LMFDB - Embedded newform 67.2.e.c.59.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [67,2,Mod(9,67)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(67, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("67.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	67.e (of order $11$, degree $10$, 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:	$0.534997693543$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 7 x^{19} + 39 x^{18} - 148 x^{17} + 492 x^{16} - 1282 x^{15} + 2921 x^{14} - 4316 x^{13} + \cdots + 4489 $ x^20 - 7x^19 + 39x^18 - 148x^17 + 492x^16 - 1282x^15 + 2921x^14 - 4316x^13 + 2696x^12 + 9361x^11 - 20998x^10 + 10813x^9 + 44155x^8 - 46933x^7 - 36976x^6 - 49131x^5 + 105828x^4 + 108234x^3 + 143215x^2 + 41004*x + 4489
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			59.2
Root			$-1.35948 - 0.399179i$ of defining polynomial
Character	$\chi$	$=$	67.59
Dual form			67.2.e.c.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.118239 + 0.822373i) q^{2} +(1.08271 + 1.24952i) q^{3} +(1.25667 + 0.368991i) q^{4} +(-3.36803 - 2.16450i) q^{5} +(-1.15559 + 0.742653i) q^{6} +(0.0592135 - 0.411839i) q^{7} +(-1.14231 + 2.50132i) q^{8} +(0.0379173 - 0.263721i) q^{9} +O(q^{10})$	\(q+(-0.118239 + 0.822373i) q^{2} +(1.08271 + 1.24952i) q^{3} +(1.25667 + 0.368991i) q^{4} +(-3.36803 - 2.16450i) q^{5} +(-1.15559 + 0.742653i) q^{6} +(0.0592135 - 0.411839i) q^{7} +(-1.14231 + 2.50132i) q^{8} +(0.0379173 - 0.263721i) q^{9} +(2.17826 - 2.51385i) q^{10} +(2.37747 + 1.52791i) q^{11} +(0.899551 + 1.96974i) q^{12} +(-1.87871 - 4.11379i) q^{13} +(0.331684 + 0.0973913i) q^{14} +(-0.942029 - 6.55195i) q^{15} +(0.281663 + 0.181014i) q^{16} +(-2.98149 + 0.875446i) q^{17} +(0.212394 + 0.0623644i) q^{18} +(0.138279 + 0.961750i) q^{19} +(-3.43382 - 3.96284i) q^{20} +(0.578712 - 0.371916i) q^{21} +(-1.53762 + 1.77451i) q^{22} +(-2.58327 - 2.98125i) q^{23} +(-4.36225 + 1.28087i) q^{24} +(4.58149 + 10.0321i) q^{25} +(3.60521 - 1.05859i) q^{26} +(4.54324 - 2.91976i) q^{27} +(0.226377 - 0.495696i) q^{28} +6.45386 q^{29} +5.49954 q^{30} +(-3.58967 + 7.86027i) q^{31} +(-3.78366 + 4.36657i) q^{32} +(0.664972 + 4.62498i) q^{33} +(-0.367413 - 2.55541i) q^{34} +(-1.09086 + 1.25892i) q^{35} +(0.144960 - 0.317419i) q^{36} -4.42749 q^{37} -0.807268 q^{38} +(3.10616 - 6.80154i) q^{39} +(9.26147 - 5.95198i) q^{40} +(-9.39879 + 2.75973i) q^{41} +(0.237427 + 0.519893i) q^{42} +(-3.36779 + 0.988872i) q^{43} +(2.42391 + 2.79734i) q^{44} +(-0.698531 + 0.806148i) q^{45} +(2.75715 - 1.77191i) q^{46} +(2.58456 + 2.98274i) q^{47} +(0.0787803 + 0.547929i) q^{48} +(6.55035 + 1.92335i) q^{49} +(-8.79181 + 2.58151i) q^{50} +(-4.32199 - 2.77758i) q^{51} +(-0.842958 - 5.86290i) q^{52} +(6.68969 + 1.96427i) q^{53} +(1.86394 + 4.08147i) q^{54} +(-4.70024 - 10.2921i) q^{55} +(0.962501 + 0.618562i) q^{56} +(-1.05201 + 1.21408i) q^{57} +(-0.763101 + 5.30748i) q^{58} +(6.00165 - 13.1418i) q^{59} +(1.23380 - 8.58124i) q^{60} +(1.42799 - 0.917715i) q^{61} +(-6.03964 - 3.88144i) q^{62} +(-0.106365 - 0.0312317i) q^{63} +(-2.70506 - 3.12181i) q^{64} +(-2.57677 + 17.9219i) q^{65} -3.88209 q^{66} +(-5.18032 - 6.33753i) q^{67} -4.06978 q^{68} +(0.928187 - 6.45569i) q^{69} +(-0.906319 - 1.04595i) q^{70} +(3.30183 + 0.969506i) q^{71} +(0.616337 + 0.396096i) q^{72} +(-1.54375 + 0.992109i) q^{73} +(0.523504 - 3.64105i) q^{74} +(-7.57480 + 16.5865i) q^{75} +(-0.181107 + 1.25963i) q^{76} +(0.770031 - 0.888663i) q^{77} +(5.22614 + 3.35863i) q^{78} +(-2.41083 - 5.27899i) q^{79} +(-0.556845 - 1.21932i) q^{80} +(7.80040 + 2.29041i) q^{81} +(-1.15822 - 8.05562i) q^{82} +(5.37548 + 3.45461i) q^{83} +(0.864483 - 0.253835i) q^{84} +(11.9367 + 3.50492i) q^{85} +(-0.415016 - 2.88650i) q^{86} +(6.98768 + 8.06422i) q^{87} +(-6.53761 + 4.20147i) q^{88} +(3.33574 - 3.84965i) q^{89} +(-0.580361 - 0.669772i) q^{90} +(-1.80547 + 0.530133i) q^{91} +(-2.14626 - 4.69965i) q^{92} +(-13.7081 + 4.02507i) q^{93} +(-2.75852 + 1.77279i) q^{94} +(1.61598 - 3.53851i) q^{95} -9.55274 q^{96} +7.79034 q^{97} +(-2.35623 + 5.15941i) q^{98} +(0.493089 - 0.569055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9} - 9 q^{10} + 3 q^{12} + 12 q^{13} + 6 q^{14} - 11 q^{15} + 8 q^{16} - 4 q^{17} - 2 q^{18} + 4 q^{19} + 2 q^{20} - 53 q^{21} + 2 q^{23} + 11 q^{24} - 3 q^{25} - 31 q^{26} + 47 q^{27} - 5 q^{28} - 6 q^{29} + 44 q^{30} + 16 q^{32} + q^{33} - 8 q^{34} + 34 q^{35} + 9 q^{36} + 24 q^{37} - 14 q^{38} - 22 q^{39} - 11 q^{40} - 6 q^{41} + 59 q^{42} - 22 q^{43} - 22 q^{44} - 46 q^{45} + 15 q^{46} + 16 q^{47} + 5 q^{48} + 42 q^{49} - 17 q^{50} + 22 q^{51} + 2 q^{52} - q^{53} - 60 q^{54} + 20 q^{55} + 11 q^{56} - 52 q^{57} + 10 q^{58} - 26 q^{59} + 44 q^{60} - 26 q^{61} + 11 q^{62} - 42 q^{63} - 6 q^{64} + 9 q^{65} + 2 q^{66} - 22 q^{67} - 52 q^{68} + 62 q^{69} - 42 q^{70} + 20 q^{71} + 11 q^{72} - 55 q^{73} + 37 q^{74} - 70 q^{75} - 3 q^{76} - 70 q^{77} + 22 q^{78} - 34 q^{79} + 40 q^{80} + 42 q^{81} - 12 q^{82} + 56 q^{83} - 29 q^{84} + 41 q^{85} - 33 q^{86} - 10 q^{87} + 11 q^{88} - 3 q^{89} + 18 q^{90} + 12 q^{91} - 18 q^{92} - 69 q^{93} + 32 q^{94} + 74 q^{95} - 12 q^{96} - 14 q^{97} + 95 q^{98} + 81 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9 - 9 * q^10 + 3 * q^12 + 12 * q^13 + 6 * q^14 - 11 * q^15 + 8 * q^16 - 4 * q^17 - 2 * q^18 + 4 * q^19 + 2 * q^20 - 53 * q^21 + 2 * q^23 + 11 * q^24 - 3 * q^25 - 31 * q^26 + 47 * q^27 - 5 * q^28 - 6 * q^29 + 44 * q^30 + 16 * q^32 + q^33 - 8 * q^34 + 34 * q^35 + 9 * q^36 + 24 * q^37 - 14 * q^38 - 22 * q^39 - 11 * q^40 - 6 * q^41 + 59 * q^42 - 22 * q^43 - 22 * q^44 - 46 * q^45 + 15 * q^46 + 16 * q^47 + 5 * q^48 + 42 * q^49 - 17 * q^50 + 22 * q^51 + 2 * q^52 - q^53 - 60 * q^54 + 20 * q^55 + 11 * q^56 - 52 * q^57 + 10 * q^58 - 26 * q^59 + 44 * q^60 - 26 * q^61 + 11 * q^62 - 42 * q^63 - 6 * q^64 + 9 * q^65 + 2 * q^66 - 22 * q^67 - 52 * q^68 + 62 * q^69 - 42 * q^70 + 20 * q^71 + 11 * q^72 - 55 * q^73 + 37 * q^74 - 70 * q^75 - 3 * q^76 - 70 * q^77 + 22 * q^78 - 34 * q^79 + 40 * q^80 + 42 * q^81 - 12 * q^82 + 56 * q^83 - 29 * q^84 + 41 * q^85 - 33 * q^86 - 10 * q^87 + 11 * q^88 - 3 * q^89 + 18 * q^90 + 12 * q^91 - 18 * q^92 - 69 * q^93 + 32 * q^94 + 74 * q^95 - 12 * q^96 - 14 * q^97 + 95 * q^98 + 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/67\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{6}{11}\right)$

Coefficient data

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

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

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

$2$	−0.118239	+	0.822373i	−0.0836079	+	0.581506i	0.904351	+	0.426789i	$0.140355\pi$
$2$	−0.118239	+	0.822373i	−0.0836079	+	0.581506i	−0.987959	+	0.154716i	$0.950554\pi$
$3$	1.08271	+	1.24952i	0.625105	+	0.721410i	0.976668	−	0.214754i	$-0.0688951\pi$
$3$	1.08271	+	1.24952i	0.625105	+	0.721410i	−0.351563	+	0.936164i	$0.614350\pi$
$4$	1.25667	+	0.368991i	0.628334	+	0.184496i
$5$	−3.36803	−	2.16450i	−1.50623	−	0.967995i	−0.994028	−	0.109129i	$-0.965194\pi$
$5$	−3.36803	−	2.16450i	−1.50623	−	0.967995i	−0.512202	−	0.858865i	$-0.671170\pi$
$6$	−1.15559	+	0.742653i	−0.471768	+	0.303187i
$7$	0.0592135	−	0.411839i	0.0223806	−	0.155661i	−0.975566	−	0.219704i	$-0.929491\pi$
$7$	0.0592135	−	0.411839i	0.0223806	−	0.155661i	0.997947	+	0.0640439i	$0.0203998\pi$
$8$	−1.14231	+	2.50132i	−0.403869	+	0.884350i
$9$	0.0379173	−	0.263721i	0.0126391	−	0.0879070i
$10$	2.17826	−	2.51385i	0.688827	−	0.794949i
$11$	2.37747	+	1.52791i	0.716835	+	0.460682i	0.847535	−	0.530740i	$-0.178086\pi$
$11$	2.37747	+	1.52791i	0.716835	+	0.460682i	−0.130700	+	0.991422i	$0.541722\pi$
$12$	0.899551	+	1.96974i	0.259678	+	0.568616i
$13$	−1.87871	−	4.11379i	−0.521060	−	1.14096i	−0.969037	−	0.246916i	$-0.920583\pi$
$13$	−1.87871	−	4.11379i	−0.521060	−	1.14096i	0.447977	−	0.894045i	$-0.352145\pi$
$14$	0.331684	+	0.0973913i	0.0886463	+	0.0260289i
$15$	−0.942029	−	6.55195i	−0.243231	−	1.69171i
$16$	0.281663	+	0.181014i	0.0704157	+	0.0452534i
$17$	−2.98149	+	0.875446i	−0.723119	+	0.212327i	−0.622524	−	0.782601i	$-0.713893\pi$
$17$	−2.98149	+	0.875446i	−0.723119	+	0.212327i	−0.100595	+	0.994927i	$0.532075\pi$
$18$	0.212394	+	0.0623644i	0.0500617	+	0.0146994i
$19$	0.138279	+	0.961750i	0.0317233	+	0.220641i	0.999516	−	0.0311078i	$-0.00990352\pi$
$19$	0.138279	+	0.961750i	0.0317233	+	0.220641i	−0.967793	+	0.251748i	$0.918994\pi$
$20$	−3.43382	−	3.96284i	−0.767825	−	0.886117i
$21$	0.578712	−	0.371916i	0.126285	−	0.0811587i
$22$	−1.53762	+	1.77451i	−0.327822	+	0.378327i
$23$	−2.58327	−	2.98125i	−0.538649	−	0.621634i	0.419552	−	0.907731i	$-0.362187\pi$
$23$	−2.58327	−	2.98125i	−0.538649	−	0.621634i	−0.958200	+	0.286098i	$0.907642\pi$
$24$	−4.36225	+	1.28087i	−0.890440	+	0.261457i
$25$	4.58149	+	10.0321i	0.916298	+	2.00641i
$26$	3.60521	−	1.05859i	0.707040	−	0.207606i
$27$	4.54324	−	2.91976i	0.874347	−	0.561908i
$28$	0.226377	−	0.495696i	0.0427812	−	0.0936778i
$29$	6.45386			1.19845			0.599226	−	0.800580i	$-0.295475\pi$
$29$	6.45386			1.19845			0.599226	+	0.800580i	$0.295475\pi$
$30$	5.49954			1.00407
$31$	−3.58967	+	7.86027i	−0.644723	+	1.41175i	0.251375	+	0.967890i	$0.419117\pi$
$31$	−3.58967	+	7.86027i	−0.644723	+	1.41175i	−0.896098	+	0.443857i	$0.853610\pi$
$32$	−3.78366	+	4.36657i	−0.668862	+	0.771908i
$33$	0.664972	+	4.62498i	0.115757	+	0.805106i
$34$	−0.367413	−	2.55541i	−0.0630108	−	0.438250i
$35$	−1.09086	+	1.25892i	−0.184389	+	0.212796i
$36$	0.144960	−	0.317419i	0.0241600	−	0.0529031i
$37$	−4.42749			−0.727874			−0.363937	−	0.931423i	$-0.618568\pi$
$37$	−4.42749			−0.727874			−0.363937	+	0.931423i	$0.618568\pi$
$38$	−0.807268			−0.130956
$39$	3.10616	−	6.80154i	0.497384	−	1.08912i
$40$	9.26147	−	5.95198i	1.46437	−	0.941091i
$41$	−9.39879	+	2.75973i	−1.46784	+	0.430998i	−0.915398	−	0.402550i	$-0.868124\pi$
$41$	−9.39879	+	2.75973i	−1.46784	+	0.430998i	−0.552447	+	0.833548i	$0.686306\pi$
$42$	0.237427	+	0.519893i	0.0366358	+	0.0802212i
$43$	−3.36779	+	0.988872i	−0.513583	+	0.150802i	−0.528247	−	0.849091i	$-0.677150\pi$
$43$	−3.36779	+	0.988872i	−0.513583	+	0.150802i	0.0146638	+	0.999892i	$0.495332\pi$
$44$	2.42391	+	2.79734i	0.365418	+	0.421715i
$45$	−0.698531	+	0.806148i	−0.104131	+	0.120173i
$46$	2.75715	−	1.77191i	0.406519	−	0.261254i
$47$	2.58456	+	2.98274i	0.376996	+	0.435077i	0.912262	−	0.409607i	$-0.134334\pi$
$47$	2.58456	+	2.98274i	0.376996	+	0.435077i	−0.535266	+	0.844684i	$0.679789\pi$
$48$	0.0787803	+	0.547929i	0.0113710	+	0.0790868i
$49$	6.55035	+	1.92335i	0.935764	+	0.274765i
$50$	−8.79181	+	2.58151i	−1.24335	+	0.365080i
$51$	−4.32199	−	2.77758i	−0.605200	−	0.388938i
$52$	−0.842958	−	5.86290i	−0.116897	−	0.813038i
$53$	6.68969	+	1.96427i	0.918900	+	0.269813i	0.706783	−	0.707431i	$-0.250146\pi$
$53$	6.68969	+	1.96427i	0.918900	+	0.269813i	0.212117	+	0.977244i	$0.431964\pi$
$54$	1.86394	+	4.08147i	0.253651	+	0.555418i
$55$	−4.70024	−	10.2921i	−0.633780	−	1.38778i
$56$	0.962501	+	0.618562i	0.128620	+	0.0826588i
$57$	−1.05201	+	1.21408i	−0.139342	+	0.160809i
$58$	−0.763101	+	5.30748i	−0.100200	+	0.696906i
$59$	6.00165	−	13.1418i	0.781348	−	1.71091i	0.0814440	−	0.996678i	$-0.474047\pi$
$59$	6.00165	−	13.1418i	0.781348	−	1.71091i	0.699904	−	0.714237i	$-0.253226\pi$
$60$	1.23380	−	8.58124i	0.159282	−	1.10783i
$61$	1.42799	−	0.917715i	0.182836	−	0.117501i	−0.446021	−	0.895022i	$-0.647159\pi$
$61$	1.42799	−	0.917715i	0.182836	−	0.117501i	0.628857	+	0.777521i	$0.283523\pi$
$62$	−6.03964	−	3.88144i	−0.767035	−	0.492943i
$63$	−0.106365	−	0.0312317i	−0.0134008	−	0.00393482i
$64$	−2.70506	−	3.12181i	−0.338133	−	0.390226i
$65$	−2.57677	+	17.9219i	−0.319609	+	2.22293i
$66$	−3.88209			−0.477852
$67$	−5.18032	−	6.33753i	−0.632877	−	0.774252i
$67$	−5.18032	−	6.33753i	−0.632877	−	0.774252i
$68$	−4.06978			−0.493534
$69$	0.928187	−	6.45569i	0.111741	−	0.777173i
$70$	−0.906319	−	1.04595i	−0.108326	−	0.125015i
$71$	3.30183	+	0.969506i	0.391856	+	0.115059i	0.471724	−	0.881746i	$-0.343632\pi$
$71$	3.30183	+	0.969506i	0.391856	+	0.115059i	−0.0798685	+	0.996805i	$0.525450\pi$
$72$	0.616337	+	0.396096i	0.0726360	+	0.0466803i
$73$	−1.54375	+	0.992109i	−0.180682	+	0.116118i	−0.627856	−	0.778330i	$-0.716067\pi$
$73$	−1.54375	+	0.992109i	−0.180682	+	0.116118i	0.447173	+	0.894447i	$0.352431\pi$
$74$	0.523504	−	3.64105i	0.0608561	−	0.423263i
$75$	−7.57480	+	16.5865i	−0.874663	+	1.91524i
$76$	−0.181107	+	1.25963i	−0.0207744	+	0.144489i
$77$	0.770031	−	0.888663i	0.0877532	−	0.101273i
$78$	5.22614	+	3.35863i	0.591744	+	0.380291i
$79$	−2.41083	−	5.27899i	−0.271240	−	0.593933i	0.724171	−	0.689620i	$-0.242222\pi$
$79$	−2.41083	−	5.27899i	−0.271240	−	0.593933i	−0.995411	+	0.0956872i	$0.969495\pi$
$80$	−0.556845	−	1.21932i	−0.0622571	−	0.136324i
$81$	7.80040	+	2.29041i	0.866712	+	0.254489i
$82$	−1.15822	−	8.05562i	−0.127904	−	0.889595i
$83$	5.37548	+	3.45461i	0.590036	+	0.379193i	0.801324	−	0.598231i	$-0.204129\pi$
$83$	5.37548	+	3.45461i	0.590036	+	0.379193i	−0.211288	+	0.977424i	$0.567766\pi$
$84$	0.864483	−	0.253835i	0.0943228	−	0.0276957i
$85$	11.9367	+	3.50492i	1.29471	+	0.380162i
$86$	−0.415016	−	2.88650i	−0.0447524	−	0.311260i
$87$	6.98768	+	8.06422i	0.749158	+	0.864575i
$88$	−6.53761	+	4.20147i	−0.696912	+	0.447878i
$89$	3.33574	−	3.84965i	0.353588	−	0.408062i	−0.550894	−	0.834576i	$-0.685713\pi$
$89$	3.33574	−	3.84965i	0.353588	−	0.408062i	0.904481	+	0.426514i	$0.140258\pi$
$90$	−0.580361	−	0.669772i	−0.0611754	−	0.0706002i
$91$	−1.80547	+	0.530133i	−0.189264	+	0.0555730i
$92$	−2.14626	−	4.69965i	−0.223763	−	0.489972i
$93$	−13.7081	+	4.02507i	−1.42147	+	0.417381i
$94$	−2.75852	+	1.77279i	−0.284520	+	0.182850i
$95$	1.61598	−	3.53851i	0.165796	−	0.363043i
$96$	−9.55274			−0.974972
$97$	7.79034			0.790989			0.395494	−	0.918468i	$-0.370573\pi$
$97$	7.79034			0.790989			0.395494	+	0.918468i	$0.370573\pi$
$98$	−2.35623	+	5.15941i	−0.238015	+	0.521179i
$99$	0.493089	−	0.569055i	0.0495573	−	0.0571922i
$100$	2.05567	+	14.2975i	0.205567	+	1.42975i
$101$	0.0803064	+	0.558543i	0.00799079	+	0.0555771i	0.993427	−	0.114470i	$-0.0365170\pi$
$101$	0.0803064	+	0.558543i	0.00799079	+	0.0555771i	−0.985436	+	0.170047i	$0.945608\pi$
$102$	2.79523	−	3.22587i	0.276769	−	0.319409i
$103$	1.00095	−	2.19178i	0.0986267	−	0.215962i	−0.853887	−	0.520459i	$-0.825761\pi$
$103$	1.00095	−	2.19178i	0.0986267	−	0.215962i	0.952513	+	0.304496i	$0.0984882\pi$
$104$	12.4360			1.21945
$105$	−2.75413			−0.268776
$106$	−2.40635	+	5.26917i	−0.233725	+	0.511787i
$107$	8.81090	−	5.66242i	0.851782	−	0.547407i	−0.0403479	−	0.999186i	$-0.512847\pi$
$107$	8.81090	−	5.66242i	0.851782	−	0.547407i	0.892130	+	0.451778i	$0.149210\pi$
$108$	6.78671	−	1.99276i	0.653052	−	0.191753i
$109$	−3.60281	−	7.88905i	−0.345087	−	0.755634i	0.654913	−	0.755704i	$-0.272705\pi$
$109$	−3.60281	−	7.88905i	−0.345087	−	0.755634i	−1.00000		6.97047e-5i	$0.999978\pi$
$110$	9.01969	−	2.64842i	0.859994	−	0.252517i
$111$	−4.79370	−	5.53223i	−0.454998	−	0.525096i
$112$	0.0912268	−	0.105281i	0.00862012	−	0.00994815i
$113$	−7.30429	+	4.69418i	−0.687129	+	0.441591i	−0.837064	−	0.547105i	$-0.815730\pi$
$113$	−7.30429	+	4.69418i	−0.687129	+	0.441591i	0.149935	+	0.988696i	$0.452094\pi$
$114$	−0.874041	−	1.00870i	−0.0818614	−	0.0944731i
$115$	2.24760	+	15.6324i	0.209590	+	1.45773i
$116$	8.11036	+	2.38142i	0.753028	+	0.221109i
$117$	−1.15613	+	0.339470i	−0.106884	+	0.0313840i
$118$	10.0978	+	6.48948i	0.929580	+	0.597405i
$119$	0.183998	+	1.27973i	0.0168671	+	0.117313i
$120$	17.4646	+	5.12808i	1.59430	+	0.468127i
$121$	−1.25170	−	2.74083i	−0.113791	−	0.249167i
$122$	0.585859	+	1.28285i	0.0530412	+	0.116144i
$123$	−13.6245	−	8.75596i	−1.22848	−	0.789499i
$124$	−7.41139	+	8.55320i	−0.665563	+	0.768100i
$125$	3.43497	−	23.8907i	0.307233	−	2.13685i
$126$	0.0382607	−	0.0837793i	0.00340853	−	0.00746365i
$127$	−1.56332	+	10.8731i	−0.138722	+	0.964835i	0.794942	+	0.606686i	$0.207501\pi$
$127$	−1.56332	+	10.8731i	−0.138722	+	0.964835i	−0.933664	+	0.358149i	$0.883408\pi$
$128$	−6.83406	+	4.39198i	−0.604051	+	0.388200i
$129$	−4.88197	−	3.13745i	−0.429833	−	0.276237i
$130$	−14.4338	−	4.23814i	−1.26593	−	0.371709i
$131$	6.79220	+	7.83862i	0.593438	+	0.684864i	0.970438	−	0.241349i	$-0.0775900\pi$
$131$	6.79220	+	7.83862i	0.593438	+	0.684864i	−0.377001	+	0.926213i	$0.623045\pi$
$132$	−0.870928	+	6.05744i	−0.0758046	+	0.527233i
$133$	0.404275			0.0350550
$134$	5.82433	−	3.51082i	0.503146	−	0.303288i
$135$	−21.6216			−1.86089
$136$	1.21603	−	8.45771i	0.104274	−	0.725243i
$137$	−10.6711	−	12.3151i	−0.911692	−	1.05215i	−0.998435	−	0.0559180i	$-0.982191\pi$
$137$	−10.6711	−	12.3151i	−0.911692	−	1.05215i	0.0867434	−	0.996231i	$-0.472354\pi$
$138$	5.19924	+	1.52663i	0.442588	+	0.129956i
$139$	−7.09991	−	4.56283i	−0.602206	−	0.387015i	0.203721	−	0.979029i	$-0.434696\pi$
$139$	−7.09991	−	4.56283i	−0.602206	−	0.387015i	−0.805927	+	0.592014i	$0.798333\pi$
$140$	−1.83538	+	1.17953i	−0.155118	+	0.0996882i
$141$	−0.928650	+	6.45890i	−0.0782064	+	0.543938i
$142$	−1.18770	+	2.60071i	−0.0996698	+	0.218246i
$143$	1.81893	−	12.6509i	0.152106	−	1.05792i
$144$	0.0584170	−	0.0674168i	0.00486808	−	0.00561807i
$145$	−21.7368	−	13.9694i	−1.80514	−	1.16009i
$146$	−0.633351	−	1.38685i	−0.0524165	−	0.114776i
$147$	4.68888	+	10.2672i	0.386733	+	0.846826i
$148$	−5.56388	−	1.63370i	−0.457348	−	0.134290i
$149$	−0.362233	−	2.51939i	−0.0296753	−	0.206396i	0.969589	−	0.244737i	$-0.0787017\pi$
$149$	−0.362233	−	2.51939i	−0.0296753	−	0.206396i	−0.999265	+	0.0383412i	$0.987793\pi$
$150$	−12.7447	−	8.19050i	−1.04060	−	0.668751i
$151$	−2.60050	+	0.763575i	−0.211625	+	0.0621388i	−0.385827	−	0.922571i	$-0.626084\pi$
$151$	−2.60050	+	0.763575i	−0.211625	+	0.0621388i	0.174201	+	0.984710i	$0.444266\pi$
$152$	−2.56360	−	0.752742i	−0.207936	−	0.0610554i
$153$	0.117823	+	0.819477i	0.00952543	+	0.0662508i
$154$	0.639765	+	0.738328i	0.0515537	+	0.0594962i
$155$	29.1037	−	18.7038i	2.33766	−	1.50233i
$156$	6.41312	−	7.40114i	0.513461	−	0.592565i
$157$	8.05712	+	9.29842i	0.643028	+	0.742094i	0.979907	−	0.199454i	$-0.0639167\pi$
$157$	8.05712	+	9.29842i	0.643028	+	0.742094i	−0.336879	+	0.941548i	$0.609371\pi$
$158$	4.62636	−	1.35842i	0.368053	−	0.108070i
$159$	4.78863	+	10.4856i	0.379763	+	0.831566i
$160$	22.1949	−	6.51702i	1.75466	−	0.515216i
$161$	−1.38076	+	0.887361i	−0.108819	+	0.0699338i
$162$	−2.80588	+	6.14403i	−0.220451	+	0.482720i
$163$	18.6015			1.45698			0.728492	−	0.685054i	$-0.240221\pi$
$163$	18.6015			1.45698			0.728492	+	0.685054i	$0.240221\pi$
$164$	−12.8295			−1.00181
$165$	7.77114	−	17.0164i	0.604982	−	1.32473i
$166$	−3.47658	+	4.01218i	−0.269835	+	0.311406i
$167$	1.06098	+	7.37929i	0.0821012	+	0.571026i	0.988800	+	0.149247i	$0.0476851\pi$
$167$	1.06098	+	7.37929i	0.0821012	+	0.571026i	−0.906699	+	0.421779i	$0.861406\pi$
$168$	0.269209	+	1.87239i	0.0207699	+	0.144458i
$169$	−4.88058	+	5.63249i	−0.375429	+	0.433268i
$170$	−4.29374	+	9.40198i	−0.329315	+	0.721099i
$171$	0.258877			0.0197968
$172$	−4.59708			−0.350524
$173$	−7.75588	+	16.9830i	−0.589669	+	1.29119i	0.345973	+	0.938244i	$0.387549\pi$
$173$	−7.75588	+	16.9830i	−0.589669	+	1.29119i	−0.935642	+	0.352950i	$0.885178\pi$
$174$	−7.45802	+	4.79298i	−0.565391	+	0.363355i
$175$	4.40288	−	1.29280i	0.332827	−	0.0977267i
$176$	0.393073	+	0.860710i	0.0296290	+	0.0648785i
$177$	22.9190	−	6.72962i	1.72270	−	0.505829i
$178$	2.77143	+	3.19840i	0.207728	+	0.239730i
$179$	−5.20917	+	6.01170i	−0.389352	+	0.449336i	−0.916259	−	0.400587i	$-0.868806\pi$
$179$	−5.20917	+	6.01170i	−0.389352	+	0.449336i	0.526907	+	0.849923i	$0.323352\pi$
$180$	−1.17528	+	0.755309i	−0.0876005	+	0.0562974i
$181$	−16.1634	−	18.6536i	−1.20142	−	1.38651i	−0.901633	−	0.432501i	$-0.857631\pi$
$181$	−16.1634	−	18.6536i	−1.20142	−	1.38651i	−0.299783	−	0.954007i	$-0.596914\pi$
$182$	−0.222490	−	1.54745i	−0.0164920	−	0.114705i
$183$	2.69281	+	0.790680i	0.199058	+	0.0584488i
$184$	10.4080	−	3.05606i	0.767286	−	0.225295i
$185$	14.9119	+	9.58330i	1.09635	+	0.704579i
$186$	−1.68927	−	11.7491i	−0.123863	−	0.861488i
$187$	−8.42602	−	2.47410i	−0.616172	−	0.180924i
$188$	2.14733	+	4.70199i	0.156610	+	0.342928i
$189$	−0.933451	−	2.04397i	−0.0678986	−	0.148677i
$190$	2.71890	+	1.74733i	0.197250	+	0.126765i
$191$	−3.33134	+	3.84458i	−0.241048	+	0.278184i	−0.863364	−	0.504582i	$-0.831646\pi$
$191$	−3.33134	+	3.84458i	−0.241048	+	0.278184i	0.622316	+	0.782766i	$0.286192\pi$
$192$	0.971949	−	6.76006i	0.0701444	−	0.487865i
$193$	−4.58973	+	10.0501i	−0.330376	+	0.723423i	−0.999811	−	0.0194479i	$-0.993809\pi$
$193$	−4.58973	+	10.0501i	−0.330376	+	0.723423i	0.669435	+	0.742871i	$0.266536\pi$
$194$	−0.921125	+	6.40657i	−0.0661329	+	0.459965i
$195$	−25.1836	+	16.1845i	−1.80344	+	1.15900i
$196$	7.52191	+	4.83404i	0.537279	+	0.345289i
$197$	−5.83292	−	1.71270i	−0.415579	−	0.122025i	0.0672574	−	0.997736i	$-0.478575\pi$
$197$	−5.83292	−	1.71270i	−0.415579	−	0.122025i	−0.482836	+	0.875711i	$0.660393\pi$
$198$	0.409673	+	0.472788i	0.0291142	+	0.0335996i
$199$	0.115553	−	0.803689i	0.00819133	−	0.0569720i	−0.985316	−	0.170742i	$-0.945384\pi$
$199$	0.115553	−	0.803689i	0.00819133	−	0.0569720i	0.993507	+	0.113770i	$0.0362927\pi$
$200$	−30.3269			−2.14444
$201$	2.31005	−	13.3346i	0.162938	−	0.940553i
$202$	−0.468827			−0.0329865
$203$	0.382156	−	2.65795i	0.0268221	−	0.186552i
$204$	−4.40641	−	5.08527i	−0.308510	−	0.356040i
$205$	37.6289	+	11.0488i	2.62811	+	0.771684i
$206$	1.68411	+	1.08231i	0.117337	+	0.0754082i
$207$	−0.884169	+	0.568221i	−0.0614540	+	0.0394941i
$208$	0.215491	−	1.49877i	0.0149416	−	0.103921i
$209$	−1.14071	+	2.49781i	−0.0789047	+	0.172777i
$210$	0.325647	−	2.26493i	0.0224718	−	0.156295i
$211$	−13.4152	+	15.4819i	−0.923538	+	1.06582i	0.0741083	+	0.997250i	$0.476389\pi$
$211$	−13.4152	+	15.4819i	−0.923538	+	1.06582i	−0.997646	+	0.0685695i	$0.978157\pi$
$212$	7.68193	+	4.93688i	0.527597	+	0.339066i
$213$	2.36353	+	5.17540i	0.161946	+	0.354613i
$214$	3.61483	+	7.91537i	0.247105	+	0.541084i
$215$	13.4832	+	3.95903i	0.919549	+	0.270004i
$216$	2.11345	+	14.6994i	0.143802	+	1.00017i
$217$	3.02461	+	1.94380i	0.205324	+	0.131954i
$218$	6.91374	−	2.03006i	0.468258	−	0.137493i
$219$	−2.91110	−	0.854776i	−0.196714	−	0.0577604i
$220$	−2.10895	−	14.6681i	−0.142186	−	0.988922i
$221$	9.20276	+	10.6206i	0.619045	+	0.714416i
$222$	5.11636	−	3.28809i	0.343388	−	0.220682i
$223$	6.72863	−	7.76525i	0.450582	−	0.519999i	−0.484327	−	0.874887i	$-0.660935\pi$
$223$	6.72863	−	7.76525i	0.450582	−	0.519999i	0.934909	+	0.354888i	$0.115481\pi$
$224$	1.57428	+	1.81682i	0.105186	+	0.121391i
$225$	2.81938	−	0.827845i	0.187959	−	0.0551897i
$226$	−2.99671	−	6.56189i	−0.199338	−	0.436490i
$227$	−12.0716	+	3.54454i	−0.801219	+	0.235259i	−0.656610	−	0.754230i	$-0.728010\pi$
$227$	−12.0716	+	3.54454i	−0.801219	+	0.235259i	−0.144608	+	0.989489i	$0.546192\pi$
$228$	−1.77001	+	1.13752i	−0.117222	+	0.0753340i
$229$	2.78651	−	6.10162i	0.184138	−	0.403206i	−0.794941	−	0.606687i	$-0.792498\pi$
$229$	2.78651	−	6.10162i	0.184138	−	0.403206i	0.979079	+	0.203481i	$0.0652254\pi$
$230$	−13.1215			−0.865203
$231$	1.94412			0.127914
$232$	−7.37234	+	16.1432i	−0.484018	+	1.05985i
$233$	3.62156	−	4.17950i	0.237256	−	0.273808i	−0.624618	−	0.780930i	$-0.714745\pi$
$233$	3.62156	−	4.17950i	0.237256	−	0.273808i	0.861874	+	0.507122i	$0.169291\pi$
$234$	−0.142471	−	0.990909i	−0.00931363	−	0.0647777i
$235$	−2.24872	−	15.6402i	−0.146691	−	1.02026i
$236$	12.3913	−	14.3003i	0.806604	−	0.930871i
$237$	3.98595	−	8.72802i	0.258915	−	0.566946i
$238$	−1.07418			−0.0696285
$239$	9.56902			0.618969			0.309484	−	0.950905i	$-0.399844\pi$
$239$	9.56902			0.618969			0.309484	+	0.950905i	$0.399844\pi$
$240$	0.920659	−	2.01596i	0.0594283	−	0.130130i
$241$	−24.7371	+	15.8976i	−1.59346	+	1.02405i	−0.623176	+	0.782081i	$0.714158\pi$
$241$	−24.7371	+	15.8976i	−1.59346	+	1.02405i	−0.970283	+	0.241973i	$0.922205\pi$
$242$	2.40199	−	0.705287i	0.154406	−	0.0453376i
$243$	−1.14671	−	2.51095i	−0.0735618	−	0.161078i
$244$	2.13314	−	0.626347i	0.136560	−	0.0400978i
$245$	−17.8987	−	20.6562i	−1.14350	−	1.31967i
$246$	8.81163	−	10.1692i	0.561809	−	0.648362i
$247$	3.69666	−	2.37570i	0.235213	−	0.151162i
$248$	−15.5605	−	17.9578i	−0.988095	−	1.14032i
$249$	1.50351	+	10.4571i	0.0952810	+	0.662694i
$250$	19.2410	+	5.64966i	1.21691	+	0.357316i
$251$	10.5564	−	3.09965i	0.666317	−	0.195648i	0.0689547	−	0.997620i	$-0.478034\pi$
$251$	10.5564	−	3.09965i	0.666317	−	0.195648i	0.597362	+	0.801971i	$0.296215\pi$
$252$	−0.122142	−	0.0784958i	−0.00769421	−	0.00494477i
$253$	−1.58657	−	11.0348i	−0.0997468	−	0.693754i
$254$	−8.75693	−	2.57127i	−0.549459	−	0.161336i
$255$	8.54454	+	18.7099i	0.535080	+	1.17166i
$256$	−6.23574	−	13.6544i	−0.389734	−	0.853398i
$257$	−4.01990	−	2.58344i	−0.250755	−	0.161150i	0.409225	−	0.912433i	$-0.365799\pi$
$257$	−4.01990	−	2.58344i	−0.250755	−	0.161150i	−0.659980	+	0.751283i	$0.729435\pi$
$258$	3.15740	−	3.64383i	0.196571	−	0.226855i
$259$	−0.262167	+	1.82341i	−0.0162903	+	0.113301i
$260$	−9.85116	+	21.5710i	−0.610943	+	1.33778i
$261$	0.244713	−	1.70202i	0.0151474	−	0.105352i
$262$	−7.24938	+	4.65889i	−0.447868	+	0.287827i
$263$	−5.55995	−	3.57317i	−0.342841	−	0.220331i	0.357877	−	0.933769i	$-0.383501\pi$
$263$	−5.55995	−	3.57317i	−0.342841	−	0.220331i	−0.700718	+	0.713438i	$0.747137\pi$
$264$	−12.3282	−	3.61988i	−0.758747	−	0.222788i
$265$	−18.2794	−	21.0956i	−1.12290	−	1.29589i
$266$	−0.0478012	+	0.332465i	−0.00293088	+	0.0203847i
$267$	8.42186			0.515409
$268$	−4.17146	−	9.87566i	−0.254812	−	0.603252i
$269$	−11.3908			−0.694508			−0.347254	−	0.937771i	$-0.612886\pi$
$269$	−11.3908			−0.694508			−0.347254	+	0.937771i	$0.612886\pi$
$270$	2.55653	−	17.7810i	0.155585	−	1.08212i
$271$	13.9045	+	16.0466i	0.844635	+	0.974761i	0.999914	−	0.0131096i	$-0.00417305\pi$
$271$	13.9045	+	16.0466i	0.844635	+	0.974761i	−0.155279	+	0.987871i	$0.549628\pi$
$272$	−0.998244	−	0.293111i	−0.0605274	−	0.0177725i
$273$	−2.61722	−	1.68198i	−0.158401	−	0.101798i
$274$	11.3893	−	7.31948i	0.688055	−	0.442186i
$275$	−4.43571	+	30.8510i	−0.267483	+	1.86039i
$276$	3.54851	−	7.77016i	0.213595	−	0.467709i
$277$	−2.28488	+	15.8917i	−0.137285	+	0.954838i	0.798432	+	0.602086i	$0.205663\pi$
$277$	−2.28488	+	15.8917i	−0.137285	+	0.954838i	−0.935717	+	0.352753i	$0.885246\pi$
$278$	4.59184	−	5.29927i	0.275400	−	0.317829i
$279$	1.93681	+	1.24471i	0.115954	+	0.0745189i
$280$	−1.90286	−	4.16667i	−0.113717	−	0.249006i
$281$	0.564303	+	1.23565i	0.0336635	+	0.0737127i	0.925717	−	0.378218i	$-0.123463\pi$
$281$	0.564303	+	1.23565i	0.0336635	+	0.0737127i	−0.892053	+	0.451930i	$0.850736\pi$
$282$	−5.20183	−	1.52739i	−0.309764	−	0.0909550i
$283$	−4.00811	−	27.8770i	−0.238257	−	1.65712i	−0.660642	−	0.750701i	$-0.729716\pi$
$283$	−4.00811	−	27.8770i	−0.238257	−	1.65712i	0.422385	−	0.906417i	$-0.361193\pi$
$284$	3.79157	+	2.43669i	0.224988	+	0.144591i
$285$	6.17108	−	1.81199i	0.365543	−	0.107333i
$286$	10.1887	+	2.99168i	0.602471	+	0.176902i
$287$	0.580031	+	4.03420i	0.0342381	+	0.238132i
$288$	1.00809	+	1.16340i	0.0594023	+	0.0685539i
$289$	−6.17840	+	3.97062i	−0.363436	+	0.233566i
$290$	14.0582	−	16.2240i	0.825526	−	0.952708i
$291$	8.43471	+	9.73417i	0.494451	+	0.570627i
$292$	−2.30606	+	0.677121i	−0.134952	+	0.0396255i
$293$	−5.36443	−	11.7465i	−0.313393	−	0.686236i	0.685741	−	0.727846i	$-0.259478\pi$
$293$	−5.36443	−	11.7465i	−0.313393	−	0.686236i	−0.999134	+	0.0416104i	$0.986751\pi$
$294$	−8.99790	+	2.64202i	−0.524768	+	0.154086i
$295$	−48.6592	+	31.2713i	−2.83305	+	1.82069i
$296$	5.05758	−	11.0746i	0.293966	−	0.643696i
$297$	15.2625			0.885623
$298$	2.11471			0.122502
$299$	−7.41105	+	16.2279i	−0.428592	+	0.938486i
$300$	−15.6393	+	18.0487i	−0.902935	+	1.04204i
$301$	0.207838	+	1.44554i	0.0119796	+	0.0833196i
$302$	−0.320462	−	2.22886i	−0.0184405	−	0.128257i
$303$	−0.610962	+	0.705087i	−0.0350988	+	0.0405062i
$304$	−0.135142	+	0.295920i	−0.00775093	+	0.0169722i
$305$	−6.79592			−0.389133
$306$	−0.687848			−0.0393216
$307$	9.46692	−	20.7297i	0.540306	−	1.18310i	−0.420858	−	0.907127i	$-0.638271\pi$
$307$	9.46692	−	20.7297i	0.540306	−	1.18310i	0.961164	−	0.275978i	$-0.0890018\pi$
$308$	1.29558	−	0.832620i	0.0738227	−	0.0474430i
$309$	3.82241	−	1.12236i	0.217450	−	0.0638489i
$310$	11.9403	+	26.1456i	0.678164	+	1.48497i
$311$	4.62400	−	1.35773i	0.262203	−	0.0769897i	−0.147989	−	0.988989i	$-0.547280\pi$
$311$	4.62400	−	1.35773i	0.262203	−	0.0769897i	0.410192	+	0.911999i	$0.365462\pi$
$312$	13.4646	+	15.5390i	0.762284	+	0.879723i
$313$	5.78274	−	6.67364i	0.326860	−	0.377216i	−0.568406	−	0.822748i	$-0.692440\pi$
$313$	5.78274	−	6.67364i	0.326860	−	0.377216i	0.895266	+	0.445532i	$0.146985\pi$
$314$	−8.59944	+	5.52652i	−0.485294	+	0.311880i
$315$	0.290641	+	0.335417i	0.0163758	+	0.0188986i
$316$	−1.08172	−	7.52352i	−0.0608514	−	0.423231i
$317$	−1.37397	−	0.403433i	−0.0771696	−	0.0226590i	0.242920	−	0.970046i	$-0.421895\pi$
$317$	−1.37397	−	0.403433i	−0.0771696	−	0.0226590i	−0.320089	+	0.947387i	$0.603713\pi$
$318$	−9.18932	+	2.69823i	−0.515311	+	0.151309i
$319$	15.3439	+	9.86091i	0.859092	+	0.552105i
$320$	2.35357	+	16.3695i	0.131569	+	0.915081i
$321$	16.6150	+	4.87860i	0.927359	+	0.272297i
$322$	−0.566482	−	1.24042i	−0.0315688	−	0.0691260i
$323$	−1.25424	−	2.74640i	−0.0697877	−	0.152814i
$324$	8.95738	+	5.75656i	0.497632	+	0.319809i
$325$	32.6626	−	37.6946i	1.81179	−	2.09092i
$326$	−2.19944	+	15.2974i	−0.121815	+	0.847245i
$327$	5.95671	−	13.0434i	0.329407	−	0.721300i
$328$	3.83340	−	26.6619i	0.211664	−	1.47216i
$329$	1.38145	−	0.887803i	0.0761617	−	0.0489462i
$330$	13.0750	+	8.40279i	0.719755	+	0.462558i
$331$	8.92115	+	2.61949i	0.490351	+	0.143980i	0.517555	−	0.855650i	$-0.326842\pi$
$331$	8.92115	+	2.61949i	0.490351	+	0.143980i	−0.0272041	+	0.999630i	$0.508660\pi$
$332$	5.48048	+	6.32481i	0.300780	+	0.347119i
$333$	−0.167879	+	1.16762i	−0.00919969	+	0.0639852i
$334$	−6.19398			−0.338919
$335$	3.72991	+	32.5578i	0.203786	+	1.77882i
$336$	0.230324			0.0125652
$337$	−1.58259	+	11.0071i	−0.0862091	+	0.599597i	0.900223	+	0.435429i	$0.143403\pi$
$337$	−1.58259	+	11.0071i	−0.0862091	+	0.599597i	−0.986432	+	0.164169i	$0.947506\pi$
$338$	−4.05493	−	4.67964i	−0.220559	−	0.254539i
$339$	−13.7739	−	4.04439i	−0.748097	−	0.219661i
$340$	13.7072	+	8.80905i	0.743375	+	0.477738i
$341$	−20.5441	+	13.2029i	−1.11253	+	0.714977i
$342$	−0.0306095	+	0.212893i	−0.00165517	+	0.0115120i
$343$	2.38989	−	5.23312i	0.129042	−	0.282562i
$344$	1.37359	−	9.55352i	0.0740590	−	0.515091i
$345$	−17.0995	+	19.7339i	−0.920607	+	1.06244i
$346$	−13.0493	−	8.38629i	−0.701536	−	0.450850i
$347$	−11.3946	−	24.9506i	−0.611692	−	1.33942i	−0.921411	−	0.388590i	$-0.872962\pi$
$347$	−11.3946	−	24.9506i	−0.611692	−	1.33942i	0.309719	−	0.950828i	$-0.399765\pi$
$348$	5.80558	+	12.7124i	0.311212	+	0.681458i
$349$	17.5421	+	5.15081i	0.939005	+	0.275717i	0.715202	−	0.698918i	$-0.246335\pi$
$349$	17.5421	+	5.15081i	0.939005	+	0.275717i	0.223803	+	0.974634i	$0.428153\pi$
$350$	0.542572	+	3.77367i	0.0290017	+	0.201711i
$351$	−20.5467	−	13.2046i	−1.09670	−	0.704808i
$352$	−15.6673	+	4.60032i	−0.835068	+	0.245198i
$353$	2.08413	+	0.611956i	0.110927	+	0.0325712i	0.336725	−	0.941603i	$-0.390681\pi$
$353$	2.08413	+	0.611956i	0.110927	+	0.0325712i	−0.225798	+	0.974174i	$0.572499\pi$
$354$	2.82433	+	19.6437i	0.150112	+	1.04405i
$355$	−9.02218	−	10.4122i	−0.478848	−	0.552620i
$356$	5.61240	−	3.60687i	0.297457	−	0.191164i
$357$	−1.39984	+	1.61550i	−0.0740871	+	0.0855011i
$358$	−4.32793	−	4.99470i	−0.228738	−	0.263978i
$359$	−15.7049	+	4.61139i	−0.828875	+	0.243380i	−0.668534	−	0.743682i	$-0.733078\pi$
$359$	−15.7049	+	4.61139i	−0.828875	+	0.243380i	−0.160342	+	0.987062i	$0.551260\pi$
$360$	−1.21849	−	2.66813i	−0.0642202	−	0.140623i
$361$	17.3245	−	5.08694i	0.911817	−	0.267734i
$362$	17.2513	−	11.0868i	0.906711	−	0.582708i
$363$	2.06949	−	4.53156i	0.108620	−	0.237845i
$364$	−2.46449			−0.129174
$365$	7.34682			0.384550
$366$	−0.968631	+	2.12101i	−0.0506311	+	0.110867i
$367$	6.15961	−	7.10857i	0.321529	−	0.371064i	−0.571858	−	0.820353i	$-0.693777\pi$
$367$	6.15961	−	7.10857i	0.321529	−	0.371064i	0.893387	+	0.449289i	$0.148322\pi$
$368$	−0.187963	−	1.30731i	−0.00979827	−	0.0681485i
$369$	0.371422	+	2.58330i	0.0193355	+	0.134481i
$370$	−9.64423	+	11.1300i	−0.501380	+	0.578623i
$371$	1.20508	−	2.63877i	0.0625649	−	0.136998i
$372$	−18.7118			−0.970162
$373$	11.1755			0.578644			0.289322	−	0.957232i	$-0.406570\pi$
$373$	11.1755			0.578644			0.289322	+	0.957232i	$0.406570\pi$
$374$	3.03092	−	6.63680i	0.156725	−	0.343181i
$375$	33.5710	−	21.5748i	1.73360	−	1.11412i
$376$	−10.4132	+	3.05758i	−0.537017	+	0.157683i
$377$	−12.1249	−	26.5499i	−0.624465	−	1.36739i
$378$	1.79128	−	0.525967i	0.0921335	−	0.0270528i
$379$	1.35354	+	1.56207i	0.0695266	+	0.0802380i	0.789447	−	0.613818i	$-0.210367\pi$
$379$	1.35354	+	1.56207i	0.0695266	+	0.0802380i	−0.719921	+	0.694056i	$0.755822\pi$
$380$	3.33643	−	3.85045i	0.171155	−	0.197524i
$381$	−15.2788	+	9.81910i	−0.782758	+	0.503048i
$382$	−2.76778	−	3.19419i	−0.141612	−	0.163429i
$383$	0.372670	+	2.59197i	0.0190425	+	0.132444i	0.997125	−	0.0757741i	$-0.0241428\pi$
$383$	0.372670	+	2.59197i	0.0190425	+	0.132444i	−0.978082	+	0.208218i	$0.933234\pi$
$384$	−12.8872	−	3.78402i	−0.657647	−	0.193103i
$385$	−4.51700	+	1.32631i	−0.230208	+	0.0675951i
$386$	−7.72226	−	4.96279i	−0.393053	−	0.252600i
$387$	0.133089	+	0.925652i	0.00676527	+	0.0470535i
$388$	9.78987	+	2.87457i	0.497005	+	0.145934i
$389$	4.94752	+	10.8336i	0.250849	+	0.549283i	0.992605	−	0.121387i	$-0.0387341\pi$
$389$	4.94752	+	10.8336i	0.250849	+	0.549283i	−0.741756	+	0.670670i	$0.766007\pi$
$390$	−10.3320	−	22.6240i	−0.523182	−	1.14561i
$391$	10.3119	+	6.62707i	0.521496	+	0.335145i
$392$	−12.2935	+	14.1874i	−0.620915	+	0.716574i
$393$	−2.44049	+	16.9740i	−0.123106	+	0.856224i
$394$	2.09816	−	4.59433i	0.105704	−	0.231459i
$395$	−3.30662	+	22.9981i	−0.166374	+	1.15716i
$396$	0.829626	−	0.533168i	0.0416903	−	0.0267927i
$397$	−0.877149	−	0.563709i	−0.0440228	−	0.0282918i	0.518444	−	0.855111i	$-0.326511\pi$
$397$	−0.877149	−	0.563709i	−0.0440228	−	0.0282918i	−0.562467	+	0.826820i	$0.690148\pi$
$398$	0.647269	+	0.190055i	0.0324447	+	0.00952661i
$399$	0.437714	+	0.505149i	0.0219131	+	0.0252891i
$400$	−0.525505	+	3.65497i	−0.0262753	+	0.182749i
$401$	22.5214			1.12467			0.562333	−	0.826911i	$-0.309904\pi$
$401$	22.5214			1.12467			0.562333	+	0.826911i	$0.309904\pi$
$402$	10.6929	+	3.47640i	0.533314	+	0.173387i
$403$	39.0795			1.94669
$404$	−0.105179	+	0.731536i	−0.00523285	+	0.0363953i
$405$	−21.3144	−	24.5981i	−1.05912	−	1.22229i
$406$	2.14064	+	0.628550i	0.106238	+	0.0311944i
$407$	−10.5262	−	6.76479i	−0.521766	−	0.335318i
$408$	11.8847	−	7.63782i	0.588380	−	0.378129i
$409$	−4.73056	+	32.9018i	−0.233911	+	1.62689i	0.447008	+	0.894530i	$0.352490\pi$
$409$	−4.73056	+	32.9018i	−0.233911	+	1.62689i	−0.680919	+	0.732359i	$0.738419\pi$
$410$	−13.5355	+	29.6386i	−0.668470	+	1.46374i
$411$	3.83420	−	26.6674i	0.189127	−	1.31541i
$412$	2.06661	−	2.38500i	0.101815	−	0.117500i
$413$	−5.05692	−	3.24989i	−0.248835	−	0.159916i
$414$	−0.362746	−	0.794303i	−0.0178280	−	0.0390379i
$415$	−10.6273	−	23.2705i	−0.521673	−	1.14230i
$416$	25.0716	+	7.36168i	1.22923	+	0.360936i
$417$	−1.98582	−	13.8117i	−0.0972463	−	0.676363i
$418$	−1.91926	−	1.23343i	−0.0938739	−	0.0603291i
$419$	−26.6651	+	7.82958i	−1.30268	+	0.382500i	−0.858211	−	0.513297i	$-0.828424\pi$
$419$	−26.6651	+	7.82958i	−1.30268	+	0.382500i	−0.444464	+	0.895797i	$0.646606\pi$
$420$	−3.46103	−	1.01625i	−0.168881	−	0.0495880i
$421$	−2.35961	−	16.4115i	−0.115001	−	0.799846i	−0.962933	−	0.269742i	$-0.913062\pi$
$421$	−2.35961	−	16.4115i	−0.115001	−	0.799846i	0.847932	−	0.530105i	$-0.177847\pi$
$422$	−11.1457	−	12.8628i	−0.542565	−	0.626154i
$423$	0.884609	−	0.568504i	0.0430112	−	0.0276416i
$424$	−12.5550	+	14.4893i	−0.609725	+	0.703660i
$425$	−22.4422	−	25.8997i	−1.08861	−	1.25632i
$426$	−4.53557	+	1.33176i	−0.219749	+	0.0645242i
$427$	−0.293395	−	0.642444i	−0.0141984	−	0.0310901i
$428$	13.1618	−	3.86464i	0.636198	−	0.186805i
$429$	17.7769	−	11.4245i	0.858279	−	0.551582i
$430$	−4.85005	+	10.6201i	−0.233890	+	0.512148i
$431$	−28.5245			−1.37398			−0.686988	−	0.726669i	$-0.741067\pi$
$431$	−28.5245			−1.37398			−0.686988	+	0.726669i	$0.741067\pi$
$432$	1.80818			0.0869960
$433$	−10.7797	+	23.6042i	−0.518039	+	1.13435i	0.452138	+	0.891948i	$0.350661\pi$
$433$	−10.7797	+	23.6042i	−0.518039	+	1.13435i	−0.970177	+	0.242398i	$0.922066\pi$
$434$	−1.95616	+	2.25753i	−0.0938986	+	0.108365i
$435$	−6.07972	−	42.2854i	−0.291500	−	2.02743i
$436$	−1.61655	−	11.2433i	−0.0774185	−	0.538458i
$437$	2.51001	−	2.89670i	0.120070	−	0.138568i
$438$	1.04715	−	2.29294i	0.0500348	−	0.109561i
$439$	−15.7702			−0.752669			−0.376334	−	0.926484i	$-0.622816\pi$
$439$	−15.7702			−0.752669			−0.376334	+	0.926484i	$0.622816\pi$
$440$	31.1130			1.48325
$441$	0.755601	−	1.65453i	0.0359810	−	0.0787874i
$442$	−9.82219	+	6.31234i	−0.467194	+	0.300247i
$443$	15.5752	−	4.57328i	0.739998	−	0.217283i	0.110056	−	0.993925i	$-0.464897\pi$
$443$	15.5752	−	4.57328i	0.739998	−	0.217283i	0.629942	+	0.776642i	$0.283079\pi$
$444$	−3.98275	−	8.72101i	−0.189013	−	0.413881i
$445$	−19.5674	+	5.74552i	−0.927586	+	0.272364i
$446$	5.59034	+	6.45160i	0.264710	+	0.305492i
$447$	2.75583	−	3.18039i	0.130346	−	0.150427i
$448$	−1.44586	+	0.929198i	−0.0683105	+	0.0439005i
$449$	4.25151	+	4.90650i	0.200641	+	0.231552i	0.847149	−	0.531355i	$-0.178317\pi$
$449$	4.25151	+	4.90650i	0.200641	+	0.231552i	−0.646508	+	0.762907i	$0.723771\pi$
$450$	0.347436	+	2.41647i	0.0163783	+	0.113913i
$451$	−26.5620	−	7.79930i	−1.25075	−	0.367255i
$452$	−10.9112	+	3.20381i	−0.513219	+	0.150695i
$453$	−3.76970	−	2.42264i	−0.177116	−	0.113825i
$454$	−1.48759	−	10.3465i	−0.0698163	−	0.485583i
$455$	7.22834	+	2.12243i	0.338870	+	0.0995012i
$456$	−1.83509	−	4.01828i	−0.0859357	−	0.188173i
$457$	7.72241	+	16.9097i	0.361239	+	0.791003i	0.999771	+	0.0214076i	$0.00681478\pi$
$457$	7.72241	+	16.9097i	0.361239	+	0.791003i	−0.638532	+	0.769595i	$0.720458\pi$
$458$	4.68833	+	3.01301i	0.219071	+	0.140789i
$459$	−10.9895	+	12.6826i	−0.512948	+	0.591974i
$460$	−2.94374	+	20.4741i	−0.137252	+	0.954611i
$461$	−2.67463	+	5.85662i	−0.124570	+	0.272770i	−0.961634	−	0.274334i	$-0.911543\pi$
$461$	−2.67463	+	5.85662i	−0.124570	+	0.272770i	0.837064	+	0.547104i	$0.184270\pi$
$462$	−0.229872	+	1.59880i	−0.0106946	+	0.0743827i
$463$	27.0475	−	17.3824i	1.25700	−	0.807828i	0.269133	−	0.963103i	$-0.413263\pi$
$463$	27.0475	−	17.3824i	1.25700	−	0.807828i	0.987871	+	0.155275i	$0.0496264\pi$
$464$	1.81781	+	1.16824i	0.0843898	+	0.0542340i
$465$	54.8817	+	16.1147i	2.54508	+	0.747302i
$466$	3.00890	+	3.47246i	0.139385	+	0.160858i
$467$	0.311545	−	2.16684i	0.0144166	−	0.100270i	−0.981343	−	0.192267i	$-0.938416\pi$
$467$	0.311545	−	2.16684i	0.0144166	−	0.100270i	0.995759	+	0.0919974i	$0.0293251\pi$
$468$	−1.57813			−0.0729492
$469$	−2.91679	+	1.75819i	−0.134685	+	0.0811858i
$470$	13.1280			0.605549
$471$	−2.89498	+	20.1351i	−0.133394	+	0.927774i
$472$	26.0160	+	30.0241i	1.19749	+	1.38197i
$473$	−9.51773	−	2.79466i	−0.437626	−	0.128498i
$474$	6.70639	+	4.30994i	0.308035	+	0.197962i
$475$	−9.01481	+	5.79347i	−0.413628	+	0.265823i
$476$	−0.240986	+	1.67610i	−0.0110456	+	0.0768237i
$477$	0.771675	−	1.68973i	0.0353326	−	0.0773675i
$478$	−1.13144	+	7.86931i	−0.0517507	+	0.359934i
$479$	24.8585	−	28.6883i	1.13581	−	1.31080i	0.191599	−	0.981473i	$-0.438633\pi$
$479$	24.8585	−	28.6883i	1.13581	−	1.31080i	0.944216	−	0.329327i	$-0.106822\pi$
$480$	32.1739	+	20.6769i	1.46853	+	0.943768i
$481$	8.31795	+	18.2138i	0.379266	+	0.830477i
$482$	−10.1489	−	22.2229i	−0.462268	−	1.01222i
$483$	−2.60374	−	0.764528i	−0.118474	−	0.0347872i
$484$	−0.561625	−	3.90618i	−0.0255284	−	0.177554i
$485$	−26.2381	−	16.8622i	−1.19141	−	0.765673i
$486$	2.20053	−	0.646133i	0.0998180	−	0.0293092i
$487$	3.40569	+	1.00000i	0.154327	+	0.0453144i	0.357983	−	0.933728i	$-0.383464\pi$
$487$	3.40569	+	1.00000i	0.154327	+	0.0453144i	−0.203657	+	0.979042i	$0.565283\pi$
$488$	0.664283	+	4.62019i	0.0300707	+	0.209146i
$489$	20.1401	+	23.2430i	0.910769	+	1.05108i
$490$	19.1034	−	12.2770i	0.863004	−	0.554619i
$491$	10.8165	−	12.4829i	0.488141	−	0.563345i	−0.457227	−	0.889350i	$-0.651157\pi$
$491$	10.8165	−	12.4829i	0.488141	−	0.563345i	0.945368	+	0.326005i	$0.105703\pi$
$492$	−13.8907	−	16.0307i	−0.626239	−	0.722719i
$493$	−19.2421	+	5.65000i	−0.866623	+	0.254463i
$494$	1.51662	+	3.32093i	0.0682360	+	0.149416i
$495$	−2.89246	+	0.849303i	−0.130006	+	0.0381733i
$496$	−2.43389	+	1.56417i	−0.109285	+	0.0702332i
$497$	0.594794	−	1.30242i	0.0266801	−	0.0584214i
$498$	−8.77744			−0.393326
$499$	17.2443			0.771963			0.385981	−	0.922507i	$-0.373863\pi$
$499$	17.2443			0.771963			0.385981	+	0.922507i	$0.373863\pi$
$500$	13.1321	−	28.7553i	0.587285	−	1.28598i
$501$	−8.07182	+	9.31537i	−0.360622	+	0.416180i
$502$	1.30088	+	9.04784i	0.0580613	+	0.403825i
$503$	4.36413	+	30.3532i	0.194587	+	1.35338i	0.819675	+	0.572829i	$0.194154\pi$
$503$	4.36413	+	30.3532i	0.194587	+	1.35338i	−0.625088	+	0.780554i	$0.714937\pi$
$504$	0.199623	−	0.230378i	0.00889193	−	0.0102618i
$505$	0.938494	−	2.05501i	0.0417624	−	0.0914470i
$506$	9.26235			0.411762
$507$	−12.3222			−0.547247
$508$	−5.97667	+	13.0871i	−0.265172	+	0.580645i
$509$	14.7914	−	9.50585i	0.655617	−	0.421339i	−0.170098	−	0.985427i	$-0.554408\pi$
$509$	14.7914	−	9.50585i	0.655617	−	0.421339i	0.825715	+	0.564088i	$0.190772\pi$
$510$	−16.3968	+	4.81455i	−0.726064	+	0.213192i
$511$	0.317178	+	0.694523i	0.0140311	+	0.0307239i
$512$	−3.62289	+	1.06378i	−0.160111	+	0.0470127i
$513$	3.43632	+	3.96572i	0.151717	+	0.175091i
$514$	2.59986	−	3.00040i	0.114675	−	0.132342i
$515$	−8.11535	+	5.21542i	−0.357605	+	0.229819i
$516$	−4.97732	−	5.74414i	−0.219114	−	0.252871i
$517$	1.58736	+	11.0403i	0.0698120	+	0.485553i
$518$	−1.46853	−	0.431199i	−0.0645234	−	0.0189458i
$519$	−29.6180	+	8.69663i	−1.30009	+	0.381740i
$520$	−41.8848	−	26.9177i	−1.83677	−	1.18042i
$521$	4.08792	+	28.4321i	0.179095	+	1.24563i	0.858862	+	0.512206i	$0.171172\pi$
$521$	4.08792	+	28.4321i	0.179095	+	1.24563i	−0.679767	+	0.733428i	$0.737919\pi$
$522$	1.37076	+	0.402491i	0.0599965	+	0.0176166i
$523$	8.66769	+	18.9796i	0.379011	+	0.829919i	0.998974	+	0.0452879i	$0.0144205\pi$
$523$	8.66769	+	18.9796i	0.379011	+	0.829919i	−0.619963	+	0.784631i	$0.712852\pi$
$524$	5.64317	+	12.3568i	0.246523	+	0.539810i
$525$	6.38244	+	4.10175i	0.278553	+	0.179015i
$526$	3.59588	−	4.14987i	0.156788	−	0.180943i
$527$	3.82133	−	26.5779i	0.166460	−	1.15775i
$528$	−0.649888	+	1.42306i	−0.0282827	+	0.0619305i
$529$	1.05866	−	7.36315i	0.0460287	−	0.320137i
$530$	19.5098	−	12.5382i	0.847451	−	0.544624i
$531$	−3.23820	−	2.08106i	−0.140526	−	0.0903104i
$532$	0.508039	+	0.149174i	0.0220263	+	0.00646750i
$533$	29.0106	+	33.4800i	1.25659	+	1.45018i
$534$	−0.995796	+	6.92591i	−0.0430923	+	0.299714i
$535$	−41.9317			−1.81287
$536$	21.7697	−	5.71820i	0.940310	−	0.246989i
$537$	−13.1518			−0.567541
$538$	1.34684	−	9.36747i	0.0580663	−	0.403860i
$539$	12.6346	+	14.5811i	0.544209	+	0.628050i
$540$	−27.1712	−	7.97818i	−1.16926	−	0.343326i
$541$	−27.3580	−	17.5819i	−1.17621	−	0.755907i	−0.201527	−	0.979483i	$-0.564591\pi$
$541$	−27.3580	−	17.5819i	−1.17621	−	0.755907i	−0.974686	+	0.223576i	$0.928227\pi$
$542$	−14.8403	+	9.53731i	−0.637447	+	0.409663i
$543$	5.80763	−	40.3930i	0.249229	−	1.73343i
$544$	7.45826	−	16.3313i	0.319770	−	0.700199i
$545$	−4.94150	+	34.3689i	−0.211670	+	1.47220i
$546$	1.69268	−	1.95345i	0.0724398	−	0.0836000i
$547$	31.9756	+	20.5495i	1.36718	+	0.878632i	0.998698	−	0.0510046i	$-0.0162423\pi$
$547$	31.9756	+	20.5495i	1.36718	+	0.878632i	0.368479	+	0.929636i	$0.379879\pi$
$548$	−8.86585	−	19.4135i	−0.378731	−	0.829304i
$549$	−0.187875	−	0.411389i	−0.00801831	−	0.0175576i
$550$	−24.8466	−	7.29562i	−1.05946	−	0.311086i
$551$	0.892432	+	6.20700i	0.0380189	+	0.264427i
$552$	15.0875	+	9.69612i	0.642165	+	0.412694i
$553$	−2.31685	+	0.680288i	−0.0985224	+	0.0289288i
$554$	−12.7987	−	3.75805i	−0.543766	−	0.159664i
$555$	4.17082	+	29.0087i	0.177041	+	1.23135i
$556$	−7.23859	−	8.35377i	−0.306984	−	0.354279i
$557$	−21.4123	+	13.7609i	−0.907270	+	0.583067i	−0.908938	−	0.416932i	$-0.863105\pi$
$557$	−21.4123	+	13.7609i	−0.907270	+	0.583067i	0.00166778	+	0.999999i	$0.499469\pi$
$558$	−1.25262	+	1.44561i	−0.0530278	+	0.0611973i
$559$	10.3951	+	11.9966i	0.439666	+	0.507402i
$560$	−0.535136	+	0.157130i	−0.0226136	+	0.00663996i
$561$	−6.03153	−	13.2072i	−0.254652	−	0.557609i
$562$	−1.08289	+	0.317965i	−0.0456789	+	0.0134125i
$563$	9.88367	−	6.35185i	0.416547	−	0.267698i	−0.315537	−	0.948913i	$-0.602184\pi$
$563$	9.88367	−	6.35185i	0.416547	−	0.267698i	0.732083	+	0.681215i	$0.238548\pi$
$564$	−3.55028	+	7.77403i	−0.149494	+	0.327346i
$565$	34.7616			1.46243
$566$	23.3992			0.983543
$567$	1.40517	−	3.07689i	0.0590115	−	0.129217i
$568$	−6.19678	+	7.15146i	−0.260011	+	0.300069i
$569$	−2.38946	−	16.6191i	−0.100172	−	0.696708i	−0.976582	−	0.215144i	$-0.930978\pi$
$569$	−2.38946	−	16.6191i	−0.100172	−	0.696708i	0.876411	−	0.481564i	$-0.159931\pi$
$570$	0.760470	+	5.28918i	0.0318526	+	0.221540i
$571$	7.54036	−	8.70204i	0.315554	−	0.364169i	−0.575709	−	0.817654i	$-0.695274\pi$
$571$	7.54036	−	8.70204i	0.315554	−	0.364169i	0.891264	+	0.453485i	$0.149819\pi$
$572$	6.95387	−	15.2268i	0.290756	−	0.636667i
$573$	−8.41076			−0.351365
$574$	−3.38620			−0.141337
$575$	18.0729	−	39.5741i	0.753691	−	1.65035i
$576$	−0.925856	+	0.595011i	−0.0385773	+	0.0247921i
$577$	13.3705	−	3.92592i	0.556619	−	0.163438i	0.00868916	−	0.999962i	$-0.497234\pi$
$577$	13.3705	−	3.92592i	0.556619	−	0.163438i	0.547930	+	0.836524i	$0.315416\pi$
$578$	−2.53480	−	5.55044i	−0.105434	−	0.230868i
$579$	−17.5272	+	5.14644i	−0.728405	+	0.213879i
$580$	−22.1614	−	25.5756i	−0.920201	−	1.06197i
$581$	1.74105	−	2.00928i	0.0722308	−	0.0833588i
$582$	−9.00244	+	5.78552i	−0.373163	+	0.239817i
$583$	12.9033	+	14.8912i	0.534401	+	0.616732i
$584$	−0.718132	−	4.99472i	−0.0297165	−	0.206683i
$585$	4.62866	+	1.35910i	0.191372	+	0.0561918i
$586$	10.2943	−	3.02267i	0.425252	−	0.124865i
$587$	10.7686	+	6.92057i	0.444468	+	0.285642i	0.743669	−	0.668548i	$-0.233084\pi$
$587$	10.7686	+	6.92057i	0.444468	+	0.285642i	−0.299201	+	0.954190i	$0.596720\pi$
$588$	2.10386	+	14.6327i	0.0867616	+	0.603440i
$589$	−8.05599	−	2.36545i	−0.331941	−	0.0974668i
$590$	−19.9633	−	43.7135i	−0.821876	−	1.79966i
$591$	−4.17534	−	9.14271i	−0.171750	−	0.376081i
$592$	−1.24706	−	0.801436i	−0.0512538	−	0.0329388i
$593$	−4.66126	+	5.37938i	−0.191415	+	0.220905i	−0.843342	−	0.537377i	$-0.819415\pi$
$593$	−4.66126	+	5.37938i	−0.191415	+	0.220905i	0.651927	+	0.758282i	$0.273961\pi$
$594$	−1.80464	+	12.5515i	−0.0740451	+	0.514995i
$595$	2.15028	−	4.70845i	0.0881528	−	0.193028i
$596$	0.474424	−	3.29969i	0.0194332	−	0.135161i
$597$	1.12933	−	0.725779i	0.0462206	−	0.0297042i
$598$	−12.4691	−	8.01343i	−0.509901	−	0.327694i
$599$	−20.0365	−	5.88324i	−0.818668	−	0.240383i	−0.154526	−	0.987989i	$-0.549385\pi$
$599$	−20.0365	−	5.88324i	−0.818668	−	0.240383i	−0.664142	+	0.747606i	$0.731203\pi$
$600$	−32.8354	−	37.8940i	−1.34050	−	1.54702i
$601$	5.24871	−	36.5056i	0.214099	−	1.48909i	−0.545174	−	0.838323i	$-0.683537\pi$
$601$	5.24871	−	36.5056i	0.214099	−	1.48909i	0.759274	−	0.650771i	$-0.225554\pi$
$602$	−1.21335			−0.0494524
$603$	−1.86776	+	1.12586i	−0.0760612	+	0.0458485i
$604$	−3.54971			−0.144436
$605$	−1.71679	+	11.9405i	−0.0697973	+	0.485451i
$606$	−0.507605	−	0.585808i	−0.0206201	−	0.0237968i
$607$	−23.4965	−	6.89919i	−0.953693	−	0.280030i	−0.232369	−	0.972628i	$-0.574648\pi$
$607$	−23.4965	−	6.89919i	−0.953693	−	0.280030i	−0.721324	+	0.692598i	$0.756466\pi$
$608$	−4.72275	−	3.03513i	−0.191533	−	0.123091i
$609$	3.73493	−	2.40029i	0.151347	−	0.0972647i
$610$	0.803546	−	5.58878i	0.0325346	−	0.226283i
$611$	7.41474	−	16.2360i	0.299968	−	0.656839i
$612$	−0.154315	+	1.07329i	−0.00623783	+	0.0433851i
$613$	6.90943	−	7.97391i	0.279069	−	0.322063i	−0.598860	−	0.800854i	$-0.704379\pi$
$613$	6.90943	−	7.97391i	0.279069	−	0.322063i	0.877929	+	0.478791i	$0.158925\pi$
$614$	15.9282	+	10.2364i	0.642808	+	0.413108i
$615$	26.9356	+	58.9807i	1.08615	+	2.37833i
$616$	1.34321	+	2.94123i	0.0541196	+	0.118505i
$617$	−25.4584	−	7.47525i	−1.02492	−	0.300942i	−0.274274	−	0.961652i	$-0.588437\pi$
$617$	−25.4584	−	7.47525i	−1.02492	−	0.300942i	−0.750642	+	0.660709i	$0.770256\pi$
$618$	0.471041	+	3.27616i	0.0189480	+	0.131786i
$619$	9.20920	+	5.91839i	0.370149	+	0.237880i	0.712470	−	0.701703i	$-0.247577\pi$
$619$	9.20920	+	5.91839i	0.370149	+	0.237880i	−0.342321	+	0.939583i	$0.611213\pi$
$620$	43.4752	−	12.7655i	1.74601	−	0.512674i
$621$	−20.4409	−	6.00200i	−0.820267	−	0.240852i
$622$	0.569820	+	3.96319i	0.0228477	+	0.158909i
$623$	−1.38791	−	1.60174i	−0.0556056	−	0.0641723i
$624$	2.10606	−	1.35348i	0.0843100	−	0.0541827i
$625$	−27.1693	+	31.3551i	−1.08677	+	1.25420i
$626$	4.80448	+	5.54466i	0.192025	+	0.221609i
$627$	−4.35613	+	1.27907i	−0.173967	+	0.0510813i
$628$	6.69410	+	14.6580i	0.267124	+	0.584919i
$629$	13.2005	−	3.87603i	0.526340	−	0.154547i
$630$	−0.310204	+	0.199356i	−0.0123588	+	0.00794252i
$631$	13.2958	−	29.1137i	0.529297	−	1.15900i	−0.436501	−	0.899704i	$-0.643782\pi$
$631$	13.2958	−	29.1137i	0.529297	−	1.15900i	0.965798	−	0.259295i	$-0.0834902\pi$
$632$	15.9584			0.634790
$633$	−33.8697			−1.34620
$634$	0.494229	−	1.08221i	0.0196283	−	0.0429801i
$635$	28.8002	−	33.2373i	1.14290	−	1.31898i
$636$	2.14861	+	14.9439i	0.0851981	+	0.592566i
$637$	−4.39389	−	30.5602i	−0.174092	−	1.21084i
$638$	−9.92360	+	11.4524i	−0.392879	+	0.453406i
$639$	0.380876	−	0.834002i	0.0150672	−	0.0329926i
$640$	32.5238			1.28562
$641$	−16.9612			−0.669928			−0.334964	−	0.942231i	$-0.608724\pi$
$641$	−16.9612			−0.669928			−0.334964	+	0.942231i	$0.608724\pi$
$642$	−5.97658	+	13.0869i	−0.235877	+	0.516498i
$643$	−19.3555	+	12.4390i	−0.763305	+	0.490546i	−0.863455	−	0.504426i	$-0.831704\pi$
$643$	−19.3555	+	12.4390i	−0.763305	+	0.490546i	0.100150	+	0.994972i	$0.468068\pi$
$644$	−2.06259	+	0.605630i	−0.0812773	+	0.0238652i
$645$	9.65160	+	21.1340i	0.380031	+	0.832152i
$646$	2.40687	−	0.706719i	0.0946969	−	0.0278055i
$647$	30.6122	+	35.3284i	1.20349	+	1.38890i	0.899898	+	0.436100i	$0.143641\pi$
$647$	30.6122	+	35.3284i	1.20349	+	1.38890i	0.303592	+	0.952802i	$0.401814\pi$
$648$	−14.6396	+	16.8949i	−0.575096	+	0.663696i
$649$	34.3482	−	22.0742i	1.34828	−	0.866490i
$650$	27.1370	+	31.3178i	1.06440	+	1.22839i
$651$	0.845975	+	5.88389i	0.0331564	+	0.230608i
$652$	23.3760	+	6.86380i	0.915473	+	0.268807i
$653$	−25.6431	+	7.52950i	−1.00349	+	0.294652i	−0.741889	−	0.670523i	$-0.766070\pi$
$653$	−25.6431	+	7.52950i	−1.00349	+	0.294652i	−0.261605	+	0.965175i	$0.584252\pi$
$654$	10.0222	+	6.44088i	0.391899	+	0.251858i
$655$	−5.90964	−	41.1025i	−0.230909	−	1.60601i
$656$	−3.14684	−	0.923996i	−0.122863	−	0.0360760i
$657$	0.203105	+	0.444738i	0.00792388	+	0.0173509i
$658$	0.566764	+	1.24104i	0.0220948	+	0.0483808i
$659$	−33.5275	−	21.5468i	−1.30605	−	0.839346i	−0.312190	−	0.950020i	$-0.601063\pi$
$659$	−33.5275	−	21.5468i	−1.30605	−	0.839346i	−0.993857	+	0.110674i	$0.964699\pi$
$660$	16.0447	−	18.5165i	0.624537	−	0.720755i
$661$	−5.95994	+	41.4523i	−0.231815	+	1.61231i	0.458429	+	0.888731i	$0.348412\pi$
$661$	−5.95994	+	41.4523i	−0.231815	+	1.61231i	−0.690244	+	0.723577i	$0.742497\pi$
$662$	−3.20903	+	7.02679i	−0.124722	+	0.273104i
$663$	−3.30662	+	22.9980i	−0.128418	+	0.893170i
$664$	−14.7816	+	9.49955i	−0.573637	+	0.368654i
$665$	−1.36161	−	0.875053i	−0.0528009	−	0.0339331i
$666$	−0.940371	−	0.276118i	−0.0364386	−	0.0106993i
$667$	−16.6721	−	19.2406i	−0.645544	−	0.744998i
$668$	−1.38959	+	9.66481i	−0.0537648	+	0.373943i
$669$	16.9880			0.656794
$670$	−27.2157	−	0.782242i	−1.05143	−	0.0302206i
$671$	4.79720			0.185194
$672$	−0.565651	+	3.93419i	−0.0218205	+	0.151765i
$673$	−29.0514	−	33.5271i	−1.11985	−	1.29238i	−0.951841	−	0.306591i	$-0.900812\pi$
$673$	−29.0514	−	33.5271i	−1.11985	−	1.29238i	−0.168009	−	0.985785i	$-0.553734\pi$
$674$	−8.86486	−	2.60296i	−0.341462	−	0.100262i
$675$	50.1060	+	32.2012i	1.92858	+	1.23942i
$676$	−8.21161	+	5.27728i	−0.315831	+	0.202972i
$677$	−0.0794992	+	0.552929i	−0.00305540	+	0.0212508i	−0.991292	−	0.131681i	$-0.957962\pi$
$677$	−0.0794992	+	0.552929i	−0.00305540	+	0.0212508i	0.988237	+	0.152932i	$0.0488716\pi$
$678$	4.95462	−	10.8491i	0.190281	−	0.416657i
$679$	0.461293	−	3.20837i	0.0177028	−	0.123126i
$680$	−22.4024	+	25.8537i	−0.859092	+	0.991445i
$681$	−17.4990	−	11.2459i	−0.670565	−	0.430946i
$682$	−8.42859	−	18.4560i	−0.322747	−	0.706718i
$683$	−2.35030	−	5.14643i	−0.0899316	−	0.196923i	0.859322	−	0.511436i	$-0.170886\pi$
$683$	−2.35030	−	5.14643i	−0.0899316	−	0.196923i	−0.949253	+	0.314513i	$0.898159\pi$
$684$	0.325322	+	0.0955233i	0.0124390	+	0.00365242i
$685$	9.28451	+	64.5752i	0.354743	+	2.46729i
$686$	4.02100	+	2.58414i	0.153523	+	0.0986629i
$687$	10.6411	−	3.12450i	0.405983	−	0.119207i
$688$	−1.12758	−	0.331087i	−0.0429886	−	0.0126226i
$689$	−4.48737	−	31.2103i	−0.170955	−	1.18902i
$690$	−14.2068	−	16.3955i	−0.540843	−	0.624166i
$691$	−32.3458	+	20.7874i	−1.23049	+	0.790789i	−0.983968	−	0.178347i	$-0.942925\pi$
$691$	−32.3458	+	20.7874i	−1.23049	+	0.790789i	−0.246524	+	0.969137i	$0.579289\pi$
$692$	−16.0132	+	18.4802i	−0.608729	+	0.702511i
$693$	−0.205162	−	0.236769i	−0.00779344	−	0.00899411i
$694$	21.8660	−	6.42043i	0.830022	−	0.243716i
$695$	14.0364	+	30.7355i	0.532433	+	1.16587i
$696$	−28.1533	+	8.26656i	−1.06715	+	0.313343i
$697$	25.6064	−	16.4563i	0.969913	−	0.623325i
$698$	−6.31005	+	13.8171i	−0.238839	+	0.522985i
$699$	9.14348			0.345838
$700$	6.00999			0.227156
$701$	7.59688	−	16.6348i	0.286930	−	0.628289i	−0.710200	−	0.704000i	$-0.751395\pi$
$701$	7.59688	−	16.6348i	0.286930	−	0.628289i	0.997130	+	0.0757111i	$0.0241227\pi$
$702$	13.2885	−	15.3358i	0.501543	−	0.578811i
$703$	−0.612228	−	4.25814i	−0.0230906	−	0.160599i
$704$	−1.66137	−	11.5551i	−0.0626154	−	0.435499i
$705$	17.1080	−	19.7437i	0.644326	−	0.743591i
$706$	−0.749683	+	1.64158i	−0.0282147	+	0.0617816i
$707$	0.234785			0.00883001
$708$	31.2847			1.17575
$709$	−11.3424	+	24.8363i	−0.425971	+	0.932746i	0.567992	+	0.823034i	$0.307720\pi$
$709$	−11.3424	+	24.8363i	−0.425971	+	0.932746i	−0.993963	+	0.109712i	$0.965007\pi$
$710$	9.62945	−	6.18847i	0.361387	−	0.232249i
$711$	−1.48359	+	0.435622i	−0.0556391	+	0.0163371i
$712$	5.81874	+	12.7413i	0.218066	+	0.477499i
$713$	32.7065	−	9.60350i	1.22487	−	0.359654i
$714$	−1.16303	−	1.34220i	−0.0435251	−	0.0502307i
$715$	−33.5092	+	38.6716i	−1.25317	+	1.44624i
$716$	−8.76446	+	5.63258i	−0.327543	+	0.210499i
$717$	10.3605	+	11.9567i	0.386921	+	0.446530i
$718$	−1.93534	−	13.4606i	−0.0722262	−	0.502344i
$719$	−25.1784	−	7.39303i	−0.938994	−	0.275714i	−0.223797	−	0.974636i	$-0.571845\pi$
$719$	−25.1784	−	7.39303i	−0.938994	−	0.275714i	−0.715198	+	0.698922i	$0.753663\pi$
$720$	−0.342674	+	0.100618i	−0.0127707	+	0.00374982i
$721$	−0.843391	−	0.542014i	−0.0314095	−	0.0201857i
$722$	2.13492	+	14.8487i	0.0794535	+	0.552612i
$723$	−46.6476	−	13.6970i	−1.73484	−	0.509396i
$724$	−13.4290	−	29.4055i	−0.499086	−	1.09285i
$725$	29.5683	+	64.7455i	1.09814	+	2.40459i
$726$	3.48194	+	2.23770i	0.129227	+	0.0830490i
$727$	−4.45727	+	5.14396i	−0.165311	+	0.190779i	−0.832361	−	0.554234i	$-0.813011\pi$
$727$	−4.45727	+	5.14396i	−0.165311	+	0.190779i	0.667050	+	0.745013i	$0.267557\pi$
$728$	0.736379	−	5.12163i	0.0272920	−	0.189820i
$729$	12.0275	−	26.3366i	0.445464	−	0.975431i
$730$	−0.868684	+	6.04183i	−0.0321514	+	0.223618i
$731$	9.17534	−	5.89663i	0.339362	−	0.218095i
$732$	3.09222	+	1.98725i	0.114292	+	0.0734507i
$733$	22.7821	+	6.68944i	0.841477	+	0.247080i	0.673940	−	0.738786i	$-0.264600\pi$
$733$	22.7821	+	6.68944i	0.841477	+	0.247080i	0.167537	+	0.985866i	$0.446419\pi$
$734$	5.11759	+	5.90601i	0.188894	+	0.217995i
$735$	6.43112	−	44.7294i	0.237215	−	1.64987i
$736$	22.7921			0.840126
$737$	−2.63292	−	22.9824i	−0.0969847	−	0.846566i
$738$	−2.16835			−0.0798182
$739$	−3.48865	+	24.2641i	−0.128332	+	0.892569i	0.819337	+	0.573313i	$0.194342\pi$
$739$	−3.48865	+	24.2641i	−0.128332	+	0.892569i	−0.947669	+	0.319256i	$0.896567\pi$
$740$	15.2032	+	17.5454i	0.558880	+	0.644982i
$741$	6.97090	+	2.04684i	0.256083	+	0.0751926i
$742$	2.02756	+	1.30304i	0.0744342	+	0.0478359i
$743$	34.3848	−	22.0978i	1.26146	−	0.810689i	0.272974	−	0.962021i	$-0.411993\pi$
$743$	34.3848	−	22.0978i	1.26146	−	0.810689i	0.988483	+	0.151332i	$0.0483562\pi$
$744$	5.59101	−	38.8863i	0.204976	−	1.42564i
$745$	−4.23320	+	9.26942i	−0.155093	+	0.339605i
$746$	−1.32138	+	9.19041i	−0.0483792	+	0.336485i
$747$	1.11488	−	1.28664i	0.0407913	−	0.0470756i
$748$	−9.67579	−	6.21825i	−0.353782	−	0.227362i
$749$	−1.81028	−	3.96397i	−0.0661463	−	0.144840i
$750$	13.7731	+	30.1589i	0.502923	+	1.10125i
$751$	35.9025	+	10.5419i	1.31010	+	0.384681i	0.860911	−	0.508755i	$-0.169894\pi$
$751$	35.9025	+	10.5419i	1.31010	+	0.384681i	0.449191	+	0.893436i	$0.351712\pi$
$752$	0.188057	+	1.30797i	0.00685774	+	0.0476966i
$753$	15.3027	+	9.83444i	0.557661	+	0.358387i
$754$	23.2675	−	6.83196i	0.847354	−	0.248805i
$755$	10.4113	+	3.05704i	0.378906	+	0.111257i
$756$	−0.418831	−	2.91303i	−0.0152327	−	0.105946i
$757$	12.0923	+	13.9553i	0.439503	+	0.507213i	0.931679	−	0.363282i	$-0.118344\pi$
$757$	12.0923	+	13.9553i	0.439503	+	0.507213i	−0.492176	+	0.870495i	$0.663799\pi$
$758$	−1.44464	+	0.928416i	−0.0524718	+	0.0337216i
$759$	12.0704	−	13.9300i	0.438129	−	0.505628i
$760$	7.00499	+	8.08419i	0.254098	+	0.293244i
$761$	31.3321	−	9.19994i	1.13579	−	0.333498i	0.340808	−	0.940133i	$-0.389299\pi$
$761$	31.3321	−	9.19994i	1.13579	−	0.333498i	0.794980	+	0.606635i	$0.207481\pi$
$762$	−6.26841	−	13.7259i	−0.227080	−	0.497237i
$763$	−3.46236	+	1.01664i	−0.125346	+	0.0368048i
$764$	−5.60501	+	3.60212i	−0.202782	+	0.130320i
$765$	1.37693	−	3.01505i	0.0497830	−	0.109009i
$766$	−2.17564			−0.0786089
$767$	−65.3379			−2.35922
$768$	10.3099	−	22.5755i	0.372025	−	0.814622i
$769$	3.37544	−	3.89546i	0.121721	−	0.140474i	−0.691618	−	0.722264i	$-0.743102\pi$
$769$	3.37544	−	3.89546i	0.121721	−	0.140474i	0.813339	+	0.581789i	$0.197647\pi$
$770$	−0.556635	−	3.87148i	−0.0200597	−	0.139519i
$771$	−1.12436	−	7.82007i	−0.0404927	−	0.281633i
$772$	−9.47618	+	10.9361i	−0.341055	+	0.393599i
$773$	−17.8139	+	39.0071i	−0.640722	+	1.40299i	0.258722	+	0.965952i	$0.416698\pi$
$773$	−17.8139	+	39.0071i	−0.640722	+	1.40299i	−0.899445	+	0.437034i	$0.856029\pi$
$774$	−0.776968			−0.0279275
$775$	−95.3007			−3.42330
$776$	−8.89902	+	19.4861i	−0.319456	+	0.699511i
$777$	−2.56224	+	1.64665i	−0.0919199	+	0.0590733i
$778$	−9.49422	+	2.78775i	−0.340384	+	0.0999459i
$779$	−3.95383	−	8.65768i	−0.141661	−	0.310194i
$780$	−37.6194	+	11.0460i	−1.34699	+	0.395512i
$781$	6.36870	+	7.34987i	0.227890	+	0.262999i
$782$	−6.66920	+	7.69667i	−0.238490	+	0.275232i
$783$	29.3214	−	18.8437i	1.04786	−	0.673420i
$784$	1.49684	+	1.72744i	0.0534584	+	0.0616943i
$785$	−7.01020	−	48.7570i	−0.250205	−	1.74021i
$786$	−13.6704	−	4.01399i	−0.487606	−	0.143174i
$787$	51.4794	−	15.1157i	1.83504	−	0.538817i	0.835106	−	0.550089i	$-0.185406\pi$
$787$	51.4794	−	15.1157i	1.83504	−	0.538817i	0.999936	+	0.0112714i	$0.00358789\pi$
$788$	−6.69808	−	4.30459i	−0.238609	−	0.153345i
$789$	−1.55510	−	10.8160i	−0.0553632	−	0.385059i
$790$	−18.5220	−	5.43855i	−0.658984	−	0.193495i
$791$	1.50073	+	3.28615i	0.0533600	+	0.116842i
$792$	0.860126	+	1.88341i	0.0305632	+	0.0669242i
$793$	−6.45807	−	4.15035i	−0.229333	−	0.147383i
$794$	0.567293	−	0.654691i	0.0201325	−	0.0232341i
$795$	6.56793	−	45.6810i	0.232941	−	1.62014i
$796$	0.441766	−	0.967332i	0.0156580	−	0.0342862i
$797$	2.75272	−	19.1456i	0.0975064	−	0.678172i	−0.881175	−	0.472789i	$-0.843247\pi$
$797$	2.75272	−	19.1456i	0.0975064	−	0.678172i	0.978682	−	0.205382i	$-0.0658438\pi$
$798$	−0.467176	+	0.300236i	−0.0165378	+	0.0106282i
$799$	−10.3171	−	6.63037i	−0.364991	−	0.234566i
$800$	−61.1405	−	17.9525i	−2.16164	−	0.634716i
$801$	−0.888750	−	1.02567i	−0.0314024	−	0.0362404i
$802$	−2.66292	+	18.5210i	−0.0940310	+	0.654000i
$803$	−5.18608			−0.183013
$804$	7.82333	−	15.9048i	0.275908	−	0.560920i
$805$	6.57114			0.231602
$806$	−4.62074	+	32.1379i	−0.162758	+	1.13201i
$807$	−12.3330	−	14.2330i	−0.434141	−	0.501025i
$808$	−1.48883	−	0.437160i	−0.0523769	−	0.0153792i
$809$	−34.2017	−	21.9801i	−1.20247	−	0.772778i	−0.223085	−	0.974799i	$-0.571613\pi$
$809$	−34.2017	−	21.9801i	−1.20247	−	0.772778i	−0.979381	+	0.202021i	$0.935249\pi$
$810$	22.7491	−	14.6199i	0.799321	−	0.513692i
$811$	3.08116	−	21.4299i	0.108194	−	0.752506i	−0.861425	−	0.507885i	$-0.830427\pi$
$811$	3.08116	−	21.4299i	0.108194	−	0.752506i	0.969619	−	0.244621i	$-0.0786635\pi$
$812$	1.46100	−	3.19915i	0.0512712	−	0.112268i
$813$	−4.99597	+	34.7477i	−0.175216	+	1.21866i
$814$	6.80780	−	7.85662i	0.238613	−	0.275374i
$815$	−62.6505	−	40.2631i	−2.19455	−	1.41035i
$816$	−0.714565	−	1.56468i	−0.0250148	−	0.0547748i
$817$	−1.41674	−	3.10223i	−0.0495655	−	0.108533i
$818$	−26.4982	−	7.78058i	−0.926489	−	0.272042i
$819$	0.0713486	+	0.496241i	0.00249312	+	0.0173401i
$820$	43.2101	+	27.7694i	1.50896	+	0.969751i
$821$	−41.3075	+	12.1290i	−1.44164	+	0.423305i	−0.906769	−	0.421628i	$-0.861459\pi$
$821$	−41.3075	+	12.1290i	−1.44164	+	0.423305i	−0.534874	+	0.844932i	$0.679641\pi$
$822$	21.4772	+	6.30628i	0.749105	+	0.219957i
$823$	−1.79621	−	12.4929i	−0.0626120	−	0.435476i	−0.996882	−	0.0789091i	$-0.974856\pi$
$823$	−1.79621	−	12.4929i	−0.0626120	−	0.435476i	0.934270	−	0.356567i	$-0.116053\pi$
$824$	4.33894	+	5.00740i	0.151154	+	0.174441i
$825$	−43.3515	+	27.8603i	−1.50931	+	0.969973i
$826$	3.27055	−	3.77441i	0.113797	−	0.131329i
$827$	28.0819	+	32.4083i	0.976505	+	1.12695i	0.991894	+	0.127065i	$0.0405558\pi$
$827$	28.0819	+	32.4083i	0.976505	+	1.12695i	−0.0153894	+	0.999882i	$0.504899\pi$
$828$	−1.32078	+	0.387815i	−0.0459001	+	0.0134775i
$829$	−4.30488	−	9.42636i	−0.149515	−	0.327391i	0.820024	−	0.572329i	$-0.193960\pi$
$829$	−4.30488	−	9.42636i	−0.149515	−	0.327391i	−0.969539	+	0.244938i	$0.921233\pi$
$830$	20.3936	−	5.98810i	0.707872	−	0.207850i
$831$	−22.3308	+	14.3511i	−0.774648	+	0.497836i
$832$	−7.76046	+	16.9930i	−0.269046	+	0.589128i
$833$	−21.2136			−0.735008
$834$	11.5932			0.401439
$835$	12.3991	−	27.1502i	0.429087	−	0.939570i
$836$	−2.35517	+	2.71801i	−0.0814552	+	0.0940043i
$837$	6.64141	+	46.1921i	0.229561	+	1.59663i
$838$	−3.28597	−	22.8544i	−0.113512	−	0.789493i
$839$	−3.07759	+	3.55173i	−0.106250	+	0.122619i	−0.806384	−	0.591393i	$-0.798578\pi$
$839$	−3.07759	+	3.55173i	−0.106250	+	0.122619i	0.700134	+	0.714012i	$0.253124\pi$
$840$	3.14609	−	6.88897i	0.108550	−	0.237692i
$841$	12.6523			0.436286
$842$	13.7754			0.474730
$843$	−0.932990	+	2.04296i	−0.0321339	+	0.0703634i
$844$	−22.5711	+	14.5056i	−0.776930	+	0.499302i
$845$	28.6295	−	8.40637i	0.984884	−	0.289188i
$846$	0.362927	+	0.794699i	0.0124777	+	0.0273223i
$847$	−1.20290	+	0.353203i	−0.0413321	+	0.0121362i
$848$	1.52868	+	1.76419i	0.0524950	+	0.0605825i
$849$	30.4932	−	35.1911i	1.04652	−	1.20775i
$850$	23.9528	−	15.3935i	0.821573	−	0.527993i
$851$	11.4374	+	13.1995i	0.392069	+	0.452471i
$852$	1.06049	+	7.37588i	0.0363319	+	0.252694i
$853$	−3.10090	−	0.910507i	−0.106173	−	0.0311752i	0.228215	−	0.973611i	$-0.426711\pi$
$853$	−3.10090	−	0.910507i	−0.106173	−	0.0311752i	−0.334387	+	0.942436i	$0.608529\pi$
$854$	0.563020	−	0.165318i	0.0192661	−	0.00565705i
$855$	−0.871905	−	0.560340i	−0.0298185	−	0.0191632i
$856$	4.09871	+	28.5072i	0.140091	+	0.974355i
$857$	−14.5038	−	4.25871i	−0.495441	−	0.145475i	0.0244603	−	0.999701i	$-0.492213\pi$
$857$	−14.5038	−	4.25871i	−0.495441	−	0.145475i	−0.519902	+	0.854226i	$0.674031\pi$
$858$	7.29331	+	15.9701i	0.248989	+	0.545211i
$859$	14.0962	+	30.8663i	0.480955	+	1.05314i	0.982200	+	0.187838i	$0.0601482\pi$
$859$	14.0962	+	30.8663i	0.480955	+	1.05314i	−0.501245	+	0.865305i	$0.667125\pi$
$860$	15.4831	+	9.95039i	0.527969	+	0.339305i
$861$	−4.41281	+	5.09265i	−0.150388	+	0.173557i
$862$	3.37272	−	23.4578i	0.114875	−	0.798975i
$863$	−5.58532	+	12.2302i	−0.190127	+	0.416319i	−0.980557	−	0.196232i	$-0.937129\pi$
$863$	−5.58532	+	12.2302i	−0.190127	+	0.416319i	0.790431	+	0.612551i	$0.209857\pi$
$864$	−4.44070	+	30.8858i	−0.151076	+	1.05075i
$865$	62.8818	−	40.4117i	2.13805	−	1.37404i
$866$	−18.1369	−	11.6559i	−0.616317	−	0.396083i
$867$	−11.6508	−	3.42099i	−0.395682	−	0.116183i
$868$	3.08369	+	3.55877i	0.104667	+	0.120792i
$869$	2.33412	−	16.2342i	0.0791797	−	0.550707i
$870$	35.4932			1.20333
$871$	−16.3390	+	33.2171i	−0.553625	+	1.12552i
$872$	23.8486			0.807615
$873$	0.295389	−	2.05447i	0.00999740	−	0.0695334i
$874$	2.08539	+	2.40667i	0.0705394	+	0.0814068i
$875$	−9.63575	−	2.82931i	−0.325748	−	0.0956482i
$876$	−3.34288	−	2.14834i	−0.112946	−	0.0725857i
$877$	38.5636	−	24.7833i	1.30220	−	0.836874i	0.308751	−	0.951143i	$-0.400089\pi$
$877$	38.5636	−	24.7833i	1.30220	−	0.836874i	0.993450	+	0.114269i	$0.0364526\pi$
$878$	1.86466	−	12.9690i	0.0629291	−	0.437681i
$879$	8.86928	−	19.4210i	0.299153	−	0.655055i
$880$	0.539126	−	3.74971i	0.0181739	−	0.126403i
$881$	3.44308	−	3.97353i	0.116000	−	0.133872i	−0.694779	−	0.719223i	$-0.744498\pi$
$881$	3.44308	−	3.97353i	0.116000	−	0.133872i	0.810780	+	0.585351i	$0.199043\pi$
$882$	1.27130	+	0.817017i	0.0428070	+	0.0275104i
$883$	−7.74978	−	16.9697i	−0.260801	−	0.571075i	0.733254	−	0.679955i	$-0.238001\pi$
$883$	−7.74978	−	16.9697i	−0.260801	−	0.571075i	−0.994055	+	0.108880i	$0.965273\pi$
$884$	7.64593	+	16.7423i	0.257160	+	0.563103i
$885$	−91.7581	−	26.9426i	−3.08441	−	0.905666i
$886$	1.91934	+	13.3493i	0.0644816	+	0.448480i
$887$	28.8292	+	18.5274i	0.967989	+	0.622089i	0.926198	−	0.377038i	$-0.123057\pi$
$887$	28.8292	+	18.5274i	0.967989	+	0.622089i	0.0417909	+	0.999126i	$0.486694\pi$
$888$	19.3138	−	5.67104i	0.648129	−	0.190308i
$889$	4.38541	+	1.28767i	0.147082	+	0.0431872i
$890$	−2.41132	−	16.7711i	−0.0808276	−	0.562168i
$891$	15.0457	+	17.3637i	0.504050	+	0.581705i
$892$	11.3210	−	7.27554i	0.379054	−	0.243603i
$893$	−2.51126	+	2.89815i	−0.0840361	+	0.0969828i
$894$	2.28962	+	2.64237i	0.0765764	+	0.0883739i
$895$	30.5570	−	8.97234i	1.02141	−	0.299912i
$896$	1.40412	+	3.07460i	0.0469084	+	0.102715i
$897$	−28.3012	+	8.30997i	−0.944948	+	0.277462i
$898$	−4.53767	+	2.91618i	−0.151424	+	0.0973143i
$899$	−23.1672	+	50.7291i	−0.772669	+	1.69191i
$900$	3.84850			0.128283
$901$	−21.6649			−0.721763
$902$	9.55461	−	20.9217i	0.318134	−	0.696616i
$903$	−1.58120	+	1.82481i	−0.0526191	+	0.0607257i
$904$	−3.39785	−	23.6326i	−0.113011	−	0.786008i
$905$	14.0632	+	97.8115i	0.467476	+	3.25136i
$906$	2.43804	−	2.81365i	0.0809984	−	0.0934771i
$907$	−5.37899	+	11.7784i	−0.178607	+	0.391094i	−0.977668	−	0.210156i	$-0.932603\pi$
$907$	−5.37899	+	11.7784i	−0.178607	+	0.391094i	0.799061	+	0.601249i	$0.205330\pi$
$908$	−16.4779			−0.546838
$909$	0.150345			0.00498662
$910$	−2.60011	+	5.69344i	−0.0861927	+	0.188736i
$911$	−18.2276	+	11.7141i	−0.603906	+	0.388107i	−0.806567	−	0.591142i	$-0.798677\pi$
$911$	−18.2276	+	11.7141i	−0.603906	+	0.388107i	0.202662	+	0.979249i	$0.435041\pi$
$912$	−0.516077	+	0.151534i	−0.0170890	+	0.00501779i
$913$	7.50173	+	16.4265i	0.248271	+	0.543638i
$914$	−14.8192	+	4.35131i	−0.490175	+	0.143928i
$915$	−7.35804	−	8.49163i	−0.243249	−	0.280725i
$916$	5.75317	−	6.63951i	0.190090	−	0.219376i
$917$	3.63044	−	2.33314i	0.119888	−	0.0770472i
$918$	−9.13045	−	10.5371i	−0.301350	−	0.347776i
$919$	−0.226211	−	1.57333i	−0.00746200	−	0.0518994i	0.985750	−	0.168216i	$-0.0538005\pi$
$919$	−0.226211	−	1.57333i	−0.00746200	−	0.0518994i	−0.993212	+	0.116316i	$0.962891\pi$
$920$	−41.6692	−	12.2352i	−1.37379	−	0.403382i
$921$	36.1521	−	10.6152i	1.19125	−	0.349783i
$922$	−4.50009	−	2.89203i	−0.148202	−	0.0952439i
$923$	−2.21483	−	15.4045i	−0.0729020	−	0.507045i
$924$	2.44312	+	0.717365i	0.0803728	+	0.0235996i
$925$	−20.2845	−	44.4168i	−0.666950	−	1.46042i
$926$	11.0967	+	24.2984i	0.364661	+	0.798496i
$927$	−0.540065	−	0.347078i	−0.0177381	−	0.0113996i
$928$	−24.4192	+	28.1812i	−0.801599	+	0.925095i
$929$	8.32583	−	57.9074i	0.273162	−	1.89988i	−0.141556	−	0.989930i	$-0.545211\pi$
$929$	8.32583	−	57.9074i	0.273162	−	1.89988i	0.414718	−	0.909950i	$-0.363880\pi$
$930$	−19.7415	+	43.2279i	−0.647349	+	1.41750i
$931$	−0.944013	+	6.56576i	−0.0309388	+	0.215184i
$932$	6.09330	−	3.91592i	0.199593	−	0.128270i
$933$	6.70297	+	4.30774i	0.219445	+	0.141029i
$934$	1.74512	+	0.512413i	0.0571020	+	0.0167667i
$935$	23.0239	+	26.5710i	0.752962	+	0.868964i
$936$	0.471540	−	3.27963i	0.0154128	−	0.107198i
$937$	7.83566			0.255980			0.127990	−	0.991775i	$-0.459147\pi$
$937$	7.83566			0.255980			0.127990	+	0.991775i	$0.459147\pi$
$938$	−1.10101	−	2.60658i	−0.0359493	−	0.0851077i
$939$	14.5999			0.476450
$940$	2.94520	−	20.4843i	0.0960619	−	0.668125i
$941$	21.0064	+	24.2427i	0.684789	+	0.790289i	0.986614	−	0.163074i	$-0.0521411\pi$
$941$	21.0064	+	24.2427i	0.684789	+	0.790289i	−0.301824	+	0.953364i	$0.597596\pi$
$942$	−16.2162	−	4.76152i	−0.528353	−	0.155139i
$943$	32.5071	+	20.8910i	1.05858	+	0.680305i
$944$	4.06929	−	2.61517i	0.132444	−	0.0851166i
$945$	−1.28029	+	8.90462i	−0.0416479	+	0.289667i
$946$	3.42362	−	7.49669i	0.111312	−	0.243738i
$947$	3.70429	−	25.7639i	0.120373	−	0.837215i	−0.836761	−	0.547569i	$-0.815553\pi$
$947$	3.70429	−	25.7639i	0.120373	−	0.837215i	0.957134	−	0.289646i	$-0.0935375\pi$
$948$	8.22958	−	9.49745i	0.267284	−	0.308463i
$949$	6.98159	+	4.48679i	0.226632	+	0.145647i
$950$	−3.69849	−	8.09856i	−0.119995	−	0.262752i
$951$	−0.983515	−	2.15360i	−0.0318927	−	0.0698352i
$952$	−3.41121	−	1.00162i	−0.110558	−	0.0324627i
$953$	−3.13695	−	21.8179i	−0.101616	−	0.706752i	−0.975401	−	0.220440i	$-0.929251\pi$
$953$	−3.13695	−	21.8179i	−0.101616	−	0.706752i	0.873785	−	0.486313i	$-0.161658\pi$
$954$	1.29835	+	0.834398i	0.0420356	+	0.0270146i
$955$	19.5417	−	5.73795i	0.632353	−	0.185676i
$956$	12.0251	+	3.53089i	0.388919	+	0.114197i
$957$	4.29164	+	29.8490i	0.138729	+	0.964881i
$958$	20.6532	+	23.8351i	0.667275	+	0.770076i
$959$	−5.70371	+	3.66555i	−0.184182	+	0.118367i
$960$	−17.9057	+	20.6643i	−0.577904	+	0.666937i
$961$	−28.5975	−	33.0033i	−0.922500	−	1.06462i
$962$	−15.9620	+	4.68688i	−0.514637	+	0.151111i
$963$	−1.15921	−	2.53832i	−0.0373551	−	0.0817963i
$964$	−36.9525	+	10.8502i	−1.19016	+	0.349462i
$965$	37.2119	−	23.9146i	1.19789	−	0.769839i
$966$	0.936592	−	2.05085i	0.0301344	−	0.0659851i
$967$	−54.2875			−1.74577			−0.872885	−	0.487926i	$-0.837753\pi$
$967$	−54.2875			−1.74577			−0.872885	+	0.487926i	$0.837753\pi$
$968$	8.28554			0.266307
$969$	2.07369	−	4.54076i	0.0666167	−	0.145870i
$970$	16.9694	−	19.5837i	0.544855	−	0.628796i
$971$	5.78273	+	40.2198i	0.185577	+	1.29071i	0.843296	+	0.537450i	$0.180612\pi$
$971$	5.78273	+	40.2198i	0.185577	+	1.29071i	−0.657719	+	0.753263i	$0.728479\pi$
$972$	−0.514520	−	3.57856i	−0.0165032	−	0.114783i
$973$	−2.29956	+	2.65384i	−0.0737207	+	0.0850782i
$974$	−1.22506	+	2.68251i	−0.0392535	+	0.0859532i
$975$	82.4643			2.64097
$976$	0.568331			0.0181918
$977$	−16.1647	+	35.3958i	−0.517156	+	1.13241i	0.453349	+	0.891333i	$0.350229\pi$
$977$	−16.1647	+	35.3958i	−0.517156	+	1.13241i	−0.970505	+	0.241080i	$0.922498\pi$
$978$	−21.4958	+	13.8145i	−0.687359	+	0.441738i
$979$	13.8125	−	4.05573i	0.441450	−	0.129622i
$980$	−14.8707	−	32.5624i	−0.475029	−	1.04017i
$981$	−2.21712	+	0.651004i	−0.0707871	+	0.0207850i
$982$	8.98665	+	10.3712i	0.286776	+	0.330957i
$983$	−19.7983	+	22.8485i	−0.631468	+	0.728753i	−0.977842	−	0.209343i	$-0.932867\pi$
$983$	−19.7983	+	22.8485i	−0.631468	+	0.728753i	0.346374	+	0.938096i	$0.387413\pi$
$984$	37.4650	−	24.0773i	1.19434	−	0.767556i
$985$	15.9383	+	18.3938i	0.507837	+	0.586075i
$986$	−2.37123	−	16.4923i	−0.0755154	−	0.525221i
$987$	2.60504	+	0.764909i	0.0829193	+	0.0243473i
$988$	5.52209	−	1.62143i	0.175681	−	0.0515846i
$989$	11.6480	+	7.48570i	0.370384	+	0.238031i
$990$	−0.356441	−	2.47910i	−0.0113284	−	0.0787910i
$991$	5.68843	+	1.67027i	0.180699	+	0.0530580i	0.370830	−	0.928701i	$-0.379073\pi$
$991$	5.68843	+	1.67027i	0.180699	+	0.0530580i	−0.190131	+	0.981759i	$0.560891\pi$
$992$	−20.7404	−	45.4151i	−0.658508	−	1.44193i
$993$	6.38596	+	13.9833i	0.202652	+	0.443747i
$994$	1.00074	+	0.643139i	0.0317417	+	0.0203991i
$995$	−2.12877	+	2.45673i	−0.0674866	+	0.0778837i
$996$	−1.96918	+	13.6959i	−0.0623958	+	0.433972i
$997$	12.1709	−	26.6504i	0.385455	−	0.844028i	−0.613086	−	0.790017i	$-0.710072\pi$
$997$	12.1709	−	26.6504i	0.385455	−	0.844028i	0.998540	−	0.0540116i	$-0.0172008\pi$
$998$	−2.03896	+	14.1813i	−0.0645422	+	0.448901i
$999$	−20.1151	+	12.9272i	−0.636415	+	0.408999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	67.2.e.c.59.2	yes	20
3.2	odd	2		603.2.u.c.595.2		20
67.5	odd	22		4489.2.a.m.1.4		10
67.25	even	11	inner	67.2.e.c.25.2	✓	20
67.62	even	11		4489.2.a.l.1.7		10
201.92	odd	22		603.2.u.c.226.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.e.c.25.2	✓	20	67.25	even	11	inner
67.2.e.c.59.2	yes	20	1.1	even	1	trivial
603.2.u.c.226.2		20	201.92	odd	22
603.2.u.c.595.2		20	3.2	odd	2
4489.2.a.l.1.7		10	67.62	even	11
4489.2.a.m.1.4		10	67.5	odd	22

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:	\( N \)	\(=\)	\( 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	67.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.118239 + 0.822373i) q^{2} +(1.08271 + 1.24952i) q^{3} +(1.25667 + 0.368991i) q^{4} +(-3.36803 - 2.16450i) q^{5} +(-1.15559 + 0.742653i) q^{6} +(0.0592135 - 0.411839i) q^{7} +(-1.14231 + 2.50132i) q^{8} +(0.0379173 - 0.263721i) q^{9} +O(q^{10})\)	\(q+(-0.118239 + 0.822373i) q^{2} +(1.08271 + 1.24952i) q^{3} +(1.25667 + 0.368991i) q^{4} +(-3.36803 - 2.16450i) q^{5} +(-1.15559 + 0.742653i) q^{6} +(0.0592135 - 0.411839i) q^{7} +(-1.14231 + 2.50132i) q^{8} +(0.0379173 - 0.263721i) q^{9} +(2.17826 - 2.51385i) q^{10} +(2.37747 + 1.52791i) q^{11} +(0.899551 + 1.96974i) q^{12} +(-1.87871 - 4.11379i) q^{13} +(0.331684 + 0.0973913i) q^{14} +(-0.942029 - 6.55195i) q^{15} +(0.281663 + 0.181014i) q^{16} +(-2.98149 + 0.875446i) q^{17} +(0.212394 + 0.0623644i) q^{18} +(0.138279 + 0.961750i) q^{19} +(-3.43382 - 3.96284i) q^{20} +(0.578712 - 0.371916i) q^{21} +(-1.53762 + 1.77451i) q^{22} +(-2.58327 - 2.98125i) q^{23} +(-4.36225 + 1.28087i) q^{24} +(4.58149 + 10.0321i) q^{25} +(3.60521 - 1.05859i) q^{26} +(4.54324 - 2.91976i) q^{27} +(0.226377 - 0.495696i) q^{28} +6.45386 q^{29} +5.49954 q^{30} +(-3.58967 + 7.86027i) q^{31} +(-3.78366 + 4.36657i) q^{32} +(0.664972 + 4.62498i) q^{33} +(-0.367413 - 2.55541i) q^{34} +(-1.09086 + 1.25892i) q^{35} +(0.144960 - 0.317419i) q^{36} -4.42749 q^{37} -0.807268 q^{38} +(3.10616 - 6.80154i) q^{39} +(9.26147 - 5.95198i) q^{40} +(-9.39879 + 2.75973i) q^{41} +(0.237427 + 0.519893i) q^{42} +(-3.36779 + 0.988872i) q^{43} +(2.42391 + 2.79734i) q^{44} +(-0.698531 + 0.806148i) q^{45} +(2.75715 - 1.77191i) q^{46} +(2.58456 + 2.98274i) q^{47} +(0.0787803 + 0.547929i) q^{48} +(6.55035 + 1.92335i) q^{49} +(-8.79181 + 2.58151i) q^{50} +(-4.32199 - 2.77758i) q^{51} +(-0.842958 - 5.86290i) q^{52} +(6.68969 + 1.96427i) q^{53} +(1.86394 + 4.08147i) q^{54} +(-4.70024 - 10.2921i) q^{55} +(0.962501 + 0.618562i) q^{56} +(-1.05201 + 1.21408i) q^{57} +(-0.763101 + 5.30748i) q^{58} +(6.00165 - 13.1418i) q^{59} +(1.23380 - 8.58124i) q^{60} +(1.42799 - 0.917715i) q^{61} +(-6.03964 - 3.88144i) q^{62} +(-0.106365 - 0.0312317i) q^{63} +(-2.70506 - 3.12181i) q^{64} +(-2.57677 + 17.9219i) q^{65} -3.88209 q^{66} +(-5.18032 - 6.33753i) q^{67} -4.06978 q^{68} +(0.928187 - 6.45569i) q^{69} +(-0.906319 - 1.04595i) q^{70} +(3.30183 + 0.969506i) q^{71} +(0.616337 + 0.396096i) q^{72} +(-1.54375 + 0.992109i) q^{73} +(0.523504 - 3.64105i) q^{74} +(-7.57480 + 16.5865i) q^{75} +(-0.181107 + 1.25963i) q^{76} +(0.770031 - 0.888663i) q^{77} +(5.22614 + 3.35863i) q^{78} +(-2.41083 - 5.27899i) q^{79} +(-0.556845 - 1.21932i) q^{80} +(7.80040 + 2.29041i) q^{81} +(-1.15822 - 8.05562i) q^{82} +(5.37548 + 3.45461i) q^{83} +(0.864483 - 0.253835i) q^{84} +(11.9367 + 3.50492i) q^{85} +(-0.415016 - 2.88650i) q^{86} +(6.98768 + 8.06422i) q^{87} +(-6.53761 + 4.20147i) q^{88} +(3.33574 - 3.84965i) q^{89} +(-0.580361 - 0.669772i) q^{90} +(-1.80547 + 0.530133i) q^{91} +(-2.14626 - 4.69965i) q^{92} +(-13.7081 + 4.02507i) q^{93} +(-2.75852 + 1.77279i) q^{94} +(1.61598 - 3.53851i) q^{95} -9.55274 q^{96} +7.79034 q^{97} +(-2.35623 + 5.15941i) q^{98} +(0.493089 - 0.569055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9} - 9 q^{10} + 3 q^{12} + 12 q^{13} + 6 q^{14} - 11 q^{15} + 8 q^{16} - 4 q^{17} - 2 q^{18} + 4 q^{19} + 2 q^{20} - 53 q^{21} + 2 q^{23} + 11 q^{24} - 3 q^{25} - 31 q^{26} + 47 q^{27} - 5 q^{28} - 6 q^{29} + 44 q^{30} + 16 q^{32} + q^{33} - 8 q^{34} + 34 q^{35} + 9 q^{36} + 24 q^{37} - 14 q^{38} - 22 q^{39} - 11 q^{40} - 6 q^{41} + 59 q^{42} - 22 q^{43} - 22 q^{44} - 46 q^{45} + 15 q^{46} + 16 q^{47} + 5 q^{48} + 42 q^{49} - 17 q^{50} + 22 q^{51} + 2 q^{52} - q^{53} - 60 q^{54} + 20 q^{55} + 11 q^{56} - 52 q^{57} + 10 q^{58} - 26 q^{59} + 44 q^{60} - 26 q^{61} + 11 q^{62} - 42 q^{63} - 6 q^{64} + 9 q^{65} + 2 q^{66} - 22 q^{67} - 52 q^{68} + 62 q^{69} - 42 q^{70} + 20 q^{71} + 11 q^{72} - 55 q^{73} + 37 q^{74} - 70 q^{75} - 3 q^{76} - 70 q^{77} + 22 q^{78} - 34 q^{79} + 40 q^{80} + 42 q^{81} - 12 q^{82} + 56 q^{83} - 29 q^{84} + 41 q^{85} - 33 q^{86} - 10 q^{87} + 11 q^{88} - 3 q^{89} + 18 q^{90} + 12 q^{91} - 18 q^{92} - 69 q^{93} + 32 q^{94} + 74 q^{95} - 12 q^{96} - 14 q^{97} + 95 q^{98} + 81 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9 - 9 * q^10 + 3 * q^12 + 12 * q^13 + 6 * q^14 - 11 * q^15 + 8 * q^16 - 4 * q^17 - 2 * q^18 + 4 * q^19 + 2 * q^20 - 53 * q^21 + 2 * q^23 + 11 * q^24 - 3 * q^25 - 31 * q^26 + 47 * q^27 - 5 * q^28 - 6 * q^29 + 44 * q^30 + 16 * q^32 + q^33 - 8 * q^34 + 34 * q^35 + 9 * q^36 + 24 * q^37 - 14 * q^38 - 22 * q^39 - 11 * q^40 - 6 * q^41 + 59 * q^42 - 22 * q^43 - 22 * q^44 - 46 * q^45 + 15 * q^46 + 16 * q^47 + 5 * q^48 + 42 * q^49 - 17 * q^50 + 22 * q^51 + 2 * q^52 - q^53 - 60 * q^54 + 20 * q^55 + 11 * q^56 - 52 * q^57 + 10 * q^58 - 26 * q^59 + 44 * q^60 - 26 * q^61 + 11 * q^62 - 42 * q^63 - 6 * q^64 + 9 * q^65 + 2 * q^66 - 22 * q^67 - 52 * q^68 + 62 * q^69 - 42 * q^70 + 20 * q^71 + 11 * q^72 - 55 * q^73 + 37 * q^74 - 70 * q^75 - 3 * q^76 - 70 * q^77 + 22 * q^78 - 34 * q^79 + 40 * q^80 + 42 * q^81 - 12 * q^82 + 56 * q^83 - 29 * q^84 + 41 * q^85 - 33 * q^86 - 10 * q^87 + 11 * q^88 - 3 * q^89 + 18 * q^90 + 12 * q^91 - 18 * q^92 - 69 * q^93 + 32 * q^94 + 74 * q^95 - 12 * q^96 - 14 * q^97 + 95 * q^98 + 81 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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