LMFDB - Embedded newform 700.2.t.e.299.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(199,700)]

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, 3, 1]))

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

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

chi := DirichletCharacter("700.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.t (of order $6$, degree $2$, not 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:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.13
Character	$\chi$	$=$	700.299
Dual form			700.2.t.e.199.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.468940 + 1.33420i) q^{2} +(-2.22627 + 1.28534i) q^{3} +(-1.56019 - 1.25132i) q^{4} +(-0.670911 - 3.57303i) q^{6} +(-2.62816 + 0.304602i) q^{7} +(2.40115 - 1.49481i) q^{8} +(1.80417 - 3.12492i) q^{9} +O(q^{10})$	\(q+(-0.468940 + 1.33420i) q^{2} +(-2.22627 + 1.28534i) q^{3} +(-1.56019 - 1.25132i) q^{4} +(-0.670911 - 3.57303i) q^{6} +(-2.62816 + 0.304602i) q^{7} +(2.40115 - 1.49481i) q^{8} +(1.80417 - 3.12492i) q^{9} +(5.44112 - 3.14143i) q^{11} +(5.08177 + 0.780410i) q^{12} +3.00876 q^{13} +(0.826049 - 3.64933i) q^{14} +(0.868384 + 3.90460i) q^{16} +(-0.539892 - 0.935120i) q^{17} +(3.32322 + 3.87253i) q^{18} +(-3.18341 + 5.51382i) q^{19} +(5.45946 - 4.05619i) q^{21} +(1.63974 + 8.73269i) q^{22} +(1.60186 - 2.77450i) q^{23} +(-3.42427 + 6.41414i) q^{24} +(-1.41093 + 4.01429i) q^{26} +1.56386i q^{27} +(4.48158 + 2.81344i) q^{28} -0.512747 q^{29} +(-2.55123 - 4.41886i) q^{31} +(-5.61675 - 0.672426i) q^{32} +(-8.07558 + 13.9873i) q^{33} +(1.50082 - 0.281809i) q^{34} +(-6.72514 + 2.61787i) q^{36} +(4.56104 + 2.63332i) q^{37} +(-5.86372 - 6.83296i) q^{38} +(-6.69829 + 3.86726i) q^{39} +7.61555i q^{41} +(2.85161 + 9.18614i) q^{42} +0.683409 q^{43} +(-12.4201 - 1.90737i) q^{44} +(2.95057 + 3.43828i) q^{46} +(9.71985 + 5.61176i) q^{47} +(-6.95197 - 7.57652i) q^{48} +(6.81444 - 1.60109i) q^{49} +(2.40388 + 1.38788i) q^{51} +(-4.69423 - 3.76492i) q^{52} +(-1.93707 + 1.11837i) q^{53} +(-2.08650 - 0.733357i) q^{54} +(-5.85529 + 4.66000i) q^{56} -16.3670i q^{57} +(0.240448 - 0.684108i) q^{58} +(-1.62035 - 2.80652i) q^{59} +(2.28536 + 1.31945i) q^{61} +(7.09203 - 1.33167i) q^{62} +(-3.78980 + 8.76234i) q^{63} +(3.53107 - 7.17855i) q^{64} +(-14.8749 - 17.3337i) q^{66} +(-3.78426 - 6.55453i) q^{67} +(-0.327803 + 2.13454i) q^{68} +8.23571i q^{69} +13.2136i q^{71} +(-0.339072 - 10.2003i) q^{72} +(1.26257 + 2.18683i) q^{73} +(-5.65223 + 4.85048i) q^{74} +(11.8663 - 4.61914i) q^{76} +(-13.3432 + 9.91356i) q^{77} +(-2.01861 - 10.7504i) q^{78} +(9.18163 + 5.30102i) q^{79} +(3.40244 + 5.89319i) q^{81} +(-10.1607 - 3.57124i) q^{82} +1.37443i q^{83} +(-13.5934 - 0.503125i) q^{84} +(-0.320478 + 0.911806i) q^{86} +(1.14151 - 0.659051i) q^{87} +(8.36911 - 15.6765i) q^{88} +(7.79161 + 4.49849i) q^{89} +(-7.90749 + 0.916474i) q^{91} +(-5.97101 + 2.32431i) q^{92} +(11.3594 + 6.55838i) q^{93} +(-12.0453 + 10.3367i) q^{94} +(13.3687 - 5.72240i) q^{96} -7.56469 q^{97} +(-1.05939 + 9.84265i) q^{98} -22.6707i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 2 q^{4} + 32 q^{9}+O(q^{10}) $ 64 * q - 2 * q^4 + 32 * q^9	$ 64 q - 2 q^{4} + 32 q^{9} + 26 q^{14} + 2 q^{16} + 24 q^{21} + 36 q^{24} - 30 q^{26} - 16 q^{29} - 60 q^{36} - 24 q^{44} + 4 q^{46} - 40 q^{49} - 114 q^{54} - 62 q^{56} - 24 q^{61} - 80 q^{64} - 132 q^{66} + 2 q^{74} - 72 q^{81} - 134 q^{84} + 8 q^{86} + 120 q^{89} - 90 q^{94} + 186 q^{96}+O(q^{100}) $ 64 * q - 2 * q^4 + 32 * q^9 + 26 * q^14 + 2 * q^16 + 24 * q^21 + 36 * q^24 - 30 * q^26 - 16 * q^29 - 60 * q^36 - 24 * q^44 + 4 * q^46 - 40 * q^49 - 114 * q^54 - 62 * q^56 - 24 * q^61 - 80 * q^64 - 132 * q^66 + 2 * q^74 - 72 * q^81 - 134 * q^84 + 8 * q^86 + 120 * q^89 - 90 * q^94 + 186 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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 $

$2$	−0.468940	+	1.33420i	−0.331591	+	0.943423i
$2$	−0.468940	+	1.33420i	−0.331591	+	0.943423i
$3$	−2.22627	+	1.28534i	−1.28534	+	0.742089i	−0.977819	−	0.209454i	$-0.932831\pi$
$3$	−2.22627	+	1.28534i	−1.28534	+	0.742089i	−0.307517	+	0.951543i	$0.599498\pi$
$4$	−1.56019	−	1.25132i	−0.780095	−	0.625661i
$5$		0			0
$5$		0			0
$6$	−0.670911	−	3.57303i	−0.273898	−	1.45869i
$7$	−2.62816	+	0.304602i	−0.993351	+	0.115129i
$7$	−2.62816	+	0.304602i	−0.993351	+	0.115129i
$8$	2.40115	−	1.49481i	0.848936	−	0.528496i
$9$	1.80417	−	3.12492i	0.601391	−	1.04164i
$10$		0			0
$11$	5.44112	−	3.14143i	1.64056	−	0.947177i	0.659924	−	0.751332i	$-0.270588\pi$
$11$	5.44112	−	3.14143i	1.64056	−	0.947177i	0.980635	−	0.195845i	$-0.0627449\pi$
$12$	5.08177	+	0.780410i	1.46698	+	0.225285i
$13$	3.00876			0.834479			0.417239	−	0.908797i	$-0.362998\pi$
$13$	3.00876			0.834479			0.417239	+	0.908797i	$0.362998\pi$
$14$	0.826049	−	3.64933i	0.220771	−	0.975326i
$15$		0			0
$16$	0.868384	+	3.90460i	0.217096	+	0.976150i
$17$	−0.539892	−	0.935120i	−0.130943	−	0.226800i	0.793097	−	0.609095i	$-0.208467\pi$
$17$	−0.539892	−	0.935120i	−0.130943	−	0.226800i	−0.924040	+	0.382295i	$0.875134\pi$
$18$	3.32322	+	3.87253i	0.783292	+	0.912765i
$19$	−3.18341	+	5.51382i	−0.730324	+	1.26496i	0.226421	+	0.974029i	$0.427297\pi$
$19$	−3.18341	+	5.51382i	−0.730324	+	1.26496i	−0.956745	+	0.290928i	$0.906036\pi$
$20$		0			0
$21$	5.45946	−	4.05619i	1.19135	−	0.885133i
$22$	1.63974	+	8.73269i	0.349594	+	1.86182i
$23$	1.60186	−	2.77450i	0.334011	−	0.578524i	−0.649283	−	0.760547i	$-0.724931\pi$
$23$	1.60186	−	2.77450i	0.334011	−	0.578524i	0.983294	+	0.182023i	$0.0582644\pi$
$24$	−3.42427	+	6.41414i	−0.698976	+	1.30928i
$25$		0			0
$26$	−1.41093	+	4.01429i	−0.276706	+	0.787267i
$27$			1.56386i			0.300965i
$28$	4.48158	+	2.81344i	0.846939	+	0.531690i
$29$	−0.512747			−0.0952147			−0.0476073	−	0.998866i	$-0.515160\pi$
$29$	−0.512747			−0.0952147			−0.0476073	+	0.998866i	$0.515160\pi$
$30$		0			0
$31$	−2.55123	−	4.41886i	−0.458215	−	0.793651i	0.540652	−	0.841246i	$-0.318178\pi$
$31$	−2.55123	−	4.41886i	−0.458215	−	0.793651i	−0.998867	+	0.0475952i	$0.984844\pi$
$32$	−5.61675	−	0.672426i	−0.992910	−	0.118869i
$33$	−8.07558	+	13.9873i	−1.40578	+	2.43488i
$34$	1.50082	−	0.281809i	0.257388	−	0.0483298i
$35$		0			0
$36$	−6.72514	+	2.61787i	−1.12086	+	0.436311i
$37$	4.56104	+	2.63332i	0.749830	+	0.432915i	0.825633	−	0.564208i	$-0.190818\pi$
$37$	4.56104	+	2.63332i	0.749830	+	0.432915i	−0.0758023	+	0.997123i	$0.524152\pi$
$38$	−5.86372	−	6.83296i	−0.951222	−	1.10845i
$39$	−6.69829	+	3.86726i	−1.07259	+	0.619257i
$40$		0			0
$41$			7.61555i			1.18935i	0.803966	+	0.594675i	$0.202719\pi$
$41$			7.61555i			1.18935i	−0.803966	+	0.594675i	$0.797281\pi$
$42$	2.85161	+	9.18614i	0.440013	+	1.41745i
$43$	0.683409			0.104219			0.0521095	−	0.998641i	$-0.483406\pi$
$43$	0.683409			0.104219			0.0521095	+	0.998641i	$0.483406\pi$
$44$	−12.4201	−	1.90737i	−1.87240	−	0.287546i
$45$		0			0
$46$	2.95057	+	3.43828i	0.435038	+	0.506947i
$47$	9.71985	+	5.61176i	1.41779	+	0.818559i	0.996104	−	0.0881845i	$-0.0281065\pi$
$47$	9.71985	+	5.61176i	1.41779	+	0.818559i	0.421682	+	0.906744i	$0.361440\pi$
$48$	−6.95197	−	7.57652i	−1.00343	−	1.09358i
$49$	6.81444	−	1.60109i	0.973491	−	0.228726i
$50$		0			0
$51$	2.40388	+	1.38788i	0.336611	+	0.194343i
$52$	−4.69423	−	3.76492i	−0.650973	−	0.522101i
$53$	−1.93707	+	1.11837i	−0.266076	+	0.153619i	−0.627103	−	0.778936i	$-0.715760\pi$
$53$	−1.93707	+	1.11837i	−0.266076	+	0.153619i	0.361027	+	0.932555i	$0.382426\pi$
$54$	−2.08650	−	0.733357i	−0.283937	−	0.0997973i
$55$		0			0
$56$	−5.85529	+	4.66000i	−0.782446	+	0.622719i
$57$		−	16.3670i		−	2.16786i
$58$	0.240448	−	0.684108i	0.0315723	−	0.0898277i
$59$	−1.62035	−	2.80652i	−0.210951	−	0.365378i	0.741061	−	0.671437i	$-0.234323\pi$
$59$	−1.62035	−	2.80652i	−0.210951	−	0.365378i	−0.952012	+	0.306059i	$0.900989\pi$
$60$		0			0
$61$	2.28536	+	1.31945i	0.292611	+	0.168939i	0.639119	−	0.769108i	$-0.279299\pi$
$61$	2.28536	+	1.31945i	0.292611	+	0.168939i	−0.346508	+	0.938047i	$0.612633\pi$
$62$	7.09203	−	1.33167i	0.900689	−	0.169123i
$63$	−3.78980	+	8.76234i	−0.477470	+	1.10395i
$64$	3.53107	−	7.17855i	0.441384	−	0.897318i
$65$		0			0
$66$	−14.8749	−	17.3337i	−1.83098	−	2.13363i
$67$	−3.78426	−	6.55453i	−0.462321	−	0.800763i	0.536755	−	0.843738i	$-0.319650\pi$
$67$	−3.78426	−	6.55453i	−0.462321	−	0.800763i	−0.999076	+	0.0429749i	$0.986316\pi$
$68$	−0.327803	+	2.13454i	−0.0397520	+	0.258851i
$69$			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	$0.713134\pi$
$72$	−0.339072	−	10.2003i	−0.0399601	−	1.20212i
$73$	1.26257	+	2.18683i	0.147772	+	0.255949i	0.930404	−	0.366536i	$-0.119456\pi$
$73$	1.26257	+	2.18683i	0.147772	+	0.255949i	−0.782632	+	0.622485i	$0.786123\pi$
$74$	−5.65223	+	4.85048i	−0.657059	+	0.563857i
$75$		0			0
$76$	11.8663	−	4.61914i	1.36116	−	0.529852i
$77$	−13.3432	+	9.91356i	−1.52060	+	1.12975i
$78$	−2.01861	−	10.7504i	−0.228562	−	1.21724i
$79$	9.18163	+	5.30102i	1.03301	+	0.596411i	0.917847	−	0.396935i	$-0.129926\pi$
$79$	9.18163	+	5.30102i	1.03301	+	0.596411i	0.115168	+	0.993346i	$0.463259\pi$
$80$		0			0
$81$	3.40244	+	5.89319i	0.378049	+	0.654799i
$82$	−10.1607	−	3.57124i	−1.12206	−	0.394378i
$83$			1.37443i			0.150863i	0.997151	+	0.0754315i	$0.0240334\pi$
$83$			1.37443i			0.150863i	−0.997151	+	0.0754315i	$0.975967\pi$
$84$	−13.5934	−	0.503125i	−1.48316	−	0.0548954i
$85$		0			0
$86$	−0.320478	+	0.911806i	−0.0345581	+	0.0983226i
$87$	1.14151	−	0.659051i	0.122383	−	0.0706577i
$88$	8.36911	−	15.6765i	0.892150	−	1.67112i
$89$	7.79161	+	4.49849i	0.825909	+	0.476839i	0.852450	−	0.522809i	$-0.175116\pi$
$89$	7.79161	+	4.49849i	0.825909	+	0.476839i	−0.0265409	+	0.999648i	$0.508449\pi$
$90$		0			0
$91$	−7.90749	+	0.916474i	−0.828930	+	0.0960725i
$92$	−5.97101	+	2.32431i	−0.622520	+	0.242326i
$93$	11.3594	+	6.55838i	1.17792	+	0.680072i
$94$	−12.0453	+	10.3367i	−1.24237	+	1.06615i
$95$		0			0
$96$	13.3687	−	5.72240i	1.36443	−	0.584040i
$97$	−7.56469			−0.768078			−0.384039	−	0.923317i	$-0.625467\pi$
$97$	−7.56469			−0.768078			−0.384039	+	0.923317i	$0.625467\pi$
$98$	−1.05939	+	9.84265i	−0.107015	+	0.994257i
$99$		−	22.6707i		−	2.27850i
$100$		0			0
$101$	3.08052	−	1.77854i	0.306523	−	0.176971i	−0.338846	−	0.940842i	$-0.610037\pi$
$101$	3.08052	−	1.77854i	0.306523	−	0.176971i	0.645370	+	0.763871i	$0.276703\pi$
$102$	−2.97900	+	2.55643i	−0.294964	+	0.253125i
$103$	7.05104	+	4.07092i	0.694760	+	0.401120i	0.805393	−	0.592742i	$-0.201954\pi$
$103$	7.05104	+	4.07092i	0.694760	+	0.401120i	−0.110633	+	0.993861i	$0.535288\pi$
$104$	7.22448	−	4.49753i	0.708419	−	0.441019i
$105$		0			0
$106$	−0.583757	−	3.10888i	−0.0566995	−	0.301962i
$107$	2.28821	−	3.96330i	0.221210	−	0.383147i	−0.733966	−	0.679187i	$-0.762333\pi$
$107$	2.28821	−	3.96330i	0.221210	−	0.383147i	0.955176	+	0.296040i	$0.0956660\pi$
$108$	1.95689	−	2.43992i	0.188302	−	0.234781i
$109$	−2.12763	−	3.68517i	−0.203790	−	0.352975i	0.745956	−	0.665995i	$-0.231993\pi$
$109$	−2.12763	−	3.68517i	−0.203790	−	0.352975i	−0.949747	+	0.313020i	$0.898659\pi$
$110$		0			0
$111$	−13.5388			−1.28504
$112$	−3.47160	−	9.99740i	−0.328035	−	0.944665i
$113$			13.3019i			1.25134i	0.780088	+	0.625669i	$0.215174\pi$
$113$			13.3019i			1.25134i	−0.780088	+	0.625669i	$0.784826\pi$
$114$	21.8369	+	7.67514i	2.04521	+	0.718843i
$115$		0			0
$116$	0.799982	+	0.641612i	0.0742765	+	0.0595721i
$117$	5.42832	−	9.40212i	0.501848	−	0.869227i
$118$	4.50431	−	0.845777i	0.414655	−	0.0778601i
$119$	1.70376	+	2.29319i	0.156183	+	0.210216i
$120$		0			0
$121$	14.2372	−	24.6595i	1.29429	−	2.24177i
$122$	−2.83212	+	2.43039i	−0.256408	+	0.220037i
$123$	−9.78854	−	16.9542i	−0.882603	−	1.52871i
$124$	−1.54902	+	10.0867i	−0.139106	+	0.905810i
$125$		0			0
$126$	−9.91354	−	9.16537i	−0.883169	−	0.816516i
$127$	8.93473			0.792829			0.396415	−	0.918072i	$-0.370254\pi$
$127$	8.93473			0.792829			0.396415	+	0.918072i	$0.370254\pi$
$128$	7.92177	+	8.07747i	0.700192	+	0.713955i
$129$	−1.52145	+	0.878410i	−0.133956	+	0.0773397i
$130$		0			0
$131$	−6.48963	+	11.2404i	−0.567002	+	0.982076i	0.429858	+	0.902896i	$0.358563\pi$
$131$	−6.48963	+	11.2404i	−0.567002	+	0.982076i	−0.996860	+	0.0791798i	$0.974770\pi$
$132$	30.1021	−	11.7177i	2.62005	−	1.01990i
$133$	6.68698	−	15.4609i	0.579834	−	1.34063i
$134$	10.5197	−	1.97528i	0.908760	−	0.170638i
$135$		0			0
$136$	−2.69419	−	1.43833i	−0.231025	−	0.123336i
$137$	12.4035	−	7.16118i	1.05971	−	0.611821i	0.134354	−	0.990933i	$-0.457104\pi$
$137$	12.4035	−	7.16118i	1.05971	−	0.611821i	0.925351	+	0.379112i	$0.123771\pi$
$138$	−10.9881	−	3.86206i	−0.935369	−	0.328760i
$139$	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
$142$	−17.6296	−	6.19639i	−1.47944	−	0.519990i
$143$	16.3710	−	9.45180i	1.36901	−	0.790399i
$144$	13.7683	+	4.33095i	1.14736	+	0.360912i
$145$		0			0
$146$	−3.50974	+	0.659026i	−0.290468	+	0.0545414i
$147$	−13.1128	+	12.3233i	−1.08153	+	1.01641i
$148$	−3.82096	−	9.81581i	−0.314081	−	0.806854i
$149$	9.34209	−	16.1810i	0.765334	−	1.32560i	−0.174736	−	0.984615i	$-0.555907\pi$
$149$	9.34209	−	16.1810i	0.765334	−	1.32560i	0.940070	−	0.340982i	$-0.110759\pi$
$150$		0			0
$151$	13.2121	−	7.62802i	1.07519	−	0.620760i	0.145593	−	0.989345i	$-0.453491\pi$
$151$	13.2121	−	7.62802i	1.07519	−	0.620760i	0.929594	+	0.368585i	$0.120158\pi$
$152$	0.598282	+	17.9981i	0.0485271	+	1.45984i
$153$	−3.89623			−0.314992
$154$	−6.96950	−	22.4514i	−0.561618	−	1.80919i
$155$		0			0
$156$	15.2898	+	2.34806i	1.22416	+	0.187996i
$157$	8.58829	+	14.8754i	0.685420	+	1.18718i	0.973305	+	0.229517i	$0.0737148\pi$
$157$	8.58829	+	14.8754i	0.685420	+	1.18718i	−0.287884	+	0.957665i	$0.592952\pi$
$158$	−11.3783	+	9.76429i	−0.905206	+	0.776805i
$159$	2.87495	−	4.97956i	0.227998	−	0.394905i
$160$		0			0
$161$	−3.36482	+	7.77977i	−0.265185	+	0.613131i
$162$	−9.45825	+	1.77598i	−0.743110	+	0.139534i
$163$	−8.75871	+	15.1705i	−0.686035	+	1.18825i	0.287075	+	0.957908i	$0.407317\pi$
$163$	−8.75871	+	15.1705i	−0.686035	+	1.18825i	−0.973110	+	0.230340i	$0.926016\pi$
$164$	9.52951	−	11.8817i	0.744130	−	0.927805i
$165$		0			0
$166$	−1.83376	−	0.644525i	−0.142328	−	0.0500248i
$167$		−	8.80963i		−	0.681710i	−0.940116	−	0.340855i	$-0.889284\pi$
$167$		−	8.80963i		−	0.681710i	0.940116	−	0.340855i	$-0.110716\pi$
$168$	7.04577	−	17.9004i	0.543593	−	1.38105i
$169$	−3.94739			−0.303645
$170$		0			0
$171$	11.4868	+	19.8958i	0.878420	+	1.52147i
$172$	−1.06625	−	0.855165i	−0.0813006	−	0.0652057i
$173$	2.38861	−	4.13719i	0.181602	−	0.314545i	−0.760824	−	0.648958i	$-0.775205\pi$
$173$	2.38861	−	4.13719i	0.181602	−	0.314545i	0.942426	+	0.334414i	$0.108538\pi$
$174$	0.344007	+	1.83206i	0.0260791	+	0.138888i
$175$		0			0
$176$	16.9910	+	18.5174i	1.28075	+	1.39580i
$177$	7.21464	+	4.16537i	0.542286	+	0.313089i
$178$	−9.65569	+	8.28606i	−0.723725	+	0.621066i
$179$	−0.824706	+	0.476144i	−0.0616414	+	0.0355887i	−0.530504	−	0.847682i	$-0.677997\pi$
$179$	−0.824706	+	0.476144i	−0.0616414	+	0.0355887i	0.468863	+	0.883271i	$0.344664\pi$
$180$		0			0
$181$		−	1.68056i		−	0.124915i	−0.998048	−	0.0624575i	$-0.980106\pi$
$181$		−	1.68056i		−	0.124915i	0.998048	−	0.0624575i	$-0.0198938\pi$
$182$	2.48538	−	10.9800i	0.184229	−	0.813889i
$183$	−6.78377			−0.501470
$184$	−0.301050	−	9.05649i	−0.0221937	−	0.667653i
$185$		0			0
$186$	−14.0771	+	12.0803i	−1.03218	+	0.885771i
$187$	−5.87523	−	3.39206i	−0.429639	−	0.248052i
$188$	−8.14269	−	20.9181i	−0.593867	−	1.52561i
$189$	−0.476355	−	4.11007i	−0.0346497	−	0.298964i
$190$		0			0
$191$	−1.65424	−	0.955079i	−0.119697	−	0.0691071i	0.438956	−	0.898508i	$-0.355348\pi$
$191$	−1.65424	−	0.955079i	−0.119697	−	0.0691071i	−0.558653	+	0.829401i	$0.688682\pi$
$192$	1.36573	+	20.5200i	0.0985633	+	1.48090i
$193$	−9.18716	+	5.30421i	−0.661306	+	0.381805i	−0.792774	−	0.609515i	$-0.791364\pi$
$193$	−9.18716	+	5.30421i	−0.661306	+	0.381805i	0.131468	+	0.991320i	$0.458031\pi$
$194$	3.54739	−	10.0928i	0.254688	−	0.724622i
$195$		0			0
$196$	−12.6353	−	6.02906i	−0.902520	−	0.430647i
$197$		−	0.656625i		−	0.0467826i	−0.999726	−	0.0233913i	$-0.992554\pi$
$197$		−	0.656625i		−	0.0467826i	0.999726	−	0.0233913i	$-0.00744636\pi$
$198$	30.2474	+	10.6312i	2.14959	+	0.755529i
$199$	5.43689	+	9.41698i	0.385411	+	0.667552i	0.991826	−	0.127597i	$-0.0407263\pi$
$199$	5.43689	+	9.41698i	0.385411	+	0.667552i	−0.606415	+	0.795148i	$0.707393\pi$
$200$		0			0
$201$	16.8495	+	9.72808i	1.18847	+	0.686166i
$202$	0.928349	+	4.94406i	0.0653184	+	0.347863i
$203$	1.34758	−	0.156184i	0.0945815	−	0.0109619i
$204$	−2.01383	−	5.17340i	−0.140996	−	0.362210i
$205$		0			0
$206$	−8.73795	+	7.49850i	−0.608802	+	0.522445i
$207$	−5.78007	−	10.0114i	−0.401743	−	0.695838i
$208$	2.61275	+	11.7480i	0.181162	+	0.814577i
$209$			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	$-0.243363\pi$
$212$	4.42163	+	0.679032i	0.303679	+	0.0466361i
$213$	−16.9839	−	29.4170i	−1.16372	−	2.01562i
$214$	4.21481	+	4.91149i	0.288119	+	0.335743i
$215$		0			0
$216$	2.33768	+	3.75507i	0.159059	+	0.255500i
$217$	8.05104	+	10.8364i	0.546540	+	0.735620i
$218$	5.91449	−	1.11057i	0.400580	−	0.0752171i
$219$	−5.62162	−	3.24564i	−0.379874	−	0.219320i
$220$		0			0
$221$	−1.62440	−	2.81355i	−0.109269	−	0.189260i
$222$	6.34888	−	18.0635i	0.426109	−	1.21234i
$223$		−	16.8755i		−	1.13007i	−0.825067	−	0.565035i	$-0.808863\pi$
$223$		−	16.8755i		−	1.13007i	0.825067	−	0.565035i	$-0.191137\pi$
$224$	14.9665	+	0.0563698i	0.999993	+	0.00376637i
$225$		0			0
$226$	−17.7474	−	6.23781i	−1.18054	−	0.414933i
$227$	9.34148	−	5.39331i	0.620016	−	0.357966i	−0.156859	−	0.987621i	$-0.550137\pi$
$227$	9.34148	−	5.39331i	0.620016	−	0.357966i	0.776875	+	0.629655i	$0.216804\pi$
$228$	−20.4804	+	25.5356i	−1.35635	+	1.69114i
$229$	−16.8003	−	9.69964i	−1.11019	−	0.640970i	−0.171314	−	0.985217i	$-0.554801\pi$
$229$	−16.8003	−	9.69964i	−1.11019	−	0.640970i	−0.938879	+	0.344246i	$0.888135\pi$
$230$		0			0
$231$	16.9633	−	39.2207i	1.11611	−	2.58054i
$232$	−1.23118	+	0.766460i	−0.0808311	+	0.0503206i
$233$	−0.337524	−	0.194869i	−0.0221119	−	0.0127663i	0.488903	−	0.872338i	$-0.337397\pi$
$233$	−0.337524	−	0.194869i	−0.0221119	−	0.0127663i	−0.511015	+	0.859572i	$0.670730\pi$
$234$	9.99877	+	11.6515i	0.653640	+	0.761683i
$235$		0			0
$236$	−0.983816	+	6.40628i	−0.0640410	+	0.417013i
$237$	−27.2543			−1.77036
$238$	−3.85854	+	1.19779i	−0.250112	+	0.0776412i
$239$			23.8384i			1.54198i	0.636850	+	0.770988i	$0.280237\pi$
$239$			23.8384i			1.54198i	−0.636850	+	0.770988i	$0.719763\pi$
$240$		0			0
$241$	−13.2723	+	7.66275i	−0.854942	+	0.493601i	−0.862315	−	0.506372i	$-0.830986\pi$
$241$	−13.2723	+	7.66275i	−0.854942	+	0.493601i	0.00737296	+	0.999973i	$0.497653\pi$
$242$	26.2244	+	30.5591i	1.68577	+	1.96441i
$243$	−19.2125	−	11.0923i	−1.23248	−	0.711573i
$244$	−1.91454	−	4.91833i	−0.122566	−	0.314864i
$245$		0			0
$246$	27.2106	−	5.10935i	1.73489	−	0.325761i
$247$	−9.57809	+	16.5897i	−0.609439	+	1.05558i
$248$	−12.7313	−	6.79675i	−0.808436	−	0.431594i
$249$	−1.76660	−	3.05984i	−0.111954	−	0.193910i
$250$		0			0
$251$	−28.9335			−1.82626			−0.913132	−	0.407664i	$-0.866343\pi$
$251$	−28.9335			−1.82626			−0.913132	+	0.407664i	$0.866343\pi$
$252$	16.8773	−	8.92866i	1.06317	−	0.562452i
$253$		−	20.1285i		−	1.26547i
$254$	−4.18986	+	11.9207i	−0.262895	+	0.747974i
$255$		0			0
$256$	−14.4918	+	6.78138i	−0.905739	+	0.423836i
$257$	−2.77160	+	4.80055i	−0.172888	+	0.299450i	−0.939428	−	0.342746i	$-0.888643\pi$
$257$	−2.77160	+	4.80055i	−0.172888	+	0.299450i	0.766541	+	0.642196i	$0.221976\pi$
$258$	−0.458506	−	2.44184i	−0.0285454	−	0.152023i
$259$	−12.7892	−	5.53147i	−0.794685	−	0.343709i
$260$		0			0
$261$	−0.925084	+	1.60229i	−0.0572613	+	0.0991794i
$262$	−11.9537	−	13.9295i	−0.738501	−	0.860570i
$263$	2.26139	+	3.91684i	0.139443	+	0.241523i	0.927286	−	0.374354i	$-0.122135\pi$
$263$	2.26139	+	3.91684i	0.139443	+	0.241523i	−0.787843	+	0.615876i	$0.788802\pi$
$264$	1.51771	+	45.6572i	0.0934085	+	2.81001i
$265$		0			0
$266$	17.4921	+	16.1720i	1.07251	+	0.991569i
$267$	−23.1283			−1.41543
$268$	−2.29767	+	14.9616i	−0.140352	+	0.913927i
$269$	−14.1145	+	8.14903i	−0.860579	+	0.496855i	−0.864206	−	0.503138i	$-0.832179\pi$
$269$	−14.1145	+	8.14903i	−0.860579	+	0.496855i	0.00362727	+	0.999993i	$0.498845\pi$
$270$		0			0
$271$	2.37107	−	4.10681i	0.144032	−	0.249471i	−0.784979	−	0.619522i	$-0.787326\pi$
$271$	2.37107	−	4.10681i	0.144032	−	0.249471i	0.929011	+	0.370051i	$0.120660\pi$
$272$	3.18244	−	2.92010i	0.192964	−	0.177057i
$273$	16.4262	−	12.2041i	0.994159	−	0.738625i
$274$	3.73794	+	19.9070i	0.225818	+	1.20262i
$275$		0			0
$276$	10.3055	−	12.8493i	0.620320	−	0.773435i
$277$	16.8589	−	9.73350i	1.01295	−	0.584829i	0.100899	−	0.994897i	$-0.467828\pi$
$277$	16.8589	−	9.73350i	1.01295	−	0.584829i	0.912055	+	0.410067i	$0.134495\pi$
$278$	−8.49192	+	24.1607i	−0.509311	+	1.44906i
$279$	−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	$0.532487\pi$
$282$	13.5299	−	38.4944i	0.805691	−	2.29231i
$283$	19.5417	−	11.2824i	1.16163	−	0.670670i	0.209939	−	0.977714i	$-0.432673\pi$
$283$	19.5417	−	11.2824i	1.16163	−	0.670670i	0.951695	+	0.307044i	$0.0993400\pi$
$284$	16.5345	−	20.6157i	0.981140	−	1.22332i
$285$		0			0
$286$	4.93359	+	26.2745i	0.291729	+	1.55365i
$287$	−2.31971	−	20.0149i	−0.136928	−	1.18144i
$288$	−12.2349	+	16.3387i	−0.720946	+	0.962768i
$289$	7.91703	−	13.7127i	0.465708	−	0.806630i
$290$		0			0
$291$	16.8410	−	9.72316i	0.987237	−	0.569982i
$292$	0.766586	−	4.99175i	0.0448611	−	0.292120i
$293$	−1.49614			−0.0874057			−0.0437028	−	0.999045i	$-0.513915\pi$
$293$	−1.49614			−0.0874057			−0.0437028	+	0.999045i	$0.513915\pi$
$294$	−10.2926	−	23.2740i	−0.600277	−	1.35737i
$295$		0			0
$296$	14.8881	−	0.494900i	0.865351	−	0.0287655i
$297$	4.91276	+	8.50915i	0.285067	+	0.493751i
$298$	17.2078	+	20.0522i	0.996821	+	1.16159i
$299$	4.81961	−	8.34780i	0.278725	−	0.482766i
$300$		0			0
$301$	−1.79611	+	0.208168i	−0.103526	+	0.0119986i
$302$	3.98162	+	21.2047i	0.229117	+	1.22020i
$303$	−4.57204	+	7.91900i	−0.262657	+	0.454935i
$304$	−24.2937	−	7.64182i	−1.39334	−	0.438288i
$305$		0			0
$306$	1.82710	−	5.19836i	0.104448	−	0.297170i
$307$			13.0912i			0.747153i	0.927599	+	0.373577i	$0.121869\pi$
$307$			13.0912i			0.747153i	−0.927599	+	0.373577i	$0.878131\pi$
$308$	33.2230	+	1.22966i	1.89306	+	0.0700666i
$309$	−20.9300			−1.19067
$310$		0			0
$311$	9.84999	+	17.0607i	0.558542	+	0.967423i	0.997619	+	0.0689731i	$0.0219723\pi$
$311$	9.84999	+	17.0607i	0.558542	+	0.967423i	−0.439077	+	0.898450i	$0.644694\pi$
$312$	−10.3028	+	19.2986i	−0.583281	+	1.09257i
$313$	−1.70931	+	2.96061i	−0.0966160	+	0.167344i	−0.910282	−	0.413989i	$-0.864135\pi$
$313$	−1.70931	+	2.96061i	−0.0966160	+	0.167344i	0.813666	+	0.581333i	$0.197469\pi$
$314$	−23.8741	+	4.48286i	−1.34729	+	0.252982i
$315$		0			0
$316$	−7.69180	−	19.7598i	−0.432698	−	1.11157i
$317$	−21.2642	−	12.2769i	−1.19432	−	0.689539i	−0.235035	−	0.971987i	$-0.575520\pi$
$317$	−21.2642	−	12.2769i	−1.19432	−	0.689539i	−0.959283	+	0.282448i	$0.908854\pi$
$318$	5.29556	+	6.17088i	0.296960	+	0.346046i
$319$	−2.78992	+	1.61076i	−0.156205	+	0.0901852i
$320$		0			0
$321$			11.7645i			0.656630i
$322$	−8.80188	−	8.13760i	−0.490509	−	0.453491i
$323$	6.87478			0.382523
$324$	2.06584	−	13.4520i	0.114769	−	0.747336i
$325$		0			0
$326$	−16.1332	−	18.8000i	−0.893537	−	1.04123i
$327$	9.47335	+	5.46944i	0.523878	+	0.302461i
$328$	11.3838	+	18.2861i	0.628566	+	1.00968i
$329$	−27.2547	−	11.7879i	−1.50260	−	0.649888i
$330$		0			0
$331$	−0.854261	−	0.493208i	−0.0469544	−	0.0271092i	0.476339	−	0.879262i	$-0.341964\pi$
$331$	−0.854261	−	0.493208i	−0.0469544	−	0.0271092i	−0.523293	+	0.852153i	$0.675297\pi$
$332$	1.71985	−	2.14437i	0.0943891	−	0.117687i
$333$	16.4578	−	9.50192i	0.901883	−	0.520702i
$334$	11.7538	+	4.13119i	0.643141	+	0.226049i
$335$		0			0
$336$	20.5787	+	17.7947i	1.12266	+	0.970780i
$337$			8.57714i			0.467226i	0.972330	+	0.233613i	$0.0750549\pi$
$337$			8.57714i			0.467226i	−0.972330	+	0.233613i	$0.924945\pi$
$338$	1.85109	−	5.26661i	0.100686	−	0.286466i
$339$	−17.0974	−	29.6136i	−0.928604	−	1.60839i
$340$		0			0
$341$	−27.7631	−	16.0290i	−1.50346	−	0.868021i
$342$	−31.9316	+	5.99582i	−1.72666	+	0.324217i
$343$	−17.4217	+	6.28360i	−0.940685	+	0.339282i
$344$	1.64097	−	1.02157i	0.0884752	−	0.0550793i
$345$		0			0
$346$	4.39973	+	5.12698i	0.236531	+	0.275628i
$347$	8.35484	+	14.4710i	0.448511	+	0.776844i	0.998289	−	0.0584664i	$-0.0186211\pi$
$347$	8.35484	+	14.4710i	0.448511	+	0.776844i	−0.549778	+	0.835311i	$0.685288\pi$
$348$	−2.60566	−	0.400153i	−0.139678	−	0.0214504i
$349$		−	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
$352$	−32.6738	+	13.9859i	−1.74152	+	0.745449i
$353$	1.87224	+	3.24282i	0.0996493	+	0.172598i	0.911540	−	0.411212i	$-0.134895\pi$
$353$	1.87224	+	3.24282i	0.0996493	+	0.172598i	−0.811890	+	0.583810i	$0.801561\pi$
$354$	−8.94069	+	7.67247i	−0.475192	+	0.407787i
$355$		0			0
$356$	−6.52733	−	16.7683i	−0.345948	−	0.888719i
$357$	−6.74054	−	2.91535i	−0.356747	−	0.154297i
$358$	−0.248535	−	1.32361i	−0.0131355	−	0.0699549i
$359$	2.42733	+	1.40142i	0.128109	+	0.0739640i	0.562685	−	0.826671i	$-0.309768\pi$
$359$	2.42733	+	1.40142i	0.128109	+	0.0739640i	−0.434576	+	0.900635i	$0.643102\pi$
$360$		0			0
$361$	−10.7682	−	18.6510i	−0.566745	−	0.981631i
$362$	2.24221	+	0.788082i	0.117848	+	0.0414207i
$363$			73.1982i			3.84191i
$364$	13.4840	+	8.46495i	0.706753	+	0.443684i
$365$		0			0
$366$	3.18118	−	9.05091i	0.166283	−	0.473099i
$367$	24.0174	−	13.8665i	1.25370	−	0.723823i	0.281856	−	0.959457i	$-0.409050\pi$
$367$	24.0174	−	13.8665i	1.25370	−	0.723823i	0.971842	+	0.235634i	$0.0757165\pi$
$368$	12.2244	+	3.84529i	0.637239	+	0.200450i
$369$	23.7980	+	13.7398i	1.23887	+	0.715264i
$370$		0			0
$371$	4.75026	−	3.52928i	0.246621	−	0.183231i
$372$	−9.51624	−	24.4466i	−0.493394	−	1.26750i
$373$	0.289797	+	0.167314i	0.0150051	+	0.00866321i	0.507484	−	0.861661i	$-0.330576\pi$
$373$	0.289797	+	0.167314i	0.0150051	+	0.00866321i	−0.492479	+	0.870325i	$0.663909\pi$
$374$	7.28083	−	6.24806i	0.376483	−	0.323080i
$375$		0			0
$376$	31.7274	−	1.05466i	1.63621	−	0.0543900i
$377$	−1.54273			−0.0794546
$378$	5.70705	+	1.29182i	0.293539	+	0.0664443i
$379$		−	5.62231i		−	0.288799i	−0.989519	−	0.144399i	$-0.953875\pi$
$379$		−	5.62231i		−	0.288799i	0.989519	−	0.144399i	$-0.0461250\pi$
$380$		0			0
$381$	−19.8911	+	11.4841i	−1.01905	+	0.588350i
$382$	2.05001	−	1.75922i	0.104888	−	0.0900096i
$383$	29.8627	+	17.2412i	1.52591	+	0.880986i	0.999527	+	0.0307396i	$0.00978627\pi$
$383$	29.8627	+	17.2412i	1.52591	+	0.880986i	0.526385	+	0.850246i	$0.323547\pi$
$384$	−28.0182	−	7.80048i	−1.42980	−	0.398066i
$385$		0			0
$386$	−2.76865	−	14.7449i	−0.140921	−	0.750495i
$387$	1.23299	−	2.13560i	0.0626763	−	0.108559i
$388$	11.8023	+	9.46586i	0.599173	+	0.480556i
$389$	−5.10332	−	8.83921i	−0.258749	−	0.448166i	0.707158	−	0.707055i	$-0.249977\pi$
$389$	−5.10332	−	8.83921i	−0.258749	−	0.448166i	−0.965907	+	0.258889i	$0.916643\pi$
$390$		0			0
$391$	−3.45932			−0.174946
$392$	13.9692	−	14.0308i	0.705550	−	0.708660i
$393$		−	33.3654i		−	1.68306i
$394$	0.876070	+	0.307918i	0.0441358	+	0.0155127i
$395$		0			0
$396$	−28.3684	+	35.3707i	−1.42557	+	1.77744i
$397$	−0.114681	+	0.198633i	−0.00575566	+	0.00996909i	−0.868889	−	0.495007i	$-0.835165\pi$
$397$	−0.114681	+	0.198633i	−0.00575566	+	0.00996909i	0.863133	+	0.504976i	$0.168499\pi$
$398$	−15.1137	+	2.83791i	−0.757583	+	0.142252i
$399$	4.98542	+	43.0150i	0.249583	+	2.15344i
$400$		0			0
$401$	−9.43363	+	16.3395i	−0.471093	+	0.815957i	−0.999453	−	0.0330632i	$-0.989474\pi$
$401$	−9.43363	+	16.3395i	−0.471093	+	0.815957i	0.528360	+	0.849020i	$0.322807\pi$
$402$	−20.8806	+	17.9188i	−1.04143	+	0.893708i
$403$	−7.67603	−	13.2953i	−0.382370	−	0.662285i
$404$	−7.03172	−	1.07987i	−0.349841	−	0.0537253i
$405$		0			0
$406$	−0.423554	+	1.87118i	−0.0210206	+	0.0928653i
$407$	33.0895			1.64019
$408$	7.84672	−	0.260836i	0.388470	−	0.0129133i
$409$	11.1260	−	6.42359i	0.550144	−	0.317626i	−0.199036	−	0.979992i	$-0.563781\pi$
$409$	11.1260	−	6.42359i	0.550144	−	0.317626i	0.749180	+	0.662366i	$0.230448\pi$
$410$		0			0
$411$	−18.4090	+	31.8854i	−0.908051	+	1.57279i
$412$	−5.90693	−	15.1745i	−0.291013	−	0.747596i
$413$	5.11340	+	6.88242i	0.251614	+	0.338662i
$414$	16.0677	−	3.01704i	0.789684	−	0.148279i
$415$		0			0
$416$	−16.8994	−	2.02317i	−0.828562	−	0.0991939i
$417$	−40.3148	+	23.2758i	−1.97423	+	1.13982i
$418$	−53.3705	−	18.7585i	−2.61044	−	0.917507i
$419$	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	$0.266021\pi$
$422$	26.8307	+	9.43034i	1.30610	+	0.459062i
$423$	35.0726	−	20.2492i	1.70529	−	0.984549i
$424$	−2.97945	+	5.58092i	−0.144695	+	0.271033i
$425$		0			0
$426$	47.2126	−	8.86514i	2.28746	−	0.429518i
$427$	−6.40820	−	2.77161i	−0.310115	−	0.134128i
$428$	−8.52942	+	3.32021i	−0.412285	+	0.160488i
$429$	−24.2975	+	42.0844i	−1.17309	+	2.03186i
$430$		0			0
$431$	−3.18583	+	1.83934i	−0.153456	+	0.0885980i	−0.574762	−	0.818321i	$-0.694905\pi$
$431$	−3.18583	+	1.83934i	−0.153456	+	0.0885980i	0.421306	+	0.906919i	$0.361572\pi$
$432$	−6.10625	+	1.35803i	−0.293787	+	0.0653383i
$433$	−18.5390			−0.890928			−0.445464	−	0.895300i	$-0.646961\pi$
$433$	−18.5390			−0.890928			−0.445464	+	0.895300i	$0.646961\pi$
$434$	−18.2334	+	5.66010i	−0.875229	+	0.271693i
$435$		0			0
$436$	−1.29182	+	8.41192i	−0.0618671	+	0.402858i
$437$	10.1987	+	17.6647i	0.487872	+	0.845019i
$438$	6.96655	−	5.97836i	0.332875	−	0.285657i
$439$	−11.4811	+	19.8859i	−0.547963	+	0.949100i	0.450451	+	0.892801i	$0.351263\pi$
$439$	−11.4811	+	19.8859i	−0.547963	+	0.949100i	−0.998414	+	0.0562989i	$0.982070\pi$
$440$		0			0
$441$	7.29116	−	24.1832i	0.347198	−	1.15158i
$442$	4.51559	−	0.847894i	0.214785	−	0.0403302i
$443$	1.54672	−	2.67900i	0.0734868	−	0.127283i	−0.826940	−	0.562290i	$-0.809921\pi$
$443$	1.54672	−	2.67900i	0.0734868	−	0.127283i	0.900427	+	0.435007i	$0.143254\pi$
$444$	21.1231	+	16.9414i	1.00246	+	0.804003i
$445$		0			0
$446$	22.5154	+	7.91362i	1.06613	+	0.374721i
$447$			48.0309i			2.27178i
$448$	−7.09362	+	19.9419i	−0.335142	+	0.942168i
$449$	−17.1346			−0.808630			−0.404315	−	0.914620i	$-0.632490\pi$
$449$	−17.1346			−0.808630			−0.404315	+	0.914620i	$0.632490\pi$
$450$		0			0
$451$	23.9237	+	41.4371i	1.12652	+	1.95120i
$452$	16.6450	−	20.7535i	0.782914	−	0.976163i
$453$	−19.6091	+	33.9640i	−0.921317	+	1.59577i
$454$	2.81516	+	14.9926i	0.132122	+	0.703636i
$455$		0			0
$456$	−24.4656	−	39.2996i	−1.14570	−	1.84037i
$457$	18.1352	+	10.4704i	0.848328	+	0.489783i	0.860086	−	0.510148i	$-0.170409\pi$
$457$	18.1352	+	10.4704i	0.848328	+	0.489783i	−0.0117581	+	0.999931i	$0.503743\pi$
$458$	20.8196	−	17.8664i	0.972836	−	0.834842i
$459$	1.46240	−	0.844315i	0.0682588	−	0.0394092i
$460$		0			0
$461$			3.96999i			0.184901i	0.995717	+	0.0924504i	$0.0294699\pi$
$461$			3.96999i			0.184901i	−0.995717	+	0.0924504i	$0.970530\pi$
$462$	44.3736	+	41.0247i	2.06445	+	1.90864i
$463$	35.7908			1.66334			0.831669	−	0.555272i	$-0.187386\pi$
$463$	35.7908			1.66334			0.831669	+	0.555272i	$0.187386\pi$
$464$	−0.445261	−	2.00207i	−0.0206707	−	0.0929438i
$465$		0			0
$466$	0.418274	−	0.358943i	0.0193762	−	0.0166277i
$467$	−1.79708	−	1.03754i	−0.0831588	−	0.0480117i	0.457844	−	0.889033i	$-0.348622\pi$
$467$	−1.79708	−	1.03754i	−0.0831588	−	0.0480117i	−0.541003	+	0.841021i	$0.681955\pi$
$468$	−20.2343	+	7.87652i	−0.935331	+	0.364092i
$469$	11.9422	+	16.0736i	0.551437	+	0.742212i
$470$		0			0
$471$	−38.2396	−	22.0777i	−1.76199	−	1.01729i
$472$	−8.08592	−	4.31677i	−0.372185	−	0.198696i
$473$	3.71851	−	2.14688i	0.170977	−	0.0987138i
$474$	12.7807	−	36.3628i	0.587035	−	1.67020i
$475$		0			0
$476$	0.211332	−	5.70977i	0.00968639	−	0.261707i
$477$			8.07090i			0.369541i
$478$	−31.8052	−	11.1788i	−1.45474	−	0.511305i
$479$	−14.4805	−	25.0810i	−0.661633	−	1.14598i	−0.980186	−	0.198077i	$-0.936530\pi$
$479$	−14.4805	−	25.0810i	−0.661633	−	1.14598i	0.318553	−	0.947905i	$-0.396803\pi$
$480$		0			0
$481$	13.7231	+	7.92301i	0.625718	+	0.361258i
$482$	−3.99975	−	21.3013i	−0.182184	−	0.970246i
$483$	−2.50862	−	21.6448i	−0.114146	−	0.984870i
$484$	−53.0697	+	20.6582i	−2.41226	+	0.939010i
$485$		0			0
$486$	23.8089	−	20.4317i	1.07999	−	0.926800i
$487$	1.24412	+	2.15488i	0.0563764	+	0.0976468i	0.892836	−	0.450381i	$-0.148712\pi$
$487$	1.24412	+	2.15488i	0.0563764	+	0.0976468i	−0.836460	+	0.548028i	$0.815379\pi$
$488$	7.45984	−	0.247975i	0.337691	−	0.0112253i
$489$		−	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	$-0.0835783\pi$
$492$	−5.94325	+	38.7005i	−0.267943	+	1.74475i
$493$	0.276828	+	0.479479i	0.0124677	+	0.0215947i
$494$	−17.6425	−	20.5587i	−0.793774	−	0.924980i
$495$		0			0
$496$	15.0384	−	13.7988i	0.675246	−	0.619585i
$497$	−4.02489	−	34.7274i	−0.180541	−	1.55774i
$498$	4.91088	−	0.922118i	0.220062	−	0.0413211i
$499$	0.404414	+	0.233489i	0.0181041	+	0.0104524i	0.509025	−	0.860752i	$-0.330006\pi$
$499$	0.404414	+	0.233489i	0.0181041	+	0.0104524i	−0.490921	+	0.871204i	$0.663340\pi$
$500$		0			0
$501$	11.3233	+	19.6126i	0.505889	+	0.876225i
$502$	13.5681	−	38.6031i	0.605573	−	1.72294i
$503$		−	16.4547i		−	0.733679i	−0.930284	−	0.366840i	$-0.880440\pi$
$503$		−	16.4547i		−	0.733679i	0.930284	−	0.366840i	$-0.119560\pi$
$504$	3.99817	+	26.7048i	0.178093	+	1.18952i
$505$		0			0
$506$	26.8555	+	9.43909i	1.19387	+	0.419619i
$507$	8.78793	−	5.07371i	0.390286	−	0.225332i
$508$	−13.9399	−	11.1802i	−0.618482	−	0.496043i
$509$	25.2083	+	14.5540i	1.11734	+	0.645095i	0.940720	−	0.339185i	$-0.110151\pi$
$509$	25.2083	+	14.5540i	1.11734	+	0.645095i	0.176617	+	0.984280i	$0.443485\pi$
$510$		0			0
$511$	−3.98434	−	5.36276i	−0.176257	−	0.237234i
$512$	−2.25193	−	22.5151i	−0.0995224	−	0.995035i
$513$	−8.62284	−	4.97840i	−0.380708	−	0.219802i
$514$	−5.10519	−	5.94905i	−0.225180	−	0.262401i
$515$		0			0
$516$	3.47293	+	0.533339i	0.152887	+	0.0234790i
$517$	70.5158			3.10128
$518$	13.3775	−	14.4695i	0.587774	−	0.635754i
$519$			12.2806i			0.539060i
$520$		0			0
$521$	−15.2705	+	8.81643i	−0.669013	+	0.386255i	−0.795702	−	0.605688i	$-0.792898\pi$
$521$	−15.2705	+	8.81643i	−0.669013	+	0.386255i	0.126690	+	0.991942i	$0.459565\pi$
$522$	−1.70397	−	1.98563i	−0.0745808	−	0.0869086i
$523$	−25.9343	−	14.9732i	−1.13403	−	0.654732i	−0.189084	−	0.981961i	$-0.560552\pi$
$523$	−25.9343	−	14.9732i	−1.13403	−	0.654732i	−0.944945	+	0.327229i	$0.893885\pi$
$524$	24.1904	−	9.41649i	1.05676	−	0.411361i
$525$		0			0
$526$	−6.28631	+	1.18038i	−0.274096	+	0.0514672i
$527$	−2.75478	+	4.77141i	−0.120000	+	0.207846i
$528$	−61.6276	−	19.3856i	−2.68200	−	0.843649i
$529$	6.36809	+	11.0298i	0.276873	+	0.479559i
$530$		0			0
$531$	−11.6935			−0.507456
$532$	−29.7795	+	15.7543i	−1.29110	+	0.683037i
$533$			22.9133i			0.992487i
$534$	10.8458	−	30.8578i	0.469343	−	1.33535i
$535$		0			0
$536$	−18.8844	−	10.0817i	−0.815681	−	0.435462i
$537$	1.22401	−	2.12005i	0.0528199	−	0.0914868i
$538$	−4.25358	−	22.6531i	−0.183385	−	0.976643i
$539$	32.0484	−	30.1188i	1.38042	−	1.29731i
$540$		0			0
$541$	9.92543	−	17.1913i	0.426727	−	0.739114i	−0.569853	−	0.821747i	$-0.693000\pi$
$541$	9.92543	−	17.1913i	0.426727	−	0.739114i	0.996580	+	0.0826334i	$0.0263330\pi$
$542$	4.36743	+	5.08933i	0.187597	+	0.218606i
$543$	2.16008	+	3.74137i	0.0926980	+	0.160558i
$544$	2.40364	+	5.61537i	0.103055	+	0.240757i
$545$		0			0
$546$	8.57981	+	27.6389i	0.367182	+	1.18283i
$547$	−31.0237			−1.32648			−0.663238	−	0.748409i	$-0.730818\pi$
$547$	−31.0237			−1.32648			−0.663238	+	0.748409i	$0.730818\pi$
$548$	−28.3128	−	4.34802i	−1.20946	−	0.185738i
$549$	8.24638	−	4.76105i	0.351947	−	0.203197i
$550$		0			0
$551$	1.63228	−	2.82719i	0.0695375	−	0.120443i
$552$	12.3108	+	19.7752i	0.523984	+	0.841689i
$553$	−25.7455	−	11.1352i	−1.09481	−	0.473516i
$554$	5.08063	+	27.0576i	0.215855	+	1.14957i
$555$		0			0
$556$	−28.2531	−	22.6599i	−1.19820	−	0.960992i
$557$	2.70836	−	1.56367i	0.114757	−	0.0662549i	−0.441523	−	0.897250i	$-0.645562\pi$
$557$	2.70836	−	1.56367i	0.114757	−	0.0662549i	0.556280	+	0.830995i	$0.312228\pi$
$558$	8.63388	−	24.5646i	0.365501	−	1.03990i
$559$	2.05621			0.0869685
$560$		0			0
$561$	17.4398			0.736307
$562$	1.60181	−	4.55739i	0.0675684	−	0.192242i
$563$	−31.5469	+	18.2136i	−1.32954	+	0.767612i	−0.985229	−	0.171242i	$-0.945222\pi$
$563$	−31.5469	+	18.2136i	−1.32954	+	0.767612i	−0.344315	+	0.938854i	$0.611889\pi$
$564$	45.0145	+	36.1031i	1.89545	+	1.52022i
$565$		0			0
$566$	5.88912	+	31.3634i	0.247538	+	1.31830i
$567$	−10.7372	−	14.4519i	−0.450921	−	0.606921i
$568$	19.7518	+	31.7279i	0.828769	+	1.33127i
$569$	6.12584	−	10.6103i	0.256809	−	0.444806i	−0.708577	−	0.705634i	$-0.750662\pi$
$569$	6.12584	−	10.6103i	0.256809	−	0.444806i	0.965385	+	0.260828i	$0.0839957\pi$
$570$		0			0
$571$	15.7382	−	9.08645i	0.658623	−	0.380256i	−0.133129	−	0.991099i	$-0.542502\pi$
$571$	15.7382	−	9.08645i	0.658623	−	0.380256i	0.791752	+	0.610842i	$0.209169\pi$
$572$	−37.3691	−	5.73880i	−1.56248	−	0.239951i
$573$	4.91039			0.205134
$574$	27.7917	+	6.29082i	1.16000	+	0.262574i
$575$		0			0
$576$	−16.0617	−	23.9857i	−0.669238	−	0.999403i
$577$	−15.6648	−	27.1323i	−0.652135	−	1.12953i	−0.982604	−	0.185714i	$-0.940540\pi$
$577$	−15.6648	−	27.1323i	−0.652135	−	1.12953i	0.330468	−	0.943817i	$-0.392793\pi$
$578$	14.5829	+	16.9934i	0.606569	+	0.706831i
$579$	13.6354	−	23.6172i	0.566667	−	0.981496i
$580$		0			0
$581$	−0.418653	−	3.61221i	−0.0173687	−	0.149860i
$582$	5.07523	+	27.0289i	0.210375	+	1.12038i
$583$	−7.02654	+	12.1703i	−0.291009	+	0.504043i
$584$	6.30052	+	3.36361i	0.260717	+	0.139187i
$585$		0			0
$586$	0.701603	−	1.99616i	0.0289829	−	0.0824606i
$587$			25.7715i			1.06370i	0.846838	+	0.531851i	$0.178504\pi$
$587$			25.7715i			1.06370i	−0.846838	+	0.531851i	$0.821496\pi$
$588$	35.8789	−	2.81829i	1.47962	−	0.116224i
$589$	32.4864			1.33858
$590$		0			0
$591$	0.843983	+	1.46182i	0.0347168	+	0.0601313i
$592$	−6.32132	+	20.0958i	−0.259805	+	0.825931i
$593$	24.2936	−	42.0778i	0.997620	−	1.72793i	0.439100	−	0.898438i	$-0.355297\pi$
$593$	24.2936	−	42.0778i	0.997620	−	1.72793i	0.558520	−	0.829491i	$-0.311369\pi$
$594$	−13.6567	+	2.56433i	−0.560342	+	0.105216i
$595$		0			0
$596$	−34.8231	+	13.5554i	−1.42641	+	0.555252i
$597$	−24.2079	−	13.9765i	−0.990765	−	0.572018i
$598$	8.87755	+	10.3450i	0.363030	+	0.423037i
$599$	−8.04858	+	4.64685i	−0.328856	+	0.189865i	−0.655333	−	0.755340i	$-0.727472\pi$
$599$	−8.04858	+	4.64685i	−0.328856	+	0.189865i	0.326477	+	0.945205i	$0.394138\pi$
$600$		0			0
$601$		−	34.0570i		−	1.38922i	−0.719388	−	0.694608i	$-0.755578\pi$
$601$		−	34.0570i		−	1.38922i	0.719388	−	0.694608i	$-0.244422\pi$
$602$	0.564530	−	2.49399i	0.0230085	−	0.101647i
$603$	−27.3098			−1.11214
$604$	−30.1585	−	4.63147i	−1.22713	−	0.188452i
$605$		0			0
$606$	−8.42153	−	9.81356i	−0.342101	−	0.398649i
$607$	5.75030	+	3.31994i	0.233397	+	0.134752i	0.612138	−	0.790751i	$-0.290310\pi$
$607$	5.75030	+	3.31994i	0.233397	+	0.134752i	−0.378741	+	0.925503i	$0.623643\pi$
$608$	21.5880	−	28.8291i	0.875510	−	1.16918i
$609$	−2.79932	+	2.07980i	−0.113434	+	0.0842777i
$610$		0			0
$611$	29.2447	+	16.8844i	1.18311	+	0.683070i
$612$	6.07886	+	4.87544i	0.245723	+	0.197078i
$613$	−23.6290	+	13.6422i	−0.954366	+	0.551003i	−0.894434	−	0.447199i	$-0.852422\pi$
$613$	−23.6290	+	13.6422i	−0.954366	+	0.551003i	−0.0599315	+	0.998202i	$0.519088\pi$
$614$	−17.4663	−	6.13899i	−0.704882	−	0.247749i
$615$		0			0
$616$	−17.2202	+	43.7496i	−0.693823	+	1.76272i
$617$			19.4392i			0.782591i	0.920265	+	0.391296i	$0.127973\pi$
$617$			19.4392i			0.782591i	−0.920265	+	0.391296i	$0.872027\pi$
$618$	9.81492	−	27.9248i	0.394814	−	1.12330i
$619$	−9.21113	−	15.9541i	−0.370226	−	0.641251i	0.619374	−	0.785096i	$-0.287387\pi$
$619$	−9.21113	−	15.9541i	−0.370226	−	0.641251i	−0.989600	+	0.143845i	$0.954053\pi$
$620$		0			0
$621$	4.33893	+	2.50508i	0.174115	+	0.100526i
$622$	−27.3815	+	5.14143i	−1.09790	+	0.206153i
$623$	−21.8478	−	9.44940i	−0.875315	−	0.378582i
$624$	−20.9168	−	22.7959i	−0.837342	−	0.912566i
$625$		0			0
$626$	−3.14849	−	3.66892i	−0.125839	−	0.146640i
$627$	−51.4157	−	89.0547i	−2.05335	−	3.55650i
$628$	5.21451	−	33.9551i	0.208081	−	1.35496i
$629$		−	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	$0.743544\pi$
$632$	29.9705	−	0.996262i	1.19216	−	0.0396292i
$633$	25.8480	+	44.7700i	1.02736	+	1.77945i
$634$	26.3515	−	22.6136i	1.04655	−	0.898102i
$635$		0			0
$636$	−10.7165	+	4.17157i	−0.424937	+	0.165413i
$637$	20.5030	−	4.81728i	0.812357	−	0.190867i
$638$	−0.840773	−	4.47766i	−0.0332865	−	0.177272i
$639$	41.2914	+	23.8396i	1.63346	+	0.943081i
$640$		0			0
$641$	4.11480	+	7.12704i	0.162525	+	0.281501i	0.935774	−	0.352602i	$-0.114703\pi$
$641$	4.11480	+	7.12704i	0.162525	+	0.281501i	−0.773249	+	0.634103i	$0.781370\pi$
$642$	−15.6962	−	5.51685i	−0.619480	−	0.217733i
$643$		−	11.2586i		−	0.443997i	−0.975047	−	0.221999i	$-0.928742\pi$
$643$		−	11.2586i		−	0.443997i	0.975047	−	0.221999i	$-0.0712581\pi$
$644$	14.9848	−	7.92743i	0.590482	−	0.312385i
$645$		0			0
$646$	−3.22386	+	9.17234i	−0.126841	+	0.360881i
$647$	−11.5368	+	6.66075i	−0.453557	+	0.261861i	−0.709331	−	0.704875i	$-0.751003\pi$
$647$	−11.5368	+	6.66075i	−0.453557	+	0.261861i	0.255774	+	0.966737i	$0.417670\pi$
$648$	16.9790	+	9.06445i	0.666998	+	0.356085i
$649$	−17.6330	−	10.1804i	−0.692155	−	0.399616i
$650$		0			0
$651$	−31.8521	−	13.7763i	−1.24838	−	0.539937i
$652$	32.6485	−	12.7089i	1.27861	−	0.497720i
$653$	27.4868	+	15.8695i	1.07564	+	0.621022i	0.929718	−	0.368273i	$-0.120051\pi$
$653$	27.4868	+	15.8695i	1.07564	+	0.621022i	0.145925	+	0.989296i	$0.453384\pi$
$654$	−11.7398	+	10.0745i	−0.459062	+	0.393945i
$655$		0			0
$656$	−29.7357	+	6.61322i	−1.16098	+	0.258203i
$657$	9.11156			0.355476
$658$	28.5083	−	30.8354i	1.11137	−	1.20209i
$659$			14.2935i			0.556794i	0.960466	+	0.278397i	$0.0898031\pi$
$659$			14.2935i			0.556794i	−0.960466	+	0.278397i	$0.910197\pi$
$660$		0			0
$661$	9.88604	−	5.70771i	0.384522	−	0.222004i	−0.295262	−	0.955416i	$-0.595407\pi$
$661$	9.88604	−	5.70771i	0.384522	−	0.222004i	0.679784	+	0.733412i	$0.262074\pi$
$662$	1.05864	−	0.908472i	0.0411451	−	0.0353088i
$663$	7.23270	+	4.17580i	0.280895	+	0.162175i
$664$	2.05451	+	3.30021i	0.0797305	+	0.128073i
$665$		0			0
$666$	4.95975	+	26.4139i	0.192186	+	1.02352i
$667$	−0.821349	+	1.42262i	−0.0318027	+	0.0550840i
$668$	−11.0237	+	13.7447i	−0.426519	+	0.531798i
$669$	21.6907	+	37.5694i	0.838612	+	1.45252i
$670$		0			0
$671$	16.5799			0.640060
$672$	−33.3919	+	19.1115i	−1.28812	+	0.737242i
$673$			37.1970i			1.43384i	0.697155	+	0.716920i	$0.254449\pi$
$673$			37.1970i			1.43384i	−0.697155	+	0.716920i	$0.745551\pi$
$674$	−11.4436	−	4.02217i	−0.440792	−	0.154928i
$675$		0			0
$676$	6.15867	+	4.93945i	0.236872	+	0.189979i
$677$	−2.22036	+	3.84578i	−0.0853354	+	0.147805i	−0.905534	−	0.424274i	$-0.860529\pi$
$677$	−2.22036	+	3.84578i	−0.0853354	+	0.147805i	0.820199	+	0.572079i	$0.193863\pi$
$678$	47.5282	−	8.92440i	1.82531	−	0.342739i
$679$	19.8812	−	2.30422i	0.762970	−	0.0884278i
$680$		0			0
$681$	−13.8644	+	24.0139i	−0.531286	+	0.920214i
$682$	34.4052	−	29.5249i	1.31744	−	1.13057i
$683$	−17.5430	−	30.3854i	−0.671265	−	1.16267i	−0.977546	−	0.210724i	$-0.932418\pi$
$683$	−17.5430	−	30.3854i	−0.671265	−	1.16267i	0.306280	−	0.951941i	$-0.400916\pi$
$684$	6.97440	−	45.4149i	0.266673	−	1.73648i
$685$		0			0
$686$	−0.213838	−	26.1907i	−0.00816437	−	0.999967i
$687$	49.8692			1.90263
$688$	0.593461	+	2.66844i	0.0226255	+	0.101733i
$689$	−5.82816	+	3.36489i	−0.222035	+	0.128192i
$690$		0			0
$691$	19.1235	−	33.1229i	0.727493	−	1.26005i	−0.230447	−	0.973085i	$-0.574019\pi$
$691$	19.1235	−	33.1229i	0.727493	−	1.26005i	0.957940	−	0.286969i	$-0.0926478\pi$
$692$	−8.90364	+	3.46588i	−0.338466	+	0.131753i
$693$	6.90556	+	59.5823i	0.262320	+	2.26335i
$694$	−23.2252	+	4.36100i	−0.881615	+	0.165541i
$695$		0			0
$696$	1.75578	−	3.28883i	0.0665528	−	0.124663i
$697$	7.12145	−	4.11157i	0.269744	−	0.155737i
$698$	34.2633	+	12.0428i	1.29689	+	0.455825i
$699$	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	$0.197795\pi$
$702$	−6.27778	−	2.20649i	−0.236940	−	0.0832787i
$703$	−29.0393	+	16.7658i	−1.09524	+	0.632336i
$704$	−3.33793	−	50.1519i	−0.125803	−	1.89017i
$705$		0			0
$706$	−5.20454	+	0.977260i	−0.195875	+	0.0367796i
$707$	−7.55434	+	5.61261i	−0.284110	+	0.211084i
$708$	−6.04398	−	15.5266i	−0.227147	−	0.583526i
$709$	8.81431	−	15.2668i	0.331028	−	0.573358i	−0.651685	−	0.758489i	$-0.725938\pi$
$709$	8.81431	−	15.2668i	0.331028	−	0.573358i	0.982714	+	0.185131i	$0.0592711\pi$
$710$		0			0
$711$	33.1305	−	19.1279i	1.24249	−	0.717353i
$712$	25.4332	−	0.845436i	0.953151	−	0.0316841i
$713$	−16.3469			−0.612195
$714$	7.05058	−	7.62612i	0.263861	−	0.285400i
$715$		0			0
$716$	1.88251	+	0.289098i	0.0703526	+	0.0108041i
$717$	−30.6403	−	53.0706i	−1.14428	−	1.98196i
$718$	−3.00805	+	2.58136i	−0.112259	+	0.0963356i
$719$	8.62714	−	14.9426i	0.321738	−	0.557266i	−0.659109	−	0.752048i	$-0.729066\pi$
$719$	8.62714	−	14.9426i	0.321738	−	0.557266i	0.980847	+	0.194781i	$0.0623997\pi$
$720$		0			0
$721$	−19.7713	−	8.55126i	−0.736321	−	0.318466i
$722$	29.9338	−	5.62069i	1.11402	−	0.209180i
$723$	19.6984	−	34.1186i	0.732592	−	1.26889i
$724$	−2.10292	+	2.62199i	−0.0781545	+	0.0974455i
$725$		0			0
$726$	−97.6612	−	34.3256i	−3.62455	−	1.27394i
$727$		−	45.1263i		−	1.67364i	−0.547476	−	0.836822i	$-0.684411\pi$
$727$		−	45.1263i		−	1.67364i	0.547476	−	0.836822i	$-0.315589\pi$
$728$	−17.6171	+	14.0208i	−0.652934	+	0.519646i
$729$	36.6148			1.35611
$730$		0			0
$731$	−0.368967	−	0.639069i	−0.0136467	−	0.0236368i
$732$	10.5840	+	8.48868i	0.391195	+	0.313751i
$733$	5.80146	−	10.0484i	0.214282	−	0.371147i	−0.738768	−	0.673959i	$-0.764592\pi$
$733$	5.80146	−	10.0484i	0.214282	−	0.371147i	0.953050	+	0.302813i	$0.0979256\pi$
$734$	7.23792	+	38.5466i	0.267156	+	1.42278i
$735$		0			0
$736$	−10.8629	+	14.5066i	−0.400412	+	0.534719i
$737$	−41.1812	−	23.7760i	−1.51693	−	0.875799i
$738$	−29.4915	+	25.3082i	−1.08560	+	0.931607i
$739$	−28.9910	+	16.7380i	−1.06645	+	0.615716i	−0.927210	−	0.374543i	$-0.877800\pi$
$739$	−28.9910	+	16.7380i	−1.06645	+	0.615716i	−0.139241	+	0.990258i	$0.544466\pi$
$740$		0			0
$741$		−	49.2442i		−	1.80903i
$742$	2.48118	+	7.99283i	0.0910869	+	0.293426i
$743$	9.16966			0.336402			0.168201	−	0.985753i	$-0.446204\pi$
$743$	9.16966			0.336402			0.168201	+	0.985753i	$0.446204\pi$
$744$	37.0793	−	1.23257i	1.35939	−	0.0451881i
$745$		0			0
$746$	−0.359129	+	0.308187i	−0.0131486	+	0.0112835i
$747$	4.29498	+	2.47971i	0.157145	+	0.0907277i
$748$	4.92190	+	12.6441i	0.179963	+	0.462313i
$749$	−4.80656	+	11.1132i	−0.175628	+	0.406067i
$750$		0			0
$751$	−34.9750	−	20.1928i	−1.27626	−	0.736847i	−0.300098	−	0.953908i	$-0.597020\pi$
$751$	−34.9750	−	20.1928i	−1.27626	−	0.736847i	−0.976158	+	0.217061i	$0.930353\pi$
$752$	−13.4711	+	42.8253i	−0.491241	+	1.56168i
$753$	64.4136	−	37.1892i	2.34736	−	1.35525i
$754$	0.723448	−	2.05831i	0.0263464	−	0.0749593i
$755$		0			0
$756$	−4.39982	+	7.00856i	−0.160020	+	0.254899i
$757$			38.3251i			1.39295i	0.717581	+	0.696475i	$0.245249\pi$
$757$			38.3251i			1.39295i	−0.717581	+	0.696475i	$0.754751\pi$
$758$	7.50130	+	2.63653i	0.272459	+	0.0957631i
$759$	25.8719	+	44.8115i	0.939091	+	1.62655i
$760$		0			0
$761$	−7.85793	−	4.53678i	−0.284850	−	0.164458i	0.350767	−	0.936463i	$-0.385921\pi$
$761$	−7.85793	−	4.53678i	−0.284850	−	0.164458i	−0.635617	+	0.772005i	$0.719254\pi$
$762$	−5.99441	−	31.9241i	−0.217154	−	1.15649i
$763$	6.71427	+	9.03712i	0.243073	+	0.327166i
$764$	1.38582	+	3.56010i	0.0501374	+	0.128800i
$765$		0			0
$766$	−37.0071	+	31.7578i	−1.33712	+	1.14745i
$767$	−4.87522	−	8.44414i	−0.176034	−	0.304900i
$768$	23.5463	−	33.7240i	0.849654	−	1.21691i
$769$		−	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
$772$	20.9710	+	3.22053i	0.754762	+	0.115909i
$773$	6.20254	+	10.7431i	0.223090	+	0.386403i	0.955745	−	0.294198i	$-0.0950524\pi$
$773$	6.20254	+	10.7431i	0.223090	+	0.386403i	−0.732655	+	0.680600i	$0.761719\pi$
$774$	2.27112	+	2.64652i	0.0816338	+	0.0951274i
$775$		0			0
$776$	−18.1640	+	11.3078i	−0.652049	+	0.405926i
$777$	35.5821	−	4.12394i	1.27650	−	0.147946i
$778$	14.1864	−	2.66380i	0.508609	−	0.0955018i
$779$	−41.9908	−	24.2434i	−1.50448	−	0.868610i
$780$		0			0
$781$	41.5096	+	71.8968i	1.48533	+	2.57267i
$782$	1.62222	−	4.61544i	0.0580104	−	0.165048i
$783$		−	0.801864i		−	0.0286563i
$784$	12.1691	+	25.2173i	0.434612	+	0.900618i
$785$		0			0
$786$	44.5162	+	15.6464i	1.58784	+	0.558088i
$787$	1.75496	−	1.01322i	0.0625574	−	0.0361176i	−0.468395	−	0.883519i	$-0.655168\pi$
$787$	1.75496	−	1.01322i	0.0625574	−	0.0361176i	0.530952	+	0.847402i	$0.321834\pi$
$788$	−0.821650	+	1.02446i	−0.0292701	+	0.0364949i
$789$	−10.0689	−	5.81328i	−0.358462	−	0.206958i
$790$		0			0
$791$	−4.05179	−	34.9595i	−0.144065	−	1.24302i
$792$	−33.8885	−	54.4359i	−1.20418	−	1.93430i
$793$	6.87610	+	3.96992i	0.244177	+	0.140976i
$794$	−0.211238	−	0.246154i	−0.00749655	−	0.00873568i
$795$		0			0
$796$	3.30109	−	21.4956i	0.117004	−	0.761890i
$797$	−32.6986			−1.15824			−0.579122	−	0.815241i	$-0.696605\pi$
$797$	−32.6986			−1.15824			−0.579122	+	0.815241i	$0.696605\pi$
$798$	−59.7286	−	13.5199i	−2.11437	−	0.478600i
$799$		−	12.1190i		−	0.428738i
$800$		0			0
$801$	28.1148	−	16.2321i	0.993389	−	0.573533i
$802$	−17.3764	−	20.2486i	−0.613583	−	0.715004i
$803$	13.7396	+	7.93253i	0.484858	+	0.279933i
$804$	−14.1155	−	36.2618i	−0.497815	−	1.27886i
$805$		0			0
$806$	21.3382	−	4.00668i	0.751606	−	0.141129i
$807$	20.9485	−	36.2838i	0.737422	−	1.27725i
$808$	4.73822	−	8.87534i	0.166690	−	0.312233i
$809$	−1.19697	−	2.07322i	−0.0420833	−	0.0728904i	0.844217	−	0.536002i	$-0.180066\pi$
$809$	−1.19697	−	2.07322i	−0.0420833	−	0.0728904i	−0.886300	+	0.463112i	$0.846733\pi$
$810$		0			0
$811$	−32.2577			−1.13272			−0.566360	−	0.824158i	$-0.691649\pi$
$811$	−32.2577			−1.13272			−0.566360	+	0.824158i	$0.691649\pi$
$812$	−2.29792	−	1.44258i	−0.0806410	−	0.0506247i
$813$			12.1905i			0.427538i
$814$	−15.5170	+	44.1481i	−0.543871	+	1.54739i
$815$		0			0
$816$	−3.33164	+	10.5914i	−0.116631	+	0.370774i
$817$	−2.17557	+	3.76820i	−0.0761135	+	0.131832i
$818$	3.35294	+	17.8566i	0.117233	+	0.624341i
$819$	−11.4026	+	26.3637i	−0.398438	+	0.921224i
$820$		0			0
$821$	−10.5830	+	18.3303i	−0.369350	+	0.639734i	−0.989464	−	0.144778i	$-0.953753\pi$
$821$	−10.5830	+	18.3303i	−0.369350	+	0.639734i	0.620114	+	0.784512i	$0.287086\pi$
$822$	−33.9088	−	39.5137i	−1.18271	−	1.37820i
$823$	−10.7796	−	18.6709i	−0.375754	−	0.650825i	0.614685	−	0.788772i	$-0.289283\pi$
$823$	−10.7796	−	18.6709i	−0.375754	−	0.650825i	−0.990440	+	0.137947i	$0.955950\pi$
$824$	23.0159	−	0.765080i	0.801797	−	0.0266528i
$825$		0			0
$826$	−11.5804	+	3.59486i	−0.402934	+	0.125081i
$827$	−11.5943			−0.403175			−0.201587	−	0.979471i	$-0.564610\pi$
$827$	−11.5943			−0.403175			−0.201587	+	0.979471i	$0.564610\pi$
$828$	−3.50945	+	22.8524i	−0.121962	+	0.794175i
$829$	18.6146	−	10.7471i	0.646510	−	0.373263i	−0.140608	−	0.990065i	$-0.544906\pi$
$829$	18.6146	−	10.7471i	0.646510	−	0.373263i	0.787118	+	0.616802i	$0.211572\pi$
$830$		0			0
$831$	−25.0216	+	43.3387i	−0.867990	+	1.50340i
$832$	10.6241	−	21.5985i	0.368326	−	0.748793i
$833$	−5.17626	−	5.50790i	−0.179347	−	0.190837i
$834$	−12.1493	−	64.7031i	−0.420697	−	2.24049i
$835$		0			0
$836$	50.0552	−	62.4104i	1.73119	−	2.15851i
$837$	6.91048	−	3.98977i	0.238861	−	0.137907i
$838$	−3.76993	+	10.7260i	−0.130230	+	0.370523i
$839$	−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
$842$	−12.9055	+	36.7180i	−0.444754	+	1.26539i
$843$	7.60451	−	4.39047i	0.261913	−	0.151216i
$844$	−25.1640	+	31.3752i	−0.866179	+	1.07998i
$845$		0			0
$846$	10.5695	+	56.2896i	0.363388	+	1.93528i
$847$	−29.9062	+	69.1458i	−1.02759	+	2.37588i
$848$	−6.04889	−	6.59230i	−0.207720	−	0.226380i
$849$	−29.0034	+	50.2353i	−0.995393	+	1.72407i
$850$		0			0
$851$	14.6123	−	8.43641i	0.500903	−	0.289197i
$852$	−10.3120	+	67.1484i	−0.353284	+	2.30047i
$853$	−22.1234			−0.757492			−0.378746	−	0.925501i	$-0.623645\pi$
$853$	−22.1234			−0.757492			−0.378746	+	0.925501i	$0.623645\pi$
$854$	6.70295	−	7.25012i	0.229370	−	0.248094i
$855$		0			0
$856$	−0.430042	−	12.9369i	−0.0146985	−	0.442176i
$857$	−12.6226	−	21.8630i	−0.431180	−	0.746825i	0.565795	−	0.824546i	$-0.308569\pi$
$857$	−12.6226	−	21.8630i	−0.431180	−	0.746825i	−0.996975	+	0.0777204i	$0.975236\pi$
$858$	−44.7551	−	52.1528i	−1.52791	−	1.78047i
$859$	10.7089	−	18.5483i	0.365382	−	0.632860i	−0.623456	−	0.781859i	$-0.714272\pi$
$859$	10.7089	−	18.5483i	0.365382	−	0.632860i	0.988837	+	0.148999i	$0.0476051\pi$
$860$		0			0
$861$	30.8901	+	41.5768i	1.05273	+	1.41693i
$862$	−0.960087	−	5.11309i	−0.0327007	−	0.174152i
$863$	−13.6655	+	23.6694i	−0.465180	+	0.805715i	−0.999210	−	0.0397506i	$-0.987344\pi$
$863$	−13.6655	+	23.6694i	−0.465180	+	0.805715i	0.534030	+	0.845466i	$0.320677\pi$
$864$	1.05158	−	8.78380i	0.0357755	−	0.298831i
$865$		0			0
$866$	8.69369	−	24.7348i	0.295424	−	0.840522i
$867$			40.7042i			1.38239i
$868$	0.998640	−	26.9812i	0.0338961	−	0.915802i
$869$	66.6111			2.25963
$870$		0			0
$871$	−11.3859	−	19.7210i	−0.385797	−	0.668220i
$872$	−10.6174	−	5.66824i	−0.359551	−	0.191951i
$873$	−13.6480	+	23.6390i	−0.461915	+	0.800060i
$874$	−28.3509	+	5.32347i	−0.958985	+	0.180069i
$875$		0			0
$876$	4.70945	+	12.0983i	0.159117	+	0.408763i
$877$	−4.99531	−	2.88404i	−0.168680	−	0.0973872i	0.413283	−	0.910602i	$-0.364382\pi$
$877$	−4.99531	−	2.88404i	−0.168680	−	0.0973872i	−0.581963	+	0.813215i	$0.697715\pi$
$878$	−21.1478	−	24.6434i	−0.713704	−	0.831674i
$879$	3.33082	−	1.92305i	0.112346	−	0.0648628i
$880$		0			0
$881$			5.17545i			0.174365i	0.996192	+	0.0871827i	$0.0277864\pi$
$881$			5.17545i			0.174365i	−0.996192	+	0.0871827i	$0.972214\pi$
$882$	28.8462	+	21.0684i	0.971301	+	0.709409i
$883$	−29.4077			−0.989646			−0.494823	−	0.868994i	$-0.664767\pi$
$883$	−29.4077			−0.989646			−0.494823	+	0.868994i	$0.664767\pi$
$884$	−0.986279	+	6.42232i	−0.0331722	+	0.216006i
$885$		0			0
$886$	2.84900	+	3.31992i	0.0957141	+	0.111535i
$887$	−24.3014	−	14.0304i	−0.815960	−	0.471095i	0.0330611	−	0.999453i	$-0.489474\pi$
$887$	−24.3014	−	14.0304i	−0.815960	−	0.471095i	−0.849021	+	0.528358i	$0.822808\pi$
$888$	−32.5087	+	20.2379i	−1.09092	+	0.679141i
$889$	−23.4819	+	2.72154i	−0.787557	+	0.0912775i
$890$		0			0
$891$	37.0261	+	21.3770i	1.24042	+	0.716158i
$892$	−21.1167	+	26.3290i	−0.707041	+	0.881562i
$893$	−61.8845	+	35.7290i	−2.07089	+	1.19563i
$894$	−64.0829	−	22.5236i	−2.14325	−	0.753303i
$895$		0			0
$896$	−23.2801	−	18.8159i	−0.777733	−	0.628595i
$897$			24.7792i			0.827355i
$898$	8.03509	−	22.8610i	0.268135	−	0.762881i
$899$	1.30814	+	2.26576i	0.0436288	+	0.0755672i
$900$		0			0
$901$	2.09161	+	1.20759i	0.0696817	+	0.0402307i
$902$	−66.5043	+	12.4875i	−2.21435	+	0.415790i
$903$	3.73105	−	2.77204i	0.124161	−	0.0922476i
$904$	19.8839	+	31.9399i	0.661328	+	1.06231i
$905$		0			0
$906$	−36.1193	−	42.0896i	−1.19998	−	1.39833i
$907$	15.2350	+	26.3877i	0.505869	+	0.876191i	0.999977	+	0.00679011i	$0.00216138\pi$
$907$	15.2350	+	26.3877i	0.505869	+	0.876191i	−0.494108	+	0.869400i	$0.664505\pi$
$908$	−21.3233	−	3.27463i	−0.707637	−	0.108672i
$909$		−	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	$0.828070\pi$
$912$	63.9065	−	14.2128i	2.11616	−	0.470633i
$913$	4.31767	+	7.47842i	0.142894	+	0.247500i
$914$	−22.4739	+	19.2860i	−0.743370	+	0.637925i
$915$		0			0
$916$	14.0742	+	36.1558i	0.465026	+	1.19462i
$917$	13.6319	−	31.5182i	0.450166	−	1.04082i
$918$	0.440710	+	2.34706i	0.0145456	+	0.0774647i
$919$	−22.3900	−	12.9268i	−0.738577	−	0.426417i	0.0829750	−	0.996552i	$-0.473558\pi$
$919$	−22.3900	−	12.9268i	−0.738577	−	0.426417i	−0.821552	+	0.570134i	$0.806891\pi$
$920$		0			0
$921$	−16.8266	−	29.1445i	−0.554454	−	0.960342i
$922$	−5.29676	−	1.86169i	−0.174440	−	0.0613114i
$923$			39.7565i			1.30860i
$924$	−75.5438	+	39.9652i	−2.48521	+	1.31476i
$925$		0			0
$926$	−16.7837	+	47.7521i	−0.551548	+	1.56923i
$927$	25.4426	−	14.6893i	0.835645	−	0.482460i
$928$	2.87997	+	0.344784i	0.0945396	+	0.0113181i
$929$	−31.8338	−	18.3793i	−1.04443	−	0.603005i	−0.123349	−	0.992363i	$-0.539363\pi$
$929$	−31.8338	−	18.3793i	−1.04443	−	0.603005i	−0.921086	+	0.389359i	$0.872697\pi$
$930$		0			0
$931$	−12.8650	+	42.6705i	−0.421634	+	1.39847i
$932$	0.282757	+	0.726384i	0.00926200	+	0.0237935i
$933$	−43.8574	−	25.3211i	−1.43583	−	0.828975i
$934$	2.22701	−	1.91112i	0.0728701	−	0.0625337i
$935$		0			0
$936$	−1.02019	−	30.6903i	−0.0333458	−	1.00314i
$937$	33.9818			1.11014			0.555069	−	0.831804i	$-0.312692\pi$
$937$	33.9818			1.11014			0.555069	+	0.831804i	$0.312692\pi$
$938$	−27.0456	+	8.39566i	−0.883072	+	0.274128i
$939$		−	8.78816i		−	0.286791i
$940$		0			0
$941$	39.2248	−	22.6464i	1.27869	−	0.738253i	0.302083	−	0.953282i	$-0.402318\pi$
$941$	39.2248	−	22.6464i	1.27869	−	0.738253i	0.976608	+	0.215029i	$0.0689846\pi$
$942$	47.3882	−	40.6663i	1.54399	−	1.32498i
$943$	21.1294	+	12.1991i	0.688067	+	0.397256i
$944$	9.55126	−	8.76394i	0.310867	−	0.285242i
$945$		0			0
$946$	1.12062	+	5.96800i	0.0364343	+	0.194037i
$947$	0.847235	−	1.46745i	0.0275314	−	0.0476858i	−0.851931	−	0.523653i	$-0.824569\pi$
$947$	0.847235	−	1.46745i	0.0275314	−	0.0476858i	0.879463	+	0.475968i	$0.157902\pi$
$948$	42.5219	+	34.1040i	1.38105	+	1.10765i
$949$	3.79876	+	6.57964i	0.123313	+	0.213584i
$950$		0			0
$951$	63.1197			2.04680
$952$	7.51888	+	2.95950i	0.243688	+	0.0959179i
$953$			1.16457i			0.0377243i	0.999822	+	0.0188621i	$0.00600436\pi$
$953$			1.16457i			0.0377243i	−0.999822	+	0.0188621i	$0.993996\pi$
$954$	−10.7682	−	3.78477i	−0.348634	−	0.122537i
$955$		0			0
$956$	29.8295	−	37.1924i	0.964755	−	1.20289i
$957$	4.14073	−	7.17195i	0.133851	−	0.231836i
$958$	40.2537	−	7.55846i	1.30054	−	0.244203i
$959$	−30.4171	+	22.5989i	−0.982220	+	0.729755i
$960$		0			0
$961$	2.48244	−	4.29970i	0.0800786	−	0.138700i
$962$	−17.0062	+	14.5939i	−0.548302	+	0.470526i
$963$	−8.25667	−	14.3010i	−0.266068	−	0.460842i
$964$	30.2958	+	4.65255i	0.975763	+	0.149849i
$965$		0			0
$966$	30.0549	+	6.80310i	0.966999	+	0.218886i
$967$	−4.42142			−0.142183			−0.0710916	−	0.997470i	$-0.522648\pi$
$967$	−4.42142			−0.142183			−0.0710916	+	0.997470i	$0.522648\pi$
$968$	−2.67570	−	80.4932i	−0.0860004	−	2.58715i
$969$	−15.3051	+	8.83639i	−0.491670	+	0.283866i
$970$		0			0
$971$	−14.4037	+	24.9479i	−0.462235	+	0.800615i	−0.999072	−	0.0430713i	$-0.986286\pi$
$971$	−14.4037	+	24.9479i	−0.462235	+	0.800615i	0.536837	+	0.843686i	$0.319619\pi$
$972$	16.0950	+	41.3472i	0.516248	+	1.32621i
$973$	−47.5926	+	5.51596i	−1.52575	+	0.176833i
$974$	−3.45846	+	0.649397i	−0.110816	+	0.0208080i
$975$		0			0
$976$	−3.16737	+	10.0692i	−0.101385	+	0.322308i
$977$	9.47493	−	5.47035i	0.303130	−	0.175012i	−0.340718	−	0.940165i	$-0.610670\pi$
$977$	9.47493	−	5.47035i	0.303130	−	0.175012i	0.643848	+	0.765153i	$0.277337\pi$
$978$	60.0811	+	21.1171i	1.92118	+	0.675250i
$979$	56.5268			1.80660
$980$		0			0
$981$	−15.3545			−0.490231
$982$	15.3474	+	5.39424i	0.489754	+	0.172137i
$983$	9.79656	−	5.65605i	0.312462	−	0.180400i	−0.335566	−	0.942017i	$-0.608927\pi$
$983$	9.79656	−	5.65605i	0.312462	−	0.180400i	0.648028	+	0.761617i	$0.275594\pi$
$984$	−48.8472	−	26.0777i	−1.55719	−	0.831327i
$985$		0			0
$986$	−0.769538	+	0.144497i	−0.0245071	+	0.00460171i
$987$	75.8276	−	8.78837i	2.41362	−	0.279737i
$988$	35.7028	−	13.8979i	1.13586	−	0.442150i
$989$	1.09473	−	1.89612i	0.0348103	−	0.0602931i
$990$		0			0
$991$	−21.1182	+	12.1926i	−0.670841	+	0.387310i	−0.796395	−	0.604777i	$-0.793262\pi$
$991$	−21.1182	+	12.1926i	−0.670841	+	0.387310i	0.125555	+	0.992087i	$0.459929\pi$
$992$	11.3583	+	26.5351i	0.360625	+	0.842492i
$993$	2.53575			0.0804696
$994$	48.2208	+	10.9151i	1.52947	+	0.346205i
$995$		0			0
$996$	−1.07262	+	6.98452i	−0.0339872	+	0.221313i
$997$	20.3320	+	35.2161i	0.643922	+	1.11531i	0.984549	+	0.175107i	$0.0560273\pi$
$997$	20.3320	+	35.2161i	0.643922	+	1.11531i	−0.340627	+	0.940198i	$0.610639\pi$
$998$	−0.501167	+	0.430078i	−0.0158642	+	0.0136139i
$999$	−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.t.e.299.13		64
4.3	odd	2	inner	700.2.t.e.299.23		64
5.2	odd	4		700.2.p.f.551.2	yes	32
5.3	odd	4		700.2.p.d.551.15	yes	32
5.4	even	2	inner	700.2.t.e.299.20		64
7.3	odd	6	inner	700.2.t.e.199.10		64
20.3	even	4		700.2.p.d.551.4	yes	32
20.7	even	4		700.2.p.f.551.13	yes	32
20.19	odd	2	inner	700.2.t.e.299.10		64
28.3	even	6	inner	700.2.t.e.199.20		64
35.3	even	12		700.2.p.d.451.4	✓	32
35.17	even	12		700.2.p.f.451.13	yes	32
35.24	odd	6	inner	700.2.t.e.199.23		64
140.3	odd	12		700.2.p.d.451.15	yes	32
140.59	even	6	inner	700.2.t.e.199.13		64
140.87	odd	12		700.2.p.f.451.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.p.d.451.4	✓	32	35.3	even	12
700.2.p.d.451.15	yes	32	140.3	odd	12
700.2.p.d.551.4	yes	32	20.3	even	4
700.2.p.d.551.15	yes	32	5.3	odd	4
700.2.p.f.451.2	yes	32	140.87	odd	12
700.2.p.f.451.13	yes	32	35.17	even	12
700.2.p.f.551.2	yes	32	5.2	odd	4
700.2.p.f.551.13	yes	32	20.7	even	4
700.2.t.e.199.10		64	7.3	odd	6	inner
700.2.t.e.199.13		64	140.59	even	6	inner
700.2.t.e.199.20		64	28.3	even	6	inner
700.2.t.e.199.23		64	35.24	odd	6	inner
700.2.t.e.299.10		64	20.19	odd	2	inner
700.2.t.e.299.13		64	1.1	even	1	trivial
700.2.t.e.299.20		64	5.4	even	2	inner
700.2.t.e.299.23		64	4.3	odd	2	inner

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.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.468940 + 1.33420i) q^{2} +(-2.22627 + 1.28534i) q^{3} +(-1.56019 - 1.25132i) q^{4} +(-0.670911 - 3.57303i) q^{6} +(-2.62816 + 0.304602i) q^{7} +(2.40115 - 1.49481i) q^{8} +(1.80417 - 3.12492i) q^{9} +O(q^{10})\)	\(q+(-0.468940 + 1.33420i) q^{2} +(-2.22627 + 1.28534i) q^{3} +(-1.56019 - 1.25132i) q^{4} +(-0.670911 - 3.57303i) q^{6} +(-2.62816 + 0.304602i) q^{7} +(2.40115 - 1.49481i) q^{8} +(1.80417 - 3.12492i) q^{9} +(5.44112 - 3.14143i) q^{11} +(5.08177 + 0.780410i) q^{12} +3.00876 q^{13} +(0.826049 - 3.64933i) q^{14} +(0.868384 + 3.90460i) q^{16} +(-0.539892 - 0.935120i) q^{17} +(3.32322 + 3.87253i) q^{18} +(-3.18341 + 5.51382i) q^{19} +(5.45946 - 4.05619i) q^{21} +(1.63974 + 8.73269i) q^{22} +(1.60186 - 2.77450i) q^{23} +(-3.42427 + 6.41414i) q^{24} +(-1.41093 + 4.01429i) q^{26} +1.56386i q^{27} +(4.48158 + 2.81344i) q^{28} -0.512747 q^{29} +(-2.55123 - 4.41886i) q^{31} +(-5.61675 - 0.672426i) q^{32} +(-8.07558 + 13.9873i) q^{33} +(1.50082 - 0.281809i) q^{34} +(-6.72514 + 2.61787i) q^{36} +(4.56104 + 2.63332i) q^{37} +(-5.86372 - 6.83296i) q^{38} +(-6.69829 + 3.86726i) q^{39} +7.61555i q^{41} +(2.85161 + 9.18614i) q^{42} +0.683409 q^{43} +(-12.4201 - 1.90737i) q^{44} +(2.95057 + 3.43828i) q^{46} +(9.71985 + 5.61176i) q^{47} +(-6.95197 - 7.57652i) q^{48} +(6.81444 - 1.60109i) q^{49} +(2.40388 + 1.38788i) q^{51} +(-4.69423 - 3.76492i) q^{52} +(-1.93707 + 1.11837i) q^{53} +(-2.08650 - 0.733357i) q^{54} +(-5.85529 + 4.66000i) q^{56} -16.3670i q^{57} +(0.240448 - 0.684108i) q^{58} +(-1.62035 - 2.80652i) q^{59} +(2.28536 + 1.31945i) q^{61} +(7.09203 - 1.33167i) q^{62} +(-3.78980 + 8.76234i) q^{63} +(3.53107 - 7.17855i) q^{64} +(-14.8749 - 17.3337i) q^{66} +(-3.78426 - 6.55453i) q^{67} +(-0.327803 + 2.13454i) q^{68} +8.23571i q^{69} +13.2136i q^{71} +(-0.339072 - 10.2003i) q^{72} +(1.26257 + 2.18683i) q^{73} +(-5.65223 + 4.85048i) q^{74} +(11.8663 - 4.61914i) q^{76} +(-13.3432 + 9.91356i) q^{77} +(-2.01861 - 10.7504i) q^{78} +(9.18163 + 5.30102i) q^{79} +(3.40244 + 5.89319i) q^{81} +(-10.1607 - 3.57124i) q^{82} +1.37443i q^{83} +(-13.5934 - 0.503125i) q^{84} +(-0.320478 + 0.911806i) q^{86} +(1.14151 - 0.659051i) q^{87} +(8.36911 - 15.6765i) q^{88} +(7.79161 + 4.49849i) q^{89} +(-7.90749 + 0.916474i) q^{91} +(-5.97101 + 2.32431i) q^{92} +(11.3594 + 6.55838i) q^{93} +(-12.0453 + 10.3367i) q^{94} +(13.3687 - 5.72240i) q^{96} -7.56469 q^{97} +(-1.05939 + 9.84265i) q^{98} -22.6707i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 2 q^{4} + 32 q^{9}+O(q^{10}) \) 64 * q - 2 * q^4 + 32 * q^9	\( 64 q - 2 q^{4} + 32 q^{9} + 26 q^{14} + 2 q^{16} + 24 q^{21} + 36 q^{24} - 30 q^{26} - 16 q^{29} - 60 q^{36} - 24 q^{44} + 4 q^{46} - 40 q^{49} - 114 q^{54} - 62 q^{56} - 24 q^{61} - 80 q^{64} - 132 q^{66} + 2 q^{74} - 72 q^{81} - 134 q^{84} + 8 q^{86} + 120 q^{89} - 90 q^{94} + 186 q^{96}+O(q^{100}) \) 64 * q - 2 * q^4 + 32 * q^9 + 26 * q^14 + 2 * q^16 + 24 * q^21 + 36 * q^24 - 30 * q^26 - 16 * q^29 - 60 * q^36 - 24 * q^44 + 4 * q^46 - 40 * q^49 - 114 * q^54 - 62 * q^56 - 24 * q^61 - 80 * q^64 - 132 * q^66 + 2 * q^74 - 72 * q^81 - 134 * q^84 + 8 * q^86 + 120 * q^89 - 90 * q^94 + 186 * q^96

Introduction

L-functions

Modular forms

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