LMFDB - Embedded newform 44.3.f.a.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [44,3,Mod(13,44)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(44, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("44.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 44 = 2^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	44.f (of order $10$, degree $4$, 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:	$1.19891316319$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 19x^{6} - 37x^{5} + 229x^{4} + 196x^{3} + 1496x^{2} + 2952x + 26896 $ x^8 - x^7 + 19x^6 - 37x^5 + 229x^4 + 196x^3 + 1496x^2 + 2952x + 26896
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			41.1
Root			$-2.28040 - 1.65680i$ of defining polynomial
Character	$\chi$	$=$	44.41
Dual form			44.3.f.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37103 - 4.21961i) q^{3} +(-5.30779 - 3.85634i) q^{5} +(10.9532 + 3.55892i) q^{7} +(-8.64421 + 6.28038i) q^{9} +(9.32350 - 5.83715i) q^{11} +(2.97320 + 4.09226i) q^{13} +(-8.99507 + 27.6840i) q^{15} +(-5.03681 + 6.93258i) q^{17} +(-10.3045 + 3.34815i) q^{19} -51.0977i q^{21} +11.7519 q^{23} +(5.57590 + 17.1609i) q^{25} +(6.04753 + 4.39379i) q^{27} +(19.2505 + 6.25487i) q^{29} +(29.4488 - 21.3958i) q^{31} +(-37.4133 - 31.3386i) q^{33} +(-44.4130 - 61.1293i) q^{35} +(-11.4023 + 35.0927i) q^{37} +(13.1914 - 18.1564i) q^{39} +(-40.3205 + 13.1009i) q^{41} +72.4430i q^{43} +70.1009 q^{45} +(-3.37433 - 10.3851i) q^{47} +(67.6654 + 49.1618i) q^{49} +(36.1584 + 11.7486i) q^{51} +(-58.4943 + 42.4986i) q^{53} +(-71.9972 - 4.97215i) q^{55} +(28.2557 + 38.8907i) q^{57} +(1.38239 - 4.25455i) q^{59} +(63.8606 - 87.8965i) q^{61} +(-117.033 + 38.0264i) q^{63} -33.1866i q^{65} -37.6104 q^{67} +(-16.1123 - 49.5886i) q^{69} +(43.3875 + 31.5228i) q^{71} +(-23.7259 - 7.70902i) q^{73} +(64.7673 - 47.0562i) q^{75} +(122.896 - 30.7541i) q^{77} +(-41.8941 - 57.6623i) q^{79} +(-19.4674 + 59.9146i) q^{81} +(6.78240 - 9.33518i) q^{83} +(53.4687 - 17.3730i) q^{85} -89.8052i q^{87} -75.6980 q^{89} +(18.0021 + 55.4048i) q^{91} +(-130.657 - 94.9280i) q^{93} +(67.6059 + 21.9665i) q^{95} +(-2.41589 + 1.75525i) q^{97} +(-43.9347 + 109.013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{3} - q^{5} + 15 q^{7} - q^{9} + 17 q^{11} - 15 q^{13} - 63 q^{15} - 75 q^{17} - 30 q^{19} + 100 q^{23} + 51 q^{25} + 100 q^{27} + 125 q^{29} + 73 q^{31} - 20 q^{33} - 155 q^{35} - 75 q^{37}+ \cdots - 419 q^{99}+O(q^{100}) $ 8 * q - 5 * q^3 - q^5 + 15 * q^7 - q^9 + 17 * q^11 - 15 * q^13 - 63 * q^15 - 75 * q^17 - 30 * q^19 + 100 * q^23 + 51 * q^25 + 100 * q^27 + 125 * q^29 + 73 * q^31 - 20 * q^33 - 155 * q^35 - 75 * q^37 - 185 * q^39 - 155 * q^41 + 332 * q^45 + 45 * q^47 + 87 * q^49 + 150 * q^51 - 85 * q^53 - 89 * q^55 - 310 * q^57 - 178 * q^59 - 145 * q^61 - 110 * q^63 + 10 * q^67 + 124 * q^69 + 207 * q^71 + 65 * q^73 + 192 * q^75 + 365 * q^77 + 235 * q^79 - 12 * q^81 + 210 * q^83 + 105 * q^85 + 18 * q^89 - 195 * q^91 - 335 * q^93 - 255 * q^95 - 90 * q^97 - 419 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/44\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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
$3$	−1.37103	−	4.21961i	−0.457011	−	1.40654i	−0.868758	−	0.495238i	$-0.835081\pi$
$3$	−1.37103	−	4.21961i	−0.457011	−	1.40654i	0.411746	−	0.911298i	$-0.364919\pi$
$4$		0			0
$5$	−5.30779	−	3.85634i	−1.06156	−	0.771267i	−0.0871824	−	0.996192i	$-0.527786\pi$
$5$	−5.30779	−	3.85634i	−1.06156	−	0.771267i	−0.974376	+	0.224925i	$0.927786\pi$
$6$		0			0
$7$	10.9532	+	3.55892i	1.56475	+	0.508417i	0.958070	−	0.286533i	$-0.0925027\pi$
$7$	10.9532	+	3.55892i	1.56475	+	0.508417i	0.606676	+	0.794950i	$0.292503\pi$
$8$		0			0
$9$	−8.64421	+	6.28038i	−0.960467	+	0.697820i
$10$		0			0
$11$	9.32350	−	5.83715i	0.847591	−	0.530650i
$11$	9.32350	−	5.83715i	0.847591	−	0.530650i
$12$		0			0
$13$	2.97320	+	4.09226i	0.228708	+	0.314789i	0.907913	−	0.419159i	$-0.137675\pi$
$13$	2.97320	+	4.09226i	0.228708	+	0.314789i	−0.679205	+	0.733949i	$0.737675\pi$
$14$		0			0
$15$	−8.99507	+	27.6840i	−0.599671	+	1.84560i
$16$		0			0
$17$	−5.03681	+	6.93258i	−0.296283	+	0.407799i	−0.931042	−	0.364911i	$-0.881099\pi$
$17$	−5.03681	+	6.93258i	−0.296283	+	0.407799i	0.634759	+	0.772710i	$0.281099\pi$
$18$		0			0
$19$	−10.3045	+	3.34815i	−0.542344	+	0.176218i	−0.567362	−	0.823469i	$-0.692036\pi$
$19$	−10.3045	+	3.34815i	−0.542344	+	0.176218i	0.0250177	+	0.999687i	$0.492036\pi$
$20$		0			0
$21$		−	51.0977i		−	2.43322i
$22$		0			0
$23$	11.7519			0.510954			0.255477	−	0.966815i	$-0.417768\pi$
$23$	11.7519			0.510954			0.255477	+	0.966815i	$0.417768\pi$
$24$		0			0
$25$	5.57590	+	17.1609i	0.223036	+	0.686434i
$26$		0			0
$27$	6.04753	+	4.39379i	0.223983	+	0.162733i
$28$		0			0
$29$	19.2505	+	6.25487i	0.663810	+	0.215685i	0.621494	−	0.783419i	$-0.286526\pi$
$29$	19.2505	+	6.25487i	0.663810	+	0.215685i	0.0423166	+	0.999104i	$0.486526\pi$
$30$		0			0
$31$	29.4488	−	21.3958i	0.949961	−	0.690187i	−0.000836644	−	1.00000i	$-0.500266\pi$
$31$	29.4488	−	21.3958i	0.949961	−	0.690187i	0.950798	+	0.309813i	$0.100266\pi$
$32$		0			0
$33$	−37.4133	−	31.3386i	−1.13374	−	0.949654i
$34$		0			0
$35$	−44.4130	−	61.1293i	−1.26894	−	1.74655i
$36$		0			0
$37$	−11.4023	+	35.0927i	−0.308170	+	0.948450i	0.670305	+	0.742086i	$0.266163\pi$
$37$	−11.4023	+	35.0927i	−0.308170	+	0.948450i	−0.978475	+	0.206365i	$0.933837\pi$
$38$		0			0
$39$	13.1914	−	18.1564i	0.338241	−	0.465548i
$40$		0			0
$41$	−40.3205	+	13.1009i	−0.983426	+	0.319534i	−0.756224	−	0.654313i	$-0.772958\pi$
$41$	−40.3205	+	13.1009i	−0.983426	+	0.319534i	−0.227202	+	0.973848i	$0.572958\pi$
$42$		0			0
$43$			72.4430i			1.68472i	0.538915	+	0.842360i	$0.318835\pi$
$43$			72.4430i			1.68472i	−0.538915	+	0.842360i	$0.681165\pi$
$44$		0			0
$45$	70.1009			1.55780
$46$		0			0
$47$	−3.37433	−	10.3851i	−0.0717943	−	0.220960i	0.908721	−	0.417405i	$-0.137060\pi$
$47$	−3.37433	−	10.3851i	−0.0717943	−	0.220960i	−0.980515	+	0.196445i	$0.937060\pi$
$48$		0			0
$49$	67.6654	+	49.1618i	1.38093	+	1.00330i
$50$		0			0
$51$	36.1584	+	11.7486i	0.708989	+	0.230364i
$52$		0			0
$53$	−58.4943	+	42.4986i	−1.10367	+	0.801860i	−0.981654	−	0.190668i	$-0.938934\pi$
$53$	−58.4943	+	42.4986i	−1.10367	+	0.801860i	−0.122011	+	0.992529i	$0.538934\pi$
$54$		0			0
$55$	−71.9972	−	4.97215i	−1.30904	−	0.0904028i
$56$		0			0
$57$	28.2557	+	38.8907i	0.495714	+	0.682292i
$58$		0			0
$59$	1.38239	−	4.25455i	0.0234303	−	0.0721110i	−0.938658	−	0.344850i	$-0.887930\pi$
$59$	1.38239	−	4.25455i	0.0234303	−	0.0721110i	0.962088	+	0.272739i	$0.0879297\pi$
$60$		0			0
$61$	63.8606	−	87.8965i	1.04689	−	1.44093i	0.155424	−	0.987848i	$-0.450326\pi$
$61$	63.8606	−	87.8965i	1.04689	−	1.44093i	0.891470	−	0.453079i	$-0.149674\pi$
$62$		0			0
$63$	−117.033	+	38.0264i	−1.85767	+	0.603594i
$64$		0			0
$65$		−	33.1866i		−	0.510562i
$66$		0			0
$67$	−37.6104			−0.561349			−0.280674	−	0.959803i	$-0.590558\pi$
$67$	−37.6104			−0.561349			−0.280674	+	0.959803i	$0.590558\pi$
$68$		0			0
$69$	−16.1123	−	49.5886i	−0.233512	−	0.718675i
$70$		0			0
$71$	43.3875	+	31.5228i	0.611091	+	0.443984i	0.849798	−	0.527108i	$-0.176724\pi$
$71$	43.3875	+	31.5228i	0.611091	+	0.443984i	−0.238707	+	0.971092i	$0.576724\pi$
$72$		0			0
$73$	−23.7259	−	7.70902i	−0.325013	−	0.105603i	0.141966	−	0.989872i	$-0.454658\pi$
$73$	−23.7259	−	7.70902i	−0.325013	−	0.105603i	−0.466979	+	0.884269i	$0.654658\pi$
$74$		0			0
$75$	64.7673	−	47.0562i	0.863564	−	0.627416i
$76$		0			0
$77$	122.896	−	30.7541i	1.59606	−	0.399404i
$78$		0			0
$79$	−41.8941	−	57.6623i	−0.530305	−	0.729903i	0.456872	−	0.889533i	$-0.348970\pi$
$79$	−41.8941	−	57.6623i	−0.530305	−	0.729903i	−0.987177	+	0.159630i	$0.948970\pi$
$80$		0			0
$81$	−19.4674	+	59.9146i	−0.240339	+	0.739686i
$82$		0			0
$83$	6.78240	−	9.33518i	0.0817157	−	0.112472i	−0.766202	−	0.642600i	$-0.777856\pi$
$83$	6.78240	−	9.33518i	0.0817157	−	0.112472i	0.847918	+	0.530127i	$0.177856\pi$
$84$		0			0
$85$	53.4687	−	17.3730i	0.629044	−	0.204389i
$86$		0			0
$87$		−	89.8052i		−	1.03224i
$88$		0			0
$89$	−75.6980			−0.850540			−0.425270	−	0.905067i	$-0.639821\pi$
$89$	−75.6980			−0.850540			−0.425270	+	0.905067i	$0.639821\pi$
$90$		0			0
$91$	18.0021	+	55.4048i	0.197826	+	0.608844i
$92$		0			0
$93$	−130.657	−	94.9280i	−1.40492	−	1.02073i
$94$		0			0
$95$	67.6059	+	21.9665i	0.711641	+	0.231226i
$96$		0			0
$97$	−2.41589	+	1.75525i	−0.0249061	+	0.0180953i	−0.600169	−	0.799873i	$-0.704900\pi$
$97$	−2.41589	+	1.75525i	−0.0249061	+	0.0180953i	0.575263	+	0.817969i	$0.304900\pi$
$98$		0			0
$99$	−43.9347	+	109.013i	−0.443785	+	1.10114i
$100$		0			0
$101$	26.1228	+	35.9549i	0.258641	+	0.355989i	0.918514	−	0.395388i	$-0.129390\pi$
$101$	26.1228	+	35.9549i	0.258641	+	0.355989i	−0.659873	+	0.751377i	$0.729390\pi$
$102$		0			0
$103$	16.6882	−	51.3610i	0.162021	−	0.498650i	−0.836783	−	0.547534i	$-0.815567\pi$
$103$	16.6882	−	51.3610i	0.162021	−	0.498650i	0.998804	+	0.0488842i	$0.0155665\pi$
$104$		0			0
$105$	−197.050	+	271.216i	−1.87667	+	2.58301i
$106$		0			0
$107$	124.961	−	40.6022i	1.16786	−	0.379460i	0.340015	−	0.940420i	$-0.389568\pi$
$107$	124.961	−	40.6022i	1.16786	−	0.379460i	0.827843	+	0.560960i	$0.189568\pi$
$108$		0			0
$109$		−	6.96523i		−	0.0639012i	−0.999489	−	0.0319506i	$-0.989828\pi$
$109$		−	6.96523i		−	0.0639012i	0.999489	−	0.0319506i	$-0.0101719\pi$
$110$		0			0
$111$	163.710			1.47487
$112$		0			0
$113$	16.8926	+	51.9900i	0.149492	+	0.460089i	0.997561	−	0.0697966i	$-0.0222350\pi$
$113$	16.8926	+	51.9900i	0.149492	+	0.460089i	−0.848069	+	0.529885i	$0.822235\pi$
$114$		0			0
$115$	−62.3768	−	45.3194i	−0.542407	−	0.394082i
$116$		0			0
$117$	−51.4020	−	16.7015i	−0.439333	−	0.142748i
$118$		0			0
$119$	−79.8418	+	58.0085i	−0.670940	+	0.487466i
$120$		0			0
$121$	52.8553	−	108.845i	0.436820	−	0.899549i
$122$		0			0
$123$	110.561	+	152.175i	0.898874	+	1.23719i
$124$		0			0
$125$	−14.1026	+	43.4033i	−0.112821	+	0.347226i
$126$		0			0
$127$	−4.79238	+	6.59615i	−0.0377353	+	0.0519382i	−0.827468	−	0.561513i	$-0.810219\pi$
$127$	−4.79238	+	6.59615i	−0.0377353	+	0.0519382i	0.789732	+	0.613451i	$0.210219\pi$
$128$		0			0
$129$	305.681	−	99.3218i	2.36962	−	0.769936i
$130$		0			0
$131$			162.483i			1.24033i	0.784473	+	0.620163i	$0.212934\pi$
$131$			162.483i			1.24033i	−0.784473	+	0.620163i	$0.787066\pi$
$132$		0			0
$133$	−124.784			−0.938223
$134$		0			0
$135$	−15.1551	−	46.6427i	−0.112260	−	0.345501i
$136$		0			0
$137$	−190.008	−	138.049i	−1.38692	−	1.00766i	−0.996195	−	0.0871507i	$-0.972224\pi$
$137$	−190.008	−	138.049i	−1.38692	−	1.00766i	−0.390726	−	0.920507i	$-0.627776\pi$
$138$		0			0
$139$	−225.896	−	73.3980i	−1.62515	−	0.528043i	−0.652001	−	0.758218i	$-0.726070\pi$
$139$	−225.896	−	73.3980i	−1.62515	−	0.528043i	−0.973149	+	0.230175i	$0.926070\pi$
$140$		0			0
$141$	−39.1949	+	28.4767i	−0.277978	+	0.201963i
$142$		0			0
$143$	51.6078	+	20.7992i	0.360894	+	0.145449i
$144$		0			0
$145$	−78.0568	−	107.436i	−0.538323	−	0.740937i
$146$		0			0
$147$	114.672	−	352.924i	0.780081	−	2.40084i
$148$		0			0
$149$	96.3895	−	132.669i	0.646909	−	0.890394i	−0.352051	−	0.935981i	$-0.614516\pi$
$149$	96.3895	−	132.669i	0.646909	−	0.890394i	0.998960	+	0.0455865i	$0.0145157\pi$
$150$		0			0
$151$	−41.8105	+	13.5851i	−0.276891	+	0.0899673i	−0.444171	−	0.895942i	$-0.646502\pi$
$151$	−41.8105	+	13.5851i	−0.276891	+	0.0899673i	0.167280	+	0.985909i	$0.446502\pi$
$152$		0			0
$153$		−	91.5598i		−	0.598430i
$154$		0			0
$155$	−238.817			−1.54076
$156$		0			0
$157$	2.48642	+	7.65241i	0.0158371	+	0.0487414i	0.958663	−	0.284545i	$-0.0918425\pi$
$157$	2.48642	+	7.65241i	0.0158371	+	0.0487414i	−0.942826	+	0.333286i	$0.891842\pi$
$158$		0			0
$159$	259.525	+	188.556i	1.63223	+	1.18589i
$160$		0			0
$161$	128.722	+	41.8242i	0.799513	+	0.259777i
$162$		0			0
$163$	102.128	−	74.2001i	0.626550	−	0.455216i	−0.228653	−	0.973508i	$-0.573432\pi$
$163$	102.128	−	74.2001i	0.626550	−	0.455216i	0.855203	+	0.518292i	$0.173432\pi$
$164$		0			0
$165$	77.7301	+	310.617i	0.471091	+	1.88253i
$166$		0			0
$167$	124.601	+	171.498i	0.746112	+	1.02694i	0.998244	+	0.0592423i	$0.0188685\pi$
$167$	124.601	+	171.498i	0.746112	+	1.02694i	−0.252131	+	0.967693i	$0.581132\pi$
$168$		0			0
$169$	44.3172	−	136.394i	0.262232	−	0.807067i
$170$		0			0
$171$	68.0469	−	93.6585i	0.397935	−	0.547710i
$172$		0			0
$173$	−239.490	+	77.8150i	−1.38434	+	0.449798i	−0.904092	−	0.427338i	$-0.859452\pi$
$173$	−239.490	+	77.8150i	−1.38434	+	0.449798i	−0.480243	+	0.877136i	$0.659452\pi$
$174$		0			0
$175$			207.811i			1.18749i
$176$		0			0
$177$	−19.8478			−0.112135
$178$		0			0
$179$	−68.5335	−	210.924i	−0.382869	−	1.17835i	−0.938015	−	0.346596i	$-0.887338\pi$
$179$	−68.5335	−	210.924i	−0.382869	−	1.17835i	0.555146	−	0.831753i	$-0.312662\pi$
$180$		0			0
$181$	1.59618	+	1.15970i	0.00881869	+	0.00640716i	0.592186	−	0.805801i	$-0.298265\pi$
$181$	1.59618	+	1.15970i	0.00881869	+	0.00640716i	−0.583367	+	0.812209i	$0.698265\pi$
$182$		0			0
$183$	−458.444	−	148.957i	−2.50516	−	0.813975i
$184$		0			0
$185$	195.850	−	142.293i	1.05865	−	0.769154i
$186$		0			0
$187$	−6.49420	+	94.0366i	−0.0347283	+	0.502869i
$188$		0			0
$189$	50.6029	+	69.6488i	0.267740	+	0.368512i
$190$		0			0
$191$	−6.42642	+	19.7785i	−0.0336462	+	0.103552i	−0.966469	−	0.256783i	$-0.917338\pi$
$191$	−6.42642	+	19.7785i	−0.0336462	+	0.103552i	0.932823	+	0.360335i	$0.117338\pi$
$192$		0			0
$193$	−109.830	+	151.168i	−0.569068	+	0.783255i	−0.992444	−	0.122699i	$-0.960845\pi$
$193$	−109.830	+	151.168i	−0.569068	+	0.783255i	0.423376	+	0.905954i	$0.360845\pi$
$194$		0			0
$195$	−140.034	+	45.4999i	−0.718124	+	0.233333i
$196$		0			0
$197$			325.621i			1.65290i	0.563011	+	0.826449i	$0.309643\pi$
$197$			325.621i			1.65290i	−0.563011	+	0.826449i	$0.690357\pi$
$198$		0			0
$199$	−76.6068			−0.384959			−0.192479	−	0.981301i	$-0.561653\pi$
$199$	−76.6068			−0.384959			−0.192479	+	0.981301i	$0.561653\pi$
$200$		0			0
$201$	51.5651	+	158.701i	0.256543	+	0.789557i
$202$		0			0
$203$	188.594	+	137.022i	0.929037	+	0.674985i
$204$		0			0
$205$	264.534	+	85.9524i	1.29041	+	0.419280i
$206$		0			0
$207$	−101.586	+	73.8066i	−0.490754	+	0.356554i
$208$		0			0
$209$	−76.5307	+	91.3656i	−0.366175	+	0.437156i
$210$		0			0
$211$	−134.868	−	185.630i	−0.639186	−	0.879764i	0.359386	−	0.933189i	$-0.382986\pi$
$211$	−134.868	−	185.630i	−0.639186	−	0.879764i	−0.998572	+	0.0534249i	$0.982986\pi$
$212$		0			0
$213$	73.5284	−	226.297i	0.345204	−	1.06243i
$214$		0			0
$215$	279.365	−	384.512i	1.29937	−	1.78843i
$216$		0			0
$217$	398.705	−	129.547i	1.83735	−	0.596991i
$218$		0			0
$219$			110.683i			0.505404i
$220$		0			0
$221$	−43.3454			−0.196133
$222$		0			0
$223$	105.098	+	323.459i	0.471293	+	1.45049i	0.850893	+	0.525339i	$0.176062\pi$
$223$	105.098	+	323.459i	0.471293	+	1.45049i	−0.379600	+	0.925151i	$0.623938\pi$
$224$		0			0
$225$	−155.976	−	113.323i	−0.693227	−	0.503659i
$226$		0			0
$227$	−176.746	−	57.4282i	−0.778616	−	0.252988i	−0.107367	−	0.994219i	$-0.534242\pi$
$227$	−176.746	−	57.4282i	−0.778616	−	0.252988i	−0.671249	+	0.741232i	$0.734242\pi$
$228$		0			0
$229$	−120.106	+	87.2618i	−0.524479	+	0.381056i	−0.818288	−	0.574808i	$-0.805077\pi$
$229$	−120.106	+	87.2618i	−0.524479	+	0.381056i	0.293810	+	0.955864i	$0.405077\pi$
$230$		0			0
$231$	−298.265	−	476.409i	−1.29119	−	2.06238i
$232$		0			0
$233$	47.8872	+	65.9111i	0.205525	+	0.282880i	0.899319	−	0.437292i	$-0.144063\pi$
$233$	47.8872	+	65.9111i	0.205525	+	0.282880i	−0.693795	+	0.720173i	$0.744063\pi$
$234$		0			0
$235$	−22.1383	+	68.1347i	−0.0942056	+	0.289935i
$236$		0			0
$237$	−185.874	+	255.834i	−0.784279	+	1.07947i
$238$		0			0
$239$	191.525	−	62.2303i	0.801360	−	0.260378i	0.120426	−	0.992722i	$-0.461574\pi$
$239$	191.525	−	62.2303i	0.801360	−	0.260378i	0.680934	+	0.732345i	$0.261574\pi$
$240$		0			0
$241$		−	381.337i		−	1.58231i	−0.611616	−	0.791155i	$-0.709480\pi$
$241$		−	381.337i		−	1.58231i	0.611616	−	0.791155i	$-0.290520\pi$
$242$		0			0
$243$	346.783			1.42709
$244$		0			0
$245$	−169.569	−	521.881i	−0.692120	−	2.13013i
$246$		0			0
$247$	−44.3390	−	32.2141i	−0.179510	−	0.130422i
$248$		0			0
$249$	−48.6897	−	15.8202i	−0.195541	−	0.0635351i
$250$		0			0
$251$	−84.0788	+	61.0868i	−0.334975	+	0.243374i	−0.742539	−	0.669803i	$-0.766379\pi$
$251$	−84.0788	+	61.0868i	−0.334975	+	0.243374i	0.407563	+	0.913177i	$0.366379\pi$
$252$		0			0
$253$	109.569	−	68.5978i	0.433080	−	0.271138i
$254$		0			0
$255$	−146.615	−	201.798i	−0.574960	−	0.791365i
$256$		0			0
$257$	−49.5999	+	152.653i	−0.192996	+	0.593980i	0.806998	+	0.590554i	$0.201091\pi$
$257$	−49.5999	+	152.653i	−0.192996	+	0.593980i	−0.999994	+	0.00342612i	$0.998909\pi$
$258$		0			0
$259$	−249.784	+	343.798i	−0.964416	+	1.32740i
$260$		0			0
$261$	−205.688	+	66.8321i	−0.788077	+	0.256062i
$262$		0			0
$263$		−	203.520i		−	0.773840i	−0.922113	−	0.386920i	$-0.873539\pi$
$263$		−	203.520i		−	0.773840i	0.922113	−	0.386920i	$-0.126461\pi$
$264$		0			0
$265$	474.364			1.79005
$266$		0			0
$267$	103.785	+	319.416i	0.388706	+	1.19631i
$268$		0			0
$269$	−182.799	−	132.812i	−0.679552	−	0.493723i	0.193657	−	0.981069i	$-0.437965\pi$
$269$	−182.799	−	132.812i	−0.679552	−	0.493723i	−0.873209	+	0.487346i	$0.837965\pi$
$270$		0			0
$271$	276.556	+	89.8585i	1.02050	+	0.331581i	0.771029	−	0.636800i	$-0.219742\pi$
$271$	276.556	+	89.8585i	1.02050	+	0.331581i	0.249474	+	0.968382i	$0.419742\pi$
$272$		0			0
$273$	209.105	−	151.924i	0.765953	−	0.556498i
$274$		0			0
$275$	152.157	+	127.452i	0.553300	+	0.463461i
$276$		0			0
$277$	112.068	+	154.248i	0.404577	+	0.556853i	0.961885	−	0.273453i	$-0.0881658\pi$
$277$	112.068	+	154.248i	0.404577	+	0.556853i	−0.557308	+	0.830306i	$0.688166\pi$
$278$		0			0
$279$	−120.188	+	369.899i	−0.430780	+	1.32580i
$280$		0			0
$281$	12.7725	−	17.5799i	0.0454538	−	0.0625618i	−0.785685	−	0.618627i	$-0.787689\pi$
$281$	12.7725	−	17.5799i	0.0454538	−	0.0625618i	0.831139	+	0.556065i	$0.187689\pi$
$282$		0			0
$283$	52.2884	−	16.9895i	0.184765	−	0.0600337i	−0.215173	−	0.976576i	$-0.569032\pi$
$283$	52.2884	−	16.9895i	0.184765	−	0.0600337i	0.399938	+	0.916542i	$0.369032\pi$
$284$		0			0
$285$		−	315.387i		−	1.10662i
$286$		0			0
$287$	−488.264			−1.70127
$288$		0			0
$289$	66.6147	+	205.019i	0.230501	+	0.709409i
$290$		0			0
$291$	10.7187	+	7.78761i	0.0368341	+	0.0267615i
$292$		0			0
$293$	417.197	+	135.556i	1.42388	+	0.462647i	0.916833	−	0.399271i	$-0.130737\pi$
$293$	417.197	+	135.556i	1.42388	+	0.462647i	0.507048	+	0.861918i	$0.330737\pi$
$294$		0			0
$295$	−23.7444	+	17.2513i	−0.0804895	+	0.0584790i
$296$		0			0
$297$	82.0314	+	5.66512i	0.276200	+	0.0190745i
$298$		0			0
$299$	34.9409	+	48.0920i	0.116859	+	0.160843i
$300$		0			0
$301$	−257.819	+	793.484i	−0.856540	+	2.63616i
$302$		0			0
$303$	115.900	−	159.523i	0.382510	−	0.526480i
$304$		0			0
$305$	−677.917	+	220.269i	−2.22268	+	0.722192i
$306$		0			0
$307$		−	232.888i		−	0.758594i	−0.925275	−	0.379297i	$-0.876166\pi$
$307$		−	232.888i		−	0.758594i	0.925275	−	0.379297i	$-0.123834\pi$
$308$		0			0
$309$	−239.603			−0.775415
$310$		0			0
$311$	−47.0093	−	144.680i	−0.151155	−	0.465208i	0.846596	−	0.532236i	$-0.178648\pi$
$311$	−47.0093	−	144.680i	−0.151155	−	0.465208i	−0.997751	+	0.0670284i	$0.978648\pi$
$312$		0			0
$313$	−81.4642	−	59.1872i	−0.260269	−	0.189097i	0.449997	−	0.893030i	$-0.351425\pi$
$313$	−81.4642	−	59.1872i	−0.260269	−	0.189097i	−0.710266	+	0.703934i	$0.751425\pi$
$314$		0			0
$315$	767.831	+	249.483i	2.43756	+	0.792011i
$316$		0			0
$317$	−270.287	+	196.375i	−0.852639	+	0.619478i	−0.925872	−	0.377836i	$-0.876668\pi$
$317$	−270.287	+	196.375i	−0.852639	+	0.619478i	0.0732335	+	0.997315i	$0.476668\pi$
$318$		0			0
$319$	215.993	−	54.0509i	0.677093	−	0.169438i
$320$		0			0
$321$	−342.651	−	471.619i	−1.06745	−	1.46922i
$322$		0			0
$323$	28.6907	−	88.3010i	0.0888258	−	0.273378i
$324$		0			0
$325$	−53.6484	+	73.8408i	−0.165072	+	0.227202i
$326$		0			0
$327$	−29.3905	+	9.54956i	−0.0898793	+	0.0292036i
$328$		0			0
$329$		−	125.760i		−	0.382248i
$330$		0			0
$331$	168.614			0.509409			0.254705	−	0.967019i	$-0.418022\pi$
$331$	168.614			0.509409			0.254705	+	0.967019i	$0.418022\pi$
$332$		0			0
$333$	−121.832	−	374.959i	−0.365860	−	1.12600i
$334$		0			0
$335$	199.628	+	145.038i	0.595905	+	0.432950i
$336$		0			0
$337$	−497.959	−	161.797i	−1.47762	−	0.480108i	−0.544220	−	0.838942i	$-0.683174\pi$
$337$	−497.959	−	161.797i	−1.47762	−	0.480108i	−0.933401	+	0.358834i	$0.883174\pi$
$338$		0			0
$339$	196.217	−	142.560i	0.578812	−	0.420531i
$340$		0			0
$341$	149.675	−	371.381i	0.438930	−	1.08909i
$342$		0			0
$343$	234.487	+	322.744i	0.683636	+	0.940945i
$344$		0			0
$345$	−105.709	+	325.340i	−0.306404	+	0.943015i
$346$		0			0
$347$	281.084	−	386.879i	0.810040	−	1.11493i	−0.181277	−	0.983432i	$-0.558023\pi$
$347$	281.084	−	386.879i	0.810040	−	1.11493i	0.991317	−	0.131493i	$-0.0419770\pi$
$348$		0			0
$349$	−9.13440	+	2.96795i	−0.0261731	+	0.00850415i	−0.322074	−	0.946714i	$-0.604380\pi$
$349$	−9.13440	+	2.96795i	−0.0261731	+	0.00850415i	0.295901	+	0.955219i	$0.404380\pi$
$350$		0			0
$351$			37.8117i			0.107726i
$352$		0			0
$353$	691.089			1.95776			0.978880	−	0.204436i	$-0.0655361\pi$
$353$	691.089			1.95776			0.978880	+	0.204436i	$0.0655361\pi$
$354$		0			0
$355$	−108.729	−	334.633i	−0.306279	−	0.942629i
$356$		0			0
$357$	354.239	+	257.370i	0.992266	+	0.720923i
$358$		0			0
$359$	43.9277	+	14.2730i	0.122361	+	0.0397576i	0.369558	−	0.929208i	$-0.379509\pi$
$359$	43.9277	+	14.2730i	0.122361	+	0.0397576i	−0.247196	+	0.968965i	$0.579509\pi$
$360$		0			0
$361$	−197.082	+	143.188i	−0.545933	+	0.396644i
$362$		0			0
$363$	−531.751	−	73.7978i	−1.46488	−	0.203300i
$364$		0			0
$365$	96.2037	+	132.413i	0.263572	+	0.362775i
$366$		0			0
$367$	140.965	−	433.846i	0.384101	−	1.18214i	−0.553030	−	0.833162i	$-0.686528\pi$
$367$	140.965	−	433.846i	0.384101	−	1.18214i	0.937131	−	0.348979i	$-0.113472\pi$
$368$		0			0
$369$	266.260	−	366.475i	0.721571	−	0.993157i
$370$		0			0
$371$	−791.950	+	257.320i	−2.13464	+	0.693585i
$372$		0			0
$373$		−	99.8021i		−	0.267566i	−0.991011	−	0.133783i	$-0.957288\pi$
$373$		−	99.8021i		−	0.267566i	0.991011	−	0.133783i	$-0.0427125\pi$
$374$		0			0
$375$	202.480			0.539947
$376$		0			0
$377$	31.6391	+	97.3751i	0.0839233	+	0.258289i
$378$		0			0
$379$	−313.281	−	227.612i	−0.826600	−	0.600560i	0.0919953	−	0.995759i	$-0.470676\pi$
$379$	−313.281	−	227.612i	−0.826600	−	0.600560i	−0.918595	+	0.395199i	$0.870676\pi$
$380$		0			0
$381$	34.4037	+	11.1784i	0.0902984	+	0.0293397i
$382$		0			0
$383$	−490.495	+	356.366i	−1.28067	+	0.930458i	−0.999573	−	0.0292222i	$-0.990697\pi$
$383$	−490.495	+	356.366i	−1.28067	+	0.930458i	−0.281093	+	0.959681i	$0.590697\pi$
$384$		0			0
$385$	−770.906	−	310.693i	−2.00235	−	0.806996i
$386$		0			0
$387$	−454.970	−	626.212i	−1.17563	−	1.61812i
$388$		0			0
$389$	179.028	−	550.992i	0.460226	−	1.41643i	−0.404662	−	0.914466i	$-0.632611\pi$
$389$	179.028	−	550.992i	0.460226	−	1.41643i	0.864888	−	0.501964i	$-0.167389\pi$
$390$		0			0
$391$	−59.1923	+	81.4712i	−0.151387	+	0.208366i
$392$		0			0
$393$	685.614	−	222.769i	1.74456	−	0.566843i
$394$		0			0
$395$			467.617i			1.18384i
$396$		0			0
$397$	−163.072			−0.410761			−0.205381	−	0.978682i	$-0.565843\pi$
$397$	−163.072			−0.410761			−0.205381	+	0.978682i	$0.565843\pi$
$398$		0			0
$399$	171.083	+	526.538i	0.428778	+	1.31964i
$400$		0			0
$401$	604.368	+	439.099i	1.50715	+	1.09501i	0.967422	+	0.253171i	$0.0814736\pi$
$401$	604.368	+	439.099i	1.50715	+	1.09501i	0.539730	+	0.841838i	$0.318526\pi$
$402$		0			0
$403$	175.114	+	56.8981i	0.434527	+	0.141186i
$404$		0			0
$405$	334.380	−	242.941i	0.825629	−	0.599855i
$406$		0			0
$407$	98.5319	+	393.743i	0.242093	+	0.967428i
$408$		0			0
$409$	−71.6699	−	98.6451i	−0.175232	−	0.241186i	0.712363	−	0.701812i	$-0.247625\pi$
$409$	−71.6699	−	98.6451i	−0.175232	−	0.241186i	−0.887595	+	0.460625i	$0.847625\pi$
$410$		0			0
$411$	−322.005	+	991.030i	−0.783468	+	2.41127i
$412$		0			0
$413$	30.2832	−	41.6812i	0.0733249	−	0.100923i
$414$		0			0
$415$	−71.9992	+	23.3940i	−0.173492	+	0.0563710i
$416$		0			0
$417$			1053.82i			2.52715i
$418$		0			0
$419$	330.708			0.789279			0.394640	−	0.918836i	$-0.370869\pi$
$419$	330.708			0.789279			0.394640	+	0.918836i	$0.370869\pi$
$420$		0			0
$421$	197.794	+	608.747i	0.469819	+	1.44595i	0.852819	+	0.522206i	$0.174891\pi$
$421$	197.794	+	608.747i	0.469819	+	1.44595i	−0.383000	+	0.923748i	$0.625109\pi$
$422$		0			0
$423$	94.3910	+	68.5791i	0.223147	+	0.162126i
$424$		0			0
$425$	−147.054	−	47.7807i	−0.346009	−	0.112425i
$426$		0			0
$427$	1012.30	−	735.476i	2.37072	−	1.72243i
$428$		0			0
$429$	17.0083	−	246.281i	0.0396463	−	0.574082i
$430$		0			0
$431$	−85.8703	−	118.190i	−0.199235	−	0.274223i	0.697696	−	0.716394i	$-0.254209\pi$
$431$	−85.8703	−	118.190i	−0.199235	−	0.274223i	−0.896931	+	0.442170i	$0.854209\pi$
$432$		0			0
$433$	28.3924	−	87.3827i	0.0655713	−	0.201808i	−0.912903	−	0.408177i	$-0.866165\pi$
$433$	28.3924	−	87.3827i	0.0655713	−	0.201808i	0.978474	+	0.206369i	$0.0661647\pi$
$434$		0			0
$435$	−346.319	+	476.667i	−0.796136	+	1.09579i
$436$		0			0
$437$	−121.098	+	39.3472i	−0.277112	+	0.0900393i
$438$		0			0
$439$		−	358.371i		−	0.816335i	−0.912907	−	0.408168i	$-0.866168\pi$
$439$		−	358.371i		−	0.816335i	0.912907	−	0.408168i	$-0.133832\pi$
$440$		0			0
$441$	−893.668			−2.02646
$442$		0			0
$443$	−253.799	−	781.114i	−0.572910	−	1.76324i	−0.643186	−	0.765710i	$-0.722388\pi$
$443$	−253.799	−	781.114i	−0.572910	−	1.76324i	0.0702760	−	0.997528i	$-0.477612\pi$
$444$		0			0
$445$	401.790	+	291.917i	0.902898	+	0.655994i
$446$		0			0
$447$	−691.963	−	224.833i	−1.54802	−	0.502981i
$448$		0			0
$449$	−131.173	+	95.3029i	−0.292145	+	0.212256i	−0.724197	−	0.689593i	$-0.757790\pi$
$449$	−131.173	+	95.3029i	−0.292145	+	0.212256i	0.432052	+	0.901849i	$0.357790\pi$
$450$		0			0
$451$	−299.456	+	357.503i	−0.663982	+	0.792690i
$452$		0			0
$453$	114.647	+	157.798i	0.253084	+	0.348341i
$454$		0			0
$455$	118.108	−	363.500i	0.259578	−	0.798900i
$456$		0			0
$457$	213.638	−	294.048i	0.467479	−	0.643430i	−0.508559	−	0.861027i	$-0.669822\pi$
$457$	213.638	−	294.048i	0.467479	−	0.643430i	0.976039	+	0.217597i	$0.0698217\pi$
$458$		0			0
$459$	−60.9206	+	19.7943i	−0.132725	+	0.0431249i
$460$		0			0
$461$		−	487.885i		−	1.05832i	−0.848523	−	0.529159i	$-0.822507\pi$
$461$		−	487.885i		−	1.05832i	0.848523	−	0.529159i	$-0.177493\pi$
$462$		0			0
$463$	367.635			0.794028			0.397014	−	0.917812i	$-0.370046\pi$
$463$	367.635			0.794028			0.397014	+	0.917812i	$0.370046\pi$
$464$		0			0
$465$	327.427	+	1007.72i	0.704144	+	2.16713i
$466$		0			0
$467$	−333.686	−	242.437i	−0.714531	−	0.519137i	0.170101	−	0.985427i	$-0.445591\pi$
$467$	−333.686	−	242.437i	−0.714531	−	0.519137i	−0.884632	+	0.466289i	$0.845591\pi$
$468$		0			0
$469$	−411.955	−	133.852i	−0.878368	−	0.285399i
$470$		0			0
$471$	28.8812	−	20.9834i	0.0613189	−	0.0445508i
$472$		0			0
$473$	422.861	+	675.422i	0.893998	+	1.42795i
$474$		0			0
$475$	−114.914	−	158.166i	−0.241924	−	0.332980i
$476$		0			0
$477$	238.729	−	734.733i	0.500481	−	1.54032i
$478$		0			0
$479$	−312.503	+	430.123i	−0.652407	+	0.897961i	−0.999200	−	0.0399806i	$-0.987270\pi$
$479$	−312.503	+	430.123i	−0.652407	+	0.897961i	0.346794	+	0.937941i	$0.387270\pi$
$480$		0			0
$481$	−177.510	+	57.6764i	−0.369043	+	0.119909i
$482$		0			0
$483$		−	600.497i		−	1.24326i
$484$		0			0
$485$	19.5919			0.0403956
$486$		0			0
$487$	−198.833	−	611.946i	−0.408282	−	1.25656i	−0.918124	−	0.396294i	$-0.870296\pi$
$487$	−198.833	−	611.946i	−0.408282	−	1.25656i	0.509842	−	0.860268i	$-0.329704\pi$
$488$		0			0
$489$	−453.116	−	329.208i	−0.926618	−	0.673227i
$490$		0			0
$491$	713.624	+	231.871i	1.45341	+	0.472241i	0.926050	−	0.377401i	$-0.123182\pi$
$491$	713.624	+	231.871i	1.45341	+	0.472241i	0.527360	+	0.849642i	$0.323182\pi$
$492$		0			0
$493$	−140.324	+	101.951i	−0.284632	+	0.206797i
$494$		0			0
$495$	653.586	−	409.190i	1.32038	−	0.826646i
$496$		0			0
$497$	363.045	+	499.689i	0.730474	+	1.00541i
$498$		0			0
$499$	56.8823	−	175.066i	0.113993	−	0.350833i	−0.877743	−	0.479132i	$-0.840952\pi$
$499$	56.8823	−	175.066i	0.113993	−	0.350833i	0.991736	+	0.128298i	$0.0409516\pi$
$500$		0			0
$501$	552.823	−	760.896i	1.10344	−	1.51875i
$502$		0			0
$503$	422.195	−	137.180i	0.839355	−	0.272723i	0.142374	−	0.989813i	$-0.454526\pi$
$503$	422.195	−	137.180i	0.839355	−	0.272723i	0.696981	+	0.717090i	$0.254526\pi$
$504$		0			0
$505$		−	291.580i		−	0.577385i
$506$		0			0
$507$	−636.291			−1.25501
$508$		0			0
$509$	−154.181	−	474.520i	−0.302909	−	0.932259i	−0.980449	−	0.196773i	$-0.936954\pi$
$509$	−154.181	−	474.520i	−0.302909	−	0.932259i	0.677540	−	0.735486i	$-0.263046\pi$
$510$		0			0
$511$	−232.440	−	168.877i	−0.454872	−	0.330484i
$512$		0			0
$513$	−77.0281	−	25.0279i	−0.150152	−	0.0487874i
$514$		0			0
$515$	−286.643	+	208.258i	−0.556588	+	0.404385i
$516$		0			0
$517$	−92.0802	−	77.1293i	−0.178105	−	0.149186i
$518$		0			0
$519$	656.698	+	903.867i	1.26531	+	1.74155i
$520$		0			0
$521$	−79.1535	+	243.610i	−0.151926	+	0.467581i	−0.997836	−	0.0657445i	$-0.979058\pi$
$521$	−79.1535	+	243.610i	−0.151926	+	0.467581i	0.845910	+	0.533325i	$0.179058\pi$
$522$		0			0
$523$	−429.405	+	591.025i	−0.821041	+	1.13007i	0.168484	+	0.985704i	$0.446113\pi$
$523$	−429.405	+	591.025i	−0.821041	+	1.13007i	−0.989525	+	0.144362i	$0.953887\pi$
$524$		0			0
$525$	876.880	−	284.916i	1.67025	−	0.542697i
$526$		0			0
$527$			311.923i			0.591884i
$528$		0			0
$529$	−390.892			−0.738926
$530$		0			0
$531$	14.7706	+	45.4591i	0.0278165	+	0.0856104i
$532$		0			0
$533$	−173.493	−	126.050i	−0.325503	−	0.236492i
$534$		0			0
$535$	−819.842	−	266.383i	−1.53242	−	0.497912i
$536$		0			0
$537$	−796.057	+	578.369i	−1.48241	+	1.07704i
$538$		0			0
$539$	917.843	+	63.3865i	1.70286	+	0.117600i
$540$		0			0
$541$	−207.051	−	284.981i	−0.382718	−	0.526766i	0.573584	−	0.819147i	$-0.305553\pi$
$541$	−207.051	−	284.981i	−0.382718	−	0.526766i	−0.956302	+	0.292380i	$0.905553\pi$
$542$		0			0
$543$	2.70504	−	8.32525i	0.00498165	−	0.0153320i
$544$		0			0
$545$	−26.8603	+	36.9700i	−0.0492849	+	0.0678348i
$546$		0			0
$547$	794.486	−	258.144i	1.45244	−	0.471927i	0.526690	−	0.850058i	$-0.323433\pi$
$547$	794.486	−	258.144i	1.45244	−	0.471927i	0.925752	+	0.378131i	$0.123433\pi$
$548$		0			0
$549$			1160.86i			2.11451i
$550$		0			0
$551$	−219.310			−0.398021
$552$		0			0
$553$	−253.660	−	780.686i	−0.458698	−	1.41173i
$554$		0			0
$555$	−868.940	−	631.322i	−1.56566	−	1.13752i
$556$		0			0
$557$	373.525	+	121.366i	0.670601	+	0.217891i	0.624476	−	0.781044i	$-0.285313\pi$
$557$	373.525	+	121.366i	0.670601	+	0.217891i	0.0461252	+	0.998936i	$0.485313\pi$
$558$		0			0
$559$	−296.456	+	215.388i	−0.530332	+	0.385309i
$560$		0			0
$561$	405.701	−	101.524i	0.723175	−	0.180970i
$562$		0			0
$563$	228.481	+	314.478i	0.405828	+	0.558575i	0.962195	−	0.272362i	$-0.0878049\pi$
$563$	228.481	+	314.478i	0.405828	+	0.558575i	−0.556366	+	0.830937i	$0.687805\pi$
$564$		0			0
$565$	110.829	−	341.096i	0.196157	−	0.603709i
$566$		0			0
$567$	−426.462	+	586.975i	−0.752138	+	1.03523i
$568$		0			0
$569$	−626.840	+	203.673i	−1.10165	+	0.357948i	−0.802738	−	0.596332i	$-0.796624\pi$
$569$	−626.840	+	203.673i	−1.10165	+	0.357948i	−0.298914	+	0.954280i	$0.596624\pi$
$570$		0			0
$571$			893.667i			1.56509i	0.622593	+	0.782546i	$0.286079\pi$
$571$			893.667i			1.56509i	−0.622593	+	0.782546i	$0.713921\pi$
$572$		0			0
$573$	92.2683			0.161027
$574$		0			0
$575$	65.5276	+	201.673i	0.113961	+	0.350736i
$576$		0			0
$577$	14.3594	+	10.4327i	0.0248864	+	0.0180810i	0.600159	−	0.799881i	$-0.295104\pi$
$577$	14.3594	+	10.4327i	0.0248864	+	0.0180810i	−0.575273	+	0.817962i	$0.695104\pi$
$578$		0			0
$579$	788.452	+	256.183i	1.36175	+	0.442459i
$580$		0			0
$581$	107.512	−	78.1123i	0.185047	−	0.134445i
$582$		0			0
$583$	−297.301	+	737.676i	−0.509950	+	1.26531i
$584$		0			0
$585$	208.424	+	286.871i	0.356281	+	0.490378i
$586$		0			0
$587$	−50.3870	+	155.075i	−0.0858382	+	0.264183i	−0.984758	−	0.173931i	$-0.944353\pi$
$587$	−50.3870	+	155.075i	−0.0858382	+	0.264183i	0.898920	+	0.438113i	$0.144353\pi$
$588$		0			0
$589$	−231.820	+	319.073i	−0.393582	+	0.541719i
$590$		0			0
$591$	1373.99	−	446.438i	2.32486	−	0.755393i
$592$		0			0
$593$		−	513.367i		−	0.865711i	−0.901463	−	0.432855i	$-0.857506\pi$
$593$		−	513.367i		−	0.865711i	0.901463	−	0.432855i	$-0.142494\pi$
$594$		0			0
$595$	647.484			1.08821
$596$		0			0
$597$	105.031	+	323.251i	0.175931	+	0.541458i
$598$		0			0
$599$	−749.454	−	544.510i	−1.25118	−	0.909032i	−0.252886	−	0.967496i	$-0.581380\pi$
$599$	−749.454	−	544.510i	−1.25118	−	0.909032i	−0.998290	+	0.0584638i	$0.981380\pi$
$600$		0			0
$601$	152.709	+	49.6182i	0.254092	+	0.0825594i	0.433293	−	0.901253i	$-0.357351\pi$
$601$	152.709	+	49.6182i	0.254092	+	0.0825594i	−0.179202	+	0.983812i	$0.557351\pi$
$602$		0			0
$603$	325.112	−	236.208i	0.539157	−	0.391721i
$604$		0			0
$605$	−700.289	+	373.901i	−1.15750	+	0.618018i
$606$		0			0
$607$	309.898	+	426.539i	0.510541	+	0.702700i	0.984010	−	0.178111i	$-0.0569985\pi$
$607$	309.898	+	426.539i	0.510541	+	0.702700i	−0.473469	+	0.880810i	$0.656999\pi$
$608$		0			0
$609$	319.609	−	983.656i	0.524810	−	1.61520i
$610$		0			0
$611$	32.4661	−	44.6858i	0.0531360	−	0.0731355i
$612$		0			0
$613$	−630.712	+	204.931i	−1.02889	+	0.334308i	−0.774353	−	0.632754i	$-0.781924\pi$
$613$	−630.712	+	204.931i	−1.02889	+	0.334308i	−0.254541	+	0.967062i	$0.581924\pi$
$614$		0			0
$615$		−	1234.07i		−	2.00662i
$616$		0			0
$617$	−260.782			−0.422661			−0.211331	−	0.977415i	$-0.567780\pi$
$617$	−260.782			−0.422661			−0.211331	+	0.977415i	$0.567780\pi$
$618$		0			0
$619$	328.398	+	1010.70i	0.530529	+	1.63280i	0.753115	+	0.657889i	$0.228550\pi$
$619$	328.398	+	1010.70i	0.530529	+	1.63280i	−0.222586	+	0.974913i	$0.571450\pi$
$620$		0			0
$621$	71.0702	+	51.6355i	0.114445	+	0.0831490i
$622$		0			0
$623$	−829.138	−	269.403i	−1.33088	−	0.432429i
$624$		0			0
$625$	607.179	−	441.141i	0.971486	−	0.705826i
$626$		0			0
$627$	490.453	+	197.664i	0.782222	+	0.315254i
$628$		0			0
$629$	−185.851	−	255.803i	−0.295471	−	0.406681i
$630$		0			0
$631$	161.533	−	497.148i	0.255996	−	0.787874i	−0.737636	−	0.675199i	$-0.764058\pi$
$631$	161.533	−	497.148i	0.255996	−	0.787874i	0.993632	−	0.112675i	$-0.0359420\pi$
$632$		0			0
$633$	−598.378	+	823.597i	−0.945305	+	1.30110i
$634$		0			0
$635$	50.8740	−	16.5300i	0.0801165	−	0.0260314i
$636$		0			0
$637$			423.072i			0.664164i
$638$		0			0
$639$	−573.026			−0.896754
$640$		0			0
$641$	−343.291	−	1056.54i	−0.535556	−	1.64827i	−0.742445	−	0.669907i	$-0.766334\pi$
$641$	−343.291	−	1056.54i	−0.535556	−	1.64827i	0.206889	−	0.978364i	$-0.433666\pi$
$642$		0			0
$643$	716.585	+	520.630i	1.11444	+	0.809689i	0.983357	−	0.181683i	$-0.0581544\pi$
$643$	716.585	+	520.630i	1.11444	+	0.809689i	0.131084	+	0.991371i	$0.458154\pi$
$644$		0			0
$645$	−2005.51	−	651.630i	−3.10932	−	1.01028i
$646$		0			0
$647$	92.5424	−	67.2360i	0.143033	−	0.103920i	−0.513968	−	0.857810i	$-0.671825\pi$
$647$	92.5424	−	67.2360i	0.143033	−	0.103920i	0.657001	+	0.753890i	$0.271825\pi$
$648$		0			0
$649$	−11.9458	−	47.7365i	−0.0184064	−	0.0735539i
$650$		0			0
$651$	−1093.28	−	1504.77i	−1.67938	−	2.31147i
$652$		0			0
$653$	−50.6565	+	155.905i	−0.0775750	+	0.238751i	−0.982322	−	0.187197i	$-0.940060\pi$
$653$	−50.6565	+	155.905i	−0.0775750	+	0.238751i	0.904747	+	0.425949i	$0.140060\pi$
$654$		0			0
$655$	626.588	−	862.425i	0.956623	−	1.31668i
$656$		0			0
$657$	253.507	−	82.3695i	0.385856	−	0.125372i
$658$		0			0
$659$		−	116.651i		−	0.177012i	−0.996076	−	0.0885062i	$-0.971791\pi$
$659$		−	116.651i		−	0.177012i	0.996076	−	0.0885062i	$-0.0282093\pi$
$660$		0			0
$661$	205.962			0.311591			0.155796	−	0.987789i	$-0.450206\pi$
$661$	205.962			0.311591			0.155796	+	0.987789i	$0.450206\pi$
$662$		0			0
$663$	59.4280	+	182.901i	0.0896350	+	0.275868i
$664$		0			0
$665$	662.325	+	481.208i	0.995978	+	0.723620i
$666$		0			0
$667$	226.231	+	73.5068i	0.339176	+	0.110205i
$668$		0			0
$669$	1220.78	−	886.947i	1.82478	−	1.32578i
$670$		0			0
$671$	82.3384	−	1192.27i	0.122710	−	1.77685i
$672$		0			0
$673$	16.4238	+	22.6055i	0.0244039	+	0.0335891i	0.821045	−	0.570864i	$-0.193392\pi$
$673$	16.4238	+	22.6055i	0.0244039	+	0.0335891i	−0.796641	+	0.604453i	$0.793392\pi$
$674$		0			0
$675$	−41.6808	+	128.280i	−0.0617493	+	0.190045i
$676$		0			0
$677$	317.546	−	437.064i	0.469049	−	0.645590i	−0.507306	−	0.861766i	$-0.669359\pi$
$677$	317.546	−	437.064i	0.469049	−	0.645590i	0.976354	+	0.216176i	$0.0693585\pi$
$678$		0			0
$679$	−32.7086	+	10.6277i	−0.0481717	+	0.0156519i
$680$		0			0
$681$			824.534i			1.21077i
$682$		0			0
$683$	−1117.89			−1.63674			−0.818369	−	0.574694i	$-0.805121\pi$
$683$	−1117.89			−1.63674			−0.818369	+	0.574694i	$0.805121\pi$
$684$		0			0
$685$	476.161	+	1465.47i	0.695125	+	2.13937i
$686$		0			0
$687$	532.880	+	387.160i	0.775662	+	0.563551i
$688$		0			0
$689$	−347.831	−	113.017i	−0.504834	−	0.164031i
$690$		0			0
$691$	−404.704	+	294.035i	−0.585679	+	0.425521i	−0.840767	−	0.541397i	$-0.817896\pi$
$691$	−404.704	+	294.035i	−0.585679	+	0.425521i	0.255088	+	0.966918i	$0.417896\pi$
$692$		0			0
$693$	−869.194	+	1037.68i	−1.25425	+	1.49737i
$694$		0			0
$695$	915.961	+	1260.71i	1.31793	+	1.81397i
$696$		0			0
$697$	112.264	−	345.512i	0.161067	−	0.495713i
$698$		0			0
$699$	212.464	−	292.432i	0.303954	−	0.418357i
$700$		0			0
$701$	615.162	−	199.878i	0.877549	−	0.285133i	0.164610	−	0.986359i	$-0.447364\pi$
$701$	615.162	−	199.878i	0.877549	−	0.285133i	0.712939	+	0.701226i	$0.247364\pi$
$702$		0			0
$703$		−	399.790i		−	0.568691i
$704$		0			0
$705$	317.854			0.450857
$706$		0			0
$707$	158.168	+	486.791i	0.223717	+	0.688531i
$708$		0			0
$709$	638.569	+	463.948i	0.900662	+	0.654369i	0.938636	−	0.344910i	$-0.112090\pi$
$709$	638.569	+	463.948i	0.900662	+	0.654369i	−0.0379740	+	0.999279i	$0.512090\pi$
$710$		0			0
$711$	724.283	+	235.334i	1.01868	+	0.330990i
$712$		0			0
$713$	346.080	−	251.442i	0.485386	−	0.352654i
$714$		0			0
$715$	−193.715	−	309.415i	−0.270930	−	0.432748i
$716$		0			0
$717$	−525.175	−	722.841i	−0.732461	−	1.00815i
$718$		0			0
$719$	−76.5507	+	235.599i	−0.106468	+	0.327676i	−0.990072	−	0.140559i	$-0.955110\pi$
$719$	−76.5507	+	235.599i	−0.106468	+	0.327676i	0.883604	+	0.468235i	$0.155110\pi$
$720$		0			0
$721$	365.579	−	503.176i	0.507044	−	0.697887i
$722$		0			0
$723$	−1609.09	+	522.825i	−2.22558	+	0.723133i
$724$		0			0
$725$			365.231i			0.503768i
$726$		0			0
$727$	−133.030			−0.182986			−0.0914928	−	0.995806i	$-0.529164\pi$
$727$	−133.030			−0.182986			−0.0914928	+	0.995806i	$0.529164\pi$
$728$		0			0
$729$	−300.244	−	924.057i	−0.411858	−	1.26757i
$730$		0			0
$731$	−502.217	−	364.882i	−0.687027	−	0.499154i
$732$		0			0
$733$	−392.639	−	127.576i	−0.535661	−	0.174047i	0.0286800	−	0.999589i	$-0.490870\pi$
$733$	−392.639	−	127.576i	−0.535661	−	0.174047i	−0.564341	+	0.825542i	$0.690870\pi$
$734$		0			0
$735$	−1969.65	+	1431.03i	−2.67979	+	1.94698i
$736$		0			0
$737$	−350.660	+	219.538i	−0.475794	+	0.297880i
$738$		0			0
$739$	46.5395	+	64.0561i	0.0629763	+	0.0866794i	0.839343	−	0.543602i	$-0.182940\pi$
$739$	46.5395	+	64.0561i	0.0629763	+	0.0866794i	−0.776367	+	0.630281i	$0.782940\pi$
$740$		0			0
$741$	−75.1408	+	231.260i	−0.101405	+	0.312091i
$742$		0			0
$743$	302.034	−	415.714i	0.406506	−	0.559507i	−0.555856	−	0.831279i	$-0.687609\pi$
$743$	302.034	−	415.714i	0.406506	−	0.559507i	0.962362	+	0.271771i	$0.0876095\pi$
$744$		0			0
$745$	−1023.23	+	332.468i	−1.37346	+	0.446266i
$746$		0			0
$747$			123.291i			0.165049i
$748$		0			0
$749$	1513.22			2.02033
$750$		0			0
$751$	−15.0351	−	46.2733i	−0.0200201	−	0.0616156i	0.940547	−	0.339663i	$-0.110313\pi$
$751$	−15.0351	−	46.2733i	−0.0200201	−	0.0616156i	−0.960567	+	0.278047i	$0.910313\pi$
$752$		0			0
$753$	373.037	+	271.027i	0.495401	+	0.359930i
$754$		0			0
$755$	274.310	+	89.1288i	0.363325	+	0.118051i
$756$		0			0
$757$	165.372	−	120.149i	0.218456	−	0.158718i	−0.473175	−	0.880968i	$-0.656892\pi$
$757$	165.372	−	120.149i	0.218456	−	0.158718i	0.691632	+	0.722250i	$0.256892\pi$
$758$		0			0
$759$	−439.679	−	368.289i	−0.579287	−	0.485229i
$760$		0			0
$761$	218.796	+	301.147i	0.287512	+	0.395726i	0.928204	−	0.372072i	$-0.121353\pi$
$761$	218.796	+	301.147i	0.287512	+	0.395726i	−0.640692	+	0.767798i	$0.721353\pi$
$762$		0			0
$763$	24.7887	−	76.2917i	0.0324884	−	0.0999891i
$764$		0			0
$765$	−353.085	+	485.980i	−0.461549	+	0.635268i
$766$		0			0
$767$	21.5208	−	6.99255i	0.0280585	−	0.00911675i
$768$		0			0
$769$			1491.70i			1.93979i	0.243531	+	0.969893i	$0.421694\pi$
$769$			1491.70i			1.93979i	−0.243531	+	0.969893i	$0.578306\pi$
$770$		0			0
$771$	712.138			0.923655
$772$		0			0
$773$	−209.903	−	646.014i	−0.271543	−	0.835723i	−0.990113	−	0.140269i	$-0.955203\pi$
$773$	−209.903	−	646.014i	−0.271543	−	0.835723i	0.718570	−	0.695454i	$-0.244797\pi$
$774$		0			0
$775$	531.374	+	386.066i	0.685644	+	0.498149i
$776$		0			0
$777$	1793.15	+	582.631i	2.30779	+	0.749847i
$778$		0			0
$779$	371.620	−	269.998i	0.477047	−	0.346595i
$780$		0			0
$781$	588.527	+	40.6439i	0.753555	+	0.0520408i
$782$		0			0
$783$	88.9355	+	122.409i	0.113583	+	0.156334i
$784$		0			0
$785$	16.3129	−	50.2058i	0.0207807	−	0.0639565i
$786$		0			0
$787$	−311.831	+	429.199i	−0.396228	+	0.545361i	−0.959792	−	0.280711i	$-0.909430\pi$
$787$	−311.831	+	429.199i	−0.396228	+	0.545361i	0.563564	+	0.826072i	$0.309430\pi$
$788$		0			0
$789$	−858.774	+	279.033i	−1.08843	+	0.353654i
$790$		0			0
$791$			629.577i			0.795926i
$792$		0			0
$793$	549.566			0.693022
$794$		0			0
$795$	−650.370	−	2001.63i	−0.818075	−	2.51778i
$796$		0			0
$797$	−723.680	−	525.784i	−0.908005	−	0.659704i	0.0325047	−	0.999472i	$-0.489652\pi$
$797$	−723.680	−	525.784i	−0.908005	−	0.659704i	−0.940509	+	0.339768i	$0.889652\pi$
$798$		0			0
$799$	88.9917	+	28.9151i	0.111379	+	0.0361892i
$800$		0			0
$801$	654.349	−	475.413i	0.816916	−	0.593524i
$802$		0			0
$803$	−266.207	+	66.6168i	−0.331516	+	0.0829599i
$804$		0			0
$805$	−521.939	−	718.388i	−0.648372	−	0.892407i
$806$		0			0
$807$	−309.789	+	953.431i	−0.383877	+	1.18145i
$808$		0			0
$809$	634.298	−	873.036i	0.784052	−	1.07915i	−0.210772	−	0.977535i	$-0.567598\pi$
$809$	634.298	−	873.036i	0.784052	−	1.07915i	0.994823	−	0.101619i	$-0.0324023\pi$
$810$		0			0
$811$	1130.95	−	367.469i	1.39452	−	0.453106i	0.487104	−	0.873344i	$-0.338053\pi$
$811$	1130.95	−	367.469i	1.39452	−	0.453106i	0.907414	+	0.420237i	$0.138053\pi$
$812$		0			0
$813$		−	1290.16i		−	1.58691i
$814$		0			0
$815$	−828.213			−1.01621
$816$		0			0
$817$	−242.550	−	746.491i	−0.296878	−	0.913698i
$818$		0			0
$819$	−503.578	−	365.871i	−0.614869	−	0.446728i
$820$		0			0
$821$	1011.88	+	328.781i	1.23250	+	0.400464i	0.851620	−	0.524159i	$-0.175620\pi$
$821$	1011.88	+	328.781i	1.23250	+	0.400464i	0.380882	+	0.924623i	$0.375620\pi$
$822$		0			0
$823$	−832.874	+	605.118i	−1.01200	+	0.735259i	−0.964627	−	0.263619i	$-0.915084\pi$
$823$	−832.874	+	605.118i	−1.01200	+	0.735259i	−0.0473700	+	0.998877i	$0.515084\pi$
$824$		0			0
$825$	329.184	−	816.786i	0.399011	−	0.990043i
$826$		0			0
$827$	−654.331	−	900.610i	−0.791211	−	1.08901i	−0.993956	−	0.109776i	$-0.964986\pi$
$827$	−654.331	−	900.610i	−0.791211	−	1.08901i	0.202746	−	0.979231i	$-0.435014\pi$
$828$		0			0
$829$	−399.558	+	1229.71i	−0.481976	+	1.48337i	0.354338	+	0.935117i	$0.384706\pi$
$829$	−399.558	+	1229.71i	−0.481976	+	1.48337i	−0.836314	+	0.548251i	$0.815294\pi$
$830$		0			0
$831$	497.218	−	684.362i	0.598337	−	0.823540i
$832$		0			0
$833$	−681.636	+	221.477i	−0.818290	+	0.265879i
$834$		0			0
$835$		−	1390.78i		−	1.66560i
$836$		0			0
$837$	272.101			0.325091
$838$		0			0
$839$	380.239	+	1170.26i	0.453205	+	1.39482i	0.873229	+	0.487309i	$0.162022\pi$
$839$	380.239	+	1170.26i	0.453205	+	1.39482i	−0.420024	+	0.907513i	$0.637978\pi$
$840$		0			0
$841$	−348.925	−	253.509i	−0.414893	−	0.301437i
$842$		0			0
$843$	−91.6917	−	29.7924i	−0.108768	−	0.0353410i
$844$		0			0
$845$	−761.209	+	553.051i	−0.900839	+	0.654498i
$846$		0			0
$847$	966.307	−	1004.10i	1.14086	−	1.18548i
$848$		0			0
$849$	−143.378	−	197.343i	−0.168879	−	0.232442i
$850$		0			0
$851$	−133.999	+	412.407i	−0.157461	+	0.484614i
$852$		0			0
$853$	−509.204	+	700.859i	−0.596956	+	0.821640i	−0.995425	−	0.0955420i	$-0.969542\pi$
$853$	−509.204	+	700.859i	−0.596956	+	0.821640i	0.398469	+	0.917182i	$0.369542\pi$
$854$		0			0
$855$	−722.357	+	234.708i	−0.844862	+	0.274512i
$856$		0			0
$857$		−	1219.98i		−	1.42354i	−0.702411	−	0.711772i	$-0.747893\pi$
$857$		−	1219.98i		−	1.42354i	0.702411	−	0.711772i	$-0.252107\pi$
$858$		0			0
$859$	−469.893			−0.547023			−0.273512	−	0.961869i	$-0.588185\pi$
$859$	−469.893			−0.547023			−0.273512	+	0.961869i	$0.588185\pi$
$860$		0			0
$861$	669.427	+	2060.28i	0.777499	+	2.39290i
$862$		0			0
$863$	−3.42992	−	2.49198i	−0.00397442	−	0.00288758i	0.585796	−	0.810458i	$-0.300782\pi$
$863$	−3.42992	−	2.49198i	−0.00397442	−	0.00288758i	−0.589771	+	0.807571i	$0.700782\pi$
$864$		0			0
$865$	1571.24	+	510.528i	1.81647	+	0.590206i
$866$		0			0
$867$	773.769	−	562.176i	0.892467	−	0.648415i
$868$		0			0
$869$	−727.184	−	293.072i	−0.836805	−	0.337252i
$870$		0			0
$871$	−111.823	−	153.912i	−0.128385	−	0.176707i
$872$		0			0
$873$	9.85983	−	30.3454i	0.0112942	−	0.0347599i
$874$		0			0
$875$	−308.938	+	425.216i	−0.353071	+	0.485961i
$876$		0			0
$877$	404.726	−	131.503i	0.461489	−	0.149947i	−0.0690394	−	0.997614i	$-0.521993\pi$
$877$	404.726	−	131.503i	0.461489	−	0.149947i	0.530529	+	0.847667i	$0.321993\pi$
$878$		0			0
$879$		−	1946.26i		−	2.21417i
$880$		0			0
$881$	−1669.31			−1.89479			−0.947396	−	0.320064i	$-0.896296\pi$
$881$	−1669.31			−1.89479			−0.947396	+	0.320064i	$0.896296\pi$
$882$		0			0
$883$	−65.8838	−	202.770i	−0.0746136	−	0.229637i	0.906793	−	0.421575i	$-0.138523\pi$
$883$	−65.8838	−	202.770i	−0.0746136	−	0.229637i	−0.981407	+	0.191938i	$0.938523\pi$
$884$		0			0
$885$	105.348	+	76.5399i	0.119037	+	0.0864857i
$886$		0			0
$887$	−498.213	−	161.879i	−0.561683	−	0.182502i	0.0143952	−	0.999896i	$-0.495418\pi$
$887$	−498.213	−	161.879i	−0.561683	−	0.182502i	−0.576078	+	0.817394i	$0.695418\pi$
$888$		0			0
$889$	−75.9672	+	55.1934i	−0.0854524	+	0.0620848i
$890$		0			0
$891$	168.226	+	672.248i	0.188806	+	0.754487i
$892$		0			0
$893$	69.5419	+	95.7162i	0.0778744	+	0.107185i
$894$		0			0
$895$	−449.634	+	1383.83i	−0.502384	+	1.54618i
$896$		0			0
$897$	155.024	−	213.373i	0.172825	−	0.237874i
$898$		0			0
$899$	700.732	−	227.682i	0.779457	−	0.253261i
$900$		0			0
$901$		−	619.574i		−	0.687651i
$902$		0			0
$903$	3701.67			4.09930
$904$		0			0
$905$	−4.00004	−	12.3108i	−0.00441993	−	0.0136031i
$906$		0			0
$907$	−705.473	−	512.556i	−0.777810	−	0.565112i	0.126511	−	0.991965i	$-0.459622\pi$
$907$	−705.473	−	512.556i	−0.777810	−	0.565112i	−0.904321	+	0.426853i	$0.859622\pi$
$908$		0			0
$909$	−451.621	−	146.741i	−0.496833	−	0.161431i
$910$		0			0
$911$	733.848	−	533.172i	0.805541	−	0.585260i	−0.106993	−	0.994260i	$-0.534122\pi$
$911$	733.848	−	533.172i	0.805541	−	0.585260i	0.912534	+	0.409000i	$0.134122\pi$
$912$		0			0
$913$	8.74487	−	126.626i	0.00957817	−	0.138693i
$914$		0			0
$915$	1858.89	+	2558.55i	2.03158	+	2.79623i
$916$		0			0
$917$	−578.263	+	1779.71i	−0.630603	+	1.94080i
$918$		0			0
$919$	−708.097	+	974.612i	−0.770508	+	1.06051i	0.225758	+	0.974183i	$0.427514\pi$
$919$	−708.097	+	974.612i	−0.770508	+	1.06051i	−0.996267	+	0.0863305i	$0.972486\pi$
$920$		0			0
$921$	−982.698	+	319.298i	−1.06699	+	0.346686i
$922$		0			0
$923$			271.277i			0.293908i
$924$		0			0
$925$	−665.798			−0.719782
$926$		0			0
$927$	178.310	+	548.783i	0.192352	+	0.591999i
$928$		0			0
$929$	1387.31	+	1007.94i	1.49334	+	1.08497i	0.972942	+	0.231050i	$0.0742160\pi$
$929$	1387.31	+	1007.94i	1.49334	+	1.08497i	0.520397	+	0.853924i	$0.325784\pi$
$930$		0			0
$931$	−861.860	−	280.035i	−0.925736	−	0.300790i
$932$		0			0
$933$	−546.040	+	396.721i	−0.585252	+	0.425210i
$934$		0			0
$935$	397.107	−	474.083i	0.424713	−	0.507040i
$936$		0			0
$937$	−525.277	−	722.982i	−0.560595	−	0.771593i	0.430807	−	0.902444i	$-0.358229\pi$
$937$	−525.277	−	722.982i	−0.560595	−	0.771593i	−0.991402	+	0.130851i	$0.958229\pi$
$938$		0			0
$939$	−138.057	+	424.895i	−0.147025	+	0.452497i
$940$		0			0
$941$	−856.109	+	1178.33i	−0.909786	+	1.25221i	0.0574535	+	0.998348i	$0.481702\pi$
$941$	−856.109	+	1178.33i	−0.909786	+	1.25221i	−0.967240	+	0.253865i	$0.918298\pi$
$942$		0			0
$943$	−473.843	+	153.961i	−0.502485	+	0.163267i
$944$		0			0
$945$		−	564.823i		−	0.597697i
$946$		0			0
$947$	1026.37			1.08381			0.541906	−	0.840439i	$-0.317703\pi$
$947$	1026.37			1.08381			0.541906	+	0.840439i	$0.317703\pi$
$948$		0			0
$949$	−38.9946	−	120.013i	−0.0410902	−	0.126463i
$950$		0			0
$951$	1199.20	+	871.267i	1.26098	+	0.916159i
$952$		0			0
$953$	73.2826	+	23.8110i	0.0768968	+	0.0249853i	0.347213	−	0.937786i	$-0.387128\pi$
$953$	73.2826	+	23.8110i	0.0768968	+	0.0249853i	−0.270316	+	0.962772i	$0.587128\pi$
$954$		0			0
$955$	110.383	−	80.1977i	0.115584	−	0.0839766i
$956$		0			0
$957$	−524.207	−	837.299i	−0.547760	−	0.874920i
$958$		0			0
$959$	−1589.90	−	2188.31i	−1.65787	−	2.28186i
$960$		0			0
$961$	112.486	−	346.196i	0.117051	−	0.360245i
$962$		0			0
$963$	−825.190	+	1135.78i	−0.856895	+	1.17941i
$964$		0			0
$965$	1165.91	−	378.828i	1.20820	−	0.392567i
$966$		0			0
$967$		−	637.935i		−	0.659705i	−0.944032	−	0.329853i	$-0.893001\pi$
$967$		−	637.935i		−	0.659705i	0.944032	−	0.329853i	$-0.106999\pi$
$968$		0			0
$969$	−411.931			−0.425110
$970$		0			0
$971$	415.360	+	1278.35i	0.427766	+	1.31653i	0.900321	+	0.435226i	$0.143332\pi$
$971$	415.360	+	1278.35i	0.427766	+	1.31653i	−0.472556	+	0.881301i	$0.656668\pi$
$972$		0			0
$973$	−2213.07	−	1607.89i	−2.27448	−	1.65251i
$974$		0			0
$975$	385.133	+	125.137i	0.395008	+	0.128346i
$976$		0			0
$977$	−620.481	+	450.806i	−0.635088	+	0.461418i	−0.858159	−	0.513384i	$-0.828392\pi$
$977$	−620.481	+	450.806i	−0.635088	+	0.461418i	0.223071	+	0.974802i	$0.428392\pi$
$978$		0			0
$979$	−705.771	+	441.861i	−0.720910	+	0.451339i
$980$		0			0
$981$	43.7443	+	60.2089i	0.0445915	+	0.0613750i
$982$		0			0
$983$	198.170	−	609.906i	0.201598	−	0.620454i	−0.798238	−	0.602342i	$-0.794235\pi$
$983$	198.170	−	609.906i	0.201598	−	0.620454i	0.999836	−	0.0181119i	$-0.00576550\pi$
$984$		0			0
$985$	1255.70	−	1728.33i	1.27483	−	1.75465i
$986$		0			0
$987$	−530.656	+	172.421i	−0.537646	+	0.174692i
$988$		0			0
$989$			851.345i			0.860814i
$990$		0			0
$991$	−1547.49			−1.56154			−0.780770	−	0.624818i	$-0.785173\pi$
$991$	−1547.49			−1.56154			−0.780770	+	0.624818i	$0.785173\pi$
$992$		0			0
$993$	−231.176	−	711.487i	−0.232806	−	0.716502i
$994$		0			0
$995$	406.613	+	295.422i	0.408656	+	0.296906i
$996$		0			0
$997$	1848.46	+	600.601i	1.85402	+	0.602408i	0.996059	+	0.0886972i	$0.0282703\pi$
$997$	1848.46	+	600.601i	1.85402	+	0.602408i	0.857963	+	0.513711i	$0.171730\pi$
$998$		0			0
$999$	−223.146	+	162.125i	−0.223369	+	0.162287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	44.3.f.a.41.1	yes	8
3.2	odd	2		396.3.t.a.217.2		8
4.3	odd	2		176.3.n.c.129.2		8
11.2	odd	10		484.3.d.c.241.1		8
11.3	even	5		484.3.f.d.457.2		8
11.4	even	5		484.3.f.a.161.1		8
11.5	even	5		484.3.f.e.233.2		8
11.6	odd	10		484.3.f.d.233.2		8
11.7	odd	10	inner	44.3.f.a.29.1	✓	8
11.8	odd	10		484.3.f.e.457.2		8
11.9	even	5		484.3.d.c.241.2		8
11.10	odd	2		484.3.f.a.481.1		8
33.2	even	10		4356.3.f.g.1693.1		8
33.20	odd	10		4356.3.f.g.1693.2		8
33.29	even	10		396.3.t.a.73.2		8
44.7	even	10		176.3.n.c.161.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.3.f.a.29.1	✓	8	11.7	odd	10	inner
44.3.f.a.41.1	yes	8	1.1	even	1	trivial
176.3.n.c.129.2		8	4.3	odd	2
176.3.n.c.161.2		8	44.7	even	10
396.3.t.a.73.2		8	33.29	even	10
396.3.t.a.217.2		8	3.2	odd	2
484.3.d.c.241.1		8	11.2	odd	10
484.3.d.c.241.2		8	11.9	even	5
484.3.f.a.161.1		8	11.4	even	5
484.3.f.a.481.1		8	11.10	odd	2
484.3.f.d.233.2		8	11.6	odd	10
484.3.f.d.457.2		8	11.3	even	5
484.3.f.e.233.2		8	11.5	even	5
484.3.f.e.457.2		8	11.8	odd	10
4356.3.f.g.1693.1		8	33.2	even	10
4356.3.f.g.1693.2		8	33.20	odd	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:	\( N \)	\(=\)	\( 44 = 2^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	44.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37103 - 4.21961i) q^{3} +(-5.30779 - 3.85634i) q^{5} +(10.9532 + 3.55892i) q^{7} +(-8.64421 + 6.28038i) q^{9} +(9.32350 - 5.83715i) q^{11} +(2.97320 + 4.09226i) q^{13} +(-8.99507 + 27.6840i) q^{15} +(-5.03681 + 6.93258i) q^{17} +(-10.3045 + 3.34815i) q^{19} -51.0977i q^{21} +11.7519 q^{23} +(5.57590 + 17.1609i) q^{25} +(6.04753 + 4.39379i) q^{27} +(19.2505 + 6.25487i) q^{29} +(29.4488 - 21.3958i) q^{31} +(-37.4133 - 31.3386i) q^{33} +(-44.4130 - 61.1293i) q^{35} +(-11.4023 + 35.0927i) q^{37} +(13.1914 - 18.1564i) q^{39} +(-40.3205 + 13.1009i) q^{41} +72.4430i q^{43} +70.1009 q^{45} +(-3.37433 - 10.3851i) q^{47} +(67.6654 + 49.1618i) q^{49} +(36.1584 + 11.7486i) q^{51} +(-58.4943 + 42.4986i) q^{53} +(-71.9972 - 4.97215i) q^{55} +(28.2557 + 38.8907i) q^{57} +(1.38239 - 4.25455i) q^{59} +(63.8606 - 87.8965i) q^{61} +(-117.033 + 38.0264i) q^{63} -33.1866i q^{65} -37.6104 q^{67} +(-16.1123 - 49.5886i) q^{69} +(43.3875 + 31.5228i) q^{71} +(-23.7259 - 7.70902i) q^{73} +(64.7673 - 47.0562i) q^{75} +(122.896 - 30.7541i) q^{77} +(-41.8941 - 57.6623i) q^{79} +(-19.4674 + 59.9146i) q^{81} +(6.78240 - 9.33518i) q^{83} +(53.4687 - 17.3730i) q^{85} -89.8052i q^{87} -75.6980 q^{89} +(18.0021 + 55.4048i) q^{91} +(-130.657 - 94.9280i) q^{93} +(67.6059 + 21.9665i) q^{95} +(-2.41589 + 1.75525i) q^{97} +(-43.9347 + 109.013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{3} - q^{5} + 15 q^{7} - q^{9} + 17 q^{11} - 15 q^{13} - 63 q^{15} - 75 q^{17} - 30 q^{19} + 100 q^{23} + 51 q^{25} + 100 q^{27} + 125 q^{29} + 73 q^{31} - 20 q^{33} - 155 q^{35} - 75 q^{37}+ \cdots - 419 q^{99}+O(q^{100}) \) 8 * q - 5 * q^3 - q^5 + 15 * q^7 - q^9 + 17 * q^11 - 15 * q^13 - 63 * q^15 - 75 * q^17 - 30 * q^19 + 100 * q^23 + 51 * q^25 + 100 * q^27 + 125 * q^29 + 73 * q^31 - 20 * q^33 - 155 * q^35 - 75 * q^37 - 185 * q^39 - 155 * q^41 + 332 * q^45 + 45 * q^47 + 87 * q^49 + 150 * q^51 - 85 * q^53 - 89 * q^55 - 310 * q^57 - 178 * q^59 - 145 * q^61 - 110 * q^63 + 10 * q^67 + 124 * q^69 + 207 * q^71 + 65 * q^73 + 192 * q^75 + 365 * q^77 + 235 * q^79 - 12 * q^81 + 210 * q^83 + 105 * q^85 + 18 * q^89 - 195 * q^91 - 335 * q^93 - 255 * q^95 - 90 * q^97 - 419 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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