LMFDB - Embedded newform 400.2.u.f.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(81,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(10))

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("400.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.u (of order $5$, degree $4$, not 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
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} - 3 x^{11} + 13 x^{10} - 24 x^{9} + 93 x^{8} - 6 x^{7} + 342 x^{6} + 786 x^{5} + 1473 x^{4} + \cdots + 16 $ x^12 - 3x^11 + 13x^10 - 24x^9 + 93x^8 - 6x^7 + 342x^6 + 786x^5 + 1473x^4 + 84x^3 + 688x^2 + 168*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 100)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$0.838695 + 2.58124i$ of defining polynomial
Character	$\chi$	$=$	400.81
Dual form			400.2.u.f.321.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.19573 + 1.59529i) q^{3} +(0.548020 + 2.16787i) q^{5} +4.40288 q^{7} +(1.34923 - 4.15250i) q^{9} +O(q^{10})$	\(q+(-2.19573 + 1.59529i) q^{3} +(0.548020 + 2.16787i) q^{5} +4.40288 q^{7} +(1.34923 - 4.15250i) q^{9} +(0.516162 + 1.58858i) q^{11} +(-0.795501 + 2.44830i) q^{13} +(-4.66170 - 3.88582i) q^{15} +(-0.239003 - 0.173646i) q^{17} +(-3.13970 - 2.28113i) q^{19} +(-9.66754 + 7.02388i) q^{21} +(2.71760 + 8.36392i) q^{23} +(-4.39935 + 2.37607i) q^{25} +(1.14582 + 3.52647i) q^{27} +(-0.177592 + 0.129028i) q^{29} +(-5.90981 - 4.29372i) q^{31} +(-3.66761 - 2.66467i) q^{33} +(2.41286 + 9.54488i) q^{35} +(-0.231242 + 0.711690i) q^{37} +(-2.15905 - 6.64487i) q^{39} +(-0.947030 + 2.91466i) q^{41} +0.913208 q^{43} +(9.74149 + 0.649305i) q^{45} +(0.00570791 - 0.00414704i) q^{47} +12.3853 q^{49} +0.801802 q^{51} +(9.20313 - 6.68646i) q^{53} +(-3.16098 + 1.98955i) q^{55} +10.5330 q^{57} +(-0.635908 + 1.95712i) q^{59} +(-3.52338 - 10.8438i) q^{61} +(5.94049 - 18.2829i) q^{63} +(-5.74355 - 0.382828i) q^{65} +(4.94968 + 3.59615i) q^{67} +(-19.3100 - 14.0295i) q^{69} +(-6.51168 + 4.73101i) q^{71} +(1.08475 + 3.33853i) q^{73} +(5.86925 - 12.2355i) q^{75} +(2.27260 + 6.99434i) q^{77} +(9.42807 - 6.84989i) q^{79} +(2.45531 + 1.78388i) q^{81} +(2.30779 + 1.67671i) q^{83} +(0.245464 - 0.613289i) q^{85} +(0.184106 - 0.566621i) q^{87} +(-1.02955 - 3.16864i) q^{89} +(-3.50249 + 10.7796i) q^{91} +19.8261 q^{93} +(3.22458 - 8.05658i) q^{95} +(-8.73973 + 6.34979i) q^{97} +7.29301 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} - 4 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q - 2 * q^3 - 4 * q^5 + 2 * q^7 - 3 * q^9	$ 12 q - 2 q^{3} - 4 q^{5} + 2 q^{7} - 3 q^{9} + 5 q^{11} - 2 q^{13} - 18 q^{15} + q^{17} + 8 q^{19} + 2 q^{21} + 6 q^{23} - 26 q^{25} + 34 q^{27} - 18 q^{29} - 12 q^{31} - 35 q^{33} + 3 q^{35} + 13 q^{37} - 22 q^{39} - 23 q^{41} - 50 q^{43} + 71 q^{45} - q^{47} + 34 q^{49} - 14 q^{51} + 21 q^{53} - 5 q^{55} + 72 q^{57} - 9 q^{59} - 26 q^{61} + 32 q^{63} - 18 q^{65} + 37 q^{67} - 44 q^{69} - 21 q^{71} + 18 q^{73} + 73 q^{75} - 60 q^{77} + 24 q^{79} + 18 q^{81} + 46 q^{83} - 16 q^{85} - 57 q^{87} - 2 q^{89} + 32 q^{91} + 22 q^{93} - 6 q^{95} - 7 q^{97} - 40 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 - 4 * q^5 + 2 * q^7 - 3 * q^9 + 5 * q^11 - 2 * q^13 - 18 * q^15 + q^17 + 8 * q^19 + 2 * q^21 + 6 * q^23 - 26 * q^25 + 34 * q^27 - 18 * q^29 - 12 * q^31 - 35 * q^33 + 3 * q^35 + 13 * q^37 - 22 * q^39 - 23 * q^41 - 50 * q^43 + 71 * q^45 - q^47 + 34 * q^49 - 14 * q^51 + 21 * q^53 - 5 * q^55 + 72 * q^57 - 9 * q^59 - 26 * q^61 + 32 * q^63 - 18 * q^65 + 37 * q^67 - 44 * q^69 - 21 * q^71 + 18 * q^73 + 73 * q^75 - 60 * q^77 + 24 * q^79 + 18 * q^81 + 46 * q^83 - 16 * q^85 - 57 * q^87 - 2 * q^89 + 32 * q^91 + 22 * q^93 - 6 * q^95 - 7 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

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
$3$	−2.19573	+	1.59529i	−1.26771	+	0.921042i	−0.999109	−	0.0422100i	$-0.986560\pi$
$3$	−2.19573	+	1.59529i	−1.26771	+	0.921042i	−0.268597	+	0.963253i	$0.586560\pi$
$4$		0			0
$5$	0.548020	+	2.16787i	0.245082	+	0.969502i
$5$	0.548020	+	2.16787i	0.245082	+	0.969502i
$6$		0			0
$7$	4.40288			1.66413			0.832066	−	0.554677i	$-0.187158\pi$
$7$	4.40288			1.66413			0.832066	+	0.554677i	$0.187158\pi$
$8$		0			0
$9$	1.34923	−	4.15250i	0.449743	−	1.38417i
$10$		0			0
$11$	0.516162	+	1.58858i	0.155629	+	0.478976i	0.998224	−	0.0595715i	$-0.0189734\pi$
$11$	0.516162	+	1.58858i	0.155629	+	0.478976i	−0.842595	+	0.538547i	$0.818973\pi$
$12$		0			0
$13$	−0.795501	+	2.44830i	−0.220632	+	0.679036i	0.778073	+	0.628173i	$0.216197\pi$
$13$	−0.795501	+	2.44830i	−0.220632	+	0.679036i	−0.998706	+	0.0508628i	$0.983803\pi$
$14$		0			0
$15$	−4.66170	−	3.88582i	−1.20364	−	1.00331i
$16$		0			0
$17$	−0.239003	−	0.173646i	−0.0579667	−	0.0421153i	0.558425	−	0.829555i	$-0.311406\pi$
$17$	−0.239003	−	0.173646i	−0.0579667	−	0.0421153i	−0.616391	+	0.787440i	$0.711406\pi$
$18$		0			0
$19$	−3.13970	−	2.28113i	−0.720297	−	0.523326i	0.166182	−	0.986095i	$-0.446856\pi$
$19$	−3.13970	−	2.28113i	−0.720297	−	0.523326i	−0.886479	+	0.462769i	$0.846856\pi$
$20$		0			0
$21$	−9.66754	+	7.02388i	−2.10963	+	1.53274i
$22$		0			0
$23$	2.71760	+	8.36392i	0.566659	+	1.74400i	0.662970	+	0.748646i	$0.269296\pi$
$23$	2.71760	+	8.36392i	0.566659	+	1.74400i	−0.0963111	+	0.995351i	$0.530704\pi$
$24$		0			0
$25$	−4.39935	+	2.37607i	−0.879870	+	0.475215i
$26$		0			0
$27$	1.14582	+	3.52647i	0.220513	+	0.678670i
$28$		0			0
$29$	−0.177592	+	0.129028i	−0.0329779	+	0.0239599i	−0.604152	−	0.796869i	$-0.706488\pi$
$29$	−0.177592	+	0.129028i	−0.0329779	+	0.0239599i	0.571174	+	0.820829i	$0.306488\pi$
$30$		0			0
$31$	−5.90981	−	4.29372i	−1.06143	−	0.771176i	−0.0870795	−	0.996201i	$-0.527753\pi$
$31$	−5.90981	−	4.29372i	−1.06143	−	0.771176i	−0.974353	+	0.225026i	$0.927753\pi$
$32$		0			0
$33$	−3.66761	−	2.66467i	−0.638448	−	0.463860i
$34$		0			0
$35$	2.41286	+	9.54488i	0.407849	+	1.61338i
$36$		0			0
$37$	−0.231242	+	0.711690i	−0.0380160	+	0.117001i	−0.968264	−	0.249931i	$-0.919592\pi$
$37$	−0.231242	+	0.711690i	−0.0380160	+	0.117001i	0.930248	+	0.366932i	$0.119592\pi$
$38$		0			0
$39$	−2.15905	−	6.64487i	−0.345724	−	1.06403i
$40$		0			0
$41$	−0.947030	+	2.91466i	−0.147901	+	0.455193i	−0.997373	−	0.0724415i	$-0.976921\pi$
$41$	−0.947030	+	2.91466i	−0.147901	+	0.455193i	0.849471	+	0.527635i	$0.176921\pi$
$42$		0			0
$43$	0.913208			0.139263			0.0696315	−	0.997573i	$-0.477818\pi$
$43$	0.913208			0.139263			0.0696315	+	0.997573i	$0.477818\pi$
$44$		0			0
$45$	9.74149	+	0.649305i	1.45218	+	0.0967927i
$46$		0			0
$47$	0.00570791	−	0.00414704i	0.000832584	−	0.000604907i	−0.587369	−	0.809319i	$-0.699836\pi$
$47$	0.00570791	−	0.00414704i	0.000832584	−	0.000604907i	0.588201	+	0.808714i	$0.299836\pi$
$48$		0			0
$49$	12.3853			1.76933
$50$		0			0
$51$	0.801802			0.112275
$52$		0			0
$53$	9.20313	−	6.68646i	1.26415	−	0.918457i	0.265193	−	0.964195i	$-0.414564\pi$
$53$	9.20313	−	6.68646i	1.26415	−	0.918457i	0.998953	+	0.0457387i	$0.0145642\pi$
$54$		0			0
$55$	−3.16098	+	1.98955i	−0.426226	+	0.268271i
$56$		0			0
$57$	10.5330			1.39513
$58$		0			0
$59$	−0.635908	+	1.95712i	−0.0827882	+	0.254796i	−0.983879	−	0.178834i	$-0.942767\pi$
$59$	−0.635908	+	1.95712i	−0.0827882	+	0.254796i	0.901091	+	0.433630i	$0.142767\pi$
$60$		0			0
$61$	−3.52338	−	10.8438i	−0.451123	−	1.38841i	−0.875628	−	0.482987i	$-0.839552\pi$
$61$	−3.52338	−	10.8438i	−0.451123	−	1.38841i	0.424505	−	0.905426i	$-0.360448\pi$
$62$		0			0
$63$	5.94049	−	18.2829i	0.748431	−	2.30343i
$64$		0			0
$65$	−5.74355	−	0.382828i	−0.712400	−	0.0474840i
$66$		0			0
$67$	4.94968	+	3.59615i	0.604699	+	0.439340i	0.847544	−	0.530725i	$-0.178080\pi$
$67$	4.94968	+	3.59615i	0.604699	+	0.439340i	−0.242844	+	0.970065i	$0.578080\pi$
$68$		0			0
$69$	−19.3100	−	14.0295i	−2.32465	−	1.68896i
$70$		0			0
$71$	−6.51168	+	4.73101i	−0.772794	+	0.561468i	−0.902808	−	0.430044i	$-0.858498\pi$
$71$	−6.51168	+	4.73101i	−0.772794	+	0.561468i	0.130013	+	0.991512i	$0.458498\pi$
$72$		0			0
$73$	1.08475	+	3.33853i	0.126961	+	0.390745i	0.994253	−	0.107054i	$-0.0341418\pi$
$73$	1.08475	+	3.33853i	0.126961	+	0.390745i	−0.867292	+	0.497799i	$0.834142\pi$
$74$		0			0
$75$	5.86925	−	12.2355i	0.677723	−	1.41283i
$76$		0			0
$77$	2.27260	+	6.99434i	0.258987	+	0.797079i
$78$		0			0
$79$	9.42807	−	6.84989i	1.06074	−	0.770673i	0.0865155	−	0.996251i	$-0.472427\pi$
$79$	9.42807	−	6.84989i	1.06074	−	0.770673i	0.974225	+	0.225577i	$0.0724268\pi$
$80$		0			0
$81$	2.45531	+	1.78388i	0.272812	+	0.198209i
$82$		0			0
$83$	2.30779	+	1.67671i	0.253313	+	0.184043i	0.707194	−	0.707020i	$-0.249961\pi$
$83$	2.30779	+	1.67671i	0.253313	+	0.184043i	−0.453881	+	0.891062i	$0.649961\pi$
$84$		0			0
$85$	0.245464	−	0.613289i	0.0266243	−	0.0665205i
$86$		0			0
$87$	0.184106	−	0.566621i	0.0197383	−	0.0607482i
$88$		0			0
$89$	−1.02955	−	3.16864i	−0.109132	−	0.335875i	0.881546	−	0.472099i	$-0.156503\pi$
$89$	−1.02955	−	3.16864i	−0.109132	−	0.335875i	−0.990678	+	0.136224i	$0.956503\pi$
$90$		0			0
$91$	−3.50249	+	10.7796i	−0.367161	+	1.13001i
$92$		0			0
$93$	19.8261			2.05587
$94$		0			0
$95$	3.22458	−	8.05658i	0.330834	−	0.826587i
$96$		0			0
$97$	−8.73973	+	6.34979i	−0.887385	+	0.644723i	−0.935195	−	0.354133i	$-0.884776\pi$
$97$	−8.73973	+	6.34979i	−0.887385	+	0.644723i	0.0478096	+	0.998856i	$0.484776\pi$
$98$		0			0
$99$	7.29301			0.732975
$100$		0			0
$101$	11.0970			1.10419			0.552095	−	0.833781i	$-0.313829\pi$
$101$	11.0970			1.10419			0.552095	+	0.833781i	$0.313829\pi$
$102$		0			0
$103$	6.12368	−	4.44911i	0.603384	−	0.438384i	−0.243694	−	0.969852i	$-0.578359\pi$
$103$	6.12368	−	4.44911i	0.603384	−	0.438384i	0.847078	+	0.531468i	$0.178359\pi$
$104$		0			0
$105$	−20.5249	−	17.1088i	−2.00302	−	1.66965i
$106$		0			0
$107$	1.82026			0.175972			0.0879858	−	0.996122i	$-0.471957\pi$
$107$	1.82026			0.175972			0.0879858	+	0.996122i	$0.471957\pi$
$108$		0			0
$109$	−3.69779	+	11.3806i	−0.354184	+	1.09007i	0.602297	+	0.798272i	$0.294252\pi$
$109$	−3.69779	+	11.3806i	−0.354184	+	1.09007i	−0.956481	+	0.291794i	$0.905748\pi$
$110$		0			0
$111$	−0.627608	−	1.93158i	−0.0595700	−	0.183337i
$112$		0			0
$113$	−3.70798	+	11.4120i	−0.348817	+	1.07355i	0.610691	+	0.791869i	$0.290892\pi$
$113$	−3.70798	+	11.4120i	−0.348817	+	1.07355i	−0.959508	+	0.281680i	$0.909108\pi$
$114$		0			0
$115$	−16.6426	+	10.4750i	−1.55193	+	0.976799i
$116$		0			0
$117$	9.09325	+	6.60663i	0.840671	+	0.610783i
$118$		0			0
$119$	−1.05230	−	0.764541i	−0.0964642	−	0.0700854i
$120$		0			0
$121$	6.64202	−	4.82571i	0.603820	−	0.438701i
$122$		0			0
$123$	−2.57031	−	7.91059i	−0.231757	−	0.713274i
$124$		0			0
$125$	−7.56196	−	8.23509i	−0.676362	−	0.736569i
$126$		0			0
$127$	−1.53732	−	4.73140i	−0.136415	−	0.419844i	0.859392	−	0.511317i	$-0.170842\pi$
$127$	−1.53732	−	4.73140i	−0.136415	−	0.419844i	−0.995808	+	0.0914736i	$0.970842\pi$
$128$		0			0
$129$	−2.00516	+	1.45683i	−0.176544	+	0.128267i
$130$		0			0
$131$	15.4346	+	11.2139i	1.34853	+	0.979765i	0.999083	+	0.0428087i	$0.0136306\pi$
$131$	15.4346	+	11.2139i	1.34853	+	0.979765i	0.349447	+	0.936956i	$0.386369\pi$
$132$		0			0
$133$	−13.8237	−	10.0435i	−1.19867	−	0.870884i
$134$		0			0
$135$	−7.01702	+	4.41657i	−0.603929	+	0.380118i
$136$		0			0
$137$	2.80931	−	8.64616i	0.240015	−	0.738691i	−0.756401	−	0.654108i	$-0.773044\pi$
$137$	2.80931	−	8.64616i	0.240015	−	0.738691i	0.996416	−	0.0845830i	$-0.0269558\pi$
$138$		0			0
$139$	−4.12063	−	12.6820i	−0.349508	−	1.07567i	−0.959126	−	0.282979i	$-0.908677\pi$
$139$	−4.12063	−	12.6820i	−0.349508	−	1.07567i	0.609618	−	0.792695i	$-0.291323\pi$
$140$		0			0
$141$	−0.00591729	+	0.0182116i	−0.000498326	+	0.00153369i
$142$		0			0
$143$	−4.29993			−0.359578
$144$		0			0
$145$	−0.377040	−	0.314286i	−0.0313115	−	0.0261001i
$146$		0			0
$147$	−27.1949	+	19.7582i	−2.24300	+	1.62963i
$148$		0			0
$149$	6.47079			0.530108			0.265054	−	0.964234i	$-0.414610\pi$
$149$	6.47079			0.530108			0.265054	+	0.964234i	$0.414610\pi$
$150$		0			0
$151$	11.0604			0.900086			0.450043	−	0.893007i	$-0.351409\pi$
$151$	11.0604			0.900086			0.450043	+	0.893007i	$0.351409\pi$
$152$		0			0
$153$	−1.04353	+	0.758171i	−0.0843646	+	0.0612945i
$154$		0			0
$155$	6.06956	−	15.1648i	0.487519	−	1.21806i
$156$		0			0
$157$	6.26300			0.499842			0.249921	−	0.968266i	$-0.419595\pi$
$157$	6.26300			0.499842			0.249921	+	0.968266i	$0.419595\pi$
$158$		0			0
$159$	−9.54073	+	29.3634i	−0.756629	+	2.32867i
$160$		0			0
$161$	11.9653	+	36.8253i	0.942995	+	2.90224i
$162$		0			0
$163$	1.25630	−	3.86650i	0.0984012	−	0.302848i	−0.889724	−	0.456499i	$-0.849103\pi$
$163$	1.25630	−	3.86650i	0.0984012	−	0.302848i	0.988125	+	0.153651i	$0.0491032\pi$
$164$		0			0
$165$	3.76675	−	9.41120i	0.293241	−	0.732661i
$166$		0			0
$167$	−16.0147	−	11.6354i	−1.23926	−	0.900372i	−0.241707	−	0.970349i	$-0.577707\pi$
$167$	−16.0147	−	11.6354i	−1.23926	−	0.900372i	−0.997549	+	0.0699770i	$0.977707\pi$
$168$		0			0
$169$	5.15587	+	3.74596i	0.396605	+	0.288151i
$170$		0			0
$171$	−13.7086	+	9.95984i	−1.04832	+	0.761648i
$172$		0			0
$173$	0.402408	+	1.23849i	0.0305945	+	0.0941603i	0.965188	−	0.261558i	$-0.0842363\pi$
$173$	0.402408	+	1.23849i	0.0305945	+	0.0941603i	−0.934593	+	0.355718i	$0.884236\pi$
$174$		0			0
$175$	−19.3698	+	10.4616i	−1.46422	+	0.790820i
$176$		0			0
$177$	−1.72590	−	5.31178i	−0.129727	−	0.399258i
$178$		0			0
$179$	17.2951	−	12.5657i	1.29270	−	0.939202i	0.292844	−	0.956160i	$-0.405398\pi$
$179$	17.2951	−	12.5657i	1.29270	−	0.939202i	0.999856	+	0.0169586i	$0.00539836\pi$
$180$		0			0
$181$	−12.3017	−	8.93773i	−0.914381	−	0.664337i	0.0277381	−	0.999615i	$-0.491170\pi$
$181$	−12.3017	−	8.93773i	−0.914381	−	0.664337i	−0.942119	+	0.335279i	$0.891170\pi$
$182$		0			0
$183$	25.0355	+	18.1894i	1.85068	+	1.34460i
$184$		0			0
$185$	−1.66958	−	0.111283i	−0.122750	−	0.00818172i
$186$		0			0
$187$	0.152486	−	0.469305i	0.0111509	−	0.0343190i
$188$		0			0
$189$	5.04491	+	15.5266i	0.366963	+	1.12940i
$190$		0			0
$191$	4.98276	−	15.3353i	0.360540	−	1.10963i	−0.592188	−	0.805800i	$-0.701736\pi$
$191$	4.98276	−	15.3353i	0.360540	−	1.10963i	0.952727	−	0.303827i	$-0.0982644\pi$
$192$		0			0
$193$	10.3557			0.745420			0.372710	−	0.927948i	$-0.378429\pi$
$193$	10.3557			0.745420			0.372710	+	0.927948i	$0.378429\pi$
$194$		0			0
$195$	13.2220	−	8.32206i	0.946849	−	0.595955i
$196$		0			0
$197$	−16.2595	+	11.8133i	−1.15844	+	0.841659i	−0.989581	−	0.143980i	$-0.954010\pi$
$197$	−16.2595	+	11.8133i	−1.15844	+	0.841659i	−0.168864	+	0.985639i	$0.554010\pi$
$198$		0			0
$199$	−2.82095			−0.199972			−0.0999859	−	0.994989i	$-0.531880\pi$
$199$	−2.82095			−0.199972			−0.0999859	+	0.994989i	$0.531880\pi$
$200$		0			0
$201$	−16.6051			−1.17123
$202$		0			0
$203$	−0.781915	+	0.568094i	−0.0548797	+	0.0398724i
$204$		0			0
$205$	−6.83760	−	0.455750i	−0.477559	−	0.0318310i
$206$		0			0
$207$	38.3978			2.66883
$208$		0			0
$209$	2.00316	−	6.16510i	0.138562	−	0.426449i
$210$		0			0
$211$	2.68797	+	8.27273i	0.185048	+	0.569518i	0.999949	−	0.0100813i	$-0.00320902\pi$
$211$	2.68797	+	8.27273i	0.185048	+	0.569518i	−0.814902	+	0.579599i	$0.803209\pi$
$212$		0			0
$213$	6.75056	−	20.7761i	0.462540	−	1.42355i
$214$		0			0
$215$	0.500456	+	1.97972i	0.0341308	+	0.135016i
$216$		0			0
$217$	−26.0202	−	18.9048i	−1.76636	−	1.28334i
$218$		0			0
$219$	−7.70775	−	5.60001i	−0.520842	−	0.378414i
$220$		0			0
$221$	0.615264	−	0.447015i	0.0413871	−	0.0300695i
$222$		0			0
$223$	−3.00568	−	9.25053i	−0.201275	−	0.619461i	−0.999846	−	0.0175601i	$-0.994410\pi$
$223$	−3.00568	−	9.25053i	−0.201275	−	0.619461i	0.798571	−	0.601901i	$-0.205590\pi$
$224$		0			0
$225$	3.93092	+	21.4742i	0.262061	+	1.43161i
$226$		0			0
$227$	2.68733	+	8.27076i	0.178365	+	0.548950i	0.999771	−	0.0213934i	$-0.00681025\pi$
$227$	2.68733	+	8.27076i	0.178365	+	0.548950i	−0.821407	+	0.570343i	$0.806810\pi$
$228$		0			0
$229$	10.9755	−	7.97420i	0.725284	−	0.526950i	−0.162784	−	0.986662i	$-0.552047\pi$
$229$	10.9755	−	7.97420i	0.725284	−	0.526950i	0.888068	+	0.459712i	$0.152047\pi$
$230$		0			0
$231$	−16.1480	−	11.7322i	−1.06246	−	0.771924i
$232$		0			0
$233$	12.7120	+	9.23583i	0.832793	+	0.605060i	0.920348	−	0.391100i	$-0.127905\pi$
$233$	12.7120	+	9.23583i	0.832793	+	0.605060i	−0.0875552	+	0.996160i	$0.527905\pi$
$234$		0			0
$235$	0.0121183	+	0.0101014i	0.000790510	+	0.000658940i
$236$		0			0
$237$	−9.77393	+	30.0811i	−0.634885	+	1.95397i
$238$		0			0
$239$	6.67480	+	20.5429i	0.431757	+	1.32881i	0.896374	+	0.443299i	$0.146192\pi$
$239$	6.67480	+	20.5429i	0.431757	+	1.32881i	−0.464617	+	0.885512i	$0.653808\pi$
$240$		0			0
$241$	2.47318	−	7.61166i	0.159312	−	0.490310i	−0.839261	−	0.543729i	$-0.817012\pi$
$241$	2.47318	−	7.61166i	0.159312	−	0.490310i	0.998572	+	0.0534188i	$0.0170118\pi$
$242$		0			0
$243$	−19.3609			−1.24200
$244$		0			0
$245$	6.78741	+	26.8499i	0.433632	+	1.71537i
$246$		0			0
$247$	8.08252	−	5.87229i	0.514278	−	0.373645i
$248$		0			0
$249$	−7.74213			−0.490638
$250$		0			0
$251$	1.26202			0.0796582			0.0398291	−	0.999207i	$-0.487319\pi$
$251$	1.26202			0.0796582			0.0398291	+	0.999207i	$0.487319\pi$
$252$		0			0
$253$	−11.8840	+	8.63427i	−0.747144	+	0.542832i
$254$		0			0
$255$	0.439403	+	1.73820i	0.0275165	+	0.108851i
$256$		0			0
$257$	27.8198			1.73535			0.867676	−	0.497130i	$-0.165613\pi$
$257$	27.8198			1.73535			0.867676	+	0.497130i	$0.165613\pi$
$258$		0			0
$259$	−1.01813	+	3.13349i	−0.0632636	+	0.194705i
$260$		0			0
$261$	0.296176	+	0.911537i	0.0183329	+	0.0564227i
$262$		0			0
$263$	−5.58904	+	17.2013i	−0.344635	+	1.06068i	0.617144	+	0.786850i	$0.288290\pi$
$263$	−5.58904	+	17.2013i	−0.344635	+	1.06068i	−0.961779	+	0.273827i	$0.911710\pi$
$264$		0			0
$265$	19.5389	+	16.2869i	1.20027	+	1.00050i
$266$		0			0
$267$	7.31553	+	5.31504i	0.447703	+	0.325275i
$268$		0			0
$269$	−9.88615	−	7.18271i	−0.602769	−	0.437937i	0.244092	−	0.969752i	$-0.421510\pi$
$269$	−9.88615	−	7.18271i	−0.602769	−	0.437937i	−0.846861	+	0.531815i	$0.821510\pi$
$270$		0			0
$271$	0.642434	−	0.466756i	0.0390251	−	0.0283534i	−0.568102	−	0.822958i	$-0.692322\pi$
$271$	0.642434	−	0.466756i	0.0390251	−	0.0283534i	0.607127	+	0.794605i	$0.292322\pi$
$272$		0			0
$273$	−9.50603	−	29.2565i	−0.575331	−	1.77069i
$274$		0			0
$275$	−6.04537	−	5.76229i	−0.364549	−	0.347479i
$276$		0			0
$277$	−7.98890	−	24.5873i	−0.480007	−	1.47731i	−0.839085	−	0.544001i	$-0.816909\pi$
$277$	−7.98890	−	24.5873i	−0.480007	−	1.47731i	0.359078	−	0.933307i	$-0.383091\pi$
$278$		0			0
$279$	−25.8034	+	18.7472i	−1.54481	+	1.12237i
$280$		0			0
$281$	−14.1996	−	10.3166i	−0.847080	−	0.615440i	0.0772594	−	0.997011i	$-0.475383\pi$
$281$	−14.1996	−	10.3166i	−0.847080	−	0.615440i	−0.924339	+	0.381571i	$0.875383\pi$
$282$		0			0
$283$	−6.73824	−	4.89562i	−0.400547	−	0.291014i	0.369217	−	0.929343i	$-0.379626\pi$
$283$	−6.73824	−	4.89562i	−0.400547	−	0.291014i	−0.769764	+	0.638329i	$0.779626\pi$
$284$		0			0
$285$	5.77230	+	22.8342i	0.341921	+	1.35258i
$286$		0			0
$287$	−4.16966	+	12.8329i	−0.246127	+	0.757501i
$288$		0			0
$289$	−5.22632	−	16.0850i	−0.307431	−	0.946174i
$290$		0			0
$291$	9.06034	−	27.8849i	0.531127	−	1.63464i
$292$		0			0
$293$	−18.5010			−1.08084			−0.540421	−	0.841395i	$-0.681735\pi$
$293$	−18.5010			−1.08084			−0.540421	+	0.841395i	$0.681735\pi$
$294$		0			0
$295$	−4.59129	−	0.306025i	−0.267315	−	0.0178175i
$296$		0			0
$297$	−5.01067	+	3.64046i	−0.290748	+	0.211241i
$298$		0			0
$299$	−22.6392			−1.30926
$300$		0			0
$301$	4.02074			0.231752
$302$		0			0
$303$	−24.3660	+	17.7029i	−1.39979	+	1.01701i
$304$		0			0
$305$	21.5772	−	13.5809i	1.23551	−	0.777639i
$306$		0			0
$307$	−2.36704			−0.135094			−0.0675469	−	0.997716i	$-0.521517\pi$
$307$	−2.36704			−0.135094			−0.0675469	+	0.997716i	$0.521517\pi$
$308$		0			0
$309$	−6.34832	+	19.5381i	−0.361143	+	1.11149i
$310$		0			0
$311$	1.86977	+	5.75455i	0.106025	+	0.326311i	0.989970	−	0.141281i	$-0.0451220\pi$
$311$	1.86977	+	5.75455i	0.106025	+	0.326311i	−0.883945	+	0.467591i	$0.845122\pi$
$312$		0			0
$313$	−7.58326	+	23.3389i	−0.428631	+	1.31919i	0.470843	+	0.882217i	$0.343950\pi$
$313$	−7.58326	+	23.3389i	−0.428631	+	1.31919i	−0.899474	+	0.436974i	$0.856050\pi$
$314$		0			0
$315$	42.8906	+	2.85881i	2.41661	+	0.161076i
$316$		0			0
$317$	1.96032	+	1.42425i	0.110102	+	0.0799941i	0.641474	−	0.767145i	$-0.278323\pi$
$317$	1.96032	+	1.42425i	0.110102	+	0.0799941i	−0.531372	+	0.847139i	$0.678323\pi$
$318$		0			0
$319$	−0.296637	−	0.215520i	−0.0166085	−	0.0120668i
$320$		0			0
$321$	−3.99681	+	2.90385i	−0.223080	+	0.162077i
$322$		0			0
$323$	0.354290	+	1.09039i	0.0197132	+	0.0606710i
$324$		0			0
$325$	−2.31766	−	12.6611i	−0.128561	−	0.702311i
$326$		0			0
$327$	−10.0361	−	30.8878i	−0.554996	−	1.70810i
$328$		0			0
$329$	0.0251312	−	0.0182589i	0.00138553	−	0.00100665i
$330$		0			0
$331$	−12.3919	−	9.00326i	−0.681122	−	0.494864i	0.192608	−	0.981276i	$-0.438305\pi$
$331$	−12.3919	−	9.00326i	−0.681122	−	0.494864i	−0.873730	+	0.486412i	$0.838305\pi$
$332$		0			0
$333$	2.64329	+	1.92047i	0.144852	+	0.105241i
$334$		0			0
$335$	−5.08348	+	12.7010i	−0.277740	+	0.693932i
$336$		0			0
$337$	7.00754	−	21.5670i	0.381725	−	1.17483i	−0.557104	−	0.830443i	$-0.688087\pi$
$337$	7.00754	−	21.5670i	0.381725	−	1.17483i	0.938828	−	0.344385i	$-0.111913\pi$
$338$		0			0
$339$	−10.0637	−	30.9730i	−0.546586	−	1.68222i
$340$		0			0
$341$	3.77052	−	11.6045i	0.204185	−	0.628417i
$342$		0			0
$343$	23.7110			1.28027
$344$		0			0
$345$	19.8320	−	49.5501i	1.06772	−	2.66769i
$346$		0			0
$347$	6.88365	−	5.00126i	0.369534	−	0.268482i	−0.387484	−	0.921876i	$-0.626656\pi$
$347$	6.88365	−	5.00126i	0.369534	−	0.268482i	0.757017	+	0.653395i	$0.226656\pi$
$348$		0			0
$349$	23.5983			1.26319			0.631594	−	0.775300i	$-0.282401\pi$
$349$	23.5983			1.26319			0.631594	+	0.775300i	$0.282401\pi$
$350$		0			0
$351$	−9.54537			−0.509494
$352$		0			0
$353$	5.14507	−	3.73811i	0.273845	−	0.198960i	−0.442384	−	0.896826i	$-0.645867\pi$
$353$	5.14507	−	3.73811i	0.273845	−	0.198960i	0.716228	+	0.697866i	$0.245867\pi$
$354$		0			0
$355$	−13.8248	−	11.5238i	−0.733743	−	0.611620i
$356$		0			0
$357$	3.53024			0.186840
$358$		0			0
$359$	9.07611	−	27.9334i	0.479019	−	1.47427i	−0.361441	−	0.932395i	$-0.617715\pi$
$359$	9.07611	−	27.9334i	0.479019	−	1.47427i	0.840460	−	0.541873i	$-0.182285\pi$
$360$		0			0
$361$	−1.21714	−	3.74596i	−0.0640598	−	0.197156i
$362$		0			0
$363$	−6.88567	+	21.1919i	−0.361404	+	1.11229i
$364$		0			0
$365$	−6.64304	+	4.18119i	−0.347712	+	0.218853i
$366$		0			0
$367$	11.0641	+	8.03852i	0.577540	+	0.419607i	0.837836	−	0.545921i	$-0.183820\pi$
$367$	11.0641	+	8.03852i	0.577540	+	0.419607i	−0.260296	+	0.965529i	$0.583820\pi$
$368$		0			0
$369$	10.8254	+	7.86508i	0.563545	+	0.409440i
$370$		0			0
$371$	40.5203	−	29.4397i	2.10371	−	1.52843i
$372$		0			0
$373$	4.60333	+	14.1676i	0.238352	+	0.733571i	0.996659	+	0.0816739i	$0.0260266\pi$
$373$	4.60333	+	14.1676i	0.238352	+	0.733571i	−0.758307	+	0.651897i	$0.773973\pi$
$374$		0			0
$375$	29.7414	+	6.01852i	1.53584	+	0.310795i
$376$		0			0
$377$	−0.174625	−	0.537439i	−0.00899363	−	0.0276795i
$378$		0			0
$379$	10.5189	−	7.64241i	0.540318	−	0.392564i	−0.283885	−	0.958858i	$-0.591623\pi$
$379$	10.5189	−	7.64241i	0.540318	−	0.392564i	0.824203	+	0.566294i	$0.191623\pi$
$380$		0			0
$381$	10.9235	+	7.93640i	0.559629	+	0.406594i
$382$		0			0
$383$	1.04621	+	0.760113i	0.0534586	+	0.0388400i	0.614194	−	0.789155i	$-0.289481\pi$
$383$	1.04621	+	0.760113i	0.0534586	+	0.0388400i	−0.560735	+	0.827995i	$0.689481\pi$
$384$		0			0
$385$	−13.9174	+	8.75974i	−0.709297	+	0.446438i
$386$		0			0
$387$	1.23213	−	3.79209i	0.0626325	−	0.192763i
$388$		0			0
$389$	−5.35538	−	16.4822i	−0.271529	−	0.835679i	−0.990117	−	0.140244i	$-0.955211\pi$
$389$	−5.35538	−	16.4822i	−0.271529	−	0.835679i	0.718588	−	0.695436i	$-0.244789\pi$
$390$		0			0
$391$	0.802844	−	2.47090i	0.0406016	−	0.124959i
$392$		0			0
$393$	−51.7798			−2.61195
$394$		0			0
$395$	20.0165	+	16.6850i	1.00714	+	0.839513i
$396$		0			0
$397$	21.6576	−	15.7352i	1.08696	−	0.789726i	0.108080	−	0.994142i	$-0.465530\pi$
$397$	21.6576	−	15.7352i	1.08696	−	0.789726i	0.978884	+	0.204416i	$0.0655296\pi$
$398$		0			0
$399$	46.3756			2.32168
$400$		0			0
$401$	5.50607			0.274960			0.137480	−	0.990505i	$-0.456100\pi$
$401$	5.50607			0.274960			0.137480	+	0.990505i	$0.456100\pi$
$402$		0			0
$403$	15.2136	−	11.0533i	0.757842	−	0.550605i
$404$		0			0
$405$	−2.52168	+	6.30040i	−0.125303	+	0.313069i
$406$		0			0
$407$	−1.24994			−0.0619571
$408$		0			0
$409$	−4.32386	+	13.3075i	−0.213801	+	0.658012i	0.785436	+	0.618943i	$0.212439\pi$
$409$	−4.32386	+	13.3075i	−0.213801	+	0.658012i	−0.999237	+	0.0390683i	$0.987561\pi$
$410$		0			0
$411$	7.62466	+	23.4663i	0.376097	+	1.15751i
$412$		0			0
$413$	−2.79983	+	8.61698i	−0.137770	+	0.424014i
$414$		0			0
$415$	−2.37018	+	5.92187i	−0.116347	+	0.290693i
$416$		0			0
$417$	29.2793	+	21.2727i	1.43381	+	1.04173i
$418$		0			0
$419$	13.7294	+	9.97500i	0.670726	+	0.487311i	0.870268	−	0.492578i	$-0.163946\pi$
$419$	13.7294	+	9.97500i	0.670726	+	0.487311i	−0.199542	+	0.979889i	$0.563946\pi$
$420$		0			0
$421$	−10.9487	+	7.95470i	−0.533607	+	0.387688i	−0.821705	−	0.569912i	$-0.806977\pi$
$421$	−10.9487	+	7.95470i	−0.533607	+	0.387688i	0.288098	+	0.957601i	$0.406977\pi$
$422$		0			0
$423$	−0.00951929	−	0.0292974i	−0.000462844	−	0.00142449i
$424$		0			0
$425$	1.46405	+	0.196039i	0.0710169	+	0.00950931i
$426$		0			0
$427$	−15.5130	−	47.7442i	−0.750727	−	2.31050i
$428$		0			0
$429$	9.44150	−	6.85965i	0.455840	−	0.331187i
$430$		0			0
$431$	−18.7825	−	13.6463i	−0.904721	−	0.657318i	0.0349532	−	0.999389i	$-0.488872\pi$
$431$	−18.7825	−	13.6463i	−0.904721	−	0.657318i	−0.939674	+	0.342071i	$0.888872\pi$
$432$		0			0
$433$	30.7134	+	22.3146i	1.47599	+	1.07237i	0.978822	+	0.204715i	$0.0656268\pi$
$433$	30.7134	+	22.3146i	1.47599	+	1.07237i	0.497168	+	0.867654i	$0.334373\pi$
$434$		0			0
$435$	1.32926	+	0.0885997i	0.0637330	+	0.00424803i
$436$		0			0
$437$	10.5467	−	32.4594i	0.504517	−	1.55274i
$438$		0			0
$439$	11.9315	+	36.7213i	0.569458	+	1.75261i	0.654318	+	0.756219i	$0.272956\pi$
$439$	11.9315	+	36.7213i	0.569458	+	1.75261i	−0.0848602	+	0.996393i	$0.527044\pi$
$440$		0			0
$441$	16.7107	−	51.4301i	0.795746	−	2.44905i
$442$		0			0
$443$	−22.5688			−1.07228			−0.536138	−	0.844130i	$-0.680117\pi$
$443$	−22.5688			−1.07228			−0.536138	+	0.844130i	$0.680117\pi$
$444$		0			0
$445$	6.30499	−	3.96842i	0.298885	−	0.188121i
$446$		0			0
$447$	−14.2081	+	10.3228i	−0.672021	+	0.488252i
$448$		0			0
$449$	−29.2091			−1.37846			−0.689232	−	0.724541i	$-0.742052\pi$
$449$	−29.2091			−1.37846			−0.689232	+	0.724541i	$0.742052\pi$
$450$		0			0
$451$	−5.11899			−0.241044
$452$		0			0
$453$	−24.2858	+	17.6446i	−1.14104	+	0.829018i
$454$		0			0
$455$	−25.2882	−	1.68555i	−1.18553	−	0.0790196i
$456$		0			0
$457$	−21.4154			−1.00177			−0.500885	−	0.865514i	$-0.666992\pi$
$457$	−21.4154			−1.00177			−0.500885	+	0.865514i	$0.666992\pi$
$458$		0			0
$459$	0.338503	−	1.04180i	0.0157999	−	0.0486272i
$460$		0			0
$461$	−7.46239	−	22.9669i	−0.347558	−	1.06967i	−0.960200	−	0.279313i	$-0.909893\pi$
$461$	−7.46239	−	22.9669i	−0.347558	−	1.06967i	0.612642	−	0.790361i	$-0.290107\pi$
$462$		0			0
$463$	−1.28333	+	3.94968i	−0.0596414	+	0.183557i	−0.976438	−	0.215796i	$-0.930765\pi$
$463$	−1.28333	+	3.94968i	−0.0596414	+	0.183557i	0.916797	+	0.399353i	$0.130765\pi$
$464$		0			0
$465$	10.8651	+	42.9805i	0.503857	+	1.99317i
$466$		0			0
$467$	−14.5240	−	10.5523i	−0.672092	−	0.488304i	0.198633	−	0.980074i	$-0.436350\pi$
$467$	−14.5240	−	10.5523i	−0.672092	−	0.488304i	−0.870725	+	0.491770i	$0.836350\pi$
$468$		0			0
$469$	21.7928	+	15.8334i	1.00630	+	0.731119i
$470$		0			0
$471$	−13.7519	+	9.99131i	−0.633652	+	0.460375i
$472$		0			0
$473$	0.471363	+	1.45071i	0.0216733	+	0.0667035i
$474$		0			0
$475$	19.2328	+	2.57531i	0.882460	+	0.118163i
$476$		0			0
$477$	−15.3484	−	47.2375i	−0.702755	−	2.16286i
$478$		0			0
$479$	−15.2189	+	11.0571i	−0.695367	+	0.505214i	−0.878420	−	0.477889i	$-0.841402\pi$
$479$	−15.2189	+	11.0571i	−0.695367	+	0.505214i	0.183053	+	0.983103i	$0.441402\pi$
$480$		0			0
$481$	−1.55848	−	1.13230i	−0.0710605	−	0.0516285i
$482$		0			0
$483$	−85.0197	−	61.7704i	−3.86853	−	2.81065i
$484$		0			0
$485$	−18.5551	−	15.4668i	−0.842543	−	0.702312i
$486$		0			0
$487$	10.1834	−	31.3412i	0.461452	−	1.42020i	−0.401937	−	0.915667i	$-0.631663\pi$
$487$	10.1834	−	31.3412i	0.461452	−	1.42020i	0.863390	−	0.504537i	$-0.168337\pi$
$488$		0			0
$489$	3.40970	+	10.4940i	0.154192	+	0.474554i
$490$		0			0
$491$	−10.3651	+	31.9005i	−0.467771	+	1.43965i	0.387693	+	0.921789i	$0.373272\pi$
$491$	−10.3651	+	31.9005i	−0.467771	+	1.43965i	−0.855464	+	0.517862i	$0.826728\pi$
$492$		0			0
$493$	0.0648500			0.00292070
$494$		0			0
$495$	3.99671	+	15.8103i	0.179639	+	0.710621i
$496$		0			0
$497$	−28.6701	+	20.8301i	−1.28603	+	0.934357i
$498$		0			0
$499$	13.4640			0.602732			0.301366	−	0.953509i	$-0.402557\pi$
$499$	13.4640			0.602732			0.301366	+	0.953509i	$0.402557\pi$
$500$		0			0
$501$	53.7258			2.40029
$502$		0			0
$503$	3.84374	−	2.79264i	0.171384	−	0.124518i	−0.498787	−	0.866725i	$-0.666221\pi$
$503$	3.84374	−	2.79264i	0.171384	−	0.124518i	0.670171	+	0.742207i	$0.266221\pi$
$504$		0			0
$505$	6.08136	+	24.0568i	0.270617	+	1.07052i
$506$		0			0
$507$	−17.2968			−0.768178
$508$		0			0
$509$	6.63417	−	20.4179i	0.294055	−	0.905007i	−0.689483	−	0.724302i	$-0.742162\pi$
$509$	6.63417	−	20.4179i	0.294055	−	0.905007i	0.983537	−	0.180705i	$-0.0578379\pi$
$510$		0			0
$511$	4.77604	+	14.6991i	0.211279	+	0.650251i
$512$		0			0
$513$	4.44680	−	13.6858i	0.196331	−	0.604245i
$514$		0			0
$515$	13.0010	+	10.8372i	0.572893	+	0.477542i
$516$		0			0
$517$	0.00953411	+	0.00692694i	0.000419310	+	0.000304646i
$518$		0			0
$519$	−2.85933	−	2.07742i	−0.125511	−	0.0911887i
$520$		0			0
$521$	10.4542	−	7.59539i	0.458005	−	0.332760i	−0.334743	−	0.942309i	$-0.608650\pi$
$521$	10.4542	−	7.59539i	0.458005	−	0.332760i	0.792748	+	0.609549i	$0.208650\pi$
$522$		0			0
$523$	6.29759	+	19.3820i	0.275374	+	0.847515i	0.989120	+	0.147110i	$0.0469971\pi$
$523$	6.29759	+	19.3820i	0.275374	+	0.847515i	−0.713746	+	0.700405i	$0.753003\pi$
$524$		0			0
$525$	25.8416	−	53.8713i	1.12782	−	2.35114i
$526$		0			0
$527$	0.666873	+	2.05242i	0.0290494	+	0.0894050i
$528$		0			0
$529$	−43.9624	+	31.9405i	−1.91141	+	1.38872i
$530$		0			0
$531$	7.26897	+	5.28121i	0.315446	+	0.229185i
$532$		0			0
$533$	−6.38259	−	4.63722i	−0.276461	−	0.200861i
$534$		0			0
$535$	0.997541	+	3.94610i	0.0431274	+	0.170605i
$536$		0			0
$537$	−17.9296	+	55.1816i	−0.773719	+	2.38126i
$538$		0			0
$539$	6.39284	+	19.6751i	0.275359	+	0.847468i
$540$		0			0
$541$	−9.79560	+	30.1478i	−0.421146	+	1.29615i	0.485491	+	0.874242i	$0.338641\pi$
$541$	−9.79560	+	30.1478i	−0.421146	+	1.29615i	−0.906637	+	0.421912i	$0.861359\pi$
$542$		0			0
$543$	41.2696			1.77105
$544$		0			0
$545$	−26.6982	−	1.77953i	−1.14363	−	0.0762267i
$546$		0			0
$547$	−24.9414	+	18.1210i	−1.06642	+	0.774798i	−0.975265	−	0.221039i	$-0.929055\pi$
$547$	−24.9414	+	18.1210i	−1.06642	+	0.774798i	−0.0911524	+	0.995837i	$0.529055\pi$
$548$		0			0
$549$	−49.7829			−2.12468
$550$		0			0
$551$	0.851914			0.0362928
$552$		0			0
$553$	41.5107	−	30.1593i	1.76521	−	1.28250i
$554$		0			0
$555$	3.84348	−	2.41912i	0.163147	−	0.102686i
$556$		0			0
$557$	−5.19763			−0.220231			−0.110115	−	0.993919i	$-0.535122\pi$
$557$	−5.19763			−0.220231			−0.110115	+	0.993919i	$0.535122\pi$
$558$		0			0
$559$	−0.726458	+	2.23581i	−0.0307259	+	0.0945646i
$560$		0			0
$561$	0.413859	+	1.27373i	0.0174732	+	0.0537768i
$562$		0			0
$563$	−1.93482	+	5.95477i	−0.0815430	+	0.250964i	−0.983514	−	0.180834i	$-0.942120\pi$
$563$	−1.93482	+	5.95477i	−0.0815430	+	0.250964i	0.901971	+	0.431797i	$0.142120\pi$
$564$		0			0
$565$	−26.7718	−	1.78443i	−1.12630	−	0.0750717i
$566$		0			0
$567$	10.8104	+	7.85423i	0.453995	+	0.329846i
$568$		0			0
$569$	24.8382	+	18.0460i	1.04127	+	0.756528i	0.970533	−	0.240967i	$-0.0774645\pi$
$569$	24.8382	+	18.0460i	1.04127	+	0.756528i	0.0707384	+	0.997495i	$0.477464\pi$
$570$		0			0
$571$	−21.2560	+	15.4434i	−0.889537	+	0.646287i	−0.935757	−	0.352645i	$-0.885282\pi$
$571$	−21.2560	+	15.4434i	−0.889537	+	0.646287i	0.0462202	+	0.998931i	$0.485282\pi$
$572$		0			0
$573$	13.5236	+	41.6213i	0.564955	+	1.73875i
$574$		0			0
$575$	−31.8290	−	30.3386i	−1.32736	−	1.26521i
$576$		0			0
$577$	−0.565447	−	1.74027i	−0.0235399	−	0.0724483i	0.938596	−	0.345017i	$-0.112127\pi$
$577$	−0.565447	−	1.74027i	−0.0235399	−	0.0724483i	−0.962136	+	0.272569i	$0.912127\pi$
$578$		0			0
$579$	−22.7384	+	16.5204i	−0.944974	+	0.686564i
$580$		0			0
$581$	10.1609	+	7.38235i	0.421546	+	0.306271i
$582$		0			0
$583$	15.3723	+	11.1686i	0.636656	+	0.462557i
$584$		0			0
$585$	−9.33906	+	23.3336i	−0.386123	+	0.964725i
$586$		0			0
$587$	−13.8225	+	42.5413i	−0.570516	+	1.75587i	0.0804491	+	0.996759i	$0.474365\pi$
$587$	−13.8225	+	42.5413i	−0.570516	+	1.75587i	−0.650965	+	0.759108i	$0.725635\pi$
$588$		0			0
$589$	8.76049	+	26.9620i	0.360970	+	1.11095i
$590$		0			0
$591$	16.8560	−	51.8775i	0.693364	−	2.13395i
$592$		0			0
$593$	−24.9335			−1.02390			−0.511948	−	0.859017i	$-0.671076\pi$
$593$	−24.9335			−1.02390			−0.511948	+	0.859017i	$0.671076\pi$
$594$		0			0
$595$	1.08075	−	2.70024i	0.0443063	−	0.110699i
$596$		0			0
$597$	6.19405	−	4.50024i	0.253506	−	0.184183i
$598$		0			0
$599$	−24.4375			−0.998490			−0.499245	−	0.866461i	$-0.666389\pi$
$599$	−24.4375			−0.998490			−0.499245	+	0.866461i	$0.666389\pi$
$600$		0			0
$601$	−27.3066			−1.11386			−0.556930	−	0.830559i	$-0.688021\pi$
$601$	−27.3066			−1.11386			−0.556930	+	0.830559i	$0.688021\pi$
$602$		0			0
$603$	21.6113	−	15.7015i	0.880079	−	0.639414i
$604$		0			0
$605$	14.1015	+	11.7545i	0.573307	+	0.477887i
$606$		0			0
$607$	−24.4802			−0.993620			−0.496810	−	0.867859i	$-0.665495\pi$
$607$	−24.4802			−0.993620			−0.496810	+	0.867859i	$0.665495\pi$
$608$		0			0
$609$	0.810598	−	2.49477i	0.0328471	−	0.101093i
$610$		0			0
$611$	0.00561254	+	0.0172736i	0.000227059	+	0.000698816i
$612$		0			0
$613$	9.33170	−	28.7200i	0.376904	−	1.15999i	−0.565282	−	0.824898i	$-0.691232\pi$
$613$	9.33170	−	28.7200i	0.376904	−	1.15999i	0.942185	−	0.335092i	$-0.108768\pi$
$614$		0			0
$615$	15.7406	−	9.90726i	0.634722	−	0.399499i
$616$		0			0
$617$	8.16876	+	5.93495i	0.328862	+	0.238932i	0.739948	−	0.672665i	$-0.234850\pi$
$617$	8.16876	+	5.93495i	0.328862	+	0.238932i	−0.411086	+	0.911597i	$0.634850\pi$
$618$		0			0
$619$	1.85616	+	1.34858i	0.0746056	+	0.0542041i	0.624463	−	0.781054i	$-0.285318\pi$
$619$	1.85616	+	1.34858i	0.0746056	+	0.0542041i	−0.549857	+	0.835259i	$0.685318\pi$
$620$		0			0
$621$	−26.3813	+	19.1671i	−1.05864	+	0.769149i
$622$		0			0
$623$	−4.53300	−	13.9511i	−0.181611	−	0.558940i
$624$		0			0
$625$	13.7085	−	20.9064i	0.548341	−	0.836255i
$626$		0			0
$627$	5.43673	+	16.7325i	0.217122	+	0.668234i
$628$		0			0
$629$	0.178849	−	0.129942i	0.00713120	−	0.00518112i
$630$		0			0
$631$	0.984245	+	0.715096i	0.0391822	+	0.0284675i	0.607204	−	0.794546i	$-0.292291\pi$
$631$	0.984245	+	0.715096i	0.0391822	+	0.0284675i	−0.568022	+	0.823014i	$0.692291\pi$
$632$		0			0
$633$	−19.0995	−	13.8766i	−0.759137	−	0.551545i
$634$		0			0
$635$	9.41459	−	5.92562i	0.373606	−	0.235151i
$636$		0			0
$637$	−9.85255	+	30.3230i	−0.390372	+	1.20144i
$638$		0			0
$639$	10.8598	+	33.4230i	0.429606	+	1.32219i
$640$		0			0
$641$	5.20042	−	16.0053i	0.205404	−	0.632170i	−0.794292	−	0.607536i	$-0.792158\pi$
$641$	5.20042	−	16.0053i	0.205404	−	0.632170i	0.999697	−	0.0246337i	$-0.00784194\pi$
$642$		0			0
$643$	23.4446			0.924566			0.462283	−	0.886732i	$-0.347030\pi$
$643$	23.4446			0.924566			0.462283	+	0.886732i	$0.347030\pi$
$644$		0			0
$645$	−4.25710	−	3.54856i	−0.167623	−	0.139724i
$646$		0			0
$647$	8.72470	−	6.33886i	0.343003	−	0.249206i	−0.402925	−	0.915233i	$-0.632006\pi$
$647$	8.72470	−	6.33886i	0.343003	−	0.249206i	0.745928	+	0.666027i	$0.232006\pi$
$648$		0			0
$649$	−3.43728			−0.134925
$650$		0			0
$651$	87.2919			3.42124
$652$		0			0
$653$	−39.3900	+	28.6185i	−1.54145	+	1.11993i	−0.592029	+	0.805917i	$0.701673\pi$
$653$	−39.3900	+	28.6185i	−1.54145	+	1.11993i	−0.949419	+	0.314011i	$0.898327\pi$
$654$		0			0
$655$	−15.8519	+	39.6058i	−0.619384	+	1.54753i
$656$		0			0
$657$	15.3268			0.597956
$658$		0			0
$659$	12.2847	−	37.8085i	0.478545	−	1.47281i	−0.362571	−	0.931956i	$-0.618101\pi$
$659$	12.2847	−	37.8085i	0.478545	−	1.47281i	0.841116	−	0.540855i	$-0.181899\pi$
$660$		0			0
$661$	5.40244	+	16.6270i	0.210131	+	0.646716i	0.999464	+	0.0327502i	$0.0104266\pi$
$661$	5.40244	+	16.6270i	0.210131	+	0.646716i	−0.789333	+	0.613965i	$0.789573\pi$
$662$		0			0
$663$	−0.637834	+	1.96305i	−0.0247714	+	0.0762386i
$664$		0			0
$665$	14.1974	−	35.4721i	0.550552	−	1.37555i
$666$		0			0
$667$	−1.56180	−	1.13472i	−0.0604732	−	0.0439364i
$668$		0			0
$669$	21.3570	+	15.5167i	0.825708	+	0.599912i
$670$		0			0
$671$	15.4077	−	11.1944i	0.594808	−	0.432153i
$672$		0			0
$673$	−8.60639	−	26.4878i	−0.331752	−	1.02103i	−0.968300	−	0.249791i	$-0.919638\pi$
$673$	−8.60639	−	26.4878i	−0.331752	−	1.02103i	0.636548	−	0.771237i	$-0.280362\pi$
$674$		0			0
$675$	−13.4200	−	12.7916i	−0.516537	−	0.492350i
$676$		0			0
$677$	−3.01733	−	9.28639i	−0.115965	−	0.356905i	0.876182	−	0.481981i	$-0.160083\pi$
$677$	−3.01733	−	9.28639i	−0.115965	−	0.356905i	−0.992147	+	0.125076i	$0.960083\pi$
$678$		0			0
$679$	−38.4800	+	27.9573i	−1.47673	+	1.07290i
$680$		0			0
$681$	−19.0949	−	13.8733i	−0.731720	−	0.531626i
$682$		0			0
$683$	9.72632	+	7.06659i	0.372167	+	0.270395i	0.758109	−	0.652128i	$-0.226123\pi$
$683$	9.72632	+	7.06659i	0.372167	+	0.270395i	−0.385942	+	0.922523i	$0.626123\pi$
$684$		0			0
$685$	20.2833	+	1.35196i	0.774986	+	0.0516556i
$686$		0			0
$687$	−11.3782	+	35.0184i	−0.434104	+	1.33604i
$688$		0			0
$689$	9.04937	+	27.8511i	0.344754	+	1.06104i
$690$		0			0
$691$	5.57282	−	17.1514i	0.212000	−	0.652469i	−0.787353	−	0.616503i	$-0.788549\pi$
$691$	5.57282	−	17.1514i	0.212000	−	0.652469i	0.999353	−	0.0359667i	$-0.0114510\pi$
$692$		0			0
$693$	32.1102			1.21977
$694$		0			0
$695$	25.2348	−	15.8830i	0.957210	−	0.602477i
$696$		0			0
$697$	0.732460	−	0.532164i	0.0277439	−	0.0201571i
$698$		0			0
$699$	−42.6461			−1.61302
$700$		0			0
$701$	39.2938			1.48411			0.742053	−	0.670341i	$-0.233852\pi$
$701$	39.2938			1.48411			0.742053	+	0.670341i	$0.233852\pi$
$702$		0			0
$703$	2.34949	−	1.70700i	0.0886126	−	0.0643808i
$704$		0			0
$705$	−0.0427231	−	0.00284765i	−0.00160905	−	0.000107249i
$706$		0			0
$707$	48.8586			1.83752
$708$		0			0
$709$	−1.15852	+	3.56557i	−0.0435093	+	0.133908i	−0.970451	−	0.241296i	$-0.922427\pi$
$709$	−1.15852	+	3.56557i	−0.0435093	+	0.133908i	0.926942	+	0.375204i	$0.122427\pi$
$710$		0			0
$711$	−15.7236	−	48.3921i	−0.589679	−	1.81485i
$712$		0			0
$713$	19.8519	−	61.0977i	0.743458	−	2.28813i
$714$		0			0
$715$	−2.35645	−	9.32171i	−0.0881262	−	0.348612i
$716$		0			0
$717$	−47.4280	−	34.4585i	−1.77123	−	1.28688i
$718$		0			0
$719$	−14.5857	−	10.5971i	−0.543954	−	0.395206i	0.281597	−	0.959533i	$-0.409136\pi$
$719$	−14.5857	−	10.5971i	−0.543954	−	0.395206i	−0.825551	+	0.564327i	$0.809136\pi$
$720$		0			0
$721$	26.9618	−	19.5889i	1.00411	−	0.729529i
$722$		0			0
$723$	6.71239	+	20.6586i	0.249637	+	0.768302i
$724$		0			0
$725$	0.474708	−	0.989610i	0.0176302	−	0.0367532i
$726$		0			0
$727$	−10.9245	−	33.6221i	−0.405167	−	1.24697i	−0.920756	−	0.390139i	$-0.872427\pi$
$727$	−10.9245	−	33.6221i	−0.405167	−	1.24697i	0.515589	−	0.856836i	$-0.327573\pi$
$728$		0			0
$729$	35.1454	−	25.5346i	1.30168	−	0.945726i
$730$		0			0
$731$	−0.218259	−	0.158575i	−0.00807261	−	0.00586509i
$732$		0			0
$733$	2.82540	+	2.05278i	0.104359	+	0.0758210i	0.638741	−	0.769422i	$-0.279456\pi$
$733$	2.82540	+	2.05278i	0.104359	+	0.0758210i	−0.534382	+	0.845243i	$0.679456\pi$
$734$		0			0
$735$	−57.7367	−	48.1272i	−2.12965	−	1.77520i
$736$		0			0
$737$	−3.15795	+	9.71917i	−0.116325	+	0.358010i
$738$		0			0
$739$	7.31335	+	22.5082i	0.269026	+	0.827976i	0.990739	+	0.135784i	$0.0433552\pi$
$739$	7.31335	+	22.5082i	0.269026	+	0.827976i	−0.721713	+	0.692193i	$0.756645\pi$
$740$		0			0
$741$	−8.37902	+	25.7880i	−0.307811	+	0.947344i
$742$		0			0
$743$	−50.0459			−1.83601			−0.918003	−	0.396574i	$-0.870199\pi$
$743$	−50.0459			−1.83601			−0.918003	+	0.396574i	$0.870199\pi$
$744$		0			0
$745$	3.54612	+	14.0279i	0.129920	+	0.513941i
$746$		0			0
$747$	10.0763	−	7.32084i	0.368671	−	0.267855i
$748$		0			0
$749$	8.01440			0.292840
$750$		0			0
$751$	1.64636			0.0600765			0.0300383	−	0.999549i	$-0.490437\pi$
$751$	1.64636			0.0600765			0.0300383	+	0.999549i	$0.490437\pi$
$752$		0			0
$753$	−2.77106	+	2.01329i	−0.100983	+	0.0733685i
$754$		0			0
$755$	6.06134	+	23.9776i	0.220595	+	0.872636i
$756$		0			0
$757$	23.4001			0.850493			0.425246	−	0.905078i	$-0.360187\pi$
$757$	23.4001			0.850493			0.425246	+	0.905078i	$0.360187\pi$
$758$		0			0
$759$	12.3200	−	37.9171i	0.447188	−	1.37630i
$760$		0			0
$761$	15.2003	+	46.7816i	0.551010	+	1.69583i	0.706255	+	0.707957i	$0.250383\pi$
$761$	15.2003	+	46.7816i	0.551010	+	1.69583i	−0.155246	+	0.987876i	$0.549617\pi$
$762$		0			0
$763$	−16.2809	+	50.1075i	−0.589408	+	1.81401i
$764$		0			0
$765$	−2.21550	−	1.84675i	−0.0801014	−	0.0667695i
$766$		0			0
$767$	−4.28576	−	3.11379i	−0.154750	−	0.112432i
$768$		0			0
$769$	−26.0912	−	18.9564i	−0.940872	−	0.683584i	0.00775840	−	0.999970i	$-0.497530\pi$
$769$	−26.0912	−	18.9564i	−0.940872	−	0.683584i	−0.948630	+	0.316386i	$0.897530\pi$
$770$		0			0
$771$	−61.0848	+	44.3807i	−2.19992	+	1.59833i
$772$		0			0
$773$	2.46824	+	7.59646i	0.0887764	+	0.273226i	0.985582	−	0.169200i	$-0.0541182\pi$
$773$	2.46824	+	7.59646i	0.0887764	+	0.273226i	−0.896805	+	0.442425i	$0.854118\pi$
$774$		0			0
$775$	36.2015	+	4.84745i	1.30040	+	0.174126i
$776$		0			0
$777$	−2.76328	−	8.50451i	−0.0991323	−	0.305098i
$778$		0			0
$779$	9.62209	−	6.99086i	0.344747	−	0.250474i
$780$		0			0
$781$	−10.8767	−	7.90237i	−0.389198	−	0.282769i
$782$		0			0
$783$	−0.658502	−	0.478430i	−0.0235329	−	0.0170977i
$784$		0			0
$785$	3.43225	+	13.5774i	0.122502	+	0.484598i
$786$		0			0
$787$	−10.0798	+	31.0225i	−0.359307	+	1.10583i	0.594163	+	0.804345i	$0.297484\pi$
$787$	−10.0798	+	31.0225i	−0.359307	+	1.10583i	−0.953470	+	0.301489i	$0.902516\pi$
$788$		0			0
$789$	−15.1691	−	46.6856i	−0.540033	−	1.66205i
$790$		0			0
$791$	−16.3258	+	50.2456i	−0.580478	+	1.78653i
$792$		0			0
$793$	29.3518			1.04231
$794$		0			0
$795$	−68.8846	−	4.59140i	−2.44308	−	0.162840i
$796$		0			0
$797$	−39.2425	+	28.5113i	−1.39004	+	1.00992i	−0.394179	+	0.919034i	$0.628971\pi$
$797$	−39.2425	+	28.5113i	−1.39004	+	1.00992i	−0.995861	+	0.0908891i	$0.971029\pi$
$798$		0			0
$799$	−0.00208432			−7.37379e−5
$800$		0			0
$801$	−14.5469			−0.513988
$802$		0			0
$803$	−4.74362	+	3.44644i	−0.167399	+	0.121622i
$804$		0			0
$805$	−73.2754	+	46.1202i	−2.58262	+	1.62552i
$806$		0			0
$807$	33.1658			1.16749
$808$		0			0
$809$	9.07658	−	27.9348i	0.319116	−	0.982137i	−0.654912	−	0.755706i	$-0.727294\pi$
$809$	9.07658	−	27.9348i	0.319116	−	0.982137i	0.974027	−	0.226431i	$-0.0727059\pi$
$810$		0			0
$811$	−9.70579	−	29.8713i	−0.340816	−	1.04892i	−0.963786	−	0.266678i	$-0.914074\pi$
$811$	−9.70579	−	29.8713i	−0.340816	−	1.04892i	0.622969	−	0.782246i	$-0.285926\pi$
$812$		0			0
$813$	−0.666001	+	2.04974i	−0.0233577	+	0.0718876i
$814$		0			0
$815$	9.07056	+	0.604585i	0.317728	+	0.0211777i
$816$		0			0
$817$	−2.86720	−	2.08314i	−0.100311	−	0.0728800i
$818$		0			0
$819$	40.0365	+	29.0882i	1.39899	+	1.01642i
$820$		0			0
$821$	−34.0816	+	24.7617i	−1.18946	+	0.864190i	−0.993207	−	0.116364i	$-0.962876\pi$
$821$	−34.0816	+	24.7617i	−1.18946	+	0.864190i	−0.196249	+	0.980554i	$0.562876\pi$
$822$		0			0
$823$	−6.16667	−	18.9791i	−0.214957	−	0.661569i	−0.999157	−	0.0410605i	$-0.986926\pi$
$823$	−6.16667	−	18.9791i	−0.214957	−	0.661569i	0.784200	−	0.620508i	$-0.213074\pi$
$824$		0			0
$825$	22.4665	+	3.00831i	0.782184	+	0.104736i
$826$		0			0
$827$	−4.30442	−	13.2476i	−0.149679	−	0.460666i	0.847904	−	0.530150i	$-0.177865\pi$
$827$	−4.30442	−	13.2476i	−0.149679	−	0.460666i	−0.997583	+	0.0694845i	$0.977865\pi$
$828$		0			0
$829$	21.5627	−	15.6662i	0.748902	−	0.544109i	−0.146584	−	0.989198i	$-0.546828\pi$
$829$	21.5627	−	15.6662i	0.748902	−	0.544109i	0.895486	+	0.445089i	$0.146828\pi$
$830$		0			0
$831$	56.7654	+	41.2425i	1.96917	+	1.43069i
$832$		0			0
$833$	−2.96013	−	2.15066i	−0.102562	−	0.0745160i
$834$		0			0
$835$	16.4476	−	41.0943i	0.569194	−	1.42213i
$836$		0			0
$837$	8.37013	−	25.7606i	0.289314	−	0.890417i
$838$		0			0
$839$	−10.2268	−	31.4748i	−0.353067	−	1.08663i	−0.957122	−	0.289686i	$-0.906449\pi$
$839$	−10.2268	−	31.4748i	−0.353067	−	1.08663i	0.604054	−	0.796943i	$-0.293551\pi$
$840$		0			0
$841$	−8.94660	+	27.5348i	−0.308504	+	0.949476i
$842$		0			0
$843$	47.6367			1.64069
$844$		0			0
$845$	−5.29525	+	13.2301i	−0.182162	+	0.455130i
$846$		0			0
$847$	29.2440	−	21.2470i	1.00484	−	0.730056i
$848$		0			0
$849$	22.6053			0.775813
$850$		0			0
$851$	−6.58094			−0.225592
$852$		0			0
$853$	13.9610	−	10.1433i	0.478017	−	0.347300i	−0.322541	−	0.946556i	$-0.604537\pi$
$853$	13.9610	−	10.1433i	0.478017	−	0.347300i	0.800557	+	0.599256i	$0.204537\pi$
$854$		0			0
$855$	−29.1042	−	24.2602i	−0.995344	−	0.829682i
$856$		0			0
$857$	−33.6214			−1.14849			−0.574243	−	0.818685i	$-0.694704\pi$
$857$	−33.6214			−1.14849			−0.574243	+	0.818685i	$0.694704\pi$
$858$		0			0
$859$	−3.08649	+	9.49923i	−0.105310	+	0.324110i	−0.989803	−	0.142443i	$-0.954504\pi$
$859$	−3.08649	+	9.49923i	−0.105310	+	0.324110i	0.884493	+	0.466553i	$0.154504\pi$
$860$		0			0
$861$	−11.3168	−	34.8294i	−0.385674	−	1.18698i
$862$		0			0
$863$	15.2688	−	46.9925i	0.519756	−	1.59964i	−0.254703	−	0.967019i	$-0.581978\pi$
$863$	15.2688	−	46.9925i	0.519756	−	1.59964i	0.774459	−	0.632625i	$-0.218022\pi$
$864$		0			0
$865$	−2.46435	+	1.55108i	−0.0837905	+	0.0527385i
$866$		0			0
$867$	37.1358	+	26.9807i	1.26120	+	0.916314i
$868$		0			0
$869$	15.7480	+	11.4416i	0.534215	+	0.388130i
$870$		0			0
$871$	−12.7419	+	9.25755i	−0.431744	+	0.313680i
$872$		0			0
$873$	14.5756	+	44.8590i	0.493309	+	1.51825i
$874$		0			0
$875$	−33.2944	−	36.2581i	−1.12556	−	1.22575i
$876$		0			0
$877$	−0.0171184	−	0.0526851i	−0.000578048	−	0.00177905i	0.950767	−	0.309906i	$-0.100298\pi$
$877$	−0.0171184	−	0.0526851i	−0.000578048	−	0.00177905i	−0.951345	+	0.308127i	$0.900298\pi$
$878$		0			0
$879$	40.6233	−	29.5146i	1.37019	−	0.995502i
$880$		0			0
$881$	−34.5433	−	25.0972i	−1.16379	−	0.845546i	−0.173541	−	0.984827i	$-0.555521\pi$
$881$	−34.5433	−	25.0972i	−1.16379	−	0.845546i	−0.990253	+	0.139281i	$0.955521\pi$
$882$		0			0
$883$	19.2078	+	13.9553i	0.646394	+	0.469633i	0.862041	−	0.506839i	$-0.169186\pi$
$883$	19.2078	+	13.9553i	0.646394	+	0.469633i	−0.215647	+	0.976471i	$0.569186\pi$
$884$		0			0
$885$	10.5694	−	6.65249i	0.355287	−	0.223621i
$886$		0			0
$887$	10.1905	−	31.3633i	0.342165	−	1.05308i	−0.620919	−	0.783875i	$-0.713240\pi$
$887$	10.1905	−	31.3633i	0.342165	−	1.05308i	0.963084	−	0.269201i	$-0.0867596\pi$
$888$		0			0
$889$	−6.76865	−	20.8318i	−0.227013	−	0.698675i
$890$		0			0
$891$	−1.56651	+	4.82123i	−0.0524801	+	0.161517i
$892$		0			0
$893$	−0.0273810			−0.000916271
$894$		0			0
$895$	36.7188	+	30.6075i	1.22738	+	1.02309i
$896$		0			0
$897$	49.7097	−	36.1162i	1.65976	−	1.20588i
$898$		0			0
$899$	1.60354			0.0534811
$900$		0			0
$901$	−3.36065			−0.111959
$902$		0			0
$903$	−8.82848	+	6.41426i	−0.293793	+	0.213453i
$904$		0			0
$905$	12.6343	−	31.5667i	0.419978	−	1.04931i
$906$		0			0
$907$	−7.31372			−0.242848			−0.121424	−	0.992601i	$-0.538746\pi$
$907$	−7.31372			−0.242848			−0.121424	+	0.992601i	$0.538746\pi$
$908$		0			0
$909$	14.9724	−	46.0802i	0.496602	−	1.52838i
$910$		0			0
$911$	−5.68376	−	17.4928i	−0.188311	−	0.579563i	0.811678	−	0.584105i	$-0.198554\pi$
$911$	−5.68376	−	17.4928i	−0.188311	−	0.579563i	−0.999990	+	0.00454173i	$0.998554\pi$
$912$		0			0
$913$	−1.47240	+	4.53157i	−0.0487292	+	0.149973i
$914$		0			0
$915$	−25.7123	+	64.2419i	−0.850022	+	2.12377i
$916$		0			0
$917$	67.9568	+	49.3735i	2.24413	+	1.63046i
$918$		0			0
$919$	28.3447	+	20.5936i	0.935004	+	0.679320i	0.947213	−	0.320605i	$-0.103886\pi$
$919$	28.3447	+	20.5936i	0.935004	+	0.679320i	−0.0122089	+	0.999925i	$0.503886\pi$
$920$		0			0
$921$	5.19738	−	3.77611i	0.171259	−	0.124427i
$922$		0			0
$923$	−6.40289	−	19.7061i	−0.210754	−	0.648633i
$924$		0			0
$925$	−0.673714	−	3.68042i	−0.0221516	−	0.121012i
$926$		0			0
$927$	−10.2127	−	31.4314i	−0.335429	−	1.03234i
$928$		0			0
$929$	−12.3232	+	8.95336i	−0.404312	+	0.293750i	−0.771295	−	0.636478i	$-0.780391\pi$
$929$	−12.3232	+	8.95336i	−0.404312	+	0.293750i	0.366983	+	0.930228i	$0.380391\pi$
$930$		0			0
$931$	−38.8863	−	28.2525i	−1.27445	−	0.925940i
$932$		0			0
$933$	−13.2857	−	9.65262i	−0.434954	−	0.316013i
$934$		0			0
$935$	1.10096	+	0.0733828i	0.0360052	+	0.00239987i
$936$		0			0
$937$	−1.33342	+	4.10386i	−0.0435611	+	0.134067i	−0.970472	−	0.241215i	$-0.922454\pi$
$937$	−1.33342	+	4.10386i	−0.0435611	+	0.134067i	0.926911	+	0.375282i	$0.122454\pi$
$938$		0			0
$939$	−20.5815	−	63.3434i	−0.671652	−	2.06713i
$940$		0			0
$941$	5.84704	−	17.9953i	0.190608	−	0.586631i	−0.809392	−	0.587269i	$-0.800203\pi$
$941$	5.84704	−	17.9953i	0.190608	−	0.586631i	1.00000		0.000637969i	$0.000203072\pi$
$942$		0			0
$943$	−26.9516			−0.877665
$944$		0			0
$945$	−30.8951	+	19.4456i	−1.00502	+	0.632566i
$946$		0			0
$947$	14.1171	−	10.2567i	0.458745	−	0.333298i	−0.334293	−	0.942469i	$-0.608498\pi$
$947$	14.1171	−	10.2567i	0.458745	−	0.333298i	0.793039	+	0.609171i	$0.208498\pi$
$948$		0			0
$949$	−9.03664			−0.293342
$950$		0			0
$951$	−6.57643			−0.213255
$952$		0			0
$953$	−29.3862	+	21.3503i	−0.951912	+	0.691605i	−0.951258	−	0.308395i	$-0.900208\pi$
$953$	−29.3862	+	21.3503i	−0.951912	+	0.691605i	−0.000653920		1.00000i	$0.500208\pi$
$954$		0			0
$955$	35.9757	+	2.39791i	1.16415	+	0.0775946i
$956$		0			0
$957$	0.995153			0.0321687
$958$		0			0
$959$	12.3690	−	38.0680i	0.399417	−	1.22928i
$960$		0			0
$961$	6.91020	+	21.2674i	0.222910	+	0.686045i
$962$		0			0
$963$	2.45595	−	7.55864i	0.0791419	−	0.243574i
$964$		0			0
$965$	5.67514	+	22.4499i	0.182689	+	0.722687i
$966$		0			0
$967$	29.1294	+	21.1638i	0.936740	+	0.680581i	0.947634	−	0.319359i	$-0.103468\pi$
$967$	29.1294	+	21.1638i	0.936740	+	0.680581i	−0.0108940	+	0.999941i	$0.503468\pi$
$968$		0			0
$969$	−2.51742	−	1.82901i	−0.0808711	−	0.0587563i
$970$		0			0
$971$	3.15763	−	2.29415i	0.101333	−	0.0736229i	−0.535965	−	0.844240i	$-0.680052\pi$
$971$	3.15763	−	2.29415i	0.101333	−	0.0736229i	0.637298	+	0.770617i	$0.280052\pi$
$972$		0			0
$973$	−18.1427	−	55.8374i	−0.581627	−	1.79006i
$974$		0			0
$975$	25.2871	+	24.1030i	0.809835	+	0.771914i
$976$		0			0
$977$	−13.6318	−	41.9543i	−0.436119	−	1.34224i	−0.891936	−	0.452162i	$-0.850653\pi$
$977$	−13.6318	−	41.9543i	−0.436119	−	1.34224i	0.455817	−	0.890074i	$-0.349347\pi$
$978$		0			0
$979$	4.50223	−	3.27106i	0.143892	−	0.104544i
$980$		0			0
$981$	42.2688	+	30.7101i	1.34954	+	0.980498i
$982$		0			0
$983$	27.2785	+	19.8190i	0.870048	+	0.632127i	0.930600	−	0.366038i	$-0.119286\pi$
$983$	27.2785	+	19.8190i	0.870048	+	0.632127i	−0.0605518	+	0.998165i	$0.519286\pi$
$984$		0			0
$985$	−34.5202	−	28.7747i	−1.09990	−	0.916839i
$986$		0			0
$987$	−0.0260531	+	0.0801833i	−0.000829280	+	0.00255226i
$988$		0			0
$989$	2.48174	+	7.63800i	0.0789146	+	0.242874i
$990$		0			0
$991$	5.66357	−	17.4307i	0.179909	−	0.553704i	−0.819914	−	0.572486i	$-0.805979\pi$
$991$	5.66357	−	17.4307i	0.179909	−	0.553704i	0.999824	+	0.0187824i	$0.00597896\pi$
$992$		0			0
$993$	41.5722			1.31925
$994$		0			0
$995$	−1.54594	−	6.11546i	−0.0490095	−	0.193873i
$996$		0			0
$997$	40.7197	−	29.5846i	1.28961	−	0.936954i	0.289810	−	0.957084i	$-0.406408\pi$
$997$	40.7197	−	29.5846i	1.28961	−	0.936954i	0.999797	+	0.0201300i	$0.00640800\pi$
$998$		0			0
$999$	−2.77472			−0.0877882

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.u.f.81.1		12
4.3	odd	2		100.2.g.a.81.3	yes	12
12.11	even	2		900.2.n.c.181.1		12
20.3	even	4		500.2.i.b.349.5		24
20.7	even	4		500.2.i.b.349.2		24
20.19	odd	2		500.2.g.a.401.1		12
25.11	even	5		10000.2.a.bc.1.6		6
25.14	even	10		10000.2.a.bd.1.1		6
25.21	even	5	inner	400.2.u.f.321.1		12
100.3	even	20		500.2.i.b.149.2		24
100.11	odd	10		2500.2.a.d.1.1		6
100.23	even	20		2500.2.c.c.1249.3		12
100.27	even	20		2500.2.c.c.1249.10		12
100.39	odd	10		2500.2.a.c.1.6		6
100.47	even	20		500.2.i.b.149.5		24
100.71	odd	10		100.2.g.a.21.3	✓	12
100.79	odd	10		500.2.g.a.101.1		12
300.71	even	10		900.2.n.c.721.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.g.a.21.3	✓	12	100.71	odd	10
100.2.g.a.81.3	yes	12	4.3	odd	2
400.2.u.f.81.1		12	1.1	even	1	trivial
400.2.u.f.321.1		12	25.21	even	5	inner
500.2.g.a.101.1		12	100.79	odd	10
500.2.g.a.401.1		12	20.19	odd	2
500.2.i.b.149.2		24	100.3	even	20
500.2.i.b.149.5		24	100.47	even	20
500.2.i.b.349.2		24	20.7	even	4
500.2.i.b.349.5		24	20.3	even	4
900.2.n.c.181.1		12	12.11	even	2
900.2.n.c.721.1		12	300.71	even	10
2500.2.a.c.1.6		6	100.39	odd	10
2500.2.a.d.1.1		6	100.11	odd	10
2500.2.c.c.1249.3		12	100.23	even	20
2500.2.c.c.1249.10		12	100.27	even	20
10000.2.a.bc.1.6		6	25.11	even	5
10000.2.a.bd.1.1		6	25.14	even	10

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.19573 + 1.59529i) q^{3} +(0.548020 + 2.16787i) q^{5} +4.40288 q^{7} +(1.34923 - 4.15250i) q^{9} +O(q^{10})\)	\(q+(-2.19573 + 1.59529i) q^{3} +(0.548020 + 2.16787i) q^{5} +4.40288 q^{7} +(1.34923 - 4.15250i) q^{9} +(0.516162 + 1.58858i) q^{11} +(-0.795501 + 2.44830i) q^{13} +(-4.66170 - 3.88582i) q^{15} +(-0.239003 - 0.173646i) q^{17} +(-3.13970 - 2.28113i) q^{19} +(-9.66754 + 7.02388i) q^{21} +(2.71760 + 8.36392i) q^{23} +(-4.39935 + 2.37607i) q^{25} +(1.14582 + 3.52647i) q^{27} +(-0.177592 + 0.129028i) q^{29} +(-5.90981 - 4.29372i) q^{31} +(-3.66761 - 2.66467i) q^{33} +(2.41286 + 9.54488i) q^{35} +(-0.231242 + 0.711690i) q^{37} +(-2.15905 - 6.64487i) q^{39} +(-0.947030 + 2.91466i) q^{41} +0.913208 q^{43} +(9.74149 + 0.649305i) q^{45} +(0.00570791 - 0.00414704i) q^{47} +12.3853 q^{49} +0.801802 q^{51} +(9.20313 - 6.68646i) q^{53} +(-3.16098 + 1.98955i) q^{55} +10.5330 q^{57} +(-0.635908 + 1.95712i) q^{59} +(-3.52338 - 10.8438i) q^{61} +(5.94049 - 18.2829i) q^{63} +(-5.74355 - 0.382828i) q^{65} +(4.94968 + 3.59615i) q^{67} +(-19.3100 - 14.0295i) q^{69} +(-6.51168 + 4.73101i) q^{71} +(1.08475 + 3.33853i) q^{73} +(5.86925 - 12.2355i) q^{75} +(2.27260 + 6.99434i) q^{77} +(9.42807 - 6.84989i) q^{79} +(2.45531 + 1.78388i) q^{81} +(2.30779 + 1.67671i) q^{83} +(0.245464 - 0.613289i) q^{85} +(0.184106 - 0.566621i) q^{87} +(-1.02955 - 3.16864i) q^{89} +(-3.50249 + 10.7796i) q^{91} +19.8261 q^{93} +(3.22458 - 8.05658i) q^{95} +(-8.73973 + 6.34979i) q^{97} +7.29301 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} - 4 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q - 2 * q^3 - 4 * q^5 + 2 * q^7 - 3 * q^9	\( 12 q - 2 q^{3} - 4 q^{5} + 2 q^{7} - 3 q^{9} + 5 q^{11} - 2 q^{13} - 18 q^{15} + q^{17} + 8 q^{19} + 2 q^{21} + 6 q^{23} - 26 q^{25} + 34 q^{27} - 18 q^{29} - 12 q^{31} - 35 q^{33} + 3 q^{35} + 13 q^{37} - 22 q^{39} - 23 q^{41} - 50 q^{43} + 71 q^{45} - q^{47} + 34 q^{49} - 14 q^{51} + 21 q^{53} - 5 q^{55} + 72 q^{57} - 9 q^{59} - 26 q^{61} + 32 q^{63} - 18 q^{65} + 37 q^{67} - 44 q^{69} - 21 q^{71} + 18 q^{73} + 73 q^{75} - 60 q^{77} + 24 q^{79} + 18 q^{81} + 46 q^{83} - 16 q^{85} - 57 q^{87} - 2 q^{89} + 32 q^{91} + 22 q^{93} - 6 q^{95} - 7 q^{97} - 40 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 - 4 * q^5 + 2 * q^7 - 3 * q^9 + 5 * q^11 - 2 * q^13 - 18 * q^15 + q^17 + 8 * q^19 + 2 * q^21 + 6 * q^23 - 26 * q^25 + 34 * q^27 - 18 * q^29 - 12 * q^31 - 35 * q^33 + 3 * q^35 + 13 * q^37 - 22 * q^39 - 23 * q^41 - 50 * q^43 + 71 * q^45 - q^47 + 34 * q^49 - 14 * q^51 + 21 * q^53 - 5 * q^55 + 72 * q^57 - 9 * q^59 - 26 * q^61 + 32 * q^63 - 18 * q^65 + 37 * q^67 - 44 * q^69 - 21 * q^71 + 18 * q^73 + 73 * q^75 - 60 * q^77 + 24 * q^79 + 18 * q^81 + 46 * q^83 - 16 * q^85 - 57 * q^87 - 2 * q^89 + 32 * q^91 + 22 * q^93 - 6 * q^95 - 7 * q^97 - 40 * q^99

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