LMFDB - Embedded newform 375.2.g.c.301.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(76,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("375.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.g (of order $5$, degree $4$, not 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:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 $ x^12 + 3x^10 - 2x^9 + 34x^8 - 22x^7 + 236x^6 - 179x^5 + 877x^4 - 409x^3 + 96x^2 - 11x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.3
Root			$-0.667650 + 2.05481i$ of defining polynomial
Character	$\chi$	$=$	375.301
Dual form			375.2.g.c.76.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.74793 - 1.26995i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.824463 - 2.53744i) q^{4} +(-0.667650 - 2.05481i) q^{6} +3.16056 q^{7} +(-0.446002 - 1.37265i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(1.74793 - 1.26995i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.824463 - 2.53744i) q^{4} +(-0.667650 - 2.05481i) q^{6} +3.16056 q^{7} +(-0.446002 - 1.37265i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-1.24455 + 0.904220i) q^{11} +(-2.15847 - 1.56822i) q^{12} +(-4.24041 - 3.08084i) q^{13} +(5.52444 - 4.01374i) q^{14} +(1.79417 + 1.30354i) q^{16} +(-0.398843 - 1.22751i) q^{17} -2.16056 q^{18} +(1.68287 + 5.17933i) q^{19} +(0.976667 - 3.00587i) q^{21} +(-1.02708 + 3.16103i) q^{22} +(-5.21204 + 3.78677i) q^{23} -1.44329 q^{24} -11.3244 q^{26} +(-0.809017 + 0.587785i) q^{27} +(2.60577 - 8.01972i) q^{28} +(-0.730396 + 2.24793i) q^{29} +(-1.37989 - 4.24687i) q^{31} +7.67809 q^{32} +(0.475377 + 1.46306i) q^{33} +(-2.25602 - 1.63910i) q^{34} +(-2.15847 + 1.56822i) q^{36} +(-4.81973 - 3.50174i) q^{37} +(9.51901 + 6.91596i) q^{38} +(-4.24041 + 3.08084i) q^{39} +(6.90269 + 5.01510i) q^{41} +(-2.11015 - 6.49436i) q^{42} +8.48426 q^{43} +(1.26831 + 3.90347i) q^{44} +(-4.30129 + 13.2380i) q^{46} +(-0.232712 + 0.716212i) q^{47} +(1.79417 - 1.30354i) q^{48} +2.98914 q^{49} -1.29068 q^{51} +(-11.3135 + 8.21974i) q^{52} +(-3.01289 + 9.27271i) q^{53} +(-0.667650 + 2.05481i) q^{54} +(-1.40962 - 4.33836i) q^{56} +5.44587 q^{57} +(1.57806 + 4.85678i) q^{58} +(-3.32724 - 2.41738i) q^{59} +(8.65159 - 6.28574i) q^{61} +(-7.80525 - 5.67084i) q^{62} +(-2.55695 - 1.85773i) q^{63} +(9.83243 - 7.14368i) q^{64} +(2.68893 + 1.95362i) q^{66} +(0.586713 + 1.80572i) q^{67} -3.44357 q^{68} +(1.99082 + 6.12712i) q^{69} +(-0.0219023 + 0.0674084i) q^{71} +(-0.446002 + 1.37265i) q^{72} +(3.24515 - 2.35774i) q^{73} -12.8716 q^{74} +14.5297 q^{76} +(-3.93348 + 2.85784i) q^{77} +(-3.49944 + 10.7702i) q^{78} +(0.500141 - 1.53928i) q^{79} +(0.309017 + 0.951057i) q^{81} +18.4343 q^{82} +(-4.06322 - 12.5053i) q^{83} +(-6.82198 - 4.95646i) q^{84} +(14.8299 - 10.7745i) q^{86} +(1.91220 + 1.38930i) q^{87} +(1.79626 + 1.30506i) q^{88} +(-5.88638 + 4.27671i) q^{89} +(-13.4021 - 9.73718i) q^{91} +(5.31155 + 16.3473i) q^{92} -4.46542 q^{93} +(0.502787 + 1.54742i) q^{94} +(2.37266 - 7.30230i) q^{96} +(-3.15009 + 9.69499i) q^{97} +(5.22480 - 3.79604i) q^{98} +1.53835 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9	$ 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9} - 4 q^{11} + 2 q^{13} + 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 3 q^{21} - 13 q^{22} - 19 q^{23} + 6 q^{24} - 56 q^{26} - 3 q^{27} - q^{28} - q^{29} + 13 q^{31} + 32 q^{32} + q^{33} - 25 q^{34} - 8 q^{37} + 22 q^{38} + 2 q^{39} + 8 q^{41} + 16 q^{42} + 4 q^{43} + 33 q^{44} - 22 q^{46} + 13 q^{47} + 16 q^{48} - 28 q^{49} + 26 q^{51} - 44 q^{52} - 44 q^{53} + 45 q^{56} + 22 q^{57} - 41 q^{58} - 22 q^{59} - 8 q^{61} - 41 q^{62} - 3 q^{63} + 49 q^{64} - 3 q^{66} + 6 q^{67} + 100 q^{68} + 6 q^{69} - 21 q^{71} - 9 q^{72} + 16 q^{73} - 44 q^{74} - 52 q^{76} - q^{77} + 19 q^{78} + 10 q^{79} - 3 q^{81} - 26 q^{82} + 10 q^{83} - 6 q^{84} + 56 q^{86} + 4 q^{87} + 16 q^{88} + 57 q^{89} - 7 q^{91} - 3 q^{92} - 22 q^{93} - 23 q^{94} - 23 q^{96} - 4 q^{97} + 18 q^{98} + 6 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9 - 4 * q^11 + 2 * q^13 + 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 3 * q^21 - 13 * q^22 - 19 * q^23 + 6 * q^24 - 56 * q^26 - 3 * q^27 - q^28 - q^29 + 13 * q^31 + 32 * q^32 + q^33 - 25 * q^34 - 8 * q^37 + 22 * q^38 + 2 * q^39 + 8 * q^41 + 16 * q^42 + 4 * q^43 + 33 * q^44 - 22 * q^46 + 13 * q^47 + 16 * q^48 - 28 * q^49 + 26 * q^51 - 44 * q^52 - 44 * q^53 + 45 * q^56 + 22 * q^57 - 41 * q^58 - 22 * q^59 - 8 * q^61 - 41 * q^62 - 3 * q^63 + 49 * q^64 - 3 * q^66 + 6 * q^67 + 100 * q^68 + 6 * q^69 - 21 * q^71 - 9 * q^72 + 16 * q^73 - 44 * q^74 - 52 * q^76 - q^77 + 19 * q^78 + 10 * q^79 - 3 * q^81 - 26 * q^82 + 10 * q^83 - 6 * q^84 + 56 * q^86 + 4 * q^87 + 16 * q^88 + 57 * q^89 - 7 * q^91 - 3 * q^92 - 22 * q^93 - 23 * q^94 - 23 * q^96 - 4 * q^97 + 18 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	1.74793	−	1.26995i	1.23597	−	0.897987i	0.238650	−	0.971106i	$-0.423295\pi$
$2$	1.74793	−	1.26995i	1.23597	−	0.897987i	0.997323	+	0.0731189i	$0.0232952\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	0.824463	−	2.53744i	0.412232	−	1.26872i
$5$		0			0
$5$		0			0
$6$	−0.667650	−	2.05481i	−0.272567	−	0.838875i
$7$	3.16056			1.19458			0.597290	−	0.802026i	$-0.296244\pi$
$7$	3.16056			1.19458			0.597290	+	0.802026i	$0.296244\pi$
$8$	−0.446002	−	1.37265i	−0.157686	−	0.485307i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	−1.24455	+	0.904220i	−0.375247	+	0.272633i	−0.759383	−	0.650644i	$-0.774499\pi$
$11$	−1.24455	+	0.904220i	−0.375247	+	0.272633i	0.384137	+	0.923276i	$0.374499\pi$
$12$	−2.15847	−	1.56822i	−0.623097	−	0.452707i
$13$	−4.24041	−	3.08084i	−1.17608	−	0.854471i	−0.184355	−	0.982860i	$-0.559019\pi$
$13$	−4.24041	−	3.08084i	−1.17608	−	0.854471i	−0.991724	+	0.128389i	$0.959019\pi$
$14$	5.52444	−	4.01374i	1.47647	−	1.07272i
$15$		0			0
$16$	1.79417	+	1.30354i	0.448542	+	0.325885i
$17$	−0.398843	−	1.22751i	−0.0967337	−	0.297716i	0.890968	−	0.454066i	$-0.150027\pi$
$17$	−0.398843	−	1.22751i	−0.0967337	−	0.297716i	−0.987702	+	0.156351i	$0.950027\pi$
$18$	−2.16056			−0.509249
$19$	1.68287	+	5.17933i	0.386076	+	1.18822i	0.935696	+	0.352806i	$0.114772\pi$
$19$	1.68287	+	5.17933i	0.386076	+	1.18822i	−0.549620	+	0.835415i	$0.685228\pi$
$20$		0			0
$21$	0.976667	−	3.00587i	0.213126	−	0.655935i
$22$	−1.02708	+	3.16103i	−0.218974	+	0.673933i
$23$	−5.21204	+	3.78677i	−1.08679	+	0.789596i	−0.978854	−	0.204562i	$-0.934423\pi$
$23$	−5.21204	+	3.78677i	−1.08679	+	0.789596i	−0.107932	+	0.994158i	$0.534423\pi$
$24$	−1.44329			−0.294611
$25$		0			0
$26$	−11.3244			−2.22090
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	2.60577	−	8.01972i	0.492443	−	1.51558i
$29$	−0.730396	+	2.24793i	−0.135631	+	0.417430i	−0.995688	−	0.0927690i	$-0.970428\pi$
$29$	−0.730396	+	2.24793i	−0.135631	+	0.417430i	0.860056	+	0.510199i	$0.170428\pi$
$30$		0			0
$31$	−1.37989	−	4.24687i	−0.247836	−	0.762760i	−0.995157	−	0.0982974i	$-0.968660\pi$
$31$	−1.37989	−	4.24687i	−0.247836	−	0.762760i	0.747321	−	0.664463i	$-0.231340\pi$
$32$	7.67809			1.35731
$33$	0.475377	+	1.46306i	0.0827525	+	0.254686i
$34$	−2.25602	−	1.63910i	−0.386905	−	0.281103i
$35$		0			0
$36$	−2.15847	+	1.56822i	−0.359745	+	0.261370i
$37$	−4.81973	−	3.50174i	−0.792358	−	0.575682i	0.116304	−	0.993214i	$-0.462895\pi$
$37$	−4.81973	−	3.50174i	−0.792358	−	0.575682i	−0.908662	+	0.417532i	$0.862895\pi$
$38$	9.51901	+	6.91596i	1.54419	+	1.12192i
$39$	−4.24041	+	3.08084i	−0.679009	+	0.493329i
$40$		0			0
$41$	6.90269	+	5.01510i	1.07802	+	0.783227i	0.977336	−	0.211692i	$-0.0678974\pi$
$41$	6.90269	+	5.01510i	1.07802	+	0.783227i	0.100683	+	0.994919i	$0.467897\pi$
$42$	−2.11015	−	6.49436i	−0.325603	−	1.00210i
$43$	8.48426			1.29384			0.646919	−	0.762559i	$-0.276057\pi$
$43$	8.48426			1.29384			0.646919	+	0.762559i	$0.276057\pi$
$44$	1.26831	+	3.90347i	0.191206	+	0.588470i
$45$		0			0
$46$	−4.30129	+	13.2380i	−0.634191	+	1.95184i
$47$	−0.232712	+	0.716212i	−0.0339445	+	0.104470i	−0.966593	−	0.256315i	$-0.917491\pi$
$47$	−0.232712	+	0.716212i	−0.0339445	+	0.104470i	0.932649	+	0.360786i	$0.117491\pi$
$48$	1.79417	−	1.30354i	0.258966	−	0.188150i
$49$	2.98914			0.427020
$50$		0			0
$51$	−1.29068			−0.180732
$52$	−11.3135	+	8.21974i	−1.56890	+	1.13987i
$53$	−3.01289	+	9.27271i	−0.413852	+	1.27371i	0.499422	+	0.866359i	$0.333546\pi$
$53$	−3.01289	+	9.27271i	−0.413852	+	1.27371i	−0.913274	+	0.407346i	$0.866454\pi$
$54$	−0.667650	+	2.05481i	−0.0908556	+	0.279625i
$55$		0			0
$56$	−1.40962	−	4.33836i	−0.188368	−	0.579737i
$57$	5.44587			0.721324
$58$	1.57806	+	4.85678i	0.207210	+	0.637727i
$59$	−3.32724	−	2.41738i	−0.433170	−	0.314717i	0.349745	−	0.936845i	$-0.386268\pi$
$59$	−3.32724	−	2.41738i	−0.433170	−	0.314717i	−0.782915	+	0.622128i	$0.786268\pi$
$60$		0			0
$61$	8.65159	−	6.28574i	1.10772	−	0.804807i	0.125419	−	0.992104i	$-0.459973\pi$
$61$	8.65159	−	6.28574i	1.10772	−	0.804807i	0.982303	+	0.187297i	$0.0599726\pi$
$62$	−7.80525	−	5.67084i	−0.991267	−	0.720198i
$63$	−2.55695	−	1.85773i	−0.322145	−	0.234052i
$64$	9.83243	−	7.14368i	1.22905	−	0.892960i
$65$		0			0
$66$	2.68893	+	1.95362i	0.330984	+	0.240474i
$67$	0.586713	+	1.80572i	0.0716785	+	0.220604i	0.980478	−	0.196630i	$-0.0629997\pi$
$67$	0.586713	+	1.80572i	0.0716785	+	0.220604i	−0.908799	+	0.417233i	$0.863000\pi$
$68$	−3.44357			−0.417594
$69$	1.99082	+	6.12712i	0.239667	+	0.737619i
$70$		0			0
$71$	−0.0219023	+	0.0674084i	−0.00259933	+	0.00799990i	−0.952348	−	0.305014i	$-0.901339\pi$
$71$	−0.0219023	+	0.0674084i	−0.00259933	+	0.00799990i	0.949748	+	0.313014i	$0.101339\pi$
$72$	−0.446002	+	1.37265i	−0.0525619	+	0.161769i
$73$	3.24515	−	2.35774i	0.379816	−	0.275952i	−0.381454	−	0.924388i	$-0.624576\pi$
$73$	3.24515	−	2.35774i	0.379816	−	0.275952i	0.761270	+	0.648436i	$0.224576\pi$
$74$	−12.8716			−1.49629
$75$		0			0
$76$	14.5297			1.66667
$77$	−3.93348	+	2.85784i	−0.448262	+	0.325681i
$78$	−3.49944	+	10.7702i	−0.396234	+	1.21948i
$79$	0.500141	−	1.53928i	0.0562703	−	0.173182i	−0.918971	−	0.394325i	$-0.870979\pi$
$79$	0.500141	−	1.53928i	0.0562703	−	0.173182i	0.975242	+	0.221143i	$0.0709786\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	18.4343			2.03573
$83$	−4.06322	−	12.5053i	−0.445996	−	1.37263i	−0.881388	−	0.472393i	$-0.843390\pi$
$83$	−4.06322	−	12.5053i	−0.445996	−	1.37263i	0.435392	−	0.900241i	$-0.356610\pi$
$84$	−6.82198	−	4.95646i	−0.744339	−	0.540794i
$85$		0			0
$86$	14.8299	−	10.7745i	1.59915	−	1.16185i
$87$	1.91220	+	1.38930i	0.205010	+	0.148948i
$88$	1.79626	+	1.30506i	0.191481	+	0.139119i
$89$	−5.88638	+	4.27671i	−0.623955	+	0.453330i	−0.854301	−	0.519779i	$-0.826014\pi$
$89$	−5.88638	+	4.27671i	−0.623955	+	0.453330i	0.230345	+	0.973109i	$0.426014\pi$
$90$		0			0
$91$	−13.4021	−	9.73718i	−1.40492	−	1.02073i
$92$	5.31155	+	16.3473i	0.553768	+	1.70432i
$93$	−4.46542			−0.463043
$94$	0.502787	+	1.54742i	0.0518585	+	0.159604i
$95$		0			0
$96$	2.37266	−	7.30230i	0.242159	−	0.745288i
$97$	−3.15009	+	9.69499i	−0.319843	+	0.984377i	0.653871	+	0.756606i	$0.273144\pi$
$97$	−3.15009	+	9.69499i	−0.319843	+	0.984377i	−0.973715	+	0.227771i	$0.926856\pi$
$98$	5.22480	−	3.79604i	0.527785	−	0.383458i
$99$	1.53835			0.154610
$100$		0			0
$101$	1.08759			0.108219			0.0541096	−	0.998535i	$-0.482768\pi$
$101$	1.08759			0.108219			0.0541096	+	0.998535i	$0.482768\pi$
$102$	−2.25602	+	1.63910i	−0.223380	+	0.162295i
$103$	1.52579	−	4.69590i	0.150341	−	0.462701i	−0.847319	−	0.531085i	$-0.821784\pi$
$103$	1.52579	−	4.69590i	0.150341	−	0.462701i	0.997659	+	0.0683845i	$0.0217845\pi$
$104$	−2.33769	+	7.19468i	−0.229230	+	0.705497i
$105$		0			0
$106$	6.50952	+	20.0343i	0.632261	+	1.94590i
$107$	−15.3059			−1.47967			−0.739837	−	0.672786i	$-0.765098\pi$
$107$	−15.3059			−1.47967			−0.739837	+	0.672786i	$0.765098\pi$
$108$	0.824463	+	2.53744i	0.0793340	+	0.244165i
$109$	−5.38724	−	3.91406i	−0.516004	−	0.374899i	0.299092	−	0.954224i	$-0.403316\pi$
$109$	−5.38724	−	3.91406i	−0.516004	−	0.374899i	−0.815097	+	0.579325i	$0.803316\pi$
$110$		0			0
$111$	−4.81973	+	3.50174i	−0.457468	+	0.332370i
$112$	5.67058	+	4.11991i	0.535819	+	0.389295i
$113$	−7.25804	−	5.27328i	−0.682779	−	0.496068i	0.191499	−	0.981493i	$-0.438665\pi$
$113$	−7.25804	−	5.27328i	−0.682779	−	0.496068i	−0.874278	+	0.485425i	$0.838665\pi$
$114$	9.51901	−	6.91596i	0.891537	−	0.647739i
$115$		0			0
$116$	5.10179	+	3.70667i	0.473689	+	0.344155i
$117$	1.61969	+	4.98490i	0.149741	+	0.460854i
$118$	−8.88573			−0.817998
$119$	−1.26057	−	3.87963i	−0.115556	−	0.355645i
$120$		0			0
$121$	−2.66789	+	8.21092i	−0.242536	+	0.746448i
$122$	7.13981	−	21.9741i	0.646408	−	1.98944i
$123$	6.90269	−	5.01510i	0.622395	−	0.452196i
$124$	−11.9138			−1.06989
$125$		0			0
$126$	−6.82858			−0.608338
$127$	8.10511	−	5.88870i	0.719212	−	0.522538i	−0.166920	−	0.985970i	$-0.553382\pi$
$127$	8.10511	−	5.88870i	0.719212	−	0.522538i	0.886132	+	0.463432i	$0.153382\pi$
$128$	3.36899	−	10.3687i	0.297780	−	0.916471i
$129$	2.62178	−	8.06901i	0.230835	−	0.710437i
$130$		0			0
$131$	−1.97111	−	6.06645i	−0.172217	−	0.530029i	0.827279	−	0.561792i	$-0.189888\pi$
$131$	−1.97111	−	6.06645i	−0.172217	−	0.530029i	−0.999495	+	0.0317631i	$0.989888\pi$
$132$	4.10435			0.357238
$133$	5.31880	+	16.3696i	0.461199	+	1.41942i
$134$	3.31870	+	2.41117i	0.286692	+	0.208294i
$135$		0			0
$136$	−1.50707	+	1.09495i	−0.129230	+	0.0938910i
$137$	−7.42461	−	5.39429i	−0.634327	−	0.460866i	0.223570	−	0.974688i	$-0.428229\pi$
$137$	−7.42461	−	5.39429i	−0.634327	−	0.460866i	−0.857897	+	0.513822i	$0.828229\pi$
$138$	11.2609	+	8.18154i	0.958594	+	0.696459i
$139$	7.49586	−	5.44606i	0.635790	−	0.461929i	−0.222611	−	0.974907i	$-0.571458\pi$
$139$	7.49586	−	5.44606i	0.635790	−	0.461929i	0.858401	+	0.512979i	$0.171458\pi$
$140$		0			0
$141$	0.609247	+	0.442644i	0.0513078	+	0.0372773i
$142$	0.0473213	+	0.145640i	0.00397111	+	0.0122218i
$143$	8.06317			0.674276
$144$	−0.685311	−	2.10917i	−0.0571093	−	0.175764i
$145$		0			0
$146$	2.67809	−	8.24232i	0.221641	−	0.682140i
$147$	0.923695	−	2.84284i	0.0761850	−	0.234473i
$148$	−12.8591	+	9.34270i	−1.05701	+	0.767965i
$149$	−10.0817			−0.825928			−0.412964	−	0.910747i	$-0.635506\pi$
$149$	−10.0817			−0.825928			−0.412964	+	0.910747i	$0.635506\pi$
$150$		0			0
$151$	10.7375			0.873804			0.436902	−	0.899509i	$-0.356076\pi$
$151$	10.7375			0.873804			0.436902	+	0.899509i	$0.356076\pi$
$152$	6.35887	−	4.61999i	0.515773	−	0.374731i
$153$	−0.398843	+	1.22751i	−0.0322446	+	0.0992385i
$154$	−3.24615	+	9.99061i	−0.261582	+	0.805067i
$155$		0			0
$156$	4.32137	+	13.2998i	0.345987	+	1.06484i
$157$	−17.4417			−1.39200			−0.696001	−	0.718041i	$-0.745039\pi$
$157$	−17.4417			−1.39200			−0.696001	+	0.718041i	$0.745039\pi$
$158$	−1.08058	−	3.32570i	−0.0859667	−	0.264578i
$159$	7.88784	+	5.73085i	0.625546	+	0.454486i
$160$		0			0
$161$	−16.4730	+	11.9683i	−1.29825	+	0.943235i
$162$	1.74793	+	1.26995i	0.137330	+	0.0997763i
$163$	−13.1525	−	9.55586i	−1.03018	−	0.748473i	−0.0618392	−	0.998086i	$-0.519697\pi$
$163$	−13.1525	−	9.55586i	−1.03018	−	0.748473i	−0.968346	+	0.249613i	$0.919697\pi$
$164$	18.4165	−	13.3804i	1.43809	−	1.04483i
$165$		0			0
$166$	−22.9832	−	16.6983i	−1.78385	−	1.29604i
$167$	3.51989	+	10.8331i	0.272377	+	0.838290i	0.989902	+	0.141757i	$0.0452751\pi$
$167$	3.51989	+	10.8331i	0.272377	+	0.838290i	−0.717525	+	0.696533i	$0.754725\pi$
$168$	−4.56162			−0.351936
$169$	4.47230	+	13.7643i	0.344023	+	1.05879i
$170$		0			0
$171$	1.68287	−	5.17933i	0.128692	−	0.396074i
$172$	6.99496	−	21.5283i	0.533361	−	1.64152i
$173$	7.65205	−	5.55954i	0.581775	−	0.422684i	−0.257589	−	0.966255i	$-0.582928\pi$
$173$	7.65205	−	5.55954i	0.581775	−	0.422684i	0.839363	+	0.543571i	$0.182928\pi$
$174$	5.10672			0.387140
$175$		0			0
$176$	−3.41162			−0.257161
$177$	−3.32724	+	2.41738i	−0.250091	+	0.181702i
$178$	−4.85780	+	14.9508i	−0.364107	+	1.12061i
$179$	1.26001	−	3.87790i	0.0941773	−	0.289848i	−0.892861	−	0.450332i	$-0.851306\pi$
$179$	1.26001	−	3.87790i	0.0941773	−	0.289848i	0.987038	+	0.160484i	$0.0513056\pi$
$180$		0			0
$181$	−3.43633	−	10.5759i	−0.255421	−	0.786104i	−0.993747	−	0.111660i	$-0.964383\pi$
$181$	−3.43633	−	10.5759i	−0.255421	−	0.786104i	0.738326	−	0.674444i	$-0.235617\pi$
$182$	−35.7916			−2.65305
$183$	−3.30461	−	10.1705i	−0.244284	−	0.751829i
$184$	7.52251	+	5.46542i	0.554567	+	0.402916i
$185$		0			0
$186$	−7.80525	+	5.67084i	−0.572308	+	0.415806i
$187$	1.60632	+	1.16706i	0.117466	+	0.0853440i
$188$	1.62548	+	1.18098i	0.118550	+	0.0861319i
$189$	−2.55695	+	1.85773i	−0.185990	+	0.135130i
$190$		0			0
$191$	−2.92164	−	2.12270i	−0.211403	−	0.153593i	0.477046	−	0.878879i	$-0.341708\pi$
$191$	−2.92164	−	2.12270i	−0.211403	−	0.153593i	−0.688448	+	0.725286i	$0.741708\pi$
$192$	−3.75565	−	11.5587i	−0.271041	−	0.834178i
$193$	17.0562			1.22774			0.613868	−	0.789409i	$-0.289613\pi$
$193$	17.0562			1.22774			0.613868	+	0.789409i	$0.289613\pi$
$194$	6.80596	+	20.9466i	0.488640	+	1.50388i
$195$		0			0
$196$	2.46443	−	7.58475i	0.176031	−	0.541768i
$197$	1.36129	−	4.18963i	0.0969880	−	0.298498i	−0.890779	−	0.454437i	$-0.849840\pi$
$197$	1.36129	−	4.18963i	0.0969880	−	0.298498i	0.987767	+	0.155939i	$0.0498403\pi$
$198$	2.68893	−	1.95362i	0.191094	−	0.138838i
$199$	16.5956			1.17643			0.588214	−	0.808705i	$-0.299831\pi$
$199$	16.5956			1.17643			0.588214	+	0.808705i	$0.299831\pi$
$200$		0			0
$201$	1.89864			0.133920
$202$	1.90103	−	1.38118i	0.133756	−	0.0971795i
$203$	−2.30846	+	7.10471i	−0.162022	+	0.498653i
$204$	−1.06412	+	3.27503i	−0.0745034	+	0.229298i
$205$		0			0
$206$	−3.29656	−	10.1458i	−0.229682	−	0.706889i
$207$	6.44244			0.447780
$208$	−3.59202	−	11.0551i	−0.249061	−	0.766532i
$209$	−6.77768	−	4.92427i	−0.468822	−	0.340619i
$210$		0			0
$211$	−15.0035	+	10.9007i	−1.03288	+	0.750434i	−0.968884	−	0.247516i	$-0.920386\pi$
$211$	−15.0035	+	10.9007i	−1.03288	+	0.750434i	−0.0640001	+	0.997950i	$0.520386\pi$
$212$	21.0449	+	15.2900i	1.44537	+	1.05012i
$213$	0.0573410	+	0.0416607i	0.00392894	+	0.00285454i
$214$	−26.7536	+	19.4376i	−1.82884	+	1.32873i
$215$		0			0
$216$	1.16765	+	0.848347i	0.0794485	+	0.0577227i
$217$	−4.36123	−	13.4225i	−0.296060	−	0.911178i
$218$	−14.3872			−0.974422
$219$	−1.23954	−	3.81490i	−0.0837601	−	0.257787i
$220$		0			0
$221$	−2.09051	+	6.43393i	−0.140623	+	0.432793i
$222$	−3.97753	+	12.2416i	−0.266954	+	0.821601i
$223$	−0.624203	+	0.453510i	−0.0417997	+	0.0303693i	−0.608489	−	0.793562i	$-0.708224\pi$
$223$	−0.624203	+	0.453510i	−0.0417997	+	0.0303693i	0.566689	+	0.823932i	$0.308224\pi$
$224$	24.2671			1.62141
$225$		0			0
$226$	−19.3833			−1.28936
$227$	9.24817	−	6.71919i	0.613823	−	0.445968i	−0.236936	−	0.971525i	$-0.576143\pi$
$227$	9.24817	−	6.71919i	0.613823	−	0.445968i	0.850758	+	0.525557i	$0.176143\pi$
$228$	4.48992	−	13.8186i	0.297352	−	0.915157i
$229$	3.15962	−	9.72432i	0.208794	−	0.642601i	−0.790743	−	0.612149i	$-0.790305\pi$
$229$	3.15962	−	9.72432i	0.208794	−	0.642601i	0.999536	−	0.0304520i	$-0.00969467\pi$
$230$		0			0
$231$	1.50246	+	4.62409i	0.0988544	+	0.304242i
$232$	3.41139			0.223969
$233$	6.95997	+	21.4206i	0.455963	+	1.40331i	0.870001	+	0.493050i	$0.164118\pi$
$233$	6.95997	+	21.4206i	0.455963	+	1.40331i	−0.414038	+	0.910260i	$0.635882\pi$
$234$	9.16166	+	6.65634i	0.598917	+	0.435138i
$235$		0			0
$236$	−8.87715	+	6.44963i	−0.577853	+	0.419835i
$237$	−1.30939	−	0.951325i	−0.0850538	−	0.0617952i
$238$	−7.13030	−	5.18047i	−0.462189	−	0.335800i
$239$	0.476571	−	0.346249i	0.0308268	−	0.0223970i	−0.572265	−	0.820069i	$-0.693935\pi$
$239$	0.476571	−	0.346249i	0.0308268	−	0.0223970i	0.603092	+	0.797672i	$0.293935\pi$
$240$		0			0
$241$	−1.22110	−	0.887185i	−0.0786583	−	0.0571486i	0.547761	−	0.836635i	$-0.315480\pi$
$241$	−1.22110	−	0.887185i	−0.0786583	−	0.0571486i	−0.626419	+	0.779486i	$0.715480\pi$
$242$	5.76414	+	17.7402i	0.370533	+	1.14038i
$243$	1.00000			0.0641500
$244$	−8.81677	−	27.1352i	−0.564436	−	1.73715i
$245$		0			0
$246$	5.69652	−	17.5321i	0.363197	−	1.11780i
$247$	8.82065	−	27.1472i	0.561244	−	1.72733i
$248$	−5.21405	+	3.78823i	−0.331093	+	0.240553i
$249$	−13.1488			−0.833274
$250$		0			0
$251$	11.8953			0.750823			0.375412	−	0.926858i	$-0.377501\pi$
$251$	11.8953			0.750823			0.375412	+	0.926858i	$0.377501\pi$
$252$	−6.82198	+	4.95646i	−0.429744	+	0.312228i
$253$	3.06258	−	9.42567i	0.192543	−	0.592587i
$254$	6.68882	−	20.5861i	0.419694	−	1.29169i
$255$		0			0
$256$	0.232398	+	0.715248i	0.0145249	+	0.0447030i
$257$	18.0492			1.12588			0.562939	−	0.826498i	$-0.309671\pi$
$257$	18.0492			1.12588			0.562939	+	0.826498i	$0.309671\pi$
$258$	−5.66451	−	17.4336i	−0.352657	−	1.08537i
$259$	−15.2330	−	11.0674i	−0.946534	−	0.687698i
$260$		0			0
$261$	1.91220	−	1.38930i	0.118362	−	0.0859953i
$262$	−11.1494	−	8.10053i	−0.688814	−	0.500453i
$263$	−15.4576	−	11.2306i	−0.953157	−	0.692509i	−0.00160518	−	0.999999i	$-0.500511\pi$
$263$	−15.4576	−	11.2306i	−0.953157	−	0.692509i	−0.951551	+	0.307490i	$0.900511\pi$
$264$	1.79626	−	1.30506i	0.110552	−	0.0803206i
$265$		0			0
$266$	30.0854	+	21.8583i	1.84465	+	1.34022i
$267$	2.24840	+	6.91986i	0.137600	+	0.423489i
$268$	5.06562			0.309432
$269$	−6.86791	−	21.1372i	−0.418744	−	1.28876i	−0.908859	−	0.417103i	$-0.863045\pi$
$269$	−6.86791	−	21.1372i	−0.418744	−	1.28876i	0.490115	−	0.871658i	$-0.336955\pi$
$270$		0			0
$271$	6.24546	−	19.2216i	0.379385	−	1.16763i	−0.561088	−	0.827756i	$-0.689617\pi$
$271$	6.24546	−	19.2216i	0.379385	−	1.16763i	0.940472	−	0.339870i	$-0.110383\pi$
$272$	0.884520	−	2.72227i	0.0536319	−	0.165062i
$273$	−13.4021	+	9.73718i	−0.811130	+	0.589321i
$274$	−19.8281			−1.19786
$275$		0			0
$276$	17.1885			1.03463
$277$	−12.9777	+	9.42882i	−0.779752	+	0.566523i	−0.904904	−	0.425615i	$-0.860058\pi$
$277$	−12.9777	+	9.42882i	−0.779752	+	0.566523i	0.125153	+	0.992137i	$0.460058\pi$
$278$	6.18604	−	19.0387i	0.371014	−	1.14186i
$279$	−1.37989	+	4.24687i	−0.0826120	+	0.254253i
$280$		0			0
$281$	2.58742	+	7.96327i	0.154353	+	0.475049i	0.998095	−	0.0617001i	$-0.0196522\pi$
$281$	2.58742	+	7.96327i	0.154353	+	0.475049i	−0.843742	+	0.536749i	$0.819652\pi$
$282$	1.62705			0.0968896
$283$	0.349174	+	1.07465i	0.0207562	+	0.0638811i	0.960898	−	0.276902i	$-0.0893078\pi$
$283$	0.349174	+	1.07465i	0.0207562	+	0.0638811i	−0.940142	+	0.340783i	$0.889308\pi$
$284$	0.152987	+	0.111151i	0.00907810	+	0.00659563i
$285$		0			0
$286$	14.0939	−	10.2398i	0.833387	−	0.605491i
$287$	21.8164	+	15.8505i	1.28778	+	0.935626i
$288$	−6.21171	−	4.51307i	−0.366028	−	0.265935i
$289$	12.4056	−	9.01318i	0.729740	−	0.530187i
$290$		0			0
$291$	8.24705	+	5.99183i	0.483451	+	0.351247i
$292$	−3.30711	−	10.1782i	−0.193534	−	0.595636i
$293$	2.37857			0.138958			0.0694789	−	0.997583i	$-0.477866\pi$
$293$	2.37857			0.138958			0.0694789	+	0.997583i	$0.477866\pi$
$294$	−1.99570	−	6.14212i	−0.116391	−	0.358216i
$295$		0			0
$296$	−2.65706	+	8.17760i	−0.154439	+	0.475313i
$297$	0.475377	−	1.46306i	0.0275842	−	0.0848953i
$298$	−17.6222	+	12.8032i	−1.02082	+	0.741672i
$299$	33.7676			1.95283
$300$		0			0
$301$	26.8150			1.54559
$302$	18.7684	−	13.6360i	1.08000	−	0.784665i
$303$	0.336084	−	1.03436i	0.0193075	−	0.0594224i
$304$	−3.73212	+	11.4863i	−0.214052	+	0.658783i
$305$		0			0
$306$	0.861724	+	2.65212i	0.0492615	+	0.151611i
$307$	−2.89366			−0.165150			−0.0825748	−	0.996585i	$-0.526314\pi$
$307$	−2.89366			−0.165150			−0.0825748	+	0.996585i	$0.526314\pi$
$308$	4.00858	+	12.3371i	0.228410	+	0.702974i
$309$	−3.99457	−	2.90222i	−0.227243	−	0.165102i
$310$		0			0
$311$	5.78079	−	4.19999i	0.327799	−	0.238160i	−0.411697	−	0.911321i	$-0.635064\pi$
$311$	5.78079	−	4.19999i	0.327799	−	0.238160i	0.739496	+	0.673161i	$0.235064\pi$
$312$	6.12016	+	4.44656i	0.346486	+	0.251737i
$313$	18.6331	+	13.5378i	1.05321	+	0.765200i	0.972820	−	0.231563i	$-0.0743841\pi$
$313$	18.6331	+	13.5378i	1.05321	+	0.765200i	0.0803879	+	0.996764i	$0.474384\pi$
$314$	−30.4869	+	22.1500i	−1.72048	+	1.25000i
$315$		0			0
$316$	−3.49347	−	2.53815i	−0.196523	−	0.142782i
$317$	6.41981	+	19.7582i	0.360573	+	1.10973i	0.952707	+	0.303890i	$0.0982854\pi$
$317$	6.41981	+	19.7582i	0.360573	+	1.10973i	−0.592135	+	0.805839i	$0.701715\pi$
$318$	21.0653			1.18128
$319$	−1.12361	−	3.45810i	−0.0629098	−	0.193617i
$320$		0			0
$321$	−4.72978	+	14.5568i	−0.263990	+	0.812479i
$322$	−13.5945	+	41.8395i	−0.757591	+	2.33163i
$323$	5.68650	−	4.13148i	0.316405	−	0.229882i
$324$	2.66802			0.148223
$325$		0			0
$326$	−35.1251			−1.94540
$327$	−5.38724	+	3.91406i	−0.297915	+	0.216448i
$328$	3.80538	−	11.7118i	0.210117	−	0.646673i
$329$	−0.735499	+	2.26363i	−0.0405494	+	0.124798i
$330$		0			0
$331$	−5.94869	−	18.3082i	−0.326969	−	1.00631i	−0.970544	−	0.240925i	$-0.922549\pi$
$331$	−5.94869	−	18.3082i	−0.326969	−	1.00631i	0.643574	−	0.765383i	$-0.277451\pi$
$332$	−35.0814			−1.92534
$333$	1.84097	+	5.66593i	0.100885	+	0.310491i
$334$	19.9099	+	14.4654i	1.08942	+	0.791513i
$335$		0			0
$336$	5.67058	−	4.11991i	0.309355	−	0.224760i
$337$	17.5609	+	12.7587i	0.956602	+	0.695012i	0.952359	−	0.304979i	$-0.0986494\pi$
$337$	17.5609	+	12.7587i	0.956602	+	0.695012i	0.00424305	+	0.999991i	$0.498649\pi$
$338$	25.2972	+	18.3795i	1.37599	+	0.999712i
$339$	−7.25804	+	5.27328i	−0.394203	+	0.286405i
$340$		0			0
$341$	5.55745	+	4.03773i	0.300953	+	0.218655i
$342$	−3.63594	−	11.1903i	−0.196609	−	0.605100i
$343$	−12.6766			−0.684470
$344$	−3.78400	−	11.6460i	−0.204020	−	0.627908i
$345$		0			0
$346$	6.31493	−	19.4354i	0.339493	−	1.04485i
$347$	0.529944	−	1.63100i	0.0284489	−	0.0875567i	−0.935824	−	0.352468i	$-0.885343\pi$
$347$	0.529944	−	1.63100i	0.0284489	−	0.0875567i	0.964273	+	0.264911i	$0.0853426\pi$
$348$	5.10179	−	3.70667i	0.273485	−	0.198698i
$349$	−15.5553			−0.832654			−0.416327	−	0.909215i	$-0.636683\pi$
$349$	−15.5553			−0.832654			−0.416327	+	0.909215i	$0.636683\pi$
$350$		0			0
$351$	5.24144			0.279767
$352$	−9.55579	+	6.94268i	−0.509325	+	0.370046i
$353$	−4.80632	+	14.7923i	−0.255814	+	0.787316i	0.737854	+	0.674961i	$0.235839\pi$
$353$	−4.80632	+	14.7923i	−0.255814	+	0.787316i	−0.993668	+	0.112355i	$0.964161\pi$
$354$	−2.74584	+	8.45083i	−0.145940	+	0.449157i
$355$		0			0
$356$	5.99877	+	18.4623i	0.317934	+	0.978501i
$357$	−4.07928			−0.215899
$358$	−2.72232	−	8.37844i	−0.143879	−	0.442814i
$359$	19.8509	+	14.4225i	1.04769	+	0.761191i	0.971772	−	0.235923i	$-0.0758112\pi$
$359$	19.8509	+	14.4225i	1.04769	+	0.761191i	0.0759181	+	0.997114i	$0.475811\pi$
$360$		0			0
$361$	−8.62214	+	6.26435i	−0.453797	+	0.329703i
$362$	−19.4373	−	14.1221i	−1.02160	−	0.742239i
$363$	6.98463	+	5.07463i	0.366598	+	0.266349i
$364$	−35.7570	+	25.9790i	−1.87418	+	1.36167i
$365$		0			0
$366$	−18.6923	−	13.5807i	−0.977060	−	0.709876i
$367$	−8.68548	−	26.7311i	−0.453378	−	1.39535i	−0.873029	−	0.487669i	$-0.837847\pi$
$367$	−8.68548	−	26.7311i	−0.453378	−	1.39535i	0.419651	−	0.907686i	$-0.362153\pi$
$368$	−14.2875			−0.744786
$369$	−2.63659	−	8.11460i	−0.137256	−	0.422429i
$370$		0			0
$371$	−9.52241	+	29.3070i	−0.494379	+	1.52154i
$372$	−3.68158	+	11.3307i	−0.190881	+	0.587471i
$373$	−7.85414	+	5.70637i	−0.406672	+	0.295464i	−0.772253	−	0.635315i	$-0.780870\pi$
$373$	−7.85414	+	5.70637i	−0.406672	+	0.295464i	0.365581	+	0.930779i	$0.380870\pi$
$374$	4.28984			0.221823
$375$		0			0
$376$	1.08690			0.0560527
$377$	10.0227	−	7.28191i	0.516195	−	0.375037i
$378$	−2.11015	+	6.49436i	−0.108534	+	0.334034i
$379$	−6.88071	+	21.1767i	−0.353438	+	1.08777i	0.603471	+	0.797385i	$0.293784\pi$
$379$	−6.88071	+	21.1767i	−0.353438	+	1.08777i	−0.956909	+	0.290387i	$0.906216\pi$
$380$		0			0
$381$	−3.09587	−	9.52812i	−0.158606	−	0.488141i
$382$	−7.80253			−0.399212
$383$	4.21189	+	12.9628i	0.215217	+	0.662371i	0.999138	+	0.0415099i	$0.0132168\pi$
$383$	4.21189	+	12.9628i	0.215217	+	0.662371i	−0.783921	+	0.620861i	$0.786783\pi$
$384$	−8.82014	−	6.40820i	−0.450101	−	0.327017i
$385$		0			0
$386$	29.8131	−	21.6605i	1.51745	−	1.10249i
$387$	−6.86391	−	4.98692i	−0.348912	−	0.253500i
$388$	22.0033	+	15.9863i	1.11705	+	0.811582i
$389$	−15.5577	+	11.3034i	−0.788808	+	0.573103i	−0.907610	−	0.419815i	$-0.862095\pi$
$389$	−15.5577	+	11.3034i	−0.788808	+	0.573103i	0.118801	+	0.992918i	$0.462095\pi$
$390$		0			0
$391$	6.72710	+	4.88752i	0.340204	+	0.247173i
$392$	−1.33316	−	4.10305i	−0.0673349	−	0.207236i
$393$	−6.37865			−0.321760
$394$	−2.94115	−	9.05194i	−0.148173	−	0.456030i
$395$		0			0
$396$	1.26831	−	3.90347i	0.0637352	−	0.196157i
$397$	−6.86887	+	21.1402i	−0.344739	+	1.06100i	0.616984	+	0.786975i	$0.288354\pi$
$397$	−6.86887	+	21.1402i	−0.344739	+	1.06100i	−0.961723	+	0.274022i	$0.911646\pi$
$398$	29.0079	−	21.0755i	1.45403	−	1.05642i
$399$	17.2120			0.861678
$400$		0			0
$401$	4.71728			0.235570			0.117785	−	0.993039i	$-0.462421\pi$
$401$	4.71728			0.235570			0.117785	+	0.993039i	$0.462421\pi$
$402$	3.31870	−	2.41117i	0.165522	−	0.120258i
$403$	−7.23261	+	22.2597i	−0.360282	+	1.10883i
$404$	0.896678	−	2.75969i	0.0446114	−	0.137300i
$405$		0			0
$406$	4.98757	+	15.3502i	0.247529	+	0.761815i
$407$	9.16474			0.454279
$408$	0.575648	+	1.77166i	0.0284988	+	0.0877104i
$409$	10.0971	+	7.33597i	0.499269	+	0.362740i	0.808738	−	0.588169i	$-0.200151\pi$
$409$	10.0971	+	7.33597i	0.499269	+	0.362740i	−0.309469	+	0.950910i	$0.600151\pi$
$410$		0			0
$411$	−7.42461	+	5.39429i	−0.366229	+	0.266081i
$412$	−10.6576	−	7.74319i	−0.525062	−	0.381480i
$413$	−10.5160	−	7.64029i	−0.517456	−	0.375954i
$414$	11.2609	−	8.18154i	0.553444	−	0.402101i
$415$		0			0
$416$	−32.5583	−	23.6550i	−1.59630	−	1.15978i
$417$	−2.86316	−	8.81191i	−0.140210	−	0.431521i
$418$	−18.1005			−0.885322
$419$	10.7996	+	33.2379i	0.527597	+	1.62378i	0.759123	+	0.650947i	$0.225628\pi$
$419$	10.7996	+	33.2379i	0.527597	+	1.62378i	−0.231527	+	0.972829i	$0.574372\pi$
$420$		0			0
$421$	−12.2247	+	37.6239i	−0.595797	+	1.83368i	−0.0450804	+	0.998983i	$0.514354\pi$
$421$	−12.2247	+	37.6239i	−0.595797	+	1.83368i	−0.550717	+	0.834692i	$0.685646\pi$
$422$	−12.3818	+	38.1073i	−0.602737	+	1.85503i
$423$	0.609247	−	0.442644i	0.0296226	−	0.0215221i
$424$	14.0720			0.683396
$425$		0			0
$426$	0.153135			0.00741940
$427$	27.3439	−	19.8665i	1.32326	−	0.961406i
$428$	−12.6191	+	38.8377i	−0.609969	+	1.87729i
$429$	2.49166	−	7.66853i	0.120298	−	0.370240i
$430$		0			0
$431$	−4.34429	−	13.3703i	−0.209257	−	0.644027i	−0.999512	−	0.0312481i	$-0.990052\pi$
$431$	−4.34429	−	13.3703i	−0.209257	−	0.644027i	0.790255	−	0.612778i	$-0.209948\pi$
$432$	−2.21771			−0.106700
$433$	0.169860	+	0.522775i	0.00816294	+	0.0251230i	0.955055	−	0.296429i	$-0.0957957\pi$
$433$	0.169860	+	0.522775i	0.00816294	+	0.0251230i	−0.946892	+	0.321552i	$0.895796\pi$
$434$	−24.6689	−	17.9230i	−1.18415	−	0.860333i
$435$		0			0
$436$	−14.3733	+	10.4428i	−0.688355	+	0.500119i
$437$	−28.3841	−	20.6223i	−1.35780	−	0.986497i
$438$	−7.01134	−	5.09404i	−0.335015	−	0.243402i
$439$	2.40583	−	1.74794i	0.114824	−	0.0834245i	−0.528891	−	0.848690i	$-0.677392\pi$
$439$	2.40583	−	1.74794i	0.114824	−	0.0834245i	0.643715	+	0.765265i	$0.277392\pi$
$440$		0			0
$441$	−2.41826	−	1.75697i	−0.115155	−	0.0836653i
$442$	4.51667	+	13.9009i	0.214836	+	0.661198i
$443$	36.6893			1.74316			0.871580	−	0.490253i	$-0.163095\pi$
$443$	36.6893			1.74316			0.871580	+	0.490253i	$0.163095\pi$
$444$	4.91175	+	15.1168i	0.233101	+	0.717412i
$445$		0			0
$446$	−0.515130	+	1.58541i	−0.0243921	+	0.0750712i
$447$	−3.11543	+	9.58830i	−0.147355	+	0.453511i
$448$	31.0760	−	22.5780i	1.46820	−	1.06671i
$449$	−17.8432			−0.842071			−0.421036	−	0.907044i	$-0.638333\pi$
$449$	−17.8432			−0.842071			−0.421036	+	0.907044i	$0.638333\pi$
$450$		0			0
$451$	−13.1255			−0.618056
$452$	−19.3646	+	14.0692i	−0.910834	+	0.661759i
$453$	3.31807	−	10.2120i	0.155896	−	0.479800i
$454$	7.63215	−	23.4893i	0.358195	−	1.10241i
$455$		0			0
$456$	−2.42887	−	7.47530i	−0.113742	−	0.350063i
$457$	24.1784			1.13102			0.565509	−	0.824742i	$-0.308680\pi$
$457$	24.1784			1.13102			0.565509	+	0.824742i	$0.308680\pi$
$458$	−6.82655	−	21.0100i	−0.318984	−	0.981731i
$459$	1.04418	+	0.758645i	0.0487384	+	0.0354105i
$460$		0			0
$461$	30.2470	−	21.9757i	1.40874	−	1.02351i	0.415240	−	0.909712i	$-0.363698\pi$
$461$	30.2470	−	21.9757i	1.40874	−	1.02351i	0.993504	−	0.113800i	$-0.0363024\pi$
$462$	8.49852	+	6.17454i	0.395387	+	0.287266i
$463$	16.5294	+	12.0093i	0.768186	+	0.558120i	0.901410	−	0.432966i	$-0.142533\pi$
$463$	16.5294	+	12.0093i	0.768186	+	0.558120i	−0.133224	+	0.991086i	$0.542533\pi$
$464$	−4.24072	+	3.08106i	−0.196870	+	0.143035i
$465$		0			0
$466$	39.3685	+	28.6029i	1.82371	+	1.32500i
$467$	−9.64517	−	29.6848i	−0.446325	−	1.37365i	−0.881024	−	0.473072i	$-0.843145\pi$
$467$	−9.64517	−	29.6848i	−0.446325	−	1.37365i	0.434699	−	0.900576i	$-0.356855\pi$
$468$	13.9843			0.646422
$469$	1.85434	+	5.70708i	0.0856256	+	0.263529i
$470$		0			0
$471$	−5.38979	+	16.5881i	−0.248348	+	0.764338i
$472$	−1.83427	+	5.64532i	−0.0844293	+	0.259847i
$473$	−10.5591	+	7.67164i	−0.485508	+	0.352742i
$474$	−3.49684			−0.160615
$475$		0			0
$476$	−10.8836			−0.498849
$477$	7.88784	−	5.73085i	0.361159	−	0.262398i
$478$	0.393295	−	1.21044i	0.0179889	−	0.0553641i
$479$	3.42915	−	10.5538i	0.156682	−	0.482217i	−0.841646	−	0.540030i	$-0.818413\pi$
$479$	3.42915	−	10.5538i	0.156682	−	0.482217i	0.998327	+	0.0578133i	$0.0184128\pi$
$480$		0			0
$481$	9.64933	+	29.6976i	0.439972	+	1.35409i
$482$	−3.26108			−0.148538
$483$	6.29211	+	19.3651i	0.286301	+	0.881144i
$484$	18.6351	+	13.5392i	0.847051	+	0.615418i
$485$		0			0
$486$	1.74793	−	1.26995i	0.0792877	−	0.0576059i
$487$	5.77397	+	4.19504i	0.261644	+	0.190095i	0.710871	−	0.703322i	$-0.248301\pi$
$487$	5.77397	+	4.19504i	0.261644	+	0.190095i	−0.449228	+	0.893417i	$0.648301\pi$
$488$	−12.4868	−	9.07218i	−0.565250	−	0.410678i
$489$	−13.1525	+	9.55586i	−0.594777	+	0.432131i
$490$		0			0
$491$	−5.85201	−	4.25173i	−0.264097	−	0.191878i	0.447854	−	0.894107i	$-0.352188\pi$
$491$	−5.85201	−	4.25173i	−0.264097	−	0.191878i	−0.711951	+	0.702229i	$0.752188\pi$
$492$	−7.03448	−	21.6499i	−0.317139	−	0.976053i
$493$	3.05067			0.137395
$494$	−19.0575	−	58.6531i	−0.857439	−	2.63893i
$495$		0			0
$496$	3.06020	−	9.41834i	0.137407	−	0.422896i
$497$	−0.0692236	+	0.213048i	−0.00310510	+	0.00955652i
$498$	−22.9832	+	16.6983i	−1.02990	+	0.748269i
$499$	16.0169			0.717014			0.358507	−	0.933527i	$-0.383286\pi$
$499$	16.0169			0.717014			0.358507	+	0.933527i	$0.383286\pi$
$500$		0			0
$501$	11.3906			0.508894
$502$	20.7921	−	15.1063i	0.927997	−	0.674229i
$503$	10.4436	−	32.1422i	0.465659	−	1.43315i	−0.392492	−	0.919755i	$-0.628387\pi$
$503$	10.4436	−	32.1422i	0.465659	−	1.43315i	0.858152	−	0.513396i	$-0.171613\pi$
$504$	−1.40962	+	4.33836i	−0.0627894	+	0.193246i
$505$		0			0
$506$	−6.61690	−	20.3647i	−0.294157	−	0.905322i
$507$	14.4727			0.642753
$508$	−8.25985	−	25.4212i	−0.366472	−	1.12788i
$509$	29.4701	+	21.4113i	1.30624	+	0.949038i	0.999996	−	0.00291563i	$-0.000928074\pi$
$509$	29.4701	+	21.4113i	1.30624	+	0.949038i	0.306243	+	0.951953i	$0.400928\pi$
$510$		0			0
$511$	10.2565	−	7.45178i	0.453720	−	0.329647i
$512$	18.9548	+	13.7715i	0.837692	+	0.608619i
$513$	−4.40581	−	3.20100i	−0.194521	−	0.141328i
$514$	31.5487	−	22.9215i	1.39156	−	1.01102i
$515$		0			0
$516$	−18.3130	−	13.3052i	−0.806187	−	0.585729i
$517$	−0.357992	−	1.10179i	−0.0157445	−	0.0484565i
$518$	−40.6813			−1.78743
$519$	−2.92282	−	8.99552i	−0.128298	−	0.394860i
$520$		0			0
$521$	7.87972	−	24.2513i	0.345217	−	1.06247i	−0.616251	−	0.787550i	$-0.711349\pi$
$521$	7.87972	−	24.2513i	0.345217	−	1.06247i	0.961468	−	0.274918i	$-0.0886507\pi$
$522$	1.57806	−	4.85678i	0.0690700	−	0.212576i
$523$	−5.68880	+	4.13315i	−0.248754	+	0.180730i	−0.705174	−	0.709034i	$-0.749131\pi$
$523$	−5.68880	+	4.13315i	−0.248754	+	0.180730i	0.456420	+	0.889764i	$0.349131\pi$
$524$	−17.0184			−0.743450
$525$		0			0
$526$	−41.2811			−1.79994
$527$	−4.66273	+	3.38767i	−0.203112	+	0.147569i
$528$	−1.05425	+	3.24465i	−0.0458803	+	0.141205i
$529$	5.71836	−	17.5993i	0.248624	−	0.765187i
$530$		0			0
$531$	1.27089	+	3.91141i	0.0551521	+	0.169741i
$532$	45.9220			1.99097
$533$	−13.8195	−	42.5322i	−0.598590	−	1.84227i
$534$	12.7179	+	9.24008i	0.550357	+	0.399858i
$535$		0			0
$536$	2.21695	−	1.61071i	0.0957577	−	0.0695721i
$537$	−3.29874	−	2.39667i	−0.142351	−	0.103424i
$538$	−38.8478	−	28.2246i	−1.67485	−	1.21685i
$539$	−3.72014	+	2.70284i	−0.160238	+	0.116420i
$540$		0			0
$541$	21.9629	+	15.9570i	0.944258	+	0.686044i	0.949442	−	0.313943i	$-0.101650\pi$
$541$	21.9629	+	15.9570i	0.944258	+	0.686044i	−0.00518365	+	0.999987i	$0.501650\pi$
$542$	−13.4937	−	41.5293i	−0.579604	−	1.78384i
$543$	−11.1202			−0.477214
$544$	−3.06235	−	9.42496i	−0.131297	−	0.404092i
$545$		0			0
$546$	−11.0602	+	34.0398i	−0.473333	+	1.45677i
$547$	−13.6205	+	41.9196i	−0.582371	+	1.79235i	0.0272113	+	0.999630i	$0.491337\pi$
$547$	−13.6205	+	41.9196i	−0.582371	+	1.79235i	−0.609582	+	0.792723i	$0.708663\pi$
$548$	−19.8090	+	14.3921i	−0.846198	+	0.614799i
$549$	−10.6939			−0.456407
$550$		0			0
$551$	−12.8719			−0.548363
$552$	7.52251	−	5.46542i	0.320179	−	0.232624i
$553$	1.58073	−	4.86497i	0.0672193	−	0.206880i
$554$	−10.7099	+	32.9618i	−0.455022	+	1.40041i
$555$		0			0
$556$	−7.63897	−	23.5103i	−0.323965	−	0.997061i
$557$	9.85667			0.417641			0.208820	−	0.977954i	$-0.433038\pi$
$557$	9.85667			0.417641			0.208820	+	0.977954i	$0.433038\pi$
$558$	2.98134	+	9.17562i	0.126210	+	0.388435i
$559$	−35.9768	−	26.1386i	−1.52165	−	1.10555i
$560$		0			0
$561$	1.60632	−	1.16706i	0.0678190	−	0.0492734i
$562$	14.6356	+	10.6334i	0.617363	+	0.448541i
$563$	−10.0251	−	7.28367i	−0.422508	−	0.306970i	0.356138	−	0.934433i	$-0.384093\pi$
$563$	−10.0251	−	7.28367i	−0.422508	−	0.306970i	−0.778646	+	0.627463i	$0.784093\pi$
$564$	1.62548	−	1.18098i	0.0684451	−	0.0497283i
$565$		0			0
$566$	1.97507	+	1.43497i	0.0830185	+	0.0603165i
$567$	0.976667	+	3.00587i	0.0410161	+	0.126235i
$568$	0.102297			0.00429228
$569$	−3.62037	−	11.1424i	−0.151774	−	0.467112i	0.846046	−	0.533110i	$-0.178977\pi$
$569$	−3.62037	−	11.1424i	−0.151774	−	0.467112i	−0.997820	+	0.0659983i	$0.978977\pi$
$570$		0			0
$571$	8.95523	−	27.5614i	0.374765	−	1.15341i	−0.568872	−	0.822426i	$-0.692620\pi$
$571$	8.95523	−	27.5614i	0.374765	−	1.15341i	0.943637	−	0.330982i	$-0.107380\pi$
$572$	6.64779	−	20.4598i	0.277958	−	0.855467i
$573$	−2.92164	+	2.12270i	−0.122053	+	0.0886769i
$574$	58.2628			2.43184
$575$		0			0
$576$	−12.1535			−0.506398
$577$	−26.5377	+	19.2808i	−1.10478	+	0.802668i	−0.981833	−	0.189745i	$-0.939234\pi$
$577$	−26.5377	+	19.2808i	−1.10478	+	0.802668i	−0.122945	+	0.992414i	$0.539234\pi$
$578$	10.2378	−	31.5088i	0.425838	−	1.31059i
$579$	5.27067	−	16.2215i	0.219042	−	0.674141i
$580$		0			0
$581$	−12.8420	−	39.5237i	−0.532777	−	1.63972i
$582$	22.0246			0.912947
$583$	−4.63488	−	14.2647i	−0.191957	−	0.590783i
$584$	−4.68371	−	3.40291i	−0.193813	−	0.140813i
$585$		0			0
$586$	4.15758	−	3.02066i	0.171748	−	0.124782i
$587$	15.0797	+	10.9560i	0.622405	+	0.452203i	0.853761	−	0.520666i	$-0.174316\pi$
$587$	15.0797	+	10.9560i	0.622405	+	0.452203i	−0.231356	+	0.972869i	$0.574316\pi$
$588$	−6.45197	−	4.68763i	−0.266075	−	0.193315i
$589$	19.6738	−	14.2938i	0.810644	−	0.588967i
$590$		0			0
$591$	−3.56391	−	2.58933i	−0.146600	−	0.106511i
$592$	−4.08275	−	12.5654i	−0.167800	−	0.516435i
$593$	−1.55882			−0.0640129			−0.0320064	−	0.999488i	$-0.510190\pi$
$593$	−1.55882			−0.0640129			−0.0320064	+	0.999488i	$0.510190\pi$
$594$	−1.02708	−	3.16103i	−0.0421416	−	0.129698i
$595$		0			0
$596$	−8.31202	+	25.5818i	−0.340474	+	1.04787i
$597$	5.12831	−	15.7833i	0.209888	−	0.645969i
$598$	59.0234	−	42.8830i	2.41365	−	1.75362i
$599$	−31.5470			−1.28898			−0.644489	−	0.764614i	$-0.722930\pi$
$599$	−31.5470			−1.28898			−0.644489	+	0.764614i	$0.722930\pi$
$600$		0			0
$601$	−32.3999			−1.32162			−0.660809	−	0.750554i	$-0.729787\pi$
$601$	−32.3999			−1.32162			−0.660809	+	0.750554i	$0.729787\pi$
$602$	46.8707	−	34.0536i	1.91031	−	1.38792i
$603$	0.586713	−	1.80572i	0.0238928	−	0.0735345i
$604$	8.85266	−	27.2457i	0.360210	−	1.10861i
$605$		0			0
$606$	−0.726129	−	2.23480i	−0.0294970	−	0.0907824i
$607$	−24.8410			−1.00827			−0.504133	−	0.863626i	$-0.668188\pi$
$607$	−24.8410			−1.00827			−0.504133	+	0.863626i	$0.668188\pi$
$608$	12.9212	+	39.7674i	0.524024	+	1.61278i
$609$	6.04363	+	4.39095i	0.244900	+	0.177930i
$610$		0			0
$611$	3.19333	−	2.32009i	0.129188	−	0.0938607i
$612$	2.78590	+	2.02408i	0.112614	+	0.0818185i
$613$	−3.19204	−	2.31915i	−0.128925	−	0.0936697i	0.521454	−	0.853280i	$-0.325390\pi$
$613$	−3.19204	−	2.31915i	−0.128925	−	0.0936697i	−0.650379	+	0.759610i	$0.725390\pi$
$614$	−5.05791	+	3.67478i	−0.204120	+	0.148302i
$615$		0			0
$616$	5.67717	+	4.12471i	0.228740	+	0.166189i
$617$	5.40225	+	16.6264i	0.217486	+	0.669354i	0.998968	+	0.0454257i	$0.0144644\pi$
$617$	5.40225	+	16.6264i	0.217486	+	0.669354i	−0.781481	+	0.623929i	$0.785536\pi$
$618$	−10.6679			−0.429126
$619$	−4.44581	−	13.6828i	−0.178692	−	0.549958i	0.821091	−	0.570798i	$-0.193366\pi$
$619$	−4.44581	−	13.6828i	−0.178692	−	0.549958i	−0.999783	+	0.0208398i	$0.993366\pi$
$620$		0			0
$621$	1.99082	−	6.12712i	0.0798890	−	0.245873i
$622$	4.77066	−	14.6826i	0.191286	−	0.588718i
$623$	−18.6043	+	13.5168i	−0.745364	+	0.541539i
$624$	−11.6240			−0.465333
$625$		0			0
$626$	49.7617			1.98888
$627$	−6.77768	+	4.92427i	−0.270674	+	0.196656i
$628$	−14.3801	+	44.2573i	−0.573827	+	1.76606i
$629$	−2.37611	+	7.31292i	−0.0947418	+	0.291585i
$630$		0			0
$631$	−5.46214	−	16.8107i	−0.217444	−	0.669225i	−0.998971	−	0.0453529i	$-0.985559\pi$
$631$	−5.46214	−	16.8107i	−0.217444	−	0.669225i	0.781527	−	0.623872i	$-0.214441\pi$
$632$	−2.33596			−0.0929194
$633$	5.73083	+	17.6377i	0.227780	+	0.701035i
$634$	36.3132	+	26.3831i	1.44218	+	1.04781i
$635$		0			0
$636$	21.0449	−	15.2900i	0.834485	−	0.606289i
$637$	−12.6752	−	9.20905i	−0.502209	−	0.364876i
$638$	−6.35559	−	4.61760i	−0.251620	−	0.182813i
$639$	0.0573410	−	0.0416607i	0.00226837	−	0.00164807i
$640$		0			0
$641$	2.21774	+	1.61128i	0.0875954	+	0.0636417i	0.630721	−	0.776010i	$-0.282759\pi$
$641$	2.21774	+	1.61128i	0.0875954	+	0.0636417i	−0.543126	+	0.839651i	$0.682759\pi$
$642$	10.2190	+	31.4507i	0.403310	+	1.24126i
$643$	−20.9276			−0.825303			−0.412651	−	0.910889i	$-0.635397\pi$
$643$	−20.9276			−0.825303			−0.412651	+	0.910889i	$0.635397\pi$
$644$	16.7875	+	51.6665i	0.661519	+	2.03595i
$645$		0			0
$646$	4.69284	−	14.4431i	0.184637	−	0.568256i
$647$	0.570653	−	1.75629i	0.0224347	−	0.0690469i	−0.939212	−	0.343337i	$-0.888443\pi$
$647$	0.570653	−	1.75629i	0.0224347	−	0.0690469i	0.961647	+	0.274290i	$0.0884428\pi$
$648$	1.16765	−	0.848347i	0.0458696	−	0.0333262i
$649$	6.32678			0.248348
$650$		0			0
$651$	−14.1132			−0.553141
$652$	−35.0912	+	25.4952i	−1.37428	+	0.998470i
$653$	5.69002	−	17.5121i	0.222667	−	0.685300i	−0.775853	−	0.630914i	$-0.782680\pi$
$653$	5.69002	−	17.5121i	0.222667	−	0.685300i	0.998520	−	0.0543858i	$-0.0173201\pi$
$654$	−4.44588	+	13.6830i	−0.173848	+	0.535048i
$655$		0			0
$656$	5.84721	+	17.9959i	0.228295	+	0.702620i
$657$	−4.01123			−0.156493
$658$	1.58909	+	4.89071i	0.0619491	+	0.190660i
$659$	10.8246	+	7.86455i	0.421668	+	0.306360i	0.778308	−	0.627882i	$-0.216078\pi$
$659$	10.8246	+	7.86455i	0.421668	+	0.306360i	−0.356641	+	0.934242i	$0.616078\pi$
$660$		0			0
$661$	−31.7001	+	23.0315i	−1.23299	+	0.895820i	−0.997111	−	0.0759628i	$-0.975797\pi$
$661$	−31.7001	+	23.0315i	−1.23299	+	0.895820i	−0.235879	+	0.971782i	$0.575797\pi$
$662$	−33.6483	−	24.4469i	−1.30778	−	0.950155i
$663$	5.47303	+	3.97639i	0.212555	+	0.154430i
$664$	−15.3532	+	11.1548i	−0.595821	+	0.432890i
$665$		0			0
$666$	10.4133	+	7.56571i	0.403507	+	0.293165i
$667$	−4.70553	−	14.4821i	−0.182199	−	0.560751i
$668$	30.3903			1.17584
$669$	0.238424	+	0.733794i	0.00921801	+	0.0283701i
$670$		0			0
$671$	−5.08365	+	15.6459i	−0.196252	+	0.604002i
$672$	7.49894	−	23.0794i	0.289278	−	0.890305i
$673$	15.6877	−	11.3978i	0.604718	−	0.439353i	−0.242832	−	0.970068i	$-0.578077\pi$
$673$	15.6877	−	11.3978i	0.604718	−	0.439353i	0.847550	+	0.530715i	$0.178077\pi$
$674$	46.8981			1.80645
$675$		0			0
$676$	38.6133			1.48513
$677$	−36.9588	+	26.8522i	−1.42044	+	1.03201i	−0.428746	+	0.903425i	$0.641044\pi$
$677$	−36.9588	+	26.8522i	−1.42044	+	1.03201i	−0.991698	+	0.128587i	$0.958956\pi$
$678$	−5.98977	+	18.4346i	−0.230036	+	0.707978i
$679$	−9.95606	+	30.6416i	−0.382078	+	1.17592i
$680$		0			0
$681$	−3.53249	−	10.8719i	−0.135365	−	0.416611i
$682$	14.8417			0.568319
$683$	−3.58128	−	11.0220i	−0.137034	−	0.421747i	0.858867	−	0.512199i	$-0.171169\pi$
$683$	−3.58128	−	11.0220i	−0.137034	−	0.421747i	−0.995901	+	0.0904520i	$0.971169\pi$
$684$	−11.7548	−	8.54034i	−0.449455	−	0.326548i
$685$		0			0
$686$	−22.1577	+	16.0985i	−0.845987	+	0.614645i
$687$	−8.27200	−	6.00996i	−0.315596	−	0.229294i
$688$	15.2222	+	11.0596i	0.580340	+	0.421642i
$689$	41.3436	−	30.0379i	1.57507	−	1.14435i
$690$		0			0
$691$	17.5091	+	12.7211i	0.666077	+	0.483934i	0.868710	−	0.495321i	$-0.164950\pi$
$691$	17.5091	+	12.7211i	0.666077	+	0.483934i	−0.202632	+	0.979255i	$0.564950\pi$
$692$	−7.79815	−	24.0002i	−0.296441	−	0.912352i
$693$	4.86205			0.184694
$694$	−1.14498	−	3.52388i	−0.0434627	−	0.133764i
$695$		0			0
$696$	1.05418	−	3.24442i	0.0399585	−	0.122980i
$697$	3.40301	−	10.4734i	0.128898	−	0.396707i
$698$	−27.1895	+	19.7543i	−1.02914	+	0.747713i
$699$	22.5229			0.851896
$700$		0			0
$701$	−8.61904			−0.325537			−0.162768	−	0.986664i	$-0.552042\pi$
$701$	−8.61904			−0.325537			−0.162768	+	0.986664i	$0.552042\pi$
$702$	9.16166	−	6.65634i	0.345785	−	0.251227i
$703$	10.0257	−	30.8559i	0.378126	−	1.16375i
$704$	−5.77751	+	17.7814i	−0.217748	+	0.670160i
$705$		0			0
$706$	10.3843	+	31.9597i	0.390820	+	1.20282i
$707$	3.43739			0.129276
$708$	3.39077	+	10.4357i	0.127433	+	0.392198i
$709$	−12.9443	−	9.40460i	−0.486134	−	0.353197i	0.317562	−	0.948238i	$-0.397136\pi$
$709$	−12.9443	−	9.40460i	−0.486134	−	0.353197i	−0.803696	+	0.595041i	$0.797136\pi$
$710$		0			0
$711$	−1.30939	+	0.951325i	−0.0491058	+	0.0356775i
$712$	8.49579	+	6.17255i	0.318393	+	0.231326i
$713$	23.2740	+	16.9095i	0.871617	+	0.633267i
$714$	−7.13030	+	5.18047i	−0.266845	+	0.193874i
$715$		0			0
$716$	−8.80110	−	6.39437i	−0.328913	−	0.238969i
$717$	−0.182034	−	0.560243i	−0.00679818	−	0.0209226i
$718$	53.0138			1.97846
$719$	−15.0132	−	46.2060i	−0.559899	−	1.72319i	−0.682642	−	0.730753i	$-0.739169\pi$
$719$	−15.0132	−	46.2060i	−0.559899	−	1.72319i	0.122743	−	0.992438i	$-0.460831\pi$
$720$		0			0
$721$	4.82235	−	14.8417i	0.179594	−	0.552733i
$722$	−7.11551	+	21.8993i	−0.264812	+	0.815007i
$723$	−1.22110	+	0.887185i	−0.0454134	+	0.0329948i
$724$	−29.6689			−1.10264
$725$		0			0
$726$	18.6531			0.692283
$727$	20.5756	−	14.9490i	0.763106	−	0.554429i	−0.136755	−	0.990605i	$-0.543667\pi$
$727$	20.5756	−	14.9490i	0.763106	−	0.554429i	0.899861	+	0.436176i	$0.143667\pi$
$728$	−7.38842	+	22.7392i	−0.273833	+	0.842772i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	−3.38389	−	10.4145i	−0.125158	−	0.385196i
$732$	−28.5317			−1.05456
$733$	5.75358	+	17.7077i	0.212513	+	0.654049i	0.999321	+	0.0368505i	$0.0117325\pi$
$733$	5.75358	+	17.7077i	0.212513	+	0.654049i	−0.786807	+	0.617199i	$0.788267\pi$
$734$	−49.1287	−	35.6941i	−1.81337	−	1.31749i
$735$		0			0
$736$	−40.0185	+	29.0752i	−1.47510	+	1.07172i
$737$	−2.36296	−	1.71679i	−0.0870408	−	0.0632389i
$738$	−14.9137	−	10.8354i	−0.548980	−	0.398857i
$739$	−37.9326	+	27.5596i	−1.39537	+	1.01380i	−0.400121	+	0.916462i	$0.631032\pi$
$739$	−37.9326	+	27.5596i	−1.39537	+	1.01380i	−0.995252	+	0.0973351i	$0.968968\pi$
$740$		0			0
$741$	−23.0927	−	16.7779i	−0.848333	−	0.616350i
$742$	20.5737	+	63.3194i	0.755286	+	2.32453i
$743$	42.7061			1.56674			0.783368	−	0.621558i	$-0.213500\pi$
$743$	42.7061			1.56674			0.783368	+	0.621558i	$0.213500\pi$
$744$	1.99159	+	6.12948i	0.0730152	+	0.224718i
$745$		0			0
$746$	−6.48171	+	19.9487i	−0.237312	+	0.730372i
$747$	−4.06322	+	12.5053i	−0.148665	+	0.457545i
$748$	4.28570	−	3.11374i	0.156701	−	0.113850i
$749$	−48.3751			−1.76759
$750$		0			0
$751$	−2.64893			−0.0966608			−0.0483304	−	0.998831i	$-0.515390\pi$
$751$	−2.64893			−0.0966608			−0.0483304	+	0.998831i	$0.515390\pi$
$752$	−1.35113	+	0.981657i	−0.0492708	+	0.0357973i
$753$	3.67584	−	11.3131i	0.133955	−	0.412272i
$754$	8.27133	−	25.4565i	0.301224	−	0.927072i
$755$		0			0
$756$	2.60577	+	8.01972i	0.0947708	+	0.291674i
$757$	−52.9153			−1.92324			−0.961620	−	0.274383i	$-0.911526\pi$
$757$	−52.9153			−1.92324			−0.961620	+	0.274383i	$0.911526\pi$
$758$	14.8662	+	45.7534i	0.539964	+	1.66184i
$759$	−8.01795	−	5.82538i	−0.291033	−	0.211448i
$760$		0			0
$761$	−41.0808	+	29.8470i	−1.48918	+	1.08195i	−0.514728	+	0.857354i	$0.672107\pi$
$761$	−41.0808	+	29.8470i	−1.48918	+	1.08195i	−0.974451	+	0.224598i	$0.927893\pi$
$762$	−17.5116	−	12.7229i	−0.634377	−	0.460902i
$763$	−17.0267	−	12.3706i	−0.616408	−	0.447847i
$764$	−7.79499	+	5.66339i	−0.282013	+	0.204894i
$765$		0			0
$766$	23.8242	+	17.3093i	0.860803	+	0.625410i
$767$	6.66131	+	20.5014i	0.240526	+	0.740263i
$768$	0.752056			0.0271375
$769$	7.59580	+	23.3775i	0.273912	+	0.843013i	0.989505	+	0.144496i	$0.0461562\pi$
$769$	7.59580	+	23.3775i	0.273912	+	0.843013i	−0.715594	+	0.698517i	$0.753844\pi$
$770$		0			0
$771$	5.57751	−	17.1658i	0.200869	−	0.618212i
$772$	14.0622	−	43.2791i	0.506111	−	1.55765i
$773$	−16.1894	+	11.7623i	−0.582293	+	0.423061i	−0.839550	−	0.543282i	$-0.817181\pi$
$773$	−16.1894	+	11.7623i	−0.582293	+	0.423061i	0.257257	+	0.966343i	$0.417181\pi$
$774$	−18.3308			−0.658885
$775$		0			0
$776$	14.7128			0.528159
$777$	−15.2330	+	11.0674i	−0.546482	+	0.397042i
$778$	−12.8392	+	39.5149i	−0.460307	+	1.41668i
$779$	−14.3586	+	44.1911i	−0.514449	+	1.58331i
$780$		0			0
$781$	−0.0336934	−	0.103698i	−0.00120565	−	0.00371060i
$782$	17.9654			0.642441
$783$	−0.730396	−	2.24793i	−0.0261022	−	0.0803344i
$784$	5.36302	+	3.89646i	0.191536	+	0.139159i
$785$		0			0
$786$	−11.1494	+	8.10053i	−0.397687	+	0.288936i
$787$	7.27526	+	5.28579i	0.259335	+	0.188418i	0.709854	−	0.704349i	$-0.248761\pi$
$787$	7.27526	+	5.28579i	0.259335	+	0.188418i	−0.450519	+	0.892767i	$0.648761\pi$
$788$	−9.50857	−	6.90838i	−0.338729	−	0.246101i
$789$	−15.4576	+	11.2306i	−0.550305	+	0.399820i
$790$		0			0
$791$	−22.9395	−	16.6665i	−0.815634	−	0.592593i
$792$	−0.686108	−	2.11162i	−0.0243798	−	0.0750333i
$793$	−56.0517			−1.99045
$794$	14.8406	+	45.6747i	0.526674	+	1.62093i
$795$		0			0
$796$	13.6824	−	42.1102i	0.484961	−	1.49256i
$797$	11.6674	−	35.9084i	0.413279	−	1.27194i	−0.500502	−	0.865735i	$-0.666851\pi$
$797$	11.6674	−	35.9084i	0.413279	−	1.27194i	0.913781	−	0.406207i	$-0.133149\pi$
$798$	30.0854	−	21.8583i	1.06501	−	0.773776i
$799$	0.971976			0.0343860
$800$		0			0
$801$	7.27597			0.257084
$802$	8.24547	−	5.99069i	0.291158	−	0.211538i
$803$	−1.90684	+	5.86866i	−0.0672910	+	0.207100i
$804$	1.56536	−	4.81769i	0.0552061	−	0.169907i
$805$		0			0
$806$	15.6265	+	48.0934i	0.550420	+	1.69402i
$807$	−22.2250			−0.782358
$808$	−0.485068	−	1.49289i	−0.0170646	−	0.0525195i
$809$	39.5610	+	28.7428i	1.39089	+	1.01054i	0.995767	+	0.0919140i	$0.0292985\pi$
$809$	39.5610	+	28.7428i	1.39089	+	1.01054i	0.395124	+	0.918628i	$0.370702\pi$
$810$		0			0
$811$	14.6069	−	10.6125i	0.512916	−	0.372655i	−0.301013	−	0.953620i	$-0.597325\pi$
$811$	14.6069	−	10.6125i	0.512916	−	0.372655i	0.813929	+	0.580965i	$0.197325\pi$
$812$	16.1245	+	11.7151i	0.565860	+	0.411121i
$813$	−16.3508	−	11.8796i	−0.573449	−	0.416635i
$814$	16.0193	−	11.6387i	0.561477	−	0.407937i
$815$		0			0
$816$	−2.31570	−	1.68246i	−0.0810658	−	0.0588978i
$817$	14.2779	+	43.9428i	0.499520	+	1.53736i
$818$	26.9653			0.942819
$819$	5.11914	+	15.7551i	0.178877	+	0.550527i
$820$		0			0
$821$	15.6393	−	48.1327i	0.545814	−	1.67984i	−0.173232	−	0.984881i	$-0.555421\pi$
$821$	15.6393	−	48.1327i	0.545814	−	1.67984i	0.719046	−	0.694962i	$-0.244579\pi$
$822$	−6.12723	+	18.8577i	−0.213712	+	0.657737i
$823$	−21.6873	+	15.7568i	−0.755972	+	0.549246i	−0.897672	−	0.440664i	$-0.854743\pi$
$823$	−21.6873	+	15.7568i	−0.755972	+	0.549246i	0.141700	+	0.989910i	$0.454743\pi$
$824$	−7.12635			−0.248258
$825$		0			0
$826$	−28.0839			−0.977163
$827$	−17.2845	+	12.5580i	−0.601042	+	0.436683i	−0.846249	−	0.532788i	$-0.821144\pi$
$827$	−17.2845	+	12.5580i	−0.601042	+	0.436683i	0.245206	+	0.969471i	$0.421144\pi$
$828$	5.31155	−	16.3473i	0.184589	−	0.568107i
$829$	−14.8675	+	45.7575i	−0.516370	+	1.58922i	0.264405	+	0.964412i	$0.414824\pi$
$829$	−14.8675	+	45.7575i	−0.516370	+	1.58922i	−0.780775	+	0.624812i	$0.785176\pi$
$830$		0			0
$831$	4.95702	+	15.2561i	0.171957	+	0.529230i
$832$	−63.7021			−2.20847
$833$	−1.19220	−	3.66921i	−0.0413072	−	0.127130i
$834$	−16.1953	−	11.7665i	−0.560796	−	0.407442i
$835$		0			0
$836$	−18.0830	+	13.1380i	−0.625412	+	0.454389i
$837$	3.61260	+	2.62471i	0.124870	+	0.0907232i
$838$	61.0873	+	44.3825i	2.11022	+	1.53317i
$839$	33.8606	−	24.6012i	1.16900	−	0.849327i	0.178110	−	0.984011i	$-0.443002\pi$
$839$	33.8606	−	24.6012i	1.16900	−	0.849327i	0.990889	+	0.134684i	$0.0430018\pi$
$840$		0			0
$841$	18.9418	+	13.7620i	0.653165	+	0.474552i
$842$	26.4123	+	81.2886i	0.910227	+	2.80139i
$843$	8.37308			0.288384
$844$	15.2900	+	47.0577i	0.526302	+	1.61979i
$845$		0			0
$846$	0.502787	−	1.54742i	0.0172862	−	0.0532014i
$847$	−8.43203	+	25.9511i	−0.289728	+	0.891691i
$848$	−17.4930	+	12.7094i	−0.600711	+	0.436442i
$849$	1.12995			0.0387798
$850$		0			0
$851$	38.3809			1.31568
$852$	0.152987	−	0.111151i	0.00524124	−	0.00380799i
$853$	17.9855	−	55.3537i	0.615812	−	1.89527i	0.227327	−	0.973819i	$-0.427002\pi$
$853$	17.9855	−	55.3537i	0.615812	−	1.89527i	0.388485	−	0.921455i	$-0.372998\pi$
$854$	22.5658	−	69.4504i	0.772186	−	2.37654i
$855$		0			0
$856$	6.82646	+	21.0097i	0.233324	+	0.718096i
$857$	3.22045			0.110008			0.0550042	−	0.998486i	$-0.482483\pi$
$857$	3.22045			0.110008			0.0550042	+	0.998486i	$0.482483\pi$
$858$	−5.38337	−	16.5683i	−0.183785	−	0.565633i
$859$	−40.0003	−	29.0619i	−1.36479	−	0.991580i	−0.998124	−	0.0612288i	$-0.980498\pi$
$859$	−40.0003	−	29.0619i	−1.36479	−	0.991580i	−0.366669	−	0.930351i	$-0.619502\pi$
$860$		0			0
$861$	21.8164	−	15.8505i	0.743500	−	0.540184i
$862$	−24.5731	−	17.8534i	−0.836963	−	0.608089i
$863$	17.3878	+	12.6329i	0.591886	+	0.430030i	0.842990	−	0.537930i	$-0.180793\pi$
$863$	17.3878	+	12.6329i	0.591886	+	0.430030i	−0.251104	+	0.967960i	$0.580793\pi$
$864$	−6.21171	+	4.51307i	−0.211327	+	0.153538i
$865$		0			0
$866$	0.960798	+	0.698061i	0.0326493	+	0.0237211i
$867$	−4.73851	−	14.5836i	−0.160928	−	0.495286i
$868$	−37.6544			−1.27807
$869$	0.769392	+	2.36795i	0.0260999	+	0.0803271i
$870$		0			0
$871$	3.07522	−	9.46456i	0.104200	−	0.320694i
$872$	−2.96993	+	9.14051i	−0.100575	+	0.309537i
$873$	8.24705	−	5.99183i	0.279120	−	0.202793i
$874$	−75.8026			−2.56406
$875$		0			0
$876$	−10.7020			−0.361588
$877$	12.4421	−	9.03971i	0.420140	−	0.305249i	−0.357554	−	0.933892i	$-0.616389\pi$
$877$	12.4421	−	9.03971i	0.420140	−	0.305249i	0.777694	+	0.628643i	$0.216389\pi$
$878$	1.98544	−	6.11054i	0.0670052	−	0.206221i
$879$	0.735020	−	2.26216i	0.0247916	−	0.0763007i
$880$		0			0
$881$	5.84891	+	18.0011i	0.197055	+	0.606472i	0.999946	+	0.0103472i	$0.00329367\pi$
$881$	5.84891	+	18.0011i	0.197055	+	0.606472i	−0.802892	+	0.596125i	$0.796706\pi$
$882$	−6.45821			−0.217459
$883$	−1.95208	−	6.00790i	−0.0656928	−	0.202182i	0.912822	−	0.408357i	$-0.133898\pi$
$883$	−1.95208	−	6.00790i	−0.0656928	−	0.202182i	−0.978515	+	0.206175i	$0.933898\pi$
$884$	14.6021	+	10.6091i	0.491123	+	0.356822i
$885$		0			0
$886$	64.1303	−	46.5934i	2.15450	−	1.56534i
$887$	0.0583776	+	0.0424138i	0.00196013	+	0.00142412i	0.588765	−	0.808304i	$-0.299614\pi$
$887$	0.0583776	+	0.0424138i	0.00196013	+	0.00142412i	−0.586805	+	0.809728i	$0.699614\pi$
$888$	6.95628	+	5.05404i	0.233438	+	0.169602i
$889$	25.6167	−	18.6116i	0.859156	−	0.624213i
$890$		0			0
$891$	−1.24455	−	0.904220i	−0.0416941	−	0.0302925i
$892$	0.636120	+	1.95778i	0.0212989	+	0.0655512i
$893$	−4.10113			−0.137239
$894$	6.73107	+	20.7161i	0.225121	+	0.692850i
$895$		0			0
$896$	10.6479	−	32.7709i	0.355721	−	1.09480i
$897$	10.4348	−	32.1149i	0.348407	−	1.07229i
$898$	−31.1886	+	22.6599i	−1.04078	+	0.756169i
$899$	10.5545			0.352013
$900$		0			0
$901$	12.5840			0.419235
$902$	−22.9425	+	16.6687i	−0.763901	+	0.555006i
$903$	8.28629	−	25.5026i	0.275751	−	0.848673i
$904$	−4.00128	+	12.3147i	−0.133081	+	0.409580i
$905$		0			0
$906$	−7.16888	−	22.0635i	−0.238170	−	0.733012i
$907$	25.4951			0.846550			0.423275	−	0.906001i	$-0.360880\pi$
$907$	25.4951			0.846550			0.423275	+	0.906001i	$0.360880\pi$
$908$	−9.42474	−	29.0064i	−0.312771	−	0.962610i
$909$	−0.879879	−	0.639269i	−0.0291837	−	0.0212032i
$910$		0			0
$911$	−2.87851	+	2.09136i	−0.0953692	+	0.0692898i	−0.634448	−	0.772966i	$-0.718773\pi$
$911$	−2.87851	+	2.09136i	−0.0953692	+	0.0692898i	0.539079	+	0.842255i	$0.318773\pi$
$912$	9.77081	+	7.09891i	0.323544	+	0.235068i
$913$	16.3644	+	11.8894i	0.541583	+	0.393483i
$914$	42.2621	−	30.7052i	1.39791	−	1.01564i
$915$		0			0
$916$	−22.0698	−	16.0347i	−0.729208	−	0.529801i
$917$	−6.22981	−	19.1734i	−0.205727	−	0.633161i
$918$	2.78860			0.0920375
$919$	2.46277	+	7.57962i	0.0812392	+	0.250029i	0.983424	−	0.181321i	$-0.0580374\pi$
$919$	2.46277	+	7.57962i	0.0812392	+	0.250029i	−0.902185	+	0.431350i	$0.858037\pi$
$920$		0			0
$921$	−0.894189	+	2.75203i	−0.0294645	+	0.0906825i
$922$	24.9617	−	76.8241i	0.822068	−	2.53007i
$923$	0.300549	−	0.218362i	0.00989270	−	0.00718747i
$924$	12.9720			0.426749
$925$		0			0
$926$	44.1434			1.45064
$927$	−3.99457	+	2.90222i	−0.131199	+	0.0953216i
$928$	−5.60805	+	17.2598i	−0.184093	+	0.566581i
$929$	15.0004	−	46.1666i	0.492149	−	1.51468i	−0.329205	−	0.944258i	$-0.606781\pi$
$929$	15.0004	−	46.1666i	0.492149	−	1.51468i	0.821354	−	0.570419i	$-0.193219\pi$
$930$		0			0
$931$	5.03032	+	15.4817i	0.164862	+	0.507394i
$932$	60.0916			1.96837
$933$	−2.20807	−	6.79573i	−0.0722888	−	0.222482i
$934$	−54.5571	−	39.6381i	−1.78516	−	1.29700i
$935$		0			0
$936$	6.12016	−	4.44656i	0.200044	−	0.145340i
$937$	25.6698	+	18.6502i	0.838594	+	0.609274i	0.921978	−	0.387243i	$-0.126573\pi$
$937$	25.6698	+	18.6502i	0.838594	+	0.609274i	−0.0833833	+	0.996518i	$0.526573\pi$
$938$	10.4889	+	7.62066i	0.342476	+	0.248823i
$939$	18.6331	−	13.5378i	0.608070	−	0.441789i
$940$		0			0
$941$	−33.1752	−	24.1032i	−1.08148	−	0.785742i	−0.103541	−	0.994625i	$-0.533017\pi$
$941$	−33.1752	−	24.1032i	−1.08148	−	0.785742i	−0.977941	+	0.208883i	$0.933017\pi$
$942$	11.6450	+	35.8395i	0.379414	+	1.16771i
$943$	−54.9681			−1.79001
$944$	−2.81848	−	8.67439i	−0.0917337	−	0.282327i
$945$		0			0
$946$	−8.71401	+	26.8190i	−0.283317	+	0.871960i
$947$	3.03389	−	9.33737i	0.0985883	−	0.303424i	−0.889584	−	0.456772i	$-0.849006\pi$
$947$	3.03389	−	9.33737i	0.0985883	−	0.303424i	0.988172	+	0.153348i	$0.0490056\pi$
$948$	−3.49347	+	2.53815i	−0.113463	+	0.0824353i
$949$	−21.0246			−0.682487
$950$		0			0
$951$	20.7750			0.673674
$952$	−4.76317	+	3.46065i	−0.154375	+	0.112160i
$953$	−16.4125	+	50.5123i	−0.531652	+	1.63626i	0.219123	+	0.975697i	$0.429680\pi$
$953$	−16.4125	+	50.5123i	−0.531652	+	1.63626i	−0.750775	+	0.660558i	$0.770320\pi$
$954$	6.50952	−	20.0343i	0.210754	−	0.648633i
$955$		0			0
$956$	−0.485670	−	1.49474i	−0.0157077	−	0.0483433i
$957$	−3.63606			−0.117537
$958$	−7.40888	−	22.8022i	−0.239370	−	0.736705i
$959$	−23.4659	−	17.0490i	−0.757754	−	0.550540i
$960$		0			0
$961$	8.94773	−	6.50090i	0.288636	−	0.209707i
$962$	54.5807	+	39.6552i	1.75975	+	1.27853i
$963$	12.3827	+	8.99657i	0.399027	+	0.289910i
$964$	−3.25793	+	2.36703i	−0.104931	+	0.0762368i
$965$		0			0
$966$	35.5908	+	25.8583i	1.14512	+	0.831976i
$967$	0.756262	+	2.32754i	0.0243198	+	0.0748485i	0.962480	−	0.271353i	$-0.0874712\pi$
$967$	0.756262	+	2.32754i	0.0243198	+	0.0748485i	−0.938160	+	0.346202i	$0.887471\pi$
$968$	12.4606			0.400500
$969$	−2.17205	−	6.68488i	−0.0697763	−	0.214749i
$970$		0			0
$971$	−14.8230	+	45.6205i	−0.475693	+	1.46403i	0.369328	+	0.929299i	$0.379588\pi$
$971$	−14.8230	+	45.6205i	−0.475693	+	1.46403i	−0.845021	+	0.534734i	$0.820412\pi$
$972$	0.824463	−	2.53744i	0.0264447	−	0.0813883i
$973$	23.6911	−	17.2126i	0.759502	−	0.551811i
$974$	15.4200			0.494088
$975$		0			0
$976$	23.7161			0.759134
$977$	19.1696	−	13.9276i	0.613291	−	0.445582i	−0.237280	−	0.971441i	$-0.576256\pi$
$977$	19.1696	−	13.9276i	0.613291	−	0.445582i	0.850572	+	0.525859i	$0.176256\pi$
$978$	−10.8543	+	33.4060i	−0.347081	+	1.06820i
$979$	3.45883	−	10.6452i	0.110545	−	0.340221i
$980$		0			0
$981$	2.05774	+	6.33308i	0.0656987	+	0.202200i
$982$	−15.6284			−0.498721
$983$	−4.00193	−	12.3167i	−0.127642	−	0.392841i	0.866731	−	0.498775i	$-0.166217\pi$
$983$	−4.00193	−	12.3167i	−0.127642	−	0.392841i	−0.994373	+	0.105934i	$0.966217\pi$
$984$	−9.96261	−	7.23826i	−0.317597	−	0.230747i
$985$		0			0
$986$	5.33236	−	3.87419i	0.169817	−	0.123379i
$987$	1.92556	+	1.39900i	0.0612913	+	0.0445307i
$988$	−61.6119	−	44.7637i	−1.96014	−	1.42412i
$989$	−44.2203	+	32.1279i	−1.40612	+	1.02161i
$990$		0			0
$991$	−35.9986	−	26.1545i	−1.14353	−	0.830826i	−0.155926	−	0.987769i	$-0.549836\pi$
$991$	−35.9986	−	26.1545i	−1.14353	−	0.830826i	−0.987608	+	0.156943i	$0.949836\pi$
$992$	−10.5949	−	32.6079i	−0.336389	−	1.03530i
$993$	−19.2504			−0.610891
$994$	0.149562	+	0.460303i	0.00474381	+	0.0145999i
$995$		0			0
$996$	−10.8407	+	33.3644i	−0.343502	+	1.05719i
$997$	17.1663	−	52.8324i	0.543662	−	1.67322i	−0.180488	−	0.983577i	$-0.557768\pi$
$997$	17.1663	−	52.8324i	0.543662	−	1.67322i	0.724150	−	0.689642i	$-0.242232\pi$
$998$	27.9964	−	20.3406i	0.886209	−	0.643869i
$999$	5.95751			0.188487

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.g.c.301.3		12
5.2	odd	4		375.2.i.d.199.6		24
5.3	odd	4		375.2.i.d.199.1		24
5.4	even	2		75.2.g.c.61.1	yes	12
15.14	odd	2		225.2.h.d.136.3		12
25.3	odd	20		1875.2.b.f.1249.10		12
25.4	even	10		1875.2.a.j.1.5		6
25.9	even	10		75.2.g.c.16.1	✓	12
25.12	odd	20		375.2.i.d.49.1		24
25.13	odd	20		375.2.i.d.49.6		24
25.16	even	5	inner	375.2.g.c.76.3		12
25.21	even	5		1875.2.a.k.1.2		6
25.22	odd	20		1875.2.b.f.1249.3		12
75.29	odd	10		5625.2.a.p.1.2		6
75.59	odd	10		225.2.h.d.91.3		12
75.71	odd	10		5625.2.a.q.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.16.1	✓	12	25.9	even	10
75.2.g.c.61.1	yes	12	5.4	even	2
225.2.h.d.91.3		12	75.59	odd	10
225.2.h.d.136.3		12	15.14	odd	2
375.2.g.c.76.3		12	25.16	even	5	inner
375.2.g.c.301.3		12	1.1	even	1	trivial
375.2.i.d.49.1		24	25.12	odd	20
375.2.i.d.49.6		24	25.13	odd	20
375.2.i.d.199.1		24	5.3	odd	4
375.2.i.d.199.6		24	5.2	odd	4
1875.2.a.j.1.5		6	25.4	even	10
1875.2.a.k.1.2		6	25.21	even	5
1875.2.b.f.1249.3		12	25.22	odd	20
1875.2.b.f.1249.10		12	25.3	odd	20
5625.2.a.p.1.2		6	75.29	odd	10
5625.2.a.q.1.5		6	75.71	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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.74793 - 1.26995i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.824463 - 2.53744i) q^{4} +(-0.667650 - 2.05481i) q^{6} +3.16056 q^{7} +(-0.446002 - 1.37265i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.74793 - 1.26995i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.824463 - 2.53744i) q^{4} +(-0.667650 - 2.05481i) q^{6} +3.16056 q^{7} +(-0.446002 - 1.37265i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-1.24455 + 0.904220i) q^{11} +(-2.15847 - 1.56822i) q^{12} +(-4.24041 - 3.08084i) q^{13} +(5.52444 - 4.01374i) q^{14} +(1.79417 + 1.30354i) q^{16} +(-0.398843 - 1.22751i) q^{17} -2.16056 q^{18} +(1.68287 + 5.17933i) q^{19} +(0.976667 - 3.00587i) q^{21} +(-1.02708 + 3.16103i) q^{22} +(-5.21204 + 3.78677i) q^{23} -1.44329 q^{24} -11.3244 q^{26} +(-0.809017 + 0.587785i) q^{27} +(2.60577 - 8.01972i) q^{28} +(-0.730396 + 2.24793i) q^{29} +(-1.37989 - 4.24687i) q^{31} +7.67809 q^{32} +(0.475377 + 1.46306i) q^{33} +(-2.25602 - 1.63910i) q^{34} +(-2.15847 + 1.56822i) q^{36} +(-4.81973 - 3.50174i) q^{37} +(9.51901 + 6.91596i) q^{38} +(-4.24041 + 3.08084i) q^{39} +(6.90269 + 5.01510i) q^{41} +(-2.11015 - 6.49436i) q^{42} +8.48426 q^{43} +(1.26831 + 3.90347i) q^{44} +(-4.30129 + 13.2380i) q^{46} +(-0.232712 + 0.716212i) q^{47} +(1.79417 - 1.30354i) q^{48} +2.98914 q^{49} -1.29068 q^{51} +(-11.3135 + 8.21974i) q^{52} +(-3.01289 + 9.27271i) q^{53} +(-0.667650 + 2.05481i) q^{54} +(-1.40962 - 4.33836i) q^{56} +5.44587 q^{57} +(1.57806 + 4.85678i) q^{58} +(-3.32724 - 2.41738i) q^{59} +(8.65159 - 6.28574i) q^{61} +(-7.80525 - 5.67084i) q^{62} +(-2.55695 - 1.85773i) q^{63} +(9.83243 - 7.14368i) q^{64} +(2.68893 + 1.95362i) q^{66} +(0.586713 + 1.80572i) q^{67} -3.44357 q^{68} +(1.99082 + 6.12712i) q^{69} +(-0.0219023 + 0.0674084i) q^{71} +(-0.446002 + 1.37265i) q^{72} +(3.24515 - 2.35774i) q^{73} -12.8716 q^{74} +14.5297 q^{76} +(-3.93348 + 2.85784i) q^{77} +(-3.49944 + 10.7702i) q^{78} +(0.500141 - 1.53928i) q^{79} +(0.309017 + 0.951057i) q^{81} +18.4343 q^{82} +(-4.06322 - 12.5053i) q^{83} +(-6.82198 - 4.95646i) q^{84} +(14.8299 - 10.7745i) q^{86} +(1.91220 + 1.38930i) q^{87} +(1.79626 + 1.30506i) q^{88} +(-5.88638 + 4.27671i) q^{89} +(-13.4021 - 9.73718i) q^{91} +(5.31155 + 16.3473i) q^{92} -4.46542 q^{93} +(0.502787 + 1.54742i) q^{94} +(2.37266 - 7.30230i) q^{96} +(-3.15009 + 9.69499i) q^{97} +(5.22480 - 3.79604i) q^{98} +1.53835 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9	\( 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9} - 4 q^{11} + 2 q^{13} + 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 3 q^{21} - 13 q^{22} - 19 q^{23} + 6 q^{24} - 56 q^{26} - 3 q^{27} - q^{28} - q^{29} + 13 q^{31} + 32 q^{32} + q^{33} - 25 q^{34} - 8 q^{37} + 22 q^{38} + 2 q^{39} + 8 q^{41} + 16 q^{42} + 4 q^{43} + 33 q^{44} - 22 q^{46} + 13 q^{47} + 16 q^{48} - 28 q^{49} + 26 q^{51} - 44 q^{52} - 44 q^{53} + 45 q^{56} + 22 q^{57} - 41 q^{58} - 22 q^{59} - 8 q^{61} - 41 q^{62} - 3 q^{63} + 49 q^{64} - 3 q^{66} + 6 q^{67} + 100 q^{68} + 6 q^{69} - 21 q^{71} - 9 q^{72} + 16 q^{73} - 44 q^{74} - 52 q^{76} - q^{77} + 19 q^{78} + 10 q^{79} - 3 q^{81} - 26 q^{82} + 10 q^{83} - 6 q^{84} + 56 q^{86} + 4 q^{87} + 16 q^{88} + 57 q^{89} - 7 q^{91} - 3 q^{92} - 22 q^{93} - 23 q^{94} - 23 q^{96} - 4 q^{97} + 18 q^{98} + 6 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9 - 4 * q^11 + 2 * q^13 + 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 3 * q^21 - 13 * q^22 - 19 * q^23 + 6 * q^24 - 56 * q^26 - 3 * q^27 - q^28 - q^29 + 13 * q^31 + 32 * q^32 + q^33 - 25 * q^34 - 8 * q^37 + 22 * q^38 + 2 * q^39 + 8 * q^41 + 16 * q^42 + 4 * q^43 + 33 * q^44 - 22 * q^46 + 13 * q^47 + 16 * q^48 - 28 * q^49 + 26 * q^51 - 44 * q^52 - 44 * q^53 + 45 * q^56 + 22 * q^57 - 41 * q^58 - 22 * q^59 - 8 * q^61 - 41 * q^62 - 3 * q^63 + 49 * q^64 - 3 * q^66 + 6 * q^67 + 100 * q^68 + 6 * q^69 - 21 * q^71 - 9 * q^72 + 16 * q^73 - 44 * q^74 - 52 * q^76 - q^77 + 19 * q^78 + 10 * q^79 - 3 * q^81 - 26 * q^82 + 10 * q^83 - 6 * q^84 + 56 * q^86 + 4 * q^87 + 16 * q^88 + 57 * q^89 - 7 * q^91 - 3 * q^92 - 22 * q^93 - 23 * q^94 - 23 * q^96 - 4 * q^97 + 18 * q^98 + 6 * q^99

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