LMFDB - Embedded newform 770.2.o.a.439.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(439,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 3]))

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

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

chi := DirichletCharacter("770.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.3
Character	$\chi$	$=$	770.439
Dual form			770.2.o.a.549.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.44024 - 2.49457i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.16254 - 0.568686i) q^{5} +2.88048 q^{6} +(-0.391243 - 2.61666i) q^{7} +1.00000 q^{8} +(-2.64857 + 4.58746i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.44024 - 2.49457i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.16254 - 0.568686i) q^{5} +2.88048 q^{6} +(-0.391243 - 2.61666i) q^{7} +1.00000 q^{8} +(-2.64857 + 4.58746i) q^{9} +(1.57377 - 1.58848i) q^{10} +(-3.21810 - 0.802409i) q^{11} +(-1.44024 + 2.49457i) q^{12} -6.76312i q^{13} +(2.46172 + 0.969505i) q^{14} +(1.69596 + 6.21365i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.33823 - 0.772629i) q^{17} +(-2.64857 - 4.58746i) q^{18} +(0.445529 - 0.771679i) q^{19} +(0.588776 + 2.15716i) q^{20} +(-5.96396 + 4.74460i) q^{21} +(2.30395 - 2.38575i) q^{22} +(-6.17407 - 3.56460i) q^{23} +(-1.44024 - 2.49457i) q^{24} +(4.35319 + 2.45962i) q^{25} +(5.85703 + 3.38156i) q^{26} +6.61688 q^{27} +(-2.07048 + 1.64716i) q^{28} +2.79982i q^{29} +(-6.22916 - 1.63809i) q^{30} +(0.849237 - 0.490307i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.63316 + 9.18341i) q^{33} +1.54526i q^{34} +(-0.641979 + 5.88114i) q^{35} +5.29715 q^{36} +(8.14224 + 4.70093i) q^{37} +(0.445529 + 0.771679i) q^{38} +(-16.8710 + 9.74050i) q^{39} +(-2.16254 - 0.568686i) q^{40} +8.03479 q^{41} +(-1.12697 - 7.53724i) q^{42} +0.302038 q^{43} +(0.914142 + 3.18816i) q^{44} +(8.33648 - 8.41439i) q^{45} +(6.17407 - 3.56460i) q^{46} +(-5.24754 + 9.08901i) q^{47} +2.88048 q^{48} +(-6.69386 + 2.04750i) q^{49} +(-4.30669 + 2.54017i) q^{50} +(-3.85475 - 2.22554i) q^{51} +(-5.85703 + 3.38156i) q^{52} +(-4.89115 + 2.82391i) q^{53} +(-3.30844 + 5.73039i) q^{54} +(6.50296 + 3.56533i) q^{55} +(-0.391243 - 2.61666i) q^{56} -2.56667 q^{57} +(-2.42472 - 1.39991i) q^{58} +(3.61218 - 2.08549i) q^{59} +(4.53320 - 4.57557i) q^{60} +(0.226973 - 0.393129i) q^{61} +0.980614i q^{62} +(13.0401 + 5.13561i) q^{63} +1.00000 q^{64} +(-3.84609 + 14.6255i) q^{65} +(-9.26965 - 2.31132i) q^{66} +(8.39321 - 4.84582i) q^{67} +(-1.33823 - 0.772629i) q^{68} +20.5355i q^{69} +(-4.77223 - 3.49654i) q^{70} -4.72658 q^{71} +(-2.64857 + 4.58746i) q^{72} +(2.80161 - 1.61751i) q^{73} +(-8.14224 + 4.70093i) q^{74} +(-0.133963 - 14.4018i) q^{75} -0.891058 q^{76} +(-0.840576 + 8.73461i) q^{77} -19.4810i q^{78} +(-7.09357 - 4.09547i) q^{79} +(1.57377 - 1.58848i) q^{80} +(-1.58417 - 2.74386i) q^{81} +(-4.01739 + 6.95833i) q^{82} -4.01538i q^{83} +(7.09092 + 2.79264i) q^{84} +(-3.33337 + 0.909810i) q^{85} +(-0.151019 + 0.261573i) q^{86} +(6.98434 - 4.03241i) q^{87} +(-3.21810 - 0.802409i) q^{88} +(6.83580 + 3.94665i) q^{89} +(3.11883 + 11.4268i) q^{90} +(-17.6968 + 2.64602i) q^{91} +7.12921i q^{92} +(-2.44621 - 1.41232i) q^{93} +(-5.24754 - 9.08901i) q^{94} +(-1.40232 + 1.41542i) q^{95} +(-1.44024 + 2.49457i) q^{96} -19.1494 q^{97} +(1.57374 - 6.82080i) q^{98} +(12.2044 - 12.6377i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9}+O(q^{10}) $ 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9	$ 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9} + 6 q^{10} + q^{11} + 2 q^{14} + 4 q^{15} - 24 q^{16} - 28 q^{18} - 2 q^{22} - 6 q^{26} + 2 q^{28} - 2 q^{30} + 12 q^{31} - 24 q^{32} + 24 q^{33} - 8 q^{35} + 56 q^{36} - 6 q^{40} + 24 q^{43} + q^{44} + 6 q^{45} - 36 q^{49} + 6 q^{52} - 4 q^{56} - 4 q^{57} - 2 q^{60} - 52 q^{63} + 48 q^{64} - 24 q^{66} - 2 q^{70} - 40 q^{71} - 28 q^{72} + 42 q^{73} + 90 q^{75} + 19 q^{77} + 6 q^{80} - 72 q^{81} - 40 q^{85} - 12 q^{86} + 18 q^{87} + q^{88} + 60 q^{89} - 56 q^{91} + 24 q^{95} + 42 q^{98} - 58 q^{99}+O(q^{100}) $ 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9 + 6 * q^10 + q^11 + 2 * q^14 + 4 * q^15 - 24 * q^16 - 28 * q^18 - 2 * q^22 - 6 * q^26 + 2 * q^28 - 2 * q^30 + 12 * q^31 - 24 * q^32 + 24 * q^33 - 8 * q^35 + 56 * q^36 - 6 * q^40 + 24 * q^43 + q^44 + 6 * q^45 - 36 * q^49 + 6 * q^52 - 4 * q^56 - 4 * q^57 - 2 * q^60 - 52 * q^63 + 48 * q^64 - 24 * q^66 - 2 * q^70 - 40 * q^71 - 28 * q^72 + 42 * q^73 + 90 * q^75 + 19 * q^77 + 6 * q^80 - 72 * q^81 - 40 * q^85 - 12 * q^86 + 18 * q^87 + q^88 + 60 * q^89 - 56 * q^91 + 24 * q^95 + 42 * q^98 - 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.44024	−	2.49457i	−0.831522	−	1.44024i	−0.896831	−	0.442373i	$-0.854137\pi$
$3$	−1.44024	−	2.49457i	−0.831522	−	1.44024i	0.0653088	−	0.997865i	$-0.479197\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.16254	−	0.568686i	−0.967119	−	0.254324i
$5$	−2.16254	−	0.568686i	−0.967119	−	0.254324i
$6$	2.88048			1.17595
$7$	−0.391243	−	2.61666i	−0.147876	−	0.989006i
$7$	−0.391243	−	2.61666i	−0.147876	−	0.989006i
$8$	1.00000			0.353553
$9$	−2.64857	+	4.58746i	−0.882858	+	1.52915i
$10$	1.57377	−	1.58848i	0.497669	−	0.502320i
$11$	−3.21810	−	0.802409i	−0.970292	−	0.241935i
$11$	−3.21810	−	0.802409i	−0.970292	−	0.241935i
$12$	−1.44024	+	2.49457i	−0.415761	+	0.720119i
$13$		−	6.76312i		−	1.87575i	−0.346972	−	0.937875i	$-0.612790\pi$
$13$		−	6.76312i		−	1.87575i	0.346972	−	0.937875i	$-0.387210\pi$
$14$	2.46172	+	0.969505i	0.657922	+	0.259111i
$15$	1.69596	+	6.21365i	0.437894	+	1.60436i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.33823	−	0.772629i	0.324569	−	0.187390i	−0.328858	−	0.944379i	$-0.606664\pi$
$17$	1.33823	−	0.772629i	0.324569	−	0.187390i	0.653427	+	0.756989i	$0.273331\pi$
$18$	−2.64857	−	4.58746i	−0.624275	−	1.08128i
$19$	0.445529	−	0.771679i	0.102211	−	0.177035i	−0.810384	−	0.585899i	$-0.800742\pi$
$19$	0.445529	−	0.771679i	0.102211	−	0.177035i	0.912595	+	0.408864i	$0.134075\pi$
$20$	0.588776	+	2.15716i	0.131654	+	0.482356i
$21$	−5.96396	+	4.74460i	−1.30144	+	1.03536i
$22$	2.30395	−	2.38575i	0.491205	−	0.508643i
$23$	−6.17407	−	3.56460i	−1.28738	−	0.743271i	−0.309197	−	0.950998i	$-0.600060\pi$
$23$	−6.17407	−	3.56460i	−1.28738	−	0.743271i	−0.978187	+	0.207727i	$0.933393\pi$
$24$	−1.44024	−	2.49457i	−0.293987	−	0.509201i
$25$	4.35319	+	2.45962i	0.870639	+	0.491923i
$26$	5.85703	+	3.38156i	1.14866	+	0.663178i
$27$	6.61688			1.27342
$28$	−2.07048	+	1.64716i	−0.391283	+	0.311284i
$29$			2.79982i			0.519914i	0.965620	+	0.259957i	$0.0837084\pi$
$29$			2.79982i			0.519914i	−0.965620	+	0.259957i	$0.916292\pi$
$30$	−6.22916	−	1.63809i	−1.13728	−	0.299072i
$31$	0.849237	−	0.490307i	0.152527	−	0.0880618i	−0.421794	−	0.906692i	$-0.638599\pi$
$31$	0.849237	−	0.490307i	0.152527	−	0.0880618i	0.574321	+	0.818630i	$0.305266\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	2.63316	+	9.18341i	0.458375	+	1.59863i
$34$			1.54526i			0.265009i
$35$	−0.641979	+	5.88114i	−0.108514	+	0.994095i
$36$	5.29715			0.882858
$37$	8.14224	+	4.70093i	1.33858	+	0.772828i	0.986596	−	0.163180i	$-0.0521751\pi$
$37$	8.14224	+	4.70093i	1.33858	+	0.772828i	0.351980	+	0.936007i	$0.385508\pi$
$38$	0.445529	+	0.771679i	0.0722743	+	0.125183i
$39$	−16.8710	+	9.74050i	−2.70153	+	1.55973i
$40$	−2.16254	−	0.568686i	−0.341928	−	0.0899171i
$41$	8.03479			1.25482			0.627412	−	0.778688i	$-0.284114\pi$
$41$	8.03479			1.25482			0.627412	+	0.778688i	$0.284114\pi$
$42$	−1.12697	−	7.53724i	−0.173895	−	1.16302i
$43$	0.302038			0.0460604			0.0230302	−	0.999735i	$-0.492669\pi$
$43$	0.302038			0.0460604			0.0230302	+	0.999735i	$0.492669\pi$
$44$	0.914142	+	3.18816i	0.137812	+	0.480633i
$45$	8.33648	−	8.41439i	1.24273	−	1.25434i
$46$	6.17407	−	3.56460i	0.910317	−	0.525572i
$47$	−5.24754	+	9.08901i	−0.765433	+	1.32577i	0.174584	+	0.984642i	$0.444142\pi$
$47$	−5.24754	+	9.08901i	−0.765433	+	1.32577i	−0.940017	+	0.341127i	$0.889191\pi$
$48$	2.88048			0.415761
$49$	−6.69386	+	2.04750i	−0.956265	+	0.292500i
$50$	−4.30669	+	2.54017i	−0.609057	+	0.359234i
$51$	−3.85475	−	2.22554i	−0.539773	−	0.311638i
$52$	−5.85703	+	3.38156i	−0.812224	+	0.468938i
$53$	−4.89115	+	2.82391i	−0.671851	+	0.387893i	−0.796778	−	0.604273i	$-0.793464\pi$
$53$	−4.89115	+	2.82391i	−0.671851	+	0.387893i	0.124927	+	0.992166i	$0.460130\pi$
$54$	−3.30844	+	5.73039i	−0.450222	+	0.779807i
$55$	6.50296	+	3.56533i	0.876858	+	0.480749i
$56$	−0.391243	−	2.61666i	−0.0522820	−	0.349666i
$57$	−2.56667			−0.339964
$58$	−2.42472	−	1.39991i	−0.318381	−	0.183817i
$59$	3.61218	−	2.08549i	0.470266	−	0.271508i	−0.246085	−	0.969248i	$-0.579144\pi$
$59$	3.61218	−	2.08549i	0.470266	−	0.271508i	0.716351	+	0.697740i	$0.245811\pi$
$60$	4.53320	−	4.57557i	0.585234	−	0.590703i
$61$	0.226973	−	0.393129i	0.0290609	−	0.0503350i	−0.851129	−	0.524956i	$-0.824082\pi$
$61$	0.226973	−	0.393129i	0.0290609	−	0.0503350i	0.880190	+	0.474621i	$0.157415\pi$
$62$			0.980614i			0.124538i
$63$	13.0401	+	5.13561i	1.64290	+	0.647027i
$64$	1.00000			0.125000
$65$	−3.84609	+	14.6255i	−0.477048	+	1.81407i
$66$	−9.26965	−	2.31132i	−1.14102	−	0.284504i
$67$	8.39321	−	4.84582i	1.02539	−	0.592012i	0.109732	−	0.993961i	$-0.465001\pi$
$67$	8.39321	−	4.84582i	1.02539	−	0.592012i	0.915662	+	0.401950i	$0.131667\pi$
$68$	−1.33823	−	0.772629i	−0.162285	−	0.0936950i
$69$			20.5355i			2.47219i
$70$	−4.77223	−	3.49654i	−0.570391	−	0.417917i
$71$	−4.72658			−0.560942			−0.280471	−	0.959863i	$-0.590491\pi$
$71$	−4.72658			−0.560942			−0.280471	+	0.959863i	$0.590491\pi$
$72$	−2.64857	+	4.58746i	−0.312137	+	0.540638i
$73$	2.80161	−	1.61751i	0.327904	−	0.189316i	−0.327006	−	0.945022i	$-0.606040\pi$
$73$	2.80161	−	1.61751i	0.327904	−	0.189316i	0.654910	+	0.755707i	$0.272706\pi$
$74$	−8.14224	+	4.70093i	−0.946517	+	0.546472i
$75$	−0.133963	−	14.4018i	−0.0154688	−	1.66297i
$76$	−0.891058			−0.102211
$77$	−0.840576	+	8.73461i	−0.0957926	+	0.995401i
$78$		−	19.4810i		−	2.20579i
$79$	−7.09357	−	4.09547i	−0.798089	−	0.460777i	0.0447138	−	0.999000i	$-0.485762\pi$
$79$	−7.09357	−	4.09547i	−0.798089	−	0.460777i	−0.842802	+	0.538223i	$0.819096\pi$
$80$	1.57377	−	1.58848i	0.175953	−	0.177597i
$81$	−1.58417	−	2.74386i	−0.176019	−	0.304873i
$82$	−4.01739	+	6.95833i	−0.443647	+	0.768419i
$83$		−	4.01538i		−	0.440745i	−0.975416	−	0.220373i	$-0.929273\pi$
$83$		−	4.01538i		−	0.440745i	0.975416	−	0.220373i	$-0.0707274\pi$
$84$	7.09092	+	2.79264i	0.773683	+	0.304702i
$85$	−3.33337	+	0.909810i	−0.361555	+	0.0986828i
$86$	−0.151019	+	0.261573i	−0.0162848	+	0.0282061i
$87$	6.98434	−	4.03241i	0.748800	−	0.432320i
$88$	−3.21810	−	0.802409i	−0.343050	−	0.0855371i
$89$	6.83580	+	3.94665i	0.724594	+	0.418344i	0.816441	−	0.577429i	$-0.195944\pi$
$89$	6.83580	+	3.94665i	0.724594	+	0.418344i	−0.0918474	+	0.995773i	$0.529277\pi$
$90$	3.11883	+	11.4268i	0.328754	+	1.20449i
$91$	−17.6968	+	2.64602i	−1.85513	+	0.277378i
$92$			7.12921i			0.743271i
$93$	−2.44621	−	1.41232i	−0.253660	−	0.146451i
$94$	−5.24754	−	9.08901i	−0.541243	−	0.937460i
$95$	−1.40232	+	1.41542i	−0.143875	+	0.145219i
$96$	−1.44024	+	2.49457i	−0.146994	+	0.254601i
$97$	−19.1494			−1.94432			−0.972162	−	0.234312i	$-0.924716\pi$
$97$	−19.1494			−1.94432			−0.972162	+	0.234312i	$0.924716\pi$
$98$	1.57374	−	6.82080i	0.158972	−	0.689005i
$99$	12.2044	−	12.6377i	1.22659	−	1.27013i
$100$	−0.0465074	−	4.99978i	−0.00465074	−	0.499978i
$101$	−5.11669	−	8.86237i	−0.509130	−	0.881839i	−0.999944	−	0.0105746i	$-0.996634\pi$
$101$	−5.11669	−	8.86237i	−0.509130	−	0.881839i	0.490814	−	0.871264i	$-0.336699\pi$
$102$	3.85475	−	2.22554i	0.381677	−	0.220361i
$103$	−1.03582	+	1.79408i	−0.102062	+	0.176776i	−0.912534	−	0.409001i	$-0.865877\pi$
$103$	−1.03582	+	1.79408i	−0.102062	+	0.176776i	0.810472	+	0.585777i	$0.199211\pi$
$104$		−	6.76312i		−	0.663178i
$105$	15.5955	−	6.86879i	1.52197	−	0.670326i
$106$		−	5.64781i		−	0.548564i
$107$	8.13821	−	14.0958i	0.786750	−	1.36269i	−0.141198	−	0.989981i	$-0.545095\pi$
$107$	8.13821	−	14.0958i	0.786750	−	1.36269i	0.927948	−	0.372710i	$-0.121571\pi$
$108$	−3.30844	−	5.73039i	−0.318355	−	0.551407i
$109$	12.3584	−	7.13512i	1.18372	−	0.683421i	0.226847	−	0.973930i	$-0.427158\pi$
$109$	12.3584	−	7.13512i	1.18372	−	0.683421i	0.956872	+	0.290510i	$0.0938249\pi$
$110$	−6.33914	+	3.84906i	−0.604414	+	0.366993i
$111$		−	27.0818i		−	2.57049i
$112$	2.46172	+	0.969505i	0.232611	+	0.0916097i
$113$		−	2.93230i		−	0.275848i	−0.990443	−	0.137924i	$-0.955957\pi$
$113$		−	2.93230i		−	0.275848i	0.990443	−	0.137924i	$-0.0440429\pi$
$114$	1.28334	−	2.22280i	0.120195	−	0.208185i
$115$	11.3246	+	11.2197i	1.05602	+	1.04624i
$116$	2.42472	−	1.39991i	0.225129	−	0.129978i
$117$	31.0256	+	17.9126i	2.86831	+	1.65602i
$118$			4.17099i			0.383970i
$119$	−2.54528	−	3.19942i	−0.233326	−	0.293290i
$120$	1.69596	+	6.21365i	0.154819	+	0.567226i
$121$	9.71228	+	5.16446i	0.882935	+	0.469496i
$122$	0.226973	+	0.393129i	0.0205492	+	0.0355922i
$123$	−11.5720	−	20.0433i	−1.04341	−	1.80724i
$124$	−0.849237	−	0.490307i	−0.0762637	−	0.0440309i
$125$	−8.01522	−	7.79462i	−0.716903	−	0.697172i
$126$	−10.9676	+	8.72524i	−0.977073	+	0.777306i
$127$	−11.9466			−1.06009			−0.530044	−	0.847970i	$-0.677825\pi$
$127$	−11.9466			−1.06009			−0.530044	+	0.847970i	$0.677825\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−0.435007	−	0.753454i	−0.0383002	−	0.0663379i
$130$	−10.7430	−	10.6436i	−0.942227	−	0.933503i
$131$	2.49012	−	4.31301i	0.217563	−	0.376830i	−0.736500	−	0.676438i	$-0.763523\pi$
$131$	2.49012	−	4.31301i	0.217563	−	0.376830i	0.954062	+	0.299608i	$0.0968560\pi$
$132$	6.63649	−	6.87209i	0.577632	−	0.598139i
$133$	−2.19353	−	0.863885i	−0.190203	−	0.0749083i
$134$			9.69165i			0.837231i
$135$	−14.3093	−	3.76293i	−1.23155	−	0.323861i
$136$	1.33823	−	0.772629i	0.114752	−	0.0662524i
$137$	−9.98924	+	5.76729i	−0.853439	+	0.492733i	−0.861810	−	0.507232i	$-0.830669\pi$
$137$	−9.98924	+	5.76729i	−0.853439	+	0.492733i	0.00837103	+	0.999965i	$0.497335\pi$
$138$	−17.7843	−	10.2678i	−1.51390	−	0.874050i
$139$	0.172337			0.0146175			0.00730873	−	0.999973i	$-0.497674\pi$
$139$	0.172337			0.0146175			0.00730873	+	0.999973i	$0.497674\pi$
$140$	5.41421	−	2.38460i	0.457584	−	0.201536i
$141$	30.2309			2.54590
$142$	2.36329	−	4.09334i	0.198323	−	0.343505i
$143$	−5.42678	+	21.7644i	−0.453810	+	1.82003i
$144$	−2.64857	−	4.58746i	−0.220715	−	0.382289i
$145$	1.59222	−	6.05474i	0.132227	−	0.502819i
$146$			3.23503i			0.267733i
$147$	14.7484	+	13.7494i	1.21643	+	1.13403i
$148$		−	9.40185i		−	0.772828i
$149$	0.339030	+	0.195739i	0.0277744	+	0.0160356i	0.513823	−	0.857896i	$-0.328229\pi$
$149$	0.339030	+	0.195739i	0.0277744	+	0.0160356i	−0.486049	+	0.873932i	$0.661562\pi$
$150$	12.5393	+	7.08487i	1.02383	+	0.578477i
$151$	2.34480	−	1.35377i	0.190818	−	0.110169i	−0.401548	−	0.915838i	$-0.631528\pi$
$151$	2.34480	−	1.35377i	0.190818	−	0.110169i	0.592365	+	0.805670i	$0.298194\pi$
$152$	0.445529	−	0.771679i	0.0361372	−	0.0625914i
$153$			8.18546i			0.661755i
$154$	−7.14411	−	5.09527i	−0.575689	−	0.410588i
$155$	−2.11534	+	0.577362i	−0.169908	+	0.0463748i
$156$	16.8710	+	9.74050i	1.35076	+	0.779864i
$157$	−3.34433	−	5.79255i	−0.266907	−	0.462296i	0.701155	−	0.713009i	$-0.252668\pi$
$157$	−3.34433	−	5.79255i	−0.266907	−	0.462296i	−0.968061	+	0.250713i	$0.919335\pi$
$158$	7.09357	−	4.09547i	0.564334	−	0.325818i
$159$	14.0888	+	8.13419i	1.11732	+	0.645084i
$160$	0.588776	+	2.15716i	0.0465468	+	0.170539i
$161$	−6.91180	+	17.5501i	−0.544726	+	1.38314i
$162$	3.16833			0.248928
$163$	−13.3290	−	7.69553i	−1.04401	−	0.602760i	−0.123044	−	0.992401i	$-0.539266\pi$
$163$	−13.3290	−	7.69553i	−1.04401	−	0.602760i	−0.920967	+	0.389641i	$0.872599\pi$
$164$	−4.01739	−	6.95833i	−0.313706	−	0.543354i
$165$	−0.471858	−	21.3570i	−0.0367341	−	1.66264i
$166$	3.47742	+	2.00769i	0.269900	+	0.155827i
$167$			2.67400i			0.206920i	0.994634	+	0.103460i	$0.0329914\pi$
$167$			2.67400i			0.206920i	−0.994634	+	0.103460i	$0.967009\pi$
$168$	−5.96396	+	4.74460i	−0.460129	+	0.366054i
$169$	−32.7397			−2.51844
$170$	0.878766	−	3.34169i	0.0673983	−	0.256296i
$171$	2.36003	+	4.08770i	0.180476	+	0.312594i
$172$	−0.151019	−	0.261573i	−0.0115151	−	0.0199447i
$173$	18.2861	+	10.5575i	1.39027	+	0.802671i	0.993344	−	0.115181i	$-0.0367449\pi$
$173$	18.2861	+	10.5575i	1.39027	+	0.802671i	0.396922	+	0.917852i	$0.370078\pi$
$174$			8.06482i			0.611393i
$175$	4.73283	−	12.3532i	0.357768	−	0.933810i
$176$	2.30395	−	2.38575i	0.173667	−	0.179833i
$177$	−10.4048	−	6.00721i	−0.782073	−	0.451530i
$178$	−6.83580	+	3.94665i	−0.512365	+	0.295814i
$179$	4.39977	+	7.62063i	0.328854	+	0.569592i	0.982285	−	0.187394i	$-0.0600042\pi$
$179$	4.39977	+	7.62063i	0.328854	+	0.569592i	−0.653431	+	0.756986i	$0.726671\pi$
$180$	−11.4553	−	3.01241i	−0.853829	−	0.224532i
$181$		−	5.30776i		−	0.394523i	−0.980351	−	0.197261i	$-0.936795\pi$
$181$		−	5.30776i		−	0.394523i	0.980351	−	0.197261i	$-0.0632048\pi$
$182$	6.55688	−	16.6489i	0.486028	−	1.23410i
$183$	−1.30758			−0.0966592
$184$	−6.17407	−	3.56460i	−0.455159	−	0.262786i
$185$	−14.9346	−	14.7963i	−1.09801	−	1.08785i
$186$	2.44621	−	1.41232i	0.179365	−	0.103556i
$187$	−4.92652	+	1.41258i	−0.360263	+	0.103298i
$188$	10.4951			0.765433
$189$	−2.58881	−	17.3142i	−0.188308	−	1.25942i
$190$	−0.524633	−	1.92215i	−0.0380609	−	0.139448i
$191$	−3.95152	+	6.84423i	−0.285922	+	0.495231i	−0.972832	−	0.231511i	$-0.925633\pi$
$191$	−3.95152	+	6.84423i	−0.285922	+	0.495231i	0.686910	+	0.726742i	$0.258966\pi$
$192$	−1.44024	−	2.49457i	−0.103940	−	0.180030i
$193$	7.13707	+	12.3618i	0.513738	+	0.889820i	0.999873	+	0.0159362i	$0.00507285\pi$
$193$	7.13707	+	12.3618i	0.513738	+	0.889820i	−0.486135	+	0.873884i	$0.661594\pi$
$194$	9.57468	−	16.5838i	0.687422	−	1.19065i
$195$	42.0236	−	11.4699i	3.00938	−	0.821380i
$196$	5.12012	+	4.77330i	0.365723	+	0.340950i
$197$	−24.2556			−1.72814			−0.864071	−	0.503369i	$-0.832093\pi$
$197$	−24.2556			−1.72814			−0.864071	+	0.503369i	$0.832093\pi$
$198$	4.84234	+	16.8881i	0.344130	+	1.20019i
$199$	9.10776	−	5.25837i	0.645632	−	0.372756i	−0.141149	−	0.989988i	$-0.545080\pi$
$199$	9.10776	−	5.25837i	0.645632	−	0.372756i	0.786781	+	0.617233i	$0.211746\pi$
$200$	4.35319	+	2.45962i	0.307817	+	0.173921i
$201$	−24.1765	−	13.9583i	−1.70528	−	0.984541i
$202$	10.2334			0.720018
$203$	7.32619	−	1.09541i	0.514198	−	0.0768828i
$204$			4.45108i			0.311638i
$205$	−17.3756	−	4.56927i	−1.21356	−	0.319132i
$206$	−1.03582	−	1.79408i	−0.0721687	−	0.125000i
$207$	32.7050	−	18.8822i	2.27315	−	1.31241i
$208$	5.85703	+	3.38156i	0.406112	+	0.234469i
$209$	−2.05296	+	2.12584i	−0.142006	+	0.147047i
$210$	−1.84920	+	16.9405i	−0.127607	+	1.16901i
$211$			7.05248i			0.485513i	0.970087	+	0.242756i	$0.0780516\pi$
$211$			7.05248i			0.485513i	−0.970087	+	0.242756i	$0.921948\pi$
$212$	4.89115	+	2.82391i	0.335925	+	0.193947i
$213$	6.80740	+	11.7908i	0.466435	+	0.807890i
$214$	8.13821	+	14.0958i	0.556316	+	0.963568i
$215$	−0.653171	−	0.171765i	−0.0445459	−	0.0117143i
$216$	6.61688			0.450222
$217$	−1.61523	−	2.03034i	−0.109649	−	0.137828i
$218$			14.2702i			0.966503i
$219$	−8.06998	−	4.65921i	−0.545319	−	0.314840i
$220$	−0.163812	−	7.41439i	−0.0110442	−	0.499878i
$221$	−5.22538	−	9.05062i	−0.351497	−	0.608811i
$222$	23.4535	+	13.5409i	1.57410	+	0.908807i
$223$	14.8664			0.995529			0.497765	−	0.867312i	$-0.334154\pi$
$223$	14.8664			0.995529			0.497765	+	0.867312i	$0.334154\pi$
$224$	−2.07048	+	1.64716i	−0.138339	+	0.110055i
$225$	−22.8132	+	13.4556i	−1.52088	+	0.897043i
$226$	2.53945	+	1.46615i	0.168922	+	0.0975269i
$227$	6.23204	−	3.59807i	0.413635	−	0.238812i	−0.278715	−	0.960374i	$-0.589909\pi$
$227$	6.23204	−	3.59807i	0.413635	−	0.238812i	0.692350	+	0.721562i	$0.256575\pi$
$228$	1.28334	+	2.22280i	0.0849910	+	0.147209i
$229$	−6.72483	−	3.88258i	−0.444390	−	0.256568i	0.261068	−	0.965320i	$-0.415925\pi$
$229$	−6.72483	−	3.88258i	−0.444390	−	0.256568i	−0.705458	+	0.708752i	$0.749259\pi$
$230$	−15.3788	+	4.19750i	−1.01405	+	0.276775i
$231$	22.9997	−	10.4831i	1.51327	−	0.689734i
$232$			2.79982i			0.183817i
$233$	1.44473	−	2.50235i	0.0946474	−	0.163934i	−0.814814	−	0.579723i	$-0.803161\pi$
$233$	1.44473	−	2.50235i	0.0946474	−	0.163934i	0.909461	+	0.415788i	$0.136494\pi$
$234$	−31.0256	+	17.9126i	−2.02820	+	1.17098i
$235$	16.5168	−	16.6712i	1.07744	−	1.08751i
$236$	−3.61218	−	2.08549i	−0.235133	−	0.135754i
$237$			23.5938i			1.53258i
$238$	4.04342	−	0.604571i	0.262096	−	0.0391885i
$239$			21.5057i			1.39109i	0.718484	+	0.695544i	$0.244836\pi$
$239$			21.5057i			1.39109i	−0.718484	+	0.695544i	$0.755164\pi$
$240$	−6.22916	−	1.63809i	−0.402090	−	0.105738i
$241$	10.4728	+	18.1393i	0.674609	+	1.16846i	0.976583	+	0.215142i	$0.0690213\pi$
$241$	10.4728	+	18.1393i	0.674609	+	1.16846i	−0.301973	+	0.953316i	$0.597645\pi$
$242$	−9.32869	+	5.82885i	−0.599671	+	0.374693i
$243$	5.36217	−	9.28755i	0.343983	−	0.595796i
$244$	−0.453946			−0.0290609
$245$	15.6401	−	0.621115i	0.999212	−	0.0396816i
$246$	23.1440			1.47561
$247$	−5.21895	−	3.01316i	−0.332074	−	0.191723i
$248$	0.849237	−	0.490307i	0.0539266	−	0.0311345i
$249$	−10.0166	+	5.78311i	−0.634779	+	0.366490i
$250$	10.7580	−	3.04408i	0.680393	−	0.192524i
$251$		−	11.5989i		−	0.732115i	−0.930592	−	0.366057i	$-0.880707\pi$
$251$		−	11.5989i		−	0.732115i	0.930592	−	0.366057i	$-0.119293\pi$
$252$	−2.07247	−	13.8609i	−0.130553	−	0.873152i
$253$	17.0085	+	16.4254i	1.06931	+	1.03265i
$254$	5.97330	−	10.3461i	0.374798	−	0.649169i
$255$	7.07043	+	7.00497i	0.442767	+	0.438668i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.24197	+	9.07936i	−0.326985	+	0.566355i	−0.981912	−	0.189337i	$-0.939366\pi$
$257$	−5.24197	+	9.07936i	−0.326985	+	0.566355i	0.654927	+	0.755692i	$0.272699\pi$
$258$	0.870014			0.0541647
$259$	9.11515	−	23.1447i	0.566388	−	1.43814i
$260$	14.5891	−	3.98196i	0.904779	−	0.246951i
$261$	−12.8441	−	7.41554i	−0.795029	−	0.459010i
$262$	2.49012	+	4.31301i	0.153840	+	0.266459i
$263$	8.33780	+	14.4415i	0.514131	+	0.890500i	0.999866	+	0.0163943i	$0.00521869\pi$
$263$	8.33780	+	14.4415i	0.514131	+	0.890500i	−0.485735	+	0.874106i	$0.661448\pi$
$264$	2.63316	+	9.18341i	0.162060	+	0.565200i
$265$	12.1832	−	3.32529i	0.748410	−	0.204271i
$266$	1.84491	−	1.46771i	0.113119	−	0.0899913i
$267$		−	22.7365i		−	1.39145i
$268$	−8.39321	−	4.84582i	−0.512697	−	0.296006i
$269$	3.39881	−	1.96231i	0.207229	−	0.119644i	−0.392794	−	0.919627i	$-0.628491\pi$
$269$	3.39881	−	1.96231i	0.207229	−	0.119644i	0.600023	+	0.799983i	$0.295158\pi$
$270$	10.4134	−	10.5108i	0.633742	−	0.639664i
$271$	4.29650	−	7.44176i	0.260994	−	0.452055i	−0.705512	−	0.708698i	$-0.749283\pi$
$271$	4.29650	−	7.44176i	0.260994	−	0.452055i	0.966506	+	0.256643i	$0.0826164\pi$
$272$			1.54526i			0.0936950i
$273$	32.0883	+	40.3349i	1.94207	+	2.44118i
$274$		−	11.5346i		−	0.696830i
$275$	−12.0354	−	11.4083i	−0.725760	−	0.687947i
$276$	17.7843	−	10.2678i	1.07049	−	0.618046i
$277$	−14.4256	−	24.9858i	−0.866748	−	1.50125i	−0.865301	−	0.501252i	$-0.832873\pi$
$277$	−14.4256	−	24.9858i	−0.866748	−	1.50125i	−0.00144636	−	0.999999i	$-0.500460\pi$
$278$	−0.0861686	+	0.149248i	−0.00516805	+	0.00895133i
$279$			5.19446i			0.310984i
$280$	−0.641979	+	5.88114i	−0.0383656	+	0.351466i
$281$		−	19.7917i		−	1.18068i	−0.807156	−	0.590338i	$-0.798994\pi$
$281$		−	19.7917i		−	1.18068i	0.807156	−	0.590338i	$-0.201006\pi$
$282$	−15.1154	+	26.1807i	−0.900111	+	1.55904i
$283$	−26.0932	+	15.0649i	−1.55108	+	0.895518i	−0.553028	+	0.833162i	$0.686528\pi$
$283$	−26.0932	+	15.0649i	−1.55108	+	0.895518i	−0.998054	+	0.0623554i	$0.980139\pi$
$284$	2.36329	+	4.09334i	0.140235	+	0.242895i
$285$	5.55054	+	1.45963i	0.328786	+	0.0864610i
$286$	−16.1351	−	15.5819i	−0.954088	−	0.921378i
$287$	−3.14356	−	21.0243i	−0.185558	−	1.24103i
$288$	5.29715			0.312137
$289$	−7.30609	+	12.6545i	−0.429770	+	0.744383i
$290$	4.44745	+	4.40627i	0.261163	+	0.258745i
$291$	27.5796	+	47.7694i	1.61675	+	2.80029i
$292$	−2.80161	−	1.61751i	−0.163952	−	0.0946578i
$293$		−	2.94700i		−	0.172165i	−0.996288	−	0.0860827i	$-0.972565\pi$
$293$		−	2.94700i		−	0.172165i	0.996288	−	0.0860827i	$-0.0274349\pi$
$294$	−19.2815	+	5.89779i	−1.12452	+	0.343966i
$295$	−8.99749	+	2.45578i	−0.523854	+	0.142981i
$296$	8.14224	+	4.70093i	0.473258	+	0.273236i
$297$	−21.2938	−	5.30944i	−1.23559	−	0.308085i
$298$	−0.339030	+	0.195739i	−0.0196395	+	0.0113388i
$299$	−24.1078	+	41.7560i	−1.39419	+	2.41481i
$300$	−12.4053	+	7.31690i	−0.716221	+	0.422441i
$301$	−0.118170	−	0.790332i	−0.00681122	−	0.0455540i
$302$			2.70755i			0.155802i
$303$	−14.7385	+	25.5279i	−0.846706	+	1.46654i
$304$	0.445529	+	0.771679i	0.0255528	+	0.0442588i
$305$	−0.714406	+	0.721082i	−0.0409067	+	0.0412890i
$306$	−7.08881	−	4.09273i	−0.405241	−	0.233966i
$307$		−	27.4659i		−	1.56756i	−0.621039	−	0.783780i	$-0.713289\pi$
$307$		−	27.4659i		−	1.56756i	0.621039	−	0.783780i	$-0.286711\pi$
$308$	7.98468	−	3.63935i	0.454970	−	0.207371i
$309$	5.96728			0.339467
$310$	0.557661	−	2.12062i	0.0316730	−	0.120443i
$311$	−11.5613	+	6.67494i	−0.655584	+	0.378501i	−0.790592	−	0.612343i	$-0.790227\pi$
$311$	−11.5613	+	6.67494i	−0.655584	+	0.378501i	0.135009	+	0.990844i	$0.456894\pi$
$312$	−16.8710	+	9.74050i	−0.955135	+	0.551447i
$313$	14.1347	−	24.4821i	0.798942	−	1.38381i	−0.121364	−	0.992608i	$-0.538727\pi$
$313$	14.1347	−	24.4821i	0.798942	−	1.38381i	0.920306	−	0.391200i	$-0.127940\pi$
$314$	6.68866			0.377463
$315$	−25.2792	−	18.5217i	−1.42432	−	1.04358i
$316$			8.19094i			0.460777i
$317$	−20.4874	−	11.8284i	−1.15069	−	0.664349i	−0.201632	−	0.979461i	$-0.564624\pi$
$317$	−20.4874	−	11.8284i	−1.15069	−	0.664349i	−0.949054	+	0.315112i	$0.897958\pi$
$318$	−14.0888	+	8.13419i	−0.790063	+	0.456143i
$319$	2.24660	−	9.01010i	0.125786	−	0.504469i
$320$	−2.16254	−	0.568686i	−0.120890	−	0.0317905i
$321$	−46.8838			−2.61680
$322$	−11.7429	−	14.7608i	−0.654408	−	0.822590i
$323$		−	1.37691i		−	0.0766135i
$324$	−1.58417	+	2.74386i	−0.0880093	+	0.152437i
$325$	16.6347	−	29.4411i	0.922725	−	1.63310i
$326$	13.3290	−	7.69553i	0.738227	−	0.426216i
$327$	−35.5981	−	20.5525i	−1.96858	−	1.13656i
$328$	8.03479			0.443647
$329$	25.8360	+	10.1750i	1.42438	+	0.560968i
$330$	18.7316	+	10.2698i	1.03114	+	0.565337i
$331$	−7.28149	+	12.6119i	−0.400227	+	0.693213i	−0.993753	−	0.111602i	$-0.964402\pi$
$331$	−7.28149	+	12.6119i	−0.400227	+	0.693213i	0.593526	+	0.804815i	$0.297735\pi$
$332$	−3.47742	+	2.00769i	−0.190848	+	0.110186i
$333$	−43.1307	+	24.9015i	−2.36355	+	1.36459i
$334$	−2.31575	−	1.33700i	−0.126712	−	0.0731573i
$335$	−20.9064	+	5.70621i	−1.14224	+	0.311763i
$336$	−1.12697	−	7.53724i	−0.0614811	−	0.411190i
$337$	19.9023			1.08415			0.542074	−	0.840331i	$-0.317639\pi$
$337$	19.9023			1.08415			0.542074	+	0.840331i	$0.317639\pi$
$338$	16.3699	−	28.3534i	0.890403	−	1.54222i
$339$	−7.31482	+	4.22321i	−0.397286	+	0.229373i
$340$	2.45460	+	2.43188i	0.133120	+	0.131887i
$341$	−3.12635	+	0.896420i	−0.169301	+	0.0485439i
$342$	−4.72006			−0.255232
$343$	7.97655	+	16.7145i	0.430693	+	0.902498i
$344$	0.302038			0.0162848
$345$	11.6783	−	44.4090i	0.628736	−	2.39090i
$346$	−18.2861	+	10.5575i	−0.983067	+	0.567574i
$347$	8.44426	+	14.6259i	0.453312	+	0.785159i	0.998589	−	0.0530967i	$-0.0169092\pi$
$347$	8.44426	+	14.6259i	0.453312	+	0.785159i	−0.545278	+	0.838255i	$0.683576\pi$
$348$	−6.98434	−	4.03241i	−0.374400	−	0.216160i
$349$	−29.0093			−1.55283			−0.776417	−	0.630219i	$-0.782965\pi$
$349$	−29.0093			−1.55283			−0.776417	+	0.630219i	$0.782965\pi$
$350$	8.33173	+	10.2753i	0.445350	+	0.549239i
$351$		−	44.7507i		−	2.38862i
$352$	0.914142	+	3.18816i	0.0487239	+	0.169929i
$353$	−6.99148	−	12.1096i	−0.372119	−	0.644528i	0.617773	−	0.786357i	$-0.288035\pi$
$353$	−6.99148	−	12.1096i	−0.372119	−	0.644528i	−0.989891	+	0.141828i	$0.954702\pi$
$354$	10.4048	−	6.00721i	0.553009	−	0.319280i
$355$	10.2214	+	2.68794i	0.542497	+	0.142661i
$356$		−	7.89331i		−	0.418344i
$357$	−4.31535	+	10.9573i	−0.228392	+	0.579922i
$358$	−8.79954			−0.465070
$359$	−22.9522	−	13.2514i	−1.21137	−	0.699384i	−0.248311	−	0.968680i	$-0.579876\pi$
$359$	−22.9522	−	13.2514i	−1.21137	−	0.699384i	−0.963057	+	0.269296i	$0.913209\pi$
$360$	8.33648	−	8.41439i	0.439371	−	0.443477i
$361$	9.10301	+	15.7669i	0.479106	+	0.829835i
$362$	4.59666	+	2.65388i	0.241595	+	0.139485i
$363$	−1.10492	−	31.6660i	−0.0579933	−	1.66203i
$364$	11.1399	+	14.0029i	0.583891	+	0.733950i
$365$	−6.97847	+	1.90470i	−0.365270	+	0.0996968i
$366$	0.653790	−	1.13240i	0.0341742	−	0.0591914i
$367$	−14.0582	−	24.3495i	−0.733832	−	1.27103i	−0.955234	−	0.295851i	$-0.904397\pi$
$367$	−14.0582	−	24.3495i	−0.733832	−	1.27103i	0.221402	−	0.975183i	$-0.428937\pi$
$368$	6.17407	−	3.56460i	0.321846	−	0.185818i
$369$	−21.2807	+	36.8593i	−1.10783	+	1.91882i
$370$	20.2813	−	5.53558i	1.05438	−	0.287781i
$371$	9.30284	+	11.6937i	0.482979	+	0.607104i
$372$			2.82464i			0.146451i
$373$	−7.76959	+	13.4573i	−0.402294	+	0.696793i	−0.994002	−	0.109359i	$-0.965120\pi$
$373$	−7.76959	+	13.4573i	−0.402294	+	0.696793i	0.591708	+	0.806152i	$0.298454\pi$
$374$	1.23993	−	4.97279i	0.0641152	−	0.257137i
$375$	−7.90037	+	31.2206i	−0.407973	+	1.61223i
$376$	−5.24754	+	9.08901i	−0.270621	+	0.468730i
$377$	18.9355			0.975229
$378$	16.2889	+	6.41510i	0.837811	+	0.329957i
$379$	−22.9334			−1.17801			−0.589004	−	0.808130i	$-0.700480\pi$
$379$	−22.9334			−1.17801			−0.589004	+	0.808130i	$0.700480\pi$
$380$	1.92695	+	0.506732i	0.0988505	+	0.0259948i
$381$	17.2059	+	29.8016i	0.881487	+	1.52678i
$382$	−3.95152	−	6.84423i	−0.202177	−	0.350181i
$383$	−14.9019	+	25.8109i	−0.761452	+	1.31887i	0.180649	+	0.983548i	$0.442180\pi$
$383$	−14.9019	+	25.8109i	−0.761452	+	1.31887i	−0.942102	+	0.335327i	$0.891153\pi$
$384$	2.88048			0.146994
$385$	6.78503	−	18.4110i	0.345797	−	0.938309i
$386$	−14.2741			−0.726535
$387$	−0.799970	+	1.38559i	−0.0406648	+	0.0704334i
$388$	9.57468	+	16.5838i	0.486081	+	0.841917i
$389$	10.7426	+	18.6067i	0.544670	+	0.943396i	0.998628	+	0.0523731i	$0.0166785\pi$
$389$	10.7426	+	18.6067i	0.544670	+	0.943396i	−0.453957	+	0.891023i	$0.649988\pi$
$390$	−11.0786	+	42.1285i	−0.560985	+	2.13326i
$391$	−11.0165			−0.557126
$392$	−6.69386	+	2.04750i	−0.338091	+	0.103415i
$393$	−14.3455			−0.723633
$394$	12.1278	−	21.0060i	0.610991	−	1.05827i
$395$	13.0111	+	12.8906i	0.654660	+	0.648599i
$396$	−17.0467	−	4.25048i	−0.856630	−	0.213595i
$397$	−16.2517	+	28.1488i	−0.815652	+	1.41275i	0.0932073	+	0.995647i	$0.470288\pi$
$397$	−16.2517	+	28.1488i	−0.815652	+	1.41275i	−0.908859	+	0.417103i	$0.863045\pi$
$398$			10.5167i			0.527156i
$399$	1.00419	+	6.71611i	0.0502725	+	0.336226i
$400$	−4.30669	+	2.54017i	−0.215334	+	0.127008i
$401$	−11.1849	+	19.3728i	−0.558546	+	0.967430i	0.439072	+	0.898452i	$0.355307\pi$
$401$	−11.1849	+	19.3728i	−0.558546	+	0.967430i	−0.997618	+	0.0689781i	$0.978026\pi$
$402$	24.1765	−	13.9583i	1.20581	−	0.696176i
$403$	−3.31600	−	5.74349i	−0.165182	−	0.286104i
$404$	−5.11669	+	8.86237i	−0.254565	+	0.440919i
$405$	1.86544	+	6.83460i	0.0926944	+	0.339614i
$406$	−2.71444	+	6.89238i	−0.134716	+	0.342063i
$407$	−22.4305	−	21.6614i	−1.11184	−	1.07372i
$408$	−3.85475	−	2.22554i	−0.190838	−	0.110181i
$409$	9.53760	+	16.5196i	0.471604	+	0.816842i	0.999472	−	0.0324840i	$-0.0103418\pi$
$409$	9.53760	+	16.5196i	0.471604	+	0.816842i	−0.527868	+	0.849326i	$0.677008\pi$
$410$	12.6449	−	12.7631i	0.624487	−	0.630323i
$411$	28.7738	+	16.6126i	1.41931	+	0.819437i
$412$	2.07163			0.102062
$413$	−6.87027	−	8.63592i	−0.338064	−	0.424946i
$414$			37.7645i			1.85602i
$415$	−2.28349	+	8.68344i	−0.112092	+	0.426253i
$416$	−5.85703	+	3.38156i	−0.287165	+	0.165795i
$417$	−0.248207	−	0.429907i	−0.0121547	−	0.0210526i
$418$	−0.814553	−	2.84083i	−0.0398411	−	0.138950i
$419$		−	19.4987i		−	0.952574i	−0.879290	−	0.476287i	$-0.841982\pi$
$419$		−	19.4987i		−	0.952574i	0.879290	−	0.476287i	$-0.158018\pi$
$420$	−13.7463	−	10.0717i	−0.670751	−	0.491449i
$421$	7.90039			0.385041			0.192521	−	0.981293i	$-0.438334\pi$
$421$	7.90039			0.385041			0.192521	+	0.981293i	$0.438334\pi$
$422$	−6.10763	−	3.52624i	−0.297315	−	0.171655i
$423$	−27.7970	−	48.1459i	−1.35154	−	2.34093i
$424$	−4.89115	+	2.82391i	−0.237535	+	0.137141i
$425$	7.72595	−	0.0718659i	0.374764	−	0.00348601i
$426$	−13.6148			−0.659639
$427$	−1.11749	−	0.440103i	−0.0540790	−	0.0212981i
$428$	−16.2764			−0.786750
$429$	62.1085	−	17.8084i	2.99863	−	0.859797i
$430$	0.475338	−	0.479780i	0.0229228	−	0.0231370i
$431$	25.2940	−	14.6035i	1.21837	−	0.703425i	0.253800	−	0.967257i	$-0.418320\pi$
$431$	25.2940	−	14.6035i	1.21837	−	0.703425i	0.964569	+	0.263831i	$0.0849863\pi$
$432$	−3.30844	+	5.73039i	−0.159177	+	0.275703i
$433$	−17.6790			−0.849599			−0.424799	−	0.905287i	$-0.639655\pi$
$433$	−17.6790			−0.849599			−0.424799	+	0.905287i	$0.639655\pi$
$434$	2.56594	−	0.383659i	0.123169	−	0.0184162i
$435$	−17.3971	+	4.74837i	−0.834128	+	0.227667i
$436$	−12.3584	−	7.13512i	−0.591860	−	0.341710i
$437$	−5.50146	+	3.17627i	−0.263170	+	0.151941i
$438$	8.06998	−	4.65921i	0.385599	−	0.222626i
$439$	3.88898	−	6.73591i	0.185611	−	0.321488i	−0.758171	−	0.652055i	$-0.773907\pi$
$439$	3.88898	−	6.73591i	0.185611	−	0.321488i	0.943782	+	0.330568i	$0.107240\pi$
$440$	6.50296	+	3.56533i	0.310016	+	0.169970i
$441$	8.33633	−	36.1308i	0.396968	−	1.72051i
$442$	10.4508			0.497092
$443$	26.6196	+	15.3688i	1.26473	+	0.730195i	0.973987	−	0.226605i	$-0.0727627\pi$
$443$	26.6196	+	15.3688i	1.26473	+	0.730195i	0.290747	+	0.956800i	$0.406096\pi$
$444$	−23.4535	+	13.5409i	−1.11306	+	0.642623i
$445$	−12.5383	−	12.4222i	−0.594373	−	0.588870i
$446$	−7.43321	+	12.8747i	−0.351973	+	0.609635i
$447$		−	1.12764i		−	0.0533357i
$448$	−0.391243	−	2.61666i	−0.0184845	−	0.123626i
$449$	8.20812			0.387365			0.193682	−	0.981064i	$-0.437957\pi$
$449$	8.20812			0.387365			0.193682	+	0.981064i	$0.437957\pi$
$450$	−0.246357	−	26.4846i	−0.0116134	−	1.24850i
$451$	−25.8567	−	6.44718i	−1.21755	−	0.303586i
$452$	−2.53945	+	1.46615i	−0.119446	+	0.0689619i
$453$	−6.75416	−	3.89951i	−0.317338	−	0.183215i
$454$			7.19614i			0.337731i
$455$	39.7749	+	4.34178i	1.86467	+	0.203546i
$456$	−2.56667			−0.120195
$457$	−8.43227	+	14.6051i	−0.394445	+	0.683199i	−0.993030	−	0.117861i	$-0.962396\pi$
$457$	−8.43227	+	14.6051i	−0.394445	+	0.683199i	0.598585	+	0.801059i	$0.295730\pi$
$458$	6.72483	−	3.88258i	0.314231	−	0.181421i
$459$	8.85493	−	5.11239i	0.413313	−	0.238626i
$460$	4.05428	−	15.4172i	0.189032	−	0.718832i
$461$	−25.9736			−1.20971			−0.604856	−	0.796335i	$-0.706770\pi$
$461$	−25.9736			−1.20971			−0.604856	+	0.796335i	$0.706770\pi$
$462$	−2.42126	+	25.1598i	−0.112647	+	1.17054i
$463$		−	6.66326i		−	0.309668i	−0.987941	−	0.154834i	$-0.950516\pi$
$463$		−	6.66326i		−	0.309668i	0.987941	−	0.154834i	$-0.0494842\pi$
$464$	−2.42472	−	1.39991i	−0.112565	−	0.0649892i
$465$	4.48687	+	4.44532i	0.208073	+	0.206147i
$466$	1.44473	+	2.50235i	0.0669259	+	0.115919i
$467$	−4.29559	+	7.44018i	−0.198776	+	0.344290i	−0.948132	−	0.317877i	$-0.897030\pi$
$467$	−4.29559	+	7.44018i	−0.198776	+	0.344290i	0.749356	+	0.662168i	$0.230363\pi$
$468$		−	35.8252i		−	1.65602i
$469$	−15.9637	−	20.0663i	−0.737134	−	0.926577i
$470$	6.17926	+	22.6396i	0.285028	+	1.04429i
$471$	−9.63327	+	16.6853i	−0.443877	+	0.768818i
$472$	3.61218	−	2.08549i	0.166264	−	0.0959926i
$473$	−0.971987	−	0.242358i	−0.0446920	−	0.0111436i
$474$	−20.4329	−	11.7969i	−0.938512	−	0.541850i
$475$	3.83751	−	2.26344i	0.176077	−	0.103854i
$476$	−1.49814	+	3.80399i	−0.0686669	+	0.174356i
$477$		−	29.9173i		−	1.36982i
$478$	−18.6245	−	10.7528i	−0.851864	−	0.491824i
$479$	−9.15755	−	15.8613i	−0.418419	−	0.724723i	0.577362	−	0.816488i	$-0.304082\pi$
$479$	−9.15755	−	15.8613i	−0.418419	−	0.724723i	−0.995781	+	0.0917657i	$0.970749\pi$
$480$	4.53320	−	4.57557i	0.206911	−	0.208845i
$481$	31.7929	−	55.0669i	1.44963	−	2.51084i
$482$	−20.9455			−0.954042
$483$	53.7345	−	8.03438i	2.44501	−	0.365577i
$484$	−0.383590	−	10.9933i	−0.0174359	−	0.499696i
$485$	41.4113	+	10.8900i	1.88039	+	0.494488i
$486$	5.36217	+	9.28755i	0.243233	+	0.421292i
$487$	16.3775	−	9.45553i	0.742133	−	0.428471i	−0.0807111	−	0.996738i	$-0.525719\pi$
$487$	16.3775	−	9.45553i	0.742133	−	0.428471i	0.822844	+	0.568267i	$0.192386\pi$
$488$	0.226973	−	0.393129i	0.0102746	−	0.0177961i
$489$			44.3336i			2.00483i
$490$	−7.28217	+	13.8553i	−0.328975	+	0.625920i
$491$		−	2.08588i		−	0.0941345i	−0.998892	−	0.0470672i	$-0.985012\pi$
$491$		−	2.08588i		−	0.0941345i	0.998892	−	0.0470672i	$-0.0149875\pi$
$492$	−11.5720	+	20.0433i	−0.521707	+	0.903622i
$493$	2.16322	+	3.74681i	0.0974267	+	0.168748i
$494$	5.21895	−	3.01316i	0.234812	−	0.135569i
$495$	−33.5794	+	20.3890i	−1.50928	+	0.916419i
$496$			0.980614i			0.0440309i
$497$	1.84924	+	12.3679i	0.0829498	+	0.554775i
$498$		−	11.5662i		−	0.518295i
$499$	11.0473	−	19.1345i	0.494546	−	0.856580i	−0.505434	−	0.862865i	$-0.668668\pi$
$499$	11.0473	−	19.1345i	0.494546	−	0.856580i	0.999980	+	0.00628578i	$0.00200084\pi$
$500$	−2.74273	+	10.8387i	−0.122659	+	0.484721i
$501$	6.67046	−	3.85119i	0.298014	−	0.172059i
$502$	10.0449	+	5.79944i	0.448327	+	0.258842i
$503$		−	5.93021i		−	0.264415i	−0.991222	−	0.132208i	$-0.957793\pi$
$503$		−	5.93021i		−	0.264415i	0.991222	−	0.132208i	$-0.0422065\pi$
$504$	13.0401	+	5.13561i	0.580852	+	0.228758i
$505$	6.02517	+	22.0751i	0.268117	+	0.982327i
$506$	−22.7290	+	6.51710i	−1.01043	+	0.289721i
$507$	47.1530	+	81.6714i	2.09414	+	3.62716i
$508$	5.97330	+	10.3461i	0.265022	+	0.459032i
$509$	3.85268	+	2.22435i	0.170767	+	0.0985924i	0.582947	−	0.812510i	$-0.301899\pi$
$509$	3.85268	+	2.22435i	0.170767	+	0.0985924i	−0.412180	+	0.911102i	$0.635233\pi$
$510$	−9.60169	+	2.62069i	−0.425170	+	0.116046i
$511$	−5.32860	−	6.69804i	−0.235723	−	0.296304i
$512$	1.00000			0.0441942
$513$	2.94801	−	5.10611i	0.130158	−	0.225440i
$514$	−5.24197	−	9.07936i	−0.231213	−	0.400473i
$515$	3.26027	−	3.29073i	0.143665	−	0.145007i
$516$	−0.435007	+	0.753454i	−0.0191501	+	0.0331690i
$517$	24.1802	−	25.0386i	1.06344	−	1.10120i
$518$	15.4863	+	19.4663i	0.680431	+	0.855301i
$519$		−	60.8212i		−	2.66975i
$520$	−3.84609	+	14.6255i	−0.168662	+	0.641372i
$521$	36.9647	−	21.3416i	1.61945	−	0.934992i	0.632393	−	0.774647i	$-0.282073\pi$
$521$	36.9647	−	21.3416i	1.61945	−	0.934992i	0.987061	−	0.160345i	$-0.0512607\pi$
$522$	12.8441	−	7.41554i	0.562170	−	0.324569i
$523$	24.1037	+	13.9163i	1.05398	+	0.608517i	0.923762	−	0.382968i	$-0.125098\pi$
$523$	24.1037	+	13.9163i	1.05398	+	0.608517i	0.130221	+	0.991485i	$0.458431\pi$
$524$	−4.98024			−0.217563
$525$	−37.6322	+	5.98513i	−1.64240	+	0.261212i
$526$	−16.6756			−0.727091
$527$	0.757651	−	1.31229i	0.0330038	−	0.0571642i
$528$	−9.26965	−	2.31132i	−0.403410	−	0.100587i
$529$	13.9128	+	24.0977i	0.604904	+	1.04772i
$530$	−3.21183	+	12.2136i	−0.139513	+	0.530527i
$531$			22.0943i			0.958812i
$532$	0.348620	+	2.33160i	0.0151146	+	0.101088i
$533$		−	54.3402i		−	2.35374i
$534$	19.6904	+	11.3682i	0.852086	+	0.491952i
$535$	−25.6153	+	25.8547i	−1.10745	+	1.11780i
$536$	8.39321	−	4.84582i	0.362532	−	0.209308i
$537$	12.6734	−	21.9510i	0.546899	−	0.947257i
$538$			3.92461i			0.169202i
$539$	23.1844	−	1.21785i	0.998623	−	0.0524565i
$540$	3.89586	+	14.2737i	0.167651	+	0.614241i
$541$	2.72711	+	1.57450i	0.117248	+	0.0676930i	0.557477	−	0.830192i	$-0.311769\pi$
$541$	2.72711	+	1.57450i	0.117248	+	0.0676930i	−0.440229	+	0.897885i	$0.645103\pi$
$542$	4.29650	+	7.44176i	0.184550	+	0.319651i
$543$	−13.2406	+	7.64445i	−0.568207	+	0.328055i
$544$	−1.33823	−	0.772629i	−0.0573762	−	0.0331262i
$545$	−30.7832	+	8.40197i	−1.31861	+	0.359901i
$546$	−50.9752	+	7.62181i	−2.18154	+	0.326183i
$547$	34.6612			1.48201			0.741003	−	0.671501i	$-0.234350\pi$
$547$	34.6612			1.48201			0.741003	+	0.671501i	$0.234350\pi$
$548$	9.98924	+	5.76729i	0.426719	+	0.246366i
$549$	1.20231	+	2.08246i	0.0513133	+	0.0888773i
$550$	15.8976	−	4.71878i	0.677875	−	0.201210i
$551$	2.16056	+	1.24740i	0.0920431	+	0.0531411i
$552$			20.5355i			0.874050i
$553$	−7.94117	+	20.1638i	−0.337693	+	0.857452i
$554$	28.8511			1.22577
$555$	−15.4010	+	58.5656i	−0.653738	+	2.48597i
$556$	−0.0861686	−	0.149248i	−0.00365436	−	0.00632955i
$557$	9.14129	+	15.8332i	0.387329	+	0.670873i	0.992089	−	0.125534i	$-0.0400644\pi$
$557$	9.14129	+	15.8332i	0.387329	+	0.670873i	−0.604760	+	0.796407i	$0.706731\pi$
$558$	−4.49853	−	2.59723i	−0.190438	−	0.109950i
$559$		−	2.04272i		−	0.0863978i
$560$	−4.77223	−	3.49654i	−0.201664	−	0.147756i
$561$	10.6192	+	10.2551i	0.448341	+	0.432970i
$562$	17.1401	+	9.89587i	0.723014	+	0.417432i
$563$	−6.56375	+	3.78958i	−0.276629	+	0.159712i	−0.631896	−	0.775053i	$-0.717723\pi$
$563$	−6.56375	+	3.78958i	−0.276629	+	0.159712i	0.355267	+	0.934765i	$0.384390\pi$
$564$	−15.1154	−	26.1807i	−0.636475	−	1.10241i
$565$	−1.66756	+	6.34123i	−0.0701547	+	0.266778i
$566$		−	30.1299i		−	1.26645i
$567$	−6.55996	+	5.21875i	−0.275492	+	0.219167i
$568$	−4.72658			−0.198323
$569$	−12.8228	−	7.40323i	−0.537558	−	0.310359i	0.206530	−	0.978440i	$-0.433783\pi$
$569$	−12.8228	−	7.40323i	−0.537558	−	0.310359i	−0.744089	+	0.668081i	$0.767116\pi$
$570$	−4.03935	+	4.07709i	−0.169190	+	0.170771i
$571$	−37.1225	+	21.4327i	−1.55353	+	0.896930i	−0.555678	+	0.831397i	$0.687541\pi$
$571$	−37.1225	+	21.4327i	−1.55353	+	0.896930i	−0.997850	+	0.0655330i	$0.979125\pi$
$572$	21.5619	−	6.18244i	0.901547	−	0.258501i
$573$	22.7645			0.951002
$574$	19.7794	+	7.78977i	0.825576	+	0.325139i
$575$	−18.1094	−	30.7033i	−0.755214	−	1.28041i
$576$	−2.64857	+	4.58746i	−0.110357	+	0.191144i
$577$	−1.62463	−	2.81394i	−0.0676341	−	0.117146i	0.830225	−	0.557428i	$-0.188212\pi$
$577$	−1.62463	−	2.81394i	−0.0676341	−	0.117146i	−0.897859	+	0.440282i	$0.854878\pi$
$578$	−7.30609	−	12.6545i	−0.303893	−	0.526359i
$579$	20.5582	−	35.6078i	0.854368	−	1.47981i
$580$	−6.03967	+	1.64847i	−0.250784	+	0.0684489i
$581$	−10.5069	+	1.57099i	−0.435900	+	0.0651757i
$582$	−55.1593			−2.28643
$583$	18.0061	−	5.16290i	0.745737	−	0.213825i
$584$	2.80161	−	1.61751i	0.115932	−	0.0669331i
$585$	−56.9075	−	56.3806i	−2.35283	−	2.33105i
$586$	2.55217	+	1.47350i	0.105429	+	0.0608696i
$587$	−17.0225			−0.702593			−0.351296	−	0.936264i	$-0.614259\pi$
$587$	−17.0225			−0.702593			−0.351296	+	0.936264i	$0.614259\pi$
$588$	4.53312	−	19.6472i	0.186943	−	0.810235i
$589$		−	0.873784i		−	0.0360036i
$590$	2.37198	−	9.01994i	0.0976528	−	0.371345i
$591$	34.9339	+	60.5073i	1.43699	+	2.48894i
$592$	−8.14224	+	4.70093i	−0.334644	+	0.193207i
$593$	−17.0074	−	9.81923i	−0.698411	−	0.403228i	0.108345	−	0.994113i	$-0.465445\pi$
$593$	−17.0074	−	9.81923i	−0.698411	−	0.403228i	−0.806755	+	0.590886i	$0.798778\pi$
$594$	15.2450	−	15.7862i	0.625510	−	0.647716i
$595$	3.68483	+	8.36635i	0.151063	+	0.342987i
$596$		−	0.391478i		−	0.0160356i
$597$	−26.2347	−	15.1466i	−1.07371	−	0.619909i
$598$	−24.1078	−	41.7560i	−0.985842	−	1.70753i
$599$	−9.84488	−	17.0518i	−0.402251	−	0.696719i	0.591746	−	0.806124i	$-0.298439\pi$
$599$	−9.84488	−	17.0518i	−0.402251	−	0.696719i	−0.993997	+	0.109405i	$0.965105\pi$
$600$	−0.133963	−	14.4018i	−0.00546904	−	0.587949i
$601$	12.1124			0.494076			0.247038	−	0.969006i	$-0.420543\pi$
$601$	12.1124			0.494076			0.247038	+	0.969006i	$0.420543\pi$
$602$	0.743533	+	0.292828i	0.0303041	+	0.0119348i
$603$			51.3381i			2.09065i
$604$	−2.34480	−	1.35377i	−0.0954088	−	0.0550843i
$605$	−18.0663	−	16.6916i	−0.734499	−	0.678610i
$606$	−14.7385	−	25.5279i	−0.598711	−	1.03700i
$607$	−24.9376	−	14.3977i	−1.01219	−	0.584386i	−0.100355	−	0.994952i	$-0.531998\pi$
$607$	−24.9376	−	14.3977i	−1.01219	−	0.584386i	−0.911831	+	0.410566i	$0.865331\pi$
$608$	−0.891058			−0.0361372
$609$	−13.2840	−	16.6980i	−0.538297	−	0.676638i
$610$	−0.267272	−	0.979234i	−0.0108215	−	0.0396480i
$611$	61.4701	+	35.4898i	2.48681	+	1.43576i
$612$	7.08881	−	4.09273i	0.286548	−	0.165439i
$613$	18.5998	+	32.2158i	0.751240	+	1.30119i	0.947222	+	0.320578i	$0.103877\pi$
$613$	18.5998	+	32.2158i	0.751240	+	1.30119i	−0.195983	+	0.980607i	$0.562790\pi$
$614$	23.7861	+	13.7329i	0.959930	+	0.554216i
$615$	13.6266	+	49.9254i	0.549479	+	2.01319i
$616$	−0.840576	+	8.73461i	−0.0338678	+	0.351928i
$617$			3.41654i			0.137545i	0.997632	+	0.0687724i	$0.0219082\pi$
$617$			3.41654i			0.137545i	−0.997632	+	0.0687724i	$0.978092\pi$
$618$	−2.98364	+	5.16782i	−0.120020	+	0.207880i
$619$	−23.5560	+	13.6001i	−0.946796	+	0.546633i	−0.892084	−	0.451869i	$-0.850757\pi$
$619$	−23.5560	+	13.6001i	−0.946796	+	0.546633i	−0.0547120	+	0.998502i	$0.517424\pi$
$620$	1.55768	+	1.54326i	0.0625580	+	0.0619788i
$621$	−40.8531	−	23.5866i	−1.63938	−	0.946496i
$622$		−	13.3499i		−	0.535282i
$623$	7.65260	−	19.4311i	0.306595	−	0.778490i
$624$		−	19.4810i		−	0.779864i
$625$	12.9006	+	21.4144i	0.516023	+	0.856574i
$626$	14.1347	+	24.4821i	0.564937	+	0.978500i
$627$	8.25979	+	2.05952i	0.329864	+	0.0822493i
$628$	−3.34433	+	5.79255i	−0.133453	+	0.231148i
$629$	14.5283			0.579281
$630$	28.6799	−	12.6316i	1.14263	−	0.503255i
$631$	−7.01999			−0.279462			−0.139731	−	0.990190i	$-0.544624\pi$
$631$	−7.01999			−0.279462			−0.139731	+	0.990190i	$0.544624\pi$
$632$	−7.09357	−	4.09547i	−0.282167	−	0.162909i
$633$	17.5929	−	10.1573i	0.699254	−	0.403715i
$634$	20.4874	−	11.8284i	0.813658	−	0.469766i
$635$	25.8350	+	6.79385i	1.02523	+	0.269606i
$636$		−	16.2684i		−	0.645084i
$637$	13.8475	+	45.2713i	0.548658	+	1.79372i
$638$	6.67967	+	6.45066i	0.264451	+	0.255384i
$639$	12.5187	−	21.6830i	0.495232	−	0.857767i
$640$	1.57377	−	1.58848i	0.0622086	−	0.0627900i
$641$	15.7071	+	27.2055i	0.620393	+	1.07455i	0.989413	+	0.145131i	$0.0463602\pi$
$641$	15.7071	+	27.2055i	0.620393	+	1.07455i	−0.369020	+	0.929422i	$0.620306\pi$
$642$	23.4419	−	40.6026i	0.925179	−	1.60246i
$643$	−10.1418			−0.399953			−0.199976	−	0.979801i	$-0.564087\pi$
$643$	−10.1418			−0.399953			−0.199976	+	0.979801i	$0.564087\pi$
$644$	18.6547	−	2.78925i	0.735100	−	0.109912i
$645$	0.512243	+	1.87676i	0.0201696	+	0.0738973i
$646$	1.19244	+	0.688457i	0.0469160	+	0.0270870i
$647$	5.00464	+	8.66829i	0.196753	+	0.340786i	0.947474	−	0.319834i	$-0.103627\pi$
$647$	5.00464	+	8.66829i	0.196753	+	0.340786i	−0.750721	+	0.660619i	$0.770294\pi$
$648$	−1.58417	−	2.74386i	−0.0622319	−	0.107789i
$649$	−13.2978	+	3.81287i	−0.521983	+	0.149668i
$650$	17.1795	+	29.1266i	0.673834	+	1.14244i
$651$	−2.73850	+	6.95346i	−0.107330	+	0.272528i
$652$			15.3911i			0.602760i
$653$	8.60496	+	4.96807i	0.336738	+	0.194416i	0.658829	−	0.752293i	$-0.271052\pi$
$653$	8.60496	+	4.96807i	0.336738	+	0.194416i	−0.322091	+	0.946709i	$0.604386\pi$
$654$	35.5981	−	20.5525i	1.39199	−	0.803668i
$655$	−7.83774	+	7.91099i	−0.306246	+	0.309108i
$656$	−4.01739	+	6.95833i	−0.156853	+	0.271677i
$657$			17.1364i			0.668555i
$658$	−21.7298	+	17.2871i	−0.847117	+	0.673920i
$659$			16.9698i			0.661050i	0.943797	+	0.330525i	$0.107226\pi$
$659$			16.9698i			0.661050i	−0.943797	+	0.330525i	$0.892774\pi$
$660$	−18.2598	+	11.0871i	−0.710760	+	0.431566i
$661$	20.0753	−	11.5905i	0.780840	−	0.450818i	−0.0558878	−	0.998437i	$-0.517799\pi$
$661$	20.0753	−	11.5905i	0.780840	−	0.450818i	0.836728	+	0.547619i	$0.184466\pi$
$662$	−7.28149	−	12.6119i	−0.283003	−	0.490176i
$663$	−15.0516	+	26.0701i	−0.584555	+	1.01248i
$664$		−	4.01538i		−	0.155827i
$665$	4.25233	+	3.11562i	0.164898	+	0.120819i
$666$		−	49.8030i		−	1.92983i
$667$	9.98026	−	17.2863i	0.386437	−	0.669329i
$668$	2.31575	−	1.33700i	0.0895990	−	0.0517300i
$669$	−21.4112	−	37.0853i	−0.827805	−	1.43380i
$670$	5.51150	−	20.9586i	0.212928	−	0.809702i
$671$	−1.04587	+	1.08300i	−0.0403754	+	0.0418088i
$672$	7.09092	+	2.79264i	0.273538	+	0.107728i
$673$	21.1462			0.815127			0.407564	−	0.913177i	$-0.366378\pi$
$673$	21.1462			0.815127			0.407564	+	0.913177i	$0.366378\pi$
$674$	−9.95115	+	17.2359i	−0.383304	+	0.663902i
$675$	28.8046	+	16.2750i	1.10869	+	0.626424i
$676$	16.3699	+	28.3534i	0.629610	+	1.09052i
$677$	−25.4368	−	14.6859i	−0.977614	−	0.564426i	−0.0760650	−	0.997103i	$-0.524236\pi$
$677$	−25.4368	−	14.6859i	−0.977614	−	0.564426i	−0.901549	+	0.432677i	$0.857569\pi$
$678$		−	8.44643i		−	0.324383i
$679$	7.49205	+	50.1074i	0.287519	+	1.92295i
$680$	−3.33337	+	0.909810i	−0.127829	+	0.0348896i
$681$	−17.9512	−	10.3642i	−0.687893	−	0.397155i
$682$	0.786854	−	3.15571i	0.0301302	−	0.120838i
$683$	26.0105	−	15.0172i	0.995266	−	0.574617i	0.0884218	−	0.996083i	$-0.471818\pi$
$683$	26.0105	−	15.0172i	0.995266	−	0.574617i	0.906844	+	0.421466i	$0.138484\pi$
$684$	2.36003	−	4.08770i	0.0902381	−	0.156297i
$685$	24.8820	−	6.79128i	0.950690	−	0.259482i
$686$	−18.4635	−	1.44936i	−0.704938	−	0.0553366i
$687$			22.3674i			0.853369i
$688$	−0.151019	+	0.261573i	−0.00575755	+	0.00997236i
$689$	19.0984	+	33.0794i	0.727591	+	1.26022i
$690$	32.6202	+	32.3181i	1.24183	+	1.23033i
$691$	−1.98906	−	1.14838i	−0.0756673	−	0.0436865i	0.461689	−	0.887042i	$-0.347244\pi$
$691$	−1.98906	−	1.14838i	−0.0756673	−	0.0436865i	−0.537356	+	0.843355i	$0.680577\pi$
$692$		−	21.1150i		−	0.802671i
$693$	−37.8434	−	26.9904i	−1.43755	−	1.02528i
$694$	−16.8885			−0.641079
$695$	−0.372687	−	0.0980057i	−0.0141368	−	0.00371757i
$696$	6.98434	−	4.03241i	0.264741	−	0.152848i
$697$	10.7524	−	6.20791i	0.407277	−	0.235141i
$698$	14.5047	−	25.1228i	0.549010	−	0.950913i
$699$	−8.32303			−0.314806
$700$	−13.0646	+	2.07782i	−0.493794	+	0.0785344i
$701$		−	38.2267i		−	1.44380i	−0.691995	−	0.721902i	$-0.743268\pi$
$701$		−	38.2267i		−	1.44380i	0.691995	−	0.721902i	$-0.256732\pi$
$702$	38.7553	+	22.3754i	1.46272	+	0.844504i
$703$	7.25521	−	4.18880i	0.273635	−	0.157983i
$704$	−3.21810	−	0.802409i	−0.121287	−	0.0302419i
$705$	−65.3756	−	17.1919i	−2.46219	−	0.647483i
$706$	13.9830			0.526255
$707$	−21.1880	+	16.8560i	−0.796856	+	0.633935i
$708$			12.0144i			0.451530i
$709$	13.5481	−	23.4660i	0.508810	−	0.881285i	−0.491138	−	0.871082i	$-0.663419\pi$
$709$	13.5481	−	23.4660i	0.508810	−	0.881285i	0.999948	−	0.0102029i	$-0.00324772\pi$
$710$	−7.43854	+	7.50805i	−0.279163	+	0.281772i
$711$	37.5757	−	21.6943i	1.40920	−	0.813601i
$712$	6.83580	+	3.94665i	0.256183	+	0.147907i
$713$	−6.99100			−0.261815
$714$	−7.33163	−	9.21585i	−0.274379	−	0.344895i
$715$	24.1127	−	43.9802i	0.901765	−	1.64477i
$716$	4.39977	−	7.62063i	0.164427	−	0.284796i
$717$	53.6474	−	30.9733i	2.00350	−	1.15672i
$718$	22.9522	−	13.2514i	0.856567	−	0.494539i
$719$	−16.7058	−	9.64509i	−0.623021	−	0.359701i	0.155024	−	0.987911i	$-0.450455\pi$
$719$	−16.7058	−	9.64509i	−0.623021	−	0.359701i	−0.778044	+	0.628210i	$0.783788\pi$
$720$	3.11883	+	11.4268i	0.116232	+	0.425852i
$721$	5.09977	+	2.00846i	0.189925	+	0.0747989i
$722$	−18.2060			−0.677558
$723$	30.1665	−	52.2500i	1.12191	−	1.94320i
$724$	−4.59666	+	2.65388i	−0.170833	+	0.0986307i
$725$	−6.88649	+	12.1882i	−0.255758	+	0.452657i
$726$	27.9760	+	14.8761i	1.03829	+	0.552104i
$727$	−2.36203			−0.0876029			−0.0438015	−	0.999040i	$-0.513947\pi$
$727$	−2.36203			−0.0876029			−0.0438015	+	0.999040i	$0.513947\pi$
$728$	−17.6968	+	2.64602i	−0.655887	+	0.0980681i
$729$	−40.3962			−1.49616
$730$	1.83971	−	6.99588i	0.0680908	−	0.258929i
$731$	0.404197	−	0.233363i	0.0149498	−	0.00863125i
$732$	0.653790	+	1.13240i	0.0241648	+	0.0418546i
$733$	12.5500	+	7.24574i	0.463544	+	0.267627i	0.713533	−	0.700621i	$-0.247094\pi$
$733$	12.5500	+	7.24574i	0.463544	+	0.267627i	−0.249989	+	0.968249i	$0.580427\pi$
$734$	28.1164			1.03779
$735$	−24.0750	−	38.1208i	−0.888018	−	1.40611i
$736$			7.12921i			0.262786i
$737$	−30.8985	+	8.85954i	−1.13816	+	0.326345i
$738$	−21.2807	−	36.8593i	−0.783355	−	1.35681i
$739$	−4.01288	+	2.31684i	−0.147616	+	0.0852262i	−0.571989	−	0.820261i	$-0.693828\pi$
$739$	−4.01288	+	2.31684i	−0.147616	+	0.0852262i	0.424373	+	0.905488i	$0.360495\pi$
$740$	−5.34670	+	20.3319i	−0.196549	+	0.747416i
$741$			17.3587i			0.637688i
$742$	−14.7784	+	2.20967i	−0.542533	+	0.0811194i
$743$	30.3368			1.11295			0.556475	−	0.830864i	$-0.312153\pi$
$743$	30.3368			1.11295			0.556475	+	0.830864i	$0.312153\pi$
$744$	−2.44621	−	1.41232i	−0.0896823	−	0.0517781i
$745$	−0.621853	−	0.616095i	−0.0227829	−	0.0225720i
$746$	−7.76959	−	13.4573i	−0.284465	−	0.492707i
$747$	18.4204	+	10.6350i	0.673968	+	0.389116i
$748$	3.68660	+	3.56020i	0.134795	+	0.130174i
$749$	−40.0680	−	15.7801i	−1.46405	−	0.576591i
$750$	−23.0877	−	22.4522i	−0.843043	−	0.819840i
$751$	10.1668	−	17.6094i	0.370992	−	0.642577i	−0.618727	−	0.785606i	$-0.712351\pi$
$751$	10.1668	−	17.6094i	0.370992	−	0.642577i	0.989718	+	0.143030i	$0.0456844\pi$
$752$	−5.24754	−	9.08901i	−0.191358	−	0.331442i
$753$	−28.9342	+	16.7052i	−1.05442	+	0.608770i
$754$	−9.46776	+	16.3986i	−0.344796	+	0.597203i
$755$	−5.84062	+	1.59414i	−0.212562	+	0.0580166i
$756$	−13.7001	+	10.8991i	−0.498268	+	0.396395i
$757$			30.7879i			1.11901i	0.828828	+	0.559503i	$0.189008\pi$
$757$			30.7879i			1.11901i	−0.828828	+	0.559503i	$0.810992\pi$
$758$	11.4667	−	19.8609i	0.416488	−	0.721379i
$759$	16.4779	−	66.0853i	0.598109	−	2.39874i
$760$	−1.40232	+	1.41542i	−0.0508674	+	0.0513428i
$761$	19.2459	−	33.3348i	0.697662	−	1.20839i	−0.271614	−	0.962406i	$-0.587557\pi$
$761$	19.2459	−	33.3348i	0.697662	−	1.20839i	0.969275	−	0.245979i	$-0.0791094\pi$
$762$	−34.4119			−1.24661
$763$	−23.5053	−	29.5462i	−0.850951	−	1.06964i
$764$	7.90304			0.285922
$765$	4.65495	−	17.7014i	0.168300	−	0.639996i
$766$	−14.9019	−	25.8109i	−0.538428	−	0.932585i
$767$	−14.1044	−	24.4296i	−0.509281	−	0.882101i
$768$	−1.44024	+	2.49457i	−0.0519701	+	0.0900149i
$769$	29.6119			1.06783			0.533916	−	0.845537i	$-0.320720\pi$
$769$	29.6119			1.06783			0.533916	+	0.845537i	$0.320720\pi$
$770$	12.5518	+	15.0815i	0.452337	+	0.543499i
$771$	30.1988			1.08758
$772$	7.13707	−	12.3618i	0.256869	−	0.444910i
$773$	−18.4694	−	31.9899i	−0.664297	−	1.15060i	−0.979475	−	0.201563i	$-0.935398\pi$
$773$	−18.4694	−	31.9899i	−0.664297	−	1.15060i	0.315179	−	0.949032i	$-0.397936\pi$
$774$	−0.799970	−	1.38559i	−0.0287543	−	0.0498040i
$775$	4.90286	−	0.0456058i	0.176116	−	0.00163821i
$776$	−19.1494			−0.687422
$777$	−70.8640	+	10.5956i	−2.54223	+	0.380114i
$778$	−21.4852			−0.770280
$779$	3.57973	−	6.20027i	0.128257	−	0.222148i
$780$	−30.9451	−	30.6586i	−1.10801	−	1.09775i
$781$	15.2106	+	3.79265i	0.544277	+	0.135712i
$782$	5.50823	−	9.54053i	0.196974	−	0.341169i
$783$			18.5261i			0.662069i
$784$	1.57374	−	6.82080i	0.0562050	−	0.243600i
$785$	3.93812	+	14.4285i	0.140558	+	0.514976i
$786$	7.17273	−	12.4235i	0.255843	−	0.443133i
$787$	−31.4120	+	18.1357i	−1.11972	+	0.646469i	−0.941329	−	0.337491i	$-0.890422\pi$
$787$	−31.4120	+	18.1357i	−1.11972	+	0.646469i	−0.178389	+	0.983960i	$0.557088\pi$
$788$	12.1278	+	21.0060i	0.432036	+	0.748308i
$789$	24.0168	−	41.5984i	0.855022	−	1.48094i
$790$	−17.6692	+	4.82263i	−0.628641	+	0.171581i
$791$	−7.67285	+	1.14724i	−0.272815	+	0.0407912i
$792$	12.2044	−	12.6377i	0.433664	−	0.449060i
$793$	−2.65877	−	1.53504i	−0.0944159	−	0.0545110i
$794$	−16.2517	−	28.1488i	−0.576753	−	0.998965i
$795$	−25.8419	−	25.6027i	−0.916519	−	0.908033i
$796$	−9.10776	−	5.25837i	−0.322816	−	0.186378i
$797$	7.35978			0.260697			0.130348	−	0.991468i	$-0.458390\pi$
$797$	7.35978			0.260697			0.130348	+	0.991468i	$0.458390\pi$
$798$	−6.31842	−	2.48840i	−0.223670	−	0.0880885i
$799$			16.2176i			0.573738i
$800$	−0.0465074	−	4.99978i	−0.00164428	−	0.176769i
$801$	−36.2103	+	20.9060i	−1.27943	+	0.738677i
$802$	−11.1849	−	19.3728i	−0.394952	−	0.684076i
$803$	−10.3138	+	2.95727i	−0.363965	+	0.104360i
$804$			27.9166i			0.984541i
$805$	24.9276	−	34.0222i	0.878581	−	1.19913i
$806$	6.63201			0.233603
$807$	−9.79020	−	5.65237i	−0.344631	−	0.198973i
$808$	−5.11669	−	8.86237i	−0.180005	−	0.311777i
$809$	−10.0964	+	5.82917i	−0.354971	+	0.204943i	−0.666873	−	0.745172i	$-0.732367\pi$
$809$	−10.0964	+	5.82917i	−0.354971	+	0.204943i	0.311901	+	0.950114i	$0.399034\pi$
$810$	−6.85166	−	1.80179i	−0.240743	−	0.0633083i
$811$	−22.2910			−0.782744			−0.391372	−	0.920233i	$-0.627999\pi$
$811$	−22.2910			−0.782744			−0.391372	+	0.920233i	$0.627999\pi$
$812$	−4.61175	−	5.79696i	−0.161841	−	0.203434i
$813$	−24.7519			−0.868088
$814$	29.9746	−	8.59462i	1.05061	−	0.301241i
$815$	24.4483	+	24.2219i	0.856387	+	0.848458i
$816$	3.85475	−	2.22554i	0.134943	−	0.0779095i
$817$	0.134567	−	0.233076i	0.00470789	−	0.00815431i
$818$	−19.0752			−0.666949
$819$	34.7327	−	88.1916i	1.21366	−	3.08166i
$820$	4.73069	+	17.3323i	0.165203	+	0.605271i
$821$	−19.5580	−	11.2918i	−0.682580	−	0.394088i	0.118246	−	0.992984i	$-0.462273\pi$
$821$	−19.5580	−	11.2918i	−0.682580	−	0.394088i	−0.800826	+	0.598896i	$0.795606\pi$
$822$	−28.7738	+	16.6126i	−1.00360	+	0.579429i
$823$	−31.1000	+	17.9556i	−1.08408	+	0.625892i	−0.931993	−	0.362475i	$-0.881932\pi$
$823$	−31.1000	+	17.9556i	−1.08408	+	0.625892i	−0.152084	+	0.988368i	$0.548598\pi$
$824$	−1.03582	+	1.79408i	−0.0360843	+	0.0624999i
$825$	−11.1250	+	46.4537i	−0.387323	+	1.61731i
$826$	10.9141	−	1.63187i	0.379749	−	0.0567800i
$827$	15.6771			0.545145			0.272573	−	0.962135i	$-0.412126\pi$
$827$	15.6771			0.545145			0.272573	+	0.962135i	$0.412126\pi$
$828$	−32.7050	−	18.8822i	−1.13658	−	0.656203i
$829$	−12.0266	+	6.94358i	−0.417702	+	0.241160i	−0.694094	−	0.719885i	$-0.744195\pi$
$829$	−12.0266	+	6.94358i	−0.417702	+	0.241160i	0.276392	+	0.961045i	$0.410861\pi$
$830$	−6.37834	−	6.31928i	−0.221395	−	0.219345i
$831$	−41.5525	+	71.9710i	−1.44144	+	2.49665i
$832$		−	6.76312i		−	0.234469i
$833$	−7.37598	+	7.91190i	−0.255562	+	0.274131i
$834$	0.496414			0.0171894
$835$	1.52066	−	5.78264i	0.0526247	−	0.200116i
$836$	2.86751	+	0.714992i	0.0991749	+	0.0247285i
$837$	5.61930	−	3.24431i	0.194231	−	0.112140i
$838$	16.8864	+	9.74936i	0.583330	+	0.336786i
$839$		−	12.2495i		−	0.422901i	−0.977389	−	0.211451i	$-0.932181\pi$
$839$		−	12.2495i		−	0.422901i	0.977389	−	0.211451i	$-0.0678187\pi$
$840$	15.5955	−	6.86879i	0.538096	−	0.236996i
$841$	21.1610			0.729689
$842$	−3.95020	+	6.84194i	−0.136133	+	0.235789i
$843$	−49.3718	+	28.5048i	−1.70046	+	0.981758i
$844$	6.10763	−	3.52624i	0.210233	−	0.121378i
$845$	70.8011	+	18.6186i	2.43563	+	0.640500i
$846$	55.5940			1.91136
$847$	9.71378	−	27.4343i	0.333770	−	0.942655i
$848$		−	5.64781i		−	0.193947i
$849$	75.1610	+	43.3942i	2.57952	+	1.48929i
$850$	−3.80074	+	6.72680i	−0.130364	+	0.230728i
$851$	−33.5139	−	58.0477i	−1.14884	−	1.98985i
$852$	6.80740	−	11.7908i	0.233218	−	0.403945i
$853$		−	33.5711i		−	1.14945i	−0.818345	−	0.574727i	$-0.805108\pi$
$853$		−	33.5711i		−	1.14945i	0.818345	−	0.574727i	$-0.194892\pi$
$854$	0.939884	−	0.747721i	0.0321622	−	0.0255865i
$855$	−2.77906	−	10.1819i	−0.0950418	−	0.348215i
$856$	8.13821	−	14.0958i	0.278158	−	0.481784i
$857$	3.22000	−	1.85907i	0.109993	−	0.0635045i	−0.443994	−	0.896030i	$-0.646439\pi$
$857$	3.22000	−	1.85907i	0.109993	−	0.0635045i	0.553987	+	0.832525i	$0.313106\pi$
$858$	−15.6317	+	62.6917i	−0.533658	+	2.14026i
$859$	−7.77461	−	4.48868i	−0.265266	−	0.153152i	0.361468	−	0.932384i	$-0.382276\pi$
$859$	−7.77461	−	4.48868i	−0.265266	−	0.153152i	−0.626735	+	0.779233i	$0.715609\pi$
$860$	0.177833	+	0.651545i	0.00606405	+	0.0222175i
$861$	−47.9191	+	38.1219i	−1.63308	+	1.29919i
$862$			29.2070i			0.994794i
$863$	9.53283	+	5.50378i	0.324501	+	0.187351i	0.653397	−	0.757015i	$-0.273343\pi$
$863$	9.53283	+	5.50378i	0.324501	+	0.187351i	−0.328896	+	0.944366i	$0.606677\pi$
$864$	−3.30844	−	5.73039i	−0.112555	−	0.194952i
$865$	−33.5406	−	33.2301i	−1.14042	−	1.12986i
$866$	8.83950	−	15.3105i	0.300379	−	0.520271i
$867$	42.0900			1.42945
$868$	−0.950711	+	2.41400i	−0.0322692	+	0.0819364i
$869$	19.5415	+	18.8716i	0.662901	+	0.640174i
$870$	4.58635	−	17.4405i	0.155492	−	0.591290i
$871$	−32.7729	−	56.7643i	−1.11047	−	1.92338i
$872$	12.3584	−	7.13512i	0.418508	−	0.241626i
$873$	50.7185	−	87.8470i	1.71656	−	2.97317i
$874$		−	6.35253i		−	0.214878i
$875$	−17.2600	+	24.0227i	−0.583495	+	0.812117i
$876$			9.31842i			0.314840i
$877$	−1.54217	+	2.67111i	−0.0520753	+	0.0901971i	−0.890888	−	0.454223i	$-0.849917\pi$
$877$	−1.54217	+	2.67111i	−0.0520753	+	0.0901971i	0.838813	+	0.544420i	$0.183250\pi$
$878$	3.88898	+	6.73591i	0.131247	+	0.227326i
$879$	−7.35148	+	4.24438i	−0.247959	+	0.143159i
$880$	−6.33914	+	3.84906i	−0.213692	+	0.129752i
$881$		−	5.47430i		−	0.184434i	−0.995739	−	0.0922169i	$-0.970605\pi$
$881$		−	5.47430i		−	0.184434i	0.995739	−	0.0922169i	$-0.0293953\pi$
$882$	27.1220	+	25.2849i	0.913246	+	0.851386i
$883$			17.3709i			0.584576i	0.956330	+	0.292288i	$0.0944167\pi$
$883$			17.3709i			0.584576i	−0.956330	+	0.292288i	$0.905583\pi$
$884$	−5.22538	+	9.05062i	−0.175748	+	0.304405i
$885$	19.0846	+	18.9079i	0.641522	+	0.635583i
$886$	−26.6196	+	15.3688i	−0.894302	+	0.516326i
$887$	3.77867	+	2.18162i	0.126875	+	0.0732515i	0.562094	−	0.827073i	$-0.309996\pi$
$887$	3.77867	+	2.18162i	0.126875	+	0.0732515i	−0.435219	+	0.900325i	$0.643329\pi$
$888$		−	27.0818i		−	0.908807i
$889$	4.67402	+	31.2602i	0.156762	+	1.04843i
$890$	17.0271	−	4.64739i	0.570751	−	0.155781i
$891$	2.89631	+	10.1011i	0.0970299	+	0.338401i
$892$	−7.43321	−	12.8747i	−0.248882	−	0.431077i
$893$	4.67586	+	8.09884i	0.156472	+	0.271017i
$894$	0.976567	+	0.563821i	0.0326613	+	0.0188570i
$895$	−5.18096	−	18.9820i	−0.173180	−	0.634499i
$896$	2.46172	+	0.969505i	0.0822403	+	0.0323889i
$897$	138.884			4.63720
$898$	−4.10406	+	7.10844i	−0.136954	+	0.237212i
$899$	1.37277	+	2.37771i	0.0457845	+	0.0793012i
$900$	23.0595	+	13.0289i	0.768650	+	0.434298i
$901$	−4.36366	+	7.55808i	−0.145375	+	0.251796i
$902$	18.5118	−	19.1690i	0.616375	−	0.638257i
$903$	−1.80134	+	1.43305i	−0.0599449	+	0.0476889i
$904$		−	2.93230i		−	0.0975269i
$905$	−3.01845	+	11.4783i	−0.100337	+	0.381551i
$906$	6.75416	−	3.89951i	0.224392	−	0.129553i
$907$	0.535517	−	0.309181i	0.0177815	−	0.0102662i	−0.491083	−	0.871113i	$-0.663399\pi$
$907$	0.535517	−	0.309181i	0.0177815	−	0.0102662i	0.508864	+	0.860847i	$0.330065\pi$
$908$	−6.23204	−	3.59807i	−0.206817	−	0.119406i
$909$	54.2078			1.79796
$910$	−23.6475	+	32.2752i	−0.783908	+	1.06991i
$911$	−36.6616			−1.21465			−0.607326	−	0.794453i	$-0.707758\pi$
$911$	−36.6616			−1.21465			−0.607326	+	0.794453i	$0.707758\pi$
$912$	1.28334	−	2.22280i	0.0424955	−	0.0736043i
$913$	−3.22198	+	12.9219i	−0.106632	+	0.427652i
$914$	−8.43227	−	14.6051i	−0.278915	−	0.483094i
$915$	2.82770	+	0.743602i	0.0934809	+	0.0245827i
$916$			7.76517i			0.256568i
$917$	−12.2599	−	4.82837i	−0.404859	−	0.159447i
$918$			10.2248i			0.337468i
$919$	28.3140	+	16.3471i	0.933993	+	0.539241i	0.888072	−	0.459704i	$-0.152044\pi$
$919$	28.3140	+	16.3471i	0.933993	+	0.539241i	0.0459211	+	0.998945i	$0.485378\pi$
$920$	11.3246	+	11.2197i	0.373360	+	0.369903i
$921$	−68.5154	+	39.5574i	−2.25766	+	1.30346i
$922$	12.9868	−	22.4938i	0.427698	−	0.740795i
$923$			31.9664i			1.05219i
$924$	−20.5784	−	14.6768i	−0.676981	−	0.482831i
$925$	23.8823	+	40.4908i	0.785245	+	1.33133i
$926$	5.77055	+	3.33163i	0.189632	+	0.109484i
$927$	−5.48687	−	9.50353i	−0.180212	−	0.312137i
$928$	2.42472	−	1.39991i	0.0795952	−	0.0459543i
$929$	16.7432	+	9.66668i	0.549326	+	0.317153i	0.748850	−	0.662739i	$-0.230606\pi$
$929$	16.7432	+	9.66668i	0.549326	+	0.317153i	−0.199524	+	0.979893i	$0.563940\pi$
$930$	−6.09320	+	1.66308i	−0.199804	+	0.0545345i
$931$	−1.40229	+	6.07773i	−0.0459583	+	0.199189i
$932$	−2.88946			−0.0946474
$933$	33.3022	+	19.2270i	1.09026	+	0.629464i
$934$	−4.29559	−	7.44018i	−0.140556	−	0.243450i
$935$	11.4571	−	0.253132i	0.374689	−	0.00827831i
$936$	31.0256	+	17.9126i	1.01410	+	0.585492i
$937$			57.0380i			1.86335i	0.363292	+	0.931676i	$0.381653\pi$
$937$			57.0380i			1.86335i	−0.363292	+	0.931676i	$0.618347\pi$
$938$	25.3598	−	3.79179i	0.828026	−	0.123806i
$939$	−81.4295			−2.65735
$940$	−22.6961	−	5.96841i	−0.740265	−	0.194668i
$941$	−24.0429	−	41.6434i	−0.783775	−	1.35754i	−0.929728	−	0.368246i	$-0.879958\pi$
$941$	−24.0429	−	41.6434i	−0.783775	−	1.35754i	0.145954	−	0.989291i	$-0.453375\pi$
$942$	−9.63327	−	16.6853i	−0.313869	−	0.543637i
$943$	−49.6074	−	28.6408i	−1.61544	−	0.932674i
$944$			4.17099i			0.135754i
$945$	−4.24790	+	38.9148i	−0.138184	+	1.26590i
$946$	0.695882	−	0.720587i	0.0226251	−	0.0234283i
$947$	−1.85319	−	1.06994i	−0.0602207	−	0.0347684i	0.469587	−	0.882886i	$-0.344403\pi$
$947$	−1.85319	−	1.06994i	−0.0602207	−	0.0347684i	−0.529808	+	0.848118i	$0.677736\pi$
$948$	20.4329	−	11.7969i	0.663628	−	0.383146i
$949$	−10.9394	−	18.9476i	−0.355109	−	0.615066i
$950$	0.0414408	+	4.45510i	0.00134452	+	0.144542i
$951$			68.1429i			2.20968i
$952$	−2.54528	−	3.19942i	−0.0824931	−	0.103694i
$953$	−31.9959			−1.03645			−0.518225	−	0.855245i	$-0.673407\pi$
$953$	−31.9959			−1.03645			−0.518225	+	0.855245i	$0.673407\pi$
$954$	25.9091	+	14.9586i	0.838839	+	0.484304i
$955$	12.4376	−	12.5538i	0.402470	−	0.406231i
$956$	18.6245	−	10.7528i	0.602358	−	0.347772i
$957$	−25.7119	+	7.37239i	−0.831149	+	0.238316i
$958$	18.3151			0.591734
$959$	18.9993	+	23.8821i	0.613519	+	0.771192i
$960$	1.69596	+	6.21365i	0.0547367	+	0.200545i
$961$	−15.0192	+	26.0140i	−0.484490	+	0.839162i
$962$	31.7929	+	55.0669i	1.02504	+	1.77543i
$963$	43.1093	+	74.6675i	1.38918	+	2.40613i
$964$	10.4728	−	18.1393i	0.337305	−	0.584229i
$965$	−8.40427	−	30.7916i	−0.270543	−	0.991217i
$966$	−19.9093	+	50.5527i	−0.640571	+	1.62651i
$967$	−25.4785			−0.819333			−0.409666	−	0.912235i	$-0.634355\pi$
$967$	−25.4785			−0.819333			−0.409666	+	0.912235i	$0.634355\pi$
$968$	9.71228	+	5.16446i	0.312165	+	0.165992i
$969$	−3.43480	+	1.98308i	−0.110342	+	0.0637058i
$970$	−30.1367	+	30.4183i	−0.967630	+	0.976672i
$971$	32.5462	+	18.7906i	1.04446	+	0.603018i	0.921093	−	0.389344i	$-0.127298\pi$
$971$	32.5462	+	18.7906i	1.04446	+	0.603018i	0.123365	+	0.992361i	$0.460631\pi$
$972$	−10.7243			−0.343983
$973$	−0.0674258	−	0.450949i	−0.00216157	−	0.0144568i
$974$			18.9111i			0.605949i
$975$	−97.4008	+	0.906011i	−3.11932	+	0.0290156i
$976$	0.226973	+	0.393129i	0.00726523	+	0.0125837i
$977$	−28.5563	+	16.4870i	−0.913597	+	0.527466i	−0.881587	−	0.472022i	$-0.843524\pi$
$977$	−28.5563	+	16.4870i	−0.913597	+	0.527466i	−0.0320105	+	0.999488i	$0.510191\pi$
$978$	−38.3940	−	22.1668i	−1.22770	−	0.708816i
$979$	−18.8314	−	18.1858i	−0.601855	−	0.581221i
$980$	−8.35797	−	13.2342i	−0.266986	−	0.422751i
$981$			75.5916i			2.41345i
$982$	1.80643	+	1.04294i	0.0576454	+	0.0332816i
$983$	0.151340	+	0.262128i	0.00482699	+	0.00836058i	0.868429	−	0.495814i	$-0.165130\pi$
$983$	0.151340	+	0.262128i	0.00482699	+	0.00836058i	−0.863602	+	0.504174i	$0.831797\pi$
$984$	−11.5720	−	20.0433i	−0.368902	−	0.638957i
$985$	52.4539	+	13.7938i	1.67132	+	0.439508i
$986$	−4.32645			−0.137782
$987$	−11.8276	−	79.1040i	−0.376477	−	2.51791i
$988$			6.02633i			0.191723i
$989$	−1.86481	−	1.07665i	−0.0592974	−	0.0342353i
$990$	−0.867738	−	39.2751i	−0.0275785	−	1.24825i
$991$	6.08333	+	10.5366i	0.193243	+	0.334707i	0.946323	−	0.323222i	$-0.104766\pi$
$991$	6.08333	+	10.5366i	0.193243	+	0.334707i	−0.753080	+	0.657929i	$0.771433\pi$
$992$	−0.849237	−	0.490307i	−0.0269633	−	0.0155673i
$993$	41.9483			1.33119
$994$	−11.6355	−	4.58244i	−0.369056	−	0.145346i
$995$	−22.6863	+	6.19200i	−0.719203	+	0.196300i
$996$	10.0166	+	5.78311i	0.317389	+	0.183245i
$997$	17.8772	−	10.3214i	0.566176	−	0.326882i	−0.189444	−	0.981891i	$-0.560669\pi$
$997$	17.8772	−	10.3214i	0.566176	−	0.326882i	0.755621	+	0.655009i	$0.227335\pi$
$998$	11.0473	+	19.1345i	0.349697	+	0.605693i
$999$	53.8763	+	31.1055i	1.70457	+	0.984134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.o.a.439.3	✓	48
5.4	even	2		770.2.o.b.439.22	yes	48
7.3	odd	6	inner	770.2.o.a.549.22	yes	48
11.10	odd	2		770.2.o.b.439.3	yes	48
35.24	odd	6		770.2.o.b.549.3	yes	48
55.54	odd	2	inner	770.2.o.a.439.22	yes	48
77.10	even	6		770.2.o.b.549.22	yes	48
385.164	even	6	inner	770.2.o.a.549.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.o.a.439.3	✓	48	1.1	even	1	trivial
770.2.o.a.439.22	yes	48	55.54	odd	2	inner
770.2.o.a.549.3	yes	48	385.164	even	6	inner
770.2.o.a.549.22	yes	48	7.3	odd	6	inner
770.2.o.b.439.3	yes	48	11.10	odd	2
770.2.o.b.439.22	yes	48	5.4	even	2
770.2.o.b.549.3	yes	48	35.24	odd	6
770.2.o.b.549.22	yes	48	77.10	even	6

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.44024 - 2.49457i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.16254 - 0.568686i) q^{5} +2.88048 q^{6} +(-0.391243 - 2.61666i) q^{7} +1.00000 q^{8} +(-2.64857 + 4.58746i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.44024 - 2.49457i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.16254 - 0.568686i) q^{5} +2.88048 q^{6} +(-0.391243 - 2.61666i) q^{7} +1.00000 q^{8} +(-2.64857 + 4.58746i) q^{9} +(1.57377 - 1.58848i) q^{10} +(-3.21810 - 0.802409i) q^{11} +(-1.44024 + 2.49457i) q^{12} -6.76312i q^{13} +(2.46172 + 0.969505i) q^{14} +(1.69596 + 6.21365i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.33823 - 0.772629i) q^{17} +(-2.64857 - 4.58746i) q^{18} +(0.445529 - 0.771679i) q^{19} +(0.588776 + 2.15716i) q^{20} +(-5.96396 + 4.74460i) q^{21} +(2.30395 - 2.38575i) q^{22} +(-6.17407 - 3.56460i) q^{23} +(-1.44024 - 2.49457i) q^{24} +(4.35319 + 2.45962i) q^{25} +(5.85703 + 3.38156i) q^{26} +6.61688 q^{27} +(-2.07048 + 1.64716i) q^{28} +2.79982i q^{29} +(-6.22916 - 1.63809i) q^{30} +(0.849237 - 0.490307i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.63316 + 9.18341i) q^{33} +1.54526i q^{34} +(-0.641979 + 5.88114i) q^{35} +5.29715 q^{36} +(8.14224 + 4.70093i) q^{37} +(0.445529 + 0.771679i) q^{38} +(-16.8710 + 9.74050i) q^{39} +(-2.16254 - 0.568686i) q^{40} +8.03479 q^{41} +(-1.12697 - 7.53724i) q^{42} +0.302038 q^{43} +(0.914142 + 3.18816i) q^{44} +(8.33648 - 8.41439i) q^{45} +(6.17407 - 3.56460i) q^{46} +(-5.24754 + 9.08901i) q^{47} +2.88048 q^{48} +(-6.69386 + 2.04750i) q^{49} +(-4.30669 + 2.54017i) q^{50} +(-3.85475 - 2.22554i) q^{51} +(-5.85703 + 3.38156i) q^{52} +(-4.89115 + 2.82391i) q^{53} +(-3.30844 + 5.73039i) q^{54} +(6.50296 + 3.56533i) q^{55} +(-0.391243 - 2.61666i) q^{56} -2.56667 q^{57} +(-2.42472 - 1.39991i) q^{58} +(3.61218 - 2.08549i) q^{59} +(4.53320 - 4.57557i) q^{60} +(0.226973 - 0.393129i) q^{61} +0.980614i q^{62} +(13.0401 + 5.13561i) q^{63} +1.00000 q^{64} +(-3.84609 + 14.6255i) q^{65} +(-9.26965 - 2.31132i) q^{66} +(8.39321 - 4.84582i) q^{67} +(-1.33823 - 0.772629i) q^{68} +20.5355i q^{69} +(-4.77223 - 3.49654i) q^{70} -4.72658 q^{71} +(-2.64857 + 4.58746i) q^{72} +(2.80161 - 1.61751i) q^{73} +(-8.14224 + 4.70093i) q^{74} +(-0.133963 - 14.4018i) q^{75} -0.891058 q^{76} +(-0.840576 + 8.73461i) q^{77} -19.4810i q^{78} +(-7.09357 - 4.09547i) q^{79} +(1.57377 - 1.58848i) q^{80} +(-1.58417 - 2.74386i) q^{81} +(-4.01739 + 6.95833i) q^{82} -4.01538i q^{83} +(7.09092 + 2.79264i) q^{84} +(-3.33337 + 0.909810i) q^{85} +(-0.151019 + 0.261573i) q^{86} +(6.98434 - 4.03241i) q^{87} +(-3.21810 - 0.802409i) q^{88} +(6.83580 + 3.94665i) q^{89} +(3.11883 + 11.4268i) q^{90} +(-17.6968 + 2.64602i) q^{91} +7.12921i q^{92} +(-2.44621 - 1.41232i) q^{93} +(-5.24754 - 9.08901i) q^{94} +(-1.40232 + 1.41542i) q^{95} +(-1.44024 + 2.49457i) q^{96} -19.1494 q^{97} +(1.57374 - 6.82080i) q^{98} +(12.2044 - 12.6377i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9}+O(q^{10}) \) 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9	\( 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9} + 6 q^{10} + q^{11} + 2 q^{14} + 4 q^{15} - 24 q^{16} - 28 q^{18} - 2 q^{22} - 6 q^{26} + 2 q^{28} - 2 q^{30} + 12 q^{31} - 24 q^{32} + 24 q^{33} - 8 q^{35} + 56 q^{36} - 6 q^{40} + 24 q^{43} + q^{44} + 6 q^{45} - 36 q^{49} + 6 q^{52} - 4 q^{56} - 4 q^{57} - 2 q^{60} - 52 q^{63} + 48 q^{64} - 24 q^{66} - 2 q^{70} - 40 q^{71} - 28 q^{72} + 42 q^{73} + 90 q^{75} + 19 q^{77} + 6 q^{80} - 72 q^{81} - 40 q^{85} - 12 q^{86} + 18 q^{87} + q^{88} + 60 q^{89} - 56 q^{91} + 24 q^{95} + 42 q^{98} - 58 q^{99}+O(q^{100}) \) 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9 + 6 * q^10 + q^11 + 2 * q^14 + 4 * q^15 - 24 * q^16 - 28 * q^18 - 2 * q^22 - 6 * q^26 + 2 * q^28 - 2 * q^30 + 12 * q^31 - 24 * q^32 + 24 * q^33 - 8 * q^35 + 56 * q^36 - 6 * q^40 + 24 * q^43 + q^44 + 6 * q^45 - 36 * q^49 + 6 * q^52 - 4 * q^56 - 4 * q^57 - 2 * q^60 - 52 * q^63 + 48 * q^64 - 24 * q^66 - 2 * q^70 - 40 * q^71 - 28 * q^72 + 42 * q^73 + 90 * q^75 + 19 * q^77 + 6 * q^80 - 72 * q^81 - 40 * q^85 - 12 * q^86 + 18 * q^87 + q^88 + 60 * q^89 - 56 * q^91 + 24 * q^95 + 42 * q^98 - 58 * q^99

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