LMFDB - Embedded newform 560.2.bd.b.141.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(141,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("560.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bd (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			141.11
Character	$\chi$	$=$	560.141
Dual form			560.2.bd.b.421.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.488835 - 1.32704i) q^{2} +(-1.83016 - 1.83016i) q^{3} +(-1.52208 + 1.29741i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.53405 + 3.32334i) q^{6} +1.00000i q^{7} +(2.46576 + 1.38565i) q^{8} +3.69896i q^{9} +O(q^{10})$	\(q+(-0.488835 - 1.32704i) q^{2} +(-1.83016 - 1.83016i) q^{3} +(-1.52208 + 1.29741i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.53405 + 3.32334i) q^{6} +1.00000i q^{7} +(2.46576 + 1.38565i) q^{8} +3.69896i q^{9} +(-1.28402 - 0.592702i) q^{10} +(-2.90936 + 2.90936i) q^{11} +(5.16011 + 0.411185i) q^{12} +(2.88170 + 2.88170i) q^{13} +(1.32704 - 0.488835i) q^{14} -2.58823 q^{15} +(0.633460 - 3.94952i) q^{16} +3.54579 q^{17} +(4.90867 - 1.80818i) q^{18} +(2.31299 + 2.31299i) q^{19} +(-0.158867 + 1.99368i) q^{20} +(1.83016 - 1.83016i) q^{21} +(5.28305 + 2.43865i) q^{22} +8.50997i q^{23} +(-1.97678 - 7.04869i) q^{24} -1.00000i q^{25} +(2.41546 - 5.23282i) q^{26} +(1.27920 - 1.27920i) q^{27} +(-1.29741 - 1.52208i) q^{28} +(-5.35406 - 5.35406i) q^{29} +(1.26522 + 3.43470i) q^{30} -6.54983 q^{31} +(-5.55084 + 1.09004i) q^{32} +10.6492 q^{33} +(-1.73330 - 4.70541i) q^{34} +(0.707107 + 0.707107i) q^{35} +(-4.79906 - 5.63011i) q^{36} +(6.77129 - 6.77129i) q^{37} +(1.93877 - 4.20011i) q^{38} -10.5479i q^{39} +(2.72336 - 0.763757i) q^{40} +11.2475i q^{41} +(-3.32334 - 1.53405i) q^{42} +(6.72342 - 6.72342i) q^{43} +(0.653652 - 8.20292i) q^{44} +(2.61556 + 2.61556i) q^{45} +(11.2931 - 4.15997i) q^{46} +5.30845 q^{47} +(-8.38758 + 6.06892i) q^{48} -1.00000 q^{49} +(-1.32704 + 0.488835i) q^{50} +(-6.48935 - 6.48935i) q^{51} +(-8.12493 - 0.647438i) q^{52} +(-4.26312 + 4.26312i) q^{53} +(-2.32287 - 1.07223i) q^{54} +4.11446i q^{55} +(-1.38565 + 2.46576i) q^{56} -8.46629i q^{57} +(-4.48781 + 9.72232i) q^{58} +(4.91504 - 4.91504i) q^{59} +(3.93950 - 3.35800i) q^{60} +(1.49244 + 1.49244i) q^{61} +(3.20179 + 8.69190i) q^{62} -3.69896 q^{63} +(4.15997 + 6.83335i) q^{64} +4.07534 q^{65} +(-5.20570 - 14.1319i) q^{66} +(-2.60202 - 2.60202i) q^{67} +(-5.39697 + 4.60033i) q^{68} +(15.5746 - 15.5746i) q^{69} +(0.592702 - 1.28402i) q^{70} +9.99630i q^{71} +(-5.12544 + 9.12075i) q^{72} +7.68603i q^{73} +(-12.2958 - 5.67575i) q^{74} +(-1.83016 + 1.83016i) q^{75} +(-6.52146 - 0.519665i) q^{76} +(-2.90936 - 2.90936i) q^{77} +(-13.9976 + 5.15620i) q^{78} -0.246529 q^{79} +(-2.34481 - 3.24066i) q^{80} +6.41459 q^{81} +(14.9259 - 5.49817i) q^{82} +(-3.31650 - 3.31650i) q^{83} +(-0.411185 + 5.16011i) q^{84} +(2.50725 - 2.50725i) q^{85} +(-12.2089 - 5.63562i) q^{86} +19.5976i q^{87} +(-11.2051 + 3.14245i) q^{88} +7.92581i q^{89} +(2.19238 - 4.74953i) q^{90} +(-2.88170 + 2.88170i) q^{91} +(-11.0409 - 12.9529i) q^{92} +(11.9872 + 11.9872i) q^{93} +(-2.59496 - 7.04454i) q^{94} +3.27107 q^{95} +(12.1539 + 8.16397i) q^{96} +9.27782 q^{97} +(0.488835 + 1.32704i) q^{98} +(-10.7616 - 10.7616i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 8 q^{4} + 12 q^{6}+O(q^{10}) $ 52 * q - 8 * q^4 + 12 * q^6	$ 52 q - 8 q^{4} + 12 q^{6} - 4 q^{10} - 4 q^{11} + 40 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{19} + 32 q^{22} + 12 q^{24} - 12 q^{26} - 24 q^{27} + 4 q^{28} + 4 q^{29} - 16 q^{34} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 4 q^{42} + 36 q^{43} + 28 q^{44} - 16 q^{46} + 32 q^{48} - 52 q^{49} - 8 q^{51} - 80 q^{52} - 4 q^{53} + 48 q^{54} - 12 q^{56} - 56 q^{58} + 24 q^{59} - 16 q^{61} - 72 q^{62} - 68 q^{63} + 4 q^{64} + 40 q^{65} - 12 q^{66} - 12 q^{67} - 72 q^{69} - 8 q^{72} + 68 q^{74} - 4 q^{77} - 4 q^{78} - 16 q^{79} - 32 q^{80} - 116 q^{81} + 104 q^{82} + 16 q^{85} - 68 q^{86} - 48 q^{88} + 36 q^{90} + 64 q^{92} + 8 q^{93} - 72 q^{94} - 32 q^{95} - 52 q^{99}+O(q^{100}) $ 52 * q - 8 * q^4 + 12 * q^6 - 4 * q^10 - 4 * q^11 + 40 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^19 + 32 * q^22 + 12 * q^24 - 12 * q^26 - 24 * q^27 + 4 * q^28 + 4 * q^29 - 16 * q^34 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 4 * q^42 + 36 * q^43 + 28 * q^44 - 16 * q^46 + 32 * q^48 - 52 * q^49 - 8 * q^51 - 80 * q^52 - 4 * q^53 + 48 * q^54 - 12 * q^56 - 56 * q^58 + 24 * q^59 - 16 * q^61 - 72 * q^62 - 68 * q^63 + 4 * q^64 + 40 * q^65 - 12 * q^66 - 12 * q^67 - 72 * q^69 - 8 * q^72 + 68 * q^74 - 4 * q^77 - 4 * q^78 - 16 * q^79 - 32 * q^80 - 116 * q^81 + 104 * q^82 + 16 * q^85 - 68 * q^86 - 48 * q^88 + 36 * q^90 + 64 * q^92 + 8 * q^93 - 72 * q^94 - 32 * q^95 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.488835	−	1.32704i	−0.345658	−	0.938360i
$2$	−0.488835	−	1.32704i	−0.345658	−	0.938360i
$3$	−1.83016	−	1.83016i	−1.05664	−	1.05664i	−0.998296	−	0.0583457i	$-0.981417\pi$
$3$	−1.83016	−	1.83016i	−1.05664	−	1.05664i	−0.0583457	−	0.998296i	$-0.518583\pi$
$4$	−1.52208	+	1.29741i	−0.761040	+	0.648704i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−1.53405	+	3.32334i	−0.626274	+	1.35675i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.46576	+	1.38565i	0.871779	+	0.489900i
$9$			3.69896i			1.23299i
$10$	−1.28402	−	0.592702i	−0.406042	−	0.187429i
$11$	−2.90936	+	2.90936i	−0.877206	+	0.877206i	−0.993245	−	0.116039i	$-0.962980\pi$
$11$	−2.90936	+	2.90936i	−0.877206	+	0.877206i	0.116039	+	0.993245i	$0.462980\pi$
$12$	5.16011	+	0.411185i	1.48960	+	0.118699i
$13$	2.88170	+	2.88170i	0.799241	+	0.799241i	0.982976	−	0.183735i	$-0.0588188\pi$
$13$	2.88170	+	2.88170i	0.799241	+	0.799241i	−0.183735	+	0.982976i	$0.558819\pi$
$14$	1.32704	−	0.488835i	0.354667	−	0.130647i
$15$	−2.58823			−0.668279
$16$	0.633460	−	3.94952i	0.158365	−	0.987381i
$17$	3.54579			0.859979			0.429990	−	0.902834i	$-0.358517\pi$
$17$	3.54579			0.859979			0.429990	+	0.902834i	$0.358517\pi$
$18$	4.90867	−	1.80818i	1.15698	−	0.426192i
$19$	2.31299	+	2.31299i	0.530637	+	0.530637i	0.920762	−	0.390125i	$-0.127568\pi$
$19$	2.31299	+	2.31299i	0.530637	+	0.530637i	−0.390125	+	0.920762i	$0.627568\pi$
$20$	−0.158867	+	1.99368i	−0.0355237	+	0.445800i
$21$	1.83016	−	1.83016i	0.399373	−	0.399373i
$22$	5.28305	+	2.43865i	1.12635	+	0.519922i
$23$			8.50997i			1.77445i	0.461337	+	0.887225i	$0.347370\pi$
$23$			8.50997i			1.77445i	−0.461337	+	0.887225i	$0.652630\pi$
$24$	−1.97678	−	7.04869i	−0.403509	−	1.43881i
$25$		−	1.00000i		−	0.200000i
$26$	2.41546	−	5.23282i	0.473712	−	1.02624i
$27$	1.27920	−	1.27920i	0.246182	−	0.246182i
$28$	−1.29741	−	1.52208i	−0.245187	−	0.287646i
$29$	−5.35406	−	5.35406i	−0.994224	−	0.994224i	0.00575897	−	0.999983i	$-0.498167\pi$
$29$	−5.35406	−	5.35406i	−0.994224	−	0.994224i	−0.999983	+	0.00575897i	$0.998167\pi$
$30$	1.26522	+	3.43470i	0.230996	+	0.627087i
$31$	−6.54983			−1.17638			−0.588192	−	0.808721i	$-0.700160\pi$
$31$	−6.54983			−1.17638			−0.588192	+	0.808721i	$0.700160\pi$
$32$	−5.55084	+	1.09004i	−0.981259	+	0.192693i
$33$	10.6492			1.85379
$34$	−1.73330	−	4.70541i	−0.297259	−	0.806970i
$35$	0.707107	+	0.707107i	0.119523	+	0.119523i
$36$	−4.79906	−	5.63011i	−0.799843	−	0.938352i
$37$	6.77129	−	6.77129i	1.11319	−	1.11319i	0.120478	−	0.992716i	$-0.461557\pi$
$37$	6.77129	−	6.77129i	1.11319	−	1.11319i	0.992716	−	0.120478i	$-0.0384427\pi$
$38$	1.93877	−	4.20011i	0.314510	−	0.681348i
$39$		−	10.5479i		−	1.68902i
$40$	2.72336	−	0.763757i	0.430601	−	0.120761i
$41$			11.2475i			1.75656i	0.478143	+	0.878282i	$0.341310\pi$
$41$			11.2475i			1.75656i	−0.478143	+	0.878282i	$0.658690\pi$
$42$	−3.32334	−	1.53405i	−0.512803	−	0.236709i
$43$	6.72342	−	6.72342i	1.02531	−	1.02531i	0.0256403	−	0.999671i	$-0.491838\pi$
$43$	6.72342	−	6.72342i	1.02531	−	1.02531i	0.999671	−	0.0256403i	$-0.00816246\pi$
$44$	0.653652	−	8.20292i	0.0985418	−	1.23664i
$45$	2.61556	+	2.61556i	0.389904	+	0.389904i
$46$	11.2931	−	4.15997i	1.66507	−	0.613354i
$47$	5.30845			0.774317			0.387159	−	0.922013i	$-0.373457\pi$
$47$	5.30845			0.774317			0.387159	+	0.922013i	$0.373457\pi$
$48$	−8.38758	+	6.06892i	−1.21064	+	0.875973i
$49$	−1.00000			−0.142857
$50$	−1.32704	+	0.488835i	−0.187672	+	0.0691317i
$51$	−6.48935	−	6.48935i	−0.908690	−	0.908690i
$52$	−8.12493	−	0.647438i	−1.12673	−	0.0897835i
$53$	−4.26312	+	4.26312i	−0.585585	+	0.585585i	−0.936433	−	0.350847i	$-0.885894\pi$
$53$	−4.26312	+	4.26312i	−0.585585	+	0.585585i	0.350847	+	0.936433i	$0.385894\pi$
$54$	−2.32287	−	1.07223i	−0.316102	−	0.145913i
$55$			4.11446i			0.554794i
$56$	−1.38565	+	2.46576i	−0.185165	+	0.329501i
$57$		−	8.46629i		−	1.12139i
$58$	−4.48781	+	9.72232i	−0.589279	+	1.27660i
$59$	4.91504	−	4.91504i	0.639884	−	0.639884i	−0.310643	−	0.950527i	$-0.600544\pi$
$59$	4.91504	−	4.91504i	0.639884	−	0.639884i	0.950527	+	0.310643i	$0.100544\pi$
$60$	3.93950	−	3.35800i	0.508587	−	0.433516i
$61$	1.49244	+	1.49244i	0.191087	+	0.191087i	0.796166	−	0.605079i	$-0.206858\pi$
$61$	1.49244	+	1.49244i	0.191087	+	0.191087i	−0.605079	+	0.796166i	$0.706858\pi$
$62$	3.20179	+	8.69190i	0.406627	+	1.10387i
$63$	−3.69896			−0.466025
$64$	4.15997	+	6.83335i	0.519996	+	0.854169i
$65$	4.07534			0.505484
$66$	−5.20570	−	14.1319i	−0.640777	−	1.73952i
$67$	−2.60202	−	2.60202i	−0.317887	−	0.317887i	0.530068	−	0.847955i	$-0.322166\pi$
$67$	−2.60202	−	2.60202i	−0.317887	−	0.317887i	−0.847955	+	0.530068i	$0.822166\pi$
$68$	−5.39697	+	4.60033i	−0.654479	+	0.557872i
$69$	15.5746	−	15.5746i	1.87496	−	1.87496i
$70$	0.592702	−	1.28402i	0.0708414	−	0.153470i
$71$			9.99630i			1.18634i	0.805076	+	0.593171i	$0.202124\pi$
$71$			9.99630i			1.18634i	−0.805076	+	0.593171i	$0.797876\pi$
$72$	−5.12544	+	9.12075i	−0.604039	+	1.07489i
$73$			7.68603i			0.899582i	0.893134	+	0.449791i	$0.148502\pi$
$73$			7.68603i			0.899582i	−0.893134	+	0.449791i	$0.851498\pi$
$74$	−12.2958	−	5.67575i	−1.42936	−	0.659792i
$75$	−1.83016	+	1.83016i	−0.211328	+	0.211328i
$76$	−6.52146	−	0.519665i	−0.748063	−	0.0596096i
$77$	−2.90936	−	2.90936i	−0.331553	−	0.331553i
$78$	−13.9976	+	5.15620i	−1.58491	+	0.583825i
$79$	−0.246529			−0.0277367			−0.0138684	−	0.999904i	$-0.504415\pi$
$79$	−0.246529			−0.0277367			−0.0138684	+	0.999904i	$0.504415\pi$
$80$	−2.34481	−	3.24066i	−0.262158	−	0.362317i
$81$	6.41459			0.712733
$82$	14.9259	−	5.49817i	1.64829	−	0.607171i
$83$	−3.31650	−	3.31650i	−0.364033	−	0.364033i	0.501262	−	0.865295i	$-0.332869\pi$
$83$	−3.31650	−	3.31650i	−0.364033	−	0.364033i	−0.865295	+	0.501262i	$0.832869\pi$
$84$	−0.411185	+	5.16011i	−0.0448640	+	0.563014i
$85$	2.50725	−	2.50725i	0.271949	−	0.271949i
$86$	−12.2089	−	5.63562i	−1.31652	−	0.607704i
$87$			19.5976i			2.10108i
$88$	−11.2051	+	3.14245i	−1.19447	+	0.334986i
$89$			7.92581i			0.840135i	0.907493	+	0.420067i	$0.137994\pi$
$89$			7.92581i			0.840135i	−0.907493	+	0.420067i	$0.862006\pi$
$90$	2.19238	−	4.74953i	0.231097	−	0.500644i
$91$	−2.88170	+	2.88170i	−0.302085	+	0.302085i
$92$	−11.0409	−	12.9529i	−1.15109	−	1.35043i
$93$	11.9872	+	11.9872i	1.24302	+	1.24302i
$94$	−2.59496	−	7.04454i	−0.267649	−	0.726589i
$95$	3.27107			0.335604
$96$	12.1539	+	8.16397i	1.24045	+	0.833232i
$97$	9.27782			0.942020			0.471010	−	0.882128i	$-0.343890\pi$
$97$	9.27782			0.942020			0.471010	+	0.882128i	$0.343890\pi$
$98$	0.488835	+	1.32704i	0.0493798	+	0.134051i
$99$	−10.7616	−	10.7616i	−1.08158	−	1.08158i
$100$	1.29741	+	1.52208i	0.129741	+	0.152208i
$101$	−10.6098	+	10.6098i	−1.05572	+	1.05572i	−0.0573632	+	0.998353i	$0.518269\pi$
$101$	−10.6098	+	10.6098i	−1.05572	+	1.05572i	−0.998353	+	0.0573632i	$0.981731\pi$
$102$	−5.43942	+	11.7839i	−0.538582	+	1.16678i
$103$			9.67759i			0.953561i	0.879022	+	0.476780i	$0.158196\pi$
$103$			9.67759i			0.953561i	−0.879022	+	0.476780i	$0.841804\pi$
$104$	3.11257	+	11.0986i	0.305213	+	1.08831i
$105$		−	2.58823i		−	0.252586i
$106$	7.74131	+	3.57338i	0.751902	+	0.347077i
$107$	−2.27930	+	2.27930i	−0.220349	+	0.220349i	−0.808645	−	0.588297i	$-0.799799\pi$
$107$	−2.27930	+	2.27930i	−0.220349	+	0.220349i	0.588297	+	0.808645i	$0.299799\pi$
$108$	−0.287400	+	3.60669i	−0.0276551	+	0.347054i
$109$	9.22176	+	9.22176i	0.883284	+	0.883284i	0.993867	−	0.110583i	$-0.0352718\pi$
$109$	9.22176	+	9.22176i	0.883284	+	0.883284i	−0.110583	+	0.993867i	$0.535272\pi$
$110$	5.46006	−	2.01129i	0.520597	−	0.191769i
$111$	−24.7851			−2.35250
$112$	3.94952	+	0.633460i	0.373195	+	0.0598564i
$113$	0.0204324			0.00192212			0.000961061	−	1.00000i	$-0.499694\pi$
$113$	0.0204324			0.00192212			0.000961061		1.00000i	$0.499694\pi$
$114$	−11.2351	+	4.13862i	−1.05227	+	0.387617i
$115$	6.01745	+	6.01745i	0.561130	+	0.561130i
$116$	15.0957	+	1.20291i	1.40160	+	0.111687i
$117$	−10.6593	+	10.6593i	−0.985452	+	0.985452i
$118$	−8.92511	−	4.11982i	−0.821623	−	0.379260i
$119$			3.54579i			0.325042i
$120$	−6.38197	−	3.58638i	−0.582592	−	0.327390i
$121$		−	5.92879i		−	0.538981i
$122$	1.25097	−	2.71008i	0.113258	−	0.245359i
$123$	20.5847	−	20.5847i	1.85606	−	1.85606i
$124$	9.96937	−	8.49781i	0.895276	−	0.763126i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	1.80818	+	4.90867i	0.161085	+	0.437299i
$127$	8.91163			0.790779			0.395390	−	0.918514i	$-0.370610\pi$
$127$	8.91163			0.790779			0.395390	+	0.918514i	$0.370610\pi$
$128$	7.03460	−	8.86083i	0.621777	−	0.783194i
$129$	−24.6098			−2.16677
$130$	−1.99217	−	5.40815i	−0.174725	−	0.474326i
$131$	6.12669	+	6.12669i	0.535291	+	0.535291i	0.922142	−	0.386851i	$-0.126437\pi$
$131$	6.12669	+	6.12669i	0.535291	+	0.535291i	−0.386851	+	0.922142i	$0.626437\pi$
$132$	−16.2089	+	13.8164i	−1.41081	+	1.20256i
$133$	−2.31299	+	2.31299i	−0.200562	+	0.200562i
$134$	−2.18103	+	4.72494i	−0.188412	+	0.408173i
$135$		−	1.80906i		−	0.155699i
$136$	8.74306	+	4.91320i	0.749712	+	0.421304i
$137$		−	6.04952i		−	0.516846i	−0.966032	−	0.258423i	$-0.916797\pi$
$137$		−	6.04952i		−	0.516846i	0.966032	−	0.258423i	$-0.0832028\pi$
$138$	−28.2815	−	13.0547i	−2.40748	−	1.11129i
$139$	5.16514	−	5.16514i	0.438102	−	0.438102i	−0.453271	−	0.891373i	$-0.649743\pi$
$139$	5.16514	−	5.16514i	0.438102	−	0.438102i	0.891373	+	0.453271i	$0.149743\pi$
$140$	−1.99368	−	0.158867i	−0.168497	−	0.0134267i
$141$	−9.71531	−	9.71531i	−0.818176	−	0.818176i
$142$	13.2655	−	4.88654i	1.11322	−	0.410069i
$143$	−16.7678			−1.40220
$144$	14.6091	+	2.34314i	1.21743	+	0.195262i
$145$	−7.57179			−0.628803
$146$	10.1997	−	3.75720i	0.844132	−	0.310948i
$147$	1.83016	+	1.83016i	0.150949	+	0.150949i
$148$	−1.52132	+	19.0916i	−0.125052	+	1.56932i
$149$	0.640257	−	0.640257i	0.0524519	−	0.0524519i	−0.680394	−	0.732846i	$-0.738191\pi$
$149$	0.640257	−	0.640257i	0.0524519	−	0.0524519i	0.732846	+	0.680394i	$0.238191\pi$
$150$	3.32334	+	1.53405i	0.271350	+	0.125255i
$151$			1.95309i			0.158940i	0.996837	+	0.0794702i	$0.0253229\pi$
$151$			1.95309i			0.158940i	−0.996837	+	0.0794702i	$0.974677\pi$
$152$	2.49830	+	8.90829i	0.202639	+	0.722557i
$153$			13.1157i			1.06034i
$154$	−2.43865	+	5.28305i	−0.196512	+	0.425720i
$155$	−4.63143	+	4.63143i	−0.372005	+	0.372005i
$156$	13.6850	+	16.0548i	1.09568	+	1.28541i
$157$	8.49590	+	8.49590i	0.678047	+	0.678047i	0.959558	−	0.281511i	$-0.0908356\pi$
$157$	8.49590	+	8.49590i	0.678047	+	0.678047i	−0.281511	+	0.959558i	$0.590836\pi$
$158$	0.120512	+	0.327155i	0.00958743	+	0.0260270i
$159$	15.6044			1.23751
$160$	−3.15426	+	4.69581i	−0.249366	+	0.371236i
$161$	−8.50997			−0.670679
$162$	−3.13568	−	8.51243i	−0.246362	−	0.668800i
$163$	0.493421	+	0.493421i	0.0386477	+	0.0386477i	0.726167	−	0.687519i	$-0.241300\pi$
$163$	0.493421	+	0.493421i	0.0386477	+	0.0386477i	−0.687519	+	0.726167i	$0.741300\pi$
$164$	−14.5926	−	17.1196i	−1.13949	−	1.33682i
$165$	7.53011	−	7.53011i	0.586219	−	0.586219i
$166$	−2.77991	+	6.02235i	−0.215763	+	0.467425i
$167$		−	20.4840i		−	1.58510i	−0.609806	−	0.792551i	$-0.708753\pi$
$167$		−	20.4840i		−	1.58510i	0.609806	−	0.792551i	$-0.291247\pi$
$168$	7.04869	−	1.97678i	0.543818	−	0.152512i
$169$			3.60843i			0.277572i
$170$	−4.55286	−	2.10159i	−0.349188	−	0.161185i
$171$	−8.55566	+	8.55566i	−0.654268	+	0.654268i
$172$	−1.51056	+	18.9566i	−0.115179	+	1.44543i
$173$	−1.80816	−	1.80816i	−0.137472	−	0.137472i	0.635022	−	0.772494i	$-0.280991\pi$
$173$	−1.80816	−	1.80816i	−0.137472	−	0.137472i	−0.772494	+	0.635022i	$0.780991\pi$
$174$	26.0068	−	9.57997i	1.97157	−	0.726256i
$175$	1.00000			0.0755929
$176$	9.64763	+	13.3336i	0.727218	+	1.00506i
$177$	−17.9906			−1.35226
$178$	10.5179	−	3.87441i	0.788349	−	0.290400i
$179$	−11.5918	−	11.5918i	−0.866414	−	0.866414i	0.125659	−	0.992073i	$-0.459895\pi$
$179$	−11.5918	−	11.5918i	−0.866414	−	0.866414i	−0.992073	+	0.125659i	$0.959895\pi$
$180$	−7.37454	−	0.587642i	−0.549665	−	0.0438003i
$181$	1.28463	−	1.28463i	0.0954860	−	0.0954860i	−0.657750	−	0.753236i	$-0.728492\pi$
$181$	1.28463	−	1.28463i	0.0954860	−	0.0954860i	0.753236	+	0.657750i	$0.228492\pi$
$182$	5.23282	+	2.41546i	0.387882	+	0.179046i
$183$		−	5.46279i		−	0.403821i
$184$	−11.7918	+	20.9836i	−0.869303	+	1.54693i
$185$		−	9.57606i		−	0.704046i
$186$	10.0478	−	21.7673i	0.736739	−	1.59606i
$187$	−10.3160	+	10.3160i	−0.754379	+	0.754379i
$188$	−8.07989	+	6.88723i	−0.589287	+	0.502303i
$189$	1.27920	+	1.27920i	0.0930481	+	0.0930481i
$190$	−1.59901	−	4.34084i	−0.116005	−	0.314918i
$191$	9.20388			0.665969			0.332985	−	0.942932i	$-0.391944\pi$
$191$	9.20388			0.665969			0.332985	+	0.942932i	$0.391944\pi$
$192$	4.89271	−	20.1195i	0.353101	−	1.45200i
$193$	−23.2750			−1.67537			−0.837687	−	0.546150i	$-0.816093\pi$
$193$	−23.2750			−1.67537			−0.837687	+	0.546150i	$0.816093\pi$
$194$	−4.53532	−	12.3121i	−0.325617	−	0.883954i
$195$	−7.45852	−	7.45852i	−0.534116	−	0.534116i
$196$	1.52208	−	1.29741i	0.108720	−	0.0926721i
$197$	−0.809095	+	0.809095i	−0.0576456	+	0.0576456i	−0.735342	−	0.677696i	$-0.762978\pi$
$197$	−0.809095	+	0.809095i	−0.0576456	+	0.0576456i	0.677696	+	0.735342i	$0.262978\pi$
$198$	−9.02046	+	19.5418i	−0.641056	+	1.38877i
$199$		−	11.7667i		−	0.834119i	−0.908879	−	0.417059i	$-0.863061\pi$
$199$		−	11.7667i		−	0.834119i	0.908879	−	0.417059i	$-0.136939\pi$
$200$	1.38565	−	2.46576i	0.0979800	−	0.174356i
$201$			9.52420i			0.671786i
$202$	19.2661	+	8.89323i	1.35556	+	0.625725i
$203$	5.35406	−	5.35406i	0.375782	−	0.375782i
$204$	18.2966	+	1.45797i	1.28102	+	0.102079i
$205$	7.95318	+	7.95318i	0.555474	+	0.555474i
$206$	12.8426	−	4.73074i	0.894784	−	0.329606i
$207$	−31.4780			−2.18787
$208$	13.2068	−	9.55591i	0.915727	−	0.662583i
$209$	−13.4587			−0.930956
$210$	−3.43470	+	1.26522i	−0.237016	+	0.0873084i
$211$	−9.41045	−	9.41045i	−0.647842	−	0.647842i	0.304629	−	0.952471i	$-0.401468\pi$
$211$	−9.41045	−	9.41045i	−0.647842	−	0.647842i	−0.952471	+	0.304629i	$0.901468\pi$
$212$	0.957804	−	12.0198i	0.0657823	−	0.825526i
$213$	18.2948	−	18.2948i	1.25354	−	1.25354i
$214$	4.13894	+	1.91053i	0.282932	+	0.130601i
$215$		−	9.50835i		−	0.648464i
$216$	4.92672	−	1.38168i	0.335221	−	0.0940117i
$217$		−	6.54983i		−	0.444631i
$218$	7.72974	−	16.7456i	0.523524	−	1.13415i
$219$	14.0667	−	14.0667i	0.950536	−	0.950536i
$220$	−5.33814	−	6.26254i	−0.359897	−	0.422221i
$221$	10.2179	+	10.2179i	0.687330	+	0.687330i
$222$	12.1158	+	32.8908i	0.813160	+	2.20749i
$223$	26.2770			1.75964			0.879818	−	0.475310i	$-0.157664\pi$
$223$	26.2770			1.75964			0.879818	+	0.475310i	$0.157664\pi$
$224$	−1.09004	−	5.55084i	−0.0728311	−	0.370881i
$225$	3.69896			0.246597
$226$	−0.00998809	−	0.0271147i	−0.000664398	−	0.00180364i
$227$	3.75208	+	3.75208i	0.249035	+	0.249035i	0.820574	−	0.571540i	$-0.193654\pi$
$227$	3.75208	+	3.75208i	0.249035	+	0.249035i	−0.571540	+	0.820574i	$0.693654\pi$
$228$	10.9842	+	12.8864i	0.727449	+	0.853421i
$229$	−10.1055	+	10.1055i	−0.667792	+	0.667792i	−0.957204	−	0.289412i	$-0.906540\pi$
$229$	−10.1055	+	10.1055i	−0.667792	+	0.667792i	0.289412	+	0.957204i	$0.406540\pi$
$230$	5.04387	−	10.9270i	0.332583	−	0.720502i
$231$			10.6492i			0.700665i
$232$	−5.78301	−	20.6207i	−0.379673	−	1.35381i
$233$		−	26.2741i		−	1.72127i	−0.509220	−	0.860636i	$-0.670066\pi$
$233$		−	26.2741i		−	1.72127i	0.509220	−	0.860636i	$-0.329934\pi$
$234$	19.3560	+	8.93470i	1.26534	+	0.584079i
$235$	3.75364	−	3.75364i	0.244861	−	0.244861i
$236$	−1.10427	+	13.8579i	−0.0718820	+	0.902073i
$237$	0.451188	+	0.451188i	0.0293078	+	0.0293078i
$238$	4.70541	−	1.73330i	0.305006	−	0.112353i
$239$	−16.6947			−1.07989			−0.539944	−	0.841701i	$-0.681554\pi$
$239$	−16.6947			−1.07989			−0.539944	+	0.841701i	$0.681554\pi$
$240$	−1.63954	+	10.2223i	−0.105832	+	0.659846i
$241$	−4.25089			−0.273824			−0.136912	−	0.990583i	$-0.543718\pi$
$241$	−4.25089			−0.273824			−0.136912	+	0.990583i	$0.543718\pi$
$242$	−7.86776	+	2.89820i	−0.505759	+	0.186303i
$243$	−15.5773	−	15.5773i	−0.999285	−	0.999285i
$244$	−4.20791	−	0.335308i	−0.269384	−	0.0214659i
$245$	−0.707107	+	0.707107i	−0.0451754	+	0.0451754i
$246$	−37.3793	−	17.2542i	−2.38322	−	1.10009i
$247$			13.3307i			0.848214i
$248$	−16.1503	−	9.07575i	−1.02555	−	0.576311i
$249$			12.1394i			0.769305i
$250$	−0.592702	+	1.28402i	−0.0374858	+	0.0812085i
$251$	−1.61619	+	1.61619i	−0.102013	+	0.102013i	−0.756271	−	0.654258i	$-0.772981\pi$
$251$	−1.61619	+	1.61619i	−0.102013	+	0.102013i	0.654258	+	0.756271i	$0.272981\pi$
$252$	5.63011	−	4.79906i	0.354664	−	0.302312i
$253$	−24.7586	−	24.7586i	−1.55656	−	1.55656i
$254$	−4.35632	−	11.8261i	−0.273340	−	0.742036i
$255$	−9.17732			−0.574706
$256$	−15.1975	−	5.00373i	−0.949841	−	0.312733i
$257$	−12.4408			−0.776037			−0.388019	−	0.921652i	$-0.626840\pi$
$257$	−12.4408			−0.776037			−0.388019	+	0.921652i	$0.626840\pi$
$258$	12.0301	+	32.6583i	0.748964	+	2.03322i
$259$	6.77129	+	6.77129i	0.420748	+	0.420748i
$260$	−6.20300	+	5.28739i	−0.384694	+	0.327910i
$261$	19.8044	−	19.8044i	1.22586	−	1.22586i
$262$	5.13543	−	11.1253i	0.317268	−	0.687324i
$263$			25.3305i			1.56195i	0.624563	+	0.780974i	$0.285277\pi$
$263$			25.3305i			1.56195i	−0.624563	+	0.780974i	$0.714723\pi$
$264$	26.2584	+	14.7560i	1.61609	+	0.908170i
$265$			6.02897i			0.370357i
$266$	4.20011	+	1.93877i	0.257525	+	0.118873i
$267$	14.5055	−	14.5055i	0.887722	−	0.887722i
$268$	7.33636	+	0.584600i	0.448140	+	0.0357101i
$269$	13.2578	+	13.2578i	0.808345	+	0.808345i	0.984383	−	0.176038i	$-0.0563282\pi$
$269$	13.2578	+	13.2578i	0.808345	+	0.808345i	−0.176038	+	0.984383i	$0.556328\pi$
$270$	−2.40070	+	0.884332i	−0.146102	+	0.0538188i
$271$	7.71653			0.468746			0.234373	−	0.972147i	$-0.424696\pi$
$271$	7.71653			0.468746			0.234373	+	0.972147i	$0.424696\pi$
$272$	2.24611	−	14.0042i	0.136191	−	0.849127i
$273$	10.5479			0.638391
$274$	−8.02797	+	2.95722i	−0.484987	+	0.178652i
$275$	2.90936	+	2.90936i	0.175441	+	0.175441i
$276$	−3.49917	+	43.9124i	−0.210625	+	2.64321i
$277$	−18.4295	+	18.4295i	−1.10732	+	1.10732i	−0.113823	+	0.993501i	$0.536310\pi$
$277$	−18.4295	+	18.4295i	−1.10732	+	1.10732i	−0.993501	+	0.113823i	$0.963690\pi$
$278$	−9.37927	−	4.32946i	−0.562531	−	0.259664i
$279$		−	24.2275i		−	1.45046i
$280$	0.763757	+	2.72336i	0.0456432	+	0.162752i
$281$		−	9.85393i		−	0.587836i	−0.955831	−	0.293918i	$-0.905041\pi$
$281$		−	9.85393i		−	0.587836i	0.955831	−	0.293918i	$-0.0949593\pi$
$282$	−8.14344	+	17.6418i	−0.484935	+	1.05055i
$283$	−10.3975	+	10.3975i	−0.618064	+	0.618064i	−0.945035	−	0.326970i	$-0.893972\pi$
$283$	−10.3975	+	10.3975i	−0.618064	+	0.618064i	0.326970	+	0.945035i	$0.393972\pi$
$284$	−12.9693	−	15.2152i	−0.769586	−	0.902854i
$285$	−5.98657	−	5.98657i	−0.354614	−	0.354614i
$286$	8.19671	+	22.2516i	0.484682	+	1.31577i
$287$	−11.2475			−0.663919
$288$	−4.03200	−	20.5323i	−0.237588	−	1.20988i
$289$	−4.42741			−0.260436
$290$	3.70135	+	10.0481i	0.217351	+	0.590044i
$291$	−16.9799	−	16.9799i	−0.995378	−	0.995378i
$292$	−9.97193	−	11.6988i	−0.583563	−	0.684618i
$293$	−1.28180	+	1.28180i	−0.0748837	+	0.0748837i	−0.743557	−	0.668673i	$-0.766863\pi$
$293$	−1.28180	+	1.28180i	−0.0748837	+	0.0748837i	0.668673	+	0.743557i	$0.266863\pi$
$294$	1.53405	−	3.32334i	0.0894677	−	0.193821i
$295$		−	6.95092i		−	0.404698i
$296$	26.0790	−	7.31378i	1.51581	−	0.425105i
$297$			7.44331i			0.431905i
$298$	−1.16263	−	0.536668i	−0.0673493	−	0.0310884i
$299$	−24.5232	+	24.5232i	−1.41821	+	1.41821i
$300$	0.411185	−	5.16011i	0.0237398	−	0.297919i
$301$	6.72342	+	6.72342i	0.387531	+	0.387531i
$302$	2.59184	−	0.954740i	0.149143	−	0.0549391i
$303$	38.8353			2.23103
$304$	10.6004	−	7.67003i	0.607975	−	0.439907i
$305$	2.11062			0.120854
$306$	17.4051	−	6.41141i	0.994983	−	0.366516i
$307$	−8.51832	−	8.51832i	−0.486166	−	0.486166i	0.420928	−	0.907094i	$-0.361704\pi$
$307$	−8.51832	−	8.51832i	−0.486166	−	0.486166i	−0.907094	+	0.420928i	$0.861704\pi$
$308$	8.20292	+	0.653652i	0.467405	+	0.0372453i
$309$	17.7115	−	17.7115i	1.00757	−	1.00757i
$310$	8.41010	+	3.88210i	0.477662	+	0.220488i
$311$			15.7859i			0.895136i	0.894250	+	0.447568i	$0.147710\pi$
$311$			15.7859i			0.895136i	−0.894250	+	0.447568i	$0.852290\pi$
$312$	14.6157	−	26.0087i	0.827452	−	1.47245i
$313$			11.1609i			0.630851i	0.948950	+	0.315426i	$0.102147\pi$
$313$			11.1609i			0.630851i	−0.948950	+	0.315426i	$0.897853\pi$
$314$	7.12133	−	15.4275i	0.401880	−	0.870625i
$315$	−2.61556	+	2.61556i	−0.147370	+	0.147370i
$316$	0.375238	−	0.319849i	0.0211088	−	0.0179929i
$317$	−22.0504	−	22.0504i	−1.23847	−	1.23847i	−0.960624	−	0.277851i	$-0.910378\pi$
$317$	−22.0504	−	22.0504i	−1.23847	−	1.23847i	−0.277851	−	0.960624i	$-0.589622\pi$
$318$	−7.62797	−	20.7077i	−0.427755	−	1.16123i
$319$	31.1538			1.74428
$320$	7.77345	+	1.89037i	0.434549	+	0.105675i
$321$	8.34297			0.465659
$322$	4.15997	+	11.2931i	0.231826	+	0.629339i
$323$	8.20138	+	8.20138i	0.456337	+	0.456337i
$324$	−9.76353	+	8.32235i	−0.542418	+	0.462353i
$325$	2.88170	−	2.88170i	0.159848	−	0.159848i
$326$	0.413589	−	0.895992i	0.0229066	−	0.0496244i
$327$		−	33.7545i		−	1.86663i
$328$	−15.5851	+	27.7337i	−0.860541	+	1.53134i
$329$			5.30845i			0.292664i
$330$	−13.6738	−	6.31180i	−0.752716	−	0.347453i
$331$	12.4571	−	12.4571i	0.684704	−	0.684704i	−0.276352	−	0.961056i	$-0.589126\pi$
$331$	12.4571	−	12.4571i	0.684704	−	0.684704i	0.961056	+	0.276352i	$0.0891257\pi$
$332$	9.35083	+	0.745124i	0.513194	+	0.0408940i
$333$	25.0467	+	25.0467i	1.37255	+	1.37255i
$334$	−27.1832	+	10.0133i	−1.48740	+	0.547904i
$335$	−3.67981			−0.201049
$336$	−6.06892	−	8.38758i	−0.331087	−	0.457580i
$337$	17.9162			0.975956			0.487978	−	0.872856i	$-0.337735\pi$
$337$	17.9162			0.975956			0.487978	+	0.872856i	$0.337735\pi$
$338$	4.78854	−	1.76393i	0.260462	−	0.0959450i
$339$	−0.0373946	−	0.0373946i	−0.00203100	−	0.00203100i
$340$	−0.563308	+	7.06916i	−0.0305497	+	0.383379i
$341$	19.0558	−	19.0558i	1.03193	−	1.03193i
$342$	15.5360	+	7.17142i	0.840092	+	0.387786i
$343$		−	1.00000i		−	0.0539949i
$344$	25.8946	−	7.26207i	1.39614	−	0.391545i
$345$		−	22.0258i		−	1.18583i
$346$	−1.51561	+	3.28339i	−0.0814797	+	0.176516i
$347$	3.36577	−	3.36577i	0.180684	−	0.180684i	−0.610970	−	0.791654i	$-0.709220\pi$
$347$	3.36577	−	3.36577i	0.180684	−	0.180684i	0.791654	+	0.610970i	$0.209220\pi$
$348$	−25.4260	−	29.8291i	−1.36298	−	1.59901i
$349$	19.5437	+	19.5437i	1.04615	+	1.04615i	0.998882	+	0.0472704i	$0.0150523\pi$
$349$	19.5437	+	19.5437i	1.04615	+	1.04615i	0.0472704	+	0.998882i	$0.484948\pi$
$350$	−0.488835	−	1.32704i	−0.0261293	−	0.0709334i
$351$	7.37255			0.393517
$352$	12.9781	−	19.3207i	0.691735	−	1.02980i
$353$	28.9133			1.53890			0.769449	−	0.638709i	$-0.220531\pi$
$353$	28.9133			1.53890			0.769449	+	0.638709i	$0.220531\pi$
$354$	8.79444	+	23.8743i	0.467419	+	1.26890i
$355$	7.06845	+	7.06845i	0.375154	+	0.375154i
$356$	−10.2830	−	12.0637i	−0.544999	−	0.639376i
$357$	6.48935	−	6.48935i	0.343453	−	0.343453i
$358$	−9.71635	+	21.0493i	−0.513525	+	1.11249i
$359$			5.13275i			0.270896i	0.990784	+	0.135448i	$0.0432474\pi$
$359$			5.13275i			0.270896i	−0.990784	+	0.135448i	$0.956753\pi$
$360$	2.82510	+	10.0736i	0.148896	+	0.530924i
$361$		−	8.30012i		−	0.436848i
$362$	−2.33274	−	1.07679i	−0.122606	−	0.0565947i
$363$	−10.8506	+	10.8506i	−0.569510	+	0.569510i
$364$	0.647438	−	8.12493i	0.0339350	−	0.425862i
$365$	5.43485	+	5.43485i	0.284473	+	0.284473i
$366$	−7.24935	+	2.67040i	−0.378929	+	0.139584i
$367$	19.9146			1.03953			0.519766	−	0.854309i	$-0.326019\pi$
$367$	19.9146			1.03953			0.519766	+	0.854309i	$0.326019\pi$
$368$	33.6103	+	5.39072i	1.75206	+	0.281011i
$369$	−41.6040			−2.16582
$370$	−12.7078	+	4.68111i	−0.660649	+	0.243359i
$371$	−4.26312	−	4.26312i	−0.221330	−	0.221330i
$372$	−33.7978	−	2.69319i	−1.75234	−	0.139636i
$373$	−2.01457	+	2.01457i	−0.104311	+	0.104311i	−0.757336	−	0.653025i	$-0.773500\pi$
$373$	−2.01457	+	2.01457i	−0.104311	+	0.104311i	0.653025	+	0.757336i	$0.273500\pi$
$374$	18.7325	+	8.64693i	0.968637	+	0.447122i
$375$			2.58823i			0.133656i
$376$	13.0894	+	7.35564i	0.675033	+	0.379338i
$377$		−	30.8576i		−	1.58925i
$378$	1.07223	−	2.32287i	0.0551498	−	0.119475i
$379$	−15.2430	+	15.2430i	−0.782978	+	0.782978i	−0.980332	−	0.197354i	$-0.936765\pi$
$379$	−15.2430	+	15.2430i	−0.782978	+	0.782978i	0.197354	+	0.980332i	$0.436765\pi$
$380$	−4.97883	+	4.24391i	−0.255409	+	0.217708i
$381$	−16.3097	−	16.3097i	−0.835571	−	0.835571i
$382$	−4.49918	−	12.2139i	−0.230198	−	0.624919i
$383$	12.4960			0.638517			0.319259	−	0.947668i	$-0.396566\pi$
$383$	12.4960			0.638517			0.319259	+	0.947668i	$0.396566\pi$
$384$	−29.0912	+	3.34229i	−1.48455	+	0.170560i
$385$	−4.11446			−0.209692
$386$	11.3777	+	30.8870i	0.579107	+	1.57210i
$387$	24.8696	+	24.8696i	1.26419	+	1.26419i
$388$	−14.1216	+	12.0371i	−0.716915	+	0.611093i
$389$	−8.19859	+	8.19859i	−0.415685	+	0.415685i	−0.883713	−	0.468028i	$-0.844964\pi$
$389$	−8.19859	+	8.19859i	−0.415685	+	0.415685i	0.468028	+	0.883713i	$0.344964\pi$
$390$	−6.25179	+	13.5438i	−0.316572	+	0.685815i
$391$			30.1745i			1.52599i
$392$	−2.46576	−	1.38565i	−0.124540	−	0.0699857i
$393$		−	22.4256i		−	1.13122i
$394$	1.46922	+	0.678189i	0.0740181	+	0.0341667i
$395$	−0.174323	+	0.174323i	−0.00877112	+	0.00877112i
$396$	30.3422	+	2.41783i	1.52476	+	0.121501i
$397$	−3.22244	−	3.22244i	−0.161729	−	0.161729i	0.621603	−	0.783332i	$-0.286482\pi$
$397$	−3.22244	−	3.22244i	−0.161729	−	0.161729i	−0.783332	+	0.621603i	$0.786482\pi$
$398$	−15.6149	+	5.75197i	−0.782704	+	0.288320i
$399$	8.46629			0.423845
$400$	−3.94952	−	0.633460i	−0.197476	−	0.0316730i
$401$	−38.1183			−1.90354			−0.951769	−	0.306816i	$-0.900736\pi$
$401$	−38.1183			−1.90354			−0.951769	+	0.306816i	$0.900736\pi$
$402$	12.6390	−	4.65576i	0.630377	−	0.232208i
$403$	−18.8747	−	18.8747i	−0.940214	−	0.940214i
$404$	2.38373	−	29.9143i	0.118595	−	1.48829i
$405$	4.53580	−	4.53580i	0.225386	−	0.225386i
$406$	−9.72232	−	4.48781i	−0.482511	−	0.222726i
$407$			39.4003i			1.95300i
$408$	−7.00925	−	24.9931i	−0.347009	−	1.23734i
$409$		−	25.3459i		−	1.25328i	−0.779311	−	0.626638i	$-0.784431\pi$
$409$		−	25.3459i		−	1.25328i	0.779311	−	0.626638i	$-0.215569\pi$
$410$	6.66641	−	14.4420i	0.329231	−	0.713240i
$411$	−11.0716	+	11.0716i	−0.546121	+	0.546121i
$412$	−12.5558	−	14.7301i	−0.618579	−	0.725698i
$413$	4.91504	+	4.91504i	0.241853	+	0.241853i
$414$	15.3875	+	41.7726i	0.756256	+	2.05301i
$415$	−4.69024			−0.230235
$416$	−19.1370	−	12.8547i	−0.938270	−	0.630254i
$417$	−18.9061			−0.925834
$418$	6.57907	+	17.8602i	0.321793	+	0.873573i
$419$	20.5431	+	20.5431i	1.00360	+	1.00360i	0.999994	+	0.00360462i	$0.00114739\pi$
$419$	20.5431	+	20.5431i	1.00360	+	1.00360i	0.00360462	+	0.999994i	$0.498853\pi$
$420$	3.35800	+	3.93950i	0.163854	+	0.192228i
$421$	10.3684	−	10.3684i	0.505326	−	0.505326i	−0.407762	−	0.913088i	$-0.633691\pi$
$421$	10.3684	−	10.3684i	0.505326	−	0.505326i	0.913088	+	0.407762i	$0.133691\pi$
$422$	−7.88791	+	17.0882i	−0.383977	+	0.831842i
$423$			19.6357i			0.954722i
$424$	−16.4190	+	4.60467i	−0.797379	+	0.223622i
$425$		−	3.54579i		−	0.171996i
$426$	−33.2211	−	15.3348i	−1.60957	−	0.742975i
$427$	−1.49244	+	1.49244i	−0.0722240	+	0.0722240i
$428$	0.512096	−	6.42647i	0.0247531	−	0.310635i
$429$	30.6878	+	30.6878i	1.48162	+	1.48162i
$430$	−12.6180	+	4.64801i	−0.608493	+	0.224147i
$431$	−28.3080			−1.36355			−0.681774	−	0.731563i	$-0.738791\pi$
$431$	−28.3080			−1.36355			−0.681774	+	0.731563i	$0.738791\pi$
$432$	−4.24191	−	5.86255i	−0.204089	−	0.282062i
$433$	5.01502			0.241006			0.120503	−	0.992713i	$-0.461549\pi$
$433$	5.01502			0.241006			0.120503	+	0.992713i	$0.461549\pi$
$434$	−8.69190	+	3.20179i	−0.417224	+	0.153691i
$435$	13.8576	+	13.8576i	0.664419	+	0.664419i
$436$	−26.0006	−	2.07187i	−1.24521	−	0.0992246i
$437$	−19.6835	+	19.6835i	−0.941589	+	0.941589i
$438$	−25.5433	−	11.7908i	−1.22051	−	0.563385i
$439$		−	6.84618i		−	0.326750i	−0.986564	−	0.163375i	$-0.947762\pi$
$439$		−	6.84618i		−	0.326750i	0.986564	−	0.163375i	$-0.0522381\pi$
$440$	−5.70119	+	10.1453i	−0.271794	+	0.483657i
$441$		−	3.69896i		−	0.176141i
$442$	8.56472	−	18.5545i	0.407382	−	0.882545i
$443$	22.0140	−	22.0140i	1.04592	−	1.04592i	0.0470231	−	0.998894i	$-0.485027\pi$
$443$	22.0140	−	22.0140i	1.04592	−	1.04592i	0.998894	−	0.0470231i	$-0.0149734\pi$
$444$	37.7249	−	32.1564i	1.79034	−	1.52607i
$445$	5.60440	+	5.60440i	0.265674	+	0.265674i
$446$	−12.8451	−	34.8707i	−0.608233	−	1.65117i
$447$	−2.34354			−0.110846
$448$	−6.83335	+	4.15997i	−0.322845	+	0.196540i
$449$	−3.71464			−0.175305			−0.0876523	−	0.996151i	$-0.527936\pi$
$449$	−3.71464			−0.175305			−0.0876523	+	0.996151i	$0.527936\pi$
$450$	−1.80818	−	4.90867i	−0.0852384	−	0.231397i
$451$	−32.7231	−	32.7231i	−1.54087	−	1.54087i
$452$	−0.0310998	+	0.0265092i	−0.00146281	+	0.00124689i
$453$	3.57447	−	3.57447i	0.167943	−	0.167943i
$454$	3.14502	−	6.81332i	0.147603	−	0.319765i
$455$			4.07534i			0.191055i
$456$	11.7313	−	20.8759i	0.549368	−	0.977601i
$457$		−	6.51689i		−	0.304847i	−0.988315	−	0.152424i	$-0.951292\pi$
$457$		−	6.51689i		−	0.304847i	0.988315	−	0.152424i	$-0.0487078\pi$
$458$	18.3504	+	8.47052i	0.857458	+	0.395802i
$459$	4.53577	−	4.53577i	0.211711	−	0.211711i
$460$	−16.9662	−	1.35195i	−0.791051	−	0.0630351i
$461$	−2.18809	−	2.18809i	−0.101910	−	0.101910i	0.654314	−	0.756223i	$-0.272958\pi$
$461$	−2.18809	−	2.18809i	−0.101910	−	0.101910i	−0.756223	+	0.654314i	$0.772958\pi$
$462$	14.1319	−	5.20570i	0.657477	−	0.242191i
$463$	20.8854			0.970628			0.485314	−	0.874340i	$-0.338705\pi$
$463$	20.8854			0.970628			0.485314	+	0.874340i	$0.338705\pi$
$464$	−24.5376	+	17.7544i	−1.13913	+	0.824228i
$465$	16.9525			0.786153
$466$	−34.8668	+	12.8437i	−1.61517	+	0.594972i
$467$	12.3412	+	12.3412i	0.571081	+	0.571081i	0.932430	−	0.361349i	$-0.117684\pi$
$467$	12.3412	+	12.3412i	0.571081	+	0.571081i	−0.361349	+	0.932430i	$0.617684\pi$
$468$	2.39484	−	30.0538i	0.110702	−	1.38924i
$469$	2.60202	−	2.60202i	0.120150	−	0.120150i
$470$	−6.81615	−	3.14633i	−0.314406	−	0.145129i
$471$		−	31.0977i		−	1.43291i
$472$	18.9298	−	5.30882i	0.871316	−	0.244358i
$473$			39.1217i			1.79882i
$474$	0.378189	−	0.819301i	0.0173708	−	0.0376317i
$475$	2.31299	−	2.31299i	0.106127	−	0.106127i
$476$	−4.60033	−	5.39697i	−0.210856	−	0.247370i
$477$	−15.7691	−	15.7691i	−0.722018	−	0.722018i
$478$	8.16093	+	22.1545i	0.373272	+	1.01332i
$479$	−5.76001			−0.263182			−0.131591	−	0.991304i	$-0.542008\pi$
$479$	−5.76001			−0.263182			−0.131591	+	0.991304i	$0.542008\pi$
$480$	14.3669	−	2.82127i	0.655755	−	0.128773i
$481$	39.0257			1.77942
$482$	2.07798	+	5.64111i	0.0946496	+	0.256946i
$483$	15.5746	+	15.5746i	0.708668	+	0.708668i
$484$	7.69207	+	9.02411i	0.349640	+	0.410187i
$485$	6.56041	−	6.56041i	0.297893	−	0.297893i
$486$	−13.0570	+	28.2865i	−0.592278	+	1.28310i
$487$		−	28.2580i		−	1.28049i	−0.768170	−	0.640246i	$-0.778832\pi$
$487$		−	28.2580i		−	1.28049i	0.768170	−	0.640246i	$-0.221168\pi$
$488$	1.61200	+	5.74798i	0.0729720	+	0.260199i
$489$		−	1.80608i		−	0.0816736i
$490$	1.28402	+	0.592702i	0.0580061	+	0.0267755i
$491$	−18.6746	+	18.6746i	−0.842774	+	0.842774i	−0.989219	−	0.146445i	$-0.953217\pi$
$491$	−18.6746	+	18.6746i	−0.842774	+	0.842774i	0.146445	+	0.989219i	$0.453217\pi$
$492$	−4.62480	+	58.0383i	−0.208502	+	2.61657i
$493$	−18.9844	−	18.9844i	−0.855012	−	0.855012i
$494$	17.6904	−	6.51652i	0.795930	−	0.293192i
$495$	−15.2192			−0.684053
$496$	−4.14906	+	25.8687i	−0.186298	+	1.16154i
$497$	−9.99630			−0.448395
$498$	16.1095	−	5.93418i	0.721886	−	0.265917i
$499$	−9.06034	−	9.06034i	−0.405596	−	0.405596i	0.474603	−	0.880200i	$-0.342591\pi$
$499$	−9.06034	−	9.06034i	−0.405596	−	0.405596i	−0.880200	+	0.474603i	$0.842591\pi$
$500$	1.99368	+	0.158867i	0.0891601	+	0.00710475i
$501$	−37.4890	+	37.4890i	−1.67488	+	1.67488i
$502$	2.93480	+	1.35470i	0.130987	+	0.0604633i
$503$			19.6641i			0.876777i	0.898786	+	0.438389i	$0.144451\pi$
$503$			19.6641i			0.876777i	−0.898786	+	0.438389i	$0.855549\pi$
$504$	−9.12075	−	5.12544i	−0.406270	−	0.228305i
$505$			15.0046i			0.667694i
$506$	−20.7528	+	44.9585i	−0.922575	+	1.99865i
$507$	6.60400	−	6.60400i	0.293294	−	0.293294i
$508$	−13.5642	+	11.5620i	−0.601815	+	0.512982i
$509$	−11.1548	−	11.1548i	−0.494426	−	0.494426i	0.415272	−	0.909697i	$-0.363686\pi$
$509$	−11.1548	−	11.1548i	−0.494426	−	0.494426i	−0.909697	+	0.415272i	$0.863686\pi$
$510$	4.48620	+	12.1787i	0.198652	+	0.539282i
$511$	−7.68603			−0.340010
$512$	0.788887	+	22.6137i	0.0348642	+	0.999392i
$513$	5.91756			0.261267
$514$	6.08151	+	16.5095i	0.268244	+	0.728203i
$515$	6.84309	+	6.84309i	0.301542	+	0.301542i
$516$	37.4582	−	31.9290i	1.64900	−	1.40560i
$517$	−15.4442	+	15.4442i	−0.679236	+	0.679236i
$518$	5.67575	−	12.2958i	0.249378	−	0.540248i
$519$			6.61843i			0.290517i
$520$	10.0488	+	5.64699i	0.440670	+	0.247637i
$521$		−	41.6834i		−	1.82618i	−0.407755	−	0.913092i	$-0.633688\pi$
$521$		−	41.6834i		−	1.82618i	0.407755	−	0.913092i	$-0.366312\pi$
$522$	−35.9624	−	16.6002i	−1.57403	−	0.726572i
$523$	−15.6695	+	15.6695i	−0.685178	+	0.685178i	−0.961162	−	0.275985i	$-0.910996\pi$
$523$	−15.6695	+	15.6695i	−0.685178	+	0.685178i	0.275985	+	0.961162i	$0.410996\pi$
$524$	−17.2741	−	1.37650i	−0.754624	−	0.0601325i
$525$	−1.83016	−	1.83016i	−0.0798746	−	0.0798746i
$526$	33.6147	−	12.3825i	1.46567	−	0.539901i
$527$	−23.2243			−1.01167
$528$	6.74584	−	42.0592i	0.293575	−	1.83039i
$529$	−49.4195			−2.14867
$530$	8.00069	−	2.94717i	0.347528	−	0.128017i
$531$	18.1805	+	18.1805i	0.788968	+	0.788968i
$532$	0.519665	−	6.52146i	0.0225303	−	0.282741i
$533$	−32.4120	+	32.4120i	−1.40392	+	1.40392i
$534$	−26.3402	−	12.1586i	−1.13985	−	0.526154i
$535$			3.22342i			0.139361i
$536$	−2.81048	−	10.0214i	−0.121394	−	0.432860i
$537$			42.4298i			1.83098i
$538$	11.1128	−	24.0746i	0.479108	−	1.03793i
$539$	2.90936	−	2.90936i	0.125315	−	0.125315i
$540$	2.34709	+	2.75354i	0.101003	+	0.118493i
$541$	0.846442	+	0.846442i	0.0363914	+	0.0363914i	0.725068	−	0.688677i	$-0.241808\pi$
$541$	0.846442	+	0.846442i	0.0363914	+	0.0363914i	−0.688677	+	0.725068i	$0.741808\pi$
$542$	−3.77211	−	10.2402i	−0.162026	−	0.439853i
$543$	−4.70216			−0.201789
$544$	−19.6821	+	3.86503i	−0.843862	+	0.165712i
$545$	13.0415			0.558638
$546$	−5.15620	−	13.9976i	−0.220665	−	0.599041i
$547$	14.9827	+	14.9827i	0.640615	+	0.640615i	0.950707	−	0.310092i	$-0.100360\pi$
$547$	14.9827	+	14.9827i	0.640615	+	0.640615i	−0.310092	+	0.950707i	$0.600360\pi$
$548$	7.84870	+	9.20786i	0.335280	+	0.393340i
$549$	−5.52045	+	5.52045i	−0.235607	+	0.235607i
$550$	2.43865	−	5.28305i	0.103984	−	0.225270i
$551$		−	24.7678i		−	1.05514i
$552$	59.9841	−	16.8224i	2.55309	−	0.716007i
$553$		−	0.246529i		−	0.0104835i
$554$	33.4658	+	15.4478i	1.42183	+	0.656313i
$555$	−17.5257	+	17.5257i	−0.743924	+	0.743924i
$556$	−1.16046	+	14.5631i	−0.0492146	+	0.617612i
$557$	12.4790	+	12.4790i	0.528751	+	0.528751i	0.920200	−	0.391449i	$-0.128026\pi$
$557$	12.4790	+	12.4790i	0.528751	+	0.528751i	−0.391449	+	0.920200i	$0.628026\pi$
$558$	−32.1509	+	11.8433i	−1.36106	+	0.501365i
$559$	38.7498			1.63894
$560$	3.24066	−	2.34481i	0.136943	−	0.0990863i
$561$	37.7597			1.59422
$562$	−13.0766	+	4.81694i	−0.551602	+	0.203191i
$563$	−17.5086	−	17.5086i	−0.737898	−	0.737898i	0.234273	−	0.972171i	$-0.424729\pi$
$563$	−17.5086	−	17.5086i	−0.737898	−	0.737898i	−0.972171	+	0.234273i	$0.924729\pi$
$564$	27.3922	+	2.18276i	1.15342	+	0.0919106i
$565$	0.0144479	−	0.0144479i	0.000607828	−	0.000607828i
$566$	18.8805	+	8.71522i	0.793606	+	0.366328i
$567$			6.41459i			0.269388i
$568$	−13.8513	+	24.6485i	−0.581189	+	1.03423i
$569$			19.4294i			0.814523i	0.913312	+	0.407262i	$0.133516\pi$
$569$			19.4294i			0.814523i	−0.913312	+	0.407262i	$0.866484\pi$
$570$	−5.01799	+	10.8709i	−0.210180	+	0.455331i
$571$	20.3820	−	20.3820i	0.852959	−	0.852959i	−0.137537	−	0.990497i	$-0.543919\pi$
$571$	20.3820	−	20.3820i	0.852959	−	0.852959i	0.990497	+	0.137537i	$0.0439187\pi$
$572$	25.5220	−	21.7548i	1.06713	−	0.909612i
$573$	−16.8446	−	16.8446i	−0.703691	−	0.703691i
$574$	5.49817	+	14.9259i	0.229489	+	0.622995i
$575$	8.50997			0.354890
$576$	−25.2763	+	15.3875i	−1.05318	+	0.641147i
$577$	−11.2204			−0.467109			−0.233555	−	0.972344i	$-0.575036\pi$
$577$	−11.2204			−0.467109			−0.233555	+	0.972344i	$0.575036\pi$
$578$	2.16427	+	5.87536i	0.0900218	+	0.244383i
$579$	42.5970	+	42.5970i	1.77027	+	1.77027i
$580$	11.5249	−	9.82371i	0.478544	−	0.407907i
$581$	3.31650	−	3.31650i	0.137592	−	0.137592i
$582$	−14.2327	+	30.8334i	−0.589963	+	1.27808i
$583$		−	24.8060i		−	1.02736i
$584$	−10.6501	+	18.9519i	−0.440705	+	0.784237i
$585$			15.0745i			0.623255i
$586$	2.32760	+	1.07442i	0.0961521	+	0.0443837i
$587$	−1.80220	+	1.80220i	−0.0743846	+	0.0743846i	−0.743320	−	0.668936i	$-0.766750\pi$
$587$	−1.80220	+	1.80220i	−0.0743846	+	0.0743846i	0.668936	+	0.743320i	$0.266750\pi$
$588$	−5.16011	−	0.411185i	−0.212799	−	0.0169570i
$589$	−15.1497	−	15.1497i	−0.624233	−	0.624233i
$590$	−9.22416	+	3.39785i	−0.379753	+	0.139887i
$591$	2.96154			0.121822
$592$	−22.4540	−	31.0327i	−0.922855	−	1.27544i
$593$	−4.86820			−0.199913			−0.0999565	−	0.994992i	$-0.531870\pi$
$593$	−4.86820			−0.199913			−0.0999565	+	0.994992i	$0.531870\pi$
$594$	9.87759	−	3.63855i	0.405282	−	0.149292i
$595$	2.50725	+	2.50725i	0.102787	+	0.102787i
$596$	−0.143848	+	1.80520i	−0.00589224	+	0.0739438i
$597$	−21.5349	+	21.5349i	−0.881365	+	0.881365i
$598$	44.5311	+	20.5555i	1.82101	+	0.840578i
$599$			20.2006i			0.825375i	0.910873	+	0.412687i	$0.135410\pi$
$599$			20.2006i			0.825375i	−0.910873	+	0.412687i	$0.864590\pi$
$600$	−7.04869	+	1.97678i	−0.287761	+	0.0807018i
$601$		−	1.70443i		−	0.0695250i	−0.999396	−	0.0347625i	$-0.988933\pi$
$601$		−	1.70443i		−	0.0695250i	0.999396	−	0.0347625i	$-0.0110675\pi$
$602$	5.63562	−	12.2089i	0.229691	−	0.497598i
$603$	9.62475	−	9.62475i	0.391950	−	0.391950i
$604$	−2.53396	−	2.97276i	−0.103105	−	0.120960i
$605$	−4.19229	−	4.19229i	−0.170441	−	0.170441i
$606$	−18.9840	−	51.5361i	−0.771174	−	2.09351i
$607$	−12.2782			−0.498356			−0.249178	−	0.968458i	$-0.580160\pi$
$607$	−12.2782			−0.498356			−0.249178	+	0.968458i	$0.580160\pi$
$608$	−15.3603	−	10.3178i	−0.622943	−	0.418442i
$609$	−19.5976			−0.794133
$610$	−1.03175	−	2.80089i	−0.0417742	−	0.113405i
$611$	15.2974	+	15.2974i	0.618866	+	0.618866i
$612$	−17.0164	−	19.9632i	−0.687848	−	0.806963i
$613$	9.49051	−	9.49051i	0.383318	−	0.383318i	−0.488978	−	0.872296i	$-0.662630\pi$
$613$	9.49051	−	9.49051i	0.383318	−	0.383318i	0.872296	+	0.488978i	$0.162630\pi$
$614$	−7.14011	+	15.4682i	−0.288151	+	0.624246i
$615$		−	29.1112i		−	1.17388i
$616$	−3.14245	−	11.2051i	−0.126613	−	0.451468i
$617$			16.0177i			0.644847i	0.946596	+	0.322424i	$0.104498\pi$
$617$			16.0177i			0.644847i	−0.946596	+	0.322424i	$0.895502\pi$
$618$	−32.1619	−	14.8459i	−1.29374	−	0.597190i
$619$	13.3205	−	13.3205i	0.535398	−	0.535398i	−0.386776	−	0.922174i	$-0.626411\pi$
$619$	13.3205	−	13.3205i	0.535398	−	0.535398i	0.922174	+	0.386776i	$0.126411\pi$
$620$	1.04055	−	13.0583i	0.0417896	−	0.524433i
$621$	10.8859	+	10.8859i	0.436838	+	0.436838i
$622$	20.9485	−	7.71670i	0.839960	−	0.309411i
$623$	−7.92581			−0.317541
$624$	−41.6593	−	6.68170i	−1.66771	−	0.267482i
$625$	−1.00000			−0.0400000
$626$	14.8110	−	5.45584i	0.591966	−	0.218059i
$627$	24.6315	+	24.6315i	0.983688	+	0.983688i
$628$	−23.9541	−	1.90879i	−0.955873	−	0.0761690i
$629$	24.0096	−	24.0096i	0.957324	−	0.957324i
$630$	4.74953	+	2.19238i	0.189226	+	0.0873464i
$631$			35.8022i			1.42526i	0.701539	+	0.712631i	$0.252496\pi$
$631$			35.8022i			1.42526i	−0.701539	+	0.712631i	$0.747504\pi$
$632$	−0.607883	−	0.341602i	−0.0241803	−	0.0135882i
$633$			34.4452i			1.36907i
$634$	−18.4828	+	40.0408i	−0.734046	+	1.59023i
$635$	6.30147	−	6.30147i	0.250066	−	0.250066i
$636$	−23.7511	+	20.2453i	−0.941794	+	0.802777i
$637$	−2.88170	−	2.88170i	−0.114177	−	0.114177i
$638$	−15.2291	−	41.3424i	−0.602925	−	1.63676i
$639$	−36.9759			−1.46274
$640$	−1.29134	−	11.2398i	−0.0510446	−	0.444291i
$641$	49.5376			1.95662			0.978309	−	0.207152i	$-0.0664196\pi$
$641$	49.5376			1.95662			0.978309	+	0.207152i	$0.0664196\pi$
$642$	−4.07834	−	11.0715i	−0.160959	−	0.436956i
$643$	11.4513	+	11.4513i	0.451595	+	0.451595i	0.895884	−	0.444289i	$-0.146543\pi$
$643$	11.4513	+	11.4513i	0.451595	+	0.451595i	−0.444289	+	0.895884i	$0.646543\pi$
$644$	12.9529	−	11.0409i	0.510414	−	0.435073i
$645$	−17.4018	+	17.4018i	−0.685194	+	0.685194i
$646$	6.87445	−	14.8927i	0.270472	−	0.585945i
$647$		−	8.58688i		−	0.337585i	−0.985652	−	0.168793i	$-0.946013\pi$
$647$		−	8.58688i		−	0.337585i	0.985652	−	0.168793i	$-0.0539868\pi$
$648$	15.8169	+	8.88836i	0.621345	+	0.349168i
$649$			28.5993i			1.12262i
$650$	−5.23282	−	2.41546i	−0.205248	−	0.0947423i
$651$	−11.9872	+	11.9872i	−0.469816	+	0.469816i
$652$	−1.39120	−	0.110858i	−0.0544834	−	0.00434153i
$653$	−27.0019	−	27.0019i	−1.05667	−	1.05667i	−0.998295	−	0.0583703i	$-0.981410\pi$
$653$	−27.0019	−	27.0019i	−1.05667	−	1.05667i	−0.0583703	−	0.998295i	$-0.518590\pi$
$654$	−44.7937	+	16.5004i	−1.75157	+	0.645217i
$655$	8.66445			0.338548
$656$	44.4222	+	7.12484i	1.73440	+	0.278178i
$657$	−28.4303			−1.10917
$658$	7.04454	−	2.59496i	0.274625	−	0.101162i
$659$	−28.1721	−	28.1721i	−1.09743	−	1.09743i	−0.994711	−	0.102717i	$-0.967246\pi$
$659$	−28.1721	−	28.1721i	−1.09743	−	1.09743i	−0.102717	−	0.994711i	$-0.532754\pi$
$660$	−1.69181	+	21.2311i	−0.0658534	+	0.826419i
$661$	22.9851	−	22.9851i	0.894018	−	0.894018i	−0.100881	−	0.994899i	$-0.532166\pi$
$661$	22.9851	−	22.9851i	0.894018	−	0.894018i	0.994899	+	0.100881i	$0.0321660\pi$
$662$	−22.6206	−	10.4416i	−0.879173	−	0.405825i
$663$		−	37.4007i		−	1.45252i
$664$	−3.58220	−	12.7732i	−0.139016	−	0.495696i
$665$			3.27107i			0.126847i
$666$	20.9943	−	45.4818i	0.813514	−	1.76238i
$667$	45.5629	−	45.5629i	1.76420	−	1.76420i
$668$	26.5762	+	31.1783i	1.02826	+	1.20633i
$669$	−48.0910	−	48.0910i	−1.85931	−	1.85931i
$670$	1.79882	+	4.88326i	0.0694944	+	0.188657i
$671$	−8.68408			−0.335245
$672$	−8.16397	+	12.1539i	−0.314932	+	0.468845i
$673$	27.3826			1.05552			0.527760	−	0.849394i	$-0.323032\pi$
$673$	27.3826			1.05552			0.527760	+	0.849394i	$0.323032\pi$
$674$	−8.75805	−	23.7755i	−0.337347	−	0.915798i
$675$	−1.27920	−	1.27920i	−0.0492364	−	0.0492364i
$676$	−4.68161	−	5.49232i	−0.180062	−	0.211243i
$677$	−23.2724	+	23.2724i	−0.894432	+	0.894432i	−0.994937	−	0.100504i	$-0.967954\pi$
$677$	−23.2724	+	23.2724i	−0.894432	+	0.894432i	0.100504	+	0.994937i	$0.467954\pi$
$678$	−0.0313444	+	0.0679040i	−0.00120377	+	0.00260784i
$679$			9.27782i			0.356050i
$680$	9.65644	−	2.70812i	0.370308	−	0.103852i
$681$		−	13.7338i		−	0.526281i
$682$	−34.6031	−	15.9727i	−1.32502	−	0.611628i
$683$	28.0097	−	28.0097i	1.07176	−	1.07176i	0.0745422	−	0.997218i	$-0.476250\pi$
$683$	28.0097	−	28.0097i	1.07176	−	1.07176i	0.997218	−	0.0745422i	$-0.0237496\pi$
$684$	1.92222	−	24.1226i	0.0734978	−	0.922351i
$685$	−4.27766	−	4.27766i	−0.163441	−	0.163441i
$686$	−1.32704	+	0.488835i	−0.0506667	+	0.0186638i
$687$	36.9894			1.41123
$688$	−22.2953	−	30.8133i	−0.849999	−	1.17475i
$689$	−24.5701			−0.936047
$690$	−29.2291	+	10.7670i	−1.11273	+	0.409892i
$691$	−25.7541	−	25.7541i	−0.979731	−	0.979731i	0.0200674	−	0.999799i	$-0.493612\pi$
$691$	−25.7541	−	25.7541i	−0.979731	−	0.979731i	−0.999799	+	0.0200674i	$0.993612\pi$
$692$	5.09808	+	0.406242i	0.193800	+	0.0154430i
$693$	10.7616	−	10.7616i	0.408800	−	0.408800i
$694$	−6.11183	−	2.82122i	−0.232002	−	0.107092i
$695$		−	7.30462i		−	0.277080i
$696$	−27.1553	+	48.3229i	−1.02932	+	1.83168i
$697$			39.8812i			1.51061i
$698$	16.3817	−	35.4890i	0.620057	−	1.34328i
$699$	−48.0857	+	48.0857i	−1.81877	+	1.81877i
$700$	−1.52208	+	1.29741i	−0.0575292	+	0.0490374i
$701$	22.5153	+	22.5153i	0.850391	+	0.850391i	0.990181	−	0.139790i	$-0.0446427\pi$
$701$	22.5153	+	22.5153i	0.850391	+	0.850391i	−0.139790	+	0.990181i	$0.544643\pi$
$702$	−3.60396	−	9.78368i	−0.136023	−	0.369261i
$703$	31.3239			1.18140
$704$	−31.9836	−	7.77784i	−1.20543	−	0.293138i
$705$	−13.7395			−0.517460
$706$	−14.1338	−	38.3691i	−0.531933	−	1.44404i
$707$	−10.6098	−	10.6098i	−0.399023	−	0.399023i
$708$	27.3832	−	23.3412i	1.02912	−	0.877215i
$709$	4.48936	−	4.48936i	0.168601	−	0.168601i	−0.617763	−	0.786364i	$-0.711961\pi$
$709$	4.48936	−	4.48936i	0.168601	−	0.168601i	0.786364	+	0.617763i	$0.211961\pi$
$710$	5.92482	−	12.8354i	0.222355	−	0.481705i
$711$		−	0.911901i		−	0.0341990i
$712$	−10.9824	+	19.5432i	−0.411582	+	0.732411i
$713$		−	55.7388i		−	2.08744i
$714$	−11.7839	−	5.43942i	−0.441000	−	0.203565i
$715$	−11.8567	+	11.8567i	−0.443414	+	0.443414i
$716$	32.6830	+	2.60436i	1.22142	+	0.0973294i
$717$	30.5539	+	30.5539i	1.14105	+	1.14105i
$718$	6.81137	−	2.50907i	0.254198	−	0.0936375i
$719$	23.4761			0.875511			0.437755	−	0.899094i	$-0.355774\pi$
$719$	23.4761			0.875511			0.437755	+	0.899094i	$0.355774\pi$
$720$	11.9871	−	8.67335i	0.446731	−	0.323237i
$721$	−9.67759			−0.360412
$722$	−11.0146	+	4.05739i	−0.409921	+	0.151000i
$723$	7.77980	+	7.77980i	0.289334	+	0.289334i
$724$	−0.288621	+	3.62201i	−0.0107265	+	0.134611i
$725$	−5.35406	+	5.35406i	−0.198845	+	0.198845i
$726$	19.7034	+	9.09508i	0.731262	+	0.337550i
$727$		−	44.9653i		−	1.66767i	−0.552014	−	0.833835i	$-0.686141\pi$
$727$		−	44.9653i		−	1.66767i	0.552014	−	0.833835i	$-0.313859\pi$
$728$	−11.0986	+	3.11257i	−0.411342	+	0.115360i
$729$			37.7741i			1.39904i
$730$	4.55553	−	9.86901i	0.168608	−	0.365269i
$731$	23.8398	−	23.8398i	0.881747	−	0.881747i
$732$	7.08747	+	8.31480i	0.261960	+	0.307324i
$733$	−14.8665	−	14.8665i	−0.549107	−	0.549107i	0.377075	−	0.926183i	$-0.376930\pi$
$733$	−14.8665	−	14.8665i	−0.549107	−	0.549107i	−0.926183	+	0.377075i	$0.876930\pi$
$734$	−9.73493	−	26.4275i	−0.359323	−	0.975455i
$735$	2.58823			0.0954685
$736$	−9.27617	−	47.2375i	−0.341924	−	1.74120i
$737$	15.1404			0.557705
$738$	20.3375	+	55.2103i	0.748633	+	2.03232i
$739$	−11.6780	−	11.6780i	−0.429581	−	0.429581i	0.458904	−	0.888486i	$-0.348242\pi$
$739$	−11.6780	−	11.6780i	−0.429581	−	0.429581i	−0.888486	+	0.458904i	$0.848242\pi$
$740$	12.4241	+	14.5755i	0.456718	+	0.535807i
$741$	24.3973	−	24.3973i	0.896258	−	0.896258i
$742$	−3.57338	+	7.74131i	−0.131183	+	0.284192i
$743$			16.8999i			0.619996i	0.950737	+	0.309998i	$0.100328\pi$
$743$			16.8999i			0.619996i	−0.950737	+	0.309998i	$0.899672\pi$
$744$	12.9476	+	46.1677i	0.474682	+	1.69259i
$745$		−	0.905461i		−	0.0331735i
$746$	3.65822	+	1.68863i	0.133937	+	0.0618252i
$747$	12.2676	−	12.2676i	0.448847	−	0.448847i
$748$	2.31771	−	29.0858i	0.0847439	−	1.06348i
$749$	−2.27930	−	2.27930i	−0.0832839	−	0.0832839i
$750$	3.43470	−	1.26522i	0.125417	−	0.0461993i
$751$	−39.5791			−1.44426			−0.722131	−	0.691757i	$-0.756837\pi$
$751$	−39.5791			−1.44426			−0.722131	+	0.691757i	$0.756837\pi$
$752$	3.36269	−	20.9659i	0.122625	−	0.764546i
$753$	5.91577			0.215583
$754$	−40.9494	+	15.0843i	−1.49129	+	0.549338i
$755$	1.38104	+	1.38104i	0.0502614	+	0.0502614i
$756$	−3.60669	−	0.287400i	−0.131174	−	0.0104526i
$757$	−10.2950	+	10.2950i	−0.374177	+	0.374177i	−0.868996	−	0.494819i	$-0.835234\pi$
$757$	−10.2950	+	10.2950i	−0.374177	+	0.374177i	0.494819	+	0.868996i	$0.335234\pi$
$758$	27.6793	+	12.7768i	1.00536	+	0.464073i
$759$			90.6242i			3.28945i
$760$	8.06568	+	4.53254i	0.292573	+	0.164413i
$761$		−	12.6879i		−	0.459936i	−0.973198	−	0.229968i	$-0.926138\pi$
$761$		−	12.6879i		−	0.459936i	0.973198	−	0.229968i	$-0.0738622\pi$
$762$	−13.6709	+	29.6164i	−0.495244	+	1.07289i
$763$	−9.22176	+	9.22176i	−0.333850	+	0.333850i
$764$	−14.0090	+	11.9412i	−0.506830	+	0.432017i
$765$	9.27420	+	9.27420i	0.335309	+	0.335309i
$766$	−6.10850	−	16.5828i	−0.220709	−	0.599159i
$767$	28.3274			1.02284
$768$	18.6561	+	36.9714i	0.673195	+	1.33409i
$769$	39.8816			1.43817			0.719084	−	0.694923i	$-0.244562\pi$
$769$	39.8816			1.43817			0.719084	+	0.694923i	$0.244562\pi$
$770$	2.01129	+	5.46006i	0.0724820	+	0.196767i
$771$	22.7687	+	22.7687i	0.819994	+	0.819994i
$772$	35.4265	−	30.1973i	1.27503	−	1.08682i
$773$	4.48945	−	4.48945i	0.161474	−	0.161474i	−0.621745	−	0.783219i	$-0.713576\pi$
$773$	4.48945	−	4.48945i	0.161474	−	0.161474i	0.783219	+	0.621745i	$0.213576\pi$
$774$	20.8459	−	45.1602i	0.749290	−	1.62325i
$775$			6.54983i			0.235277i
$776$	22.8769	+	12.8558i	0.821233	+	0.461496i
$777$		−	24.7851i		−	0.889160i
$778$	14.8876	+	6.87212i	0.533747	+	0.246377i
$779$	−26.0154	+	26.0154i	−0.932098	+	0.932098i
$780$	21.0292	+	1.67572i	0.752967	+	0.0600004i
$781$	−29.0829	−	29.0829i	−1.04067	−	1.04067i
$782$	40.0428	−	14.7504i	1.43193	−	0.527472i
$783$	−13.6978			−0.489520
$784$	−0.633460	+	3.94952i	−0.0226236	+	0.141054i
$785$	12.0150			0.428834
$786$	−29.7597	+	10.9624i	−1.06149	+	0.391017i
$787$	18.5238	+	18.5238i	0.660303	+	0.660303i	0.955451	−	0.295148i	$-0.0953691\pi$
$787$	18.5238	+	18.5238i	0.660303	+	0.660303i	−0.295148	+	0.955451i	$0.595369\pi$
$788$	0.181781	−	2.28123i	0.00647568	−	0.0812656i
$789$	46.3589	−	46.3589i	1.65042	−	1.65042i
$790$	0.316548	+	0.146118i	0.0112623	+	0.00519866i
$791$			0.0204324i			0.000726494i
$792$	−11.6238	−	41.4474i	−0.413033	−	1.47277i
$793$			8.60152i			0.305449i
$794$	−2.70107	+	5.85155i	−0.0958573	+	0.207664i
$795$	11.0340	−	11.0340i	0.391334	−	0.391334i
$796$	15.2662	+	17.9099i	0.541097	+	0.634798i
$797$	21.7474	+	21.7474i	0.770333	+	0.770333i	0.978165	−	0.207832i	$-0.0666406\pi$
$797$	21.7474	+	21.7474i	0.770333	+	0.770333i	−0.207832	+	0.978165i	$0.566641\pi$
$798$	−4.13862	−	11.2351i	−0.146505	−	0.397719i
$799$	18.8226			0.665897
$800$	1.09004	+	5.55084i	0.0385386	+	0.196252i
$801$	−29.3172			−1.03587
$802$	18.6336	+	50.5846i	0.657974	+	1.78620i
$803$	−22.3615	−	22.3615i	−0.789119	−	0.789119i
$804$	−12.3568	−	14.4966i	−0.435790	−	0.511256i
$805$	−6.01745	+	6.01745i	−0.212087	+	0.212087i
$806$	−15.8209	+	34.2741i	−0.557267	+	1.20725i
$807$		−	48.5279i		−	1.70826i
$808$	−40.8628	+	11.4598i	−1.43755	+	0.403156i
$809$		−	13.5455i		−	0.476235i	−0.971236	−	0.238117i	$-0.923470\pi$
$809$		−	13.5455i		−	0.476235i	0.971236	−	0.238117i	$-0.0765303\pi$
$810$	−8.23646	−	3.80194i	−0.289400	−	0.133587i
$811$	20.6848	−	20.6848i	0.726340	−	0.726340i	−0.243549	−	0.969889i	$-0.578312\pi$
$811$	20.6848	−	20.6848i	0.726340	−	0.726340i	0.969889	+	0.243549i	$0.0783116\pi$
$812$	−1.20291	+	15.0957i	−0.0422138	+	0.529756i
$813$	−14.1225	−	14.1225i	−0.495297	−	0.495297i
$814$	52.2859	−	19.2603i	1.83262	−	0.675071i
$815$	0.697803			0.0244430
$816$	−29.7406	+	21.5191i	−1.04113	+	0.753318i
$817$	31.1024			1.08814
$818$	−33.6351	+	12.3900i	−1.17602	+	0.433205i
$819$	−10.6593	−	10.6593i	−0.372466	−	0.372466i
$820$	−22.4239	−	1.78686i	−0.783077	−	0.0623997i
$821$	−14.5472	+	14.5472i	−0.507701	+	0.507701i	−0.913820	−	0.406119i	$-0.866882\pi$
$821$	−14.5472	+	14.5472i	−0.507701	+	0.507701i	0.406119	+	0.913820i	$0.366882\pi$
$822$	20.1046	+	9.28028i	0.701229	+	0.323687i
$823$			17.6705i			0.615956i	0.951393	+	0.307978i	$0.0996523\pi$
$823$			17.6705i			0.615956i	−0.951393	+	0.307978i	$0.900348\pi$
$824$	−13.4097	+	23.8626i	−0.467149	+	0.831294i
$825$		−	10.6492i		−	0.370757i
$826$	4.11982	−	8.92511i	0.143347	−	0.310544i
$827$	27.5755	−	27.5755i	0.958895	−	0.958895i	−0.0402929	−	0.999188i	$-0.512829\pi$
$827$	27.5755	−	27.5755i	0.958895	−	0.958895i	0.999188	+	0.0402929i	$0.0128291\pi$
$828$	47.9120	−	40.8398i	1.66506	−	1.41928i
$829$	−30.6156	−	30.6156i	−1.06332	−	1.06332i	−0.997855	−	0.0654679i	$-0.979146\pi$
$829$	−30.6156	−	30.6156i	−1.06332	−	1.06332i	−0.0654679	−	0.997855i	$-0.520854\pi$
$830$	2.29275	+	6.22414i	0.0795826	+	0.216043i
$831$	67.4580			2.34009
$832$	−7.70389	+	31.6795i	−0.267084	+	1.09829i
$833$	−3.54579			−0.122854
$834$	9.24194	+	25.0891i	0.320022	+	0.868766i
$835$	−14.4844	−	14.4844i	−0.501253	−	0.501253i
$836$	20.4852	−	17.4614i	0.708496	−	0.603916i
$837$	−8.37854	+	8.37854i	−0.289605	+	0.289605i
$838$	17.2194	−	37.3038i	0.594835	−	1.28864i
$839$			28.1499i			0.971844i	0.874002	+	0.485922i	$0.161516\pi$
$839$			28.1499i			0.971844i	−0.874002	+	0.485922i	$0.838484\pi$
$840$	3.58638	−	6.38197i	0.123742	−	0.220199i
$841$			28.3320i			0.976964i
$842$	−18.8278	−	8.69089i	−0.648849	−	0.299508i
$843$	−18.0342	+	18.0342i	−0.621132	+	0.621132i
$844$	26.5327	+	2.11426i	0.913292	+	0.0727760i
$845$	2.55155	+	2.55155i	0.0877759	+	0.0877759i
$846$	26.0574	−	9.59863i	0.895873	−	0.330008i
$847$	5.92879			0.203716
$848$	14.1368	+	19.5378i	0.485459	+	0.670932i
$849$	38.0580			1.30615
$850$	−4.70541	+	1.73330i	−0.161394	+	0.0594518i
$851$	57.6235	+	57.6235i	1.97531	+	1.97531i
$852$	−4.11033	+	51.5820i	−0.140818	+	1.76717i
$853$	−10.7757	+	10.7757i	−0.368952	+	0.368952i	−0.867095	−	0.498143i	$-0.834016\pi$
$853$	−10.7757	+	10.7757i	−0.368952	+	0.368952i	0.498143	+	0.867095i	$0.334016\pi$
$854$	2.71008	+	1.25097i	0.0927370	+	0.0428073i
$855$			12.0995i			0.413795i
$856$	−8.77853	+	2.46191i	−0.300044	+	0.0841464i
$857$		−	29.5877i		−	1.01070i	−0.862916	−	0.505348i	$-0.831364\pi$
$857$		−	29.5877i		−	1.01070i	0.862916	−	0.505348i	$-0.168636\pi$
$858$	25.7227	−	55.7253i	0.878160	−	1.90243i
$859$	22.8014	−	22.8014i	0.777975	−	0.777975i	−0.201511	−	0.979486i	$-0.564585\pi$
$859$	22.8014	−	22.8014i	0.777975	−	0.777975i	0.979486	+	0.201511i	$0.0645853\pi$
$860$	12.3362	+	14.4725i	0.420661	+	0.493507i
$861$	20.5847	+	20.5847i	0.701525	+	0.701525i
$862$	13.8379	+	37.5659i	0.471322	+	1.27950i
$863$	14.6922			0.500127			0.250064	−	0.968229i	$-0.419548\pi$
$863$	14.6922			0.500127			0.250064	+	0.968229i	$0.419548\pi$
$864$	−5.70626	+	8.49501i	−0.194131	+	0.289006i
$865$	−2.55712			−0.0869447
$866$	−2.45151	−	6.65514i	−0.0833059	−	0.226151i
$867$	8.10285	+	8.10285i	0.275187	+	0.275187i
$868$	8.49781	+	9.96937i	0.288434	+	0.338382i
$869$	0.717244	−	0.717244i	0.0243308	−	0.0243308i
$870$	11.6155	−	25.1636i	0.393803	−	0.853127i
$871$		−	14.9965i		−	0.508136i
$872$	9.96057	+	35.5168i	0.337307	+	1.20275i
$873$			34.3183i			1.16150i
$874$	35.7428	+	16.4988i	1.20902	+	0.558082i
$875$	0.707107	−	0.707107i	0.0239046	−	0.0239046i
$876$	−3.16038	+	39.6608i	−0.106779	+	1.34001i
$877$	1.31962	+	1.31962i	0.0445606	+	0.0445606i	0.729036	−	0.684475i	$-0.239969\pi$
$877$	1.31962	+	1.31962i	0.0445606	+	0.0445606i	−0.684475	+	0.729036i	$0.739969\pi$
$878$	−9.08517	+	3.34665i	−0.306610	+	0.112944i
$879$	4.69180			0.158251
$880$	16.2502	+	2.60635i	0.547793	+	0.0878600i
$881$	14.4564			0.487050			0.243525	−	0.969895i	$-0.421696\pi$
$881$	14.4564			0.487050			0.243525	+	0.969895i	$0.421696\pi$
$882$	−4.90867	+	1.80818i	−0.165284	+	0.0608845i
$883$	−36.8129	−	36.8129i	−1.23885	−	1.23885i	−0.960470	−	0.278382i	$-0.910202\pi$
$883$	−36.8129	−	36.8129i	−1.23885	−	1.23885i	−0.278382	−	0.960470i	$-0.589798\pi$
$884$	−28.8093	−	2.29568i	−0.968961	−	0.0772119i
$885$	−12.7213	+	12.7213i	−0.427621	+	0.427621i
$886$	−39.9747	−	18.4523i	−1.34298	−	0.619917i
$887$		−	36.7266i		−	1.23316i	−0.787293	−	0.616579i	$-0.788518\pi$
$887$		−	36.7266i		−	1.23316i	0.787293	−	0.616579i	$-0.211482\pi$
$888$	−61.1141	−	34.3434i	−2.05086	−	1.15249i
$889$			8.91163i			0.298886i
$890$	4.69765	−	10.1769i	0.157465	−	0.341130i
$891$	−18.6624	+	18.6624i	−0.625213	+	0.625213i
$892$	−39.9957	+	34.0920i	−1.33915	+	1.14148i
$893$	12.2784	+	12.2784i	0.410882	+	0.410882i
$894$	1.14561	+	3.10998i	0.0383148	+	0.104013i
$895$	−16.3933			−0.547968
$896$	8.86083	+	7.03460i	0.296020	+	0.235010i
$897$	89.7626			2.99709
$898$	1.81584	+	4.92948i	0.0605955	+	0.164499i
$899$	35.0682	+	35.0682i	1.16959	+	1.16959i
$900$	−5.63011	+	4.79906i	−0.187670	+	0.159969i
$901$	−15.1161	+	15.1161i	−0.503591	+	0.503591i
$902$	−27.4287	+	59.4211i	−0.913276	+	1.97850i
$903$		−	24.6098i		−	0.818964i
$904$	0.0503815	+	0.0283121i	0.00167566	+	0.000941648i
$905$		−	1.81675i		−	0.0603907i
$906$	−6.49079	−	2.99614i	−0.215642	−	0.0995402i
$907$	15.9543	−	15.9543i	0.529754	−	0.529754i	−0.390745	−	0.920499i	$-0.627783\pi$
$907$	15.9543	−	15.9543i	0.529754	−	0.529754i	0.920499	+	0.390745i	$0.127783\pi$
$908$	−10.5790	−	0.842988i	−0.351075	−	0.0279755i
$909$	−39.2453	−	39.2453i	−1.30168	−	1.30168i
$910$	5.40815	−	1.99217i	0.179279	−	0.0660398i
$911$	−16.8240			−0.557405			−0.278702	−	0.960378i	$-0.589904\pi$
$911$	−16.8240			−0.557405			−0.278702	+	0.960378i	$0.589904\pi$
$912$	−33.4378	−	5.36306i	−1.10724	−	0.177589i
$913$	19.2978			0.638664
$914$	−8.64819	+	3.18568i	−0.286057	+	0.105373i
$915$	−3.86277	−	3.86277i	−0.127699	−	0.127699i
$916$	2.27043	−	28.4924i	0.0750171	−	0.941416i
$917$	−6.12669	+	6.12669i	−0.202321	+	0.202321i
$918$	−8.23639	−	3.80191i	−0.271842	−	0.125482i
$919$		−	51.5219i		−	1.69955i	−0.527144	−	0.849776i	$-0.676737\pi$
$919$		−	51.5219i		−	1.69955i	0.527144	−	0.849776i	$-0.323263\pi$
$920$	6.49955	+	23.1757i	0.214284	+	0.764079i
$921$			31.1797i			1.02741i
$922$	−1.83408	+	3.97331i	−0.0604021	+	0.130854i
$923$	−28.8064	+	28.8064i	−0.948173	+	0.948173i
$924$	−13.8164	−	16.2089i	−0.454525	−	0.533235i
$925$	−6.77129	−	6.77129i	−0.222639	−	0.222639i
$926$	−10.2095	−	27.7158i	−0.335506	−	0.910799i
$927$	−35.7970			−1.17573
$928$	35.5557	+	23.8834i	1.16717	+	0.784012i
$929$	50.8534			1.66845			0.834223	−	0.551427i	$-0.185916\pi$
$929$	50.8534			1.66845			0.834223	+	0.551427i	$0.185916\pi$
$930$	−8.28697	−	22.4967i	−0.271740	−	0.737695i
$931$	−2.31299	−	2.31299i	−0.0758053	−	0.0758053i
$932$	34.0882	+	39.9913i	1.11660	+	1.30996i
$933$	28.8907	−	28.8907i	0.945838	−	0.945838i
$934$	10.3445	−	22.4100i	0.338481	−	0.733279i
$935$			14.5890i			0.477111i
$936$	−41.0533	+	11.5133i	−1.34187	+	0.376323i
$937$			3.95662i			0.129257i	0.997909	+	0.0646286i	$0.0205863\pi$
$937$			3.95662i			0.129257i	−0.997909	+	0.0646286i	$0.979414\pi$
$938$	−4.72494	−	2.18103i	−0.154275	−	0.0712131i
$939$	20.4262	−	20.4262i	0.666584	−	0.666584i
$940$	−0.843338	+	10.5834i	−0.0275067	+	0.345191i
$941$	4.40405	+	4.40405i	0.143568	+	0.143568i	0.775238	−	0.631670i	$-0.217630\pi$
$941$	4.40405	+	4.40405i	0.143568	+	0.143568i	−0.631670	+	0.775238i	$0.717630\pi$
$942$	−41.2679	+	15.2016i	−1.34458	+	0.495296i
$943$	−95.7158			−3.11694
$944$	−16.2986	−	22.5256i	−0.530474	−	0.733144i
$945$	1.80906			0.0588488
$946$	51.9162	−	19.1241i	1.68794	−	0.621777i
$947$	4.49491	+	4.49491i	0.146065	+	0.146065i	0.776358	−	0.630293i	$-0.217065\pi$
$947$	4.49491	+	4.49491i	0.146065	+	0.146065i	−0.630293	+	0.776358i	$0.717065\pi$
$948$	−1.27212	−	0.101369i	−0.0413165	−	0.00329232i
$949$	−22.1489	+	22.1489i	−0.718983	+	0.718983i
$950$	−4.20011	−	1.93877i	−0.136270	−	0.0629019i
$951$			80.7115i			2.61725i
$952$	−4.91320	+	8.74306i	−0.159238	+	0.283364i
$953$		−	33.6811i		−	1.09104i	−0.838098	−	0.545520i	$-0.816332\pi$
$953$		−	33.6811i		−	1.09104i	0.838098	−	0.545520i	$-0.183668\pi$
$954$	−13.2178	+	28.6348i	−0.427941	+	0.927085i
$955$	6.50813	−	6.50813i	0.210598	−	0.210598i
$956$	25.4106	−	21.6598i	0.821838	−	0.700528i
$957$	−57.0164	−	57.0164i	−1.84308	−	1.84308i
$958$	2.81569	+	7.64378i	0.0909710	+	0.246959i
$959$	6.04952			0.195349
$960$	−10.7670	−	17.6863i	−0.347503	−	0.570823i
$961$	11.9003			0.383880
$962$	−19.0771	−	51.7888i	−0.615072	−	1.66974i
$963$	−8.43104	−	8.43104i	−0.271687	−	0.271687i
$964$	6.47020	−	5.51515i	0.208391	−	0.177631i
$965$	−16.4579	+	16.4579i	−0.529800	+	0.529800i
$966$	13.0547	−	28.2815i	0.420029	−	0.909943i
$967$		−	7.56797i		−	0.243369i	−0.992569	−	0.121685i	$-0.961170\pi$
$967$		−	7.56797i		−	0.243369i	0.992569	−	0.121685i	$-0.0388297\pi$
$968$	8.21521	−	14.6190i	0.264047	−	0.469872i
$969$		−	30.0196i		−	0.964370i
$970$	−11.9129	−	5.49898i	−0.382500	−	0.176562i
$971$	−43.1957	+	43.1957i	−1.38622	+	1.38622i	−0.553108	+	0.833110i	$0.686558\pi$
$971$	−43.1957	+	43.1957i	−1.38622	+	1.38622i	−0.833110	+	0.553108i	$0.813442\pi$
$972$	43.9201	+	3.49979i	1.40874	+	0.112256i
$973$	5.16514	+	5.16514i	0.165587	+	0.165587i
$974$	−37.4995	+	13.8135i	−1.20156	+	0.442613i
$975$	−10.5479			−0.337805
$976$	6.83981	−	4.94901i	0.218937	−	0.158414i
$977$	35.4986			1.13570			0.567851	−	0.823131i	$-0.307775\pi$
$977$	35.4986			1.13570			0.567851	+	0.823131i	$0.307775\pi$
$978$	−2.39674	+	0.882874i	−0.0766393	+	0.0282312i
$979$	−23.0591	−	23.0591i	−0.736971	−	0.736971i
$980$	0.158867	−	1.99368i	0.00507482	−	0.0636858i
$981$	−34.1109	+	34.1109i	−1.08908	+	1.08908i
$982$	33.9108	+	15.6532i	1.08214	+	0.499514i
$983$			2.44975i			0.0781348i	0.999237	+	0.0390674i	$0.0124387\pi$
$983$			2.44975i			0.0781348i	−0.999237	+	0.0390674i	$0.987561\pi$
$984$	79.2801	−	22.2339i	2.52736	−	0.708790i
$985$			1.14423i			0.0364583i
$986$	−15.9128	+	34.4733i	−0.506767	+	1.09785i
$987$	9.71531	−	9.71531i	0.309242	−	0.309242i
$988$	−17.2954	−	20.2904i	−0.550240	−	0.645525i
$989$	57.2160	+	57.2160i	1.81936	+	1.81936i
$990$	7.43968	+	20.1965i	0.236449	+	0.641888i
$991$	−43.9845			−1.39722			−0.698608	−	0.715505i	$-0.746197\pi$
$991$	−43.9845			−1.39722			−0.698608	+	0.715505i	$0.746197\pi$
$992$	36.3571	−	7.13955i	1.15434	−	0.226681i
$993$	−45.5969			−1.44697
$994$	4.88654	+	13.2655i	0.154992	+	0.420756i
$995$	−8.32031	−	8.32031i	−0.263772	−	0.263772i
$996$	−15.7498	−	18.4772i	−0.499052	−	0.585472i
$997$	−29.2477	+	29.2477i	−0.926285	+	0.926285i	−0.997464	−	0.0711789i	$-0.977324\pi$
$997$	−29.2477	+	29.2477i	−0.926285	+	0.926285i	0.0711789	+	0.997464i	$0.477324\pi$
$998$	−7.59444	+	16.4525i	−0.240398	+	0.520793i
$999$		−	17.3237i		−	0.548097i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bd.b.141.11	✓	52
4.3	odd	2		2240.2.bd.b.1681.24		52
16.5	even	4	inner	560.2.bd.b.421.11	yes	52
16.11	odd	4		2240.2.bd.b.561.24		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.b.141.11	✓	52	1.1	even	1	trivial
560.2.bd.b.421.11	yes	52	16.5	even	4	inner
2240.2.bd.b.561.24		52	16.11	odd	4
2240.2.bd.b.1681.24		52	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.488835 - 1.32704i) q^{2} +(-1.83016 - 1.83016i) q^{3} +(-1.52208 + 1.29741i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.53405 + 3.32334i) q^{6} +1.00000i q^{7} +(2.46576 + 1.38565i) q^{8} +3.69896i q^{9} +O(q^{10})\)	\(q+(-0.488835 - 1.32704i) q^{2} +(-1.83016 - 1.83016i) q^{3} +(-1.52208 + 1.29741i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.53405 + 3.32334i) q^{6} +1.00000i q^{7} +(2.46576 + 1.38565i) q^{8} +3.69896i q^{9} +(-1.28402 - 0.592702i) q^{10} +(-2.90936 + 2.90936i) q^{11} +(5.16011 + 0.411185i) q^{12} +(2.88170 + 2.88170i) q^{13} +(1.32704 - 0.488835i) q^{14} -2.58823 q^{15} +(0.633460 - 3.94952i) q^{16} +3.54579 q^{17} +(4.90867 - 1.80818i) q^{18} +(2.31299 + 2.31299i) q^{19} +(-0.158867 + 1.99368i) q^{20} +(1.83016 - 1.83016i) q^{21} +(5.28305 + 2.43865i) q^{22} +8.50997i q^{23} +(-1.97678 - 7.04869i) q^{24} -1.00000i q^{25} +(2.41546 - 5.23282i) q^{26} +(1.27920 - 1.27920i) q^{27} +(-1.29741 - 1.52208i) q^{28} +(-5.35406 - 5.35406i) q^{29} +(1.26522 + 3.43470i) q^{30} -6.54983 q^{31} +(-5.55084 + 1.09004i) q^{32} +10.6492 q^{33} +(-1.73330 - 4.70541i) q^{34} +(0.707107 + 0.707107i) q^{35} +(-4.79906 - 5.63011i) q^{36} +(6.77129 - 6.77129i) q^{37} +(1.93877 - 4.20011i) q^{38} -10.5479i q^{39} +(2.72336 - 0.763757i) q^{40} +11.2475i q^{41} +(-3.32334 - 1.53405i) q^{42} +(6.72342 - 6.72342i) q^{43} +(0.653652 - 8.20292i) q^{44} +(2.61556 + 2.61556i) q^{45} +(11.2931 - 4.15997i) q^{46} +5.30845 q^{47} +(-8.38758 + 6.06892i) q^{48} -1.00000 q^{49} +(-1.32704 + 0.488835i) q^{50} +(-6.48935 - 6.48935i) q^{51} +(-8.12493 - 0.647438i) q^{52} +(-4.26312 + 4.26312i) q^{53} +(-2.32287 - 1.07223i) q^{54} +4.11446i q^{55} +(-1.38565 + 2.46576i) q^{56} -8.46629i q^{57} +(-4.48781 + 9.72232i) q^{58} +(4.91504 - 4.91504i) q^{59} +(3.93950 - 3.35800i) q^{60} +(1.49244 + 1.49244i) q^{61} +(3.20179 + 8.69190i) q^{62} -3.69896 q^{63} +(4.15997 + 6.83335i) q^{64} +4.07534 q^{65} +(-5.20570 - 14.1319i) q^{66} +(-2.60202 - 2.60202i) q^{67} +(-5.39697 + 4.60033i) q^{68} +(15.5746 - 15.5746i) q^{69} +(0.592702 - 1.28402i) q^{70} +9.99630i q^{71} +(-5.12544 + 9.12075i) q^{72} +7.68603i q^{73} +(-12.2958 - 5.67575i) q^{74} +(-1.83016 + 1.83016i) q^{75} +(-6.52146 - 0.519665i) q^{76} +(-2.90936 - 2.90936i) q^{77} +(-13.9976 + 5.15620i) q^{78} -0.246529 q^{79} +(-2.34481 - 3.24066i) q^{80} +6.41459 q^{81} +(14.9259 - 5.49817i) q^{82} +(-3.31650 - 3.31650i) q^{83} +(-0.411185 + 5.16011i) q^{84} +(2.50725 - 2.50725i) q^{85} +(-12.2089 - 5.63562i) q^{86} +19.5976i q^{87} +(-11.2051 + 3.14245i) q^{88} +7.92581i q^{89} +(2.19238 - 4.74953i) q^{90} +(-2.88170 + 2.88170i) q^{91} +(-11.0409 - 12.9529i) q^{92} +(11.9872 + 11.9872i) q^{93} +(-2.59496 - 7.04454i) q^{94} +3.27107 q^{95} +(12.1539 + 8.16397i) q^{96} +9.27782 q^{97} +(0.488835 + 1.32704i) q^{98} +(-10.7616 - 10.7616i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 8 q^{4} + 12 q^{6}+O(q^{10}) \) 52 * q - 8 * q^4 + 12 * q^6	\( 52 q - 8 q^{4} + 12 q^{6} - 4 q^{10} - 4 q^{11} + 40 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{19} + 32 q^{22} + 12 q^{24} - 12 q^{26} - 24 q^{27} + 4 q^{28} + 4 q^{29} - 16 q^{34} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 4 q^{42} + 36 q^{43} + 28 q^{44} - 16 q^{46} + 32 q^{48} - 52 q^{49} - 8 q^{51} - 80 q^{52} - 4 q^{53} + 48 q^{54} - 12 q^{56} - 56 q^{58} + 24 q^{59} - 16 q^{61} - 72 q^{62} - 68 q^{63} + 4 q^{64} + 40 q^{65} - 12 q^{66} - 12 q^{67} - 72 q^{69} - 8 q^{72} + 68 q^{74} - 4 q^{77} - 4 q^{78} - 16 q^{79} - 32 q^{80} - 116 q^{81} + 104 q^{82} + 16 q^{85} - 68 q^{86} - 48 q^{88} + 36 q^{90} + 64 q^{92} + 8 q^{93} - 72 q^{94} - 32 q^{95} - 52 q^{99}+O(q^{100}) \) 52 * q - 8 * q^4 + 12 * q^6 - 4 * q^10 - 4 * q^11 + 40 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^19 + 32 * q^22 + 12 * q^24 - 12 * q^26 - 24 * q^27 + 4 * q^28 + 4 * q^29 - 16 * q^34 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 4 * q^42 + 36 * q^43 + 28 * q^44 - 16 * q^46 + 32 * q^48 - 52 * q^49 - 8 * q^51 - 80 * q^52 - 4 * q^53 + 48 * q^54 - 12 * q^56 - 56 * q^58 + 24 * q^59 - 16 * q^61 - 72 * q^62 - 68 * q^63 + 4 * q^64 + 40 * q^65 - 12 * q^66 - 12 * q^67 - 72 * q^69 - 8 * q^72 + 68 * q^74 - 4 * q^77 - 4 * q^78 - 16 * q^79 - 32 * q^80 - 116 * q^81 + 104 * q^82 + 16 * q^85 - 68 * q^86 - 48 * q^88 + 36 * q^90 + 64 * q^92 + 8 * q^93 - 72 * q^94 - 32 * q^95 - 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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