LMFDB - Embedded newform 512.2.o.a.117.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(5,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(128))

chi = DirichletCharacter(H, H._module([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("512.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.o (of order $128$, degree $64$, 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$4032$
Relative dimension:	$63$ over $\Q(\zeta_{128})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{128}]$

Embedding invariants

Embedding label			117.33
Character	$\chi$	$=$	512.117
Dual form			512.2.o.a.477.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.126435 + 1.40855i) q^{2} +(0.0798222 + 3.25160i) q^{3} +(-1.96803 + 0.356182i) q^{4} +(-0.147744 - 0.533878i) q^{5} +(-4.56995 + 0.523551i) q^{6} +(-1.92420 + 4.06838i) q^{7} +(-0.750528 - 2.72703i) q^{8} +(-7.57013 + 0.371896i) q^{9} +O(q^{10})$	\(q+(0.126435 + 1.40855i) q^{2} +(0.0798222 + 3.25160i) q^{3} +(-1.96803 + 0.356182i) q^{4} +(-0.147744 - 0.533878i) q^{5} +(-4.56995 + 0.523551i) q^{6} +(-1.92420 + 4.06838i) q^{7} +(-0.750528 - 2.72703i) q^{8} +(-7.57013 + 0.371896i) q^{9} +(0.733315 - 0.275606i) q^{10} +(4.02861 + 2.83726i) q^{11} +(-1.31525 - 6.37080i) q^{12} +(4.49507 - 0.554413i) q^{13} +(-5.97380 - 2.19594i) q^{14} +(1.72416 - 0.523020i) q^{15} +(3.74627 - 1.40195i) q^{16} +(1.08162 - 3.56562i) q^{17} +(-1.48097 - 10.6159i) q^{18} +(0.0701835 - 0.951454i) q^{19} +(0.480922 + 0.998064i) q^{20} +(-13.3823 - 5.93197i) q^{21} +(-3.48707 + 6.03322i) q^{22} +(-3.39895 + 2.52083i) q^{23} +(8.80730 - 2.65809i) q^{24} +(4.02545 - 2.41276i) q^{25} +(1.34926 + 6.26143i) q^{26} +(-1.09570 - 14.8540i) q^{27} +(2.33780 - 8.69204i) q^{28} +(-4.19140 + 0.941211i) q^{29} +(0.954695 + 2.36244i) q^{30} +(2.82068 + 4.22145i) q^{31} +(2.44838 + 5.09955i) q^{32} +(-8.90407 + 13.3259i) q^{33} +(5.15911 + 1.07269i) q^{34} +(2.45631 + 0.426210i) q^{35} +(14.7658 - 3.42824i) q^{36} +(0.201020 + 0.399358i) q^{37} +(1.34904 - 0.0214406i) q^{38} +(2.16154 + 14.5719i) q^{39} +(-1.34502 + 0.803594i) q^{40} +(6.47514 + 3.88105i) q^{41} +(6.66348 - 19.5997i) q^{42} +(-3.43521 - 3.60811i) q^{43} +(-8.93899 - 4.14890i) q^{44} +(1.31699 + 3.98658i) q^{45} +(-3.98047 - 4.46887i) q^{46} +(-5.79678 - 4.75730i) q^{47} +(4.85761 + 12.0695i) q^{48} +(-8.40840 - 10.2457i) q^{49} +(3.90745 + 5.36498i) q^{50} +(11.6803 + 3.23237i) q^{51} +(-8.64894 + 2.69216i) q^{52} +(-3.38089 - 0.759205i) q^{53} +(20.7841 - 3.42142i) q^{54} +(0.919552 - 2.56997i) q^{55} +(12.5388 + 2.19392i) q^{56} +(3.09935 + 0.152261i) q^{57} +(-1.85568 - 5.78480i) q^{58} +(0.624380 - 5.06234i) q^{59} +(-3.20691 + 1.64343i) q^{60} +(3.74790 + 8.45512i) q^{61} +(-5.58949 + 4.50682i) q^{62} +(13.0534 - 31.5137i) q^{63} +(-6.87341 + 4.09343i) q^{64} +(-0.960109 - 2.31791i) q^{65} +(-19.8960 - 10.8570i) q^{66} +(-4.48141 + 11.6176i) q^{67} +(-0.858649 + 7.40249i) q^{68} +(-8.46805 - 10.8508i) q^{69} +(-0.289774 + 3.51372i) q^{70} +(1.09599 + 1.20924i) q^{71} +(6.69577 + 20.3649i) q^{72} +(-1.70342 - 3.60157i) q^{73} +(-0.537100 + 0.333640i) q^{74} +(8.16664 + 12.8965i) q^{75} +(0.200767 + 1.89749i) q^{76} +(-19.2949 + 10.9304i) q^{77} +(-20.2519 + 4.88704i) q^{78} +(-0.523594 + 5.31613i) q^{79} +(-1.30196 - 1.79292i) q^{80} +(25.5836 - 2.51976i) q^{81} +(-4.64796 + 9.61126i) q^{82} +(3.94108 - 7.82959i) q^{83} +(28.4496 + 6.90776i) q^{84} +(-2.06341 - 0.0506539i) q^{85} +(4.64788 - 5.29486i) q^{86} +(-3.39501 - 13.5536i) q^{87} +(4.71373 - 13.1156i) q^{88} +(10.5598 + 7.83164i) q^{89} +(-5.44879 + 2.35909i) q^{90} +(-6.39384 + 19.3544i) q^{91} +(5.79136 - 6.17172i) q^{92} +(-13.5013 + 9.50869i) q^{93} +(5.96797 - 8.76655i) q^{94} +(-0.518330 + 0.103102i) q^{95} +(-16.3863 + 8.36820i) q^{96} +(12.3713 + 2.46081i) q^{97} +(13.3684 - 13.1391i) q^{98} +(-31.5522 - 19.9802i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) $ 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{53}{128}\right)$	$1$

Coefficient data

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

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

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

$2$	0.126435	+	1.40855i	0.0894034	+	0.995995i
$2$	0.126435	+	1.40855i	0.0894034	+	0.995995i
$3$	0.0798222	+	3.25160i	0.0460854	+	1.87731i	0.367025	+	0.930211i	$0.380376\pi$
$3$	0.0798222	+	3.25160i	0.0460854	+	1.87731i	−0.320940	+	0.947100i	$0.603999\pi$
$4$	−1.96803	+	0.356182i	−0.984014	+	0.178091i
$5$	−0.147744	−	0.533878i	−0.0660732	−	0.238758i	0.923317	−	0.384038i	$-0.125467\pi$
$5$	−0.147744	−	0.533878i	−0.0660732	−	0.238758i	−0.989391	+	0.145280i	$0.953592\pi$
$6$	−4.56995	+	0.523551i	−1.86567	+	0.213739i
$7$	−1.92420	+	4.06838i	−0.727279	+	1.53770i	0.111823	+	0.993728i	$0.464331\pi$
$7$	−1.92420	+	4.06838i	−0.727279	+	1.53770i	−0.839102	+	0.543974i	$0.816919\pi$
$8$	−0.750528	−	2.72703i	−0.265352	−	0.964152i
$9$	−7.57013	+	0.371896i	−2.52338	+	0.123965i
$10$	0.733315	−	0.275606i	0.231894	−	0.0871543i
$11$	4.02861	+	2.83726i	1.21467	+	0.855467i	0.992821	−	0.119613i	$-0.0381655\pi$
$11$	4.02861	+	2.83726i	1.21467	+	0.855467i	0.221850	+	0.975081i	$0.428791\pi$
$12$	−1.31525	−	6.37080i	−0.379680	−	1.83909i
$13$	4.49507	−	0.554413i	1.24671	−	0.153767i	0.528099	−	0.849183i	$-0.322905\pi$
$13$	4.49507	−	0.554413i	1.24671	−	0.153767i	0.718608	+	0.695416i	$0.244780\pi$
$14$	−5.97380	−	2.19594i	−1.59657	−	0.586891i
$15$	1.72416	−	0.523020i	0.445177	−	0.135043i
$16$	3.74627	−	1.40195i	0.936567	−	0.350488i
$17$	1.08162	−	3.56562i	0.262331	−	0.864790i	−0.722514	−	0.691356i	$-0.757014\pi$
$17$	1.08162	−	3.56562i	0.262331	−	0.864790i	0.984846	−	0.173434i	$-0.0554863\pi$
$18$	−1.48097	−	10.6159i	−0.349067	−	2.50219i
$19$	0.0701835	−	0.951454i	0.0161012	−	0.218279i	−0.983250	−	0.182262i	$-0.941658\pi$
$19$	0.0701835	−	0.951454i	0.0161012	−	0.218279i	0.999351	−	0.0360166i	$-0.0114669\pi$
$20$	0.480922	+	0.998064i	0.107537	+	0.223174i
$21$	−13.3823	−	5.93197i	−2.92026	−	1.29446i
$22$	−3.48707	+	6.03322i	−0.743446	+	1.28629i
$23$	−3.39895	+	2.52083i	−0.708730	+	0.525630i	−0.888955	−	0.457995i	$-0.848568\pi$
$23$	−3.39895	+	2.52083i	−0.708730	+	0.525630i	0.180224	+	0.983626i	$0.442318\pi$
$24$	8.80730	−	2.65809i	1.79778	−	0.542581i
$25$	4.02545	−	2.41276i	0.805089	−	0.482552i
$26$	1.34926	+	6.26143i	0.264611	+	1.22797i
$27$	−1.09570	−	14.8540i	−0.210867	−	2.85866i
$28$	2.33780	−	8.69204i	0.441802	−	1.64264i
$29$	−4.19140	+	0.941211i	−0.778324	+	0.174778i	−0.590081	−	0.807344i	$-0.700904\pi$
$29$	−4.19140	+	0.941211i	−0.778324	+	0.174778i	−0.188243	+	0.982123i	$0.560279\pi$
$30$	0.954695	+	2.36244i	0.174303	+	0.431321i
$31$	2.82068	+	4.22145i	0.506610	+	0.758195i	0.993323	−	0.115367i	$-0.0368043\pi$
$31$	2.82068	+	4.22145i	0.506610	+	0.758195i	−0.486713	+	0.873562i	$0.661804\pi$
$32$	2.44838	+	5.09955i	0.432816	+	0.901482i
$33$	−8.90407	+	13.3259i	−1.55000	+	2.31974i
$34$	5.15911	+	1.07269i	0.884780	+	0.183965i
$35$	2.45631	+	0.426210i	0.415192	+	0.0720426i
$36$	14.7658	−	3.42824i	2.46096	−	0.571374i
$37$	0.201020	+	0.399358i	0.0330475	+	0.0656540i	0.909145	−	0.416481i	$-0.136737\pi$
$37$	0.201020	+	0.399358i	0.0330475	+	0.0656540i	−0.876097	+	0.482135i	$0.839862\pi$
$38$	1.34904	−	0.0214406i	0.218844	−	0.00347813i
$39$	2.16154	+	14.5719i	0.346123	+	2.33337i
$40$	−1.34502	+	0.803594i	−0.212666	+	0.127059i
$41$	6.47514	+	3.88105i	1.01125	+	0.606118i	0.920903	−	0.389793i	$-0.127453\pi$
$41$	6.47514	+	3.88105i	1.01125	+	0.606118i	0.0903439	+	0.995911i	$0.471203\pi$
$42$	6.66348	−	19.5997i	1.02820	−	3.02430i
$43$	−3.43521	−	3.60811i	−0.523865	−	0.550232i	0.408027	−	0.912970i	$-0.366217\pi$
$43$	−3.43521	−	3.60811i	−0.523865	−	0.550232i	−0.931891	+	0.362738i	$0.881842\pi$
$44$	−8.93899	−	4.14890i	−1.34760	−	0.625470i
$45$	1.31699	+	3.98658i	0.196325	+	0.594284i
$46$	−3.98047	−	4.46887i	−0.586888	−	0.658899i
$47$	−5.79678	−	4.75730i	−0.845548	−	0.693923i	0.108331	−	0.994115i	$-0.465449\pi$
$47$	−5.79678	−	4.75730i	−0.845548	−	0.693923i	−0.953879	+	0.300192i	$0.902949\pi$
$48$	4.85761	+	12.0695i	0.701136	+	1.74208i
$49$	−8.40840	−	10.2457i	−1.20120	−	1.46367i
$50$	3.90745	+	5.36498i	0.552597	+	0.758723i
$51$	11.6803	+	3.23237i	1.63557	+	0.452623i
$52$	−8.64894	+	2.69216i	−1.19939	+	0.373336i
$53$	−3.38089	−	0.759205i	−0.464401	−	0.104285i	−0.0193944	−	0.999812i	$-0.506174\pi$
$53$	−3.38089	−	0.759205i	−0.464401	−	0.104285i	−0.445007	+	0.895527i	$0.646799\pi$
$54$	20.7841	−	3.42142i	2.82836	−	0.465597i
$55$	0.919552	−	2.56997i	0.123992	−	0.346535i
$56$	12.5388	+	2.19392i	1.67556	+	0.293175i
$57$	3.09935	+	0.152261i	0.410519	+	0.0201675i
$58$	−1.85568	−	5.78480i	−0.243663	−	0.759581i
$59$	0.624380	−	5.06234i	0.0812874	−	0.659061i	−0.895532	−	0.444997i	$-0.853205\pi$
$59$	0.624380	−	5.06234i	0.0812874	−	0.659061i	0.976820	−	0.214064i	$-0.0686701\pi$
$60$	−3.20691	+	1.64343i	−0.414011	+	0.212166i
$61$	3.74790	+	8.45512i	0.479869	+	1.08257i	0.976678	+	0.214708i	$0.0688799\pi$
$61$	3.74790	+	8.45512i	0.479869	+	1.08257i	−0.496809	+	0.867860i	$0.665495\pi$
$62$	−5.58949	+	4.50682i	−0.709866	+	0.572366i
$63$	13.0534	−	31.5137i	1.64458	−	3.97036i
$64$	−6.87341	+	4.09343i	−0.859177	+	0.511679i
$65$	−0.960109	−	2.31791i	−0.119087	−	0.287501i
$66$	−19.8960	−	10.8570i	−2.44902	−	1.33640i
$67$	−4.48141	+	11.6176i	−0.547492	+	1.41932i	0.331943	+	0.943299i	$0.392296\pi$
$67$	−4.48141	+	11.6176i	−0.547492	+	1.41932i	−0.879435	+	0.476019i	$0.842079\pi$
$68$	−0.858649	+	7.40249i	−0.104126	+	0.897684i
$69$	−8.46805	−	10.8508i	−1.01943	−	1.30628i
$70$	−0.289774	+	3.51372i	−0.0346346	+	0.419970i
$71$	1.09599	+	1.20924i	0.130071	+	0.143511i	0.802504	−	0.596647i	$-0.203501\pi$
$71$	1.09599	+	1.20924i	0.130071	+	0.143511i	−0.672433	+	0.740158i	$0.734751\pi$
$72$	6.69577	+	20.3649i	0.789104	+	2.40002i
$73$	−1.70342	−	3.60157i	−0.199370	−	0.421532i	0.779391	−	0.626538i	$-0.215529\pi$
$73$	−1.70342	−	3.60157i	−0.199370	−	0.421532i	−0.978761	+	0.205006i	$0.934279\pi$
$74$	−0.537100	+	0.333640i	−0.0624366	+	0.0387848i
$75$	8.16664	+	12.8965i	0.943002	+	1.48916i
$76$	0.200767	+	1.89749i	0.0230296	+	0.217657i
$77$	−19.2949	+	10.9304i	−2.19886	+	1.24564i
$78$	−20.2519	+	4.88704i	−2.29308	+	0.553348i
$79$	−0.523594	+	5.31613i	−0.0589089	+	0.598112i	0.919734	+	0.392543i	$0.128405\pi$
$79$	−0.523594	+	5.31613i	−0.0589089	+	0.598112i	−0.978643	+	0.205569i	$0.934095\pi$
$80$	−1.30196	−	1.79292i	−0.145564	−	0.200455i
$81$	25.5836	−	2.51976i	2.84262	−	0.279973i
$82$	−4.64796	+	9.61126i	−0.513282	+	1.06139i
$83$	3.94108	−	7.82959i	0.432590	−	0.859409i	−0.566778	−	0.823870i	$-0.691810\pi$
$83$	3.94108	−	7.82959i	0.432590	−	0.859409i	0.999368	−	0.0355385i	$-0.0113146\pi$
$84$	28.4496	+	6.90776i	3.10411	+	0.753698i
$85$	−2.06341	−	0.0506539i	−0.223808	−	0.00549418i
$86$	4.64788	−	5.29486i	0.501193	−	0.570959i
$87$	−3.39501	−	13.5536i	−0.363983	−	1.45310i
$88$	4.71373	−	13.1156i	0.502485	−	1.39813i
$89$	10.5598	+	7.83164i	1.11933	+	0.830153i	0.986947	−	0.161046i	$-0.0514867\pi$
$89$	10.5598	+	7.83164i	1.11933	+	0.830153i	0.132384	+	0.991198i	$0.457737\pi$
$90$	−5.44879	+	2.35909i	−0.574353	+	0.248670i
$91$	−6.39384	+	19.3544i	−0.670256	+	2.02890i
$92$	5.79136	−	6.17172i	0.603791	−	0.643446i
$93$	−13.5013	+	9.50869i	−1.40002	+	0.986005i
$94$	5.96797	−	8.76655i	0.615549	−	0.904201i
$95$	−0.518330	+	0.103102i	−0.0531796	+	0.0105781i
$96$	−16.3863	+	8.36820i	−1.67242	+	0.854076i
$97$	12.3713	+	2.46081i	1.25612	+	0.249858i	0.777903	−	0.628384i	$-0.216283\pi$
$97$	12.3713	+	2.46081i	1.25612	+	0.249858i	0.478217	+	0.878242i	$0.341283\pi$
$98$	13.3684	−	13.1391i	1.35041	−	1.32725i
$99$	−31.5522	−	19.9802i	−3.17112	−	2.00809i
$100$	−7.06281	+	6.18217i	−0.706281	+	0.618217i
$101$	−4.13767	−	3.56918i	−0.411714	−	0.355147i	0.422715	−	0.906263i	$-0.361077\pi$
$101$	−4.13767	−	3.56918i	−0.411714	−	0.355147i	−0.834429	+	0.551116i	$0.814202\pi$
$102$	−3.07616	+	16.8610i	−0.304585	+	1.66948i
$103$	−12.7969	−	3.20546i	−1.26092	−	0.315844i	−0.445797	−	0.895134i	$-0.647080\pi$
$103$	−12.7969	−	3.20546i	−1.26092	−	0.315844i	−0.815121	+	0.579290i	$0.803330\pi$
$104$	−4.88558	−	11.8421i	−0.479070	−	1.16121i
$105$	−1.18979	+	8.02094i	−0.116112	+	0.782764i
$106$	0.641913	−	4.85815i	0.0623481	−	0.471865i
$107$	−2.36029	−	6.11882i	−0.228178	−	0.591529i	0.770783	−	0.637097i	$-0.219865\pi$
$107$	−2.36029	−	6.11882i	−0.228178	−	0.591529i	−0.998961	+	0.0455683i	$0.985490\pi$
$108$	7.44709	+	28.8429i	0.716597	+	2.77541i
$109$	3.34587	+	3.87879i	0.320476	+	0.371521i	0.894308	−	0.447452i	$-0.147669\pi$
$109$	3.34587	+	3.87879i	0.320476	+	0.371521i	−0.573831	+	0.818973i	$0.694544\pi$
$110$	3.73620	+	0.970299i	0.356233	+	0.0925144i
$111$	−1.28251	+	0.685513i	−0.121730	+	0.0650660i
$112$	−1.50491	+	17.9389i	−0.142200	+	1.69506i
$113$	−4.47114	+	8.36491i	−0.420609	+	0.786904i	−0.999596	−	0.0284329i	$-0.990948\pi$
$113$	−4.47114	+	8.36491i	−0.420609	+	0.786904i	0.578987	+	0.815337i	$0.303448\pi$
$114$	0.177400	+	4.38484i	0.0166150	+	0.410678i
$115$	1.84799	+	1.44219i	0.172326	+	0.134485i
$116$	7.91356	−	3.34523i	0.734755	−	0.310597i
$117$	−33.8220	+	5.86868i	−3.12685	+	0.542560i
$118$	7.20951	+	0.239411i	0.663689	+	0.0220396i
$119$	12.4250	+	11.2614i	1.13900	+	1.03233i
$120$	−2.72033	−	4.30931i	−0.248331	−	0.393385i
$121$	4.47381	+	12.5035i	0.406710	+	1.13668i
$122$	−11.4356	+	6.34813i	−1.03533	+	0.574733i
$123$	−12.1027	+	21.3643i	−1.09127	+	1.92636i
$124$	−7.05479	−	7.30326i	−0.633539	−	0.655852i
$125$	−3.88882	−	3.70246i	−0.347827	−	0.331158i
$126$	46.0391	+	14.4019i	4.10149	+	1.28303i
$127$	−9.20856	−	9.20856i	−0.817128	−	0.817128i	0.168563	−	0.985691i	$-0.446087\pi$
$127$	−9.20856	−	9.20856i	−0.817128	−	0.817128i	−0.985691	+	0.168563i	$0.946087\pi$
$128$	−6.63485	−	9.16400i	−0.586443	−	0.809990i
$129$	11.4579	−	11.4579i	1.00881	−	1.00881i
$130$	3.14350	−	1.64543i	0.275703	−	0.144314i
$131$	1.60256	−	1.68322i	0.140016	−	0.147064i	−0.650496	−	0.759509i	$-0.725439\pi$
$131$	1.60256	−	1.68322i	0.140016	−	0.147064i	0.790513	+	0.612445i	$0.209814\pi$
$132$	12.7770	−	29.3972i	1.11210	−	2.55870i
$133$	3.73583	+	2.11632i	0.323937	+	0.183508i
$134$	−16.9306	−	4.84341i	−1.46258	−	0.418407i
$135$	−7.76836	+	2.77956i	−0.668594	+	0.239227i
$136$	−10.5353	−	0.273512i	−0.903399	−	0.0234535i
$137$	10.2422	−	11.3006i	0.875053	−	0.965472i	−0.124590	−	0.992208i	$-0.539761\pi$
$137$	10.2422	−	11.3006i	0.875053	−	0.965472i	0.999643	+	0.0267365i	$0.00851149\pi$
$138$	14.2132	−	13.2996i	1.20991	−	1.13214i
$139$	1.52703	+	8.80048i	0.129521	+	0.746447i	0.976614	+	0.215002i	$0.0689758\pi$
$139$	1.52703	+	8.80048i	0.129521	+	0.746447i	−0.847093	+	0.531445i	$0.821649\pi$
$140$	−4.98589	+	0.0360985i	−0.421385	+	0.00305088i
$141$	15.0061	−	19.2285i	1.26374	−	1.61933i
$142$	−1.56471	+	1.69665i	−0.131307	+	0.142380i
$143$	19.6819	+	10.5202i	1.64588	+	0.879741i
$144$	−27.8383	+	12.0062i	−2.31986	+	1.00051i
$145$	1.12175	+	2.09864i	0.0931560	+	0.174283i
$146$	4.85762	−	2.85472i	0.402020	−	0.236258i
$147$	32.6436	−	28.1586i	2.69240	−	2.32248i
$148$	−0.537857	−	0.714348i	−0.0442115	−	0.0587190i
$149$	6.07797	−	2.34453i	0.497927	−	0.192072i	−0.0978816	−	0.995198i	$-0.531207\pi$
$149$	6.07797	−	2.34453i	0.497927	−	0.192072i	0.595809	+	0.803126i	$0.296832\pi$
$150$	−17.1329	+	13.1337i	−1.39889	+	1.07236i
$151$	13.9170	+	2.06440i	1.13255	+	0.167998i	0.686584	−	0.727050i	$-0.259109\pi$
$151$	13.9170	+	2.06440i	1.13255	+	0.167998i	0.445968	+	0.895049i	$0.352859\pi$
$152$	−2.64732	+	0.522701i	−0.214726	+	0.0423966i
$153$	−6.86195	+	27.3944i	−0.554756	+	2.21471i
$154$	−17.8356	−	25.7958i	−1.43723	−	2.07869i
$155$	1.83700	−	2.12960i	0.147552	−	0.171053i
$156$	−9.44420	−	27.9080i	−0.756141	−	2.23443i
$157$	−6.69073	+	10.5658i	−0.533979	+	0.843244i	−0.999118	−	0.0419931i	$-0.986629\pi$
$157$	−6.69073	+	10.5658i	−0.533979	+	0.843244i	0.465139	+	0.885238i	$0.346004\pi$
$158$	−7.55424	−	0.0653598i	−0.600983	−	0.00519975i
$159$	2.19876	−	11.0539i	0.174373	−	0.876632i
$160$	2.36081	−	2.06057i	0.186638	−	0.162902i
$161$	−3.71545	−	18.6788i	−0.292818	−	1.47210i
$162$	6.78388	+	35.7171i	0.532992	+	2.80620i
$163$	−1.85128	−	2.62862i	−0.145004	−	0.205889i	0.738576	−	0.674170i	$-0.235499\pi$
$163$	−1.85128	−	2.62862i	−0.145004	−	0.205889i	−0.883580	+	0.468281i	$0.844874\pi$
$164$	−14.1256	−	5.33169i	−1.10302	−	0.416335i
$165$	8.42992	+	2.78487i	0.656269	+	0.216802i
$166$	11.5267	+	4.56128i	0.894642	+	0.354024i
$167$	10.2892	−	13.8734i	0.796203	−	1.07355i	−0.199404	−	0.979917i	$-0.563901\pi$
$167$	10.2892	−	13.8734i	0.796203	−	1.07355i	0.995606	−	0.0936375i	$-0.0298495\pi$
$168$	−6.13288	+	40.9461i	−0.473162	+	3.15906i
$169$	7.28784	−	1.82551i	0.560603	−	0.140424i
$170$	−0.189540	−	2.91282i	−0.0145370	−	0.223403i
$171$	−0.177455	+	7.22873i	−0.0135703	+	0.552795i
$172$	8.04573	+	5.87731i	0.613481	+	0.448141i
$173$	−0.391298	−	0.196963i	−0.0297498	−	0.0149748i	0.434674	−	0.900588i	$-0.356864\pi$
$173$	−0.391298	−	0.196963i	−0.0297498	−	0.0149748i	−0.464424	+	0.885613i	$0.653739\pi$
$174$	18.6617	−	6.49570i	1.41474	−	0.492437i
$175$	2.07026	+	21.0197i	0.156497	+	1.58894i
$176$	19.0699	+	4.98125i	1.43745	+	0.375476i
$177$	16.5105	+	1.62615i	1.24101	+	0.122229i
$178$	−9.69614	+	15.8641i	−0.726756	+	1.18907i
$179$	−3.56966	−	6.30134i	−0.266809	−	0.470984i	0.704208	−	0.709994i	$-0.251302\pi$
$179$	−3.56966	−	6.30134i	−0.266809	−	0.470984i	−0.971017	+	0.239010i	$0.923177\pi$
$180$	−4.01182	−	7.37662i	−0.299023	−	0.549821i
$181$	−15.5971	+	9.87677i	−1.15933	+	0.734135i	−0.968872	−	0.247562i	$-0.920371\pi$
$181$	−15.5971	+	9.87677i	−1.15933	+	0.734135i	−0.190453	+	0.981696i	$0.560996\pi$
$182$	−28.0701	−	6.55896i	−2.08069	−	0.486182i
$183$	−27.1935	+	12.8616i	−2.01020	+	0.950754i
$184$	9.42541	+	7.37710i	0.694850	+	0.543847i
$185$	0.183509	−	0.166323i	0.0134919	−	0.0122283i
$186$	−15.1005	−	17.8150i	−1.10722	−	1.30626i
$187$	14.4740	−	11.2956i	1.05845	−	0.826019i
$188$	13.1027	+	7.29779i	0.955612	+	0.532246i
$189$	62.5401	+	24.1244i	4.54912	+	1.75479i
$190$	−0.210760	−	0.717058i	−0.0152901	−	0.0520209i
$191$	15.1965	−	6.29459i	1.09958	−	0.455461i	0.242242	−	0.970216i	$-0.422117\pi$
$191$	15.1965	−	6.29459i	1.09958	−	0.455461i	0.857337	+	0.514755i	$0.172117\pi$
$192$	−13.8588	−	22.0228i	−1.00018	−	1.58936i
$193$	3.62010	+	1.49949i	0.260580	+	0.107936i	0.509149	−	0.860678i	$-0.329960\pi$
$193$	3.62010	+	1.49949i	0.260580	+	0.107936i	−0.248569	+	0.968614i	$0.579960\pi$
$194$	−1.90200	+	17.7368i	−0.136556	+	1.27343i
$195$	7.46026	−	3.30691i	0.534241	−	0.236813i
$196$	20.1973	+	17.1688i	1.44266	+	1.22635i
$197$	3.66671	+	0.452245i	0.261242	+	0.0322211i	0.251967	−	0.967736i	$-0.418923\pi$
$197$	3.66671	+	0.452245i	0.261242	+	0.0322211i	0.00927510	+	0.999957i	$0.497048\pi$
$198$	24.1538	−	46.9691i	1.71654	−	3.33795i
$199$	−0.637276	+	12.9720i	−0.0451753	+	0.919564i	0.864088	+	0.503341i	$0.167896\pi$
$199$	−0.637276	+	12.9720i	−0.0451753	+	0.919564i	−0.909263	+	0.416222i	$0.863354\pi$
$200$	−9.60088	−	9.16668i	−0.678885	−	0.648182i
$201$	−38.1335	−	13.6444i	−2.68973	−	0.962402i
$202$	4.50422	−	6.27939i	0.316916	−	0.441816i
$203$	4.23589	−	18.8633i	0.297301	−	1.32394i
$204$	−24.1385	−	2.20110i	−1.69003	−	0.154108i
$205$	1.11534	−	4.03034i	0.0778991	−	0.281491i
$206$	2.89707	−	18.4304i	0.201849	−	1.28411i
$207$	24.7930	−	20.3471i	1.72323	−	1.41422i
$208$	16.0625	−	8.37884i	1.11373	−	0.580968i
$209$	2.98227	−	3.63391i	0.206288	−	0.251362i
$210$	−11.4483	−	0.661754i	−0.790010	−	0.0456653i
$211$	−6.30361	+	2.08243i	−0.433958	+	0.143361i	−0.522361	−	0.852724i	$-0.674949\pi$
$211$	−6.30361	+	2.08243i	−0.433958	+	0.143361i	0.0884028	+	0.996085i	$0.471824\pi$
$212$	6.92411	+	0.289925i	0.475550	+	0.0199121i
$213$	−3.84449	+	3.66026i	−0.263420	+	0.250797i
$214$	8.32025	−	4.09823i	0.568760	−	0.280149i
$215$	−1.41876	+	2.36706i	−0.0967588	+	0.161432i
$216$	−39.6850	+	14.1364i	−2.70023	+	0.961858i
$217$	−22.6020	+	3.35269i	−1.53432	+	0.227596i
$218$	−5.04044	+	5.20325i	−0.341382	+	0.352408i
$219$	11.5749	−	5.82631i	0.782159	−	0.393706i
$220$	−0.894326	+	5.38531i	−0.0602955	+	0.363078i
$221$	2.88512	−	16.6274i	0.194074	−	1.11848i
$222$	−1.12773	−	1.71980i	−0.0756886	−	0.115425i
$223$	10.0848	+	6.73845i	0.675329	+	0.451240i	0.845359	−	0.534199i	$-0.179387\pi$
$223$	10.0848	+	6.73845i	0.675329	+	0.451240i	−0.170030	+	0.985439i	$0.554387\pi$
$224$	−25.4581	+	0.148375i	−1.70099	+	0.00991372i
$225$	−29.5758	+	19.7619i	−1.97172	+	1.31746i
$226$	−12.3477	−	5.24020i	−0.821357	−	0.348573i
$227$	1.05934	+	4.71744i	0.0703106	+	0.313107i	0.998216	−	0.0597088i	$-0.0190172\pi$
$227$	1.05934	+	4.71744i	0.0703106	+	0.313107i	−0.927905	+	0.372816i	$0.878392\pi$
$228$	−6.15384	+	0.804276i	−0.407548	+	0.0532645i
$229$	7.68076	−	0.566567i	0.507559	−	0.0374398i	0.182636	−	0.983181i	$-0.441537\pi$
$229$	7.68076	−	0.566567i	0.507559	−	0.0374398i	0.324922	+	0.945741i	$0.394662\pi$
$230$	−1.79774	+	2.78534i	−0.118540	+	0.183660i
$231$	−37.0815	−	61.8668i	−2.43978	−	4.07053i
$232$	5.71248	+	10.7237i	0.375043	+	0.704045i
$233$	17.8801	+	24.1086i	1.17137	+	1.57941i	0.732353	+	0.680925i	$0.238422\pi$
$233$	17.8801	+	24.1086i	1.17137	+	1.57941i	0.439014	+	0.898480i	$0.355328\pi$
$234$	−12.5426	−	46.8980i	−0.819938	−	3.06582i
$235$	−1.68338	+	3.79764i	−0.109811	+	0.247731i
$236$	0.574314	+	10.1852i	0.0373847	+	0.663001i
$237$	−17.3277	−	1.27817i	−1.12556	−	0.0830260i
$238$	−14.2913	+	18.9251i	−0.926366	+	1.22673i
$239$	2.52423	+	0.765716i	0.163279	+	0.0495300i	0.370866	−	0.928687i	$-0.379061\pi$
$239$	2.52423	+	0.765716i	0.163279	+	0.0495300i	−0.207587	+	0.978217i	$0.566561\pi$
$240$	5.72594	−	4.37657i	0.369608	−	0.282506i
$241$	6.53827	+	21.5538i	0.421167	+	1.38840i	0.869234	+	0.494402i	$0.164613\pi$
$241$	6.53827	+	21.5538i	0.421167	+	1.38840i	−0.448066	+	0.894000i	$0.647887\pi$
$242$	−17.0461	+	7.88246i	−1.09576	+	0.506704i
$243$	4.76569	+	38.6392i	0.305719	+	2.47870i
$244$	−10.3875	−	15.3050i	−0.664993	−	0.979802i
$245$	−4.22765	+	6.00280i	−0.270094	+	0.383505i
$246$	−31.6229	−	14.3461i	−2.01621	−	0.914675i
$247$	−0.212020	−	4.31576i	−0.0134905	−	0.274605i
$248$	9.39503	−	10.8604i	0.596585	−	0.689637i
$249$	25.7732	+	12.1898i	1.63331	+	0.772500i
$250$	4.72342	−	5.94572i	0.298735	−	0.376040i
$251$	8.00080	−	2.21412i	0.505006	−	0.139754i	−0.00489345	−	0.999988i	$-0.501558\pi$
$251$	8.00080	−	2.21412i	0.505006	−	0.139754i	0.509899	+	0.860234i	$0.329683\pi$
$252$	−14.4649	+	66.6693i	−0.911202	+	4.19977i
$253$	−20.8453	+	0.511724i	−1.31053	+	0.0321718i
$254$	11.8064	−	14.1350i	0.740802	−	0.886910i
$255$		−	6.71342i		−	0.420411i
$256$	12.0691	−	10.5042i	0.754317	−	0.656511i
$257$		−	9.43270i		−	0.588396i	−0.955745	−	0.294198i	$-0.904948\pi$
$257$		−	9.43270i		−	0.588396i	0.955745	−	0.294198i	$-0.0950525\pi$
$258$	17.5878	+	14.6904i	1.09497	+	0.914583i
$259$	−2.01154	+	0.0493806i	−0.124991	+	0.00306836i
$260$	2.71512	+	4.21973i	0.168384	+	0.261697i
$261$	31.3794	−	8.68385i	1.94234	−	0.537517i
$262$	2.57352	+	2.04447i	0.158993	+	0.126308i
$263$	20.6773	+	9.77965i	1.27502	+	0.603039i	0.940642	−	0.339400i	$-0.110224\pi$
$263$	20.6773	+	9.77965i	1.27502	+	0.603039i	0.334377	+	0.942439i	$0.391474\pi$
$264$	43.0229	+	14.2802i	2.64787	+	0.878888i
$265$	0.0941837	+	1.91715i	0.00578566	+	0.117770i
$266$	−2.50860	+	5.52968i	−0.153812	+	0.339046i
$267$	−24.6225	+	34.9612i	−1.50687	+	2.13959i
$268$	4.68156	−	24.4600i	0.285972	−	1.49413i
$269$	−3.09460	−	25.0904i	−0.188681	−	1.52979i	−0.726760	−	0.686891i	$-0.758975\pi$
$269$	−3.09460	−	25.0904i	−0.188681	−	1.52979i	0.538079	−	0.842894i	$-0.319150\pi$
$270$	−4.89735	−	10.5907i	−0.298043	−	0.644529i
$271$	−5.09676	−	16.8018i	−0.309606	−	1.02063i	−0.964316	−	0.264754i	$-0.914709\pi$
$271$	−5.09676	−	16.8018i	−0.309606	−	1.02063i	0.654710	−	0.755880i	$-0.272791\pi$
$272$	−0.946786	−	14.8741i	−0.0574073	−	0.901878i
$273$	−63.4432	−	19.2453i	−3.83975	−	1.16478i
$274$	17.2124	+	12.9979i	1.03984	+	0.785232i
$275$	23.0626	+	1.70120i	1.39073	+	0.102586i
$276$	20.5302	+	18.3385i	1.23577	+	1.10385i
$277$	7.09677	−	16.0101i	0.426404	−	0.961952i	−0.564257	−	0.825599i	$-0.690837\pi$
$277$	7.09677	−	16.0101i	0.426404	−	0.961952i	0.990660	−	0.136352i	$-0.0435379\pi$
$278$	−12.2028	+	3.26359i	−0.731878	+	0.195737i
$279$	−22.9229	−	30.9079i	−1.37236	−	1.85041i
$280$	−0.681240	−	7.01831i	−0.0407119	−	0.419425i
$281$	−13.0530	−	21.7777i	−0.778679	−	1.29915i	−0.949475	−	0.313841i	$-0.898384\pi$
$281$	−13.0530	−	21.7777i	−0.778679	−	1.29915i	0.170796	−	0.985306i	$-0.445366\pi$
$282$	28.9817	+	18.7057i	1.72583	+	1.11391i
$283$	−16.4451	+	1.21307i	−0.977561	+	0.0721092i	−0.552904	−	0.833245i	$-0.686480\pi$
$283$	−16.4451	+	1.21307i	−0.977561	+	0.0721092i	−0.424657	+	0.905354i	$0.639605\pi$
$284$	−2.58766	−	1.98945i	−0.153549	−	0.118052i
$285$	−0.376621	−	1.67717i	−0.0223091	−	0.0993470i
$286$	−12.3297	+	29.0530i	−0.729071	+	1.71794i
$287$	−28.2490	+	18.8754i	−1.66749	+	1.11418i
$288$	−20.4310	−	37.6937i	−1.20391	−	2.22112i
$289$	2.59124	+	1.73141i	0.152426	+	0.101848i
$290$	−2.81421	+	1.84538i	−0.165256	+	0.108364i
$291$	−7.01407	+	40.4231i	−0.411172	+	2.36964i
$292$	4.63519	+	6.48127i	0.271254	+	0.379288i
$293$	2.54745	−	1.28228i	0.148823	−	0.0749114i	−0.373637	−	0.927575i	$-0.621889\pi$
$293$	2.54745	−	1.28228i	0.148823	−	0.0749114i	0.522460	+	0.852664i	$0.325014\pi$
$294$	43.7900	+	42.4199i	2.55389	+	2.47398i
$295$	−2.79492	+	0.414588i	−0.162727	+	0.0241382i
$296$	0.938191	−	0.847917i	0.0545312	−	0.0492842i
$297$	37.7306	−	62.9498i	2.18935	−	3.65272i
$298$	4.07087	+	8.26470i	0.235819	+	0.478761i
$299$	−13.8809	+	13.2157i	−0.802755	+	0.764286i
$300$	−20.6657	−	22.4719i	−1.19313	−	1.29742i
$301$	21.2892	−	7.03300i	1.22709	−	0.405375i
$302$	−1.14820	+	19.8639i	−0.0660715	+	1.14304i
$303$	11.2753	−	13.7389i	0.647746	−	0.789281i
$304$	−1.07097	−	3.66280i	−0.0614241	−	0.210076i
$305$	3.96028	−	3.25012i	0.226765	−	0.186101i
$306$	−39.4540	−	6.20177i	−2.25544	−	0.354532i
$307$	−3.84868	+	13.9073i	−0.219656	+	0.793734i	0.768444	+	0.639918i	$0.221032\pi$
$307$	−3.84868	+	13.9073i	−0.219656	+	0.793734i	−0.988099	+	0.153817i	$0.950843\pi$
$308$	34.0797	−	28.3839i	1.94187	−	1.61732i
$309$	9.40140	−	41.8663i	0.534827	−	2.38169i
$310$	3.23191	+	2.31825i	0.183560	+	0.131668i
$311$	9.09151	+	3.25300i	0.515532	+	0.184460i	0.581785	−	0.813342i	$-0.302354\pi$
$311$	9.09151	+	3.25300i	0.515532	+	0.184460i	−0.0662529	+	0.997803i	$0.521104\pi$
$312$	38.1157	−	16.8312i	2.15788	−	0.952879i
$313$	1.30074	−	26.4771i	0.0735220	−	1.49658i	−0.624796	−	0.780788i	$-0.714818\pi$
$313$	1.30074	−	26.4771i	0.0735220	−	1.49658i	0.698318	−	0.715787i	$-0.253932\pi$
$314$	−15.7284	−	8.08834i	−0.887607	−	0.456451i
$315$	−18.7531	−	2.31297i	−1.05662	−	0.130321i
$316$	−0.863062	−	10.6488i	−0.0485510	−	0.599042i
$317$	−8.35609	+	3.70400i	−0.469325	+	0.208037i	−0.626326	−	0.779561i	$-0.715442\pi$
$317$	−8.35609	+	3.70400i	−0.469325	+	0.208037i	0.157002	+	0.987598i	$0.449817\pi$
$318$	15.8480	+	1.69946i	0.888711	+	0.0953007i
$319$	−19.5560	−	8.10035i	−1.09492	−	0.453532i
$320$	3.20090	+	3.06479i	0.178936	+	0.171327i
$321$	19.7075	−	8.16313i	1.09997	−	0.455622i
$322$	25.8403	−	7.59506i	1.44002	−	0.423256i
$323$	−3.31661	−	1.27936i	−0.184541	−	0.0711854i
$324$	−49.4517	+	14.0713i	−2.74731	+	0.781741i
$325$	16.7570	−	13.0773i	0.929510	−	0.725397i
$326$	3.46848	−	2.93998i	0.192101	−	0.162830i
$327$	−12.3452	+	11.1890i	−0.682691	+	0.618755i
$328$	5.72397	−	20.5707i	0.316053	−	1.13583i
$329$	30.5086	−	14.4295i	1.68200	−	0.795525i
$330$	−2.85679	+	12.2261i	−0.157261	+	0.673023i
$331$	22.9147	−	14.5106i	1.25951	−	0.797574i	0.273115	−	0.961981i	$-0.411946\pi$
$331$	22.9147	−	14.5106i	1.25951	−	0.797574i	0.986393	+	0.164407i	$0.0525711\pi$
$332$	−4.96741	+	16.8126i	−0.272622	+	0.922711i
$333$	−1.67027	−	2.94843i	−0.0915300	−	0.161573i
$334$	20.8423	+	12.7388i	1.14044	+	0.697035i
$335$	6.86450	+	0.676094i	0.375048	+	0.0369390i
$336$	−58.4501	−	3.46142i	−3.18871	−	0.188836i
$337$	−0.611618	−	6.20986i	−0.0333169	−	0.338273i	−0.997365	−	0.0725451i	$-0.976888\pi$
$337$	−0.611618	−	6.20986i	−0.0333169	−	0.338273i	0.964048	−	0.265727i	$-0.0856121\pi$
$338$	3.49276	+	10.0345i	0.189981	+	0.545804i
$339$	−27.5562	−	13.8706i	−1.49665	−	0.753349i
$340$	4.07889	−	0.635260i	0.221209	−	0.0344518i
$341$	−0.613951	+	25.0096i	−0.0332473	+	1.35435i
$342$	−10.2045	+	0.664013i	−0.551794	+	0.0359057i
$343$	27.3035	−	6.83916i	1.47425	−	0.369280i
$344$	−7.26122	+	12.0759i	−0.391499	+	0.651090i
$345$	−4.54191	+	6.12405i	−0.244528	+	0.329708i
$346$	0.227958	−	0.576065i	0.0122551	−	0.0309695i
$347$	11.8793	+	3.92441i	0.637717	+	0.210673i	0.614325	−	0.789053i	$-0.289428\pi$
$347$	11.8793	+	3.92441i	0.637717	+	0.210673i	0.0233919	+	0.999726i	$0.492553\pi$
$348$	11.5090	+	25.4647i	0.616948	+	1.36505i
$349$	10.0792	+	14.3113i	0.539526	+	0.766068i	0.992072	−	0.125673i	$-0.0401091\pi$
$349$	10.0792	+	14.3113i	0.539526	+	0.766068i	−0.452546	+	0.891741i	$0.649484\pi$
$350$	−29.3455	+	5.57369i	−1.56858	+	0.297926i
$351$	−13.1605	−	66.1623i	−0.702456	−	3.53148i
$352$	−4.60522	+	27.4908i	−0.245459	+	1.46526i
$353$	−3.86871	+	19.4493i	−0.205911	+	1.03518i	0.730134	+	0.683304i	$0.239457\pi$
$353$	−3.86871	+	19.4493i	−0.205911	+	1.03518i	−0.936045	+	0.351880i	$0.885543\pi$
$354$	−0.202991	+	23.4615i	−0.0107888	+	1.24697i
$355$	0.483663	−	0.763787i	0.0256701	−	0.0405376i
$356$	−23.5714	−	11.6517i	−1.24928	−	0.617539i
$357$	−35.6257	+	41.3001i	−1.88551	+	2.18583i
$358$	8.42442	−	5.82476i	0.445244	−	0.307848i
$359$	−4.17272	+	16.6584i	−0.220228	+	0.879198i	0.754590	+	0.656196i	$0.227836\pi$
$359$	−4.17272	+	16.6584i	−0.220228	+	0.879198i	−0.974818	+	0.223002i	$0.928414\pi$
$360$	9.88310	−	6.58351i	0.520885	−	0.346982i
$361$	17.8940	+	2.65433i	0.941790	+	0.139701i
$362$	−15.8840	−	20.7206i	−0.834842	−	1.08905i
$363$	−40.2991	+	15.5451i	−2.11515	+	0.815905i
$364$	5.68957	−	40.3674i	0.298214	−	2.11583i
$365$	−1.67113	+	1.44153i	−0.0874711	+	0.0754531i
$366$	−21.5544	−	36.6772i	−1.12667	−	1.91715i
$367$	−0.942283	−	1.76289i	−0.0491868	−	0.0920220i	0.856127	−	0.516766i	$-0.172864\pi$
$367$	−0.942283	−	1.76289i	−0.0491868	−	0.0920220i	−0.905314	+	0.424744i	$0.860364\pi$
$368$	−9.19930	+	14.2089i	−0.479547	+	0.740689i
$369$	−50.4609	−	26.9719i	−2.62689	−	1.40410i
$370$	0.257476	+	0.237453i	0.0133856	+	0.0123446i
$371$	9.59424	−	12.2939i	0.498108	−	0.638267i
$372$	23.1841	−	23.5223i	1.20204	−	1.21957i
$373$	−5.94221	−	34.2458i	−0.307676	−	1.77318i	−0.583641	−	0.812012i	$-0.698373\pi$
$373$	−5.94221	−	34.2458i	−0.307676	−	1.77318i	0.275965	−	0.961168i	$-0.411002\pi$
$374$	17.7405	+	18.9592i	0.917340	+	0.980358i
$375$	11.7285	−	12.9404i	0.605657	−	0.668240i
$376$	−8.62265	+	19.3785i	−0.444679	+	0.999370i
$377$	−18.3188	+	6.55458i	−0.943467	+	0.337578i
$378$	−26.0731	+	91.1411i	−1.34106	+	4.68779i
$379$	9.38471	+	5.31637i	0.482060	+	0.273084i	0.714639	−	0.699494i	$-0.246591\pi$
$379$	9.38471	+	5.31637i	0.482060	+	0.273084i	−0.232578	+	0.972578i	$0.574716\pi$
$380$	0.983365	−	0.387528i	0.0504456	−	0.0198798i
$381$	29.2075	−	30.6776i	1.49635	−	1.57166i
$382$	10.7876	+	20.6092i	0.551943	+	1.05446i
$383$	−15.0254	+	15.0254i	−0.767762	+	0.767762i	−0.977712	−	0.209950i	$-0.932670\pi$
$383$	−15.0254	+	15.0254i	−0.767762	+	0.767762i	0.209950	+	0.977712i	$0.432670\pi$
$384$	29.2680	−	22.3053i	1.49358	−	1.13826i
$385$	8.68623	+	8.68623i	0.442691	+	0.442691i
$386$	−1.65440	+	5.28868i	−0.0842069	+	0.269186i
$387$	27.3468	+	26.0363i	1.39012	+	1.32350i
$388$	−25.2237	−	0.436506i	−1.28054	−	0.0221602i
$389$	10.3101	−	18.1999i	0.522743	−	0.922770i	−0.476311	−	0.879277i	$-0.658026\pi$
$389$	10.3101	−	18.1999i	0.522743	−	0.922770i	0.999054	−	0.0434929i	$-0.0138486\pi$
$390$	5.60119	+	10.0900i	0.283627	+	0.510929i
$391$	5.31197	+	14.8460i	0.268638	+	0.750792i
$392$	−21.6295	+	30.6196i	−1.09246	+	1.54652i
$393$	5.60108	+	5.07652i	0.282537	+	0.256077i
$394$	−0.173408	+	5.22192i	−0.00873618	+	0.263076i
$395$	2.91553	−	0.505892i	0.146696	−	0.0254542i
$396$	69.2122	+	28.0833i	3.47805	+	1.41124i
$397$	−0.815703	−	0.636580i	−0.0409389	−	0.0319491i	0.594555	−	0.804055i	$-0.297328\pi$
$397$	−0.815703	−	0.636580i	−0.0409389	−	0.0319491i	−0.635494	+	0.772106i	$0.719203\pi$
$398$	−18.3523	+	0.742492i	−0.919920	+	0.0372178i
$399$	−6.58322	+	12.3163i	−0.329573	+	0.616588i
$400$	11.6978	−	14.6823i	0.584892	−	0.734116i
$401$	−12.2530	+	6.54934i	−0.611884	+	0.327059i	−0.748065	−	0.663625i	$-0.769017\pi$
$401$	−12.2530	+	6.54934i	−0.611884	+	0.327059i	0.136181	+	0.990684i	$0.456517\pi$
$402$	14.3974	−	55.4382i	0.718077	−	2.76500i
$403$	15.0196	+	17.4119i	0.748179	+	0.867347i
$404$	9.41433	+	5.55048i	0.468380	+	0.276147i
$405$	−5.12506	−	13.2862i	−0.254666	−	0.660198i
$406$	27.1055	+	3.58148i	1.34522	+	0.177746i
$407$	−0.323254	+	2.17920i	−0.0160231	+	0.108019i
$408$	0.0483963	−	34.2785i	0.00239597	−	1.69704i
$409$	−36.1080	−	9.04459i	−1.78543	−	0.447226i	−0.797653	−	0.603116i	$-0.793926\pi$
$409$	−36.1080	−	9.04459i	−1.78543	−	0.447226i	−0.987774	+	0.155890i	$0.950176\pi$
$410$	5.81795	+	1.06144i	0.287328	+	0.0524209i
$411$	37.5624	+	32.4016i	1.85282	+	1.59825i
$412$	26.3264	+	1.75041i	1.29701	+	0.0862367i
$413$	19.3941	+	12.2812i	0.954320	+	0.604317i
$414$	31.7946	+	32.3496i	1.56262	+	1.58990i
$415$	−4.76232	−	0.947284i	−0.233773	−	0.0465004i
$416$	13.8329	+	21.5654i	0.678213	+	1.05733i
$417$	−28.4937	+	5.66775i	−1.39534	+	0.277551i
$418$	5.49560	+	3.74122i	0.268799	+	0.182989i
$419$	−15.5877	+	10.9781i	−0.761510	+	0.536316i	−0.890310	−	0.455355i	$-0.849512\pi$
$419$	−15.5877	+	10.9781i	−0.761510	+	0.536316i	0.128800	+	0.991671i	$0.458887\pi$
$420$	−0.515363	−	16.2092i	−0.0251471	−	0.790929i
$421$	−2.78575	+	8.43259i	−0.135769	+	0.410979i	−0.994911	−	0.100758i	$-0.967873\pi$
$421$	−2.78575	+	8.43259i	−0.135769	+	0.410979i	0.859142	+	0.511738i	$0.170998\pi$
$422$	−3.73021	−	8.61566i	−0.181584	−	0.419404i
$423$	45.6516	+	33.8575i	2.21966	+	1.64621i
$424$	0.467079	+	9.78961i	0.0226834	+	0.475425i
$425$	−4.24898	−	16.9629i	−0.206106	−	0.822821i
$426$	−5.64174	−	4.95237i	−0.273343	−	0.239943i
$427$	−41.6103	−	1.02148i	−2.01367	−	0.0494327i
$428$	6.82453	+	11.2013i	0.329876	+	0.541437i
$429$	−32.6363	+	64.8372i	−1.57570	+	3.13037i
$430$	−3.51351	−	1.69912i	−0.169436	−	0.0819387i
$431$	4.90379	−	0.482982i	0.236207	−	0.0232644i	0.0207793	−	0.999784i	$-0.493385\pi$
$431$	4.90379	−	0.482982i	0.236207	−	0.0232644i	0.215428	+	0.976520i	$0.430885\pi$
$432$	−24.9294	−	54.1110i	−1.19942	−	2.60342i
$433$	−3.27391	+	33.2406i	−0.157334	+	1.59744i	0.514999	+	0.857191i	$0.327792\pi$
$433$	−3.27391	+	33.2406i	−0.157334	+	1.59744i	−0.672333	+	0.740248i	$0.734708\pi$
$434$	−7.58013	−	31.4122i	−0.363858	−	1.50783i
$435$	−6.73440	+	3.81499i	−0.322890	+	0.182915i
$436$	−7.96632	−	6.44184i	−0.381518	−	0.308508i
$437$	2.15991	+	3.41087i	0.103322	+	0.163164i
$438$	9.67013	+	15.5672i	0.462057	+	0.743828i
$439$	17.2988	+	36.5753i	0.825629	+	1.74565i	0.648137	+	0.761523i	$0.275548\pi$
$439$	17.2988	+	36.5753i	0.825629	+	1.74565i	0.177491	+	0.984122i	$0.443202\pi$
$440$	−7.69856	−	0.578809i	−0.367014	−	0.0275936i
$441$	67.4629	+	74.4339i	3.21252	+	3.54447i
$442$	23.7853	+	1.96155i	1.13135	+	0.0933014i
$443$	−9.69350	−	12.4211i	−0.460552	−	0.590143i	0.500766	−	0.865583i	$-0.333052\pi$
$443$	−9.69350	−	12.4211i	−0.460552	−	0.590143i	−0.961318	+	0.275439i	$0.911177\pi$
$444$	2.27984	−	1.80591i	0.108196	−	0.0857049i
$445$	2.62101	−	6.79470i	0.124248	−	0.322100i
$446$	−8.21637	+	15.0569i	−0.389057	+	0.712967i
$447$	8.10864	+	19.5760i	0.383525	+	0.925912i
$448$	−3.42780	−	35.8402i	−0.161948	−	1.69329i
$449$	1.08939	−	2.63002i	0.0514115	−	0.124118i	−0.896087	−	0.443878i	$-0.853602\pi$
$449$	1.08939	−	2.63002i	0.0514115	−	0.124118i	0.947499	+	0.319760i	$0.103602\pi$
$450$	−31.5751	−	39.1604i	−1.48847	−	1.84604i
$451$	15.0742	+	34.0069i	0.709817	+	1.60132i
$452$	5.81990	−	18.0549i	0.273745	−	0.849231i
$453$	−5.60170	+	45.4174i	−0.263191	+	2.13390i
$454$	−6.51081	+	2.08858i	−0.305567	+	0.0980219i
$455$	11.2776	+	0.554031i	0.528700	+	0.0259734i
$456$	−1.91093	−	8.56630i	−0.0894873	−	0.401154i
$457$	11.3503	−	31.7219i	0.530944	−	1.48389i	−0.314204	−	0.949356i	$-0.601738\pi$
$457$	11.3503	−	31.7219i	0.530944	−	1.48389i	0.845148	−	0.534533i	$-0.179512\pi$
$458$	1.76916	+	10.7471i	0.0826673	+	0.502179i
$459$	−54.1489	−	12.1595i	−2.52745	−	0.567559i
$460$	−4.15059	−	2.18005i	−0.193522	−	0.101645i
$461$	−27.4633	−	7.60012i	−1.27909	−	0.353973i	−0.440019	−	0.897988i	$-0.645028\pi$
$461$	−27.4633	−	7.60012i	−1.27909	−	0.353973i	−0.839075	+	0.544015i	$0.816903\pi$
$462$	82.4540	−	60.0533i	3.83611	−	2.79393i
$463$	8.05794	+	9.81863i	0.374484	+	0.456311i	0.925815	−	0.377976i	$-0.123380\pi$
$463$	8.05794	+	9.81863i	0.374484	+	0.456311i	−0.551331	+	0.834287i	$0.685880\pi$
$464$	−14.3826	+	9.40217i	−0.667695	+	0.436485i
$465$	7.07122	+	5.80320i	0.327920	+	0.269117i
$466$	−31.6975	+	28.2333i	−1.46836	+	1.30788i
$467$	−7.94993	−	24.0648i	−0.367879	−	1.11358i	−0.953086	−	0.302701i	$-0.902112\pi$
$467$	−7.94993	−	24.0648i	−0.367879	−	1.11358i	0.585207	−	0.810884i	$-0.301013\pi$
$468$	64.4724	−	23.5965i	2.98024	−	1.09075i
$469$	−38.6417	−	40.5867i	−1.78431	−	1.87412i
$470$	−5.56201	−	1.89097i	−0.256556	−	0.0872238i
$471$	−34.8899	−	20.9122i	−1.60764	−	0.963582i
$472$	−14.2738	+	2.09672i	−0.657004	+	0.0965096i
$473$	−3.60193	−	24.2823i	−0.165617	−	1.11650i
$474$	−0.390473	−	24.5686i	−0.0179350	−	1.12847i
$475$	−2.01311	−	3.99936i	−0.0923678	−	0.183503i
$476$	−28.4639	−	17.7372i	−1.30464	−	0.812982i
$477$	25.8761	+	4.48993i	1.18479	+	0.205580i
$478$	−0.759397	+	3.65231i	−0.0347340	+	0.167053i
$479$	0.855730	−	1.28069i	0.0390993	−	0.0585162i	−0.811405	−	0.584484i	$-0.801297\pi$
$479$	0.855730	−	1.28069i	0.0390993	−	0.0585162i	0.850504	+	0.525968i	$0.176297\pi$
$480$	6.88857	+	7.51192i	0.314419	+	0.342871i
$481$	1.12501	+	1.68369i	0.0512959	+	0.0767697i
$482$	−29.5329	+	11.9347i	−1.34519	+	0.543608i
$483$	60.4394	−	13.5721i	2.75009	−	0.617553i
$484$	−13.2581	−	23.0137i	−0.602640	−	1.04608i
$485$	−0.514018	−	6.96837i	−0.0233403	−	0.316417i
$486$	−53.8227	+	11.5981i	−2.44145	+	0.526099i
$487$	−3.98865	+	2.39070i	−0.180743	+	0.108333i	−0.601613	−	0.798788i	$-0.705475\pi$
$487$	−3.98865	+	2.39070i	−0.180743	+	0.108333i	0.420870	+	0.907121i	$0.361725\pi$
$488$	20.2445	−	16.5665i	0.916425	−	0.749928i
$489$	8.39944	−	6.22945i	0.379836	−	0.281705i
$490$	−8.98977	−	5.19589i	−0.406116	−	0.234726i
$491$	4.01375	+	1.77917i	0.181138	+	0.0802929i	0.493817	−	0.869566i	$-0.335601\pi$
$491$	4.01375	+	1.77917i	0.181138	+	0.0802929i	−0.312679	+	0.949859i	$0.601226\pi$
$492$	16.2090	−	46.3564i	0.730756	−	2.08991i
$493$	−1.17750	+	15.9630i	−0.0530319	+	0.718936i
$494$	6.05216	−	0.844306i	0.272300	−	0.0379871i
$495$	−6.00536	+	19.7970i	−0.269921	+	0.889809i
$496$	16.4853	+	11.8602i	0.740212	+	0.532540i
$497$	−7.02857	+	2.13209i	−0.315275	+	0.0956375i
$498$	−13.9113	+	37.8441i	−0.623382	+	1.69584i
$499$	−15.3334	+	1.89119i	−0.686415	+	0.0846612i	−0.458066	−	0.888918i	$-0.651458\pi$
$499$	−15.3334	+	1.89119i	−0.686415	+	0.0846612i	−0.228349	+	0.973579i	$0.573333\pi$
$500$	8.97205	+	5.90143i	0.401242	+	0.263920i
$501$	45.9320	+	32.3489i	2.05209	+	1.44524i
$502$	4.13028	+	10.9896i	0.184344	+	0.490489i
$503$	−27.3039	+	1.34136i	−1.21742	+	0.0598081i	−0.647613	−	0.761969i	$-0.724233\pi$
$503$	−27.3039	+	1.34136i	−1.21742	+	0.0598081i	−0.569809	+	0.821777i	$0.692983\pi$
$504$	−95.7359	−	11.9451i	−4.26442	−	0.532079i
$505$	−1.29419	+	2.73634i	−0.0575908	+	0.121765i
$506$	−3.35638	−	29.2970i	−0.149209	−	1.30241i
$507$	6.51755	+	23.5514i	0.289454	+	1.04595i
$508$	21.4026	+	14.8428i	0.949588	+	0.658542i
$509$	−0.278832	−	11.3584i	−0.0123590	−	0.503450i	−0.973667	−	0.227975i	$-0.926790\pi$
$509$	−0.278832	−	11.3584i	−0.0123590	−	0.503450i	0.961308	−	0.275476i	$-0.0888353\pi$
$510$	9.45619	−	0.848815i	0.418727	−	0.0375862i
$511$	17.9303			0.793189
$512$	16.3216	+	15.6718i	0.721320	+	0.692602i
$513$	−14.2098			−0.627379
$514$	13.2864	−	1.19263i	0.586040	−	0.0526046i
$515$	0.179342	+	7.30559i	0.00790276	+	0.321923i
$516$	−18.4684	+	26.6306i	−0.813027	+	1.17235i
$517$	−9.85524	−	35.6123i	−0.433433	−	1.56623i
$518$	−0.323885	−	2.82711i	−0.0142307	−	0.124216i
$519$	0.609209	−	1.28806i	0.0267413	−	0.0565397i
$520$	−5.60042	+	4.35790i	−0.245595	+	0.191107i
$521$	17.7594	−	0.872462i	0.778052	−	0.0382232i	0.343833	−	0.939031i	$-0.388274\pi$
$521$	17.7594	−	0.872462i	0.778052	−	0.0382232i	0.434219	+	0.900807i	$0.357024\pi$
$522$	16.1991	+	43.1015i	0.709016	+	1.88650i
$523$	4.38894	+	3.09104i	0.191915	+	0.135162i	0.667786	−	0.744353i	$-0.267242\pi$
$523$	4.38894	+	3.09104i	0.191915	+	0.135162i	−0.475871	+	0.879515i	$0.657867\pi$
$524$	−2.55435	+	3.88343i	−0.111587	+	0.169649i
$525$	−68.1822	+	8.40947i	−2.97572	+	0.367019i
$526$	−11.1608	+	30.3616i	−0.486633	+	1.32383i
$527$	18.1030	−	5.49148i	0.788579	−	0.239213i
$528$	−14.6748	+	62.4054i	−0.638639	+	2.71585i
$529$	−1.47828	+	4.87324i	−0.0642731	+	0.211880i
$530$	−2.68850	+	0.375059i	−0.116781	+	0.0162915i
$531$	−2.84397	+	38.5548i	−0.123418	+	1.67313i
$532$	−8.10601	−	2.83435i	−0.351440	−	0.122884i
$533$	31.2579	+	13.8557i	1.35393	+	0.600155i
$534$	−52.3578	−	30.2616i	−2.26574	−	1.30955i
$535$	−2.91799	+	2.16413i	−0.126156	+	0.0935634i
$536$	35.0451	+	3.50160i	1.51372	+	0.151246i
$537$	20.2045	−	12.1101i	0.871887	−	0.522589i
$538$	34.9498	−	7.53121i	1.50679	−	0.324694i
$539$	−4.80447	−	65.1326i	−0.206943	−	2.80546i
$540$	14.2983	−	8.23720i	0.615302	−	0.354473i
$541$	−10.7154	+	2.40623i	−0.460692	+	0.103452i	−0.443254	−	0.896396i	$-0.646176\pi$
$541$	−10.7154	+	2.40623i	−0.460692	+	0.103452i	−0.0174380	+	0.999848i	$0.505551\pi$
$542$	23.0217	−	9.30338i	0.988867	−	0.399614i
$543$	−33.3603	−	49.9272i	−1.43163	−	2.14258i
$544$	20.8313	−	3.21422i	0.893134	−	0.137808i
$545$	1.57647	−	2.35936i	0.0675287	−	0.101064i
$546$	19.0865	−	91.7962i	0.816825	−	3.92851i
$547$	−10.0856	−	1.75002i	−0.431229	−	0.0748253i	−0.0487964	−	0.998809i	$-0.515539\pi$
$547$	−10.0856	−	1.75002i	−0.431229	−	0.0748253i	−0.382432	+	0.923983i	$0.624914\pi$
$548$	−16.1319	+	25.8879i	−0.689123	+	1.10588i
$549$	−31.5165	−	62.6125i	−1.34509	−	2.67224i
$550$	0.519705	+	32.6999i	0.0221603	+	1.39433i
$551$	0.601352	+	4.05399i	0.0256185	+	0.172706i
$552$	−23.2350	+	31.2365i	−0.988947	+	1.32951i
$553$	−20.6205	−	12.3595i	−0.876875	−	0.525578i
$554$	23.4483	+	7.97192i	0.996221	+	0.338695i
$555$	0.555463	+	0.583421i	0.0235781	+	0.0247649i
$556$	−6.13980	−	16.7757i	−0.260386	−	0.711448i
$557$	−1.65558	−	5.01152i	−0.0701493	−	0.212345i	0.908499	−	0.417887i	$-0.137229\pi$
$557$	−1.65558	−	5.01152i	−0.0701493	−	0.212345i	−0.978648	+	0.205542i	$0.934104\pi$
$558$	40.6371	−	36.1959i	1.72031	−	1.53229i
$559$	−17.4419	−	14.3142i	−0.737713	−	0.605425i
$560$	9.79952	−	1.84693i	0.414105	−	0.0780468i
$561$	37.8842	+	46.1620i	1.59947	+	1.94896i
$562$	29.0246	−	21.1393i	1.22433	−	0.891709i
$563$	29.0842	+	8.04867i	1.22575	+	0.339211i	0.818714	−	0.574201i	$-0.194687\pi$
$563$	29.0842	+	8.04867i	1.22575	+	0.339211i	0.407037	+	0.913412i	$0.366562\pi$
$564$	−22.6836	+	43.1872i	−0.955151	+	1.81851i
$565$	5.12643	+	1.15118i	0.215670	+	0.0484304i
$566$	−3.78791	−	23.0104i	−0.159218	−	0.967200i
$567$	−38.9765	+	108.932i	−1.63686	+	4.57472i
$568$	2.47507	−	3.89638i	0.103852	−	0.163489i
$569$	−13.7453	−	0.675263i	−0.576232	−	0.0283085i	−0.241134	−	0.970492i	$-0.577519\pi$
$569$	−13.7453	−	0.675263i	−0.576232	−	0.0283085i	−0.335098	+	0.942183i	$0.608769\pi$
$570$	2.31476	−	0.742544i	0.0969547	−	0.0311017i
$571$	4.81041	−	39.0018i	0.201310	−	1.63218i	−0.464161	−	0.885751i	$-0.653644\pi$
$571$	4.81041	−	39.0018i	0.201310	−	1.63218i	0.665470	−	0.746424i	$-0.268231\pi$
$572$	−42.4816	−	13.6937i	−1.77624	−	0.572562i
$573$	21.6805	+	48.9104i	0.905716	+	2.04326i
$574$	−30.1586	−	37.4036i	−1.25880	−	1.56120i
$575$	−7.60013	+	18.3483i	−0.316947	+	0.765178i
$576$	50.5103	−	33.5440i	2.10460	−	1.39767i
$577$	3.94949	+	9.53492i	0.164420	+	0.396944i	0.984519	−	0.175277i	$-0.0560820\pi$
$577$	3.94949	+	9.53492i	0.164420	+	0.396944i	−0.820100	+	0.572221i	$0.806082\pi$
$578$	−2.11116	+	3.86880i	−0.0878125	+	0.160921i
$579$	−4.58678	+	11.8908i	−0.190620	+	0.494164i
$580$	−2.95513	−	3.73064i	−0.122705	−	0.154906i
$581$	24.2703	+	31.0995i	1.00690	+	1.29022i
$582$	−57.8247	−	4.76876i	−2.39691	−	0.197671i
$583$	−11.4662	−	12.6510i	−0.474882	−	0.523952i
$584$	−8.54315	+	7.34836i	−0.353518	+	0.304077i
$585$	8.13017	+	17.1898i	0.336141	+	0.710710i
$586$	2.12824	+	3.42608i	0.0879168	+	0.141530i
$587$	−8.13580	−	12.8478i	−0.335800	−	0.530287i	0.634270	−	0.773112i	$-0.281301\pi$
$587$	−8.13580	−	12.8478i	−0.335800	−	0.530287i	−0.970070	+	0.242825i	$0.921926\pi$
$588$	−54.2139	+	67.0439i	−2.23575	+	2.76484i
$589$	4.21448	−	2.38748i	0.173655	−	0.0983742i
$590$	−0.937345	−	3.88437i	−0.0385899	−	0.159917i
$591$	−1.17783	+	11.9587i	−0.0484496	+	0.491917i
$592$	1.31295	+	1.21428i	0.0539621	+	0.0499067i
$593$	29.5896	−	2.91432i	1.21510	−	0.119677i	0.529917	−	0.848049i	$-0.322223\pi$
$593$	29.5896	−	2.91432i	1.21510	−	0.119677i	0.685181	+	0.728373i	$0.259723\pi$
$594$	93.4384	+	45.1864i	3.83383	+	1.85402i
$595$	4.17649	−	8.29726i	0.171219	−	0.340155i
$596$	−11.1265	+	6.77897i	−0.455761	+	0.277677i
$597$	−42.2307	−	1.03671i	−1.72839	−	0.0424296i
$598$	−20.3701	−	17.8810i	−0.832995	−	0.731210i
$599$	6.25608	+	24.9757i	0.255616	+	1.02048i	0.952803	+	0.303588i	$0.0981848\pi$
$599$	6.25608	+	24.9757i	0.255616	+	1.02048i	−0.697187	+	0.716889i	$0.745565\pi$
$600$	29.0400	−	31.9499i	1.18555	−	1.30435i
$601$	11.4837	+	8.51692i	0.468432	+	0.347413i	0.804026	−	0.594594i	$-0.202687\pi$
$601$	11.4837	+	8.51692i	0.468432	+	0.347413i	−0.335594	+	0.942007i	$0.608937\pi$
$602$	12.5980	+	29.0977i	0.513458	+	1.18593i
$603$	29.6043	−	89.6135i	1.20558	−	3.64934i
$604$	−28.1244	+	0.894199i	−1.14437	+	0.0363844i
$605$	6.01435	−	4.23578i	0.244518	−	0.172209i
$606$	20.7776	+	14.1447i	0.844031	+	0.574588i
$607$	−29.2799	+	5.82414i	−1.18844	+	0.236395i	−0.749426	−	0.662088i	$-0.769671\pi$
$607$	−29.2799	+	5.82414i	−1.18844	+	0.236395i	−0.439010	+	0.898482i	$0.644671\pi$
$608$	5.02383	−	1.97162i	0.203743	−	0.0799596i
$609$	61.6739	+	12.2677i	2.49915	+	0.497112i
$610$	5.07867	+	5.16732i	0.205629	+	0.209219i
$611$	−28.6944	−	18.1705i	−1.16085	−	0.735102i
$612$	3.74712	−	56.3571i	0.151468	−	2.27810i
$613$	31.8388	+	27.4643i	1.28596	+	1.10927i	0.987960	+	0.154707i	$0.0494433\pi$
$613$	31.8388	+	27.4643i	1.28596	+	1.10927i	0.297996	+	0.954567i	$0.403682\pi$
$614$	−20.0758	−	3.66268i	−0.810194	−	0.147814i
$615$	13.1941	+	3.30494i	0.532036	+	0.133268i
$616$	44.2890	+	44.4142i	1.78445	+	1.78950i
$617$	1.30317	−	8.78527i	0.0524637	−	0.353682i	−0.947009	−	0.321207i	$-0.895911\pi$
$617$	1.30317	−	8.78527i	0.0524637	−	0.353682i	0.999473	−	0.0324742i	$-0.0103387\pi$
$618$	60.1595	+	7.94895i	2.41997	+	0.319754i
$619$	−3.45749	−	8.96321i	−0.138968	−	0.360262i	0.845955	−	0.533255i	$-0.179031\pi$
$619$	−3.45749	−	8.96321i	−0.138968	−	0.360262i	−0.984923	+	0.172993i	$0.944656\pi$
$620$	−2.85675	+	4.84541i	−0.114730	+	0.194596i
$621$	41.1688	+	47.7260i	1.65205	+	1.91518i
$622$	−3.43252	+	13.2171i	−0.137631	+	0.529959i
$623$	−52.1811	+	27.8914i	−2.09059	+	1.11745i
$624$	28.5268	+	51.5599i	1.14198	+	2.06405i
$625$	9.65955	−	18.0717i	0.386382	−	0.722870i
$626$	37.4588	−	1.51549i	1.49716	−	0.0605713i
$627$	12.0540	+	9.40707i	0.481392	+	0.375682i
$628$	9.40420	−	23.1770i	0.375268	−	0.924861i
$629$	1.64139	−	0.284807i	0.0654463	−	0.0113560i
$630$	0.886882	−	26.7071i	0.0353342	−	1.06404i
$631$	−1.94011	−	1.75841i	−0.0772345	−	0.0700013i	0.632029	−	0.774945i	$-0.282222\pi$
$631$	−1.94011	−	1.75841i	−0.0772345	−	0.0700013i	−0.709263	+	0.704943i	$0.750972\pi$
$632$	14.8902	−	2.56205i	0.592302	−	0.101913i
$633$	−7.27440	−	20.3306i	−0.289131	−	0.808068i
$634$	−6.27378	−	11.3017i	−0.249163	−	0.448846i
$635$	−3.55574	+	6.27677i	−0.141105	+	0.249086i
$636$	−0.390022	+	22.5375i	−0.0154654	+	0.893672i
$637$	−43.4766	−	41.3932i	−1.72261	−	1.64006i
$638$	8.93718	−	28.5697i	0.353826	−	1.13109i
$639$	−8.74653	−	8.74653i	−0.346007	−	0.346007i
$640$	−3.91220	+	4.89613i	−0.154643	+	0.193536i
$641$	−21.0299	+	21.0299i	−0.830630	+	0.830630i	−0.987603	−	0.156973i	$-0.949827\pi$
$641$	−21.0299	+	21.0299i	−0.830630	+	0.830630i	0.156973	+	0.987603i	$0.449827\pi$
$642$	13.9899	+	26.7270i	0.552138	+	1.05483i
$643$	−11.6167	+	12.2014i	−0.458117	+	0.481175i	−0.912177	−	0.409796i	$-0.865600\pi$
$643$	−11.6167	+	12.2014i	−0.458117	+	0.481175i	0.454060	+	0.890971i	$0.349975\pi$
$644$	13.9651	+	35.4370i	0.550304	+	1.39642i
$645$	−7.80998	−	4.42430i	−0.307518	−	0.174207i
$646$	1.38270	−	4.83337i	0.0544017	−	0.190166i
$647$	17.0210	−	6.09022i	0.669165	−	0.239431i	0.0196812	−	0.999806i	$-0.493735\pi$
$647$	17.0210	−	6.09022i	0.669165	−	0.239431i	0.649484	+	0.760375i	$0.274985\pi$
$648$	−26.0726	−	67.8760i	−1.02423	−	2.66642i
$649$	16.8786	−	18.6226i	0.662542	−	0.731003i
$650$	20.5387	+	21.9496i	0.805593	+	0.860935i
$651$	−12.7057	−	73.2250i	−0.497977	−	2.86991i
$652$	4.57964	+	4.51381i	0.179353	+	0.176774i
$653$	19.7377	−	25.2915i	0.772396	−	0.989733i	−0.227477	−	0.973783i	$-0.573048\pi$
$653$	19.7377	−	25.2915i	0.772396	−	0.989733i	0.999873	−	0.0159500i	$-0.00507725\pi$
$654$	−17.3212	−	15.9741i	−0.677312	−	0.624639i
$655$	−1.13541	−	0.606887i	−0.0443640	−	0.0237130i
$656$	29.6986	+	5.46163i	1.15954	+	0.213241i
$657$	14.2345	+	26.6309i	0.555341	+	1.03897i
$658$	24.1821	+	41.1485i	0.942715	+	1.60414i
$659$	15.6305	−	13.4830i	0.608880	−	0.525223i	−0.293615	−	0.955924i	$-0.594858\pi$
$659$	15.6305	−	13.4830i	0.608880	−	0.525223i	0.902495	+	0.430701i	$0.141733\pi$
$660$	−17.5822	−	2.47812i	−0.684388	−	0.0964607i
$661$	−24.5035	+	9.45206i	−0.953077	+	0.367642i	−0.785948	−	0.618293i	$-0.787825\pi$
$661$	−24.5035	+	9.45206i	−0.953077	+	0.367642i	−0.167129	+	0.985935i	$0.553450\pi$
$662$	23.3361	+	30.4419i	0.906985	+	1.18316i
$663$	54.2958	+	8.05402i	2.10867	+	0.312792i
$664$	−24.3094	−	4.87114i	−0.943389	−	0.189037i
$665$	0.577911	−	2.30715i	0.0224104	−	0.0894675i
$666$	3.94183	−	2.72544i	0.152743	−	0.105609i
$667$	11.8737	−	13.7650i	0.459753	−	0.532981i
$668$	−15.3080	+	30.9680i	−0.592284	+	1.19819i
$669$	−21.1057	+	33.3296i	−0.815995	+	1.28860i
$670$	−0.0843964	+	9.75448i	−0.00326052	+	0.376848i
$671$	−8.89062	+	44.6961i	−0.343218	+	1.72548i
$672$	−2.51458	−	82.7676i	−0.0970019	−	3.19283i
$673$	−2.03326	−	10.2219i	−0.0783763	−	0.394024i	−0.999983	−	0.00589832i	$-0.998122\pi$
$673$	−2.03326	−	10.2219i	−0.0783763	−	0.394024i	0.921606	−	0.388126i	$-0.126878\pi$
$674$	8.66957	−	1.64664i	0.333939	−	0.0634262i
$675$	−40.2498	−	57.1504i	−1.54922	−	2.19972i
$676$	−13.6925	+	6.18844i	−0.526633	+	0.238017i
$677$	8.06469	+	2.66421i	0.309951	+	0.102394i	0.464451	−	0.885599i	$-0.346252\pi$
$677$	8.06469	+	2.66421i	0.309951	+	0.102394i	−0.154500	+	0.987993i	$0.549377\pi$
$678$	16.0534	−	40.5680i	0.616527	−	1.55801i
$679$	−33.8165	+	45.5962i	−1.29776	+	1.74982i
$680$	1.41051	+	5.66500i	0.0540907	+	0.217243i
$681$	−15.2546	+	3.82109i	−0.584559	+	0.146424i
$682$	−35.3049	+	2.29732i	−1.35189	+	0.0879689i
$683$	1.11643	−	45.4785i	0.0427192	−	1.74019i	−0.470917	−	0.882177i	$-0.656077\pi$
$683$	1.11643	−	45.4785i	0.0427192	−	1.74019i	0.513636	−	0.858008i	$-0.328298\pi$
$684$	−2.22550	−	14.2895i	−0.0850942	−	0.546375i
$685$	−7.54635	−	3.79852i	−0.288331	−	0.145134i
$686$	13.0854	+	37.5936i	0.499604	+	1.43533i
$687$	2.45534	+	24.9295i	0.0936771	+	0.951120i
$688$	−17.9276	−	8.70097i	−0.683484	−	0.331721i
$689$	−15.6182	−	1.53826i	−0.595008	−	0.0586032i
$690$	−9.20029	−	5.62321i	−0.350249	−	0.214072i
$691$	−4.25230	−	7.50636i	−0.161765	−	0.285555i	0.777410	−	0.628994i	$-0.216533\pi$
$691$	−4.25230	−	7.50636i	−0.161765	−	0.285555i	−0.939175	+	0.343439i	$0.888408\pi$
$692$	0.840239	+	0.248255i	0.0319411	+	0.00943724i
$693$	142.000	−	89.9204i	5.39413	−	3.41579i
$694$	−4.02575	+	17.2288i	−0.152815	+	0.653998i
$695$	4.47278	−	2.11547i	0.169662	−	0.0802442i
$696$	−34.4131	+	19.4307i	−1.30443	+	0.736518i
$697$	20.8420	−	18.8901i	0.789446	−	0.715512i
$698$	−18.8839	+	16.0065i	−0.714765	+	0.605855i
$699$	−76.9642	+	60.0634i	−2.91105	+	2.27181i
$700$	−11.5611	−	40.6299i	−0.436970	−	1.53567i
$701$	−25.0331	−	9.65634i	−0.945488	−	0.364715i	−0.162470	−	0.986714i	$-0.551946\pi$
$701$	−25.0331	−	9.65634i	−0.945488	−	0.364715i	−0.783018	+	0.621999i	$0.786321\pi$
$702$	91.5290	−	26.9025i	3.45454	−	1.01537i
$703$	0.394079	−	0.163233i	0.0148630	−	0.00615645i
$704$	−39.3044	−	3.01088i	−1.48134	−	0.113477i
$705$	−12.4828	−	5.17053i	−0.470128	−	0.194733i
$706$	−27.8845	−	2.99019i	−1.04945	−	0.112537i
$707$	22.4825	−	9.96579i	0.845540	−	0.374802i
$708$	−33.0724	+	2.68045i	−1.24294	+	0.100737i
$709$	−3.90298	−	0.481387i	−0.146579	−	0.0180789i	0.0487867	−	0.998809i	$-0.484465\pi$
$709$	−3.90298	−	0.481387i	−0.146579	−	0.0180789i	−0.195366	+	0.980730i	$0.562590\pi$
$710$	1.13698	+	0.584693i	0.0426702	+	0.0219431i
$711$	1.98662	−	40.4385i	0.0745040	−	1.51656i
$712$	13.4318	−	34.6747i	0.503377	−	1.29949i
$713$	−20.2289	−	7.23803i	−0.757580	−	0.271066i
$714$	−62.6776	−	44.9588i	−2.34565	−	1.68254i
$715$	2.70862	−	12.0620i	0.101297	−	0.451094i
$716$	9.26962	+	11.1298i	0.346422	+	0.415939i
$717$	−2.28831	+	8.26889i	−0.0854585	+	0.308807i
$718$	−23.9918	−	3.77127i	−0.895366	−	0.140742i
$719$	19.9427	−	16.3666i	0.743739	−	0.610370i	−0.184293	−	0.982871i	$-0.559000\pi$
$719$	19.9427	−	16.3666i	0.743739	−	0.610370i	0.928032	+	0.372501i	$0.121500\pi$
$720$	10.5228	+	13.0885i	0.392161	+	0.487778i
$721$	37.6649	−	45.8948i	1.40271	−	1.70921i
$722$	−1.47631	+	25.5402i	−0.0549427	+	0.950509i
$723$	−69.5624	+	22.9803i	−2.58705	+	0.854647i
$724$	27.1777	−	24.9932i	1.01005	−	0.928864i
$725$	−14.6013	+	13.9016i	−0.542280	+	0.516294i
$726$	−26.9913	−	54.7978i	−1.00174	−	2.03374i
$727$	4.82386	−	8.04812i	0.178907	−	0.298488i	−0.755191	−	0.655505i	$-0.772456\pi$
$727$	4.82386	−	8.04812i	0.178907	−	0.298488i	0.934098	+	0.357016i	$0.116206\pi$
$728$	57.5789	+	2.91017i	2.13402	+	0.107858i
$729$	−48.9713	+	7.26421i	−1.81375	+	0.269045i
$730$	−2.24176	−	2.17161i	−0.0829711	−	0.0803750i
$731$	−16.5807	+	8.34605i	−0.613261	+	0.308690i
$732$	48.9365	−	34.9977i	1.80875	−	1.29355i
$733$	1.76869	−	10.1932i	0.0653279	−	0.376494i	−0.934463	−	0.356060i	$-0.884120\pi$
$733$	1.76869	−	10.1932i	0.0653279	−	0.376494i	0.999791	−	0.0204346i	$-0.00650497\pi$
$734$	2.36398	−	1.55014i	0.0872560	−	0.0572169i
$735$	−19.8561	−	13.2674i	−0.732405	−	0.489377i
$736$	−21.1771	−	11.1612i	−0.780596	−	0.411406i
$737$	−51.0161	+	34.0879i	−1.87920	+	1.25564i
$738$	31.6113	−	74.4870i	1.16363	−	2.74190i
$739$	3.09688	+	13.7911i	0.113921	+	0.507312i	0.999114	+	0.0420883i	$0.0134011\pi$
$739$	3.09688	+	13.7911i	0.113921	+	0.507312i	−0.885193	+	0.465224i	$0.845974\pi$
$740$	−0.301910	+	0.392691i	−0.0110984	+	0.0144356i
$741$	14.0162	−	1.03390i	0.514898	−	0.0379811i
$742$	18.5296	+	11.9596i	0.680243	+	0.439050i
$743$	−9.00390	−	15.0221i	−0.330321	−	0.551107i	0.647101	−	0.762404i	$-0.275981\pi$
$743$	−9.00390	−	15.0221i	−0.330321	−	0.551107i	−0.977422	+	0.211297i	$0.932231\pi$
$744$	36.0636	+	29.6820i	1.32216	+	1.08819i
$745$	−2.14968	−	2.89851i	−0.0787582	−	0.106193i
$746$	47.4856	−	12.6998i	1.73857	−	0.464972i
$747$	−26.9227	+	60.7366i	−0.985050	+	2.22224i
$748$	−24.4620	+	27.3855i	−0.894419	+	1.00131i
$749$	29.4354	+	2.17128i	1.07554	+	0.0793369i
$750$	19.7101	+	14.8841i	0.719712	+	0.543489i
$751$	19.5044	+	5.91659i	0.711725	+	0.215900i	0.625329	−	0.780361i	$-0.284965\pi$
$751$	19.5044	+	5.91659i	0.711725	+	0.215900i	0.0863965	+	0.996261i	$0.472465\pi$
$752$	−28.3858	−	9.69531i	−1.03512	−	0.353552i
$753$	7.83806	+	25.8386i	0.285635	+	0.941612i
$754$	−11.5486	−	24.9742i	−0.420575	−	0.909508i
$755$	−0.954023	−	7.73501i	−0.0347204	−	0.281506i
$756$	−131.673	−	25.2018i	−4.78891	−	0.916582i
$757$	−3.55651	+	5.04986i	−0.129264	+	0.183540i	−0.877050	−	0.480399i	$-0.840492\pi$
$757$	−3.55651	+	5.04986i	−0.129264	+	0.183540i	0.747786	+	0.663940i	$0.231117\pi$
$758$	−6.30182	+	13.8910i	−0.228892	+	0.504545i
$759$	−3.32784	−	67.7397i	−0.120793	−	2.45880i
$760$	0.670185	+	1.33612i	0.0243102	+	0.0484662i
$761$	−26.6800	−	12.6187i	−0.967148	−	0.457427i	−0.122335	−	0.992489i	$-0.539038\pi$
$761$	−26.6800	−	12.6187i	−0.967148	−	0.457427i	−0.844813	+	0.535062i	$0.820288\pi$
$762$	46.9038	+	37.2615i	1.69915	+	1.34984i
$763$	−22.2185	+	6.14869i	−0.804365	+	0.222598i
$764$	−27.6651	+	17.8006i	−1.00089	+	0.644005i
$765$	15.6391	−	0.383919i	0.565433	−	0.0138806i
$766$	−23.0638	−	19.2643i	−0.833328	−	0.696047i
$767$		−	23.1017i		−	0.834155i
$768$	35.1187	+	38.4053i	1.26724	+	1.38583i
$769$			12.3297i			0.444622i	0.974976	+	0.222311i	$0.0713600\pi$
$769$			12.3297i			0.444622i	−0.974976	+	0.222311i	$0.928640\pi$
$770$	−11.1367	+	13.3332i	−0.401340	+	0.480496i
$771$	30.6713	−	0.752939i	1.10460	−	0.0271164i
$772$	−7.65854	−	1.66163i	−0.275637	−	0.0598035i
$773$	−26.6957	+	7.38768i	−0.960176	+	0.265716i	−0.711355	−	0.702833i	$-0.751918\pi$
$773$	−26.6957	+	7.38768i	−0.960176	+	0.265716i	−0.248821	+	0.968549i	$0.580043\pi$
$774$	−33.2159	+	41.8113i	−1.19392	+	1.50288i
$775$	21.5399	+	10.1876i	0.773734	+	0.365949i
$776$	−2.57432	−	35.5840i	−0.0924129	−	1.27739i
$777$	−0.321131	−	6.53678i	−0.0115205	−	0.234506i
$778$	26.9390	+	12.2212i	0.965809	+	0.438151i
$779$	4.14709	−	5.88841i	0.148585	−	0.210974i
$780$	−13.5041	+	9.16529i	−0.483526	+	0.328170i
$781$	0.984386	+	7.98119i	0.0352241	+	0.285590i
$782$	−20.2396	+	9.35923i	−0.723768	+	0.334685i
$783$	18.5733	+	61.2279i	0.663755	+	2.18811i
$784$	−45.8640	−	26.5949i	−1.63800	−	0.949816i
$785$	6.62938	+	2.01100i	0.236613	+	0.0717757i
$786$	−6.44237	+	8.53126i	−0.229792	+	0.304300i
$787$	21.3160	+	1.57236i	0.759832	+	0.0560486i	0.447934	−	0.894067i	$-0.352160\pi$
$787$	21.3160	+	1.57236i	0.759832	+	0.0560486i	0.311899	+	0.950115i	$0.399035\pi$
$788$	−7.37726	+	0.415982i	−0.262804	+	0.0148187i
$789$	−30.1490	+	68.0150i	−1.07333	+	2.42140i
$790$	1.08120	+	4.04271i	0.0384674	+	0.143833i
$791$	−25.4282	−	34.2860i	−0.904124	−	1.21907i
$792$	−30.8059	+	101.040i	−1.09464	+	3.59029i
$793$	21.5347	+	35.9285i	0.764719	+	1.27586i
$794$	0.793522	−	1.22944i	0.0281610	−	0.0436314i
$795$	−6.22629	+	0.459279i	−0.220824	+	0.0162889i
$796$	−3.36623	−	25.7563i	−0.119313	−	0.912909i
$797$	−7.67257	−	34.1675i	−0.271776	−	1.21028i	−0.901266	−	0.433266i	$-0.857361\pi$
$797$	−7.67257	−	34.1675i	−0.271776	−	1.21028i	0.629490	−	0.777009i	$-0.283264\pi$
$798$	−18.1805	−	7.71557i	−0.643584	−	0.273128i
$799$	−23.2326	+	15.5235i	−0.821911	+	0.549183i
$800$	22.1598	+	14.6206i	0.783468	+	0.516917i
$801$	−82.8512	−	55.3594i	−2.92740	−	1.95603i
$802$	−10.7743	−	16.4308i	−0.380453	−	0.580193i
$803$	3.35622	−	19.3424i	0.118438	−	0.682577i
$804$	79.9078	+	13.2701i	2.81813	+	0.468000i
$805$	−9.42328	+	4.74328i	−0.332127	+	0.167179i
$806$	−22.6265	+	23.3573i	−0.796984	+	0.822727i
$807$	81.3367	−	12.0652i	2.86319	−	0.424714i
$808$	−6.62783	+	13.9623i	−0.233166	+	0.491193i
$809$	−7.49882	+	12.5110i	−0.263644	+	0.439864i	−0.960875	−	0.276983i	$-0.910665\pi$
$809$	−7.49882	+	12.5110i	−0.263644	+	0.439864i	0.697230	+	0.716847i	$0.254415\pi$
$810$	18.0663	−	8.89876i	0.634786	−	0.312671i
$811$	24.4120	−	23.2422i	0.857222	−	0.816144i	−0.127216	−	0.991875i	$-0.540604\pi$
$811$	24.4120	−	23.2422i	0.857222	−	0.816144i	0.984438	+	0.175732i	$0.0562291\pi$
$812$	−1.61760	+	38.6322i	−0.0567667	+	1.35573i
$813$	54.2257	−	17.9138i	1.90178	−	0.628263i
$814$	−3.11039	−	0.179791i	−0.109019	−	0.00630168i
$815$	−1.12985	+	1.37672i	−0.0395768	+	0.0482245i
$816$	48.2892	−	4.26585i	1.69046	−	0.149335i
$817$	−3.67405	+	3.01521i	−0.128539	+	0.105489i
$818$	8.17443	−	52.0036i	0.285812	−	1.81826i
$819$	41.2043	−	148.893i	1.43980	−	5.20275i
$820$	−0.759498	+	8.32908i	−0.0265228	+	0.290864i
$821$	−9.93325	+	44.2348i	−0.346673	+	1.54380i	0.423456	+	0.905917i	$0.360817\pi$
$821$	−9.93325	+	44.2348i	−0.346673	+	1.54380i	−0.770129	+	0.637888i	$0.779808\pi$
$822$	−40.8900	+	57.0053i	−1.42620	+	1.98829i
$823$	−32.2915	−	11.5541i	−1.12561	−	0.402750i	−0.292726	−	0.956196i	$-0.594562\pi$
$823$	−32.2915	−	11.5541i	−1.12561	−	0.402750i	−0.832885	+	0.553447i	$0.813312\pi$
$824$	0.863051	+	37.3034i	0.0300658	+	1.29953i
$825$	−3.69070	+	75.1260i	−0.128494	+	2.61555i
$826$	−14.8465	+	28.8703i	−0.516577	+	1.00453i
$827$	−6.32522	−	0.780141i	−0.219949	−	0.0271282i	0.0116822	−	0.999932i	$-0.496281\pi$
$827$	−6.32522	−	0.780141i	−0.219949	−	0.0271282i	−0.231631	+	0.972804i	$0.574406\pi$
$828$	−41.5461	+	48.8745i	−1.44383	+	1.69850i
$829$	−33.8946	+	15.0245i	−1.17721	+	0.521821i	−0.898679	−	0.438606i	$-0.855472\pi$
$829$	−33.8946	+	15.0245i	−1.17721	+	0.521821i	−0.278530	+	0.960427i	$0.589847\pi$
$830$	0.732171	−	6.82774i	0.0254140	−	0.236994i
$831$	52.6248	+	21.7979i	1.82553	+	0.756160i
$832$	−28.6270	+	22.2110i	−0.992463	+	0.770026i
$833$	−45.6268	+	18.8992i	−1.58088	+	0.654820i
$834$	−11.5859	−	39.4182i	−0.401188	−	1.36494i
$835$	−8.92687	−	3.44347i	−0.308927	−	0.119166i
$836$	−4.57486	+	8.21386i	−0.158225	+	0.284082i
$837$	59.6149	−	46.5239i	2.06059	−	1.60810i
$838$	−17.4341	−	20.5681i	−0.602249	−	0.710512i
$839$	39.6170	−	35.9067i	1.36773	−	1.23964i	0.425377	−	0.905016i	$-0.360142\pi$
$839$	39.6170	−	35.9067i	1.36773	−	1.23964i	0.942353	−	0.334622i	$-0.108608\pi$
$840$	22.7664	−	2.77534i	0.785514	−	0.0957582i
$841$	−9.53371	+	4.50911i	−0.328749	+	0.155487i
$842$	−12.2299	−	2.85769i	−0.421472	−	0.0984826i
$843$	69.7703	−	44.1816i	2.40302	−	1.52169i
$844$	11.6640	−	6.34351i	0.401490	−	0.218353i
$845$	−2.05133	−	3.62111i	−0.0705680	−	0.124570i
$846$	−41.9180	+	68.5834i	−1.44117	+	2.35794i
$847$	−59.4773	−	5.85800i	−2.04366	−	0.201283i
$848$	−13.7301	+	1.89566i	−0.471494	+	0.0650972i
$849$	−5.25709	−	53.3761i	−0.180423	−	1.83186i
$850$	23.3559	−	8.12962i	0.801100	−	0.278844i
$851$	−1.68997	−	0.850660i	−0.0579315	−	0.0291603i
$852$	6.26235	−	8.57283i	0.214544	−	0.293700i
$853$	1.14075	−	46.4692i	0.0390587	−	1.59107i	−0.585878	−	0.810399i	$-0.699250\pi$
$853$	1.14075	−	46.4692i	0.0390587	−	1.59107i	0.624937	−	0.780676i	$-0.285125\pi$
$854$	−3.82222	−	58.7394i	−0.130794	−	2.01002i
$855$	3.88548	−	0.973262i	0.132881	−	0.0332849i
$856$	−14.9148	+	11.0289i	−0.509776	+	0.376961i
$857$	8.54763	−	11.5251i	0.291981	−	0.393691i	−0.632722	−	0.774379i	$-0.718063\pi$
$857$	8.54763	−	11.5251i	0.291981	−	0.393691i	0.924704	+	0.380687i	$0.124313\pi$
$858$	−95.4529	−	37.7722i	−3.25871	−	1.28952i
$859$	−14.2620	−	4.71154i	−0.486614	−	0.160756i	0.0599018	−	0.998204i	$-0.480921\pi$
$859$	−14.2620	−	4.71154i	−0.486614	−	0.160756i	−0.546516	+	0.837449i	$0.684046\pi$
$860$	1.94906	−	5.16378i	0.0664624	−	0.176083i
$861$	−63.6301	−	90.3477i	−2.16851	−	3.07904i
$862$	1.30032	+	6.84618i	0.0442890	+	0.233182i
$863$	−7.02058	−	35.2948i	−0.238983	−	1.20145i	−0.894778	−	0.446511i	$-0.852667\pi$
$863$	−7.02058	−	35.2948i	−0.238983	−	1.20145i	0.655795	−	0.754939i	$-0.272333\pi$
$864$	73.0662	−	41.9558i	2.48576	−	1.42737i
$865$	−0.0473422	+	0.238005i	−0.00160968	+	0.00809243i
$866$	−47.2349	−	0.408680i	−1.60511	−	0.0138875i
$867$	−5.42301	+	8.56387i	−0.184175	+	0.290844i
$868$	43.2872	−	14.6486i	1.46926	−	0.497206i
$869$	−17.1926	+	19.9310i	−0.583220	+	0.676114i
$870$	−6.22507	−	9.00339i	−0.211050	−	0.305243i
$871$	−13.7033	+	54.7065i	−0.464318	+	1.85366i
$872$	8.06643	−	12.0354i	0.273164	−	0.407572i
$873$	−94.5678	−	14.0278i	−3.20064	−	0.474769i
$874$	−4.53129	+	3.47359i	−0.153273	+	0.117496i
$875$	22.5459	−	8.69691i	0.762190	−	0.294009i
$876$	−20.7045	+	15.5891i	−0.699540	+	0.526707i
$877$	−33.9159	+	29.2561i	−1.14526	+	0.987908i	−0.999999	−	0.00148573i	$-0.999527\pi$
$877$	−33.9159	+	29.2561i	−1.14526	+	0.987908i	−0.145261	+	0.989393i	$0.546402\pi$
$878$	−49.3310	+	28.9907i	−1.66484	+	0.978389i
$879$	4.37279	+	8.18092i	0.147491	+	0.275936i
$880$	−0.158089	−	10.9170i	−0.00532918	−	0.368011i
$881$	43.1198	+	23.0480i	1.45274	+	0.776506i	0.993718	−	0.111917i	$-0.0356992\pi$
$881$	43.1198	+	23.0480i	1.45274	+	0.776506i	0.459024	+	0.888424i	$0.348199\pi$
$882$	−96.3142	+	104.436i	−3.24307	+	3.51654i
$883$	10.7526	−	13.7782i	0.361853	−	0.463672i	−0.572560	−	0.819863i	$-0.694050\pi$
$883$	10.7526	−	13.7782i	0.361853	−	0.463672i	0.934413	+	0.356191i	$0.115925\pi$
$884$	0.244359	+	33.7507i	0.00821870	+	1.13516i
$885$	−1.57117	−	9.05487i	−0.0528143	−	0.304376i
$886$	16.2701	−	15.2243i	0.546605	−	0.511469i
$887$	−25.2599	+	27.8701i	−0.848146	+	0.935785i	−0.998603	−	0.0528317i	$-0.983175\pi$
$887$	−25.2599	+	27.8701i	−0.848146	+	0.935785i	0.150458	+	0.988616i	$0.451925\pi$
$888$	2.83197	+	2.98294i	0.0950348	+	0.100101i
$889$	55.1830	−	19.7448i	1.85078	−	0.662219i
$890$	9.90207	+	2.83273i	0.331918	+	0.0949532i
$891$	110.215	+	62.4362i	3.69235	+	2.09169i
$892$	−22.2473	−	9.66945i	−0.744895	−	0.323757i
$893$	−4.93319	+	5.18149i	−0.165083	+	0.173392i
$894$	−26.5485	+	13.8965i	−0.887916	+	0.464769i
$895$	−2.83675	+	2.83675i	−0.0948222	+	0.0948222i
$896$	50.0494	−	9.35970i	1.67203	−	0.312686i
$897$	−44.0803	−	44.0803i	−1.47180	−	1.47180i
$898$	3.84226	+	1.20193i	0.128218	+	0.0401091i
$899$	−15.7959	−	15.0389i	−0.526823	−	0.501577i
$900$	51.1672	−	49.4264i	1.70557	−	1.64755i
$901$	−6.36387	+	11.2338i	−0.212011	+	0.374252i
$902$	−45.9945	+	25.5325i	−1.53145	+	0.850138i
$903$	24.5678	+	68.6625i	0.817566	+	2.28494i
$904$	26.1671	+	5.91483i	0.870304	+	0.196724i
$905$	7.57738	+	6.86774i	0.251881	+	0.228291i
$906$	−64.6809	−	2.14791i	−2.14888	−	0.0713594i
$907$	−46.1726	+	8.01170i	−1.53314	+	0.266024i	−0.873972	−	0.485976i	$-0.838464\pi$
$907$	−46.1726	+	8.01170i	−1.53314	+	0.266024i	−0.659163	+	0.752000i	$0.729089\pi$
$908$	−3.76507	−	8.90673i	−0.124948	−	0.295580i
$909$	32.6501	+	25.4804i	1.08293	+	0.845130i
$910$	0.645503	+	15.9551i	0.0213982	+	0.528905i
$911$	19.7643	−	36.9765i	0.654822	−	1.22509i	−0.307078	−	0.951684i	$-0.599351\pi$
$911$	19.7643	−	36.9765i	0.654822	−	1.22509i	0.961900	−	0.273401i	$-0.0881487\pi$
$912$	11.8245	−	3.77472i	0.391547	−	0.124994i
$913$	38.0917	−	20.3604i	1.26065	−	0.673832i
$914$	46.1170	+	11.9767i	1.52541	+	0.396153i
$915$	10.8842	+	12.6178i	0.359820	+	0.417132i
$916$	−14.9141	+	3.85076i	−0.492777	+	0.127233i
$917$	3.76434	+	9.75868i	0.124309	+	0.322260i
$918$	10.2810	−	77.8089i	0.339323	−	2.56808i
$919$	3.74333	−	25.2355i	0.123481	−	0.832442i	−0.835606	−	0.549330i	$-0.814883\pi$
$919$	3.74333	−	25.2355i	0.123481	−	0.832442i	0.959087	−	0.283112i	$-0.0913669\pi$
$920$	2.54592	−	6.12194i	0.0839366	−	0.201835i
$921$	−45.5283	−	11.4042i	−1.50021	−	0.375783i
$922$	7.23282	−	39.6444i	0.238200	−	1.30562i
$923$	5.59699	+	4.82800i	0.184227	+	0.158915i
$924$	95.0132	+	108.548i	3.12571	+	3.57096i
$925$	1.77275	+	1.12258i	0.0582876	+	0.0369102i
$926$	−12.8112	+	12.5914i	−0.421003	+	0.413781i
$927$	98.0665	+	19.5066i	3.22093	+	0.640682i
$928$	−15.0619	−	19.0698i	−0.494431	−	0.625998i
$929$	28.0582	−	5.58113i	0.920560	−	0.183111i	0.288008	−	0.957628i	$-0.407007\pi$
$929$	28.0582	−	5.58113i	0.920560	−	0.183111i	0.632553	+	0.774517i	$0.282007\pi$
$930$	−7.28005	+	10.6939i	−0.238722	+	0.350667i
$931$	−10.3384	+	7.28113i	−0.338828	+	0.238629i
$932$	−43.7757	−	41.0778i	−1.43392	−	1.34555i
$933$	−9.85172	+	29.8216i	−0.322531	+	0.976315i
$934$	32.8913	−	14.2405i	1.07624	−	0.465964i
$935$	−8.16895	−	6.05850i	−0.267153	−	0.198134i
$936$	41.3885	+	87.8292i	1.35282	+	2.87079i
$937$	13.7096	+	54.7318i	0.447873	+	1.78801i	0.600387	+	0.799709i	$0.295013\pi$
$937$	13.7096	+	54.7318i	0.447873	+	1.78801i	−0.152514	+	0.988301i	$0.548737\pi$
$938$	52.2827	−	59.5604i	1.70709	−	1.94472i
$939$	86.1968	+	2.11601i	2.81292	+	0.0690534i
$940$	1.96029	−	8.07345i	0.0639375	−	0.263327i
$941$	−14.7294	+	29.2623i	−0.480166	+	0.953925i	0.515137	+	0.857108i	$0.327741\pi$
$941$	−14.7294	+	29.2623i	−0.480166	+	0.953925i	−0.995302	+	0.0968171i	$0.969134\pi$
$942$	25.0445	−	51.7882i	0.815995	−	1.68735i
$943$	−31.7922	+	3.13125i	−1.03530	+	0.101968i
$944$	−4.75805	−	19.8402i	−0.154861	−	0.645745i
$945$	3.63956	−	36.9530i	0.118395	−	1.20208i
$946$	33.7474	−	8.14364i	1.09722	−	0.264773i
$947$	−32.1577	+	18.2171i	−1.04498	+	0.591976i	−0.916623	−	0.399752i	$-0.869096\pi$
$947$	−32.1577	+	18.2171i	−1.04498	+	0.591976i	−0.128360	+	0.991728i	$0.540971\pi$
$948$	34.5567	−	3.65634i	1.12235	−	0.118752i
$949$	−9.65373	−	15.2449i	−0.313373	−	0.494871i
$950$	5.37878	−	3.34123i	0.174511	−	0.108404i
$951$	−12.7109	−	26.8750i	−0.412180	−	0.871481i
$952$	21.3849	−	42.3355i	0.693087	−	1.37210i
$953$	−36.3407	−	40.0958i	−1.17719	−	1.29883i	−0.945343	−	0.326077i	$-0.894273\pi$
$953$	−36.3407	−	40.0958i	−1.17719	−	1.29883i	−0.231847	−	0.972752i	$-0.574477\pi$
$954$	−3.05264	+	37.0155i	−0.0988328	+	1.19842i
$955$	−5.60574	−	7.18309i	−0.181397	−	0.232439i
$956$	−5.24048	−	0.607867i	−0.169489	−	0.0196598i
$957$	24.7781	−	64.2347i	0.800961	−	2.07641i
$958$	1.91211	+	1.04341i	0.0617775	+	0.0337112i
$959$	26.2668	+	63.4138i	0.848201	+	2.04774i
$960$	−9.70995	+	10.6527i	−0.313387	+	0.343814i
$961$	1.99879	−	4.82551i	0.0644771	−	0.155661i
$962$	−2.22932	+	1.79751i	−0.0718763	+	0.0579540i
$963$	20.1433	+	45.4425i	0.649108	+	1.46436i
$964$	−20.5446	−	40.0897i	−0.661696	−	1.29120i
$965$	0.265699	−	2.15423i	0.00855316	−	0.0693472i
$966$	26.7587	+	83.4159i	0.860947	+	2.68386i
$967$	22.2310	+	1.09214i	0.714902	+	0.0351209i	0.403269	−	0.915082i	$-0.367874\pi$
$967$	22.2310	+	1.09214i	0.714902	+	0.0351209i	0.311633	+	0.950203i	$0.399124\pi$
$968$	30.7396	−	21.5844i	0.988008	−	0.693749i
$969$	3.89522	−	10.8864i	0.125132	−	0.349722i
$970$	9.75031	−	1.60507i	0.313063	−	0.0515356i
$971$	19.6491	+	4.41236i	0.630571	+	0.141599i	0.522632	−	0.852558i	$-0.324950\pi$
$971$	19.6491	+	4.41236i	0.630571	+	0.141599i	0.107938	+	0.994158i	$0.465575\pi$
$972$	−23.1416	−	74.3455i	−0.742266	−	2.38463i
$973$	−38.7420	−	10.7213i	−1.24201	−	0.343711i
$974$	−3.87174	−	5.31594i	−0.124058	−	0.170334i
$975$	43.8596	+	53.4431i	1.40463	+	1.71155i
$976$	25.8943	+	26.4208i	0.828857	+	0.845709i
$977$	−15.4500	−	12.6795i	−0.494290	−	0.405654i	0.353951	−	0.935264i	$-0.384838\pi$
$977$	−15.4500	−	12.6795i	−0.494290	−	0.405654i	−0.848241	+	0.529611i	$0.822338\pi$
$978$	9.83648	+	11.0434i	0.314536	+	0.353129i
$979$	20.3206	+	61.5114i	0.649450	+	1.96591i
$980$	6.18204	−	13.3195i	0.197478	−	0.425475i
$981$	−26.7712	−	28.1186i	−0.854738	−	0.897759i
$982$	−1.99857	+	5.87851i	−0.0637770	+	0.187591i
$983$	−11.5535	−	6.92490i	−0.368499	−	0.220870i	0.317852	−	0.948140i	$-0.397039\pi$
$983$	−11.5535	−	6.92490i	−0.368499	−	0.220870i	−0.686351	+	0.727270i	$0.740789\pi$
$984$	67.3447	+	16.9700i	2.14687	+	0.540985i
$985$	−0.300290	−	2.02439i	−0.00956804	−	0.0645025i
$986$	−22.6335	+	0.359719i	−0.720799	+	0.0114558i
$987$	49.3542	+	98.0500i	1.57096	+	3.12097i
$988$	1.95445	+	8.41802i	0.0621795	+	0.267813i
$989$	20.7716	+	3.60421i	0.660497	+	0.114607i
$990$	−28.6444	−	5.95580i	−0.910378	−	0.189288i
$991$	15.1236	−	22.6340i	0.480417	−	0.718994i	−0.509527	−	0.860454i	$-0.670180\pi$
$991$	15.1236	−	22.6340i	0.480417	−	0.718994i	0.989944	+	0.141460i	$0.0451797\pi$
$992$	−14.6214	+	24.7199i	−0.464230	+	0.784859i
$993$	49.0117	+	73.3512i	1.55534	+	2.32773i
$994$	−3.89182	−	9.63052i	−0.123441	−	0.305462i
$995$	7.01965	−	1.57631i	0.222538	−	0.0499725i
$996$	−55.0643	−	14.8100i	−1.74478	−	0.469273i
$997$	0.849870	+	11.5214i	0.0269156	+	0.364887i	0.993918	+	0.110120i	$0.0351236\pi$
$997$	0.849870	+	11.5214i	0.0269156	+	0.364887i	−0.967003	+	0.254766i	$0.918001\pi$
$998$	−4.60251	−	21.3587i	−0.145690	−	0.676097i
$999$	5.71181	−	3.42353i	0.180714	−	0.108316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.o.a.117.33	✓	4032
512.477	even	128	inner	512.2.o.a.477.33	yes	4032

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.o.a.117.33	✓	4032	1.1	even	1	trivial
512.2.o.a.477.33	yes	4032	512.477	even	128	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.o (of order \(128\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(0.126435 + 1.40855i) q^{2} +(0.0798222 + 3.25160i) q^{3} +(-1.96803 + 0.356182i) q^{4} +(-0.147744 - 0.533878i) q^{5} +(-4.56995 + 0.523551i) q^{6} +(-1.92420 + 4.06838i) q^{7} +(-0.750528 - 2.72703i) q^{8} +(-7.57013 + 0.371896i) q^{9} +O(q^{10})\)	\(q+(0.126435 + 1.40855i) q^{2} +(0.0798222 + 3.25160i) q^{3} +(-1.96803 + 0.356182i) q^{4} +(-0.147744 - 0.533878i) q^{5} +(-4.56995 + 0.523551i) q^{6} +(-1.92420 + 4.06838i) q^{7} +(-0.750528 - 2.72703i) q^{8} +(-7.57013 + 0.371896i) q^{9} +(0.733315 - 0.275606i) q^{10} +(4.02861 + 2.83726i) q^{11} +(-1.31525 - 6.37080i) q^{12} +(4.49507 - 0.554413i) q^{13} +(-5.97380 - 2.19594i) q^{14} +(1.72416 - 0.523020i) q^{15} +(3.74627 - 1.40195i) q^{16} +(1.08162 - 3.56562i) q^{17} +(-1.48097 - 10.6159i) q^{18} +(0.0701835 - 0.951454i) q^{19} +(0.480922 + 0.998064i) q^{20} +(-13.3823 - 5.93197i) q^{21} +(-3.48707 + 6.03322i) q^{22} +(-3.39895 + 2.52083i) q^{23} +(8.80730 - 2.65809i) q^{24} +(4.02545 - 2.41276i) q^{25} +(1.34926 + 6.26143i) q^{26} +(-1.09570 - 14.8540i) q^{27} +(2.33780 - 8.69204i) q^{28} +(-4.19140 + 0.941211i) q^{29} +(0.954695 + 2.36244i) q^{30} +(2.82068 + 4.22145i) q^{31} +(2.44838 + 5.09955i) q^{32} +(-8.90407 + 13.3259i) q^{33} +(5.15911 + 1.07269i) q^{34} +(2.45631 + 0.426210i) q^{35} +(14.7658 - 3.42824i) q^{36} +(0.201020 + 0.399358i) q^{37} +(1.34904 - 0.0214406i) q^{38} +(2.16154 + 14.5719i) q^{39} +(-1.34502 + 0.803594i) q^{40} +(6.47514 + 3.88105i) q^{41} +(6.66348 - 19.5997i) q^{42} +(-3.43521 - 3.60811i) q^{43} +(-8.93899 - 4.14890i) q^{44} +(1.31699 + 3.98658i) q^{45} +(-3.98047 - 4.46887i) q^{46} +(-5.79678 - 4.75730i) q^{47} +(4.85761 + 12.0695i) q^{48} +(-8.40840 - 10.2457i) q^{49} +(3.90745 + 5.36498i) q^{50} +(11.6803 + 3.23237i) q^{51} +(-8.64894 + 2.69216i) q^{52} +(-3.38089 - 0.759205i) q^{53} +(20.7841 - 3.42142i) q^{54} +(0.919552 - 2.56997i) q^{55} +(12.5388 + 2.19392i) q^{56} +(3.09935 + 0.152261i) q^{57} +(-1.85568 - 5.78480i) q^{58} +(0.624380 - 5.06234i) q^{59} +(-3.20691 + 1.64343i) q^{60} +(3.74790 + 8.45512i) q^{61} +(-5.58949 + 4.50682i) q^{62} +(13.0534 - 31.5137i) q^{63} +(-6.87341 + 4.09343i) q^{64} +(-0.960109 - 2.31791i) q^{65} +(-19.8960 - 10.8570i) q^{66} +(-4.48141 + 11.6176i) q^{67} +(-0.858649 + 7.40249i) q^{68} +(-8.46805 - 10.8508i) q^{69} +(-0.289774 + 3.51372i) q^{70} +(1.09599 + 1.20924i) q^{71} +(6.69577 + 20.3649i) q^{72} +(-1.70342 - 3.60157i) q^{73} +(-0.537100 + 0.333640i) q^{74} +(8.16664 + 12.8965i) q^{75} +(0.200767 + 1.89749i) q^{76} +(-19.2949 + 10.9304i) q^{77} +(-20.2519 + 4.88704i) q^{78} +(-0.523594 + 5.31613i) q^{79} +(-1.30196 - 1.79292i) q^{80} +(25.5836 - 2.51976i) q^{81} +(-4.64796 + 9.61126i) q^{82} +(3.94108 - 7.82959i) q^{83} +(28.4496 + 6.90776i) q^{84} +(-2.06341 - 0.0506539i) q^{85} +(4.64788 - 5.29486i) q^{86} +(-3.39501 - 13.5536i) q^{87} +(4.71373 - 13.1156i) q^{88} +(10.5598 + 7.83164i) q^{89} +(-5.44879 + 2.35909i) q^{90} +(-6.39384 + 19.3544i) q^{91} +(5.79136 - 6.17172i) q^{92} +(-13.5013 + 9.50869i) q^{93} +(5.96797 - 8.76655i) q^{94} +(-0.518330 + 0.103102i) q^{95} +(-16.3863 + 8.36820i) q^{96} +(12.3713 + 2.46081i) q^{97} +(13.3684 - 13.1391i) q^{98} +(-31.5522 - 19.9802i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Introduction

L-functions

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