LMFDB - Embedded newform 475.2.l.e.176.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			176.7
Character	$\chi$	$=$	475.176
Dual form			475.2.l.e.251.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.17674 - 0.792270i) q^{2} +(0.363030 - 2.05885i) q^{3} +(2.57843 - 2.16356i) q^{4} +(-0.840938 - 4.76919i) q^{6} +(1.49485 + 2.58916i) q^{7} +(1.58201 - 2.74013i) q^{8} +(-1.28798 - 0.468785i) q^{9} +O(q^{10})$	\(q+(2.17674 - 0.792270i) q^{2} +(0.363030 - 2.05885i) q^{3} +(2.57843 - 2.16356i) q^{4} +(-0.840938 - 4.76919i) q^{6} +(1.49485 + 2.58916i) q^{7} +(1.58201 - 2.74013i) q^{8} +(-1.28798 - 0.468785i) q^{9} +(1.03220 - 1.78782i) q^{11} +(-3.51839 - 6.09402i) q^{12} +(-0.487552 - 2.76505i) q^{13} +(5.30523 + 4.45161i) q^{14} +(0.103752 - 0.588408i) q^{16} +(-7.66330 + 2.78921i) q^{17} -3.17500 q^{18} +(-2.39057 + 3.64488i) q^{19} +(5.87336 - 2.13773i) q^{21} +(0.830393 - 4.70939i) q^{22} +(-3.38493 + 2.84029i) q^{23} +(-5.06718 - 4.25187i) q^{24} +(-3.25194 - 5.63252i) q^{26} +(1.70318 - 2.94999i) q^{27} +(9.45618 + 3.44177i) q^{28} +(7.67059 + 2.79186i) q^{29} +(-2.50483 - 4.33850i) q^{31} +(0.858520 + 4.86891i) q^{32} +(-3.30612 - 2.77416i) q^{33} +(-14.4712 + 12.1428i) q^{34} +(-4.33520 + 1.57788i) q^{36} +1.47168 q^{37} +(-2.31593 + 9.82795i) q^{38} -5.86980 q^{39} +(-1.17665 + 6.67313i) q^{41} +(11.0911 - 9.30657i) q^{42} +(-5.25688 - 4.41104i) q^{43} +(-1.20660 - 6.84297i) q^{44} +(-5.11784 + 8.86435i) q^{46} +(-0.751233 - 0.273426i) q^{47} +(-1.17378 - 0.427219i) q^{48} +(-0.969174 + 1.67866i) q^{49} +(2.96055 + 16.7901i) q^{51} +(-7.23946 - 6.07463i) q^{52} +(7.46661 - 6.26523i) q^{53} +(1.37019 - 7.77076i) q^{54} +9.45952 q^{56} +(6.63640 + 6.24502i) q^{57} +18.9088 q^{58} +(8.51236 - 3.09825i) q^{59} +(-1.57051 + 1.31782i) q^{61} +(-8.88964 - 7.45929i) q^{62} +(-0.711575 - 4.03554i) q^{63} +(6.32375 + 10.9531i) q^{64} +(-9.39445 - 3.41930i) q^{66} +(-1.52085 - 0.553545i) q^{67} +(-13.7247 + 23.7718i) q^{68} +(4.61889 + 8.00015i) q^{69} +(4.14723 + 3.47994i) q^{71} +(-3.32213 + 2.78760i) q^{72} +(2.54821 - 14.4516i) q^{73} +(3.20347 - 1.16597i) q^{74} +(1.72200 + 14.5702i) q^{76} +6.17193 q^{77} +(-12.7770 + 4.65046i) q^{78} +(2.16322 - 12.2682i) q^{79} +(-8.60518 - 7.22060i) q^{81} +(2.72565 + 15.4579i) q^{82} +(3.85430 + 6.67585i) q^{83} +(10.5189 - 18.2193i) q^{84} +(-14.9376 - 5.43684i) q^{86} +(8.53267 - 14.7790i) q^{87} +(-3.26590 - 5.65670i) q^{88} +(-0.0972439 - 0.551497i) q^{89} +(6.43033 - 5.39569i) q^{91} +(-2.58266 + 14.6470i) q^{92} +(-9.84163 + 3.58206i) q^{93} -1.85187 q^{94} +10.3360 q^{96} +(-14.0997 + 5.13189i) q^{97} +(-0.779693 + 4.42186i) q^{98} +(-2.16754 + 1.81879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 3 q^{3} - 6 q^{4} - 3 q^{6} - 18 q^{8} + 9 q^{9}+O(q^{10}) $ 42 * q + 3 * q^3 - 6 * q^4 - 3 * q^6 - 18 * q^8 + 9 * q^9	$ 42 q + 3 q^{3} - 6 q^{4} - 3 q^{6} - 18 q^{8} + 9 q^{9} - 24 q^{12} + 27 q^{13} + 12 q^{14} + 18 q^{16} + 36 q^{18} + 12 q^{19} + 15 q^{21} - 12 q^{22} + 12 q^{23} + 33 q^{24} - 18 q^{26} - 30 q^{27} + 42 q^{28} - 3 q^{29} - 6 q^{31} + 60 q^{32} - 36 q^{33} - 42 q^{34} - 63 q^{36} + 48 q^{37} + 24 q^{38} - 60 q^{39} - 9 q^{41} + 165 q^{42} - 33 q^{44} - 15 q^{46} + 9 q^{47} - 84 q^{48} - 33 q^{49} - 36 q^{51} - 105 q^{52} - 6 q^{53} - 18 q^{54} + 36 q^{56} - 21 q^{57} - 24 q^{58} - 45 q^{59} + 9 q^{61} - 57 q^{62} - 51 q^{63} - 48 q^{66} - 27 q^{67} - 78 q^{68} + 15 q^{69} - 6 q^{71} + 24 q^{72} - 81 q^{73} + 72 q^{74} - 114 q^{76} + 18 q^{77} - 66 q^{78} + 27 q^{79} - 21 q^{81} - 9 q^{82} + 36 q^{84} - 60 q^{86} - 6 q^{87} - 60 q^{88} + 84 q^{89} - 33 q^{91} + 18 q^{92} - 21 q^{93} - 36 q^{94} + 222 q^{96} - 51 q^{97} + 180 q^{98} - 18 q^{99}+O(q^{100}) $ 42 * q + 3 * q^3 - 6 * q^4 - 3 * q^6 - 18 * q^8 + 9 * q^9 - 24 * q^12 + 27 * q^13 + 12 * q^14 + 18 * q^16 + 36 * q^18 + 12 * q^19 + 15 * q^21 - 12 * q^22 + 12 * q^23 + 33 * q^24 - 18 * q^26 - 30 * q^27 + 42 * q^28 - 3 * q^29 - 6 * q^31 + 60 * q^32 - 36 * q^33 - 42 * q^34 - 63 * q^36 + 48 * q^37 + 24 * q^38 - 60 * q^39 - 9 * q^41 + 165 * q^42 - 33 * q^44 - 15 * q^46 + 9 * q^47 - 84 * q^48 - 33 * q^49 - 36 * q^51 - 105 * q^52 - 6 * q^53 - 18 * q^54 + 36 * q^56 - 21 * q^57 - 24 * q^58 - 45 * q^59 + 9 * q^61 - 57 * q^62 - 51 * q^63 - 48 * q^66 - 27 * q^67 - 78 * q^68 + 15 * q^69 - 6 * q^71 + 24 * q^72 - 81 * q^73 + 72 * q^74 - 114 * q^76 + 18 * q^77 - 66 * q^78 + 27 * q^79 - 21 * q^81 - 9 * q^82 + 36 * q^84 - 60 * q^86 - 6 * q^87 - 60 * q^88 + 84 * q^89 - 33 * q^91 + 18 * q^92 - 21 * q^93 - 36 * q^94 + 222 * q^96 - 51 * q^97 + 180 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	2.17674	−	0.792270i	1.53919	−	0.560219i	0.573339	−	0.819318i	$-0.305648\pi$
$2$	2.17674	−	0.792270i	1.53919	−	0.560219i	0.965851	+	0.259099i	$0.0834256\pi$
$3$	0.363030	−	2.05885i	0.209595	−	1.18868i	−0.680447	−	0.732797i	$-0.738214\pi$
$3$	0.363030	−	2.05885i	0.209595	−	1.18868i	0.890042	−	0.455878i	$-0.150675\pi$
$4$	2.57843	−	2.16356i	1.28921	−	1.08178i
$5$		0			0
$5$		0			0
$6$	−0.840938	−	4.76919i	−0.343311	−	1.94702i
$7$	1.49485	+	2.58916i	0.565002	+	0.978611i	0.997050	+	0.0767608i	$0.0244578\pi$
$7$	1.49485	+	2.58916i	0.565002	+	0.978611i	−0.432048	+	0.901851i	$0.642209\pi$
$8$	1.58201	−	2.74013i	0.559326	−	0.968782i
$9$	−1.28798	−	0.468785i	−0.429325	−	0.156262i
$10$		0			0
$11$	1.03220	−	1.78782i	0.311219	−	0.539047i	−0.667408	−	0.744692i	$-0.732596\pi$
$11$	1.03220	−	1.78782i	0.311219	−	0.539047i	0.978626	+	0.205646i	$0.0659295\pi$
$12$	−3.51839	−	6.09402i	−1.01567	−	1.75919i
$13$	−0.487552	−	2.76505i	−0.135223	−	0.766886i	−0.974704	−	0.223498i	$-0.928252\pi$
$13$	−0.487552	−	2.76505i	−0.135223	−	0.766886i	0.839482	−	0.543388i	$-0.182859\pi$
$14$	5.30523	+	4.45161i	1.41788	+	1.18974i
$15$		0			0
$16$	0.103752	−	0.588408i	0.0259380	−	0.147102i
$17$	−7.66330	+	2.78921i	−1.85862	+	0.676484i	−0.878615	+	0.477531i	$0.841532\pi$
$17$	−7.66330	+	2.78921i	−1.85862	+	0.676484i	−0.980009	+	0.198953i	$0.936246\pi$
$18$	−3.17500			−0.748354
$19$	−2.39057	+	3.64488i	−0.548434	+	0.836194i
$19$	−2.39057	+	3.64488i	−0.548434	+	0.836194i
$20$		0			0
$21$	5.87336	−	2.13773i	1.28167	−	0.466491i
$22$	0.830393	−	4.70939i	0.177040	−	1.00405i
$23$	−3.38493	+	2.84029i	−0.705806	+	0.592241i	−0.923419	−	0.383794i	$-0.874617\pi$
$23$	−3.38493	+	2.84029i	−0.705806	+	0.592241i	0.217613	+	0.976035i	$0.430173\pi$
$24$	−5.06718	−	4.25187i	−1.03433	−	0.867910i
$25$		0			0
$26$	−3.25194	−	5.63252i	−0.637758	−	1.10463i
$27$	1.70318	−	2.94999i	0.327777	−	0.567727i
$28$	9.45618	+	3.44177i	1.78705	+	0.650433i
$29$	7.67059	+	2.79186i	1.42439	+	0.518436i	0.935319	−	0.353806i	$-0.115113\pi$
$29$	7.67059	+	2.79186i	1.42439	+	0.518436i	0.489073	+	0.872243i	$0.337335\pi$
$30$		0			0
$31$	−2.50483	−	4.33850i	−0.449881	−	0.779217i	0.548496	−	0.836153i	$-0.315200\pi$
$31$	−2.50483	−	4.33850i	−0.449881	−	0.779217i	−0.998378	+	0.0569355i	$0.981867\pi$
$32$	0.858520	+	4.86891i	0.151766	+	0.860709i
$33$	−3.30612	−	2.77416i	−0.575521	−	0.482920i
$34$	−14.4712	+	12.1428i	−2.48180	+	2.08247i
$35$		0			0
$36$	−4.33520	+	1.57788i	−0.722533	+	0.262981i
$37$	1.47168			0.241943			0.120971	−	0.992656i	$-0.461399\pi$
$37$	1.47168			0.241943			0.120971	+	0.992656i	$0.461399\pi$
$38$	−2.31593	+	9.82795i	−0.375693	+	1.59430i
$39$	−5.86980			−0.939920
$40$		0			0
$41$	−1.17665	+	6.67313i	−0.183762	+	1.04217i	0.743773	+	0.668432i	$0.233034\pi$
$41$	−1.17665	+	6.67313i	−0.183762	+	1.04217i	−0.927535	+	0.373735i	$0.878077\pi$
$42$	11.0911	−	9.30657i	1.71140	−	1.43604i
$43$	−5.25688	−	4.41104i	−0.801666	−	0.672678i	0.146937	−	0.989146i	$-0.453059\pi$
$43$	−5.25688	−	4.41104i	−0.801666	−	0.672678i	−0.948603	+	0.316468i	$0.897503\pi$
$44$	−1.20660	−	6.84297i	−0.181902	−	1.03162i
$45$		0			0
$46$	−5.11784	+	8.86435i	−0.754584	+	1.30698i
$47$	−0.751233	−	0.273426i	−0.109579	−	0.0398833i	0.286649	−	0.958036i	$-0.407459\pi$
$47$	−0.751233	−	0.273426i	−0.109579	−	0.0398833i	−0.396228	+	0.918152i	$0.629681\pi$
$48$	−1.17378	−	0.427219i	−0.169420	−	0.0616638i
$49$	−0.969174	+	1.67866i	−0.138453	+	0.239808i
$50$		0			0
$51$	2.96055	+	16.7901i	0.414560	+	2.35109i
$52$	−7.23946	−	6.07463i	−1.00393	−	0.842399i
$53$	7.46661	−	6.26523i	1.02562	−	0.860595i	0.0352942	−	0.999377i	$-0.488763\pi$
$53$	7.46661	−	6.26523i	1.02562	−	0.860595i	0.990323	+	0.138782i	$0.0443187\pi$
$54$	1.37019	−	7.77076i	0.186460	−	1.05747i
$55$		0			0
$56$	9.45952			1.26408
$57$	6.63640	+	6.24502i	0.879013	+	0.827173i
$58$	18.9088			2.48285
$59$	8.51236	−	3.09825i	1.10821	−	0.403357i	0.277876	−	0.960617i	$-0.410369\pi$
$59$	8.51236	−	3.09825i	1.10821	−	0.403357i	0.830338	+	0.557260i	$0.188147\pi$
$60$		0			0
$61$	−1.57051	+	1.31782i	−0.201084	+	0.168729i	−0.737769	−	0.675053i	$-0.764121\pi$
$61$	−1.57051	+	1.31782i	−0.201084	+	0.168729i	0.536685	+	0.843782i	$0.319676\pi$
$62$	−8.88964	−	7.45929i	−1.12899	−	0.947331i
$63$	−0.711575	−	4.03554i	−0.0896501	−	0.508431i
$64$	6.32375	+	10.9531i	0.790469	+	1.36913i
$65$		0			0
$66$	−9.39445	−	3.41930i	−1.15638	−	0.420887i
$67$	−1.52085	−	0.553545i	−0.185802	−	0.0676263i	0.247444	−	0.968902i	$-0.420409\pi$
$67$	−1.52085	−	0.553545i	−0.185802	−	0.0676263i	−0.433246	+	0.901276i	$0.642632\pi$
$68$	−13.7247	+	23.7718i	−1.66436	+	2.88275i
$69$	4.61889	+	8.00015i	0.556049	+	0.963105i
$70$		0			0
$71$	4.14723	+	3.47994i	0.492185	+	0.412992i	0.854809	−	0.518943i	$-0.173674\pi$
$71$	4.14723	+	3.47994i	0.492185	+	0.412992i	−0.362623	+	0.931936i	$0.618119\pi$
$72$	−3.32213	+	2.78760i	−0.391517	+	0.328521i
$73$	2.54821	−	14.4516i	0.298246	−	1.69144i	−0.355464	−	0.934690i	$-0.615677\pi$
$73$	2.54821	−	14.4516i	0.298246	−	1.69144i	0.653709	−	0.756746i	$-0.273212\pi$
$74$	3.20347	−	1.16597i	0.372396	−	0.135541i
$75$		0			0
$76$	1.72200	+	14.5702i	0.197527	+	1.67132i
$77$	6.17193			0.703356
$78$	−12.7770	+	4.65046i	−1.44672	+	0.526561i
$79$	2.16322	−	12.2682i	0.243381	−	1.38028i	−0.580841	−	0.814017i	$-0.697276\pi$
$79$	2.16322	−	12.2682i	0.243381	−	1.38028i	0.824222	−	0.566266i	$-0.191613\pi$
$80$		0			0
$81$	−8.60518	−	7.22060i	−0.956131	−	0.802289i
$82$	2.72565	+	15.4579i	0.300997	+	1.70704i
$83$	3.85430	+	6.67585i	0.423065	+	0.732769i	0.996237	−	0.0866652i	$-0.0276210\pi$
$83$	3.85430	+	6.67585i	0.423065	+	0.732769i	−0.573173	+	0.819434i	$0.694288\pi$
$84$	10.5189	−	18.2193i	1.14771	−	1.98789i
$85$		0			0
$86$	−14.9376	−	5.43684i	−1.61076	−	0.586270i
$87$	8.53267	−	14.7790i	0.914798	−	1.58448i
$88$	−3.26590	−	5.65670i	−0.348146	−	0.603006i
$89$	−0.0972439	−	0.551497i	−0.0103078	−	0.0584586i	0.979220	−	0.202801i	$-0.0650044\pi$
$89$	−0.0972439	−	0.551497i	−0.0103078	−	0.0584586i	−0.989528	+	0.144342i	$0.953893\pi$
$90$		0			0
$91$	6.43033	−	5.39569i	0.674082	−	0.565622i
$92$	−2.58266	+	14.6470i	−0.269261	+	1.52705i
$93$	−9.84163	+	3.58206i	−1.02053	+	0.371442i
$94$	−1.85187			−0.191006
$95$		0			0
$96$	10.3360			1.05491
$97$	−14.0997	+	5.13189i	−1.43161	+	0.521064i	−0.937393	−	0.348273i	$-0.886768\pi$
$97$	−14.0997	+	5.13189i	−1.43161	+	0.521064i	−0.494219	+	0.869337i	$0.664546\pi$
$98$	−0.779693	+	4.42186i	−0.0787608	+	0.446675i
$99$	−2.16754	+	1.81879i	−0.217846	+	0.182795i
$100$		0			0
$101$	1.12312	+	6.36955i	0.111755	+	0.633794i	0.988306	+	0.152485i	$0.0487274\pi$
$101$	1.12312	+	6.36955i	0.111755	+	0.633794i	−0.876551	+	0.481309i	$0.840161\pi$
$102$	19.7467	+	34.2022i	1.95521	+	3.38653i
$103$	−2.53495	+	4.39067i	−0.249776	+	0.432625i	−0.963464	−	0.267839i	$-0.913690\pi$
$103$	−2.53495	+	4.39067i	−0.249776	+	0.432625i	0.713687	+	0.700464i	$0.247024\pi$
$104$	−8.34790	−	3.03839i	−0.818579	−	0.297938i
$105$		0			0
$106$	11.2891	−	19.5534i	1.09650	−	1.89919i
$107$	−4.13664	−	7.16487i	−0.399904	−	0.692654i	0.593810	−	0.804606i	$-0.297623\pi$
$107$	−4.13664	−	7.16487i	−0.399904	−	0.692654i	−0.993714	+	0.111952i	$0.964290\pi$
$108$	−1.99096	−	11.2913i	−0.191580	−	1.08650i
$109$	−3.71736	−	3.11923i	−0.356058	−	0.298768i	0.447159	−	0.894454i	$-0.352436\pi$
$109$	−3.71736	−	3.11923i	−0.356058	−	0.298768i	−0.803217	+	0.595686i	$0.796880\pi$
$110$		0			0
$111$	0.534265	−	3.02997i	0.0507102	−	0.287592i
$112$	1.67858	−	0.610952i	0.158611	−	0.0577295i
$113$	−10.4314			−0.981300			−0.490650	−	0.871357i	$-0.663241\pi$
$113$	−10.4314			−0.981300			−0.490650	+	0.871357i	$0.663241\pi$
$114$	19.3935	+	8.33597i	1.81637	+	0.780736i
$115$		0			0
$116$	25.8184	−	9.39714i	2.39718	−	0.872502i
$117$	−0.668257	+	3.78987i	−0.0617803	+	0.350374i
$118$	16.0746	−	13.4882i	1.47978	−	1.24169i
$119$	−18.6772	−	15.6721i	−1.71214	−	1.43666i
$120$		0			0
$121$	3.36914	+	5.83553i	0.306286	+	0.530503i
$122$	−2.37454	+	4.11282i	−0.214980	+	0.372357i
$123$	13.3118	+	4.84509i	1.20028	+	0.436867i
$124$	−15.8451	−	5.76716i	−1.42294	−	0.517906i
$125$		0			0
$126$	−4.74616	−	8.22058i	−0.422821	−	0.732348i
$127$	1.82152	+	10.3304i	0.161634	+	0.916671i	0.952468	+	0.304640i	$0.0985361\pi$
$127$	1.82152	+	10.3304i	0.161634	+	0.916671i	−0.790834	+	0.612031i	$0.790353\pi$
$128$	14.8683	+	12.4760i	1.31418	+	1.10273i
$129$	−10.9901	+	9.22176i	−0.967621	+	0.811930i
$130$		0			0
$131$	−0.656429	+	0.238921i	−0.0573525	+	0.0208746i	−0.370537	−	0.928818i	$-0.620826\pi$
$131$	−0.656429	+	0.238921i	−0.0573525	+	0.0208746i	0.313185	+	0.949692i	$0.398604\pi$
$132$	−14.5267			−1.26438
$133$	−13.0107	−	0.741007i	−1.12817	−	0.0642534i
$134$	−3.74906			−0.323870
$135$		0			0
$136$	−4.48065	+	25.4110i	−0.384212	+	2.17898i
$137$	−9.56429	+	8.02539i	−0.817132	+	0.685655i	−0.952299	−	0.305168i	$-0.901288\pi$
$137$	−9.56429	+	8.02539i	−0.817132	+	0.685655i	0.135166	+	0.990823i	$0.456843\pi$
$138$	16.3924	+	13.7549i	1.39541	+	1.17089i
$139$	1.85958	+	10.5462i	0.157728	+	0.894519i	0.956249	+	0.292553i	$0.0945048\pi$
$139$	1.85958	+	10.5462i	0.157728	+	0.894519i	−0.798521	+	0.601966i	$0.794384\pi$
$140$		0			0
$141$	−0.835663	+	1.44741i	−0.0703755	+	0.121894i
$142$	11.7845	+	4.28920i	0.988933	+	0.359942i
$143$	−5.44664	−	1.98242i	−0.455471	−	0.165778i
$144$	−0.409467	+	0.709218i	−0.0341222	+	0.0591015i
$145$		0			0
$146$	−5.90279	−	33.4764i	−0.488518	−	2.77052i
$147$	3.10426	+	2.60478i	0.256035	+	0.214839i
$148$	3.79463	−	3.18407i	0.311916	−	0.261729i
$149$	−0.505273	+	2.86555i	−0.0413936	+	0.234755i	−0.998485	−	0.0550330i	$-0.982474\pi$
$149$	−0.505273	+	2.86555i	−0.0413936	+	0.234755i	0.957091	+	0.289788i	$0.0935847\pi$
$150$		0			0
$151$	−4.19725			−0.341568			−0.170784	−	0.985309i	$-0.554630\pi$
$151$	−4.19725			−0.341568			−0.170784	+	0.985309i	$0.554630\pi$
$152$	6.20553	+	12.3167i	0.503335	+	0.999018i
$153$	11.1777			0.903663
$154$	13.4347	−	4.88983i	1.08260	−	0.394034i
$155$		0			0
$156$	−15.1349	+	12.6997i	−1.21176	+	1.01679i
$157$	−15.4648	−	12.9765i	−1.23422	−	1.03564i	−0.997953	−	0.0639475i	$-0.979631\pi$
$157$	−15.4648	−	12.9765i	−1.23422	−	1.03564i	−0.236269	−	0.971688i	$-0.575925\pi$
$158$	−5.01097	−	28.4186i	−0.398651	−	2.26086i
$159$	−10.1885	−	17.6471i	−0.808003	−	1.39950i
$160$		0			0
$161$	−12.4139	−	4.51830i	−0.978355	−	0.356092i
$162$	−24.4519	−	8.89977i	−1.92112	−	0.699232i
$163$	2.79226	−	4.83634i	0.218707	−	0.378812i	−0.735706	−	0.677301i	$-0.763149\pi$
$163$	2.79226	−	4.83634i	0.218707	−	0.378812i	0.954413	+	0.298490i	$0.0964828\pi$
$164$	11.4038	+	19.7519i	0.890486	+	1.54237i
$165$		0			0
$166$	13.6789	+	11.4780i	1.06169	+	0.890862i
$167$	15.8632	−	13.3108i	1.22753	−	1.03002i	0.229132	−	0.973395i	$-0.426411\pi$
$167$	15.8632	−	13.3108i	1.22753	−	1.03002i	0.998396	−	0.0566231i	$-0.0180333\pi$
$168$	3.43409	−	19.4757i	0.264946	−	1.50258i
$169$	4.80823	−	1.75005i	0.369864	−	0.134619i
$170$		0			0
$171$	4.78766	−	3.57386i	0.366122	−	0.273300i
$172$	−23.0980			−1.76121
$173$	−19.9068	+	7.24548i	−1.51348	+	0.550863i	−0.959511	−	0.281671i	$-0.909111\pi$
$173$	−19.9068	+	7.24548i	−1.51348	+	0.550863i	−0.553973	+	0.832534i	$0.686889\pi$
$174$	6.86446	−	38.9303i	0.520394	−	2.95130i
$175$		0			0
$176$	−0.944871	−	0.792841i	−0.0712224	−	0.0597627i
$177$	−3.28857	−	18.6504i	−0.247184	−	1.40185i
$178$	−0.648610	−	1.12342i	−0.0486153	−	0.0842042i
$179$	4.21641	−	7.30304i	0.315149	−	0.545855i	−0.664320	−	0.747448i	$-0.731279\pi$
$179$	4.21641	−	7.30304i	0.315149	−	0.545855i	0.979469	+	0.201594i	$0.0646120\pi$
$180$		0			0
$181$	−12.4976	−	4.54876i	−0.928940	−	0.338106i	−0.167150	−	0.985931i	$-0.553457\pi$
$181$	−12.4976	−	4.54876i	−0.928940	−	0.338106i	−0.761789	+	0.647825i	$0.775679\pi$
$182$	9.72234	−	16.8396i	0.720668	−	1.24823i
$183$	2.14304	+	3.71185i	0.158418	+	0.274388i
$184$	2.42776	+	13.7685i	0.178977	+	1.01503i
$185$		0			0
$186$	−18.5847	+	15.5944i	−1.36270	+	1.14344i
$187$	−2.92343	+	16.5796i	−0.213782	+	1.21242i
$188$	−2.52858	+	0.920326i	−0.184415	+	0.0671217i
$189$	10.1840			0.740778
$190$		0			0
$191$	17.8925			1.29465			0.647327	−	0.762213i	$-0.275887\pi$
$191$	17.8925			1.29465			0.647327	+	0.762213i	$0.275887\pi$
$192$	24.8464	−	9.04333i	1.79313	−	0.652646i
$193$	−0.496073	+	2.81337i	−0.0357081	+	0.202511i	−0.997443	−	0.0714726i	$-0.977230\pi$
$193$	−0.496073	+	2.81337i	−0.0357081	+	0.202511i	0.961734	+	0.273983i	$0.0883413\pi$
$194$	−26.6257	+	22.3416i	−1.91161	+	1.60403i
$195$		0			0
$196$	1.13293	+	6.42517i	0.0809236	+	0.458941i
$197$	−2.99878	−	5.19405i	−0.213654	−	0.370060i	0.739201	−	0.673485i	$-0.235203\pi$
$197$	−2.99878	−	5.19405i	−0.213654	−	0.370060i	−0.952855	+	0.303424i	$0.901870\pi$
$198$	−3.27722	+	5.67631i	−0.232902	+	0.403398i
$199$	7.68687	+	2.79779i	0.544908	+	0.198330i	0.599783	−	0.800163i	$-0.295254\pi$
$199$	7.68687	+	2.79779i	0.544908	+	0.198330i	−0.0548748	+	0.998493i	$0.517476\pi$
$200$		0			0
$201$	−1.69178	+	2.93025i	−0.119329	+	0.206684i
$202$	7.49115	+	12.9750i	0.527075	+	0.912921i
$203$	4.23781	+	24.0338i	0.297436	+	1.68684i
$204$	43.9600	+	36.8868i	3.07782	+	2.58259i
$205$		0			0
$206$	−2.03935	+	11.5657i	−0.142088	+	0.805822i
$207$	5.69119	−	2.07142i	0.395565	−	0.143974i
$208$	−1.67756			−0.116318
$209$	4.04884	+	8.03613i	0.280064	+	0.555871i
$210$		0			0
$211$	−8.79759	+	3.20206i	−0.605651	+	0.220439i	−0.626599	−	0.779342i	$-0.715554\pi$
$211$	−8.79759	+	3.20206i	−0.605651	+	0.220439i	0.0209484	+	0.999781i	$0.493331\pi$
$212$	5.69693	−	32.3089i	0.391267	−	2.21898i
$213$	8.67022	−	7.27518i	0.594074	−	0.498487i
$214$	−14.6809	−	12.3187i	−1.00357	−	0.842092i
$215$		0			0
$216$	−5.38891	−	9.33386i	−0.366669	−	0.635089i
$217$	7.48872	−	12.9708i	0.508367	−	0.880518i
$218$	−10.5630	−	3.84462i	−0.715417	−	0.260390i
$219$	−28.8286	−	10.4928i	−1.94806	−	0.709035i
$220$		0			0
$221$	11.4486	+	19.8295i	0.770114	+	1.33388i
$222$	−1.23759	−	7.01874i	−0.0830618	−	0.471067i
$223$	−3.42461	−	2.87359i	−0.229329	−	0.192430i	0.520882	−	0.853629i	$-0.325603\pi$
$223$	−3.42461	−	2.87359i	−0.229329	−	0.192430i	−0.750210	+	0.661199i	$0.770048\pi$
$224$	−11.3230	+	9.50115i	−0.756552	+	0.634822i
$225$		0			0
$226$	−22.7064	+	8.26445i	−1.51041	+	0.549743i
$227$	14.9692			0.993542			0.496771	−	0.867882i	$-0.334519\pi$
$227$	14.9692			0.993542			0.496771	+	0.867882i	$0.334519\pi$
$228$	30.6230	+	1.74408i	2.02805	+	0.115505i
$229$	−24.7467			−1.63531			−0.817653	−	0.575711i	$-0.804725\pi$
$229$	−24.7467			−1.63531			−0.817653	+	0.575711i	$0.804725\pi$
$230$		0			0
$231$	2.24059	−	12.7070i	0.147420	−	0.836062i
$232$	19.7850	−	16.6016i	1.29895	−	1.08995i
$233$	17.1162	+	14.3622i	1.12132	+	0.940900i	0.998670	−	0.0515494i	$-0.0164160\pi$
$233$	17.1162	+	14.3622i	1.12132	+	0.940900i	0.122651	+	0.992450i	$0.460860\pi$
$234$	1.54798	+	8.77901i	0.101194	+	0.573902i
$235$		0			0
$236$	15.2453	−	26.4056i	0.992383	−	1.71886i
$237$	−24.4731	−	8.90747i	−1.58970	−	0.578602i
$238$	−53.0721	−	19.3167i	−3.44015	−	1.25211i
$239$	5.58991	−	9.68201i	0.361581	−	0.626277i	−0.626640	−	0.779309i	$-0.715570\pi$
$239$	5.58991	−	9.68201i	0.361581	−	0.626277i	0.988221	+	0.153032i	$0.0489036\pi$
$240$		0			0
$241$	0.0793237	+	0.449867i	0.00510969	+	0.0289785i	0.987256	−	0.159140i	$-0.0508722\pi$
$241$	0.0793237	+	0.449867i	0.00510969	+	0.0289785i	−0.982146	+	0.188119i	$0.939761\pi$
$242$	11.9571	+	10.0332i	0.768630	+	0.644957i
$243$	−10.1618	+	8.52674i	−0.651878	+	0.546991i
$244$	−1.19828	+	6.79580i	−0.0767122	+	0.435056i
$245$		0			0
$246$	32.8149			2.09220
$247$	11.2438	+	4.83297i	0.715426	+	0.307514i
$248$	−15.8507			−1.00652
$249$	15.1438	−	5.51188i	0.959697	−	0.349301i
$250$		0			0
$251$	14.6420	−	12.2861i	0.924195	−	0.775492i	−0.0505708	−	0.998720i	$-0.516104\pi$
$251$	14.6420	−	12.2861i	0.924195	−	0.775492i	0.974766	+	0.223229i	$0.0716596\pi$
$252$	−10.5659	−	8.86583i	−0.665588	−	0.558495i
$253$	1.58401	+	8.98336i	0.0995857	+	0.564779i
$254$	12.1494	+	21.0434i	0.762321	+	1.32038i
$255$		0			0
$256$	18.4792	+	6.72588i	1.15495	+	0.420368i
$257$	4.89098	+	1.78017i	0.305091	+	0.111044i	0.490029	−	0.871706i	$-0.336986\pi$
$257$	4.89098	+	1.78017i	0.305091	+	0.111044i	−0.184938	+	0.982750i	$0.559208\pi$
$258$	−16.6164	+	28.7805i	−1.03449	+	1.79179i
$259$	2.19995	+	3.81042i	0.136698	+	0.236768i
$260$		0			0
$261$	−8.57075	−	7.19171i	−0.530516	−	0.445156i
$262$	−1.23959	+	1.04014i	−0.0765820	+	0.0642599i
$263$	0.473937	−	2.68783i	0.0292242	−	0.165739i	−0.966703	−	0.255902i	$-0.917628\pi$
$263$	0.473937	−	2.68783i	0.0292242	−	0.165739i	0.995927	+	0.0901630i	$0.0287388\pi$
$264$	−12.8319	+	4.67042i	−0.789748	+	0.287445i
$265$		0			0
$266$	−28.9081	+	8.69504i	−1.77247	+	0.533127i
$267$	−1.17075			−0.0716488
$268$	−5.11904	+	1.86318i	−0.312695	+	0.113812i
$269$	−1.04039	+	5.90035i	−0.0634337	+	0.359750i	0.936524	+	0.350602i	$0.114023\pi$
$269$	−1.04039	+	5.90035i	−0.0634337	+	0.359750i	−0.999958	+	0.00914814i	$0.997088\pi$
$270$		0			0
$271$	−16.8435	−	14.1334i	−1.02317	−	0.858541i	−0.0331468	−	0.999450i	$-0.510553\pi$
$271$	−16.8435	−	14.1334i	−1.02317	−	0.858541i	−0.990022	+	0.140910i	$0.954997\pi$
$272$	0.846111	+	4.79853i	0.0513030	+	0.290954i
$273$	−8.77449	−	15.1979i	−0.531056	−	0.919817i
$274$	−14.4607	+	25.0467i	−0.873604	+	1.51313i
$275$		0			0
$276$	29.2183	+	10.6346i	1.75873	+	0.640127i
$277$	1.12518	−	1.94886i	0.0676053	−	0.117096i	−0.830241	−	0.557404i	$-0.811797\pi$
$277$	1.12518	−	1.94886i	0.0676053	−	0.117096i	0.897847	+	0.440308i	$0.145131\pi$
$278$	12.4033	+	21.4831i	0.743900	+	1.28847i
$279$	1.19234	+	6.76211i	0.0713837	+	0.404837i
$280$		0			0
$281$	−1.98061	+	1.66193i	−0.118154	+	0.0991426i	−0.699950	−	0.714192i	$-0.746794\pi$
$281$	−1.98061	+	1.66193i	−0.118154	+	0.0991426i	0.581797	+	0.813334i	$0.302350\pi$
$282$	−0.672284	+	3.81271i	−0.0400339	+	0.227044i
$283$	22.6099	−	8.22934i	1.34402	−	0.489184i	0.432944	−	0.901421i	$-0.357475\pi$
$283$	22.6099	−	8.22934i	1.34402	−	0.489184i	0.911077	+	0.412237i	$0.135252\pi$
$284$	18.2224			1.08130
$285$		0			0
$286$	−13.4265			−0.793928
$287$	−19.0367	+	6.92880i	−1.12370	+	0.408994i
$288$	1.17672	−	6.67350i	0.0693388	−	0.393240i
$289$	37.9237	−	31.8218i	2.23081	−	1.87187i
$290$		0			0
$291$	5.44713	+	30.8922i	0.319317	+	1.81093i
$292$	−24.6966	−	42.7757i	−1.44526	−	2.50326i
$293$	−7.51114	+	13.0097i	−0.438805	+	0.760033i	−0.997598	−	0.0692744i	$-0.977932\pi$
$293$	−7.51114	+	13.0097i	−0.438805	+	0.760033i	0.558792	+	0.829308i	$0.311265\pi$
$294$	8.82087	+	3.21053i	0.514443	+	0.187242i
$295$		0			0
$296$	2.32822	−	4.03260i	0.135325	−	0.234390i
$297$	−3.51603	−	6.08994i	−0.204021	−	0.353374i
$298$	1.17044	+	6.63787i	0.0678015	+	0.384521i
$299$	9.50386	+	7.97469i	0.549622	+	0.461188i
$300$		0			0
$301$	3.56265	−	20.2048i	0.205348	−	1.16458i
$302$	−9.13634	+	3.32536i	−0.525737	+	0.191353i
$303$	13.5216			0.776798
$304$	1.89665	+	1.78479i	0.108780	+	0.102365i
$305$		0			0
$306$	24.3310	−	8.85575i	1.39091	−	0.506249i
$307$	5.28604	−	29.9786i	0.301690	−	1.71097i	−0.336998	−	0.941505i	$-0.609412\pi$
$307$	5.28604	−	29.9786i	0.301690	−	1.71097i	0.638689	−	0.769465i	$-0.279477\pi$
$308$	15.9139	−	13.3533i	0.906777	−	0.760876i
$309$	8.11944	+	6.81302i	0.461899	+	0.387579i
$310$		0			0
$311$	−10.9968	−	19.0470i	−0.623570	−	1.08005i	−0.988816	−	0.149143i	$-0.952348\pi$
$311$	−10.9968	−	19.0470i	−0.623570	−	1.08005i	0.365246	−	0.930911i	$-0.380985\pi$
$312$	−9.28610	+	16.0840i	−0.525722	+	0.910578i
$313$	4.98087	+	1.81289i	0.281535	+	0.102470i	0.478928	−	0.877854i	$-0.341025\pi$
$313$	4.98087	+	1.81289i	0.281535	+	0.102470i	−0.197393	+	0.980324i	$0.563248\pi$
$314$	−43.9437	−	15.9942i	−2.47988	−	0.902604i
$315$		0			0
$316$	−20.9653	−	36.3130i	−1.17939	−	2.04277i
$317$	4.80363	+	27.2428i	0.269799	+	1.53011i	0.755013	+	0.655710i	$0.227631\pi$
$317$	4.80363	+	27.2428i	0.269799	+	1.53011i	−0.485214	+	0.874396i	$0.661258\pi$
$318$	−36.1590	−	30.3410i	−2.02770	−	1.70144i
$319$	12.9089	−	10.8318i	0.722759	−	0.606467i
$320$		0			0
$321$	−16.2531	+	5.91564i	−0.907159	+	0.330179i
$322$	−30.6017			−1.70536
$323$	8.15330	−	34.5997i	0.453662	−	1.92518i
$324$	−37.8101			−2.10056
$325$		0			0
$326$	2.24635	−	12.7397i	0.124414	−	0.705587i
$327$	−7.77153	+	6.52109i	−0.429767	+	0.360617i
$328$	16.4237	+	13.7812i	0.906850	+	0.760937i
$329$	−0.415038	−	2.35380i	−0.0228818	−	0.129769i
$330$		0			0
$331$	4.79147	−	8.29907i	0.263363	−	0.456158i	−0.703771	−	0.710427i	$-0.748502\pi$
$331$	4.79147	−	8.29907i	0.263363	−	0.456158i	0.967133	+	0.254269i	$0.0818350\pi$
$332$	24.3816	+	8.87419i	1.33812	+	0.487034i
$333$	−1.89549	−	0.689902i	−0.103872	−	0.0378064i
$334$	23.9843	−	41.5420i	1.31236	−	2.27308i
$335$		0			0
$336$	−0.648482	−	3.67772i	−0.0353776	−	0.200636i
$337$	19.7132	+	16.5413i	1.07384	+	0.901062i	0.995395	−	0.0958557i	$-0.0305587\pi$
$337$	19.7132	+	16.5413i	1.07384	+	0.901062i	0.0784491	+	0.996918i	$0.475003\pi$
$338$	9.07977	−	7.61883i	0.493874	−	0.414410i
$339$	−3.78690	+	21.4766i	−0.205676	+	1.16645i
$340$		0			0
$341$	−10.3419			−0.560046
$342$	7.59005	−	11.5725i	0.410423	−	0.625769i
$343$	15.1329			0.817097
$344$	−20.4033	+	7.42619i	−1.10007	+	0.400393i
$345$		0			0
$346$	−37.5916	+	31.5431i	−2.02094	+	1.69577i
$347$	18.1341	+	15.2163i	0.973490	+	0.816855i	0.983094	−	0.183099i	$-0.0586129\pi$
$347$	18.1341	+	15.2163i	0.973490	+	0.816855i	−0.00960483	+	0.999954i	$0.503057\pi$
$348$	−9.97439	−	56.5676i	−0.534684	−	3.03234i
$349$	1.52143	+	2.63519i	0.0814401	+	0.141058i	0.903869	−	0.427810i	$-0.140715\pi$
$349$	1.52143	+	2.63519i	0.0814401	+	0.141058i	−0.822429	+	0.568868i	$0.807381\pi$
$350$		0			0
$351$	−8.98726	−	3.27109i	−0.479704	−	0.174598i
$352$	9.59087	+	3.49079i	0.511195	+	0.186060i
$353$	3.62900	−	6.28562i	0.193152	−	0.334550i	−0.753141	−	0.657859i	$-0.771462\pi$
$353$	3.62900	−	6.28562i	0.193152	−	0.334550i	0.946293	+	0.323310i	$0.104796\pi$
$354$	−21.9345	−	37.9917i	−1.16581	−	2.01923i
$355$		0			0
$356$	−1.44393	−	1.21160i	−0.0765283	−	0.0642149i
$357$	−39.0468	+	32.7641i	−2.06657	+	1.73406i
$358$	3.39207	−	19.2374i	0.179276	−	1.01673i
$359$	−11.8876	+	4.32672i	−0.627402	+	0.228356i	−0.636100	−	0.771606i	$-0.719454\pi$
$359$	−11.8876	+	4.32672i	−0.627402	+	0.228356i	0.00869809	+	0.999962i	$0.497231\pi$
$360$		0			0
$361$	−7.57035	−	17.4267i	−0.398439	−	0.917195i
$362$	−30.8079			−1.61923
$363$	13.2376	−	4.81808i	0.694791	−	0.252883i
$364$	4.90627	−	27.8248i	0.257158	−	1.45842i
$365$		0			0
$366$	7.60563	+	6.38188i	0.397553	+	0.333586i
$367$	3.04307	+	17.2581i	0.158847	+	0.900865i	0.955184	+	0.296012i	$0.0956569\pi$
$367$	3.04307	+	17.2581i	0.158847	+	0.900865i	−0.796337	+	0.604853i	$0.793232\pi$
$368$	1.32005	+	2.28640i	0.0688126	+	0.119187i
$369$	4.64376	−	8.04323i	0.241745	−	0.418714i
$370$		0			0
$371$	27.3832	+	9.96666i	1.42166	+	0.517443i
$372$	−17.6259	+	30.5290i	−0.913863	+	1.58286i
$373$	3.69923	+	6.40726i	0.191539	+	0.331755i	0.945760	−	0.324865i	$-0.105319\pi$
$373$	3.69923	+	6.40726i	0.191539	+	0.331755i	−0.754221	+	0.656620i	$0.771985\pi$
$374$	6.77195	+	38.4056i	0.350169	+	1.98591i
$375$		0			0
$376$	−1.93768	+	1.62591i	−0.0999285	+	0.0838499i
$377$	3.97982	−	22.5707i	0.204971	−	1.16245i
$378$	22.1680	−	8.06849i	1.14020	−	0.414998i
$379$	−15.6602			−0.804409			−0.402204	−	0.915550i	$-0.631756\pi$
$379$	−15.6602			−0.804409			−0.402204	+	0.915550i	$0.631756\pi$
$380$		0			0
$381$	21.9299			1.12350
$382$	38.9473	−	14.1757i	1.99272	−	0.725290i
$383$	0.570823	−	3.23730i	0.0291677	−	0.165418i	−0.966745	−	0.255744i	$-0.917680\pi$
$383$	0.570823	−	3.23730i	0.0291677	−	0.165418i	0.995912	+	0.0903255i	$0.0287908\pi$
$384$	31.0837	−	26.0823i	1.58623	−	1.33101i
$385$		0			0
$386$	1.14912	+	6.51700i	0.0584888	+	0.331707i
$387$	4.70290	+	8.14567i	0.239062	+	0.414067i
$388$	−25.2521	+	43.7378i	−1.28198	+	2.22045i
$389$	−24.7914	−	9.02334i	−1.25697	−	0.457501i	−0.374222	−	0.927339i	$-0.622090\pi$
$389$	−24.7914	−	9.02334i	−1.25697	−	0.457501i	−0.882753	+	0.469838i	$0.844312\pi$
$390$		0			0
$391$	18.0175	−	31.2073i	0.911186	−	1.57822i
$392$	3.06649	+	5.31132i	0.154881	+	0.268262i
$393$	0.253597	+	1.43822i	0.0127923	+	0.0725487i
$394$	−10.6427	−	8.93026i	−0.536170	−	0.449900i
$395$		0			0
$396$	−1.65381	+	9.37922i	−0.0831071	+	0.471324i
$397$	13.0900	−	4.76437i	0.656969	−	0.239117i	0.00804173	−	0.999968i	$-0.497440\pi$
$397$	13.0900	−	4.76437i	0.656969	−	0.239117i	0.648927	+	0.760851i	$0.275218\pi$
$398$	18.9489			0.949825
$399$	−6.24891	+	26.5181i	−0.312837	+	1.32757i
$400$		0			0
$401$	−16.2268	+	5.90606i	−0.810327	+	0.294935i	−0.713759	−	0.700392i	$-0.753009\pi$
$401$	−16.2268	+	5.90606i	−0.810327	+	0.294935i	−0.0965678	+	0.995326i	$0.530786\pi$
$402$	−1.36102	+	7.71874i	−0.0678817	+	0.384976i
$403$	−10.7749	+	9.04123i	−0.536737	+	0.450376i
$404$	16.6768	+	13.9935i	0.829701	+	0.696202i
$405$		0			0
$406$	28.2659	+	48.9580i	1.40281	+	2.42974i
$407$	1.51906	−	2.63109i	0.0752972	−	0.130419i
$408$	50.6907	+	18.4499i	2.50957	+	0.913407i
$409$	22.4741	+	8.17990i	1.11127	+	0.404470i	0.831460	−	0.555585i	$-0.187506\pi$
$409$	22.4741	+	8.17990i	1.11127	+	0.404470i	0.279812	+	0.960055i	$0.409728\pi$
$410$		0			0
$411$	13.0509	+	22.6048i	0.643754	+	1.11501i
$412$	2.96327	+	16.8056i	0.145990	+	0.827950i
$413$	20.7466	+	17.4085i	1.02087	+	0.856614i
$414$	10.7471	−	9.01791i	0.528193	−	0.443206i
$415$		0			0
$416$	13.0442	−	4.74769i	0.639544	−	0.232775i
$417$	22.3881			1.09635
$418$	15.1801	+	14.2848i	0.742482	+	0.698693i
$419$	10.2371			0.500113			0.250056	−	0.968231i	$-0.419551\pi$
$419$	10.2371			0.500113			0.250056	+	0.968231i	$0.419551\pi$
$420$		0			0
$421$	3.94305	−	22.3622i	0.192173	−	1.08987i	−0.724215	−	0.689574i	$-0.757798\pi$
$421$	3.94305	−	22.3622i	0.192173	−	1.08987i	0.916388	−	0.400291i	$-0.131091\pi$
$422$	−16.6132	+	13.9401i	−0.808717	+	0.678594i
$423$	0.839392	+	0.704334i	0.0408126	+	0.0342459i
$424$	−5.35525	−	30.3711i	−0.260074	−	1.47495i
$425$		0			0
$426$	13.1089	−	22.7053i	0.635130	−	1.10008i
$427$	−5.75973	−	2.09637i	−0.278733	−	0.101450i
$428$	−26.1676	−	9.52424i	−1.26486	−	0.460372i
$429$	−6.05878	+	10.4941i	−0.292521	+	0.506661i
$430$		0			0
$431$	1.46902	+	8.33121i	0.0707601	+	0.401300i	0.999530	+	0.0306444i	$0.00975594\pi$
$431$	1.46902	+	8.33121i	0.0707601	+	0.401300i	−0.928770	+	0.370656i	$0.879133\pi$
$432$	−1.55909	−	1.30823i	−0.0750118	−	0.0629423i
$433$	4.90226	−	4.11349i	0.235588	−	0.197682i	−0.517349	−	0.855775i	$-0.673081\pi$
$433$	4.90226	−	4.11349i	0.235588	−	0.197682i	0.752937	+	0.658093i	$0.228637\pi$
$434$	6.02461	−	34.1673i	0.289191	−	1.64008i
$435$		0			0
$436$	−16.3336			−0.782237
$437$	−2.26062	−	19.1276i	−0.108140	−	0.914996i
$438$	−71.0656			−3.39564
$439$	−8.22096	+	2.99219i	−0.392365	+	0.142809i	−0.530666	−	0.847581i	$-0.678058\pi$
$439$	−8.22096	+	2.99219i	−0.392365	+	0.142809i	0.138301	+	0.990390i	$0.455836\pi$
$440$		0			0
$441$	2.03520	−	1.70774i	0.0969145	−	0.0813209i
$442$	40.6309	+	34.0934i	1.93261	+	1.62166i
$443$	1.31031	+	7.43111i	0.0622545	+	0.353063i	0.999984	+	0.00569583i	$0.00181305\pi$
$443$	1.31031	+	7.43111i	0.0622545	+	0.353063i	−0.937729	+	0.347367i	$0.887076\pi$
$444$	−5.17794	−	8.96846i	−0.245734	−	0.425624i
$445$		0			0
$446$	−9.73114	−	3.54185i	−0.460783	−	0.167711i
$447$	5.71629	+	2.08056i	0.270371	+	0.0984070i
$448$	−18.9062	+	32.7464i	−0.893232	+	1.54712i
$449$	14.2005	+	24.5960i	0.670163	+	1.16076i	0.977858	+	0.209271i	$0.0671092\pi$
$449$	14.2005	+	24.5960i	0.670163	+	1.16076i	−0.307694	+	0.951485i	$0.599557\pi$
$450$		0			0
$451$	10.7158	+	8.99161i	0.504586	+	0.423398i
$452$	−26.8965	+	22.5689i	−1.26511	+	1.06155i
$453$	−1.52373	+	8.64149i	−0.0715910	+	0.406013i
$454$	32.5841	−	11.8597i	1.52925	−	0.556601i
$455$		0			0
$456$	27.6110	−	8.30490i	1.29301	−	0.388912i
$457$	−39.0146			−1.82503			−0.912514	−	0.409046i	$-0.865862\pi$
$457$	−39.0146			−1.82503			−0.912514	+	0.409046i	$0.865862\pi$
$458$	−53.8671	+	19.6060i	−2.51705	+	0.916130i
$459$	−4.82382	+	27.3572i	−0.225157	+	1.27693i
$460$		0			0
$461$	−7.99183	−	6.70594i	−0.372217	−	0.312327i	0.437421	−	0.899257i	$-0.355892\pi$
$461$	−7.99183	−	6.70594i	−0.372217	−	0.312327i	−0.809638	+	0.586930i	$0.800336\pi$
$462$	−5.19021	−	29.4351i	−0.241470	−	1.36945i
$463$	−4.50708	−	7.80650i	−0.209462	−	0.362799i	0.742083	−	0.670308i	$-0.233838\pi$
$463$	−4.50708	−	7.80650i	−0.209462	−	0.362799i	−0.951545	+	0.307509i	$0.900505\pi$
$464$	2.43859	−	4.22377i	0.113209	−	0.196084i
$465$		0			0
$466$	48.6364	+	17.7022i	2.25304	+	0.820038i
$467$	−13.1538	+	22.7831i	−0.608687	+	1.05428i	0.382770	+	0.923844i	$0.374970\pi$
$467$	−13.1538	+	22.7831i	−0.608687	+	1.05428i	−0.991457	+	0.130433i	$0.958363\pi$
$468$	6.47656	+	11.2177i	0.299379	+	0.518540i
$469$	−0.840234	−	4.76521i	−0.0387984	−	0.220037i
$470$		0			0
$471$	−32.3307	+	27.1287i	−1.48972	+	1.25002i
$472$	4.97708	−	28.2264i	0.229089	−	1.29923i
$473$	−13.3123	+	4.84527i	−0.612098	+	0.222786i
$474$	−60.3287			−2.77099
$475$		0			0
$476$	−82.0654			−3.76146
$477$	−12.5539	+	4.56923i	−0.574802	+	0.209211i
$478$	4.49704	−	25.5040i	0.205690	−	1.16652i
$479$	14.6914	−	12.3276i	0.671268	−	0.563260i	−0.242173	−	0.970233i	$-0.577860\pi$
$479$	14.6914	−	12.3276i	0.671268	−	0.563260i	0.913440	+	0.406973i	$0.133416\pi$
$480$		0			0
$481$	−0.717522	−	4.06927i	−0.0327162	−	0.185543i
$482$	0.529083	+	0.916399i	0.0240991	+	0.0417408i
$483$	−13.8091	+	23.9181i	−0.628337	+	1.08831i
$484$	21.3126	+	7.75716i	0.968755	+	0.352598i
$485$		0			0
$486$	−15.3641	+	26.6114i	−0.696930	+	1.20712i
$487$	16.3650	+	28.3451i	0.741571	+	1.28444i	0.951780	+	0.306782i	$0.0992523\pi$
$487$	16.3650	+	28.3451i	0.741571	+	1.28444i	−0.210209	+	0.977657i	$0.567414\pi$
$488$	1.12641	+	6.38821i	0.0509904	+	0.289181i
$489$	−8.94361	−	7.50458i	−0.404444	−	0.339369i
$490$		0			0
$491$	−5.24888	+	29.7679i	−0.236878	+	1.34340i	0.601743	+	0.798690i	$0.294473\pi$
$491$	−5.24888	+	29.7679i	−0.236878	+	1.34340i	−0.838622	+	0.544715i	$0.816638\pi$
$492$	44.8061	−	16.3081i	2.02002	−	0.735226i
$493$	−66.5691			−2.99812
$494$	28.3039	+	1.61200i	1.27345	+	0.0725274i
$495$		0			0
$496$	−2.81269	+	1.02373i	−0.126293	+	0.0459670i
$497$	−2.81062	+	15.9398i	−0.126074	+	0.714999i
$498$	28.5972	−	23.9959i	1.28147	−	1.07528i
$499$	8.66486	+	7.27068i	0.387892	+	0.325480i	0.815791	−	0.578346i	$-0.196302\pi$
$499$	8.66486	+	7.27068i	0.387892	+	0.325480i	−0.427899	+	0.903826i	$0.640746\pi$
$500$		0			0
$501$	−21.6460	−	37.4920i	−0.967073	−	1.67502i
$502$	22.1380	−	38.3441i	0.988066	−	1.71138i
$503$	−31.9629	−	11.6335i	−1.42515	−	0.518714i	−0.489616	−	0.871938i	$-0.662863\pi$
$503$	−31.9629	−	11.6335i	−1.42515	−	0.518714i	−0.935539	+	0.353225i	$0.885085\pi$
$504$	−12.1836	−	4.43448i	−0.542702	−	0.197527i
$505$		0			0
$506$	10.5652	+	18.2995i	0.469681	+	0.813512i
$507$	−1.85756	−	10.5347i	−0.0824970	−	0.467864i
$508$	27.0470	+	22.6951i	1.20002	+	1.00693i
$509$	0.243132	−	0.204012i	0.0107767	−	0.00904269i	−0.637383	−	0.770547i	$-0.719983\pi$
$509$	0.243132	−	0.204012i	0.0107767	−	0.00904269i	0.648160	+	0.761504i	$0.275539\pi$
$510$		0			0
$511$	41.2268	−	15.0053i	1.82377	−	0.663797i
$512$	6.73489			0.297643
$513$	6.68081	+	13.2601i	0.294965	+	0.585446i
$514$	12.0568			0.531801
$515$		0			0
$516$	−8.38528	+	47.5553i	−0.369141	+	2.09351i
$517$	−1.26426	+	1.06084i	−0.0556019	+	0.0466555i
$518$	7.80760	+	6.55136i	0.343046	+	0.287850i
$519$	7.69056	+	43.6153i	0.337578	+	1.91450i
$520$		0			0
$521$	−19.0299	+	32.9608i	−0.833716	+	1.44404i	0.0613560	+	0.998116i	$0.480458\pi$
$521$	−19.0299	+	32.9608i	−0.833716	+	1.44404i	−0.895072	+	0.445922i	$0.852876\pi$
$522$	−24.3541	−	8.86416i	−1.06595	−	0.387974i
$523$	10.6551	+	3.87813i	0.465914	+	0.169579i	0.564300	−	0.825570i	$-0.309146\pi$
$523$	10.6551	+	3.87813i	0.465914	+	0.169579i	−0.0983868	+	0.995148i	$0.531368\pi$
$524$	−1.17564	+	2.03626i	−0.0513579	+	0.0889545i
$525$		0			0
$526$	−1.09785	−	6.22620i	−0.0478684	−	0.271475i
$527$	31.2963	+	26.2607i	1.36329	+	1.14393i
$528$	−1.97535	+	1.65752i	−0.0859663	+	0.0721343i
$529$	−0.603433	+	3.42224i	−0.0262362	+	0.148793i
$530$		0			0
$531$	−12.4161			−0.538814
$532$	−35.1505	+	26.2389i	−1.52397	+	1.13760i
$533$	19.0252			0.824072
$534$	−2.54842	+	0.927550i	−0.110281	+	0.0401390i
$535$		0			0
$536$	−3.92280	+	3.29162i	−0.169439	+	0.142176i
$537$	−13.5051	−	11.3322i	−0.582790	−	0.489019i
$538$	2.41000	+	13.6678i	0.103903	+	0.589261i
$539$	2.00076	+	3.46541i	0.0861786	+	0.149266i
$540$		0			0
$541$	−12.7209	−	4.63002i	−0.546913	−	0.199060i	0.0537612	−	0.998554i	$-0.482879\pi$
$541$	−12.7209	−	4.63002i	−0.546913	−	0.199060i	−0.600675	+	0.799494i	$0.705101\pi$
$542$	−47.8614	−	17.4201i	−2.05582	−	0.748258i
$543$	−13.9022	+	24.0793i	−0.596600	+	1.03334i
$544$	−20.1595	−	34.9173i	−0.864332	−	1.49707i
$545$		0			0
$546$	−31.1406	−	26.1301i	−1.33270	−	1.11826i
$547$	28.4188	−	23.8462i	1.21510	−	1.01959i	0.216033	−	0.976386i	$-0.430688\pi$
$547$	28.4188	−	23.8462i	1.21510	−	1.01959i	0.999066	−	0.0432034i	$-0.0137564\pi$
$548$	−7.29743	+	41.3858i	−0.311731	+	1.76791i
$549$	2.64056	−	0.961084i	0.112696	−	0.0410181i
$550$		0			0
$551$	−28.5131	+	21.2842i	−1.21470	+	0.906739i
$552$	29.2286			1.24405
$553$	34.9981	−	12.7383i	1.48827	−	0.541686i
$554$	0.905195	−	5.13361i	0.0384580	−	0.218106i
$555$		0			0
$556$	27.6122	+	23.1694i	1.17102	+	0.982601i
$557$	0.309403	+	1.75471i	0.0131098	+	0.0743495i	0.990661	−	0.136350i	$-0.0435371\pi$
$557$	0.309403	+	1.75471i	0.0131098	+	0.0743495i	−0.977551	+	0.210699i	$0.932426\pi$
$558$	7.95284	+	13.7747i	0.336671	+	0.583130i
$559$	−9.63374	+	16.6861i	−0.407464	+	0.705748i
$560$		0			0
$561$	33.0735	+	12.0378i	1.39636	+	0.508235i
$562$	−2.99459	+	5.18678i	−0.126319	+	0.218791i
$563$	10.4217	+	18.0509i	0.439222	+	0.760756i	0.997630	−	0.0688114i	$-0.0219207\pi$
$563$	10.4217	+	18.0509i	0.439222	+	0.760756i	−0.558407	+	0.829567i	$0.688587\pi$
$564$	0.976861	+	5.54005i	0.0411333	+	0.233278i
$565$		0			0
$566$	42.6961	−	35.8263i	1.79465	−	1.50589i
$567$	5.83183	−	33.0740i	0.244914	−	1.38898i
$568$	16.0964	−	5.85863i	0.675392	−	0.245822i
$569$	4.50848			0.189005			0.0945026	−	0.995525i	$-0.469874\pi$
$569$	4.50848			0.189005			0.0945026	+	0.995525i	$0.469874\pi$
$570$		0			0
$571$	18.1758			0.760633			0.380316	−	0.924856i	$-0.375815\pi$
$571$	18.1758			0.760633			0.380316	+	0.924856i	$0.375815\pi$
$572$	−18.3329	+	6.67261i	−0.766535	+	0.278996i
$573$	6.49550	−	36.8378i	0.271353	−	1.53892i
$574$	−35.9486	+	30.1644i	−1.50046	+	1.25904i
$575$		0			0
$576$	−3.01021	−	17.0718i	−0.125425	−	0.711323i
$577$	−6.62362	−	11.4724i	−0.275745	−	0.477604i	0.694578	−	0.719417i	$-0.255591\pi$
$577$	−6.62362	−	11.4724i	−0.275745	−	0.477604i	−0.970323	+	0.241813i	$0.922258\pi$
$578$	57.3388	−	99.3137i	2.38498	−	4.13091i
$579$	5.61220	+	2.04267i	0.233235	+	0.0848906i
$580$		0			0
$581$	−11.5232	+	19.9588i	−0.478064	+	0.828031i
$582$	36.3320	+	62.9288i	1.50601	+	2.60848i
$583$	−3.49407	−	19.8159i	−0.144710	−	0.820689i
$584$	−35.5680	−	29.8451i	−1.47182	−	1.23500i
$585$		0			0
$586$	−6.04265	+	34.2696i	−0.249619	+	1.41566i
$587$	−4.31307	+	1.56983i	−0.178020	+	0.0647938i	−0.429492	−	0.903071i	$-0.641307\pi$
$587$	−4.31307	+	1.56983i	−0.178020	+	0.0647938i	0.251473	+	0.967864i	$0.419085\pi$
$588$	13.6397			0.562493
$589$	21.8013	+	1.24166i	0.898307	+	0.0511617i
$590$		0			0
$591$	−11.7824	+	4.28844i	−0.484663	+	0.176403i
$592$	0.152690	−	0.865948i	0.00627552	−	0.0355903i
$593$	1.28453	−	1.07785i	0.0527495	−	0.0442621i	−0.616032	−	0.787721i	$-0.711261\pi$
$593$	1.28453	−	1.07785i	0.0527495	−	0.0442621i	0.668781	+	0.743459i	$0.266816\pi$
$594$	−12.4784	−	10.4706i	−0.511994	−	0.429614i
$595$		0			0
$596$	4.89697	+	8.48179i	0.200588	+	0.347428i
$597$	8.55079	−	14.8104i	0.349960	−	0.606149i
$598$	27.0056	+	9.82922i	1.10434	+	0.401947i
$599$	−22.7361	−	8.27527i	−0.928973	−	0.338118i	−0.167170	−	0.985928i	$-0.553463\pi$
$599$	−22.7361	−	8.27527i	−0.928973	−	0.338118i	−0.761802	+	0.647810i	$0.775685\pi$
$600$		0			0
$601$	10.6313	+	18.4140i	0.433660	+	0.751121i	0.997185	−	0.0749779i	$-0.0238886\pi$
$601$	10.6313	+	18.4140i	0.433660	+	0.751121i	−0.563525	+	0.826099i	$0.690555\pi$
$602$	−8.25266	−	46.8032i	−0.336353	−	1.90755i
$603$	1.69933	+	1.42591i	0.0692021	+	0.0580674i
$604$	−10.8223	+	9.08100i	−0.440354	+	0.369501i
$605$		0			0
$606$	29.4331	−	10.7128i	1.19564	−	0.435177i
$607$	36.9992			1.50175			0.750876	−	0.660443i	$-0.229631\pi$
$607$	36.9992			1.50175			0.750876	+	0.660443i	$0.229631\pi$
$608$	−19.7990	−	8.51026i	−0.802953	−	0.345137i
$609$	51.0204			2.06745
$610$		0			0
$611$	−0.389771	+	2.21050i	−0.0157685	+	0.0894274i
$612$	28.8209	−	24.1836i	1.16502	−	0.977564i
$613$	−27.1741	−	22.8018i	−1.09755	−	0.920956i	−0.100294	−	0.994958i	$-0.531978\pi$
$613$	−27.1741	−	22.8018i	−1.09755	−	0.920956i	−0.997258	+	0.0740018i	$0.976423\pi$
$614$	−12.2448	−	69.4437i	−0.494160	−	2.80252i
$615$		0			0
$616$	9.76407	−	16.9119i	0.393406	−	0.681399i
$617$	19.6789	+	7.16254i	0.792243	+	0.288353i	0.706268	−	0.707944i	$-0.250377\pi$
$617$	19.6789	+	7.16254i	0.792243	+	0.288353i	0.0859751	+	0.996297i	$0.472599\pi$
$618$	23.0717	+	8.39741i	0.928080	+	0.337793i
$619$	−5.65065	+	9.78720i	−0.227119	+	0.393381i	−0.956953	−	0.290243i	$-0.906264\pi$
$619$	−5.65065	+	9.78720i	−0.227119	+	0.393381i	0.729834	+	0.683624i	$0.239597\pi$
$620$		0			0
$621$	2.61370	+	14.8230i	0.104884	+	0.594828i
$622$	−39.0275	−	32.7479i	−1.56486	−	1.31307i
$623$	1.28255	−	1.07619i	0.0513843	−	0.0431166i
$624$	−0.609004	+	3.45383i	−0.0243797	+	0.138264i
$625$		0			0
$626$	12.2784			0.490742
$627$	18.0150	−	5.41858i	0.719450	−	0.216397i
$628$	−67.9501			−2.71151
$629$	−11.2779	+	4.10484i	−0.449681	+	0.163670i
$630$		0			0
$631$	−8.29815	+	6.96298i	−0.330344	+	0.277192i	−0.792840	−	0.609430i	$-0.791398\pi$
$631$	−8.29815	+	6.96298i	−0.330344	+	0.277192i	0.462496	+	0.886621i	$0.346954\pi$
$632$	−30.1943	−	25.3360i	−1.20106	−	1.00781i
$633$	3.39876	+	19.2753i	0.135089	+	0.766125i
$634$	32.0399	+	55.4947i	1.27247	+	2.20398i
$635$		0			0
$636$	−64.4508	−	23.4582i	−2.55564	−	0.930178i
$637$	5.11409	+	1.86138i	0.202628	+	0.0737505i
$638$	19.5176	−	33.8054i	0.772709	−	1.33837i
$639$	−3.71019	−	6.42623i	−0.146773	−	0.254218i
$640$		0			0
$641$	−10.4066	−	8.73219i	−0.411037	−	0.344901i	0.413704	−	0.910411i	$-0.364235\pi$
$641$	−10.4066	−	8.73219i	−0.411037	−	0.344901i	−0.824741	+	0.565511i	$0.808679\pi$
$642$	−30.6920	+	25.7536i	−1.21132	+	1.01642i
$643$	2.50424	−	14.2023i	0.0987578	−	0.560083i	−0.894773	−	0.446521i	$-0.852663\pi$
$643$	2.50424	−	14.2023i	0.0987578	−	0.560083i	0.993531	−	0.113562i	$-0.0362261\pi$
$644$	−41.7841	+	15.2082i	−1.64652	+	0.599286i
$645$		0			0
$646$	−9.66462	−	81.7742i	−0.380249	−	3.21736i
$647$	17.6253			0.692923			0.346462	−	0.938064i	$-0.387383\pi$
$647$	17.6253			0.692923			0.346462	+	0.938064i	$0.387383\pi$
$648$	−33.3989	+	12.1562i	−1.31203	+	0.477541i
$649$	3.24733	−	18.4165i	0.127469	−	0.722912i
$650$		0			0
$651$	−23.9863	−	20.1269i	−0.940098	−	0.788836i
$652$	−3.26406	−	18.5114i	−0.127830	−	0.724962i
$653$	17.1666	+	29.7335i	0.671782	+	1.16356i	0.977398	+	0.211406i	$0.0678041\pi$
$653$	17.1666	+	29.7335i	0.671782	+	1.16356i	−0.305616	+	0.952155i	$0.598863\pi$
$654$	−11.7502	+	20.3519i	−0.459468	+	0.795822i
$655$		0			0
$656$	3.80444	+	1.38470i	0.148538	+	0.0540635i
$657$	−10.0567	+	17.4188i	−0.392351	+	0.679572i
$658$	−2.76827	−	4.79479i	−0.107918	−	0.186920i
$659$	1.11832	+	6.34230i	0.0435635	+	0.247061i	0.998811	−	0.0487463i	$-0.0155226\pi$
$659$	1.11832	+	6.34230i	0.0435635	+	0.247061i	−0.955248	+	0.295807i	$0.904411\pi$
$660$		0			0
$661$	15.0634	−	12.6397i	0.585900	−	0.491629i	−0.300979	−	0.953631i	$-0.597313\pi$
$661$	15.0634	−	12.6397i	0.585900	−	0.491629i	0.886879	+	0.462002i	$0.152869\pi$
$662$	3.85470	−	21.8611i	0.149817	−	0.849655i
$663$	44.9821	−	16.3721i	1.74696	−	0.635841i
$664$	24.3902			0.946525
$665$		0			0
$666$	−4.67259			−0.181059
$667$	−33.8941	+	12.3364i	−1.31238	+	0.477669i
$668$	12.1034	−	68.6418i	0.468294	−	2.65583i
$669$	−7.15950	+	6.00754i	−0.276802	+	0.232265i
$670$		0			0
$671$	0.734937	+	4.16803i	0.0283719	+	0.160905i
$672$	15.4508	+	26.7616i	0.596028	+	1.03235i
$673$	2.22659	−	3.85656i	0.0858287	−	0.148660i	−0.819915	−	0.572485i	$-0.805980\pi$
$673$	2.22659	−	3.85656i	0.0858287	−	0.148660i	0.905744	+	0.423825i	$0.139313\pi$
$674$	56.0157	+	20.3880i	2.15764	+	0.785318i
$675$		0			0
$676$	8.61134	−	14.9153i	0.331205	−	0.573665i
$677$	−2.62402	−	4.54494i	−0.100849	−	0.174676i	0.811185	−	0.584789i	$-0.198823\pi$
$677$	−2.62402	−	4.54494i	−0.100849	−	0.174676i	−0.912035	+	0.410113i	$0.865489\pi$
$678$	8.77212	+	49.7492i	0.336891	+	1.91061i
$679$	−34.3643	−	28.8351i	−1.31878	−	1.10659i
$680$		0			0
$681$	5.43427	−	30.8193i	0.208242	−	1.18100i
$682$	−22.5117	+	8.19358i	−0.862017	+	0.313749i
$683$	−18.6438			−0.713386			−0.356693	−	0.934222i	$-0.616096\pi$
$683$	−18.6438			−0.713386			−0.356693	+	0.934222i	$0.616096\pi$
$684$	4.61240	−	19.5733i	0.176359	−	0.748405i
$685$		0			0
$686$	32.9403	−	11.9893i	1.25767	−	0.457754i
$687$	−8.98378	+	50.9496i	−0.342753	+	1.94385i
$688$	−3.14090	+	2.63553i	−0.119746	+	0.100479i
$689$	−20.9640	−	17.5909i	−0.798665	−	0.670159i
$690$		0			0
$691$	−6.39630	−	11.0787i	−0.243327	−	0.421454i	0.718333	−	0.695699i	$-0.244905\pi$
$691$	−6.39630	−	11.0787i	−0.243327	−	0.421454i	−0.961660	+	0.274245i	$0.911572\pi$
$692$	−35.6522	+	61.7514i	−1.35529	+	2.34744i
$693$	−7.94929	−	2.89331i	−0.301969	−	0.109908i
$694$	51.5287	+	18.7549i	1.95600	+	0.711927i
$695$		0			0
$696$	−26.9976	−	46.7612i	−1.02334	−	1.77248i
$697$	−9.59574	−	54.4201i	−0.363464	−	2.06131i
$698$	5.39953	+	4.53075i	0.204375	+	0.171491i
$699$	35.7833	−	30.0258i	1.35345	−	1.13568i
$700$		0			0
$701$	29.9768	−	10.9107i	1.13221	−	0.412090i	0.293115	−	0.956077i	$-0.405308\pi$
$701$	29.9768	−	10.9107i	1.13221	−	0.412090i	0.839094	+	0.543987i	$0.183086\pi$
$702$	−22.1545			−0.836169
$703$	−3.51816	+	5.36411i	−0.132690	+	0.202311i
$704$	26.1094			0.984034
$705$		0			0
$706$	2.91950	−	16.5573i	0.109877	−	0.623143i
$707$	−14.8129	+	12.4295i	−0.557096	+	0.467459i
$708$	−48.8306	−	40.9737i	−1.83516	−	1.53989i
$709$	−2.34773	−	13.3146i	−0.0881708	−	0.500042i	−0.996627	−	0.0820619i	$-0.973849\pi$
$709$	−2.34773	−	13.3146i	−0.0881708	−	0.500042i	0.908456	−	0.417980i	$-0.137262\pi$
$710$		0			0
$711$	−8.53733	+	14.7871i	−0.320175	+	0.554559i
$712$	−1.66502	−	0.606016i	−0.0623991	−	0.0227114i
$713$	20.8013	+	7.57104i	0.779014	+	0.283538i
$714$	−59.0368	+	102.255i	−2.20939	+	3.82678i
$715$		0			0
$716$	−4.92884	−	27.9528i	−0.184199	−	1.04465i
$717$	−17.9045	−	15.0236i	−0.668655	−	0.561068i
$718$	−22.4483	+	18.8363i	−0.837762	+	0.702965i
$719$	−5.08500	+	28.8385i	−0.189639	+	1.07549i	0.730211	+	0.683222i	$0.239422\pi$
$719$	−5.08500	+	28.8385i	−0.189639	+	1.07549i	−0.919849	+	0.392272i	$0.871689\pi$
$720$		0			0
$721$	−15.1575			−0.564496
$722$	−30.2853	−	31.9357i	−1.12710	−	1.18852i
$723$	0.955003			0.0355170
$724$	−42.0657	+	15.3107i	−1.56336	+	0.569016i
$725$		0			0
$726$	24.9975	−	20.9754i	0.927746	−	0.778471i
$727$	−12.8894	−	10.8155i	−0.478040	−	0.401123i	0.371677	−	0.928362i	$-0.378783\pi$
$727$	−12.8894	−	10.8155i	−0.478040	−	0.401123i	−0.849717	+	0.527239i	$0.823227\pi$
$728$	−4.61201	−	26.1560i	−0.170932	−	0.969406i
$729$	−2.98368	−	5.16788i	−0.110507	−	0.191403i
$730$		0			0
$731$	52.5884	+	19.1406i	1.94505	+	0.707941i
$732$	13.5565	+	4.93416i	0.501062	+	0.182372i
$733$	−3.71262	+	6.43045i	−0.137129	+	0.237514i	−0.926409	−	0.376520i	$-0.877121\pi$
$733$	−3.71262	+	6.43045i	−0.137129	+	0.237514i	0.789280	+	0.614034i	$0.210454\pi$
$734$	20.2970	+	35.1555i	0.749177	+	1.29761i
$735$		0			0
$736$	−16.7351	−	14.0424i	−0.616865	−	0.517611i
$737$	−2.55946	+	2.14764i	−0.0942788	+	0.0791093i
$738$	3.73587	−	21.1872i	0.137519	−	0.779910i
$739$	−11.7407	+	4.27327i	−0.431889	+	0.157195i	−0.548811	−	0.835946i	$-0.684919\pi$
$739$	−11.7407	+	4.27327i	−0.431889	+	0.157195i	0.116922	+	0.993141i	$0.462697\pi$
$740$		0			0
$741$	14.0322	−	21.3947i	0.515485	−	0.785955i
$742$	67.5024			2.47809
$743$	−10.6225	+	3.86626i	−0.389701	+	0.141839i	−0.529437	−	0.848349i	$-0.677597\pi$
$743$	−10.6225	+	3.86626i	−0.389701	+	0.141839i	0.139736	+	0.990189i	$0.455375\pi$
$744$	−5.75429	+	32.6342i	−0.210962	+	1.19643i
$745$		0			0
$746$	13.1286	+	11.0162i	0.480670	+	0.403330i
$747$	−1.83471	−	10.4052i	−0.0671286	−	0.380705i
$748$	28.3331	+	49.0743i	1.03596	+	1.79433i
$749$	12.3673	−	21.4209i	0.451893	−	0.782701i
$750$		0			0
$751$	−45.2073	−	16.4541i	−1.64964	−	0.600419i	−0.660954	−	0.750427i	$-0.729848\pi$
$751$	−45.2073	−	16.4541i	−1.64964	−	0.600419i	−0.988685	+	0.150007i	$0.952070\pi$
$752$	−0.238828	+	0.413663i	−0.00870917	+	0.0150847i
$753$	−19.9797	−	34.6059i	−0.728101	−	1.26111i
$754$	−9.21903	−	52.2837i	−0.335737	−	1.90406i
$755$		0			0
$756$	26.2588	−	22.0337i	0.955022	−	0.801359i
$757$	−1.71413	+	9.72129i	−0.0623009	+	0.353326i	0.937682	+	0.347494i	$0.112967\pi$
$757$	−1.71413	+	9.72129i	−0.0623009	+	0.353326i	−0.999983	+	0.00583181i	$0.998144\pi$
$758$	−34.0882	+	12.4071i	−1.23814	+	0.450645i
$759$	19.0704			0.692211
$760$		0			0
$761$	−24.4437			−0.886083			−0.443042	−	0.896501i	$-0.646101\pi$
$761$	−24.4437			−0.886083			−0.443042	+	0.896501i	$0.646101\pi$
$762$	47.7357	−	17.3744i	1.72928	−	0.629407i
$763$	2.51930	−	14.2876i	0.0912046	−	0.517247i
$764$	46.1344	−	38.7114i	1.66909	−	1.40053i
$765$		0			0
$766$	−1.32228	−	7.49901i	−0.0477759	−	0.270950i
$767$	−12.7170	−	22.0265i	−0.459185	−	0.795331i
$768$	20.5561	−	35.6041i	0.741753	−	1.28475i
$769$	−19.5929	−	7.13124i	−0.706539	−	0.257159i	−0.0363389	−	0.999340i	$-0.511570\pi$
$769$	−19.5929	−	7.13124i	−0.706539	−	0.257159i	−0.670200	+	0.742180i	$0.733792\pi$
$770$		0			0
$771$	5.44067	−	9.42351i	0.195941	−	0.339379i
$772$	4.80780	+	8.32735i	0.173036	+	0.299708i
$773$	4.49549	+	25.4952i	0.161692	+	0.916998i	0.952410	+	0.304819i	$0.0985959\pi$
$773$	4.49549	+	25.4952i	0.161692	+	0.916998i	−0.790719	+	0.612179i	$0.790293\pi$
$774$	16.6906	+	14.0051i	0.599930	+	0.503401i
$775$		0			0
$776$	−8.24396	+	46.7538i	−0.295941	+	1.67836i
$777$	8.64372	−	3.14606i	0.310092	−	0.112864i
$778$	−61.1134			−2.19102
$779$	−21.5099	−	20.2413i	−0.770672	−	0.725221i
$780$		0			0
$781$	10.5022	−	3.82250i	0.375799	−	0.136780i
$782$	14.4950	−	82.2050i	0.518339	−	2.93964i
$783$	21.3004	−	17.8731i	0.761213	−	0.638734i
$784$	0.887182	+	0.744434i	0.0316851	+	0.0265869i
$785$		0			0
$786$	1.69147	+	2.92972i	0.0603329	+	0.104500i
$787$	−5.96541	+	10.3324i	−0.212644	+	0.368310i	−0.952541	−	0.304410i	$-0.901541\pi$
$787$	−5.96541	+	10.3324i	−0.212644	+	0.368310i	0.739897	+	0.672720i	$0.234874\pi$
$788$	−18.9698	−	6.90443i	−0.675770	−	0.245960i
$789$	−5.36177	−	1.95152i	−0.190884	−	0.0694761i
$790$		0			0
$791$	−15.5934	−	27.0085i	−0.554436	−	0.960311i
$792$	1.55462	+	8.81670i	0.0552411	+	0.313288i
$793$	4.40953	+	3.70004i	0.156587	+	0.131392i
$794$	24.7189	−	20.7416i	0.877242	−	0.736093i
$795$		0			0
$796$	25.8732	−	9.41709i	0.917053	−	0.333780i
$797$	−0.806993			−0.0285852			−0.0142926	−	0.999898i	$-0.504550\pi$
$797$	−0.806993			−0.0285852			−0.0142926	+	0.999898i	$0.504550\pi$
$798$	7.40722	+	62.6739i	0.262213	+	2.21863i
$799$	6.51957			0.230646
$800$		0			0
$801$	−0.133286	+	0.755902i	−0.00470943	+	0.0267085i
$802$	−30.6423	+	25.7120i	−1.08202	+	0.907921i
$803$	−23.2066	−	19.4726i	−0.818943	−	0.687175i
$804$	1.97763	+	11.2157i	0.0697457	+	0.395547i
$805$		0			0
$806$	−16.2911	+	28.2171i	−0.573830	+	0.993903i
$807$	11.7702	+	4.28401i	0.414331	+	0.150804i
$808$	19.2302	+	6.99921i	0.676515	+	0.246231i
$809$	−14.1310	+	24.4756i	−0.496818	+	0.860515i	−0.999993	−	0.00366987i	$-0.998832\pi$
$809$	−14.1310	+	24.4756i	−0.496818	+	0.860515i	0.503175	+	0.864185i	$0.332165\pi$
$810$		0			0
$811$	2.46012	+	13.9520i	0.0863866	+	0.489923i	0.997049	+	0.0767709i	$0.0244610\pi$
$811$	2.46012	+	13.9520i	0.0863866	+	0.489923i	−0.910662	+	0.413152i	$0.864428\pi$
$812$	62.9255	+	52.8008i	2.20825	+	1.85294i
$813$	−35.2131	+	29.5473i	−1.23498	+	1.03627i
$814$	1.22207	−	6.93072i	0.0428337	−	0.242922i
$815$		0			0
$816$	10.1866			0.356602
$817$	28.6447	−	8.61580i	1.00215	−	0.301429i
$818$	55.4010			1.93705
$819$	−10.8115	+	3.93508i	−0.377786	+	0.137503i
$820$		0			0
$821$	30.8044	−	25.8480i	1.07508	−	0.902101i	0.0795794	−	0.996829i	$-0.474642\pi$
$821$	30.8044	−	25.8480i	1.07508	−	0.902101i	0.995503	+	0.0947271i	$0.0301978\pi$
$822$	46.3176	+	38.8651i	1.61551	+	1.35558i
$823$	0.418314	+	2.37238i	0.0145815	+	0.0826958i	0.991230	−	0.132147i	$-0.0421871\pi$
$823$	0.418314	+	2.37238i	0.0145815	+	0.0826958i	−0.976649	+	0.214843i	$0.931076\pi$
$824$	8.02066	+	13.8922i	0.279413	+	0.483958i
$825$		0			0
$826$	58.9522	+	21.4568i	2.05121	+	0.746579i
$827$	33.2228	+	12.0921i	1.15527	+	0.420484i	0.847405	−	0.530947i	$-0.178164\pi$
$827$	33.2228	+	12.0921i	1.15527	+	0.420484i	0.307864	+	0.951430i	$0.400386\pi$
$828$	10.1927	−	17.6542i	0.354220	−	0.613527i
$829$	15.5780	+	26.9819i	0.541046	+	0.937119i	0.998844	+	0.0480633i	$0.0153049\pi$
$829$	15.5780	+	26.9819i	0.541046	+	0.937119i	−0.457798	+	0.889056i	$0.651362\pi$
$830$		0			0
$831$	−3.60393	−	3.02406i	−0.125019	−	0.104903i
$832$	27.2025	−	22.8256i	0.943078	−	0.791337i
$833$	2.74494	−	15.5673i	0.0951064	−	0.539375i
$834$	48.7332	−	17.7374i	1.68749	−	0.614197i
$835$		0			0
$836$	27.8263	+	11.9607i	0.962393	+	0.413669i
$837$	−17.0647			−0.589843
$838$	22.2834	−	8.11051i	0.769768	−	0.280173i
$839$	2.09798	−	11.8983i	0.0724304	−	0.410773i	−0.926937	−	0.375216i	$-0.877568\pi$
$839$	2.09798	−	11.8983i	0.0724304	−	0.410773i	0.999368	−	0.0355570i	$-0.0113205\pi$
$840$		0			0
$841$	28.8281	+	24.1896i	0.994072	+	0.834125i
$842$	−9.13385	−	51.8006i	−0.314773	−	1.78517i
$843$	2.70264	+	4.68111i	0.0930839	+	0.161226i
$844$	−15.7561	+	27.2904i	−0.542348	+	0.939374i
$845$		0			0
$846$	2.38516	+	0.868128i	0.0820036	+	0.0298469i
$847$	−10.0728	+	17.4465i	−0.346104	+	0.599470i
$848$	−2.91183	−	5.04344i	−0.0999927	−	0.173192i
$849$	−8.73486	−	49.5379i	−0.299780	−	1.70013i
$850$		0			0
$851$	−4.98153	+	4.18000i	−0.170765	+	0.143289i
$852$	6.61527	−	37.5171i	0.226635	−	1.28531i
$853$	−1.00015	+	0.364026i	−0.0342446	+	0.0124640i	−0.359086	−	0.933305i	$-0.616911\pi$
$853$	−1.00015	+	0.364026i	−0.0342446	+	0.0124640i	0.324841	+	0.945769i	$0.394689\pi$
$854$	−14.1983			−0.485857
$855$		0			0
$856$	−26.1769			−0.894707
$857$	−22.6211	+	8.23340i	−0.772721	+	0.281248i	−0.698134	−	0.715967i	$-0.745986\pi$
$857$	−22.6211	+	8.23340i	−0.772721	+	0.281248i	−0.0745871	+	0.997215i	$0.523764\pi$
$858$	−4.87424	+	27.6432i	−0.166404	+	0.943723i
$859$	18.7118	−	15.7010i	0.638437	−	0.535712i	−0.265101	−	0.964221i	$-0.585405\pi$
$859$	18.7118	−	15.7010i	0.638437	−	0.535712i	0.903538	+	0.428508i	$0.140961\pi$
$860$		0			0
$861$	7.35443	+	41.7090i	0.250638	+	1.42144i
$862$	9.79824	+	16.9710i	0.333729	+	0.578036i
$863$	5.10783	−	8.84702i	0.173873	−	0.301156i	−0.765898	−	0.642962i	$-0.777705\pi$
$863$	5.10783	−	8.84702i	0.173873	−	0.301156i	0.939771	+	0.341806i	$0.111039\pi$
$864$	15.8255	+	5.76000i	0.538393	+	0.195959i
$865$		0			0
$866$	7.41197	−	12.8379i	0.251869	−	0.436250i
$867$	−51.7487	−	89.6314i	−1.75748	−	3.04404i
$868$	−8.75405	−	49.6467i	−0.297132	−	1.68512i
$869$	−19.7005	−	16.5306i	−0.668292	−	0.560764i
$870$		0			0
$871$	−0.789083	+	4.47511i	−0.0267371	+	0.151633i
$872$	−14.4280	+	5.25137i	−0.488594	+	0.177834i
$873$	20.5659			0.696050
$874$	−20.0750	−	39.8448i	−0.679047	−	1.34777i
$875$		0			0
$876$	−97.0342	+	35.3176i	−3.27848	+	1.19327i
$877$	−7.36026	+	41.7421i	−0.248538	+	1.40953i	0.563591	+	0.826054i	$0.309419\pi$
$877$	−7.36026	+	41.7421i	−0.248538	+	1.40953i	−0.812129	+	0.583477i	$0.801692\pi$
$878$	−15.5243	+	13.0264i	−0.523920	+	0.439621i
$879$	24.0581	+	20.1872i	0.811461	+	0.680897i
$880$		0			0
$881$	−6.57499	−	11.3882i	−0.221517	−	0.383679i	0.733752	−	0.679418i	$-0.237768\pi$
$881$	−6.57499	−	11.3882i	−0.221517	−	0.383679i	−0.955269	+	0.295739i	$0.904434\pi$
$882$	3.07713	−	5.32974i	0.103612	−	0.179462i
$883$	47.5127	+	17.2932i	1.59893	+	0.581963i	0.979208	−	0.202857i	$-0.0650227\pi$
$883$	47.5127	+	17.2932i	1.59893	+	0.581963i	0.619723	+	0.784821i	$0.287245\pi$
$884$	72.4216	+	26.3593i	2.43580	+	0.886560i
$885$		0			0
$886$	8.73964	+	15.1375i	0.293614	+	0.508554i
$887$	−3.19742	−	18.1335i	−0.107359	−	0.608863i	−0.990252	−	0.139288i	$-0.955519\pi$
$887$	−3.19742	−	18.1335i	−0.107359	−	0.608863i	0.882893	−	0.469574i	$-0.155593\pi$
$888$	−7.45728	−	6.25740i	−0.250250	−	0.209985i
$889$	−24.0241	+	20.1586i	−0.805741	+	0.676097i
$890$		0			0
$891$	−21.7913	+	7.93140i	−0.730037	+	0.265712i
$892$	−15.0473			−0.503820
$893$	2.79248	−	2.08451i	0.0934469	−	0.0697555i
$894$	14.0912			0.471282
$895$		0			0
$896$	−10.0764	+	57.1461i	−0.336629	+	1.90912i
$897$	19.8688	−	16.6719i	0.663401	−	0.556660i
$898$	50.3975	+	42.2885i	1.68179	+	1.41119i
$899$	−7.10104	−	40.2720i	−0.236833	−	1.34315i
$900$		0			0
$901$	−39.7438	+	68.8383i	−1.32406	+	2.29334i
$902$	30.4493	+	11.0826i	1.01385	+	0.369011i
$903$	−40.3052	−	14.6699i	−1.34127	−	0.488183i
$904$	−16.5026	+	28.5833i	−0.548867	+	0.950665i
$905$		0			0
$906$	3.52963	+	20.0175i	0.117264	+	0.665037i
$907$	−33.9038	−	28.4486i	−1.12576	−	0.944621i	−0.126875	−	0.991919i	$-0.540495\pi$
$907$	−33.9038	−	28.4486i	−1.12576	−	0.944621i	−0.998881	+	0.0472972i	$0.984939\pi$
$908$	38.5971	−	32.3868i	1.28089	−	1.07479i
$909$	1.53939	−	8.73033i	0.0510584	−	0.289567i
$910$		0			0
$911$	38.3563			1.27080			0.635401	−	0.772182i	$-0.280835\pi$
$911$	38.3563			1.27080			0.635401	+	0.772182i	$0.280835\pi$
$912$	4.36316	−	3.25698i	0.144479	−	0.107849i
$913$	15.9136			0.526662
$914$	−84.9248	+	30.9101i	−2.80906	+	1.02242i
$915$		0			0
$916$	−63.8075	+	53.5409i	−2.10826	+	1.76904i
$917$	−1.59987	−	1.34245i	−0.0528323	−	0.0443316i
$918$	11.1741	+	63.3714i	0.368800	+	2.09157i
$919$	−4.70946	−	8.15703i	−0.155351	−	0.269076i	0.777836	−	0.628467i	$-0.216317\pi$
$919$	−4.70946	−	8.15703i	−0.155351	−	0.269076i	−0.933187	+	0.359392i	$0.882984\pi$
$920$		0			0
$921$	−59.8024	−	21.7663i	−1.97056	−	0.717223i
$922$	−22.7091	−	8.26543i	−0.747883	−	0.272207i
$923$	7.60019	−	13.1639i	0.250163	−	0.433296i
$924$	−21.7152	−	37.6119i	−0.714378	−	1.23734i
$925$		0			0
$926$	−15.9956	−	13.4219i	−0.525649	−	0.441072i
$927$	5.32324	−	4.46673i	0.174838	−	0.146707i
$928$	−7.00798	+	39.7442i	−0.230048	+	1.30467i
$929$	17.8090	−	6.48196i	0.584296	−	0.212666i	−0.0329231	−	0.999458i	$-0.510482\pi$
$929$	17.8090	−	6.48196i	0.584296	−	0.212666i	0.617219	+	0.786792i	$0.288259\pi$
$930$		0			0
$931$	−3.80164	−	7.54548i	−0.124594	−	0.247293i
$932$	75.2065			2.46347
$933$	−43.2069	+	15.7260i	−1.41453	+	0.514847i
$934$	−10.5821	+	60.0143i	−0.346258	+	1.96373i
$935$		0			0
$936$	9.32754	+	7.82674i	0.304880	+	0.255825i
$937$	1.53351	+	8.69696i	0.0500976	+	0.284117i	0.999557	−	0.0297733i	$-0.00947855\pi$
$937$	1.53351	+	8.69696i	0.0500976	+	0.284117i	−0.949459	+	0.313891i	$0.898367\pi$
$938$	−5.60430	−	9.70694i	−0.182987	−	0.316943i
$939$	5.54066	−	9.59670i	0.180813	−	0.313176i
$940$		0			0
$941$	16.9239	+	6.15980i	0.551704	+	0.200804i	0.602803	−	0.797890i	$-0.294050\pi$
$941$	16.9239	+	6.15980i	0.551704	+	0.200804i	−0.0510996	+	0.998694i	$0.516273\pi$
$942$	−48.8824	+	84.6668i	−1.59268	+	2.75859i
$943$	−14.9707	−	25.9301i	−0.487514	−	0.844399i
$944$	−0.939855	−	5.33019i	−0.0305897	−	0.173483i
$945$		0			0
$946$	−25.1386	+	21.0938i	−0.817327	+	0.685818i
$947$	1.40574	−	7.97232i	0.0456803	−	0.259066i	−0.953412	−	0.301672i	$-0.902455\pi$
$947$	1.40574	−	7.97232i	0.0456803	−	0.259066i	0.999092	+	0.0426067i	$0.0135662\pi$
$948$	−82.3739	+	29.9816i	−2.67538	+	0.973759i
$949$	−41.2018			−1.33747
$950$		0			0
$951$	57.8325			1.87535
$952$	−72.4912	+	26.3846i	−2.34945	+	0.855130i
$953$	4.27625	−	24.2518i	0.138521	−	0.785594i	−0.833821	−	0.552035i	$-0.813852\pi$
$953$	4.27625	−	24.2518i	0.138521	−	0.785594i	0.972343	−	0.233559i	$-0.0750373\pi$
$954$	−23.7065	+	19.8921i	−0.767525	+	0.644030i
$955$		0			0
$956$	−6.53441	−	37.0585i	−0.211338	−	1.19856i
$957$	−17.6148	−	30.5097i	−0.569405	−	0.986238i
$958$	22.2127	−	38.4735i	0.717659	−	1.24302i
$959$	−35.0762	−	12.7667i	−1.13267	−	0.412259i
$960$		0			0
$961$	2.95162	−	5.11235i	0.0952135	−	0.164915i
$962$	−4.78582	−	8.28928i	−0.154301	−	0.267257i
$963$	1.96911	+	11.1674i	0.0634537	+	0.359864i
$964$	1.17784	+	0.988328i	0.0379358	+	0.0318319i
$965$		0			0
$966$	−11.1093	+	63.0041i	−0.357437	+	2.02712i
$967$	−46.0742	+	16.7696i	−1.48165	+	0.539276i	−0.951236	−	0.308465i	$-0.900185\pi$
$967$	−46.0742	+	16.7696i	−1.48165	+	0.539276i	−0.530412	+	0.847740i	$0.677963\pi$
$968$	21.3201			0.685255
$969$	−68.2755	−	29.3471i	−2.19332	−	0.942765i
$970$		0			0
$971$	5.93099	−	2.15870i	0.190335	−	0.0692761i	−0.245094	−	0.969499i	$-0.578819\pi$
$971$	5.93099	−	2.15870i	0.190335	−	0.0692761i	0.435429	+	0.900223i	$0.356597\pi$
$972$	−7.75331	+	43.9712i	−0.248688	+	1.41038i
$973$	−24.5261	+	20.5798i	−0.786270	+	0.659759i
$974$	58.0795	+	48.7345i	1.86099	+	1.56155i
$975$		0			0
$976$	0.612469	+	1.06083i	0.0196047	+	0.0339563i
$977$	12.6888	−	21.9776i	0.405950	−	0.703126i	−0.588481	−	0.808511i	$-0.700274\pi$
$977$	12.6888	−	21.9776i	0.405950	−	0.703126i	0.994432	+	0.105384i	$0.0336073\pi$
$978$	−25.4136	−	9.24979i	−0.812637	−	0.295776i
$979$	−1.08635	−	0.395399i	−0.0347199	−	0.0126370i
$980$		0			0
$981$	3.32562	+	5.76014i	0.106179	+	0.183907i
$982$	12.1587	+	68.9555i	0.388000	+	2.20046i
$983$	0.234177	+	0.196498i	0.00746909	+	0.00626731i	0.646515	−	0.762902i	$-0.276226\pi$
$983$	0.234177	+	0.196498i	0.00746909	+	0.00626731i	−0.639045	+	0.769169i	$0.720670\pi$
$984$	34.3356	−	28.8110i	1.09458	−	0.918460i
$985$		0			0
$986$	−144.904	+	52.7407i	−4.61468	+	1.67961i
$987$	−4.99678			−0.159049
$988$	39.4477	−	11.8652i	1.25500	−	0.377481i
$989$	30.3228			0.964208
$990$		0			0
$991$	9.62910	−	54.6094i	0.305879	−	1.73472i	−0.313462	−	0.949601i	$-0.601489\pi$
$991$	9.62910	−	54.6094i	0.305879	−	1.73472i	0.619340	−	0.785123i	$-0.287400\pi$
$992$	18.9733	−	15.9205i	0.602403	−	0.505476i
$993$	−15.3470	−	12.8777i	−0.487024	−	0.408662i
$994$	6.51064	+	36.9237i	0.206505	+	1.17115i
$995$		0			0
$996$	27.1218	−	46.9764i	0.859388	−	1.48850i
$997$	52.2892	+	19.0317i	1.65602	+	0.602740i	0.989729	−	0.142956i	$-0.0456607\pi$
$997$	52.2892	+	19.0317i	1.65602	+	0.602740i	0.666286	+	0.745696i	$0.267883\pi$
$998$	24.6215	+	8.96149i	0.779380	+	0.283671i
$999$	2.50654	−	4.34145i	0.0793034	−	0.137357i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.e.176.7	yes	42
5.2	odd	4		475.2.u.d.24.13		84
5.3	odd	4		475.2.u.d.24.2		84
5.4	even	2		475.2.l.d.176.1	✓	42
19.2	odd	18		9025.2.a.cp.1.21		21
19.4	even	9	inner	475.2.l.e.251.7	yes	42
19.17	even	9		9025.2.a.cs.1.1		21
95.4	even	18		475.2.l.d.251.1	yes	42
95.23	odd	36		475.2.u.d.99.13		84
95.42	odd	36		475.2.u.d.99.2		84
95.59	odd	18		9025.2.a.cr.1.1		21
95.74	even	18		9025.2.a.cq.1.21		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.l.d.176.1	✓	42	5.4	even	2
475.2.l.d.251.1	yes	42	95.4	even	18
475.2.l.e.176.7	yes	42	1.1	even	1	trivial
475.2.l.e.251.7	yes	42	19.4	even	9	inner
475.2.u.d.24.2		84	5.3	odd	4
475.2.u.d.24.13		84	5.2	odd	4
475.2.u.d.99.2		84	95.42	odd	36
475.2.u.d.99.13		84	95.23	odd	36
9025.2.a.cp.1.21		21	19.2	odd	18
9025.2.a.cq.1.21		21	95.74	even	18
9025.2.a.cr.1.1		21	95.59	odd	18
9025.2.a.cs.1.1		21	19.17	even	9

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.17674 - 0.792270i) q^{2} +(0.363030 - 2.05885i) q^{3} +(2.57843 - 2.16356i) q^{4} +(-0.840938 - 4.76919i) q^{6} +(1.49485 + 2.58916i) q^{7} +(1.58201 - 2.74013i) q^{8} +(-1.28798 - 0.468785i) q^{9} +O(q^{10})\)	\(q+(2.17674 - 0.792270i) q^{2} +(0.363030 - 2.05885i) q^{3} +(2.57843 - 2.16356i) q^{4} +(-0.840938 - 4.76919i) q^{6} +(1.49485 + 2.58916i) q^{7} +(1.58201 - 2.74013i) q^{8} +(-1.28798 - 0.468785i) q^{9} +(1.03220 - 1.78782i) q^{11} +(-3.51839 - 6.09402i) q^{12} +(-0.487552 - 2.76505i) q^{13} +(5.30523 + 4.45161i) q^{14} +(0.103752 - 0.588408i) q^{16} +(-7.66330 + 2.78921i) q^{17} -3.17500 q^{18} +(-2.39057 + 3.64488i) q^{19} +(5.87336 - 2.13773i) q^{21} +(0.830393 - 4.70939i) q^{22} +(-3.38493 + 2.84029i) q^{23} +(-5.06718 - 4.25187i) q^{24} +(-3.25194 - 5.63252i) q^{26} +(1.70318 - 2.94999i) q^{27} +(9.45618 + 3.44177i) q^{28} +(7.67059 + 2.79186i) q^{29} +(-2.50483 - 4.33850i) q^{31} +(0.858520 + 4.86891i) q^{32} +(-3.30612 - 2.77416i) q^{33} +(-14.4712 + 12.1428i) q^{34} +(-4.33520 + 1.57788i) q^{36} +1.47168 q^{37} +(-2.31593 + 9.82795i) q^{38} -5.86980 q^{39} +(-1.17665 + 6.67313i) q^{41} +(11.0911 - 9.30657i) q^{42} +(-5.25688 - 4.41104i) q^{43} +(-1.20660 - 6.84297i) q^{44} +(-5.11784 + 8.86435i) q^{46} +(-0.751233 - 0.273426i) q^{47} +(-1.17378 - 0.427219i) q^{48} +(-0.969174 + 1.67866i) q^{49} +(2.96055 + 16.7901i) q^{51} +(-7.23946 - 6.07463i) q^{52} +(7.46661 - 6.26523i) q^{53} +(1.37019 - 7.77076i) q^{54} +9.45952 q^{56} +(6.63640 + 6.24502i) q^{57} +18.9088 q^{58} +(8.51236 - 3.09825i) q^{59} +(-1.57051 + 1.31782i) q^{61} +(-8.88964 - 7.45929i) q^{62} +(-0.711575 - 4.03554i) q^{63} +(6.32375 + 10.9531i) q^{64} +(-9.39445 - 3.41930i) q^{66} +(-1.52085 - 0.553545i) q^{67} +(-13.7247 + 23.7718i) q^{68} +(4.61889 + 8.00015i) q^{69} +(4.14723 + 3.47994i) q^{71} +(-3.32213 + 2.78760i) q^{72} +(2.54821 - 14.4516i) q^{73} +(3.20347 - 1.16597i) q^{74} +(1.72200 + 14.5702i) q^{76} +6.17193 q^{77} +(-12.7770 + 4.65046i) q^{78} +(2.16322 - 12.2682i) q^{79} +(-8.60518 - 7.22060i) q^{81} +(2.72565 + 15.4579i) q^{82} +(3.85430 + 6.67585i) q^{83} +(10.5189 - 18.2193i) q^{84} +(-14.9376 - 5.43684i) q^{86} +(8.53267 - 14.7790i) q^{87} +(-3.26590 - 5.65670i) q^{88} +(-0.0972439 - 0.551497i) q^{89} +(6.43033 - 5.39569i) q^{91} +(-2.58266 + 14.6470i) q^{92} +(-9.84163 + 3.58206i) q^{93} -1.85187 q^{94} +10.3360 q^{96} +(-14.0997 + 5.13189i) q^{97} +(-0.779693 + 4.42186i) q^{98} +(-2.16754 + 1.81879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 3 q^{3} - 6 q^{4} - 3 q^{6} - 18 q^{8} + 9 q^{9}+O(q^{10}) \) 42 * q + 3 * q^3 - 6 * q^4 - 3 * q^6 - 18 * q^8 + 9 * q^9	\( 42 q + 3 q^{3} - 6 q^{4} - 3 q^{6} - 18 q^{8} + 9 q^{9} - 24 q^{12} + 27 q^{13} + 12 q^{14} + 18 q^{16} + 36 q^{18} + 12 q^{19} + 15 q^{21} - 12 q^{22} + 12 q^{23} + 33 q^{24} - 18 q^{26} - 30 q^{27} + 42 q^{28} - 3 q^{29} - 6 q^{31} + 60 q^{32} - 36 q^{33} - 42 q^{34} - 63 q^{36} + 48 q^{37} + 24 q^{38} - 60 q^{39} - 9 q^{41} + 165 q^{42} - 33 q^{44} - 15 q^{46} + 9 q^{47} - 84 q^{48} - 33 q^{49} - 36 q^{51} - 105 q^{52} - 6 q^{53} - 18 q^{54} + 36 q^{56} - 21 q^{57} - 24 q^{58} - 45 q^{59} + 9 q^{61} - 57 q^{62} - 51 q^{63} - 48 q^{66} - 27 q^{67} - 78 q^{68} + 15 q^{69} - 6 q^{71} + 24 q^{72} - 81 q^{73} + 72 q^{74} - 114 q^{76} + 18 q^{77} - 66 q^{78} + 27 q^{79} - 21 q^{81} - 9 q^{82} + 36 q^{84} - 60 q^{86} - 6 q^{87} - 60 q^{88} + 84 q^{89} - 33 q^{91} + 18 q^{92} - 21 q^{93} - 36 q^{94} + 222 q^{96} - 51 q^{97} + 180 q^{98} - 18 q^{99}+O(q^{100}) \) 42 * q + 3 * q^3 - 6 * q^4 - 3 * q^6 - 18 * q^8 + 9 * q^9 - 24 * q^12 + 27 * q^13 + 12 * q^14 + 18 * q^16 + 36 * q^18 + 12 * q^19 + 15 * q^21 - 12 * q^22 + 12 * q^23 + 33 * q^24 - 18 * q^26 - 30 * q^27 + 42 * q^28 - 3 * q^29 - 6 * q^31 + 60 * q^32 - 36 * q^33 - 42 * q^34 - 63 * q^36 + 48 * q^37 + 24 * q^38 - 60 * q^39 - 9 * q^41 + 165 * q^42 - 33 * q^44 - 15 * q^46 + 9 * q^47 - 84 * q^48 - 33 * q^49 - 36 * q^51 - 105 * q^52 - 6 * q^53 - 18 * q^54 + 36 * q^56 - 21 * q^57 - 24 * q^58 - 45 * q^59 + 9 * q^61 - 57 * q^62 - 51 * q^63 - 48 * q^66 - 27 * q^67 - 78 * q^68 + 15 * q^69 - 6 * q^71 + 24 * q^72 - 81 * q^73 + 72 * q^74 - 114 * q^76 + 18 * q^77 - 66 * q^78 + 27 * q^79 - 21 * q^81 - 9 * q^82 + 36 * q^84 - 60 * q^86 - 6 * q^87 - 60 * q^88 + 84 * q^89 - 33 * q^91 + 18 * q^92 - 21 * q^93 - 36 * q^94 + 222 * q^96 - 51 * q^97 + 180 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more