LMFDB - Embedded newform 525.2.t.i.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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 8 x^{18} - 15 x^{17} + 18 x^{16} - 45 x^{15} + 59 x^{14} - 147 x^{13} + 271 x^{12} + \cdots + 59049 $ x^20 - 3x^19 + 8x^18 - 15x^17 + 18x^16 - 45x^15 + 59x^14 - 147x^13 + 271x^12 - 330x^11 + 879x^10 - 990x^9 + 2439x^8 - 3969x^7 + 4779x^6 - 10935x^5 + 13122x^4 - 32805x^3 + 52488x^2 - 59049*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.1
Root			$-1.63084 - 0.583411i$ of defining polynomial
Character	$\chi$	$=$	525.26
Dual form			525.2.t.i.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.36764 - 1.36696i) q^{2} +(-0.310170 + 1.70405i) q^{3} +(2.73715 + 4.74088i) q^{4} +(3.06374 - 3.61059i) q^{6} +(-2.24882 + 1.39384i) q^{7} -9.49844i q^{8} +(-2.80759 - 1.05709i) q^{9} +O(q^{10})$	\(q+(-2.36764 - 1.36696i) q^{2} +(-0.310170 + 1.70405i) q^{3} +(2.73715 + 4.74088i) q^{4} +(3.06374 - 3.61059i) q^{6} +(-2.24882 + 1.39384i) q^{7} -9.49844i q^{8} +(-2.80759 - 1.05709i) q^{9} +(-1.79388 + 1.03570i) q^{11} +(-8.92769 + 3.19377i) q^{12} +2.04106i q^{13} +(7.22973 - 0.226073i) q^{14} +(-7.50967 + 13.0071i) q^{16} +(-1.05144 - 1.82114i) q^{17} +(5.20236 + 6.34067i) q^{18} +(-2.41421 - 1.39384i) q^{19} +(-1.67766 - 4.26444i) q^{21} +5.66303 q^{22} +(1.53909 + 0.888591i) q^{23} +(16.1858 + 2.94613i) q^{24} +(2.79004 - 4.83250i) q^{26} +(2.67217 - 4.45640i) q^{27} +(-12.7634 - 6.84624i) q^{28} -2.79774i q^{29} +(6.04532 - 3.49027i) q^{31} +(19.1086 - 11.0324i) q^{32} +(-1.20848 - 3.37811i) q^{33} +5.74909i q^{34} +(-2.67324 - 16.2039i) q^{36} +(3.03329 - 5.25381i) q^{37} +(3.81065 + 6.60024i) q^{38} +(-3.47807 - 0.633076i) q^{39} -11.7165 q^{41} +(-1.85720 + 12.3900i) q^{42} +4.37014 q^{43} +(-9.82025 - 5.66973i) q^{44} +(-2.42933 - 4.20773i) q^{46} +(1.47384 - 2.55277i) q^{47} +(-19.8356 - 16.8313i) q^{48} +(3.11440 - 6.26901i) q^{49} +(3.42945 - 1.22684i) q^{51} +(-9.67643 + 5.58669i) q^{52} +(-5.36432 + 3.09709i) q^{53} +(-12.4185 + 6.89842i) q^{54} +(13.2393 + 21.3603i) q^{56} +(3.12400 - 3.68161i) q^{57} +(-3.82440 + 6.62405i) q^{58} +(1.44301 + 2.49936i) q^{59} +(-6.30263 - 3.63883i) q^{61} -19.0842 q^{62} +(7.78719 - 1.53613i) q^{63} -30.2845 q^{64} +(-1.75650 + 9.65010i) q^{66} +(-3.70150 - 6.41119i) q^{67} +(5.75589 - 9.96949i) q^{68} +(-1.99158 + 2.34707i) q^{69} +3.80885i q^{71} +(-10.0407 + 26.6677i) q^{72} +(-5.81273 + 3.35598i) q^{73} +(-14.3635 + 8.29276i) q^{74} -15.2606i q^{76} +(2.59052 - 4.82949i) q^{77} +(7.36944 + 6.25328i) q^{78} +(2.95787 - 5.12317i) q^{79} +(6.76512 + 5.93576i) q^{81} +(27.7405 + 16.0160i) q^{82} -5.96419 q^{83} +(15.6252 - 19.6260i) q^{84} +(-10.3469 - 5.97380i) q^{86} +(4.76750 + 0.867776i) q^{87} +(9.83752 + 17.0391i) q^{88} +(6.20912 - 10.7545i) q^{89} +(-2.84492 - 4.58998i) q^{91} +9.72883i q^{92} +(4.07252 + 11.3841i) q^{93} +(-6.97906 + 4.02936i) q^{94} +(12.8728 + 35.9840i) q^{96} -9.97170i q^{97} +(-15.9433 + 10.5855i) q^{98} +(6.13132 - 1.01152i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 3 q^{3} + 14 q^{4} - 7 q^{9}+O(q^{10}) $ 20 * q + 3 * q^3 + 14 * q^4 - 7 * q^9	$ 20 q + 3 q^{3} + 14 q^{4} - 7 q^{9} - 21 q^{12} - 18 q^{16} + 14 q^{18} - 9 q^{21} + 20 q^{22} + 18 q^{24} - 10 q^{28} + 42 q^{31} + 12 q^{33} - 36 q^{36} + 24 q^{37} + 33 q^{42} + 36 q^{43} - 8 q^{46} - 4 q^{49} + 21 q^{51} - 84 q^{52} - 75 q^{54} + 6 q^{57} - 4 q^{58} - 90 q^{61} - 5 q^{63} - 120 q^{64} + 6 q^{66} + 20 q^{67} - 35 q^{72} - 48 q^{73} - 108 q^{78} + 46 q^{79} + 29 q^{81} + 36 q^{82} + 75 q^{84} + 69 q^{87} + 4 q^{88} - 30 q^{91} - 30 q^{93} + 6 q^{94} + 135 q^{96} + 94 q^{99}+O(q^{100}) $ 20 * q + 3 * q^3 + 14 * q^4 - 7 * q^9 - 21 * q^12 - 18 * q^16 + 14 * q^18 - 9 * q^21 + 20 * q^22 + 18 * q^24 - 10 * q^28 + 42 * q^31 + 12 * q^33 - 36 * q^36 + 24 * q^37 + 33 * q^42 + 36 * q^43 - 8 * q^46 - 4 * q^49 + 21 * q^51 - 84 * q^52 - 75 * q^54 + 6 * q^57 - 4 * q^58 - 90 * q^61 - 5 * q^63 - 120 * q^64 + 6 * q^66 + 20 * q^67 - 35 * q^72 - 48 * q^73 - 108 * q^78 + 46 * q^79 + 29 * q^81 + 36 * q^82 + 75 * q^84 + 69 * q^87 + 4 * q^88 - 30 * q^91 - 30 * q^93 + 6 * q^94 + 135 * q^96 + 94 * 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 $

$2$	−2.36764	−	1.36696i	−1.67417	−	0.966585i	−0.965260	−	0.261291i	$-0.915852\pi$
$2$	−2.36764	−	1.36696i	−1.67417	−	0.966585i	−0.708915	−	0.705294i	$-0.750815\pi$
$3$	−0.310170	+	1.70405i	−0.179077	+	0.983835i
$3$	−0.310170	+	1.70405i	−0.179077	+	0.983835i
$4$	2.73715	+	4.74088i	1.36857	+	2.37044i
$5$		0			0
$5$		0			0
$6$	3.06374	−	3.61059i	1.25077	−	1.47402i
$7$	−2.24882	+	1.39384i	−0.849975	+	0.526823i
$7$	−2.24882	+	1.39384i	−0.849975	+	0.526823i
$8$		−	9.49844i		−	3.35821i
$9$	−2.80759	−	1.05709i	−0.935863	−	0.352364i
$10$		0			0
$11$	−1.79388	+	1.03570i	−0.540876	+	0.312275i	−0.745434	−	0.666579i	$-0.767758\pi$
$11$	−1.79388	+	1.03570i	−0.540876	+	0.312275i	0.204558	+	0.978854i	$0.434424\pi$
$12$	−8.92769	+	3.19377i	−2.57720	+	0.921961i
$13$			2.04106i			0.566088i	0.959107	+	0.283044i	$0.0913443\pi$
$13$			2.04106i			0.566088i	−0.959107	+	0.283044i	$0.908656\pi$
$14$	7.22973	−	0.226073i	1.93223	−	0.0604206i
$15$		0			0
$16$	−7.50967	+	13.0071i	−1.87742	+	3.25178i
$17$	−1.05144	−	1.82114i	−0.255011	−	0.441692i	0.709887	−	0.704315i	$-0.248746\pi$
$17$	−1.05144	−	1.82114i	−0.255011	−	0.441692i	−0.964899	+	0.262623i	$0.915413\pi$
$18$	5.20236	+	6.34067i	1.22621	+	1.49451i
$19$	−2.41421	−	1.39384i	−0.553857	−	0.319769i	0.196819	−	0.980440i	$-0.436939\pi$
$19$	−2.41421	−	1.39384i	−0.553857	−	0.319769i	−0.750676	+	0.660670i	$0.770272\pi$
$20$		0			0
$21$	−1.67766	−	4.26444i	−0.366096	−	0.930577i
$22$	5.66303			1.20736
$23$	1.53909	+	0.888591i	0.320921	+	0.185284i	0.651803	−	0.758388i	$-0.274013\pi$
$23$	1.53909	+	0.888591i	0.320921	+	0.185284i	−0.330882	+	0.943672i	$0.607346\pi$
$24$	16.1858	+	2.94613i	3.30392	+	0.601376i
$25$		0			0
$26$	2.79004	−	4.83250i	0.547173	−	0.947731i
$27$	2.67217	−	4.45640i	0.514259	−	0.857635i
$28$	−12.7634	−	6.84624i	−2.41206	−	1.29382i
$29$		−	2.79774i		−	0.519528i	−0.965672	−	0.259764i	$-0.916355\pi$
$29$		−	2.79774i		−	0.519528i	0.965672	−	0.259764i	$-0.0836448\pi$
$30$		0			0
$31$	6.04532	−	3.49027i	1.08577	−	0.626870i	0.153324	−	0.988176i	$-0.451002\pi$
$31$	6.04532	−	3.49027i	1.08577	−	0.626870i	0.932447	+	0.361306i	$0.117669\pi$
$32$	19.1086	−	11.0324i	3.37796	−	1.95027i
$33$	−1.20848	−	3.37811i	−0.210369	−	0.588054i
$34$			5.74909i			0.985961i
$35$		0			0
$36$	−2.67324	−	16.2039i	−0.445541	−	2.70064i
$37$	3.03329	−	5.25381i	0.498670	−	0.863722i	−0.501329	−	0.865257i	$-0.667155\pi$
$37$	3.03329	−	5.25381i	0.498670	−	0.863722i	0.999999	+	0.00153522i	$0.000488676\pi$
$38$	3.81065	+	6.60024i	0.618169	+	1.07070i
$39$	−3.47807	−	0.633076i	−0.556938	−	0.101373i
$40$		0			0
$41$	−11.7165			−1.82981			−0.914905	−	0.403670i	$-0.867734\pi$
$41$	−11.7165			−1.82981			−0.914905	+	0.403670i	$0.867734\pi$
$42$	−1.85720	+	12.3900i	−0.286573	+	1.91181i
$43$	4.37014			0.666440			0.333220	−	0.942849i	$-0.391865\pi$
$43$	4.37014			0.666440			0.333220	+	0.942849i	$0.391865\pi$
$44$	−9.82025	−	5.66973i	−1.48046	−	0.854743i
$45$		0			0
$46$	−2.42933	−	4.20773i	−0.358186	−	0.620396i
$47$	1.47384	−	2.55277i	0.214982	−	0.372360i	−0.738285	−	0.674489i	$-0.764364\pi$
$47$	1.47384	−	2.55277i	0.214982	−	0.372360i	0.953267	+	0.302129i	$0.0976974\pi$
$48$	−19.8356	−	16.8313i	−2.86302	−	2.42939i
$49$	3.11440	−	6.26901i	0.444915	−	0.895573i
$50$		0			0
$51$	3.42945	−	1.22684i	0.480219	−	0.171792i
$52$	−9.67643	+	5.58669i	−1.34188	+	0.774734i
$53$	−5.36432	+	3.09709i	−0.736846	+	0.425418i	−0.820921	−	0.571041i	$-0.806540\pi$
$53$	−5.36432	+	3.09709i	−0.736846	+	0.425418i	0.0840757	+	0.996459i	$0.473206\pi$
$54$	−12.4185	+	6.89842i	−1.68994	+	0.938755i
$55$		0			0
$56$	13.2393	+	21.3603i	1.76918	+	2.85439i
$57$	3.12400	−	3.68161i	0.413783	−	0.487641i
$58$	−3.82440	+	6.62405i	−0.502168	+	0.869781i
$59$	1.44301	+	2.49936i	0.187864	+	0.325389i	0.944538	−	0.328403i	$-0.106510\pi$
$59$	1.44301	+	2.49936i	0.187864	+	0.325389i	−0.756674	+	0.653792i	$0.773177\pi$
$60$		0			0
$61$	−6.30263	−	3.63883i	−0.806969	−	0.465904i	0.0389331	−	0.999242i	$-0.487604\pi$
$61$	−6.30263	−	3.63883i	−0.806969	−	0.465904i	−0.845902	+	0.533338i	$0.820937\pi$
$62$	−19.0842			−2.42369
$63$	7.78719	−	1.53613i	0.981094	−	0.193534i
$64$	−30.2845			−3.78556
$65$		0			0
$66$	−1.75650	+	9.65010i	−0.216210	+	1.18784i
$67$	−3.70150	−	6.41119i	−0.452211	−	0.783252i	0.546312	−	0.837581i	$-0.316031\pi$
$67$	−3.70150	−	6.41119i	−0.452211	−	0.783252i	−0.998523	+	0.0543297i	$0.982698\pi$
$68$	5.75589	−	9.96949i	0.698004	−	1.20898i
$69$	−1.99158	+	2.34707i	−0.239759	+	0.282554i
$70$		0			0
$71$			3.80885i			0.452027i	0.974124	+	0.226014i	$0.0725694\pi$
$71$			3.80885i			0.452027i	−0.974124	+	0.226014i	$0.927431\pi$
$72$	−10.0407	+	26.6677i	−1.18331	+	3.14282i
$73$	−5.81273	+	3.35598i	−0.680328	+	0.392788i	−0.799979	−	0.600028i	$-0.795156\pi$
$73$	−5.81273	+	3.35598i	−0.680328	+	0.392788i	0.119651	+	0.992816i	$0.461823\pi$
$74$	−14.3635	+	8.29276i	−1.66972	+	0.964014i
$75$		0			0
$76$		−	15.2606i		−	1.75051i
$77$	2.59052	−	4.82949i	0.295218	−	0.550372i
$78$	7.36944	+	6.25328i	0.834425	+	0.708044i
$79$	2.95787	−	5.12317i	0.332786	−	0.576402i	−0.650271	−	0.759702i	$-0.725345\pi$
$79$	2.95787	−	5.12317i	0.332786	−	0.576402i	0.983057	+	0.183300i	$0.0586781\pi$
$80$		0			0
$81$	6.76512	+	5.93576i	0.751679	+	0.659529i
$82$	27.7405	+	16.0160i	3.06342	+	1.76867i
$83$	−5.96419			−0.654655			−0.327327	−	0.944911i	$-0.606148\pi$
$83$	−5.96419			−0.654655			−0.327327	+	0.944911i	$0.606148\pi$
$84$	15.6252	−	19.6260i	1.70485	−	2.14137i
$85$		0			0
$86$	−10.3469	−	5.97380i	−1.11574	−	0.644171i
$87$	4.76750	+	0.867776i	0.511130	+	0.0930354i
$88$	9.83752	+	17.0391i	1.04868	+	1.81637i
$89$	6.20912	−	10.7545i	0.658166	−	1.13998i	−0.322924	−	0.946425i	$-0.604666\pi$
$89$	6.20912	−	10.7545i	0.658166	−	1.13998i	0.981090	−	0.193552i	$-0.0620008\pi$
$90$		0			0
$91$	−2.84492	−	4.58998i	−0.298228	−	0.481161i
$92$			9.72883i			1.01430i
$93$	4.07252	+	11.3841i	0.422301	+	1.18048i
$94$	−6.97906	+	4.02936i	−0.719835	+	0.415597i
$95$		0			0
$96$	12.8728	+	35.9840i	1.31383	+	3.67260i
$97$		−	9.97170i		−	1.01247i	−0.862395	−	0.506237i	$-0.831036\pi$
$97$		−	9.97170i		−	1.01247i	0.862395	−	0.506237i	$-0.168964\pi$
$98$	−15.9433	+	10.5855i	−1.61051	+	1.06930i
$99$	6.13132	−	1.01152i	0.616220	−	0.101661i
$100$		0			0
$101$	−8.06825	−	13.9746i	−0.802821	−	1.39053i	−0.917752	−	0.397153i	$-0.869998\pi$
$101$	−8.06825	−	13.9746i	−0.802821	−	1.39053i	0.114931	−	0.993373i	$-0.463335\pi$
$102$	−9.79675	−	1.78319i	−0.970023	−	0.176563i
$103$	0.453075	+	0.261583i	0.0446428	+	0.0257745i	0.522155	−	0.852850i	$-0.325128\pi$
$103$	0.453075	+	0.261583i	0.0446428	+	0.0257745i	−0.477513	+	0.878625i	$0.658461\pi$
$104$	19.3869			1.90104
$105$		0			0
$106$	16.9344			1.64481
$107$	2.66952	+	1.54125i	0.258073	+	0.148998i	0.623455	−	0.781859i	$-0.285728\pi$
$107$	2.66952	+	1.54125i	0.258073	+	0.148998i	−0.365382	+	0.930858i	$0.619062\pi$
$108$	28.4414	+	0.470601i	2.73677	+	0.0452836i
$109$	−6.77743	−	11.7389i	−0.649160	−	1.12438i	−0.983324	−	0.181864i	$-0.941787\pi$
$109$	−6.77743	−	11.7389i	−0.649160	−	1.12438i	0.334163	−	0.942515i	$-0.391546\pi$
$110$		0			0
$111$	8.01194	+	6.79846i	0.760459	+	0.645281i
$112$	−1.24198	−	39.7180i	−0.117356	−	3.75300i
$113$		−	11.0653i		−	1.04093i	−0.853883	−	0.520466i	$-0.825758\pi$
$113$		−	11.0653i		−	1.04093i	0.853883	−	0.520466i	$-0.174242\pi$
$114$	−12.4291	+	4.44635i	−1.16409	+	0.416439i
$115$		0			0
$116$	13.2638	−	7.65784i	1.23151	−	0.711013i
$117$	2.15759	−	5.73046i	0.199469	−	0.529781i
$118$		−	7.89013i		−	0.726345i
$119$	4.90289	+	2.62989i	0.449447	+	0.241082i
$120$		0			0
$121$	−3.35465	+	5.81043i	−0.304969	+	0.528221i
$122$	9.94824	+	17.2309i	0.900672	+	1.56001i
$123$	3.63410	−	19.9655i	0.327676	−	1.80023i
$124$	33.0939	+	19.1068i	2.97192	+	1.71584i
$125$		0			0
$126$	−20.5371	−	7.00776i	−1.82959	−	0.624301i
$127$	−4.98617			−0.442451			−0.221226	−	0.975223i	$-0.571006\pi$
$127$	−4.98617			−0.442451			−0.221226	+	0.975223i	$0.571006\pi$
$128$	33.4855	+	19.3329i	2.95973	+	1.70880i
$129$	−1.35549	+	7.44695i	−0.119344	+	0.655667i
$130$		0			0
$131$	−5.85196	+	10.1359i	−0.511288	+	0.885577i	0.488626	+	0.872493i	$0.337498\pi$
$131$	−5.85196	+	10.1359i	−0.511288	+	0.885577i	−0.999914	+	0.0130842i	$0.995835\pi$
$132$	12.7075	−	14.9756i	1.10604	−	1.30346i
$133$	7.37192	−	0.230519i	0.639226	−	0.0199886i
$134$			20.2392i			1.74840i
$135$		0			0
$136$	−17.2980	+	9.98702i	−1.48329	+	0.856380i
$137$	−10.9606	+	6.32808i	−0.936423	+	0.540644i	−0.888837	−	0.458223i	$-0.848486\pi$
$137$	−10.9606	+	6.32808i	−0.936423	+	0.540644i	−0.0475860	+	0.998867i	$0.515153\pi$
$138$	7.92370	−	2.83460i	0.674510	−	0.241297i
$139$			18.0304i			1.52932i	0.644434	+	0.764660i	$0.277093\pi$
$139$			18.0304i			1.52932i	−0.644434	+	0.764660i	$0.722907\pi$
$140$		0			0
$141$	3.89291	+	3.30330i	0.327842	+	0.278188i
$142$	5.20654	−	9.01798i	0.436923	−	0.756772i
$143$	−2.11392	−	3.66143i	−0.176775	−	0.306184i
$144$	34.8338	−	28.5803i	2.90282	−	2.38169i
$145$		0			0
$146$	18.3499			1.51865
$147$	9.71673	+	7.25157i	0.801422	+	0.598099i
$148$	33.2103			2.72987
$149$	12.6249	+	7.28898i	1.03427	+	0.597136i	0.918205	−	0.396105i	$-0.129638\pi$
$149$	12.6249	+	7.28898i	1.03427	+	0.597136i	0.116065	+	0.993242i	$0.462972\pi$
$150$		0			0
$151$	3.51450	+	6.08730i	0.286006	+	0.495377i	0.972853	−	0.231425i	$-0.0743389\pi$
$151$	3.51450	+	6.08730i	0.286006	+	0.495377i	−0.686847	+	0.726802i	$0.741006\pi$
$152$	−13.2393	+	22.9312i	−1.07385	+	1.85997i
$153$	1.02689	+	6.22449i	0.0830192	+	0.503220i
$154$	−12.7351	+	7.89337i	−1.02623	+	0.636066i
$155$		0			0
$156$	−6.51867	−	18.2220i	−0.521911	−	1.45892i
$157$	−18.9680	+	10.9512i	−1.51381	+	0.874000i	−0.513943	+	0.857824i	$0.671816\pi$
$157$	−18.9680	+	10.9512i	−1.51381	+	0.874000i	−0.999869	+	0.0161753i	$0.994851\pi$
$158$	−14.0063	+	8.08656i	−1.11428	+	0.643332i
$159$	−3.61375	−	10.1017i	−0.286589	−	0.801117i
$160$		0			0
$161$	−4.69969	+	0.146959i	−0.370387	+	0.0115820i
$162$	−7.90343	−	23.3014i	−0.620952	−	1.83073i
$163$	4.04815	−	7.01159i	0.317075	−	0.549190i	−0.662801	−	0.748795i	$-0.730633\pi$
$163$	4.04815	−	7.01159i	0.317075	−	0.549190i	0.979876	+	0.199605i	$0.0639659\pi$
$164$	−32.0698	−	55.5465i	−2.50423	−	4.33745i
$165$		0			0
$166$	14.1211	+	8.15279i	1.09601	+	0.632780i
$167$	−3.58777			−0.277630			−0.138815	−	0.990318i	$-0.544329\pi$
$167$	−3.58777			−0.277630			−0.138815	+	0.990318i	$0.544329\pi$
$168$	−40.5055	+	15.9352i	−3.12507	+	1.22943i
$169$	8.83407			0.679544
$170$		0			0
$171$	5.30468	+	6.46538i	0.405659	+	0.494420i
$172$	11.9617	+	20.7183i	0.912073	+	1.57976i
$173$	−6.50462	+	11.2663i	−0.494537	+	0.856563i	−0.999980	−	0.00629680i	$-0.997996\pi$
$173$	−6.50462	+	11.2663i	−0.494537	+	0.856563i	0.505443	+	0.862860i	$0.331329\pi$
$174$	−10.1015	−	8.57156i	−0.765794	−	0.649808i
$175$		0			0
$176$		−	31.1110i		−	2.34508i
$177$	−4.70663	+	1.68373i	−0.353772	+	0.126557i
$178$	−29.4020	+	16.9752i	−2.20377	+	1.27235i
$179$	3.50400	−	2.02304i	0.261902	−	0.151209i	−0.363300	−	0.931672i	$-0.618350\pi$
$179$	3.50400	−	2.02304i	0.261902	−	0.151209i	0.625202	+	0.780463i	$0.285017\pi$
$180$		0			0
$181$			9.00970i			0.669686i	0.942274	+	0.334843i	$0.108683\pi$
$181$			9.00970i			0.669686i	−0.942274	+	0.334843i	$0.891317\pi$
$182$	0.461429	+	14.7563i	0.0342034	+	1.09381i
$183$	8.15564	−	9.61136i	0.602882	−	0.710492i
$184$	8.44023	−	14.6189i	0.622222	−	1.07772i
$185$		0			0
$186$	5.91934	−	32.5205i	0.434027	−	2.38452i
$187$	3.77232	+	2.17795i	0.275859	+	0.159267i
$188$	16.1365			1.17688
$189$	0.202289	+	13.7462i	0.0147144	+	0.999892i
$190$		0			0
$191$	22.6067	+	13.0520i	1.63576	+	0.944409i	0.982269	+	0.187478i	$0.0600314\pi$
$191$	22.6067	+	13.0520i	1.63576	+	0.944409i	0.653495	+	0.756931i	$0.273302\pi$
$192$	9.39333	−	51.6063i	0.677905	−	3.72437i
$193$	−3.75401	−	6.50213i	−0.270219	−	0.468034i	0.698699	−	0.715416i	$-0.253763\pi$
$193$	−3.75401	−	6.50213i	−0.270219	−	0.468034i	−0.968918	+	0.247383i	$0.920430\pi$
$194$	−13.6309	+	23.6094i	−0.978642	+	1.69506i
$195$		0			0
$196$	38.2452	−	2.39419i	2.73180	−	0.171014i
$197$		−	20.7941i		−	1.48152i	−0.671772	−	0.740758i	$-0.734466\pi$
$197$		−	20.7941i		−	1.48152i	0.671772	−	0.740758i	$-0.265534\pi$
$198$	−15.8995	−	5.98634i	−1.12993	−	0.425431i
$199$	−19.8822	+	11.4790i	−1.40941	+	0.813725i	−0.995332	−	0.0965149i	$-0.969230\pi$
$199$	−19.8822	+	11.4790i	−1.40941	+	0.813725i	−0.414081	+	0.910240i	$0.635897\pi$
$200$		0			0
$201$	12.0731	−	4.31900i	0.851571	−	0.304639i
$202$			44.1158i			3.10398i
$203$	3.89962	+	6.29163i	0.273699	+	0.441586i
$204$	15.2032	+	12.9006i	1.06444	+	0.903220i
$205$		0			0
$206$	−0.715145	−	1.23867i	−0.0498265	−	0.0863021i
$207$	−3.38180	−	4.12175i	−0.235051	−	0.286482i
$208$	−26.5483	−	15.3277i	−1.84080	−	1.06278i
$209$	5.77441			0.399424
$210$		0			0
$211$	−18.9736			−1.30620			−0.653098	−	0.757273i	$-0.726531\pi$
$211$	−18.9736			−1.30620			−0.653098	+	0.757273i	$0.726531\pi$
$212$	−29.3659	−	16.9544i	−2.01686	−	1.16443i
$213$	−6.49048	−	1.18139i	−0.444720	−	0.0809475i
$214$	−4.21365	−	7.29826i	−0.288039	−	0.498899i
$215$		0			0
$216$	−42.3289	−	25.3814i	−2.88011	−	1.72699i
$217$	−8.72996	+	16.2752i	−0.592628	+	1.10483i
$218$			37.0579i			2.50988i
$219$	−3.91583	−	10.9461i	−0.264607	−	0.739670i
$220$		0			0
$221$	3.71707	−	2.14605i	0.250037	−	0.144359i
$222$	−9.67618	−	27.0483i	−0.649423	−	1.81536i
$223$		−	6.06277i		−	0.405993i	−0.979179	−	0.202997i	$-0.934932\pi$
$223$		−	6.06277i		−	0.405993i	0.979179	−	0.202997i	$-0.0650681\pi$
$224$	−27.5945	+	51.4443i	−1.84374	+	3.43726i
$225$		0			0
$226$	−15.1257	+	26.1985i	−1.00615	+	1.74270i
$227$	10.9025	+	18.8837i	0.723626	+	1.25336i	0.959537	+	0.281582i	$0.0908592\pi$
$227$	10.9025	+	18.8837i	0.723626	+	1.25336i	−0.235911	+	0.971775i	$0.575807\pi$
$228$	26.0049	+	4.73339i	1.72222	+	0.313476i
$229$	−7.94782	−	4.58868i	−0.525207	−	0.303228i	0.213856	−	0.976865i	$-0.431398\pi$
$229$	−7.94782	−	4.58868i	−0.525207	−	0.303228i	−0.739062	+	0.673637i	$0.764731\pi$
$230$		0			0
$231$	7.42621	+	5.91235i	0.488609	+	0.389004i
$232$	−26.5742			−1.74468
$233$	−15.7465	−	9.09122i	−1.03158	−	0.595586i	−0.114146	−	0.993464i	$-0.536413\pi$
$233$	−15.7465	−	9.09122i	−1.03158	−	0.595586i	−0.917438	+	0.397878i	$0.869747\pi$
$234$	−12.9417	+	10.6183i	−0.846025	+	0.694143i
$235$		0			0
$236$	−7.89946	+	13.6823i	−0.514211	+	0.890640i
$237$	7.81271	+	6.62941i	0.507490	+	0.430627i
$238$	−8.01333	−	12.9287i	−0.519427	−	0.838042i
$239$		−	13.1450i		−	0.850278i	−0.905128	−	0.425139i	$-0.860225\pi$
$239$		−	13.1450i		−	0.850278i	0.905128	−	0.425139i	$-0.139775\pi$
$240$		0			0
$241$	0.0154860	−	0.00894087i	0.000997544	−	0.000575932i	−0.499501	−	0.866313i	$-0.666483\pi$
$241$	0.0154860	−	0.00894087i	0.000997544	−	0.000575932i	0.500499	+	0.865737i	$0.333150\pi$
$242$	15.8852	−	9.17135i	1.02114	−	0.589556i
$243$	−12.2132	+	9.68702i	−0.783476	+	0.621422i
$244$		−	39.8400i		−	2.55050i
$245$		0			0
$246$	−35.8963	+	42.3035i	−2.28866	+	2.69717i
$247$	2.84492	−	4.92754i	0.181018	−	0.313532i
$248$	−33.1521	−	57.4211i	−2.10516	−	3.64624i
$249$	1.84991	−	10.1633i	0.117233	−	0.644072i
$250$		0			0
$251$	5.38577			0.339947			0.169973	−	0.985449i	$-0.445632\pi$
$251$	5.38577			0.339947			0.169973	+	0.985449i	$0.445632\pi$
$252$	28.5973	+	32.7135i	1.80146	+	2.06076i
$253$	−3.68125			−0.231438
$254$	11.8055	+	6.81589i	0.740741	+	0.427667i
$255$		0			0
$256$	−22.5700	−	39.0923i	−1.41062	−	2.44327i
$257$	−10.8420	+	18.7790i	−0.676308	+	1.17140i	0.299777	+	0.954009i	$0.403088\pi$
$257$	−10.8420	+	18.7790i	−0.676308	+	1.17140i	−0.976085	+	0.217391i	$0.930245\pi$
$258$	13.3890	−	15.7788i	0.833561	−	0.982346i
$259$	0.501658	+	16.0428i	0.0311715	+	0.996852i
$260$		0			0
$261$	−2.95747	+	7.85492i	−0.183063	+	0.486207i
$262$	27.7107	−	15.9988i	1.71197	−	0.988408i
$263$	−1.24114	+	0.716573i	−0.0765320	+	0.0441858i	−0.537778	−	0.843087i	$-0.680736\pi$
$263$	−1.24114	+	0.716573i	−0.0765320	+	0.0441858i	0.461246	+	0.887272i	$0.347403\pi$
$264$	−32.0868	+	11.4786i	−1.97481	+	0.706462i
$265$		0			0
$266$	−17.7692	−	9.53132i	−1.08950	−	0.584403i
$267$	16.4004	+	13.9164i	1.00369	+	0.851670i
$268$	20.2631	−	35.0968i	1.23777	−	2.14388i
$269$	9.99414	+	17.3104i	0.609354	+	1.05543i	0.991347	+	0.131266i	$0.0419044\pi$
$269$	9.99414	+	17.3104i	0.609354	+	1.05543i	−0.381993	+	0.924165i	$0.624762\pi$
$270$		0			0
$271$	−13.6061	−	7.85550i	−0.826513	−	0.477187i	0.0261443	−	0.999658i	$-0.491677\pi$
$271$	−13.6061	−	7.85550i	−0.826513	−	0.477187i	−0.852657	+	0.522471i	$0.825010\pi$
$272$	31.5838			1.91505
$273$	8.70398	−	3.42421i	0.526789	−	0.207243i
$274$	34.6009			2.09032
$275$		0			0
$276$	−16.5784	−	3.01759i	−0.997904	−	0.181638i
$277$	−1.09487	−	1.89637i	−0.0657844	−	0.113942i	0.831257	−	0.555888i	$-0.187622\pi$
$277$	−1.09487	−	1.89637i	−0.0657844	−	0.113942i	−0.897042	+	0.441946i	$0.854288\pi$
$278$	24.6468	−	42.6896i	1.47822	−	2.56035i
$279$	−20.6623	+	3.40878i	−1.23702	+	0.204078i
$280$		0			0
$281$			0.0597482i			0.00356428i	0.999998	+	0.00178214i	$0.000567273\pi$
$281$			0.0597482i			0.00356428i	−0.999998	+	0.00178214i	$0.999433\pi$
$282$	−4.70155	−	13.1425i	−0.279973	−	0.782622i
$283$	13.8059	−	7.97086i	0.820677	−	0.473818i	−0.0299727	−	0.999551i	$-0.509542\pi$
$283$	13.8059	−	7.97086i	0.820677	−	0.473818i	0.850650	+	0.525733i	$0.176209\pi$
$284$	−18.0573	+	10.4254i	−1.07150	+	0.618633i
$285$		0			0
$286$			11.5586i			0.683474i
$287$	26.3483	−	16.3310i	1.55529	−	0.963986i
$288$	−65.3114	+	10.7748i	−3.84851	+	0.634911i
$289$	6.28895	−	10.8928i	0.369939	−	0.640752i
$290$		0			0
$291$	16.9923	+	3.09292i	0.996107	+	0.181310i
$292$	−31.8206	−	18.3716i	−1.86216	−	1.07512i
$293$	−19.3670			−1.13143			−0.565715	−	0.824601i	$-0.691400\pi$
$293$	−19.3670			−1.13143			−0.565715	+	0.824601i	$0.691400\pi$
$294$	−13.0931	−	30.4515i	−0.763607	−	1.77597i
$295$		0			0
$296$	−49.9030	−	28.8115i	−2.90055	−	1.67464i
$297$	−0.178069	+	10.7618i	−0.0103326	+	0.624465i
$298$	−19.9275	−	34.5154i	−1.15437	−	1.99942i
$299$	−1.81367	+	3.14137i	−0.104887	+	0.181670i
$300$		0			0
$301$	−9.82767	+	6.09129i	−0.566458	+	0.351096i
$302$		−	19.2167i		−	1.10580i
$303$	26.3160	−	9.41422i	1.51182	−	0.540833i
$304$	36.2598	−	20.9346i	2.07964	−	1.20068i
$305$		0			0
$306$	6.07731	−	16.1411i	0.347417	−	0.922724i
$307$		−	17.7639i		−	1.01384i	−0.861993	−	0.506921i	$-0.830784\pi$
$307$		−	17.7639i		−	1.01384i	0.861993	−	0.506921i	$-0.169216\pi$
$308$	29.9867	−	0.937683i	1.70865	−	0.0534294i
$309$	−0.586281	+	0.690928i	−0.0333523	+	0.0393055i
$310$		0			0
$311$	−3.58777	−	6.21419i	−0.203444	−	0.352375i	0.746192	−	0.665731i	$-0.231880\pi$
$311$	−3.58777	−	6.21419i	−0.203444	−	0.352375i	−0.949636	+	0.313356i	$0.898547\pi$
$312$	−6.01323	+	33.0363i	−0.340432	+	1.87031i
$313$	11.7724	+	6.79679i	0.665414	+	0.384177i	0.794337	−	0.607477i	$-0.207818\pi$
$313$	11.7724	+	6.79679i	0.665414	+	0.384177i	−0.128922	+	0.991655i	$0.541152\pi$
$314$	59.8792			3.37918
$315$		0			0
$316$	32.3845			1.82177
$317$	−2.78896	−	1.61021i	−0.156644	−	0.0904383i	0.419629	−	0.907696i	$-0.362160\pi$
$317$	−2.78896	−	1.61021i	−0.156644	−	0.0904383i	−0.576273	+	0.817257i	$0.695493\pi$
$318$	−5.25253	+	28.8570i	−0.294547	+	1.61822i
$319$	2.89762	+	5.01883i	0.162236	+	0.281000i
$320$		0			0
$321$	−3.45438	+	4.07096i	−0.192805	+	0.227219i
$322$	11.3281	+	6.07633i	0.631288	+	0.338621i
$323$			5.86216i			0.326179i
$324$	−9.62359	+	48.3197i	−0.534644	+	2.68443i
$325$		0			0
$326$	−19.1691	+	11.0673i	−1.06168	+	0.612961i
$327$	22.1058	−	7.90806i	1.22245	−	0.437317i
$328$			111.288i			6.14488i
$329$	0.243750	+	7.79503i	0.0134384	+	0.429754i
$330$		0			0
$331$	1.59353	−	2.76008i	0.0875885	−	0.151708i	−0.818903	−	0.573932i	$-0.805417\pi$
$331$	1.59353	−	2.76008i	0.0875885	−	0.151708i	0.906491	+	0.422224i	$0.138751\pi$
$332$	−16.3249	−	28.2755i	−0.895944	−	1.55182i
$333$	−14.0700	+	11.5441i	−0.771031	+	0.632612i
$334$	8.49454	+	4.90433i	0.464801	+	0.268353i
$335$		0			0
$336$	68.0668	+	10.2029i	3.71335	+	0.556616i
$337$	33.9495			1.84935			0.924673	−	0.380763i	$-0.124339\pi$
$337$	33.9495			1.84935			0.924673	+	0.380763i	$0.124339\pi$
$338$	−20.9159	−	12.0758i	−1.13768	−	0.656837i
$339$	18.8558	+	3.43211i	1.02410	+	0.186406i
$340$		0			0
$341$	−7.22973	+	12.5223i	−0.391512	+	0.678118i
$342$	−3.72168	−	22.5590i	−0.201246	−	1.21985i
$343$	1.73427	+	18.4389i	0.0936419	+	0.995606i
$344$		−	41.5095i		−	2.23804i
$345$		0			0
$346$	30.8012	−	17.7831i	1.65588	−	0.956024i
$347$	−24.2234	+	13.9854i	−1.30038	+	0.750773i	−0.980469	−	0.196675i	$-0.936986\pi$
$347$	−24.2234	+	13.9854i	−1.30038	+	0.750773i	−0.319909	+	0.947448i	$0.603652\pi$
$348$	8.93534	+	24.9774i	0.478985	+	1.33893i
$349$		−	19.3368i		−	1.03508i	−0.855660	−	0.517539i	$-0.826848\pi$
$349$		−	19.3368i		−	1.03508i	0.855660	−	0.517539i	$-0.173152\pi$
$350$		0			0
$351$	9.09579	+	5.45406i	0.485497	+	0.291116i
$352$	−22.8524	+	39.5816i	−1.21804	+	2.10971i
$353$	3.44352	+	5.96436i	0.183280	+	0.317451i	0.942996	−	0.332805i	$-0.107995\pi$
$353$	3.44352	+	5.96436i	0.183280	+	0.317451i	−0.759715	+	0.650256i	$0.774662\pi$
$354$	13.4452	+	2.44728i	0.714604	+	0.130071i
$355$		0			0
$356$	67.9812			3.60300
$357$	−6.00220	+	7.53906i	−0.317670	+	0.399010i
$358$	−11.0616			−0.584625
$359$	−18.0588	−	10.4263i	−0.953108	−	0.550277i	−0.0590629	−	0.998254i	$-0.518811\pi$
$359$	−18.0588	−	10.4263i	−0.953108	−	0.550277i	−0.894045	+	0.447977i	$0.852145\pi$
$360$		0			0
$361$	−5.61440	−	9.72443i	−0.295495	−	0.511812i
$362$	12.3159	−	21.3317i	0.647309	−	1.12117i
$363$	−8.86077	−	7.51873i	−0.465070	−	0.394631i
$364$	13.9736	−	26.0509i	0.732416	−	1.36544i
$365$		0			0
$366$	−32.4479	+	11.6078i	−1.69608	+	0.606751i
$367$	−20.7408	+	11.9747i	−1.08266	+	0.625075i	−0.931613	−	0.363451i	$-0.881598\pi$
$367$	−20.7408	+	11.9747i	−1.08266	+	0.625075i	−0.151048	+	0.988526i	$0.548265\pi$
$368$	−23.1160	+	13.3461i	−1.20501	+	0.695711i
$369$	32.8951	+	12.3854i	1.71245	+	0.644759i
$370$		0			0
$371$	7.74654	−	14.4418i	0.402180	−	0.749782i
$372$	−42.8236	+	50.4673i	−2.22030	+	2.61661i
$373$	−1.99026	+	3.44723i	−0.103052	+	0.178491i	−0.912940	−	0.408093i	$-0.866194\pi$
$373$	−1.99026	+	3.44723i	−0.103052	+	0.178491i	0.809889	+	0.586583i	$0.199527\pi$
$374$	−5.95433	−	10.3132i	−0.307891	−	0.533283i
$375$		0			0
$376$	−24.2473	−	13.9992i	−1.25046	−	0.721954i
$377$	5.71037			0.294099
$378$	18.3116	−	32.8227i	0.941846	−	1.68822i
$379$	−13.9203			−0.715038			−0.357519	−	0.933906i	$-0.616377\pi$
$379$	−13.9203			−0.715038			−0.357519	+	0.933906i	$0.616377\pi$
$380$		0			0
$381$	1.54656	−	8.49670i	0.0792327	−	0.435299i
$382$	−35.6830	−	61.8048i	−1.82570	−	3.16221i
$383$	7.90064	−	13.6843i	0.403704	−	0.699236i	−0.590466	−	0.807063i	$-0.701056\pi$
$383$	7.90064	−	13.6843i	0.403704	−	0.699236i	0.994170	+	0.107827i	$0.0343892\pi$
$384$	−43.3304	+	51.0646i	−2.21120	+	2.60588i
$385$		0			0
$386$			20.5263i			1.04476i
$387$	−12.2696	−	4.61964i	−0.623697	−	0.234829i
$388$	47.2747	−	27.2940i	2.40001	−	1.38564i
$389$	−21.7212	+	12.5407i	−1.10131	+	0.635841i	−0.936564	−	0.350495i	$-0.886013\pi$
$389$	−21.7212	+	12.5407i	−1.10131	+	0.635841i	−0.164744	+	0.986336i	$0.552680\pi$
$390$		0			0
$391$		−	3.73720i		−	0.188998i
$392$	−59.5458	−	29.5820i	−3.00752	−	1.49412i
$393$	−15.4570	−	13.1159i	−0.779702	−	0.661610i
$394$	−28.4246	+	49.2329i	−1.43201	+	2.48032i
$395$		0			0
$396$	21.5778	+	26.2992i	1.08433	+	1.32158i
$397$	1.27064	+	0.733605i	0.0637716	+	0.0368186i	0.531547	−	0.847029i	$-0.321611\pi$
$397$	1.27064	+	0.733605i	0.0637716	+	0.0368186i	−0.467775	+	0.883847i	$0.654944\pi$
$398$	62.7653			3.14614
$399$	−1.89373	+	12.6336i	−0.0948051	+	0.632473i
$400$		0			0
$401$	18.5840	+	10.7295i	0.928039	+	0.535804i	0.886191	−	0.463320i	$-0.153342\pi$
$401$	18.5840	+	10.7295i	0.928039	+	0.535804i	0.0418482	+	0.999124i	$0.486675\pi$
$402$	−34.4887	−	6.27759i	−1.72014	−	0.313098i
$403$	7.12384	+	12.3389i	0.354864	+	0.614642i
$404$	44.1680	−	76.5012i	2.19744	−	3.80608i
$405$		0			0
$406$	−0.632495	−	20.2269i	−0.0313902	−	1.00385i
$407$			12.5663i			0.622889i
$408$	−11.6531	−	32.5744i	−0.576914	−	1.61267i
$409$	−6.02404	+	3.47798i	−0.297870	+	0.171975i	−0.641485	−	0.767135i	$-0.721682\pi$
$409$	−6.02404	+	3.47798i	−0.297870	+	0.171975i	0.343616	+	0.939110i	$0.388348\pi$
$410$		0			0
$411$	−7.38374	−	20.6401i	−0.364213	−	1.01810i
$412$			2.86396i			0.141097i
$413$	−6.72879	−	3.60930i	−0.331102	−	0.177602i
$414$	2.37262	+	14.3816i	0.116608	+	0.706817i
$415$		0			0
$416$	22.5177	+	39.0019i	1.10402	+	1.91222i
$417$	−30.7248	−	5.59250i	−1.50460	−	0.273866i
$418$	−13.6717	−	7.89337i	−0.668706	−	0.386077i
$419$	−34.8831			−1.70415			−0.852076	−	0.523419i	$-0.824656\pi$
$419$	−34.8831			−1.70415			−0.852076	+	0.523419i	$0.824656\pi$
$420$		0			0
$421$	−29.6603			−1.44555			−0.722777	−	0.691082i	$-0.757134\pi$
$421$	−29.6603			−1.44555			−0.722777	+	0.691082i	$0.757134\pi$
$422$	44.9227	+	25.9361i	2.18680	+	1.26255i
$423$	−6.83645	+	5.60914i	−0.332400	+	0.272726i
$424$	29.4175	+	50.9526i	1.42864	+	2.47448i
$425$		0			0
$426$	13.7522	+	11.6693i	0.666297	+	0.565380i
$427$	19.2454	−	0.601804i	0.931353	−	0.0291233i
$428$			16.8745i			0.815661i
$429$	6.89494	−	2.46657i	0.332891	−	0.119087i
$430$		0			0
$431$	−7.32938	+	4.23162i	−0.353044	+	0.203830i	−0.666025	−	0.745929i	$-0.732006\pi$
$431$	−7.32938	+	4.23162i	−0.353044	+	0.203830i	0.312981	+	0.949759i	$0.398672\pi$
$432$	37.8979	+	68.2234i	1.82336	+	3.28240i
$433$			10.6435i			0.511495i	0.966744	+	0.255748i	$0.0823216\pi$
$433$			10.6435i			0.511495i	−0.966744	+	0.255748i	$0.917678\pi$
$434$	42.9169	−	26.6004i	2.06008	−	1.27686i
$435$		0			0
$436$	37.1017	−	64.2620i	1.77685	−	3.07759i
$437$	−2.47711	−	4.29049i	−0.118496	−	0.205242i
$438$	−5.69160	+	31.2692i	−0.271955	+	1.49410i
$439$	10.9548	+	6.32477i	0.522845	+	0.301865i	0.738098	−	0.674694i	$-0.235724\pi$
$439$	10.9548	+	6.32477i	0.522845	+	0.301865i	−0.215253	+	0.976558i	$0.569058\pi$
$440$		0			0
$441$	−15.3709	+	14.3086i	−0.731947	+	0.681362i
$442$	−11.7342			−0.558141
$443$	22.2838	+	12.8656i	1.05874	+	0.611261i	0.925082	−	0.379767i	$-0.123996\pi$
$443$	22.2838	+	12.8656i	1.05874	+	0.611261i	0.133654	+	0.991028i	$0.457329\pi$
$444$	−10.3008	+	56.5920i	−0.488856	+	2.68574i
$445$		0			0
$446$	−8.28756	+	14.3545i	−0.392427	+	0.679704i
$447$	−16.3367	+	19.2526i	−0.772697	+	0.910618i
$448$	68.1044	−	42.2118i	3.21763	−	1.99432i
$449$		−	35.6974i		−	1.68466i	−0.538960	−	0.842331i	$-0.681183\pi$
$449$		−	35.6974i		−	1.68466i	0.538960	−	0.842331i	$-0.318817\pi$
$450$		0			0
$451$	21.0180	−	12.1348i	0.989700	−	0.571404i
$452$	52.4590	−	30.2872i	2.46747	−	1.42459i
$453$	−11.4632	+	4.10080i	−0.538586	+	0.192672i
$454$		−	59.6132i		−	2.79778i
$455$		0			0
$456$	−34.9695	−	29.6731i	−1.63760	−	1.38957i
$457$	−5.55255	+	9.61730i	−0.259737	+	0.449878i	−0.966172	−	0.257900i	$-0.916969\pi$
$457$	−5.55255	+	9.61730i	−0.259737	+	0.449878i	0.706434	+	0.707779i	$0.250303\pi$
$458$	12.5451	+	21.7287i	0.586192	+	1.01531i
$459$	−10.9254	−	0.180775i	−0.509953	−	0.00843785i
$460$		0			0
$461$	−18.8795			−0.879304			−0.439652	−	0.898168i	$-0.644898\pi$
$461$	−18.8795			−0.879304			−0.439652	+	0.898168i	$0.644898\pi$
$462$	−9.50066	−	24.1496i	−0.442011	−	1.12354i
$463$	−14.6440			−0.680565			−0.340282	−	0.940323i	$-0.610523\pi$
$463$	−14.6440			−0.680565			−0.340282	+	0.940323i	$0.610523\pi$
$464$	36.3906	+	21.0101i	1.68939	+	0.975371i
$465$		0			0
$466$	24.8546	+	43.0495i	1.15137	+	1.99423i
$467$	2.71213	−	4.69754i	0.125502	−	0.217376i	−0.796427	−	0.604735i	$-0.793279\pi$
$467$	2.71213	−	4.69754i	0.125502	−	0.217376i	0.921929	+	0.387359i	$0.126612\pi$
$468$	33.0731	−	5.45626i	1.52880	−	0.252216i
$469$	17.2602	+	9.25832i	0.797003	+	0.427509i
$470$		0			0
$471$	−12.7781	−	35.7192i	−0.588783	−	1.64585i
$472$	23.7401	−	13.7063i	1.09272	−	0.630885i
$473$	−7.83952	+	4.52615i	−0.360462	+	0.208113i
$474$	−9.43557	−	26.3757i	−0.433390	−	1.21148i
$475$		0			0
$476$	0.951932	+	30.4424i	0.0436317	+	1.39533i
$477$	18.3347	−	3.02478i	0.839488	−	0.138495i
$478$	−17.9686	+	31.1226i	−0.821866	+	1.42351i
$479$	−1.85555	−	3.21391i	−0.0847823	−	0.146847i	0.820516	−	0.571623i	$-0.193686\pi$
$479$	−1.85555	−	3.21391i	−0.0847823	−	0.146847i	−0.905298	+	0.424776i	$0.860353\pi$
$480$		0			0
$481$	10.7234	+	6.19113i	0.488943	+	0.282291i
$482$	−0.0488872			−0.00222675
$483$	1.20728	−	8.05409i	0.0549329	−	0.366474i
$484$	−36.7288			−1.66949
$485$		0			0
$486$	42.1582	−	6.24048i	1.91233	−	0.283074i
$487$	−9.16240	−	15.8697i	−0.415188	−	0.719127i	0.580260	−	0.814431i	$-0.302951\pi$
$487$	−9.16240	−	15.8697i	−0.415188	−	0.719127i	−0.995448	+	0.0953043i	$0.969618\pi$
$488$	−34.5632	+	59.8652i	−1.56460	+	2.70997i
$489$	10.6925	+	9.07304i	0.483532	+	0.410297i
$490$		0			0
$491$		−	36.7134i		−	1.65685i	−0.560098	−	0.828426i	$-0.689237\pi$
$491$		−	36.7134i		−	1.65685i	0.560098	−	0.828426i	$-0.310763\pi$
$492$	104.601	−	37.4198i	4.71579	−	1.68701i
$493$	−5.09510	+	2.94166i	−0.229472	+	0.132486i
$494$	−13.4715	+	7.77777i	−0.606111	+	0.349938i
$495$		0			0
$496$			104.843i			4.70759i
$497$	−5.30894	−	8.56542i	−0.238138	−	0.384212i
$498$	−18.2727	+	21.5343i	−0.818820	+	0.964973i
$499$	−0.535767	+	0.927975i	−0.0239842	+	0.0415419i	−0.877768	−	0.479085i	$-0.840968\pi$
$499$	−0.535767	+	0.927975i	−0.0239842	+	0.0415419i	0.853784	+	0.520627i	$0.174302\pi$
$500$		0			0
$501$	1.11282	−	6.11374i	0.0497170	−	0.273142i
$502$	−12.7516	−	7.36212i	−0.569131	−	0.328588i
$503$	27.1662			1.21128			0.605640	−	0.795739i	$-0.292917\pi$
$503$	27.1662			1.21128			0.605640	+	0.795739i	$0.292917\pi$
$504$	−14.5908	−	73.9661i	−0.649926	−	3.29471i
$505$		0			0
$506$	8.71588	+	5.03212i	0.387468	+	0.223705i
$507$	−2.74006	+	15.0537i	−0.121690	+	0.668559i
$508$	−13.6479	−	23.6388i	−0.605527	−	1.04880i
$509$	−11.8003	+	20.4387i	−0.523037	+	0.905927i	0.476603	+	0.879119i	$0.341868\pi$
$509$	−11.8003	+	20.4387i	−0.523037	+	0.905927i	−0.999641	+	0.0268088i	$0.991465\pi$
$510$		0			0
$511$	8.39408	−	15.6490i	0.371332	−	0.692272i
$512$			46.0773i			2.03635i
$513$	−12.6627	+	7.03409i	−0.559071	+	0.310563i
$514$	51.3401	−	29.6412i	2.26452	−	1.30742i
$515$		0			0
$516$	−39.0153	+	13.9572i	−1.71755	+	0.614432i
$517$			6.10583i			0.268534i
$518$	20.7421	−	38.6694i	0.911356	−	1.69904i
$519$	−17.1809	−	14.5787i	−0.754157	−	0.639933i
$520$		0			0
$521$	−12.5487	−	21.7350i	−0.549770	−	0.952230i	−0.998290	−	0.0584568i	$-0.981382\pi$
$521$	−12.5487	−	21.7350i	−0.549770	−	0.952230i	0.448520	−	0.893773i	$-0.351951\pi$
$522$	17.7396	−	14.5549i	0.776440	−	0.637050i
$523$	5.29103	+	3.05478i	0.231361	+	0.133576i	0.611200	−	0.791476i	$-0.290687\pi$
$523$	5.29103	+	3.05478i	0.231361	+	0.133576i	−0.379839	+	0.925053i	$0.624021\pi$
$524$	−64.0708			−2.79895
$525$		0			0
$526$	3.91810			0.170837
$527$	−12.7126	−	7.33960i	−0.553768	−	0.319718i
$528$	53.0148	+	9.64971i	2.30717	+	0.419950i
$529$	−9.92081	−	17.1833i	−0.431340	−	0.747102i
$530$		0			0
$531$	−1.40932	−	8.54258i	−0.0611592	−	0.370716i
$532$	21.2709	+	34.3184i	0.922211	+	1.48789i
$533$		−	23.9141i		−	1.03583i
$534$	−19.8071	−	55.3677i	−0.857136	−	2.39599i
$535$		0			0
$536$	−60.8963	+	35.1585i	−2.63032	+	1.51862i
$537$	2.36053	+	6.59849i	0.101864	+	0.284746i
$538$		−	54.6463i		−	2.35597i
$539$	0.905929	+	14.4715i	0.0390211	+	0.623330i
$540$		0			0
$541$	11.2979	−	19.5686i	0.485737	−	0.841321i	−0.514129	−	0.857713i	$-0.671885\pi$
$541$	11.2979	−	19.5686i	0.485737	−	0.841321i	0.999866	+	0.0163924i	$0.00521808\pi$
$542$	21.4763	+	37.1980i	0.922485	+	1.59779i
$543$	−15.3530	−	2.79454i	−0.658860	−	0.119925i
$544$	−40.1831	−	23.1997i	−1.72284	−	0.994680i
$545$		0			0
$546$	−25.2887	−	3.79067i	−1.08225	−	0.162226i
$547$	20.6880			0.884556			0.442278	−	0.896878i	$-0.354170\pi$
$547$	20.6880			0.884556			0.442278	+	0.896878i	$0.354170\pi$
$548$	−60.0013	−	34.6418i	−2.56313	−	1.47982i
$549$	13.8486	+	16.8788i	0.591045	+	0.720369i
$550$		0			0
$551$	−3.89962	+	6.75433i	−0.166129	+	0.287744i
$552$	22.2935	+	18.9169i	0.948874	+	0.805158i
$553$	0.489184	+	15.6439i	0.0208022	+	0.665246i
$554$			5.98657i			0.254345i
$555$		0			0
$556$	−85.4801	+	49.3520i	−3.62516	+	2.09299i
$557$	4.08989	−	2.36130i	0.173294	−	0.100051i	−0.410844	−	0.911706i	$-0.634766\pi$
$557$	4.08989	−	2.36130i	0.173294	−	0.100051i	0.584138	+	0.811654i	$0.301433\pi$
$558$	53.5806	+	20.1737i	2.26825	+	0.854022i
$559$			8.91972i			0.377264i
$560$		0			0
$561$	−4.88140	+	5.75269i	−0.206093	+	0.242879i
$562$	0.0816733	−	0.141462i	0.00344518	−	0.00596723i
$563$	16.9161	+	29.2995i	0.712927	+	1.23483i	0.963754	+	0.266794i	$0.0859643\pi$
$563$	16.9161	+	29.2995i	0.712927	+	1.23483i	−0.250826	+	0.968032i	$0.580702\pi$
$564$	−5.00506	+	27.4974i	−0.210751	+	1.15785i
$565$		0			0
$566$	−43.5833			−1.83194
$567$	−23.4871	−	3.91896i	−0.986364	−	0.164581i
$568$	36.1781			1.51800
$569$	21.5858	+	12.4626i	0.904926	+	0.522459i	0.878795	−	0.477199i	$-0.158348\pi$
$569$	21.5858	+	12.4626i	0.904926	+	0.522459i	0.0261307	+	0.999659i	$0.491681\pi$
$570$		0			0
$571$	−1.10062	−	1.90633i	−0.0460596	−	0.0797776i	0.842076	−	0.539358i	$-0.181333\pi$
$571$	−1.10062	−	1.90633i	−0.0460596	−	0.0797776i	−0.888136	+	0.459581i	$0.848000\pi$
$572$	11.5723	−	20.0437i	0.483860	−	0.838071i
$573$	−29.2532	+	34.4747i	−1.22207	+	1.44020i
$574$	−84.7071	+	2.64879i	−3.53561	+	0.110558i
$575$		0			0
$576$	85.0264	+	32.0135i	3.54277	+	1.33389i
$577$	−21.9455	+	12.6702i	−0.913602	+	0.527469i	−0.881588	−	0.472019i	$-0.843525\pi$
$577$	−21.9455	+	12.6702i	−0.913602	+	0.527469i	−0.0320140	+	0.999487i	$0.510192\pi$
$578$	−29.7800	+	17.1935i	−1.23868	+	0.715154i
$579$	12.2443	−	4.38026i	0.508858	−	0.182037i
$580$		0			0
$581$	13.4124	−	8.31314i	0.556440	−	0.344887i
$582$	−36.0038	−	30.5507i	−1.49240	−	1.26637i
$583$	6.41531	−	11.1116i	0.265695	−	0.460197i
$584$	31.8766	+	55.2118i	1.31906	+	2.28468i
$585$		0			0
$586$	45.8540	+	26.4738i	1.89421	+	1.09362i
$587$	−21.7712			−0.898593			−0.449297	−	0.893383i	$-0.648325\pi$
$587$	−21.7712			−0.898593			−0.449297	+	0.893383i	$0.648325\pi$
$588$	−7.78269	+	65.9145i	−0.320953	+	2.71827i
$589$	−19.4595			−0.801816
$590$		0			0
$591$	35.4342	+	6.44970i	1.45757	+	0.265305i
$592$	45.5580	+	78.9088i	1.87242	+	3.24313i
$593$	17.4071	−	30.1501i	0.714826	−	1.23811i	−0.248201	−	0.968709i	$-0.579839\pi$
$593$	17.4071	−	30.1501i	0.714826	−	1.23811i	0.963027	−	0.269406i	$-0.0868273\pi$
$594$	15.1326	−	25.2367i	0.620897	−	1.03548i
$595$		0			0
$596$			79.8041i			3.26890i
$597$	−13.3940	−	37.4408i	−0.548178	−	1.53235i
$598$	8.58823	−	4.95842i	0.351199	−	0.202765i
$599$	−5.38292	+	3.10783i	−0.219940	+	0.126982i	−0.605922	−	0.795524i	$-0.707196\pi$
$599$	−5.38292	+	3.10783i	−0.219940	+	0.126982i	0.385983	+	0.922506i	$0.373863\pi$
$600$		0			0
$601$		−	29.5235i		−	1.20429i	−0.798388	−	0.602144i	$-0.794313\pi$
$601$		−	29.5235i		−	1.20429i	0.798388	−	0.602144i	$-0.205687\pi$
$602$	31.5949	−	0.987972i	1.28771	−	0.0402667i
$603$	3.61508	+	21.9128i	0.147218	+	0.892359i
$604$	−19.2394	+	33.3237i	−0.782841	+	1.35592i
$605$		0			0
$606$	−75.1757	−	13.6834i	−3.05380	−	0.555850i
$607$	−16.1380	−	9.31727i	−0.655021	−	0.378176i	0.135356	−	0.990797i	$-0.456782\pi$
$607$	−16.1380	−	9.31727i	−0.655021	−	0.378176i	−0.790377	+	0.612621i	$0.790115\pi$
$608$	−61.5096			−2.49454
$609$	−11.9308	+	4.69368i	−0.483461	+	0.190197i
$610$		0			0
$611$	5.21036	+	3.00820i	0.210788	+	0.121699i
$612$	−26.6988	+	21.9057i	−1.07924	+	0.885487i
$613$	2.59472	+	4.49418i	0.104800	+	0.181518i	0.913656	−	0.406487i	$-0.133247\pi$
$613$	2.59472	+	4.49418i	0.104800	+	0.181518i	−0.808857	+	0.588006i	$0.799913\pi$
$614$	−24.2826	+	42.0586i	−0.979965	+	1.69735i
$615$		0			0
$616$	−45.8727	−	24.6059i	−1.84826	−	0.991401i
$617$			8.86686i			0.356966i	0.983943	+	0.178483i	$0.0571190\pi$
$617$			8.86686i			0.356966i	−0.983943	+	0.178483i	$0.942881\pi$
$618$	2.33257	−	0.834447i	0.0938298	−	0.0335664i
$619$	20.2601	−	11.6972i	0.814321	−	0.470148i	−0.0341335	−	0.999417i	$-0.510867\pi$
$619$	20.2601	−	11.6972i	0.814321	−	0.470148i	0.848454	+	0.529269i	$0.177534\pi$
$620$		0			0
$621$	8.07262	−	4.48432i	0.323943	−	0.179949i
$622$			19.6173i			0.786582i
$623$	1.02689	+	32.8395i	0.0411415	+	1.31569i
$624$	34.3537	−	40.4856i	1.37525	−	1.62072i
$625$		0			0
$626$	−18.5819	−	32.1847i	−0.742680	−	1.28636i
$627$	−1.79105	+	9.83989i	−0.0715275	+	0.392967i
$628$	−103.837	−	59.9501i	−4.14353	−	2.39227i
$629$	−12.7573			−0.508666
$630$		0			0
$631$	−8.27702			−0.329503			−0.164752	−	0.986335i	$-0.552682\pi$
$631$	−8.27702			−0.329503			−0.164752	+	0.986335i	$0.552682\pi$
$632$	−48.6621	−	28.0951i	−1.93568	−	1.11756i
$633$	5.88504	−	32.3320i	0.233909	−	1.28508i
$634$	4.40217	+	7.62479i	0.174833	+	0.302819i
$635$		0			0
$636$	37.9996	−	44.7822i	1.50678	−	1.77573i
$637$	12.7954	+	6.35669i	0.506973	+	0.251861i
$638$		−	15.8437i		−	0.627258i
$639$	4.02630	−	10.6937i	0.159278	−	0.423035i
$640$		0			0
$641$	35.6157	−	20.5627i	1.40673	−	0.812179i	0.411663	−	0.911336i	$-0.364948\pi$
$641$	35.6157	−	20.5627i	1.40673	−	0.812179i	0.995072	+	0.0991572i	$0.0316147\pi$
$642$	13.7436	−	4.91658i	0.542415	−	0.194042i
$643$		−	3.55349i		−	0.140136i	−0.997542	−	0.0700680i	$-0.977678\pi$
$643$		−	3.55349i		−	0.140136i	0.997542	−	0.0700680i	$-0.0223216\pi$
$644$	−13.5605	−	21.8784i	−0.534357	−	0.862130i
$645$		0			0
$646$	8.01333	−	13.8795i	0.315280	−	0.546081i
$647$	−23.3627	−	40.4653i	−0.918481	−	1.59086i	−0.801724	−	0.597695i	$-0.796084\pi$
$647$	−23.3627	−	40.4653i	−0.918481	−	1.59086i	−0.116757	−	0.993161i	$-0.537250\pi$
$648$	56.3804	−	64.2580i	2.21483	−	2.52429i
$649$	−5.17718	−	2.98905i	−0.203222	−	0.117330i
$650$		0			0
$651$	−25.0260	−	19.9244i	−0.980848	−	0.780899i
$652$	44.3215			1.73576
$653$	1.64369	+	0.948985i	0.0643226	+	0.0371367i	0.531816	−	0.846860i	$-0.321510\pi$
$653$	1.64369	+	0.948985i	0.0643226	+	0.0371367i	−0.467494	+	0.883996i	$0.654843\pi$
$654$	−63.1486	−	11.4942i	−2.46930	−	0.449460i
$655$		0			0
$656$	87.9870	−	152.398i	3.43532	−	5.95014i
$657$	19.8673	−	3.27763i	0.775098	−	0.127872i
$658$	10.0784	−	18.7890i	0.392896	−	0.732472i
$659$			2.32588i			0.0906035i	0.998973	+	0.0453017i	$0.0144249\pi$
$659$			2.32588i			0.0906035i	−0.998973	+	0.0453017i	$0.985575\pi$
$660$		0			0
$661$	−8.03266	+	4.63766i	−0.312434	+	0.180384i	−0.648015	−	0.761627i	$-0.724401\pi$
$661$	−8.03266	+	4.63766i	−0.312434	+	0.180384i	0.335581	+	0.942011i	$0.391067\pi$
$662$	−7.54583	+	4.35659i	−0.293277	+	0.169324i
$663$	2.50406	+	6.99972i	0.0972496	+	0.271846i
$664$			56.6505i			2.19846i
$665$		0			0
$666$	49.0930	−	8.09915i	1.90231	−	0.313836i
$667$	2.48605	−	4.30597i	0.0962603	−	0.166728i
$668$	−9.82025	−	17.0092i	−0.379957	−	0.658105i
$669$	10.3313	+	1.88049i	0.399430	+	0.0727039i
$670$		0			0
$671$	15.0749			0.581961
$672$	−79.1047	−	62.9790i	−3.05153	−	2.42947i
$673$	−26.5356			−1.02287			−0.511436	−	0.859321i	$-0.670886\pi$
$673$	−26.5356			−1.02287			−0.511436	+	0.859321i	$0.670886\pi$
$674$	−80.3801	−	46.4075i	−3.09613	−	1.78755i
$675$		0			0
$676$	24.1802	+	41.8813i	0.930006	+	1.61082i
$677$	−18.3673	+	31.8130i	−0.705911	+	1.22267i	0.260450	+	0.965487i	$0.416129\pi$
$677$	−18.3673	+	31.8130i	−0.705911	+	1.22267i	−0.966362	+	0.257187i	$0.917204\pi$
$678$	−39.9521	−	33.9010i	−1.53435	−	1.30196i
$679$	13.8990	+	22.4246i	0.533394	+	0.860577i
$680$		0			0
$681$	−35.5605	+	12.7213i	−1.36268	+	0.487482i
$682$	34.2348	−	19.7655i	1.31092	−	0.756859i
$683$	44.3300	−	25.5940i	1.69624	−	0.979326i	0.746976	−	0.664851i	$-0.231505\pi$
$683$	44.3300	−	25.5940i	1.69624	−	0.979326i	0.949266	−	0.314475i	$-0.101829\pi$
$684$	−16.1319	+	42.8456i	−0.616818	+	1.63824i
$685$		0			0
$686$	21.0990	−	46.0273i	0.805565	−	1.75733i
$687$	10.2845	−	12.1202i	0.392379	−	0.462416i
$688$	−32.8183	+	56.8430i	−1.25119	+	2.16712i
$689$	−6.32135	−	10.9489i	−0.240824	−	0.417120i
$690$		0			0
$691$	15.4415	+	8.91516i	0.587423	+	0.339149i	0.764078	−	0.645124i	$-0.223194\pi$
$691$	15.4415	+	8.91516i	0.587423	+	0.339149i	−0.176655	+	0.984273i	$0.556528\pi$
$692$	−71.2164			−2.70724
$693$	−12.3783	+	10.8208i	−0.470214	+	0.411049i
$694$	76.4696			2.90275
$695$		0			0
$696$	8.24252	−	45.2838i	0.312432	−	1.71648i
$697$	12.3192	+	21.3374i	0.466622	+	0.808213i
$698$	−26.4327	+	45.7827i	−1.00049	+	1.73290i
$699$	20.3760	−	24.0130i	0.770691	−	0.908254i
$700$		0			0
$701$			42.3606i			1.59994i	0.600041	+	0.799970i	$0.295151\pi$
$701$			42.3606i			1.59994i	−0.600041	+	0.799970i	$0.704849\pi$
$702$	−14.0801	−	25.3468i	−0.531419	−	0.956654i
$703$	−14.6460	+	8.45586i	−0.552384	+	0.318919i
$704$	54.3268	−	31.3656i	2.04752	−	1.18214i
$705$		0			0
$706$		−	18.8286i		−	0.708624i
$707$	37.6225	+	20.1806i	1.41494	+	0.758968i
$708$	−20.8651	−	17.7049i	−0.784159	−	0.665392i
$709$	15.3029	−	26.5055i	0.574714	−	0.995434i	−0.421359	−	0.906894i	$-0.638447\pi$
$709$	15.3029	−	26.5055i	0.574714	−	0.995434i	0.996073	−	0.0885399i	$-0.0282201\pi$
$710$		0			0
$711$	−13.7201	+	11.2570i	−0.514545	+	0.422172i
$712$	−102.151	−	58.9770i	−3.82828	−	2.21026i
$713$	12.4057			0.464596
$714$	24.5166	−	9.64504i	0.917512	−	0.360957i
$715$		0			0
$716$	19.1820	+	11.0747i	0.716863	+	0.413881i
$717$	22.3997	+	4.07718i	0.836533	+	0.152265i
$718$	28.5045	+	49.3713i	1.06378	+	1.84252i
$719$	11.4617	−	19.8522i	0.427449	−	0.740364i	−0.569196	−	0.822202i	$-0.692746\pi$
$719$	11.4617	−	19.8522i	0.427449	−	0.740364i	0.996646	+	0.0818377i	$0.0260789\pi$
$720$		0			0
$721$	−1.38349	+	0.0432616i	−0.0515238	+	0.00161115i
$722$			30.6986i			1.14248i
$723$	0.0104324	+	0.0291622i	0.000387985	+	0.00108455i
$724$	−42.7139	+	24.6609i	−1.58745	+	0.916515i
$725$		0			0
$726$	10.7013	+	29.9140i	0.397164	+	1.11021i
$727$		−	32.1534i		−	1.19250i	−0.802798	−	0.596252i	$-0.796656\pi$
$727$		−	32.1534i		−	1.19250i	0.802798	−	0.596252i	$-0.203344\pi$
$728$	−43.5977	+	27.0223i	−1.61584	+	1.00151i
$729$	−12.7190	−	23.8165i	−0.471075	−	0.882093i
$730$		0			0
$731$	−4.59493	−	7.95866i	−0.169950	−	0.294362i
$732$	67.8895	+	12.3572i	2.50927	+	0.456734i
$733$	11.8271	+	6.82836i	0.436843	+	0.252211i	0.702258	−	0.711923i	$-0.252176\pi$
$733$	11.8271	+	6.82836i	0.436843	+	0.252211i	−0.265415	+	0.964134i	$0.585509\pi$
$734$	65.4757			2.41675
$735$		0			0
$736$	39.2131			1.44541
$737$	13.2801	+	7.66729i	0.489180	+	0.282428i
$738$	−60.9535	−	74.2904i	−2.24373	−	2.73467i
$739$	9.19147	+	15.9201i	0.338114	+	0.585630i	0.984078	−	0.177737i	$-0.0568778\pi$
$739$	9.19147	+	15.9201i	0.338114	+	0.585630i	−0.645964	+	0.763368i	$0.723544\pi$
$740$		0			0
$741$	7.51438	+	6.37626i	0.276048	+	0.234238i
$742$	−38.0824	+	23.6038i	−1.39805	+	0.866524i
$743$			10.0307i			0.367992i	0.982927	+	0.183996i	$0.0589034\pi$
$743$			10.0307i			0.367992i	−0.982927	+	0.183996i	$0.941097\pi$
$744$	108.131	−	38.6826i	3.96429	−	1.41817i
$745$		0			0
$746$	9.42443	−	5.44120i	0.345053	−	0.199216i
$747$	16.7450	+	6.30469i	0.612667	+	0.230677i
$748$			23.8455i			0.871877i
$749$	−8.15155	+	0.254898i	−0.297851	+	0.00931378i
$750$		0			0
$751$	−16.6659	+	28.8661i	−0.608146	+	1.05334i	0.383400	+	0.923582i	$0.374753\pi$
$751$	−16.6659	+	28.8661i	−0.608146	+	1.05334i	−0.991546	+	0.129757i	$0.958580\pi$
$752$	22.1361	+	38.3409i	0.807222	+	1.39815i
$753$	−1.67050	+	9.17764i	−0.0608766	+	0.334452i
$754$	−13.5201	−	7.80583i	−0.492373	−	0.284272i
$755$		0			0
$756$	−64.6156	+	38.5845i	−2.35005	+	1.40331i
$757$	−7.30587			−0.265536			−0.132768	−	0.991147i	$-0.542387\pi$
$757$	−7.30587			−0.265536			−0.132768	+	0.991147i	$0.542387\pi$
$758$	32.9583	+	19.0285i	1.19710	+	0.691145i
$759$	1.14181	−	6.27305i	0.0414452	−	0.227697i
$760$		0			0
$761$	−3.12585	+	5.41414i	−0.113312	+	0.196262i	−0.917104	−	0.398649i	$-0.869479\pi$
$761$	−3.12585	+	5.41414i	−0.113312	+	0.196262i	0.803792	+	0.594911i	$0.202813\pi$
$762$	−15.2763	+	18.0030i	−0.553403	+	0.652182i
$763$	31.6034	+	16.9519i	1.14412	+	0.613701i
$764$			142.901i			5.16998i
$765$		0			0
$766$	−37.4118	+	21.5997i	−1.35174	+	0.780429i
$767$	−5.10135	+	2.94527i	−0.184199	+	0.106347i
$768$	73.6159	−	26.3351i	2.65638	−	0.950287i
$769$		−	12.2298i		−	0.441018i	−0.975385	−	0.220509i	$-0.929228\pi$
$769$		−	12.2298i		−	0.441018i	0.975385	−	0.220509i	$-0.0707718\pi$
$770$		0			0
$771$	−28.6375	−	24.3001i	−1.03135	−	0.875146i
$772$	20.5505	−	35.5946i	0.739630	−	1.28108i
$773$	20.4185	+	35.3660i	0.734404	+	1.27203i	0.954984	+	0.296656i	$0.0958716\pi$
$773$	20.4185	+	35.3660i	0.734404	+	1.27203i	−0.220580	+	0.975369i	$0.570795\pi$
$774$	22.7351	+	27.7096i	0.817195	+	0.996002i
$775$		0			0
$776$	−94.7156			−3.40009
$777$	−27.4934	−	4.12115i	−0.986321	−	0.147845i
$778$	68.5707			2.45838
$779$	28.2860	+	16.3310i	1.01345	+	0.585117i
$780$		0			0
$781$	−3.94482	−	6.83263i	−0.141157	−	0.244491i
$782$	−5.10859	+	8.84834i	−0.182683	+	0.316416i
$783$	−12.4679	−	7.47605i	−0.445565	−	0.267172i
$784$	58.1537	+	87.5877i	2.07692	+	3.12813i
$785$		0			0
$786$	18.6677	+	52.1828i	0.665856	+	1.86130i
$787$	38.0128	−	21.9467i	1.35501	−	0.782316i	0.366065	−	0.930589i	$-0.380705\pi$
$787$	38.0128	−	21.9467i	1.35501	−	0.782316i	0.988946	+	0.148273i	$0.0473714\pi$
$788$	98.5822	−	56.9165i	3.51185	−	2.02757i
$789$	−0.836113	−	2.33723i	−0.0297664	−	0.0832075i
$790$		0			0
$791$	15.4232	+	24.8838i	0.548387	+	0.884765i
$792$	−9.60785	−	58.2379i	−0.341400	−	2.06940i
$793$	7.42706	−	12.8641i	0.263743	−	0.456816i
$794$	−2.00561	−	3.47382i	−0.0711766	−	0.123281i
$795$		0			0
$796$	−108.841	−	62.8395i	−3.85777	−	2.22729i
$797$	32.7354			1.15955			0.579773	−	0.814778i	$-0.303141\pi$
$797$	32.7354			1.15955			0.579773	+	0.814778i	$0.303141\pi$
$798$	21.7533	−	27.3233i	0.770059	−	0.967233i
$799$	−6.19862			−0.219291
$800$		0			0
$801$	−28.8012	+	23.6307i	−1.01764	+	0.834948i
$802$	−29.3334	−	50.8070i	−1.03580	−	1.79406i
$803$	6.95157	−	12.0405i	0.245316	−	0.424899i
$804$	53.5217	+	45.4154i	1.88757	+	1.60168i
$805$		0			0
$806$		−	38.9520i		−	1.37203i
$807$	−32.5977	+	11.6614i	−1.14749	+	0.410500i
$808$	−132.737	+	76.6358i	−4.66967	+	2.69604i
$809$	27.4680	−	15.8586i	0.965722	−	0.557560i	0.0677924	−	0.997699i	$-0.478404\pi$
$809$	27.4680	−	15.8586i	0.965722	−	0.557560i	0.897929	+	0.440140i	$0.145071\pi$
$810$		0			0
$811$			25.7354i			0.903691i	0.892096	+	0.451845i	$0.149234\pi$
$811$			25.7354i			0.903691i	−0.892096	+	0.451845i	$0.850766\pi$
$812$	−19.1540	+	35.7087i	−0.672175	+	1.25313i
$813$	17.6064	−	20.7490i	0.617483	−	0.727699i
$814$	17.1776	−	29.7525i	0.602075	−	1.04282i
$815$		0			0
$816$	−9.79635	+	53.8205i	−0.342941	+	1.88409i
$817$	−10.5504	−	6.09129i	−0.369113	−	0.213107i
$818$	19.0170			0.664914
$819$	3.13533	+	15.8941i	0.109557	+	0.555386i
$820$		0			0
$821$	22.3697	+	12.9152i	0.780708	+	0.450742i	0.836681	−	0.547690i	$-0.184493\pi$
$821$	22.3697	+	12.9152i	0.780708	+	0.450742i	−0.0559731	+	0.998432i	$0.517826\pi$
$822$	−10.7321	+	58.9617i	−0.374327	+	2.05653i
$823$	−19.0097	−	32.9258i	−0.662638	−	1.14772i	−0.979920	−	0.199392i	$-0.936103\pi$
$823$	−19.0097	−	32.9258i	−0.662638	−	1.14772i	0.317282	−	0.948331i	$-0.397230\pi$
$824$	2.48463	−	4.30350i	0.0865561	−	0.149920i
$825$		0			0
$826$	10.9976	+	17.7435i	0.382655	+	0.617375i
$827$			2.97310i			0.103385i	0.998663	+	0.0516924i	$0.0164615\pi$
$827$			2.97310i			0.103385i	−0.998663	+	0.0516924i	$0.983538\pi$
$828$	10.2843	−	27.3145i	0.357403	−	0.949246i
$829$	−5.17590	+	2.98831i	−0.179767	+	0.103788i	−0.587183	−	0.809454i	$-0.699763\pi$
$829$	−5.17590	+	2.98831i	−0.179767	+	0.103788i	0.407416	+	0.913243i	$0.366430\pi$
$830$		0			0
$831$	3.57111	−	1.27752i	0.123880	−	0.0443166i
$832$		−	61.8125i		−	2.14296i
$833$	−14.6914	+	0.919696i	−0.509026	+	0.0318656i
$834$	65.1006	+	55.2405i	2.25425	+	1.91282i
$835$		0			0
$836$	15.8054	+	27.3758i	0.546642	+	0.946811i
$837$	0.600085	−	36.2669i	0.0207420	−	1.25357i
$838$	82.5907	+	47.6837i	2.85305	+	1.64721i
$839$	−44.9345			−1.55131			−0.775655	−	0.631157i	$-0.782580\pi$
$839$	−44.9345			−1.55131			−0.775655	+	0.631157i	$0.782580\pi$
$840$		0			0
$841$	21.1726			0.730090
$842$	70.2249	+	40.5444i	2.42011	+	1.39725i
$843$	−0.101814	−	0.0185321i	−0.00350666	−	0.000638279i
$844$	−51.9336	−	89.9516i	−1.78763	−	3.09626i
$845$		0			0
$846$	23.8537	−	3.93529i	0.820108	−	0.135298i
$847$	−0.554807	−	17.7425i	−0.0190634	−	0.609639i
$848$		−	93.0325i		−	3.19475i
$849$	9.30057	+	25.9983i	0.319195	+	0.892261i
$850$		0			0
$851$	9.33698	−	5.39071i	0.320068	−	0.184791i
$852$	−12.1646	−	34.0042i	−0.416751	−	1.16497i
$853$		−	44.2981i		−	1.51674i	−0.651826	−	0.758368i	$-0.725997\pi$
$853$		−	44.2981i		−	1.51674i	0.651826	−	0.758368i	$-0.274003\pi$
$854$	−46.3890	−	24.8829i	−1.58740	−	0.851474i
$855$		0			0
$856$	14.6395	−	25.3563i	0.500367	−	0.866661i
$857$	7.37279	+	12.7700i	0.251850	+	0.436216i	0.964035	−	0.265775i	$-0.0856278\pi$
$857$	7.37279	+	12.7700i	0.251850	+	0.436216i	−0.712185	+	0.701991i	$0.752295\pi$
$858$	−19.6964	−	3.58513i	−0.672425	−	0.122394i
$859$	1.52877	+	0.882637i	0.0521610	+	0.0301152i	0.525854	−	0.850575i	$-0.323746\pi$
$859$	1.52877	+	0.882637i	0.0521610	+	0.0301152i	−0.473693	+	0.880690i	$0.657079\pi$
$860$		0			0
$861$	19.6563	+	49.9643i	0.669887	+	1.70278i
$862$	23.1378			0.788076
$863$	−18.7870	−	10.8467i	−0.639518	−	0.369226i	0.144911	−	0.989445i	$-0.453710\pi$
$863$	−18.7870	−	10.8467i	−0.639518	−	0.369226i	−0.784429	+	0.620219i	$0.787044\pi$
$864$	1.89681	−	114.636i	0.0645307	−	3.90000i
$865$		0			0
$866$	14.5492	−	25.2000i	0.494404	−	0.856332i
$867$	16.6112	+	14.0953i	0.564147	+	0.478702i
$868$	−101.054	+	3.15995i	−3.43000	+	0.107256i
$869$			12.2538i			0.415683i
$870$		0			0
$871$	13.0856	−	7.55499i	0.443390	−	0.255991i
$872$	−111.501	+	64.3750i	−3.77589	+	2.18001i
$873$	−10.5410	+	27.9964i	−0.356759	+	0.947536i
$874$			13.5444i			0.458147i
$875$		0			0
$876$	41.1760	−	48.5256i	1.39121	−	1.63953i
$877$	−15.7318	+	27.2482i	−0.531224	+	0.920107i	0.468112	+	0.883669i	$0.344934\pi$
$877$	−15.7318	+	27.2482i	−0.531224	+	0.920107i	−0.999336	+	0.0364380i	$0.988399\pi$
$878$	−17.2914	−	29.9496i	−0.583556	−	1.01075i
$879$	6.00705	−	33.0023i	0.202613	−	1.11314i
$880$		0			0
$881$	−19.8571			−0.669004			−0.334502	−	0.942395i	$-0.608568\pi$
$881$	−19.8571			−0.669004			−0.334502	+	0.942395i	$0.608568\pi$
$882$	55.9520	−	12.8663i	1.88400	−	0.433229i
$883$	30.0998			1.01294			0.506469	−	0.862258i	$-0.330951\pi$
$883$	30.0998			1.01294			0.506469	+	0.862258i	$0.330951\pi$
$884$	20.3483	+	11.7481i	0.684388	+	0.395132i
$885$		0			0
$886$	−35.1734	−	60.9221i	−1.18167	−	2.04672i
$887$	14.7405	−	25.5312i	0.494937	−	0.857255i	−0.505046	−	0.863092i	$-0.668525\pi$
$887$	14.7405	−	25.5312i	0.494937	−	0.857255i	0.999983	+	0.00583681i	$0.00185793\pi$
$888$	64.5748	−	76.1009i	2.16699	−	2.55378i
$889$	11.2130	−	6.94994i	0.376072	−	0.233094i
$890$		0			0
$891$	−18.2835	−	3.64143i	−0.612520	−	0.121993i
$892$	28.7429	−	16.5947i	0.962383	−	0.555632i
$893$	−7.11632	+	4.10861i	−0.238139	+	0.137489i
$894$	64.9969	−	23.2518i	2.17382	−	0.777656i
$895$		0			0
$896$	−102.250	+	3.19735i	−3.41593	+	0.106816i
$897$	−4.79051	−	4.06494i	−0.159950	−	0.135725i
$898$	−48.7968	+	84.5185i	−1.62837	+	2.82042i
$899$	−9.76487	−	16.9133i	−0.325677	−	0.564089i
$900$		0			0
$901$	11.2805	+	6.51280i	0.375808	+	0.216973i
$902$	−66.3509			−2.20924
$903$	−7.33163	−	18.6362i	−0.243981	−	0.620174i
$904$	−105.103			−3.49566
$905$		0			0
$906$	32.7463	+	5.96044i	1.08792	+	0.198023i
$907$	16.6945	+	28.9158i	0.554333	+	0.960133i	0.997955	+	0.0639189i	$0.0203599\pi$
$907$	16.6945	+	28.9158i	0.554333	+	0.960133i	−0.443622	+	0.896214i	$0.646307\pi$
$908$	−59.6837	+	103.375i	−1.98067	+	3.43062i
$909$	7.87988	+	47.7639i	0.261359	+	1.58423i
$910$		0			0
$911$		−	40.1277i		−	1.32949i	−0.747071	−	0.664744i	$-0.768540\pi$
$911$		−	40.1277i		−	1.32949i	0.747071	−	0.664744i	$-0.231460\pi$
$912$	24.4270	+	68.2819i	0.808858	+	2.26104i
$913$	10.6991	−	6.17710i	0.354087	−	0.204432i
$914$	26.2929	−	15.1802i	0.869692	−	0.502117i
$915$		0			0
$916$		−	50.2396i		−	1.65996i
$917$	−0.967822	−	30.9506i	−0.0319603	−	1.02208i
$918$	25.6202	+	15.3625i	0.845594	+	0.507039i
$919$	−9.73901	+	16.8685i	−0.321260	+	0.556439i	−0.980748	−	0.195276i	$-0.937440\pi$
$919$	−9.73901	+	16.8685i	−0.321260	+	0.556439i	0.659488	+	0.751715i	$0.270773\pi$
$920$		0			0
$921$	30.2707	+	5.50984i	0.997453	+	0.181555i
$922$	44.6998	+	25.8074i	1.47211	+	0.849922i
$923$	−7.77409			−0.255887
$924$	−7.70311	+	51.3898i	−0.253414	+	1.69060i
$925$		0			0
$926$	34.6718	+	20.0177i	1.13938	+	0.657824i
$927$	−0.995530	−	1.21336i	−0.0326975	−	0.0398519i
$928$	−30.8658	−	53.4611i	−1.01322	−	1.75495i
$929$	−22.2310	+	38.5053i	−0.729376	+	1.26332i	0.227771	+	0.973715i	$0.426856\pi$
$929$	−22.2310	+	38.5053i	−0.729376	+	1.26332i	−0.957147	+	0.289602i	$0.906477\pi$
$930$		0			0
$931$	−16.2568	+	10.7937i	−0.532796	+	0.353749i
$932$		−	99.5361i		−	3.26041i
$933$	11.7021	−	4.18629i	0.383111	−	0.137053i
$934$	−12.8427	+	7.41472i	−0.420225	+	0.242617i
$935$		0			0
$936$	−54.4304	−	20.4937i	−1.77911	−	0.669858i
$937$			7.31878i			0.239094i	0.992829	+	0.119547i	$0.0381443\pi$
$937$			7.31878i			0.239094i	−0.992829	+	0.119547i	$0.961856\pi$
$938$	−28.2103	−	45.5144i	−0.921098	−	1.48610i
$939$	−15.2335	+	17.9526i	−0.497127	+	0.585861i
$940$		0			0
$941$	−4.22911	−	7.32504i	−0.137865	−	0.238790i	0.788823	−	0.614620i	$-0.210691\pi$
$941$	−4.22911	−	7.32504i	−0.137865	−	0.238790i	−0.926688	+	0.375831i	$0.877357\pi$
$942$	−18.5727	+	102.037i	−0.605133	+	3.32456i
$943$	−18.0327	−	10.4112i	−0.587225	−	0.339035i
$944$	−43.3461			−1.41079
$945$		0			0
$946$	24.7482			0.804635
$947$	16.0677	+	9.27668i	0.522129	+	0.301452i	0.737805	−	0.675013i	$-0.235862\pi$
$947$	16.0677	+	9.27668i	0.522129	+	0.301452i	−0.215676	+	0.976465i	$0.569195\pi$
$948$	−10.0447	+	55.1848i	−0.326236	+	1.79232i
$949$	−6.84976	−	11.8641i	−0.222353	−	0.385126i
$950$		0			0
$951$	3.60893	−	4.25310i	0.117028	−	0.137916i
$952$	24.9799	−	46.5698i	0.809602	−	1.50934i
$953$		−	12.3994i		−	0.401658i	−0.979626	−	0.200829i	$-0.935637\pi$
$953$		−	12.3994i		−	0.401658i	0.979626	−	0.200829i	$-0.0643635\pi$
$954$	−47.5447	−	17.9012i	−1.53932	−	0.579572i
$955$		0			0
$956$	62.3188	−	35.9798i	2.01553	−	1.16367i
$957$	−9.45110	+	3.38101i	−0.305511	+	0.109293i
$958$			10.1458i			0.327797i
$959$	15.8280	−	29.5080i	0.511112	−	0.952863i
$960$		0			0
$961$	8.86390	−	15.3527i	0.285932	−	0.495249i
$962$	−16.9260	−	29.3167i	−0.545717	−	0.945210i
$963$	−5.86569	−	7.14913i	−0.189019	−	0.230378i
$964$	0.0847752	+	0.0489450i	0.00273043	+	0.00157641i
$965$		0			0
$966$	−13.8680	+	17.4189i	−0.446196	+	0.560444i
$967$	−55.9627			−1.79964			−0.899819	−	0.436263i	$-0.856302\pi$
$967$	−55.9627			−1.79964			−0.899819	+	0.436263i	$0.856302\pi$
$968$	55.1900	+	31.8640i	1.77388	+	1.02415i
$969$	−9.98943	−	1.81827i	−0.320907	−	0.0584111i
$970$		0			0
$971$	−20.9297	+	36.2512i	−0.671665	+	1.16336i	0.305767	+	0.952106i	$0.401087\pi$
$971$	−20.9297	+	36.2512i	−0.671665	+	1.16336i	−0.977432	+	0.211251i	$0.932246\pi$
$972$	−79.3543	−	31.3864i	−2.54529	−	1.00672i
$973$	−25.1316	−	40.5472i	−0.805681	−	1.29988i
$974$			50.0985i			1.60526i
$975$		0			0
$976$	94.6614	−	54.6528i	3.03004	−	1.74939i
$977$	15.9878	−	9.23058i	0.511496	−	0.295312i	−0.221952	−	0.975058i	$-0.571243\pi$
$977$	15.9878	−	9.23058i	0.511496	−	0.295312i	0.733448	+	0.679745i	$0.237910\pi$
$978$	−12.9136	−	36.0979i	−0.412930	−	1.15428i
$979$			25.7231i			0.822115i
$980$		0			0
$981$	6.61920	+	40.1223i	0.211335	+	1.28101i
$982$	−50.1857	+	86.9241i	−1.60149	+	2.77386i
$983$	−19.4902	−	33.7581i	−0.621642	−	1.07672i	−0.989180	−	0.146707i	$-0.953133\pi$
$983$	−19.4902	−	33.7581i	−0.621642	−	1.07672i	0.367538	−	0.930008i	$-0.380201\pi$
$984$	−189.641	−	34.5183i	−6.04555	−	1.10040i
$985$		0			0
$986$	16.0845			0.512234
$987$	−13.3587	−	2.00242i	−0.425213	−	0.0637377i
$988$	31.1479			0.990945
$989$	6.72602	+	3.88327i	0.213875	+	0.123481i
$990$		0			0
$991$	2.60812	+	4.51739i	0.0828495	+	0.143500i	0.904473	−	0.426531i	$-0.140265\pi$
$991$	2.60812	+	4.51739i	0.0828495	+	0.143500i	−0.821623	+	0.570031i	$0.806931\pi$
$992$	77.0118	−	133.388i	2.44513	−	4.23508i
$993$	4.20906	+	3.57156i	0.133570	+	0.113340i
$994$	0.861078	+	27.5369i	0.0273117	+	0.873419i
$995$		0			0
$996$	53.2464	−	19.0482i	1.68718	−	0.603566i
$997$	−28.5316	+	16.4727i	−0.903604	+	0.521696i	−0.878368	−	0.477985i	$-0.841367\pi$
$997$	−28.5316	+	16.4727i	−0.903604	+	0.521696i	−0.0252363	+	0.999682i	$0.508034\pi$
$998$	2.53701	−	1.46474i	0.0803075	−	0.0463656i
$999$	−15.3076	−	27.5566i	−0.484312	−	0.871853i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.t.i.26.1	yes	20
3.2	odd	2	inner	525.2.t.i.26.10	yes	20
5.2	odd	4		525.2.q.g.299.20		40
5.3	odd	4		525.2.q.g.299.1		40
5.4	even	2		525.2.t.h.26.10	yes	20
7.3	odd	6	inner	525.2.t.i.101.10	yes	20
15.2	even	4		525.2.q.g.299.2		40
15.8	even	4		525.2.q.g.299.19		40
15.14	odd	2		525.2.t.h.26.1	✓	20
21.17	even	6	inner	525.2.t.i.101.1	yes	20
35.3	even	12		525.2.q.g.374.2		40
35.17	even	12		525.2.q.g.374.19		40
35.24	odd	6		525.2.t.h.101.1	yes	20
105.17	odd	12		525.2.q.g.374.1		40
105.38	odd	12		525.2.q.g.374.20		40
105.59	even	6		525.2.t.h.101.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.q.g.299.1		40	5.3	odd	4
525.2.q.g.299.2		40	15.2	even	4
525.2.q.g.299.19		40	15.8	even	4
525.2.q.g.299.20		40	5.2	odd	4
525.2.q.g.374.1		40	105.17	odd	12
525.2.q.g.374.2		40	35.3	even	12
525.2.q.g.374.19		40	35.17	even	12
525.2.q.g.374.20		40	105.38	odd	12
525.2.t.h.26.1	✓	20	15.14	odd	2
525.2.t.h.26.10	yes	20	5.4	even	2
525.2.t.h.101.1	yes	20	35.24	odd	6
525.2.t.h.101.10	yes	20	105.59	even	6
525.2.t.i.26.1	yes	20	1.1	even	1	trivial
525.2.t.i.26.10	yes	20	3.2	odd	2	inner
525.2.t.i.101.1	yes	20	21.17	even	6	inner
525.2.t.i.101.10	yes	20	7.3	odd	6	inner

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)

\(f(q)\)	\(=\)	\(q+(-2.36764 - 1.36696i) q^{2} +(-0.310170 + 1.70405i) q^{3} +(2.73715 + 4.74088i) q^{4} +(3.06374 - 3.61059i) q^{6} +(-2.24882 + 1.39384i) q^{7} -9.49844i q^{8} +(-2.80759 - 1.05709i) q^{9} +O(q^{10})\)	\(q+(-2.36764 - 1.36696i) q^{2} +(-0.310170 + 1.70405i) q^{3} +(2.73715 + 4.74088i) q^{4} +(3.06374 - 3.61059i) q^{6} +(-2.24882 + 1.39384i) q^{7} -9.49844i q^{8} +(-2.80759 - 1.05709i) q^{9} +(-1.79388 + 1.03570i) q^{11} +(-8.92769 + 3.19377i) q^{12} +2.04106i q^{13} +(7.22973 - 0.226073i) q^{14} +(-7.50967 + 13.0071i) q^{16} +(-1.05144 - 1.82114i) q^{17} +(5.20236 + 6.34067i) q^{18} +(-2.41421 - 1.39384i) q^{19} +(-1.67766 - 4.26444i) q^{21} +5.66303 q^{22} +(1.53909 + 0.888591i) q^{23} +(16.1858 + 2.94613i) q^{24} +(2.79004 - 4.83250i) q^{26} +(2.67217 - 4.45640i) q^{27} +(-12.7634 - 6.84624i) q^{28} -2.79774i q^{29} +(6.04532 - 3.49027i) q^{31} +(19.1086 - 11.0324i) q^{32} +(-1.20848 - 3.37811i) q^{33} +5.74909i q^{34} +(-2.67324 - 16.2039i) q^{36} +(3.03329 - 5.25381i) q^{37} +(3.81065 + 6.60024i) q^{38} +(-3.47807 - 0.633076i) q^{39} -11.7165 q^{41} +(-1.85720 + 12.3900i) q^{42} +4.37014 q^{43} +(-9.82025 - 5.66973i) q^{44} +(-2.42933 - 4.20773i) q^{46} +(1.47384 - 2.55277i) q^{47} +(-19.8356 - 16.8313i) q^{48} +(3.11440 - 6.26901i) q^{49} +(3.42945 - 1.22684i) q^{51} +(-9.67643 + 5.58669i) q^{52} +(-5.36432 + 3.09709i) q^{53} +(-12.4185 + 6.89842i) q^{54} +(13.2393 + 21.3603i) q^{56} +(3.12400 - 3.68161i) q^{57} +(-3.82440 + 6.62405i) q^{58} +(1.44301 + 2.49936i) q^{59} +(-6.30263 - 3.63883i) q^{61} -19.0842 q^{62} +(7.78719 - 1.53613i) q^{63} -30.2845 q^{64} +(-1.75650 + 9.65010i) q^{66} +(-3.70150 - 6.41119i) q^{67} +(5.75589 - 9.96949i) q^{68} +(-1.99158 + 2.34707i) q^{69} +3.80885i q^{71} +(-10.0407 + 26.6677i) q^{72} +(-5.81273 + 3.35598i) q^{73} +(-14.3635 + 8.29276i) q^{74} -15.2606i q^{76} +(2.59052 - 4.82949i) q^{77} +(7.36944 + 6.25328i) q^{78} +(2.95787 - 5.12317i) q^{79} +(6.76512 + 5.93576i) q^{81} +(27.7405 + 16.0160i) q^{82} -5.96419 q^{83} +(15.6252 - 19.6260i) q^{84} +(-10.3469 - 5.97380i) q^{86} +(4.76750 + 0.867776i) q^{87} +(9.83752 + 17.0391i) q^{88} +(6.20912 - 10.7545i) q^{89} +(-2.84492 - 4.58998i) q^{91} +9.72883i q^{92} +(4.07252 + 11.3841i) q^{93} +(-6.97906 + 4.02936i) q^{94} +(12.8728 + 35.9840i) q^{96} -9.97170i q^{97} +(-15.9433 + 10.5855i) q^{98} +(6.13132 - 1.01152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 3 q^{3} + 14 q^{4} - 7 q^{9}+O(q^{10}) \) 20 * q + 3 * q^3 + 14 * q^4 - 7 * q^9	\( 20 q + 3 q^{3} + 14 q^{4} - 7 q^{9} - 21 q^{12} - 18 q^{16} + 14 q^{18} - 9 q^{21} + 20 q^{22} + 18 q^{24} - 10 q^{28} + 42 q^{31} + 12 q^{33} - 36 q^{36} + 24 q^{37} + 33 q^{42} + 36 q^{43} - 8 q^{46} - 4 q^{49} + 21 q^{51} - 84 q^{52} - 75 q^{54} + 6 q^{57} - 4 q^{58} - 90 q^{61} - 5 q^{63} - 120 q^{64} + 6 q^{66} + 20 q^{67} - 35 q^{72} - 48 q^{73} - 108 q^{78} + 46 q^{79} + 29 q^{81} + 36 q^{82} + 75 q^{84} + 69 q^{87} + 4 q^{88} - 30 q^{91} - 30 q^{93} + 6 q^{94} + 135 q^{96} + 94 q^{99}+O(q^{100}) \) 20 * q + 3 * q^3 + 14 * q^4 - 7 * q^9 - 21 * q^12 - 18 * q^16 + 14 * q^18 - 9 * q^21 + 20 * q^22 + 18 * q^24 - 10 * q^28 + 42 * q^31 + 12 * q^33 - 36 * q^36 + 24 * q^37 + 33 * q^42 + 36 * q^43 - 8 * q^46 - 4 * q^49 + 21 * q^51 - 84 * q^52 - 75 * q^54 + 6 * q^57 - 4 * q^58 - 90 * q^61 - 5 * q^63 - 120 * q^64 + 6 * q^66 + 20 * q^67 - 35 * q^72 - 48 * q^73 - 108 * q^78 + 46 * q^79 + 29 * q^81 + 36 * q^82 + 75 * q^84 + 69 * q^87 + 4 * q^88 - 30 * q^91 - 30 * q^93 + 6 * q^94 + 135 * q^96 + 94 * q^99

Introduction

L-functions

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