LMFDB - Embedded newform 1152.2.i.k.769.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(385,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1152.385");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.i (of order $3$, 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:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} + \cdots + 729 $ x^12 - 2x^11 + 3x^10 - 8x^9 + 22x^8 - 42x^7 + 51x^6 - 126x^5 + 198x^4 - 216x^3 + 243x^2 - 486*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			769.5
Root			$-0.433633 - 1.67689i$ of defining polynomial
Character	$\chi$	$=$	1152.769
Dual form			1152.2.i.k.385.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23541 + 1.21398i) q^{3} +(2.22043 - 3.84590i) q^{5} +(1.45488 + 2.51992i) q^{7} +(0.0524919 + 2.99954i) q^{9} +O(q^{10})$	\(q+(1.23541 + 1.21398i) q^{3} +(2.22043 - 3.84590i) q^{5} +(1.45488 + 2.51992i) q^{7} +(0.0524919 + 2.99954i) q^{9} +(1.08263 + 1.87517i) q^{11} +(1.96377 - 3.40135i) q^{13} +(7.41200 - 2.05571i) q^{15} +1.79720 q^{17} -1.76882 q^{19} +(-1.26177 + 4.87934i) q^{21} +(-3.44197 + 5.96166i) q^{23} +(-7.36062 - 12.7490i) q^{25} +(-3.57654 + 3.76940i) q^{27} +(2.87353 + 4.97710i) q^{29} +(3.27671 - 5.67542i) q^{31} +(-0.938929 + 3.63091i) q^{33} +12.9218 q^{35} +2.51332 q^{37} +(6.55525 - 1.81809i) q^{39} +(-3.68420 + 6.38122i) q^{41} +(-2.53640 - 4.39317i) q^{43} +(11.6525 + 6.45839i) q^{45} +(-4.98598 - 8.63597i) q^{47} +(-0.733339 + 1.27018i) q^{49} +(2.22029 + 2.18177i) q^{51} +3.30620 q^{53} +9.61562 q^{55} +(-2.18523 - 2.14732i) q^{57} +(2.30090 - 3.98528i) q^{59} +(-1.87353 - 3.24505i) q^{61} +(-7.48224 + 4.49624i) q^{63} +(-8.72084 - 15.1049i) q^{65} +(-2.36045 + 4.08841i) q^{67} +(-11.4896 + 3.18663i) q^{69} +0.907539 q^{71} -1.87740 q^{73} +(6.38362 - 24.6859i) q^{75} +(-3.15019 + 5.45629i) q^{77} +(1.23661 + 2.14187i) q^{79} +(-8.99449 + 0.314903i) q^{81} +(1.09251 + 1.89227i) q^{83} +(3.99056 - 6.91185i) q^{85} +(-2.49211 + 9.63718i) q^{87} -5.30620 q^{89} +11.4282 q^{91} +(10.9380 - 3.03363i) q^{93} +(-3.92754 + 6.80271i) q^{95} +(4.45302 + 7.71286i) q^{97} +(-5.56782 + 3.34583i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} - 2 q^{5} + 6 q^{7} - 2 q^{9}+O(q^{10}) $ 12 * q + 4 * q^3 - 2 * q^5 + 6 * q^7 - 2 * q^9	$ 12 q + 4 q^{3} - 2 q^{5} + 6 q^{7} - 2 q^{9} + 4 q^{11} + 10 q^{13} + 4 q^{15} + 4 q^{17} + 4 q^{19} + 2 q^{21} + 8 q^{23} - 14 q^{25} - 14 q^{27} - 2 q^{29} + 8 q^{31} - 10 q^{33} + 8 q^{35} + 22 q^{39} - 2 q^{41} - 2 q^{43} + 10 q^{45} - 14 q^{47} - 18 q^{49} - 38 q^{51} + 24 q^{53} - 16 q^{55} - 38 q^{57} + 6 q^{59} + 14 q^{61} - 16 q^{63} - 8 q^{65} + 4 q^{67} - 50 q^{69} - 28 q^{71} + 60 q^{73} + 50 q^{75} + 2 q^{77} + 16 q^{79} + 22 q^{81} + 24 q^{83} + 16 q^{85} - 36 q^{87} - 48 q^{89} - 52 q^{91} + 42 q^{93} - 20 q^{95} - 14 q^{97} + 68 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 - 2 * q^5 + 6 * q^7 - 2 * q^9 + 4 * q^11 + 10 * q^13 + 4 * q^15 + 4 * q^17 + 4 * q^19 + 2 * q^21 + 8 * q^23 - 14 * q^25 - 14 * q^27 - 2 * q^29 + 8 * q^31 - 10 * q^33 + 8 * q^35 + 22 * q^39 - 2 * q^41 - 2 * q^43 + 10 * q^45 - 14 * q^47 - 18 * q^49 - 38 * q^51 + 24 * q^53 - 16 * q^55 - 38 * q^57 + 6 * q^59 + 14 * q^61 - 16 * q^63 - 8 * q^65 + 4 * q^67 - 50 * q^69 - 28 * q^71 + 60 * q^73 + 50 * q^75 + 2 * q^77 + 16 * q^79 + 22 * q^81 + 24 * q^83 + 16 * q^85 - 36 * q^87 - 48 * q^89 - 52 * q^91 + 42 * q^93 - 20 * q^95 - 14 * q^97 + 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.23541	+	1.21398i	0.713266	+	0.700893i
$3$	1.23541	+	1.21398i	0.713266	+	0.700893i
$4$		0			0
$5$	2.22043	−	3.84590i	0.993006	−	1.71994i	0.394260	−	0.918999i	$-0.371001\pi$
$5$	2.22043	−	3.84590i	0.993006	−	1.71994i	0.598746	−	0.800939i	$-0.295666\pi$
$6$		0			0
$7$	1.45488	+	2.51992i	0.549892	+	0.952441i	0.998281	+	0.0586028i	$0.0186645\pi$
$7$	1.45488	+	2.51992i	0.549892	+	0.952441i	−0.448389	+	0.893838i	$0.648002\pi$
$8$		0			0
$9$	0.0524919	+	2.99954i	0.0174973	+	0.999847i
$10$		0			0
$11$	1.08263	+	1.87517i	0.326425	+	0.565385i	0.981800	−	0.189919i	$-0.0608225\pi$
$11$	1.08263	+	1.87517i	0.326425	+	0.565385i	−0.655374	+	0.755304i	$0.727489\pi$
$12$		0			0
$13$	1.96377	−	3.40135i	0.544652	−	0.943366i	−0.453976	−	0.891014i	$-0.649995\pi$
$13$	1.96377	−	3.40135i	0.544652	−	0.943366i	0.998629	−	0.0523518i	$-0.0166717\pi$
$14$		0			0
$15$	7.41200	−	2.05571i	1.91377	−	0.530782i
$16$		0			0
$17$	1.79720			0.435885			0.217943	−	0.975962i	$-0.430065\pi$
$17$	1.79720			0.435885			0.217943	+	0.975962i	$0.430065\pi$
$18$		0			0
$19$	−1.76882			−0.405795			−0.202898	−	0.979200i	$-0.565036\pi$
$19$	−1.76882			−0.405795			−0.202898	+	0.979200i	$0.565036\pi$
$20$		0			0
$21$	−1.26177	+	4.87934i	−0.275340	+	1.06476i
$22$		0			0
$23$	−3.44197	+	5.96166i	−0.717700	+	1.24309i	0.244209	+	0.969723i	$0.421472\pi$
$23$	−3.44197	+	5.96166i	−0.717700	+	1.24309i	−0.961909	+	0.273370i	$0.911862\pi$
$24$		0			0
$25$	−7.36062	−	12.7490i	−1.47212	−	2.54979i
$26$		0			0
$27$	−3.57654	+	3.76940i	−0.688306	+	0.725421i
$28$		0			0
$29$	2.87353	+	4.97710i	0.533601	+	0.924224i	0.999230	+	0.0392435i	$0.0124948\pi$
$29$	2.87353	+	4.97710i	0.533601	+	0.924224i	−0.465629	+	0.884980i	$0.654172\pi$
$30$		0			0
$31$	3.27671	−	5.67542i	0.588514	−	1.01934i	−0.405913	−	0.913912i	$-0.633047\pi$
$31$	3.27671	−	5.67542i	0.588514	−	1.01934i	0.994427	−	0.105425i	$-0.0336201\pi$
$32$		0			0
$33$	−0.938929	+	3.63091i	−0.163447	+	0.632060i
$34$		0			0
$35$	12.9218			2.18419
$36$		0			0
$37$	2.51332			0.413187			0.206593	−	0.978427i	$-0.433762\pi$
$37$	2.51332			0.413187			0.206593	+	0.978427i	$0.433762\pi$
$38$		0			0
$39$	6.55525	−	1.81809i	1.04968	−	0.291128i
$40$		0			0
$41$	−3.68420	+	6.38122i	−0.575376	+	0.996580i	0.420625	+	0.907235i	$0.361811\pi$
$41$	−3.68420	+	6.38122i	−0.575376	+	0.996580i	−0.996001	+	0.0893453i	$0.971523\pi$
$42$		0			0
$43$	−2.53640	−	4.39317i	−0.386797	−	0.669953i	0.605219	−	0.796059i	$-0.293085\pi$
$43$	−2.53640	−	4.39317i	−0.386797	−	0.669953i	−0.992017	+	0.126106i	$0.959752\pi$
$44$		0			0
$45$	11.6525	+	6.45839i	1.73705	+	0.962760i
$46$		0			0
$47$	−4.98598	−	8.63597i	−0.727280	−	1.25969i	−0.958029	−	0.286673i	$-0.907451\pi$
$47$	−4.98598	−	8.63597i	−0.727280	−	1.25969i	0.230748	−	0.973013i	$-0.425883\pi$
$48$		0			0
$49$	−0.733339	+	1.27018i	−0.104763	+	0.181454i
$50$		0			0
$51$	2.22029	+	2.18177i	0.310902	+	0.305509i
$52$		0			0
$53$	3.30620			0.454141			0.227070	−	0.973878i	$-0.427085\pi$
$53$	3.30620			0.454141			0.227070	+	0.973878i	$0.427085\pi$
$54$		0			0
$55$	9.61562			1.29657
$56$		0			0
$57$	−2.18523	−	2.14732i	−0.289440	−	0.284419i
$58$		0			0
$59$	2.30090	−	3.98528i	0.299552	−	0.518839i	−0.676482	−	0.736459i	$-0.736496\pi$
$59$	2.30090	−	3.98528i	0.299552	−	0.518839i	0.976033	+	0.217621i	$0.0698296\pi$
$60$		0			0
$61$	−1.87353	−	3.24505i	−0.239881	−	0.415485i	0.720799	−	0.693144i	$-0.243775\pi$
$61$	−1.87353	−	3.24505i	−0.239881	−	0.415485i	−0.960680	+	0.277658i	$0.910442\pi$
$62$		0			0
$63$	−7.48224	+	4.49624i	−0.942674	+	0.566473i
$64$		0			0
$65$	−8.72084	−	15.1049i	−1.08169	−	1.87354i
$66$		0			0
$67$	−2.36045	+	4.08841i	−0.288374	+	0.499479i	−0.973422	−	0.229019i	$-0.926448\pi$
$67$	−2.36045	+	4.08841i	−0.288374	+	0.499479i	0.685047	+	0.728498i	$0.259781\pi$
$68$		0			0
$69$	−11.4896	+	3.18663i	−1.38319	+	0.383625i
$70$		0			0
$71$	0.907539			0.107705			0.0538525	−	0.998549i	$-0.482850\pi$
$71$	0.907539			0.107705			0.0538525	+	0.998549i	$0.482850\pi$
$72$		0			0
$73$	−1.87740			−0.219733			−0.109866	−	0.993946i	$-0.535042\pi$
$73$	−1.87740			−0.219733			−0.109866	+	0.993946i	$0.535042\pi$
$74$		0			0
$75$	6.38362	−	24.6859i	0.737117	−	2.85048i
$76$		0			0
$77$	−3.15019	+	5.45629i	−0.358998	+	0.621802i
$78$		0			0
$79$	1.23661	+	2.14187i	0.139129	+	0.240979i	0.927167	−	0.374648i	$-0.122236\pi$
$79$	1.23661	+	2.14187i	0.139129	+	0.240979i	−0.788038	+	0.615627i	$0.788903\pi$
$80$		0			0
$81$	−8.99449	+	0.314903i	−0.999388	+	0.0349892i
$82$		0			0
$83$	1.09251	+	1.89227i	0.119918	+	0.207704i	0.919735	−	0.392540i	$-0.128403\pi$
$83$	1.09251	+	1.89227i	0.119918	+	0.207704i	−0.799817	+	0.600244i	$0.795070\pi$
$84$		0			0
$85$	3.99056	−	6.91185i	0.432837	−	0.749696i
$86$		0			0
$87$	−2.49211	+	9.63718i	−0.267183	+	1.03321i
$88$		0			0
$89$	−5.30620			−0.562456			−0.281228	−	0.959641i	$-0.590742\pi$
$89$	−5.30620			−0.562456			−0.281228	+	0.959641i	$0.590742\pi$
$90$		0			0
$91$	11.4282			1.19800
$92$		0			0
$93$	10.9380	−	3.03363i	1.13421	−	0.314572i
$94$		0			0
$95$	−3.92754	+	6.80271i	−0.402958	+	0.697943i
$96$		0			0
$97$	4.45302	+	7.71286i	0.452136	+	0.783123i	0.998519	−	0.0544132i	$-0.0173288\pi$
$97$	4.45302	+	7.71286i	0.452136	+	0.783123i	−0.546382	+	0.837536i	$0.683995\pi$
$98$		0			0
$99$	−5.56782	+	3.34583i	−0.559587	+	0.336268i
$100$		0			0
$101$	−0.689326	−	1.19395i	−0.0685905	−	0.118802i	0.829691	−	0.558224i	$-0.188517\pi$
$101$	−0.689326	−	1.19395i	−0.0685905	−	0.118802i	−0.898281	+	0.439421i	$0.855184\pi$
$102$		0			0
$103$	2.54512	−	4.40828i	0.250778	−	0.434361i	−0.712962	−	0.701203i	$-0.752647\pi$
$103$	2.54512	−	4.40828i	0.250778	−	0.434361i	0.963740	+	0.266842i	$0.0859801\pi$
$104$		0			0
$105$	15.9638	+	15.6869i	1.55791	+	1.53088i
$106$		0			0
$107$	17.2062			1.66338			0.831692	−	0.555238i	$-0.187373\pi$
$107$	17.2062			1.66338			0.831692	+	0.555238i	$0.187373\pi$
$108$		0			0
$109$	6.59351			0.631544			0.315772	−	0.948835i	$-0.397737\pi$
$109$	6.59351			0.631544			0.315772	+	0.948835i	$0.397737\pi$
$110$		0			0
$111$	3.10498	+	3.05112i	0.294712	+	0.289600i
$112$		0			0
$113$	−8.90072	+	15.4165i	−0.837309	+	1.45026i	0.0548276	+	0.998496i	$0.482539\pi$
$113$	−8.90072	+	15.4165i	−0.837309	+	1.45026i	−0.892137	+	0.451766i	$0.850794\pi$
$114$		0			0
$115$	15.2853	+	26.4749i	1.42536	+	2.46880i
$116$		0			0
$117$	10.3056	+	5.71187i	0.952751	+	0.528063i
$118$		0			0
$119$	2.61471	+	4.52881i	0.239690	+	0.415155i
$120$		0			0
$121$	3.15582	−	5.46604i	0.286893	−	0.496913i
$122$		0			0
$123$	−12.2982	+	3.41089i	−1.10889	+	0.307550i
$124$		0			0
$125$	−43.1706			−3.86130
$126$		0			0
$127$	−18.2258			−1.61728			−0.808639	−	0.588305i	$-0.799795\pi$
$127$	−18.2258			−1.61728			−0.808639	+	0.588305i	$0.799795\pi$
$128$		0			0
$129$	2.19973	−	8.50653i	0.193676	−	0.748958i
$130$		0			0
$131$	−4.33057	+	7.50076i	−0.378363	+	0.655345i	−0.990824	−	0.135156i	$-0.956846\pi$
$131$	−4.33057	+	7.50076i	−0.378363	+	0.655345i	0.612461	+	0.790501i	$0.290180\pi$
$132$		0			0
$133$	−2.57342	−	4.45729i	−0.223144	−	0.386496i
$134$		0			0
$135$	6.55525	+	22.1247i	0.564186	+	1.90419i
$136$		0			0
$137$	−0.774446	−	1.34138i	−0.0661654	−	0.114602i	0.831045	−	0.556205i	$-0.187743\pi$
$137$	−0.774446	−	1.34138i	−0.0661654	−	0.114602i	−0.897210	+	0.441603i	$0.854410\pi$
$138$		0			0
$139$	−9.78618	+	16.9502i	−0.830053	+	1.43769i	0.0679426	+	0.997689i	$0.478357\pi$
$139$	−9.78618	+	16.9502i	−0.830053	+	1.43769i	−0.897996	+	0.440005i	$0.854977\pi$
$140$		0			0
$141$	4.32418	−	16.7219i	0.364161	−	1.40824i
$142$		0			0
$143$	8.50416			0.711154
$144$		0			0
$145$	25.5219			2.11948
$146$		0			0
$147$	−2.44796	+	0.678937i	−0.201904	+	0.0559978i
$148$		0			0
$149$	−0.945984	+	1.63849i	−0.0774980	+	0.134230i	−0.902170	−	0.431381i	$-0.858026\pi$
$149$	−0.945984	+	1.63849i	−0.0774980	+	0.134230i	0.824672	+	0.565612i	$0.191360\pi$
$150$		0			0
$151$	−4.27927	−	7.41191i	−0.348242	−	0.603173i	0.637695	−	0.770289i	$-0.279888\pi$
$151$	−4.27927	−	7.41191i	−0.348242	−	0.603173i	−0.985937	+	0.167116i	$0.946555\pi$
$152$		0			0
$153$	0.0943385	+	5.39078i	0.00762682	+	0.435819i
$154$		0			0
$155$	−14.5514	−	25.2038i	−1.16880	−	2.02441i
$156$		0			0
$157$	2.22265	−	3.84974i	0.177387	−	0.307242i	−0.763598	−	0.645692i	$-0.776569\pi$
$157$	2.22265	−	3.84974i	0.177387	−	0.307242i	0.940985	+	0.338449i	$0.109902\pi$
$158$		0			0
$159$	4.08452	+	4.01366i	0.323923	+	0.318304i
$160$		0			0
$161$	−20.0306			−1.57863
$162$		0			0
$163$	−18.8817			−1.47893			−0.739465	−	0.673195i	$-0.764922\pi$
$163$	−18.8817			−1.47893			−0.739465	+	0.673195i	$0.764922\pi$
$164$		0			0
$165$	11.8793	+	11.6732i	0.924800	+	0.908757i
$166$		0			0
$167$	4.31394	−	7.47197i	0.333823	−	0.578198i	−0.649435	−	0.760417i	$-0.724995\pi$
$167$	4.31394	−	7.47197i	0.333823	−	0.578198i	0.983258	+	0.182219i	$0.0583279\pi$
$168$		0			0
$169$	−1.21280	−	2.10063i	−0.0932924	−	0.161587i
$170$		0			0
$171$	−0.0928488	−	5.30565i	−0.00710033	−	0.405733i
$172$		0			0
$173$	−3.91423	−	6.77965i	−0.297594	−	0.515447i	0.677991	−	0.735070i	$-0.262851\pi$
$173$	−3.91423	−	6.77965i	−0.297594	−	0.515447i	−0.975585	+	0.219623i	$0.929517\pi$
$174$		0			0
$175$	21.4176	−	37.0964i	1.61902	−	2.80422i
$176$		0			0
$177$	7.68062	−	2.13021i	0.577311	−	0.160116i
$178$		0			0
$179$	−13.6390			−1.01943			−0.509714	−	0.860344i	$-0.670249\pi$
$179$	−13.6390			−1.01943			−0.509714	+	0.860344i	$0.670249\pi$
$180$		0			0
$181$	−0.504672			−0.0375120			−0.0187560	−	0.999824i	$-0.505971\pi$
$181$	−0.504672			−0.0375120			−0.0187560	+	0.999824i	$0.505971\pi$
$182$		0			0
$183$	1.62485	−	6.28340i	0.120112	−	0.464482i
$184$		0			0
$185$	5.58064	−	9.66596i	0.410297	−	0.710655i
$186$		0			0
$187$	1.94571	+	3.37006i	0.142284	+	0.246443i
$188$		0			0
$189$	−14.7020	−	3.52860i	−1.06941	−	0.256668i
$190$		0			0
$191$	−10.0083	−	17.3349i	−0.724175	−	1.25431i	−0.959313	−	0.282345i	$-0.908888\pi$
$191$	−10.0083	−	17.3349i	−0.724175	−	1.25431i	0.235138	−	0.971962i	$-0.424446\pi$
$192$		0			0
$193$	−1.08462	+	1.87862i	−0.0780726	+	0.135226i	−0.902418	−	0.430861i	$-0.858210\pi$
$193$	−1.08462	+	1.87862i	−0.0780726	+	0.135226i	0.824346	+	0.566087i	$0.191543\pi$
$194$		0			0
$195$	7.56329	−	29.2478i	0.541618	−	2.09448i
$196$		0			0
$197$	−5.67460			−0.404298			−0.202149	−	0.979355i	$-0.564793\pi$
$197$	−5.67460			−0.404298			−0.202149	+	0.979355i	$0.564793\pi$
$198$		0			0
$199$	−11.5032			−0.815439			−0.407719	−	0.913107i	$-0.633676\pi$
$199$	−11.5032			−0.815439			−0.407719	+	0.913107i	$0.633676\pi$
$200$		0			0
$201$	−7.87939	+	2.18534i	−0.555769	+	0.154142i
$202$		0			0
$203$	−8.36126	+	14.4821i	−0.586846	+	1.01645i
$204$		0			0
$205$	16.3610	+	28.3381i	1.14270	+	1.97922i
$206$		0			0
$207$	−18.0629	−	10.0114i	−1.25546	−	0.695839i
$208$		0			0
$209$	−1.91498	−	3.31684i	−0.132462	−	0.229431i
$210$		0			0
$211$	10.3177	−	17.8707i	0.710297	−	1.23027i	−0.254449	−	0.967086i	$-0.581894\pi$
$211$	10.3177	−	17.8707i	0.710297	−	1.23027i	0.964746	−	0.263184i	$-0.0847726\pi$
$212$		0			0
$213$	1.12119	+	1.10174i	0.0768224	+	0.0754897i
$214$		0			0
$215$	−22.5276			−1.53637
$216$		0			0
$217$	19.0688			1.29448
$218$		0			0
$219$	−2.31936	−	2.27913i	−0.156728	−	0.154009i
$220$		0			0
$221$	3.52929	−	6.11292i	0.237406	−	0.411199i
$222$		0			0
$223$	2.54291	+	4.40444i	0.170286	+	0.294943i	0.938520	−	0.345226i	$-0.112198\pi$
$223$	2.54291	+	4.40444i	0.170286	+	0.294943i	−0.768234	+	0.640169i	$0.778864\pi$
$224$		0			0
$225$	37.8547	−	22.7477i	2.52364	−	1.51651i
$226$		0			0
$227$	9.14484	+	15.8393i	0.606964	+	1.05129i	0.991738	+	0.128282i	$0.0409462\pi$
$227$	9.14484	+	15.8393i	0.606964	+	1.05129i	−0.384773	+	0.923011i	$0.625720\pi$
$228$		0			0
$229$	9.62341	−	16.6682i	0.635933	−	1.10147i	−0.350384	−	0.936606i	$-0.613949\pi$
$229$	9.62341	−	16.6682i	0.635933	−	1.10147i	0.986317	−	0.164862i	$-0.0527178\pi$
$230$		0			0
$231$	−10.5156	+	2.91650i	−0.691878	+	0.191891i
$232$		0			0
$233$	16.4263			1.07612			0.538061	−	0.842906i	$-0.319157\pi$
$233$	16.4263			1.07612			0.538061	+	0.842906i	$0.319157\pi$
$234$		0			0
$235$	−44.2841			−2.88878
$236$		0			0
$237$	−1.07247	+	4.14732i	−0.0696644	+	0.269397i
$238$		0			0
$239$	−9.08563	+	15.7368i	−0.587700	+	1.01793i	0.406833	+	0.913503i	$0.366633\pi$
$239$	−9.08563	+	15.7368i	−0.587700	+	1.01793i	−0.994533	+	0.104424i	$0.966700\pi$
$240$		0			0
$241$	−11.4344	−	19.8050i	−0.736556	−	1.27575i	−0.954037	−	0.299688i	$-0.903117\pi$
$241$	−11.4344	−	19.8050i	−0.736556	−	1.27575i	0.217481	−	0.976065i	$-0.430216\pi$
$242$		0			0
$243$	−11.4942	−	10.5301i	−0.737353	−	0.675507i
$244$		0			0
$245$	3.25666	+	5.64070i	0.208060	+	0.360371i
$246$		0			0
$247$	−3.47356	+	6.01639i	−0.221017	+	0.382813i
$248$		0			0
$249$	−0.947493	+	3.66402i	−0.0600449	+	0.232198i
$250$		0			0
$251$	−0.139530			−0.00880707			−0.00440353	−	0.999990i	$-0.501402\pi$
$251$	−0.139530			−0.00880707			−0.00440353	+	0.999990i	$0.501402\pi$
$252$		0			0
$253$	−14.9055			−0.937102
$254$		0			0
$255$	13.3209	−	3.69452i	0.834185	−	0.231360i
$256$		0			0
$257$	−7.17682	+	12.4306i	−0.447678	+	0.775400i	−0.998234	−	0.0593974i	$-0.981082\pi$
$257$	−7.17682	+	12.4306i	−0.447678	+	0.775400i	0.550557	+	0.834798i	$0.314415\pi$
$258$		0			0
$259$	3.65657	+	6.33336i	0.227208	+	0.393536i
$260$		0			0
$261$	−14.7782	+	8.88052i	−0.914745	+	0.549690i
$262$		0			0
$263$	−0.968751	−	1.67793i	−0.0597357	−	0.103465i	0.834611	−	0.550840i	$-0.185692\pi$
$263$	−0.968751	−	1.67793i	−0.0597357	−	0.103465i	−0.894347	+	0.447374i	$0.852359\pi$
$264$		0			0
$265$	7.34118	−	12.7153i	0.450965	−	0.781094i
$266$		0			0
$267$	−6.55534	−	6.44163i	−0.401181	−	0.394221i
$268$		0			0
$269$	9.91415			0.604477			0.302238	−	0.953232i	$-0.402266\pi$
$269$	9.91415			0.604477			0.302238	+	0.953232i	$0.402266\pi$
$270$		0			0
$271$	−4.56777			−0.277472			−0.138736	−	0.990329i	$-0.544304\pi$
$271$	−4.56777			−0.277472			−0.138736	+	0.990329i	$0.544304\pi$
$272$		0			0
$273$	14.1185	+	13.8736i	0.854493	+	0.839670i
$274$		0			0
$275$	15.9377	−	27.6048i	0.961077	−	1.66463i
$276$		0			0
$277$	−14.4728	−	25.0676i	−0.869585	−	1.50616i	−0.862422	−	0.506190i	$-0.831053\pi$
$277$	−14.4728	−	25.0676i	−0.869585	−	1.50616i	−0.00716263	−	0.999974i	$-0.502280\pi$
$278$		0			0
$279$	17.1957	+	9.53070i	1.02948	+	0.570588i
$280$		0			0
$281$	11.1351	+	19.2865i	0.664262	+	1.15054i	0.979485	+	0.201518i	$0.0645875\pi$
$281$	11.1351	+	19.2865i	0.664262	+	1.15054i	−0.315223	+	0.949018i	$0.602079\pi$
$282$		0			0
$283$	6.79946	−	11.7770i	0.404186	−	0.700071i	−0.590040	−	0.807374i	$-0.700888\pi$
$283$	6.79946	−	11.7770i	0.404186	−	0.700071i	0.994226	+	0.107303i	$0.0342215\pi$
$284$		0			0
$285$	−13.1105	+	3.63618i	−0.776599	+	0.215389i
$286$		0			0
$287$	−21.4403			−1.26558
$288$		0			0
$289$	−13.7701			−0.810004
$290$		0			0
$291$	−3.86196	+	14.9345i	−0.226392	+	0.875474i
$292$		0			0
$293$	−7.21821	+	12.5023i	−0.421693	+	0.730393i	−0.996105	−	0.0881730i	$-0.971897\pi$
$293$	−7.21821	+	12.5023i	−0.421693	+	0.730393i	0.574413	+	0.818566i	$0.305230\pi$
$294$		0			0
$295$	−10.2180	−	17.6980i	−0.594913	−	1.03042i
$296$		0			0
$297$	−10.9403	−	2.62576i	−0.634823	−	0.152362i
$298$		0			0
$299$	13.5185	+	23.4147i	0.781794	+	1.35411i
$300$		0			0
$301$	7.38030	−	12.7831i	0.425394	−	0.736804i
$302$		0			0
$303$	0.597829	−	2.31185i	0.0343444	−	0.132812i
$304$		0			0
$305$	−16.6401			−0.952812
$306$		0			0
$307$	−16.5451			−0.944280			−0.472140	−	0.881524i	$-0.656518\pi$
$307$	−16.5451			−0.944280			−0.472140	+	0.881524i	$0.656518\pi$
$308$		0			0
$309$	8.49585	−	2.35631i	0.483312	−	0.134046i
$310$		0			0
$311$	−5.19366	+	8.99568i	−0.294505	+	0.510098i	−0.974870	−	0.222776i	$-0.928488\pi$
$311$	−5.19366	+	8.99568i	−0.294505	+	0.510098i	0.680364	+	0.732874i	$0.261822\pi$
$312$		0			0
$313$	−6.76501	−	11.7173i	−0.382381	−	0.662303i	0.609021	−	0.793154i	$-0.291562\pi$
$313$	−6.76501	−	11.7173i	−0.382381	−	0.662303i	−0.991402	+	0.130851i	$0.958229\pi$
$314$		0			0
$315$	0.678291	+	38.7595i	0.0382174	+	2.18385i
$316$		0			0
$317$	−11.9869	−	20.7619i	−0.673251	−	1.16611i	−0.976977	−	0.213346i	$-0.931564\pi$
$317$	−11.9869	−	20.7619i	−0.673251	−	1.16611i	0.303726	−	0.952760i	$-0.401769\pi$
$318$		0			0
$319$	−6.22194	+	10.7767i	−0.348362	+	0.603380i
$320$		0			0
$321$	21.2567	+	20.8880i	1.18644	+	1.16585i
$322$		0			0
$323$	−3.17893			−0.176880
$324$		0			0
$325$	−57.8183			−3.20718
$326$		0			0
$327$	8.14571	+	8.00441i	0.450459	+	0.442645i
$328$		0			0
$329$	14.5080	−	25.1286i	0.799851	−	1.38538i
$330$		0			0
$331$	−1.29103	−	2.23612i	−0.0709612	−	0.122908i	0.828362	−	0.560194i	$-0.189273\pi$
$331$	−1.29103	−	2.23612i	−0.0709612	−	0.122908i	−0.899323	+	0.437285i	$0.855940\pi$
$332$		0			0
$333$	0.131929	+	7.53879i	0.00722965	+	0.413123i
$334$		0			0
$335$	10.4824	+	18.1561i	0.572715	+	0.991972i
$336$		0			0
$337$	−1.79736	+	3.11313i	−0.0979087	+	0.169583i	−0.910819	−	0.412806i	$-0.864549\pi$
$337$	−1.79736	+	3.11313i	−0.0979087	+	0.169583i	0.812910	+	0.582389i	$0.197882\pi$
$338$		0			0
$339$	−29.7114	+	8.24042i	−1.61370	+	0.447558i
$340$		0			0
$341$	14.1899			0.768424
$342$		0			0
$343$	16.1006			0.869351
$344$		0			0
$345$	−13.2564	+	51.2636i	−0.713702	+	2.75994i
$346$		0			0
$347$	5.85180	−	10.1356i	0.314141	−	0.544108i	−0.665114	−	0.746742i	$-0.731617\pi$
$347$	5.85180	−	10.1356i	0.314141	−	0.544108i	0.979255	+	0.202634i	$0.0649502\pi$
$348$		0			0
$349$	9.34856	+	16.1922i	0.500417	+	0.866747i	1.00000		0.000481224i	$0.000153178\pi$
$349$	9.34856	+	16.1922i	0.500417	+	0.866747i	−0.499583	+	0.866266i	$0.666513\pi$
$350$		0			0
$351$	5.79754	+	19.5673i	0.309450	+	1.04443i
$352$		0			0
$353$	14.3410	+	24.8394i	0.763295	+	1.32207i	0.941143	+	0.338008i	$0.109753\pi$
$353$	14.3410	+	24.8394i	0.763295	+	1.32207i	−0.177848	+	0.984058i	$0.556914\pi$
$354$		0			0
$355$	2.01513	−	3.49030i	0.106952	−	0.185246i
$356$		0			0
$357$	−2.26765	+	8.76916i	−0.120017	+	0.464113i
$358$		0			0
$359$	−15.8202			−0.834958			−0.417479	−	0.908687i	$-0.637086\pi$
$359$	−15.8202			−0.834958			−0.417479	+	0.908687i	$0.637086\pi$
$360$		0			0
$361$	−15.8713			−0.835330
$362$		0			0
$363$	10.5344	−	2.92171i	0.552914	−	0.153350i
$364$		0			0
$365$	−4.16863	+	7.22028i	−0.218196	+	0.377927i
$366$		0			0
$367$	13.1383	+	22.7563i	0.685815	+	1.18787i	0.973180	+	0.230046i	$0.0738876\pi$
$367$	13.1383	+	22.7563i	0.685815	+	1.18787i	−0.287364	+	0.957821i	$0.592779\pi$
$368$		0			0
$369$	−19.3341	−	10.7160i	−1.00649	−	0.557850i
$370$		0			0
$371$	4.81011	+	8.33136i	0.249729	+	0.432543i
$372$		0			0
$373$	10.8735	−	18.8335i	0.563010	−	0.975162i	−0.434222	−	0.900806i	$-0.642977\pi$
$373$	10.8735	−	18.8335i	0.563010	−	0.975162i	0.997232	−	0.0743558i	$-0.0236901\pi$
$374$		0			0
$375$	−53.3336	−	52.4084i	−2.75413	−	2.70636i
$376$		0			0
$377$	22.5718			1.16251
$378$		0			0
$379$	32.8861			1.68925			0.844623	−	0.535362i	$-0.179825\pi$
$379$	32.8861			1.68925			0.844623	+	0.535362i	$0.179825\pi$
$380$		0			0
$381$	−22.5164	−	22.1258i	−1.15355	−	1.13354i
$382$		0			0
$383$	5.81269	−	10.0679i	0.297015	−	0.514444i	−0.678437	−	0.734659i	$-0.737342\pi$
$383$	5.81269	−	10.0679i	0.297015	−	0.514444i	0.975452	+	0.220214i	$0.0706757\pi$
$384$		0			0
$385$	13.9896	+	24.2306i	0.712974	+	1.23491i
$386$		0			0
$387$	13.0444	−	7.83864i	0.663082	−	0.398461i
$388$		0			0
$389$	−3.61687	−	6.26460i	−0.183383	−	0.317628i	0.759648	−	0.650335i	$-0.225371\pi$
$389$	−3.61687	−	6.26460i	−0.183383	−	0.317628i	−0.943030	+	0.332707i	$0.892038\pi$
$390$		0			0
$391$	−6.18591	+	10.7143i	−0.312835	+	0.541846i
$392$		0			0
$393$	−14.4558	+	4.00931i	−0.729200	+	0.202243i
$394$		0			0
$395$	10.9832			0.552625
$396$		0			0
$397$	29.8911			1.50019			0.750095	−	0.661330i	$-0.230008\pi$
$397$	29.8911			1.50019			0.750095	+	0.661330i	$0.230008\pi$
$398$		0			0
$399$	2.23184	−	8.63069i	0.111732	−	0.432075i
$400$		0			0
$401$	3.03226	−	5.25202i	0.151424	−	0.262273i	−0.780327	−	0.625371i	$-0.784948\pi$
$401$	3.03226	−	5.25202i	0.151424	−	0.262273i	0.931751	+	0.363098i	$0.118281\pi$
$402$		0			0
$403$	−12.8694	−	22.2905i	−0.641071	−	1.11037i
$404$		0			0
$405$	−18.7605	+	35.2911i	−0.932219	+	1.75363i
$406$		0			0
$407$	2.72099	+	4.71290i	0.134875	+	0.233610i
$408$		0			0
$409$	−14.4396	+	25.0101i	−0.713993	+	1.23667i	0.249354	+	0.968412i	$0.419782\pi$
$409$	−14.4396	+	25.0101i	−0.713993	+	1.23667i	−0.963347	+	0.268259i	$0.913552\pi$
$410$		0			0
$411$	0.671651	−	2.59732i	0.0331301	−	0.128116i
$412$		0			0
$413$	13.3901			0.658884
$414$		0			0
$415$	9.70332			0.476317
$416$		0			0
$417$	−32.6672	+	9.06020i	−1.59972	+	0.443680i
$418$		0			0
$419$	5.63281	−	9.75631i	0.275181	−	0.476627i	−0.695000	−	0.719010i	$-0.744596\pi$
$419$	5.63281	−	9.75631i	0.275181	−	0.476627i	0.970181	+	0.242383i	$0.0779290\pi$
$420$		0			0
$421$	−6.03050	−	10.4451i	−0.293909	−	0.509065i	0.680822	−	0.732449i	$-0.261623\pi$
$421$	−6.03050	−	10.4451i	−0.293909	−	0.509065i	−0.974730	+	0.223384i	$0.928289\pi$
$422$		0			0
$423$	25.6422	−	15.4090i	1.24677	−	0.749210i
$424$		0			0
$425$	−13.2285	−	22.9125i	−0.641677	−	1.11142i
$426$		0			0
$427$	5.45151	−	9.44229i	0.263817	−	0.456944i
$428$		0			0
$429$	10.5062	+	10.3239i	0.507242	+	0.498443i
$430$		0			0
$431$	−25.5079			−1.22867			−0.614336	−	0.789045i	$-0.710576\pi$
$431$	−25.5079			−1.22867			−0.614336	+	0.789045i	$0.710576\pi$
$432$		0			0
$433$	29.4513			1.41534			0.707670	−	0.706543i	$-0.249746\pi$
$433$	29.4513			1.41534			0.707670	+	0.706543i	$0.249746\pi$
$434$		0			0
$435$	31.5301	+	30.9831i	1.51175	+	1.48553i
$436$		0			0
$437$	6.08823	−	10.5451i	0.291239	−	0.504441i
$438$		0			0
$439$	17.8086	+	30.8454i	0.849959	+	1.47217i	0.881244	+	0.472662i	$0.156707\pi$
$439$	17.8086	+	30.8454i	0.849959	+	1.47217i	−0.0312845	+	0.999511i	$0.509960\pi$
$440$		0			0
$441$	−3.84845	−	2.13301i	−0.183260	−	0.101572i
$442$		0			0
$443$	−6.60886	−	11.4469i	−0.313996	−	0.543857i	0.665227	−	0.746641i	$-0.268335\pi$
$443$	−6.60886	−	11.4469i	−0.313996	−	0.543857i	−0.979224	+	0.202783i	$0.935001\pi$
$444$		0			0
$445$	−11.7820	+	20.4071i	−0.558522	+	0.967389i
$446$		0			0
$447$	−3.15778	+	0.875807i	−0.149358	+	0.0414242i
$448$		0			0
$449$	−5.83739			−0.275483			−0.137742	−	0.990468i	$-0.543984\pi$
$449$	−5.83739			−0.275483			−0.137742	+	0.990468i	$0.543984\pi$
$450$		0			0
$451$	−15.9545			−0.751269
$452$		0			0
$453$	3.71127	−	14.3517i	0.174370	−	0.674303i
$454$		0			0
$455$	25.3755	−	43.9517i	1.18962	−	2.06049i
$456$		0			0
$457$	−13.5037	−	23.3891i	−0.631677	−	1.09410i	−0.987209	−	0.159433i	$-0.949034\pi$
$457$	−13.5037	−	23.3891i	−0.631677	−	1.09410i	0.355532	−	0.934664i	$-0.384300\pi$
$458$		0			0
$459$	−6.42777	+	6.77437i	−0.300022	+	0.316200i
$460$		0			0
$461$	1.78550	+	3.09258i	0.0831591	+	0.144036i	0.904605	−	0.426250i	$-0.140166\pi$
$461$	1.78550	+	3.09258i	0.0831591	+	0.144036i	−0.821446	+	0.570286i	$0.806832\pi$
$462$		0			0
$463$	−19.8396	+	34.3631i	−0.922023	+	1.59699i	−0.125742	+	0.992063i	$0.540131\pi$
$463$	−19.8396	+	34.3631i	−0.922023	+	1.59699i	−0.796281	+	0.604927i	$0.793202\pi$
$464$		0			0
$465$	12.6199	−	48.8022i	0.585236	−	2.26315i
$466$		0			0
$467$	−18.8522			−0.872376			−0.436188	−	0.899855i	$-0.643672\pi$
$467$	−18.8522			−0.872376			−0.436188	+	0.899855i	$0.643672\pi$
$468$		0			0
$469$	−13.7366			−0.634299
$470$		0			0
$471$	7.41940	−	2.05776i	0.341868	−	0.0948167i
$472$		0			0
$473$	5.49197	−	9.51237i	0.252521	−	0.437379i
$474$		0			0
$475$	13.0196	+	22.5506i	0.597381	+	1.03469i
$476$		0			0
$477$	0.173549	+	9.91707i	0.00794624	+	0.454071i
$478$		0			0
$479$	11.0879	+	19.2049i	0.506621	+	0.877492i	0.999971	+	0.00766167i	$0.00243881\pi$
$479$	11.0879	+	19.2049i	0.506621	+	0.877492i	−0.493350	+	0.869831i	$0.664228\pi$
$480$		0			0
$481$	4.93558	−	8.54867i	0.225043	−	0.389786i
$482$		0			0
$483$	−24.7460	−	24.3168i	−1.12598	−	1.10645i
$484$		0			0
$485$	39.5505			1.79590
$486$		0			0
$487$	−17.9432			−0.813086			−0.406543	−	0.913632i	$-0.633266\pi$
$487$	−17.9432			−0.813086			−0.406543	+	0.913632i	$0.633266\pi$
$488$		0			0
$489$	−23.3267	−	22.9221i	−1.05487	−	1.03657i
$490$		0			0
$491$	1.71919	−	2.97773i	0.0775861	−	0.134383i	−0.824622	−	0.565684i	$-0.808612\pi$
$491$	1.71919	−	2.97773i	0.0775861	−	0.134383i	0.902208	+	0.431301i	$0.141945\pi$
$492$		0			0
$493$	5.16431	+	8.94485i	0.232589	+	0.402856i
$494$		0			0
$495$	0.504742	+	28.8425i	0.0226865	+	1.29637i
$496$		0			0
$497$	1.32036	+	2.28693i	0.0592262	+	0.102583i
$498$		0			0
$499$	5.41124	−	9.37254i	0.242240	−	0.419572i	−0.719112	−	0.694894i	$-0.755451\pi$
$499$	5.41124	−	9.37254i	0.242240	−	0.419572i	0.961352	+	0.275322i	$0.0887845\pi$
$500$		0			0
$501$	14.4003	−	3.99392i	0.643360	−	0.178435i
$502$		0			0
$503$	9.71510			0.433175			0.216587	−	0.976263i	$-0.430507\pi$
$503$	9.71510			0.433175			0.216587	+	0.976263i	$0.430507\pi$
$504$		0			0
$505$	−6.12240			−0.272443
$506$		0			0
$507$	1.05182	−	4.06747i	0.0467130	−	0.180643i
$508$		0			0
$509$	−17.5991	+	30.4825i	−0.780066	+	1.35111i	0.151837	+	0.988406i	$0.451481\pi$
$509$	−17.5991	+	30.4825i	−0.780066	+	1.35111i	−0.931903	+	0.362708i	$0.881852\pi$
$510$		0			0
$511$	−2.73138	−	4.73090i	−0.120829	−	0.209283i
$512$		0			0
$513$	6.32626	−	6.66739i	0.279311	−	0.294372i
$514$		0			0
$515$	−11.3025	−	19.5766i	−0.498049	−	0.862646i
$516$		0			0
$517$	10.7960	−	18.6991i	0.474806	−	0.822387i
$518$		0			0
$519$	3.39468	−	13.1275i	0.149010	−	0.576233i
$520$		0			0
$521$	−7.57440			−0.331840			−0.165920	−	0.986139i	$-0.553059\pi$
$521$	−7.57440			−0.331840			−0.165920	+	0.986139i	$0.553059\pi$
$522$		0			0
$523$	10.0630			0.440025			0.220013	−	0.975497i	$-0.429390\pi$
$523$	10.0630			0.440025			0.220013	+	0.975497i	$0.429390\pi$
$524$		0			0
$525$	71.4939	−	19.8288i	3.12025	−	0.865398i
$526$		0			0
$527$	5.88890	−	10.1999i	0.256525	−	0.444314i
$528$		0			0
$529$	−12.1943	−	21.1211i	−0.530187	−	0.918310i
$530$		0			0
$531$	12.0748	+	6.69245i	0.524001	+	0.290427i
$532$		0			0
$533$	14.4699	+	25.0625i	0.626759	+	1.08558i
$534$		0			0
$535$	38.2051	−	66.1732i	1.65175	−	2.86092i
$536$		0			0
$537$	−16.8498	−	16.5575i	−0.727124	−	0.714511i
$538$		0			0
$539$	−3.17574			−0.136789
$540$		0			0
$541$	−26.2133			−1.12700			−0.563498	−	0.826117i	$-0.690545\pi$
$541$	−26.2133			−1.12700			−0.563498	+	0.826117i	$0.690545\pi$
$542$		0			0
$543$	−0.623479	−	0.612663i	−0.0267560	−	0.0262919i
$544$		0			0
$545$	14.6404	−	25.3580i	0.627127	−	1.08622i
$546$		0			0
$547$	9.57620	+	16.5865i	0.409449	+	0.709186i	0.994828	−	0.101574i	$-0.0323878\pi$
$547$	9.57620	+	16.5865i	0.409449	+	0.709186i	−0.585379	+	0.810760i	$0.699054\pi$
$548$		0			0
$549$	9.63530	−	5.79006i	0.411225	−	0.247114i
$550$		0			0
$551$	−5.08276	−	8.80359i	−0.216533	−	0.375046i
$552$		0			0
$553$	−3.59823	+	6.23232i	−0.153012	+	0.265025i
$554$		0			0
$555$	18.6287	−	5.16665i	0.790744	−	0.219312i
$556$		0			0
$557$	22.5019			0.953435			0.476717	−	0.879057i	$-0.341827\pi$
$557$	22.5019			0.953435			0.476717	+	0.879057i	$0.341827\pi$
$558$		0			0
$559$	−19.9236			−0.842680
$560$		0			0
$561$	−1.68745	+	6.52547i	−0.0712440	+	0.275506i
$562$		0			0
$563$	12.7085	−	22.0118i	0.535599	−	0.927685i	−0.463535	−	0.886079i	$-0.653419\pi$
$563$	12.7085	−	22.0118i	0.535599	−	0.927685i	0.999134	−	0.0416066i	$-0.0132476\pi$
$564$		0			0
$565$	39.5268	+	68.4625i	1.66291	+	2.88024i
$566$		0			0
$567$	−13.8794	−	22.2073i	−0.582881	−	0.932618i
$568$		0			0
$569$	9.14798	+	15.8448i	0.383503	+	0.664247i	0.991560	−	0.129646i	$-0.0413842\pi$
$569$	9.14798	+	15.8448i	0.383503	+	0.664247i	−0.608057	+	0.793893i	$0.708051\pi$
$570$		0			0
$571$	1.27484	−	2.20808i	0.0533503	−	0.0924054i	−0.838117	−	0.545491i	$-0.816343\pi$
$571$	1.27484	−	2.20808i	0.0533503	−	0.0924054i	0.891467	+	0.453085i	$0.149677\pi$
$572$		0			0
$573$	8.67986	−	33.5656i	0.362606	−	1.40222i
$574$		0			0
$575$	101.340			4.22617
$576$		0			0
$577$	2.22842			0.0927702			0.0463851	−	0.998924i	$-0.485230\pi$
$577$	2.22842			0.0927702			0.0463851	+	0.998924i	$0.485230\pi$
$578$		0			0
$579$	−3.62056	+	1.00416i	−0.150465	+	0.0417314i
$580$		0			0
$581$	−3.17892	+	5.50606i	−0.131884	+	0.228430i
$582$		0			0
$583$	3.57939	+	6.19968i	0.148243	+	0.256765i
$584$		0			0
$585$	44.8501	−	26.9514i	1.85432	−	1.11430i
$586$		0			0
$587$	15.2694	+	26.4473i	0.630234	+	1.09160i	0.987504	+	0.157596i	$0.0503743\pi$
$587$	15.2694	+	26.4473i	0.630234	+	1.09160i	−0.357270	+	0.934001i	$0.616292\pi$
$588$		0			0
$589$	−5.79591	+	10.0388i	−0.238816	+	0.413642i
$590$		0			0
$591$	−7.01048	−	6.88887i	−0.288372	−	0.283370i
$592$		0			0
$593$	−5.96281			−0.244863			−0.122432	−	0.992477i	$-0.539069\pi$
$593$	−5.96281			−0.244863			−0.122432	+	0.992477i	$0.539069\pi$
$594$		0			0
$595$	23.2231			0.952055
$596$		0			0
$597$	−14.2112	−	13.9647i	−0.581625	−	0.571536i
$598$		0			0
$599$	−4.29265	+	7.43508i	−0.175393	+	0.303789i	−0.940297	−	0.340355i	$-0.889453\pi$
$599$	−4.29265	+	7.43508i	−0.175393	+	0.303789i	0.764904	+	0.644144i	$0.222786\pi$
$600$		0			0
$601$	1.44648	+	2.50538i	0.0590033	+	0.102197i	0.894018	−	0.448031i	$-0.147874\pi$
$601$	1.44648	+	2.50538i	0.0590033	+	0.102197i	−0.835015	+	0.550227i	$0.814541\pi$
$602$		0			0
$603$	−12.3873	−	6.86565i	−0.504448	−	0.279591i
$604$		0			0
$605$	−14.0146	−	24.2739i	−0.569773	−	0.986876i
$606$		0			0
$607$	9.96773	−	17.2646i	0.404577	−	0.700749i	−0.589695	−	0.807626i	$-0.700752\pi$
$607$	9.96773	−	17.2646i	0.404577	−	0.700749i	0.994272	+	0.106877i	$0.0340853\pi$
$608$		0			0
$609$	−27.9107	+	7.74099i	−1.13100	+	0.313681i
$610$		0			0
$611$	−39.1653			−1.58446
$612$		0			0
$613$	35.4941			1.43359			0.716797	−	0.697282i	$-0.245607\pi$
$613$	35.4941			1.43359			0.716797	+	0.697282i	$0.245607\pi$
$614$		0			0
$615$	−14.1894	+	54.8713i	−0.572171	+	2.21262i
$616$		0			0
$617$	−15.6891	+	27.1743i	−0.631618	+	1.09399i	0.355603	+	0.934637i	$0.384276\pi$
$617$	−15.6891	+	27.1743i	−0.631618	+	1.09399i	−0.987221	+	0.159357i	$0.949058\pi$
$618$		0			0
$619$	16.7289	+	28.9752i	0.672389	+	1.16461i	0.977225	+	0.212207i	$0.0680652\pi$
$619$	16.7289	+	28.9752i	0.672389	+	1.16461i	−0.304835	+	0.952405i	$0.598601\pi$
$620$		0			0
$621$	−10.1615	−	34.2963i	−0.407768	−	1.37626i
$622$		0			0
$623$	−7.71987	−	13.3712i	−0.309290	−	0.535706i
$624$		0			0
$625$	−59.0543	+	102.285i	−2.36217	+	4.09140i
$626$		0			0
$627$	1.66080	−	6.42243i	0.0663259	−	0.256487i
$628$		0			0
$629$	4.51694			0.180102
$630$		0			0
$631$	−8.12216			−0.323338			−0.161669	−	0.986845i	$-0.551688\pi$
$631$	−8.12216			−0.323338			−0.161669	+	0.986845i	$0.551688\pi$
$632$		0			0
$633$	34.4413	−	9.55225i	1.36892	−	0.379668i
$634$		0			0
$635$	−40.4691	+	70.0945i	−1.60597	+	2.78162i
$636$		0			0
$637$	2.88022	+	4.98869i	0.114119	+	0.197659i
$638$		0			0
$639$	0.0476384	+	2.72220i	0.00188455	+	0.107689i
$640$		0			0
$641$	−10.4782	−	18.1488i	−0.413865	−	0.716836i	0.581443	−	0.813587i	$-0.302488\pi$
$641$	−10.4782	−	18.1488i	−0.413865	−	0.716836i	−0.995309	+	0.0967511i	$0.969155\pi$
$642$		0			0
$643$	16.3547	−	28.3272i	0.644967	−	1.11712i	−0.339342	−	0.940663i	$-0.610204\pi$
$643$	16.3547	−	28.3272i	0.644967	−	1.11712i	0.984309	−	0.176453i	$-0.0564623\pi$
$644$		0			0
$645$	−27.8309	−	27.3481i	−1.09584	−	1.07683i
$646$		0			0
$647$	18.7820			0.738395			0.369198	−	0.929351i	$-0.379633\pi$
$647$	18.7820			0.738395			0.369198	+	0.929351i	$0.379633\pi$
$648$		0			0
$649$	9.96410			0.391125
$650$		0			0
$651$	23.5579	+	23.1492i	0.923307	+	0.907290i
$652$		0			0
$653$	4.85977	−	8.41736i	0.190177	−	0.329397i	−0.755132	−	0.655573i	$-0.772427\pi$
$653$	4.85977	−	8.41736i	0.190177	−	0.329397i	0.945309	+	0.326176i	$0.105760\pi$
$654$		0			0
$655$	19.2314	+	33.3098i	0.751435	+	1.30152i
$656$		0			0
$657$	−0.0985482	−	5.63133i	−0.00384473	−	0.219699i
$658$		0			0
$659$	16.1773	+	28.0198i	0.630177	+	1.09150i	0.987515	+	0.157523i	$0.0503510\pi$
$659$	16.1773	+	28.0198i	0.630177	+	1.09150i	−0.357338	+	0.933975i	$0.616316\pi$
$660$		0			0
$661$	−13.0319	+	22.5719i	−0.506883	+	0.877946i	0.493086	+	0.869981i	$0.335869\pi$
$661$	−13.0319	+	22.5719i	−0.506883	+	0.877946i	−0.999968	+	0.00796563i	$0.997464\pi$
$662$		0			0
$663$	11.7811	−	3.26748i	0.457540	−	0.126898i
$664$		0			0
$665$	−22.8564			−0.886333
$666$		0			0
$667$	−39.5624			−1.53186
$668$		0			0
$669$	−2.20538	+	8.52835i	−0.0852648	+	0.329725i
$670$		0			0
$671$	4.05668	−	7.02637i	0.156606	−	0.271250i
$672$		0			0
$673$	16.6951	+	28.9167i	0.643549	+	1.11466i	0.984635	+	0.174627i	$0.0558719\pi$
$673$	16.6951	+	28.9167i	0.643549	+	1.11466i	−0.341086	+	0.940032i	$0.610795\pi$
$674$		0			0
$675$	74.3815	+	17.8521i	2.86294	+	0.687128i
$676$		0			0
$677$	−12.6991	−	21.9955i	−0.488065	−	0.845354i	0.511840	−	0.859081i	$-0.328964\pi$
$677$	−12.6991	−	21.9955i	−0.488065	−	0.845354i	−0.999906	+	0.0137265i	$0.995631\pi$
$678$		0			0
$679$	−12.9572	+	22.4425i	−0.497252	+	0.861266i
$680$		0			0
$681$	−7.93101	+	30.6698i	−0.303917	+	1.17527i
$682$		0			0
$683$	−37.2800			−1.42648			−0.713241	−	0.700919i	$-0.752773\pi$
$683$	−37.2800			−1.42648			−0.713241	+	0.700919i	$0.752773\pi$
$684$		0			0
$685$	−6.87841			−0.262811
$686$		0			0
$687$	32.1238	−	8.90950i	1.22560	−	0.339919i
$688$		0			0
$689$	6.49261	−	11.2455i	0.247349	−	0.428421i
$690$		0			0
$691$	−6.41730	−	11.1151i	−0.244126	−	0.422838i	0.717760	−	0.696291i	$-0.245168\pi$
$691$	−6.41730	−	11.1151i	−0.244126	−	0.422838i	−0.961885	+	0.273453i	$0.911834\pi$
$692$		0			0
$693$	−16.5317	−	9.16271i	−0.627988	−	0.348063i
$694$		0			0
$695$	43.4591	+	75.2733i	1.64850	+	2.85528i
$696$		0			0
$697$	−6.62125	+	11.4683i	−0.250798	+	0.434395i
$698$		0			0
$699$	20.2933	+	19.9412i	0.767561	+	0.754247i
$700$		0			0
$701$	−6.89156			−0.260290			−0.130145	−	0.991495i	$-0.541544\pi$
$701$	−6.89156			−0.260290			−0.130145	+	0.991495i	$0.541544\pi$
$702$		0			0
$703$	−4.44561			−0.167669
$704$		0			0
$705$	−54.7092	−	53.7601i	−2.06047	−	2.02472i
$706$		0			0
$707$	2.00577	−	3.47410i	0.0754347	−	0.130657i
$708$		0			0
$709$	10.1178	+	17.5246i	0.379983	+	0.658150i	0.991059	−	0.133422i	$-0.0425964\pi$
$709$	10.1178	+	17.5246i	0.379983	+	0.658150i	−0.611076	+	0.791572i	$0.709263\pi$
$710$		0			0
$711$	−6.35971	+	3.82169i	−0.238508	+	0.143325i
$712$		0			0
$713$	22.5566	+	39.0693i	0.844753	+	1.46316i
$714$		0			0
$715$	18.8829	−	32.7061i	0.706180	−	1.22314i
$716$		0			0
$717$	−30.3287	+	8.41162i	−1.13264	+	0.314138i
$718$		0			0
$719$	44.1706			1.64729			0.823643	−	0.567108i	$-0.191938\pi$
$719$	44.1706			1.64729			0.823643	+	0.567108i	$0.191938\pi$
$720$		0			0
$721$	14.8114			0.551604
$722$		0			0
$723$	9.91670	−	38.3486i	0.368806	−	1.42620i
$724$		0			0
$725$	42.3019	−	73.2690i	1.57105	−	2.72114i
$726$		0			0
$727$	7.29193	+	12.6300i	0.270443	+	0.468421i	0.968975	−	0.247158i	$-0.0794965\pi$
$727$	7.29193	+	12.6300i	0.270443	+	0.468421i	−0.698532	+	0.715578i	$0.746163\pi$
$728$		0			0
$729$	−1.41670	−	26.9628i	−0.0524705	−	0.998622i
$730$		0			0
$731$	−4.55842	−	7.89542i	−0.168599	−	0.292023i
$732$		0			0
$733$	16.4444	−	28.4826i	0.607388	−	1.05203i	−0.384281	−	0.923216i	$-0.625551\pi$
$733$	16.4444	−	28.4826i	0.607388	−	1.05203i	0.991669	−	0.128811i	$-0.0411161\pi$
$734$		0			0
$735$	−2.82439	+	10.9221i	−0.104179	+	0.402868i
$736$		0			0
$737$	−10.2220			−0.376531
$738$		0			0
$739$	35.3966			1.30208			0.651042	−	0.759041i	$-0.274332\pi$
$739$	35.3966			1.30208			0.651042	+	0.759041i	$0.274332\pi$
$740$		0			0
$741$	−11.5951	+	3.21588i	−0.425956	+	0.118138i
$742$		0			0
$743$	18.8177	−	32.5932i	0.690353	−	1.19573i	−0.281369	−	0.959600i	$-0.590788\pi$
$743$	18.8177	−	32.5932i	0.690353	−	1.19573i	0.971722	−	0.236127i	$-0.0758782\pi$
$744$		0			0
$745$	4.20098	+	7.27631i	0.153912	+	0.266584i
$746$		0			0
$747$	−5.61861	+	3.37634i	−0.205574	+	0.123534i
$748$		0			0
$749$	25.0329	+	43.3582i	0.914682	+	1.58427i
$750$		0			0
$751$	8.38950	−	14.5310i	0.306137	−	0.530245i	−0.671377	−	0.741116i	$-0.734297\pi$
$751$	8.38950	−	14.5310i	0.306137	−	0.530245i	0.977514	+	0.210871i	$0.0676300\pi$
$752$		0			0
$753$	−0.172377	−	0.169387i	−0.00628178	−	0.00617281i
$754$		0			0
$755$	−38.0073			−1.38323
$756$		0			0
$757$	19.4825			0.708103			0.354051	−	0.935226i	$-0.384804\pi$
$757$	19.4825			0.708103			0.354051	+	0.935226i	$0.384804\pi$
$758$		0			0
$759$	−18.4145	−	18.0950i	−0.668403	−	0.656809i
$760$		0			0
$761$	−9.49573	+	16.4471i	−0.344220	+	0.596206i	−0.985212	−	0.171341i	$-0.945190\pi$
$761$	−9.49573	+	16.4471i	−0.344220	+	0.596206i	0.640992	+	0.767548i	$0.278523\pi$
$762$		0			0
$763$	9.59276	+	16.6151i	0.347281	+	0.601508i
$764$		0			0
$765$	20.9419	+	11.6070i	0.757154	+	0.419653i
$766$		0			0
$767$	−9.03688	−	15.6523i	−0.326303	−	0.565173i
$768$		0			0
$769$	21.2098	−	36.7365i	0.764846	−	1.32475i	−0.175482	−	0.984483i	$-0.556148\pi$
$769$	21.2098	−	36.7365i	0.764846	−	1.32475i	0.940328	−	0.340270i	$-0.110518\pi$
$770$		0			0
$771$	−23.9569	+	6.64441i	−0.862786	+	0.239293i
$772$		0			0
$773$	2.55333			0.0918368			0.0459184	−	0.998945i	$-0.485379\pi$
$773$	2.55333			0.0918368			0.0459184	+	0.998945i	$0.485379\pi$
$774$		0			0
$775$	−96.4744			−3.46546
$776$		0			0
$777$	−3.17122	+	12.2633i	−0.113767	+	0.439944i
$778$		0			0
$779$	6.51670	−	11.2872i	0.233485	−	0.404408i
$780$		0			0
$781$	0.982529	+	1.70179i	0.0351577	+	0.0608949i
$782$		0			0
$783$	−29.0379	−	6.96932i	−1.03773	−	0.249063i
$784$		0			0
$785$	−9.87046	−	17.0961i	−0.352292	−	0.610188i
$786$		0			0
$787$	−6.70128	+	11.6069i	−0.238875	+	0.413743i	−0.960392	−	0.278654i	$-0.910112\pi$
$787$	−6.70128	+	11.6069i	−0.238875	+	0.413743i	0.721517	+	0.692397i	$0.243445\pi$
$788$		0			0
$789$	0.840165	−	3.24898i	0.0299107	−	0.115667i
$790$		0			0
$791$	−51.7978			−1.84172
$792$		0			0
$793$	−14.7167			−0.522606
$794$		0			0
$795$	24.5055	−	6.79658i	0.869122	−	0.241050i
$796$		0			0
$797$	−16.0873	+	27.8640i	−0.569840	+	0.986992i	0.426741	+	0.904374i	$0.359662\pi$
$797$	−16.0873	+	27.8640i	−0.569840	+	0.986992i	−0.996581	+	0.0826182i	$0.973672\pi$
$798$		0			0
$799$	−8.96082	−	15.5206i	−0.317011	−	0.549079i
$800$		0			0
$801$	−0.278532	−	15.9162i	−0.00984146	−	0.562370i
$802$		0			0
$803$	−2.03253	−	3.52044i	−0.0717264	−	0.124234i
$804$		0			0
$805$	−44.4765	+	77.0355i	−1.56759	+	2.71515i
$806$		0			0
$807$	12.2481	+	12.0356i	0.431153	+	0.423674i
$808$		0			0
$809$	34.7417			1.22145			0.610727	−	0.791841i	$-0.290877\pi$
$809$	34.7417			1.22145			0.610727	+	0.791841i	$0.290877\pi$
$810$		0			0
$811$	40.7570			1.43117			0.715587	−	0.698524i	$-0.246159\pi$
$811$	40.7570			1.43117			0.715587	+	0.698524i	$0.246159\pi$
$812$		0			0
$813$	−5.64309	−	5.54520i	−0.197912	−	0.194479i
$814$		0			0
$815$	−41.9255	+	72.6172i	−1.46859	+	2.54367i
$816$		0			0
$817$	4.48644	+	7.77074i	0.156961	+	0.271864i
$818$		0			0
$819$	0.599888	+	34.2793i	0.0209618	+	1.19782i
$820$		0			0
$821$	8.25420	+	14.2967i	0.288073	+	0.498958i	0.973350	−	0.229325i	$-0.0736519\pi$
$821$	8.25420	+	14.2967i	0.288073	+	0.498958i	−0.685276	+	0.728283i	$0.740319\pi$
$822$		0			0
$823$	−2.28675	+	3.96078i	−0.0797113	+	0.138064i	−0.903125	−	0.429377i	$-0.858733\pi$
$823$	−2.28675	+	3.96078i	−0.0797113	+	0.138064i	0.823414	+	0.567441i	$0.192066\pi$
$824$		0			0
$825$	53.2014	−	14.7553i	1.85223	−	0.513715i
$826$		0			0
$827$	47.2992			1.64475			0.822377	−	0.568943i	$-0.192648\pi$
$827$	47.2992			1.64475			0.822377	+	0.568943i	$0.192648\pi$
$828$		0			0
$829$	2.10329			0.0730501			0.0365251	−	0.999333i	$-0.488371\pi$
$829$	2.10329			0.0730501			0.0365251	+	0.999333i	$0.488371\pi$
$830$		0			0
$831$	12.5517	−	48.5385i	0.435415	−	1.68378i
$832$		0			0
$833$	−1.31796	+	2.28277i	−0.0456646	+	0.0790934i
$834$		0			0
$835$	−19.1576	−	33.1820i	−0.662977	−	1.14831i
$836$		0			0
$837$	9.67364	+	32.6496i	0.334370	+	1.12854i
$838$		0			0
$839$	4.60255	+	7.97185i	0.158898	+	0.275219i	0.934471	−	0.356038i	$-0.115873\pi$
$839$	4.60255	+	7.97185i	0.158898	+	0.275219i	−0.775574	+	0.631257i	$0.782539\pi$
$840$		0			0
$841$	−2.01432	+	3.48891i	−0.0694595	+	0.120307i
$842$		0			0
$843$	−9.65707	+	37.3446i	−0.332607	+	1.28622i
$844$		0			0
$845$	−10.7718			−0.370560
$846$		0			0
$847$	18.3653			0.631041
$848$		0			0
$849$	22.6972	−	6.29505i	0.778967	−	0.216046i
$850$		0			0
$851$	−8.65075	+	14.9835i	−0.296544	+	0.513629i
$852$		0			0
$853$	−7.43348	−	12.8752i	−0.254518	−	0.440837i	0.710247	−	0.703953i	$-0.248583\pi$
$853$	−7.43348	−	12.8752i	−0.254518	−	0.440837i	−0.964764	+	0.263115i	$0.915250\pi$
$854$		0			0
$855$	−20.6112	−	11.4237i	−0.704887	−	0.390684i
$856$		0			0
$857$	−22.9611	−	39.7698i	−0.784337	−	1.35851i	−0.929394	−	0.369088i	$-0.879670\pi$
$857$	−22.9611	−	39.7698i	−0.784337	−	1.35851i	0.145058	−	0.989423i	$-0.453663\pi$
$858$		0			0
$859$	14.6542	−	25.3818i	0.499994	−	0.866015i	−0.500006	−	0.866022i	$-0.666669\pi$
$859$	14.6542	−	25.3818i	0.499994	−	0.866015i	1.00000		6.84699e-6i	$2.17947e-6\pi$
$860$		0			0
$861$	−26.4876	−	26.0281i	−0.902694	−	0.887035i
$862$		0			0
$863$	−23.5606			−0.802012			−0.401006	−	0.916075i	$-0.631339\pi$
$863$	−23.5606			−0.802012			−0.401006	+	0.916075i	$0.631339\pi$
$864$		0			0
$865$	−34.7651			−1.18205
$866$		0			0
$867$	−17.0117	−	16.7166i	−0.577748	−	0.567726i
$868$		0			0
$869$	−2.67758	+	4.63771i	−0.0908307	+	0.157323i
$870$		0			0
$871$	9.27076	+	16.0574i	0.314128	+	0.544085i
$872$		0			0
$873$	−22.9013	+	13.7619i	−0.775092	+	0.465769i
$874$		0			0
$875$	−62.8080	−	108.787i	−2.12330	−	3.67766i
$876$		0			0
$877$	−9.29438	+	16.0983i	−0.313849	+	0.543602i	−0.979192	−	0.202935i	$-0.934952\pi$
$877$	−9.29438	+	16.0983i	−0.313849	+	0.543602i	0.665343	+	0.746538i	$0.268285\pi$
$878$		0			0
$879$	−24.0951	+	6.68274i	−0.812706	+	0.225403i
$880$		0			0
$881$	24.6693			0.831129			0.415564	−	0.909564i	$-0.363584\pi$
$881$	24.6693			0.831129			0.415564	+	0.909564i	$0.363584\pi$
$882$		0			0
$883$	4.42122			0.148786			0.0743930	−	0.997229i	$-0.476298\pi$
$883$	4.42122			0.148786			0.0743930	+	0.997229i	$0.476298\pi$
$884$		0			0
$885$	8.86171	−	34.2688i	0.297883	−	1.15193i
$886$		0			0
$887$	22.1558	−	38.3750i	0.743919	−	1.28851i	−0.206779	−	0.978388i	$-0.566298\pi$
$887$	22.1558	−	38.3750i	0.743919	−	1.28851i	0.950698	−	0.310118i	$-0.100369\pi$
$888$		0			0
$889$	−26.5163	−	45.9276i	−0.889328	−	1.54036i
$890$		0			0
$891$	−10.3282	−	16.5253i	−0.346008	−	0.553618i
$892$		0			0
$893$	8.81931	+	15.2755i	0.295127	+	0.511175i
$894$		0			0
$895$	−30.2845	+	52.4543i	−1.01230	+	1.75335i
$896$		0			0
$897$	−11.7241	+	45.3380i	−0.391457	+	1.51379i
$898$		0			0
$899$	37.6628			1.25613
$900$		0			0
$901$	5.94190			0.197953
$902$		0			0
$903$	24.6361	−	6.83280i	0.819840	−	0.227381i
$904$		0			0
$905$	−1.12059	+	1.94092i	−0.0372497	+	0.0645183i
$906$		0			0
$907$	−23.2939	−	40.3462i	−0.773461	−	1.33967i	−0.935656	−	0.352914i	$-0.885191\pi$
$907$	−23.2939	−	40.3462i	−0.773461	−	1.33967i	0.162195	−	0.986759i	$-0.448143\pi$
$908$		0			0
$909$	3.54511	−	2.13033i	0.117584	−	0.0706587i
$910$		0			0
$911$	−4.29458	−	7.43844i	−0.142286	−	0.246446i	0.786071	−	0.618136i	$-0.212112\pi$
$911$	−4.29458	−	7.43844i	−0.142286	−	0.246446i	−0.928357	+	0.371690i	$0.878779\pi$
$912$		0			0
$913$	−2.36556	+	4.09727i	−0.0782886	+	0.135600i
$914$		0			0
$915$	−20.5575	−	20.2009i	−0.679609	−	0.667820i
$916$		0			0
$917$	−25.2018			−0.832236
$918$		0			0
$919$	41.7394			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$919$	41.7394			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$920$		0			0
$921$	−20.4401	−	20.0855i	−0.673523	−	0.661840i
$922$		0			0
$923$	1.78220	−	3.08686i	0.0586618	−	0.101605i
$924$		0			0
$925$	−18.4996	−	32.0422i	−0.608262	−	1.05354i
$926$		0			0
$927$	13.3564	+	7.40280i	0.438682	+	0.243140i
$928$		0			0
$929$	20.5014	+	35.5094i	0.672628	+	1.16503i	0.977156	+	0.212523i	$0.0681680\pi$
$929$	20.5014	+	35.5094i	0.672628	+	1.16503i	−0.304528	+	0.952503i	$0.598499\pi$
$930$		0			0
$931$	1.29715	−	2.24672i	0.0425123	−	0.0736334i
$932$		0			0
$933$	−17.3369	+	4.80837i	−0.567585	+	0.157419i
$934$		0			0
$935$	17.2812			0.565156
$936$		0			0
$937$	−10.1921			−0.332962			−0.166481	−	0.986045i	$-0.553240\pi$
$937$	−10.1921			−0.332962			−0.166481	+	0.986045i	$0.553240\pi$
$938$		0			0
$939$	5.86706	−	22.6884i	0.191464	−	0.740406i
$940$		0			0
$941$	20.7130	−	35.8761i	0.675226	−	1.16953i	−0.301177	−	0.953568i	$-0.597379\pi$
$941$	20.7130	−	35.8761i	0.675226	−	1.16953i	0.976403	−	0.215958i	$-0.0692873\pi$
$942$		0			0
$943$	−25.3618	−	43.9279i	−0.825894	−	1.43049i
$944$		0			0
$945$	−46.2154	+	48.7075i	−1.50339	+	1.58445i
$946$		0			0
$947$	1.04880	+	1.81658i	0.0340815	+	0.0590309i	0.882563	−	0.470194i	$-0.155816\pi$
$947$	1.04880	+	1.81658i	0.0340815	+	0.0590309i	−0.848482	+	0.529225i	$0.822483\pi$
$948$		0			0
$949$	−3.68678	+	6.38569i	−0.119678	+	0.207288i
$950$		0			0
$951$	10.3958	−	40.2014i	0.337108	−	1.30362i
$952$		0			0
$953$	31.7663			1.02901			0.514506	−	0.857487i	$-0.327975\pi$
$953$	31.7663			1.02901			0.514506	+	0.857487i	$0.327975\pi$
$954$		0			0
$955$	−88.8908			−2.87644
$956$		0			0
$957$	−20.7694	+	5.76037i	−0.671380	+	0.186206i
$958$		0			0
$959$	2.25345	−	3.90309i	0.0727677	−	0.126037i
$960$		0			0
$961$	−5.97362	−	10.3466i	−0.192697	−	0.333762i
$962$		0			0
$963$	0.903185	+	51.6106i	0.0291047	+	1.66313i
$964$		0			0
$965$	4.81664	+	8.34267i	0.155053	+	0.268560i
$966$		0			0
$967$	−1.76817	+	3.06256i	−0.0568605	+	0.0984853i	−0.893055	−	0.449948i	$-0.851442\pi$
$967$	−1.76817	+	3.06256i	−0.0568605	+	0.0984853i	0.836194	+	0.548434i	$0.184776\pi$
$968$		0			0
$969$	−3.92729	−	3.85916i	−0.126163	−	0.123974i
$970$		0			0
$971$	21.4727			0.689093			0.344546	−	0.938769i	$-0.388033\pi$
$971$	21.4727			0.689093			0.344546	+	0.938769i	$0.388033\pi$
$972$		0			0
$973$	−56.9508			−1.82576
$974$		0			0
$975$	−71.4295	−	70.1904i	−2.28757	−	2.24789i
$976$		0			0
$977$	23.6237	−	40.9174i	0.755788	−	1.30906i	−0.189193	−	0.981940i	$-0.560587\pi$
$977$	23.6237	−	40.9174i	0.755788	−	1.30906i	0.944982	−	0.327124i	$-0.106079\pi$
$978$		0			0
$979$	−5.74465	−	9.95003i	−0.183600	−	0.318004i
$980$		0			0
$981$	0.346106	+	19.7775i	0.0110503	+	0.631447i
$982$		0			0
$983$	−21.4576	−	37.1656i	−0.684390	−	1.18540i	−0.973628	−	0.228141i	$-0.926735\pi$
$983$	−21.4576	−	37.1656i	−0.684390	−	1.18540i	0.289238	−	0.957257i	$-0.406598\pi$
$984$		0			0
$985$	−12.6001	+	21.8239i	−0.401471	+	0.695368i
$986$		0			0
$987$	48.4290	−	13.4317i	1.54151	−	0.427537i
$988$		0			0
$989$	34.9208			1.11042
$990$		0			0
$991$	−11.5080			−0.365563			−0.182782	−	0.983154i	$-0.558510\pi$
$991$	−11.5080			−0.365563			−0.182782	+	0.983154i	$0.558510\pi$
$992$		0			0
$993$	1.11966	−	4.32982i	0.0355314	−	0.137403i
$994$		0			0
$995$	−25.5420	+	44.2401i	−0.809736	+	1.40250i
$996$		0			0
$997$	−8.46934	−	14.6693i	−0.268227	−	0.464582i	0.700177	−	0.713969i	$-0.253104\pi$
$997$	−8.46934	−	14.6693i	−0.268227	−	0.464582i	−0.968404	+	0.249387i	$0.919771\pi$
$998$		0			0
$999$	−8.98898	+	9.47368i	−0.284399	+	0.299734i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.i.k.769.5	yes	12
3.2	odd	2		3456.2.i.l.2305.1		12
4.3	odd	2		1152.2.i.i.769.2	yes	12
8.3	odd	2		1152.2.i.l.769.5	yes	12
8.5	even	2		1152.2.i.j.769.2	yes	12
9.2	odd	6		3456.2.i.l.1153.1		12
9.7	even	3	inner	1152.2.i.k.385.5	yes	12
12.11	even	2		3456.2.i.k.2305.1		12
24.5	odd	2		3456.2.i.j.2305.6		12
24.11	even	2		3456.2.i.i.2305.6		12
36.7	odd	6		1152.2.i.i.385.2	✓	12
36.11	even	6		3456.2.i.k.1153.1		12
72.11	even	6		3456.2.i.i.1153.6		12
72.29	odd	6		3456.2.i.j.1153.6		12
72.43	odd	6		1152.2.i.l.385.5	yes	12
72.61	even	6		1152.2.i.j.385.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.i.i.385.2	✓	12	36.7	odd	6
1152.2.i.i.769.2	yes	12	4.3	odd	2
1152.2.i.j.385.2	yes	12	72.61	even	6
1152.2.i.j.769.2	yes	12	8.5	even	2
1152.2.i.k.385.5	yes	12	9.7	even	3	inner
1152.2.i.k.769.5	yes	12	1.1	even	1	trivial
1152.2.i.l.385.5	yes	12	72.43	odd	6
1152.2.i.l.769.5	yes	12	8.3	odd	2
3456.2.i.i.1153.6		12	72.11	even	6
3456.2.i.i.2305.6		12	24.11	even	2
3456.2.i.j.1153.6		12	72.29	odd	6
3456.2.i.j.2305.6		12	24.5	odd	2
3456.2.i.k.1153.1		12	36.11	even	6
3456.2.i.k.2305.1		12	12.11	even	2
3456.2.i.l.1153.1		12	9.2	odd	6
3456.2.i.l.2305.1		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23541 + 1.21398i) q^{3} +(2.22043 - 3.84590i) q^{5} +(1.45488 + 2.51992i) q^{7} +(0.0524919 + 2.99954i) q^{9} +O(q^{10})\)	\(q+(1.23541 + 1.21398i) q^{3} +(2.22043 - 3.84590i) q^{5} +(1.45488 + 2.51992i) q^{7} +(0.0524919 + 2.99954i) q^{9} +(1.08263 + 1.87517i) q^{11} +(1.96377 - 3.40135i) q^{13} +(7.41200 - 2.05571i) q^{15} +1.79720 q^{17} -1.76882 q^{19} +(-1.26177 + 4.87934i) q^{21} +(-3.44197 + 5.96166i) q^{23} +(-7.36062 - 12.7490i) q^{25} +(-3.57654 + 3.76940i) q^{27} +(2.87353 + 4.97710i) q^{29} +(3.27671 - 5.67542i) q^{31} +(-0.938929 + 3.63091i) q^{33} +12.9218 q^{35} +2.51332 q^{37} +(6.55525 - 1.81809i) q^{39} +(-3.68420 + 6.38122i) q^{41} +(-2.53640 - 4.39317i) q^{43} +(11.6525 + 6.45839i) q^{45} +(-4.98598 - 8.63597i) q^{47} +(-0.733339 + 1.27018i) q^{49} +(2.22029 + 2.18177i) q^{51} +3.30620 q^{53} +9.61562 q^{55} +(-2.18523 - 2.14732i) q^{57} +(2.30090 - 3.98528i) q^{59} +(-1.87353 - 3.24505i) q^{61} +(-7.48224 + 4.49624i) q^{63} +(-8.72084 - 15.1049i) q^{65} +(-2.36045 + 4.08841i) q^{67} +(-11.4896 + 3.18663i) q^{69} +0.907539 q^{71} -1.87740 q^{73} +(6.38362 - 24.6859i) q^{75} +(-3.15019 + 5.45629i) q^{77} +(1.23661 + 2.14187i) q^{79} +(-8.99449 + 0.314903i) q^{81} +(1.09251 + 1.89227i) q^{83} +(3.99056 - 6.91185i) q^{85} +(-2.49211 + 9.63718i) q^{87} -5.30620 q^{89} +11.4282 q^{91} +(10.9380 - 3.03363i) q^{93} +(-3.92754 + 6.80271i) q^{95} +(4.45302 + 7.71286i) q^{97} +(-5.56782 + 3.34583i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 2 q^{5} + 6 q^{7} - 2 q^{9}+O(q^{10}) \) 12 * q + 4 * q^3 - 2 * q^5 + 6 * q^7 - 2 * q^9	\( 12 q + 4 q^{3} - 2 q^{5} + 6 q^{7} - 2 q^{9} + 4 q^{11} + 10 q^{13} + 4 q^{15} + 4 q^{17} + 4 q^{19} + 2 q^{21} + 8 q^{23} - 14 q^{25} - 14 q^{27} - 2 q^{29} + 8 q^{31} - 10 q^{33} + 8 q^{35} + 22 q^{39} - 2 q^{41} - 2 q^{43} + 10 q^{45} - 14 q^{47} - 18 q^{49} - 38 q^{51} + 24 q^{53} - 16 q^{55} - 38 q^{57} + 6 q^{59} + 14 q^{61} - 16 q^{63} - 8 q^{65} + 4 q^{67} - 50 q^{69} - 28 q^{71} + 60 q^{73} + 50 q^{75} + 2 q^{77} + 16 q^{79} + 22 q^{81} + 24 q^{83} + 16 q^{85} - 36 q^{87} - 48 q^{89} - 52 q^{91} + 42 q^{93} - 20 q^{95} - 14 q^{97} + 68 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 - 2 * q^5 + 6 * q^7 - 2 * q^9 + 4 * q^11 + 10 * q^13 + 4 * q^15 + 4 * q^17 + 4 * q^19 + 2 * q^21 + 8 * q^23 - 14 * q^25 - 14 * q^27 - 2 * q^29 + 8 * q^31 - 10 * q^33 + 8 * q^35 + 22 * q^39 - 2 * q^41 - 2 * q^43 + 10 * q^45 - 14 * q^47 - 18 * q^49 - 38 * q^51 + 24 * q^53 - 16 * q^55 - 38 * q^57 + 6 * q^59 + 14 * q^61 - 16 * q^63 - 8 * q^65 + 4 * q^67 - 50 * q^69 - 28 * q^71 + 60 * q^73 + 50 * q^75 + 2 * q^77 + 16 * q^79 + 22 * q^81 + 24 * q^83 + 16 * q^85 - 36 * q^87 - 48 * q^89 - 52 * q^91 + 42 * q^93 - 20 * q^95 - 14 * q^97 + 68 * q^99

Introduction

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