LMFDB - Embedded newform 775.2.k.d.376.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(101,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("775.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.k (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:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			376.2
Character	$\chi$	$=$	775.376
Dual form			775.2.k.d.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.420591 - 1.29445i) q^{2} +(0.973089 - 2.99486i) q^{3} +(0.119342 - 0.0867070i) q^{4} -4.28595 q^{6} +(0.741309 - 0.538593i) q^{7} +(-2.36467 - 1.71804i) q^{8} +(-5.59523 - 4.06517i) q^{9} +O(q^{10})$	\(q+(-0.420591 - 1.29445i) q^{2} +(0.973089 - 2.99486i) q^{3} +(0.119342 - 0.0867070i) q^{4} -4.28595 q^{6} +(0.741309 - 0.538593i) q^{7} +(-2.36467 - 1.71804i) q^{8} +(-5.59523 - 4.06517i) q^{9} +(4.53839 - 3.29733i) q^{11} +(-0.143545 - 0.441786i) q^{12} +(0.592172 - 1.82252i) q^{13} +(-1.00897 - 0.733057i) q^{14} +(-1.13817 + 3.50294i) q^{16} +(1.86192 + 1.35276i) q^{17} +(-2.90884 + 8.95250i) q^{18} +(1.97142 + 6.06741i) q^{19} +(-0.891650 - 2.74422i) q^{21} +(-6.17702 - 4.48787i) q^{22} +(2.98754 + 2.17057i) q^{23} +(-7.44631 + 5.41006i) q^{24} -2.60821 q^{26} +(-9.97655 + 7.24839i) q^{27} +(0.0417696 - 0.128554i) q^{28} +(0.643286 + 1.97983i) q^{29} +(5.54716 + 0.478553i) q^{31} -0.832724 q^{32} +(-5.45879 - 16.8004i) q^{33} +(0.967971 - 2.97911i) q^{34} -1.02023 q^{36} -8.06343 q^{37} +(7.02476 - 5.10379i) q^{38} +(-4.88195 - 3.54694i) q^{39} +(-0.782302 - 2.40768i) q^{41} +(-3.17722 + 2.30838i) q^{42} +(2.94598 + 9.06681i) q^{43} +(0.255718 - 0.787020i) q^{44} +(1.55316 - 4.78013i) q^{46} +(-1.28959 + 3.96894i) q^{47} +(9.38327 + 6.81735i) q^{48} +(-1.90366 + 5.85887i) q^{49} +(5.86314 - 4.25982i) q^{51} +(-0.0873542 - 0.268848i) q^{52} +(6.25519 + 4.54466i) q^{53} +(13.5787 + 9.86549i) q^{54} -2.67828 q^{56} +20.0894 q^{57} +(2.29222 - 1.66540i) q^{58} +(3.04742 - 9.37899i) q^{59} -6.81609 q^{61} +(-1.71362 - 7.38177i) q^{62} -6.33727 q^{63} +(2.62658 + 8.08380i) q^{64} +(-19.4513 + 14.1322i) q^{66} -0.414188 q^{67} +0.339499 q^{68} +(9.40770 - 6.83509i) q^{69} +(4.68617 + 3.40470i) q^{71} +(6.24678 + 19.2256i) q^{72} +(-5.11470 + 3.71605i) q^{73} +(3.39140 + 10.4377i) q^{74} +(0.761360 + 0.553160i) q^{76} +(1.58843 - 4.88869i) q^{77} +(-2.53802 + 7.81123i) q^{78} +(-8.59071 - 6.24151i) q^{79} +(5.58827 + 17.1989i) q^{81} +(-2.78758 + 2.02529i) q^{82} +(3.10371 + 9.55223i) q^{83} +(-0.344354 - 0.250188i) q^{84} +(10.4974 - 7.62683i) q^{86} +6.55529 q^{87} -16.3967 q^{88} +(1.86543 - 1.35532i) q^{89} +(-0.542612 - 1.66999i) q^{91} +0.544743 q^{92} +(6.83108 - 16.1473i) q^{93} +5.67996 q^{94} +(-0.810314 + 2.49389i) q^{96} +(9.18599 - 6.67401i) q^{97} +8.38465 q^{98} -38.7976 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} - 6 q^{4} - 16 q^{6} + 9 q^{7} - 11 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 - 6 * q^4 - 16 * q^6 + 9 * q^7 - 11 * q^8 - 6 * q^9	$ 24 q - 2 q^{2} - 6 q^{4} - 16 q^{6} + 9 q^{7} - 11 q^{8} - 6 q^{9} + q^{11} - 18 q^{12} + 5 q^{13} + 6 q^{14} - 24 q^{16} - 7 q^{17} + 18 q^{18} + 2 q^{19} - 10 q^{21} - 28 q^{22} + 15 q^{23} - 32 q^{24} + 22 q^{26} - 9 q^{27} - 38 q^{28} + 15 q^{29} + 6 q^{31} - 74 q^{32} - 5 q^{33} - 20 q^{34} - 58 q^{36} + 56 q^{37} + 21 q^{38} - 10 q^{39} - 24 q^{41} + 38 q^{42} - 21 q^{43} + 41 q^{44} + 48 q^{46} + 8 q^{47} + 26 q^{48} - 23 q^{49} + 26 q^{51} + 27 q^{52} - 26 q^{53} + 11 q^{54} - 48 q^{56} - 62 q^{57} - 52 q^{58} + 10 q^{59} - 40 q^{61} + 28 q^{62} - 26 q^{63} + 9 q^{64} - 2 q^{66} + 26 q^{67} + 8 q^{68} + 64 q^{69} - 7 q^{71} + 127 q^{72} + 51 q^{73} - q^{74} + 43 q^{76} + 39 q^{77} + 31 q^{78} + 31 q^{79} + 34 q^{81} - 58 q^{82} - 6 q^{83} + 113 q^{84} - 22 q^{86} - 4 q^{87} + 28 q^{88} + 13 q^{89} + 54 q^{91} + 2 q^{92} + 72 q^{93} - 10 q^{94} + 101 q^{96} + 39 q^{97} + 220 q^{98} - 170 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 - 6 * q^4 - 16 * q^6 + 9 * q^7 - 11 * q^8 - 6 * q^9 + q^11 - 18 * q^12 + 5 * q^13 + 6 * q^14 - 24 * q^16 - 7 * q^17 + 18 * q^18 + 2 * q^19 - 10 * q^21 - 28 * q^22 + 15 * q^23 - 32 * q^24 + 22 * q^26 - 9 * q^27 - 38 * q^28 + 15 * q^29 + 6 * q^31 - 74 * q^32 - 5 * q^33 - 20 * q^34 - 58 * q^36 + 56 * q^37 + 21 * q^38 - 10 * q^39 - 24 * q^41 + 38 * q^42 - 21 * q^43 + 41 * q^44 + 48 * q^46 + 8 * q^47 + 26 * q^48 - 23 * q^49 + 26 * q^51 + 27 * q^52 - 26 * q^53 + 11 * q^54 - 48 * q^56 - 62 * q^57 - 52 * q^58 + 10 * q^59 - 40 * q^61 + 28 * q^62 - 26 * q^63 + 9 * q^64 - 2 * q^66 + 26 * q^67 + 8 * q^68 + 64 * q^69 - 7 * q^71 + 127 * q^72 + 51 * q^73 - q^74 + 43 * q^76 + 39 * q^77 + 31 * q^78 + 31 * q^79 + 34 * q^81 - 58 * q^82 - 6 * q^83 + 113 * q^84 - 22 * q^86 - 4 * q^87 + 28 * q^88 + 13 * q^89 + 54 * q^91 + 2 * q^92 + 72 * q^93 - 10 * q^94 + 101 * q^96 + 39 * q^97 + 220 * q^98 - 170 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.420591	−	1.29445i	−0.297403	−	0.915311i	−0.982404	−	0.186769i	$-0.940198\pi$
$2$	−0.420591	−	1.29445i	−0.297403	−	0.915311i	0.685001	−	0.728542i	$-0.259802\pi$
$3$	0.973089	−	2.99486i	0.561813	−	1.72908i	−0.115422	−	0.993317i	$-0.536822\pi$
$3$	0.973089	−	2.99486i	0.561813	−	1.72908i	0.677235	−	0.735767i	$-0.263178\pi$
$4$	0.119342	−	0.0867070i	0.0596710	−	0.0433535i
$5$		0			0
$5$		0			0
$6$	−4.28595			−1.74973
$7$	0.741309	−	0.538593i	0.280189	−	0.203569i	−0.438811	−	0.898579i	$-0.644600\pi$
$7$	0.741309	−	0.538593i	0.280189	−	0.203569i	0.719000	+	0.695010i	$0.244600\pi$
$8$	−2.36467	−	1.71804i	−0.836038	−	0.607417i
$9$	−5.59523	−	4.06517i	−1.86508	−	1.35506i
$10$		0			0
$11$	4.53839	−	3.29733i	1.36838	−	0.994183i	0.370513	−	0.928827i	$-0.379182\pi$
$11$	4.53839	−	3.29733i	1.36838	−	0.994183i	0.997862	−	0.0653556i	$-0.0208182\pi$
$12$	−0.143545	−	0.441786i	−0.0414379	−	0.127533i
$13$	0.592172	−	1.82252i	0.164239	−	0.505476i	−0.834740	−	0.550644i	$-0.814382\pi$
$13$	0.592172	−	1.82252i	0.164239	−	0.505476i	0.998979	+	0.0451681i	$0.0143823\pi$
$14$	−1.00897	−	0.733057i	−0.269658	−	0.195918i
$15$		0			0
$16$	−1.13817	+	3.50294i	−0.284544	+	0.875735i
$17$	1.86192	+	1.35276i	0.451581	+	0.328093i	0.790220	−	0.612824i	$-0.209966\pi$
$17$	1.86192	+	1.35276i	0.451581	+	0.328093i	−0.338639	+	0.940917i	$0.609966\pi$
$18$	−2.90884	+	8.95250i	−0.685621	+	2.11012i
$19$	1.97142	+	6.06741i	0.452275	+	1.39196i	0.874305	+	0.485377i	$0.161317\pi$
$19$	1.97142	+	6.06741i	0.452275	+	1.39196i	−0.422031	+	0.906582i	$0.638683\pi$
$20$		0			0
$21$	−0.891650	−	2.74422i	−0.194574	−	0.598837i
$22$	−6.17702	−	4.48787i	−1.31694	−	0.956816i
$23$	2.98754	+	2.17057i	0.622944	+	0.452596i	0.853949	−	0.520357i	$-0.174201\pi$
$23$	2.98754	+	2.17057i	0.622944	+	0.452596i	−0.231004	+	0.972953i	$0.574201\pi$
$24$	−7.44631	+	5.41006i	−1.51997	+	1.10432i
$25$		0			0
$26$	−2.60821			−0.511512
$27$	−9.97655	+	7.24839i	−1.91999	+	1.39495i
$28$	0.0417696	−	0.128554i	0.00789371	−	0.0242943i
$29$	0.643286	+	1.97983i	0.119455	+	0.367645i	0.992850	−	0.119367i	$-0.0380866\pi$
$29$	0.643286	+	1.97983i	0.119455	+	0.367645i	−0.873395	+	0.487012i	$0.838087\pi$
$30$		0			0
$31$	5.54716	+	0.478553i	0.996299	+	0.0859507i
$31$	5.54716	+	0.478553i	0.996299	+	0.0859507i
$32$	−0.832724			−0.147206
$33$	−5.45879	−	16.8004i	−0.950253	−	2.92458i
$34$	0.967971	−	2.97911i	0.166006	−	0.510913i
$35$		0			0
$36$	−1.02023			−0.170038
$37$	−8.06343			−1.32562			−0.662810	−	0.748788i	$-0.730636\pi$
$37$	−8.06343			−1.32562			−0.662810	+	0.748788i	$0.730636\pi$
$38$	7.02476	−	5.10379i	1.13957	−	0.827944i
$39$	−4.88195	−	3.54694i	−0.781738	−	0.567966i
$40$		0			0
$41$	−0.782302	−	2.40768i	−0.122175	−	0.376016i	0.871201	−	0.490927i	$-0.163342\pi$
$41$	−0.782302	−	2.40768i	−0.122175	−	0.376016i	−0.993376	+	0.114911i	$0.963342\pi$
$42$	−3.17722	+	2.30838i	−0.490255	+	0.356191i
$43$	2.94598	+	9.06681i	0.449258	+	1.38268i	0.877746	+	0.479127i	$0.159047\pi$
$43$	2.94598	+	9.06681i	0.449258	+	1.38268i	−0.428487	+	0.903548i	$0.640953\pi$
$44$	0.255718	−	0.787020i	0.0385510	−	0.118648i
$45$		0			0
$46$	1.55316	−	4.78013i	0.229001	−	0.704791i
$47$	−1.28959	+	3.96894i	−0.188106	+	0.578929i	−0.999988	−	0.00489158i	$-0.998443\pi$
$47$	−1.28959	+	3.96894i	−0.188106	+	0.578929i	0.811883	+	0.583821i	$0.198443\pi$
$48$	9.38327	+	6.81735i	1.35436	+	0.983999i
$49$	−1.90366	+	5.85887i	−0.271952	+	0.836981i
$50$		0			0
$51$	5.86314	−	4.25982i	0.821004	−	0.596494i
$52$	−0.0873542	−	0.268848i	−0.0121138	−	0.0372826i
$53$	6.25519	+	4.54466i	0.859217	+	0.624258i	0.927672	−	0.373396i	$-0.121807\pi$
$53$	6.25519	+	4.54466i	0.859217	+	0.624258i	−0.0684548	+	0.997654i	$0.521807\pi$
$54$	13.5787	+	9.86549i	1.84782	+	1.34252i
$55$		0			0
$56$	−2.67828			−0.357900
$57$	20.0894			2.66091
$58$	2.29222	−	1.66540i	0.300983	−	0.218677i
$59$	3.04742	−	9.37899i	0.396740	−	1.22104i	−0.530858	−	0.847461i	$-0.678130\pi$
$59$	3.04742	−	9.37899i	0.396740	−	1.22104i	0.927598	−	0.373580i	$-0.121870\pi$
$60$		0			0
$61$	−6.81609			−0.872711			−0.436355	−	0.899774i	$-0.643731\pi$
$61$	−6.81609			−0.872711			−0.436355	+	0.899774i	$0.643731\pi$
$62$	−1.71362	−	7.38177i	−0.217630	−	0.937486i
$63$	−6.33727			−0.798421
$64$	2.62658	+	8.08380i	0.328323	+	1.01047i
$65$		0			0
$66$	−19.4513	+	14.1322i	−2.39429	+	1.73956i
$67$	−0.414188			−0.0506011			−0.0253006	−	0.999680i	$-0.508054\pi$
$67$	−0.414188			−0.0506011			−0.0253006	+	0.999680i	$0.508054\pi$
$68$	0.339499			0.0411703
$69$	9.40770	−	6.83509i	1.13255	−	0.822849i
$70$		0			0
$71$	4.68617	+	3.40470i	0.556146	+	0.404064i	0.830046	−	0.557694i	$-0.188314\pi$
$71$	4.68617	+	3.40470i	0.556146	+	0.404064i	−0.273901	+	0.961758i	$0.588314\pi$
$72$	6.24678	+	19.2256i	0.736190	+	2.26576i
$73$	−5.11470	+	3.71605i	−0.598631	+	0.434931i	−0.845393	−	0.534145i	$-0.820633\pi$
$73$	−5.11470	+	3.71605i	−0.598631	+	0.434931i	0.246762	+	0.969076i	$0.420633\pi$
$74$	3.39140	+	10.4377i	0.394243	+	1.21335i
$75$		0			0
$76$	0.761360	+	0.553160i	0.0873340	+	0.0634518i
$77$	1.58843	−	4.88869i	0.181018	−	0.557117i
$78$	−2.53802	+	7.81123i	−0.287374	+	0.884448i
$79$	−8.59071	−	6.24151i	−0.966530	−	0.702225i	−0.0118721	−	0.999930i	$-0.503779\pi$
$79$	−8.59071	−	6.24151i	−0.966530	−	0.702225i	−0.954658	+	0.297704i	$0.903779\pi$
$80$		0			0
$81$	5.58827	+	17.1989i	0.620919	+	1.91099i
$82$	−2.78758	+	2.02529i	−0.307836	+	0.223656i
$83$	3.10371	+	9.55223i	0.340676	+	1.04849i	0.963858	+	0.266416i	$0.0858396\pi$
$83$	3.10371	+	9.55223i	0.340676	+	1.04849i	−0.623182	+	0.782077i	$0.714160\pi$
$84$	−0.344354	−	0.250188i	−0.0375721	−	0.0272977i
$85$		0			0
$86$	10.4974	−	7.62683i	1.13197	−	0.822422i
$87$	6.55529			0.702800
$88$	−16.3967			−1.74790
$89$	1.86543	−	1.35532i	0.197735	−	0.143663i	−0.484512	−	0.874785i	$-0.661003\pi$
$89$	1.86543	−	1.35532i	0.197735	−	0.143663i	0.682247	+	0.731122i	$0.261003\pi$
$90$		0			0
$91$	−0.542612	−	1.66999i	−0.0568812	−	0.175062i
$92$	0.544743			0.0567933
$93$	6.83108	−	16.1473i	0.708350	−	1.67440i
$94$	5.67996			0.585843
$95$		0			0
$96$	−0.810314	+	2.49389i	−0.0827024	+	0.254532i
$97$	9.18599	−	6.67401i	0.932696	−	0.677643i	−0.0139556	−	0.999903i	$-0.504442\pi$
$97$	9.18599	−	6.67401i	0.932696	−	0.677643i	0.946651	+	0.322260i	$0.104442\pi$
$98$	8.38465			0.846977
$99$	−38.7976			−3.89930
$100$		0			0
$101$	−3.83286	−	2.78473i	−0.381383	−	0.277091i	0.380532	−	0.924768i	$-0.375741\pi$
$101$	−3.83286	−	2.78473i	−0.381383	−	0.277091i	−0.761915	+	0.647676i	$0.775741\pi$
$102$	−7.98009	−	5.79787i	−0.790147	−	0.574075i
$103$	−0.381335	−	1.17363i	−0.0375740	−	0.115641i	0.930510	−	0.366266i	$-0.119364\pi$
$103$	−0.381335	−	1.17363i	−0.0375740	−	0.115641i	−0.968084	+	0.250625i	$0.919364\pi$
$104$	−4.53144	+	3.29229i	−0.444345	+	0.322835i
$105$		0			0
$106$	3.25194	−	10.0085i	0.315857	−	0.972107i
$107$	−10.3951	−	7.55250i	−1.00493	−	0.730127i	−0.0417936	−	0.999126i	$-0.513307\pi$
$107$	−10.3951	−	7.55250i	−1.00493	−	0.730127i	−0.963140	+	0.268999i	$0.913307\pi$
$108$	−0.562135	+	1.73007i	−0.0540915	+	0.166476i
$109$	0.325129	−	1.00064i	0.0311417	−	0.0958444i	−0.934278	−	0.356547i	$-0.883954\pi$
$109$	0.325129	−	1.00064i	0.0311417	−	0.0958444i	0.965419	+	0.260702i	$0.0839541\pi$
$110$		0			0
$111$	−7.84643	+	24.1488i	−0.744750	+	2.29211i
$112$	1.04292	+	3.20978i	0.0985466	+	0.303295i
$113$	9.95912	−	7.23572i	0.936875	−	0.680680i	−0.0107913	−	0.999942i	$-0.503435\pi$
$113$	9.95912	−	7.23572i	0.936875	−	0.680680i	0.947666	+	0.319262i	$0.103435\pi$
$114$	−8.44941	−	26.0046i	−0.791360	−	2.43556i
$115$		0			0
$116$	0.248436	+	0.180499i	0.0230667	+	0.0167589i
$117$	−10.7222	+	7.79013i	−0.991267	+	0.720198i
$118$	−13.4223			−1.23562
$119$	2.10884			0.193317
$120$		0			0
$121$	6.32538	−	19.4675i	0.575034	−	1.76977i
$122$	2.86678	+	8.82306i	0.259546	+	0.798802i
$123$	−7.97190			−0.718802
$124$	0.703503	−	0.423866i	0.0631765	−	0.0380643i
$125$		0			0
$126$	2.66540	+	8.20325i	0.237453	+	0.730804i
$127$	0.142802	−	0.439500i	0.0126716	−	0.0389993i	−0.944521	−	0.328452i	$-0.893473\pi$
$127$	0.142802	−	0.439500i	0.0126716	−	0.0389993i	0.957192	+	0.289452i	$0.0934732\pi$
$128$	8.01194	−	5.82101i	0.708162	−	0.514510i
$129$	30.0205			2.64316
$130$		0			0
$131$	3.15547	−	2.29258i	0.275694	−	0.200304i	−0.441343	−	0.897339i	$-0.645498\pi$
$131$	3.15547	−	2.29258i	0.275694	−	0.200304i	0.717037	+	0.697035i	$0.245498\pi$
$132$	−2.10818	−	1.53168i	−0.183493	−	0.133316i
$133$	4.72929	+	3.43603i	0.410082	+	0.297942i
$134$	0.174204	+	0.536144i	0.0150489	+	0.0463158i
$135$		0			0
$136$	−2.07873	−	6.39768i	−0.178250	−	0.548596i
$137$	−3.52887	+	10.8607i	−0.301491	+	0.927895i	0.679472	+	0.733702i	$0.262209\pi$
$137$	−3.52887	+	10.8607i	−0.301491	+	0.927895i	−0.980963	+	0.194193i	$0.937791\pi$
$138$	−12.8044	−	9.30298i	−1.08999	−	0.791922i
$139$	−2.91380	+	8.96774i	−0.247145	+	0.760634i	0.748131	+	0.663551i	$0.230951\pi$
$139$	−2.91380	+	8.96774i	−0.247145	+	0.760634i	−0.995276	+	0.0970833i	$0.969049\pi$
$140$		0			0
$141$	10.6315	+	7.72426i	0.895337	+	0.650500i
$142$	2.43624	−	7.49797i	0.204445	−	0.629216i
$143$	−3.32194	−	10.2239i	−0.277795	−	0.854964i
$144$	20.6084	−	14.9729i	1.71737	−	1.24774i
$145$		0			0
$146$	6.96142	+	5.05777i	0.576131	+	0.418584i
$147$	15.6941	+	11.4024i	1.29442	+	0.940454i
$148$	−0.962306	+	0.699156i	−0.0791010	+	0.0574703i
$149$	−16.3472			−1.33922			−0.669608	−	0.742715i	$-0.733538\pi$
$149$	−16.3472			−1.33922			−0.669608	+	0.742715i	$0.733538\pi$
$150$		0			0
$151$	−2.41419	+	1.75402i	−0.196464	+	0.142740i	−0.681668	−	0.731661i	$-0.738745\pi$
$151$	−2.41419	+	1.75402i	−0.196464	+	0.142740i	0.485204	+	0.874401i	$0.338745\pi$
$152$	5.76226	−	17.7344i	0.467381	−	1.43845i
$153$	−4.91864	−	15.1380i	−0.397649	−	1.22384i
$154$	−6.99621			−0.563771
$155$		0			0
$156$	−0.890167			−0.0712704
$157$	2.56540	+	7.89548i	0.204741	+	0.630128i	0.999724	+	0.0234963i	$0.00747979\pi$
$157$	2.56540	+	7.89548i	0.204741	+	0.630128i	−0.794983	+	0.606632i	$0.792520\pi$
$158$	−4.46613	+	13.7453i	−0.355306	+	1.09352i
$159$	19.6975	−	14.3111i	1.56211	−	1.13494i
$160$		0			0
$161$	3.38374			0.266676
$162$	19.9127	−	14.4674i	1.56449	−	1.13667i
$163$	−18.4867	−	13.4314i	−1.44799	−	1.05203i	−0.986295	−	0.164992i	$-0.947240\pi$
$163$	−18.4867	−	13.4314i	−1.44799	−	1.05203i	−0.461698	−	0.887037i	$-0.652760\pi$
$164$	−0.302124	−	0.219506i	−0.0235919	−	0.0171405i
$165$		0			0
$166$	11.0594	−	8.03516i	0.858379	−	0.623649i
$167$	−4.62307	−	14.2283i	−0.357744	−	1.10102i	−0.954401	−	0.298526i	$-0.903505\pi$
$167$	−4.62307	−	14.2283i	−0.357744	−	1.10102i	0.596657	−	0.802496i	$-0.296495\pi$
$168$	−2.60620	+	8.02106i	−0.201073	+	0.618838i
$169$	7.54632	+	5.48272i	0.580486	+	0.421748i
$170$		0			0
$171$	13.6345	−	41.9627i	1.04266	−	3.20897i
$172$	1.13774	+	0.826613i	0.0867515	+	0.0630287i
$173$	0.833317	−	2.56469i	0.0633560	−	0.194990i	−0.914368	−	0.404884i	$-0.867312\pi$
$173$	0.833317	−	2.56469i	0.0633560	−	0.194990i	0.977724	+	0.209894i	$0.0673120\pi$
$174$	−2.75709	−	8.48546i	−0.209015	−	0.643281i
$175$		0			0
$176$	6.38488	+	19.6506i	0.481278	+	1.48122i
$177$	−25.1234	−	18.2532i	−1.88839	−	1.37199i
$178$	−2.53896	−	1.84467i	−0.190303	−	0.138264i
$179$	19.7892	−	14.3777i	1.47911	−	1.07464i	0.501271	−	0.865290i	$-0.332866\pi$
$179$	19.7892	−	14.3777i	1.47911	−	1.07464i	0.977841	−	0.209348i	$-0.0671342\pi$
$180$		0			0
$181$	−18.9958			−1.41194			−0.705972	−	0.708239i	$-0.749490\pi$
$181$	−18.9958			−1.41194			−0.705972	+	0.708239i	$0.749490\pi$
$182$	−1.93349	+	1.40476i	−0.143320	+	0.104128i
$183$	−6.63266	+	20.4132i	−0.490301	+	1.50899i
$184$	−3.33543	−	10.2654i	−0.245891	−	0.756775i
$185$		0			0
$186$	−23.7749	−	2.05106i	−1.74326	−	0.150391i
$187$	12.9106			0.944117
$188$	0.190233	+	0.585477i	0.0138742	+	0.0427003i
$189$	−3.49178	+	10.7466i	−0.253990	+	0.781700i
$190$		0			0
$191$	−22.8593			−1.65404			−0.827021	−	0.562171i	$-0.809966\pi$
$191$	−22.8593			−1.65404			−0.827021	+	0.562171i	$0.809966\pi$
$192$	26.7657			1.93165
$193$	−10.3326	+	7.50709i	−0.743759	+	0.540372i	−0.893886	−	0.448294i	$-0.852032\pi$
$193$	−10.3326	+	7.50709i	−0.743759	+	0.540372i	0.150127	+	0.988667i	$0.452032\pi$
$194$	−12.5027	−	9.08373i	−0.897640	−	0.652174i
$195$		0			0
$196$	0.280818	+	0.864270i	0.0200585	+	0.0617336i
$197$	14.8306	−	10.7751i	1.05664	−	0.767693i	0.0831754	−	0.996535i	$-0.473494\pi$
$197$	14.8306	−	10.7751i	1.05664	−	0.767693i	0.973464	+	0.228842i	$0.0734938\pi$
$198$	16.3179	+	50.2213i	1.15966	+	3.56907i
$199$	−7.21304	+	22.1995i	−0.511319	+	1.57368i	0.278562	+	0.960418i	$0.410142\pi$
$199$	−7.21304	+	22.1995i	−0.511319	+	1.57368i	−0.789881	+	0.613260i	$0.789858\pi$
$200$		0			0
$201$	−0.403042	+	1.24043i	−0.0284284	+	0.0874935i
$202$	−1.99262	+	6.13265i	−0.140200	+	0.431492i
$203$	1.54320	+	1.12120i	0.108311	+	0.0786926i
$204$	0.330363	−	1.01675i	0.0231300	−	0.0711868i
$205$		0			0
$206$	−1.35881	+	0.987234i	−0.0946729	+	0.0687839i
$207$	−7.89221	−	24.2897i	−0.548546	−	1.68825i
$208$	5.71018	+	4.14869i	0.395930	+	0.287660i
$209$	28.9533	+	21.0358i	2.00274	+	1.45508i
$210$		0			0
$211$	−4.87701			−0.335747			−0.167874	−	0.985809i	$-0.553690\pi$
$211$	−4.87701			−0.335747			−0.167874	+	0.985809i	$0.553690\pi$
$212$	1.14056			0.0783341
$213$	14.7567	−	10.7213i	1.01111	−	0.734614i
$214$	−5.40420	+	16.6324i	−0.369424	+	1.13697i
$215$		0			0
$216$	36.0443			2.45250
$217$	4.36991	−	2.63290i	0.296649	−	0.178733i
$218$	−1.43203			−0.0969891
$219$	6.15199	+	18.9339i	0.415713	+	1.27943i
$220$		0			0
$221$	3.56801	−	2.59231i	0.240010	−	0.174378i
$222$	34.5595			2.31948
$223$	10.8420			0.726032			0.363016	−	0.931783i	$-0.381747\pi$
$223$	10.8420			0.726032			0.363016	+	0.931783i	$0.381747\pi$
$224$	−0.617306	+	0.448499i	−0.0412455	+	0.0299666i
$225$		0			0
$226$	−13.5550	−	9.84826i	−0.901663	−	0.655096i
$227$	1.70815	+	5.25714i	0.113374	+	0.348929i	0.991604	−	0.129309i	$-0.0412758\pi$
$227$	1.70815	+	5.25714i	0.113374	+	0.348929i	−0.878231	+	0.478238i	$0.841276\pi$
$228$	2.39751	−	1.74189i	0.158779	−	0.115360i
$229$	−3.15229	−	9.70174i	−0.208309	−	0.641109i	−0.999561	−	0.0296192i	$-0.990571\pi$
$229$	−3.15229	−	9.70174i	−0.208309	−	0.641109i	0.791252	−	0.611490i	$-0.209429\pi$
$230$		0			0
$231$	−13.0952	−	9.51425i	−0.861604	−	0.625992i
$232$	1.88026	−	5.78684i	0.123445	−	0.379924i
$233$	2.79870	−	8.61352i	0.183349	−	0.564290i	−0.816567	−	0.577251i	$-0.804126\pi$
$233$	2.79870	−	8.61352i	0.183349	−	0.564290i	0.999916	+	0.0129605i	$0.00412556\pi$
$234$	14.5936	+	10.6028i	0.954010	+	0.693129i
$235$		0			0
$236$	−0.449540	−	1.38354i	−0.0292625	−	0.0900608i
$237$	−27.0520	+	19.6544i	−1.75722	+	1.27669i
$238$	−0.886960	−	2.72978i	−0.0574931	−	0.176946i
$239$	−9.64391	−	7.00671i	−0.623813	−	0.453226i	0.230439	−	0.973087i	$-0.425984\pi$
$239$	−9.64391	−	7.00671i	−0.623813	−	0.453226i	−0.854251	+	0.519860i	$0.825984\pi$
$240$		0			0
$241$	−14.1964	+	10.3143i	−0.914473	+	0.664404i	−0.942142	−	0.335213i	$-0.891192\pi$
$241$	−14.1964	+	10.3143i	−0.914473	+	0.664404i	0.0276690	+	0.999617i	$0.491192\pi$
$242$	−27.8600			−1.79091
$243$	19.9512			1.27987
$244$	−0.813446	+	0.591003i	−0.0520755	+	0.0378351i
$245$		0			0
$246$	3.35291	+	10.3192i	0.213774	+	0.657928i
$247$	12.2254			0.777882
$248$	−12.2951	−	10.6618i	−0.780737	−	0.677028i
$249$	31.6278			2.00433
$250$		0			0
$251$	7.48819	−	23.0463i	0.472650	−	1.45467i	−0.376450	−	0.926437i	$-0.622855\pi$
$251$	7.48819	−	23.0463i	0.472650	−	1.45467i	0.849100	−	0.528231i	$-0.177145\pi$
$252$	−0.756303	+	0.549486i	−0.0476426	+	0.0346144i
$253$	20.7157			1.30238
$254$	−0.628970			−0.0394651
$255$		0			0
$256$	2.84824	+	2.06937i	0.178015	+	0.129336i
$257$	4.46143	+	3.24142i	0.278296	+	0.202194i	0.718174	−	0.695864i	$-0.244978\pi$
$257$	4.46143	+	3.24142i	0.278296	+	0.202194i	−0.439878	+	0.898058i	$0.644978\pi$
$258$	−12.6264	−	38.8599i	−0.786082	−	2.41931i
$259$	−5.97750	+	4.34290i	−0.371423	+	0.269855i
$260$		0			0
$261$	4.44902	−	13.6927i	0.275387	−	0.847555i
$262$	−4.29478	−	3.12034i	−0.265332	−	0.192775i
$263$	2.44499	−	7.52489i	0.150764	−	0.464005i	−0.846943	−	0.531684i	$-0.821559\pi$
$263$	2.44499	−	7.52489i	0.150764	−	0.464005i	0.997707	+	0.0676792i	$0.0215594\pi$
$264$	−15.9555	+	49.1059i	−0.981992	+	3.02226i
$265$		0			0
$266$	2.45866	−	7.56697i	0.150750	−	0.463961i
$267$	−2.24375	−	6.90555i	−0.137315	−	0.422613i
$268$	−0.0494300	+	0.0359130i	−0.00301942	+	0.00219374i
$269$	0.166570	+	0.512649i	0.0101559	+	0.0312568i	0.956006	−	0.293347i	$-0.0947691\pi$
$269$	0.166570	+	0.512649i	0.0101559	+	0.0312568i	−0.945850	+	0.324604i	$0.894769\pi$
$270$		0			0
$271$	10.5152	+	7.63975i	0.638754	+	0.464082i	0.859422	−	0.511267i	$-0.170824\pi$
$271$	10.5152	+	7.63975i	0.638754	+	0.464082i	−0.220668	+	0.975349i	$0.570824\pi$
$272$	−6.85783	+	4.98250i	−0.415817	+	0.302109i
$273$	−5.52939			−0.334654
$274$	15.5428			0.938977
$275$		0			0
$276$	0.530083	−	1.63143i	0.0319072	−	0.0982004i
$277$	0.394056	+	1.21278i	0.0236765	+	0.0728689i	0.962197	−	0.272356i	$-0.0878027\pi$
$277$	0.394056	+	1.21278i	0.0236765	+	0.0728689i	−0.938520	+	0.345225i	$0.887803\pi$
$278$	12.8338			0.769718
$279$	−29.0923	−	25.2278i	−1.74171	−	1.51035i
$280$		0			0
$281$	3.36754	+	10.3642i	0.200891	+	0.618278i	0.999857	+	0.0169022i	$0.00538040\pi$
$281$	3.36754	+	10.3642i	0.200891	+	0.618278i	−0.798967	+	0.601375i	$0.794620\pi$
$282$	5.52711	−	17.0107i	0.329135	−	1.01297i
$283$	−8.36935	+	6.08069i	−0.497506	+	0.361460i	−0.808064	−	0.589095i	$-0.799484\pi$
$283$	−8.36935	+	6.08069i	−0.497506	+	0.361460i	0.310557	+	0.950555i	$0.399484\pi$
$284$	0.854468			0.0507034
$285$		0			0
$286$	−11.8371	+	8.60014i	−0.699941	+	0.508537i
$287$	−1.87668	−	1.36349i	−0.110777	−	0.0804843i
$288$	4.65928	+	3.38517i	0.274551	+	0.199473i
$289$	−3.61652	−	11.1305i	−0.212736	−	0.654736i
$290$		0			0
$291$	−11.0489	−	34.0052i	−0.647701	−	1.99342i
$292$	−0.288191	+	0.886962i	−0.0168651	+	0.0519055i
$293$	15.5304	+	11.2835i	0.907297	+	0.659190i	0.940330	−	0.340265i	$-0.110517\pi$
$293$	15.5304	+	11.2835i	0.907297	+	0.659190i	−0.0330331	+	0.999454i	$0.510517\pi$
$294$	8.15901	−	25.1108i	0.475843	−	1.46449i
$295$		0			0
$296$	19.0674	+	13.8533i	1.10827	+	0.805204i
$297$	−21.3771	+	65.7920i	−1.24043	+	3.81764i
$298$	6.87549	+	21.1606i	0.398286	+	1.22580i
$299$	5.72504	−	4.15949i	0.331088	−	0.240549i
$300$		0			0
$301$	7.06720	+	5.13462i	0.407347	+	0.295955i
$302$	3.28586	+	2.38732i	0.189080	+	0.137375i
$303$	−12.0696	+	8.76907i	−0.693380	+	0.503770i
$304$	−23.4976			−1.34768
$305$		0			0
$306$	−17.5266	+	12.7338i	−1.00193	+	0.727945i
$307$	2.95997	−	9.10984i	0.168934	−	0.519926i	−0.830370	−	0.557212i	$-0.811871\pi$
$307$	2.95997	−	9.10984i	0.168934	−	0.519926i	0.999305	+	0.0372856i	$0.0118711\pi$
$308$	−0.234317	−	0.721154i	−0.0133515	−	0.0410915i
$309$	−3.88593			−0.221063
$310$		0			0
$311$	0.0597943			0.00339063			0.00169531	−	0.999999i	$-0.499460\pi$
$311$	0.0597943			0.00339063			0.00169531	+	0.999999i	$0.499460\pi$
$312$	5.45044	+	16.7747i	0.308570	+	0.949682i
$313$	−3.00795	+	9.25752i	−0.170019	+	0.523266i	−0.999371	−	0.0354611i	$-0.988710\pi$
$313$	−3.00795	+	9.25752i	−0.170019	+	0.523266i	0.829352	+	0.558727i	$0.188710\pi$
$314$	9.14129	−	6.64153i	0.515873	−	0.374804i
$315$		0			0
$316$	−1.56642			−0.0881178
$317$	−5.30371	+	3.85337i	−0.297886	+	0.216427i	−0.726681	−	0.686975i	$-0.758938\pi$
$317$	−5.30371	+	3.85337i	−0.297886	+	0.216427i	0.428795	+	0.903402i	$0.358938\pi$
$318$	−26.8095	−	19.4782i	−1.50340	−	1.09228i
$319$	9.44763	+	6.86411i	0.528966	+	0.384316i
$320$		0			0
$321$	−32.7340	+	23.7827i	−1.82704	+	1.32742i
$322$	−1.42317	−	4.38007i	−0.0793102	−	0.244092i
$323$	−4.53713	+	13.9639i	−0.252453	+	0.776970i
$324$	2.15818	+	1.56801i	0.119899	+	0.0871117i
$325$		0			0
$326$	−9.61086	+	29.5792i	−0.532297	+	1.63824i
$327$	−2.68041	−	1.94743i	−0.148227	−	0.107693i
$328$	−2.28659	+	7.03739i	−0.126256	+	0.388575i
$329$	1.18166	+	3.63677i	0.0651470	+	0.200502i
$330$		0			0
$331$	−3.02132	−	9.29868i	−0.166067	−	0.511101i	0.833046	−	0.553203i	$-0.186595\pi$
$331$	−3.02132	−	9.29868i	−0.166067	−	0.511101i	−0.999113	+	0.0421017i	$0.986595\pi$
$332$	1.19865	+	0.870869i	0.0657844	+	0.0477951i
$333$	45.1168	+	32.7792i	2.47238	+	1.79629i
$334$	−16.4734	+	11.9686i	−0.901384	+	0.654894i
$335$		0			0
$336$	10.6277			0.579788
$337$	4.87501	−	3.54190i	0.265559	−	0.192940i	−0.447035	−	0.894516i	$-0.647520\pi$
$337$	4.87501	−	3.54190i	0.265559	−	0.192940i	0.712594	+	0.701577i	$0.247520\pi$
$338$	3.92317	−	12.0743i	0.213392	−	0.656754i
$339$	−11.9789	−	36.8672i	−0.650603	−	2.00235i
$340$		0			0
$341$	26.7531	−	16.1190i	1.44876	−	0.872891i
$342$	−60.0530			−3.24729
$343$	3.72643	+	11.4688i	0.201208	+	0.619255i
$344$	8.61081	−	26.5013i	0.464264	−	1.42886i
$345$		0			0
$346$	−3.67033			−0.197318
$347$	−19.0290			−1.02153			−0.510765	−	0.859720i	$-0.670638\pi$
$347$	−19.0290			−1.02153			−0.510765	+	0.859720i	$0.670638\pi$
$348$	0.782321	−	0.568389i	0.0419368	−	0.0304689i
$349$	−14.0832	−	10.2321i	−0.753859	−	0.547710i	0.143162	−	0.989699i	$-0.454273\pi$
$349$	−14.0832	−	10.2321i	−0.753859	−	0.547710i	−0.897021	+	0.441989i	$0.854273\pi$
$350$		0			0
$351$	7.30248	+	22.4747i	0.389778	+	1.19961i
$352$	−3.77922	+	2.74577i	−0.201433	+	0.146350i
$353$	−3.68802	−	11.3506i	−0.196293	−	0.604129i	−0.999959	−	0.00904788i	$-0.997120\pi$
$353$	−3.68802	−	11.3506i	−0.196293	−	0.604129i	0.803666	−	0.595081i	$-0.202880\pi$
$354$	−13.0611	+	40.1979i	−0.694190	+	2.13650i
$355$		0			0
$356$	0.105109	−	0.323492i	0.00557076	−	0.0171450i
$357$	2.05209	−	6.31569i	0.108608	−	0.334262i
$358$	−26.9343	−	19.5689i	−1.42352	−	1.03425i
$359$	−9.86202	+	30.3522i	−0.520497	+	1.60193i	0.252554	+	0.967583i	$0.418729\pi$
$359$	−9.86202	+	30.3522i	−0.520497	+	1.60193i	−0.773052	+	0.634343i	$0.781271\pi$
$360$		0			0
$361$	−17.5556	+	12.7549i	−0.923978	+	0.671310i
$362$	7.98945	+	24.5890i	0.419916	+	1.29237i
$363$	−52.1473	−	37.8872i	−2.73702	−	1.98856i
$364$	−0.209556	−	0.152252i	−0.0109837	−	0.00798015i
$365$		0			0
$366$	29.2135			1.52701
$367$	−16.2510			−0.848293			−0.424147	−	0.905593i	$-0.639426\pi$
$367$	−16.2510			−0.848293			−0.424147	+	0.905593i	$0.639426\pi$
$368$	−11.0037	+	7.99467i	−0.573609	+	0.416751i
$369$	−5.41047	+	16.6517i	−0.281658	+	0.866853i
$370$		0			0
$371$	7.08476			0.367822
$372$	−0.584849	−	2.51935i	−0.0303230	−	0.130622i
$373$	−21.1742			−1.09636			−0.548180	−	0.836360i	$-0.684679\pi$
$373$	−21.1742			−1.09636			−0.548180	+	0.836360i	$0.684679\pi$
$374$	−5.43008	−	16.7121i	−0.280783	−	0.864160i
$375$		0			0
$376$	9.86823	−	7.16969i	0.508915	−	0.369748i
$377$	3.98921			0.205455
$378$	15.3795			0.791036
$379$	5.43943	−	3.95198i	0.279405	−	0.203000i	−0.439253	−	0.898363i	$-0.644757\pi$
$379$	5.43943	−	3.95198i	0.279405	−	0.203000i	0.718658	+	0.695364i	$0.244757\pi$
$380$		0			0
$381$	−1.17728	−	0.855345i	−0.0603140	−	0.0438207i
$382$	9.61442	+	29.5901i	0.491916	+	1.51396i
$383$	−14.9958	+	10.8951i	−0.766251	+	0.556714i	−0.900821	−	0.434190i	$-0.857035\pi$
$383$	−14.9958	+	10.8951i	−0.766251	+	0.556714i	0.134571	+	0.990904i	$0.457035\pi$
$384$	−9.63679	−	29.6590i	−0.491776	−	1.51353i
$385$		0			0
$386$	14.0633	+	10.2176i	0.715805	+	0.520062i
$387$	20.3747	−	62.7068i	1.03570	−	3.18757i
$388$	0.517590	−	1.59298i	0.0262767	−	0.0808713i
$389$	2.34427	+	1.70321i	0.118859	+	0.0863562i	0.645627	−	0.763653i	$-0.276596\pi$
$389$	2.34427	+	1.70321i	0.118859	+	0.0863562i	−0.526768	+	0.850009i	$0.676596\pi$
$390$		0			0
$391$	2.62628	+	8.08285i	0.132817	+	0.408767i
$392$	14.5673	−	10.5838i	0.735759	−	0.534560i
$393$	−3.79541	−	11.6811i	−0.191453	−	0.589232i
$394$	−20.1854	−	14.6655i	−1.01693	−	0.738839i
$395$		0			0
$396$	−4.63018	+	3.36402i	−0.232675	+	0.169048i
$397$	21.8732			1.09778			0.548891	−	0.835894i	$-0.315050\pi$
$397$	21.8732			1.09778			0.548891	+	0.835894i	$0.315050\pi$
$398$	31.7697			1.59247
$399$	14.8925	−	10.8200i	0.745555	−	0.541678i
$400$		0			0
$401$	−1.69586	−	5.21933i	−0.0846874	−	0.260641i	0.899742	−	0.436423i	$-0.143755\pi$
$401$	−1.69586	−	5.21933i	−0.0846874	−	0.260641i	−0.984429	+	0.175782i	$0.943755\pi$
$402$	1.77519			0.0885385
$403$	4.15705	−	9.82641i	0.207077	−	0.489489i
$404$	−0.698877			−0.0347704
$405$		0			0
$406$	0.802275	−	2.46915i	0.0398162	−	0.122542i
$407$	−36.5950	+	26.5878i	−1.81394	+	1.31791i
$408$	−21.1829			−1.04871
$409$	20.9396			1.03540			0.517698	−	0.855563i	$-0.326789\pi$
$409$	20.9396			1.03540			0.517698	+	0.855563i	$0.326789\pi$
$410$		0			0
$411$	29.0925	+	21.1369i	1.43503	+	1.04261i
$412$	−0.147271	−	0.106999i	−0.00725553	−	0.00527145i
$413$	−2.79238	−	8.59406i	−0.137404	−	0.422886i
$414$	−28.1223	+	20.4321i	−1.38214	+	1.00418i
$415$		0			0
$416$	−0.493116	+	1.51765i	−0.0241770	+	0.0744091i
$417$	24.0218	+	17.4528i	1.17635	+	0.854669i
$418$	15.0522	−	46.3259i	0.736228	−	2.26588i
$419$	0.278033	−	0.855696i	0.0135828	−	0.0418035i	−0.944035	−	0.329844i	$-0.893004\pi$
$419$	0.278033	−	0.855696i	0.0135828	−	0.0418035i	0.957618	+	0.288041i	$0.0930038\pi$
$420$		0			0
$421$	−7.08975	+	21.8200i	−0.345533	+	1.06344i	0.615765	+	0.787930i	$0.288847\pi$
$421$	−7.08975	+	21.8200i	−0.345533	+	1.06344i	−0.961298	+	0.275512i	$0.911153\pi$
$422$	2.05122	+	6.31302i	0.0998521	+	0.307313i
$423$	23.3500	−	16.9647i	1.13531	−	0.824854i
$424$	−6.98360	−	21.4933i	−0.339153	−	1.04381i
$425$		0			0
$426$	−20.0847	−	14.5924i	−0.973107	−	0.707004i
$427$	−5.05283	+	3.67110i	−0.244524	+	0.177657i
$428$	−1.89543			−0.0916190
$429$	−33.8516			−1.63437
$430$		0			0
$431$	−10.6468	+	32.7676i	−0.512840	+	1.57836i	0.274337	+	0.961634i	$0.411542\pi$
$431$	−10.6468	+	32.7676i	−0.512840	+	1.57836i	−0.787177	+	0.616727i	$0.788458\pi$
$432$	−14.0356	−	43.1972i	−0.675289	−	2.07833i
$433$	−0.131862			−0.00633687			−0.00316844	−	0.999995i	$-0.501009\pi$
$433$	−0.131862			−0.00633687			−0.00316844	+	0.999995i	$0.501009\pi$
$434$	−5.24609	−	4.54923i	−0.251821	−	0.218370i
$435$		0			0
$436$	−0.0479614	−	0.147610i	−0.00229693	−	0.00706924i
$437$	−7.28005	+	22.4057i	−0.348252	+	1.07181i
$438$	21.9214	−	15.9268i	1.04744	−	0.761013i
$439$	27.8217			1.32786			0.663929	−	0.747795i	$-0.268888\pi$
$439$	27.8217			1.32786			0.663929	+	0.747795i	$0.268888\pi$
$440$		0			0
$441$	34.4688	−	25.0430i	1.64137	−	1.19252i
$442$	−4.85627	−	3.52829i	−0.230989	−	0.167824i
$443$	18.9099	+	13.7389i	0.898437	+	0.652753i	0.938064	−	0.346462i	$-0.112617\pi$
$443$	18.9099	+	13.7389i	0.898437	+	0.652753i	−0.0396273	+	0.999215i	$0.512617\pi$
$444$	1.15747	+	3.56231i	0.0549309	+	0.169060i
$445$		0			0
$446$	−4.56003	−	14.0343i	−0.215924	−	0.664545i
$447$	−15.9073	+	48.9576i	−0.752389	+	2.31562i
$448$	6.30099	+	4.57794i	0.297694	+	0.216287i
$449$	−1.68488	+	5.18553i	−0.0795145	+	0.244721i	−0.982910	−	0.184089i	$-0.941067\pi$
$449$	−1.68488	+	5.18553i	−0.0795145	+	0.244721i	0.903395	+	0.428809i	$0.141067\pi$
$450$		0			0
$451$	−11.4893	−	8.34746i	−0.541010	−	0.393067i
$452$	0.561153	−	1.72705i	0.0263944	−	0.0812337i
$453$	2.90380	+	8.93699i	0.136433	+	0.419896i
$454$	6.08665	−	4.42221i	0.285661	−	0.207545i
$455$		0			0
$456$	−47.5049	−	34.5143i	−2.22462	−	1.61628i
$457$	26.8169	+	19.4836i	1.25444	+	0.911404i	0.998471	−	0.0552814i	$-0.0176056\pi$
$457$	26.8169	+	19.4836i	1.25444	+	0.911404i	0.255969	+	0.966685i	$0.417606\pi$
$458$	−11.2325	+	8.16093i	−0.524863	+	0.381335i
$459$	−28.3808			−1.32470
$460$		0			0
$461$	5.65240	−	4.10671i	0.263259	−	0.191269i	−0.448324	−	0.893871i	$-0.647979\pi$
$461$	5.65240	−	4.10671i	0.263259	−	0.191269i	0.711582	+	0.702603i	$0.247979\pi$
$462$	−6.80794	+	20.9527i	−0.316734	+	0.974807i
$463$	6.10820	+	18.7991i	0.283872	+	0.873668i	0.986734	+	0.162342i	$0.0519049\pi$
$463$	6.10820	+	18.7991i	0.283872	+	0.873668i	−0.702863	+	0.711326i	$0.748095\pi$
$464$	−7.66740			−0.355950
$465$		0			0
$466$	−12.3268			−0.571029
$467$	−5.16887	−	15.9082i	−0.239187	−	0.736142i	−0.996538	−	0.0831341i	$-0.973507\pi$
$467$	−5.16887	−	15.9082i	−0.239187	−	0.736142i	0.757351	−	0.653007i	$-0.226493\pi$
$468$	−0.604149	+	1.85938i	−0.0279268	+	0.0859499i
$469$	−0.307041	+	0.223079i	−0.0141779	+	0.0103008i
$470$		0			0
$471$	26.1422			1.20457
$472$	−23.3196	+	16.9427i	−1.07337	+	0.779850i
$473$	43.2663	+	31.4348i	1.98939	+	1.44537i
$474$	36.8194	+	26.7508i	1.69117	+	1.22871i
$475$		0			0
$476$	0.251674	−	0.182852i	0.0115354	−	0.00838099i
$477$	−16.5244	−	50.8569i	−0.756601	−	2.32858i
$478$	−5.01366	+	15.4305i	−0.229320	+	0.705773i
$479$	−3.37161	−	2.44962i	−0.154053	−	0.111926i	0.508089	−	0.861305i	$-0.330352\pi$
$479$	−3.37161	−	2.44962i	−0.154053	−	0.111926i	−0.662141	+	0.749379i	$0.730352\pi$
$480$		0			0
$481$	−4.77494	+	14.6957i	−0.217718	+	0.670068i
$482$	19.3222	+	14.0384i	0.880103	+	0.639432i
$483$	3.29268	−	10.1338i	0.149822	−	0.461106i
$484$	−0.933087	−	2.87175i	−0.0424130	−	0.130534i
$485$		0			0
$486$	−8.39127	−	25.8257i	−0.380636	−	1.17148i
$487$	5.26178	+	3.82291i	0.238434	+	0.173232i	0.700585	−	0.713569i	$-0.252922\pi$
$487$	5.26178	+	3.82291i	0.238434	+	0.173232i	−0.462151	+	0.886801i	$0.652922\pi$
$488$	16.1178	+	11.7103i	0.729620	+	0.530100i
$489$	−58.2144	+	42.2952i	−2.63255	+	1.91266i
$490$		0			0
$491$	25.5391			1.15256			0.576282	−	0.817251i	$-0.304503\pi$
$491$	25.5391			1.15256			0.576282	+	0.817251i	$0.304503\pi$
$492$	−0.951383	+	0.691220i	−0.0428917	+	0.0311626i
$493$	−1.48049	+	4.55649i	−0.0666780	+	0.205214i
$494$	−5.14188	−	15.8251i	−0.231344	−	0.712004i
$495$		0			0
$496$	−7.98998	+	18.8867i	−0.358761	+	0.848038i
$497$	5.30765			0.238081
$498$	−13.3023	−	40.9404i	−0.596092	−	1.83458i
$499$	2.83976	−	8.73989i	0.127125	−	0.391251i	−0.867157	−	0.498035i	$-0.834055\pi$
$499$	2.83976	−	8.73989i	0.127125	−	0.391251i	0.994282	+	0.106783i	$0.0340552\pi$
$500$		0			0
$501$	−47.1106			−2.10474
$502$	−32.9816			−1.47204
$503$	−20.1892	+	14.6683i	−0.900193	+	0.654029i	−0.938516	−	0.345237i	$-0.887799\pi$
$503$	−20.1892	+	14.6683i	−0.900193	+	0.654029i	0.0383223	+	0.999265i	$0.487799\pi$
$504$	14.9856	+	10.8877i	0.667511	+	0.484975i
$505$		0			0
$506$	−8.71283	−	26.8153i	−0.387333	−	1.19209i
$507$	23.7632	−	17.2650i	1.05536	−	0.766765i
$508$	−0.0210654	−	0.0648328i	−0.000934628	−	0.00287649i
$509$	−2.71759	+	8.36389i	−0.120455	+	0.370723i	−0.993046	−	0.117729i	$-0.962438\pi$
$509$	−2.71759	+	8.36389i	−0.120455	+	0.370723i	0.872590	+	0.488453i	$0.162438\pi$
$510$		0			0
$511$	−1.79014	+	5.50949i	−0.0791912	+	0.243725i
$512$	7.60132	−	23.3945i	0.335934	−	1.03390i
$513$	−63.6469	−	46.2422i	−2.81008	−	2.04164i
$514$	2.31940	−	7.13839i	0.102305	−	0.314861i
$515$		0			0
$516$	3.58271	−	2.60299i	0.157720	−	0.114590i
$517$	7.23426	+	22.2648i	0.318163	+	0.979204i
$518$	8.13573	+	5.91096i	0.357464	+	0.259712i
$519$	−6.86999	−	4.99134i	−0.301559	−	0.219095i
$520$		0			0
$521$	21.3783			0.936602			0.468301	−	0.883569i	$-0.344866\pi$
$521$	21.3783			0.936602			0.468301	+	0.883569i	$0.344866\pi$
$522$	−19.5956			−0.857678
$523$	32.4578	−	23.5819i	1.41928	−	1.03117i	0.427389	−	0.904068i	$-0.359433\pi$
$523$	32.4578	−	23.5819i	1.41928	−	1.03117i	0.991890	−	0.127099i	$-0.0405665\pi$
$524$	0.177797	−	0.547202i	0.00776709	−	0.0239046i
$525$		0			0
$526$	−10.7689			−0.469546
$527$	9.68098	+	8.39501i	0.421710	+	0.365692i
$528$	65.0640			2.83155
$529$	−2.89340	−	8.90497i	−0.125800	−	0.387173i
$530$		0			0
$531$	−55.1783	+	40.0894i	−2.39453	+	1.73973i
$532$	0.862332			0.0373868
$533$	−4.85129			−0.210133
$534$	−7.99515	+	5.80882i	−0.345984	+	0.251372i
$535$		0			0
$536$	0.979419	+	0.711590i	0.0423045	+	0.0307360i
$537$	−23.8025	−	73.2566i	−1.02715	−	3.16125i
$538$	0.593539	−	0.431231i	0.0255893	−	0.0185917i
$539$	10.6791	+	32.8668i	0.459980	+	1.41567i
$540$		0			0
$541$	32.6156	+	23.6966i	1.40225	+	1.01880i	0.994393	+	0.105751i	$0.0337248\pi$
$541$	32.6156	+	23.6966i	1.40225	+	1.01880i	0.407860	+	0.913045i	$0.366275\pi$
$542$	5.46664	−	16.8246i	0.234812	−	0.722677i
$543$	−18.4846	+	56.8897i	−0.793249	+	2.44137i
$544$	−1.55046	−	1.12648i	−0.0664755	−	0.0482973i
$545$		0			0
$546$	2.32561	+	7.15750i	0.0995270	+	0.306313i
$547$	−22.3860	+	16.2644i	−0.957157	+	0.695416i	−0.952489	−	0.304573i	$-0.901486\pi$
$547$	−22.3860	+	16.2644i	−0.957157	+	0.695416i	−0.00466864	+	0.999989i	$0.501486\pi$
$548$	0.520560	+	1.60212i	0.0222372	+	0.0684391i
$549$	38.1376	+	27.7086i	1.62767	+	1.18257i
$550$		0			0
$551$	−10.7442	+	7.80615i	−0.457720	+	0.332553i
$552$	−33.9891			−1.44667
$553$	−9.73001			−0.413762
$554$	1.40414	−	1.02017i	0.0596563	−	0.0433428i
$555$		0			0
$556$	0.429828	+	1.32288i	0.0182288	+	0.0561024i
$557$	−15.4033			−0.652657			−0.326329	−	0.945256i	$-0.605812\pi$
$557$	−15.4033			−0.652657			−0.326329	+	0.945256i	$0.605812\pi$
$558$	−20.4201	+	48.2689i	−0.864450	+	2.04339i
$559$	18.2689			0.772694
$560$		0			0
$561$	12.5632	−	38.6654i	0.530417	−	1.63246i
$562$	11.9996	−	8.71819i	0.506171	−	0.367755i
$563$	−1.02980			−0.0434009			−0.0217005	−	0.999765i	$-0.506908\pi$
$563$	−1.02980			−0.0434009			−0.0217005	+	0.999765i	$0.506908\pi$
$564$	1.93854			0.0816271
$565$		0			0
$566$	11.3912	+	8.27619i	0.478808	+	0.347874i
$567$	13.4058	+	9.73992i	0.562993	+	0.409038i
$568$	−5.23186	−	16.1020i	−0.219524	−	0.675625i
$569$	−10.0268	+	7.28492i	−0.420347	+	0.305400i	−0.777777	−	0.628540i	$-0.783653\pi$
$569$	−10.0268	+	7.28492i	−0.420347	+	0.305400i	0.357431	+	0.933940i	$0.383653\pi$
$570$		0			0
$571$	−1.51723	+	4.66955i	−0.0634941	+	0.195415i	−0.977771	−	0.209675i	$-0.932760\pi$
$571$	−1.51723	+	4.66955i	−0.0634941	+	0.195415i	0.914277	+	0.405089i	$0.132760\pi$
$572$	−1.28293	−	0.932103i	−0.0536420	−	0.0389732i
$573$	−22.2442	+	68.4605i	−0.929263	+	2.85998i
$574$	−0.975649	+	3.00274i	−0.0407228	+	0.125332i
$575$		0			0
$576$	18.1657	−	55.9083i	0.756904	−	2.32951i
$577$	5.19382	+	15.9849i	0.216221	+	0.665461i	0.999065	+	0.0432422i	$0.0137687\pi$
$577$	5.19382	+	15.9849i	0.216221	+	0.665461i	−0.782843	+	0.622219i	$0.786231\pi$
$578$	−12.8868	+	9.36277i	−0.536018	+	0.389440i
$579$	12.4281	+	38.2498i	0.516495	+	1.58961i
$580$		0			0
$581$	7.44557	+	5.40952i	0.308894	+	0.224425i
$582$	−39.3707	+	28.6045i	−1.63197	+	1.18569i
$583$	43.3738			1.79636
$584$	18.4789			0.764663
$585$		0			0
$586$	8.07393	−	24.8490i	0.333531	−	1.02650i
$587$	−12.5220	−	38.5388i	−0.516839	−	1.59067i	−0.779911	−	0.625891i	$-0.784736\pi$
$587$	−12.5220	−	38.5388i	−0.516839	−	1.59067i	0.263072	−	0.964776i	$-0.415264\pi$
$588$	2.86163			0.118012
$589$	8.03220	+	34.6003i	0.330961	+	1.42568i
$590$		0			0
$591$	−17.8384	−	54.9008i	−0.733772	−	2.25832i
$592$	9.17759	−	28.2457i	0.377197	−	1.16089i
$593$	34.5799	−	25.1238i	1.42003	−	1.03171i	0.428260	−	0.903656i	$-0.359127\pi$
$593$	34.5799	−	25.1238i	1.42003	−	1.03171i	0.991767	−	0.128055i	$-0.0408733\pi$
$594$	94.1551			3.86323
$595$		0			0
$596$	−1.95091	+	1.41742i	−0.0799124	+	0.0580597i
$597$	59.4654	+	43.2041i	2.43376	+	1.76823i
$598$	−7.79213	−	5.66131i	−0.318644	−	0.231508i
$599$	1.73669	+	5.34499i	0.0709594	+	0.218391i	0.980247	−	0.197778i	$-0.0633726\pi$
$599$	1.73669	+	5.34499i	0.0709594	+	0.218391i	−0.909287	+	0.416169i	$0.863373\pi$
$600$		0			0
$601$	−6.95038	−	21.3911i	−0.283512	−	0.872560i	−0.986841	−	0.161695i	$-0.948304\pi$
$601$	−6.95038	−	21.3911i	−0.283512	−	0.872560i	0.703329	−	0.710864i	$-0.251696\pi$
$602$	3.67409	−	11.3077i	0.149745	−	0.460867i
$603$	2.31748	+	1.68375i	0.0943750	+	0.0685674i
$604$	−0.136029	+	0.418655i	−0.00553496	+	0.0170348i
$605$		0			0
$606$	16.4274	+	11.9352i	0.667319	+	0.484836i
$607$	5.44889	−	16.7700i	0.221164	−	0.680671i	−0.777495	−	0.628889i	$-0.783510\pi$
$607$	5.44889	−	16.7700i	0.221164	−	0.680671i	0.998658	−	0.0517821i	$-0.0164901\pi$
$608$	−1.64165	−	5.05247i	−0.0665776	−	0.204905i
$609$	4.85949	−	3.53063i	0.196917	−	0.143068i
$610$		0			0
$611$	6.46981	+	4.70059i	0.261740	+	0.190165i
$612$	−1.89957	−	1.38012i	−0.0767858	−	0.0557881i
$613$	−29.7965	+	21.6484i	−1.20347	+	0.874372i	−0.994621	−	0.103577i	$-0.966971\pi$
$613$	−29.7965	+	21.6484i	−1.20347	+	0.874372i	−0.208848	+	0.977948i	$0.566971\pi$
$614$	−13.0371			−0.526136
$615$		0			0
$616$	−12.1551	+	8.83117i	−0.489741	+	0.355818i
$617$	−1.02769	+	3.16290i	−0.0413731	+	0.127333i	−0.969610	−	0.244657i	$-0.921325\pi$
$617$	−1.02769	+	3.16290i	−0.0413731	+	0.127333i	0.928237	+	0.371991i	$0.121325\pi$
$618$	1.63438	+	5.03012i	0.0657446	+	0.202341i
$619$	12.2404			0.491982			0.245991	−	0.969272i	$-0.420887\pi$
$619$	12.2404			0.491982			0.245991	+	0.969272i	$0.420887\pi$
$620$		0			0
$621$	−45.5385			−1.82740
$622$	−0.0251489	−	0.0774005i	−0.00100838	−	0.00310348i
$623$	0.652899	−	2.00942i	0.0261578	−	0.0805056i
$624$	17.9812	−	13.0641i	0.719826	−	0.522984i
$625$		0			0
$626$	13.2485			0.529515
$627$	91.1735	−	66.2414i	3.64112	−	2.64543i
$628$	0.990754	+	0.719825i	0.0395354	+	0.0287241i
$629$	−15.0134	−	10.9079i	−0.598625	−	0.434926i
$630$		0			0
$631$	30.3909	−	22.0803i	1.20984	−	0.879001i	0.214625	−	0.976696i	$-0.431147\pi$
$631$	30.3909	−	22.0803i	1.20984	−	0.879001i	0.995216	+	0.0976951i	$0.0311470\pi$
$632$	9.59107	+	29.5183i	0.381512	+	1.17417i
$633$	−4.74576	+	14.6060i	−0.188627	+	0.580535i
$634$	7.21867	+	5.24467i	0.286690	+	0.208292i
$635$		0			0
$636$	1.10987	−	3.41582i	0.0440091	−	0.135446i
$637$	9.55060	+	6.93891i	0.378408	+	0.274930i
$638$	4.91162	−	15.1164i	0.194453	−	0.598465i
$639$	−12.3795	−	38.1002i	−0.489725	−	1.50722i
$640$		0			0
$641$	2.20975	+	6.80091i	0.0872799	+	0.268620i	0.985165	−	0.171610i	$-0.0548969\pi$
$641$	2.20975	+	6.80091i	0.0872799	+	0.268620i	−0.897885	+	0.440230i	$0.854897\pi$
$642$	44.5530	+	32.3697i	1.75837	+	1.27753i
$643$	−26.8868	−	19.5344i	−1.06031	−	0.770363i	−0.0861670	−	0.996281i	$-0.527462\pi$
$643$	−26.8868	−	19.5344i	−1.06031	−	0.770363i	−0.974146	+	0.225918i	$0.927462\pi$
$644$	0.403823	−	0.293394i	0.0159128	−	0.0115614i
$645$		0			0
$646$	19.9837			0.786249
$647$	13.4503	−	9.77225i	0.528788	−	0.384187i	−0.291117	−	0.956688i	$-0.594027\pi$
$647$	13.4503	−	9.77225i	0.528788	−	0.384187i	0.819904	+	0.572501i	$0.194027\pi$
$648$	16.3339	−	50.2707i	0.641657	−	1.97482i
$649$	−17.0953	−	52.6139i	−0.671048	−	2.06527i
$650$		0			0
$651$	−3.63287	−	15.6493i	−0.142383	−	0.613345i
$652$	−3.37084			−0.132012
$653$	−10.4095	−	32.0372i	−0.407356	−	1.25371i	−0.918912	−	0.394462i	$-0.870931\pi$
$653$	−10.4095	−	32.0372i	−0.407356	−	1.25371i	0.511556	−	0.859250i	$-0.329069\pi$
$654$	−1.39349	+	4.28872i	−0.0544897	+	0.167702i
$655$		0			0
$656$	9.32434			0.364054
$657$	43.7244			1.70585
$658$	4.21061	−	3.05919i	0.164147	−	0.119260i
$659$	12.4643	+	9.05581i	0.485538	+	0.352764i	0.803466	−	0.595351i	$-0.202987\pi$
$659$	12.4643	+	9.05581i	0.485538	+	0.352764i	−0.317928	+	0.948115i	$0.602987\pi$
$660$		0			0
$661$	0.797817	+	2.45543i	0.0310315	+	0.0955050i	0.965373	−	0.260875i	$-0.0840109\pi$
$661$	0.797817	+	2.45543i	0.0310315	+	0.0955050i	−0.934341	+	0.356380i	$0.884011\pi$
$662$	−10.7659	+	7.82187i	−0.418428	+	0.304006i
$663$	−4.29161	−	13.2082i	−0.166672	−	0.512965i
$664$	9.07182	−	27.9202i	0.352055	−	1.08351i
$665$		0			0
$666$	23.4552	−	72.1878i	0.908872	−	2.79722i
$667$	−2.37552	+	7.31111i	−0.0919807	+	0.283087i
$668$	−1.78542	−	1.29719i	−0.0690801	−	0.0501897i
$669$	10.5502	−	32.4702i	0.407895	−	1.25537i
$670$		0			0
$671$	−30.9341	+	22.4749i	−1.19420	+	0.867634i
$672$	0.742498	+	2.28517i	0.0286425	+	0.0881525i
$673$	−12.0917	−	8.78514i	−0.466101	−	0.338642i	0.329819	−	0.944044i	$-0.393012\pi$
$673$	−12.0917	−	8.78514i	−0.466101	−	0.338642i	−0.795920	+	0.605402i	$0.793012\pi$
$674$	−6.63518	−	4.82074i	−0.255578	−	0.185688i
$675$		0			0
$676$	1.37598			0.0529224
$677$	−9.58212			−0.368271			−0.184135	−	0.982901i	$-0.558948\pi$
$677$	−9.58212			−0.368271			−0.184135	+	0.982901i	$0.558948\pi$
$678$	−42.6843	+	31.0120i	−1.63928	+	1.19101i
$679$	3.21509	−	9.89501i	0.123384	−	0.379736i
$680$		0			0
$681$	17.4066			0.667022
$682$	−32.1172	−	27.8509i	−1.22983	−	1.06647i
$683$	42.9429			1.64317			0.821583	−	0.570089i	$-0.193091\pi$
$683$	42.9429			1.64317			0.821583	+	0.570089i	$0.193091\pi$
$684$	−2.01129	−	6.19012i	−0.0769037	−	0.236685i
$685$		0			0
$686$	13.2784	−	9.64731i	0.506971	−	0.368336i
$687$	−32.1228			−1.22556
$688$	−35.1135			−1.33869
$689$	11.9869	−	8.70898i	0.456664	−	0.331786i
$690$		0			0
$691$	16.0878	+	11.6885i	0.612010	+	0.444651i	0.850122	−	0.526586i	$-0.176528\pi$
$691$	16.0878	+	11.6885i	0.612010	+	0.444651i	−0.238111	+	0.971238i	$0.576528\pi$
$692$	−0.122927	−	0.378329i	−0.00467297	−	0.0143819i
$693$	−28.7610	+	20.8961i	−1.09254	+	0.793777i
$694$	8.00343	+	24.6320i	0.303806	+	0.935019i
$695$		0			0
$696$	−15.5011	−	11.2622i	−0.587568	−	0.426893i
$697$	1.80043	−	5.54116i	0.0681962	−	0.209886i
$698$	−7.32158	+	22.5335i	−0.277126	+	0.852906i
$699$	−23.0729	−	16.7634i	−0.872697	−	0.634051i
$700$		0			0
$701$	4.81083	+	14.8062i	0.181702	+	0.559223i	0.999876	−	0.0157487i	$-0.00501318\pi$
$701$	4.81083	+	14.8062i	0.181702	+	0.559223i	−0.818174	+	0.574971i	$0.805013\pi$
$702$	26.0210	−	18.9053i	0.982098	−	0.713536i
$703$	−15.8964	−	48.9241i	−0.599544	−	1.84521i
$704$	38.5754	+	28.0267i	1.45387	+	1.05630i
$705$		0			0
$706$	−13.1415	+	9.54788i	−0.494588	+	0.359339i
$707$	−4.34117			−0.163266
$708$	−4.58095			−0.172163
$709$	34.1492	−	24.8109i	1.28250	−	0.931792i	0.282876	−	0.959157i	$-0.408712\pi$
$709$	34.1492	−	24.8109i	1.28250	−	0.931792i	0.999626	+	0.0273649i	$0.00871162\pi$
$710$		0			0
$711$	22.6942	+	69.8455i	0.851098	+	2.61941i
$712$	−6.73962			−0.252578
$713$	15.5336	+	13.4702i	0.581738	+	0.504463i
$714$	−9.03841			−0.338254
$715$		0			0
$716$	1.11503	−	3.43172i	0.0416708	−	0.128249i
$717$	−30.3685	+	22.0640i	−1.13413	+	0.823995i
$718$	43.4371			1.62106
$719$	−46.3827			−1.72978			−0.864891	−	0.501960i	$-0.832613\pi$
$719$	−46.3827			−1.72978			−0.864891	+	0.501960i	$0.832613\pi$
$720$		0			0
$721$	−0.914795	−	0.664637i	−0.0340687	−	0.0247524i
$722$	23.8942	+	17.3602i	0.889251	+	0.646078i
$723$	17.0755	+	52.5531i	0.635046	+	1.95447i
$724$	−2.26699	+	1.64707i	−0.0842522	+	0.0612128i
$725$		0			0
$726$	−27.1103	+	83.4369i	−1.00616	+	3.09663i
$727$	−12.3763	−	8.99188i	−0.459010	−	0.333491i	0.334133	−	0.942526i	$-0.391557\pi$
$727$	−12.3763	−	8.99188i	−0.459010	−	0.333491i	−0.793143	+	0.609036i	$0.791557\pi$
$728$	−1.58600	+	4.88121i	−0.0587811	+	0.180910i
$729$	2.64945	−	8.15416i	0.0981277	−	0.302006i
$730$		0			0
$731$	−6.78005	+	20.8668i	−0.250769	+	0.771788i
$732$	0.978416	+	3.01126i	0.0361633	+	0.111299i
$733$	−6.29770	+	4.57555i	−0.232611	+	0.169002i	−0.697985	−	0.716112i	$-0.745920\pi$
$733$	−6.29770	+	4.57555i	−0.232611	+	0.169002i	0.465374	+	0.885114i	$0.345920\pi$
$734$	6.83501	+	21.0360i	0.252285	+	0.776452i
$735$		0			0
$736$	−2.48779	−	1.80749i	−0.0917013	−	0.0666249i
$737$	−1.87975	+	1.36571i	−0.0692413	+	0.0503067i
$738$	23.8303			0.877206
$739$	−1.12482			−0.0413773			−0.0206887	−	0.999786i	$-0.506586\pi$
$739$	−1.12482			−0.0413773			−0.0206887	+	0.999786i	$0.506586\pi$
$740$		0			0
$741$	11.8964	−	36.6133i	0.437024	−	1.34502i
$742$	−2.97978	−	9.17083i	−0.109391	−	0.336672i
$743$	37.3958			1.37192			0.685960	−	0.727639i	$-0.259382\pi$
$743$	37.3958			1.37192			0.685960	+	0.727639i	$0.259382\pi$
$744$	−43.8949	+	26.4470i	−1.60927	+	0.969595i
$745$		0			0
$746$	8.90569	+	27.4089i	0.326060	+	1.00351i
$747$	21.4655	−	66.0640i	0.785382	−	2.41716i
$748$	1.54078	−	1.11944i	0.0563364	−	0.0409308i
$749$	−11.7737			−0.430202
$750$		0			0
$751$	−43.0328	+	31.2652i	−1.57029	+	1.14088i	−0.643412	+	0.765520i	$0.722482\pi$
$751$	−43.0328	+	31.2652i	−1.57029	+	1.14088i	−0.926878	+	0.375362i	$0.877518\pi$
$752$	−12.4352	−	9.03469i	−0.453464	−	0.329461i
$753$	−61.7337	−	44.8522i	−2.24970	−	1.63450i
$754$	−1.67782	−	5.16381i	−0.0611028	−	0.188055i
$755$		0			0
$756$	0.515089	+	1.58528i	0.0187336	+	0.0576562i
$757$	6.64091	−	20.4386i	0.241368	−	0.742854i	−0.754845	−	0.655903i	$-0.772288\pi$
$757$	6.64091	−	20.4386i	0.241368	−	0.742854i	0.996213	−	0.0869504i	$-0.0277122\pi$
$758$	−7.40340	−	5.37888i	−0.268903	−	0.195370i
$759$	20.1582	−	62.0406i	0.731697	−	2.25193i
$760$		0			0
$761$	−22.9004	−	16.6381i	−0.830138	−	0.603130i	0.0894604	−	0.995990i	$-0.471486\pi$
$761$	−22.9004	−	16.6381i	−0.830138	−	0.603130i	−0.919598	+	0.392860i	$0.871486\pi$
$762$	−0.612044	+	1.88368i	−0.0221720	+	0.0682384i
$763$	−0.297919	−	0.916900i	−0.0107854	−	0.0331940i
$764$	−2.72808	+	1.98206i	−0.0986984	+	0.0717086i
$765$		0			0
$766$	20.4102	+	14.8289i	0.737451	+	0.535790i
$767$	−15.2888	−	11.1080i	−0.552046	−	0.401085i
$768$	8.96907	−	6.51641i	0.323643	−	0.235141i
$769$	−8.29866			−0.299257			−0.149629	−	0.988742i	$-0.547808\pi$
$769$	−8.29866			−0.299257			−0.149629	+	0.988742i	$0.547808\pi$
$770$		0			0
$771$	14.0490	−	10.2072i	0.505961	−	0.367602i
$772$	−0.582199	+	1.79182i	−0.0209538	+	0.0644891i
$773$	−3.97213	−	12.2249i	−0.142867	−	0.439701i	0.853863	−	0.520498i	$-0.174254\pi$
$773$	−3.97213	−	12.2249i	−0.142867	−	0.439701i	−0.996731	+	0.0807968i	$0.974254\pi$
$774$	−89.7400			−3.22564
$775$		0			0
$776$	−33.1881			−1.19138
$777$	7.18976	+	22.1278i	0.257931	+	0.793830i
$778$	1.21874	−	3.75088i	0.0436938	−	0.134476i
$779$	13.0661	−	9.49308i	0.468142	−	0.340125i
$780$		0			0
$781$	32.4941			1.16273
$782$	9.35822	−	6.79914i	0.334649	−	0.243137i
$783$	−20.7683	−	15.0891i	−0.742200	−	0.539240i
$784$	−18.3566	−	13.3368i	−0.655592	−	0.476315i
$785$		0			0
$786$	−13.5242	+	9.82590i	−0.482392	+	0.350478i
$787$	−3.60362	−	11.0908i	−0.128455	−	0.395345i	0.866059	−	0.499941i	$-0.166645\pi$
$787$	−3.60362	−	11.0908i	−0.128455	−	0.395345i	−0.994515	+	0.104596i	$0.966645\pi$
$788$	0.835642	−	2.57184i	0.0297685	−	0.0916181i
$789$	−20.1568	−	14.6448i	−0.717601	−	0.521368i
$790$		0			0
$791$	3.48568	−	10.7278i	0.123937	−	0.381437i
$792$	91.7436	+	66.6556i	3.25997	+	2.36850i
$793$	−4.03630	+	12.4224i	−0.143333	+	0.441134i
$794$	−9.19965	−	28.3136i	−0.326483	−	1.00481i
$795$		0			0
$796$	1.06403	+	3.27475i	0.0377136	+	0.116070i
$797$	4.31568	+	3.13553i	0.152869	+	0.111066i	0.661591	−	0.749865i	$-0.269882\pi$
$797$	4.31568	+	3.13553i	0.152869	+	0.111066i	−0.508721	+	0.860931i	$0.669882\pi$
$798$	−20.2695	−	14.7267i	−0.717534	−	0.521319i
$799$	−7.77013	+	5.64533i	−0.274887	+	0.199717i
$800$		0			0
$801$	−15.9471			−0.563464
$802$	−6.04288	+	4.39041i	−0.213381	+	0.155031i
$803$	−10.9595	+	33.7298i	−0.386751	+	1.19030i
$804$	0.0594546	+	0.182983i	0.00209680	+	0.00645330i
$805$		0			0
$806$	−14.4682	−	1.24817i	−0.509620	−	0.0439649i
$807$	1.69740			0.0597513
$808$	4.27918	+	13.1700i	0.150541	+	0.463318i
$809$	−5.06021	+	15.5737i	−0.177908	+	0.547543i	−0.999754	−	0.0221653i	$-0.992944\pi$
$809$	−5.06021	+	15.5737i	−0.177908	+	0.547543i	0.821847	+	0.569709i	$0.192944\pi$
$810$		0			0
$811$	35.0584			1.23107			0.615534	−	0.788110i	$-0.288940\pi$
$811$	35.0584			1.23107			0.615534	+	0.788110i	$0.288940\pi$
$812$	0.281384			0.00987463
$813$	33.1122	−	24.0574i	1.16130	−	0.843731i
$814$	49.8079	+	36.1876i	1.74577	+	1.26837i
$815$		0			0
$816$	8.24862	+	25.3867i	0.288760	+	0.888711i
$817$	−49.2042	+	35.7490i	−1.72144	+	1.25070i
$818$	−8.80700	−	27.1051i	−0.307929	−	0.947709i
$819$	−3.75276	+	11.5498i	−0.131132	+	0.403582i
$820$		0			0
$821$	−7.94004	+	24.4369i	−0.277109	+	0.852855i	0.711544	+	0.702641i	$0.247996\pi$
$821$	−7.94004	+	24.4369i	−0.277109	+	0.852855i	−0.988654	+	0.150214i	$0.952004\pi$
$822$	15.1246	−	46.5486i	0.527530	−	1.62357i
$823$	5.56297	+	4.04173i	0.193913	+	0.140886i	0.680505	−	0.732743i	$-0.261760\pi$
$823$	5.56297	+	4.04173i	0.193913	+	0.140886i	−0.486592	+	0.873629i	$0.661760\pi$
$824$	−1.11460	+	3.43039i	−0.0388290	+	0.119503i
$825$		0			0
$826$	−9.95009	+	7.22916i	−0.346208	+	0.251535i
$827$	10.7633	+	33.1261i	0.374278	+	1.15191i	0.943965	+	0.330046i	$0.107064\pi$
$827$	10.7633	+	33.1261i	0.374278	+	1.15191i	−0.569687	+	0.821862i	$0.692936\pi$
$828$	−3.04796	−	2.21447i	−0.105924	−	0.0769583i
$829$	−9.87637	−	7.17560i	−0.343021	−	0.249219i	0.402915	−	0.915238i	$-0.367997\pi$
$829$	−9.87637	−	7.17560i	−0.343021	−	0.249219i	−0.745935	+	0.666019i	$0.767997\pi$
$830$		0			0
$831$	4.01556			0.139298
$832$	16.2883			0.564694
$833$	−11.4701	+	8.33352i	−0.397416	+	0.288739i
$834$	12.4884	−	38.4353i	0.432438	−	1.33091i
$835$		0			0
$836$	5.27930			0.182588
$837$	−58.8103	+	35.4337i	−2.03278	+	1.22477i
$838$	−1.22459			−0.0423028
$839$	−2.12550	−	6.54162i	−0.0733804	−	0.225842i	0.907639	−	0.419752i	$-0.137883\pi$
$839$	−2.12550	−	6.54162i	−0.0733804	−	0.225842i	−0.981019	+	0.193910i	$0.937883\pi$
$840$		0			0
$841$	19.9556	−	14.4986i	0.688124	−	0.499951i
$842$	31.2267			1.07614
$843$	34.3163			1.18192
$844$	−0.582032	+	0.422871i	−0.0200344	+	0.0145558i
$845$		0			0
$846$	−31.7807	−	23.0900i	−1.09264	−	0.793852i
$847$	−5.79600	−	17.8383i	−0.199153	−	0.612930i
$848$	−23.0392	+	16.7390i	−0.791169	+	0.574818i
$849$	10.0667	+	30.9821i	0.345488	+	1.06330i
$850$		0			0
$851$	−24.0898	−	17.5023i	−0.825787	−	0.599970i
$852$	0.831474	−	2.55901i	0.0284858	−	0.0876703i
$853$	6.23773	−	19.1978i	0.213576	−	0.657319i	−0.785676	−	0.618639i	$-0.787685\pi$
$853$	6.23773	−	19.1978i	0.213576	−	0.657319i	0.999252	−	0.0386804i	$-0.0123154\pi$
$854$	6.87721	+	4.99659i	0.235333	+	0.170980i
$855$		0			0
$856$	11.6056	+	35.7184i	0.396671	+	1.22083i
$857$	−5.27558	+	3.83293i	−0.180210	+	0.130931i	−0.674233	−	0.738518i	$-0.735526\pi$
$857$	−5.27558	+	3.83293i	−0.180210	+	0.130931i	0.494023	+	0.869449i	$0.335526\pi$
$858$	14.2377	+	43.8191i	0.486066	+	1.49596i
$859$	−6.94602	−	5.04658i	−0.236995	−	0.172187i	0.462948	−	0.886385i	$-0.346792\pi$
$859$	−6.94602	−	5.04658i	−0.236995	−	0.172187i	−0.699944	+	0.714198i	$0.746792\pi$
$860$		0			0
$861$	−5.90965	+	4.29361i	−0.201400	+	0.146326i
$862$	46.8939			1.59721
$863$	−46.4756			−1.58205			−0.791023	−	0.611786i	$-0.790451\pi$
$863$	−46.4756			−1.58205			−0.791023	+	0.611786i	$0.790451\pi$
$864$	8.30771	−	6.03590i	0.282634	−	0.205346i
$865$		0			0
$866$	0.0554598	+	0.170688i	0.00188460	+	0.00580021i
$867$	−36.8535			−1.25161
$868$	0.293222	−	0.693118i	0.00995261	−	0.0235260i
$869$	−59.5683			−2.02072
$870$		0			0
$871$	−0.245270	+	0.754865i	−0.00831067	+	0.0255776i
$872$	−2.48797	+	1.80761i	−0.0842532	+	0.0612136i
$873$	−78.5288			−2.65780
$874$	32.0649			1.08461
$875$		0			0
$876$	2.37589	+	1.72619i	0.0802739	+	0.0583224i
$877$	34.5132	+	25.0753i	1.16543	+	0.846732i	0.990454	−	0.137841i	$-0.0440164\pi$
$877$	34.5132	+	25.0753i	1.16543	+	0.846732i	0.174972	+	0.984573i	$0.444016\pi$
$878$	−11.7016	−	36.0137i	−0.394909	−	1.21540i
$879$	48.9050	−	35.5316i	1.64952	−	1.19845i
$880$		0			0
$881$	6.10369	−	18.7852i	0.205639	−	0.632891i	−0.794048	−	0.607855i	$-0.792030\pi$
$881$	6.10369	−	18.7852i	0.205639	−	0.632891i	0.999687	−	0.0250354i	$-0.00796985\pi$
$882$	−46.9140	−	34.0851i	−1.57968	−	1.14770i
$883$	1.49764	−	4.60925i	0.0503995	−	0.155114i	−0.922689	−	0.385545i	$-0.874014\pi$
$883$	1.49764	−	4.60925i	0.0503995	−	0.155114i	0.973089	+	0.230431i	$0.0740136\pi$
$884$	0.201042	−	0.618743i	0.00676176	−	0.0208106i
$885$		0			0
$886$	9.83086	−	30.2563i	0.330274	−	1.01648i
$887$	10.8335	+	33.3422i	0.363754	+	1.11952i	0.950757	+	0.309936i	$0.100308\pi$
$887$	10.8335	+	33.3422i	0.363754	+	1.11952i	−0.587003	+	0.809585i	$0.699692\pi$
$888$	60.0428	−	43.6237i	2.01491	−	1.46391i
$889$	−0.130851	−	0.402718i	−0.00438860	−	0.0135067i
$890$		0			0
$891$	82.0722	+	59.6290i	2.74952	+	1.99765i
$892$	1.29390	−	0.940076i	0.0433231	−	0.0314761i
$893$	−26.6235			−0.890921
$894$	70.0634			2.34327
$895$		0			0
$896$	2.80417	−	8.63035i	0.0936807	−	0.288320i
$897$	−6.88611	−	21.1933i	−0.229920	−	0.707622i
$898$	7.42104			0.247643
$899$	2.62095	+	11.2903i	0.0874137	+	0.376552i
$900$		0			0
$901$	5.49880	+	16.9236i	0.183192	+	0.563806i
$902$	−5.97304	+	18.3831i	−0.198880	+	0.612091i
$903$	22.2545	−	16.1688i	0.740583	−	0.538065i
$904$	−35.9813			−1.19672
$905$		0			0
$906$	10.3471	−	7.51763i	0.343760	−	0.249756i
$907$	17.5796	+	12.7723i	0.583721	+	0.424098i	0.840064	−	0.542488i	$-0.182517\pi$
$907$	17.5796	+	12.7723i	0.583721	+	0.424098i	−0.256343	+	0.966586i	$0.582517\pi$
$908$	0.659685	+	0.479289i	0.0218924	+	0.0159058i
$909$	10.1253	+	31.1625i	0.335835	+	1.03359i
$910$		0			0
$911$	−1.34474	−	4.13869i	−0.0445533	−	0.137121i	0.926305	−	0.376773i	$-0.122966\pi$
$911$	−1.34474	−	4.13869i	−0.0445533	−	0.137121i	−0.970859	+	0.239653i	$0.922966\pi$
$912$	−22.8652	+	70.3720i	−0.757144	+	2.33025i
$913$	45.5827	+	33.1178i	1.50857	+	1.09604i
$914$	13.9415	−	42.9076i	0.461144	−	1.41926i
$915$		0			0
$916$	−1.21741	−	0.884500i	−0.0402243	−	0.0292247i
$917$	1.10441	−	3.39902i	0.0364708	−	0.112246i
$918$	11.9367	+	36.7374i	0.393970	+	1.21252i
$919$	33.2493	−	24.1571i	1.09679	−	0.796868i	0.116261	−	0.993219i	$-0.462909\pi$
$919$	33.2493	−	24.1571i	1.09679	−	0.796868i	0.980534	+	0.196351i	$0.0629092\pi$
$920$		0			0
$921$	−24.4024	−	17.7294i	−0.804086	−	0.584203i
$922$	−7.69326	−	5.58948i	−0.253364	−	0.184080i
$923$	8.98014	−	6.52446i	0.295585	−	0.214755i
$924$	−2.38777			−0.0785517
$925$		0			0
$926$	21.7653	−	15.8135i	0.715254	−	0.519662i
$927$	−2.63735	+	8.11692i	−0.0866218	+	0.266595i
$928$	−0.535679	−	1.64865i	−0.0175845	−	0.0541196i
$929$	−19.8163			−0.650152			−0.325076	−	0.945688i	$-0.605390\pi$
$929$	−19.8163			−0.650152			−0.325076	+	0.945688i	$0.605390\pi$
$930$		0			0
$931$	−39.3010			−1.28804
$932$	−0.412850	−	1.27062i	−0.0135233	−	0.0416206i
$933$	0.0581852	−	0.179076i	0.00190490	−	0.00586267i
$934$	−18.4183	+	13.3816i	−0.602664	+	0.437861i
$935$		0			0
$936$	38.7382			1.26620
$937$	34.6362	−	25.1647i	1.13152	−	0.822094i	0.145601	−	0.989343i	$-0.453488\pi$
$937$	34.6362	−	25.1647i	1.13152	−	0.822094i	0.985915	+	0.167249i	$0.0534884\pi$
$938$	0.417902	+	0.303623i	0.0136450	+	0.00991366i
$939$	24.7980	+	18.0168i	0.809251	+	0.587955i
$940$		0			0
$941$	−20.5084	+	14.9002i	−0.668554	+	0.485733i	−0.869541	−	0.493861i	$-0.835585\pi$
$941$	−20.5084	+	14.9002i	−0.668554	+	0.485733i	0.200987	+	0.979594i	$0.435585\pi$
$942$	−10.9952	−	33.8397i	−0.358242	−	1.10256i
$943$	2.88888	−	8.89106i	0.0940749	−	0.289533i
$944$	29.3856	+	21.3499i	0.956419	+	0.694879i
$945$		0			0
$946$	22.4932	−	69.2270i	0.731318	−	2.25076i
$947$	−24.8796	−	18.0761i	−0.808480	−	0.587395i	0.104910	−	0.994482i	$-0.466545\pi$
$947$	−24.8796	−	18.0761i	−0.808480	−	0.587395i	−0.913389	+	0.407087i	$0.866545\pi$
$948$	−1.52426	+	4.69120i	−0.0495057	+	0.152363i
$949$	3.74378	+	11.5222i	0.121528	+	0.374026i
$950$		0			0
$951$	6.37932	+	19.6335i	0.206864	+	0.636661i
$952$	−4.98673	−	3.62307i	−0.161621	−	0.117424i
$953$	−26.3418	−	19.1384i	−0.853294	−	0.619955i	0.0727581	−	0.997350i	$-0.476820\pi$
$953$	−26.3418	−	19.1384i	−0.853294	−	0.619955i	−0.926052	+	0.377395i	$0.876820\pi$
$954$	−58.8815	+	42.7799i	−1.90636	+	1.38505i
$955$		0			0
$956$	−1.75845			−0.0568725
$957$	29.7504	−	21.6149i	0.961695	−	0.698712i
$958$	−1.75283	+	5.39465i	−0.0566313	+	0.174293i
$959$	3.23353	+	9.95178i	0.104416	+	0.321360i
$960$		0			0
$961$	30.5420	+	5.30923i	0.985225	+	0.171265i
$962$	21.0311			0.678071
$963$	27.4609	+	84.5159i	0.884915	+	2.72349i
$964$	−0.799908	+	2.46186i	−0.0257633	+	0.0792913i
$965$		0			0
$966$	−14.5026			−0.466613
$967$	29.4715			0.947741			0.473870	−	0.880595i	$-0.342857\pi$
$967$	29.4715			0.947741			0.473870	+	0.880595i	$0.342857\pi$
$968$	−48.4033	+	35.1671i	−1.55574	+	1.13031i
$969$	37.4048	+	27.1762i	1.20161	+	0.873024i
$970$		0			0
$971$	−15.8132	−	48.6679i	−0.507468	−	1.56183i	−0.796581	−	0.604532i	$-0.793360\pi$
$971$	−15.8132	−	48.6679i	−0.507468	−	1.56183i	0.289113	−	0.957295i	$-0.406640\pi$
$972$	2.38101	−	1.72991i	0.0763710	−	0.0554868i
$973$	2.66994	+	8.21722i	0.0855943	+	0.263432i
$974$	2.73549	−	8.41896i	0.0876506	−	0.269761i
$975$		0			0
$976$	7.75790	−	23.8764i	0.248324	−	0.764264i
$977$	−0.437149	+	1.34541i	−0.0139856	+	0.0430433i	−0.957806	−	0.287416i	$-0.907204\pi$
$977$	−0.437149	+	1.34541i	−0.0139856	+	0.0430433i	0.943820	+	0.330460i	$0.107204\pi$
$978$	79.2333	+	57.5664i	2.53360	+	1.84077i
$979$	3.99713	−	12.3019i	0.127749	−	0.393170i
$980$		0			0
$981$	−5.88697	+	4.27713i	−0.187956	+	0.136558i
$982$	−10.7415	−	33.0590i	−0.342775	−	1.05495i
$983$	0.479375	+	0.348286i	0.0152897	+	0.0111086i	0.595404	−	0.803427i	$-0.296992\pi$
$983$	0.479375	+	0.348286i	0.0152897	+	0.0111086i	−0.580114	+	0.814535i	$0.696992\pi$
$984$	18.8509	+	13.6960i	0.600946	+	0.436613i
$985$		0			0
$986$	6.52081			0.207665
$987$	12.0415			0.383285
$988$	1.45900	−	1.06003i	0.0464170	−	0.0337239i
$989$	−10.8789	+	33.4819i	−0.345930	+	1.06466i
$990$		0			0
$991$	−61.1371			−1.94208			−0.971042	−	0.238909i	$-0.923210\pi$
$991$	−61.1371			−1.94208			−0.971042	+	0.238909i	$0.923210\pi$
$992$	−4.61925	−	0.398503i	−0.146661	−	0.0126525i
$993$	−30.7882			−0.977036
$994$	−2.23235	−	6.87046i	−0.0708058	−	0.217918i
$995$		0			0
$996$	3.77452	−	2.74235i	0.119600	−	0.0868947i
$997$	−21.4914			−0.680640			−0.340320	−	0.940310i	$-0.610535\pi$
$997$	−21.4914			−0.680640			−0.340320	+	0.940310i	$0.610535\pi$
$998$	−12.5077			−0.395924
$999$	80.4452	−	58.4468i	2.54517	−	1.84918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.k.d.376.2		24
5.2	odd	4		775.2.bf.c.624.9		48
5.3	odd	4		775.2.bf.c.624.4		48
5.4	even	2		155.2.h.b.66.5	✓	24
31.8	even	5	inner	775.2.k.d.101.2		24
155.8	odd	20		775.2.bf.c.349.9		48
155.39	even	10		155.2.h.b.101.5	yes	24
155.109	even	10		4805.2.a.u.1.9		12
155.132	odd	20		775.2.bf.c.349.4		48
155.139	odd	10		4805.2.a.v.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.h.b.66.5	✓	24	5.4	even	2
155.2.h.b.101.5	yes	24	155.39	even	10
775.2.k.d.101.2		24	31.8	even	5	inner
775.2.k.d.376.2		24	1.1	even	1	trivial
775.2.bf.c.349.4		48	155.132	odd	20
775.2.bf.c.349.9		48	155.8	odd	20
775.2.bf.c.624.4		48	5.3	odd	4
775.2.bf.c.624.9		48	5.2	odd	4
4805.2.a.u.1.9		12	155.109	even	10
4805.2.a.v.1.9		12	155.139	odd	10

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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.420591 - 1.29445i) q^{2} +(0.973089 - 2.99486i) q^{3} +(0.119342 - 0.0867070i) q^{4} -4.28595 q^{6} +(0.741309 - 0.538593i) q^{7} +(-2.36467 - 1.71804i) q^{8} +(-5.59523 - 4.06517i) q^{9} +O(q^{10})\)	\(q+(-0.420591 - 1.29445i) q^{2} +(0.973089 - 2.99486i) q^{3} +(0.119342 - 0.0867070i) q^{4} -4.28595 q^{6} +(0.741309 - 0.538593i) q^{7} +(-2.36467 - 1.71804i) q^{8} +(-5.59523 - 4.06517i) q^{9} +(4.53839 - 3.29733i) q^{11} +(-0.143545 - 0.441786i) q^{12} +(0.592172 - 1.82252i) q^{13} +(-1.00897 - 0.733057i) q^{14} +(-1.13817 + 3.50294i) q^{16} +(1.86192 + 1.35276i) q^{17} +(-2.90884 + 8.95250i) q^{18} +(1.97142 + 6.06741i) q^{19} +(-0.891650 - 2.74422i) q^{21} +(-6.17702 - 4.48787i) q^{22} +(2.98754 + 2.17057i) q^{23} +(-7.44631 + 5.41006i) q^{24} -2.60821 q^{26} +(-9.97655 + 7.24839i) q^{27} +(0.0417696 - 0.128554i) q^{28} +(0.643286 + 1.97983i) q^{29} +(5.54716 + 0.478553i) q^{31} -0.832724 q^{32} +(-5.45879 - 16.8004i) q^{33} +(0.967971 - 2.97911i) q^{34} -1.02023 q^{36} -8.06343 q^{37} +(7.02476 - 5.10379i) q^{38} +(-4.88195 - 3.54694i) q^{39} +(-0.782302 - 2.40768i) q^{41} +(-3.17722 + 2.30838i) q^{42} +(2.94598 + 9.06681i) q^{43} +(0.255718 - 0.787020i) q^{44} +(1.55316 - 4.78013i) q^{46} +(-1.28959 + 3.96894i) q^{47} +(9.38327 + 6.81735i) q^{48} +(-1.90366 + 5.85887i) q^{49} +(5.86314 - 4.25982i) q^{51} +(-0.0873542 - 0.268848i) q^{52} +(6.25519 + 4.54466i) q^{53} +(13.5787 + 9.86549i) q^{54} -2.67828 q^{56} +20.0894 q^{57} +(2.29222 - 1.66540i) q^{58} +(3.04742 - 9.37899i) q^{59} -6.81609 q^{61} +(-1.71362 - 7.38177i) q^{62} -6.33727 q^{63} +(2.62658 + 8.08380i) q^{64} +(-19.4513 + 14.1322i) q^{66} -0.414188 q^{67} +0.339499 q^{68} +(9.40770 - 6.83509i) q^{69} +(4.68617 + 3.40470i) q^{71} +(6.24678 + 19.2256i) q^{72} +(-5.11470 + 3.71605i) q^{73} +(3.39140 + 10.4377i) q^{74} +(0.761360 + 0.553160i) q^{76} +(1.58843 - 4.88869i) q^{77} +(-2.53802 + 7.81123i) q^{78} +(-8.59071 - 6.24151i) q^{79} +(5.58827 + 17.1989i) q^{81} +(-2.78758 + 2.02529i) q^{82} +(3.10371 + 9.55223i) q^{83} +(-0.344354 - 0.250188i) q^{84} +(10.4974 - 7.62683i) q^{86} +6.55529 q^{87} -16.3967 q^{88} +(1.86543 - 1.35532i) q^{89} +(-0.542612 - 1.66999i) q^{91} +0.544743 q^{92} +(6.83108 - 16.1473i) q^{93} +5.67996 q^{94} +(-0.810314 + 2.49389i) q^{96} +(9.18599 - 6.67401i) q^{97} +8.38465 q^{98} -38.7976 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} - 6 q^{4} - 16 q^{6} + 9 q^{7} - 11 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 - 6 * q^4 - 16 * q^6 + 9 * q^7 - 11 * q^8 - 6 * q^9	\( 24 q - 2 q^{2} - 6 q^{4} - 16 q^{6} + 9 q^{7} - 11 q^{8} - 6 q^{9} + q^{11} - 18 q^{12} + 5 q^{13} + 6 q^{14} - 24 q^{16} - 7 q^{17} + 18 q^{18} + 2 q^{19} - 10 q^{21} - 28 q^{22} + 15 q^{23} - 32 q^{24} + 22 q^{26} - 9 q^{27} - 38 q^{28} + 15 q^{29} + 6 q^{31} - 74 q^{32} - 5 q^{33} - 20 q^{34} - 58 q^{36} + 56 q^{37} + 21 q^{38} - 10 q^{39} - 24 q^{41} + 38 q^{42} - 21 q^{43} + 41 q^{44} + 48 q^{46} + 8 q^{47} + 26 q^{48} - 23 q^{49} + 26 q^{51} + 27 q^{52} - 26 q^{53} + 11 q^{54} - 48 q^{56} - 62 q^{57} - 52 q^{58} + 10 q^{59} - 40 q^{61} + 28 q^{62} - 26 q^{63} + 9 q^{64} - 2 q^{66} + 26 q^{67} + 8 q^{68} + 64 q^{69} - 7 q^{71} + 127 q^{72} + 51 q^{73} - q^{74} + 43 q^{76} + 39 q^{77} + 31 q^{78} + 31 q^{79} + 34 q^{81} - 58 q^{82} - 6 q^{83} + 113 q^{84} - 22 q^{86} - 4 q^{87} + 28 q^{88} + 13 q^{89} + 54 q^{91} + 2 q^{92} + 72 q^{93} - 10 q^{94} + 101 q^{96} + 39 q^{97} + 220 q^{98} - 170 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 - 6 * q^4 - 16 * q^6 + 9 * q^7 - 11 * q^8 - 6 * q^9 + q^11 - 18 * q^12 + 5 * q^13 + 6 * q^14 - 24 * q^16 - 7 * q^17 + 18 * q^18 + 2 * q^19 - 10 * q^21 - 28 * q^22 + 15 * q^23 - 32 * q^24 + 22 * q^26 - 9 * q^27 - 38 * q^28 + 15 * q^29 + 6 * q^31 - 74 * q^32 - 5 * q^33 - 20 * q^34 - 58 * q^36 + 56 * q^37 + 21 * q^38 - 10 * q^39 - 24 * q^41 + 38 * q^42 - 21 * q^43 + 41 * q^44 + 48 * q^46 + 8 * q^47 + 26 * q^48 - 23 * q^49 + 26 * q^51 + 27 * q^52 - 26 * q^53 + 11 * q^54 - 48 * q^56 - 62 * q^57 - 52 * q^58 + 10 * q^59 - 40 * q^61 + 28 * q^62 - 26 * q^63 + 9 * q^64 - 2 * q^66 + 26 * q^67 + 8 * q^68 + 64 * q^69 - 7 * q^71 + 127 * q^72 + 51 * q^73 - q^74 + 43 * q^76 + 39 * q^77 + 31 * q^78 + 31 * q^79 + 34 * q^81 - 58 * q^82 - 6 * q^83 + 113 * q^84 - 22 * q^86 - 4 * q^87 + 28 * q^88 + 13 * q^89 + 54 * q^91 + 2 * q^92 + 72 * q^93 - 10 * q^94 + 101 * q^96 + 39 * q^97 + 220 * q^98 - 170 * q^99

Introduction

L-functions

Modular forms

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