LMFDB - Embedded newform 527.2.h.c.35.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [527,2,Mod(35,527)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(527, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("527.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 527 = 17 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	527.h (of order $5$, degree $4$, 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:	$4.20811618652$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			35.10
Character	$\chi$	$=$	527.35
Dual form			527.2.h.c.256.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0792451 - 0.243891i) q^{2} +(1.00279 - 3.08629i) q^{3} +(1.56483 - 1.13692i) q^{4} +3.14033 q^{5} -0.832185 q^{6} +(-1.06954 + 0.777066i) q^{7} +(-0.816222 - 0.593020i) q^{8} +(-6.09251 - 4.42647i) q^{9} +O(q^{10})$	\(q+(-0.0792451 - 0.243891i) q^{2} +(1.00279 - 3.08629i) q^{3} +(1.56483 - 1.13692i) q^{4} +3.14033 q^{5} -0.832185 q^{6} +(-1.06954 + 0.777066i) q^{7} +(-0.816222 - 0.593020i) q^{8} +(-6.09251 - 4.42647i) q^{9} +(-0.248856 - 0.765899i) q^{10} +(-1.78612 + 1.29769i) q^{11} +(-1.93964 - 5.96961i) q^{12} +(-1.08487 + 3.33887i) q^{13} +(0.274276 + 0.199273i) q^{14} +(3.14911 - 9.69195i) q^{15} +(1.11547 - 3.43307i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(-0.596776 + 1.83669i) q^{18} +(1.52428 + 4.69126i) q^{19} +(4.91408 - 3.57029i) q^{20} +(1.32572 + 4.08014i) q^{21} +(0.458037 + 0.332783i) q^{22} +(3.06681 + 2.22817i) q^{23} +(-2.64873 + 1.92442i) q^{24} +4.86167 q^{25} +0.900293 q^{26} +(-11.8948 + 8.64209i) q^{27} +(-0.790190 + 2.43196i) q^{28} +(1.97713 + 6.08500i) q^{29} -2.61334 q^{30} +(3.97348 - 3.90019i) q^{31} -2.94351 q^{32} +(2.21393 + 6.81379i) q^{33} +(-0.0792451 + 0.243891i) q^{34} +(-3.35871 + 2.44024i) q^{35} -14.5663 q^{36} +4.23745 q^{37} +(1.02337 - 0.743518i) q^{38} +(9.21682 + 6.69641i) q^{39} +(-2.56321 - 1.86228i) q^{40} +(-0.843887 - 2.59722i) q^{41} +(0.890056 - 0.646663i) q^{42} +(-1.52239 - 4.68544i) q^{43} +(-1.31961 + 4.06133i) q^{44} +(-19.1325 - 13.9006i) q^{45} +(0.300402 - 0.924541i) q^{46} +(2.43252 - 7.48653i) q^{47} +(-9.47685 - 6.88534i) q^{48} +(-1.62303 + 4.99519i) q^{49} +(-0.385263 - 1.18572i) q^{50} +(-2.62535 + 1.90743i) q^{51} +(2.09839 + 6.45817i) q^{52} +(5.68641 + 4.13142i) q^{53} +(3.05034 + 2.21620i) q^{54} +(-5.60900 + 4.07518i) q^{55} +1.33380 q^{56} +16.0071 q^{57} +(1.32740 - 0.964413i) q^{58} +(2.12380 - 6.53639i) q^{59} +(-6.09112 - 18.7465i) q^{60} -3.46089 q^{61} +(-1.26610 - 0.660027i) q^{62} +9.95584 q^{63} +(-1.99769 - 6.14825i) q^{64} +(-3.40683 + 10.4852i) q^{65} +(1.48638 - 1.07992i) q^{66} -14.3217 q^{67} -1.93424 q^{68} +(9.95215 - 7.23066i) q^{69} +(0.861316 + 0.625783i) q^{70} +(-9.24974 - 6.72033i) q^{71} +(2.34786 + 7.22596i) q^{72} +(-11.5155 + 8.36648i) q^{73} +(-0.335797 - 1.03348i) q^{74} +(4.87525 - 15.0045i) q^{75} +(7.71881 + 5.60804i) q^{76} +(0.901933 - 2.77586i) q^{77} +(0.902809 - 2.77856i) q^{78} +(7.19298 + 5.22601i) q^{79} +(3.50295 - 10.7810i) q^{80} +(7.76250 + 23.8905i) q^{81} +(-0.566565 + 0.411634i) q^{82} +(2.15573 + 6.63467i) q^{83} +(6.71331 + 4.87750i) q^{84} +(-2.54058 - 1.84584i) q^{85} +(-1.02210 + 0.742596i) q^{86} +20.7627 q^{87} +2.22743 q^{88} +(11.7313 - 8.52331i) q^{89} +(-1.87407 + 5.76780i) q^{90} +(-1.43422 - 4.41407i) q^{91} +7.33229 q^{92} +(-8.05250 - 16.1744i) q^{93} -2.01867 q^{94} +(4.78674 + 14.7321i) q^{95} +(-2.95173 + 9.08450i) q^{96} +(2.05145 - 1.49047i) q^{97} +1.34690 q^{98} +16.6261 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9}+O(q^{10}) $ 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9	\( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9} - 13 q^{10} - 4 q^{11} - 14 q^{12} - 14 q^{13} + 17 q^{14} - 9 q^{15} - 58 q^{16} - 24 q^{17} - 24 q^{18} - 6 q^{19} + 43 q^{20} + 26 q^{21} + 42 q^{22} - 11 q^{23} - 38 q^{24} + 126 q^{25} - 44 q^{26} - q^{27} + 31 q^{28} - 10 q^{29} - 70 q^{30} + 21 q^{31} + 28 q^{32} - 36 q^{33} - 2 q^{34} + 2 q^{35} + 160 q^{36} + 54 q^{37} + 15 q^{38} - 10 q^{39} - 29 q^{40} - 14 q^{41} - 3 q^{42} + 6 q^{43} - 5 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 93 q^{48} - 72 q^{49} + 108 q^{50} + q^{51} + 13 q^{52} - 30 q^{53} - 63 q^{54} - 12 q^{55} + 66 q^{56} - 62 q^{57} + 29 q^{58} + 8 q^{59} - 86 q^{60} - 14 q^{61} - 34 q^{62} + 86 q^{63} - 122 q^{64} + 13 q^{65} - 40 q^{66} + 126 q^{67} + 120 q^{68} - 34 q^{69} - 38 q^{70} - 39 q^{71} - 51 q^{72} - 60 q^{73} - 111 q^{74} - 41 q^{75} + 64 q^{76} - 26 q^{77} - 99 q^{78} - 33 q^{79} - 91 q^{80} + 81 q^{81} - 88 q^{82} + 22 q^{83} + 160 q^{84} - 4 q^{85} + 35 q^{86} + 70 q^{87} - 120 q^{88} + 101 q^{89} + 125 q^{90} - 13 q^{91} - 98 q^{92} + 47 q^{93} - 8 q^{94} - 64 q^{95} + 208 q^{96} + 16 q^{97} + 8 q^{98} + 280 q^{99}+O(q^{100}) \) 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9 - 13 * q^10 - 4 * q^11 - 14 * q^12 - 14 * q^13 + 17 * q^14 - 9 * q^15 - 58 * q^16 - 24 * q^17 - 24 * q^18 - 6 * q^19 + 43 * q^20 + 26 * q^21 + 42 * q^22 - 11 * q^23 - 38 * q^24 + 126 * q^25 - 44 * q^26 - q^27 + 31 * q^28 - 10 * q^29 - 70 * q^30 + 21 * q^31 + 28 * q^32 - 36 * q^33 - 2 * q^34 + 2 * q^35 + 160 * q^36 + 54 * q^37 + 15 * q^38 - 10 * q^39 - 29 * q^40 - 14 * q^41 - 3 * q^42 + 6 * q^43 - 5 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 93 * q^48 - 72 * q^49 + 108 * q^50 + q^51 + 13 * q^52 - 30 * q^53 - 63 * q^54 - 12 * q^55 + 66 * q^56 - 62 * q^57 + 29 * q^58 + 8 * q^59 - 86 * q^60 - 14 * q^61 - 34 * q^62 + 86 * q^63 - 122 * q^64 + 13 * q^65 - 40 * q^66 + 126 * q^67 + 120 * q^68 - 34 * q^69 - 38 * q^70 - 39 * q^71 - 51 * q^72 - 60 * q^73 - 111 * q^74 - 41 * q^75 + 64 * q^76 - 26 * q^77 - 99 * q^78 - 33 * q^79 - 91 * q^80 + 81 * q^81 - 88 * q^82 + 22 * q^83 + 160 * q^84 - 4 * q^85 + 35 * q^86 + 70 * q^87 - 120 * q^88 + 101 * q^89 + 125 * q^90 - 13 * q^91 - 98 * q^92 + 47 * q^93 - 8 * q^94 - 64 * q^95 + 208 * q^96 + 16 * q^97 + 8 * q^98 + 280 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/527\mathbb{Z}\right)^\times$.

$n$	$156$	$375$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.0792451	−	0.243891i	−0.0560348	−	0.172457i	0.919122	−	0.393973i	$-0.128900\pi$
$2$	−0.0792451	−	0.243891i	−0.0560348	−	0.172457i	−0.975157	+	0.221516i	$0.928900\pi$
$3$	1.00279	−	3.08629i	0.578964	−	1.78187i	−0.0433025	−	0.999062i	$-0.513788\pi$
$3$	1.00279	−	3.08629i	0.578964	−	1.78187i	0.622266	−	0.782806i	$-0.286212\pi$
$4$	1.56483	−	1.13692i	0.782415	−	0.568458i
$5$	3.14033			1.40440			0.702199	−	0.711981i	$-0.252202\pi$
$5$	3.14033			1.40440			0.702199	+	0.711981i	$0.252202\pi$
$6$	−0.832185			−0.339738
$7$	−1.06954	+	0.777066i	−0.404248	+	0.293704i	−0.771269	−	0.636509i	$-0.780378\pi$
$7$	−1.06954	+	0.777066i	−0.404248	+	0.293704i	0.367021	+	0.930213i	$0.380378\pi$
$8$	−0.816222	−	0.593020i	−0.288578	−	0.209664i
$9$	−6.09251	−	4.42647i	−2.03084	−	1.47549i
$10$	−0.248856	−	0.765899i	−0.0786951	−	0.242199i
$11$	−1.78612	+	1.29769i	−0.538535	+	0.391268i	−0.823541	−	0.567257i	$-0.808004\pi$
$11$	−1.78612	+	1.29769i	−0.538535	+	0.391268i	0.285006	+	0.958526i	$0.408004\pi$
$12$	−1.93964	−	5.96961i	−0.559927	−	1.72328i
$13$	−1.08487	+	3.33887i	−0.300888	+	0.926037i	0.680292	+	0.732941i	$0.261853\pi$
$13$	−1.08487	+	3.33887i	−0.300888	+	0.926037i	−0.981180	+	0.193096i	$0.938147\pi$
$14$	0.274276	+	0.199273i	0.0733033	+	0.0532579i
$15$	3.14911	−	9.69195i	0.813096	−	2.50245i
$16$	1.11547	−	3.43307i	0.278868	−	0.858269i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$18$	−0.596776	+	1.83669i	−0.140661	+	0.432911i
$19$	1.52428	+	4.69126i	0.349694	+	1.07625i	0.959023	+	0.283330i	$0.0914391\pi$
$19$	1.52428	+	4.69126i	0.349694	+	1.07625i	−0.609328	+	0.792918i	$0.708561\pi$
$20$	4.91408	−	3.57029i	1.09882	−	0.798341i
$21$	1.32572	+	4.08014i	0.289296	+	0.890361i
$22$	0.458037	+	0.332783i	0.0976538	+	0.0709496i
$23$	3.06681	+	2.22817i	0.639475	+	0.464606i	0.859670	−	0.510850i	$-0.170669\pi$
$23$	3.06681	+	2.22817i	0.639475	+	0.464606i	−0.220195	+	0.975456i	$0.570669\pi$
$24$	−2.64873	+	1.92442i	−0.540670	+	0.392820i
$25$	4.86167			0.972333
$26$	0.900293			0.176562
$27$	−11.8948	+	8.64209i	−2.28916	+	1.66317i
$28$	−0.790190	+	2.43196i	−0.149332	+	0.459596i
$29$	1.97713	+	6.08500i	0.367145	+	1.12996i	0.948627	+	0.316396i	$0.102473\pi$
$29$	1.97713	+	6.08500i	0.367145	+	1.12996i	−0.581482	+	0.813559i	$0.697527\pi$
$30$	−2.61334			−0.477128
$31$	3.97348	−	3.90019i	0.713658	−	0.700494i
$31$	3.97348	−	3.90019i	0.713658	−	0.700494i
$32$	−2.94351			−0.520343
$33$	2.21393	+	6.81379i	0.385396	+	1.18613i
$34$	−0.0792451	+	0.243891i	−0.0135904	+	0.0418270i
$35$	−3.35871	+	2.44024i	−0.567725	+	0.412477i
$36$	−14.5663			−2.42771
$37$	4.23745			0.696632			0.348316	−	0.937377i	$-0.386754\pi$
$37$	4.23745			0.696632			0.348316	+	0.937377i	$0.386754\pi$
$38$	1.02337	−	0.743518i	0.166012	−	0.120615i
$39$	9.21682	+	6.69641i	1.47587	+	1.07228i
$40$	−2.56321	−	1.86228i	−0.405279	−	0.294452i
$41$	−0.843887	−	2.59722i	−0.131793	−	0.405617i	0.863284	−	0.504718i	$-0.168403\pi$
$41$	−0.843887	−	2.59722i	−0.131793	−	0.405617i	−0.995077	+	0.0991006i	$0.968403\pi$
$42$	0.890056	−	0.646663i	0.137339	−	0.0997823i
$43$	−1.52239	−	4.68544i	−0.232162	−	0.714523i	−0.997485	−	0.0708759i	$-0.977421\pi$
$43$	−1.52239	−	4.68544i	−0.232162	−	0.714523i	0.765323	−	0.643647i	$-0.222579\pi$
$44$	−1.31961	+	4.06133i	−0.198938	+	0.612269i
$45$	−19.1325	−	13.9006i	−2.85210	−	2.07217i
$46$	0.300402	−	0.924541i	0.0442918	−	0.136316i
$47$	2.43252	−	7.48653i	0.354820	−	1.09202i	−0.601294	−	0.799028i	$-0.705348\pi$
$47$	2.43252	−	7.48653i	0.354820	−	1.09202i	0.956114	−	0.292995i	$-0.0946521\pi$
$48$	−9.47685	−	6.88534i	−1.36787	−	0.993813i
$49$	−1.62303	+	4.99519i	−0.231862	+	0.713598i
$50$	−0.385263	−	1.18572i	−0.0544845	−	0.167686i
$51$	−2.62535	+	1.90743i	−0.367623	+	0.267094i
$52$	2.09839	+	6.45817i	0.290994	+	0.895587i
$53$	5.68641	+	4.13142i	0.781089	+	0.567494i	0.905305	−	0.424761i	$-0.139642\pi$
$53$	5.68641	+	4.13142i	0.781089	+	0.567494i	−0.124217	+	0.992255i	$0.539642\pi$
$54$	3.05034	+	2.21620i	0.415099	+	0.301587i
$55$	−5.60900	+	4.07518i	−0.756317	+	0.549497i
$56$	1.33380			0.178236
$57$	16.0071			2.12019
$58$	1.32740	−	0.964413i	0.174296	−	0.126634i
$59$	2.12380	−	6.53639i	0.276495	−	0.850965i	−0.712324	−	0.701850i	$-0.752358\pi$
$59$	2.12380	−	6.53639i	0.276495	−	0.850965i	0.988820	−	0.149115i	$-0.0476425\pi$
$60$	−6.09112	−	18.7465i	−0.786360	−	2.42017i
$61$	−3.46089			−0.443122			−0.221561	−	0.975146i	$-0.571115\pi$
$61$	−3.46089			−0.443122			−0.221561	+	0.975146i	$0.571115\pi$
$62$	−1.26610	−	0.660027i	−0.160795	−	0.0838235i
$63$	9.95584			1.25432
$64$	−1.99769	−	6.14825i	−0.249711	−	0.768532i
$65$	−3.40683	+	10.4852i	−0.422566	+	1.30052i
$66$	1.48638	−	1.07992i	0.182961	−	0.132929i
$67$	−14.3217			−1.74967			−0.874836	−	0.484419i	$-0.839031\pi$
$67$	−14.3217			−1.74967			−0.874836	+	0.484419i	$0.839031\pi$
$68$	−1.93424			−0.234561
$69$	9.95215	−	7.23066i	1.19810	−	0.870470i
$70$	0.861316	+	0.625783i	0.102947	+	0.0747953i
$71$	−9.24974	−	6.72033i	−1.09774	−	0.797557i	−0.117053	−	0.993126i	$-0.537345\pi$
$71$	−9.24974	−	6.72033i	−1.09774	−	0.797557i	−0.980690	+	0.195569i	$0.937345\pi$
$72$	2.34786	+	7.22596i	0.276698	+	0.851588i
$73$	−11.5155	+	8.36648i	−1.34778	+	0.979222i	−0.348665	+	0.937247i	$0.613365\pi$
$73$	−11.5155	+	8.36648i	−1.34778	+	0.979222i	−0.999119	+	0.0419747i	$0.986635\pi$
$74$	−0.335797	−	1.03348i	−0.0390356	−	0.120139i
$75$	4.87525	−	15.0045i	0.562946	−	1.73257i
$76$	7.71881	+	5.60804i	0.885408	+	0.643286i
$77$	0.901933	−	2.77586i	0.102785	−	0.316339i
$78$	0.902809	−	2.77856i	0.102223	−	0.314610i
$79$	7.19298	+	5.22601i	0.809274	+	0.587972i	0.913620	−	0.406569i	$-0.133275\pi$
$79$	7.19298	+	5.22601i	0.809274	+	0.587972i	−0.104346	+	0.994541i	$0.533275\pi$
$80$	3.50295	−	10.7810i	0.391642	−	1.20535i
$81$	7.76250	+	23.8905i	0.862500	+	2.65450i
$82$	−0.566565	+	0.411634i	−0.0625667	+	0.0454573i
$83$	2.15573	+	6.63467i	0.236623	+	0.728249i	0.996902	+	0.0786532i	$0.0250620\pi$
$83$	2.15573	+	6.63467i	0.236623	+	0.728249i	−0.760280	+	0.649596i	$0.774938\pi$
$84$	6.71331	+	4.87750i	0.732482	+	0.532179i
$85$	−2.54058	−	1.84584i	−0.275565	−	0.200209i
$86$	−1.02210	+	0.742596i	−0.110215	+	0.0800762i
$87$	20.7627			2.22599
$88$	2.22743			0.237444
$89$	11.7313	−	8.52331i	1.24352	−	0.903469i	0.245691	−	0.969348i	$-0.420985\pi$
$89$	11.7313	−	8.52331i	1.24352	−	0.903469i	0.997828	+	0.0658791i	$0.0209852\pi$
$90$	−1.87407	+	5.76780i	−0.197545	+	0.607979i
$91$	−1.43422	−	4.41407i	−0.150347	−	0.462720i
$92$	7.33229			0.764444
$93$	−8.05250	−	16.1744i	−0.835006	−	1.67721i
$94$	−2.01867			−0.208210
$95$	4.78674	+	14.7321i	0.491110	+	1.51148i
$96$	−2.95173	+	9.08450i	−0.301260	+	0.927183i
$97$	2.05145	−	1.49047i	0.208293	−	0.151334i	−0.478748	−	0.877952i	$-0.658909\pi$
$97$	2.05145	−	1.49047i	0.208293	−	0.151334i	0.687041	+	0.726618i	$0.258909\pi$
$98$	1.34690			0.136058
$99$	16.6261			1.67099
$100$	7.60768	−	5.52731i	0.760768	−	0.552731i
$101$	−11.0678	−	8.04120i	−1.10128	−	0.800130i	−0.120015	−	0.992772i	$-0.538294\pi$
$101$	−11.0678	−	8.04120i	−1.10128	−	0.800130i	−0.981269	+	0.192643i	$0.938294\pi$
$102$	0.673252	+	0.489146i	0.0666619	+	0.0484327i
$103$	2.69329	+	8.28908i	0.265377	+	0.816748i	0.991606	+	0.129295i	$0.0412713\pi$
$103$	2.69329	+	8.28908i	0.265377	+	0.816748i	−0.726229	+	0.687453i	$0.758729\pi$
$104$	2.86551	−	2.08192i	0.280986	−	0.204149i
$105$	4.16319	+	12.8130i	0.406286	+	1.25042i
$106$	0.556997	−	1.71426i	0.0541004	−	0.166504i
$107$	−13.7335	−	9.97801i	−1.32767	−	0.964610i	−0.999802	−	0.0198872i	$-0.993669\pi$
$107$	−13.7335	−	9.97801i	−1.32767	−	0.964610i	−0.327870	−	0.944723i	$-0.606331\pi$
$108$	−8.78804	+	27.0468i	−0.845630	+	2.60258i
$109$	−2.05788	+	6.33351i	−0.197109	+	0.606640i	0.802836	+	0.596200i	$0.203323\pi$
$109$	−2.05788	+	6.33351i	−0.197109	+	0.606640i	−0.999945	+	0.0104406i	$0.996677\pi$
$110$	1.43839	+	1.04505i	0.137145	+	0.0996415i
$111$	4.24929	−	13.0780i	0.403325	−	1.24131i
$112$	1.47468	+	4.53861i	0.139344	+	0.428858i
$113$	−5.06261	+	3.67820i	−0.476250	+	0.346016i	−0.799872	−	0.600170i	$-0.795099\pi$
$113$	−5.06261	+	3.67820i	−0.476250	+	0.346016i	0.323622	+	0.946187i	$0.395099\pi$
$114$	−1.26848	−	3.90399i	−0.118804	−	0.365642i
$115$	9.63080	+	6.99719i	0.898077	+	0.652491i
$116$	10.0120	+	7.27415i	0.929592	+	0.675388i
$117$	21.3890	−	15.5400i	1.97741	−	1.43667i
$118$	−1.76247			−0.162249
$119$	1.32202			0.121190
$120$	−8.31789	+	6.04330i	−0.759316	+	0.551676i
$121$	−1.89297	+	5.82596i	−0.172088	+	0.529633i
$122$	0.274259	+	0.844083i	0.0248303	+	0.0764197i
$123$	−8.86200			−0.799060
$124$	1.78364	−	10.6206i	0.160175	−	0.953762i
$125$	−0.434415			−0.0388553
$126$	−0.788952	−	2.42814i	−0.0702854	−	0.216316i
$127$	−0.554707	+	1.70721i	−0.0492223	+	0.151491i	−0.972647	−	0.232290i	$-0.925378\pi$
$127$	−0.554707	+	1.70721i	−0.0492223	+	0.151491i	0.923424	+	0.383781i	$0.125378\pi$
$128$	−6.10389	+	4.43474i	−0.539513	+	0.391979i
$129$	−15.9872			−1.40760
$130$	2.82722			0.247963
$131$	7.21086	−	5.23900i	0.630016	−	0.457733i	−0.226390	−	0.974037i	$-0.572692\pi$
$131$	7.21086	−	5.23900i	0.630016	−	0.457733i	0.856406	+	0.516303i	$0.172692\pi$
$132$	11.2111	+	8.14537i	0.975804	+	0.708963i
$133$	−5.27570	−	3.83302i	−0.457461	−	0.332365i
$134$	1.13492	+	3.49294i	0.0980425	+	0.301744i
$135$	−37.3536	+	27.1390i	−3.21489	+	2.33575i
$136$	0.311769	+	0.959527i	0.0267340	+	0.0822787i
$137$	−0.694789	+	2.13834i	−0.0593599	+	0.182691i	−0.976340	−	0.216243i	$-0.930620\pi$
$137$	−0.694789	+	2.13834i	−0.0593599	+	0.182691i	0.916980	+	0.398934i	$0.130620\pi$
$138$	−2.55216	−	1.85425i	−0.217254	−	0.157844i
$139$	−0.241833	+	0.744284i	−0.0205120	+	0.0631294i	−0.960789	−	0.277282i	$-0.910566\pi$
$139$	−0.241833	+	0.744284i	−0.0205120	+	0.0631294i	0.940277	+	0.340411i	$0.110566\pi$
$140$	−2.48146	+	7.63714i	−0.209721	+	0.645456i
$141$	−20.6663	−	15.0149i	−1.74041	−	1.26448i
$142$	−0.906035	+	2.78849i	−0.0760327	+	0.234005i
$143$	−2.39513	−	7.37144i	−0.200290	−	0.616431i
$144$	−21.9924	+	15.9784i	−1.83270	+	1.33154i
$145$	6.20885	+	19.1089i	0.515617	+	1.58691i
$146$	2.95306	+	2.14552i	0.244397	+	0.177565i
$147$	13.7890	+	10.0183i	1.13730	+	0.826295i
$148$	6.63089	−	4.81762i	0.545056	−	0.396006i
$149$	−14.3424			−1.17497			−0.587487	−	0.809234i	$-0.699883\pi$
$149$	−14.3424			−1.17497			−0.587487	+	0.809234i	$0.699883\pi$
$150$	−4.04581			−0.330339
$151$	10.5083	−	7.63474i	0.855155	−	0.621306i	−0.0714075	−	0.997447i	$-0.522749\pi$
$151$	10.5083	−	7.63474i	0.855155	−	0.621306i	0.926563	+	0.376141i	$0.122749\pi$
$152$	1.53786	−	4.73304i	0.124737	−	0.383900i
$153$	2.32713	+	7.16217i	0.188137	+	0.579027i
$154$	−0.748484			−0.0603145
$155$	12.4780	−	12.2479i	1.00226	−	0.983773i
$156$	22.0360			1.76429
$157$	6.73239	+	20.7202i	0.537303	+	1.65365i	0.738619	+	0.674123i	$0.235478\pi$
$157$	6.73239	+	20.7202i	0.537303	+	1.65365i	−0.201315	+	0.979526i	$0.564522\pi$
$158$	0.704570	−	2.16844i	0.0560525	−	0.172512i
$159$	18.4530	−	13.4069i	1.46342	−	1.06324i
$160$	−9.24358			−0.730769
$161$	−5.01152			−0.394963
$162$	5.21156	−	3.78642i	0.409458	−	0.297489i
$163$	4.38296	+	3.18441i	0.343300	+	0.249422i	0.746053	−	0.665887i	$-0.231947\pi$
$163$	4.38296	+	3.18441i	0.343300	+	0.249422i	−0.402753	+	0.915309i	$0.631947\pi$
$164$	−4.27336	−	3.10478i	−0.333693	−	0.242442i
$165$	6.95248	+	21.3975i	0.541250	+	1.66580i
$166$	1.44731	−	1.05153i	0.112333	−	0.0816146i
$167$	−5.77583	−	17.7762i	−0.446947	−	1.37556i	−0.880334	−	0.474355i	$-0.842681\pi$
$167$	−5.77583	−	17.7762i	−0.446947	−	1.37556i	0.433386	−	0.901208i	$-0.357319\pi$
$168$	1.33753	−	4.11648i	0.103192	−	0.317594i
$169$	0.546084	+	0.396754i	0.0420065	+	0.0305195i
$170$	−0.248856	+	0.765899i	−0.0190864	+	0.0587418i
$171$	11.4790	−	35.3287i	0.877820	−	2.70165i
$172$	−7.70924	−	5.60109i	−0.587824	−	0.427079i
$173$	−1.97512	+	6.07880i	−0.150166	+	0.462162i	−0.997639	−	0.0686755i	$-0.978123\pi$
$173$	−1.97512	+	6.07880i	−0.150166	+	0.462162i	0.847473	+	0.530838i	$0.178123\pi$
$174$	−1.64534	−	5.06384i	−0.124733	−	0.383889i
$175$	−5.19975	+	3.77784i	−0.393064	+	0.285578i
$176$	2.46270	+	7.57941i	0.185633	+	0.571320i
$177$	−18.0434	−	13.1093i	−1.35623	−	0.985356i
$178$	−3.00841	−	2.18574i	−0.225490	−	0.163828i
$179$	2.44842	−	1.77888i	0.183004	−	0.132960i	−0.492512	−	0.870306i	$-0.663921\pi$
$179$	2.44842	−	1.77888i	0.183004	−	0.132960i	0.675516	+	0.737346i	$0.263921\pi$
$180$	−45.7429			−3.40947
$181$	11.8818			0.883168			0.441584	−	0.897220i	$-0.354417\pi$
$181$	11.8818			0.883168			0.441584	+	0.897220i	$0.354417\pi$
$182$	−0.962899	+	0.699587i	−0.0713749	+	0.0518569i
$183$	−3.47057	+	10.6813i	−0.256552	+	0.789585i
$184$	−1.18185	−	3.63736i	−0.0871272	−	0.268150i
$185$	13.3070			0.978349
$186$	−3.30667	+	3.24568i	−0.242457	+	0.237985i
$187$	2.20776			0.161448
$188$	−4.70508	−	14.4807i	−0.343153	−	1.05612i
$189$	6.00651	−	18.4861i	0.436909	−	1.34467i
$190$	3.21370	−	2.33489i	0.233147	−	0.169391i
$191$	23.3163			1.68711			0.843554	−	0.537044i	$-0.180459\pi$
$191$	23.3163			1.68711			0.843554	+	0.537044i	$0.180459\pi$
$192$	−20.9785			−1.51400
$193$	−14.3126	+	10.3987i	−1.03025	+	0.748517i	−0.968358	−	0.249566i	$-0.919712\pi$
$193$	−14.3126	+	10.3987i	−1.03025	+	0.748517i	−0.0618876	+	0.998083i	$0.519712\pi$
$194$	−0.526080	−	0.382219i	−0.0377703	−	0.0274418i
$195$	28.9438	+	21.0289i	2.07271	+	1.50591i
$196$	3.13933	+	9.66188i	0.224238	+	0.690134i
$197$	12.4288	−	9.03003i	0.885513	−	0.643363i	−0.0491909	−	0.998789i	$-0.515664\pi$
$197$	12.4288	−	9.03003i	0.885513	−	0.643363i	0.934704	+	0.355426i	$0.115664\pi$
$198$	−1.31754	−	4.05497i	−0.0936334	−	0.288174i
$199$	1.55012	−	4.77079i	0.109885	−	0.338192i	−0.880961	−	0.473190i	$-0.843103\pi$
$199$	1.55012	−	4.77079i	0.109885	−	0.338192i	0.990846	+	0.134997i	$0.0431026\pi$
$200$	−3.96820	−	2.88307i	−0.280594	−	0.203864i
$201$	−14.3617	+	44.2008i	−1.01300	+	3.11768i
$202$	−1.08411	+	3.33656i	−0.0762780	+	0.234760i
$203$	−6.84307	−	4.97178i	−0.480289	−	0.348951i
$204$	−1.93964	+	5.96961i	−0.135802	+	0.417956i
$205$	−2.65008	−	8.15612i	−0.185090	−	0.569648i
$206$	1.80821	−	1.31374i	0.125984	−	0.0915325i
$207$	−8.82166	−	27.1503i	−0.613148	−	1.88708i
$208$	10.2525	+	7.44885i	0.710880	+	0.516485i
$209$	−8.81034	−	6.40109i	−0.609424	−	0.442773i
$210$	2.79507	−	2.03074i	0.192878	−	0.140134i
$211$	−3.43110			−0.236207			−0.118103	−	0.993001i	$-0.537681\pi$
$211$	−3.43110			−0.236207			−0.118103	+	0.993001i	$0.537681\pi$
$212$	13.5953			0.933732
$213$	−30.0165	+	21.8082i	−2.05669	+	1.49428i
$214$	−1.34523	+	4.14020i	−0.0919583	+	0.283018i
$215$	−4.78081	−	14.7138i	−0.326049	−	1.00347i
$216$	14.8338			1.00931
$217$	−1.21909	+	7.25907i	−0.0827574	+	0.492777i
$218$	1.70777			0.115665
$219$	14.2737	+	43.9299i	0.964526	+	2.96851i
$220$	−4.14400	+	12.7539i	−0.279388	+	0.859869i
$221$	2.84021	−	2.06354i	0.191054	−	0.138808i
$222$	−3.52634			−0.236673
$223$	−18.6020			−1.24568			−0.622842	−	0.782348i	$-0.714022\pi$
$223$	−18.6020			−1.24568			−0.622842	+	0.782348i	$0.714022\pi$
$224$	3.14820	−	2.28730i	0.210348	−	0.152827i
$225$	−29.6197	−	21.5200i	−1.97465	−	1.43467i
$226$	1.29827	+	0.943248i	0.0863596	+	0.0627439i
$227$	−7.62890	−	23.4793i	−0.506348	−	1.55838i	−0.798493	−	0.602004i	$-0.794369\pi$
$227$	−7.62890	−	23.4793i	−0.506348	−	1.55838i	0.292146	−	0.956374i	$-0.405631\pi$
$228$	25.0484	−	18.1987i	1.65887	−	1.20524i
$229$	5.86012	+	18.0356i	0.387248	+	1.19183i	0.934836	+	0.355079i	$0.115546\pi$
$229$	5.86012	+	18.0356i	0.387248	+	1.19183i	−0.547589	+	0.836748i	$0.684454\pi$
$230$	0.943360	−	2.90336i	0.0622033	−	0.191442i
$231$	−7.66266	−	5.56725i	−0.504166	−	0.366298i
$232$	1.99474	−	6.13919i	0.130961	−	0.403058i
$233$	0.904197	−	2.78283i	0.0592359	−	0.182309i	−0.917060	−	0.398749i	$-0.869444\pi$
$233$	0.904197	−	2.78283i	0.0592359	−	0.182309i	0.976296	+	0.216440i	$0.0694444\pi$
$234$	−5.48504	−	3.98512i	−0.358568	−	0.260515i
$235$	7.63892	−	23.5102i	0.498308	−	1.53364i
$236$	−4.10794	−	12.6429i	−0.267404	−	0.822984i
$237$	23.3420	−	16.9590i	1.51623	−	1.10160i
$238$	−0.104764	−	0.322430i	−0.00679084	−	0.0209001i
$239$	−0.938207	−	0.681648i	−0.0606876	−	0.0440921i	0.557028	−	0.830494i	$-0.311942\pi$
$239$	−0.938207	−	0.681648i	−0.0606876	−	0.0440921i	−0.617715	+	0.786402i	$0.711942\pi$
$240$	−29.7604	−	21.6222i	−1.92103	−	1.39571i
$241$	15.2882	−	11.1075i	0.984798	−	0.715498i	0.0260221	−	0.999661i	$-0.491716\pi$
$241$	15.2882	−	11.1075i	0.984798	−	0.715498i	0.958776	+	0.284164i	$0.0917160\pi$
$242$	1.57091			0.100982
$243$	37.4088			2.39977
$244$	−5.41571	+	3.93475i	−0.346706	+	0.251896i
$245$	−5.09686	+	15.6865i	−0.325627	+	1.00218i
$246$	0.702270	+	2.16137i	0.0447751	+	0.137804i
$247$	−17.3171			−1.10186
$248$	−5.55613	+	0.827065i	−0.352815	+	0.0525187i
$249$	22.6382			1.43464
$250$	0.0344253	+	0.105950i	0.00217725	+	0.00670087i
$251$	−3.06680	+	9.43865i	−0.193575	+	0.595763i	0.806415	+	0.591350i	$0.201405\pi$
$251$	−3.06680	+	9.43865i	−0.193575	+	0.595763i	−0.999990	+	0.00441292i	$0.998595\pi$
$252$	15.5792	−	11.3190i	0.981398	−	0.713027i
$253$	−8.36917			−0.526165
$254$	0.460332			0.0288838
$255$	−8.24447	+	5.98995i	−0.516288	+	0.375106i
$256$	−8.89473	−	6.46240i	−0.555921	−	0.403900i
$257$	21.0434	+	15.2889i	1.31265	+	0.953695i	0.999993	+	0.00382820i	$0.00121856\pi$
$257$	21.0434	+	15.2889i	1.31265	+	0.953695i	0.312656	+	0.949867i	$0.398781\pi$
$258$	1.26691	+	3.89915i	0.0788745	+	0.242751i
$259$	−4.53212	+	3.29278i	−0.281612	+	0.204603i
$260$	6.58963	+	20.2808i	0.408671	+	1.25776i
$261$	14.8893	−	45.8246i	0.921625	−	2.83647i
$262$	−1.84917	−	1.34350i	−0.114242	−	0.0830019i
$263$	3.72716	−	11.4710i	0.229826	−	0.707333i	−0.767939	−	0.640523i	$-0.778718\pi$
$263$	3.72716	−	11.4710i	0.229826	−	0.707333i	0.997766	−	0.0668103i	$-0.0212822\pi$
$264$	2.23365	−	6.87447i	0.137472	−	0.423095i
$265$	17.8572	+	12.9740i	1.09696	+	0.796987i
$266$	−0.516767	+	1.59045i	−0.0316850	+	0.0975165i
$267$	−14.5412	−	44.7534i	−0.889910	−	2.73886i
$268$	−22.4110	+	16.2825i	−1.36897	+	0.994615i
$269$	6.04098	+	18.5922i	0.368325	+	1.13359i	0.947873	+	0.318649i	$0.103229\pi$
$269$	6.04098	+	18.5922i	0.368325	+	1.13359i	−0.579548	+	0.814938i	$0.696771\pi$
$270$	9.57907	+	6.95960i	0.582963	+	0.423548i
$271$	14.9993	+	10.8976i	0.911142	+	0.661983i	0.941303	−	0.337562i	$-0.109602\pi$
$271$	14.9993	+	10.8976i	0.911142	+	0.661983i	−0.0301615	+	0.999545i	$0.509602\pi$
$272$	−2.92035	+	2.12176i	−0.177072	+	0.128650i
$273$	−15.0613			−0.911552
$274$	0.576582			0.0348326
$275$	−8.68351	+	6.30894i	−0.523635	+	0.380443i
$276$	7.35278	−	22.6295i	0.442585	−	1.36214i
$277$	−5.66377	−	17.4313i	−0.340303	−	1.04734i	−0.964051	−	0.265719i	$-0.914391\pi$
$277$	−5.66377	−	17.4313i	−0.340303	−	1.04734i	0.623748	−	0.781626i	$-0.285609\pi$
$278$	0.200689			0.0120365
$279$	−41.4725	+	6.17344i	−2.48289	+	0.369594i
$280$	4.18857			0.250315
$281$	−1.60011	−	4.92463i	−0.0954546	−	0.293779i	0.891917	−	0.452199i	$-0.149360\pi$
$281$	−1.60011	−	4.92463i	−0.0954546	−	0.293779i	−0.987372	+	0.158420i	$0.949360\pi$
$282$	−2.02431	+	6.23018i	−0.120546	+	0.371002i
$283$	0.948040	−	0.688791i	0.0563551	−	0.0409444i	−0.559251	−	0.828998i	$-0.688911\pi$
$283$	0.948040	−	0.688791i	0.0563551	−	0.0409444i	0.615606	+	0.788054i	$0.288911\pi$
$284$	−22.1147			−1.31227
$285$	50.2675			2.97759
$286$	−1.60803	+	1.16830i	−0.0950848	+	0.0690831i
$287$	2.92078	+	2.12207i	0.172408	+	0.125262i
$288$	17.9333	+	13.0293i	1.05673	+	0.767761i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	4.16847	−	3.02857i	0.244781	−	0.177844i
$291$	−2.54282	−	7.82600i	−0.149063	−	0.458768i
$292$	−8.50778	+	26.1842i	−0.497880	+	1.53232i
$293$	−15.6458	−	11.3673i	−0.914038	−	0.664088i	0.0279948	−	0.999608i	$-0.491088\pi$
$293$	−15.6458	−	11.3673i	−0.914038	−	0.664088i	−0.942033	+	0.335520i	$0.891088\pi$
$294$	1.35067	−	4.15692i	0.0787724	−	0.242437i
$295$	6.66944	−	20.5264i	0.388310	−	1.19509i
$296$	−3.45870	−	2.51289i	−0.201033	−	0.146059i
$297$	10.0308	−	30.8716i	0.582045	−	1.79135i
$298$	1.13656	+	3.49798i	0.0658394	+	0.202633i
$299$	−10.7667	+	7.82243i	−0.622652	+	0.452383i
$300$	−9.42990	−	29.0222i	−0.544435	−	1.67560i
$301$	5.26916	+	3.82827i	0.303709	+	0.220658i
$302$	−2.69478	−	1.95787i	−0.155067	−	0.112663i
$303$	−35.9161	+	26.0946i	−2.06333	+	1.49910i
$304$	17.8057			1.02123
$305$	−10.8683			−0.622320
$306$	1.56238	−	1.13513i	0.0893153	−	0.0648913i
$307$	−0.477941	+	1.47095i	−0.0272775	+	0.0839516i	−0.963769	−	0.266740i	$-0.914053\pi$
$307$	−0.477941	+	1.47095i	−0.0272775	+	0.0839516i	0.936491	+	0.350692i	$0.114053\pi$
$308$	−1.74455	−	5.36918i	−0.0994051	−	0.305937i
$309$	28.2833			1.60898
$310$	−3.97597	−	2.07270i	−0.225820	−	0.117722i
$311$	−25.9534			−1.47168			−0.735840	−	0.677156i	$-0.763212\pi$
$311$	−25.9534			−1.47168			−0.735840	+	0.677156i	$0.763212\pi$
$312$	−3.55186	−	10.9315i	−0.201085	−	0.618875i
$313$	8.71696	−	26.8280i	0.492711	−	1.51641i	−0.327782	−	0.944754i	$-0.606301\pi$
$313$	8.71696	−	26.8280i	0.492711	−	1.51641i	0.820493	−	0.571657i	$-0.193699\pi$
$314$	4.51996	−	3.28395i	0.255076	−	0.185324i
$315$	31.2646			1.76156
$316$	17.1973			0.967425
$317$	−11.2071	+	8.14240i	−0.629451	+	0.457323i	−0.856210	−	0.516628i	$-0.827187\pi$
$317$	−11.2071	+	8.14240i	−0.629451	+	0.457323i	0.226759	+	0.973951i	$0.427187\pi$
$318$	−4.73215	−	3.43811i	−0.265366	−	0.192799i
$319$	−11.4278	−	8.30281i	−0.639836	−	0.464868i
$320$	−6.27340	−	19.3075i	−0.350694	−	1.07932i
$321$	−44.5669	+	32.3797i	−2.48748	+	1.80726i
$322$	0.397138	+	1.22227i	0.0221317	+	0.0681142i
$323$	1.52428	−	4.69126i	0.0848133	−	0.261028i
$324$	39.3085	+	28.5593i	2.18381	+	1.58663i
$325$	−5.27425	+	16.2325i	−0.292563	+	0.900416i
$326$	0.429321	−	1.32132i	0.0237779	−	0.0731809i
$327$	17.4834	+	12.7024i	0.966834	+	0.702446i
$328$	−0.851403	+	2.62035i	−0.0470109	+	0.144685i
$329$	3.21585	+	9.89738i	0.177296	+	0.545660i
$330$	4.66773	−	3.39130i	0.256950	−	0.186685i
$331$	8.47236	+	26.0752i	0.465683	+	1.43322i	0.858122	+	0.513446i	$0.171631\pi$
$331$	8.47236	+	26.0752i	0.465683	+	1.43322i	−0.392439	+	0.919778i	$0.628369\pi$
$332$	10.9164	+	7.93124i	0.599116	+	0.435283i
$333$	−25.8167	−	18.7569i	−1.41475	−	1.02787i
$334$	−3.87775	+	2.81735i	−0.212181	+	0.154159i
$335$	−44.9748			−2.45724
$336$	15.4862			0.844844
$337$	−26.1181	+	18.9759i	−1.42274	+	1.03368i	−0.431430	+	0.902147i	$0.641991\pi$
$337$	−26.1181	+	18.9759i	−1.42274	+	1.03368i	−0.991311	+	0.131535i	$0.958009\pi$
$338$	0.0534903	−	0.164626i	0.00290949	−	0.00895448i
$339$	6.27522	+	19.3131i	0.340823	+	1.04895i
$340$	−6.07414			−0.329417
$341$	−2.03587	+	12.1225i	−0.110248	+	0.656472i
$342$	−9.52602			−0.515108
$343$	−5.00539	−	15.4050i	−0.270266	−	0.831792i
$344$	−1.53595	+	4.72717i	−0.0828129	+	0.254872i
$345$	31.2530	−	22.7067i	1.68261	−	1.22249i
$346$	1.63909			0.0881178
$347$	9.67320			0.519284			0.259642	−	0.965705i	$-0.416395\pi$
$347$	9.67320			0.519284			0.259642	+	0.965705i	$0.416395\pi$
$348$	32.4901	−	23.6054i	1.74165	−	1.26538i
$349$	−9.89480	−	7.18899i	−0.529656	−	0.384818i	0.290573	−	0.956853i	$-0.406154\pi$
$349$	−9.89480	−	7.18899i	−0.529656	−	0.384818i	−0.820229	+	0.572035i	$0.806154\pi$
$350$	1.33344	+	0.968799i	0.0712752	+	0.0517845i
$351$	−15.9506	−	49.0908i	−0.851378	−	2.62027i
$352$	5.25745	−	3.81976i	0.280223	−	0.203594i
$353$	2.14467	+	6.60062i	0.114149	+	0.351316i	0.991769	−	0.128043i	$-0.0408695\pi$
$353$	2.14467	+	6.60062i	0.114149	+	0.351316i	−0.877619	+	0.479358i	$0.840869\pi$
$354$	−1.76740	+	5.43949i	−0.0939361	+	0.289105i
$355$	−29.0472	−	21.1041i	−1.54167	−	1.12009i
$356$	8.66726	−	26.6751i	0.459364	−	1.41378i
$357$	1.32572	−	4.08014i	0.0701645	−	0.215944i
$358$	−0.627880	−	0.456182i	−0.0331845	−	0.0241100i
$359$	7.69072	−	23.6696i	0.405901	−	1.24923i	−0.514240	−	0.857646i	$-0.671926\pi$
$359$	7.69072	−	23.6696i	0.405901	−	1.24923i	0.920141	−	0.391588i	$-0.128074\pi$
$360$	7.37304	+	22.6919i	0.388593	+	1.19597i
$361$	−4.31312	+	3.13366i	−0.227006	+	0.164930i
$362$	−0.941576	−	2.89787i	−0.0494881	−	0.152309i
$363$	16.0823	+	11.6845i	0.844103	+	0.613277i
$364$	−7.26274	−	5.27669i	−0.380671	−	0.276574i
$365$	−36.1624	+	26.2735i	−1.89282	+	1.37522i
$366$	2.88011			0.150546
$367$	−17.6504			−0.921344			−0.460672	−	0.887571i	$-0.652392\pi$
$367$	−17.6504			−0.921344			−0.460672	+	0.887571i	$0.652392\pi$
$368$	11.0704	−	8.04313i	0.577086	−	0.419277i
$369$	−6.35511	+	19.5590i	−0.330834	+	1.01820i
$370$	−1.05451	−	3.24546i	−0.0548216	−	0.168723i
$371$	−9.29223			−0.482429
$372$	−30.9897	−	16.1551i	−1.60674	−	0.837605i
$373$	−5.10751			−0.264457			−0.132228	−	0.991219i	$-0.542213\pi$
$373$	−5.10751			−0.264457			−0.132228	+	0.991219i	$0.542213\pi$
$374$	−0.174955	−	0.538455i	−0.00904668	−	0.0278428i
$375$	−0.435629	+	1.34073i	−0.0224958	+	0.0692349i
$376$	−6.42515	+	4.66814i	−0.331352	+	0.240741i
$377$	−22.4619			−1.15685
$378$	−4.98460			−0.256380
$379$	18.3128	−	13.3050i	0.940665	−	0.683433i	−0.00791533	−	0.999969i	$-0.502520\pi$
$379$	18.3128	−	13.3050i	0.940665	−	0.683433i	0.948581	+	0.316535i	$0.102520\pi$
$380$	24.2396	+	17.6111i	1.24346	+	0.903430i
$381$	4.71269	+	3.42397i	0.241438	+	0.175415i
$382$	−1.84770	−	5.68665i	−0.0945367	−	0.290954i
$383$	−8.42497	+	6.12110i	−0.430496	+	0.312774i	−0.781847	−	0.623470i	$-0.785722\pi$
$383$	−8.42497	+	6.12110i	−0.430496	+	0.312774i	0.351351	+	0.936244i	$0.385722\pi$
$384$	7.56591	+	23.2855i	0.386096	+	1.18828i
$385$	2.83237	−	8.71713i	0.144351	−	0.444266i
$386$	3.67037	+	2.66668i	0.186817	+	0.135730i
$387$	−11.4648	+	35.2849i	−0.582786	+	1.79363i
$388$	1.51564	−	4.66466i	0.0769449	−	0.236812i
$389$	−0.171621	−	0.124690i	−0.00870151	−	0.00632202i	0.583426	−	0.812166i	$-0.301712\pi$
$389$	−0.171621	−	0.124690i	−0.00870151	−	0.00632202i	−0.592128	+	0.805844i	$0.701712\pi$
$390$	2.83512	−	8.72559i	0.143562	−	0.441838i
$391$	−1.17142	−	3.60526i	−0.0592412	−	0.182326i
$392$	4.28700	−	3.11469i	0.216526	−	0.157316i
$393$	−8.93803	−	27.5084i	−0.450864	−	1.38762i
$394$	−3.18727	−	2.31569i	−0.160572	−	0.116663i
$395$	22.5883	+	16.4114i	1.13654	+	0.825746i
$396$	26.0171	−	18.9025i	1.30741	−	0.949887i
$397$	−28.7535			−1.44310			−0.721549	−	0.692363i	$-0.756570\pi$
$397$	−28.7535			−1.44310			−0.721549	+	0.692363i	$0.756570\pi$
$398$	−1.28639			−0.0644811
$399$	−17.1202	+	12.4386i	−0.857084	+	0.622708i
$400$	5.42306	−	16.6905i	0.271153	−	0.834523i
$401$	8.18870	+	25.2022i	0.408924	+	1.25854i	0.917574	+	0.397566i	$0.130145\pi$
$401$	8.18870	+	25.2022i	0.408924	+	1.25854i	−0.508649	+	0.860974i	$0.669855\pi$
$402$	11.9183			0.594430
$403$	8.71154	+	17.4981i	0.433952	+	0.871643i
$404$	−26.4614			−1.31650
$405$	24.3768	+	75.0241i	1.21129	+	3.72798i
$406$	−0.670295	+	2.06296i	−0.0332662	+	0.102383i
$407$	−7.56858	+	5.49890i	−0.375161	+	0.272570i
$408$	3.27401			0.162088
$409$	−18.8501			−0.932076			−0.466038	−	0.884765i	$-0.654319\pi$
$409$	−18.8501			−0.932076			−0.466038	+	0.884765i	$0.654319\pi$
$410$	−1.77920	+	1.29267i	−0.0878685	+	0.0638402i
$411$	5.90280	+	4.28864i	0.291164	+	0.211543i
$412$	13.6385	+	9.90897i	0.671922	+	0.488180i
$413$	2.80772	+	8.64127i	0.138159	+	0.425209i
$414$	−5.92265	+	4.30306i	−0.291082	+	0.211484i
$415$	6.76971	+	20.8350i	0.332312	+	1.02275i
$416$	3.19331	−	9.82799i	0.156565	−	0.481857i
$417$	2.05457	+	1.49273i	0.100613	+	0.0730993i
$418$	−0.862994	+	2.65602i	−0.0422104	+	0.129910i
$419$	3.02629	−	9.31397i	0.147844	−	0.455017i	−0.849522	−	0.527554i	$-0.823109\pi$
$419$	3.02629	−	9.31397i	0.147844	−	0.455017i	0.997366	+	0.0725365i	$0.0231094\pi$
$420$	21.0820	+	15.3170i	1.02870	+	0.747391i
$421$	−4.70700	+	14.4867i	−0.229405	+	0.706037i	0.768409	+	0.639959i	$0.221049\pi$
$421$	−4.70700	+	14.4867i	−0.229405	+	0.706037i	−0.997814	+	0.0660781i	$0.978951\pi$
$422$	0.271898	+	0.836817i	0.0132358	+	0.0407356i
$423$	−47.9591	+	34.8443i	−2.33185	+	1.69419i
$424$	−2.19136	−	6.74431i	−0.106422	−	0.327533i
$425$	−3.93317	−	2.85762i	−0.190787	−	0.138615i
$426$	7.69750	+	5.59256i	0.372945	+	0.270961i
$427$	3.70157	−	2.68935i	0.179131	−	0.130147i
$428$	−32.8348			−1.58713
$429$	−25.1522			−1.21436
$430$	−3.20972	+	2.33200i	−0.154786	+	0.112459i
$431$	2.53639	−	7.80622i	0.122174	−	0.376012i	−0.871202	−	0.490925i	$-0.836659\pi$
$431$	2.53639	−	7.80622i	0.122174	−	0.376012i	0.993376	+	0.114913i	$0.0366589\pi$
$432$	16.4006	+	50.4758i	0.789074	+	2.42852i
$433$	−27.8717			−1.33943			−0.669713	−	0.742620i	$-0.733583\pi$
$433$	−27.8717			−1.33943			−0.669713	+	0.742620i	$0.733583\pi$
$434$	1.86703	−	0.277919i	0.0896204	−	0.0133406i
$435$	65.2017			3.12618
$436$	3.98043	+	12.2505i	0.190628	+	0.586693i
$437$	−5.77823	+	17.7836i	−0.276410	+	0.850703i
$438$	9.58300	−	6.96246i	0.457894	−	0.332679i
$439$	39.8032			1.89970			0.949851	−	0.312703i	$-0.101234\pi$
$439$	39.8032			1.89970			0.949851	+	0.312703i	$0.101234\pi$
$440$	6.99485			0.333466
$441$	31.9994	−	23.2489i	1.52378	−	1.10709i
$442$	−0.728352	−	0.529179i	−0.0346442	−	0.0251705i
$443$	7.66369	+	5.56799i	0.364113	+	0.264543i	0.754765	−	0.655995i	$-0.227751\pi$
$443$	7.66369	+	5.56799i	0.364113	+	0.264543i	−0.390653	+	0.920538i	$0.627751\pi$
$444$	−8.21914	−	25.2959i	−0.390063	−	1.20049i
$445$	36.8402	−	26.7660i	1.74639	−	1.26883i
$446$	1.47412	+	4.53687i	0.0698016	+	0.214827i
$447$	−14.3825	+	44.2647i	−0.680267	+	2.09365i
$448$	6.91421	+	5.02347i	0.326666	+	0.237336i
$449$	9.18828	−	28.2786i	0.433622	−	1.33455i	−0.460870	−	0.887468i	$-0.652463\pi$
$449$	9.18828	−	28.2786i	0.433622	−	1.33455i	0.894492	−	0.447084i	$-0.147537\pi$
$450$	−2.90132	+	8.92936i	−0.136770	+	0.420934i
$451$	4.87767	+	3.54383i	0.229680	+	0.166873i
$452$	−3.74032	+	11.5115i	−0.175930	+	0.541457i
$453$	−13.0253	−	40.0878i	−0.611982	−	1.88349i
$454$	−5.12185	+	3.72125i	−0.240381	+	0.174647i
$455$	−4.50392	−	13.8616i	−0.211147	−	0.649843i
$456$	−13.0653	−	9.49253i	−0.611841	−	0.444528i
$457$	16.7545	+	12.1729i	0.783744	+	0.569423i	0.906100	−	0.423063i	$-0.139045\pi$
$457$	16.7545	+	12.1729i	0.783744	+	0.569423i	−0.122356	+	0.992486i	$0.539045\pi$
$458$	3.93434	−	2.85847i	0.183840	−	0.133567i
$459$	14.7028			0.686268
$460$	23.0258			1.07358
$461$	12.4610	−	9.05345i	0.580367	−	0.421661i	−0.258489	−	0.966014i	$-0.583225\pi$
$461$	12.4610	−	9.05345i	0.580367	−	0.421661i	0.838856	+	0.544353i	$0.183225\pi$
$462$	−0.750575	+	2.31003i	−0.0349199	+	0.107472i
$463$	3.14060	+	9.66576i	0.145956	+	0.449206i	0.997133	−	0.0756730i	$-0.0241105\pi$
$463$	3.14060	+	9.66576i	0.145956	+	0.449206i	−0.851177	+	0.524879i	$0.824111\pi$
$464$	23.0957			1.07219
$465$	−25.2875	−	50.7929i	−1.17268	−	2.35546i
$466$	−0.750362			−0.0347599
$467$	5.94540	+	18.2980i	0.275120	+	0.846733i	0.989188	+	0.146656i	$0.0468510\pi$
$467$	5.94540	+	18.2980i	0.275120	+	0.846733i	−0.714067	+	0.700077i	$0.753149\pi$
$468$	15.8024	−	48.6349i	0.730468	−	2.24815i
$469$	15.3176	−	11.1289i	0.707302	−	0.513885i
$470$	−6.33928			−0.292409
$471$	70.6996			3.25766
$472$	−5.60971	+	4.07569i	−0.258208	+	0.187599i
$473$	8.79942	+	6.39315i	0.404598	+	0.293958i
$474$	−5.98589	−	4.34901i	−0.274941	−	0.199756i
$475$	7.41055	+	22.8073i	0.340019	+	1.04647i
$476$	2.06874	−	1.50303i	0.0948208	−	0.0688913i
$477$	−16.3569	−	50.3414i	−0.748932	−	2.30497i
$478$	−0.0918996	+	0.282838i	−0.00420339	+	0.0129367i
$479$	10.8817	+	7.90600i	0.497196	+	0.361234i	0.807945	−	0.589258i	$-0.200580\pi$
$479$	10.8817	+	7.90600i	0.497196	+	0.361234i	−0.310749	+	0.950492i	$0.600580\pi$
$480$	−9.26941	+	28.5283i	−0.423089	+	1.30213i
$481$	−4.59706	+	14.1483i	−0.209608	+	0.645107i
$482$	−3.92054	−	2.84844i	−0.178576	−	0.129743i
$483$	−5.02552	+	15.4670i	−0.228669	+	0.703772i
$484$	3.66145	+	11.2688i	0.166430	+	0.512218i
$485$	6.44223	−	4.68056i	0.292527	−	0.212533i
$486$	−2.96446	−	9.12368i	−0.134471	−	0.413859i
$487$	−24.9597	−	18.1343i	−1.13103	−	0.821744i	−0.145189	−	0.989404i	$-0.546379\pi$
$487$	−24.9597	−	18.1343i	−1.13103	−	0.821744i	−0.985845	+	0.167660i	$0.946379\pi$
$488$	2.82486	+	2.05238i	0.127875	+	0.0929069i
$489$	14.2232	−	10.3338i	0.643195	−	0.467309i
$490$	4.22971			0.191079
$491$	−28.2292			−1.27397			−0.636983	−	0.770878i	$-0.719818\pi$
$491$	−28.2292			−1.27397			−0.636983	+	0.770878i	$0.719818\pi$
$492$	−13.8675	+	10.0753i	−0.625196	+	0.454232i
$493$	1.97713	−	6.08500i	0.0890457	−	0.274054i
$494$	1.37230	+	4.22350i	0.0617427	+	0.190024i
$495$	52.2115			2.34673
$496$	−8.95732	−	17.9918i	−0.402195	−	0.807856i
$497$	15.1151			0.678006
$498$	−1.79397	−	5.52127i	−0.0803897	−	0.247414i
$499$	−7.58365	+	23.3401i	−0.339491	+	1.04485i	0.624976	+	0.780644i	$0.285109\pi$
$499$	−7.58365	+	23.3401i	−0.339491	+	1.04485i	−0.964467	+	0.264202i	$0.914891\pi$
$500$	−0.679786	+	0.493893i	−0.0304010	+	0.0220876i
$501$	−60.6544			−2.70984
$502$	2.54504			0.113591
$503$	19.3951	−	14.0914i	0.864786	−	0.628304i	−0.0643967	−	0.997924i	$-0.520512\pi$
$503$	19.3951	−	14.0914i	0.864786	−	0.628304i	0.929183	+	0.369621i	$0.120512\pi$
$504$	−8.12618	−	5.90401i	−0.361969	−	0.262986i
$505$	−34.7564	−	25.2520i	−1.54664	−	1.12370i
$506$	0.663216	+	2.04117i	0.0294835	+	0.0907410i
$507$	1.77211	−	1.28751i	0.0787020	−	0.0571803i
$508$	1.07293	+	3.30215i	0.0476038	+	0.146509i
$509$	−4.83211	+	14.8717i	−0.214180	+	0.659177i	0.785031	+	0.619456i	$0.212647\pi$
$509$	−4.83211	+	14.8717i	−0.214180	+	0.659177i	−0.999211	+	0.0397210i	$0.987353\pi$
$510$	2.11423	+	1.53608i	0.0936198	+	0.0680188i
$511$	5.81495	−	17.8966i	0.257238	−	0.791698i
$512$	−5.53422	+	17.0326i	−0.244580	+	0.752741i
$513$	−58.6733	−	42.6287i	−2.59049	−	1.88210i
$514$	2.06125	−	6.34386i	0.0909177	−	0.279816i
$515$	8.45781	+	26.0304i	0.372695	+	1.14704i
$516$	−25.0173	+	18.1762i	−1.10133	+	0.800161i
$517$	5.37043	+	16.5285i	0.236191	+	0.726922i
$518$	1.16223	+	0.844409i	0.0510654	+	0.0371012i
$519$	16.7803	+	12.1916i	0.736572	+	0.535151i
$520$	8.99864	−	6.53790i	0.394617	−	0.286706i
$521$	34.1230			1.49495			0.747477	−	0.664288i	$-0.231265\pi$
$521$	34.1230			1.49495			0.747477	+	0.664288i	$0.231265\pi$
$522$	−12.3561			−0.540813
$523$	−9.04426	+	6.57104i	−0.395478	+	0.287332i	−0.767697	−	0.640814i	$-0.778597\pi$
$523$	−9.04426	+	6.57104i	−0.395478	+	0.287332i	0.372219	+	0.928145i	$0.378597\pi$
$524$	5.32748	−	16.3963i	0.232732	−	0.716275i
$525$	6.44520	+	19.8363i	0.281292	+	0.865727i
$526$	−3.09304			−0.134863
$527$	−5.50709	+	0.819764i	−0.239892	+	0.0357095i
$528$	25.8618			1.12549
$529$	−2.66679	−	8.20753i	−0.115947	−	0.356849i
$530$	1.74916	−	5.38335i	0.0759784	−	0.233838i
$531$	−41.8724	+	30.4221i	−1.81711	+	1.32021i
$532$	−12.6134			−0.546860
$533$	9.58728			0.415271
$534$	−9.76264	+	7.09297i	−0.422471	+	0.306943i
$535$	−43.1279	−	31.3342i	−1.86458	−	1.35470i
$536$	11.6897	+	8.49305i	0.504917	+	0.366844i
$537$	−3.03488	−	9.34039i	−0.130965	−	0.403068i
$538$	4.05576	−	2.94669i	0.174856	−	0.127041i
$539$	−3.58328	−	11.0282i	−0.154343	−	0.475018i
$540$	−27.5974	+	84.9359i	−1.18760	+	3.65506i
$541$	0.858841	+	0.623984i	0.0369244	+	0.0268272i	0.606094	−	0.795393i	$-0.292735\pi$
$541$	0.858841	+	0.623984i	0.0369244	+	0.0268272i	−0.569170	+	0.822220i	$0.692735\pi$
$542$	1.46922	−	4.52178i	0.0631082	−	0.194227i
$543$	11.9150	−	36.6707i	0.511323	−	1.57369i
$544$	2.38135	+	1.73015i	0.102099	+	0.0741795i
$545$	−6.46243	+	19.8893i	−0.276820	+	0.851965i
$546$	1.19354	+	3.67332i	0.0510786	+	0.157204i
$547$	4.90926	−	3.56678i	0.209905	−	0.152505i	−0.477866	−	0.878433i	$-0.658590\pi$
$547$	4.90926	−	3.56678i	0.209905	−	0.152505i	0.687771	+	0.725928i	$0.258590\pi$
$548$	1.34389	+	4.13606i	0.0574080	+	0.176684i
$549$	21.0855	+	15.3195i	0.899908	+	0.653822i
$550$	2.22682	+	1.61788i	0.0949520	+	0.0689867i
$551$	−25.5326	+	18.5505i	−1.08772	+	0.790277i
$552$	−12.4111			−0.528251
$553$	−11.7541			−0.499837
$554$	−3.80252	+	2.76269i	−0.161553	+	0.117375i
$555$	13.3442	−	41.0691i	0.566429	−	1.74329i
$556$	0.467762	+	1.43962i	0.0198375	+	0.0610536i
$557$	31.8626			1.35006			0.675032	−	0.737789i	$-0.264130\pi$
$557$	31.8626			1.35006			0.675032	+	0.737789i	$0.264130\pi$
$558$	4.79214	+	9.62557i	0.202868	+	0.407483i
$559$	17.2957			0.731529
$560$	4.63099	+	14.2527i	0.195695	+	0.602287i
$561$	2.21393	−	6.81379i	0.0934723	−	0.287678i
$562$	−1.07427	+	0.780506i	−0.0453155	+	0.0329237i
$563$	31.2863			1.31856			0.659279	−	0.751898i	$-0.270862\pi$
$563$	31.2863			1.31856			0.659279	+	0.751898i	$0.270862\pi$
$564$	−49.4099			−2.08053
$565$	−15.8983	+	11.5508i	−0.668845	+	0.485944i
$566$	−0.243118	−	0.176636i	−0.0102190	−	0.00742454i
$567$	−26.8668	−	19.5199i	−1.12830	−	0.819759i
$568$	3.56455	+	10.9706i	0.149565	+	0.460315i
$569$	17.4192	−	12.6558i	0.730250	−	0.530557i	−0.159393	−	0.987215i	$-0.550954\pi$
$569$	17.4192	−	12.6558i	0.730250	−	0.530557i	0.889642	+	0.456658i	$0.150954\pi$
$570$	−3.98346	−	12.2598i	−0.166849	−	0.513507i
$571$	9.05728	−	27.8754i	0.379035	−	1.16655i	−0.561681	−	0.827354i	$-0.689845\pi$
$571$	9.05728	−	27.8754i	0.379035	−	1.16655i	0.940716	−	0.339196i	$-0.110155\pi$
$572$	−12.1287	−	8.81200i	−0.507125	−	0.368448i
$573$	23.3815	−	71.9608i	0.976775	−	3.00620i
$574$	0.286098	−	0.880518i	0.0119415	−	0.0367521i
$575$	14.9098	+	10.8326i	0.621783	+	0.451751i
$576$	−15.0441	+	46.3010i	−0.626837	+	1.92921i
$577$	−5.84688	−	17.9949i	−0.243409	−	0.749136i	−0.995894	−	0.0905265i	$-0.971145\pi$
$577$	−5.84688	−	17.9949i	−0.243409	−	0.749136i	0.752485	−	0.658609i	$-0.228855\pi$
$578$	0.207466	−	0.150733i	0.00862947	−	0.00626968i
$579$	17.7408	+	54.6006i	0.737283	+	2.26913i
$580$	31.4410	+	22.8432i	1.30552	+	0.948513i
$581$	−7.46122	−	5.42089i	−0.309544	−	0.224897i
$582$	−1.70719	+	1.24034i	−0.0707652	+	0.0514140i
$583$	−15.5179			−0.642686
$584$	14.3607			0.594249
$585$	67.1684	−	48.8007i	2.77707	−	2.01766i
$586$	−1.53254	+	4.71669i	−0.0633088	+	0.194845i
$587$	1.01189	+	3.11428i	0.0417652	+	0.128540i	0.969765	−	0.244041i	$-0.0784730\pi$
$587$	1.01189	+	3.11428i	0.0417652	+	0.128540i	−0.928000	+	0.372581i	$0.878473\pi$
$588$	32.9674			1.35955
$589$	24.3535	+	12.6956i	1.00347	+	0.523114i
$590$	−5.53474			−0.227862
$591$	−15.4057	−	47.4140i	−0.633708	−	1.95035i
$592$	4.72676	−	14.5475i	0.194269	−	0.597898i
$593$	7.21040	−	5.23866i	0.296095	−	0.215126i	−0.429812	−	0.902918i	$-0.641420\pi$
$593$	7.21040	−	5.23866i	0.296095	−	0.215126i	0.725907	+	0.687793i	$0.241420\pi$
$594$	−8.32421			−0.341546
$595$	4.15159			0.170199
$596$	−22.4434	+	16.3061i	−0.919318	+	0.667923i
$597$	−13.1696	−	9.56824i	−0.538994	−	0.391602i
$598$	2.76103	+	2.00601i	0.112907	+	0.0820317i
$599$	−2.01993	−	6.21670i	−0.0825320	−	0.254007i	0.901272	−	0.433253i	$-0.142634\pi$
$599$	−2.01993	−	6.21670i	−0.0825320	−	0.254007i	−0.983804	+	0.179246i	$0.942634\pi$
$600$	−12.8773	+	9.35587i	−0.525712	+	0.381952i
$601$	−4.20532	−	12.9426i	−0.171539	−	0.527941i	0.827920	−	0.560846i	$-0.189524\pi$
$601$	−4.20532	−	12.9426i	−0.171539	−	0.527941i	−0.999458	+	0.0329050i	$0.989524\pi$
$602$	0.516126	−	1.58847i	0.0210357	−	0.0647414i
$603$	87.2549	+	63.3944i	3.55330	+	2.58162i
$604$	7.76368	−	23.8942i	0.315900	−	0.972239i
$605$	−5.94455	+	18.2954i	−0.241680	+	0.743816i
$606$	9.21043	+	6.69177i	0.374148	+	0.271835i
$607$	−9.59401	+	29.5273i	−0.389409	+	1.19848i	0.543822	+	0.839200i	$0.316977\pi$
$607$	−9.59401	+	29.5273i	−0.389409	+	1.19848i	−0.933231	+	0.359277i	$0.883023\pi$
$608$	−4.48673	−	13.8087i	−0.181961	−	0.560018i
$609$	−22.2065	+	16.1340i	−0.899854	+	0.653782i
$610$	0.861264	+	2.65070i	0.0348715	+	0.107324i
$611$	22.3576	+	16.2438i	0.904493	+	0.657152i
$612$	11.7844	+	8.56183i	0.476354	+	0.346092i
$613$	36.3723	−	26.4260i	1.46906	−	1.06734i	0.488180	−	0.872743i	$-0.337661\pi$
$613$	36.3723	−	26.4260i	1.46906	−	1.06734i	0.980884	−	0.194594i	$-0.0623390\pi$
$614$	0.396627			0.0160065
$615$	−27.8296			−1.12220
$616$	−2.38232	+	1.73086i	−0.0959865	+	0.0697383i
$617$	10.5787	−	32.5578i	0.425881	−	1.31073i	−0.476267	−	0.879301i	$-0.658010\pi$
$617$	10.5787	−	32.5578i	0.425881	−	1.31073i	0.902148	−	0.431426i	$-0.141990\pi$
$618$	−2.24131	−	6.89805i	−0.0901588	−	0.277480i
$619$	−32.9777			−1.32549			−0.662743	−	0.748847i	$-0.730608\pi$
$619$	−32.9777			−1.32549			−0.662743	+	0.748847i	$0.730608\pi$
$620$	5.60121	−	33.3523i	0.224950	−	1.33946i
$621$	−55.7352			−2.23658
$622$	2.05668	+	6.32980i	0.0824652	+	0.253802i
$623$	−5.92395	+	18.2320i	−0.237338	+	0.730452i
$624$	33.2704	−	24.1723i	1.33188	−	0.967668i
$625$	−25.6725			−1.02690
$626$	−7.23390			−0.289125
$627$	−28.5906	+	20.7723i	−1.14180	+	0.829564i
$628$	34.0922	+	24.7694i	1.36042	+	0.988407i
$629$	−3.42817	−	2.49071i	−0.136690	−	0.0993111i
$630$	−2.47757	−	7.62517i	−0.0987087	−	0.303794i
$631$	−3.76774	+	2.73742i	−0.149991	+	0.108975i	−0.660250	−	0.751046i	$-0.729550\pi$
$631$	−3.76774	+	2.73742i	−0.149991	+	0.108975i	0.510259	+	0.860021i	$0.329550\pi$
$632$	−2.77194	−	8.53117i	−0.110262	−	0.339352i
$633$	−3.44069	+	10.5894i	−0.136755	+	0.420889i
$634$	2.87397	+	2.08806i	0.114140	+	0.0829274i
$635$	−1.74196	+	5.36121i	−0.0691277	+	0.212753i
$636$	13.6333	−	41.9591i	0.540597	−	1.66379i
$637$	−14.9175	−	10.8382i	−0.591054	−	0.429426i
$638$	−1.11938	+	3.44511i	−0.0443168	+	0.136393i
$639$	26.6068	+	81.8874i	1.05255	+	3.23941i
$640$	−19.1682	+	13.9265i	−0.757691	+	0.550495i
$641$	−0.420747	−	1.29493i	−0.0166185	−	0.0511465i	0.942403	−	0.334479i	$-0.108560\pi$
$641$	−0.420747	−	1.29493i	−0.0166185	−	0.0511465i	−0.959022	+	0.283332i	$0.908560\pi$
$642$	11.4289	+	8.30355i	0.451061	+	0.327715i
$643$	17.7823	+	12.9196i	0.701265	+	0.509499i	0.880344	−	0.474336i	$-0.157312\pi$
$643$	17.7823	+	12.9196i	0.701265	+	0.509499i	−0.179079	+	0.983835i	$0.557312\pi$
$644$	−7.84218	+	5.69767i	−0.309025	+	0.224520i
$645$	−50.2052			−1.97683
$646$	−1.26495			−0.0497688
$647$	−17.1438	+	12.4557i	−0.673993	+	0.489685i	−0.871360	−	0.490645i	$-0.836761\pi$
$647$	−17.1438	+	12.4557i	−0.673993	+	0.489685i	0.197366	+	0.980330i	$0.436761\pi$
$648$	7.83164	−	24.1033i	0.307656	−	0.946867i
$649$	4.68885	+	14.4308i	0.184053	+	0.566458i
$650$	4.37692			0.171677
$651$	21.1810	+	11.0418i	0.830151	+	0.432763i
$652$	10.4790			0.410389
$653$	−6.25734	−	19.2581i	−0.244869	−	0.753629i	−0.995658	−	0.0930868i	$-0.970327\pi$
$653$	−6.25734	−	19.2581i	−0.244869	−	0.753629i	0.750789	−	0.660542i	$-0.229673\pi$
$654$	1.71254	−	5.27066i	0.0669656	−	0.206099i
$655$	22.6445	−	16.4522i	0.884793	−	0.642840i
$656$	−9.85777			−0.384881
$657$	107.192			4.18196
$658$	2.15905	−	1.56864i	0.0841684	−	0.0611519i
$659$	8.69525	+	6.31747i	0.338719	+	0.246094i	0.744121	−	0.668045i	$-0.232869\pi$
$659$	8.69525	+	6.31747i	0.338719	+	0.246094i	−0.405402	+	0.914138i	$0.632869\pi$
$660$	35.2067	+	25.5791i	1.37042	+	0.995666i
$661$	−7.30234	−	22.4743i	−0.284028	−	0.874149i	−0.986688	−	0.162623i	$-0.948005\pi$
$661$	−7.30234	−	22.4743i	−0.284028	−	0.874149i	0.702660	−	0.711526i	$-0.251995\pi$
$662$	5.68813	−	4.13267i	0.221076	−	0.160621i
$663$	−3.52051	−	10.8350i	−0.136725	−	0.420797i
$664$	2.17493	−	6.69376i	0.0844038	−	0.259768i
$665$	−16.5674	−	12.0369i	−0.642457	−	0.466772i
$666$	−2.52881	+	7.78287i	−0.0979893	+	0.301580i
$667$	−7.49490	+	23.0669i	−0.290204	+	0.893155i
$668$	−29.2482	−	21.2501i	−1.13165	−	0.822191i
$669$	−18.6540	+	57.4111i	−0.721206	+	2.21964i
$670$	3.56403	+	10.9690i	0.137691	+	0.423768i
$671$	6.18157	−	4.49117i	0.238637	−	0.173380i
$672$	−3.90226	−	12.0099i	−0.150533	−	0.463293i
$673$	6.58663	+	4.78547i	0.253896	+	0.184466i	0.707452	−	0.706762i	$-0.249845\pi$
$673$	6.58663	+	4.78547i	0.253896	+	0.184466i	−0.453556	+	0.891228i	$0.649845\pi$
$674$	6.69778	+	4.86622i	0.257989	+	0.187440i
$675$	−57.8286	+	42.0150i	−2.22583	+	1.61716i
$676$	1.30561			0.0502156
$677$	−25.3361			−0.973744			−0.486872	−	0.873473i	$-0.661862\pi$
$677$	−25.3361			−0.973744			−0.486872	+	0.873473i	$0.661862\pi$
$678$	4.21303	−	3.06095i	0.161800	−	0.117555i
$679$	−1.03592	+	3.18823i	−0.0397549	+	0.122353i
$680$	0.979058	+	3.01323i	0.0375452	+	0.115552i
$681$	−80.1141			−3.06998
$682$	3.11792	−	0.464122i	0.119391	−	0.0177721i
$683$	−23.8448			−0.912396			−0.456198	−	0.889878i	$-0.650789\pi$
$683$	−23.8448			−0.912396			−0.456198	+	0.889878i	$0.650789\pi$
$684$	−22.2031	−	68.3341i	−0.848956	−	2.61282i
$685$	−2.18187	+	6.71510i	−0.0833648	+	0.256571i
$686$	−3.36050	+	2.44154i	−0.128304	+	0.0932185i
$687$	61.5395			2.34788
$688$	−17.7836			−0.677995
$689$	−19.9633	+	14.5042i	−0.760540	+	0.552565i
$690$	−8.01461	−	5.82296i	−0.305111	−	0.221676i
$691$	−27.6338	−	20.0771i	−1.05124	−	0.763770i	−0.0787913	−	0.996891i	$-0.525106\pi$
$691$	−27.6338	−	20.0771i	−1.05124	−	0.763770i	−0.972448	+	0.233121i	$0.925106\pi$
$692$	3.82035	+	11.7578i	0.145228	+	0.446966i
$693$	−17.7823	+	12.9196i	−0.675494	+	0.490775i
$694$	−0.766554	−	2.35921i	−0.0290980	−	0.0895544i
$695$	−0.759434	+	2.33730i	−0.0288070	+	0.0886588i
$696$	−16.9470	−	12.3127i	−0.642373	−	0.466712i
$697$	−0.843887	+	2.59722i	−0.0319645	+	0.0983766i
$698$	−0.969219	+	2.98295i	−0.0366855	+	0.112906i
$699$	−7.68189	−	5.58122i	−0.290556	−	0.211101i
$700$	−3.84164	+	11.8234i	−0.145200	+	0.446881i
$701$	4.91683	+	15.1324i	0.185706	+	0.571544i	0.999960	−	0.00896479i	$-0.00285362\pi$
$701$	4.91683	+	15.1324i	0.185706	+	0.571544i	−0.814254	+	0.580509i	$0.802854\pi$
$702$	−10.7088	+	7.78041i	−0.404178	+	0.293653i
$703$	6.45906	+	19.8790i	0.243608	+	0.749749i
$704$	11.5466	+	8.38912i	0.435180	+	0.316177i
$705$	−64.8989	−	47.1518i	−2.44423	−	1.77584i
$706$	1.43988	−	1.04613i	0.0541906	−	0.0393718i
$707$	18.0860			0.680193
$708$	−43.1391			−1.62127
$709$	17.0815	−	12.4105i	0.641510	−	0.466084i	−0.218858	−	0.975757i	$-0.570233\pi$
$709$	17.0815	−	12.4105i	0.641510	−	0.466084i	0.860369	+	0.509672i	$0.170233\pi$
$710$	−2.84525	+	8.75677i	−0.106780	+	0.328636i
$711$	−20.6906	−	63.6790i	−0.775956	−	2.38815i
$712$	−14.6299			−0.548278
$713$	20.8762	−	3.10755i	0.781820	−	0.116379i
$714$	−1.10017			−0.0411728
$715$	−7.52148	−	23.1487i	−0.281288	−	0.865714i
$716$	1.80893	−	5.56731i	0.0676028	−	0.208060i
$717$	−3.04459	+	2.21202i	−0.113702	+	0.0826095i
$718$	−6.38227			−0.238184
$719$	−15.6123			−0.582242			−0.291121	−	0.956686i	$-0.594028\pi$
$719$	−15.6123			−0.582242			−0.291121	+	0.956686i	$0.594028\pi$
$720$	−69.0634	+	50.1775i	−2.57384	+	1.87001i
$721$	−9.32175	−	6.77265i	−0.347160	−	0.252227i
$722$	1.10607	+	0.803605i	0.0411636	+	0.0299071i
$723$	−18.9500	−	58.3222i	−0.704759	−	2.16903i
$724$	18.5930	−	13.5086i	0.691004	−	0.502044i
$725$	9.61217	+	29.5832i	0.356987	+	1.09869i
$726$	1.57530	−	4.84828i	0.0584649	−	0.179937i
$727$	−11.3615	−	8.25464i	−0.421376	−	0.306148i	0.356815	−	0.934175i	$-0.383863\pi$
$727$	−11.3615	−	8.25464i	−0.421376	−	0.306148i	−0.778191	+	0.628027i	$0.783863\pi$
$728$	−1.44699	+	4.45338i	−0.0536291	+	0.165053i
$729$	14.2258	−	43.7826i	0.526882	−	1.62158i
$730$	9.27357	+	6.73764i	0.343230	+	0.249371i
$731$	−1.52239	+	4.68544i	−0.0563077	+	0.173297i
$732$	6.71290	+	20.6602i	0.248116	+	0.763622i
$733$	−13.0939	+	9.51330i	−0.483636	+	0.351382i	−0.802732	−	0.596341i	$-0.796621\pi$
$733$	−13.0939	+	9.51330i	−0.483636	+	0.351382i	0.319096	+	0.947722i	$0.396621\pi$
$734$	1.39871	+	4.30478i	0.0516273	+	0.158892i
$735$	43.3020	+	31.4607i	1.59722	+	1.16045i
$736$	−9.02718	−	6.55863i	−0.332746	−	0.241754i
$737$	25.5802	−	18.5851i	0.942259	−	0.684591i
$738$	5.27389			0.194134
$739$	−19.3937			−0.713408			−0.356704	−	0.934217i	$-0.616100\pi$
$739$	−19.3937			−0.713408			−0.356704	+	0.934217i	$0.616100\pi$
$740$	20.8232	−	15.1289i	0.765475	−	0.556150i
$741$	−17.3655	+	53.4456i	−0.637939	+	1.96337i
$742$	0.736364	+	2.26630i	0.0270328	+	0.0831983i
$743$	−46.0122			−1.68803			−0.844013	−	0.536323i	$-0.819813\pi$
$743$	−46.0122			−1.68803			−0.844013	+	0.536323i	$0.819813\pi$
$744$	−3.01910	+	17.9772i	−0.110686	+	0.659076i
$745$	−45.0398			−1.65013
$746$	0.404745	+	1.24568i	0.0148188	+	0.0456075i
$747$	16.2343	−	49.9640i	0.593982	−	1.82809i
$748$	3.45478	−	2.51004i	0.126319	−	0.0917762i
$749$	22.4422			0.820018
$750$	0.361514			0.0132006
$751$	17.0365	−	12.3777i	0.621670	−	0.451669i	−0.231835	−	0.972755i	$-0.574473\pi$
$751$	17.0365	−	12.3777i	0.621670	−	0.451669i	0.853504	+	0.521086i	$0.174473\pi$
$752$	−22.9884	−	16.7021i	−0.838301	−	0.609061i
$753$	26.0550	+	18.9301i	0.949497	+	0.689850i
$754$	1.78000	+	5.47828i	0.0648238	+	0.199507i
$755$	32.9996	−	23.9756i	1.20098	−	0.872561i
$756$	−11.6180	−	35.7566i	−0.422543	−	1.30045i
$757$	−9.13239	+	28.1066i	−0.331922	+	1.02155i	0.636296	+	0.771445i	$0.280466\pi$
$757$	−9.13239	+	28.1066i	−0.331922	+	1.02155i	−0.968218	+	0.250107i	$0.919534\pi$
$758$	−4.69618	−	3.41198i	−0.170573	−	0.123929i
$759$	−8.39256	+	25.8296i	−0.304631	+	0.937556i
$760$	4.82938	−	14.8633i	0.175180	−	0.539148i
$761$	−14.0571	−	10.2131i	−0.509571	−	0.370225i	0.303090	−	0.952962i	$-0.401982\pi$
$761$	−14.0571	−	10.2131i	−0.509571	−	0.370225i	−0.812661	+	0.582737i	$0.801982\pi$
$762$	0.461619	−	1.42072i	0.0167227	−	0.0514671i
$763$	−2.72057	−	8.37306i	−0.0984913	−	0.303125i
$764$	36.4861	−	26.5087i	1.32002	−	0.959050i
$765$	7.30796	+	22.4916i	0.264220	+	0.813185i
$766$	2.16052	+	1.56971i	0.0780629	+	0.0567160i
$767$	19.5201	+	14.1822i	0.704831	+	0.512090i
$768$	−28.8644	+	20.9712i	−1.04155	+	0.756734i
$769$	30.1202			1.08616			0.543081	−	0.839680i	$-0.317257\pi$
$769$	30.1202			1.08616			0.543081	+	0.839680i	$0.317257\pi$
$770$	−2.35048			−0.0847056
$771$	68.2880	−	49.6142i	2.45933	−	1.78681i
$772$	−10.5744	+	32.5445i	−0.380579	+	1.17130i
$773$	−2.02834	−	6.24260i	−0.0729544	−	0.224531i	0.907930	−	0.419122i	$-0.137662\pi$
$773$	−2.02834	−	6.24260i	−0.0729544	−	0.224531i	−0.980884	+	0.194591i	$0.937662\pi$
$774$	9.51421			0.341981
$775$	19.3177	−	18.9614i	0.693913	−	0.681114i
$776$	−2.55832			−0.0918383
$777$	5.61767	+	17.2894i	0.201533	+	0.620254i
$778$	−0.0168107	+	0.0517379i	−0.000602691	+	0.00185489i
$779$	10.8979	−	7.91778i	0.390457	−	0.283684i
$780$	69.2003			2.47777
$781$	25.2420			0.903232
$782$	−0.786462	+	0.571398i	−0.0281238	+	0.0204331i
$783$	−76.1047	−	55.2933i	−2.71976	−	1.97602i
$784$	15.3384	+	11.1440i	0.547800	+	0.398000i
$785$	21.1419	+	65.0682i	0.754588	+	2.32238i
$786$	−6.00077	+	4.35982i	−0.214041	+	0.155510i
$787$	−13.7937	−	42.4527i	−0.491693	−	1.51328i	−0.822047	−	0.569420i	$-0.807168\pi$
$787$	−13.7937	−	42.4527i	−0.491693	−	1.51328i	0.330354	−	0.943857i	$-0.392832\pi$
$788$	9.18254	−	28.2609i	0.327114	−	1.00675i
$789$	−31.6652	−	23.0061i	−1.12731	−	0.819040i
$790$	2.21258	−	6.80962i	0.0787201	−	0.242275i
$791$	2.55646	−	7.86797i	0.0908972	−	0.279753i
$792$	−13.5706	−	9.85963i	−0.482211	−	0.350347i
$793$	3.75460	−	11.5555i	0.133330	−	0.410347i
$794$	2.27858	+	7.01274i	0.0808637	+	0.248873i
$795$	57.9486	−	42.1021i	2.05523	−	1.49321i
$796$	−2.99831	−	9.22784i	−0.106272	−	0.327072i
$797$	−36.1949	−	26.2971i	−1.28209	−	0.931493i	−0.282476	−	0.959274i	$-0.591156\pi$
$797$	−36.1949	−	26.2971i	−1.28209	−	0.931493i	−0.999614	+	0.0277817i	$0.991156\pi$
$798$	4.39036	+	3.18978i	0.155417	+	0.112917i
$799$	−6.36843	+	4.62693i	−0.225299	+	0.163689i
$800$	−14.3103			−0.505947
$801$	−109.201			−3.85844
$802$	5.49770	−	3.99431i	0.194130	−	0.141044i
$803$	9.71089	−	29.8870i	0.342690	−	1.05469i
$804$	27.7789	+	85.4948i	0.979688	+	3.01517i
$805$	−15.7378			−0.554685
$806$	3.57730	−	3.51131i	0.126005	−	0.123681i
$807$	63.4387			2.23315
$808$	4.26516	+	13.1268i	0.150048	+	0.461800i
$809$	4.71267	−	14.5041i	0.165689	−	0.509937i	−0.833398	−	0.552674i	$-0.813608\pi$
$809$	4.71267	−	14.5041i	0.165689	−	0.509937i	0.999086	+	0.0427364i	$0.0136076\pi$
$810$	16.3660	−	11.8906i	0.575043	−	0.417793i
$811$	−9.06694			−0.318383			−0.159192	−	0.987248i	$-0.550889\pi$
$811$	−9.06694			−0.318383			−0.159192	+	0.987248i	$0.550889\pi$
$812$	−16.3607			−0.574150
$813$	48.6744	−	35.3640i	1.70708	−	1.24027i
$814$	1.94091	+	1.41015i	0.0680288	+	0.0494258i
$815$	13.7639	+	10.0001i	0.482130	+	0.350288i
$816$	3.61984	+	11.1407i	0.126720	+	0.390003i
$817$	19.6600	−	14.2839i	0.687818	−	0.499729i
$818$	1.49378	+	4.59737i	0.0522287	+	0.160743i
$819$	−10.8007	+	33.2413i	−0.377409	+	1.16154i
$820$	−13.4198	−	9.75002i	−0.468638	−	0.340485i
$821$	11.5225	−	35.4627i	0.402139	−	1.23766i	−0.521122	−	0.853482i	$-0.674486\pi$
$821$	11.5225	−	35.4627i	0.402139	−	1.23766i	0.923261	−	0.384174i	$-0.125514\pi$
$822$	0.578193	−	1.77950i	0.0201668	−	0.0620671i
$823$	14.9677	+	10.8747i	0.521742	+	0.379068i	0.817260	−	0.576269i	$-0.195492\pi$
$823$	14.9677	+	10.8747i	0.521742	+	0.379068i	−0.295518	+	0.955337i	$0.595492\pi$
$824$	2.71727	−	8.36291i	0.0946607	−	0.291336i
$825$	10.7634	+	33.1264i	0.374734	+	1.15331i
$826$	1.88503	−	1.36956i	0.0655887	−	0.0476530i
$827$	1.17077	+	3.60326i	0.0407116	+	0.125297i	0.969347	−	0.245697i	$-0.0790169\pi$
$827$	1.17077	+	3.60326i	0.0407116	+	0.125297i	−0.928635	+	0.370995i	$0.879017\pi$
$828$	−44.6720	−	32.4561i	−1.55246	−	1.12793i
$829$	−2.74701	−	1.99582i	−0.0954077	−	0.0693177i	0.539059	−	0.842268i	$-0.318780\pi$
$829$	−2.74701	−	1.99582i	−0.0954077	−	0.0693177i	−0.634466	+	0.772950i	$0.718780\pi$
$830$	4.54502	−	3.30215i	0.157760	−	0.114619i
$831$	−59.4775			−2.06325
$832$	22.6955			0.786823
$833$	4.24916	−	3.08720i	0.147225	−	0.106965i
$834$	0.201250	−	0.619383i	0.00696870	−	0.0214475i
$835$	−18.1380	−	55.8231i	−0.627692	−	1.93184i
$836$	−21.0642			−0.728521
$837$	−13.5581	+	80.7312i	−0.468635	+	2.79048i
$838$	−2.51142			−0.0867554
$839$	5.87082	+	18.0685i	0.202683	+	0.623795i	0.999801	+	0.0199705i	$0.00635723\pi$
$839$	5.87082	+	18.0685i	0.202683	+	0.623795i	−0.797117	+	0.603825i	$0.793643\pi$
$840$	4.20027	−	12.9271i	0.144923	−	0.446028i
$841$	−9.65661	+	7.01594i	−0.332987	+	0.241929i
$842$	3.90618			0.134616
$843$	−16.8034			−0.578740
$844$	−5.36910	+	3.90088i	−0.184812	+	0.134274i
$845$	1.71488	+	1.24594i	0.0589938	+	0.0428615i
$846$	12.2987	+	8.93556i	0.422840	+	0.307211i
$847$	−2.50255	−	7.70207i	−0.0859888	−	0.264646i
$848$	20.5265	−	14.9134i	0.704883	−	0.512128i
$849$	−1.17512	−	3.61664i	−0.0403299	−	0.124123i
$850$	−0.385263	+	1.18572i	−0.0132144	+	0.0406698i
$851$	12.9955	+	9.44176i	0.445479	+	0.323659i
$852$	−22.1765	+	68.2524i	−0.759756	+	2.33829i
$853$	7.10680	−	21.8725i	0.243332	−	0.748899i	−0.752574	−	0.658507i	$-0.771188\pi$
$853$	7.10680	−	21.8725i	0.243332	−	0.748899i	0.995906	−	0.0903917i	$-0.0288119\pi$
$854$	−0.949240	−	0.689663i	−0.0324823	−	0.0235998i
$855$	36.0478	−	110.944i	1.23281	−	3.79419i
$856$	5.29247	+	16.2885i	0.180893	+	0.556731i
$857$	−0.0834558	+	0.0606342i	−0.00285079	+	0.00207122i	−0.589210	−	0.807980i	$-0.700561\pi$
$857$	−0.0834558	+	0.0606342i	−0.00285079	+	0.00207122i	0.586359	+	0.810051i	$0.300561\pi$
$858$	1.99319	+	6.13440i	0.0680463	+	0.209425i
$859$	34.8598	+	25.3271i	1.18940	+	0.864150i	0.993201	−	0.116414i	$-0.0371400\pi$
$859$	34.8598	+	25.3271i	1.18940	+	0.864150i	0.196199	+	0.980564i	$0.437140\pi$
$860$	−24.2095	−	17.5893i	−0.825538	−	0.599789i
$861$	9.47826	−	6.88636i	0.323018	−	0.234687i
$862$	−2.10487			−0.0716920
$863$	−7.65259			−0.260497			−0.130249	−	0.991481i	$-0.541578\pi$
$863$	−7.65259			−0.260497			−0.130249	+	0.991481i	$0.541578\pi$
$864$	35.0125	−	25.4380i	1.19115	−	0.865420i
$865$	−6.20253	+	19.0894i	−0.210892	+	0.649060i
$866$	2.20869	+	6.79766i	0.0750544	+	0.230994i
$867$	3.24511			0.110210
$868$	6.34527	+	12.7452i	0.215373	+	0.432601i
$869$	−19.6293			−0.665877
$870$	−5.16692	−	15.9021i	−0.175175	−	0.539133i
$871$	15.5371	−	47.8183i	0.526454	−	1.62026i
$872$	5.43559	−	3.94919i	0.184072	−	0.133736i
$873$	−19.0960			−0.646301
$874$	4.79516			0.162199
$875$	0.464624	−	0.337569i	0.0157072	−	0.0114119i
$876$	72.2805	+	52.5148i	2.44213	+	1.77431i
$877$	−7.19496	−	5.22745i	−0.242957	−	0.176518i	0.459643	−	0.888104i	$-0.347977\pi$
$877$	−7.19496	−	5.22745i	−0.242957	−	0.176518i	−0.702600	+	0.711586i	$0.747977\pi$
$878$	−3.15421	−	9.70765i	−0.106449	−	0.327617i
$879$	−50.7724	+	36.8883i	−1.71251	+	1.24421i
$880$	7.73369	+	23.8019i	0.260703	+	0.802360i
$881$	1.07565	−	3.31052i	0.0362397	−	0.111534i	−0.931300	−	0.364252i	$-0.881325\pi$
$881$	1.07565	−	3.31052i	0.0362397	−	0.111534i	0.967540	+	0.252718i	$0.0813245\pi$
$882$	−8.20601	−	5.96201i	−0.276311	−	0.200751i
$883$	−5.39868	+	16.6154i	−0.181680	+	0.559153i	−0.999875	−	0.0157869i	$-0.994975\pi$
$883$	−5.39868	+	16.6154i	−0.181680	+	0.559153i	0.818195	+	0.574940i	$0.194975\pi$
$884$	2.09839	−	6.45817i	0.0705764	−	0.217212i
$885$	−56.6623	−	41.1676i	−1.90468	−	1.38383i
$886$	0.750676	−	2.31034i	0.0252195	−	0.0776175i
$887$	13.2363	+	40.7372i	0.444432	+	1.36782i	0.883106	+	0.469174i	$0.155448\pi$
$887$	13.2363	+	40.7372i	0.444432	+	1.36782i	−0.438674	+	0.898646i	$0.644552\pi$
$888$	−11.2239	+	8.15462i	−0.376648	+	0.273651i
$889$	−0.733336	−	2.25698i	−0.0245953	−	0.0756966i
$890$	−9.44741	−	6.86394i	−0.316678	−	0.230080i
$891$	−44.8673	−	32.5980i	−1.50311	−	1.09207i
$892$	−29.1090	+	21.1489i	−0.974642	+	0.708119i
$893$	38.8291			1.29937
$894$	11.9355			0.399183
$895$	7.68886	−	5.58628i	0.257010	−	0.186729i
$896$	3.08227	−	9.48626i	0.102971	−	0.316914i
$897$	13.3455	+	41.0733i	0.445594	+	1.37140i
$898$	−7.62504			−0.254451
$899$	31.5887	+	16.4674i	1.05354	+	0.549219i
$900$	−70.8163			−2.36054
$901$	−2.17202	−	6.68478i	−0.0723603	−	0.222702i
$902$	0.477779	−	1.47045i	0.0159083	−	0.0489607i
$903$	17.0990	−	12.4232i	0.569019	−	0.413417i
$904$	6.31347			0.209983
$905$	37.3128			1.24032
$906$	−8.74487	+	6.35352i	−0.290529	+	0.211082i
$907$	−7.76613	−	5.64242i	−0.257870	−	0.187354i	0.451337	−	0.892353i	$-0.350947\pi$
$907$	−7.76613	−	5.64242i	−0.257870	−	0.187354i	−0.709208	+	0.705000i	$0.750947\pi$
$908$	−38.6320	−	28.0678i	−1.28205	−	0.931461i
$909$	31.8363	+	97.9822i	1.05594	+	3.24986i
$910$	−3.02382	+	2.19693i	−0.100239	+	0.0728277i
$911$	9.76933	+	30.0669i	0.323672	+	0.996161i	0.972036	+	0.234831i	$0.0754536\pi$
$911$	9.76933	+	30.0669i	0.323672	+	0.996161i	−0.648364	+	0.761331i	$0.724546\pi$
$912$	17.8555	−	54.9535i	0.591254	−	1.81969i
$913$	−12.4601	−	9.05282i	−0.412370	−	0.299605i
$914$	1.64115	−	5.05093i	0.0542843	−	0.167070i
$915$	−10.8987	+	33.5428i	−0.360301	+	1.10889i
$916$	29.6751	+	21.5602i	0.980492	+	0.712369i
$917$	−3.64126	+	11.2066i	−0.120245	+	0.370076i
$918$	−1.16513	−	3.58589i	−0.0384549	−	0.118352i
$919$	42.9366	−	31.1953i	1.41635	−	1.02904i	0.423988	−	0.905668i	$-0.360630\pi$
$919$	42.9366	−	31.1953i	1.41635	−	1.02904i	0.992361	−	0.123370i	$-0.0393702\pi$
$920$	−3.71140	−	11.4225i	−0.122361	−	0.376589i
$921$	4.06049	+	2.95012i	0.133798	+	0.0972098i
$922$	−3.19554	−	2.32169i	−0.105239	−	0.0764609i
$923$	32.4731	−	23.5931i	1.06886	−	0.776575i
$924$	−18.3203			−0.602692
$925$	20.6011			0.677359
$926$	2.10852	−	1.53193i	0.0692903	−	0.0503423i
$927$	20.2825	−	62.4230i	0.666164	−	2.05024i
$928$	−5.81971	−	17.9112i	−0.191041	−	0.587965i
$929$	20.9731			0.688107			0.344053	−	0.938950i	$-0.388200\pi$
$929$	20.9731			0.688107			0.344053	+	0.938950i	$0.388200\pi$
$930$	−10.3840	+	10.1925i	−0.340506	+	0.334225i
$931$	−25.9077			−0.849089
$932$	−1.74893	−	5.38266i	−0.0572882	−	0.176315i
$933$	−26.0259	+	80.0994i	−0.852049	+	2.62234i
$934$	3.99159	−	2.90006i	0.130609	−	0.0948930i
$935$	6.93310			0.226737
$936$	−26.6737			−0.871856
$937$	41.6228	−	30.2407i	1.35976	−	0.987922i	0.361298	−	0.932450i	$-0.382334\pi$
$937$	41.6228	−	30.2407i	1.35976	−	0.987922i	0.998460	−	0.0554718i	$-0.0176663\pi$
$938$	−3.92809	−	2.85392i	−0.128257	−	0.0931839i
$939$	−74.0576	−	53.8060i	−2.41678	−	1.75589i
$940$	−14.7755	−	45.4743i	−0.481923	−	1.48321i
$941$	−20.3378	+	14.7763i	−0.662995	+	0.481694i	−0.867673	−	0.497135i	$-0.834385\pi$
$941$	−20.3378	+	14.7763i	−0.662995	+	0.481694i	0.204678	+	0.978829i	$0.434385\pi$
$942$	−5.60260	−	17.2430i	−0.182542	−	0.561808i
$943$	3.19900	−	9.84550i	0.104174	−	0.320614i
$944$	−20.0709	−	14.5823i	−0.653251	−	0.474615i
$945$	18.8624	−	58.0525i	0.613594	−	1.88845i
$946$	0.861924	−	2.65273i	0.0280236	−	0.0862477i
$947$	−39.1334	−	28.4321i	−1.27167	−	0.923919i	−0.272398	−	0.962185i	$-0.587817\pi$
$947$	−39.1334	−	28.4321i	−1.27167	−	0.923919i	−0.999268	+	0.0382653i	$0.987817\pi$
$948$	17.2454	−	53.0759i	0.560104	−	1.72382i
$949$	−15.4419	−	47.5252i	−0.501264	−	1.54273i
$950$	4.97526	−	3.61474i	0.161419	−	0.117278i
$951$	13.8914	+	42.7533i	0.450459	+	1.38637i
$952$	−1.07907	−	0.783987i	−0.0349727	−	0.0254092i
$953$	−13.4663	−	9.78385i	−0.436217	−	0.316930i	0.347913	−	0.937527i	$-0.386890\pi$
$953$	−13.4663	−	9.78385i	−0.436217	−	0.316930i	−0.784130	+	0.620597i	$0.786890\pi$
$954$	−10.9816	+	7.97862i	−0.355543	+	0.258317i
$955$	73.2209			2.36937
$956$	−2.24311			−0.0725474
$957$	−37.0846	+	26.9435i	−1.19878	+	0.870961i
$958$	1.06589	−	3.28046i	0.0344372	−	0.105987i
$959$	−0.918528	−	2.82694i	−0.0296608	−	0.0912866i
$960$	−65.8795			−2.12625
$961$	0.577086	−	30.9946i	0.0186157	−	0.999827i
$962$	3.81495			0.122999
$963$	39.5044	+	121.582i	1.27301	+	3.91793i
$964$	11.2951	−	34.7627i	0.363791	−	1.11963i
$965$	−44.9464	+	32.6554i	−1.44687	+	1.05122i
$966$	4.17051			0.134184
$967$	15.9979			0.514459			0.257229	−	0.966350i	$-0.417190\pi$
$967$	15.9979			0.514459			0.257229	+	0.966350i	$0.417190\pi$
$968$	5.00000	−	3.63271i	0.160706	−	0.116760i
$969$	−12.9500	−	9.40873i	−0.416014	−	0.302252i
$970$	−1.65206	−	1.20029i	−0.0530446	−	0.0385391i
$971$	−3.17351	−	9.76706i	−0.101843	−	0.313440i	0.887134	−	0.461513i	$-0.152693\pi$
$971$	−3.17351	−	9.76706i	−0.101843	−	0.313440i	−0.988976	+	0.148073i	$0.952693\pi$
$972$	58.5384	−	42.5306i	1.87762	−	1.36417i
$973$	−0.319709	−	0.983962i	−0.0102494	−	0.0315444i
$974$	−2.44487	+	7.52452i	−0.0783385	+	0.241101i
$975$	44.8091	+	32.5557i	1.43504	+	1.04262i
$976$	−3.86054	+	11.8815i	−0.123573	+	0.380318i
$977$	5.98322	−	18.4145i	0.191420	−	0.589131i	−0.808580	−	0.588387i	$-0.799763\pi$
$977$	5.98322	−	18.4145i	0.191420	−	0.589131i	1.00000		0.000743753i	$-0.000236744\pi$
$978$	−3.64743	−	2.65002i	−0.116632	−	0.0847382i
$979$	−9.89292	+	30.4473i	−0.316179	+	0.973099i
$980$	9.85854	+	30.3415i	0.314920	+	0.969223i
$981$	40.5727	−	29.4778i	1.29539	−	0.941155i
$982$	2.23703	+	6.88486i	0.0713864	+	0.219705i
$983$	15.3373	+	11.1432i	0.489183	+	0.355412i	0.804870	−	0.593451i	$-0.202235\pi$
$983$	15.3373	+	11.1432i	0.489183	+	0.355412i	−0.315687	+	0.948863i	$0.602235\pi$
$984$	7.23336	+	5.25534i	0.230591	+	0.167534i
$985$	39.0304	−	28.3573i	1.24361	−	0.903538i
$986$	−1.64076			−0.0522523
$987$	33.7710			1.07494
$988$	−27.0984	+	19.6881i	−0.862115	+	0.626363i
$989$	5.77107	−	17.7615i	0.183509	−	0.564783i
$990$	−4.13751	−	12.7339i	−0.131499	−	0.404711i
$991$	−27.8209			−0.883761			−0.441880	−	0.897074i	$-0.645688\pi$
$991$	−27.8209			−0.883761			−0.441880	+	0.897074i	$0.645688\pi$
$992$	−11.6960	+	11.4802i	−0.371347	+	0.364497i
$993$	88.9716			2.82343
$994$	−1.19780	−	3.68645i	−0.0379919	−	0.116927i
$995$	4.86790	−	14.9818i	0.154323	−	0.474956i
$996$	35.4250	−	25.7378i	1.12248	−	0.815532i
$997$	43.8208			1.38782			0.693909	−	0.720063i	$-0.255887\pi$
$997$	43.8208			1.38782			0.693909	+	0.720063i	$0.255887\pi$
$998$	6.29341			0.199215
$999$	−50.4037	+	36.6204i	−1.59470	+	1.15862i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	527.2.h.c.35.10	✓	96
31.8	even	5	inner	527.2.h.c.256.10	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
527.2.h.c.35.10	✓	96	1.1	even	1	trivial
527.2.h.c.256.10	yes	96	31.8	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 527 = 17 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	527.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0792451 - 0.243891i) q^{2} +(1.00279 - 3.08629i) q^{3} +(1.56483 - 1.13692i) q^{4} +3.14033 q^{5} -0.832185 q^{6} +(-1.06954 + 0.777066i) q^{7} +(-0.816222 - 0.593020i) q^{8} +(-6.09251 - 4.42647i) q^{9} +O(q^{10})\)	\(q+(-0.0792451 - 0.243891i) q^{2} +(1.00279 - 3.08629i) q^{3} +(1.56483 - 1.13692i) q^{4} +3.14033 q^{5} -0.832185 q^{6} +(-1.06954 + 0.777066i) q^{7} +(-0.816222 - 0.593020i) q^{8} +(-6.09251 - 4.42647i) q^{9} +(-0.248856 - 0.765899i) q^{10} +(-1.78612 + 1.29769i) q^{11} +(-1.93964 - 5.96961i) q^{12} +(-1.08487 + 3.33887i) q^{13} +(0.274276 + 0.199273i) q^{14} +(3.14911 - 9.69195i) q^{15} +(1.11547 - 3.43307i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(-0.596776 + 1.83669i) q^{18} +(1.52428 + 4.69126i) q^{19} +(4.91408 - 3.57029i) q^{20} +(1.32572 + 4.08014i) q^{21} +(0.458037 + 0.332783i) q^{22} +(3.06681 + 2.22817i) q^{23} +(-2.64873 + 1.92442i) q^{24} +4.86167 q^{25} +0.900293 q^{26} +(-11.8948 + 8.64209i) q^{27} +(-0.790190 + 2.43196i) q^{28} +(1.97713 + 6.08500i) q^{29} -2.61334 q^{30} +(3.97348 - 3.90019i) q^{31} -2.94351 q^{32} +(2.21393 + 6.81379i) q^{33} +(-0.0792451 + 0.243891i) q^{34} +(-3.35871 + 2.44024i) q^{35} -14.5663 q^{36} +4.23745 q^{37} +(1.02337 - 0.743518i) q^{38} +(9.21682 + 6.69641i) q^{39} +(-2.56321 - 1.86228i) q^{40} +(-0.843887 - 2.59722i) q^{41} +(0.890056 - 0.646663i) q^{42} +(-1.52239 - 4.68544i) q^{43} +(-1.31961 + 4.06133i) q^{44} +(-19.1325 - 13.9006i) q^{45} +(0.300402 - 0.924541i) q^{46} +(2.43252 - 7.48653i) q^{47} +(-9.47685 - 6.88534i) q^{48} +(-1.62303 + 4.99519i) q^{49} +(-0.385263 - 1.18572i) q^{50} +(-2.62535 + 1.90743i) q^{51} +(2.09839 + 6.45817i) q^{52} +(5.68641 + 4.13142i) q^{53} +(3.05034 + 2.21620i) q^{54} +(-5.60900 + 4.07518i) q^{55} +1.33380 q^{56} +16.0071 q^{57} +(1.32740 - 0.964413i) q^{58} +(2.12380 - 6.53639i) q^{59} +(-6.09112 - 18.7465i) q^{60} -3.46089 q^{61} +(-1.26610 - 0.660027i) q^{62} +9.95584 q^{63} +(-1.99769 - 6.14825i) q^{64} +(-3.40683 + 10.4852i) q^{65} +(1.48638 - 1.07992i) q^{66} -14.3217 q^{67} -1.93424 q^{68} +(9.95215 - 7.23066i) q^{69} +(0.861316 + 0.625783i) q^{70} +(-9.24974 - 6.72033i) q^{71} +(2.34786 + 7.22596i) q^{72} +(-11.5155 + 8.36648i) q^{73} +(-0.335797 - 1.03348i) q^{74} +(4.87525 - 15.0045i) q^{75} +(7.71881 + 5.60804i) q^{76} +(0.901933 - 2.77586i) q^{77} +(0.902809 - 2.77856i) q^{78} +(7.19298 + 5.22601i) q^{79} +(3.50295 - 10.7810i) q^{80} +(7.76250 + 23.8905i) q^{81} +(-0.566565 + 0.411634i) q^{82} +(2.15573 + 6.63467i) q^{83} +(6.71331 + 4.87750i) q^{84} +(-2.54058 - 1.84584i) q^{85} +(-1.02210 + 0.742596i) q^{86} +20.7627 q^{87} +2.22743 q^{88} +(11.7313 - 8.52331i) q^{89} +(-1.87407 + 5.76780i) q^{90} +(-1.43422 - 4.41407i) q^{91} +7.33229 q^{92} +(-8.05250 - 16.1744i) q^{93} -2.01867 q^{94} +(4.78674 + 14.7321i) q^{95} +(-2.95173 + 9.08450i) q^{96} +(2.05145 - 1.49047i) q^{97} +1.34690 q^{98} +16.6261 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9}+O(q^{10}) \) 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9	\( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9} - 13 q^{10} - 4 q^{11} - 14 q^{12} - 14 q^{13} + 17 q^{14} - 9 q^{15} - 58 q^{16} - 24 q^{17} - 24 q^{18} - 6 q^{19} + 43 q^{20} + 26 q^{21} + 42 q^{22} - 11 q^{23} - 38 q^{24} + 126 q^{25} - 44 q^{26} - q^{27} + 31 q^{28} - 10 q^{29} - 70 q^{30} + 21 q^{31} + 28 q^{32} - 36 q^{33} - 2 q^{34} + 2 q^{35} + 160 q^{36} + 54 q^{37} + 15 q^{38} - 10 q^{39} - 29 q^{40} - 14 q^{41} - 3 q^{42} + 6 q^{43} - 5 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 93 q^{48} - 72 q^{49} + 108 q^{50} + q^{51} + 13 q^{52} - 30 q^{53} - 63 q^{54} - 12 q^{55} + 66 q^{56} - 62 q^{57} + 29 q^{58} + 8 q^{59} - 86 q^{60} - 14 q^{61} - 34 q^{62} + 86 q^{63} - 122 q^{64} + 13 q^{65} - 40 q^{66} + 126 q^{67} + 120 q^{68} - 34 q^{69} - 38 q^{70} - 39 q^{71} - 51 q^{72} - 60 q^{73} - 111 q^{74} - 41 q^{75} + 64 q^{76} - 26 q^{77} - 99 q^{78} - 33 q^{79} - 91 q^{80} + 81 q^{81} - 88 q^{82} + 22 q^{83} + 160 q^{84} - 4 q^{85} + 35 q^{86} + 70 q^{87} - 120 q^{88} + 101 q^{89} + 125 q^{90} - 13 q^{91} - 98 q^{92} + 47 q^{93} - 8 q^{94} - 64 q^{95} + 208 q^{96} + 16 q^{97} + 8 q^{98} + 280 q^{99}+O(q^{100}) \) 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9 - 13 * q^10 - 4 * q^11 - 14 * q^12 - 14 * q^13 + 17 * q^14 - 9 * q^15 - 58 * q^16 - 24 * q^17 - 24 * q^18 - 6 * q^19 + 43 * q^20 + 26 * q^21 + 42 * q^22 - 11 * q^23 - 38 * q^24 + 126 * q^25 - 44 * q^26 - q^27 + 31 * q^28 - 10 * q^29 - 70 * q^30 + 21 * q^31 + 28 * q^32 - 36 * q^33 - 2 * q^34 + 2 * q^35 + 160 * q^36 + 54 * q^37 + 15 * q^38 - 10 * q^39 - 29 * q^40 - 14 * q^41 - 3 * q^42 + 6 * q^43 - 5 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 93 * q^48 - 72 * q^49 + 108 * q^50 + q^51 + 13 * q^52 - 30 * q^53 - 63 * q^54 - 12 * q^55 + 66 * q^56 - 62 * q^57 + 29 * q^58 + 8 * q^59 - 86 * q^60 - 14 * q^61 - 34 * q^62 + 86 * q^63 - 122 * q^64 + 13 * q^65 - 40 * q^66 + 126 * q^67 + 120 * q^68 - 34 * q^69 - 38 * q^70 - 39 * q^71 - 51 * q^72 - 60 * q^73 - 111 * q^74 - 41 * q^75 + 64 * q^76 - 26 * q^77 - 99 * q^78 - 33 * q^79 - 91 * q^80 + 81 * q^81 - 88 * q^82 + 22 * q^83 + 160 * q^84 - 4 * q^85 + 35 * q^86 + 70 * q^87 - 120 * q^88 + 101 * q^89 + 125 * q^90 - 13 * q^91 - 98 * q^92 + 47 * q^93 - 8 * q^94 - 64 * q^95 + 208 * q^96 + 16 * q^97 + 8 * q^98 + 280 * q^99

Introduction

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