LMFDB - Embedded newform 605.2.g.q.81.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(81,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, 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("605.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.5
Character	$\chi$	$=$	605.81
Dual form			605.2.g.q.366.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11052 + 0.806841i) q^{2} +(1.00795 - 3.10216i) q^{3} +(-0.0357685 - 0.110084i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(3.62230 - 2.63176i) q^{6} +(0.424181 + 1.30550i) q^{7} +(0.897462 - 2.76210i) q^{8} +(-6.18037 - 4.49030i) q^{9} +O(q^{10})$	\(q+(1.11052 + 0.806841i) q^{2} +(1.00795 - 3.10216i) q^{3} +(-0.0357685 - 0.110084i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(3.62230 - 2.63176i) q^{6} +(0.424181 + 1.30550i) q^{7} +(0.897462 - 2.76210i) q^{8} +(-6.18037 - 4.49030i) q^{9} -1.37268 q^{10} -0.377552 q^{12} +(-1.56345 - 1.13592i) q^{13} +(-0.582265 + 1.79203i) q^{14} +(1.00795 + 3.10216i) q^{15} +(3.03794 - 2.20719i) q^{16} +(5.02356 - 3.64983i) q^{17} +(-3.24047 - 9.97315i) q^{18} +(-0.251177 + 0.773043i) q^{19} +(0.0936432 + 0.0680358i) q^{20} +4.47741 q^{21} -3.63935 q^{23} +(-7.66388 - 5.56814i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-0.819745 - 2.52292i) q^{26} +(-12.2426 + 8.89475i) q^{27} +(0.128542 - 0.0933914i) q^{28} +(2.42118 + 7.45164i) q^{29} +(-1.38360 + 4.25827i) q^{30} +(2.75701 + 2.00309i) q^{31} -0.653939 q^{32} +8.52360 q^{34} +(-1.11052 - 0.806841i) q^{35} +(-0.273248 + 0.840972i) q^{36} +(-1.39787 - 4.30220i) q^{37} +(-0.902660 + 0.655821i) q^{38} +(-5.09968 + 3.70513i) q^{39} +(0.897462 + 2.76210i) q^{40} +(-0.564307 + 1.73676i) q^{41} +(4.97226 + 3.61256i) q^{42} +6.46243 q^{43} +7.63935 q^{45} +(-4.04158 - 2.93638i) q^{46} +(1.46418 - 4.50629i) q^{47} +(-3.78497 - 11.6489i) q^{48} +(4.13873 - 3.00696i) q^{49} +(1.11052 - 0.806841i) q^{50} +(-6.25884 - 19.2627i) q^{51} +(-0.0691239 + 0.212742i) q^{52} +(6.79126 + 4.93414i) q^{53} -20.7723 q^{54} +3.98660 q^{56} +(2.14493 + 1.55838i) q^{57} +(-3.32351 + 10.2287i) q^{58} +(0.344786 + 1.06114i) q^{59} +(0.305446 - 0.221919i) q^{60} +(-2.05885 + 1.49584i) q^{61} +(1.44555 + 4.44894i) q^{62} +(3.24047 - 9.97315i) q^{63} +(-6.80210 - 4.94201i) q^{64} +1.93253 q^{65} +2.73820 q^{67} +(-0.581474 - 0.422466i) q^{68} +(-3.66830 + 11.2899i) q^{69} +(-0.582265 - 1.79203i) q^{70} +(0.902660 - 0.655821i) q^{71} +(-17.9493 + 13.0409i) q^{72} +(3.83766 + 11.8111i) q^{73} +(1.91883 - 5.90555i) q^{74} +(-2.63885 - 1.91724i) q^{75} +0.0940841 q^{76} -8.65275 q^{78} +(4.69917 + 3.41415i) q^{79} +(-1.16039 + 3.57132i) q^{80} +(8.17092 + 25.1475i) q^{81} +(-2.02796 + 1.47340i) q^{82} +(12.9258 - 9.39111i) q^{83} +(-0.160150 - 0.492892i) q^{84} +(-1.91883 + 5.90555i) q^{85} +(7.17667 + 5.21416i) q^{86} +25.5566 q^{87} -2.70789 q^{89} +(8.48367 + 6.16374i) q^{90} +(0.819745 - 2.52292i) q^{91} +(0.130174 + 0.400635i) q^{92} +(8.99283 - 6.53367i) q^{93} +(5.26187 - 3.82297i) q^{94} +(-0.251177 - 0.773043i) q^{95} +(-0.659139 + 2.02862i) q^{96} +(-11.4581 - 8.32478i) q^{97} +7.02229 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9}+O(q^{10}) $ 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9	$ 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9} + 72 q^{12} + 18 q^{14} - 6 q^{15} - 18 q^{16} - 6 q^{20} + 48 q^{23} - 6 q^{25} + 36 q^{26} - 30 q^{27} + 96 q^{34} + 12 q^{36} + 30 q^{42} + 48 q^{45} - 42 q^{47} + 6 q^{48} + 24 q^{49} - 24 q^{53} - 120 q^{56} + 24 q^{58} - 18 q^{60} - 30 q^{64} + 120 q^{67} + 24 q^{69} + 18 q^{70} - 6 q^{75} - 288 q^{78} - 18 q^{80} - 30 q^{81} - 42 q^{82} + 6 q^{86} - 120 q^{89} - 36 q^{91} - 36 q^{92} + 60 q^{93} - 24 q^{97}+O(q^{100}) $ 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9 + 72 * q^12 + 18 * q^14 - 6 * q^15 - 18 * q^16 - 6 * q^20 + 48 * q^23 - 6 * q^25 + 36 * q^26 - 30 * q^27 + 96 * q^34 + 12 * q^36 + 30 * q^42 + 48 * q^45 - 42 * q^47 + 6 * q^48 + 24 * q^49 - 24 * q^53 - 120 * q^56 + 24 * q^58 - 18 * q^60 - 30 * q^64 + 120 * q^67 + 24 * q^69 + 18 * q^70 - 6 * q^75 - 288 * q^78 - 18 * q^80 - 30 * q^81 - 42 * q^82 + 6 * q^86 - 120 * q^89 - 36 * q^91 - 36 * q^92 + 60 * q^93 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	1.11052	+	0.806841i	0.785257	+	0.570523i	0.906552	−	0.422094i	$-0.138705\pi$
$2$	1.11052	+	0.806841i	0.785257	+	0.570523i	−0.121295	+	0.992617i	$0.538705\pi$
$3$	1.00795	−	3.10216i	0.581942	−	1.79103i	−0.0292786	−	0.999571i	$-0.509321\pi$
$3$	1.00795	−	3.10216i	0.581942	−	1.79103i	0.611220	−	0.791461i	$-0.290679\pi$
$4$	−0.0357685	−	0.110084i	−0.0178843	−	0.0550421i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$6$	3.62230	−	2.63176i	1.47880	−	1.07441i
$7$	0.424181	+	1.30550i	0.160326	+	0.493431i	0.998661	−	0.0517227i	$-0.0164712\pi$
$7$	0.424181	+	1.30550i	0.160326	+	0.493431i	−0.838336	+	0.545154i	$0.816471\pi$
$8$	0.897462	−	2.76210i	0.317301	−	0.976551i
$9$	−6.18037	−	4.49030i	−2.06012	−	1.49677i
$10$	−1.37268			−0.434080
$11$		0			0
$11$		0			0
$12$	−0.377552			−0.108990
$13$	−1.56345	−	1.13592i	−0.433624	−	0.315046i	0.349472	−	0.936947i	$-0.386361\pi$
$13$	−1.56345	−	1.13592i	−0.433624	−	0.315046i	−0.783096	+	0.621900i	$0.786361\pi$
$14$	−0.582265	+	1.79203i	−0.155617	+	0.478940i
$15$	1.00795	+	3.10216i	0.260252	+	0.800974i
$16$	3.03794	−	2.20719i	0.759486	−	0.551799i
$17$	5.02356	−	3.64983i	1.21839	−	0.885214i	0.222427	−	0.974949i	$-0.428602\pi$
$17$	5.02356	−	3.64983i	1.21839	−	0.885214i	0.995966	+	0.0897356i	$0.0286022\pi$
$18$	−3.24047	−	9.97315i	−0.763787	−	2.35069i
$19$	−0.251177	+	0.773043i	−0.0576239	+	0.177348i	−0.975726	−	0.218997i	$-0.929722\pi$
$19$	−0.251177	+	0.773043i	−0.0576239	+	0.177348i	0.918102	+	0.396345i	$0.129722\pi$
$20$	0.0936432	+	0.0680358i	0.0209393	+	0.0152133i
$21$	4.47741			0.977051
$22$		0			0
$23$	−3.63935			−0.758858			−0.379429	−	0.925221i	$-0.623880\pi$
$23$	−3.63935			−0.758858			−0.379429	+	0.925221i	$0.623880\pi$
$24$	−7.66388	−	5.56814i	−1.56438	−	1.13659i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	−0.819745	−	2.52292i	−0.160765	−	0.494785i
$27$	−12.2426	+	8.89475i	−2.35608	+	1.71180i
$28$	0.128542	−	0.0933914i	0.0242922	−	0.0176493i
$29$	2.42118	+	7.45164i	0.449602	+	1.38373i	0.877357	+	0.479839i	$0.159305\pi$
$29$	2.42118	+	7.45164i	0.449602	+	1.38373i	−0.427754	+	0.903895i	$0.640695\pi$
$30$	−1.38360	+	4.25827i	−0.252609	+	0.777450i
$31$	2.75701	+	2.00309i	0.495174	+	0.359765i	0.807171	−	0.590318i	$-0.200998\pi$
$31$	2.75701	+	2.00309i	0.495174	+	0.359765i	−0.311997	+	0.950083i	$0.600998\pi$
$32$	−0.653939			−0.115601
$33$		0			0
$34$	8.52360			1.46179
$35$	−1.11052	−	0.806841i	−0.187712	−	0.136381i
$36$	−0.273248	+	0.840972i	−0.0455414	+	0.140162i
$37$	−1.39787	−	4.30220i	−0.229809	−	0.707278i	−0.997768	−	0.0667792i	$-0.978728\pi$
$37$	−1.39787	−	4.30220i	−0.229809	−	0.707278i	0.767959	−	0.640499i	$-0.221272\pi$
$38$	−0.902660	+	0.655821i	−0.146431	+	0.106388i
$39$	−5.09968	+	3.70513i	−0.816602	+	0.593296i
$40$	0.897462	+	2.76210i	0.141901	+	0.436727i
$41$	−0.564307	+	1.73676i	−0.0881299	+	0.271236i	−0.985402	−	0.170241i	$-0.945545\pi$
$41$	−0.564307	+	1.73676i	−0.0881299	+	0.271236i	0.897273	+	0.441477i	$0.145545\pi$
$42$	4.97226	+	3.61256i	0.767237	+	0.557430i
$43$	6.46243			0.985512			0.492756	−	0.870168i	$-0.335990\pi$
$43$	6.46243			0.985512			0.492756	+	0.870168i	$0.335990\pi$
$44$		0			0
$45$	7.63935			1.13881
$46$	−4.04158	−	2.93638i	−0.595899	−	0.432946i
$47$	1.46418	−	4.50629i	0.213573	−	0.657311i	−0.785679	−	0.618635i	$-0.787686\pi$
$47$	1.46418	−	4.50629i	0.213573	−	0.657311i	0.999252	−	0.0386757i	$-0.0123139\pi$
$48$	−3.78497	−	11.6489i	−0.546313	−	1.68138i
$49$	4.13873	−	3.00696i	0.591247	−	0.429566i
$50$	1.11052	−	0.806841i	0.157051	−	0.114105i
$51$	−6.25884	−	19.2627i	−0.876413	−	2.69732i
$52$	−0.0691239	+	0.212742i	−0.00958576	+	0.0295019i
$53$	6.79126	+	4.93414i	0.932851	+	0.677756i	0.946689	−	0.322148i	$-0.104405\pi$
$53$	6.79126	+	4.93414i	0.932851	+	0.677756i	−0.0138381	+	0.999904i	$0.504405\pi$
$54$	−20.7723			−2.82675
$55$		0			0
$56$	3.98660			0.532732
$57$	2.14493	+	1.55838i	0.284103	+	0.206413i
$58$	−3.32351	+	10.2287i	−0.436398	+	1.34310i
$59$	0.344786	+	1.06114i	0.0448873	+	0.138149i	0.970988	−	0.239127i	$-0.0768611\pi$
$59$	0.344786	+	1.06114i	0.0448873	+	0.138149i	−0.926101	+	0.377275i	$0.876861\pi$
$60$	0.305446	−	0.221919i	0.0394329	−	0.0286497i
$61$	−2.05885	+	1.49584i	−0.263608	+	0.191523i	−0.711736	−	0.702447i	$-0.752091\pi$
$61$	−2.05885	+	1.49584i	−0.263608	+	0.191523i	0.448128	+	0.893969i	$0.352091\pi$
$62$	1.44555	+	4.44894i	0.183585	+	0.565016i
$63$	3.24047	−	9.97315i	0.408261	−	1.25650i
$64$	−6.80210	−	4.94201i	−0.850262	−	0.617752i
$65$	1.93253			0.239701
$66$		0			0
$67$	2.73820			0.334524			0.167262	−	0.985912i	$-0.446507\pi$
$67$	2.73820			0.334524			0.167262	+	0.985912i	$0.446507\pi$
$68$	−0.581474	−	0.422466i	−0.0705141	−	0.0512315i
$69$	−3.66830	+	11.2899i	−0.441611	+	1.35914i
$70$	−0.582265	−	1.79203i	−0.0695940	−	0.214188i
$71$	0.902660	−	0.655821i	0.107126	−	0.0778316i	−0.532933	−	0.846158i	$-0.678910\pi$
$71$	0.902660	−	0.655821i	0.107126	−	0.0778316i	0.640059	+	0.768326i	$0.278910\pi$
$72$	−17.9493	+	13.0409i	−2.11535	+	1.53689i
$73$	3.83766	+	11.8111i	0.449164	+	1.38238i	0.877852	+	0.478932i	$0.158976\pi$
$73$	3.83766	+	11.8111i	0.449164	+	1.38238i	−0.428688	+	0.903453i	$0.641024\pi$
$74$	1.91883	−	5.90555i	0.223059	−	0.686506i
$75$	−2.63885	−	1.91724i	−0.304709	−	0.221384i
$76$	0.0940841			0.0107922
$77$		0			0
$78$	−8.65275			−0.979731
$79$	4.69917	+	3.41415i	0.528698	+	0.384122i	0.819871	−	0.572549i	$-0.194045\pi$
$79$	4.69917	+	3.41415i	0.528698	+	0.384122i	−0.291173	+	0.956671i	$0.594045\pi$
$80$	−1.16039	+	3.57132i	−0.129736	+	0.399285i
$81$	8.17092	+	25.1475i	0.907880	+	2.79417i
$82$	−2.02796	+	1.47340i	−0.223951	+	0.162710i
$83$	12.9258	−	9.39111i	1.41879	−	1.03081i	0.426815	−	0.904339i	$-0.359635\pi$
$83$	12.9258	−	9.39111i	1.41879	−	1.03081i	0.991971	−	0.126469i	$-0.0403645\pi$
$84$	−0.160150	−	0.492892i	−0.0174738	−	0.0537790i
$85$	−1.91883	+	5.90555i	−0.208126	+	0.640547i
$86$	7.17667	+	5.21416i	0.773880	+	0.562257i
$87$	25.5566			2.73995
$88$		0			0
$89$	−2.70789			−0.287036			−0.143518	−	0.989648i	$-0.545842\pi$
$89$	−2.70789			−0.287036			−0.143518	+	0.989648i	$0.545842\pi$
$90$	8.48367	+	6.16374i	0.894257	+	0.649716i
$91$	0.819745	−	2.52292i	0.0859327	−	0.264474i
$92$	0.130174	+	0.400635i	0.0135716	+	0.0417691i
$93$	8.99283	−	6.53367i	0.932513	−	0.677510i
$94$	5.26187	−	3.82297i	0.542721	−	0.394310i
$95$	−0.251177	−	0.773043i	−0.0257702	−	0.0793125i
$96$	−0.659139	+	2.02862i	−0.0672731	+	0.207045i
$97$	−11.4581	−	8.32478i	−1.16339	−	0.845253i	−0.173188	−	0.984889i	$-0.555407\pi$
$97$	−11.4581	−	8.32478i	−1.16339	−	0.845253i	−0.990203	+	0.139636i	$0.955407\pi$
$98$	7.02229			0.709358
$99$		0			0
$100$	−0.115749			−0.0115749
$101$	9.22734	+	6.70405i	0.918154	+	0.667078i	0.943064	−	0.332612i	$-0.107930\pi$
$101$	9.22734	+	6.70405i	0.918154	+	0.667078i	−0.0249097	+	0.999690i	$0.507930\pi$
$102$	8.59139	−	26.4416i	0.850674	−	2.61811i
$103$	4.28633	+	13.1920i	0.422345	+	1.29984i	0.905514	+	0.424316i	$0.139485\pi$
$103$	4.28633	+	13.1920i	0.422345	+	1.29984i	−0.483170	+	0.875527i	$0.660515\pi$
$104$	−4.54065	+	3.29898i	−0.445248	+	0.323491i
$105$	−3.62230	+	2.63176i	−0.353500	+	0.256833i
$106$	3.56077	+	10.9589i	0.345853	+	1.06443i
$107$	0.329349	−	1.01363i	0.0318394	−	0.0979916i	−0.933874	−	0.357602i	$-0.883594\pi$
$107$	0.329349	−	1.01363i	0.0318394	−	0.0979916i	0.965713	+	0.259611i	$0.0835943\pi$
$108$	1.41707	+	1.02956i	0.136358	+	0.0990697i
$109$	−11.3115			−1.08345			−0.541724	−	0.840556i	$-0.682228\pi$
$109$	−11.3115			−1.08345			−0.541724	+	0.840556i	$0.682228\pi$
$110$		0			0
$111$	−14.7551			−1.40049
$112$	4.17012	+	3.02977i	0.394040	+	0.286287i
$113$	−1.16453	+	3.58406i	−0.109550	+	0.337160i	−0.990771	−	0.135544i	$-0.956722\pi$
$113$	−1.16453	+	3.58406i	−0.109550	+	0.337160i	0.881222	+	0.472704i	$0.156722\pi$
$114$	1.12462	+	3.46123i	0.105331	+	0.324174i
$115$	2.94430	−	2.13916i	0.274557	−	0.199478i
$116$	0.733705	−	0.533068i	0.0681228	−	0.0494941i
$117$	4.56212	+	14.0407i	0.421768	+	1.29807i
$118$	−0.473280	+	1.45661i	−0.0435690	+	0.134092i
$119$	6.89574	+	5.01005i	0.632132	+	0.459270i
$120$	9.47308			0.864770
$121$		0			0
$122$	−3.49330			−0.316269
$123$	4.81890	+	3.50114i	0.434506	+	0.315687i
$124$	0.121894	−	0.375151i	0.0109464	−	0.0336896i
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$	11.6454	−	8.46085i	1.03745	−	0.753752i
$127$	−1.35880	+	0.987223i	−0.120574	+	0.0876019i	−0.646438	−	0.762967i	$-0.723742\pi$
$127$	−1.35880	+	0.987223i	−0.120574	+	0.0876019i	0.525864	+	0.850569i	$0.323742\pi$
$128$	−3.16230	−	9.73256i	−0.279510	−	0.860245i
$129$	6.51382	−	20.0475i	0.573510	−	1.76508i
$130$	2.14612	+	1.55925i	0.188227	+	0.136755i
$131$	−11.7943			−1.03047			−0.515235	−	0.857049i	$-0.672295\pi$
$131$	−11.7943			−1.03047			−0.515235	+	0.857049i	$0.672295\pi$
$132$		0			0
$133$	−1.11575			−0.0967477
$134$	3.04083	+	2.20929i	0.262687	+	0.190854i
$135$	4.67625	−	14.3920i	0.402467	−	1.23867i
$136$	−5.57275	−	17.1512i	−0.477860	−	1.47070i
$137$	5.99308	−	4.35423i	0.512023	−	0.372007i	−0.301567	−	0.953445i	$-0.597510\pi$
$137$	5.99308	−	4.35423i	0.512023	−	0.372007i	0.813591	+	0.581438i	$0.197510\pi$
$138$	−13.1828	+	9.57789i	−1.12220	+	0.815324i
$139$	0.819289	+	2.52151i	0.0694912	+	0.213872i	0.979771	−	0.200121i	$-0.0641337\pi$
$139$	0.819289	+	2.52151i	0.0694912	+	0.213872i	−0.910280	+	0.413993i	$0.864134\pi$
$140$	−0.0490987	+	0.151110i	−0.00414960	+	0.0127712i
$141$	−12.5034	−	9.08426i	−1.05298	−	0.765033i
$142$	1.53157			0.128526
$143$		0			0
$144$	−28.6866			−2.39055
$145$	−6.33874	−	4.60536i	−0.526404	−	0.382455i
$146$	−5.26788	+	16.2129i	−0.435973	+	1.34179i
$147$	−5.15643	−	15.8699i	−0.425295	−	1.30892i
$148$	−0.423605	+	0.307767i	−0.0348201	+	0.0252983i
$149$	6.75802	−	4.90999i	0.553638	−	0.402242i	−0.275487	−	0.961305i	$-0.588839\pi$
$149$	6.75802	−	4.90999i	0.553638	−	0.402242i	0.829125	+	0.559063i	$0.188839\pi$
$150$	−1.38360	−	4.25827i	−0.112970	−	0.347686i
$151$	−2.29391	+	7.05994i	−0.186676	+	0.574529i	−0.999973	−	0.00731897i	$-0.997670\pi$
$151$	−2.29391	+	7.05994i	−0.186676	+	0.574529i	0.813297	+	0.581848i	$0.197670\pi$
$152$	1.90980	+	1.38755i	0.154905	+	0.112545i
$153$	−47.4363			−3.83500
$154$		0			0
$155$	−3.40786			−0.273726
$156$	0.590284	+	0.428867i	0.0472606	+	0.0343368i
$157$	−2.65267	+	8.16407i	−0.211706	+	0.651564i	0.787665	+	0.616104i	$0.211290\pi$
$157$	−2.65267	+	8.16407i	−0.211706	+	0.651564i	−0.999371	+	0.0354602i	$0.988710\pi$
$158$	2.46386	+	7.58297i	0.196014	+	0.603269i
$159$	22.1517	−	16.0942i	1.75675	−	1.27635i
$160$	0.529047	−	0.384375i	0.0418249	−	0.0303875i
$161$	−1.54375	−	4.75116i	−0.121664	−	0.374444i
$162$	−11.2161	+	34.5195i	−0.881217	+	2.71211i
$163$	−13.2497	−	9.62648i	−1.03780	−	0.754004i	−0.0679435	−	0.997689i	$-0.521644\pi$
$163$	−13.2497	−	9.62648i	−1.03780	−	0.754004i	−0.969854	+	0.243685i	$0.921644\pi$
$164$	0.211374			0.0165055
$165$		0			0
$166$	21.9315			1.70221
$167$	17.3441	+	12.6013i	1.34213	+	0.975115i	0.999363	+	0.0356948i	$0.0113644\pi$
$167$	17.3441	+	12.6013i	1.34213	+	0.975115i	0.342768	+	0.939420i	$0.388636\pi$
$168$	4.01830	−	12.3671i	0.310019	−	0.954140i
$169$	−2.86314	−	8.81183i	−0.220241	−	0.677833i
$170$	−6.89574	+	5.01005i	−0.528879	+	0.384253i
$171$	5.02356	−	3.64983i	0.384161	−	0.279109i
$172$	−0.231152	−	0.711412i	−0.0176252	−	0.0542446i
$173$	−4.24518	+	13.0653i	−0.322755	+	0.993338i	0.649689	+	0.760200i	$0.274899\pi$
$173$	−4.24518	+	13.0653i	−0.322755	+	0.993338i	−0.972444	+	0.233138i	$0.925101\pi$
$174$	28.3811	+	20.6201i	2.15157	+	1.56321i
$175$	1.37268			0.103765
$176$		0			0
$177$	3.63935			0.273551
$178$	−3.00717	−	2.18484i	−0.225397	−	0.163761i
$179$	−1.16453	+	3.58406i	−0.0870411	+	0.267885i	−0.985098	−	0.171995i	$-0.944979\pi$
$179$	−1.16453	+	3.58406i	−0.0870411	+	0.267885i	0.898057	+	0.439880i	$0.144979\pi$
$180$	−0.273248	−	0.840972i	−0.0203667	−	0.0626824i
$181$	0.0108391	−	0.00787510i	0.000805667	−	0.000585352i	−0.587382	−	0.809310i	$-0.699842\pi$
$181$	0.0108391	−	0.00787510i	0.000805667	−	0.000585352i	0.588188	+	0.808724i	$0.299842\pi$
$182$	2.94594	−	2.14035i	0.218367	−	0.158653i
$183$	2.56511	+	7.89461i	0.189619	+	0.583586i
$184$	−3.26618	+	10.0523i	−0.240786	+	0.741063i
$185$	3.65967	+	2.65891i	0.269065	+	0.195487i
$186$	15.2584			1.11880
$187$		0			0
$188$	−0.548444			−0.0399994
$189$	−16.8051	−	12.2096i	−1.22239	−	0.888121i
$190$	0.344786	−	1.06114i	0.0250134	−	0.0769832i
$191$	−5.13770	−	15.8122i	−0.371751	−	1.14413i	−0.945644	−	0.325202i	$-0.894568\pi$
$191$	−5.13770	−	15.8122i	−0.371751	−	1.14413i	0.573893	−	0.818930i	$-0.305432\pi$
$192$	−22.1871	+	16.1199i	−1.60122	+	1.16335i
$193$	−21.6665	+	15.7416i	−1.55959	+	1.13311i	−0.623244	+	0.782028i	$0.714186\pi$
$193$	−21.6665	+	15.7416i	−1.55959	+	1.13311i	−0.936345	+	0.351080i	$0.885814\pi$
$194$	−6.00766	−	18.4897i	−0.431325	−	1.32748i
$195$	1.94790	−	5.99503i	0.139492	−	0.429313i
$196$	−0.479055	−	0.348054i	−0.0342182	−	0.0248610i
$197$	2.55719			0.182192			0.0910962	−	0.995842i	$-0.470963\pi$
$197$	2.55719			0.182192			0.0910962	+	0.995842i	$0.470963\pi$
$198$		0			0
$199$	−21.8629			−1.54982			−0.774911	−	0.632071i	$-0.782205\pi$
$199$	−21.8629			−1.54982			−0.774911	+	0.632071i	$0.782205\pi$
$200$	−2.34959	−	1.70707i	−0.166141	−	0.120708i
$201$	2.75997	−	8.49432i	0.194673	−	0.599143i
$202$	4.83805	+	14.8900i	0.340404	+	1.04766i
$203$	−8.70106	+	6.32169i	−0.610695	+	0.443696i
$204$	−1.89665	+	1.37800i	−0.132792	+	0.0964793i
$205$	−0.564307	−	1.73676i	−0.0394129	−	0.121300i
$206$	−5.88376	+	18.1083i	−0.409941	+	1.26167i
$207$	22.4925	+	16.3418i	1.56334	+	1.13583i
$208$	−7.25687			−0.503173
$209$		0			0
$210$	−6.14605			−0.424118
$211$	−10.3803	−	7.54174i	−0.714611	−	0.519195i	0.170047	−	0.985436i	$-0.445608\pi$
$211$	−10.3803	−	7.54174i	−0.714611	−	0.519195i	−0.884658	+	0.466241i	$0.845608\pi$
$212$	0.300257	−	0.924097i	0.0206218	−	0.0634673i
$213$	−1.12462	−	3.46123i	−0.0770578	−	0.237160i
$214$	1.18359	−	0.859928i	0.0809085	−	0.0587835i
$215$	−5.22822	+	3.79852i	−0.356562	+	0.259057i
$216$	13.5810	+	41.7980i	0.924069	+	2.84399i
$217$	−1.44555	+	4.44894i	−0.0981303	+	0.302014i
$218$	−12.5617	−	9.12661i	−0.850786	−	0.618132i
$219$	40.5081			2.73728
$220$		0			0
$221$	−12.0000			−0.807207
$222$	−16.3859	−	11.9050i	−1.09975	−	0.799013i
$223$	−2.27565	+	7.00373i	−0.152389	+	0.469004i	−0.997887	−	0.0649740i	$-0.979304\pi$
$223$	−2.27565	+	7.00373i	−0.152389	+	0.469004i	0.845498	+	0.533978i	$0.179304\pi$
$224$	−0.277389	−	0.853714i	−0.0185338	−	0.0570412i
$225$	−6.18037	+	4.49030i	−0.412024	+	0.299353i
$226$	−4.18500	+	3.04058i	−0.278382	+	0.202256i
$227$	0.424181	+	1.30550i	0.0281539	+	0.0866488i	0.964146	−	0.265372i	$-0.0854947\pi$
$227$	0.424181	+	1.30550i	0.0281539	+	0.0866488i	−0.935992	+	0.352021i	$0.885495\pi$
$228$	0.0948323	−	0.291864i	0.00628042	−	0.0193291i
$229$	−23.8634	−	17.3378i	−1.57694	−	1.14571i	−0.920101	−	0.391682i	$-0.871893\pi$
$229$	−23.8634	−	17.3378i	−1.57694	−	1.14571i	−0.656839	−	0.754031i	$-0.728107\pi$
$230$	4.99567			0.329405
$231$		0			0
$232$	22.7551			1.49395
$233$	−17.7971	−	12.9303i	−1.16593	−	0.847095i	−0.175410	−	0.984495i	$-0.556125\pi$
$233$	−17.7971	−	12.9303i	−1.16593	−	0.847095i	−0.990516	+	0.137401i	$0.956125\pi$
$234$	−6.26233	+	19.2735i	−0.409381	+	1.25995i
$235$	1.46418	+	4.50629i	0.0955128	+	0.293958i
$236$	0.104482	−	0.0759109i	0.00680122	−	0.00494138i
$237$	15.3278	−	11.1363i	0.995645	−	0.723379i
$238$	3.61556	+	11.1275i	0.234362	+	0.721291i
$239$	5.78556	−	17.8061i	0.374237	−	1.15178i	−0.569755	−	0.821814i	$-0.692962\pi$
$239$	5.78556	−	17.8061i	0.374237	−	1.15178i	0.943992	−	0.329968i	$-0.107038\pi$
$240$	9.90917	+	7.19943i	0.639634	+	0.464721i
$241$	−26.2630			−1.69175			−0.845875	−	0.533382i	$-0.820921\pi$
$241$	−26.2630			−1.69175			−0.845875	+	0.533382i	$0.820921\pi$
$242$		0			0
$243$	40.8495			2.62050
$244$	0.238310	+	0.173143i	0.0152563	+	0.0110843i
$245$	−1.58085	+	4.86537i	−0.100997	+	0.310837i
$246$	2.52663	+	7.77618i	0.161092	+	0.495791i
$247$	1.27081	−	0.923301i	0.0808600	−	0.0587482i
$248$	8.00705	−	5.81746i	0.508448	−	0.369409i
$249$	−16.1042	−	49.5635i	−1.02056	−	3.14096i
$250$	−0.424181	+	1.30550i	−0.0268276	+	0.0825668i
$251$	18.3048	+	13.2992i	1.15539	+	0.839438i	0.989188	−	0.146654i	$-0.0468503\pi$
$251$	18.3048	+	13.2992i	1.15539	+	0.839438i	0.166200	+	0.986092i	$0.446850\pi$
$252$	−1.21379			−0.0764618
$253$		0			0
$254$	−2.30550			−0.144660
$255$	16.3859	+	11.9050i	1.02612	+	0.745522i
$256$	−0.855514	+	2.63300i	−0.0534696	+	0.164563i
$257$	5.31823	+	16.3678i	0.331742	+	1.02100i	0.968305	+	0.249773i	$0.0803559\pi$
$257$	5.31823	+	16.3678i	0.331742	+	1.02100i	−0.636562	+	0.771225i	$0.719644\pi$
$258$	23.4089	−	17.0075i	1.45737	−	1.05884i
$259$	5.02356	−	3.64983i	0.312149	−	0.226789i
$260$	−0.0691239	−	0.212742i	−0.00428688	−	0.0131937i
$261$	18.4963	−	56.9257i	1.14489	−	3.52361i
$262$	−13.0978	−	9.51610i	−0.809184	−	0.587907i
$263$	5.71441			0.352366			0.176183	−	0.984357i	$-0.443625\pi$
$263$	5.71441			0.352366			0.176183	+	0.984357i	$0.443625\pi$
$264$		0			0
$265$	−8.39446			−0.515667
$266$	−1.23906	−	0.900232i	−0.0759719	−	0.0551968i
$267$	−2.72943	+	8.40032i	−0.167038	+	0.514091i
$268$	−0.0979413	−	0.301432i	−0.00598272	−	0.0184129i
$269$	2.32257	−	1.68744i	0.141610	−	0.102885i	−0.514725	−	0.857355i	$-0.672106\pi$
$269$	2.32257	−	1.68744i	0.141610	−	0.102885i	0.656335	+	0.754470i	$0.272106\pi$
$270$	16.8051	−	12.2096i	1.02273	−	0.743056i
$271$	−2.36304	−	7.27268i	−0.143544	−	0.441784i	0.853277	−	0.521458i	$-0.174612\pi$
$271$	−2.36304	−	7.27268i	−0.143544	−	0.441784i	−0.996821	+	0.0796748i	$0.974612\pi$
$272$	7.20540	−	22.1759i	0.436892	−	1.34461i
$273$	−7.00022	−	5.08596i	−0.423673	−	0.307816i
$274$	10.1686			0.614309
$275$		0			0
$276$	1.37404			0.0827077
$277$	23.7827	+	17.2791i	1.42896	+	1.03820i	0.990209	+	0.139596i	$0.0445804\pi$
$277$	23.7827	+	17.2791i	1.42896	+	1.03820i	0.438755	+	0.898607i	$0.355420\pi$
$278$	−1.12462	+	3.46123i	−0.0674504	+	0.207591i
$279$	−8.04489	−	24.7596i	−0.481635	−	1.48232i
$280$	−3.22523	+	2.34327i	−0.192744	+	0.140037i
$281$	−19.5977	+	14.2386i	−1.16910	+	0.849401i	−0.990901	−	0.134593i	$-0.957027\pi$
$281$	−19.5977	+	14.2386i	−1.16910	+	0.849401i	−0.178199	+	0.983994i	$0.557027\pi$
$282$	−6.55575	−	20.1765i	−0.390389	−	1.20149i
$283$	1.58187	−	4.86849i	0.0940323	−	0.289402i	−0.892968	−	0.450120i	$-0.851381\pi$
$283$	1.58187	−	4.86849i	0.0940323	−	0.289402i	0.987000	+	0.160718i	$0.0513811\pi$
$284$	−0.104482	−	0.0759109i	−0.00619989	−	0.00450448i
$285$	−2.65128			−0.157048
$286$		0			0
$287$	−2.50670			−0.147966
$288$	4.04158	+	2.93638i	0.238152	+	0.173028i
$289$	6.66161	−	20.5023i	0.391859	−	1.20602i
$290$	−3.32351	−	10.2287i	−0.195163	−	0.600651i
$291$	−37.3740	+	27.1538i	−2.19090	+	1.59178i
$292$	1.16295	−	0.844931i	0.0680564	−	0.0494459i
$293$	3.39682	+	10.4543i	0.198444	+	0.610748i	0.999919	+	0.0127200i	$0.00404900\pi$
$293$	3.39682	+	10.4543i	0.198444	+	0.610748i	−0.801475	+	0.598028i	$0.795951\pi$
$294$	7.07813	−	21.7842i	0.412805	−	1.27048i
$295$	−0.902660	−	0.655821i	−0.0525549	−	0.0381834i
$296$	−13.1377			−0.763611
$297$		0			0
$298$	11.4665			0.664237
$299$	5.68996	+	4.13400i	0.329059	+	0.239075i
$300$	−0.116670	+	0.359073i	−0.00673594	+	0.0207311i
$301$	2.74124	+	8.43668i	0.158003	+	0.486282i
$302$	−8.24368	+	5.98939i	−0.474371	+	0.344651i
$303$	30.0977	−	21.8673i	1.72907	−	1.25624i
$304$	0.943195	+	2.90286i	0.0540960	+	0.166490i
$305$	0.786410	−	2.42032i	0.0450297	−	0.138587i
$306$	−52.6790	−	38.2735i	−3.01146	−	2.18795i
$307$	−14.3515			−0.819081			−0.409540	−	0.912292i	$-0.634311\pi$
$307$	−14.3515			−0.819081			−0.409540	+	0.912292i	$0.634311\pi$
$308$		0			0
$309$	45.2440			2.57384
$310$	−3.78450	−	2.74960i	−0.214945	−	0.156167i
$311$	8.46121	−	26.0409i	0.479791	−	1.47665i	−0.359594	−	0.933109i	$-0.617085\pi$
$311$	8.46121	−	26.0409i	0.479791	−	1.47665i	0.839385	−	0.543537i	$-0.182915\pi$
$312$	5.65719	+	17.4110i	0.320275	+	0.985706i
$313$	−3.13159	+	2.27523i	−0.177008	+	0.128604i	−0.672761	−	0.739860i	$-0.734892\pi$
$313$	−3.13159	+	2.27523i	−0.177008	+	0.128604i	0.495754	+	0.868463i	$0.334892\pi$
$314$	−9.53295	+	6.92609i	−0.537976	+	0.390862i
$315$	3.24047	+	9.97315i	0.182580	+	0.561923i
$316$	0.207761	−	0.639424i	0.0116875	−	0.0359704i
$317$	12.5480	+	9.11667i	0.704767	+	0.512043i	0.881481	−	0.472219i	$-0.156547\pi$
$317$	12.5480	+	9.11667i	0.704767	+	0.512043i	−0.176714	+	0.984262i	$0.556547\pi$
$318$	37.5854			2.10769
$319$		0			0
$320$	8.40786			0.470013
$321$	−2.81248	−	2.04339i	−0.156977	−	0.114051i
$322$	2.11907	−	6.52183i	0.118091	−	0.363447i
$323$	1.55967	+	4.80018i	0.0867825	+	0.267089i
$324$	2.47608	−	1.79898i	0.137560	−	0.0999433i
$325$	−1.56345	+	1.13592i	−0.0867248	+	0.0630092i
$326$	−6.94705	−	21.3808i	−0.384762	−	1.18417i
$327$	−11.4015	+	35.0902i	−0.630503	+	1.94049i
$328$	4.29066	+	3.11735i	0.236912	+	0.172127i
$329$	6.50403			0.358579
$330$		0			0
$331$	26.8575			1.47622			0.738110	−	0.674681i	$-0.235719\pi$
$331$	26.8575			1.47622			0.738110	+	0.674681i	$0.235719\pi$
$332$	−1.49615	−	1.08702i	−0.0821118	−	0.0596577i
$333$	−10.6788	+	32.8661i	−0.585196	+	1.80105i
$334$	9.09383	+	27.9879i	0.497593	+	1.53143i
$335$	−2.21525	+	1.60947i	−0.121032	+	0.0879349i
$336$	13.6021	−	9.88252i	0.742056	−	0.539135i
$337$	−0.597186	−	1.83795i	−0.0325308	−	0.100119i	0.933473	−	0.358648i	$-0.116762\pi$
$337$	−0.597186	−	1.83795i	−0.0325308	−	0.100119i	−0.966004	+	0.258529i	$0.916762\pi$
$338$	3.93017	−	12.0958i	0.213773	−	0.657926i
$339$	9.94452	+	7.22512i	0.540112	+	0.392415i
$340$	0.718741			0.0389792
$341$		0			0
$342$	8.52360			0.460904
$343$	13.4548	+	9.77548i	0.726491	+	0.527827i
$344$	5.79979	−	17.8499i	0.312703	−	0.962402i
$345$	−3.66830	−	11.2899i	−0.197494	−	0.607825i
$346$	−15.2560	+	11.0841i	−0.820168	+	0.595887i
$347$	3.07448	−	2.23374i	0.165047	−	0.119913i	−0.502196	−	0.864754i	$-0.667474\pi$
$347$	3.07448	−	2.23374i	0.165047	−	0.119913i	0.667243	+	0.744840i	$0.267474\pi$
$348$	−0.914122	−	2.81338i	−0.0490021	−	0.150813i
$349$	−5.31228	+	16.3495i	−0.284360	+	0.875170i	0.702230	+	0.711950i	$0.252188\pi$
$349$	−5.31228	+	16.3495i	−0.284360	+	0.875170i	−0.986590	+	0.163219i	$0.947812\pi$
$350$	1.52439	+	1.10753i	0.0814821	+	0.0592002i
$351$	29.2444			1.56095
$352$		0			0
$353$	−1.99207			−0.106027			−0.0530135	−	0.998594i	$-0.516883\pi$
$353$	−1.99207			−0.106027			−0.0530135	+	0.998594i	$0.516883\pi$
$354$	4.04158	+	2.93638i	0.214808	+	0.156067i
$355$	−0.344786	+	1.06114i	−0.0182993	+	0.0563195i
$356$	0.0968574	+	0.298096i	0.00513343	+	0.0157991i
$357$	22.4925	−	16.3418i	1.19043	−	0.864899i
$358$	−4.18500	+	3.04058i	−0.221184	+	0.160700i
$359$	4.81329	+	14.8138i	0.254036	+	0.781842i	0.994018	+	0.109216i	$0.0348339\pi$
$359$	4.81329	+	14.8138i	0.254036	+	0.781842i	−0.739982	+	0.672626i	$0.765166\pi$
$360$	6.85603	−	21.1007i	0.361344	−	1.11210i
$361$	14.8368	+	10.7796i	0.780885	+	0.567346i
$362$	0.0183911			0.000966613
$363$		0			0
$364$	−0.307054			−0.0160940
$365$	−10.0471	−	7.29966i	−0.525890	−	0.382082i
$366$	−3.52108	+	10.8368i	−0.184050	+	0.566447i
$367$	5.80087	+	17.8532i	0.302803	+	0.931932i	0.980488	+	0.196579i	$0.0629833\pi$
$367$	5.80087	+	17.8532i	0.302803	+	0.931932i	−0.677685	+	0.735352i	$0.737017\pi$
$368$	−11.0561	+	8.03276i	−0.576342	+	0.418737i
$369$	11.2862	−	8.19989i	0.587535	−	0.426869i
$370$	1.91883	+	5.90555i	0.0997552	+	0.307015i
$371$	−3.56077	+	10.9589i	−0.184866	+	0.568959i
$372$	−1.04091	−	0.756269i	−0.0539689	−	0.0392107i
$373$	2.62664			0.136003			0.0680013	−	0.997685i	$-0.478338\pi$
$373$	2.62664			0.136003			0.0680013	+	0.997685i	$0.478338\pi$
$374$		0			0
$375$	3.26180			0.168439
$376$	−11.1328	−	8.08845i	−0.574130	−	0.417130i
$377$	4.67902	−	14.4005i	0.240982	−	0.741666i
$378$	−8.81122	−	27.1182i	−0.453200	−	1.39481i
$379$	−2.15254	+	1.56391i	−0.110569	+	0.0803327i	−0.641696	−	0.766959i	$-0.721769\pi$
$379$	−2.15254	+	1.56391i	−0.110569	+	0.0803327i	0.531127	+	0.847292i	$0.321769\pi$
$380$	−0.0761156	+	0.0553012i	−0.00390465	+	0.00283689i
$381$	1.69292	+	5.21027i	0.0867309	+	0.266930i
$382$	7.05242	−	21.7051i	0.360833	−	1.11053i
$383$	−17.7429	−	12.8910i	−0.906621	−	0.658699i	0.0335370	−	0.999437i	$-0.489323\pi$
$383$	−17.7429	−	12.8910i	−0.906621	−	0.658699i	−0.940158	+	0.340739i	$0.889323\pi$
$384$	−33.3794			−1.70338
$385$		0			0
$386$	−36.7621			−1.87114
$387$	−39.9402	−	29.0183i	−2.03027	−	1.47508i
$388$	−0.506588	+	1.55912i	−0.0257181	+	0.0791522i
$389$	−1.05723	−	3.25380i	−0.0536035	−	0.164974i	0.920671	−	0.390340i	$-0.127642\pi$
$389$	−1.05723	−	3.25380i	−0.0536035	−	0.164974i	−0.974274	+	0.225365i	$0.927642\pi$
$390$	7.00022	−	5.08596i	0.354470	−	0.257538i
$391$	−18.2825	+	13.2830i	−0.924586	+	0.671751i
$392$	−4.59119	−	14.1302i	−0.231890	−	0.713684i
$393$	−11.8881	+	36.5877i	−0.599673	+	1.84560i
$394$	2.83982	+	2.06325i	0.143068	+	0.103945i
$395$	−5.80849			−0.292257
$396$		0			0
$397$	5.51021			0.276549			0.138275	−	0.990394i	$-0.455844\pi$
$397$	5.51021			0.276549			0.138275	+	0.990394i	$0.455844\pi$
$398$	−24.2792	−	17.6399i	−1.21701	−	0.884208i
$399$	−1.12462	+	3.46123i	−0.0563015	+	0.173278i
$400$	−1.16039	−	3.57132i	−0.0580195	−	0.178566i
$401$	14.5024	−	10.5366i	0.724217	−	0.526174i	−0.163512	−	0.986541i	$-0.552282\pi$
$401$	14.5024	−	10.5366i	0.724217	−	0.526174i	0.887729	+	0.460367i	$0.152282\pi$
$402$	9.91858	−	7.20627i	0.494694	−	0.359416i
$403$	−2.03512	−	6.26347i	−0.101377	−	0.312005i
$404$	0.407962	−	1.25558i	0.0202969	−	0.0624673i
$405$	−21.3918	−	15.5420i	−1.06296	−	0.772289i
$406$	−14.7633			−0.732691
$407$		0			0
$408$	−58.8227			−2.91216
$409$	−23.7254	−	17.2375i	−1.17314	−	0.852338i	−0.181761	−	0.983343i	$-0.558180\pi$
$409$	−23.7254	−	17.2375i	−1.17314	−	0.852338i	−0.991382	+	0.131004i	$0.958180\pi$
$410$	0.774613	−	2.38401i	0.0382554	−	0.117738i
$411$	−7.46676	−	22.9803i	−0.368308	−	1.13354i
$412$	1.29891	−	0.943714i	0.0639928	−	0.0464935i
$413$	−1.23906	+	0.900232i	−0.0609703	+	0.0442975i
$414$	11.7932	+	36.2958i	0.579605	+	1.78384i
$415$	−4.93720	+	15.1951i	−0.242358	+	0.745900i
$416$	1.02240	+	0.742819i	0.0501274	+	0.0364197i
$417$	8.64794			0.423491
$418$		0			0
$419$	2.65275			0.129595			0.0647977	−	0.997898i	$-0.479360\pi$
$419$	2.65275			0.129595			0.0647977	+	0.997898i	$0.479360\pi$
$420$	0.419279	+	0.304624i	0.0204587	+	0.0148641i
$421$	−3.44954	+	10.6166i	−0.168120	+	0.517422i	−0.999253	−	0.0386532i	$-0.987693\pi$
$421$	−3.44954	+	10.6166i	−0.168120	+	0.517422i	0.831132	+	0.556075i	$0.187693\pi$
$422$	−5.44258	−	16.7505i	−0.264941	−	0.815403i
$423$	−29.2838	+	21.2759i	−1.42383	+	1.03447i
$424$	19.7235	−	14.3300i	0.957857	−	0.695924i
$425$	−1.91883	−	5.90555i	−0.0930769	−	0.286461i
$426$	1.54375	−	4.75116i	0.0747948	−	0.230195i
$427$	−2.82614	−	2.05331i	−0.136766	−	0.0993667i
$428$	−0.123365			−0.00596309
$429$		0			0
$430$	−8.87085			−0.427791
$431$	−3.68845	−	2.67982i	−0.177667	−	0.129082i	0.495398	−	0.868666i	$-0.335022\pi$
$431$	−3.68845	−	2.67982i	−0.177667	−	0.129082i	−0.673064	+	0.739584i	$0.735022\pi$
$432$	−17.5598	+	54.0435i	−0.844846	+	2.60017i
$433$	6.23070	+	19.1761i	0.299428	+	0.921545i	0.981698	+	0.190445i	$0.0609930\pi$
$433$	6.23070	+	19.1761i	0.299428	+	0.921545i	−0.682270	+	0.731101i	$0.739007\pi$
$434$	−5.19490	+	3.77432i	−0.249363	+	0.181173i
$435$	−20.6757	+	15.0218i	−0.991325	+	0.720240i
$436$	0.404597	+	1.24522i	0.0193767	+	0.0596353i
$437$	0.914122	−	2.81338i	0.0437284	−	0.134582i
$438$	44.9851	+	32.6836i	2.14947	+	1.56168i
$439$	−34.4868			−1.64596			−0.822982	−	0.568067i	$-0.807691\pi$
$439$	−34.4868			−1.64596			−0.822982	+	0.568067i	$0.807691\pi$
$440$		0			0
$441$	−39.0810			−1.86100
$442$	−13.3263	−	9.68209i	−0.633865	−	0.460530i
$443$	9.72123	−	29.9189i	0.461870	−	1.42149i	−0.401007	−	0.916075i	$-0.631340\pi$
$443$	9.72123	−	29.9189i	0.461870	−	1.42149i	0.862877	−	0.505414i	$-0.168660\pi$
$444$	0.527768	+	1.62430i	0.0250468	+	0.0770861i
$445$	2.19073	−	1.59166i	0.103851	−	0.0754519i
$446$	−8.17805	+	5.94170i	−0.387242	+	0.281348i
$447$	−8.41980	−	25.9135i	−0.398243	−	1.22567i
$448$	3.56646	−	10.9764i	0.168499	−	0.518587i
$449$	3.86422	+	2.80752i	0.182364	+	0.132495i	0.675222	−	0.737615i	$-0.264048\pi$
$449$	3.86422	+	2.80752i	0.182364	+	0.132495i	−0.492858	+	0.870110i	$0.664048\pi$
$450$	−10.4864			−0.494333
$451$		0			0
$452$	0.436202			0.0205172
$453$	19.5889	+	14.2322i	0.920366	+	0.668685i
$454$	−0.582265	+	1.79203i	−0.0273271	+	0.0841041i
$455$	0.819745	+	2.52292i	0.0384303	+	0.118276i
$456$	6.22940	−	4.52592i	0.291718	−	0.211946i
$457$	−1.23906	+	0.900232i	−0.0579610	+	0.0421111i	−0.616388	−	0.787442i	$-0.711405\pi$
$457$	−1.23906	+	0.900232i	−0.0579610	+	0.0421111i	0.558428	+	0.829553i	$0.311405\pi$
$458$	−12.5120	−	38.5080i	−0.584647	−	1.79936i
$459$	−29.0370	+	89.3666i	−1.35533	+	4.17128i
$460$	−0.340801	−	0.247606i	−0.0158899	−	0.0115447i
$461$	18.5220			0.862655			0.431327	−	0.902195i	$-0.358045\pi$
$461$	18.5220			0.862655			0.431327	+	0.902195i	$0.358045\pi$
$462$		0			0
$463$	9.68306			0.450010			0.225005	−	0.974358i	$-0.427760\pi$
$463$	9.68306			0.450010			0.225005	+	0.974358i	$0.427760\pi$
$464$	23.8026	+	17.2936i	1.10501	+	0.802836i
$465$	−3.43496	+	10.5717i	−0.159292	+	0.490251i
$466$	−9.33131	−	28.7188i	−0.432265	−	1.33037i
$467$	25.6442	−	18.6316i	1.18667	−	0.862169i	0.193764	−	0.981048i	$-0.437930\pi$
$467$	25.6442	−	18.6316i	1.18667	−	0.862169i	0.992909	+	0.118880i	$0.0379302\pi$
$468$	1.38248	−	1.00443i	0.0639054	−	0.0464300i
$469$	1.16149	+	3.57471i	0.0536328	+	0.165065i
$470$	−2.00986	+	6.18570i	−0.0927077	+	0.285325i
$471$	22.6525	+	16.4580i	1.04377	+	0.758344i
$472$	3.24041			0.149152
$473$		0			0
$474$	26.0070			1.19454
$475$	0.657590	+	0.477767i	0.0301723	+	0.0219214i
$476$	0.304877	−	0.938314i	0.0139740	−	0.0430076i
$477$	−19.8167	−	60.9896i	−0.907345	−	2.79252i
$478$	20.7917	−	15.1061i	0.950990	−	0.690935i
$479$	−24.9456	+	18.1241i	−1.13980	+	0.828110i	−0.987091	−	0.160162i	$-0.948798\pi$
$479$	−24.9456	+	18.1241i	−1.13980	+	0.828110i	−0.152705	+	0.988272i	$0.548798\pi$
$480$	−0.659139	−	2.02862i	−0.0300854	−	0.0925935i
$481$	−2.70143	+	8.31416i	−0.123175	+	0.379093i
$482$	−29.1656	−	21.1901i	−1.32846	−	0.965182i
$483$	−16.2949			−0.741443
$484$		0			0
$485$	14.1630			0.643107
$486$	45.3643	+	32.9591i	2.05777	+	1.49505i
$487$	9.26806	−	28.5242i	0.419976	−	1.29255i	−0.487748	−	0.872984i	$-0.662182\pi$
$487$	9.26806	−	28.5242i	0.419976	−	1.29255i	0.907724	−	0.419568i	$-0.137818\pi$
$488$	2.28393	+	7.02921i	0.103389	+	0.318197i
$489$	−43.2180	+	31.3997i	−1.95438	+	1.41994i
$490$	−5.68115	+	4.12760i	−0.256648	+	0.186466i
$491$	10.6646	+	32.8223i	0.481287	+	1.48125i	0.837287	+	0.546764i	$0.184140\pi$
$491$	10.6646	+	32.8223i	0.481287	+	1.48125i	−0.356000	+	0.934486i	$0.615860\pi$
$492$	0.213055	−	0.655716i	0.00960526	−	0.0295619i
$493$	39.3602	+	28.5968i	1.77269	+	1.28794i
$494$	2.15622			0.0970131
$495$		0			0
$496$	12.7968			0.574595
$497$	1.23906	+	0.900232i	0.0555796	+	0.0403809i
$498$	22.1059	−	68.0349i	0.990588	−	3.04871i
$499$	5.51995	+	16.9886i	0.247107	+	0.760516i	0.995283	+	0.0970160i	$0.0309298\pi$
$499$	5.51995	+	16.9886i	0.247107	+	0.760516i	−0.748176	+	0.663500i	$0.769070\pi$
$500$	0.0936432	−	0.0680358i	0.00418785	−	0.00304265i
$501$	56.5732	−	41.1028i	2.52750	−	1.83634i
$502$	9.59751	+	29.5381i	0.428358	+	1.31835i
$503$	1.58187	−	4.86849i	0.0705320	−	0.217075i	−0.909577	−	0.415536i	$-0.863594\pi$
$503$	1.58187	−	4.86849i	0.0705320	−	0.217075i	0.980109	+	0.198460i	$0.0635941\pi$
$504$	−24.6387	−	17.9010i	−1.09749	−	0.797376i
$505$	−11.4056			−0.507543
$506$		0			0
$507$	−30.2216			−1.34219
$508$	0.157280	+	0.114270i	0.00697816	+	0.00506993i
$509$	−5.59562	+	17.2216i	−0.248022	+	0.763332i	0.747103	+	0.664708i	$0.231444\pi$
$509$	−5.59562	+	17.2216i	−0.248022	+	0.763332i	−0.995125	+	0.0986239i	$0.968556\pi$
$510$	8.59139	+	26.4416i	0.380433	+	1.17085i
$511$	−13.7915	+	10.0201i	−0.610099	+	0.443263i
$512$	−19.6325	+	14.2638i	−0.867642	+	0.630379i
$513$	−3.80097	−	11.6982i	−0.167817	−	0.516488i
$514$	−7.30023	+	22.4678i	−0.322000	+	0.991013i
$515$	−11.2218	−	8.15308i	−0.494490	−	0.359268i
$516$	−2.43990			−0.107411
$517$		0			0
$518$	8.52360			0.374506
$519$	36.2518	+	26.3384i	1.59128	+	1.15613i
$520$	1.73438	−	5.33786i	0.0760574	−	0.234081i
$521$	−10.6830	−	32.8788i	−0.468029	−	1.44045i	−0.855132	−	0.518410i	$-0.826524\pi$
$521$	−10.6830	−	32.8788i	−0.468029	−	1.44045i	0.387103	−	0.922036i	$-0.373476\pi$
$522$	66.4705	−	48.2936i	2.90933	−	2.11376i
$523$	−26.5290	+	19.2745i	−1.16003	+	0.842813i	−0.989782	−	0.142587i	$-0.954458\pi$
$523$	−26.5290	+	19.2745i	−1.16003	+	0.842813i	−0.170251	+	0.985401i	$0.554458\pi$
$524$	0.421864	+	1.29836i	0.0184292	+	0.0567192i
$525$	1.38360	−	4.25827i	0.0603851	−	0.185846i
$526$	6.34598	+	4.61062i	0.276698	+	0.201033i
$527$	21.1609			0.921785
$528$		0			0
$529$	−9.75510			−0.424135
$530$	−9.32223	−	6.77299i	−0.404932	−	0.294200i
$531$	2.63394	−	8.10643i	0.114303	−	0.351789i
$532$	0.0399087	+	0.122826i	0.00173026	+	0.00532520i
$533$	2.85508	−	2.07433i	0.123667	−	0.0898494i
$534$	−9.80881	+	7.12652i	−0.424469	+	0.308395i
$535$	0.329349	+	1.01363i	0.0142390	+	0.0438232i
$536$	2.45743	−	7.56318i	0.106145	−	0.326680i
$537$	9.94452	+	7.22512i	0.429138	+	0.311787i
$538$	3.94076			0.169898
$539$		0			0
$540$	−1.75160			−0.0753767
$541$	−3.53738	−	2.57005i	−0.152084	−	0.110495i	0.509141	−	0.860683i	$-0.329963\pi$
$541$	−3.53738	−	2.57005i	−0.152084	−	0.110495i	−0.661225	+	0.750188i	$0.729963\pi$
$542$	3.24369	−	9.98306i	0.139329	−	0.428809i
$543$	−0.0135045	−	0.0415625i	−0.000579532	−	0.00178362i
$544$	−3.28510	+	2.38676i	−0.140848	+	0.102332i
$545$	9.15122	−	6.64875i	0.391995	−	0.284801i
$546$	−3.67034	−	11.2961i	−0.157076	−	0.483430i
$547$	9.77956	−	30.0984i	0.418144	−	1.28691i	−0.491264	−	0.871010i	$-0.663465\pi$
$547$	9.77956	−	30.0984i	0.418144	−	1.28691i	0.909408	−	0.415904i	$-0.136535\pi$
$548$	−0.693695	−	0.503999i	−0.0296332	−	0.0215298i
$549$	19.4412			0.829731
$550$		0			0
$551$	−6.36858			−0.271311
$552$	27.8916	+	20.2644i	1.18714	+	0.862511i
$553$	−2.46386	+	7.58297i	−0.104774	+	0.322461i
$554$	12.4697	+	38.3777i	0.529786	+	1.63051i
$555$	11.9371	−	8.67283i	0.506703	−	0.368141i
$556$	0.248274	−	0.180382i	0.0105292	−	0.00764989i
$557$	0.469915	+	1.44625i	0.0199109	+	0.0612796i	0.960518	−	0.278217i	$-0.0897434\pi$
$557$	0.469915	+	1.44625i	0.0199109	+	0.0612796i	−0.940607	+	0.339496i	$0.889743\pi$
$558$	11.0431	−	33.9870i	0.467490	−	1.43879i
$559$	−10.1037	−	7.34078i	−0.427341	−	0.310482i
$560$	−5.15456			−0.217820
$561$		0			0
$562$	−33.2519			−1.40265
$563$	−0.529047	−	0.384375i	−0.0222967	−	0.0161995i	0.576581	−	0.817040i	$-0.304386\pi$
$563$	−0.529047	−	0.384375i	−0.0222967	−	0.0161995i	−0.598878	+	0.800840i	$0.704386\pi$
$564$	−0.552805	+	1.70136i	−0.0232773	+	0.0716401i
$565$	−1.16453	−	3.58406i	−0.0489922	−	0.150782i
$566$	5.68480	−	4.13025i	0.238950	−	0.173607i
$567$	−29.3640	+	21.3342i	−1.23317	+	0.895953i
$568$	−1.00134	−	3.08181i	−0.0420154	−	0.129310i
$569$	10.0927	−	31.0621i	0.423108	−	1.30219i	−0.481687	−	0.876343i	$-0.659976\pi$
$569$	10.0927	−	31.0621i	0.423108	−	1.30219i	0.904795	−	0.425848i	$-0.140024\pi$
$570$	−2.94430	−	2.13916i	−0.123323	−	0.0895995i
$571$	26.1457			1.09416			0.547082	−	0.837079i	$-0.315738\pi$
$571$	26.1457			1.09416			0.547082	+	0.837079i	$0.315738\pi$
$572$		0			0
$573$	−54.2306			−2.26552
$574$	−2.78374	−	2.02251i	−0.116191	−	0.0844178i
$575$	−1.12462	+	3.46123i	−0.0469000	+	0.144343i
$576$	19.8483	+	61.0869i	0.827014	+	2.54529i
$577$	−4.63872	+	3.37023i	−0.193112	+	0.140304i	−0.680140	−	0.733082i	$-0.738081\pi$
$577$	−4.63872	+	3.37023i	−0.193112	+	0.140304i	0.487028	+	0.873387i	$0.338081\pi$
$578$	23.9400	−	17.3934i	0.995772	−	0.723470i
$579$	26.9942	+	83.0797i	1.12184	+	3.45268i
$580$	−0.280250	+	0.862522i	−0.0116368	+	0.0358143i
$581$	17.7429	+	12.8910i	0.736101	+	0.534808i
$582$	−63.4134			−2.62857
$583$		0			0
$584$	36.0676			1.49249
$585$	−11.9438	−	8.67766i	−0.493814	−	0.358777i
$586$	−4.66274	+	14.3504i	−0.192616	+	0.592812i
$587$	13.4294	+	41.3316i	0.554292	+	1.70594i	0.697805	+	0.716288i	$0.254160\pi$
$587$	13.4294	+	41.3316i	0.554292	+	1.70594i	−0.143513	+	0.989648i	$0.545840\pi$
$588$	−1.56258	+	1.13528i	−0.0644399	+	0.0468183i
$589$	−2.24097	+	1.62816i	−0.0923376	+	0.0670872i
$590$	−0.473280	−	1.45661i	−0.0194846	−	0.0599676i
$591$	2.57753	−	7.93281i	0.106025	−	0.326312i
$592$	−13.7424	−	9.98447i	−0.564811	−	0.410359i
$593$	9.23707			0.379321			0.189661	−	0.981850i	$-0.439261\pi$
$593$	9.23707			0.379321			0.189661	+	0.981850i	$0.439261\pi$
$594$		0			0
$595$	−8.52360			−0.349434
$596$	−0.782237	−	0.568328i	−0.0320417	−	0.0232796i
$597$	−22.0368	+	67.8222i	−0.901905	+	2.77578i
$598$	2.98334	+	9.18179i	0.121998	+	0.375471i
$599$	29.1946	−	21.2111i	1.19286	−	0.866662i	0.199295	−	0.979940i	$-0.436135\pi$
$599$	29.1946	−	21.2111i	1.19286	−	0.866662i	0.993563	+	0.113277i	$0.0361349\pi$
$600$	−7.66388	+	5.56814i	−0.312877	+	0.227318i
$601$	−7.14725	−	21.9970i	−0.291543	−	0.897276i	−0.984361	−	0.176164i	$-0.943631\pi$
$601$	−7.14725	−	21.9970i	−0.291543	−	0.897276i	0.692818	−	0.721112i	$-0.256369\pi$
$602$	−3.76285	+	11.5809i	−0.153362	+	0.472001i
$603$	−16.9231	−	12.2953i	−0.689161	−	0.500704i
$604$	0.859237			0.0349619
$605$		0			0
$606$	51.0676			2.07448
$607$	−17.7971	−	12.9303i	−0.722361	−	0.524826i	0.164776	−	0.986331i	$-0.447310\pi$
$607$	−17.7971	−	12.9303i	−0.722361	−	0.524826i	−0.887138	+	0.461505i	$0.847310\pi$
$608$	0.164254	−	0.505523i	0.00666139	−	0.0205017i
$609$	10.8406	+	33.3640i	0.439285	+	1.35198i
$610$	2.82614	−	2.05331i	0.114427	−	0.0831361i
$611$	−7.40795	+	5.38219i	−0.299694	+	0.217740i
$612$	1.69673	+	5.22199i	0.0685861	+	0.211086i
$613$	2.60324	−	8.01194i	0.105144	−	0.323599i	−0.884620	−	0.466312i	$-0.845582\pi$
$613$	2.60324	−	8.01194i	0.105144	−	0.323599i	0.989764	+	0.142713i	$0.0455825\pi$
$614$	−15.9376	−	11.5793i	−0.643189	−	0.467304i
$615$	−5.95649			−0.240189
$616$		0			0
$617$	−17.8709			−0.719453			−0.359727	−	0.933058i	$-0.617130\pi$
$617$	−17.8709			−0.719453			−0.359727	+	0.933058i	$0.617130\pi$
$618$	50.2444	+	36.5047i	2.02113	+	1.46843i
$619$	9.11916	−	28.0659i	0.366530	−	1.12806i	−0.582488	−	0.812839i	$-0.697921\pi$
$619$	9.11916	−	28.0659i	0.366530	−	1.12806i	0.949018	−	0.315223i	$-0.102079\pi$
$620$	0.121894	+	0.375151i	0.00489538	+	0.0150664i
$621$	44.5551	−	32.3711i	1.78793	−	1.29901i
$622$	30.4073	−	22.0922i	1.21922	−	0.885815i
$623$	−1.14864	−	3.53515i	−0.0460192	−	0.141633i
$624$	−7.31458	+	22.5120i	−0.292817	+	0.901199i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	−5.31344			−0.212368
$627$		0			0
$628$	0.993617			0.0396496
$629$	−22.7246	−	16.5104i	−0.906089	−	0.658312i
$630$	−4.44813	+	13.6899i	−0.177218	+	0.545420i
$631$	7.11370	+	21.8937i	0.283192	+	0.871575i	0.986935	+	0.161120i	$0.0515107\pi$
$631$	7.11370	+	21.8937i	0.283192	+	0.871575i	−0.703743	+	0.710455i	$0.748489\pi$
$632$	13.6476	−	9.91553i	0.542870	−	0.394418i
$633$	−33.8586	+	24.5997i	−1.34576	+	0.977749i
$634$	6.57914	+	20.2485i	0.261291	+	0.804171i
$635$	0.519014	−	1.59736i	0.0205964	−	0.0633893i
$636$	−2.56405	−	1.86289i	−0.101671	−	0.0738685i
$637$	−9.88636			−0.391712
$638$		0			0
$639$	−8.52360			−0.337189
$640$	8.27901	+	6.01505i	0.327257	+	0.237766i
$641$	−1.16453	+	3.58406i	−0.0459962	+	0.141562i	−0.971417	−	0.237379i	$-0.923712\pi$
$641$	−1.16453	+	3.58406i	−0.0459962	+	0.141562i	0.925421	+	0.378941i	$0.123712\pi$
$642$	−1.47463	−	4.53845i	−0.0581991	−	0.179118i
$643$	−22.8961	+	16.6350i	−0.902932	+	0.656019i	−0.939217	−	0.343323i	$-0.888448\pi$
$643$	−22.8961	+	16.6350i	−0.902932	+	0.656019i	0.0362853	+	0.999341i	$0.488448\pi$
$644$	−0.467811	+	0.339884i	−0.0184343	+	0.0133933i
$645$	6.51382	+	20.0475i	0.256482	+	0.789369i
$646$	−2.14093	+	6.58911i	−0.0842339	+	0.259245i
$647$	−9.52818	−	6.92263i	−0.374591	−	0.272156i	0.384521	−	0.923116i	$-0.374367\pi$
$647$	−9.52818	−	6.92263i	−0.374591	−	0.272156i	−0.759112	+	0.650960i	$0.774367\pi$
$648$	76.7931			3.01672
$649$		0			0
$650$	−2.65275			−0.104049
$651$	12.3443	+	8.96864i	0.483810	+	0.351509i
$652$	−0.585801	+	1.80291i	−0.0229417	+	0.0706074i
$653$	−14.2544	−	43.8706i	−0.557818	−	1.71679i	−0.688383	−	0.725348i	$-0.741679\pi$
$653$	−14.2544	−	43.8706i	−0.557818	−	1.71679i	0.130565	−	0.991440i	$-0.458321\pi$
$654$	−40.9738	+	29.7692i	−1.60220	+	1.16407i
$655$	9.54176	−	6.93250i	0.372827	−	0.270875i
$656$	2.11903	+	6.52170i	0.0827342	+	0.254630i
$657$	29.3172	−	90.2292i	1.14377	−	3.52017i
$658$	7.22286	+	5.24772i	0.281577	+	0.204577i
$659$	15.7781			0.614626			0.307313	−	0.951609i	$-0.400570\pi$
$659$	15.7781			0.614626			0.307313	+	0.951609i	$0.400570\pi$
$660$		0			0
$661$	−38.6732			−1.50421			−0.752106	−	0.659042i	$-0.770962\pi$
$661$	−38.6732			−1.50421			−0.752106	+	0.659042i	$0.770962\pi$
$662$	29.8258	+	21.6697i	1.15921	+	0.842217i
$663$	−12.0954	+	37.2259i	−0.469747	+	1.44573i
$664$	−14.3388	−	44.1304i	−0.556455	−	1.71259i
$665$	0.902660	−	0.655821i	0.0350037	−	0.0254316i
$666$	−38.3768	+	27.8823i	−1.48707	+	1.08042i
$667$	−8.81154	−	27.1191i	−0.341184	−	1.05006i
$668$	0.766825	−	2.36005i	0.0296694	−	0.0913129i
$669$	19.4329	+	14.1188i	0.751320	+	0.545866i
$670$	−3.75867			−0.145210
$671$		0			0
$672$	−2.92795			−0.112948
$673$	35.8225	+	26.0266i	1.38086	+	1.00325i	0.996800	+	0.0799413i	$0.0254733\pi$
$673$	35.8225	+	26.0266i	1.38086	+	1.00325i	0.384057	+	0.923309i	$0.374527\pi$
$674$	0.819745	−	2.52292i	0.0315754	−	0.0971791i
$675$	4.67625	+	14.3920i	0.179989	+	0.553949i
$676$	−0.867634	+	0.630373i	−0.0333705	+	0.0242451i
$677$	5.45280	−	3.96169i	0.209568	−	0.152260i	−0.478050	−	0.878333i	$-0.658656\pi$
$677$	5.45280	−	3.96169i	0.209568	−	0.152260i	0.687618	+	0.726072i	$0.258656\pi$
$678$	5.21408	+	16.0473i	0.200246	+	0.616293i
$679$	6.00766	−	18.4897i	0.230553	−	0.709569i
$680$	14.5897	+	10.6000i	0.559488	+	0.406492i
$681$	4.47741			0.171575
$682$		0			0
$683$	33.3303			1.27535			0.637675	−	0.770305i	$-0.279896\pi$
$683$	33.3303			1.27535			0.637675	+	0.770305i	$0.279896\pi$
$684$	−0.581474	−	0.422466i	−0.0222332	−	0.0161534i
$685$	−2.28915	+	7.04529i	−0.0874640	+	0.269187i
$686$	7.05458	+	21.7118i	0.269345	+	0.828959i
$687$	−77.8378	+	56.5524i	−2.96970	+	2.15761i
$688$	19.6325	−	14.2638i	0.748482	−	0.543804i
$689$	−5.01305	−	15.4286i	−0.190982	−	0.587782i
$690$	5.03540	−	15.4974i	0.191694	−	0.589974i
$691$	−7.28557	−	5.29328i	−0.277156	−	0.201366i	0.440520	−	0.897743i	$-0.354794\pi$
$691$	−7.28557	−	5.29328i	−0.277156	−	0.201366i	−0.717676	+	0.696377i	$0.754794\pi$
$692$	1.59013			0.0604477
$693$		0			0
$694$	5.21655			0.198018
$695$	−2.14493	−	1.55838i	−0.0813617	−	0.0591128i
$696$	22.9361	−	70.5899i	0.869389	−	2.67570i
$697$	3.50404	+	10.7843i	0.132725	+	0.408486i
$698$	−19.0909	+	13.8703i	−0.722600	+	0.525000i
$699$	−58.0506	+	42.1762i	−2.19567	+	1.59525i
$700$	−0.0490987	−	0.151110i	−0.00185576	−	0.00571144i
$701$	−14.1820	+	43.6476i	−0.535646	+	1.64855i	0.206604	+	0.978425i	$0.433759\pi$
$701$	−14.1820	+	43.6476i	−0.535646	+	1.64855i	−0.742250	+	0.670123i	$0.766241\pi$
$702$	32.4765	+	23.5956i	1.22575	+	0.890557i
$703$	3.67690			0.138677
$704$		0			0
$705$	15.4551			0.582071
$706$	−2.21223	−	1.60728i	−0.0832585	−	0.0604908i
$707$	−4.83805	+	14.8900i	−0.181954	+	0.559996i
$708$	−0.130174	−	0.400635i	−0.00489225	−	0.0150568i
$709$	6.88490	−	5.00217i	0.258568	−	0.187861i	−0.450948	−	0.892550i	$-0.648914\pi$
$709$	6.88490	−	5.00217i	0.258568	−	0.187861i	0.709515	+	0.704690i	$0.248914\pi$
$710$	−1.23906	+	0.900232i	−0.0465012	+	0.0337851i
$711$	−13.7121	−	42.2014i	−0.514242	−	1.58267i
$712$	−2.43023	+	7.47948i	−0.0910768	+	0.280305i
$713$	−10.0337	−	7.28994i	−0.375767	−	0.273010i
$714$	38.1637			1.42824
$715$		0			0
$716$	0.436202			0.0163016
$717$	−49.4059	−	35.8955i	−1.84510	−	1.34054i
$718$	−6.60711	+	20.3346i	−0.246575	+	0.758880i
$719$	−2.96828	−	9.13541i	−0.110698	−	0.340693i	0.880327	−	0.474366i	$-0.157323\pi$
$719$	−2.96828	−	9.13541i	−0.110698	−	0.340693i	−0.991025	+	0.133673i	$0.957323\pi$
$720$	23.2079	−	16.8615i	0.864908	−	0.628392i
$721$	−15.4039	+	11.1916i	−0.573670	+	0.416796i
$722$	7.77920	+	23.9419i	0.289512	+	0.891026i
$723$	−26.4719	+	81.4720i	−0.984499	+	3.02998i
$724$	−0.00125462		0.000911538i	−4.66278e−5		3.38771e-5i
$725$	7.83511			0.290989
$726$		0			0
$727$	32.9688			1.22274			0.611372	−	0.791343i	$-0.290618\pi$
$727$	32.9688			1.22274			0.611372	+	0.791343i	$0.290618\pi$
$728$	−6.23287	−	4.52844i	−0.231005	−	0.167835i
$729$	16.6616	−	51.2791i	0.617096	−	1.89923i
$730$	−5.26788	−	16.2129i	−0.194973	−	0.600065i
$731$	32.4644	−	23.5868i	1.20074	−	0.872389i
$732$	0.777322	−	0.564757i	0.0287306	−	0.0208740i
$733$	8.45792	+	26.0308i	0.312400	+	0.961470i	0.976811	+	0.214102i	$0.0686825\pi$
$733$	8.45792	+	26.0308i	0.312400	+	0.961470i	−0.664411	+	0.747368i	$0.731317\pi$
$734$	−7.96274	+	24.5068i	−0.293910	+	0.904562i
$735$	13.4997	+	9.80812i	0.497944	+	0.361778i
$736$	2.37991			0.0877248
$737$		0			0
$738$	19.1496			0.704905
$739$	31.1995	+	22.6677i	1.14769	+	0.833846i	0.988172	−	0.153349i	$-0.0490059\pi$
$739$	31.1995	+	22.6677i	1.14769	+	0.833846i	0.159518	+	0.987195i	$0.449006\pi$
$740$	0.161803	−	0.497977i	0.00594799	−	0.0183060i
$741$	−1.58331	−	4.87291i	−0.0581642	−	0.179011i
$742$	−12.7964	+	9.29715i	−0.469772	+	0.341309i
$743$	27.6395	−	20.0813i	1.01400	−	0.736712i	0.0489530	−	0.998801i	$-0.484412\pi$
$743$	27.6395	−	20.0813i	1.01400	−	0.736712i	0.965044	+	0.262089i	$0.0844116\pi$
$744$	−9.97596	−	30.7028i	−0.365736	−	1.12562i
$745$	−2.58133	+	7.94453i	−0.0945727	+	0.291065i
$746$	2.91695	+	2.11928i	0.106797	+	0.0775925i
$747$	−122.055			−4.46575
$748$		0			0
$749$	1.46300			0.0534568
$750$	3.62230	+	2.63176i	0.132268	+	0.0960981i
$751$	−14.1933	+	43.6825i	−0.517922	+	1.59400i	0.259981	+	0.965614i	$0.416284\pi$
$751$	−14.1933	+	43.6825i	−0.517922	+	1.59400i	−0.777903	+	0.628385i	$0.783716\pi$
$752$	−5.49816	−	16.9216i	−0.200497	−	0.617067i
$753$	59.7066	−	43.3794i	2.17583	−	1.58083i
$754$	16.8151	−	12.2169i	0.612370	−	0.444913i
$755$	−2.29391	−	7.05994i	−0.0834840	−	0.256937i
$756$	−0.742994	+	2.28670i	−0.0270224	+	0.0831665i
$757$	24.4514	+	17.7650i	0.888700	+	0.645679i	0.935539	−	0.353224i	$-0.114915\pi$
$757$	24.4514	+	17.7650i	0.888700	+	0.645679i	−0.0468384	+	0.998902i	$0.514915\pi$
$758$	−3.65227			−0.132656
$759$		0			0
$760$	−2.36065			−0.0856296
$761$	−10.8658	−	7.89443i	−0.393883	−	0.286173i	0.373162	−	0.927766i	$-0.378274\pi$
$761$	−10.8658	−	7.89443i	−0.393883	−	0.286173i	−0.767045	+	0.641593i	$0.778274\pi$
$762$	−2.32384	+	7.15204i	−0.0841838	+	0.259091i
$763$	−4.79814	−	14.7672i	−0.173704	−	0.534607i
$764$	−1.55691	+	1.13116i	−0.0563270	+	0.0409239i
$765$	38.3768	−	27.8823i	1.38751	−	1.00809i
$766$	−9.30292	−	28.6314i	−0.336128	−	1.03450i
$767$	0.666310	−	2.05069i	0.0240591	−	0.0740462i
$768$	7.30567	+	5.30788i	0.263621	+	0.191532i
$769$	−10.8982			−0.393001			−0.196500	−	0.980504i	$-0.562958\pi$
$769$	−10.8982			−0.393001			−0.196500	+	0.980504i	$0.562958\pi$
$770$		0			0
$771$	56.1362			2.02169
$772$	2.50788	+	1.82208i	0.0902607	+	0.0655783i
$773$	4.06344	−	12.5060i	0.146152	−	0.449809i	−0.851006	−	0.525157i	$-0.824007\pi$
$773$	4.06344	−	12.5060i	0.146152	−	0.449809i	0.997157	+	0.0753479i	$0.0240067\pi$
$774$	−20.9413	−	64.4508i	−0.752721	−	2.31664i
$775$	2.75701	−	2.00309i	0.0990348	−	0.0719530i
$776$	−33.2771	+	24.1772i	−1.19458	+	0.867911i
$777$	−6.25884	−	19.2627i	−0.224535	−	0.691047i
$778$	1.45123	−	4.46643i	0.0520292	−	0.160129i
$779$	−1.20085	−	0.872467i	−0.0430248	−	0.0312594i
$780$	−0.729632			−0.0261250
$781$		0			0
$782$	−31.0204			−1.10929
$783$	−95.9220	−	69.6914i	−3.42797	−	2.49057i
$784$	5.93627	−	18.2700i	0.212010	−	0.652498i
$785$	−2.65267	−	8.16407i	−0.0946778	−	0.291388i
$786$	−42.7224	+	31.0396i	−1.52386	+	1.10715i
$787$	9.33710	−	6.78380i	0.332832	−	0.241816i	−0.408799	−	0.912624i	$-0.634052\pi$
$787$	9.33710	−	6.78380i	0.332832	−	0.241816i	0.741631	+	0.670808i	$0.234052\pi$
$788$	−0.0914670	−	0.281506i	−0.00325838	−	0.0100283i
$789$	5.75985	−	17.7270i	0.205056	−	0.631098i
$790$	−6.45046	−	4.68653i	−0.229497	−	0.166739i
$791$	−5.17295			−0.183929
$792$		0			0
$793$	4.91806			0.174645
$794$	6.11920	+	4.44586i	0.217162	+	0.157778i
$795$	−8.46121	+	26.0409i	−0.300088	+	0.923577i
$796$	0.782004	+	2.40676i	0.0277174	+	0.0853054i
$797$	4.48595	−	3.25923i	0.158900	−	0.115448i	−0.505494	−	0.862830i	$-0.668690\pi$
$797$	4.48595	−	3.25923i	0.158900	−	0.115448i	0.664394	+	0.747382i	$0.268690\pi$
$798$	−4.04158	+	2.93638i	−0.143070	+	0.103947i
$799$	−9.09179	−	27.9817i	−0.321644	−	0.989920i
$800$	−0.202078	+	0.621933i	−0.00714454	+	0.0219886i
$801$	16.7358	+	12.1593i	0.591330	+	0.429626i
$802$	24.6067			0.868891
$803$		0			0
$804$	−1.03381			−0.0364597
$805$	4.04158	+	2.93638i	0.142447	+	0.103494i
$806$	2.79357	−	8.59774i	0.0983994	−	0.302842i
$807$	−2.89368	−	8.90584i	−0.101862	−	0.313500i
$808$	26.7985	−	19.4702i	0.942767	−	0.684960i
$809$	−14.9184	+	10.8389i	−0.524505	+	0.381075i	−0.818298	−	0.574794i	$-0.805082\pi$
$809$	−14.9184	+	10.8389i	−0.524505	+	0.381075i	0.293793	+	0.955869i	$0.405082\pi$
$810$	−11.2161	−	34.5195i	−0.394092	−	1.21289i
$811$	1.95551	−	6.01845i	0.0686674	−	0.211337i	−0.910834	−	0.412772i	$-0.864561\pi$
$811$	1.95551	−	6.01845i	0.0686674	−	0.211337i	0.979502	+	0.201435i	$0.0645606\pi$
$812$	1.00714	+	0.731732i	0.0353438	+	0.0256788i
$813$	−24.9428			−0.874783
$814$		0			0
$815$	16.3776			0.573681
$816$	−61.5306	−	44.7046i	−2.15400	−	1.56497i
$817$	−1.62321	+	4.99574i	−0.0567891	+	0.174779i
$818$	−12.4396	−	38.2852i	−0.434941	−	1.33861i
$819$	−16.3950	+	11.9117i	−0.572887	+	0.416227i
$820$	−0.171005	+	0.124243i	−0.00597176	+	0.00433874i
$821$	2.45743	+	7.56318i	0.0857648	+	0.263957i	0.984737	−	0.174049i	$-0.0556850\pi$
$821$	2.45743	+	7.56318i	0.0857648	+	0.263957i	−0.898972	+	0.438006i	$0.855685\pi$
$822$	10.2495	−	31.5447i	0.357492	−	1.10025i
$823$	−1.06985	−	0.777293i	−0.0372927	−	0.0270947i	0.568983	−	0.822349i	$-0.307337\pi$
$823$	−1.06985	−	0.777293i	−0.0372927	−	0.0270947i	−0.606275	+	0.795255i	$0.707337\pi$
$824$	40.2844			1.40337
$825$		0			0
$826$	−2.10235			−0.0731502
$827$	3.66476	+	2.66261i	0.127436	+	0.0925879i	0.649678	−	0.760210i	$-0.274904\pi$
$827$	3.66476	+	2.66261i	0.127436	+	0.0925879i	−0.522241	+	0.852798i	$0.674904\pi$
$828$	0.994448	−	3.06060i	0.0345595	−	0.106363i
$829$	−11.6854	−	35.9640i	−0.405851	−	1.24908i	−0.920182	−	0.391490i	$-0.871960\pi$
$829$	−11.6854	−	35.9640i	−0.405851	−	1.24908i	0.514331	−	0.857592i	$-0.328040\pi$
$830$	−17.7429	+	12.8910i	−0.615866	+	0.447453i
$831$	77.5744	−	56.3611i	2.69103	−	1.95515i
$832$	5.02105	+	15.4532i	0.174074	+	0.535744i
$833$	9.81625	−	30.2113i	0.340113	−	1.04676i
$834$	9.60372	+	6.97751i	0.332550	+	0.241611i
$835$	−21.4385			−0.741912
$836$		0			0
$837$	−51.5699			−1.78252
$838$	2.94594	+	2.14035i	0.101766	+	0.0739371i
$839$	−12.1295	+	37.3308i	−0.418757	+	1.28880i	0.490090	+	0.871672i	$0.336964\pi$
$839$	−12.1295	+	37.3308i	−0.418757	+	1.28880i	−0.908847	+	0.417130i	$0.863036\pi$
$840$	4.01830	+	12.3671i	0.138645	+	0.426704i
$841$	−26.2032	+	19.0378i	−0.903560	+	0.656475i
$842$	−12.3967	+	9.00673i	−0.427219	+	0.310393i
$843$	24.4167	+	75.1469i	0.840956	+	2.58820i
$844$	−0.458938	+	1.41247i	−0.0157973	+	0.0486191i
$845$	7.49579	+	5.44601i	0.257863	+	0.187349i
$846$	−49.6866			−1.70826
$847$		0			0
$848$	31.5221			1.08247
$849$	−13.5084	−	9.81441i	−0.463606	−	0.336830i
$850$	2.63394	−	8.10643i	0.0903434	−	0.278048i
$851$	5.08735	+	15.6572i	0.174392	+	0.536723i
$852$	−0.340801	+	0.247606i	−0.0116756	+	0.00848285i
$853$	−27.0145	+	19.6271i	−0.924957	+	0.672021i	−0.944753	−	0.327783i	$-0.893698\pi$
$853$	−27.0145	+	19.6271i	−0.924957	+	0.672021i	0.0197957	+	0.999804i	$0.493698\pi$
$854$	−1.48179	−	4.56049i	−0.0507059	−	0.156057i
$855$	−1.91883	+	5.90555i	−0.0656226	+	0.201966i
$856$	−2.50418	−	1.81939i	−0.0855911	−	0.0621856i
$857$	−16.9781			−0.579961			−0.289980	−	0.957033i	$-0.593649\pi$
$857$	−16.9781			−0.579961			−0.289980	+	0.957033i	$0.593649\pi$
$858$		0			0
$859$	−40.8148			−1.39258			−0.696291	−	0.717759i	$-0.745168\pi$
$859$	−40.8148			−1.39258			−0.696291	+	0.717759i	$0.745168\pi$
$860$	0.605163	+	0.439677i	0.0206359	+	0.0149929i
$861$	−2.52663	+	7.77618i	−0.0861074	+	0.265011i
$862$	−1.93392	−	5.95199i	−0.0658696	−	0.202726i
$863$	−28.3401	+	20.5903i	−0.964709	+	0.700902i	−0.954240	−	0.299043i	$-0.903332\pi$
$863$	−28.3401	+	20.5903i	−0.964709	+	0.700902i	−0.0104691	+	0.999945i	$0.503332\pi$
$864$	8.00589	−	5.81662i	0.272366	−	0.197885i
$865$	−4.24518	−	13.0653i	−0.144340	−	0.444234i
$866$	−8.55275	+	26.3227i	−0.290634	+	0.894481i
$867$	−56.8869	−	41.3307i	−1.93198	−	1.40366i
$868$	0.541464			0.0183785
$869$		0			0
$870$	−35.0810			−1.18936
$871$	−4.28104	−	3.11036i	−0.145058	−	0.105391i
$872$	−10.1517	+	31.2436i	−0.343779	+	1.05804i
$873$	33.4344	+	102.900i	1.13158	+	3.48265i
$874$	3.28510	−	2.38676i	0.111120	−	0.0807335i
$875$	−1.11052	+	0.806841i	−0.0375425	+	0.0272762i
$876$	−1.44891	−	4.45930i	−0.0489543	−	0.150666i
$877$	−8.23918	+	25.3576i	−0.278217	+	0.856265i	0.710133	+	0.704068i	$0.248635\pi$
$877$	−8.23918	+	25.3576i	−0.278217	+	0.856265i	−0.988350	+	0.152197i	$0.951365\pi$
$878$	−38.2983	−	27.8254i	−1.29251	−	0.939060i
$879$	35.8548			1.20935
$880$		0			0
$881$	−4.66615			−0.157207			−0.0786033	−	0.996906i	$-0.525046\pi$
$881$	−4.66615			−0.157207			−0.0786033	+	0.996906i	$0.525046\pi$
$882$	−43.4003	−	31.5322i	−1.46136	−	1.06174i
$883$	1.99963	−	6.15422i	0.0672928	−	0.207106i	−0.911756	−	0.410733i	$-0.865273\pi$
$883$	1.99963	−	6.15422i	0.0672928	−	0.207106i	0.979049	+	0.203627i	$0.0652729\pi$
$884$	0.429222	+	1.32101i	0.0144363	+	0.0444304i
$885$	−2.94430	+	2.13916i	−0.0989715	+	0.0719070i
$886$	34.9354	−	25.3821i	1.17368	−	0.852727i
$887$	5.67070	+	17.4526i	0.190404	+	0.586002i	1.00000		0.000985588i	$-0.000313722\pi$
$887$	5.67070	+	17.4526i	0.190404	+	0.586002i	−0.809596	+	0.586988i	$0.800314\pi$
$888$	−13.2421	+	40.7551i	−0.444377	+	1.36765i
$889$	−1.86519	−	1.35514i	−0.0625565	−	0.0454500i
$890$	3.71707			0.124597
$891$		0			0
$892$	0.852396			0.0285403
$893$	3.11579	+	2.26375i	0.104266	+	0.0757536i
$894$	11.5577	−	35.5709i	0.386547	−	1.18967i
$895$	−1.16453	−	3.58406i	−0.0389260	−	0.119802i
$896$	11.3644	−	8.25674i	0.379659	−	0.275838i
$897$	18.5595	−	13.4843i	0.619684	−	0.450227i
$898$	2.02608	+	6.23562i	0.0676110	+	0.208085i
$899$	−8.25104	+	25.3941i	−0.275188	+	0.846940i
$900$	0.715374	+	0.519749i	0.0238458	+	0.0173250i
$901$	52.1251			1.73654
$902$		0			0
$903$	28.9350			0.962895
$904$	8.85441	+	6.43311i	0.294493	+	0.213962i
$905$	−0.00414019	+	0.0127422i	−0.000137624	+	0.000423564i
$906$	10.2708	+	31.6102i	0.341224	+	1.05018i
$907$	24.0962	−	17.5069i	0.800100	−	0.581307i	−0.110844	−	0.993838i	$-0.535355\pi$
$907$	24.0962	−	17.5069i	0.800100	−	0.581307i	0.910943	+	0.412531i	$0.135355\pi$
$908$	0.128542	−	0.0933914i	0.00426582	−	0.00309930i
$909$	−26.9251	−	82.8670i	−0.893050	−	2.74852i
$910$	−1.12525	+	3.46316i	−0.0373016	+	0.114803i
$911$	−37.1096	−	26.9617i	−1.22949	−	0.893280i	−0.232642	−	0.972562i	$-0.574737\pi$
$911$	−37.1096	−	26.9617i	−1.22949	−	0.893280i	−0.996852	+	0.0792824i	$0.974737\pi$
$912$	9.95582			0.329670
$913$		0			0
$914$	−2.10235			−0.0695396
$915$	−6.71556	−	4.87914i	−0.222009	−	0.161299i
$916$	−1.05506	+	3.24713i	−0.0348601	+	0.107288i
$917$	−5.00291	−	15.3974i	−0.165211	−	0.508466i
$918$	−104.351	+	75.8153i	−3.44409	+	2.50228i
$919$	47.0326	−	34.1712i	1.55146	−	1.12720i	0.608863	−	0.793276i	$-0.291626\pi$
$919$	47.0326	−	34.1712i	1.55146	−	1.12720i	0.942599	−	0.333927i	$-0.108374\pi$
$920$	−3.26618	−	10.0523i	−0.107683	−	0.331414i
$921$	−14.4656	+	44.5205i	−0.476657	+	1.46700i
$922$	20.5691	+	14.9443i	0.677406	+	0.492164i
$923$	−2.15622			−0.0709730
$924$		0			0
$925$	−4.52360			−0.148735
$926$	10.7532	+	7.81269i	0.353373	+	0.256741i
$927$	32.7448	−	100.778i	1.07548	−	3.30999i
$928$	−1.58331	−	4.87291i	−0.0519745	−	0.159961i
$929$	−32.2281	+	23.4151i	−1.05737	+	0.768224i	−0.973600	−	0.228261i	$-0.926696\pi$
$929$	−32.2281	+	23.4151i	−1.05737	+	0.768224i	−0.0837697	+	0.996485i	$0.526696\pi$
$930$	−12.3443	+	8.96864i	−0.404785	+	0.294093i
$931$	1.28496	+	3.95469i	0.0421128	+	0.129610i
$932$	−0.786851	+	2.42168i	−0.0257741	+	0.0793247i
$933$	−72.2546	−	52.4960i	−2.36551	−	1.71864i
$934$	43.5112			1.42373
$935$		0			0
$936$	42.8763			1.40146
$937$	−7.82608	−	5.68598i	−0.255667	−	0.185753i	0.452568	−	0.891730i	$-0.350508\pi$
$937$	−7.82608	−	5.68598i	−0.255667	−	0.185753i	−0.708235	+	0.705977i	$0.750508\pi$
$938$	−1.59436	+	4.90693i	−0.0520576	+	0.160217i
$939$	3.90163	+	12.0080i	0.127325	+	0.391866i
$940$	0.443700	−	0.322367i	0.0144719	−	0.0105145i
$941$	−3.21299	+	2.33437i	−0.104740	+	0.0760983i	−0.638923	−	0.769271i	$-0.720620\pi$
$941$	−3.21299	+	2.33437i	−0.104740	+	0.0760983i	0.534182	+	0.845369i	$0.320620\pi$
$942$	11.8771	+	36.5539i	0.386976	+	1.19099i
$943$	2.05371	−	6.32068i	0.0668781	−	0.205829i
$944$	3.38958	+	2.46268i	0.110322	+	0.0801533i
$945$	20.7723			0.675723
$946$		0			0
$947$	2.65275			0.0862029			0.0431014	−	0.999071i	$-0.486276\pi$
$947$	2.65275			0.0862029			0.0431014	+	0.999071i	$0.486276\pi$
$948$	−1.77418	−	1.28902i	−0.0576227	−	0.0418653i
$949$	7.41641	−	22.8254i	0.240747	−	0.740942i
$950$	0.344786	+	1.06114i	0.0111863	+	0.0344280i
$951$	40.9292	−	29.7368i	1.32722	−	0.964281i
$952$	20.0269	−	14.5504i	0.649077	−	0.471582i
$953$	−6.44851	−	19.8465i	−0.208888	−	0.642890i	−0.999531	−	0.0306134i	$-0.990254\pi$
$953$	−6.44851	−	19.8465i	−0.208888	−	0.642890i	0.790644	−	0.612277i	$-0.209746\pi$
$954$	27.2020	−	83.7192i	0.880697	−	2.71051i
$955$	13.4507	+	9.77249i	0.435254	+	0.316230i
$956$	−2.16711			−0.0700895
$957$		0			0
$958$	−42.3259			−1.36749
$959$	8.22658	+	5.97696i	0.265650	+	0.193006i
$960$	8.47472	−	26.0825i	0.273520	−	0.841809i
$961$	−5.99077	−	18.4377i	−0.193250	−	0.594764i
$962$	−9.70820	+	7.05342i	−0.313005	+	0.227411i
$963$	−6.58701	+	4.78575i	−0.212264	+	0.154218i
$964$	0.939389	+	2.89114i	0.0302557	+	0.0931175i
$965$	8.27587	−	25.4705i	0.266410	−	0.819925i
$966$	−18.0958	−	13.1474i	−0.582223	−	0.423010i
$967$	58.5364			1.88240			0.941202	−	0.337843i	$-0.109697\pi$
$967$	58.5364			1.88240			0.941202	+	0.337843i	$0.109697\pi$
$968$		0			0
$969$	16.4630			0.528868
$970$	15.7283	+	11.4273i	0.505004	+	0.366907i
$971$	−17.3869	+	53.5115i	−0.557973	+	1.71727i	0.129986	+	0.991516i	$0.458507\pi$
$971$	−17.3869	+	53.5115i	−0.557973	+	1.71727i	−0.687959	+	0.725750i	$0.741493\pi$
$972$	−1.46113	−	4.49689i	−0.0468657	−	0.144238i
$973$	−2.94430	+	2.13916i	−0.0943899	+	0.0685783i
$974$	33.3068	−	24.1988i	1.06722	−	0.775381i
$975$	1.94790	+	5.99503i	0.0623828	+	0.191995i
$976$	−2.95305	+	9.08856i	−0.0945249	+	0.290918i
$977$	−29.9228	−	21.7402i	−0.957315	−	0.695530i	−0.00478928	−	0.999989i	$-0.501524\pi$
$977$	−29.9228	−	21.7402i	−0.957315	−	0.695530i	−0.952526	+	0.304459i	$0.901524\pi$
$978$	−73.3290			−2.34480
$979$		0			0
$980$	0.592145			0.0189154
$981$	69.9094	+	50.7922i	2.23204	+	1.62167i
$982$	−14.6391	+	45.0545i	−0.467152	+	1.43775i
$983$	−6.07657	−	18.7018i	−0.193812	−	0.596493i	−0.999988	−	0.00481755i	$-0.998467\pi$
$983$	−6.07657	−	18.7018i	−0.193812	−	0.596493i	0.806176	−	0.591676i	$-0.201533\pi$
$984$	13.9953	−	10.1682i	0.446153	−	0.324149i
$985$	−2.06881	+	1.50308i	−0.0659178	+	0.0478921i
$986$	20.6372	+	63.5148i	0.657223	+	2.02272i
$987$	6.55575	−	20.1765i	0.208672	−	0.642226i
$988$	−0.147096	−	0.106872i	−0.00467975	−	0.00340004i
$989$	−23.5191			−0.747863
$990$		0			0
$991$	18.5763			0.590095			0.295047	−	0.955483i	$-0.404665\pi$
$991$	18.5763			0.590095			0.295047	+	0.955483i	$0.404665\pi$
$992$	−1.80292	−	1.30990i	−0.0572427	−	0.0415892i
$993$	27.0710	−	83.3161i	0.859073	−	2.64396i
$994$	0.649662	+	1.99946i	0.0206060	+	0.0634189i
$995$	17.6875	−	12.8507i	0.560731	−	0.407395i
$996$	−4.88014	+	3.54563i	−0.154633	+	0.112348i
$997$	−9.30292	−	28.6314i	−0.294626	−	0.906767i	−0.983347	−	0.181740i	$-0.941827\pi$
$997$	−9.30292	−	28.6314i	−0.294626	−	0.906767i	0.688720	−	0.725027i	$-0.258173\pi$
$998$	−7.57712	+	23.3200i	−0.239850	+	0.738181i
$999$	55.3806	+	40.2363i	1.75216	+	1.27302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.q.81.5		24
11.2	odd	10	inner	605.2.g.q.511.5		24
11.3	even	5	inner	605.2.g.q.366.5		24
11.4	even	5	inner	605.2.g.q.251.2		24
11.5	even	5		605.2.a.m.1.2	✓	6
11.6	odd	10		605.2.a.m.1.5	yes	6
11.7	odd	10	inner	605.2.g.q.251.5		24
11.8	odd	10	inner	605.2.g.q.366.2		24
11.9	even	5	inner	605.2.g.q.511.2		24
11.10	odd	2	inner	605.2.g.q.81.2		24
33.5	odd	10		5445.2.a.bx.1.5		6
33.17	even	10		5445.2.a.bx.1.2		6
44.27	odd	10		9680.2.a.cw.1.1		6
44.39	even	10		9680.2.a.cw.1.2		6
55.39	odd	10		3025.2.a.bg.1.2		6
55.49	even	10		3025.2.a.bg.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.m.1.2	✓	6	11.5	even	5
605.2.a.m.1.5	yes	6	11.6	odd	10
605.2.g.q.81.2		24	11.10	odd	2	inner
605.2.g.q.81.5		24	1.1	even	1	trivial
605.2.g.q.251.2		24	11.4	even	5	inner
605.2.g.q.251.5		24	11.7	odd	10	inner
605.2.g.q.366.2		24	11.8	odd	10	inner
605.2.g.q.366.5		24	11.3	even	5	inner
605.2.g.q.511.2		24	11.9	even	5	inner
605.2.g.q.511.5		24	11.2	odd	10	inner
3025.2.a.bg.1.2		6	55.39	odd	10
3025.2.a.bg.1.5		6	55.49	even	10
5445.2.a.bx.1.2		6	33.17	even	10
5445.2.a.bx.1.5		6	33.5	odd	10
9680.2.a.cw.1.1		6	44.27	odd	10
9680.2.a.cw.1.2		6	44.39	even	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.11052 + 0.806841i) q^{2} +(1.00795 - 3.10216i) q^{3} +(-0.0357685 - 0.110084i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(3.62230 - 2.63176i) q^{6} +(0.424181 + 1.30550i) q^{7} +(0.897462 - 2.76210i) q^{8} +(-6.18037 - 4.49030i) q^{9} +O(q^{10})\)	\(q+(1.11052 + 0.806841i) q^{2} +(1.00795 - 3.10216i) q^{3} +(-0.0357685 - 0.110084i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(3.62230 - 2.63176i) q^{6} +(0.424181 + 1.30550i) q^{7} +(0.897462 - 2.76210i) q^{8} +(-6.18037 - 4.49030i) q^{9} -1.37268 q^{10} -0.377552 q^{12} +(-1.56345 - 1.13592i) q^{13} +(-0.582265 + 1.79203i) q^{14} +(1.00795 + 3.10216i) q^{15} +(3.03794 - 2.20719i) q^{16} +(5.02356 - 3.64983i) q^{17} +(-3.24047 - 9.97315i) q^{18} +(-0.251177 + 0.773043i) q^{19} +(0.0936432 + 0.0680358i) q^{20} +4.47741 q^{21} -3.63935 q^{23} +(-7.66388 - 5.56814i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-0.819745 - 2.52292i) q^{26} +(-12.2426 + 8.89475i) q^{27} +(0.128542 - 0.0933914i) q^{28} +(2.42118 + 7.45164i) q^{29} +(-1.38360 + 4.25827i) q^{30} +(2.75701 + 2.00309i) q^{31} -0.653939 q^{32} +8.52360 q^{34} +(-1.11052 - 0.806841i) q^{35} +(-0.273248 + 0.840972i) q^{36} +(-1.39787 - 4.30220i) q^{37} +(-0.902660 + 0.655821i) q^{38} +(-5.09968 + 3.70513i) q^{39} +(0.897462 + 2.76210i) q^{40} +(-0.564307 + 1.73676i) q^{41} +(4.97226 + 3.61256i) q^{42} +6.46243 q^{43} +7.63935 q^{45} +(-4.04158 - 2.93638i) q^{46} +(1.46418 - 4.50629i) q^{47} +(-3.78497 - 11.6489i) q^{48} +(4.13873 - 3.00696i) q^{49} +(1.11052 - 0.806841i) q^{50} +(-6.25884 - 19.2627i) q^{51} +(-0.0691239 + 0.212742i) q^{52} +(6.79126 + 4.93414i) q^{53} -20.7723 q^{54} +3.98660 q^{56} +(2.14493 + 1.55838i) q^{57} +(-3.32351 + 10.2287i) q^{58} +(0.344786 + 1.06114i) q^{59} +(0.305446 - 0.221919i) q^{60} +(-2.05885 + 1.49584i) q^{61} +(1.44555 + 4.44894i) q^{62} +(3.24047 - 9.97315i) q^{63} +(-6.80210 - 4.94201i) q^{64} +1.93253 q^{65} +2.73820 q^{67} +(-0.581474 - 0.422466i) q^{68} +(-3.66830 + 11.2899i) q^{69} +(-0.582265 - 1.79203i) q^{70} +(0.902660 - 0.655821i) q^{71} +(-17.9493 + 13.0409i) q^{72} +(3.83766 + 11.8111i) q^{73} +(1.91883 - 5.90555i) q^{74} +(-2.63885 - 1.91724i) q^{75} +0.0940841 q^{76} -8.65275 q^{78} +(4.69917 + 3.41415i) q^{79} +(-1.16039 + 3.57132i) q^{80} +(8.17092 + 25.1475i) q^{81} +(-2.02796 + 1.47340i) q^{82} +(12.9258 - 9.39111i) q^{83} +(-0.160150 - 0.492892i) q^{84} +(-1.91883 + 5.90555i) q^{85} +(7.17667 + 5.21416i) q^{86} +25.5566 q^{87} -2.70789 q^{89} +(8.48367 + 6.16374i) q^{90} +(0.819745 - 2.52292i) q^{91} +(0.130174 + 0.400635i) q^{92} +(8.99283 - 6.53367i) q^{93} +(5.26187 - 3.82297i) q^{94} +(-0.251177 - 0.773043i) q^{95} +(-0.659139 + 2.02862i) q^{96} +(-11.4581 - 8.32478i) q^{97} +7.02229 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9}+O(q^{10}) \) 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9	\( 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9} + 72 q^{12} + 18 q^{14} - 6 q^{15} - 18 q^{16} - 6 q^{20} + 48 q^{23} - 6 q^{25} + 36 q^{26} - 30 q^{27} + 96 q^{34} + 12 q^{36} + 30 q^{42} + 48 q^{45} - 42 q^{47} + 6 q^{48} + 24 q^{49} - 24 q^{53} - 120 q^{56} + 24 q^{58} - 18 q^{60} - 30 q^{64} + 120 q^{67} + 24 q^{69} + 18 q^{70} - 6 q^{75} - 288 q^{78} - 18 q^{80} - 30 q^{81} - 42 q^{82} + 6 q^{86} - 120 q^{89} - 36 q^{91} - 36 q^{92} + 60 q^{93} - 24 q^{97}+O(q^{100}) \) 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9 + 72 * q^12 + 18 * q^14 - 6 * q^15 - 18 * q^16 - 6 * q^20 + 48 * q^23 - 6 * q^25 + 36 * q^26 - 30 * q^27 + 96 * q^34 + 12 * q^36 + 30 * q^42 + 48 * q^45 - 42 * q^47 + 6 * q^48 + 24 * q^49 - 24 * q^53 - 120 * q^56 + 24 * q^58 - 18 * q^60 - 30 * q^64 + 120 * q^67 + 24 * q^69 + 18 * q^70 - 6 * q^75 - 288 * q^78 - 18 * q^80 - 30 * q^81 - 42 * q^82 + 6 * q^86 - 120 * q^89 - 36 * q^91 - 36 * q^92 + 60 * q^93 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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