LMFDB - Embedded newform 525.2.t.f.26.1

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			26.1
Root			$-2.33086i$ of defining polynomial
Character	$\chi$	$=$	525.26
Dual form			525.2.t.f.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.01859 - 1.16543i) q^{2} +(1.67602 - 0.437000i) q^{3} +(1.71646 + 2.97300i) q^{4} +(-3.89248 - 1.07116i) q^{6} +(-1.11699 + 2.39840i) q^{7} -3.33995i q^{8} +(2.61806 - 1.46484i) q^{9} +O(q^{10})$	\(q+(-2.01859 - 1.16543i) q^{2} +(1.67602 - 0.437000i) q^{3} +(1.71646 + 2.97300i) q^{4} +(-3.89248 - 1.07116i) q^{6} +(-1.11699 + 2.39840i) q^{7} -3.33995i q^{8} +(2.61806 - 1.46484i) q^{9} +(-2.42019 + 1.39730i) q^{11} +(4.17602 + 4.23270i) q^{12} +3.20486i q^{13} +(5.04991 - 3.53962i) q^{14} +(-0.459555 + 0.795973i) q^{16} +(-0.440969 - 0.763780i) q^{17} +(-6.99195 - 0.0942709i) q^{18} +(1.90160 + 1.09789i) q^{19} +(-0.823984 + 4.50789i) q^{21} +6.51381 q^{22} +(6.53240 + 3.77148i) q^{23} +(-1.45956 - 5.59780i) 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} +(-3.44566 + 3.39951i) q^{33} +2.05568i q^{34} +(8.84876 + 5.26916i) q^{36} +(0.203727 - 0.352865i) q^{37} +(-2.55903 - 4.43237i) q^{38} +(1.40052 + 5.37140i) q^{39} +8.55098 q^{41} +(6.91692 - 8.13927i) 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} +(-1.07284 - 1.08741i) q^{51} +(-9.52805 + 5.50102i) q^{52} +(6.46794 - 3.73427i) q^{53} +(-11.7598 + 2.89748i) 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} +(0.588936 + 7.91537i) q^{63} +12.4147 q^{64} +(10.9173 - 2.84653i) q^{66} +(-0.802125 - 1.38932i) q^{67} +(1.51381 - 2.62200i) q^{68} +(12.5965 + 3.46641i) q^{69} -6.25869i q^{71} +(-4.89248 - 8.74419i) 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} +(4.70850 - 7.67007i) q^{81} +(-17.2609 - 9.96559i) q^{82} -0.666893 q^{83} +(-14.8163 + 5.28791i) q^{84} +(-0.238319 - 0.137594i) q^{86} +(3.56273 + 13.6641i) q^{87} +(4.66689 + 8.08330i) q^{88} +(0.437271 - 0.757376i) q^{89} +(-7.68656 - 3.57978i) q^{91} +25.8944i q^{92} +(-10.8579 + 10.7125i) q^{93} +(5.30832 - 3.06476i) q^{94} +(-5.59470 + 5.51978i) 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} - 2 q^{3} + 3 q^{4} - 5 q^{6} - 2 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - 5 * q^6 - 2 * q^7 + 4 * q^9	$ 8 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - 5 q^{6} - 2 q^{7} + 4 q^{9} + 18 q^{12} + 12 q^{14} + q^{16} - 12 q^{17} - 26 q^{18} + 9 q^{19} - 22 q^{21} + 40 q^{22} + 27 q^{23} - 7 q^{24} + 6 q^{26} + 4 q^{27} - 3 q^{28} - 21 q^{31} + 21 q^{32} - 4 q^{33} + 9 q^{36} - 7 q^{37} - 12 q^{38} + 15 q^{39} + 30 q^{41} + 5 q^{42} - 16 q^{43} - 7 q^{46} - 6 q^{47} - 25 q^{48} - 4 q^{49} + 12 q^{51} - 30 q^{52} + 24 q^{53} + 7 q^{54} + 21 q^{56} - 6 q^{57} + 13 q^{58} + 12 q^{59} + 15 q^{61} + 24 q^{62} + 44 q^{63} + 38 q^{64} - 16 q^{66} - 4 q^{67} + 13 q^{69} - 13 q^{72} - 15 q^{73} - 54 q^{74} - 36 q^{77} + 6 q^{78} - 29 q^{79} + 28 q^{81} - 27 q^{82} + 30 q^{83} - 51 q^{84} - 9 q^{86} + 29 q^{87} + 2 q^{88} + 3 q^{89} - 3 q^{91} - 45 q^{93} - 24 q^{94} - 42 q^{96} - 39 q^{98} - 34 q^{99}+O(q^{100}) $ 8 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - 5 * q^6 - 2 * q^7 + 4 * q^9 + 18 * q^12 + 12 * q^14 + q^16 - 12 * q^17 - 26 * q^18 + 9 * q^19 - 22 * q^21 + 40 * q^22 + 27 * q^23 - 7 * q^24 + 6 * q^26 + 4 * q^27 - 3 * q^28 - 21 * q^31 + 21 * q^32 - 4 * q^33 + 9 * q^36 - 7 * q^37 - 12 * q^38 + 15 * q^39 + 30 * q^41 + 5 * q^42 - 16 * q^43 - 7 * q^46 - 6 * q^47 - 25 * q^48 - 4 * q^49 + 12 * q^51 - 30 * q^52 + 24 * q^53 + 7 * q^54 + 21 * q^56 - 6 * q^57 + 13 * q^58 + 12 * q^59 + 15 * q^61 + 24 * q^62 + 44 * q^63 + 38 * q^64 - 16 * q^66 - 4 * q^67 + 13 * q^69 - 13 * q^72 - 15 * q^73 - 54 * q^74 - 36 * q^77 + 6 * q^78 - 29 * q^79 + 28 * q^81 - 27 * q^82 + 30 * q^83 - 51 * q^84 - 9 * q^86 + 29 * q^87 + 2 * q^88 + 3 * q^89 - 3 * q^91 - 45 * q^93 - 24 * q^94 - 42 * q^96 - 39 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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	$-0.641643\pi$
$2$	−2.01859	−	1.16543i	−1.42736	−	0.824085i	−0.996912	+	0.0785324i	$0.974977\pi$
$3$	1.67602	−	0.437000i	0.967649	−	0.252302i
$3$	1.67602	−	0.437000i	0.967649	−	0.252302i
$4$	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
$9$	2.61806	−	1.46484i	0.872687	−	0.488279i
$10$		0			0
$11$	−2.42019	+	1.39730i	−0.729714	+	0.421301i	−0.818318	−	0.574766i	$-0.805093\pi$
$11$	−2.42019	+	1.39730i	−0.729714	+	0.421301i	0.0886035	+	0.996067i	$0.471760\pi$
$12$	4.17602	+	4.23270i	1.20551	+	1.22188i
$13$			3.20486i			0.888869i	0.895811	+	0.444434i	$0.146595\pi$
$13$			3.20486i			0.888869i	−0.895811	+	0.444434i	$0.853405\pi$
$14$	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	$-0.200775\pi$
$17$	−0.440969	−	0.763780i	−0.106951	−	0.185244i	−0.914533	+	0.404510i	$0.867442\pi$
$18$	−6.99195	−	0.0942709i	−1.64802	−	0.0222199i
$19$	1.90160	+	1.09789i	0.436257	+	0.251873i	0.702009	−	0.712168i	$-0.252287\pi$
$19$	1.90160	+	1.09789i	0.436257	+	0.251873i	−0.265751	+	0.964042i	$0.585620\pi$
$20$		0			0
$21$	−0.823984	+	4.50789i	−0.179808	+	0.983702i
$22$	6.51381			1.38875
$23$	6.53240	+	3.77148i	1.36210	+	0.786408i	0.989903	−	0.141746i	$-0.0452716\pi$
$23$	6.53240	+	3.77148i	1.36210	+	0.786408i	0.372196	+	0.928154i	$0.378605\pi$
$24$	−1.45956	−	5.59780i	−0.297930	−	1.14265i
$25$		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	−0.990896	−	0.134630i	$-0.957015\pi$
$31$	−7.62645	+	4.40313i	−1.36975	+	0.790826i	−0.378855	+	0.925456i	$0.623682\pi$
$32$	−3.92965	+	2.26878i	−0.694671	+	0.401068i
$33$	−3.44566	+	3.39951i	−0.599812	+	0.591779i
$34$			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	−0.848793	−	0.528725i	$-0.822670\pi$
$37$	0.203727	−	0.352865i	0.0334925	−	0.0580107i	0.882286	+	0.470714i	$0.156004\pi$
$38$	−2.55903	−	4.43237i	−0.415130	−	0.719026i
$39$	1.40052	+	5.37140i	0.224263	+	0.860113i
$40$		0			0
$41$	8.55098			1.33544			0.667720	−	0.744413i	$-0.267270\pi$
$41$	8.55098			1.33544			0.667720	+	0.744413i	$0.267270\pi$
$42$	6.91692	−	8.13927i	1.06730	−	1.25592i
$43$	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	$-0.894763\pi$
$47$	−1.31486	+	2.27740i	−0.191792	+	0.332194i	0.754052	+	0.656815i	$0.228097\pi$
$48$	−0.422382	+	1.53489i	−0.0609656	+	0.221542i
$49$	−4.50469	−	5.35796i	−0.643527	−	0.765424i
$50$		0			0
$51$	−1.07284	−	1.08741i	−0.150228	−	0.152267i
$52$	−9.52805	+	5.50102i	−1.32130	+	0.762854i
$53$	6.46794	−	3.73427i	0.888440	−	0.512941i	0.0150081	−	0.999887i	$-0.495223\pi$
$53$	6.46794	−	3.73427i	0.888440	−	0.512941i	0.873432	+	0.486946i	$0.161889\pi$
$54$	−11.7598	+	2.89748i	−1.60031	+	0.394297i
$55$		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	$-0.252658\pi$
$59$	−2.04991	−	3.55054i	−0.266875	−	0.462241i	−0.968053	+	0.250745i	$0.919324\pi$
$60$		0			0
$61$	10.7004	+	6.17786i	1.37004	+	0.790994i	0.990933	−	0.134358i	$-0.0428972\pi$
$61$	10.7004	+	6.17786i	1.37004	+	0.790994i	0.379109	+	0.925352i	$0.376231\pi$
$62$	20.5262			2.60683
$63$	0.588936	+	7.91537i	0.0741989	+	0.997243i
$64$	12.4147			1.55183
$65$		0			0
$66$	10.9173	−	2.84653i	1.34382	−	0.350384i
$67$	−0.802125	−	1.38932i	−0.0979952	−	0.169733i	0.812860	−	0.582460i	$-0.197910\pi$
$67$	−0.802125	−	1.38932i	−0.0979952	−	0.169733i	−0.910855	+	0.412727i	$0.864576\pi$
$68$	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	$-0.121117\pi$
$72$	−4.89248	−	8.74419i	−0.576584	−	1.03051i
$73$	−0.192022	+	0.110864i	−0.0224745	+	0.0129757i	−0.511195	−	0.859465i	$-0.670797\pi$
$73$	−0.192022	+	0.110864i	−0.0224745	+	0.0129757i	0.488721	+	0.872440i	$0.337464\pi$
$74$	−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	−0.764199	−	0.644980i	$-0.776866\pi$
$79$	1.56849	−	2.71671i	0.176469	−	0.305654i	0.940669	+	0.339326i	$0.110199\pi$
$80$		0			0
$81$	4.70850	−	7.67007i	0.523167	−	0.852230i
$82$	−17.2609	−	9.96559i	−1.90615	−	1.10051i
$83$	−0.666893			−0.0732010			−0.0366005	−	0.999330i	$-0.511653\pi$
$83$	−0.666893			−0.0732010			−0.0366005	+	0.999330i	$0.511653\pi$
$84$	−14.8163	+	5.28791i	−1.61659	+	0.576959i
$85$		0			0
$86$	−0.238319	−	0.137594i	−0.0256986	−	0.0148371i
$87$	3.56273	+	13.6641i	0.381965	+	1.46494i
$88$	4.66689	+	8.08330i	0.497492	+	0.861682i
$89$	0.437271	−	0.757376i	0.0463506	−	0.0802816i	−0.841919	−	0.539603i	$-0.818574\pi$
$89$	0.437271	−	0.757376i	0.0463506	−	0.0802816i	0.888270	+	0.459322i	$0.151908\pi$
$90$		0			0
$91$	−7.68656	−	3.57978i	−0.805770	−	0.375263i
$92$			25.8944i			2.69968i
$93$	−10.8579	+	10.7125i	−1.12591	+	1.11083i
$94$	5.30832	−	3.06476i	0.547511	−	0.316106i
$95$		0			0
$96$	−5.59470	+	5.51978i	−0.571007	+	0.563360i
$97$		−	6.37221i		−	0.647000i	−0.946228	−	0.323500i	$-0.895140\pi$
$97$		−	6.37221i		−	0.647000i	0.946228	−	0.323500i	$-0.104860\pi$
$98$	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	−0.999443	−	0.0333808i	$-0.989373\pi$
$101$	−5.31267	−	9.20181i	−0.528630	−	0.915614i	0.470813	−	0.882233i	$-0.343961\pi$
$102$	0.898330	+	3.44535i	0.0889479	+	0.341140i
$103$	0.868777	+	0.501589i	0.0856031	+	0.0494230i	0.542191	−	0.840256i	$-0.317595\pi$
$103$	0.868777	+	0.501589i	0.0856031	+	0.0494230i	−0.456587	+	0.889679i	$0.650928\pi$
$104$	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	$-0.545226\pi$
$107$	−11.0651	−	6.38846i	−1.06971	−	0.617596i	−0.928101	+	0.372328i	$0.878560\pi$
$108$	17.1333	+	4.96429i	1.64865	+	0.477689i
$109$	−0.00912370	−	0.0158027i	−0.000873892	−	0.00151363i	0.865588	−	0.500757i	$-0.166945\pi$
$109$	−0.00912370	−	0.0158027i	−0.000873892	−	0.00151363i	−0.866462	+	0.499243i	$0.833612\pi$
$110$		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	$0.889545\pi$
$114$	−6.22592	−	6.31043i	−0.583111	−	0.591026i
$115$		0			0
$116$	−24.2380	+	13.9938i	−2.25044	+	1.29929i
$117$	4.69460	+	8.39053i	0.434016	+	0.775705i
$118$			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
$123$	14.3316	−	3.73678i	1.29224	−	0.336934i
$124$	−26.1810	−	15.1156i	−2.35112	−	1.35742i
$125$		0			0
$126$	8.03601	−	16.6642i	0.715905	−	1.48457i
$127$	−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
$129$	0.197875	−	0.0515933i	0.0174219	−	0.00454253i
$130$		0			0
$131$	−4.94673	+	8.56799i	−0.432198	+	0.748589i	−0.997062	−	0.0765948i	$-0.975595\pi$
$131$	−4.94673	+	8.56799i	−0.432198	+	0.748589i	0.564864	+	0.825184i	$0.308929\pi$
$132$	−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	$-0.847563\pi$
$137$	−10.9111	+	6.29951i	−0.932195	+	0.538203i	−0.0446900	+	0.999001i	$0.514230\pi$
$138$	−21.3874	−	21.6777i	−1.82061	−	1.84532i
$139$		−	0.988113i		−	0.0838106i	−0.999122	−	0.0419053i	$-0.986657\pi$
$139$		−	0.988113i		−	0.0838106i	0.999122	−	0.0419053i	$-0.0133428\pi$
$140$		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
$144$	−0.0371731	+	2.75708i	−0.00309776	+	0.229757i
$145$		0			0
$146$	0.516818			0.0427722
$147$	−9.89136	−	7.01149i	−0.815826	−	0.578298i
$148$	1.39876			0.114977
$149$	−15.3604	−	8.86834i	−1.25837	−	0.726523i	−0.285616	−	0.958344i	$-0.592198\pi$
$149$	−15.3604	−	8.86834i	−1.25837	−	0.726523i	−0.972758	+	0.231821i	$0.925532\pi$
$150$		0			0
$151$	11.2504	+	19.4862i	0.915542	+	1.58576i	0.806106	+	0.591771i	$0.201571\pi$
$151$	11.2504	+	19.4862i	0.915542	+	1.58576i	0.109435	+	0.993994i	$0.465096\pi$
$152$	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
$156$	−13.5652	+	13.3836i	−1.08609	+	1.07154i
$157$	10.2988	−	5.94600i	0.821931	−	0.474542i	−0.0291509	−	0.999575i	$-0.509280\pi$
$157$	10.2988	−	5.94600i	0.821931	−	0.474542i	0.851082	+	0.525033i	$0.175947\pi$
$158$	−6.33228	+	3.65594i	−0.503769	+	0.290851i
$159$	9.20850	−	9.08518i	0.730282	−	0.720502i
$160$		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	−0.649459	−	0.760397i	$-0.725004\pi$
$163$	4.26159	−	7.38130i	0.333794	−	0.578148i	0.983252	+	0.182249i	$0.0583378\pi$
$164$	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	$-0.455901\pi$
$167$	3.56923			0.276195			0.138098	+	0.990419i	$0.455901\pi$
$168$	15.0561	+	2.75206i	1.16160	+	0.212326i
$169$	2.72886			0.209912
$170$		0			0
$171$	6.58674	+	0.0888076i	0.503701	+	0.00679128i
$172$	0.202650	+	0.350999i	0.0154519	+	0.0267634i
$173$	−4.27114	+	7.39784i	−0.324729	+	0.562447i	−0.981457	−	0.191680i	$-0.938606\pi$
$173$	−4.27114	+	7.39784i	−0.324729	+	0.562447i	0.656728	+	0.754127i	$0.271940\pi$
$174$	8.73285	−	31.7342i	0.662036	−	2.40576i
$175$		0			0
$176$		−	2.56854i		−	0.193611i
$177$	−4.98727	−	5.05496i	−0.374866	−	0.379954i
$178$	−1.76534	+	1.01922i	−0.132318	+	0.0763937i
$179$	−1.06480	+	0.614760i	−0.0795866	+	0.0459493i	−0.539265	−	0.842136i	$-0.681298\pi$
$179$	−1.06480	+	0.614760i	−0.0795866	+	0.0459493i	0.459679	+	0.888085i	$0.347965\pi$
$180$		0			0
$181$		−	15.3995i		−	1.14464i	−0.820032	−	0.572318i	$-0.806044\pi$
$181$		−	15.3995i		−	1.14464i	0.820032	−	0.572318i	$-0.193956\pi$
$182$	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
$186$	34.4022	−	8.96994i	2.52249	−	0.657708i
$187$	2.13445	+	1.23233i	0.156087	+	0.0901167i
$188$	−9.02762			−0.658407
$189$	4.44608	+	13.0089i	0.323405	+	0.946261i
$190$		0			0
$191$	12.5795	+	7.26275i	0.910218	+	0.525514i	0.880501	−	0.474044i	$-0.157206\pi$
$191$	12.5795	+	7.26275i	0.910218	+	0.525514i	0.0297166	+	0.999558i	$0.490540\pi$
$192$	20.8072	−	5.42521i	1.50163	−	0.391531i
$193$	−0.201572	−	0.349134i	−0.0145095	−	0.0251312i	0.858679	−	0.512513i	$-0.171285\pi$
$193$	−0.201572	−	0.349134i	−0.0145095	−	0.0251312i	−0.873189	+	0.487382i	$0.837952\pi$
$194$	−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	$-0.136492\pi$
$198$	17.0536	−	9.54168i	1.21194	−	0.678097i
$199$	−16.0886	+	9.28875i	−1.14049	+	0.658462i	−0.946552	−	0.322552i	$-0.895459\pi$
$199$	−16.0886	+	9.28875i	−1.14049	+	0.658462i	−0.193938	+	0.981014i	$0.562126\pi$
$200$		0			0
$201$	−1.95151	−	1.97800i	−0.137649	−	0.139517i
$202$			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
$207$	22.6268	+	0.305073i	1.57267	+	0.0212040i
$208$	−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
$213$	−2.73505	−	10.4897i	−0.187402	−	0.718741i
$214$	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
$219$	−0.273385	+	0.269724i	−0.0184737	+	0.0182263i
$220$		0			0
$221$	2.44781	−	1.41324i	0.164658	−	0.0950651i
$222$	−1.17098	+	1.15530i	−0.0785908	+	0.0775383i
$223$		−	1.44594i		−	0.0968271i	−0.998827	−	0.0484135i	$-0.984583\pi$
$223$		−	1.44594i		−	0.0968271i	0.998827	−	0.0484135i	$-0.0154165\pi$
$224$	−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	$-0.177942\pi$
$227$	−0.533562	−	0.924157i	−0.0354138	−	0.0613385i	−0.883189	+	0.469017i	$0.844608\pi$
$228$	3.29408	+	12.6337i	0.218156	+	0.836688i
$229$	−6.58058	−	3.79930i	−0.434857	−	0.251065i	0.266557	−	0.963819i	$-0.414114\pi$
$229$	−6.58058	−	3.79930i	−0.434857	−	0.251065i	−0.701414	+	0.712755i	$0.747447\pi$
$230$		0			0
$231$	−4.30466	−	12.0613i	−0.283226	−	0.793574i
$232$	27.2296			1.78771
$233$	15.5882	+	8.99983i	1.02121	+	0.589598i	0.914455	−	0.404687i	$-0.132619\pi$
$233$	15.5882	+	8.99983i	1.02121	+	0.589598i	0.106759	+	0.994285i	$0.465953\pi$
$234$	0.302125	−	22.4082i	0.0197506	−	1.46487i
$235$		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	−0.346683	−	0.937982i	$-0.612692\pi$
$241$	4.53760	−	2.61978i	0.292292	−	0.168755i	0.638975	+	0.769227i	$0.279359\pi$
$242$	6.43980	−	3.71802i	0.413966	−	0.239004i
$243$	4.53971	−	14.9128i	0.291222	−	0.956655i
$244$			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
$249$	−1.11772	+	0.291432i	−0.0708328	+	0.0184688i
$250$		0			0
$251$	15.0765			0.951620			0.475810	−	0.879548i	$-0.342155\pi$
$251$	15.0765			0.951620			0.475810	+	0.879548i	$0.342155\pi$
$252$	−22.5215	+	15.3373i	−1.41872	+	0.966161i
$253$	−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	$-0.668060\pi$
$257$	7.95478	−	13.7781i	0.496206	−	0.859453i	0.999990	+	0.00437591i	$0.00139290\pi$
$258$	−0.459555	−	0.126464i	−0.0286107	−	0.00787329i
$259$	0.618753	+	0.882764i	0.0384475	+	0.0548523i
$260$		0			0
$261$	11.9424	+	21.3443i	0.739215	+	1.32118i
$262$	19.9708	−	11.5302i	1.23380	−	0.712336i
$263$	7.19124	−	4.15187i	0.443431	−	0.256015i	−0.261621	−	0.965171i	$-0.584257\pi$
$263$	7.19124	−	4.15187i	0.443431	−	0.256015i	0.705052	+	0.709156i	$0.250924\pi$
$264$	11.3542	+	11.5083i	0.698802	+	0.708287i
$265$		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	−0.999385	−	0.0350578i	$-0.988838\pi$
$269$	−8.69353	−	15.0576i	−0.530054	−	0.918080i	0.469332	−	0.883022i	$-0.344495\pi$
$270$		0			0
$271$	−8.82614	−	5.09577i	−0.536150	−	0.309546i	0.207367	−	0.978263i	$-0.433510\pi$
$271$	−8.82614	−	5.09577i	−0.536150	−	0.309546i	−0.743517	+	0.668717i	$0.766844\pi$
$272$	0.810598			0.0491497
$273$	−14.4472	−	2.64075i	−0.874382	−	0.159826i
$274$	29.3666			1.77410
$275$		0			0
$276$	11.3158	+	43.3995i	0.681134	+	2.61234i
$277$	4.78018	+	8.27951i	0.287213	+	0.497468i	0.973143	−	0.230199i	$-0.0739378\pi$
$277$	4.78018	+	8.27951i	0.287213	+	0.497468i	−0.685930	+	0.727667i	$0.740605\pi$
$278$	−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	$0.884256\pi$
$282$	7.55753	−	7.45632i	0.450044	−	0.444017i
$283$	−17.2940	+	9.98469i	−1.02802	+	0.593528i	−0.916417	−	0.400225i	$-0.868932\pi$
$283$	−17.2940	+	9.98469i	−1.02802	+	0.593528i	−0.111604	+	0.993753i	$0.535599\pi$
$284$	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
$291$	−2.78466	−	10.6799i	−0.163239	−	0.626069i
$292$	−0.659198	−	0.380588i	−0.0385766	−	0.0222722i
$293$	3.01023			0.175859			0.0879297	−	0.996127i	$-0.471975\pi$
$293$	3.01023			0.175859			0.0879297	+	0.996127i	$0.471975\pi$
$294$	11.7952	+	25.6810i	0.687907	+	1.49775i
$295$		0			0
$296$	−1.17855	−	0.680436i	−0.0685018	−	0.0395495i
$297$	−4.04121	+	13.9475i	−0.234495	+	0.809314i
$298$	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
$303$	−12.9253	−	13.1007i	−0.742539	−	0.752618i
$304$	−1.74778	+	1.00908i	−0.100242	+	0.0578748i
$305$		0			0
$306$	3.01123	+	5.38189i	0.172141	+	0.307662i
$307$			20.3794i			1.16311i	0.813507	+	0.581556i	$0.197556\pi$
$307$			20.3794i			1.16311i	−0.813507	+	0.581556i	$0.802444\pi$
$308$	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	−0.935789	−	0.352562i	$-0.885311\pi$
$311$	−13.6359	−	23.6181i	−0.773222	−	1.33926i	0.162567	−	0.986697i	$-0.448023\pi$
$312$	17.9402	−	4.67767i	1.01566	−	0.264821i
$313$	−0.546210	−	0.315354i	−0.0308736	−	0.0178249i	0.484484	−	0.874800i	$-0.339007\pi$
$313$	−0.546210	−	0.315354i	−0.0308736	−	0.0178249i	−0.515357	+	0.856975i	$0.672341\pi$
$314$	−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	$-0.0801453\pi$
$317$	22.0233	+	12.7151i	1.23695	+	0.714153i	0.268480	+	0.963285i	$0.413479\pi$
$318$	−29.1763	+	7.60735i	−1.63613	+	0.426599i
$319$	−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
$324$	30.8851	+	0.832984i	1.71584	+	0.0462769i
$325$		0			0
$326$	−17.2048	+	9.93319i	−0.952885	+	0.550149i
$327$	−0.0221973	−	0.0224986i	−0.00122751	−	0.00124417i
$328$		−	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	−0.979621	−	0.200855i	$-0.935628\pi$
$331$	−5.74666	+	9.95352i	−0.315865	+	0.547095i	0.663756	+	0.747949i	$0.268961\pi$
$332$	−1.14470	−	1.98267i	−0.0628233	−	0.108813i
$333$	0.0164793	−	1.22225i	0.000903061	−	0.0669788i
$334$	−7.20480	−	4.15970i	−0.394229	−	0.227608i
$335$		0			0
$336$	−3.20949	−	2.72749i	−0.175092	−	0.148797i
$337$	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
$339$	3.15962	+	12.1180i	0.171607	+	0.658162i
$340$		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	$-0.827001\pi$
$347$	−15.5732	+	8.99121i	−0.836015	+	0.482673i	0.0198929	+	0.999802i	$0.493667\pi$
$348$	−34.5079	+	34.0458i	−1.84982	+	1.82505i
$349$		−	6.15422i		−	0.329428i	−0.986341	−	0.164714i	$-0.947330\pi$
$349$		−	6.15422i		−	0.329428i	0.986341	−	0.164714i	$-0.0526701\pi$
$350$		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	−0.929494	−	0.368836i	$-0.879756\pi$
$353$	−14.7332	−	25.5186i	−0.784169	−	1.35822i	0.145326	−	0.989384i	$-0.453577\pi$
$354$	4.17602	+	16.0162i	0.221953	+	0.851251i
$355$		0			0
$356$	3.00223			0.159118
$357$	3.80639	−	1.35850i	0.201455	−	0.0718992i
$358$	2.86584			0.151465
$359$	30.5228	+	17.6224i	1.61093	+	0.930073i	0.989154	+	0.146881i	$0.0469233\pi$
$359$	30.5228	+	17.6224i	1.61093	+	0.930073i	0.621779	+	0.783192i	$0.286410\pi$
$360$		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
$366$	−35.0335	−	35.5090i	−1.83123	−	1.85608i
$367$	−30.1613	+	17.4136i	−1.57441	+	0.908984i	−0.578788	+	0.815478i	$0.696474\pi$
$367$	−30.1613	+	17.4136i	−1.57441	+	0.908984i	−0.995619	+	0.0935065i	$0.970192\pi$
$368$	−6.00400	+	3.46641i	−0.312980	+	0.180699i
$369$	22.3870	−	12.5258i	1.16542	−	0.652067i
$370$		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	−0.474702	−	0.880146i	$-0.657444\pi$
$373$	10.1371	−	17.5579i	0.524878	−	0.909115i	0.999580	−	0.0289688i	$-0.00922234\pi$
$374$	−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
$378$	6.18622	−	31.4413i	0.318185	−	1.61716i
$379$	−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
$381$	−11.7248	+	3.05708i	−0.600678	+	0.156619i
$382$	−16.9285	−	29.3210i	−0.866137	−	1.50019i
$383$	−13.8881	+	24.0549i	−0.709648	+	1.22915i	0.255339	+	0.966851i	$0.417813\pi$
$383$	−13.8881	+	24.0549i	−0.709648	+	1.22915i	−0.964988	+	0.262295i	$0.915521\pi$
$384$	−33.1686	−	9.12758i	−1.69263	−	0.465790i
$385$		0			0
$386$			0.939675i			0.0478282i
$387$	0.309095	−	0.172942i	0.0157122	−	0.00879115i
$388$	18.9446	−	10.9377i	0.961765	−	0.555275i
$389$	13.4945	−	7.79107i	0.684200	−	0.395023i	−0.117236	−	0.993104i	$-0.537403\pi$
$389$	13.4945	−	7.79107i	0.684200	−	0.395023i	0.801436	+	0.598081i	$0.204070\pi$
$390$		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
$396$	−28.7782	−	0.388011i	−1.44616	−	0.0194983i
$397$	16.3596	+	9.44524i	0.821067	+	0.474043i	0.850784	−	0.525515i	$-0.176127\pi$
$397$	16.3596	+	9.44524i	0.821067	+	0.474043i	−0.0297174	+	0.999558i	$0.509461\pi$
$398$	43.3016			2.17051
$399$	−6.51605	+	7.66756i	−0.326211	+	0.383858i
$400$		0			0
$401$	−18.0127	−	10.3996i	−0.899511	−	0.519333i	−0.0224695	−	0.999748i	$-0.507153\pi$
$401$	−18.0127	−	10.3996i	−0.899511	−	0.519333i	−0.877042	+	0.480415i	$0.840486\pi$
$402$	1.63407	+	6.26711i	0.0814999	+	0.312575i
$403$	−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
$408$	−3.63187	+	3.58324i	−0.179805	+	0.177397i
$409$	24.9664	−	14.4143i	1.23451	−	0.712744i	0.266542	−	0.963823i	$-0.414119\pi$
$409$	24.9664	−	14.4143i	1.23451	−	0.712744i	0.967966	+	0.251080i	$0.0807856\pi$
$410$		0			0
$411$	−15.5342	+	15.3262i	−0.766248	+	0.755986i
$412$			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
$417$	−0.431805	−	1.65609i	−0.0211456	−	0.0810992i
$418$	12.3867	+	7.15145i	0.605852	+	0.349789i
$419$	3.24500			0.158528			0.0792642	−	0.996854i	$-0.474743\pi$
$419$	3.24500			0.158528			0.0792642	+	0.996854i	$0.474743\pi$
$420$		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
$423$	−0.106358	+	7.88844i	−0.00517131	+	0.383549i
$424$	−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
$429$	−10.8950	−	11.0429i	−0.526014	−	0.533154i
$430$		0			0
$431$	33.1792	−	19.1560i	1.59819	−	0.922714i	0.606351	−	0.795197i	$-0.292633\pi$
$431$	33.1792	−	19.1560i	1.59819	−	0.922714i	0.991836	−	0.127516i	$-0.0407006\pi$
$432$	1.14254	+	4.63716i	0.0549705	+	0.223105i
$433$		−	28.9533i		−	1.39140i	−0.718330	−	0.695702i	$-0.755093\pi$
$433$		−	28.9533i		−	1.39140i	0.718330	−	0.695702i	$-0.244907\pi$
$434$	−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
$438$	0.866196	−	0.225850i	0.0413885	−	0.0107915i
$439$	−13.2197	−	7.63242i	−0.630943	−	0.364275i	0.150174	−	0.988660i	$-0.452017\pi$
$439$	−13.2197	−	7.63242i	−0.630943	−	0.364275i	−0.781117	+	0.624384i	$0.785350\pi$
$440$		0			0
$441$	−19.6421	−	7.42885i	−0.935338	−	0.353755i
$442$	−6.58816			−0.313367
$443$	−1.97776	−	1.14186i	−0.0939660	−	0.0542513i	0.452281	−	0.891876i	$-0.350611\pi$
$443$	−1.97776	−	1.14186i	−0.0939660	−	0.0542513i	−0.546247	+	0.837624i	$0.683944\pi$
$444$	2.34434	−	0.611256i	0.111257	−	0.0290089i
$445$		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
$453$	27.3713	+	27.7428i	1.28601	+	1.30347i
$454$			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	−0.172033	−	0.985091i	$-0.555034\pi$
$457$	16.3987	−	28.4033i	0.767097	−	1.32865i	0.939131	−	0.343560i	$-0.111633\pi$
$458$	8.85564	+	15.3384i	0.413797	+	0.716718i
$459$	−4.40164	−	1.27535i	−0.205451	−	0.0595284i
$460$		0			0
$461$	−16.5678			−0.771637			−0.385819	−	0.922575i	$-0.626081\pi$
$461$	−16.5678			−0.771637			−0.385819	+	0.922575i	$0.626081\pi$
$462$	−5.36727	+	29.3635i	−0.249708	+	1.36612i
$463$	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	0.208275	−	0.978070i	$-0.433215\pi$
$467$	20.5550	−	35.6023i	0.951171	−	1.64748i	0.742896	−	0.669406i	$-0.233451\pi$
$468$	−16.8869	+	28.3591i	−0.780598	+	1.31090i
$469$	4.22812	−	0.371969i	0.195236	−	0.0171759i
$470$		0			0
$471$	14.6625	−	14.4661i	0.675613	−	0.666565i
$472$	−11.8586	+	6.84658i	−0.545837	+	0.315139i
$473$	−0.285733	+	0.164968i	−0.0131380	+	0.00758524i
$474$	−9.01536	+	8.89463i	−0.414089	+	0.408544i
$475$		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	$-0.0434906\pi$
$479$	8.25944	+	14.3058i	0.377383	+	0.653647i	−0.613297	+	0.789852i	$0.710157\pi$
$480$		0			0
$481$	1.13088	+	0.652916i	0.0515639	+	0.0297704i
$482$	−12.2127			−0.556274
$483$	−22.3840	+	26.3397i	−1.01851	+	1.19850i
$484$	−10.9519			−0.497813
$485$		0			0
$486$	−26.5436	+	24.8120i	−1.20404	+	1.12550i
$487$	−1.01601	−	1.75977i	−0.0460396	−	0.0797430i	0.842087	−	0.539341i	$-0.181327\pi$
$487$	−1.01601	−	1.75977i	−0.0460396	−	0.0797430i	−0.888127	+	0.459598i	$0.847993\pi$
$488$	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	$0.956925\pi$
$492$	35.7091	+	36.1938i	1.60989	+	1.63174i
$493$	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	−0.945209	−	0.326465i	$-0.894143\pi$
$499$	−4.24155	+	7.34658i	−0.189878	+	0.328878i	0.755331	+	0.655343i	$0.227476\pi$
$500$		0			0
$501$	5.98209	−	1.55975i	0.267260	−	0.0696846i
$502$	−30.4332	−	17.5706i	−1.35830	−	0.784216i
$503$	17.0296			0.759312			0.379656	−	0.925128i	$-0.376042\pi$
$503$	17.0296			0.759312			0.379656	+	0.925128i	$0.376042\pi$
$504$	26.4369	−	1.96701i	1.17759	−	0.0876177i
$505$		0			0
$506$	42.5508	+	24.5667i	1.89161	+	1.09212i
$507$	4.57361	−	1.19251i	0.203121	−	0.0529612i
$508$	−12.0077	−	20.7979i	−0.532755	−	0.922759i
$509$	−6.43409	+	11.1442i	−0.285186	+	0.493956i	−0.972654	−	0.232258i	$-0.925389\pi$
$509$	−6.43409	+	11.1442i	−0.285186	+	0.493956i	0.687468	+	0.726214i	$0.258722\pi$
$510$		0			0
$511$	−0.0514110	−	0.584381i	−0.00227429	−	0.0258515i
$512$		−	10.3101i		−	0.455646i
$513$	11.0783	−	2.72956i	0.489119	−	0.120513i
$514$	−32.1148	+	18.5415i	−1.41652	+	0.817831i
$515$		0			0
$516$	0.493031	+	0.499723i	0.0217045	+	0.0219991i
$517$		−	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	$-0.0477961\pi$
$521$	8.32724	+	14.4232i	0.364823	+	0.631892i	−0.623925	+	0.781485i	$0.714463\pi$
$522$	0.768563	−	57.0033i	0.0336391	−	2.49497i
$523$	−31.4934	−	18.1827i	−1.37711	−	0.795075i	−0.385300	−	0.922791i	$-0.625902\pi$
$523$	−31.4934	−	18.1827i	−1.37711	−	0.795075i	−0.991811	+	0.127716i	$0.959235\pi$
$524$	−33.9635			−1.48370
$525$		0			0
$526$	−19.3549			−0.843912
$527$	6.72605	+	3.88329i	0.292991	+	0.169159i
$528$	−1.12245	−	4.30491i	−0.0488484	−	0.187347i
$529$	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
$534$	−2.51334	+	2.47968i	−0.108763	+	0.107306i
$535$		0			0
$536$	−4.64026	+	2.67906i	−0.200429	+	0.115718i
$537$	−1.51597	+	1.49566i	−0.0654188	+	0.0645427i
$538$			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	−0.903896	−	0.427751i	$-0.859306\pi$
$541$	−1.89575	+	3.28353i	−0.0815046	+	0.141170i	0.822392	+	0.568922i	$0.192639\pi$
$542$	11.8775	+	20.5725i	0.510184	+	0.883665i
$543$	−6.72958	−	25.8098i	−0.288794	−	1.10761i
$544$	3.46571	+	2.00093i	0.148591	+	0.0857890i
$545$		0			0
$546$	26.0852	+	22.1678i	1.11634	+	0.948693i
$547$	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
$549$	37.0638	+	0.499723i	1.58184	+	0.0213277i
$550$		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	$-0.600561\pi$
$557$	8.42853	−	4.86622i	0.357128	−	0.206188i	0.667820	+	0.744322i	$0.267227\pi$
$558$	53.7389	−	30.0675i	2.27495	−	1.27286i
$559$			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	$-0.163512\pi$
$563$	0.235135	+	0.407265i	0.00990975	+	0.0171642i	−0.861028	+	0.508558i	$0.830179\pi$
$564$	−15.1304	+	3.94507i	−0.637107	+	0.166117i
$565$		0			0
$566$	46.5459			1.95647
$567$	13.1366	+	19.8602i	0.551686	+	0.834052i
$568$	−20.9037			−0.877100
$569$	5.38387	+	3.10838i	0.225703	+	0.130310i	0.608588	−	0.793486i	$-0.291736\pi$
$569$	5.38387	+	3.10838i	0.225703	+	0.130310i	−0.382885	+	0.923796i	$0.625069\pi$
$570$		0			0
$571$	−5.31121	−	9.19928i	−0.222267	−	0.384978i	0.733229	−	0.679982i	$-0.238012\pi$
$571$	−5.31121	−	9.19928i	−0.222267	−	0.384978i	−0.955496	+	0.295004i	$0.904679\pi$
$572$	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
$576$	32.5024	−	18.1855i	1.35427	−	0.757728i
$577$	2.56914	−	1.48330i	0.106955	−	0.0617504i	−0.445568	−	0.895248i	$-0.646998\pi$
$577$	2.56914	−	1.48330i	0.106955	−	0.0617504i	0.552523	+	0.833497i	$0.313665\pi$
$578$	−32.7459	+	18.9058i	−1.36205	+	0.786380i
$579$	−0.490410	−	0.497067i	−0.0203807	−	0.0206574i
$580$		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	$-0.372589\pi$
$587$	18.8819			0.779341			0.389670	+	0.920954i	$0.372589\pi$
$588$	3.86701	−	41.4419i	0.159473	−	1.70904i
$589$	−19.3366			−0.796751
$590$		0			0
$591$	−5.10047	−	19.5617i	−0.209805	−	0.804661i
$592$	0.187247	+	0.324322i	0.00769582	+	0.0133296i
$593$	15.1472	−	26.2357i	0.622020	−	1.07737i	−0.367088	−	0.930186i	$-0.619645\pi$
$593$	15.1472	−	26.2357i	0.622020	−	1.07737i	0.989109	−	0.147185i	$-0.0470213\pi$
$594$	24.4123	−	23.4444i	1.00165	−	0.961936i
$595$		0			0
$596$		−	60.8887i		−	2.49410i
$597$	−22.9056	+	22.5988i	−0.937462	+	0.924907i
$598$	48.7976	−	28.1733i	1.99548	−	1.15209i
$599$	−6.29024	+	3.63167i	−0.257012	+	0.148386i	−0.622971	−	0.782245i	$-0.714075\pi$
$599$	−6.29024	+	3.63167i	−0.257012	+	0.148386i	0.365959	+	0.930631i	$0.380741\pi$
$600$		0			0
$601$		−	45.3302i		−	1.84906i	−0.381110	−	0.924530i	$-0.624458\pi$
$601$		−	45.3302i		−	1.84906i	0.381110	−	0.924530i	$-0.375542\pi$
$602$	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
$606$	10.8228	+	41.5085i	0.439647	+	1.68617i
$607$	−22.5370	−	13.0117i	−0.914748	−	0.528130i	−0.0327925	−	0.999462i	$-0.510440\pi$
$607$	−22.5370	−	13.0117i	−0.914748	−	0.528130i	−0.881956	+	0.471332i	$0.843773\pi$
$608$	−9.96351			−0.404073
$609$	−36.7515	−	6.71769i	−1.48924	−	0.272215i
$610$		0			0
$611$	−7.29877	−	4.21394i	−0.295276	−	0.170478i
$612$	0.122451	−	9.08204i	0.00494980	−	0.367120i
$613$	12.8525	+	22.2611i	0.519106	+	0.899118i	0.999753	+	0.0222040i	$0.00706833\pi$
$613$	12.8525	+	22.2611i	0.519106	+	0.899118i	−0.480648	+	0.876914i	$0.659598\pi$
$614$	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	$-0.0572213\pi$
$618$	−2.84441	−	2.88302i	−0.114419	−	0.115972i
$619$	−26.4112	+	15.2485i	−1.06156	+	0.612890i	−0.925863	−	0.377861i	$-0.876660\pi$
$619$	−26.4112	+	15.2485i	−1.06156	+	0.612890i	−0.135694	+	0.990751i	$0.543327\pi$
$620$		0			0
$621$	38.0563	−	9.37661i	1.52715	−	0.376271i
$622$			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
$627$	−10.2846	+	2.68157i	−0.410726	+	0.107091i
$628$	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
$633$	11.7015	−	3.05102i	0.465094	−	0.121267i
$634$	−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
$639$	−9.16797	−	16.3857i	−0.362679	−	0.648206i
$640$		0			0
$641$	−6.03197	+	3.48256i	−0.238249	+	0.137553i	−0.614371	−	0.789017i	$-0.710590\pi$
$641$	−6.03197	+	3.48256i	−0.238249	+	0.137553i	0.376123	+	0.926570i	$0.377257\pi$
$642$	36.2277	+	36.7195i	1.42979	+	1.44920i
$643$		−	25.8907i		−	1.02103i	−0.859869	−	0.510514i	$-0.829455\pi$
$643$		−	25.8907i		−	1.02103i	0.859869	−	0.510514i	$-0.170545\pi$
$644$	−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	$-0.103449\pi$
$647$	5.01859	+	8.69245i	0.197301	+	0.341735i	−0.750351	+	0.661039i	$0.770116\pi$
$648$	−25.6176	−	15.7261i	−1.00636	−	0.617781i
$649$	9.92232	+	5.72866i	0.389485	+	0.224869i
$650$		0			0
$651$	−13.5648	−	38.0073i	−0.531645	−	1.48962i
$652$	29.2594			1.14589
$653$	34.2946	+	19.8000i	1.34205	+	0.774833i	0.987108	−	0.160055i	$-0.0511671\pi$
$653$	34.2946	+	19.8000i	1.34205	+	0.774833i	0.354942	+	0.934888i	$0.384500\pi$
$654$	0.0185866	+	0.0712847i	0.000726792	+	0.00278745i
$655$		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	−0.562991	−	0.826463i	$-0.690350\pi$
$661$	−3.31012	+	1.91110i	−0.128749	+	0.0743332i	0.434242	+	0.900796i	$0.357016\pi$
$662$	23.2003	−	13.3947i	0.901705	−	0.520599i
$663$	3.48498	−	3.43831i	0.135346	−	0.133533i
$664$			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
$669$	−0.631874	−	2.42341i	−0.0244297	−	0.0936946i
$670$		0			0
$671$	−34.5292			−1.33299
$672$	−6.98946	−	19.5839i	−0.269624	−	0.755464i
$673$	−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	0.397672	+	0.917528i	$0.369818\pi$
$677$	−15.5014	+	26.8492i	−0.595766	+	1.03190i	−0.993438	+	0.114370i	$0.963515\pi$
$678$	7.74478	−	28.1436i	0.297436	−	1.08085i
$679$	15.2831	+	7.11767i	0.586513	+	0.273151i
$680$		0			0
$681$	−1.29812	−	1.31574i	−0.0497439	−	0.0504191i
$682$	−49.6772	+	28.6812i	−1.90224	+	1.09826i
$683$	−16.5419	+	9.55050i	−0.632960	+	0.365440i	−0.781898	−	0.623407i	$-0.785748\pi$
$683$	−16.5419	+	9.55050i	−0.632960	+	0.365440i	0.148937	+	0.988847i	$0.452415\pi$
$684$	11.0419	+	19.7348i	0.422196	+	0.754579i
$685$		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	0.196403	−	0.980523i	$-0.437074\pi$
$691$	−14.5775	−	8.41632i	−0.554554	−	0.320172i	−0.750957	+	0.660351i	$0.770407\pi$
$692$	−29.3250			−1.11477
$693$	−12.4855	−	18.3338i	−0.474283	−	0.696443i
$694$	41.9145			1.59105
$695$		0			0
$696$	45.6372	−	11.8993i	1.72987	−	0.451043i
$697$	−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	$0.864360\pi$
$702$	−9.28603	−	37.6886i	−0.350479	−	1.42247i
$703$	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	−0.746366	−	0.665536i	$-0.768203\pi$
$709$	5.41030	−	9.37091i	0.203188	−	0.351932i	0.949554	+	0.313604i	$0.101536\pi$
$710$		0			0
$711$	0.126874	−	9.41011i	0.00475816	−	0.352907i
$712$	−2.52959	−	1.46046i	−0.0948005	−	0.0547331i
$713$	−66.4253			−2.48765
$714$	−9.26675	−	1.69384i	−0.346800	−	0.0633905i
$715$		0			0
$716$	−3.65536	−	2.11042i	−0.136607	−	0.0788703i
$717$	−13.0583	−	50.0821i	−0.487669	−	1.87035i
$718$	−41.0753	−	71.1445i	−1.53292	−	2.65509i
$719$	−11.1296	+	19.2770i	−0.415064	+	0.718912i	−0.995435	−	0.0954404i	$-0.969574\pi$
$719$	−11.1296	+	19.2770i	−0.415064	+	0.718912i	0.580371	+	0.814352i	$0.302907\pi$
$720$		0			0
$721$	−2.17342	+	1.52341i	−0.0809425	+	0.0567348i
$722$			33.0483i			1.22993i
$723$	6.46025	−	6.37373i	0.240259	−	0.237042i
$724$	45.7827	−	26.4327i	1.70150	−	0.982362i
$725$		0			0
$726$	9.16844	−	9.04566i	0.340273	−	0.335716i
$727$		−	43.7899i		−	1.62408i	−0.583604	−	0.812038i	$-0.698358\pi$
$727$		−	43.7899i		−	1.62408i	0.583604	−	0.812038i	$-0.301642\pi$
$728$	−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
$732$	18.5359	+	71.0903i	0.685106	+	2.62757i
$733$	−22.6647	−	13.0854i	−0.837138	−	0.483322i	0.0191524	−	0.999817i	$-0.493903\pi$
$733$	−22.6647	−	13.0854i	−0.837138	−	0.483322i	−0.856290	+	0.516495i	$0.827237\pi$
$734$	81.1776			2.99632
$735$		0			0
$736$	−34.2267			−1.26161
$737$	3.88259	+	2.24161i	0.143017	+	0.0825709i
$738$	−59.7881	−	0.806109i	−2.20083	−	0.0296733i
$739$	−20.1777	−	34.9489i	−0.742250	−	1.28561i	−0.951469	−	0.307746i	$-0.900425\pi$
$739$	−20.1777	−	34.9489i	−0.742250	−	1.28561i	0.209219	−	0.977869i	$-0.432908\pi$
$740$		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	$-0.0517593\pi$
$744$	35.7791	+	36.2647i	1.31173	+	1.32953i
$745$		0			0
$746$	−40.9251	+	23.6281i	−1.49838	+	0.865087i
$747$	−1.74597	+	0.976890i	−0.0638816	+	0.0357425i
$748$			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	0.281475	+	0.959569i	$0.409176\pi$
$751$	−18.9165	+	32.7644i	−0.690274	+	1.19559i	−0.971748	+	0.236020i	$0.924157\pi$
$752$	−1.20850	−	2.09319i	−0.0440695	−	0.0763307i
$753$	25.2685	−	6.58843i	0.920834	−	0.240096i
$754$	52.7422	+	30.4507i	1.92076	+	1.10895i
$755$		0			0
$756$	−31.0440	+	35.5475i	−1.12906	+	1.29285i
$757$	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
$759$	−35.3296	+	9.21174i	−1.28238	+	0.334365i
$760$		0			0
$761$	0.915074	−	1.58495i	0.0331714	−	0.0574545i	−0.848963	−	0.528452i	$-0.822773\pi$
$761$	0.915074	−	1.58495i	0.0331714	−	0.0574545i	0.882135	+	0.470998i	$0.156106\pi$
$762$	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
$768$	26.1122	+	26.4666i	0.942243	+	0.955032i
$769$			23.5601i			0.849598i	0.905288	+	0.424799i	$0.139655\pi$
$769$			23.5601i			0.849598i	−0.905288	+	0.424799i	$0.860345\pi$
$770$		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	−0.867255	−	0.497864i	$-0.834118\pi$
$773$	−24.0437	−	41.6448i	−0.864790	−	1.49786i	0.00246461	−	0.999997i	$-0.499215\pi$
$774$	−0.825487	−	0.0111299i	−0.0296715	−	0.000400054i
$775$		0			0
$776$	−21.2828			−0.764010
$777$	1.42281	+	1.20913i	0.0510430	+	0.0433774i
$778$	−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
$786$	28.4327	−	28.0520i	1.01416	−	1.00058i
$787$	26.1234	−	15.0823i	0.931197	−	0.537627i	0.0440072	−	0.999031i	$-0.485988\pi$
$787$	26.1234	−	15.0823i	0.931197	−	0.537627i	0.887190	+	0.461404i	$0.152654\pi$
$788$	34.6995	−	20.0338i	1.23612	−	0.713673i
$789$	10.2383	−	10.1012i	0.364492	−	0.359611i
$790$		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	$-0.479664\pi$
$797$	3.60475			0.127687			0.0638435	+	0.997960i	$0.479664\pi$
$798$	22.0892	−	7.88362i	0.781950	−	0.279077i
$799$	2.31925			0.0820491
$800$		0			0
$801$	0.0353705	−	2.62339i	0.00124976	−	0.0926928i
$802$	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
$807$	−21.1507	−	21.4378i	−0.744539	−	0.754645i
$808$	−30.7335	+	17.7440i	−1.08120	+	0.624232i
$809$	18.7612	−	10.8318i	0.659607	−	0.380824i	−0.132520	−	0.991180i	$-0.542307\pi$
$809$	18.7612	−	10.8318i	0.659607	−	0.380824i	0.792127	+	0.610356i	$0.208974\pi$
$810$		0			0
$811$			27.6526i			0.971015i	0.874232	+	0.485508i	$0.161365\pi$
$811$			27.6526i			0.971015i	−0.874232	+	0.485508i	$0.838635\pi$
$812$	−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
$816$	1.35858	−	0.354231i	0.0475597	−	0.0124006i
$817$	0.224508	+	0.129620i	0.00785453	+	0.00453481i
$818$	−67.1957			−2.34944
$819$	−25.3677	+	1.88746i	−0.886419	+	0.0659531i
$820$		0			0
$821$	−12.2722	−	7.08534i	−0.428302	−	0.247280i	0.270321	−	0.962770i	$-0.412870\pi$
$821$	−12.2722	−	7.08534i	−0.428302	−	0.247280i	−0.698623	+	0.715490i	$0.746203\pi$
$822$	49.2189	−	12.8332i	1.71670	−	0.447609i
$823$	11.6538	+	20.1850i	0.406227	+	0.703605i	0.994463	−	0.105084i	$-0.0335110\pi$
$823$	11.6538	+	20.1850i	0.406227	+	0.703605i	−0.588237	+	0.808689i	$0.700178\pi$
$824$	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	$0.811607\pi$
$828$	37.9311	+	67.7932i	1.31820	+	2.35598i
$829$	25.9947	−	15.0080i	0.902833	−	0.521251i	0.0247149	−	0.999695i	$-0.492132\pi$
$829$	25.9947	−	15.0080i	0.902833	−	0.521251i	0.878118	+	0.478444i	$0.158799\pi$
$830$		0			0
$831$	11.6298	+	11.7877i	0.403434	+	0.408910i
$832$			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
$837$	−12.7346	+	43.9510i	−0.440172	+	1.51917i
$838$	−6.55031	−	3.78182i	−0.226277	−	0.130641i
$839$	−28.6277			−0.988337			−0.494168	−	0.869366i	$-0.664527\pi$
$839$	−28.6277			−0.988337			−0.494168	+	0.869366i	$0.664527\pi$
$840$		0			0
$841$	−37.4666			−1.29195
$842$	−56.3835	−	32.5530i	−1.94310	−	1.12185i
$843$	5.21074	+	19.9846i	0.179467	+	0.688307i
$844$	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
$849$	−24.6217	+	24.2920i	−0.845015	+	0.833698i
$850$		0			0
$851$	2.66165	−	1.53670i	0.0912401	−	0.0526775i
$852$	26.4912	−	26.1364i	0.907573	−	0.895419i
$853$		−	17.3563i		−	0.594269i	−0.954836	−	0.297135i	$-0.903969\pi$
$853$		−	17.3563i		−	0.594269i	0.954836	−	0.297135i	$-0.0960310\pi$
$854$	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	−0.922602	−	0.385752i	$-0.873942\pi$
$857$	−23.2842	−	40.3294i	−0.795372	−	1.37763i	0.127230	−	0.991873i	$-0.459391\pi$
$858$	9.12275	+	34.9883i	0.311446	+	1.19448i
$859$	31.5359	+	18.2072i	1.07599	+	0.621223i	0.929812	−	0.368035i	$-0.119969\pi$
$859$	31.5359	+	18.2072i	1.07599	+	0.621223i	0.146178	+	0.989258i	$0.453303\pi$
$860$		0			0
$861$	−7.04587	+	38.5469i	−0.240123	+	1.31367i
$862$	−89.3002			−3.04158
$863$	−2.05942	−	1.18901i	−0.0701034	−	0.0404742i	0.464539	−	0.885553i	$-0.346220\pi$
$863$	−2.05942	−	1.18901i	−0.0701034	−	0.0404742i	−0.534642	+	0.845079i	$0.679554\pi$
$864$	−6.56170	+	22.6464i	−0.223234	+	0.770448i
$865$		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
$873$	−9.33426	−	16.6829i	−0.315917	−	0.564629i
$874$		−	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	−0.990028	−	0.140872i	$-0.955009\pi$
$877$	−11.0465	+	19.1332i	−0.373015	+	0.646082i	0.617012	+	0.786953i	$0.288343\pi$
$878$	17.7901	+	30.8134i	0.600387	+	1.03990i
$879$	5.04519	−	1.31547i	0.170170	−	0.0443697i
$880$		0			0
$881$	33.5633			1.13078			0.565388	−	0.824825i	$-0.308727\pi$
$881$	33.5633			1.13078			0.565388	+	0.824825i	$0.308727\pi$
$882$	30.9915	+	37.8873i	1.04354	+	1.27573i
$883$	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	$-0.986310\pi$
$887$	−13.7685	+	23.8478i	−0.462302	+	0.800730i	0.536773	+	0.843726i	$0.319643\pi$
$888$	−2.27262	−	0.625396i	−0.0762641	−	0.0209869i
$889$	7.81399	−	16.7783i	0.262073	−	0.562726i
$890$		0			0
$891$	−0.678096	+	25.1422i	−0.0227171	+	0.842295i
$892$	4.29877	−	2.48189i	0.143933	−	0.0831000i
$893$	−5.00068	+	2.88714i	−0.167341	+	0.0966146i
$894$	50.2907	+	50.9733i	1.68197	+	1.70480i
$895$		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
$903$	−0.0972815	+	0.532212i	−0.00323733	+	0.0177109i
$904$	24.1487			0.803174
$905$		0			0
$906$	−22.9189	−	87.9005i	−0.761431	−	2.92030i
$907$	19.3650	+	33.5412i	0.643005	+	1.11372i	0.984758	+	0.173928i	$0.0556459\pi$
$907$	19.3650	+	33.5412i	0.643005	+	1.11372i	−0.341754	+	0.939790i	$0.611021\pi$
$908$	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	$-0.126690\pi$
$912$	−2.48834	+	2.45502i	−0.0823973	+	0.0812938i
$913$	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	−0.785867	−	0.618395i	$-0.787783\pi$
$919$	4.32329	−	7.48816i	0.142612	−	0.247012i	0.928480	+	0.371383i	$0.121116\pi$
$920$		0			0
$921$	8.90578	+	34.1561i	0.293455	+	1.12548i
$922$	33.4434	+	19.3086i	1.10140	+	0.635894i
$923$	20.0583			0.660225
$924$	28.4694	−	33.5005i	0.936574	−	1.10208i
$925$		0			0
$926$	−73.8532	−	42.6392i	−2.42697	−	1.40121i
$927$	3.00926	+	0.0405732i	0.0988370	+	0.00133260i
$928$	−18.4967	−	32.0373i	−0.607185	−	1.05168i
$929$	−6.27980	+	10.8769i	−0.206034	+	0.356861i	−0.950462	−	0.310842i	$-0.899389\pi$
$929$	−6.27980	+	10.8769i	−0.206034	+	0.356861i	0.744428	+	0.667703i	$0.232722\pi$
$930$		0			0
$931$	−2.68366	−	15.1344i	−0.0879535	−	0.496009i
$932$			61.7914i			2.02405i
$933$	−33.1751	−	33.6254i	−1.08610	−	1.10085i
$934$	−82.9840	+	47.9108i	−2.71532	+	1.56769i
$935$		0			0
$936$	28.0239	−	15.6797i	0.915990	−	0.512508i
$937$		−	11.3901i		−	0.372097i	−0.982541	−	0.186048i	$-0.940432\pi$
$937$		−	11.3901i		−	0.372097i	0.982541	−	0.186048i	$-0.0595681\pi$
$938$	−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	0.973123	+	0.230285i	$0.0739658\pi$
$941$	21.0434	+	36.4482i	0.685994	+	1.18818i	−0.287129	+	0.957892i	$0.592701\pi$
$942$	−46.4568	+	12.1130i	−1.51365	+	0.394664i
$943$	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	$-0.257058\pi$
$947$	12.6504	+	7.30370i	0.411082	+	0.237338i	−0.280172	+	0.959950i	$0.590392\pi$
$948$	18.0491	−	4.70607i	0.586207	−	0.152846i
$949$	−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	$-0.154948\pi$
$954$	−45.5756	+	25.5001i	−1.47556	+	0.825596i
$955$		0			0
$956$	88.8379	−	51.2906i	2.87322	−	1.65886i
$957$	−27.7152	−	28.0914i	−0.895906	−	0.908066i
$958$		−	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
$963$	−38.3273	−	0.516758i	−1.23508	−	0.0166523i
$964$	15.5772	+	8.99352i	0.501709	+	0.289662i
$965$		0			0
$966$	75.8811	−	27.0819i	2.44144	−	0.871346i
$967$	−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
$969$	−0.846268	−	3.24567i	−0.0271860	−	0.104266i
$970$		0			0
$971$	2.64865	−	4.58759i	0.0849991	−	0.147223i	−0.820392	−	0.571802i	$-0.806245\pi$
$971$	2.64865	−	4.58759i	0.0849991	−	0.147223i	0.905391	+	0.424579i	$0.139578\pi$
$972$	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	$-0.519654\pi$
$977$	24.1247	−	13.9284i	0.771818	−	0.445610i	0.833523	+	0.552485i	$0.186320\pi$
$978$	−24.4947	+	24.1667i	−0.783255	+	0.772765i
$979$			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	$-0.170023\pi$
$983$	−0.330614	−	0.572640i	−0.0105449	−	0.0182644i	−0.871250	+	0.490840i	$0.836690\pi$
$984$	−12.4806	−	47.8667i	−0.397868	−	1.52594i
$985$		0			0
$986$	−16.7593			−0.533725
$987$	−9.18286	−	7.80378i	−0.292294	−	0.248397i
$988$	−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	0.916380	+	0.400309i	$0.131097\pi$
$991$	25.3374	+	43.8856i	0.804868	+	1.39407i	−0.111513	+	0.993763i	$0.535570\pi$
$992$	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
$996$	−2.78496	−	2.82276i	−0.0882447	−	0.0894425i
$997$	−5.21879	+	3.01307i	−0.165281	+	0.0954249i	−0.580359	−	0.814361i	$-0.697088\pi$
$997$	−5.21879	+	3.01307i	−0.165281	+	0.0954249i	0.415078	+	0.909786i	$0.363754\pi$
$998$	17.1239	−	9.88647i	0.542047	−	0.312951i
$999$	−0.506503	−	2.05571i	−0.0160250	−	0.0650398i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.1	✓	8	15.14	odd	2
105.2.s.c.101.1	yes	8	35.24	odd	6
105.2.s.d.26.4	yes	8	5.4	even	2
105.2.s.d.101.4	yes	8	105.59	even	6
525.2.q.e.299.1		16	5.3	odd	4
525.2.q.e.299.8		16	5.2	odd	4
525.2.q.e.374.1		16	105.17	odd	12
525.2.q.e.374.8		16	105.38	odd	12
525.2.q.f.299.1		16	15.2	even	4
525.2.q.f.299.8		16	15.8	even	4
525.2.q.f.374.1		16	35.3	even	12
525.2.q.f.374.8		16	35.17	even	12
525.2.t.f.26.1		8	1.1	even	1	trivial
525.2.t.f.101.1		8	21.17	even	6	inner
525.2.t.g.26.4		8	3.2	odd	2
525.2.t.g.101.4		8	7.3	odd	6
735.2.b.c.146.1		8	35.9	even	6
735.2.b.c.146.8		8	105.89	even	6
735.2.b.d.146.1		8	35.19	odd	6
735.2.b.d.146.8		8	105.44	odd	6
735.2.s.k.521.1		8	35.4	even	6
735.2.s.k.656.1		8	105.104	even	2
735.2.s.l.521.4		8	105.74	odd	6
735.2.s.l.656.4		8	35.34	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-2.01859 - 1.16543i) q^{2} +(1.67602 - 0.437000i) q^{3} +(1.71646 + 2.97300i) q^{4} +(-3.89248 - 1.07116i) q^{6} +(-1.11699 + 2.39840i) q^{7} -3.33995i q^{8} +(2.61806 - 1.46484i) q^{9} +O(q^{10})\)	\(q+(-2.01859 - 1.16543i) q^{2} +(1.67602 - 0.437000i) q^{3} +(1.71646 + 2.97300i) q^{4} +(-3.89248 - 1.07116i) q^{6} +(-1.11699 + 2.39840i) q^{7} -3.33995i q^{8} +(2.61806 - 1.46484i) q^{9} +(-2.42019 + 1.39730i) q^{11} +(4.17602 + 4.23270i) q^{12} +3.20486i q^{13} +(5.04991 - 3.53962i) q^{14} +(-0.459555 + 0.795973i) q^{16} +(-0.440969 - 0.763780i) q^{17} +(-6.99195 - 0.0942709i) q^{18} +(1.90160 + 1.09789i) q^{19} +(-0.823984 + 4.50789i) q^{21} +6.51381 q^{22} +(6.53240 + 3.77148i) q^{23} +(-1.45956 - 5.59780i) 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} +(-3.44566 + 3.39951i) q^{33} +2.05568i q^{34} +(8.84876 + 5.26916i) q^{36} +(0.203727 - 0.352865i) q^{37} +(-2.55903 - 4.43237i) q^{38} +(1.40052 + 5.37140i) q^{39} +8.55098 q^{41} +(6.91692 - 8.13927i) 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} +(-1.07284 - 1.08741i) q^{51} +(-9.52805 + 5.50102i) q^{52} +(6.46794 - 3.73427i) q^{53} +(-11.7598 + 2.89748i) 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} +(0.588936 + 7.91537i) q^{63} +12.4147 q^{64} +(10.9173 - 2.84653i) q^{66} +(-0.802125 - 1.38932i) q^{67} +(1.51381 - 2.62200i) q^{68} +(12.5965 + 3.46641i) q^{69} -6.25869i q^{71} +(-4.89248 - 8.74419i) 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} +(4.70850 - 7.67007i) q^{81} +(-17.2609 - 9.96559i) q^{82} -0.666893 q^{83} +(-14.8163 + 5.28791i) q^{84} +(-0.238319 - 0.137594i) q^{86} +(3.56273 + 13.6641i) q^{87} +(4.66689 + 8.08330i) q^{88} +(0.437271 - 0.757376i) q^{89} +(-7.68656 - 3.57978i) q^{91} +25.8944i q^{92} +(-10.8579 + 10.7125i) q^{93} +(5.30832 - 3.06476i) q^{94} +(-5.59470 + 5.51978i) q^{96} -6.37221i q^{97} +(2.84876 + 16.0654i) q^{98} +(-4.28939 + 7.20339i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - 5 q^{6} - 2 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - 5 * q^6 - 2 * q^7 + 4 * q^9	\( 8 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - 5 q^{6} - 2 q^{7} + 4 q^{9} + 18 q^{12} + 12 q^{14} + q^{16} - 12 q^{17} - 26 q^{18} + 9 q^{19} - 22 q^{21} + 40 q^{22} + 27 q^{23} - 7 q^{24} + 6 q^{26} + 4 q^{27} - 3 q^{28} - 21 q^{31} + 21 q^{32} - 4 q^{33} + 9 q^{36} - 7 q^{37} - 12 q^{38} + 15 q^{39} + 30 q^{41} + 5 q^{42} - 16 q^{43} - 7 q^{46} - 6 q^{47} - 25 q^{48} - 4 q^{49} + 12 q^{51} - 30 q^{52} + 24 q^{53} + 7 q^{54} + 21 q^{56} - 6 q^{57} + 13 q^{58} + 12 q^{59} + 15 q^{61} + 24 q^{62} + 44 q^{63} + 38 q^{64} - 16 q^{66} - 4 q^{67} + 13 q^{69} - 13 q^{72} - 15 q^{73} - 54 q^{74} - 36 q^{77} + 6 q^{78} - 29 q^{79} + 28 q^{81} - 27 q^{82} + 30 q^{83} - 51 q^{84} - 9 q^{86} + 29 q^{87} + 2 q^{88} + 3 q^{89} - 3 q^{91} - 45 q^{93} - 24 q^{94} - 42 q^{96} - 39 q^{98} - 34 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - 5 * q^6 - 2 * q^7 + 4 * q^9 + 18 * q^12 + 12 * q^14 + q^16 - 12 * q^17 - 26 * q^18 + 9 * q^19 - 22 * q^21 + 40 * q^22 + 27 * q^23 - 7 * q^24 + 6 * q^26 + 4 * q^27 - 3 * q^28 - 21 * q^31 + 21 * q^32 - 4 * q^33 + 9 * q^36 - 7 * q^37 - 12 * q^38 + 15 * q^39 + 30 * q^41 + 5 * q^42 - 16 * q^43 - 7 * q^46 - 6 * q^47 - 25 * q^48 - 4 * q^49 + 12 * q^51 - 30 * q^52 + 24 * q^53 + 7 * q^54 + 21 * q^56 - 6 * q^57 + 13 * q^58 + 12 * q^59 + 15 * q^61 + 24 * q^62 + 44 * q^63 + 38 * q^64 - 16 * q^66 - 4 * q^67 + 13 * q^69 - 13 * q^72 - 15 * q^73 - 54 * q^74 - 36 * q^77 + 6 * q^78 - 29 * q^79 + 28 * q^81 - 27 * q^82 + 30 * q^83 - 51 * q^84 - 9 * q^86 + 29 * q^87 + 2 * q^88 + 3 * q^89 - 3 * q^91 - 45 * q^93 - 24 * q^94 - 42 * q^96 - 39 * q^98 - 34 * q^99

Introduction

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