LMFDB - Embedded newform 525.2.t.i.101.10

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			101.10
Root			$-0.310170 - 1.70405i$ of defining polynomial
Character	$\chi$	$=$	525.101
Dual form			525.2.t.i.26.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.36764 - 1.36696i) q^{2} +(-1.63084 + 0.583411i) q^{3} +(2.73715 - 4.74088i) q^{4} +(-3.06374 + 3.61059i) q^{6} +(-2.24882 - 1.39384i) q^{7} -9.49844i q^{8} +(2.31926 - 1.90290i) q^{9} +O(q^{10})$	\(q+(2.36764 - 1.36696i) q^{2} +(-1.63084 + 0.583411i) q^{3} +(2.73715 - 4.74088i) q^{4} +(-3.06374 + 3.61059i) q^{6} +(-2.24882 - 1.39384i) q^{7} -9.49844i q^{8} +(2.31926 - 1.90290i) q^{9} +(1.79388 + 1.03570i) q^{11} +(-1.69796 + 9.32849i) q^{12} -2.04106i q^{13} +(-7.22973 - 0.226073i) q^{14} +(-7.50967 - 13.0071i) q^{16} +(1.05144 - 1.82114i) q^{17} +(2.89000 - 7.67571i) q^{18} +(-2.41421 + 1.39384i) q^{19} +(4.48065 + 0.961143i) q^{21} +5.66303 q^{22} +(-1.53909 + 0.888591i) q^{23} +(5.54150 + 15.4904i) 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} +(-3.52977 - 0.642485i) q^{33} -5.74909i q^{34} +(-2.67324 - 16.2039i) q^{36} +(3.03329 + 5.25381i) q^{37} +(-3.81065 + 6.60024i) q^{38} +(1.19078 + 3.32864i) q^{39} +11.7165 q^{41} +(11.9224 - 3.84922i) 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} +(-0.652249 + 3.58341i) q^{51} +(-9.67643 - 5.58669i) q^{52} +(5.36432 + 3.09709i) q^{53} +(-0.235023 + 14.2039i) 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} +(-7.86795 + 1.04659i) q^{63} -30.2845 q^{64} +(-9.23548 + 3.30387i) q^{66} +(-3.70150 + 6.41119i) q^{67} +(-5.75589 - 9.96949i) q^{68} +(1.99158 - 2.34707i) q^{69} +3.80885i q^{71} +(-18.0746 - 22.0294i) 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} +(1.75796 - 8.82664i) q^{81} +(27.7405 - 16.0160i) q^{82} +5.96419 q^{83} +(16.8209 - 18.6114i) q^{84} +(10.3469 - 5.97380i) q^{86} +(1.63224 + 4.56267i) q^{87} +(9.83752 - 17.0391i) q^{88} +(-6.20912 - 10.7545i) q^{89} +(-2.84492 + 4.58998i) q^{91} +9.72883i q^{92} +(-11.8952 - 2.16515i) q^{93} +(-6.97906 - 4.02936i) q^{94} +(37.5995 + 6.84382i) 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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	2.36764	−	1.36696i	1.67417	−	0.966585i	0.708915	−	0.705294i	$-0.249185\pi$
$2$	2.36764	−	1.36696i	1.67417	−	0.966585i	0.965260	−	0.261291i	$-0.0841483\pi$
$3$	−1.63084	+	0.583411i	−0.941565	+	0.336833i
$3$	−1.63084	+	0.583411i	−0.941565	+	0.336833i
$4$	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
$9$	2.31926	−	1.90290i	0.773088	−	0.634299i
$10$		0			0
$11$	1.79388	+	1.03570i	0.540876	+	0.312275i	0.745434	−	0.666579i	$-0.232242\pi$
$11$	1.79388	+	1.03570i	0.540876	+	0.312275i	−0.204558	+	0.978854i	$0.565576\pi$
$12$	−1.69796	+	9.32849i	−0.490160	+	2.69290i
$13$		−	2.04106i		−	0.566088i	−0.959107	−	0.283044i	$-0.908656\pi$
$13$		−	2.04106i		−	0.566088i	0.959107	−	0.283044i	$-0.0913443\pi$
$14$	−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	$-0.751254\pi$
$17$	1.05144	−	1.82114i	0.255011	−	0.441692i	0.964899	+	0.262623i	$0.0845875\pi$
$18$	2.89000	−	7.67571i	0.681179	−	1.80918i
$19$	−2.41421	+	1.39384i	−0.553857	+	0.319769i	−0.750676	−	0.660670i	$-0.770272\pi$
$19$	−2.41421	+	1.39384i	−0.553857	+	0.319769i	0.196819	+	0.980440i	$0.436939\pi$
$20$		0			0
$21$	4.48065	+	0.961143i	0.977757	+	0.209739i
$22$	5.66303			1.20736
$23$	−1.53909	+	0.888591i	−0.320921	+	0.185284i	−0.651803	−	0.758388i	$-0.725987\pi$
$23$	−1.53909	+	0.888591i	−0.320921	+	0.185284i	0.330882	+	0.943672i	$0.392654\pi$
$24$	5.54150	+	15.4904i	1.13115	+	3.16197i
$25$		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	0.932447	−	0.361306i	$-0.117669\pi$
$31$	6.04532	+	3.49027i	1.08577	+	0.626870i	0.153324	+	0.988176i	$0.451002\pi$
$32$	−19.1086	−	11.0324i	−3.37796	−	1.95027i
$33$	−3.52977	−	0.642485i	−0.614454	−	0.111842i
$34$		−	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	0.999999	−	0.00153522i	$-0.000488676\pi$
$37$	3.03329	+	5.25381i	0.498670	+	0.863722i	−0.501329	+	0.865257i	$0.667155\pi$
$38$	−3.81065	+	6.60024i	−0.618169	+	1.07070i
$39$	1.19078	+	3.32864i	0.190677	+	0.533009i
$40$		0			0
$41$	11.7165			1.82981			0.914905	−	0.403670i	$-0.132266\pi$
$41$	11.7165			1.82981			0.914905	+	0.403670i	$0.132266\pi$
$42$	11.9224	−	3.84922i	1.83967	−	0.593947i
$43$	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	$-0.235636\pi$
$47$	−1.47384	−	2.55277i	−0.214982	−	0.372360i	−0.953267	+	0.302129i	$0.902303\pi$
$48$	19.8356	+	16.8313i	2.86302	+	2.42939i
$49$	3.11440	+	6.26901i	0.444915	+	0.895573i
$50$		0			0
$51$	−0.652249	+	3.58341i	−0.0913331	+	0.501778i
$52$	−9.67643	−	5.58669i	−1.34188	−	0.774734i
$53$	5.36432	+	3.09709i	0.736846	+	0.425418i	0.820921	−	0.571041i	$-0.193460\pi$
$53$	5.36432	+	3.09709i	0.736846	+	0.425418i	−0.0840757	+	0.996459i	$0.526794\pi$
$54$	−0.235023	+	14.2039i	−0.0319825	+	1.93291i
$55$		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	$-0.893490\pi$
$59$	−1.44301	+	2.49936i	−0.187864	+	0.325389i	0.756674	+	0.653792i	$0.226823\pi$
$60$		0			0
$61$	−6.30263	+	3.63883i	−0.806969	+	0.465904i	−0.845902	−	0.533338i	$-0.820937\pi$
$61$	−6.30263	+	3.63883i	−0.806969	+	0.465904i	0.0389331	+	0.999242i	$0.487604\pi$
$62$	19.0842			2.42369
$63$	−7.86795	+	1.04659i	−0.991269	+	0.131858i
$64$	−30.2845			−3.78556
$65$		0			0
$66$	−9.23548	+	3.30387i	−1.13681	+	0.406679i
$67$	−3.70150	+	6.41119i	−0.452211	+	0.783252i	−0.998523	−	0.0543297i	$-0.982698\pi$
$67$	−3.70150	+	6.41119i	−0.452211	+	0.783252i	0.546312	+	0.837581i	$0.316031\pi$
$68$	−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	$0.927431\pi$
$72$	−18.0746	−	22.0294i	−2.13011	−	2.59619i
$73$	−5.81273	−	3.35598i	−0.680328	−	0.392788i	0.119651	−	0.992816i	$-0.461823\pi$
$73$	−5.81273	−	3.35598i	−0.680328	−	0.392788i	−0.799979	+	0.600028i	$0.795156\pi$
$74$	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	0.983057	−	0.183300i	$-0.0586781\pi$
$79$	2.95787	+	5.12317i	0.332786	+	0.576402i	−0.650271	+	0.759702i	$0.725345\pi$
$80$		0			0
$81$	1.75796	−	8.82664i	0.195329	−	0.980738i
$82$	27.7405	−	16.0160i	3.06342	−	1.76867i
$83$	5.96419			0.654655			0.327327	−	0.944911i	$-0.393852\pi$
$83$	5.96419			0.654655			0.327327	+	0.944911i	$0.393852\pi$
$84$	16.8209	−	18.6114i	1.83531	−	2.03067i
$85$		0			0
$86$	10.3469	−	5.97380i	1.11574	−	0.644171i
$87$	1.63224	+	4.56267i	0.174994	+	0.489169i
$88$	9.83752	−	17.0391i	1.04868	−	1.81637i
$89$	−6.20912	−	10.7545i	−0.658166	−	1.13998i	−0.981090	−	0.193552i	$-0.937999\pi$
$89$	−6.20912	−	10.7545i	−0.658166	−	1.13998i	0.322924	−	0.946425i	$-0.395334\pi$
$90$		0			0
$91$	−2.84492	+	4.58998i	−0.298228	+	0.481161i
$92$			9.72883i			1.01430i
$93$	−11.8952	−	2.16515i	−1.23347	−	0.224516i
$94$	−6.97906	−	4.02936i	−0.719835	−	0.415597i
$95$		0			0
$96$	37.5995	+	6.84382i	3.83748	+	0.698494i
$97$			9.97170i			1.01247i	0.862395	+	0.506237i	$0.168964\pi$
$97$			9.97170i			1.01247i	−0.862395	+	0.506237i	$0.831036\pi$
$98$	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	−0.114931	−	0.993373i	$-0.536665\pi$
$101$	8.06825	−	13.9746i	0.802821	−	1.39053i	0.917752	−	0.397153i	$-0.130002\pi$
$102$	3.35408	+	9.37583i	0.332104	+	0.928345i
$103$	0.453075	−	0.261583i	0.0446428	−	0.0257745i	−0.477513	−	0.878625i	$-0.658461\pi$
$103$	0.453075	−	0.261583i	0.0446428	−	0.0257745i	0.522155	+	0.852850i	$0.325128\pi$
$104$	−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	$-0.714272\pi$
$107$	−2.66952	+	1.54125i	−0.258073	+	0.148998i	0.365382	+	0.930858i	$0.380938\pi$
$108$	13.8131	+	24.8663i	1.32917	+	2.39276i
$109$	−6.77743	+	11.7389i	−0.649160	+	1.12438i	0.334163	+	0.942515i	$0.391546\pi$
$109$	−6.77743	+	11.7389i	−0.649160	+	1.12438i	−0.983324	+	0.181864i	$0.941787\pi$
$110$		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	$-0.174242\pi$
$114$	2.36390	−	12.9871i	0.221399	−	1.21635i
$115$		0			0
$116$	−13.2638	−	7.65784i	−1.23151	−	0.711013i
$117$	−3.88393	−	4.73376i	−0.359069	−	0.437636i
$118$			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
$123$	−19.1077	+	6.83554i	−1.72288	+	0.616340i
$124$	33.0939	−	19.1068i	2.97192	−	1.71584i
$125$		0			0
$126$	−17.1978	+	13.2331i	−1.53210	+	1.17890i
$127$	−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
$129$	−7.12699	+	2.54959i	−0.627497	+	0.224479i
$130$		0			0
$131$	5.85196	+	10.1359i	0.511288	+	0.885577i	0.999914	+	0.0130842i	$0.00416493\pi$
$131$	5.85196	+	10.1359i	0.511288	+	0.885577i	−0.488626	+	0.872493i	$0.662502\pi$
$132$	−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	$-0.151514\pi$
$137$	10.9606	+	6.32808i	0.936423	+	0.540644i	0.0475860	+	0.998867i	$0.484847\pi$
$138$	1.50701	−	8.27943i	0.128285	−	0.704791i
$139$		−	18.0304i		−	1.52932i	−0.644434	−	0.764660i	$-0.722907\pi$
$139$		−	18.0304i		−	1.52932i	0.644434	−	0.764660i	$-0.277093\pi$
$140$		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
$144$	−42.1681	−	15.8768i	−3.51401	−	1.32307i
$145$		0			0
$146$	−18.3499			−1.51865
$147$	−8.73650	−	8.40676i	−0.720574	−	0.693378i
$148$	33.2103			2.72987
$149$	−12.6249	+	7.28898i	−1.03427	+	0.597136i	−0.918205	−	0.396105i	$-0.870362\pi$
$149$	−12.6249	+	7.28898i	−1.03427	+	0.597136i	−0.116065	+	0.993242i	$0.537028\pi$
$150$		0			0
$151$	3.51450	−	6.08730i	0.286006	−	0.495377i	−0.686847	−	0.726802i	$-0.741006\pi$
$151$	3.51450	−	6.08730i	0.286006	−	0.495377i	0.972853	+	0.231425i	$0.0743389\pi$
$152$	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
$156$	19.0400	+	3.46564i	1.52442	+	0.277474i
$157$	−18.9680	−	10.9512i	−1.51381	−	0.874000i	−0.999869	−	0.0161753i	$-0.994851\pi$
$157$	−18.9680	−	10.9512i	−1.51381	−	0.874000i	−0.513943	−	0.857824i	$-0.671816\pi$
$158$	14.0063	+	8.08656i	1.11428	+	0.643332i
$159$	−10.5552	−	1.92125i	−0.837082	−	0.152365i
$160$		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	0.979876	−	0.199605i	$-0.0639659\pi$
$163$	4.04815	+	7.01159i	0.317075	+	0.549190i	−0.662801	+	0.748795i	$0.730633\pi$
$164$	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	$-0.455671\pi$
$167$	3.58777			0.277630			0.138815	+	0.990318i	$0.455671\pi$
$168$	9.12936	−	42.5592i	0.704345	−	3.28351i
$169$	8.83407			0.679544
$170$		0			0
$171$	−2.94684	+	7.82668i	−0.225350	+	0.598521i
$172$	11.9617	−	20.7183i	0.912073	−	1.57976i
$173$	6.50462	+	11.2663i	0.494537	+	0.856563i	0.999980	−	0.00629680i	$-0.00200435\pi$
$173$	6.50462	+	11.2663i	0.494537	+	0.856563i	−0.505443	+	0.862860i	$0.668671\pi$
$174$	10.1015	+	8.57156i	0.765794	+	0.649808i
$175$		0			0
$176$		−	31.1110i		−	2.34508i
$177$	0.895156	−	4.91792i	0.0672840	−	0.369654i
$178$	−29.4020	−	16.9752i	−2.20377	−	1.27235i
$179$	−3.50400	−	2.02304i	−0.261902	−	0.151209i	0.363300	−	0.931672i	$-0.381650\pi$
$179$	−3.50400	−	2.02304i	−0.261902	−	0.151209i	−0.625202	+	0.780463i	$0.714983\pi$
$180$		0			0
$181$		−	9.00970i		−	0.669686i	−0.942274	−	0.334843i	$-0.891317\pi$
$181$		−	9.00970i		−	0.669686i	0.942274	−	0.334843i	$-0.108683\pi$
$182$	−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
$186$	−31.1232	+	11.1339i	−2.28206	+	0.816379i
$187$	3.77232	−	2.17795i	0.275859	−	0.159267i
$188$	−16.1365			−1.17688
$189$	12.2208	−	6.29707i	0.888929	−	0.458045i
$190$		0			0
$191$	−22.6067	+	13.0520i	−1.63576	+	0.944409i	−0.653495	+	0.756931i	$0.726698\pi$
$191$	−22.6067	+	13.0520i	−1.63576	+	0.944409i	−0.982269	+	0.187478i	$0.939969\pi$
$192$	49.3891	−	17.6683i	3.56435	−	1.27510i
$193$	−3.75401	+	6.50213i	−0.270219	+	0.468034i	−0.968918	−	0.247383i	$-0.920430\pi$
$193$	−3.75401	+	6.50213i	−0.270219	+	0.468034i	0.698699	+	0.715416i	$0.253763\pi$
$194$	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	$-0.265534\pi$
$198$	13.1341	−	10.7762i	0.933396	−	0.765829i
$199$	−19.8822	−	11.4790i	−1.40941	−	0.813725i	−0.414081	−	0.910240i	$-0.635897\pi$
$199$	−19.8822	−	11.4790i	−1.40941	−	0.813725i	−0.995332	+	0.0965149i	$0.969230\pi$
$200$		0			0
$201$	2.29619	−	12.6151i	0.161961	−	0.889801i
$202$		−	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
$207$	−1.87864	+	4.98960i	−0.130575	+	0.346801i
$208$	−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
$213$	−2.22212	−	6.21161i	−0.152257	−	0.425613i
$214$	−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
$219$	11.4375	+	2.08185i	0.772877	+	0.140678i
$220$		0			0
$221$	−3.71707	−	2.14605i	−0.250037	−	0.144359i
$222$	−28.2626	−	5.14433i	−1.89686	−	0.345265i
$223$			6.06277i			0.405993i	0.979179	+	0.202997i	$0.0650681\pi$
$223$			6.06277i			0.405993i	−0.979179	+	0.202997i	$0.934932\pi$
$224$	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	0.235911	+	0.971775i	$0.424193\pi$
$227$	−10.9025	+	18.8837i	−0.723626	+	1.25336i	−0.959537	+	0.281582i	$0.909141\pi$
$228$	−8.90322	−	24.8876i	−0.589630	−	1.64822i
$229$	−7.94782	+	4.58868i	−0.525207	+	0.303228i	−0.739062	−	0.673637i	$-0.764731\pi$
$229$	−7.94782	+	4.58868i	−0.525207	+	0.303228i	0.213856	+	0.976865i	$0.431398\pi$
$230$		0			0
$231$	7.04230	+	6.36478i	0.463350	+	0.418772i
$232$	−26.5742			−1.74468
$233$	15.7465	−	9.09122i	1.03158	−	0.595586i	0.114146	−	0.993464i	$-0.463587\pi$
$233$	15.7465	−	9.09122i	1.03158	−	0.595586i	0.917438	+	0.397878i	$0.130253\pi$
$234$	−15.6666	−	5.89866i	−1.02416	−	0.385608i
$235$		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	0.500499	−	0.865737i	$-0.333150\pi$
$241$	0.0154860	+	0.00894087i	0.000997544	+	0.000575932i	−0.499501	+	0.866313i	$0.666483\pi$
$242$	−15.8852	−	9.17135i	−1.02114	−	0.589556i
$243$	2.28261	+	15.4204i	0.146430	+	0.989221i
$244$			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
$249$	−9.72662	+	3.47957i	−0.616400	+	0.220509i
$250$		0			0
$251$	−5.38577			−0.339947			−0.169973	−	0.985449i	$-0.554368\pi$
$251$	−5.38577			−0.339947			−0.169973	+	0.985449i	$0.554368\pi$
$252$	−16.5740	+	40.1657i	−1.04406	+	2.53020i
$253$	−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	0.976085	+	0.217391i	$0.0697545\pi$
$257$	10.8420	+	18.7790i	0.676308	+	1.17140i	−0.299777	+	0.954009i	$0.596912\pi$
$258$	−13.3890	+	15.7788i	−0.833561	+	0.982346i
$259$	0.501658	−	16.0428i	0.0311715	−	0.996852i
$260$		0			0
$261$	−5.32382	−	6.48871i	−0.329536	−	0.401641i
$262$	27.7107	+	15.9988i	1.71197	+	0.988408i
$263$	1.24114	+	0.716573i	0.0765320	+	0.0441858i	0.537778	−	0.843087i	$-0.319264\pi$
$263$	1.24114	+	0.716573i	0.0765320	+	0.0441858i	−0.461246	+	0.887272i	$0.652597\pi$
$264$	−6.10261	+	33.5273i	−0.375590	+	2.06346i
$265$		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	0.381993	+	0.924165i	$0.375238\pi$
$269$	−9.99414	+	17.3104i	−0.609354	+	1.05543i	−0.991347	+	0.131266i	$0.958096\pi$
$270$		0			0
$271$	−13.6061	+	7.85550i	−0.826513	+	0.477187i	−0.852657	−	0.522471i	$-0.825010\pi$
$271$	−13.6061	+	7.85550i	−0.826513	+	0.477187i	0.0261443	+	0.999658i	$0.491677\pi$
$272$	−31.5838			−1.91505
$273$	1.96175	−	9.14527i	0.118731	−	0.553497i
$274$	34.6009			2.09032
$275$		0			0
$276$	−5.67591	−	15.8661i	−0.341649	−	0.955029i
$277$	−1.09487	+	1.89637i	−0.0657844	+	0.113942i	−0.897042	−	0.441946i	$-0.854288\pi$
$277$	−1.09487	+	1.89637i	−0.0657844	+	0.113942i	0.831257	+	0.555888i	$0.187622\pi$
$278$	−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	$0.999433\pi$
$282$	13.7325	+	2.49957i	0.817757	+	0.148847i
$283$	13.8059	+	7.97086i	0.820677	+	0.473818i	0.850650	−	0.525733i	$-0.176209\pi$
$283$	13.8059	+	7.97086i	0.820677	+	0.473818i	−0.0299727	+	0.999551i	$0.509542\pi$
$284$	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
$291$	−5.81760	−	16.2622i	−0.341034	−	0.953309i
$292$	−31.8206	+	18.3716i	−1.86216	+	1.07512i
$293$	19.3670			1.13143			0.565715	−	0.824601i	$-0.308600\pi$
$293$	19.3670			1.13143			0.565715	+	0.824601i	$0.308600\pi$
$294$	−32.1766	−	7.96176i	−1.87658	−	0.464339i
$295$		0			0
$296$	49.9030	−	28.8115i	2.90055	−	1.67464i
$297$	−9.40905	+	5.22670i	−0.545968	+	0.303284i
$298$	−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
$303$	−5.00506	+	27.4974i	−0.287533	+	1.57969i
$304$	36.2598	+	20.9346i	2.07964	+	1.20068i
$305$		0			0
$306$	−10.9399	−	13.3336i	−0.625394	−	0.762234i
$307$			17.7639i			1.01384i	0.861993	+	0.506921i	$0.169216\pi$
$307$			17.7639i			1.01384i	−0.861993	+	0.506921i	$0.830784\pi$
$308$	−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	$-0.768120\pi$
$311$	3.58777	−	6.21419i	0.203444	−	0.352375i	0.949636	+	0.313356i	$0.101453\pi$
$312$	31.6169	−	11.3105i	1.78995	−	0.640333i
$313$	11.7724	−	6.79679i	0.665414	−	0.384177i	−0.128922	−	0.991655i	$-0.541152\pi$
$313$	11.7724	−	6.79679i	0.665414	−	0.384177i	0.794337	+	0.607477i	$0.207818\pi$
$314$	−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	$-0.637840\pi$
$317$	2.78896	−	1.61021i	0.156644	−	0.0904383i	0.576273	+	0.817257i	$0.304507\pi$
$318$	−27.6172	+	9.87970i	−1.54870	+	0.554026i
$319$	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
$324$	−37.0343	−	32.4941i	−2.05746	−	1.80523i
$325$		0			0
$326$	19.1691	+	11.0673i	1.06168	+	0.612961i
$327$	4.20431	−	23.0982i	0.232499	−	1.27733i
$328$		−	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	0.906491	−	0.422224i	$-0.138751\pi$
$331$	1.59353	+	2.76008i	0.0875885	+	0.151708i	−0.818903	+	0.573932i	$0.805417\pi$
$332$	16.3249	−	28.2755i	0.895944	−	1.55182i
$333$	17.0325	+	6.41293i	0.933373	+	0.351426i
$334$	8.49454	−	4.90433i	0.464801	−	0.268353i
$335$		0			0
$336$	−21.1465	−	65.4982i	−1.15363	−	3.57322i
$337$	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
$339$	6.45559	+	18.0456i	0.350620	+	0.980104i
$340$		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	$-0.0630144\pi$
$347$	24.2234	+	13.9854i	1.30038	+	0.750773i	0.319909	+	0.947448i	$0.396348\pi$
$348$	26.0987	+	4.75047i	1.39904	+	0.254652i
$349$			19.3368i			1.03508i	0.855660	+	0.517539i	$0.173152\pi$
$349$			19.3368i			1.03508i	−0.855660	+	0.517539i	$0.826848\pi$
$350$		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	$-0.892005\pi$
$353$	−3.44352	+	5.96436i	−0.183280	+	0.317451i	0.759715	+	0.650256i	$0.225338\pi$
$354$	−4.60319	−	12.8675i	−0.244657	−	0.683901i
$355$		0			0
$356$	−67.9812			−3.60300
$357$	6.46151	−	7.14932i	0.341979	−	0.378382i
$358$	−11.0616			−0.584625
$359$	18.0588	−	10.4263i	0.953108	−	0.550277i	0.0590629	−	0.998254i	$-0.481189\pi$
$359$	18.0588	−	10.4263i	0.953108	−	0.550277i	0.894045	+	0.447977i	$0.147855\pi$
$360$		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
$366$	6.17129	−	33.9047i	0.322579	−	1.77222i
$367$	−20.7408	−	11.9747i	−1.08266	−	0.625075i	−0.151048	−	0.988526i	$-0.548265\pi$
$367$	−20.7408	−	11.9747i	−1.08266	−	0.625075i	−0.931613	+	0.363451i	$0.881598\pi$
$368$	23.1160	+	13.3461i	1.20501	+	0.695711i
$369$	27.1736	−	22.2953i	1.41460	−	1.16065i
$370$		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	0.809889	−	0.586583i	$-0.199527\pi$
$373$	−1.99026	−	3.44723i	−0.103052	−	0.178491i	−0.912940	+	0.408093i	$0.866194\pi$
$374$	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
$378$	20.3265	−	31.6145i	1.04548	−	1.62607i
$379$	−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
$381$	8.13164	−	2.90899i	0.416596	−	0.149032i
$382$	−35.6830	+	61.8048i	−1.82570	+	3.16221i
$383$	−7.90064	−	13.6843i	−0.403704	−	0.699236i	0.590466	−	0.807063i	$-0.298944\pi$
$383$	−7.90064	−	13.6843i	−0.403704	−	0.699236i	−0.994170	+	0.107827i	$0.965611\pi$
$384$	43.3304	−	51.0646i	2.21120	−	2.60588i
$385$		0			0
$386$			20.5263i			1.04476i
$387$	10.1355	−	8.31593i	0.515217	−	0.422723i
$388$	47.2747	+	27.2940i	2.40001	+	1.38564i
$389$	21.7212	+	12.5407i	1.10131	+	0.635841i	0.936564	−	0.350495i	$-0.113987\pi$
$389$	21.7212	+	12.5407i	1.10131	+	0.635841i	0.164744	+	0.986336i	$0.447320\pi$
$390$		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
$396$	11.9868	−	31.8365i	0.602361	−	1.59985i
$397$	1.27064	−	0.733605i	0.0637716	−	0.0368186i	−0.467775	−	0.883847i	$-0.654944\pi$
$397$	1.27064	−	0.733605i	0.0637716	−	0.0368186i	0.531547	+	0.847029i	$0.321611\pi$
$398$	−62.7653			−3.14614
$399$	−12.1569	+	3.92492i	−0.608606	+	0.196492i
$400$		0			0
$401$	−18.5840	+	10.7295i	−0.928039	+	0.535804i	−0.886191	−	0.463320i	$-0.846658\pi$
$401$	−18.5840	+	10.7295i	−0.928039	+	0.535804i	−0.0418482	+	0.999124i	$0.513325\pi$
$402$	−11.8078	−	33.0068i	−0.588918	−	1.64623i
$403$	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
$408$	34.0368	+	6.19535i	1.68507	+	0.306715i
$409$	−6.02404	−	3.47798i	−0.297870	−	0.171975i	0.343616	−	0.939110i	$-0.388348\pi$
$409$	−6.02404	−	3.47798i	−0.297870	−	0.171975i	−0.641485	+	0.767135i	$0.721682\pi$
$410$		0			0
$411$	−21.5668	−	3.92556i	−1.06381	−	0.193634i
$412$		−	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
$417$	10.5192	+	29.4047i	0.515125	+	1.43995i
$418$	−13.6717	+	7.89337i	−0.668706	+	0.386077i
$419$	34.8831			1.70415			0.852076	−	0.523419i	$-0.175344\pi$
$419$	34.8831			1.70415			0.852076	+	0.523419i	$0.175344\pi$
$420$		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
$423$	−8.27589	−	3.11597i	−0.402387	−	0.151504i
$424$	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
$429$	−1.31135	+	7.20448i	−0.0633127	+	0.347835i
$430$		0			0
$431$	7.32938	+	4.23162i	0.353044	+	0.203830i	0.666025	−	0.745929i	$-0.267994\pi$
$431$	7.32938	+	4.23162i	0.353044	+	0.203830i	−0.312981	+	0.949759i	$0.601328\pi$
$432$	78.0321	+	1.29115i	3.75432	+	0.0621203i
$433$		−	10.6435i		−	0.511495i	−0.966744	−	0.255748i	$-0.917678\pi$
$433$		−	10.6435i		−	0.511495i	0.966744	−	0.255748i	$-0.0823216\pi$
$434$	−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
$438$	29.9258	−	10.7056i	1.42991	−	0.511531i
$439$	10.9548	−	6.32477i	0.522845	−	0.301865i	−0.215253	−	0.976558i	$-0.569058\pi$
$439$	10.9548	−	6.32477i	0.522845	−	0.301865i	0.738098	+	0.674694i	$0.235724\pi$
$440$		0			0
$441$	19.1524	+	8.61309i	0.912019	+	0.410147i
$442$	−11.7342			−0.558141
$443$	−22.2838	+	12.8656i	−1.05874	+	0.611261i	−0.925082	−	0.379767i	$-0.876004\pi$
$443$	−22.2838	+	12.8656i	−1.05874	+	0.611261i	−0.133654	+	0.991028i	$0.542671\pi$
$444$	−54.1606	+	19.3752i	−2.57035	+	0.919508i
$445$		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
$453$	−2.18019	+	11.9778i	−0.102434	+	0.562766i
$454$			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	0.706434	−	0.707779i	$-0.250303\pi$
$457$	−5.55255	−	9.61730i	−0.259737	−	0.449878i	−0.966172	+	0.257900i	$0.916969\pi$
$458$	−12.5451	+	21.7287i	−0.586192	+	1.01531i
$459$	5.30613	+	9.55204i	0.247669	+	0.445851i
$460$		0			0
$461$	18.8795			0.879304			0.439652	−	0.898168i	$-0.355102\pi$
$461$	18.8795			0.879304			0.439652	+	0.898168i	$0.355102\pi$
$462$	25.3740	+	5.44298i	1.18051	+	0.253230i
$463$	−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	$-0.206721\pi$
$467$	−2.71213	−	4.69754i	−0.125502	−	0.217376i	−0.921929	+	0.387359i	$0.873388\pi$
$468$	−33.0731	+	5.45626i	−1.52880	+	0.252216i
$469$	17.2602	−	9.25832i	0.797003	−	0.427509i
$470$		0			0
$471$	37.3228	+	6.79346i	1.71974	+	0.313026i
$472$	23.7401	+	13.7063i	1.09272	+	0.630885i
$473$	7.83952	+	4.52615i	0.360462	+	0.208113i
$474$	−27.5598	−	5.01641i	−1.26586	−	0.230411i
$475$		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	$-0.806314\pi$
$479$	1.85555	−	3.21391i	0.0847823	−	0.146847i	0.905298	+	0.424776i	$0.139647\pi$
$480$		0			0
$481$	10.7234	−	6.19113i	0.488943	−	0.282291i
$482$	0.0488872			0.00222675
$483$	−7.75016	+	2.50218i	−0.352645	+	0.113853i
$484$	−36.7288			−1.66949
$485$		0			0
$486$	26.4835	+	33.3898i	1.20132	+	1.51459i
$487$	−9.16240	+	15.8697i	−0.415188	+	0.719127i	−0.995448	−	0.0953043i	$-0.969618\pi$
$487$	−9.16240	+	15.8697i	−0.415188	+	0.719127i	0.580260	+	0.814431i	$0.302951\pi$
$488$	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	$-0.310763\pi$
$492$	−19.8942	+	109.297i	−0.896899	+	4.92750i
$493$	−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	0.853784	−	0.520627i	$-0.174302\pi$
$499$	−0.535767	−	0.927975i	−0.0239842	−	0.0415419i	−0.877768	+	0.479085i	$0.840968\pi$
$500$		0			0
$501$	−5.85107	+	2.09314i	−0.261406	+	0.0935147i
$502$	−12.7516	+	7.36212i	−0.569131	+	0.328588i
$503$	−27.1662			−1.21128			−0.605640	−	0.795739i	$-0.707083\pi$
$503$	−27.1662			−1.21128			−0.605640	+	0.795739i	$0.707083\pi$
$504$	9.94099	+	74.7333i	0.442807	+	3.32888i
$505$		0			0
$506$	−8.71588	+	5.03212i	−0.387468	+	0.223705i
$507$	−14.4069	+	5.15390i	−0.639834	+	0.228893i
$508$	−13.6479	+	23.6388i	−0.605527	+	1.04880i
$509$	11.8003	+	20.4387i	0.523037	+	0.905927i	0.999641	+	0.0268088i	$0.00853453\pi$
$509$	11.8003	+	20.4387i	0.523037	+	0.905927i	−0.476603	+	0.879119i	$0.658132\pi$
$510$		0			0
$511$	8.39408	+	15.6490i	0.371332	+	0.692272i
$512$			46.0773i			2.03635i
$513$	0.239645	−	14.4833i	0.0105806	−	0.639451i
$514$	51.3401	+	29.6412i	2.26452	+	1.30742i
$515$		0			0
$516$	−7.42033	+	40.7668i	−0.326662	+	1.79466i
$517$		−	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	−0.448520	−	0.893773i	$-0.648049\pi$
$521$	12.5487	−	21.7350i	0.549770	−	0.952230i	0.998290	−	0.0584568i	$-0.0186180\pi$
$522$	−21.4747	−	8.08548i	−0.939922	−	0.353892i
$523$	5.29103	−	3.05478i	0.231361	−	0.133576i	−0.379839	−	0.925053i	$-0.624021\pi$
$523$	5.29103	−	3.05478i	0.231361	−	0.133576i	0.611200	+	0.791476i	$0.290687\pi$
$524$	64.0708			2.79895
$525$		0			0
$526$	3.91810			0.170837
$527$	12.7126	−	7.33960i	0.553768	−	0.319718i
$528$	18.1505	+	50.7370i	0.789900	+	2.20805i
$529$	−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
$534$	57.8533	+	10.5304i	2.50356	+	0.455695i
$535$		0			0
$536$	60.8963	+	35.1585i	2.63032	+	1.51862i
$537$	6.89472	+	1.25497i	0.297529	+	0.0541560i
$538$			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	0.999866	−	0.0163924i	$-0.00521808\pi$
$541$	11.2979	+	19.5686i	0.485737	+	0.841321i	−0.514129	+	0.857713i	$0.671885\pi$
$542$	−21.4763	+	37.1980i	−0.922485	+	1.59779i
$543$	5.25636	+	14.6934i	0.225572	+	0.630552i
$544$	−40.1831	+	23.1997i	−1.72284	+	0.994680i
$545$		0			0
$546$	−7.85648	−	24.3344i	−0.336226	−	1.04141i
$547$	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
$549$	−7.69314	+	20.4327i	−0.328335	+	0.872044i
$550$		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	$-0.365234\pi$
$557$	−4.08989	−	2.36130i	−0.173294	−	0.100051i	−0.584138	+	0.811654i	$0.698567\pi$
$558$	44.2612	−	36.3153i	1.87373	−	1.53735i
$559$		−	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	0.250826	+	0.968032i	$0.419298\pi$
$563$	−16.9161	+	29.2995i	−0.712927	+	1.23483i	−0.963754	+	0.266794i	$0.914036\pi$
$564$	26.3160	−	9.41422i	1.10810	−	0.396410i
$565$		0			0
$566$	43.5833			1.83194
$567$	−16.2563	+	17.3992i	−0.682700	+	0.730699i
$568$	36.1781			1.51800
$569$	−21.5858	+	12.4626i	−0.904926	+	0.522459i	−0.878795	−	0.477199i	$-0.841652\pi$
$569$	−21.5858	+	12.4626i	−0.904926	+	0.522459i	−0.0261307	+	0.999659i	$0.508319\pi$
$570$		0			0
$571$	−1.10062	+	1.90633i	−0.0460596	+	0.0797776i	−0.888136	−	0.459581i	$-0.848000\pi$
$571$	−1.10062	+	1.90633i	−0.0460596	+	0.0797776i	0.842076	+	0.539358i	$0.181333\pi$
$572$	−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
$576$	−70.2377	+	57.6283i	−2.92657	+	2.40118i
$577$	−21.9455	−	12.6702i	−0.913602	−	0.527469i	−0.0320140	−	0.999487i	$-0.510192\pi$
$577$	−21.9455	−	12.6702i	−0.913602	−	0.527469i	−0.881588	+	0.472019i	$0.843525\pi$
$578$	29.7800	+	17.1935i	1.23868	+	0.715154i
$579$	2.32876	−	12.7940i	0.0967799	−	0.531702i
$580$		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	$-0.351675\pi$
$587$	21.7712			0.898593			0.449297	+	0.893383i	$0.351675\pi$
$588$	−63.7685	+	18.4082i	−2.62977	+	0.759139i
$589$	−19.4595			−0.801816
$590$		0			0
$591$	12.1315	+	33.9118i	0.499023	+	1.39494i
$592$	45.5580	−	78.9088i	1.87242	−	3.24313i
$593$	−17.4071	−	30.1501i	−0.714826	−	1.23811i	−0.963027	−	0.269406i	$-0.913173\pi$
$593$	−17.4071	−	30.1501i	−0.714826	−	1.23811i	0.248201	−	0.968709i	$-0.420161\pi$
$594$	−15.1326	+	25.2367i	−0.620897	+	1.03548i
$595$		0			0
$596$			79.8041i			3.26890i
$597$	39.1216	+	7.12088i	1.60114	+	0.291438i
$598$	8.58823	+	4.95842i	0.351199	+	0.202765i
$599$	5.38292	+	3.10783i	0.219940	+	0.126982i	0.605922	−	0.795524i	$-0.292804\pi$
$599$	5.38292	+	3.10783i	0.219940	+	0.126982i	−0.385983	+	0.922506i	$0.626137\pi$
$600$		0			0
$601$			29.5235i			1.20429i	0.798388	+	0.602144i	$0.205687\pi$
$601$			29.5235i			1.20429i	−0.798388	+	0.602144i	$0.794313\pi$
$602$	−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
$606$	25.7377	+	71.9458i	1.04552	+	2.92260i
$607$	−16.1380	+	9.31727i	−0.655021	+	0.378176i	−0.790377	−	0.612621i	$-0.790115\pi$
$607$	−16.1380	+	9.31727i	−0.655021	+	0.378176i	0.135356	+	0.990797i	$0.456782\pi$
$608$	61.5096			2.49454
$609$	2.68903	−	12.5357i	0.108965	−	0.507973i
$610$		0			0
$611$	−5.21036	+	3.00820i	−0.210788	+	0.121699i
$612$	−32.3203	−	12.1690i	−1.30647	−	0.491903i
$613$	2.59472	−	4.49418i	0.104800	−	0.181518i	−0.808857	−	0.588006i	$-0.799913\pi$
$613$	2.59472	−	4.49418i	0.104800	−	0.181518i	0.913656	+	0.406487i	$0.133247\pi$
$614$	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	$0.942881\pi$
$618$	−0.443633	+	2.43729i	−0.0178455	+	0.0980422i
$619$	20.2601	+	11.6972i	0.814321	+	0.470148i	0.848454	−	0.529269i	$-0.177534\pi$
$619$	20.2601	+	11.6972i	0.814321	+	0.470148i	−0.0341335	+	0.999417i	$0.510867\pi$
$620$		0			0
$621$	0.152776	−	9.23325i	0.00613071	−	0.370517i
$622$		−	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
$627$	9.41712	−	3.36885i	0.376084	−	0.134539i
$628$	−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
$633$	30.9429	−	11.0694i	1.22987	−	0.439969i
$634$	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
$639$	7.24785	+	8.83372i	0.286720	+	0.349457i
$640$		0			0
$641$	−35.6157	−	20.5627i	−1.40673	−	0.812179i	−0.411663	−	0.911336i	$-0.635052\pi$
$641$	−35.6157	−	20.5627i	−1.40673	−	0.812179i	−0.995072	+	0.0991572i	$0.968385\pi$
$642$	2.61389	−	14.3606i	0.103162	−	0.566766i
$643$			3.55349i			0.140136i	0.997542	+	0.0700680i	$0.0223216\pi$
$643$			3.55349i			0.140136i	−0.997542	+	0.0700680i	$0.977678\pi$
$644$	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	0.116757	−	0.993161i	$-0.462750\pi$
$647$	23.3627	−	40.4653i	0.918481	−	1.59086i	0.801724	−	0.597695i	$-0.203916\pi$
$648$	−83.8393	−	16.6979i	−3.29352	−	0.655954i
$649$	−5.17718	+	2.98905i	−0.203222	+	0.117330i
$650$		0			0
$651$	23.7323	+	21.4491i	0.930142	+	0.840655i
$652$	44.3215			1.73576
$653$	−1.64369	+	0.948985i	−0.0643226	+	0.0371367i	−0.531816	−	0.846860i	$-0.678490\pi$
$653$	−1.64369	+	0.948985i	−0.0643226	+	0.0371367i	0.467494	+	0.883996i	$0.345157\pi$
$654$	−21.6200	−	60.4354i	−0.845408	−	2.36321i
$655$		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	0.335581	−	0.942011i	$-0.391067\pi$
$661$	−8.03266	−	4.63766i	−0.312434	−	0.180384i	−0.648015	+	0.761627i	$0.724401\pi$
$662$	7.54583	+	4.35659i	0.293277	+	0.169324i
$663$	7.31396	+	1.33128i	0.284051	+	0.0517026i
$664$		−	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
$669$	−3.53709	−	9.88740i	−0.136752	−	0.382269i
$670$		0			0
$671$	−15.0749			−0.581961
$672$	−75.0153	−	67.7983i	−2.89378	−	2.61538i
$673$	−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	0.966362	+	0.257187i	$0.0827957\pi$
$677$	18.3673	+	31.8130i	0.705911	+	1.22267i	−0.260450	+	0.965487i	$0.583871\pi$
$678$	39.9521	+	33.9010i	1.53435	+	1.30196i
$679$	13.8990	−	22.4246i	0.533394	−	0.860577i
$680$		0			0
$681$	6.76327	−	37.1569i	0.259169	−	1.42386i
$682$	34.2348	+	19.7655i	1.31092	+	0.756859i
$683$	−44.3300	−	25.5940i	−1.69624	−	0.979326i	−0.949266	−	0.314475i	$-0.898171\pi$
$683$	−44.3300	−	25.5940i	−1.69624	−	0.979326i	−0.746976	−	0.664851i	$-0.768495\pi$
$684$	29.0394	+	35.3934i	1.11035	+	1.35330i
$685$		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	−0.176655	−	0.984273i	$-0.556528\pi$
$691$	15.4415	−	8.91516i	0.587423	−	0.339149i	0.764078	+	0.645124i	$0.223194\pi$
$692$	71.2164			2.70724
$693$	−15.1981	−	6.27137i	−0.577330	−	0.238229i
$694$	76.4696			2.90275
$695$		0			0
$696$	43.3382	−	15.5037i	1.64273	−	0.587666i
$697$	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	$0.704849\pi$
$702$	28.9910	+	0.479695i	1.09420	+	0.0181049i
$703$	−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	0.996073	+	0.0885399i	$0.0282201\pi$
$709$	15.3029	+	26.5055i	0.574714	+	0.995434i	−0.421359	+	0.906894i	$0.638447\pi$
$710$		0			0
$711$	16.6089	+	6.25347i	0.622884	+	0.234523i
$712$	−102.151	+	58.9770i	−3.82828	+	2.21026i
$713$	−12.4057			−0.464596
$714$	5.52570	−	25.7596i	0.206794	−	0.964030i
$715$		0			0
$716$	−19.1820	+	11.0747i	−0.716863	+	0.413881i
$717$	7.66893	+	21.4373i	0.286401	+	0.800592i
$718$	28.5045	−	49.3713i	1.06378	−	1.84252i
$719$	−11.4617	−	19.8522i	−0.427449	−	0.740364i	0.569196	−	0.822202i	$-0.307254\pi$
$719$	−11.4617	−	19.8522i	−0.427449	−	0.740364i	−0.996646	+	0.0818377i	$0.973921\pi$
$720$		0			0
$721$	−1.38349	−	0.0432616i	−0.0515238	−	0.00161115i
$722$			30.6986i			1.14248i
$723$	−0.0304714	−	0.00554638i	−0.00113324	−	0.000206272i
$724$	−42.7139	−	24.6609i	−1.58745	−	0.916515i
$725$		0			0
$726$	31.2569	+	5.68935i	1.16005	+	0.211152i
$727$			32.1534i			1.19250i	0.802798	+	0.596252i	$0.203344\pi$
$727$			32.1534i			1.19250i	−0.802798	+	0.596252i	$0.796656\pi$
$728$	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
$732$	−23.2431	−	64.9726i	−0.859090	−	2.40146i
$733$	11.8271	−	6.82836i	0.436843	−	0.252211i	−0.265415	−	0.964134i	$-0.585509\pi$
$733$	11.8271	−	6.82836i	0.436843	−	0.252211i	0.702258	+	0.711923i	$0.252176\pi$
$734$	−65.4757			−2.41675
$735$		0			0
$736$	39.2131			1.44541
$737$	−13.2801	+	7.66729i	−0.489180	+	0.282428i
$738$	33.8607	−	89.9325i	1.24643	−	3.31046i
$739$	9.19147	−	15.9201i	0.338114	−	0.585630i	−0.645964	−	0.763368i	$-0.723544\pi$
$739$	9.19147	−	15.9201i	0.338114	−	0.585630i	0.984078	+	0.177737i	$0.0568778\pi$
$740$		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	$0.941097\pi$
$744$	−20.5655	+	112.986i	−0.753970	+	4.14226i
$745$		0			0
$746$	−9.42443	−	5.44120i	−0.345053	−	0.199216i
$747$	13.8325	−	11.3492i	0.506105	−	0.415247i
$748$		−	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	−0.991546	−	0.129757i	$-0.958580\pi$
$751$	−16.6659	−	28.8661i	−0.608146	−	1.05334i	0.383400	−	0.923582i	$-0.374753\pi$
$752$	−22.1361	+	38.3409i	−0.807222	+	1.39815i
$753$	8.78332	−	3.14212i	0.320082	−	0.114505i
$754$	−13.5201	+	7.80583i	−0.492373	+	0.284272i
$755$		0			0
$756$	3.59636	−	75.1732i	0.130798	−	2.73402i
$757$	−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
$759$	6.00353	−	2.14768i	0.217914	−	0.0779560i
$760$		0			0
$761$	3.12585	+	5.41414i	0.113312	+	0.196262i	0.917104	−	0.398649i	$-0.130521\pi$
$761$	3.12585	+	5.41414i	0.113312	+	0.196262i	−0.803792	+	0.594911i	$0.797187\pi$
$762$	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
$768$	14.0010	−	76.9208i	0.505219	−	2.77564i
$769$			12.2298i			0.441018i	0.975385	+	0.220509i	$0.0707718\pi$
$769$			12.2298i			0.441018i	−0.975385	+	0.220509i	$0.929228\pi$
$770$		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	0.220580	+	0.975369i	$0.429205\pi$
$773$	−20.4185	+	35.3660i	−0.734404	+	1.27203i	−0.954984	+	0.296656i	$0.904128\pi$
$774$	12.6297	−	33.5440i	0.453965	−	1.20571i
$775$		0			0
$776$	94.7156			3.40009
$777$	8.54144	+	26.4559i	0.306422	+	0.949101i
$778$	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
$786$	−54.5255	−	9.92468i	−1.94486	−	0.354002i
$787$	38.0128	+	21.9467i	1.35501	+	0.782316i	0.988946	−	0.148273i	$-0.0473714\pi$
$787$	38.0128	+	21.9467i	1.35501	+	0.782316i	0.366065	+	0.930589i	$0.380705\pi$
$788$	−98.5822	−	56.9165i	−3.51185	−	2.02757i
$789$	−2.44215	−	0.444518i	−0.0869430	−	0.0158253i
$790$		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	$-0.696859\pi$
$797$	−32.7354			−1.15955			−0.579773	+	0.814778i	$0.696859\pi$
$798$	−23.4180	+	25.9108i	−0.828986	+	0.917231i
$799$	−6.19862			−0.219291
$800$		0			0
$801$	−34.8653	−	13.1272i	−1.23191	−	0.463828i
$802$	−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
$807$	6.19976	−	34.0611i	0.218242	−	1.19901i
$808$	−132.737	−	76.6358i	−4.66967	−	2.69604i
$809$	−27.4680	−	15.8586i	−0.965722	−	0.557560i	−0.0677924	−	0.997699i	$-0.521596\pi$
$809$	−27.4680	−	15.8586i	−0.965722	−	0.557560i	−0.897929	+	0.440140i	$0.854929\pi$
$810$		0			0
$811$		−	25.7354i		−	0.903691i	−0.892096	−	0.451845i	$-0.850766\pi$
$811$		−	25.7354i		−	0.903691i	0.892096	−	0.451845i	$-0.149234\pi$
$812$	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
$816$	51.5081	−	18.4264i	1.80314	−	0.645051i
$817$	−10.5504	+	6.09129i	−0.369113	+	0.213107i
$818$	−19.0170			−0.664914
$819$	2.13616	+	16.0590i	0.0746434	+	0.561146i
$820$		0			0
$821$	−22.3697	+	12.9152i	−0.780708	+	0.450742i	−0.836681	−	0.547690i	$-0.815507\pi$
$821$	−22.3697	+	12.9152i	−0.780708	+	0.450742i	0.0559731	+	0.998432i	$0.482174\pi$
$822$	−56.4284	+	20.1865i	−1.96817	+	0.704086i
$823$	−19.0097	+	32.9258i	−0.662638	+	1.14772i	0.317282	+	0.948331i	$0.397230\pi$
$823$	−19.0097	+	32.9258i	−0.662638	+	1.14772i	−0.979920	+	0.199392i	$0.936103\pi$
$824$	−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	$0.983538\pi$
$828$	18.5130	+	22.5637i	0.643370	+	0.784143i
$829$	−5.17590	−	2.98831i	−0.179767	−	0.103788i	0.407416	−	0.913243i	$-0.366430\pi$
$829$	−5.17590	−	2.98831i	−0.179767	−	0.103788i	−0.587183	+	0.809454i	$0.699763\pi$
$830$		0			0
$831$	0.679192	−	3.73143i	0.0235609	−	0.129442i
$832$			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
$837$	−31.7081	+	17.6138i	−1.09599	+	0.608821i
$838$	82.5907	−	47.6837i	2.85305	−	1.64721i
$839$	44.9345			1.55131			0.775655	−	0.631157i	$-0.217420\pi$
$839$	44.9345			1.55131			0.775655	+	0.631157i	$0.217420\pi$
$840$		0			0
$841$	21.1726			0.730090
$842$	−70.2249	+	40.5444i	−2.42011	+	1.39725i
$843$	−0.0348578	−	0.0974396i	−0.00120057	−	0.00335600i
$844$	−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
$849$	−27.1655	−	4.94464i	−0.932318	−	0.169700i
$850$		0			0
$851$	−9.33698	−	5.39071i	−0.320068	−	0.184791i
$852$	−35.5308	−	6.46728i	−1.21727	−	0.221565i
$853$			44.2981i			1.51674i	0.651826	+	0.758368i	$0.274003\pi$
$853$			44.2981i			1.51674i	−0.651826	+	0.758368i	$0.725997\pi$
$854$	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	$-0.914372\pi$
$857$	−7.37279	+	12.7700i	−0.251850	+	0.436216i	0.712185	+	0.701991i	$0.247705\pi$
$858$	6.74341	+	18.8502i	0.230216	+	0.643534i
$859$	1.52877	−	0.882637i	0.0521610	−	0.0301152i	−0.473693	−	0.880690i	$-0.657079\pi$
$859$	1.52877	−	0.882637i	0.0521610	−	0.0301152i	0.525854	+	0.850575i	$0.323746\pi$
$860$		0			0
$861$	52.4975	+	11.2612i	1.78911	+	0.383782i
$862$	23.1378			0.788076
$863$	18.7870	−	10.8467i	0.639518	−	0.369226i	−0.144911	−	0.989445i	$-0.546290\pi$
$863$	18.7870	−	10.8467i	0.639518	−	0.369226i	0.784429	+	0.620219i	$0.212956\pi$
$864$	100.226	−	55.6754i	3.40976	−	1.89411i
$865$		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
$873$	18.9751	+	23.1270i	0.642211	+	0.782730i
$874$		−	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	−0.999336	−	0.0364380i	$-0.988399\pi$
$877$	−15.7318	−	27.2482i	−0.531224	−	0.920107i	0.468112	−	0.883669i	$-0.344934\pi$
$878$	17.2914	−	29.9496i	0.583556	−	1.01075i
$879$	−31.5844	+	11.2989i	−1.06531	+	0.381102i
$880$		0			0
$881$	19.8571			0.669004			0.334502	−	0.942395i	$-0.391432\pi$
$881$	19.8571			0.669004			0.334502	+	0.942395i	$0.391432\pi$
$882$	57.1198	−	5.78784i	1.92332	−	0.194887i
$883$	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	$-0.331475\pi$
$887$	−14.7405	−	25.5312i	−0.494937	−	0.857255i	−0.999983	+	0.00583681i	$0.998142\pi$
$888$	−64.5748	+	76.1009i	−2.16699	+	2.55378i
$889$	11.2130	+	6.94994i	0.376072	+	0.233094i
$890$		0			0
$891$	12.2953	−	14.0132i	0.411909	−	0.469461i
$892$	28.7429	+	16.5947i	0.962383	+	0.555632i
$893$	7.11632	+	4.10861i	0.238139	+	0.137489i
$894$	12.3618	−	67.9148i	0.413440	−	2.27141i
$895$		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
$903$	19.5811	+	4.20033i	0.651617	+	0.139778i
$904$	−105.103			−3.49566
$905$		0			0
$906$	11.2112	+	31.3393i	0.372469	+	1.04118i
$907$	16.6945	−	28.9158i	0.554333	−	0.960133i	−0.443622	−	0.896214i	$-0.646307\pi$
$907$	16.6945	−	28.9158i	0.554333	−	0.960133i	0.997955	−	0.0639189i	$-0.0203599\pi$
$908$	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	$-0.231460\pi$
$912$	−71.3473	−	12.9866i	−2.36255	−	0.430028i
$913$	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	0.659488	−	0.751715i	$-0.270773\pi$
$919$	−9.73901	−	16.8685i	−0.321260	−	0.556439i	−0.980748	+	0.195276i	$0.937440\pi$
$920$		0			0
$921$	−10.3637	−	28.9701i	−0.341495	−	0.954597i
$922$	44.6998	−	25.8074i	1.47211	−	0.849922i
$923$	7.77409			0.255887
$924$	49.4505	−	15.9654i	1.62680	−	0.525222i
$925$		0			0
$926$	−34.6718	+	20.0177i	−1.13938	+	0.657824i
$927$	0.553034	−	1.46883i	0.0181640	−	0.0482428i
$928$	−30.8658	+	53.4611i	−1.01322	+	1.75495i
$929$	22.2310	+	38.5053i	0.729376	+	1.26332i	0.957147	+	0.289602i	$0.0935230\pi$
$929$	22.2310	+	38.5053i	0.729376	+	1.26332i	−0.227771	+	0.973715i	$0.573144\pi$
$930$		0			0
$931$	−16.2568	−	10.7937i	−0.532796	−	0.353749i
$932$		−	99.5361i		−	3.26041i
$933$	−2.22563	+	12.2275i	−0.0728640	+	0.400310i
$934$	−12.8427	−	7.41472i	−0.420225	−	0.242617i
$935$		0			0
$936$	−44.9633	+	36.8913i	−1.46967	+	1.20583i
$937$		−	7.31878i		−	0.239094i	−0.992829	−	0.119547i	$-0.961856\pi$
$937$		−	7.31878i		−	0.239094i	0.992829	−	0.119547i	$-0.0381443\pi$
$938$	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	$-0.789309\pi$
$941$	4.22911	−	7.32504i	0.137865	−	0.238790i	0.926688	+	0.375831i	$0.122643\pi$
$942$	97.6533	−	34.9342i	3.18172	−	1.13822i
$943$	−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	$-0.764138\pi$
$947$	−16.0677	+	9.27668i	−0.522129	+	0.301452i	0.215676	+	0.976465i	$0.430805\pi$
$948$	−52.8138	+	18.8935i	−1.71531	+	0.613631i
$949$	−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	$-0.0643635\pi$
$954$	39.2752	−	32.2244i	1.27158	−	1.04330i
$955$		0			0
$956$	−62.3188	−	35.9798i	−2.01553	−	1.16367i
$957$	−1.79751	+	9.87540i	−0.0581052	+	0.319226i
$958$		−	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
$963$	−3.25849	+	8.65440i	−0.105003	+	0.278884i
$964$	0.0847752	−	0.0489450i	0.00273043	−	0.00157641i
$965$		0			0
$966$	−14.9292	+	16.5184i	−0.480340	+	0.531471i
$967$	−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
$969$	−3.42005	−	9.56023i	−0.109868	−	0.307119i
$970$		0			0
$971$	20.9297	+	36.2512i	0.671665	+	1.16336i	0.977432	+	0.211251i	$0.0677539\pi$
$971$	20.9297	+	36.2512i	0.671665	+	1.16336i	−0.305767	+	0.952106i	$0.598913\pi$
$972$	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	$-0.428757\pi$
$977$	−15.9878	−	9.23058i	−0.511496	−	0.295312i	−0.733448	+	0.679745i	$0.762090\pi$
$978$	−37.7185	−	6.86548i	−1.20610	−	0.219534i
$979$		−	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	−0.367538	−	0.930008i	$-0.619799\pi$
$983$	19.4902	−	33.7581i	0.621642	−	1.07672i	0.989180	−	0.146707i	$-0.0468674\pi$
$984$	64.9269	+	181.493i	2.06979	+	5.78580i
$985$		0			0
$986$	−16.0845			−0.512234
$987$	−4.15019	−	12.8546i	−0.132102	−	0.409167i
$988$	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	−0.821623	−	0.570031i	$-0.806931\pi$
$991$	2.60812	−	4.51739i	0.0828495	−	0.143500i	0.904473	+	0.426531i	$0.140265\pi$
$992$	−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
$996$	−10.1270	+	55.6369i	−0.320885	+	1.76292i
$997$	−28.5316	−	16.4727i	−0.903604	−	0.521696i	−0.0252363	−	0.999682i	$-0.508034\pi$
$997$	−28.5316	−	16.4727i	−0.903604	−	0.521696i	−0.878368	+	0.477985i	$0.841367\pi$
$998$	−2.53701	−	1.46474i	−0.0803075	−	0.0463656i
$999$	−31.5186	−	0.521517i	−0.997203	−	0.0165001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.t.i.101.10	yes	20
3.2	odd	2	inner	525.2.t.i.101.1	yes	20
5.2	odd	4		525.2.q.g.374.19		40
5.3	odd	4		525.2.q.g.374.2		40
5.4	even	2		525.2.t.h.101.1	yes	20
7.5	odd	6	inner	525.2.t.i.26.1	yes	20
15.2	even	4		525.2.q.g.374.1		40
15.8	even	4		525.2.q.g.374.20		40
15.14	odd	2		525.2.t.h.101.10	yes	20
21.5	even	6	inner	525.2.t.i.26.10	yes	20
35.12	even	12		525.2.q.g.299.20		40
35.19	odd	6		525.2.t.h.26.10	yes	20
35.33	even	12		525.2.q.g.299.1		40
105.47	odd	12		525.2.q.g.299.2		40
105.68	odd	12		525.2.q.g.299.19		40
105.89	even	6		525.2.t.h.26.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.q.g.299.1		40	35.33	even	12
525.2.q.g.299.2		40	105.47	odd	12
525.2.q.g.299.19		40	105.68	odd	12
525.2.q.g.299.20		40	35.12	even	12
525.2.q.g.374.1		40	15.2	even	4
525.2.q.g.374.2		40	5.3	odd	4
525.2.q.g.374.19		40	5.2	odd	4
525.2.q.g.374.20		40	15.8	even	4
525.2.t.h.26.1	✓	20	105.89	even	6
525.2.t.h.26.10	yes	20	35.19	odd	6
525.2.t.h.101.1	yes	20	5.4	even	2
525.2.t.h.101.10	yes	20	15.14	odd	2
525.2.t.i.26.1	yes	20	7.5	odd	6	inner
525.2.t.i.26.10	yes	20	21.5	even	6	inner
525.2.t.i.101.1	yes	20	3.2	odd	2	inner
525.2.t.i.101.10	yes	20	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(2.36764 - 1.36696i) q^{2} +(-1.63084 + 0.583411i) q^{3} +(2.73715 - 4.74088i) q^{4} +(-3.06374 + 3.61059i) q^{6} +(-2.24882 - 1.39384i) q^{7} -9.49844i q^{8} +(2.31926 - 1.90290i) q^{9} +O(q^{10})\)	\(q+(2.36764 - 1.36696i) q^{2} +(-1.63084 + 0.583411i) q^{3} +(2.73715 - 4.74088i) q^{4} +(-3.06374 + 3.61059i) q^{6} +(-2.24882 - 1.39384i) q^{7} -9.49844i q^{8} +(2.31926 - 1.90290i) q^{9} +(1.79388 + 1.03570i) q^{11} +(-1.69796 + 9.32849i) q^{12} -2.04106i q^{13} +(-7.22973 - 0.226073i) q^{14} +(-7.50967 - 13.0071i) q^{16} +(1.05144 - 1.82114i) q^{17} +(2.89000 - 7.67571i) q^{18} +(-2.41421 + 1.39384i) q^{19} +(4.48065 + 0.961143i) q^{21} +5.66303 q^{22} +(-1.53909 + 0.888591i) q^{23} +(5.54150 + 15.4904i) 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} +(-3.52977 - 0.642485i) q^{33} -5.74909i q^{34} +(-2.67324 - 16.2039i) q^{36} +(3.03329 + 5.25381i) q^{37} +(-3.81065 + 6.60024i) q^{38} +(1.19078 + 3.32864i) q^{39} +11.7165 q^{41} +(11.9224 - 3.84922i) 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} +(-0.652249 + 3.58341i) q^{51} +(-9.67643 - 5.58669i) q^{52} +(5.36432 + 3.09709i) q^{53} +(-0.235023 + 14.2039i) 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} +(-7.86795 + 1.04659i) q^{63} -30.2845 q^{64} +(-9.23548 + 3.30387i) q^{66} +(-3.70150 + 6.41119i) q^{67} +(-5.75589 - 9.96949i) q^{68} +(1.99158 - 2.34707i) q^{69} +3.80885i q^{71} +(-18.0746 - 22.0294i) 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} +(1.75796 - 8.82664i) q^{81} +(27.7405 - 16.0160i) q^{82} +5.96419 q^{83} +(16.8209 - 18.6114i) q^{84} +(10.3469 - 5.97380i) q^{86} +(1.63224 + 4.56267i) q^{87} +(9.83752 - 17.0391i) q^{88} +(-6.20912 - 10.7545i) q^{89} +(-2.84492 + 4.58998i) q^{91} +9.72883i q^{92} +(-11.8952 - 2.16515i) q^{93} +(-6.97906 - 4.02936i) q^{94} +(37.5995 + 6.84382i) 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

Modular forms

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