	+	0.643848i	$0.222663\pi$
$978$	41.4732	+	48.3285i	1.32617	+	1.54538i
$979$	56.5268			1.80660
$980$		0			0
$981$	−15.3545			−0.490231
$982$	10.5941	+	12.3452i	0.338071	+	0.393952i
$983$	−5.65605	+	9.79656i	−0.180400	+	0.312462i	−0.942017	−	0.335566i	$-0.891073\pi$
$983$	−5.65605	+	9.79656i	−0.180400	+	0.312462i	0.761617	+	0.648028i	$0.224406\pi$
$984$	−1.83964	−	55.3418i	−0.0586455	−	1.76423i
$985$		0			0
$986$	0.769538	−	0.144497i	0.0245071	−	0.00460171i
$987$	8.78837	−	75.8276i	0.279737	−	2.41362i
$988$	13.8979	+	35.7028i	0.442150	+	1.13586i
$989$	−1.09473	−	1.89612i	−0.0348103	−	0.0602931i
$990$		0			0
$991$	21.1182	+	12.1926i	0.670841	+	0.387310i	0.796395	−	0.604777i	$-0.206738\pi$
$991$	21.1182	+	12.1926i	0.670841	+	0.387310i	−0.125555	+	0.992087i	$0.540071\pi$
$992$	3.43103	−	28.6592i	0.108935	−	0.909932i
$993$		−	2.53575i		−	0.0804696i
$994$	40.9769	−	27.6638i	1.29971	−	0.877442i
$995$		0			0
$996$	−5.51246	−	4.42117i	−0.174669	−	0.140090i
$997$	35.2161	+	20.3320i	1.11531	+	0.643922i	0.940198	−	0.340627i	$-0.110639\pi$
$997$	35.2161	+	20.3320i	1.11531	+	0.643922i	0.175107	+	0.984549i	$0.443973\pi$
$998$	−0.218984	+	0.623042i	−0.00693183	+	0.0197220i
$999$	−4.11814	−	7.13283i	−0.130292	−	0.225673i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.p.d.451.4	✓	32
4.3	odd	2	inner	700.2.p.d.451.15	yes	32
5.2	odd	4		700.2.t.e.199.10		64
5.3	odd	4		700.2.t.e.199.23		64
5.4	even	2		700.2.p.f.451.13	yes	32
7.5	odd	6	inner	700.2.p.d.551.15	yes	32
20.3	even	4		700.2.t.e.199.13		64
20.7	even	4		700.2.t.e.199.20		64
20.19	odd	2		700.2.p.f.451.2	yes	32
28.19	even	6	inner	700.2.p.d.551.4	yes	32
35.12	even	12		700.2.t.e.299.13		64
35.19	odd	6		700.2.p.f.551.2	yes	32
35.33	even	12		700.2.t.e.299.20		64
140.19	even	6		700.2.p.f.551.13	yes	32
140.47	odd	12		700.2.t.e.299.23		64
140.103	odd	12		700.2.t.e.299.10		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.p.d.451.4	✓	32	1.1	even	1	trivial
700.2.p.d.451.15	yes	32	4.3	odd	2	inner
700.2.p.d.551.4	yes	32	28.19	even	6	inner
700.2.p.d.551.15	yes	32	7.5	odd	6	inner
700.2.p.f.451.2	yes	32	20.19	odd	2
700.2.p.f.451.13	yes	32	5.4	even	2
700.2.p.f.551.2	yes	32	35.19	odd	6
700.2.p.f.551.13	yes	32	140.19	even	6
700.2.t.e.199.10		64	5.2	odd	4
700.2.t.e.199.13		64	20.3	even	4
700.2.t.e.199.20		64	20.7	even	4
700.2.t.e.199.23		64	5.3	odd	4
700.2.t.e.299.10		64	140.103	odd	12
700.2.t.e.299.13		64	35.12	even	12
700.2.t.e.299.20		64	35.33	even	12
700.2.t.e.299.23		64	140.47	odd	12

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07322 + 0.920983i) q^{2} +(1.28534 - 2.22627i) q^{3} +(0.303582 - 1.97683i) q^{4} +(0.670911 + 3.57303i) q^{6} +(-0.304602 + 2.62816i) q^{7} +(1.49481 + 2.40115i) q^{8} +(-1.80417 - 3.12492i) q^{9} +O(q^{10})\)	\(q+(-1.07322 + 0.920983i) q^{2} +(1.28534 - 2.22627i) q^{3} +(0.303582 - 1.97683i) q^{4} +(0.670911 + 3.57303i) q^{6} +(-0.304602 + 2.62816i) q^{7} +(1.49481 + 2.40115i) q^{8} +(-1.80417 - 3.12492i) q^{9} +(-5.44112 - 3.14143i) q^{11} +(-4.01073 - 3.21674i) q^{12} -3.00876i q^{13} +(-2.09358 - 3.10111i) q^{14} +(-3.81568 - 1.20026i) q^{16} +(-0.935120 - 0.539892i) q^{17} +(4.81426 + 1.69210i) q^{18} +(-3.18341 - 5.51382i) q^{19} +(5.45946 + 4.05619i) q^{21} +(8.73269 - 1.63974i) q^{22} +(-2.77450 + 1.60186i) q^{23} +(7.26694 - 0.241563i) q^{24} +(2.77101 + 3.22904i) q^{26} -1.56386 q^{27} +(5.10294 + 1.40001i) q^{28} +0.512747 q^{29} +(2.55123 - 4.41886i) q^{31} +(5.20046 - 2.22604i) q^{32} +(-13.9873 + 8.07558i) q^{33} +(1.50082 - 0.281809i) q^{34} +(-6.72514 + 2.61787i) q^{36} +(2.63332 + 4.56104i) q^{37} +(8.49461 + 2.98566i) q^{38} +(-6.69829 - 3.86726i) q^{39} -7.61555i q^{41} +(-9.59486 + 0.674906i) q^{42} +0.683409i q^{43} +(-7.86189 + 9.80246i) q^{44} +(1.50235 - 4.27441i) q^{46} +(-5.61176 - 9.71985i) q^{47} +(-7.57652 + 6.95197i) q^{48} +(-6.81444 - 1.60109i) q^{49} +(-2.40388 + 1.38788i) q^{51} +(-5.94778 - 0.913405i) q^{52} +(-1.11837 + 1.93707i) q^{53} +(1.67836 - 1.44029i) q^{54} +(-6.76593 + 3.19721i) q^{56} -16.3670 q^{57} +(-0.550288 + 0.472231i) q^{58} +(-1.62035 + 2.80652i) q^{59} +(2.28536 - 1.31945i) q^{61} +(1.33167 + 7.09203i) q^{62} +(8.76234 - 3.78980i) q^{63} +(-3.53107 + 7.17855i) q^{64} +(7.57394 - 21.5489i) q^{66} +(6.55453 + 3.78426i) q^{67} +(-1.35116 + 1.68467i) q^{68} +8.23571i q^{69} +13.2136i q^{71} +(4.80651 - 9.00327i) q^{72} +(-2.18683 - 1.26257i) q^{73} +(-7.02675 - 2.46974i) q^{74} +(-11.8663 + 4.61914i) q^{76} +(9.91356 - 13.3432i) q^{77} +(10.7504 - 2.01861i) q^{78} +(9.18163 - 5.30102i) q^{79} +(3.40244 - 5.89319i) q^{81} +(7.01379 + 8.17313i) q^{82} +1.37443 q^{83} +(9.67578 - 9.56102i) q^{84} +(-0.629408 - 0.733445i) q^{86} +(0.659051 - 1.14151i) q^{87} +(-0.590394 - 17.7608i) q^{88} +(-7.79161 + 4.49849i) q^{89} +(7.90749 + 0.916474i) q^{91} +(2.32431 + 5.97101i) q^{92} +(-6.55838 - 11.3594i) q^{93} +(14.9744 + 5.26316i) q^{94} +(1.72859 - 14.4388i) q^{96} -7.56469i q^{97} +(8.78793 - 4.55767i) q^{98} +22.6707i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} + q^{4} - 4 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q - q^2 + q^4 - 4 * q^8 - 16 * q^9	\( 32 q - q^{2} + q^{4} - 4 q^{8} - 16 q^{9} + 15 q^{12} - 13 q^{14} + q^{16} - 15 q^{18} + 12 q^{21} + 34 q^{22} - 18 q^{24} - 15 q^{26} + 17 q^{28} + 8 q^{29} + 14 q^{32} - 30 q^{36} - 16 q^{37} + 30 q^{38} + q^{42} + 12 q^{44} + 2 q^{46} + 20 q^{49} + 18 q^{52} - 20 q^{53} + 57 q^{54} - 31 q^{56} - 24 q^{57} - 4 q^{58} - 12 q^{61} + 40 q^{64} - 66 q^{66} + 15 q^{68} + 13 q^{72} - 72 q^{73} - q^{74} + 8 q^{77} + 60 q^{78} - 36 q^{81} - 66 q^{82} + 67 q^{84} + 4 q^{86} + 34 q^{88} - 60 q^{89} - 148 q^{92} - 20 q^{93} + 45 q^{94} + 93 q^{96}+O(q^{100}) \) 32 * q - q^2 + q^4 - 4 * q^8 - 16 * q^9 + 15 * q^12 - 13 * q^14 + q^16 - 15 * q^18 + 12 * q^21 + 34 * q^22 - 18 * q^24 - 15 * q^26 + 17 * q^28 + 8 * q^29 + 14 * q^32 - 30 * q^36 - 16 * q^37 + 30 * q^38 + q^42 + 12 * q^44 + 2 * q^46 + 20 * q^49 + 18 * q^52 - 20 * q^53 + 57 * q^54 - 31 * q^56 - 24 * q^57 - 4 * q^58 - 12 * q^61 + 40 * q^64 - 66 * q^66 + 15 * q^68 + 13 * q^72 - 72 * q^73 - q^74 + 8 * q^77 + 60 * q^78 - 36 * q^81 - 66 * q^82 + 67 * q^84 + 4 * q^86 + 34 * q^88 - 60 * q^89 - 148 * q^92 - 20 * q^93 + 45 * q^94 + 93 * q^96

Introduction

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