LMFDB - Embedded newform 525.2.t.g.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(26,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("525.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.t (of order $6$, degree $2$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.4
Root			$-2.33086i$ of defining polynomial
Character	$\chi$	$=$	525.101
Dual form			525.2.t.g.26.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.01859 - 1.16543i) q^{2} +(1.21646 + 1.23297i) q^{3} +(1.71646 - 2.97300i) q^{4} +(3.89248 + 1.07116i) q^{6} +(-1.11699 - 2.39840i) q^{7} -3.33995i q^{8} +(-0.0404447 + 2.99973i) q^{9} +O(q^{10})$	\(q+(2.01859 - 1.16543i) q^{2} +(1.21646 + 1.23297i) q^{3} +(1.71646 - 2.97300i) q^{4} +(3.89248 + 1.07116i) q^{6} +(-1.11699 - 2.39840i) q^{7} -3.33995i q^{8} +(-0.0404447 + 2.99973i) q^{9} +(2.42019 + 1.39730i) q^{11} +(5.75363 - 1.50019i) q^{12} -3.20486i q^{13} +(-5.04991 - 3.53962i) q^{14} +(-0.459555 - 0.795973i) q^{16} +(0.440969 - 0.763780i) q^{17} +(3.41434 + 6.10234i) q^{18} +(1.90160 - 1.09789i) q^{19} +(1.59840 - 4.29478i) q^{21} +6.51381 q^{22} +(-6.53240 + 3.77148i) q^{23} +(4.11806 - 4.06291i) q^{24} +(-3.73505 - 6.46929i) q^{26} +(-3.74778 + 3.59918i) q^{27} +(-9.04771 - 0.795973i) q^{28} +8.15270i q^{29} +(-7.62645 - 4.40313i) q^{31} +(3.92965 + 2.26878i) q^{32} +(1.22124 + 4.68378i) q^{33} -2.05568i q^{34} +(8.84876 + 5.26916i) q^{36} +(0.203727 + 0.352865i) q^{37} +(2.55903 - 4.43237i) q^{38} +(3.95151 - 3.89859i) q^{39} -8.55098 q^{41} +(-1.77876 - 10.5322i) q^{42} +0.118062 q^{43} +(8.30832 - 4.79681i) q^{44} +(-8.79081 + 15.2261i) q^{46} +(1.31486 + 2.27740i) q^{47} +(0.422382 - 1.53489i) q^{48} +(-4.50469 + 5.35796i) q^{49} +(1.47814 - 0.385407i) q^{51} +(-9.52805 - 5.50102i) q^{52} +(-6.46794 - 3.73427i) q^{53} +(-3.37062 + 11.6330i) q^{54} +(-8.01054 + 3.73067i) q^{56} +(3.66689 + 1.00908i) q^{57} +(9.50142 + 16.4569i) q^{58} +(2.04991 - 3.55054i) q^{59} +(10.7004 - 6.17786i) q^{61} -20.5262 q^{62} +(7.23974 - 3.25365i) q^{63} +12.4147 q^{64} +(7.92380 + 8.03135i) q^{66} +(-0.802125 + 1.38932i) q^{67} +(-1.51381 - 2.62200i) q^{68} +(-12.5965 - 3.46641i) q^{69} -6.25869i q^{71} +(10.0189 + 0.135083i) q^{72} +(-0.192022 - 0.110864i) q^{73} +(0.822480 + 0.474859i) q^{74} -7.53794i q^{76} +(0.647967 - 7.36535i) q^{77} +(3.43292 - 12.4749i) q^{78} +(1.56849 + 2.71671i) q^{79} +(-8.99673 - 0.242646i) q^{81} +(-17.2609 + 9.96559i) q^{82} +0.666893 q^{83} +(-10.0248 - 12.1239i) q^{84} +(0.238319 - 0.137594i) q^{86} +(-10.0521 + 9.91745i) q^{87} +(4.66689 - 8.08330i) q^{88} +(-0.437271 - 0.757376i) q^{89} +(-7.68656 + 3.57978i) q^{91} +25.8944i q^{92} +(-3.84834 - 14.7594i) q^{93} +(5.30832 + 3.06476i) q^{94} +(1.98292 + 7.60504i) q^{96} +6.37221i q^{97} +(-2.84876 + 16.0654i) q^{98} +(-4.28939 + 7.20339i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - q^{3} + 3 q^{4} + 5 q^{6} - 2 q^{7} - 5 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 - q^3 + 3 * q^4 + 5 * q^6 - 2 * q^7 - 5 * q^9	$ 8 q + 3 q^{2} - q^{3} + 3 q^{4} + 5 q^{6} - 2 q^{7} - 5 q^{9} + 9 q^{12} - 12 q^{14} + q^{16} + 12 q^{17} + 19 q^{18} + 9 q^{19} + 19 q^{21} + 40 q^{22} - 27 q^{23} + 16 q^{24} - 6 q^{26} - 4 q^{27} - 3 q^{28} - 21 q^{31} - 21 q^{32} - 2 q^{33} + 9 q^{36} - 7 q^{37} + 12 q^{38} - 3 q^{39} - 30 q^{41} - 26 q^{42} - 16 q^{43} - 7 q^{46} + 6 q^{47} + 25 q^{48} - 4 q^{49} - 6 q^{51} - 30 q^{52} - 24 q^{53} + 17 q^{54} - 21 q^{56} - 6 q^{57} + 13 q^{58} - 12 q^{59} + 15 q^{61} - 24 q^{62} + 2 q^{63} + 38 q^{64} + 22 q^{66} - 4 q^{67} - 13 q^{69} + 14 q^{72} - 15 q^{73} + 54 q^{74} + 36 q^{77} + 6 q^{78} - 29 q^{79} - 41 q^{81} - 27 q^{82} - 30 q^{83} - 3 q^{84} + 9 q^{86} - 32 q^{87} + 2 q^{88} - 3 q^{89} - 3 q^{91} + 9 q^{93} - 24 q^{94} - 3 q^{96} + 39 q^{98} - 34 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 - q^3 + 3 * q^4 + 5 * q^6 - 2 * q^7 - 5 * q^9 + 9 * q^12 - 12 * q^14 + q^16 + 12 * q^17 + 19 * q^18 + 9 * q^19 + 19 * q^21 + 40 * q^22 - 27 * q^23 + 16 * q^24 - 6 * q^26 - 4 * q^27 - 3 * q^28 - 21 * q^31 - 21 * q^32 - 2 * q^33 + 9 * q^36 - 7 * q^37 + 12 * q^38 - 3 * q^39 - 30 * q^41 - 26 * q^42 - 16 * q^43 - 7 * q^46 + 6 * q^47 + 25 * q^48 - 4 * q^49 - 6 * q^51 - 30 * q^52 - 24 * q^53 + 17 * q^54 - 21 * q^56 - 6 * q^57 + 13 * q^58 - 12 * q^59 + 15 * q^61 - 24 * q^62 + 2 * q^63 + 38 * q^64 + 22 * q^66 - 4 * q^67 - 13 * q^69 + 14 * q^72 - 15 * q^73 + 54 * q^74 + 36 * q^77 + 6 * q^78 - 29 * q^79 - 41 * q^81 - 27 * q^82 - 30 * q^83 - 3 * q^84 + 9 * q^86 - 32 * q^87 + 2 * q^88 - 3 * q^89 - 3 * q^91 + 9 * q^93 - 24 * q^94 - 3 * q^96 + 39 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	2.01859	−	1.16543i	1.42736	−	0.824085i	0.430445	−	0.902617i	$-0.358357\pi$
$2$	2.01859	−	1.16543i	1.42736	−	0.824085i	0.996912	+	0.0785324i	$0.0250234\pi$
$3$	1.21646	+	1.23297i	0.702324	+	0.711857i
$3$	1.21646	+	1.23297i	0.702324	+	0.711857i
$4$	1.71646	−	2.97300i	0.858231	−	1.48650i
$5$		0			0
$5$		0			0
$6$	3.89248	+	1.07116i	1.58910	+	0.437299i
$7$	−1.11699	−	2.39840i	−0.422181	−	0.906512i
$7$	−1.11699	−	2.39840i	−0.422181	−	0.906512i
$8$		−	3.33995i		−	1.18085i
$9$	−0.0404447	+	2.99973i	−0.0134816	+	0.999909i
$10$		0			0
$11$	2.42019	+	1.39730i	0.729714	+	0.421301i	0.818318	−	0.574766i	$-0.194907\pi$
$11$	2.42019	+	1.39730i	0.729714	+	0.421301i	−0.0886035	+	0.996067i	$0.528240\pi$
$12$	5.75363	−	1.50019i	1.66093	−	0.433066i
$13$		−	3.20486i		−	0.888869i	−0.895811	−	0.444434i	$-0.853405\pi$
$13$		−	3.20486i		−	0.888869i	0.895811	−	0.444434i	$-0.146595\pi$
$14$	−5.04991	−	3.53962i	−1.34964	−	0.946002i
$15$		0			0
$16$	−0.459555	−	0.795973i	−0.114889	−	0.198993i
$17$	0.440969	−	0.763780i	0.106951	−	0.185244i	−0.807583	−	0.589754i	$-0.799225\pi$
$17$	0.440969	−	0.763780i	0.106951	−	0.185244i	0.914533	+	0.404510i	$0.132558\pi$
$18$	3.41434	+	6.10234i	0.804767	+	1.43834i
$19$	1.90160	−	1.09789i	0.436257	−	0.251873i	−0.265751	−	0.964042i	$-0.585620\pi$
$19$	1.90160	−	1.09789i	0.436257	−	0.251873i	0.702009	+	0.712168i	$0.252287\pi$
$20$		0			0
$21$	1.59840	−	4.29478i	0.348799	−	0.937197i
$22$	6.51381			1.38875
$23$	−6.53240	+	3.77148i	−1.36210	+	0.786408i	−0.989903	−	0.141746i	$-0.954728\pi$
$23$	−6.53240	+	3.77148i	−1.36210	+	0.786408i	−0.372196	+	0.928154i	$0.621395\pi$
$24$	4.11806	−	4.06291i	0.840596	−	0.829339i
$25$		0			0
$26$	−3.73505	−	6.46929i	−0.732503	−	1.26873i
$27$	−3.74778	+	3.59918i	−0.721261	+	0.692663i
$28$	−9.04771	−	0.795973i	−1.70986	−	0.150425i
$29$			8.15270i			1.51392i	0.653462	+	0.756959i	$0.273316\pi$
$29$			8.15270i			1.51392i	−0.653462	+	0.756959i	$0.726684\pi$
$30$		0			0
$31$	−7.62645	−	4.40313i	−1.36975	−	0.790826i	−0.378855	−	0.925456i	$-0.623682\pi$
$31$	−7.62645	−	4.40313i	−1.36975	−	0.790826i	−0.990896	+	0.134630i	$0.957015\pi$
$32$	3.92965	+	2.26878i	0.694671	+	0.401068i
$33$	1.22124	+	4.68378i	0.212590	+	0.815342i
$34$		−	2.05568i		−	0.352545i
$35$		0			0
$36$	8.84876	+	5.26916i	1.47479	+	0.878193i
$37$	0.203727	+	0.352865i	0.0334925	+	0.0580107i	0.882286	−	0.470714i	$-0.156004\pi$
$37$	0.203727	+	0.352865i	0.0334925	+	0.0580107i	−0.848793	+	0.528725i	$0.822670\pi$
$38$	2.55903	−	4.43237i	0.415130	−	0.719026i
$39$	3.95151	−	3.89859i	0.632748	−	0.624274i
$40$		0			0
$41$	−8.55098			−1.33544			−0.667720	−	0.744413i	$-0.732730\pi$
$41$	−8.55098			−1.33544			−0.667720	+	0.744413i	$0.732730\pi$
$42$	−1.77876	−	10.5322i	−0.274469	−	1.62515i
$43$	0.118062			0.0180044			0.00900218	−	0.999959i	$-0.497134\pi$
$43$	0.118062			0.0180044			0.00900218	+	0.999959i	$0.497134\pi$
$44$	8.30832	−	4.79681i	1.25253	−	0.723146i
$45$		0			0
$46$	−8.79081	+	15.2261i	−1.29613	+	2.24497i
$47$	1.31486	+	2.27740i	0.191792	+	0.332194i	0.945844	−	0.324621i	$-0.105237\pi$
$47$	1.31486	+	2.27740i	0.191792	+	0.332194i	−0.754052	+	0.656815i	$0.771903\pi$
$48$	0.422382	−	1.53489i	0.0609656	−	0.221542i
$49$	−4.50469	+	5.35796i	−0.643527	+	0.765424i
$50$		0			0
$51$	1.47814	−	0.385407i	0.206981	−	0.0539677i
$52$	−9.52805	−	5.50102i	−1.32130	−	0.762854i
$53$	−6.46794	−	3.73427i	−0.888440	−	0.512941i	−0.0150081	−	0.999887i	$-0.504777\pi$
$53$	−6.46794	−	3.73427i	−0.888440	−	0.512941i	−0.873432	+	0.486946i	$0.838111\pi$
$54$	−3.37062	+	11.6330i	−0.458683	+	1.58306i
$55$		0			0
$56$	−8.01054	+	3.73067i	−1.07045	+	0.498532i
$57$	3.66689	+	1.00908i	0.485692	+	0.133656i
$58$	9.50142	+	16.4569i	1.24760	+	2.16090i
$59$	2.04991	−	3.55054i	0.266875	−	0.462241i	−0.701178	−	0.712986i	$-0.747342\pi$
$59$	2.04991	−	3.55054i	0.266875	−	0.462241i	0.968053	+	0.250745i	$0.0806755\pi$
$60$		0			0
$61$	10.7004	−	6.17786i	1.37004	−	0.790994i	0.379109	−	0.925352i	$-0.376231\pi$
$61$	10.7004	−	6.17786i	1.37004	−	0.790994i	0.990933	+	0.134358i	$0.0428972\pi$
$62$	−20.5262			−2.60683
$63$	7.23974	−	3.25365i	0.912121	−	0.409921i
$64$	12.4147			1.55183
$65$		0			0
$66$	7.92380	+	8.03135i	0.975352	+	0.988591i
$67$	−0.802125	+	1.38932i	−0.0979952	+	0.169733i	−0.910855	−	0.412727i	$-0.864576\pi$
$67$	−0.802125	+	1.38932i	−0.0979952	+	0.169733i	0.812860	+	0.582460i	$0.197910\pi$
$68$	−1.51381	−	2.62200i	−0.183577	−	0.317964i
$69$	−12.5965	−	3.46641i	−1.51645	−	0.417307i
$70$		0			0
$71$		−	6.25869i		−	0.742770i	−0.928479	−	0.371385i	$-0.878883\pi$
$71$		−	6.25869i		−	0.742770i	0.928479	−	0.371385i	$-0.121117\pi$
$72$	10.0189	+	0.135083i	1.18074	+	0.0159197i
$73$	−0.192022	−	0.110864i	−0.0224745	−	0.0129757i	0.488721	−	0.872440i	$-0.337464\pi$
$73$	−0.192022	−	0.110864i	−0.0224745	−	0.0129757i	−0.511195	+	0.859465i	$0.670797\pi$
$74$	0.822480	+	0.474859i	0.0956114	+	0.0552012i
$75$		0			0
$76$		−	7.53794i		−	0.864661i
$77$	0.647967	−	7.36535i	0.0738427	−	0.839359i
$78$	3.43292	−	12.4749i	0.388702	−	1.41250i
$79$	1.56849	+	2.71671i	0.176469	+	0.305654i	0.940669	−	0.339326i	$-0.110199\pi$
$79$	1.56849	+	2.71671i	0.176469	+	0.305654i	−0.764199	+	0.644980i	$0.776866\pi$
$80$		0			0
$81$	−8.99673	−	0.242646i	−0.999636	−	0.0269607i
$82$	−17.2609	+	9.96559i	−1.90615	+	1.10051i
$83$	0.666893			0.0732010			0.0366005	−	0.999330i	$-0.488347\pi$
$83$	0.666893			0.0732010			0.0366005	+	0.999330i	$0.488347\pi$
$84$	−10.0248	−	12.1239i	−1.09379	−	1.32282i
$85$		0			0
$86$	0.238319	−	0.137594i	0.0256986	−	0.0148371i
$87$	−10.0521	+	9.91745i	−1.07769	+	1.06326i
$88$	4.66689	−	8.08330i	0.497492	−	0.861682i
$89$	−0.437271	−	0.757376i	−0.0463506	−	0.0802816i	0.841919	−	0.539603i	$-0.181426\pi$
$89$	−0.437271	−	0.757376i	−0.0463506	−	0.0802816i	−0.888270	+	0.459322i	$0.848092\pi$
$90$		0			0
$91$	−7.68656	+	3.57978i	−0.805770	+	0.375263i
$92$			25.8944i			2.69968i
$93$	−3.84834	−	14.7594i	−0.399054	−	1.53048i
$94$	5.30832	+	3.06476i	0.547511	+	0.316106i
$95$		0			0
$96$	1.98292	+	7.60504i	0.202381	+	0.776186i
$97$			6.37221i			0.647000i	0.946228	+	0.323500i	$0.104860\pi$
$97$			6.37221i			0.647000i	−0.946228	+	0.323500i	$0.895140\pi$
$98$	−2.84876	+	16.0654i	−0.287768	+	1.62285i
$99$	−4.28939	+	7.20339i	−0.431100	+	0.723968i
$100$		0			0
$101$	5.31267	−	9.20181i	0.528630	−	0.915614i	−0.470813	−	0.882233i	$-0.656039\pi$
$101$	5.31267	−	9.20181i	0.528630	−	0.915614i	0.999443	−	0.0333808i	$-0.0106274\pi$
$102$	2.53459	−	2.50065i	0.250962	−	0.247601i
$103$	0.868777	−	0.501589i	0.0856031	−	0.0494230i	−0.456587	−	0.889679i	$-0.650928\pi$
$103$	0.868777	−	0.501589i	0.0856031	−	0.0494230i	0.542191	+	0.840256i	$0.317595\pi$
$104$	−10.7041			−1.04962
$105$		0			0
$106$	−17.4081			−1.69083
$107$	11.0651	−	6.38846i	1.06971	−	0.617596i	0.141606	−	0.989923i	$-0.454774\pi$
$107$	11.0651	−	6.38846i	1.06971	−	0.617596i	0.928101	+	0.372328i	$0.121440\pi$
$108$	4.26745	+	17.3200i	0.410635	+	1.66662i
$109$	−0.00912370	+	0.0158027i	−0.000873892	+	0.00151363i	−0.866462	−	0.499243i	$-0.833612\pi$
$109$	−0.00912370	+	0.0158027i	−0.000873892	+	0.00151363i	0.865588	+	0.500757i	$0.166945\pi$
$110$		0			0
$111$	−0.187247	+	0.680436i	−0.0177727	+	0.0645841i
$112$	−1.39575	+	1.99129i	−0.131886	+	0.188159i
$113$			7.23027i			0.680166i	0.940395	+	0.340083i	$0.110455\pi$
$113$			7.23027i			0.680166i	−0.940395	+	0.340083i	$0.889545\pi$
$114$	8.57796	−	2.23659i	0.803399	−	0.209476i
$115$		0			0
$116$	24.2380	+	13.9938i	2.25044	+	1.29929i
$117$	9.61371	+	0.129620i	0.888788	+	0.0119833i
$118$		−	9.55611i		−	0.879711i
$119$	−2.32441	−	0.204490i	−0.213078	−	0.0187456i
$120$		0			0
$121$	−1.59513	−	2.76284i	−0.145012	−	0.251167i
$122$	14.3997	−	24.9411i	1.30369	−	2.25806i
$123$	−10.4019	−	10.5431i	−0.937911	−	0.950642i
$124$	−26.1810	+	15.1156i	−2.35112	+	1.35742i
$125$		0			0
$126$	10.8221	−	15.0052i	0.964112	−	1.33677i
$127$	−6.99561			−0.620760			−0.310380	−	0.950613i	$-0.600456\pi$
$127$	−6.99561			−0.620760			−0.310380	+	0.950613i	$0.600456\pi$
$128$	17.2008	−	9.93088i	1.52035	−	0.877774i
$129$	0.143618	+	0.145568i	0.0126449	+	0.0128165i
$130$		0			0
$131$	4.94673	+	8.56799i	0.432198	+	0.748589i	0.997062	−	0.0765948i	$-0.0244048\pi$
$131$	4.94673	+	8.56799i	0.432198	+	0.748589i	−0.564864	+	0.825184i	$0.691071\pi$
$132$	16.0211	+	4.40880i	1.39446	+	0.383737i
$133$	−4.75724	−	3.33448i	−0.412505	−	0.289136i
$134$			3.73929i			0.323025i
$135$		0			0
$136$	−2.55098	−	1.47281i	−0.218745	−	0.126293i
$137$	10.9111	+	6.29951i	0.932195	+	0.538203i	0.887505	−	0.460798i	$-0.152437\pi$
$137$	10.9111	+	6.29951i	0.932195	+	0.538203i	0.0446900	+	0.999001i	$0.485770\pi$
$138$	−29.4671	+	7.68316i	−2.50840	+	0.654034i
$139$			0.988113i			0.0838106i	0.999122	+	0.0419053i	$0.0133428\pi$
$139$			0.988113i			0.0838106i	−0.999122	+	0.0419053i	$0.986657\pi$
$140$		0			0
$141$	−1.20850	+	4.39156i	−0.101774	+	0.369836i
$142$	−7.29408	−	12.6337i	−0.612106	−	1.06020i
$143$	4.47814	−	7.75637i	0.374481	−	0.648620i
$144$	2.40629	−	1.34635i	0.200524	−	0.112196i
$145$		0			0
$146$	−0.516818			−0.0427722
$147$	−12.0860	+	0.963598i	−0.996837	+	0.0794762i
$148$	1.39876			0.114977
$149$	15.3604	−	8.86834i	1.25837	−	0.726523i	0.285616	−	0.958344i	$-0.407802\pi$
$149$	15.3604	−	8.86834i	1.25837	−	0.726523i	0.972758	+	0.231821i	$0.0744684\pi$
$150$		0			0
$151$	11.2504	−	19.4862i	0.915542	−	1.58576i	0.109435	−	0.993994i	$-0.465096\pi$
$151$	11.2504	−	19.4862i	0.915542	−	1.58576i	0.806106	−	0.591771i	$-0.201571\pi$
$152$	−3.66689	−	6.35124i	−0.297424	−	0.515154i
$153$	2.27330	+	1.35368i	0.183785	+	0.109438i
$154$	−7.27583	−	15.6228i	−0.586303	−	1.25892i
$155$		0			0
$156$	−4.80789	−	18.4396i	−0.384939	−	1.47635i
$157$	10.2988	+	5.94600i	0.821931	+	0.474542i	0.851082	−	0.525033i	$-0.175947\pi$
$157$	10.2988	+	5.94600i	0.821931	+	0.474542i	−0.0291509	+	0.999575i	$0.509280\pi$
$158$	6.33228	+	3.65594i	0.503769	+	0.290851i
$159$	−3.26375	−	12.5174i	−0.258832	−	0.992693i
$160$		0			0
$161$	16.3421	+	11.4546i	1.28794	+	0.902752i
$162$	−18.4435	+	9.99527i	−1.44906	+	0.785302i
$163$	4.26159	+	7.38130i	0.333794	+	0.578148i	0.983252	−	0.182249i	$-0.0583378\pi$
$163$	4.26159	+	7.38130i	0.333794	+	0.578148i	−0.649459	+	0.760397i	$0.725004\pi$
$164$	−14.6774	+	25.4221i	−1.14611	+	1.98513i
$165$		0			0
$166$	1.34618	−	0.777218i	0.104484	−	0.0603238i
$167$	−3.56923			−0.276195			−0.138098	−	0.990419i	$-0.544099\pi$
$167$	−3.56923			−0.276195			−0.138098	+	0.990419i	$0.544099\pi$
$168$	−14.3443	−	5.33856i	−1.10669	−	0.411879i
$169$	2.72886			0.209912
$170$		0			0
$171$	3.21646	+	5.74869i	0.245969	+	0.439613i
$172$	0.202650	−	0.350999i	0.0154519	−	0.0267634i
$173$	4.27114	+	7.39784i	0.324729	+	0.562447i	0.981457	−	0.191680i	$-0.0613936\pi$
$173$	4.27114	+	7.39784i	0.324729	+	0.562447i	−0.656728	+	0.754127i	$0.728060\pi$
$174$	−8.73285	+	31.7342i	−0.662036	+	2.40576i
$175$		0			0
$176$		−	2.56854i		−	0.193611i
$177$	6.87136	−	1.79162i	0.516483	−	0.134666i
$178$	−1.76534	−	1.01922i	−0.132318	−	0.0763937i
$179$	1.06480	+	0.614760i	0.0795866	+	0.0459493i	0.539265	−	0.842136i	$-0.318702\pi$
$179$	1.06480	+	0.614760i	0.0795866	+	0.0459493i	−0.459679	+	0.888085i	$0.652035\pi$
$180$		0			0
$181$			15.3995i			1.14464i	0.820032	+	0.572318i	$0.193956\pi$
$181$			15.3995i			1.14464i	−0.820032	+	0.572318i	$0.806044\pi$
$182$	−11.3440	+	16.1843i	−0.840872	+	1.19966i
$183$	20.6337	+	5.67814i	1.52529	+	0.419740i
$184$	12.5965	+	21.8179i	0.928630	+	1.60843i
$185$		0			0
$186$	−24.9693	−	25.3082i	−1.83084	−	1.85569i
$187$	2.13445	−	1.23233i	0.156087	−	0.0901167i
$188$	9.02762			0.658407
$189$	12.8185	+	4.96846i	0.932410	+	0.361402i
$190$		0			0
$191$	−12.5795	+	7.26275i	−0.910218	+	0.525514i	−0.880501	−	0.474044i	$-0.842794\pi$
$191$	−12.5795	+	7.26275i	−0.910218	+	0.525514i	−0.0297166	+	0.999558i	$0.509460\pi$
$192$	15.1020	+	15.3070i	1.08989	+	1.10468i
$193$	−0.201572	+	0.349134i	−0.0145095	+	0.0251312i	−0.873189	−	0.487382i	$-0.837952\pi$
$193$	−0.201572	+	0.349134i	−0.0145095	+	0.0251312i	0.858679	+	0.512513i	$0.171285\pi$
$194$	7.42638	+	12.8629i	0.533183	+	0.923500i
$195$		0			0
$196$	8.19710	+	22.5892i	0.585507	+	1.61351i
$197$		−	11.6716i		−	0.831564i	−0.909464	−	0.415782i	$-0.863508\pi$
$197$		−	11.6716i		−	0.831564i	0.909464	−	0.415782i	$-0.136492\pi$
$198$	−0.263449	+	19.5397i	−0.0187225	+	1.38862i
$199$	−16.0886	−	9.28875i	−1.14049	−	0.658462i	−0.193938	−	0.981014i	$-0.562126\pi$
$199$	−16.0886	−	9.28875i	−1.14049	−	0.658462i	−0.946552	+	0.322552i	$0.895459\pi$
$200$		0			0
$201$	−2.68875	+	0.701057i	−0.189650	+	0.0494488i
$202$		−	24.7662i		−	1.74254i
$203$	19.5535	−	9.10645i	1.37239	−	0.639147i
$204$	1.39136	−	5.05605i	0.0974147	−	0.353994i
$205$		0			0
$206$	1.16913	−	2.02500i	0.0814574	−	0.141088i
$207$	−11.0492	−	19.7479i	−0.767974	−	1.37258i
$208$	−2.55098	+	1.47281i	−0.176879	+	0.102121i
$209$	6.13631			0.424457
$210$		0			0
$211$	6.98175			0.480644			0.240322	−	0.970693i	$-0.422747\pi$
$211$	6.98175			0.480644			0.240322	+	0.970693i	$0.422747\pi$
$212$	−22.2039	+	12.8194i	−1.52497	+	0.880443i
$213$	7.71680	−	7.61346i	0.528746	−	0.521666i
$214$	14.8906	−	25.7913i	1.01790	−	1.76306i
$215$		0			0
$216$	12.0211	+	12.5174i	0.817931	+	0.851700i
$217$	−2.04186	+	23.2095i	−0.138611	+	1.57557i
$218$			0.0425322i			0.00288064i
$219$	−0.0968952	−	0.371620i	−0.00654757	−	0.0251118i
$220$		0			0
$221$	−2.44781	−	1.41324i	−0.164658	−	0.0950651i
$222$	0.415027	+	1.59174i	0.0278548	+	0.106831i
$223$			1.44594i			0.0968271i	0.998827	+	0.0484135i	$0.0154165\pi$
$223$			1.44594i			0.0968271i	−0.998827	+	0.0484135i	$0.984583\pi$
$224$	1.05210	−	11.9591i	0.0702965	−	0.799050i
$225$		0			0
$226$	8.42638	+	14.5949i	0.560514	+	0.970839i
$227$	0.533562	−	0.924157i	0.0354138	−	0.0613385i	−0.847775	−	0.530356i	$-0.822058\pi$
$227$	0.533562	−	0.924157i	0.0354138	−	0.0613385i	0.883189	+	0.469017i	$0.155392\pi$
$228$	9.29408	−	9.16961i	0.615515	−	0.607272i
$229$	−6.58058	+	3.79930i	−0.434857	+	0.251065i	−0.701414	−	0.712755i	$-0.747447\pi$
$229$	−6.58058	+	3.79930i	−0.434857	+	0.251065i	0.266557	+	0.963819i	$0.414114\pi$
$230$		0			0
$231$	9.86950	−	8.16073i	0.649366	−	0.536937i
$232$	27.2296			1.78771
$233$	−15.5882	+	8.99983i	−1.02121	+	0.589598i	−0.914455	−	0.404687i	$-0.867381\pi$
$233$	−15.5882	+	8.99983i	−1.02121	+	0.589598i	−0.106759	+	0.994285i	$0.534047\pi$
$234$	19.5572	−	10.9425i	1.27849	−	0.715332i
$235$		0			0
$236$	−7.03717	−	12.1887i	−0.458081	−	0.793419i
$237$	−1.44162	+	5.23868i	−0.0936433	+	0.340289i
$238$	−4.93034	+	2.29616i	−0.319587	+	0.148838i
$239$		−	29.8816i		−	1.93288i	−0.256892	−	0.966440i	$-0.582698\pi$
$239$		−	29.8816i		−	1.93288i	0.256892	−	0.966440i	$-0.417302\pi$
$240$		0			0
$241$	4.53760	+	2.61978i	0.292292	+	0.168755i	0.638975	−	0.769227i	$-0.279359\pi$
$241$	4.53760	+	2.61978i	0.292292	+	0.168755i	−0.346683	+	0.937982i	$0.612692\pi$
$242$	−6.43980	−	3.71802i	−0.413966	−	0.239004i
$243$	−10.6450	−	11.3879i	−0.682877	−	0.730534i
$244$		−	42.4162i		−	2.71542i
$245$		0			0
$246$	−33.2845	−	9.15948i	−2.12214	−	0.583987i
$247$	−3.51859	−	6.09437i	−0.223882	−	0.387776i
$248$	−14.7062	+	25.4719i	−0.933846	+	1.61747i
$249$	0.811249	+	0.822261i	0.0514108	+	0.0521087i
$250$		0			0
$251$	−15.0765			−0.951620			−0.475810	−	0.879548i	$-0.657845\pi$
$251$	−15.0765			−0.951620			−0.475810	+	0.879548i	$0.657845\pi$
$252$	2.75363	−	27.1085i	0.173463	−	1.70767i
$253$	−21.0795			−1.32526
$254$	−14.1212	+	8.15291i	−0.886046	+	0.511559i
$255$		0			0
$256$	10.7329	−	18.5898i	0.670803	−	1.16187i
$257$	−7.95478	−	13.7781i	−0.496206	−	0.859453i	0.503785	−	0.863829i	$-0.331940\pi$
$257$	−7.95478	−	13.7781i	−0.496206	−	0.859453i	−0.999990	+	0.00437591i	$0.998607\pi$
$258$	0.459555	+	0.126464i	0.0286107	+	0.00787329i
$259$	0.618753	−	0.882764i	0.0384475	−	0.0548523i
$260$		0			0
$261$	−24.4559	−	0.329733i	−1.51378	−	0.0204100i
$262$	19.9708	+	11.5302i	1.23380	+	0.712336i
$263$	−7.19124	−	4.15187i	−0.443431	−	0.256015i	0.261621	−	0.965171i	$-0.415743\pi$
$263$	−7.19124	−	4.15187i	−0.443431	−	0.256015i	−0.705052	+	0.709156i	$0.749076\pi$
$264$	15.6436	−	4.07886i	0.962796	−	0.251037i
$265$		0			0
$266$	−13.4890	−	1.18670i	−0.827065	−	0.0727611i
$267$	0.401900	−	1.46046i	0.0245959	−	0.0893788i
$268$	2.75363	+	4.76943i	0.168205	+	0.291340i
$269$	8.69353	−	15.0576i	0.530054	−	0.918080i	−0.469332	−	0.883022i	$-0.655505\pi$
$269$	8.69353	−	15.0576i	0.530054	−	0.918080i	0.999385	−	0.0350578i	$-0.0111615\pi$
$270$		0			0
$271$	−8.82614	+	5.09577i	−0.536150	+	0.309546i	−0.743517	−	0.668717i	$-0.766844\pi$
$271$	−8.82614	+	5.09577i	−0.536150	+	0.309546i	0.207367	+	0.978263i	$0.433510\pi$
$272$	−0.810598			−0.0491497
$273$	−13.7642	−	5.12265i	−0.833046	−	0.310037i
$274$	29.3666			1.77410
$275$		0			0
$276$	−31.9271	+	31.4995i	−1.92179	+	1.89605i
$277$	4.78018	−	8.27951i	0.287213	−	0.497468i	−0.685930	−	0.727667i	$-0.740605\pi$
$277$	4.78018	−	8.27951i	0.287213	−	0.497468i	0.973143	+	0.230199i	$0.0739378\pi$
$278$	1.15158	+	1.99459i	0.0690670	+	0.119628i
$279$	13.5166	−	22.6992i	0.809220	−	1.35896i
$280$		0			0
$281$			11.9239i			0.711320i	0.934616	+	0.355660i	$0.115744\pi$
$281$			11.9239i			0.711320i	−0.934616	+	0.355660i	$0.884256\pi$
$282$	2.67860	+	10.2732i	0.159508	+	0.611758i
$283$	−17.2940	−	9.98469i	−1.02802	−	0.593528i	−0.111604	−	0.993753i	$-0.535599\pi$
$283$	−17.2940	−	9.98469i	−1.02802	−	0.593528i	−0.916417	+	0.400225i	$0.868932\pi$
$284$	−18.6071	−	10.7428i	−1.10413	−	0.637468i
$285$		0			0
$286$		−	20.8759i		−	1.23442i
$287$	9.55132	+	20.5087i	0.563797	+	1.21059i
$288$	−6.96467	+	11.6961i	−0.410397	+	0.689201i
$289$	8.11109	+	14.0488i	0.477123	+	0.826401i
$290$		0			0
$291$	−7.85677	+	7.75155i	−0.460572	+	0.454404i
$292$	−0.659198	+	0.380588i	−0.0385766	+	0.0222722i
$293$	−3.01023			−0.175859			−0.0879297	−	0.996127i	$-0.528025\pi$
$293$	−3.01023			−0.175859			−0.0879297	+	0.996127i	$0.528025\pi$
$294$	−23.2736	+	16.0305i	−1.35735	+	0.934919i
$295$		0			0
$296$	1.17855	−	0.680436i	0.0685018	−	0.0395495i
$297$	−14.0995	+	3.47394i	−0.818134	+	0.201579i
$298$	20.6709	−	35.8030i	1.19743	−	2.07401i
$299$	12.0871	+	20.9354i	0.699014	+	1.21073i
$300$		0			0
$301$	−0.131874	−	0.283161i	−0.00760109	−	0.0163212i
$302$		−	52.4461i		−	3.01793i
$303$	17.8082	−	4.64327i	1.02306	−	0.266749i
$304$	−1.74778	−	1.00908i	−0.100242	−	0.0578748i
$305$		0			0
$306$	6.16647	+	0.0831411i	0.352513	+	0.00475286i
$307$		−	20.3794i		−	1.16311i	−0.813507	−	0.581556i	$-0.802444\pi$
$307$		−	20.3794i		−	1.16311i	0.813507	−	0.581556i	$-0.197556\pi$
$308$	−20.7850	−	14.5687i	−1.18433	−	0.830131i
$309$	1.67528	+	0.461015i	0.0953033	+	0.0262263i
$310$		0			0
$311$	13.6359	−	23.6181i	0.773222	−	1.33926i	−0.162567	−	0.986697i	$-0.551977\pi$
$311$	13.6359	−	23.6181i	0.773222	−	1.33926i	0.935789	−	0.352562i	$-0.114689\pi$
$312$	−13.0211	−	13.1978i	−0.737173	−	0.747180i
$313$	−0.546210	+	0.315354i	−0.0308736	+	0.0178249i	−0.515357	−	0.856975i	$-0.672341\pi$
$313$	−0.546210	+	0.315354i	−0.0308736	+	0.0178249i	0.484484	+	0.874800i	$0.339007\pi$
$314$	27.7186			1.56425
$315$		0			0
$316$	10.7690			0.605806
$317$	−22.0233	+	12.7151i	−1.23695	+	0.714153i	−0.968470	−	0.249132i	$-0.919855\pi$
$317$	−22.0233	+	12.7151i	−1.23695	+	0.714153i	−0.268480	+	0.963285i	$0.586521\pi$
$318$	−21.1763	−	21.4638i	−1.18751	−	1.20363i
$319$	−11.3917	+	19.7311i	−0.637815	+	1.10473i
$320$		0			0
$321$	21.3371	+	5.87170i	1.19092	+	0.327726i
$322$	46.3376	+	4.07655i	2.58229	+	0.227177i
$323$		−	1.93654i		−	0.107752i
$324$	−16.1639	+	26.3308i	−0.897996	+	1.46282i
$325$		0			0
$326$	17.2048	+	9.93319i	0.952885	+	0.550149i
$327$	−0.0305829	+	0.00797411i	−0.00169124	+	0.000440969i
$328$			28.5598i			1.57695i
$329$	3.99346	−	5.69739i	0.220166	−	0.314107i
$330$		0			0
$331$	−5.74666	−	9.95352i	−0.315865	−	0.547095i	0.663756	−	0.747949i	$-0.268961\pi$
$331$	−5.74666	−	9.95352i	−0.315865	−	0.547095i	−0.979621	+	0.200855i	$0.935628\pi$
$332$	1.14470	−	1.98267i	0.0628233	−	0.108813i
$333$	−1.06674	+	0.596853i	−0.0584569	+	0.0327074i
$334$	−7.20480	+	4.15970i	−0.394229	+	0.227608i
$335$		0			0
$336$	−4.15308	+	0.701406i	−0.226569	+	0.0382648i
$337$	16.2041			0.882694			0.441347	−	0.897336i	$-0.354501\pi$
$337$	16.2041			0.882694			0.441347	+	0.897336i	$0.354501\pi$
$338$	5.50843	−	3.18030i	0.299619	−	0.172985i
$339$	−8.91472	+	8.79534i	−0.484181	+	0.477697i
$340$		0			0
$341$	−12.3050	−	21.3128i	−0.666351	−	1.15415i
$342$	13.1924	+	7.85566i	0.713364	+	0.424786i
$343$	17.8822	+	4.81930i	0.965550	+	0.260218i
$344$		−	0.394322i		−	0.0212604i
$345$		0			0
$346$	17.2433	+	9.95545i	0.927008	+	0.535208i
$347$	15.5732	+	8.99121i	0.836015	+	0.482673i	0.855908	−	0.517129i	$-0.172999\pi$
$347$	15.5732	+	8.99121i	0.836015	+	0.482673i	−0.0198929	+	0.999802i	$0.506333\pi$
$348$	12.2306	+	46.9077i	0.655627	+	2.51451i
$349$			6.15422i			0.329428i	0.986341	+	0.164714i	$0.0526701\pi$
$349$			6.15422i			0.329428i	−0.986341	+	0.164714i	$0.947330\pi$
$350$		0			0
$351$	11.5349	+	12.0111i	0.615687	+	0.641106i
$352$	6.34033	+	10.9818i	0.337941	+	0.585330i
$353$	14.7332	−	25.5186i	0.784169	−	1.35822i	−0.145326	−	0.989384i	$-0.546423\pi$
$353$	14.7332	−	25.5186i	0.784169	−	1.35822i	0.929494	−	0.368836i	$-0.120244\pi$
$354$	11.7824	−	11.6246i	0.626229	−	0.617842i
$355$		0			0
$356$	−3.00223			−0.159118
$357$	−2.57542	−	3.11469i	−0.136306	−	0.164847i
$358$	2.86584			0.151465
$359$	−30.5228	+	17.6224i	−1.61093	+	0.930073i	−0.621779	+	0.783192i	$0.713590\pi$
$359$	−30.5228	+	17.6224i	−1.61093	+	0.930073i	−0.989154	+	0.146881i	$0.953077\pi$
$360$		0			0
$361$	−7.08928	+	12.2790i	−0.373120	+	0.646262i
$362$	17.9471	+	31.0852i	0.943277	+	1.63380i
$363$	1.46610	−	5.32764i	0.0769502	−	0.279628i
$364$	−2.55098	+	28.9967i	−0.133708	+	1.51984i
$365$		0			0
$366$	48.2684	−	12.5854i	2.52303	−	0.657848i
$367$	−30.1613	−	17.4136i	−1.57441	−	0.908984i	−0.995619	−	0.0935065i	$-0.970192\pi$
$367$	−30.1613	−	17.4136i	−1.57441	−	0.908984i	−0.578788	−	0.815478i	$-0.696474\pi$
$368$	6.00400	+	3.46641i	0.312980	+	0.180699i
$369$	0.345842	−	25.6506i	0.0180038	−	1.33532i
$370$		0			0
$371$	−1.73169	+	19.6839i	−0.0899048	+	1.02194i
$372$	−50.4853	−	13.8929i	−2.61754	−	0.720314i
$373$	10.1371	+	17.5579i	0.524878	+	0.909115i	0.999580	+	0.0289688i	$0.00922234\pi$
$373$	10.1371	+	17.5579i	0.524878	+	0.909115i	−0.474702	+	0.880146i	$0.657444\pi$
$374$	2.87239	−	4.97512i	0.148528	−	0.257257i
$375$		0			0
$376$	7.60641	−	4.39156i	0.392270	−	0.226477i
$377$	26.1283			1.34568
$378$	31.6657	−	4.90984i	1.62871	−	0.252535i
$379$	−9.07202			−0.465998			−0.232999	−	0.972477i	$-0.574854\pi$
$379$	−9.07202			−0.465998			−0.232999	+	0.972477i	$0.574854\pi$
$380$		0			0
$381$	−8.50989	−	8.62540i	−0.435975	−	0.441893i
$382$	−16.9285	+	29.3210i	−0.866137	+	1.50019i
$383$	13.8881	+	24.0549i	0.709648	+	1.22915i	0.964988	+	0.262295i	$0.0844794\pi$
$383$	13.8881	+	24.0549i	0.709648	+	1.22915i	−0.255339	+	0.966851i	$0.582187\pi$
$384$	33.1686	+	9.12758i	1.69263	+	0.465790i
$385$		0			0
$386$			0.939675i			0.0478282i
$387$	−0.00477499	+	0.354155i	−0.000242727	+	0.0180027i
$388$	18.9446	+	10.9377i	0.961765	+	0.555275i
$389$	−13.4945	−	7.79107i	−0.684200	−	0.395023i	0.117236	−	0.993104i	$-0.462597\pi$
$389$	−13.4945	−	7.79107i	−0.684200	−	0.395023i	−0.801436	+	0.598081i	$0.795930\pi$
$390$		0			0
$391$			6.65242i			0.336427i
$392$	17.8953	+	15.0454i	0.903850	+	0.759908i
$393$	−4.54660	+	16.5218i	−0.229345	+	0.833416i
$394$	−13.6024	−	23.5600i	−0.685279	−	1.18694i
$395$		0			0
$396$	14.0531	+	25.1167i	0.706194	+	1.26216i
$397$	16.3596	−	9.44524i	0.821067	−	0.474043i	−0.0297174	−	0.999558i	$-0.509461\pi$
$397$	16.3596	−	9.44524i	0.821067	−	0.474043i	0.850784	+	0.525515i	$0.176127\pi$
$398$	−43.3016			−2.17051
$399$	−1.67568	−	9.92182i	−0.0838888	−	0.496712i
$400$		0			0
$401$	18.0127	−	10.3996i	0.899511	−	0.519333i	0.0224695	−	0.999748i	$-0.492847\pi$
$401$	18.0127	−	10.3996i	0.899511	−	0.519333i	0.877042	+	0.480415i	$0.159514\pi$
$402$	−4.61044	+	4.54870i	−0.229948	+	0.226869i
$403$	−14.1114	+	24.4417i	−0.702941	+	1.21753i
$404$	−18.2380	−	31.5891i	−0.907373	−	1.57162i
$405$		0			0
$406$	28.8574	−	41.1704i	1.43217	−	2.04325i
$407$			1.13867i			0.0564416i
$408$	−1.28724	−	4.93691i	−0.0637277	−	0.244414i
$409$	24.9664	+	14.4143i	1.23451	+	0.712744i	0.967966	−	0.251080i	$-0.0807856\pi$
$409$	24.9664	+	14.4143i	1.23451	+	0.712744i	0.266542	+	0.963823i	$0.414119\pi$
$410$		0			0
$411$	5.50577	+	21.1162i	0.271579	+	1.04158i
$412$		−	3.44383i		−	0.169665i
$413$	−10.8054	−	0.950602i	−0.531697	−	0.0467761i
$414$	−45.3187	−	26.9858i	−2.22729	−	1.32628i
$415$		0			0
$416$	7.27114	−	12.5940i	0.356497	−	0.617471i
$417$	−1.21832	+	1.20200i	−0.0596612	+	0.0588622i
$418$	12.3867	−	7.15145i	0.605852	−	0.349789i
$419$	−3.24500			−0.158528			−0.0792642	−	0.996854i	$-0.525257\pi$
$419$	−3.24500			−0.158528			−0.0792642	+	0.996854i	$0.525257\pi$
$420$		0			0
$421$	27.9322			1.36133			0.680665	−	0.732594i	$-0.261691\pi$
$421$	27.9322			1.36133			0.680665	+	0.732594i	$0.261691\pi$
$422$	14.0933	−	8.13675i	0.686050	−	0.396091i
$423$	−6.88477	+	3.85211i	−0.334749	+	0.187296i
$424$	−12.4722	+	21.6026i	−0.605706	+	1.04911i
$425$		0			0
$426$	6.70407	−	24.3618i	0.324813	−	1.18033i
$427$	−26.7692	−	18.7632i	−1.29545	−	0.908016i
$428$		−	43.8622i		−	2.12016i
$429$	15.0109	−	3.91389i	0.724732	−	0.188965i
$430$		0			0
$431$	−33.1792	−	19.1560i	−1.59819	−	0.922714i	−0.991836	−	0.127516i	$-0.959299\pi$
$431$	−33.1792	−	19.1560i	−1.59819	−	0.922714i	−0.606351	−	0.795197i	$-0.707367\pi$
$432$	4.58717	+	1.32911i	0.220700	+	0.0639468i
$433$			28.9533i			1.39140i	0.718330	+	0.695702i	$0.244907\pi$
$433$			28.9533i			1.39140i	−0.718330	+	0.695702i	$0.755093\pi$
$434$	22.9275	+	49.2301i	1.10055	+	2.36312i
$435$		0			0
$436$	0.0313210	+	0.0542495i	0.00150000	+	0.00259808i
$437$	−8.28134	+	14.3437i	−0.396150	+	0.686153i
$438$	−0.628690	−	0.637223i	−0.0300400	−	0.0304477i
$439$	−13.2197	+	7.63242i	−0.630943	+	0.364275i	−0.781117	−	0.624384i	$-0.785350\pi$
$439$	−13.2197	+	7.63242i	−0.630943	+	0.364275i	0.150174	+	0.988660i	$0.452017\pi$
$440$		0			0
$441$	−15.8902	−	13.7295i	−0.756678	−	0.653787i
$442$	−6.58816			−0.313367
$443$	1.97776	−	1.14186i	0.0939660	−	0.0542513i	−0.452281	−	0.891876i	$-0.649389\pi$
$443$	1.97776	−	1.14186i	0.0939660	−	0.0542513i	0.546247	+	0.837624i	$0.316056\pi$
$444$	1.70153	+	1.72463i	0.0807512	+	0.0818472i
$445$		0			0
$446$	1.68514	+	2.91875i	0.0797937	+	0.138207i
$447$	29.6198	+	8.15099i	1.40097	+	0.385528i
$448$	−13.8670	−	29.7754i	−0.655155	−	1.40676i
$449$			10.3113i			0.486619i	0.969949	+	0.243310i	$0.0782331\pi$
$449$			10.3113i			0.486619i	−0.969949	+	0.243310i	$0.921767\pi$
$450$		0			0
$451$	−20.6950	−	11.9483i	−0.974489	−	0.562621i
$452$	21.4956	+	12.4105i	1.01107	+	0.583739i
$453$	37.7116	−	9.83281i	1.77184	−	0.461986i
$454$		−	2.48732i		−	0.116736i
$455$		0			0
$456$	3.37028	−	12.2472i	0.157828	−	0.573529i
$457$	16.3987	+	28.4033i	0.767097	+	1.32865i	0.939131	+	0.343560i	$0.111633\pi$
$457$	16.3987	+	28.4033i	0.767097	+	1.32865i	−0.172033	+	0.985091i	$0.555034\pi$
$458$	−8.85564	+	15.3384i	−0.413797	+	0.716718i
$459$	1.09633	+	4.44961i	0.0511724	+	0.207690i
$460$		0			0
$461$	16.5678			0.771637			0.385819	−	0.922575i	$-0.373919\pi$
$461$	16.5678			0.771637			0.385819	+	0.922575i	$0.373919\pi$
$462$	10.4117	−	27.9754i	0.484395	−	1.30153i
$463$	36.5866			1.70032			0.850162	−	0.526522i	$-0.176504\pi$
$463$	36.5866			1.70032			0.850162	+	0.526522i	$0.176504\pi$
$464$	6.48933	−	3.74662i	0.301260	−	0.173932i
$465$		0			0
$466$	−20.9774	+	36.3339i	−0.971758	+	1.68313i
$467$	−20.5550	−	35.6023i	−0.951171	−	1.64748i	−0.742896	−	0.669406i	$-0.766549\pi$
$467$	−20.5550	−	35.6023i	−0.951171	−	1.64748i	−0.208275	−	0.978070i	$-0.566785\pi$
$468$	16.8869	−	28.3591i	0.780598	−	1.31090i
$469$	4.22812	+	0.371969i	0.195236	+	0.0171759i
$470$		0			0
$471$	5.19680	+	19.9312i	0.239456	+	0.918380i
$472$	−11.8586	−	6.84658i	−0.545837	−	0.315139i
$473$	0.285733	+	0.164968i	0.0131380	+	0.00758524i
$474$	3.19529	+	12.2548i	0.146765	+	0.562884i
$475$		0			0
$476$	−4.59771	+	6.55947i	−0.210736	+	0.300653i
$477$	11.4634	−	19.2510i	0.524872	−	0.881444i
$478$	−34.8250	−	60.3186i	−1.59286	−	2.75891i
$479$	−8.25944	+	14.3058i	−0.377383	+	0.653647i	−0.990681	−	0.136205i	$-0.956509\pi$
$479$	−8.25944	+	14.3058i	−0.377383	+	0.653647i	0.613297	+	0.789852i	$0.289843\pi$
$480$		0			0
$481$	1.13088	−	0.652916i	0.0515639	−	0.0297704i
$482$	12.2127			0.556274
$483$	5.75630	+	34.0835i	0.261921	+	1.55085i
$484$	−10.9519			−0.497813
$485$		0			0
$486$	−34.7597	−	10.5814i	−1.57673	−	0.479984i
$487$	−1.01601	+	1.75977i	−0.0460396	+	0.0797430i	−0.888127	−	0.459598i	$-0.847993\pi$
$487$	−1.01601	+	1.75977i	−0.0460396	+	0.0797430i	0.842087	+	0.539341i	$0.181327\pi$
$488$	−20.6337	−	35.7386i	−0.934044	−	1.61781i
$489$	−3.91688	+	14.2335i	−0.177127	+	0.643661i
$490$		0			0
$491$			5.97889i			0.269824i	0.990858	+	0.134912i	$0.0430751\pi$
$491$			5.97889i			0.269824i	−0.990858	+	0.134912i	$0.956925\pi$
$492$	−49.1992	+	12.8281i	−2.21807	+	0.578334i
$493$	6.22687	+	3.59509i	0.280444	+	0.161915i
$494$	−14.2051	−	8.20134i	−0.639120	−	0.368996i
$495$		0			0
$496$			8.09393i			0.363428i
$497$	−15.0109	+	6.99087i	−0.673330	+	0.313583i
$498$	2.59587	+	0.714349i	0.116323	+	0.0320108i
$499$	−4.24155	−	7.34658i	−0.189878	−	0.328878i	0.755331	−	0.655343i	$-0.227476\pi$
$499$	−4.24155	−	7.34658i	−0.189878	−	0.328878i	−0.945209	+	0.326465i	$0.894143\pi$
$500$		0			0
$501$	−4.34183	−	4.40077i	−0.193979	−	0.196612i
$502$	−30.4332	+	17.5706i	−1.35830	+	0.784216i
$503$	−17.0296			−0.759312			−0.379656	−	0.925128i	$-0.623958\pi$
$503$	−17.0296			−0.759312			−0.379656	+	0.925128i	$0.623958\pi$
$504$	−10.8670	−	24.1803i	−0.484055	−	1.07708i
$505$		0			0
$506$	−42.5508	+	24.5667i	−1.89161	+	1.09212i
$507$	3.31955	+	3.36461i	0.147426	+	0.149427i
$508$	−12.0077	+	20.7979i	−0.532755	+	0.922759i
$509$	6.43409	+	11.1442i	0.285186	+	0.493956i	0.972654	−	0.232258i	$-0.0746113\pi$
$509$	6.43409	+	11.1442i	0.285186	+	0.493956i	−0.687468	+	0.726214i	$0.741278\pi$
$510$		0			0
$511$	−0.0514110	+	0.584381i	−0.00227429	+	0.0258515i
$512$		−	10.3101i		−	0.455646i
$513$	−3.17528	+	10.9589i	−0.140192	+	0.483846i
$514$	−32.1148	−	18.5415i	−1.41652	−	0.817831i
$515$		0			0
$516$	0.679288	−	0.177116i	0.0299040	−	0.00779708i
$517$			7.34899i			0.323208i
$518$	0.220206	−	2.50305i	0.00967530	−	0.109978i
$519$	−3.92565	+	14.2654i	−0.172317	+	0.626181i
$520$		0			0
$521$	−8.32724	+	14.4232i	−0.364823	+	0.631892i	−0.988748	−	0.149592i	$-0.952204\pi$
$521$	−8.32724	+	14.4232i	−0.364823	+	0.631892i	0.623925	+	0.781485i	$0.285537\pi$
$522$	−49.7506	+	27.8361i	−2.17752	+	1.21835i
$523$	−31.4934	+	18.1827i	−1.37711	+	0.795075i	−0.991811	−	0.127716i	$-0.959235\pi$
$523$	−31.4934	+	18.1827i	−1.37711	+	0.795075i	−0.385300	+	0.922791i	$0.625902\pi$
$524$	33.9635			1.48370
$525$		0			0
$526$	−19.3549			−0.843912
$527$	−6.72605	+	3.88329i	−0.292991	+	0.169159i
$528$	3.16694	−	3.12453i	0.137823	−	0.135978i
$529$	16.9482	−	29.3551i	0.736876	−	1.27631i
$530$		0			0
$531$	10.5678	+	6.29276i	0.458602	+	0.273083i
$532$	−18.0790	+	8.41977i	−0.783826	+	0.365043i
$533$			27.4047i			1.18703i
$534$	−0.890797	−	3.41645i	−0.0385485	−	0.147844i
$535$		0			0
$536$	4.64026	+	2.67906i	0.200429	+	0.115718i
$537$	0.537300	+	2.06070i	0.0231862	+	0.0889256i
$538$		−	40.5268i		−	1.74724i
$539$	−18.3889	+	6.67290i	−0.792064	+	0.287422i
$540$		0			0
$541$	−1.89575	−	3.28353i	−0.0815046	−	0.141170i	0.822392	−	0.568922i	$-0.192639\pi$
$541$	−1.89575	−	3.28353i	−0.0815046	−	0.141170i	−0.903896	+	0.427751i	$0.859306\pi$
$542$	−11.8775	+	20.5725i	−0.510184	+	0.883665i
$543$	−18.9872	+	18.7329i	−0.814818	+	0.803906i
$544$	3.46571	−	2.00093i	0.148591	−	0.0857890i
$545$		0			0
$546$	−33.7543	+	5.70069i	−1.44455	+	0.243967i
$547$	10.9382			0.467684			0.233842	−	0.972275i	$-0.424870\pi$
$547$	10.9382			0.467684			0.233842	+	0.972275i	$0.424870\pi$
$548$	37.4568	−	21.6257i	1.60008	−	0.923805i
$549$	18.0991	+	32.3480i	0.772452	+	1.38058i
$550$		0			0
$551$	8.95077	+	15.5032i	0.381316	+	0.660458i
$552$	−11.5776	+	42.0718i	−0.492776	+	1.79069i
$553$	4.76379	−	6.79641i	0.202577	−	0.289013i
$554$		−	22.2839i		−	0.946752i
$555$		0			0
$556$	2.93766	+	1.69606i	0.124584	+	0.0719288i
$557$	−8.42853	−	4.86622i	−0.357128	−	0.206188i	0.310692	−	0.950511i	$-0.399439\pi$
$557$	−8.42853	−	4.86622i	−0.357128	−	0.206188i	−0.667820	+	0.744322i	$0.732773\pi$
$558$	0.830175	−	61.5730i	0.0351441	−	2.60659i
$559$		−	0.378374i		−	0.0160035i
$560$		0			0
$561$	4.11591	+	1.13265i	0.173774	+	0.0478203i
$562$	13.8965	+	24.0694i	0.586187	+	1.01531i
$563$	−0.235135	+	0.407265i	−0.00990975	+	0.0171642i	−0.870938	−	0.491393i	$-0.836488\pi$
$563$	−0.235135	+	0.407265i	−0.00990975	+	0.0171642i	0.861028	+	0.508558i	$0.169821\pi$
$564$	10.9818	+	11.1308i	0.462415	+	0.468692i
$565$		0			0
$566$	−46.5459			−1.95647
$567$	9.46725	+	21.8488i	0.397587	+	0.917564i
$568$	−20.9037			−0.877100
$569$	−5.38387	+	3.10838i	−0.225703	+	0.130310i	−0.608588	−	0.793486i	$-0.708264\pi$
$569$	−5.38387	+	3.10838i	−0.225703	+	0.130310i	0.382885	+	0.923796i	$0.374931\pi$
$570$		0			0
$571$	−5.31121	+	9.19928i	−0.222267	+	0.384978i	−0.955496	−	0.295004i	$-0.904679\pi$
$571$	−5.31121	+	9.19928i	−0.222267	+	0.384978i	0.733229	+	0.679982i	$0.238012\pi$
$572$	−15.3731	−	26.6270i	−0.642782	−	1.11333i
$573$	−24.2572	−	6.67528i	−1.01336	−	0.278864i
$574$	43.1817	+	30.2672i	1.80237	+	1.26333i
$575$		0			0
$576$	−0.502107	+	37.2406i	−0.0209211	+	1.55169i
$577$	2.56914	+	1.48330i	0.106955	+	0.0617504i	0.552523	−	0.833497i	$-0.313665\pi$
$577$	2.56914	+	1.48330i	0.106955	+	0.0617504i	−0.445568	+	0.895248i	$0.646998\pi$
$578$	32.7459	+	18.9058i	1.36205	+	0.786380i
$579$	−0.675677	+	0.176174i	−0.0280802	+	0.00732155i
$580$		0			0
$581$	−0.744909	−	1.59948i	−0.0309040	−	0.0663576i
$582$	−6.82566	+	24.8037i	−0.282933	+	1.02815i
$583$	−10.4358	−	18.0753i	−0.432205	−	0.748601i
$584$	−0.370280	+	0.641344i	−0.0153223	+	0.0265390i
$585$		0			0
$586$	−6.07641	+	3.50821i	−0.251014	+	0.144923i
$587$	−18.8819			−0.779341			−0.389670	−	0.920954i	$-0.627411\pi$
$587$	−18.8819			−0.779341			−0.389670	+	0.920954i	$0.627411\pi$
$588$	−17.8804	+	37.5856i	−0.737375	+	1.55001i
$589$	−19.3366			−0.796751
$590$		0			0
$591$	14.3907	−	14.1980i	0.591955	−	0.584027i
$592$	0.187247	−	0.324322i	0.00769582	−	0.0133296i
$593$	−15.1472	−	26.2357i	−0.622020	−	1.07737i	−0.989109	−	0.147185i	$-0.952979\pi$
$593$	−15.1472	−	26.2357i	−0.622020	−	1.07737i	0.367088	−	0.930186i	$-0.380355\pi$
$594$	−24.4123	+	23.4444i	−1.00165	+	0.961936i
$595$		0			0
$596$		−	60.8887i		−	2.49410i
$597$	−8.11836	−	31.1362i	−0.332262	−	1.27432i
$598$	48.7976	+	28.1733i	1.99548	+	1.15209i
$599$	6.29024	+	3.63167i	0.257012	+	0.148386i	0.622971	−	0.782245i	$-0.285925\pi$
$599$	6.29024	+	3.63167i	0.257012	+	0.148386i	−0.365959	+	0.930631i	$0.619259\pi$
$600$		0			0
$601$			45.3302i			1.84906i	0.381110	+	0.924530i	$0.375542\pi$
$601$			45.3302i			1.84906i	−0.381110	+	0.924530i	$0.624458\pi$
$602$	−0.596204	−	0.417896i	−0.0242995	−	0.0170322i
$603$	−4.13515	−	2.46235i	−0.168396	−	0.100275i
$604$	−38.6216	−	66.8946i	−1.57149	−	2.72190i
$605$		0			0
$606$	30.5360	−	30.1271i	1.24044	−	1.22383i
$607$	−22.5370	+	13.0117i	−0.914748	+	0.528130i	−0.881956	−	0.471332i	$-0.843773\pi$
$607$	−22.5370	+	13.0117i	−0.914748	+	0.528130i	−0.0327925	+	0.999462i	$0.510440\pi$
$608$	9.96351			0.404073
$609$	35.0141	+	13.0313i	1.41884	+	0.528054i
$610$		0			0
$611$	7.29877	−	4.21394i	0.295276	−	0.170478i
$612$	7.92651	−	4.43498i	0.320410	−	0.179273i
$613$	12.8525	−	22.2611i	0.519106	−	0.899118i	−0.480648	−	0.876914i	$-0.659598\pi$
$613$	12.8525	−	22.2611i	0.519106	−	0.899118i	0.999753	−	0.0222040i	$-0.00706833\pi$
$614$	−23.7507	−	41.1375i	−0.958502	−	1.66017i
$615$		0			0
$616$	−24.5999	−	2.16417i	−0.991157	−	0.0871971i
$617$		−	8.88258i		−	0.357599i	−0.983886	−	0.178800i	$-0.942779\pi$
$617$		−	8.88258i		−	0.357599i	0.983886	−	0.178800i	$-0.0572213\pi$
$618$	3.91898	−	1.02182i	0.157644	−	0.0411037i
$619$	−26.4112	−	15.2485i	−1.06156	−	0.612890i	−0.135694	−	0.990751i	$-0.543327\pi$
$619$	−26.4112	−	15.2485i	−1.06156	−	0.612890i	−0.925863	+	0.377861i	$0.876660\pi$
$620$		0			0
$621$	10.9077	−	37.6460i	0.437713	−	1.51068i
$622$		−	63.5669i		−	2.54880i
$623$	−1.32807	+	1.89473i	−0.0532079	+	0.0759108i
$624$	−4.91911	−	1.35368i	−0.196922	−	0.0541904i
$625$		0			0
$626$	−0.735048	+	1.27314i	−0.0293784	+	0.0508849i
$627$	7.46458	+	7.56590i	0.298107	+	0.302153i
$628$	35.3549	−	20.4121i	1.41081	−	0.814533i
$629$	0.359349			0.0143282
$630$		0			0
$631$	44.3335			1.76489			0.882445	−	0.470416i	$-0.155896\pi$
$631$	44.3335			1.76489			0.882445	+	0.470416i	$0.155896\pi$
$632$	9.07367	−	5.23868i	0.360931	−	0.208384i
$633$	8.49303	+	8.60831i	0.337568	+	0.342150i
$634$	−29.6372	+	51.3332i	−1.17705	+	2.03870i
$635$		0			0
$636$	−42.8163	−	11.7825i	−1.69778	−	0.467206i
$637$	17.1715	+	14.4369i	0.680361	+	0.572011i
$638$			53.1052i			2.10245i
$639$	18.7744	+	0.253131i	0.742703	+	0.0100137i
$640$		0			0
$641$	6.03197	+	3.48256i	0.238249	+	0.137553i	0.614371	−	0.789017i	$-0.289410\pi$
$641$	6.03197	+	3.48256i	0.238249	+	0.137553i	−0.376123	+	0.926570i	$0.622743\pi$
$642$	49.9139	−	13.0144i	1.96994	−	0.513637i
$643$			25.8907i			1.02103i	0.859869	+	0.510514i	$0.170545\pi$
$643$			25.8907i			1.02103i	−0.859869	+	0.510514i	$0.829455\pi$
$644$	62.1053	−	28.9237i	2.44729	−	1.13975i
$645$		0			0
$646$	−2.25691	−	3.90908i	−0.0887968	−	0.153801i
$647$	−5.01859	+	8.69245i	−0.197301	+	0.341735i	−0.947652	−	0.319304i	$-0.896551\pi$
$647$	−5.01859	+	8.69245i	−0.197301	+	0.341735i	0.750351	+	0.661039i	$0.229884\pi$
$648$	−0.810424	+	30.0486i	−0.0318365	+	1.18042i
$649$	9.92232	−	5.72866i	0.389485	−	0.224869i
$650$		0			0
$651$	−31.1006	+	25.7159i	−1.21893	+	1.00789i
$652$	29.2594			1.14589
$653$	−34.2946	+	19.8000i	−1.34205	+	0.774833i	−0.987108	−	0.160055i	$-0.948833\pi$
$653$	−34.2946	+	19.8000i	−1.34205	+	0.774833i	−0.354942	+	0.934888i	$0.615500\pi$
$654$	−0.0524410	+	0.0517388i	−0.00205061	+	0.00202315i
$655$		0			0
$656$	3.92965	+	6.80635i	0.153427	+	0.265744i
$657$	0.340329	−	0.571531i	0.0132775	−	0.0222975i
$658$	1.42122	−	16.1548i	0.0554048	−	0.629779i
$659$			17.9364i			0.698705i	0.936991	+	0.349352i	$0.113598\pi$
$659$			17.9364i			0.698705i	−0.936991	+	0.349352i	$0.886402\pi$
$660$		0			0
$661$	−3.31012	−	1.91110i	−0.128749	−	0.0743332i	0.434242	−	0.900796i	$-0.357016\pi$
$661$	−3.31012	−	1.91110i	−0.128749	−	0.0743332i	−0.562991	+	0.826463i	$0.690350\pi$
$662$	−23.2003	−	13.3947i	−0.901705	−	0.520599i
$663$	−1.23517	−	4.73724i	−0.0479702	−	0.183979i
$664$		−	2.22739i		−	0.0864393i
$665$		0			0
$666$	−1.45771	+	2.44801i	−0.0564852	+	0.0948585i
$667$	−30.7478	−	53.2567i	−1.19056	−	2.06211i
$668$	−6.12645	+	10.6113i	−0.237039	+	0.410564i
$669$	−1.78280	+	1.75893i	−0.0689271	+	0.0680040i
$670$		0			0
$671$	34.5292			1.33299
$672$	16.0251	−	13.2506i	0.618181	−	0.511151i
$673$	−1.08304			−0.0417483			−0.0208741	−	0.999782i	$-0.506645\pi$
$673$	−1.08304			−0.0417483			−0.0208741	+	0.999782i	$0.506645\pi$
$674$	32.7094	−	18.8848i	1.25992	−	0.727415i
$675$		0			0
$676$	4.68398	−	8.11288i	0.180153	−	0.312034i
$677$	15.5014	+	26.8492i	0.595766	+	1.03190i	0.993438	+	0.114370i	$0.0364849\pi$
$677$	15.5014	+	26.8492i	0.595766	+	1.03190i	−0.397672	+	0.917528i	$0.630182\pi$
$678$	−7.74478	+	28.1436i	−0.297436	+	1.08085i
$679$	15.2831	−	7.11767i	0.586513	−	0.273151i
$680$		0			0
$681$	1.78852	−	0.466333i	0.0685362	−	0.0178699i
$682$	−49.6772	−	28.6812i	−1.90224	−	1.09826i
$683$	16.5419	+	9.55050i	0.632960	+	0.365440i	0.781898	−	0.623407i	$-0.214252\pi$
$683$	16.5419	+	9.55050i	0.632960	+	0.365440i	−0.148937	+	0.988847i	$0.547585\pi$
$684$	22.6118	+	0.304869i	0.864583	+	0.0116570i
$685$		0			0
$686$	41.7134	−	11.1124i	1.59263	−	0.424272i
$687$	−12.6894	−	3.49198i	−0.484133	−	0.133227i
$688$	−0.0542562	−	0.0939745i	−0.00206850	−	0.00358275i
$689$	−11.9678	+	20.7289i	−0.455937	+	0.789707i
$690$		0			0
$691$	−14.5775	+	8.41632i	−0.554554	+	0.320172i	−0.750957	−	0.660351i	$-0.770407\pi$
$691$	−14.5775	+	8.41632i	−0.554554	+	0.320172i	0.196403	+	0.980523i	$0.437074\pi$
$692$	29.3250			1.11477
$693$	22.0678	+	2.24161i	0.838288	+	0.0851519i
$694$	41.9145			1.59105
$695$		0			0
$696$	33.1237	+	33.5733i	1.25555	+	1.27259i
$697$	−3.77072	+	6.53107i	−0.142826	+	0.247382i
$698$	7.17232	+	12.4228i	0.271476	+	0.470211i
$699$	−30.0589	−	8.27184i	−1.13693	−	0.312870i
$700$		0			0
$701$			21.8878i			0.826691i	0.910574	+	0.413345i	$0.135640\pi$
$701$			21.8878i			0.826691i	−0.910574	+	0.413345i	$0.864360\pi$
$702$	37.2823	+	10.8024i	1.40713	+	0.407709i
$703$	0.774814	+	0.447339i	0.0292227	+	0.0168717i
$704$	30.0458	+	17.3470i	1.13240	+	0.653789i
$705$		0			0
$706$		−	68.6821i		−	2.58489i
$707$	−28.0038	−	2.46364i	−1.05319	−	0.0926547i
$708$	6.46794	−	23.5038i	0.243080	−	0.883326i
$709$	5.41030	+	9.37091i	0.203188	+	0.351932i	0.949554	−	0.313604i	$-0.101536\pi$
$709$	5.41030	+	9.37091i	0.203188	+	0.351932i	−0.746366	+	0.665536i	$0.768203\pi$
$710$		0			0
$711$	−8.21283	+	4.59518i	−0.308005	+	0.172333i
$712$	−2.52959	+	1.46046i	−0.0948005	+	0.0547331i
$713$	66.4253			2.48765
$714$	−8.82867	−	3.28579i	−0.330405	−	0.122968i
$715$		0			0
$716$	3.65536	−	2.11042i	0.136607	−	0.0788703i
$717$	36.8432	−	36.3498i	1.37593	−	1.35751i
$718$	−41.0753	+	71.1445i	−1.53292	+	2.65509i
$719$	11.1296	+	19.2770i	0.415064	+	0.718912i	0.995435	−	0.0954404i	$-0.0304259\pi$
$719$	11.1296	+	19.2770i	0.415064	+	0.718912i	−0.580371	+	0.814352i	$0.697093\pi$
$720$		0			0
$721$	−2.17342	−	1.52341i	−0.0809425	−	0.0567348i
$722$			33.0483i			1.22993i
$723$	2.28969	+	8.78160i	0.0851545	+	0.326591i
$724$	45.7827	+	26.4327i	1.70150	+	0.982362i
$725$		0			0
$726$	−3.24955	−	12.4629i	−0.120602	−	0.462543i
$727$			43.7899i			1.62408i	0.583604	+	0.812038i	$0.301642\pi$
$727$			43.7899i			1.62408i	−0.583604	+	0.812038i	$0.698358\pi$
$728$	11.9563	+	25.6727i	0.443129	+	0.951493i
$729$	1.09174	−	26.9779i	0.0404349	−	0.999182i
$730$		0			0
$731$	0.0520618	−	0.0901738i	0.00192558	−	0.00333520i
$732$	52.2981	−	51.5977i	1.93299	−	1.90711i
$733$	−22.6647	+	13.0854i	−0.837138	+	0.483322i	−0.856290	−	0.516495i	$-0.827237\pi$
$733$	−22.6647	+	13.0854i	−0.837138	+	0.483322i	0.0191524	+	0.999817i	$0.493903\pi$
$734$	−81.1776			−2.99632
$735$		0			0
$736$	−34.2267			−1.26161
$737$	−3.88259	+	2.24161i	−0.143017	+	0.0825709i
$738$	−29.1959	−	52.1811i	−1.07472	−	1.92081i
$739$	−20.1777	+	34.9489i	−0.742250	+	1.28561i	0.209219	+	0.977869i	$0.432908\pi$
$739$	−20.1777	+	34.9489i	−0.742250	+	1.28561i	−0.951469	+	0.307746i	$0.900425\pi$
$740$		0			0
$741$	3.23397	−	11.7519i	0.118803	−	0.431716i
$742$	19.4446	+	41.7517i	0.713835	+	1.53275i
$743$		−	8.82565i		−	0.323782i	−0.986809	−	0.161891i	$-0.948241\pi$
$743$		−	8.82565i		−	0.323782i	0.986809	−	0.161891i	$-0.0517593\pi$
$744$	−49.2957	+	12.8532i	−1.80727	+	0.471222i
$745$		0			0
$746$	40.9251	+	23.6281i	1.49838	+	0.865087i
$747$	−0.0269722	+	2.00050i	−0.000986863	+	0.0731943i
$748$		−	8.46097i		−	0.309364i
$749$	−27.6817	−	19.4029i	−1.01147	−	0.708965i
$750$		0			0
$751$	−18.9165	−	32.7644i	−0.690274	−	1.19559i	−0.971748	−	0.236020i	$-0.924157\pi$
$751$	−18.9165	−	32.7644i	−0.690274	−	1.19559i	0.281475	−	0.959569i	$-0.409176\pi$
$752$	1.20850	−	2.09319i	0.0440695	−	0.0763307i
$753$	−18.3400	−	18.5889i	−0.668346	−	0.677418i
$754$	52.7422	−	30.4507i	1.92076	−	1.10895i
$755$		0			0
$756$	36.7737	−	29.5813i	1.33745	−	1.07586i
$757$	34.7636			1.26351			0.631753	−	0.775170i	$-0.282336\pi$
$757$	34.7636			1.26351			0.631753	+	0.775170i	$0.282336\pi$
$758$	−18.3127	+	10.5728i	−0.665146	+	0.384022i
$759$	−25.6424	−	25.9905i	−0.930760	−	0.943394i
$760$		0			0
$761$	−0.915074	−	1.58495i	−0.0331714	−	0.0574545i	0.848963	−	0.528452i	$-0.177227\pi$
$761$	−0.915074	−	1.58495i	−0.0331714	−	0.0574545i	−0.882135	+	0.470998i	$0.843894\pi$
$762$	−27.2303	−	7.49342i	−0.986448	−	0.271458i
$763$	0.0480923	+	0.00423093i	0.00174106	+	0.000153170i
$764$			49.8649i			1.80405i
$765$		0			0
$766$	56.0686	+	32.3712i	2.02584	+	1.16962i
$767$	−11.3790	−	6.56967i	−0.410872	−	0.237217i
$768$	35.9769	−	9.38051i	1.29820	−	0.338490i
$769$		−	23.5601i		−	0.849598i	−0.905288	−	0.424799i	$-0.860345\pi$
$769$		−	23.5601i		−	0.849598i	0.905288	−	0.424799i	$-0.139655\pi$
$770$		0			0
$771$	7.31132	−	26.5685i	0.263311	−	0.956842i
$772$	0.691982	+	1.19855i	0.0249050	+	0.0431367i
$773$	24.0437	−	41.6448i	0.864790	−	1.49786i	−0.00246461	−	0.999997i	$-0.500785\pi$
$773$	24.0437	−	41.6448i	0.864790	−	1.49786i	0.867255	−	0.497864i	$-0.165882\pi$
$774$	0.403105	+	0.720458i	0.0144893	+	0.0258963i
$775$		0			0
$776$	21.2828			0.764010
$777$	1.84111	−	0.310942i	0.0660496	−	0.0111550i
$778$	−36.3198			−1.30213
$779$	−16.2606	+	9.38804i	−0.582595	+	0.336361i
$780$		0			0
$781$	8.74525	−	15.1472i	0.312930	−	0.542010i
$782$	7.75294	+	13.4285i	0.277245	+	0.480202i
$783$	−29.3431	−	30.5546i	−1.04864	−	1.09193i
$784$	6.33495	+	1.12333i	0.226248	+	0.0401189i
$785$		0			0
$786$	10.0774	+	38.6495i	0.359447	+	1.37858i
$787$	26.1234	+	15.0823i	0.931197	+	0.537627i	0.887190	−	0.461404i	$-0.152654\pi$
$787$	26.1234	+	15.0823i	0.931197	+	0.537627i	0.0440072	+	0.999031i	$0.485988\pi$
$788$	−34.6995	−	20.0338i	−1.23612	−	0.713673i
$789$	−3.62873	−	13.9172i	−0.129186	−	0.495465i
$790$		0			0
$791$	17.3411	−	8.07610i	0.616579	−	0.287153i
$792$	24.0589	+	14.3263i	0.854897	+	0.509064i
$793$	−19.7992	−	34.2932i	−0.703090	−	1.21779i
$794$	22.0156	−	38.1321i	0.781303	−	1.35326i
$795$		0			0
$796$	−55.2309	+	31.8876i	−1.95761	+	1.13022i
$797$	−3.60475			−0.127687			−0.0638435	−	0.997960i	$-0.520336\pi$
$797$	−3.60475			−0.127687			−0.0638435	+	0.997960i	$0.520336\pi$
$798$	−14.9457	−	18.0752i	−0.529072	−	0.639854i
$799$	2.31925			0.0820491
$800$		0			0
$801$	2.28961	−	1.28106i	0.0808992	−	0.0452641i
$802$	24.2401	−	41.9851i	0.855948	−	1.48255i
$803$	−0.309820	−	0.536624i	−0.0109333	−	0.0189371i
$804$	−2.53089	+	9.19699i	−0.0892578	+	0.324353i
$805$		0			0
$806$			65.7836i			2.31713i
$807$	29.1410	−	7.59814i	1.02581	−	0.267467i
$808$	−30.7335	−	17.7440i	−1.08120	−	0.624232i
$809$	−18.7612	−	10.8318i	−0.659607	−	0.380824i	0.132520	−	0.991180i	$-0.457693\pi$
$809$	−18.7612	−	10.8318i	−0.659607	−	0.380824i	−0.792127	+	0.610356i	$0.791026\pi$
$810$		0			0
$811$		−	27.6526i		−	0.971015i	−0.874232	−	0.485508i	$-0.838635\pi$
$811$		−	27.6526i		−	0.971015i	0.874232	−	0.485508i	$-0.161365\pi$
$812$	6.48933	−	73.7633i	0.227731	−	2.58858i
$813$	−17.0196	−	4.68358i	−0.596904	−	0.164260i
$814$	1.32704	+	2.29850i	0.0465126	+	0.0805623i
$815$		0			0
$816$	−0.986061	−	0.999446i	−0.0345190	−	0.0349876i
$817$	0.224508	−	0.129620i	0.00785453	−	0.00453481i
$818$	67.1957			2.34944
$819$	−10.4275	−	23.2024i	−0.364366	−	0.810756i
$820$		0			0
$821$	12.2722	−	7.08534i	0.428302	−	0.247280i	−0.270321	−	0.962770i	$-0.587130\pi$
$821$	12.2722	−	7.08534i	0.428302	−	0.247280i	0.698623	+	0.715490i	$0.253797\pi$
$822$	35.7233	+	36.2082i	1.24599	+	1.26291i
$823$	11.6538	−	20.1850i	0.406227	−	0.703605i	−0.588237	−	0.808689i	$-0.700178\pi$
$823$	11.6538	−	20.1850i	0.406227	−	0.703605i	0.994463	+	0.105084i	$0.0335110\pi$
$824$	−1.67528	−	2.90167i	−0.0583611	−	0.101084i
$825$		0			0
$826$	−22.9194	+	10.6740i	−0.797468	+	0.371397i
$827$			32.0877i			1.11580i	0.829908	+	0.557900i	$0.188393\pi$
$827$			32.0877i			1.11580i	−0.829908	+	0.557900i	$0.811607\pi$
$828$	−77.6762	−	1.04729i	−2.69943	−	0.0363959i
$829$	25.9947	+	15.0080i	0.902833	+	0.521251i	0.878118	−	0.478444i	$-0.158799\pi$
$829$	25.9947	+	15.0080i	0.902833	+	0.521251i	0.0247149	+	0.999695i	$0.492132\pi$
$830$		0			0
$831$	16.0233	−	4.17788i	0.555843	−	0.144929i
$832$		−	39.7873i		−	1.37938i
$833$	2.10588	+	5.80329i	0.0729645	+	0.201072i
$834$	−1.05843	+	3.84621i	−0.0366503	+	0.133183i
$835$		0			0
$836$	10.5327	−	18.2432i	0.364282	−	0.630956i
$837$	44.4299	−	10.9470i	1.53572	−	0.378384i
$838$	−6.55031	+	3.78182i	−0.226277	+	0.130641i
$839$	28.6277			0.988337			0.494168	−	0.869366i	$-0.335473\pi$
$839$	28.6277			0.988337			0.494168	+	0.869366i	$0.335473\pi$
$840$		0			0
$841$	−37.4666			−1.29195
$842$	56.3835	−	32.5530i	1.94310	−	1.12185i
$843$	−14.7018	+	14.5049i	−0.506358	+	0.499577i
$844$	11.9839	−	20.7567i	0.412503	−	0.714476i
$845$		0			0
$846$	−9.40813	+	15.7995i	−0.323458	+	0.543200i
$847$	−4.84468	+	6.91181i	−0.166465	+	0.237493i
$848$			6.86441i			0.235725i
$849$	−8.72661	−	33.4690i	−0.299497	−	1.14865i
$850$		0			0
$851$	−2.66165	−	1.53670i	−0.0912401	−	0.0526775i
$852$	−9.38921	−	36.0102i	−0.321669	−	1.23369i
$853$			17.3563i			0.594269i	0.954836	+	0.297135i	$0.0960310\pi$
$853$			17.3563i			0.594269i	−0.954836	+	0.297135i	$0.903969\pi$
$854$	−75.9031	−	6.67758i	−2.59735	−	0.228502i
$855$		0			0
$856$	−21.3371	−	36.9569i	−0.729287	−	1.26316i
$857$	23.2842	−	40.3294i	0.795372	−	1.37763i	−0.127230	−	0.991873i	$-0.540609\pi$
$857$	23.2842	−	40.3294i	0.795372	−	1.37763i	0.922602	−	0.385752i	$-0.126058\pi$
$858$	25.7394	−	25.3947i	0.878728	−	0.866960i
$859$	31.5359	−	18.2072i	1.07599	−	0.621223i	0.146178	−	0.989258i	$-0.453303\pi$
$859$	31.5359	−	18.2072i	1.07599	−	0.621223i	0.929812	+	0.368035i	$0.119969\pi$
$860$		0			0
$861$	−13.6679	+	36.7246i	−0.465800	+	1.25157i
$862$	−89.3002			−3.04158
$863$	2.05942	−	1.18901i	0.0701034	−	0.0404742i	−0.464539	−	0.885553i	$-0.653780\pi$
$863$	2.05942	−	1.18901i	0.0701034	−	0.0404742i	0.534642	+	0.845079i	$0.320446\pi$
$864$	−22.8933	+	5.64063i	−0.778844	+	0.191898i
$865$		0			0
$866$	33.7430	+	58.4447i	1.14664	+	1.98603i
$867$	−7.45499	+	27.0906i	−0.253185	+	0.920045i
$868$	65.4971	+	45.9087i	2.22312	+	1.55824i
$869$			8.76660i			0.297387i
$870$		0			0
$871$	4.45259	+	2.57070i	0.150870	+	0.0871049i
$872$	0.0527802	+	0.0304727i	0.00178736	+	0.00103193i
$873$	−19.1149	−	0.257722i	−0.646942	−	0.00872257i
$874$			38.6054i			1.30585i
$875$		0			0
$876$	−1.27114	−	0.349803i	−0.0429480	−	0.0118187i
$877$	−11.0465	−	19.1332i	−0.373015	−	0.646082i	0.617012	−	0.786953i	$-0.288343\pi$
$877$	−11.0465	−	19.1332i	−0.373015	−	0.646082i	−0.990028	+	0.140872i	$0.955009\pi$
$878$	−17.7901	+	30.8134i	−0.600387	+	1.03990i
$879$	−3.66183	−	3.71153i	−0.123510	−	0.125187i
$880$		0			0
$881$	−33.5633			−1.13078			−0.565388	−	0.824825i	$-0.691273\pi$
$881$	−33.5633			−1.13078			−0.565388	+	0.824825i	$0.691273\pi$
$882$	−48.0767	−	9.19527i	−1.61883	−	0.309621i
$883$	3.74124			0.125903			0.0629514	−	0.998017i	$-0.479949\pi$
$883$	3.74124			0.125903			0.0629514	+	0.998017i	$0.479949\pi$
$884$	−8.40314	+	4.85156i	−0.282628	+	0.163176i
$885$		0			0
$886$	2.66151	−	4.60988i	0.0894153	−	0.154872i
$887$	13.7685	+	23.8478i	0.462302	+	0.800730i	0.999075	−	0.0429963i	$-0.0136904\pi$
$887$	13.7685	+	23.8478i	0.462302	+	0.800730i	−0.536773	+	0.843726i	$0.680357\pi$
$888$	2.27262	+	0.625396i	0.0762641	+	0.0209869i
$889$	7.81399	+	16.7783i	0.262073	+	0.562726i
$890$		0			0
$891$	−21.4347	−	13.1583i	−0.718090	−	0.440821i
$892$	4.29877	+	2.48189i	0.143933	+	0.0831000i
$893$	5.00068	+	2.88714i	0.167341	+	0.0966146i
$894$	69.2895	−	18.0663i	2.31739	−	0.604229i
$895$		0			0
$896$	−43.0313	−	30.1618i	−1.43758	−	1.00764i
$897$	−11.1094	+	40.3702i	−0.370931	+	1.34792i
$898$	12.0171	+	20.8142i	0.401015	+	0.694579i
$899$	35.8974	−	62.1762i	1.19725	−	2.07369i
$900$		0			0
$901$	−5.70432	+	3.29339i	−0.190038	+	0.109719i
$902$	−55.6995			−1.85459
$903$	0.188711	−	0.507052i	0.00627990	−	0.0168736i
$904$	24.1487			0.803174
$905$		0			0
$906$	64.6646	−	63.7987i	2.14834	−	2.11957i
$907$	19.3650	−	33.5412i	0.643005	−	1.11372i	−0.341754	−	0.939790i	$-0.611021\pi$
$907$	19.3650	−	33.5412i	0.643005	−	1.11372i	0.984758	−	0.173928i	$-0.0556459\pi$
$908$	−1.83168	−	3.17256i	−0.0607864	−	0.105285i
$909$	27.3880	+	16.3087i	0.908404	+	0.540926i
$910$		0			0
$911$		−	23.3967i		−	0.775167i	−0.921835	−	0.387583i	$-0.873310\pi$
$911$		−	23.3967i		−	0.775167i	0.921835	−	0.387583i	$-0.126690\pi$
$912$	−0.881938	−	3.38248i	−0.0292039	−	0.112005i
$913$	1.61401	+	0.931847i	0.0534158	+	0.0308396i
$914$	66.2043	+	38.2231i	2.18984	+	1.26431i
$915$		0			0
$916$			26.0854i			0.861886i
$917$	15.0241	−	21.4346i	0.496139	−	0.707833i
$918$	7.39876	+	7.70422i	0.244195	+	0.254277i
$919$	4.32329	+	7.48816i	0.142612	+	0.247012i	0.928480	−	0.371383i	$-0.121116\pi$
$919$	4.32329	+	7.48816i	0.142612	+	0.247012i	−0.785867	+	0.618395i	$0.787783\pi$
$920$		0			0
$921$	25.1272	−	24.7907i	0.827969	−	0.816881i
$922$	33.4434	−	19.3086i	1.10140	−	0.635894i
$923$	−20.0583			−0.660225
$924$	−7.32123	−	43.3496i	−0.240851	−	1.42610i
$925$		0			0
$926$	73.8532	−	42.6392i	2.42697	−	1.40121i
$927$	1.46949	+	2.62638i	0.0482644	+	0.0862616i
$928$	−18.4967	+	32.0373i	−0.607185	+	1.05168i
$929$	6.27980	+	10.8769i	0.206034	+	0.356861i	0.950462	−	0.310842i	$-0.100611\pi$
$929$	6.27980	+	10.8769i	0.206034	+	0.356861i	−0.744428	+	0.667703i	$0.767278\pi$
$930$		0			0
$931$	−2.68366	+	15.1344i	−0.0879535	+	0.496009i
$932$			61.7914i			2.02405i
$933$	45.7080	−	11.9178i	1.49641	−	0.390171i
$934$	−82.9840	−	47.9108i	−2.71532	−	1.56769i
$935$		0			0
$936$	0.432922	−	32.1093i	0.0141505	−	1.04952i
$937$			11.3901i			0.372097i	0.982541	+	0.186048i	$0.0595681\pi$
$937$			11.3901i			0.372097i	−0.982541	+	0.186048i	$0.940432\pi$
$938$	8.96833	−	4.17673i	0.292826	−	0.136375i
$939$	−1.05327	−	0.289846i	−0.0343720	−	0.00945875i
$940$		0			0
$941$	−21.0434	+	36.4482i	−0.685994	+	1.18818i	0.287129	+	0.957892i	$0.407299\pi$
$941$	−21.0434	+	36.4482i	−0.685994	+	1.18818i	−0.973123	+	0.230285i	$0.926034\pi$
$942$	33.7186	+	34.1763i	1.09861	+	1.11352i
$943$	55.8584	−	32.2499i	1.81900	−	1.05020i
$944$	−3.76818			−0.122644
$945$		0			0
$946$	0.769036			0.0250035
$947$	−12.6504	+	7.30370i	−0.411082	+	0.237338i	−0.691255	−	0.722611i	$-0.742942\pi$
$947$	−12.6504	+	7.30370i	−0.411082	+	0.237338i	0.280172	+	0.959950i	$0.409608\pi$
$948$	13.1001	+	13.2779i	0.425472	+	0.431247i
$949$	−0.355304	+	0.615405i	−0.0115337	+	0.0199769i
$950$		0			0
$951$	−42.4679	−	11.6866i	−1.37711	−	0.378965i
$952$	−0.682986	+	7.76340i	−0.0221357	+	0.251613i
$953$		−	28.8817i		−	0.935570i	−0.883842	−	0.467785i	$-0.845052\pi$
$953$		−	28.8817i		−	0.935570i	0.883842	−	0.467785i	$-0.154948\pi$
$954$	0.704066	−	52.2196i	0.0227950	−	1.69067i
$955$		0			0
$956$	−88.8379	−	51.2906i	−2.87322	−	1.65886i
$957$	−38.1855	+	9.95637i	−1.23436	+	0.321844i
$958$			38.5032i			1.24398i
$959$	2.92127	−	33.2056i	0.0943326	−	1.07226i
$960$		0			0
$961$	23.2751	+	40.3137i	0.750811	+	1.30044i
$962$	1.52186	−	2.63594i	0.0490667	−	0.0849860i
$963$	18.7161	+	33.4508i	0.603118	+	1.07794i
$964$	15.5772	−	8.99352i	0.501709	−	0.289662i
$965$		0			0
$966$	51.3416	+	62.0920i	1.65189	+	1.99778i
$967$	−0.409782			−0.0131777			−0.00658885	−	0.999978i	$-0.502097\pi$
$967$	−0.409782			−0.0131777			−0.00658885	+	0.999978i	$0.502097\pi$
$968$	−9.22774	+	5.32764i	−0.296591	+	0.171237i
$969$	2.38770	−	2.35573i	0.0767041	−	0.0756768i
$970$		0			0
$971$	−2.64865	−	4.58759i	−0.0849991	−	0.147223i	0.820392	−	0.571802i	$-0.193755\pi$
$971$	−2.64865	−	4.58759i	−0.0849991	−	0.147223i	−0.905391	+	0.424579i	$0.860422\pi$
$972$	−52.1279	+	12.1007i	−1.67200	+	0.388129i
$973$	2.36989	−	1.10371i	0.0759753	−	0.0353832i
$974$			4.73634i			0.151762i
$975$		0			0
$976$	−9.83482	−	5.67814i	−0.314805	−	0.181753i
$977$	−24.1247	−	13.9284i	−0.771818	−	0.445610i	0.0617045	−	0.998094i	$-0.480346\pi$
$977$	−24.1247	−	13.9284i	−0.771818	−	0.445610i	−0.833523	+	0.552485i	$0.813680\pi$
$978$	8.68160	+	33.2964i	0.277607	+	1.06470i
$979$		−	2.44399i		−	0.0781102i
$980$		0			0
$981$	−0.0470348	−	0.0280077i	−0.00150171	−	0.000894219i
$982$	6.96799	+	12.0689i	0.222357	+	0.385134i
$983$	0.330614	−	0.572640i	0.0105449	−	0.0182644i	−0.860705	−	0.509104i	$-0.829977\pi$
$983$	0.330614	−	0.572640i	0.0105449	−	0.0182644i	0.871250	+	0.490840i	$0.163310\pi$
$984$	−35.2135	+	34.7419i	−1.12257	+	1.10753i
$985$		0			0
$986$	16.7593			0.533725
$987$	11.8826	−	2.00683i	0.378228	−	0.0638782i
$988$	−24.1581			−0.768571
$989$	−0.771231	+	0.445270i	−0.0245237	+	0.0141588i
$990$		0			0
$991$	25.3374	−	43.8856i	0.804868	−	1.39407i	−0.111513	−	0.993763i	$-0.535570\pi$
$991$	25.3374	−	43.8856i	0.804868	−	1.39407i	0.916380	−	0.400309i	$-0.131097\pi$
$992$	−19.9795	−	34.6055i	−0.634350	−	1.09873i
$993$	5.28182	−	19.1935i	0.167614	−	0.609089i
$994$	−22.1534	+	31.6058i	−0.702663	+	1.00248i
$995$		0			0
$996$	3.83706	−	1.00046i	0.121582	−	0.0317009i
$997$	−5.21879	−	3.01307i	−0.165281	−	0.0954249i	0.415078	−	0.909786i	$-0.363754\pi$
$997$	−5.21879	−	3.01307i	−0.165281	−	0.0954249i	−0.580359	+	0.814361i	$0.697088\pi$
$998$	−17.1239	−	9.88647i	−0.542047	−	0.312951i
$999$	−2.03355	−	0.589211i	−0.0643387	−	0.0186418i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.t.g.101.4		8
3.2	odd	2		525.2.t.f.101.1		8
5.2	odd	4		525.2.q.f.374.8		16
5.3	odd	4		525.2.q.f.374.1		16
5.4	even	2		105.2.s.c.101.1	yes	8
7.5	odd	6		525.2.t.f.26.1		8
15.2	even	4		525.2.q.e.374.1		16
15.8	even	4		525.2.q.e.374.8		16
15.14	odd	2		105.2.s.d.101.4	yes	8
21.5	even	6	inner	525.2.t.g.26.4		8
35.4	even	6		735.2.b.d.146.1		8
35.9	even	6		735.2.s.l.656.4		8
35.12	even	12		525.2.q.e.299.8		16
35.19	odd	6		105.2.s.d.26.4	yes	8
35.24	odd	6		735.2.b.c.146.1		8
35.33	even	12		525.2.q.e.299.1		16
35.34	odd	2		735.2.s.k.521.1		8
105.44	odd	6		735.2.s.k.656.1		8
105.47	odd	12		525.2.q.f.299.1		16
105.59	even	6		735.2.b.d.146.8		8
105.68	odd	12		525.2.q.f.299.8		16
105.74	odd	6		735.2.b.c.146.8		8
105.89	even	6		105.2.s.c.26.1	✓	8
105.104	even	2		735.2.s.l.521.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.1	✓	8	105.89	even	6
105.2.s.c.101.1	yes	8	5.4	even	2
105.2.s.d.26.4	yes	8	35.19	odd	6
105.2.s.d.101.4	yes	8	15.14	odd	2
525.2.q.e.299.1		16	35.33	even	12
525.2.q.e.299.8		16	35.12	even	12
525.2.q.e.374.1		16	15.2	even	4
525.2.q.e.374.8		16	15.8	even	4
525.2.q.f.299.1		16	105.47	odd	12
525.2.q.f.299.8		16	105.68	odd	12
525.2.q.f.374.1		16	5.3	odd	4
525.2.q.f.374.8		16	5.2	odd	4
525.2.t.f.26.1		8	7.5	odd	6
525.2.t.f.101.1		8	3.2	odd	2
525.2.t.g.26.4		8	21.5	even	6	inner
525.2.t.g.101.4		8	1.1	even	1	trivial
735.2.b.c.146.1		8	35.24	odd	6
735.2.b.c.146.8		8	105.74	odd	6
735.2.b.d.146.1		8	35.4	even	6
735.2.b.d.146.8		8	105.59	even	6
735.2.s.k.521.1		8	35.34	odd	2
735.2.s.k.656.1		8	105.44	odd	6
735.2.s.l.521.4		8	105.104	even	2
735.2.s.l.656.4		8	35.9	even	6

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.01859 - 1.16543i) q^{2} +(1.21646 + 1.23297i) q^{3} +(1.71646 - 2.97300i) q^{4} +(3.89248 + 1.07116i) q^{6} +(-1.11699 - 2.39840i) q^{7} -3.33995i q^{8} +(-0.0404447 + 2.99973i) q^{9} +O(q^{10})\)	\(q+(2.01859 - 1.16543i) q^{2} +(1.21646 + 1.23297i) q^{3} +(1.71646 - 2.97300i) q^{4} +(3.89248 + 1.07116i) q^{6} +(-1.11699 - 2.39840i) q^{7} -3.33995i q^{8} +(-0.0404447 + 2.99973i) q^{9} +(2.42019 + 1.39730i) q^{11} +(5.75363 - 1.50019i) q^{12} -3.20486i q^{13} +(-5.04991 - 3.53962i) q^{14} +(-0.459555 - 0.795973i) q^{16} +(0.440969 - 0.763780i) q^{17} +(3.41434 + 6.10234i) q^{18} +(1.90160 - 1.09789i) q^{19} +(1.59840 - 4.29478i) q^{21} +6.51381 q^{22} +(-6.53240 + 3.77148i) q^{23} +(4.11806 - 4.06291i) q^{24} +(-3.73505 - 6.46929i) q^{26} +(-3.74778 + 3.59918i) q^{27} +(-9.04771 - 0.795973i) q^{28} +8.15270i q^{29} +(-7.62645 - 4.40313i) q^{31} +(3.92965 + 2.26878i) q^{32} +(1.22124 + 4.68378i) q^{33} -2.05568i q^{34} +(8.84876 + 5.26916i) q^{36} +(0.203727 + 0.352865i) q^{37} +(2.55903 - 4.43237i) q^{38} +(3.95151 - 3.89859i) q^{39} -8.55098 q^{41} +(-1.77876 - 10.5322i) q^{42} +0.118062 q^{43} +(8.30832 - 4.79681i) q^{44} +(-8.79081 + 15.2261i) q^{46} +(1.31486 + 2.27740i) q^{47} +(0.422382 - 1.53489i) q^{48} +(-4.50469 + 5.35796i) q^{49} +(1.47814 - 0.385407i) q^{51} +(-9.52805 - 5.50102i) q^{52} +(-6.46794 - 3.73427i) q^{53} +(-3.37062 + 11.6330i) q^{54} +(-8.01054 + 3.73067i) q^{56} +(3.66689 + 1.00908i) q^{57} +(9.50142 + 16.4569i) q^{58} +(2.04991 - 3.55054i) q^{59} +(10.7004 - 6.17786i) q^{61} -20.5262 q^{62} +(7.23974 - 3.25365i) q^{63} +12.4147 q^{64} +(7.92380 + 8.03135i) q^{66} +(-0.802125 + 1.38932i) q^{67} +(-1.51381 - 2.62200i) q^{68} +(-12.5965 - 3.46641i) q^{69} -6.25869i q^{71} +(10.0189 + 0.135083i) q^{72} +(-0.192022 - 0.110864i) q^{73} +(0.822480 + 0.474859i) q^{74} -7.53794i q^{76} +(0.647967 - 7.36535i) q^{77} +(3.43292 - 12.4749i) q^{78} +(1.56849 + 2.71671i) q^{79} +(-8.99673 - 0.242646i) q^{81} +(-17.2609 + 9.96559i) q^{82} +0.666893 q^{83} +(-10.0248 - 12.1239i) q^{84} +(0.238319 - 0.137594i) q^{86} +(-10.0521 + 9.91745i) q^{87} +(4.66689 - 8.08330i) q^{88} +(-0.437271 - 0.757376i) q^{89} +(-7.68656 + 3.57978i) q^{91} +25.8944i q^{92} +(-3.84834 - 14.7594i) q^{93} +(5.30832 + 3.06476i) q^{94} +(1.98292 + 7.60504i) q^{96} +6.37221i q^{97} +(-2.84876 + 16.0654i) q^{98} +(-4.28939 + 7.20339i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - q^{3} + 3 q^{4} + 5 q^{6} - 2 q^{7} - 5 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 - q^3 + 3 * q^4 + 5 * q^6 - 2 * q^7 - 5 * q^9	\( 8 q + 3 q^{2} - q^{3} + 3 q^{4} + 5 q^{6} - 2 q^{7} - 5 q^{9} + 9 q^{12} - 12 q^{14} + q^{16} + 12 q^{17} + 19 q^{18} + 9 q^{19} + 19 q^{21} + 40 q^{22} - 27 q^{23} + 16 q^{24} - 6 q^{26} - 4 q^{27} - 3 q^{28} - 21 q^{31} - 21 q^{32} - 2 q^{33} + 9 q^{36} - 7 q^{37} + 12 q^{38} - 3 q^{39} - 30 q^{41} - 26 q^{42} - 16 q^{43} - 7 q^{46} + 6 q^{47} + 25 q^{48} - 4 q^{49} - 6 q^{51} - 30 q^{52} - 24 q^{53} + 17 q^{54} - 21 q^{56} - 6 q^{57} + 13 q^{58} - 12 q^{59} + 15 q^{61} - 24 q^{62} + 2 q^{63} + 38 q^{64} + 22 q^{66} - 4 q^{67} - 13 q^{69} + 14 q^{72} - 15 q^{73} + 54 q^{74} + 36 q^{77} + 6 q^{78} - 29 q^{79} - 41 q^{81} - 27 q^{82} - 30 q^{83} - 3 q^{84} + 9 q^{86} - 32 q^{87} + 2 q^{88} - 3 q^{89} - 3 q^{91} + 9 q^{93} - 24 q^{94} - 3 q^{96} + 39 q^{98} - 34 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - q^3 + 3 * q^4 + 5 * q^6 - 2 * q^7 - 5 * q^9 + 9 * q^12 - 12 * q^14 + q^16 + 12 * q^17 + 19 * q^18 + 9 * q^19 + 19 * q^21 + 40 * q^22 - 27 * q^23 + 16 * q^24 - 6 * q^26 - 4 * q^27 - 3 * q^28 - 21 * q^31 - 21 * q^32 - 2 * q^33 + 9 * q^36 - 7 * q^37 + 12 * q^38 - 3 * q^39 - 30 * q^41 - 26 * q^42 - 16 * q^43 - 7 * q^46 + 6 * q^47 + 25 * q^48 - 4 * q^49 - 6 * q^51 - 30 * q^52 - 24 * q^53 + 17 * q^54 - 21 * q^56 - 6 * q^57 + 13 * q^58 - 12 * q^59 + 15 * q^61 - 24 * q^62 + 2 * q^63 + 38 * q^64 + 22 * q^66 - 4 * q^67 - 13 * q^69 + 14 * q^72 - 15 * q^73 + 54 * q^74 + 36 * q^77 + 6 * q^78 - 29 * q^79 - 41 * q^81 - 27 * q^82 - 30 * q^83 - 3 * q^84 + 9 * q^86 - 32 * q^87 + 2 * q^88 - 3 * q^89 - 3 * q^91 + 9 * q^93 - 24 * q^94 - 3 * q^96 + 39 * q^98 - 34 * q^99

Introduction

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