LMFDB - Embedded newform 44.3.h.a.3.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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([5, 8]))

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

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

chi := DirichletCharacter("44.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 44 = 2^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	44.h (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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			3.7
Character	$\chi$	$=$	44.3
Dual form			44.3.h.a.15.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.844007 - 1.81319i) q^{2} +(1.03917 - 0.337648i) q^{3} +(-2.57530 - 3.06069i) q^{4} +(0.605291 + 0.439770i) q^{5} +(0.264851 - 2.16920i) q^{6} +(3.68852 + 1.19847i) q^{7} +(-7.72318 + 2.08627i) q^{8} +(-6.31528 + 4.58832i) q^{9} +O(q^{10})$	\(q+(0.844007 - 1.81319i) q^{2} +(1.03917 - 0.337648i) q^{3} +(-2.57530 - 3.06069i) q^{4} +(0.605291 + 0.439770i) q^{5} +(0.264851 - 2.16920i) q^{6} +(3.68852 + 1.19847i) q^{7} +(-7.72318 + 2.08627i) q^{8} +(-6.31528 + 4.58832i) q^{9} +(1.30826 - 0.726338i) q^{10} +(10.4619 + 3.39827i) q^{11} +(-3.70962 - 2.31104i) q^{12} +(-2.78472 + 2.02322i) q^{13} +(5.28619 - 5.67646i) q^{14} +(0.777490 + 0.252622i) q^{15} +(-2.73563 + 15.7644i) q^{16} +(6.28791 + 4.56843i) q^{17} +(2.98934 + 15.3234i) q^{18} +(-18.2467 + 5.92872i) q^{19} +(-0.212810 - 2.98515i) q^{20} +4.23767 q^{21} +(14.9916 - 16.1013i) q^{22} -15.0061i q^{23} +(-7.32131 + 4.77571i) q^{24} +(-7.55245 - 23.2440i) q^{25} +(1.31815 + 6.75684i) q^{26} +(-10.7936 + 14.8562i) q^{27} +(-5.83090 - 14.3758i) q^{28} +(4.31911 - 13.2929i) q^{29} +(1.11426 - 1.19652i) q^{30} +(-32.6981 - 45.0051i) q^{31} +(26.2749 + 18.2655i) q^{32} +(12.0192 - 0.00105272i) q^{33} +(13.5905 - 7.54537i) q^{34} +(1.70557 + 2.34752i) q^{35} +(30.3072 + 7.51279i) q^{36} +(11.3339 - 34.8823i) q^{37} +(-4.65049 + 38.0886i) q^{38} +(-2.21068 + 3.04274i) q^{39} +(-5.59225 - 2.13362i) q^{40} +(17.0545 + 52.4884i) q^{41} +(3.57663 - 7.68370i) q^{42} +43.0444i q^{43} +(-16.5416 - 40.7723i) q^{44} -5.84038 q^{45} +(-27.2090 - 12.6653i) q^{46} +(46.1847 - 15.0063i) q^{47} +(2.48003 + 17.3056i) q^{48} +(-27.4730 - 19.9603i) q^{49} +(-48.5201 - 5.92413i) q^{50} +(8.07676 + 2.62430i) q^{51} +(13.3640 + 3.31277i) q^{52} +(-74.7736 + 54.3262i) q^{53} +(17.8271 + 32.1096i) q^{54} +(4.83805 + 6.65778i) q^{55} +(-30.9874 - 1.56078i) q^{56} +(-16.9597 + 12.3220i) q^{57} +(-20.4571 - 19.0506i) q^{58} +(76.2995 + 24.7912i) q^{59} +(-1.22908 - 3.03023i) q^{60} +(62.8898 + 45.6921i) q^{61} +(-109.200 + 21.3032i) q^{62} +(-28.7930 + 9.35541i) q^{63} +(55.2950 - 32.2252i) q^{64} -2.57532 q^{65} +(10.1424 - 21.7939i) q^{66} +57.7376i q^{67} +(-2.21072 - 31.0104i) q^{68} +(-5.06680 - 15.5940i) q^{69} +(5.69602 - 1.11120i) q^{70} +(57.7740 - 79.5191i) q^{71} +(39.2016 - 48.6117i) q^{72} +(23.1219 - 71.1618i) q^{73} +(-53.6822 - 49.9914i) q^{74} +(-15.6966 - 21.6045i) q^{75} +(65.1368 + 40.5793i) q^{76} +(34.5162 + 25.0729i) q^{77} +(3.65123 + 6.57647i) q^{78} +(-44.4641 - 61.1996i) q^{79} +(-8.58856 + 8.33900i) q^{80} +(15.5097 - 47.7339i) q^{81} +(109.565 + 13.3775i) q^{82} +(-38.8192 + 53.4301i) q^{83} +(-10.9133 - 12.9702i) q^{84} +(1.79696 + 5.53046i) q^{85} +(78.0477 + 36.3298i) q^{86} -15.2719i q^{87} +(-87.8890 - 4.41910i) q^{88} +46.7420 q^{89} +(-4.92933 + 10.5897i) q^{90} +(-12.6963 + 4.12527i) q^{91} +(-45.9291 + 38.6454i) q^{92} +(-49.1749 - 35.7277i) q^{93} +(11.7709 - 96.4070i) q^{94} +(-13.6519 - 4.43576i) q^{95} +(33.4715 + 10.1093i) q^{96} +(-86.8069 + 63.0689i) q^{97} +(-59.3792 + 32.9671i) q^{98} +(-81.6622 + 26.5416i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{2} - 9 q^{4} - 6 q^{5} - 11 q^{6} + 7 q^{8} + 20 q^{9}+O(q^{10}) $ 40 * q - 5 * q^2 - 9 * q^4 - 6 * q^5 - 11 * q^6 + 7 * q^8 + 20 * q^9	$ 40 q - 5 q^{2} - 9 q^{4} - 6 q^{5} - 11 q^{6} + 7 q^{8} + 20 q^{9} - 8 q^{10} - 50 q^{12} - 6 q^{13} - 36 q^{14} - 65 q^{16} - 30 q^{17} - 58 q^{18} + 34 q^{20} - 52 q^{21} + 25 q^{22} + 49 q^{24} + 156 q^{26} + 130 q^{28} - 38 q^{29} + 94 q^{30} + 20 q^{32} - 110 q^{33} + 258 q^{34} + 324 q^{36} - 150 q^{37} + 80 q^{38} + 112 q^{40} - 150 q^{41} - 230 q^{42} + 4 q^{44} + 144 q^{45} + 40 q^{46} - 304 q^{48} + 132 q^{49} - 177 q^{50} - 314 q^{52} + 290 q^{53} - 540 q^{54} - 856 q^{56} + 242 q^{57} - 476 q^{58} - 344 q^{60} + 42 q^{61} - 364 q^{62} + 303 q^{64} + 164 q^{65} - 50 q^{66} + 14 q^{68} - 104 q^{69} + 576 q^{70} + 535 q^{72} + 186 q^{73} + 588 q^{74} + 366 q^{76} + 190 q^{77} + 1412 q^{78} + 1100 q^{80} - 160 q^{81} + 365 q^{82} + 380 q^{84} + 286 q^{85} - 501 q^{86} + 47 q^{88} - 88 q^{89} - 150 q^{90} - 702 q^{92} - 178 q^{93} - 678 q^{94} - 616 q^{96} - 130 q^{97} - 652 q^{98}+O(q^{100}) $ 40 * q - 5 * q^2 - 9 * q^4 - 6 * q^5 - 11 * q^6 + 7 * q^8 + 20 * q^9 - 8 * q^10 - 50 * q^12 - 6 * q^13 - 36 * q^14 - 65 * q^16 - 30 * q^17 - 58 * q^18 + 34 * q^20 - 52 * q^21 + 25 * q^22 + 49 * q^24 + 156 * q^26 + 130 * q^28 - 38 * q^29 + 94 * q^30 + 20 * q^32 - 110 * q^33 + 258 * q^34 + 324 * q^36 - 150 * q^37 + 80 * q^38 + 112 * q^40 - 150 * q^41 - 230 * q^42 + 4 * q^44 + 144 * q^45 + 40 * q^46 - 304 * q^48 + 132 * q^49 - 177 * q^50 - 314 * q^52 + 290 * q^53 - 540 * q^54 - 856 * q^56 + 242 * q^57 - 476 * q^58 - 344 * q^60 + 42 * q^61 - 364 * q^62 + 303 * q^64 + 164 * q^65 - 50 * q^66 + 14 * q^68 - 104 * q^69 + 576 * q^70 + 535 * q^72 + 186 * q^73 + 588 * q^74 + 366 * q^76 + 190 * q^77 + 1412 * q^78 + 1100 * q^80 - 160 * q^81 + 365 * q^82 + 380 * q^84 + 286 * q^85 - 501 * q^86 + 47 * q^88 - 88 * q^89 - 150 * q^90 - 702 * q^92 - 178 * q^93 - 678 * q^94 - 616 * q^96 - 130 * q^97 - 652 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$

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 $

$2$	0.844007	−	1.81319i	0.422004	−	0.906594i
$2$	0.844007	−	1.81319i	0.422004	−	0.906594i
$3$	1.03917	−	0.337648i	0.346391	−	0.112549i	−0.130654	−	0.991428i	$-0.541708\pi$
$3$	1.03917	−	0.337648i	0.346391	−	0.112549i	0.477045	+	0.878879i	$0.341708\pi$
$4$	−2.57530	−	3.06069i	−0.643826	−	0.765172i
$5$	0.605291	+	0.439770i	0.121058	+	0.0879539i	0.646667	−	0.762773i	$-0.276162\pi$
$5$	0.605291	+	0.439770i	0.121058	+	0.0879539i	−0.525609	+	0.850726i	$0.676162\pi$
$6$	0.264851	−	2.16920i	0.0441418	−	0.361533i
$7$	3.68852	+	1.19847i	0.526931	+	0.171210i	0.560389	−	0.828230i	$-0.310652\pi$
$7$	3.68852	+	1.19847i	0.526931	+	0.171210i	−0.0334574	+	0.999440i	$0.510652\pi$
$8$	−7.72318	+	2.08627i	−0.965397	+	0.260783i
$9$	−6.31528	+	4.58832i	−0.701697	+	0.509813i
$10$	1.30826	−	0.726338i	0.130826	−	0.0726338i
$11$	10.4619	+	3.39827i	0.951084	+	0.308934i
$11$	10.4619	+	3.39827i	0.951084	+	0.308934i
$12$	−3.70962	−	2.31104i	−0.309135	−	0.192587i
$13$	−2.78472	+	2.02322i	−0.214210	+	0.155632i	−0.689716	−	0.724080i	$-0.742265\pi$
$13$	−2.78472	+	2.02322i	−0.214210	+	0.155632i	0.475507	+	0.879712i	$0.342265\pi$
$14$	5.28619	−	5.67646i	0.377585	−	0.405461i
$15$	0.777490	+	0.252622i	0.0518327	+	0.0168415i
$16$	−2.73563	+	15.7644i	−0.170977	+	0.985275i
$17$	6.28791	+	4.56843i	0.369877	+	0.268731i	0.757160	−	0.653230i	$-0.226586\pi$
$17$	6.28791	+	4.56843i	0.369877	+	0.268731i	−0.387283	+	0.921961i	$0.626586\pi$
$18$	2.98934	+	15.3234i	0.166075	+	0.851298i
$19$	−18.2467	+	5.92872i	−0.960354	+	0.312038i	−0.746916	−	0.664919i	$-0.768466\pi$
$19$	−18.2467	+	5.92872i	−0.960354	+	0.312038i	−0.213438	+	0.976957i	$0.568466\pi$
$20$	−0.212810	−	2.98515i	−0.0106405	−	0.149257i
$21$	4.23767			0.201794
$22$	14.9916	−	16.1013i	0.681438	−	0.731876i
$23$		−	15.0061i		−	0.652441i	−0.945294	−	0.326220i	$-0.894225\pi$
$23$		−	15.0061i		−	0.652441i	0.945294	−	0.326220i	$-0.105775\pi$
$24$	−7.32131	+	4.77571i	−0.305054	+	0.198988i
$25$	−7.55245	−	23.2440i	−0.302098	−	0.929761i
$26$	1.31815	+	6.75684i	0.0506982	+	0.259879i
$27$	−10.7936	+	14.8562i	−0.399764	+	0.550229i
$28$	−5.83090	−	14.3758i	−0.208247	−	0.513423i
$29$	4.31911	−	13.2929i	0.148935	−	0.458374i	−0.848561	−	0.529097i	$-0.822531\pi$
$29$	4.31911	−	13.2929i	0.148935	−	0.458374i	0.997496	+	0.0707231i	$0.0225307\pi$
$30$	1.11426	−	1.19652i	0.0371420	−	0.0398840i
$31$	−32.6981	−	45.0051i	−1.05478	−	1.45178i	−0.884593	−	0.466364i	$-0.845564\pi$
$31$	−32.6981	−	45.0051i	−1.05478	−	1.45178i	−0.170185	−	0.985412i	$-0.554436\pi$
$32$	26.2749	+	18.2655i	0.821092	+	0.570796i
$33$	12.0192	−	0.00105272i	0.364218	−	3.19005e-5i
$34$	13.5905	−	7.54537i	0.399720	−	0.221923i
$35$	1.70557	+	2.34752i	0.0487307	+	0.0670721i
$36$	30.3072	+	7.51279i	0.841865	+	0.208688i
$37$	11.3339	−	34.8823i	0.306323	−	0.942764i	−0.672858	−	0.739772i	$-0.734933\pi$
$37$	11.3339	−	34.8823i	0.306323	−	0.942764i	0.979180	−	0.202992i	$-0.0650666\pi$
$38$	−4.65049	+	38.0886i	−0.122381	+	1.00233i
$39$	−2.21068	+	3.04274i	−0.0566840	+	0.0780189i
$40$	−5.59225	−	2.13362i	−0.139806	−	0.0533405i
$41$	17.0545	+	52.4884i	0.415964	+	1.28020i	0.911386	+	0.411553i	$0.135013\pi$
$41$	17.0545	+	52.4884i	0.415964	+	1.28020i	−0.495422	+	0.868652i	$0.664987\pi$
$42$	3.57663	−	7.68370i	0.0851578	−	0.182945i
$43$			43.0444i			1.00103i	0.865727	+	0.500517i	$0.166857\pi$
$43$			43.0444i			1.00103i	−0.865727	+	0.500517i	$0.833143\pi$
$44$	−16.5416	−	40.7723i	−0.375945	−	0.926642i
$45$	−5.84038			−0.129786
$46$	−27.2090	−	12.6653i	−0.591499	−	0.275332i
$47$	46.1847	−	15.0063i	0.982653	−	0.319283i	0.226740	−	0.973955i	$-0.427193\pi$
$47$	46.1847	−	15.0063i	0.982653	−	0.319283i	0.755913	+	0.654672i	$0.227193\pi$
$48$	2.48003	+	17.3056i	0.0516673	+	0.360534i
$49$	−27.4730	−	19.9603i	−0.560674	−	0.407353i
$50$	−48.5201	−	5.92413i	−0.970403	−	0.118483i
$51$	8.07676	+	2.62430i	0.158368	+	0.0514568i
$52$	13.3640	+	3.31277i	0.256999	+	0.0637071i
$53$	−74.7736	+	54.3262i	−1.41082	+	1.02502i	−0.417621	+	0.908621i	$0.637136\pi$
$53$	−74.7736	+	54.3262i	−1.41082	+	1.02502i	−0.993202	+	0.116402i	$0.962864\pi$
$54$	17.8271	+	32.1096i	0.330132	+	0.594623i
$55$	4.83805	+	6.65778i	0.0879645	+	0.121050i
$56$	−30.9874	−	1.56078i	−0.553347	−	0.0278712i
$57$	−16.9597	+	12.3220i	−0.297539	+	0.216175i
$58$	−20.4571	−	19.0506i	−0.352708	−	0.328459i
$59$	76.2995	+	24.7912i	1.29321	+	0.420190i	0.873215	−	0.487335i	$-0.162031\pi$
$59$	76.2995	+	24.7912i	1.29321	+	0.420190i	0.419997	+	0.907525i	$0.362031\pi$
$60$	−1.22908	−	3.03023i	−0.0204846	−	0.0505039i
$61$	62.8898	+	45.6921i	1.03098	+	0.749052i	0.968505	−	0.248995i	$-0.0801002\pi$
$61$	62.8898	+	45.6921i	1.03098	+	0.749052i	0.0624763	+	0.998046i	$0.480100\pi$
$62$	−109.200	+	21.3032i	−1.76129	+	0.343600i
$63$	−28.7930	+	9.35541i	−0.457031	+	0.148499i
$64$	55.2950	−	32.2252i	0.863984	−	0.503519i
$65$	−2.57532			−0.0396203
$66$	10.1424	−	21.7939i	0.153672	−	0.330211i
$67$			57.7376i			0.861755i	0.902411	+	0.430877i	$0.141796\pi$
$67$			57.7376i			0.861755i	−0.902411	+	0.430877i	$0.858204\pi$
$68$	−2.21072	−	31.0104i	−0.0325106	−	0.456036i
$69$	−5.06680	−	15.5940i	−0.0734318	−	0.226000i
$70$	5.69602	−	1.11120i	0.0813717	−	0.0158743i
$71$	57.7740	−	79.5191i	0.813719	−	1.11999i	−0.177020	−	0.984207i	$-0.556646\pi$
$71$	57.7740	−	79.5191i	0.813719	−	1.11999i	0.990739	−	0.135780i	$-0.0433541\pi$
$72$	39.2016	−	48.6117i	0.544466	−	0.675163i
$73$	23.1219	−	71.1618i	0.316738	−	0.974820i	−0.658295	−	0.752760i	$-0.728722\pi$
$73$	23.1219	−	71.1618i	0.316738	−	0.974820i	0.975033	−	0.222060i	$-0.0712780\pi$
$74$	−53.6822	−	49.9914i	−0.725435	−	0.675560i
$75$	−15.6966	−	21.6045i	−0.209288	−	0.288060i
$76$	65.1368	+	40.5793i	0.857064	+	0.533938i
$77$	34.5162	+	25.0729i	0.448263	+	0.325622i
$78$	3.65123	+	6.57647i	0.0468106	+	0.0843137i
$79$	−44.4641	−	61.1996i	−0.562837	−	0.774678i	0.428847	−	0.903377i	$-0.358920\pi$
$79$	−44.4641	−	61.1996i	−0.562837	−	0.774678i	−0.991684	+	0.128699i	$0.958920\pi$
$80$	−8.58856	+	8.33900i	−0.107357	+	0.104238i
$81$	15.5097	−	47.7339i	0.191477	−	0.589307i
$82$	109.565	+	13.3775i	1.33616	+	0.163141i
$83$	−38.8192	+	53.4301i	−0.467701	+	0.643736i	−0.976084	−	0.217396i	$-0.930244\pi$
$83$	−38.8192	+	53.4301i	−0.467701	+	0.643736i	0.508382	+	0.861132i	$0.330244\pi$
$84$	−10.9133	−	12.9702i	−0.129920	−	0.154407i
$85$	1.79696	+	5.53046i	0.0211407	+	0.0650643i
$86$	78.0477	+	36.3298i	0.907531	+	0.422440i
$87$		−	15.2719i		−	0.175539i
$88$	−87.8890	−	4.41910i	−0.998738	−	0.0502171i
$89$	46.7420			0.525191			0.262596	−	0.964906i	$-0.415421\pi$
$89$	46.7420			0.525191			0.262596	+	0.964906i	$0.415421\pi$
$90$	−4.92933	+	10.5897i	−0.0547703	+	0.117663i
$91$	−12.6963	+	4.12527i	−0.139520	+	0.0453327i
$92$	−45.9291	+	38.6454i	−0.499229	+	0.420058i
$93$	−49.1749	−	35.7277i	−0.528762	−	0.384168i
$94$	11.7709	−	96.4070i	0.125223	−	1.02561i
$95$	−13.6519	−	4.43576i	−0.143704	−	0.0466922i
$96$	33.4715	+	10.1093i	0.348662	+	0.105306i
$97$	−86.8069	+	63.0689i	−0.894916	+	0.650195i	−0.937155	−	0.348913i	$-0.886551\pi$
$97$	−86.8069	+	63.0689i	−0.894916	+	0.650195i	0.0422389	+	0.999108i	$0.486551\pi$
$98$	−59.3792	+	32.9671i	−0.605910	+	0.336399i
$99$	−81.6622	+	26.5416i	−0.824871	+	0.268097i
$100$	−51.6929	+	82.9761i	−0.516929	+	0.829761i
$101$	58.6040	−	42.5783i	0.580238	−	0.421568i	−0.258572	−	0.965992i	$-0.583252\pi$
$101$	58.6040	−	42.5783i	0.580238	−	0.421568i	0.838810	+	0.544424i	$0.183252\pi$
$102$	11.5752	−	12.4298i	0.113482	−	0.121860i
$103$	−19.9403	−	6.47899i	−0.193595	−	0.0629029i	0.210615	−	0.977569i	$-0.432453\pi$
$103$	−19.9403	−	6.47899i	−0.193595	−	0.0629029i	−0.404210	+	0.914666i	$0.632453\pi$
$104$	17.2859	−	21.4354i	0.166211	−	0.206109i
$105$	2.56503	+	1.86360i	0.0244288	+	0.0177486i
$106$	35.3942	+	181.430i	0.333907	+	1.71161i
$107$	−24.9694	+	8.11306i	−0.233359	+	0.0758230i	−0.423362	−	0.905961i	$-0.639150\pi$
$107$	−24.9694	+	8.11306i	−0.233359	+	0.0758230i	0.190003	+	0.981783i	$0.439150\pi$
$108$	73.2670	−	5.22318i	0.678398	−	0.0483628i
$109$	−79.3568			−0.728044			−0.364022	−	0.931390i	$-0.618597\pi$
$109$	−79.3568			−0.728044			−0.364022	+	0.931390i	$0.618597\pi$
$110$	16.1552	−	3.15308i	0.146865	−	0.0286644i
$111$		−	40.0756i		−	0.361042i
$112$	−28.9836	+	54.8687i	−0.258782	+	0.489899i
$113$	−7.02958	−	21.6348i	−0.0622087	−	0.191459i	0.915122	−	0.403177i	$-0.132094\pi$
$113$	−7.02958	−	21.6348i	−0.0622087	−	0.191459i	−0.977331	+	0.211718i	$0.932094\pi$
$114$	8.02790	+	41.1510i	0.0704202	+	0.360973i
$115$	6.59924	−	9.08308i	0.0573847	−	0.0789833i
$116$	−51.8083	+	21.0137i	−0.446623	+	0.181152i
$117$	8.30313	−	25.5544i	0.0709669	−	0.218414i
$118$	109.348	−	117.421i	0.926682	−	0.995097i
$119$	17.7179	+	24.3866i	0.148890	+	0.204930i
$120$	−6.53173	−	0.328993i	−0.0544311	−	0.00274160i
$121$	97.9035	+	71.1049i	0.809120	+	0.587644i
$122$	135.928	−	75.4666i	1.11416	−	0.618579i
$123$	35.4452	+	48.7862i	0.288173	+	0.396636i
$124$	−53.5390	+	215.980i	−0.431766	+	1.74178i
$125$	11.4306	−	35.1798i	0.0914449	−	0.281438i
$126$	−7.33837	+	60.1031i	−0.0582411	+	0.477009i
$127$	−52.1961	+	71.8418i	−0.410993	+	0.565683i	−0.963460	−	0.267851i	$-0.913686\pi$
$127$	−52.1961	+	71.8418i	−0.410993	+	0.565683i	0.552467	+	0.833535i	$0.313686\pi$
$128$	−11.7610	−	127.459i	−0.0918828	−	0.995770i
$129$	14.5339	+	44.7307i	0.112666	+	0.346749i
$130$	−2.17359	+	4.66954i	−0.0167199	+	0.0359195i
$131$		−	170.654i		−	1.30271i	−0.758775	−	0.651353i	$-0.774202\pi$
$131$		−	170.654i		−	1.30271i	0.758775	−	0.651353i	$-0.225798\pi$
$132$	−30.9562	−	36.7842i	−0.234517	−	0.278669i
$133$	−74.4088			−0.559465
$134$	104.689	+	48.7309i	0.781262	+	0.363664i
$135$	−13.0666	+	4.24559i	−0.0967895	+	0.0314488i
$136$	−58.0936	−	22.1646i	−0.427159	−	0.162975i
$137$	−72.1395	−	52.4124i	−0.526565	−	0.382572i	0.292506	−	0.956264i	$-0.405511\pi$
$137$	−72.1395	−	52.4124i	−0.526565	−	0.382572i	−0.819071	+	0.573692i	$0.805511\pi$
$138$	−32.5513	−	3.97439i	−0.235879	−	0.0287999i
$139$	170.380	+	55.3599i	1.22576	+	0.398273i	0.849176	−	0.528111i	$-0.177099\pi$
$139$	170.380	+	55.3599i	1.22576	+	0.398273i	0.376582	+	0.926383i	$0.377099\pi$
$140$	2.79266	−	11.2658i	0.0199476	−	0.0804701i
$141$	42.9271	−	31.1884i	0.304447	−	0.221194i
$142$	−95.4214	−	171.870i	−0.671982	−	1.21035i
$143$	−36.0090	+	11.7035i	−0.251811	+	0.0818428i
$144$	−55.0558	−	112.108i	−0.382332	−	0.778531i
$145$	8.46011	−	6.14663i	0.0583456	−	0.0423906i
$146$	−109.515	−	101.985i	−0.750101	−	0.698530i
$147$	−35.2888	−	11.4660i	−0.240060	−	0.0780002i
$148$	−135.952	+	55.1428i	−0.918595	+	0.372586i
$149$	95.8450	+	69.6355i	0.643255	+	0.467352i	0.860967	−	0.508661i	$-0.169859\pi$
$149$	95.8450	+	69.6355i	0.643255	+	0.467352i	−0.217712	+	0.976013i	$0.569859\pi$
$150$	−52.4211	+	10.2265i	−0.349474	+	0.0681769i
$151$	138.124	−	44.8793i	0.914731	−	0.297214i	0.186427	−	0.982469i	$-0.440309\pi$
$151$	138.124	−	44.8793i	0.914731	−	0.297214i	0.728303	+	0.685255i	$0.240309\pi$
$152$	128.554	−	83.8561i	0.845749	−	0.551685i
$153$	−60.6713			−0.396544
$154$	74.5939	−	41.4227i	0.484376	−	0.268979i
$155$		−	41.6208i		−	0.268521i
$156$	15.0060	−	1.06977i	0.0961925	−	0.00685753i
$157$	27.4296	+	84.4196i	0.174711	+	0.537705i	0.999620	−	0.0275605i	$-0.00877388\pi$
$157$	27.4296	+	84.4196i	0.174711	+	0.537705i	−0.824909	+	0.565265i	$0.808774\pi$
$158$	−148.494	+	28.9689i	−0.939838	+	0.183347i
$159$	−59.3597	+	81.7016i	−0.373331	+	0.513847i
$160$	7.87138	+	22.6108i	0.0491961	+	0.141318i
$161$	17.9844	−	55.3504i	0.111705	−	0.343791i
$162$	−73.4602	−	68.4097i	−0.453458	−	0.422282i
$163$	−13.3585	−	18.3864i	−0.0819539	−	0.112800i	0.766072	−	0.642755i	$-0.222209\pi$
$163$	−13.3585	−	18.3864i	−0.0819539	−	0.112800i	−0.848026	+	0.529955i	$0.822209\pi$
$164$	116.730	−	187.372i	0.711769	−	1.14251i
$165$	7.27556	+	5.28503i	0.0440943	+	0.0320305i
$166$	64.1151	+	115.482i	0.386235	+	0.695674i
$167$	175.977	+	242.212i	1.05376	+	1.45037i	0.885508	+	0.464624i	$0.153811\pi$
$167$	175.977	+	242.212i	1.05376	+	1.45037i	0.168247	+	0.985745i	$0.446189\pi$
$168$	−32.7283	+	8.84092i	−0.194811	+	0.0526245i
$169$	−48.5626	+	149.460i	−0.287353	+	0.884381i
$170$	11.5444	+	1.40953i	0.0679083	+	0.00829136i
$171$	88.0303	−	121.163i	0.514797	−	0.708557i
$172$	131.746	−	110.852i	0.765963	−	0.644491i
$173$	−14.5428	−	44.7583i	−0.0840627	−	0.258718i	0.900187	−	0.435504i	$-0.143430\pi$
$173$	−14.5428	−	44.7583i	−0.0840627	−	0.258718i	−0.984249	+	0.176786i	$0.943430\pi$
$174$	−27.6909	−	12.8896i	−0.159143	−	0.0740783i
$175$		−	94.7874i		−	0.541642i
$176$	−82.1916	+	155.629i	−0.466998	+	0.884258i
$177$	87.6592			0.495250
$178$	39.4506	−	84.7521i	0.221633	−	0.476135i
$179$	−86.7866	+	28.1987i	−0.484842	+	0.157535i	−0.541230	−	0.840874i	$-0.682041\pi$
$179$	−86.7866	+	28.1987i	−0.484842	+	0.157535i	0.0563889	+	0.998409i	$0.482041\pi$
$180$	15.0408	+	17.8756i	0.0835597	+	0.0993088i
$181$	16.1873	+	11.7607i	0.0894324	+	0.0649764i	0.631603	−	0.775292i	$-0.282397\pi$
$181$	16.1873	+	11.7607i	0.0894324	+	0.0649764i	−0.542171	+	0.840268i	$0.682397\pi$
$182$	−3.23586	+	26.5025i	−0.0177795	+	0.145618i
$183$	80.7814	+	26.2475i	0.441428	+	0.143429i
$184$	31.3068	+	115.895i	0.170146	+	0.629865i
$185$	22.2005	−	16.1296i	0.120003	−	0.0871870i
$186$	−106.285	+	59.0090i	−0.571424	+	0.317252i
$187$	50.2588	+	69.1626i	0.268764	+	0.369854i
$188$	−164.869	−	102.711i	−0.876964	−	0.546336i
$189$	−57.6172	+	41.8614i	−0.304853	+	0.221489i
$190$	−19.5651	+	21.0096i	−0.102974	+	0.110577i
$191$	−208.998	−	67.9075i	−1.09423	−	0.355537i	−0.294350	−	0.955698i	$-0.595103\pi$
$191$	−208.998	−	67.9075i	−1.09423	−	0.355537i	−0.799879	+	0.600161i	$0.795103\pi$
$192$	46.5803	−	52.1579i	0.242606	−	0.271656i
$193$	−72.6595	−	52.7902i	−0.376474	−	0.273524i	0.383416	−	0.923576i	$-0.374747\pi$
$193$	−72.6595	−	52.7902i	−0.376474	−	0.273524i	−0.759890	+	0.650051i	$0.774747\pi$
$194$	41.0901	+	210.628i	0.211805	+	1.08571i
$195$	−2.67621	+	0.869552i	−0.0137241	+	0.00445924i
$196$	9.65904	+	135.490i	0.0492808	+	0.691276i
$197$	−113.348			−0.575370			−0.287685	−	0.957725i	$-0.592886\pi$
$197$	−113.348			−0.575370			−0.287685	+	0.957725i	$0.592886\pi$
$198$	−20.7987	+	170.470i	−0.105044	+	0.860961i
$199$			128.213i			0.644289i	0.946691	+	0.322144i	$0.104404\pi$
$199$			128.213i			0.644289i	−0.946691	+	0.322144i	$0.895596\pi$
$200$	106.822	+	163.761i	0.534111	+	0.818807i
$201$	19.4950	+	59.9994i	0.0969900	+	0.298504i
$202$	−27.7403	−	142.197i	−0.137328	−	0.703943i
$203$	31.8622	−	43.8546i	0.156957	−	0.216032i
$204$	−12.7679	−	31.4788i	−0.0625880	−	0.154308i
$205$	−12.7599	+	39.2708i	−0.0622432	+	0.191565i
$206$	−28.5774	+	30.6872i	−0.138725	+	0.148967i
$207$	68.8529	+	94.7679i	0.332623	+	0.457816i
$208$	−24.2769	−	49.4343i	−0.116716	−	0.237665i
$209$	−211.043	+	0.0184845i	−1.00978	+	8.84427e-5i
$210$	5.54396	−	3.07798i	0.0263998	−	0.0146571i
$211$	−169.233	−	232.929i	−0.802053	−	1.10393i	−0.992501	−	0.122234i	$-0.960994\pi$
$211$	−169.233	−	232.929i	−0.802053	−	1.10393i	0.190449	−	0.981697i	$-0.439006\pi$
$212$	358.840	+	88.9523i	1.69264	+	0.419586i
$213$	33.1878	−	102.142i	0.155811	−	0.479538i
$214$	−6.36388	+	52.1217i	−0.0297377	+	0.243560i
$215$	−18.9296	+	26.0544i	−0.0880448	+	0.121183i
$216$	52.3673	−	137.255i	0.242441	−	0.635441i
$217$	−66.6702	−	205.190i	−0.307236	−	0.945575i
$218$	−66.9777	+	143.889i	−0.307237	+	0.660040i
$219$		−	81.7566i		−	0.373318i
$220$	7.91794	−	31.9536i	0.0359906	−	0.145243i
$221$	−26.7530			−0.121055
$222$	−72.6647	−	33.8241i	−0.327318	−	0.152361i
$223$	−146.310	+	47.5389i	−0.656097	+	0.213179i	−0.618101	−	0.786099i	$-0.712098\pi$
$223$	−146.310	+	47.5389i	−0.656097	+	0.213179i	−0.0379966	+	0.999278i	$0.512098\pi$
$224$	75.0249	+	98.8623i	0.334933	+	0.441350i
$225$	154.347	+	112.139i	0.685986	+	0.498398i
$226$	−45.1610	−	5.51400i	−0.199827	−	0.0243982i
$227$	−307.232	−	99.8258i	−1.35345	−	0.439761i	−0.459596	−	0.888128i	$-0.652006\pi$
$227$	−307.232	−	99.8258i	−1.35345	−	0.439761i	−0.893850	+	0.448367i	$0.852006\pi$
$228$	81.3901	+	20.1756i	0.356974	+	0.0884896i
$229$	230.677	−	167.597i	1.00732	−	0.731864i	0.0436787	−	0.999046i	$-0.486092\pi$
$229$	230.677	−	167.597i	1.00732	−	0.731864i	0.963646	+	0.267181i	$0.0860922\pi$
$230$	−10.8995	−	19.6319i	−0.0473892	−	0.0853559i
$231$	44.3342	+	14.4008i	0.191923	+	0.0623410i
$232$	−5.62483	+	111.674i	−0.0242450	+	0.481353i
$233$	157.782	−	114.636i	0.677178	−	0.491999i	−0.195242	−	0.980755i	$-0.562549\pi$
$233$	157.782	−	114.636i	0.677178	−	0.491999i	0.872420	+	0.488756i	$0.162549\pi$
$234$	−39.3270	−	36.6232i	−0.168064	−	0.156510i
$235$	34.5545	+	11.2274i	0.147040	+	0.0477763i
$236$	−120.616	−	297.374i	−0.511086	−	1.26006i
$237$	−66.8699	−	48.5838i	−0.282151	−	0.204995i
$238$	59.1716	−	11.5434i	0.248620	−	0.0485018i
$239$	−200.985	+	65.3040i	−0.840941	+	0.273238i	−0.697647	−	0.716442i	$-0.745770\pi$
$239$	−200.985	+	65.3040i	−0.840941	+	0.273238i	−0.143294	+	0.989680i	$0.545770\pi$
$240$	−6.10936	+	11.5656i	−0.0254557	+	0.0481900i
$241$	328.286			1.36218			0.681092	−	0.732198i	$-0.261505\pi$
$241$	328.286			1.36218			0.681092	+	0.732198i	$0.261505\pi$
$242$	211.558	−	117.504i	0.874206	−	0.485556i
$243$		−	220.110i		−	0.905802i
$244$	−22.1110	−	310.157i	−0.0906188	−	1.27114i
$245$	−7.85123	−	24.1636i	−0.0320458	−	0.0986269i
$246$	118.375	−	23.0930i	0.481197	−	0.0938739i
$247$	38.8170	−	53.4270i	0.157154	−	0.216304i
$248$	346.426	+	279.365i	1.39688	+	1.12647i
$249$	−22.2994	+	68.6304i	−0.0895557	+	0.275624i
$250$	−54.1401	−	50.4179i	−0.216560	−	0.201671i
$251$	49.3072	+	67.8655i	0.196443	+	0.270380i	0.895863	−	0.444330i	$-0.146558\pi$
$251$	49.3072	+	67.8655i	0.196443	+	0.270380i	−0.699420	+	0.714711i	$0.746558\pi$
$252$	102.785	+	64.0333i	0.407876	+	0.254100i
$253$	50.9949	−	156.993i	0.201561	−	0.620526i
$254$	86.2088	+	155.276i	0.339405	+	0.611324i
$255$	3.73470	+	5.14038i	0.0146459	+	0.0201583i
$256$	−241.033	−	86.2510i	−0.941534	−	0.336918i
$257$	−50.0346	+	153.991i	−0.194687	+	0.599185i	0.805293	+	0.592877i	$0.202008\pi$
$257$	−50.0346	+	153.991i	−0.194687	+	0.599185i	−0.999980	+	0.00630817i	$0.997992\pi$
$258$	93.3718	+	11.4004i	0.361906	+	0.0441874i
$259$	83.6108	−	115.080i	0.322822	−	0.444326i
$260$	6.63223	+	7.88225i	0.0255086	+	0.0303164i
$261$	33.7154	+	103.765i	0.129178	+	0.397569i
$262$	−309.429	−	144.034i	−1.18103	−	0.549747i
$263$			399.263i			1.51811i	0.651027	+	0.759055i	$0.274339\pi$
$263$			399.263i			1.51811i	−0.651027	+	0.759055i	$0.725661\pi$
$264$	−92.8241	+	25.0833i	−0.351606	+	0.0950126i
$265$	−69.1508			−0.260947
$266$	−62.8016	+	134.917i	−0.236096	+	0.507207i
$267$	48.5731	−	15.7824i	0.181922	−	0.0591100i
$268$	176.717	−	148.692i	0.659391	−	0.554820i
$269$	51.6076	+	37.4951i	0.191850	+	0.139387i	0.679564	−	0.733617i	$-0.262169\pi$
$269$	51.6076	+	37.4951i	0.191850	+	0.139387i	−0.487714	+	0.873003i	$0.662169\pi$
$270$	−3.33024	+	27.2755i	−0.0123342	+	0.101020i
$271$	−162.436	−	52.7786i	−0.599394	−	0.194755i	−0.00642369	−	0.999979i	$-0.502045\pi$
$271$	−162.436	−	52.7786i	−0.599394	−	0.194755i	−0.592970	+	0.805225i	$0.702045\pi$
$272$	−89.2200	+	86.6276i	−0.328015	+	0.318484i
$273$	−11.8008	+	8.57375i	−0.0432262	+	0.0314057i
$274$	−155.920	+	86.5660i	−0.569050	+	0.315934i
$275$	−0.0235469	−	268.842i	−8.56253e−5	−	0.977609i
$276$	−34.6798	+	55.6671i	−0.125652	+	0.201693i
$277$	−261.885	+	190.270i	−0.945432	+	0.686897i	−0.949722	−	0.313094i	$-0.898634\pi$
$277$	−261.885	+	190.270i	−0.945432	+	0.686897i	0.00428992	+	0.999991i	$0.498634\pi$
$278$	244.180	−	262.207i	0.878346	−	0.943192i
$279$	412.995	+	134.190i	1.48027	+	0.480969i
$280$	−18.0700	−	14.5721i	−0.0645358	−	0.0520430i
$281$	−309.396	−	224.789i	−1.10105	−	0.799961i	−0.119821	−	0.992796i	$-0.538232\pi$
$281$	−309.396	−	224.789i	−1.10105	−	0.799961i	−0.981231	+	0.192834i	$0.938232\pi$
$282$	−20.3196	−	104.158i	−0.0720552	−	0.369355i
$283$	419.260	−	136.226i	1.48148	−	0.481364i	0.546928	−	0.837179i	$-0.315797\pi$
$283$	419.260	−	136.226i	1.48148	−	0.481364i	0.934556	+	0.355816i	$0.115797\pi$
$284$	−392.169	+	27.9576i	−1.38088	+	0.0984421i
$285$	−15.6844			−0.0550329
$286$	−9.17118	+	75.1690i	−0.0320671	+	0.262829i
$287$			214.044i			0.745797i
$288$	−249.741	+	5.20621i	−0.867157	+	0.0180771i
$289$	−70.6387	−	217.404i	−0.244425	−	0.752261i
$290$	−4.00460	−	20.5276i	−0.0138090	−	0.0707847i
$291$	−68.9124	+	94.8498i	−0.236812	+	0.325944i
$292$	−277.350	+	112.494i	−0.949829	+	0.385255i
$293$	−161.544	+	497.182i	−0.551345	+	1.69687i	0.154059	+	0.988062i	$0.450765\pi$
$293$	−161.544	+	497.182i	−0.551345	+	1.69687i	−0.705404	+	0.708805i	$0.749235\pi$
$294$	−50.5741	+	54.3078i	−0.172021	+	0.184721i
$295$	35.2810	+	48.5601i	0.119597	+	0.164611i
$296$	−14.7603	+	293.048i	−0.0498659	+	0.990026i
$297$	−163.408	+	118.744i	−0.550194	+	0.399813i
$298$	207.156	−	115.012i	0.695155	−	0.385947i
$299$	30.3607	+	41.7880i	0.101541	+	0.139759i
$300$	−25.7012	+	103.681i	−0.0856707	+	0.345602i
$301$	−51.5875	+	158.770i	−0.171387	+	0.527476i
$302$	35.2033	−	288.324i	0.116567	−	0.954715i
$303$	46.5233	−	64.0339i	0.153542	−	0.211333i
$304$	−43.5465	−	303.868i	−0.143245	−	0.999564i
$305$	17.9726	+	55.3141i	0.0589267	+	0.181358i
$306$	−51.2070	+	110.008i	−0.167343	+	0.359505i
$307$			528.080i			1.72013i	0.510183	+	0.860066i	$0.329578\pi$
$307$			528.080i			1.72013i	−0.510183	+	0.860066i	$0.670422\pi$
$308$	−12.1495	−	170.214i	−0.0394463	−	0.552642i
$309$	−22.9091			−0.0741394
$310$	−75.4663	−	35.1283i	−0.243440	−	0.113317i
$311$	303.245	−	98.5302i	0.975064	−	0.316817i	0.222205	−	0.975000i	$-0.428674\pi$
$311$	303.245	−	98.5302i	0.975064	−	0.316817i	0.752859	+	0.658182i	$0.228674\pi$
$312$	10.7255	−	28.1117i	0.0343766	−	0.0901015i
$313$	260.815	+	189.493i	0.833274	+	0.605409i	0.920484	−	0.390781i	$-0.127795\pi$
$313$	260.815	+	189.493i	0.833274	+	0.605409i	−0.0872100	+	0.996190i	$0.527795\pi$
$314$	176.219	+	21.5158i	0.561208	+	0.0685215i
$315$	−21.5424	−	6.99953i	−0.0683884	−	0.0222207i
$316$	−72.8043	+	293.698i	−0.230393	+	0.929425i
$317$	293.298	−	213.093i	0.925230	−	0.672219i	−0.0195904	−	0.999808i	$-0.506236\pi$
$317$	293.298	−	213.093i	0.925230	−	0.672219i	0.944820	+	0.327589i	$0.106236\pi$
$318$	98.0404	+	176.587i	0.308303	+	0.555305i
$319$	90.3589	−	124.391i	0.283257	−	0.389941i
$320$	47.6412	+	4.81143i	0.148879	+	0.0150357i
$321$	−23.2082	+	16.8618i	−0.0722998	+	0.0525289i
$322$	−85.1817	−	79.3253i	−0.264539	−	0.246352i
$323$	−141.819	−	46.0797i	−0.439067	−	0.142662i
$324$	−186.041	+	75.4589i	−0.574199	+	0.232898i
$325$	68.0593	+	49.4480i	0.209413	+	0.152148i
$326$	−44.6126	+	8.70321i	−0.136848	+	0.0266970i
$327$	−82.4655	+	26.7947i	−0.252188	+	0.0819409i
$328$	−241.220	−	369.797i	−0.735426	−	1.12743i
$329$	188.338			0.572455
$330$	15.7234	−	8.73136i	0.0476466	−	0.0264587i
$331$		−	88.0333i		−	0.265962i	−0.991119	−	0.132981i	$-0.957545\pi$
$331$		−	88.0333i		−	0.265962i	0.991119	−	0.132981i	$-0.0424549\pi$
$332$	263.504	−	18.7851i	0.793687	−	0.0565816i
$333$	88.4739	+	272.295i	0.265688	+	0.817702i
$334$	587.701	−	114.651i	1.75958	−	0.343267i
$335$	−25.3912	+	34.9480i	−0.0757947	+	0.104322i
$336$	−11.5927	+	66.8044i	−0.0345021	+	0.198823i
$337$	−3.58012	+	11.0185i	−0.0106235	+	0.0326957i	−0.956228	−	0.292623i	$-0.905472\pi$
$337$	−3.58012	+	11.0185i	−0.0106235	+	0.0326957i	0.945604	+	0.325319i	$0.105472\pi$
$338$	230.013	+	214.199i	0.680510	+	0.633724i
$339$	−14.6099	−	20.1088i	−0.0430971	−	0.0593181i
$340$	12.2993	−	19.7425i	0.0361745	−	0.0580663i
$341$	−189.145	−	581.956i	−0.554679	−	1.70662i
$342$	−145.394	−	261.878i	−0.425128	−	0.765726i
$343$	−189.115	−	260.294i	−0.551355	−	0.758875i
$344$	−89.8021	−	332.440i	−0.261053	−	0.966395i
$345$	3.79088	−	11.6671i	0.0109881	−	0.0338178i
$346$	−93.4295	−	11.4074i	−0.270027	−	0.0329694i
$347$	15.5579	−	21.4136i	0.0448355	−	0.0617108i	−0.786011	−	0.618213i	$-0.787857\pi$
$347$	15.5579	−	21.4136i	0.0448355	−	0.0617108i	0.830846	+	0.556502i	$0.187857\pi$
$348$	−46.7426	+	39.3299i	−0.134318	+	0.113017i
$349$	−89.5402	−	275.576i	−0.256562	−	0.789617i	−0.993518	−	0.113676i	$-0.963737\pi$
$349$	−89.5402	−	275.576i	−0.256562	−	0.789617i	0.736956	−	0.675941i	$-0.236263\pi$
$350$	−171.867	−	80.0013i	−0.491050	−	0.228575i
$351$		−	63.2083i		−	0.180081i
$352$	212.815	+	280.381i	0.604589	+	0.796538i
$353$	217.033			0.614825			0.307413	−	0.951576i	$-0.400537\pi$
$353$	217.033			0.614825			0.307413	+	0.951576i	$0.400537\pi$
$354$	73.9850	−	158.943i	0.208997	−	0.448991i
$355$	69.9402	−	22.7249i	0.197015	−	0.0640139i
$356$	−120.375	−	143.063i	−0.338132	−	0.401862i
$357$	26.6461	+	19.3595i	0.0746390	+	0.0542284i
$358$	−22.1190	+	181.160i	−0.0617850	+	0.506035i
$359$	−222.876	−	72.4169i	−0.620825	−	0.201718i	−0.0183184	−	0.999832i	$-0.505831\pi$
$359$	−222.876	−	72.4169i	−0.620825	−	0.201718i	−0.602507	+	0.798114i	$0.705831\pi$
$360$	45.1063	−	12.1846i	0.125295	−	0.0338461i
$361$	5.73832	−	4.16913i	0.0158956	−	0.0115488i
$362$	34.9866	−	19.4244i	0.0966480	−	0.0536586i
$363$	125.747	+	40.8334i	0.346411	+	0.112489i
$364$	45.3229	+	28.2355i	0.124514	+	0.0775701i
$365$	45.2903	−	32.9053i	0.124083	−	0.0901516i
$366$	115.772	−	124.319i	0.316316	−	0.339669i
$367$	−269.892	−	87.6932i	−0.735400	−	0.238946i	−0.0827128	−	0.996573i	$-0.526358\pi$
$367$	−269.892	−	87.6932i	−0.735400	−	0.238946i	−0.652687	+	0.757627i	$0.726358\pi$
$368$	236.563	+	41.0512i	0.642834	+	0.111552i
$369$	−348.537	−	253.227i	−0.944546	−	0.686253i
$370$	−10.5086	−	53.8672i	−0.0284017	−	0.145587i
$371$	−340.912	+	110.769i	−0.918901	+	0.298569i
$372$	17.2891	+	242.519i	0.0464760	+	0.651932i
$373$	377.208			1.01128			0.505640	−	0.862744i	$-0.331256\pi$
$373$	377.208			1.01128			0.505640	+	0.862744i	$0.331256\pi$
$374$	167.824	−	32.7550i	0.448726	−	0.0875801i
$375$		−	40.4175i		−	0.107780i
$376$	−325.385	+	212.250i	−0.865387	+	0.564495i
$377$	14.8668	+	45.7554i	0.0394346	+	0.121367i
$378$	27.2732	+	139.802i	0.0721513	+	0.369847i
$379$	−237.957	+	327.520i	−0.627855	+	0.864168i	−0.997895	−	0.0648476i	$-0.979344\pi$
$379$	−237.957	+	327.520i	−0.627855	+	0.864168i	0.370040	+	0.929016i	$0.379344\pi$
$380$	21.5812	+	53.2075i	0.0567926	+	0.140020i
$381$	−29.9836	+	92.2801i	−0.0786971	+	0.242205i
$382$	−299.525	+	321.638i	−0.784097	+	0.841985i
$383$	−106.026	−	145.932i	−0.276830	−	0.381023i	0.647851	−	0.761767i	$-0.275668\pi$
$383$	−106.026	−	145.932i	−0.276830	−	0.381023i	−0.924681	+	0.380744i	$0.875668\pi$
$384$	−55.2579	−	128.481i	−0.143901	−	0.334585i
$385$	9.86607	+	30.3556i	0.0256262	+	0.0788457i
$386$	−157.044	+	87.1900i	−0.406849	+	0.225881i
$387$	−197.501	−	271.837i	−0.510340	−	0.702422i
$388$	416.588	+	103.267i	1.07368	+	0.266153i
$389$	65.7531	−	202.367i	0.169031	−	0.520224i	−0.830280	−	0.557347i	$-0.811819\pi$
$389$	65.7531	−	202.367i	0.169031	−	0.520224i	0.999311	+	0.0371228i	$0.0118193\pi$
$390$	−0.682076	+	5.58637i	−0.00174891	+	0.0143240i
$391$	68.5545	−	94.3572i	0.175331	−	0.241323i
$392$	253.821	+	96.8410i	0.647504	+	0.247043i
$393$	−57.6212	−	177.340i	−0.146619	−	0.451246i
$394$	−95.6664	+	205.521i	−0.242808	+	0.521627i
$395$		−	56.5975i		−	0.143285i
$396$	291.541	+	181.590i	0.736214	+	0.458561i
$397$	−510.883			−1.28686			−0.643430	−	0.765505i	$-0.722489\pi$
$397$	−510.883			−1.28686			−0.643430	+	0.765505i	$0.722489\pi$
$398$	232.475	+	108.213i	0.584108	+	0.271892i
$399$	−77.3237	+	25.1240i	−0.193794	+	0.0629674i
$400$	387.089	−	55.4728i	0.967722	−	0.138682i
$401$	22.1925	+	16.1238i	0.0553429	+	0.0402090i	0.615113	−	0.788439i	$-0.289110\pi$
$401$	22.1925	+	16.1238i	0.0553429	+	0.0402090i	−0.559770	+	0.828648i	$0.689110\pi$
$402$	125.244	+	15.2918i	0.311552	+	0.0380394i
$403$	182.110	+	59.1713i	0.451887	+	0.146827i
$404$	−281.242	−	69.7166i	−0.696144	−	0.172566i
$405$	30.3798	−	22.0722i	0.0750118	−	0.0544992i
$406$	−52.6247	−	94.7858i	−0.129617	−	0.233463i
$407$	237.114	−	326.420i	0.582590	−	0.802014i
$408$	−67.8532	−	3.41765i	−0.166307	−	0.00837661i
$409$	−107.946	+	78.4274i	−0.263927	+	0.191754i	−0.711876	−	0.702305i	$-0.752154\pi$
$409$	−107.946	+	78.4274i	−0.263927	+	0.191754i	0.447950	+	0.894059i	$0.352154\pi$
$410$	60.4360	+	56.2809i	0.147405	+	0.137270i
$411$	−92.6624	−	30.1078i	−0.225456	−	0.0732551i
$412$	31.5221	+	77.7164i	0.0765100	+	0.188632i
$413$	251.721	+	182.886i	0.609493	+	0.442822i
$414$	229.944	−	44.8585i	0.555421	−	0.108354i
$415$	−46.9938	+	15.2692i	−0.113238	+	0.0367933i
$416$	−110.124	+	2.29568i	−0.264720	+	0.00551847i
$417$	195.747			0.469417
$418$	−178.089	+	382.677i	−0.426049	+	0.915495i
$419$			302.402i			0.721723i	0.932619	+	0.360861i	$0.117517\pi$
$419$			302.402i			0.721723i	−0.932619	+	0.360861i	$0.882483\pi$
$420$	−0.901820	−	12.6501i	−0.00214719	−	0.0301192i
$421$	−32.1608	−	98.9806i	−0.0763914	−	0.235108i	0.905568	−	0.424202i	$-0.139445\pi$
$421$	−32.1608	−	98.9806i	−0.0763914	−	0.235108i	−0.981959	+	0.189093i	$0.939445\pi$
$422$	−565.179	+	110.257i	−1.33929	+	0.261273i
$423$	−222.815	+	306.679i	−0.526750	+	0.725009i
$424$	464.151	−	575.569i	1.09470	−	1.35747i
$425$	58.6997	−	180.659i	0.138117	−	0.425081i
$426$	−157.191	−	146.384i	−0.368993	−	0.343624i
$427$	177.210	+	243.908i	0.415011	+	0.571213i
$428$	89.1354	+	55.5300i	0.208260	+	0.129743i
$429$	−33.4680	+	24.3204i	−0.0780139	+	0.0566909i
$430$	31.2648	+	56.3131i	0.0727088	+	0.130961i
$431$	197.345	+	271.622i	0.457876	+	0.630213i	0.974067	−	0.226261i	$-0.0726503\pi$
$431$	197.345	+	271.622i	0.457876	+	0.630213i	−0.516190	+	0.856474i	$0.672650\pi$
$432$	−204.671	−	210.796i	−0.473776	−	0.487954i
$433$	−197.554	+	608.008i	−0.456244	+	1.40418i	0.413424	+	0.910539i	$0.364333\pi$
$433$	−197.554	+	608.008i	−0.456244	+	1.40418i	−0.869668	+	0.493637i	$0.835667\pi$
$434$	−428.318	−	52.2961i	−0.986907	−	0.120498i
$435$	6.71613	−	9.24396i	0.0154394	−	0.0212505i
$436$	204.368	+	242.886i	0.468733	+	0.557079i
$437$	88.9672	+	273.813i	0.203586	+	0.626574i
$438$	−148.240	−	69.0032i	−0.338448	−	0.157542i
$439$		−	419.823i		−	0.956317i	−0.878273	−	0.478159i	$-0.841304\pi$
$439$		−	419.823i		−	0.956317i	0.878273	−	0.478159i	$-0.158696\pi$
$440$	−51.2550	−	41.3257i	−0.116489	−	0.0939221i
$441$	265.084			0.601097
$442$	−22.5798	+	48.5083i	−0.0510855	+	0.109747i
$443$	238.218	−	77.4017i	0.537738	−	0.174722i	−0.0275424	−	0.999621i	$-0.508768\pi$
$443$	238.218	−	77.4017i	0.537738	−	0.174722i	0.565280	+	0.824899i	$0.308768\pi$
$444$	−122.659	+	103.207i	−0.276259	+	0.232448i
$445$	28.2925	+	20.5557i	0.0635787	+	0.0461926i
$446$	−37.2895	+	305.410i	−0.0836087	+	0.684776i
$447$	123.112	+	40.0015i	0.275418	+	0.0894888i
$448$	242.578	−	52.5938i	0.541468	−	0.117397i
$449$	−88.8032	+	64.5193i	−0.197780	+	0.143695i	−0.682268	−	0.731103i	$-0.739006\pi$
$449$	−88.8032	+	64.5193i	−0.197780	+	0.143695i	0.484488	+	0.874798i	$0.339006\pi$
$450$	333.600	−	185.213i	0.741333	−	0.411585i
$451$	0.0531724	+	607.085i	0.000117899	+	1.34609i
$452$	−48.1141	+	77.2316i	−0.106447	+	0.170866i
$453$	128.382	−	93.2749i	0.283404	−	0.205905i
$454$	−440.309	+	472.816i	−0.969844	+	1.04145i
$455$	−9.49911	−	3.08645i	−0.0208772	−	0.00678340i
$456$	105.276	−	130.547i	0.230868	−	0.286288i
$457$	−258.376	−	187.721i	−0.565375	−	0.410769i	0.268047	−	0.963406i	$-0.413622\pi$
$457$	−258.376	−	187.721i	−0.565375	−	0.410769i	−0.833422	+	0.552637i	$0.813622\pi$
$458$	−109.191	−	559.715i	−0.238409	−	1.22208i
$459$	−135.739	+	44.1042i	−0.295727	+	0.0960877i
$460$	−44.7955	+	3.19346i	−0.0973816	+	0.00694230i
$461$	−635.144			−1.37775			−0.688876	−	0.724879i	$-0.741896\pi$
$461$	−635.144			−1.37775			−0.688876	+	0.724879i	$0.741896\pi$
$462$	63.5297	−	68.2319i	0.137510	−	0.147688i
$463$		−	735.608i		−	1.58879i	−0.607404	−	0.794393i	$-0.707789\pi$
$463$		−	735.608i		−	1.58879i	0.607404	−	0.794393i	$-0.292211\pi$
$464$	197.738	+	104.452i	0.426160	+	0.225113i
$465$	−14.0532	−	43.2513i	−0.0302219	−	0.0930135i
$466$	−74.6865	−	382.843i	−0.160271	−	0.821551i
$467$	172.418	−	237.313i	0.369204	−	0.508166i	−0.583480	−	0.812127i	$-0.698309\pi$
$467$	172.418	−	237.313i	0.369204	−	0.508166i	0.952684	+	0.303962i	$0.0983094\pi$
$468$	−99.5971	+	40.3970i	−0.212814	+	0.0863185i
$469$	−69.1969	+	212.966i	−0.147541	+	0.454085i
$470$	49.5217	−	53.1778i	0.105365	−	0.113144i
$471$	57.0083	+	78.4652i	0.121037	+	0.166593i
$472$	−640.996	−	32.2859i	−1.35804	−	0.0684023i
$473$	−146.277	+	450.327i	−0.309253	+	0.952066i
$474$	−144.530	+	80.2426i	−0.304916	+	0.169288i
$475$	275.615	+	379.351i	0.580242	+	0.798634i
$476$	29.0109	−	117.032i	0.0609472	−	0.245866i
$477$	222.950	−	686.170i	0.467401	−	1.43851i
$478$	−51.2244	+	419.541i	−0.107164	+	0.877700i
$479$	59.1076	−	81.3546i	0.123398	−	0.169843i	−0.742849	−	0.669459i	$-0.766526\pi$
$479$	59.1076	−	81.3546i	0.123398	−	0.169843i	0.866247	+	0.499617i	$0.166526\pi$
$480$	15.8142	+	20.8389i	0.0329464	+	0.0434143i
$481$	39.0126	+	120.069i	0.0811074	+	0.249623i
$482$	277.076	−	595.245i	0.574847	−	1.23495i
$483$		−	63.5911i		−	0.131659i
$484$	−34.5014	−	482.769i	−0.0712839	−	0.997456i
$485$	−80.2792			−0.165524
$486$	−399.100	−	185.774i	−0.821194	−	0.382252i
$487$	−113.789	+	36.9723i	−0.233653	+	0.0759186i	−0.423503	−	0.905895i	$-0.639200\pi$
$487$	−113.789	+	36.9723i	−0.233653	+	0.0759186i	0.189850	+	0.981813i	$0.439200\pi$
$488$	−581.036	−	221.684i	−1.19065	−	0.454270i
$489$	−20.0899	−	14.5962i	−0.0410837	−	0.0298490i
$490$	−50.4396	−	6.15849i	−0.102938	−	0.0125684i
$491$	265.485	+	86.2615i	0.540704	+	0.175685i	0.566621	−	0.823979i	$-0.308251\pi$
$491$	265.485	+	86.2615i	0.540704	+	0.175685i	−0.0259170	+	0.999664i	$0.508251\pi$
$492$	58.0371	−	234.126i	0.117962	−	0.475866i
$493$	87.8857	−	63.8527i	0.178267	−	0.129519i
$494$	−64.1114	−	115.475i	−0.129780	−	0.233756i
$495$	−61.1016	−	19.8472i	−0.123438	−	0.0400953i
$496$	798.928	−	392.349i	1.61074	−	0.791026i
$497$	308.402	−	224.067i	0.620527	−	0.450839i
$498$	105.619	+	98.3575i	0.212086	+	0.197505i
$499$	160.821	+	52.2540i	0.322287	+	0.104717i	0.465693	−	0.884947i	$-0.345805\pi$
$499$	160.821	+	52.2540i	0.322287	+	0.104717i	−0.143405	+	0.989664i	$0.545805\pi$
$500$	−137.112	+	55.6131i	−0.274223	+	0.111226i
$501$	264.653	+	192.282i	0.528250	+	0.383796i
$502$	164.668	−	32.1242i	0.328025	−	0.0639924i
$503$	591.543	−	192.204i	1.17603	−	0.382115i	0.345139	−	0.938552i	$-0.387832\pi$
$503$	591.543	−	192.204i	1.17603	−	0.382115i	0.830890	+	0.556436i	$0.187832\pi$
$504$	202.855	−	132.323i	0.402491	−	0.262546i
$505$	54.1971			0.107321
$506$	−241.618	−	224.967i	−0.477505	−	0.444598i
$507$			171.712i			0.338683i
$508$	354.306	−	25.2583i	0.697453	−	0.0497212i
$509$	97.9151	+	301.352i	0.192367	+	0.592046i	0.999997	+	0.00235633i	$0.000750043\pi$
$509$	97.9151	+	301.352i	0.192367	+	0.592046i	−0.807630	+	0.589690i	$0.799250\pi$
$510$	12.4726	−	2.43320i	0.0244561	−	0.00477099i
$511$	170.571	−	234.771i	0.333798	−	0.459434i
$512$	−359.823	+	364.241i	−0.702779	+	0.711408i
$513$	108.871	−	335.069i	0.212223	−	0.653156i
$514$	236.984	+	220.691i	0.461059	+	0.429360i
$515$	−9.22042	−	12.6908i	−0.0179037	−	0.0246424i
$516$	99.4775	−	159.679i	0.192786	−	0.309455i
$517$	534.176	−	0.0467866i	1.03322	−	9.04962e-5i
$518$	−138.094	−	248.731i	−0.266591	−	0.480176i
$519$	−30.2251	−	41.6013i	−0.0582372	−	0.0801566i
$520$	19.8897	−	5.37280i	0.0382493	−	0.0103323i
$521$	−108.271	+	333.223i	−0.207814	+	0.639584i	0.791773	+	0.610816i	$0.209158\pi$
$521$	−108.271	+	333.223i	−0.207814	+	0.639584i	−0.999586	+	0.0287683i	$0.990842\pi$
$522$	216.602	+	26.4464i	0.414947	+	0.0506635i
$523$	−397.190	+	546.685i	−0.759445	+	1.04529i	0.237815	+	0.971310i	$0.423569\pi$
$523$	−397.190	+	546.685i	−0.759445	+	1.04529i	−0.997260	+	0.0739759i	$0.976431\pi$
$524$	−522.320	+	439.487i	−0.996794	+	0.838716i
$525$	−32.0048	−	98.5007i	−0.0609615	−	0.187620i
$526$	723.939	+	336.981i	1.37631	+	0.640648i
$527$		−	432.367i		−	0.820431i
$528$	−32.8634	+	189.478i	−0.0622413	+	0.358860i
$529$	303.816			0.574321
$530$	−58.3638	+	125.383i	−0.110120	+	0.236573i
$531$	−595.602	+	193.523i	−1.12166	+	0.364450i
$532$	191.625	+	227.742i	0.360198	+	0.428087i
$533$	−153.688	−	111.661i	−0.288345	−	0.209495i
$534$	12.3797	−	101.393i	0.0231829	−	0.189874i
$535$	−18.6816	−	6.07003i	−0.0349190	−	0.0113459i
$536$	−120.456	−	445.917i	−0.224731	−	0.831936i
$537$	−80.6652	+	58.6067i	−0.150215	+	0.109137i
$538$	111.543	−	61.9281i	0.207329	−	0.115108i
$539$	−219.590	−	302.184i	−0.407402	−	0.560638i
$540$	46.6449	+	29.0591i	0.0863794	+	0.0538131i
$541$	−307.422	+	223.355i	−0.568247	+	0.412856i	−0.834468	−	0.551056i	$-0.814225\pi$
$541$	−307.422	+	223.355i	−0.568247	+	0.412856i	0.266221	+	0.963912i	$0.414225\pi$
$542$	−232.794	+	249.981i	−0.429510	+	0.461220i
$543$	20.7924	+	6.75585i	0.0382917	+	0.0124417i
$544$	81.7698	+	234.887i	0.150312	+	0.431778i
$545$	−48.0339	−	34.8987i	−0.0881357	−	0.0640343i
$546$	5.58590	+	28.6333i	0.0102306	+	0.0524420i
$547$	222.878	−	72.4175i	0.407455	−	0.132390i	−0.0981162	−	0.995175i	$-0.531282\pi$
$547$	222.878	−	72.4175i	0.407455	−	0.132390i	0.505571	+	0.862785i	$0.331282\pi$
$548$	25.3630	+	355.774i	0.0462829	+	0.649223i
$549$	−606.817			−1.10531
$550$	−487.482	−	226.862i	−0.886331	−	0.412477i
$551$			268.158i			0.486675i
$552$	71.6650	+	109.865i	0.129828	+	0.199030i
$553$	−90.6606	−	279.025i	−0.163943	−	0.504566i
$554$	123.963	+	635.436i	0.223761	+	1.14700i
$555$	17.6240	−	24.2574i	0.0317550	−	0.0437071i
$556$	−269.341	−	664.049i	−0.484427	−	1.19433i
$557$	−15.6464	+	48.1548i	−0.0280906	+	0.0864539i	−0.964119	−	0.265471i	$-0.914473\pi$
$557$	−15.6464	+	48.1548i	−0.0280906	+	0.0864539i	0.936028	+	0.351925i	$0.114473\pi$
$558$	591.883	−	635.580i	1.06072	−	1.13903i
$559$	−87.0884	−	119.867i	−0.155793	−	0.214431i
$560$	−41.6731	+	20.4654i	−0.0744163	+	0.0365454i
$561$	75.5803	+	54.9022i	0.134724	+	0.0978649i
$562$	−668.717	+	371.269i	−1.18989	+	0.660621i
$563$	306.745	+	422.198i	0.544840	+	0.749908i	0.989301	−	0.145890i	$-0.0466046\pi$
$563$	306.745	+	422.198i	0.544840	+	0.749908i	−0.444460	+	0.895798i	$0.646605\pi$
$564$	−206.008	−	51.0670i	−0.365263	−	0.0905443i
$565$	5.25940	−	16.1868i	0.00930866	−	0.0286491i
$566$	106.855	−	875.173i	0.188791	−	1.54624i
$567$	114.415	−	157.479i	0.201791	−	0.277741i
$568$	−280.301	+	734.672i	−0.493488	+	1.29344i
$569$	87.5395	+	269.419i	0.153848	+	0.473495i	0.998042	−	0.0625419i	$-0.0199207\pi$
$569$	87.5395	+	269.419i	0.153848	+	0.473495i	−0.844194	+	0.536037i	$0.819921\pi$
$570$	−13.2377	+	28.4387i	−0.0232241	+	0.0498925i
$571$			187.846i			0.328977i	0.986379	+	0.164488i	$0.0525973\pi$
$571$			187.846i			0.328977i	−0.986379	+	0.164488i	$0.947403\pi$
$572$	128.555	+	80.0723i	0.224746	+	0.139986i
$573$	−240.114			−0.419047
$574$	388.102	+	180.655i	0.676135	+	0.314729i
$575$	−348.803	+	113.333i	−0.606614	+	0.197101i
$576$	−201.344	+	457.222i	−0.349555	+	0.793788i
$577$	−762.773	−	554.187i	−1.32196	−	0.960463i	−0.999906	−	0.0137424i	$-0.995626\pi$
$577$	−762.773	−	554.187i	−1.32196	−	0.960463i	−0.322058	−	0.946720i	$-0.604374\pi$
$578$	−453.813	−	55.4089i	−0.785144	−	0.0958632i
$579$	−93.3304	−	30.3249i	−0.161192	−	0.0523746i
$580$	−40.6003	−	10.0643i	−0.0700005	−	0.0173523i
$581$	−207.220	+	150.554i	−0.356661	+	0.259129i
$582$	113.818	+	205.005i	0.195563	+	0.352242i
$583$	−966.891	+	314.256i	−1.65848	+	0.539032i
$584$	−30.1119	+	597.834i	−0.0515615	+	1.02369i
$585$	16.2639	−	11.8164i	0.0278015	−	0.0201989i
$586$	765.140	+	712.535i	1.30570	+	1.21593i
$587$	29.3693	+	9.54266i	0.0500329	+	0.0162567i	0.333927	−	0.942599i	$-0.391626\pi$
$587$	29.3693	+	9.54266i	0.0500329	+	0.0162567i	−0.283894	+	0.958856i	$0.591626\pi$
$588$	55.7854	+	137.537i	0.0948732	+	0.233906i
$589$	863.456	+	627.337i	1.46597	+	1.06509i
$590$	117.826	−	22.9860i	0.199705	−	0.0389593i
$591$	−117.788	+	38.2717i	−0.199303	+	0.0647575i
$592$	518.893	+	274.098i	0.876508	+	0.463003i
$593$	−313.027			−0.527870			−0.263935	−	0.964540i	$-0.585020\pi$
$593$	−313.027			−0.527870			−0.263935	+	0.964540i	$0.585020\pi$
$594$	77.3888	+	396.510i	0.130284	+	0.667525i
$595$			22.5528i			0.0379039i
$596$	−33.6975	−	472.684i	−0.0565394	−	0.793094i
$597$	43.2910	+	133.236i	0.0725143	+	0.223176i
$598$	101.394	−	19.7804i	0.169555	−	0.0330776i
$599$	533.190	−	733.872i	0.890133	−	1.22516i	−0.0833771	−	0.996518i	$-0.526571\pi$
$599$	533.190	−	733.872i	0.890133	−	1.22516i	0.973510	−	0.228645i	$-0.0734294\pi$
$600$	166.301	+	134.108i	0.277168	+	0.223514i
$601$	320.006	−	984.877i	0.532456	−	1.63873i	−0.216627	−	0.976255i	$-0.569505\pi$
$601$	320.006	−	984.877i	0.532456	−	1.63873i	0.749083	−	0.662477i	$-0.230495\pi$
$602$	244.340	+	227.541i	0.405880	+	0.377975i
$603$	−264.918	−	364.629i	−0.439334	−	0.604691i
$604$	−493.074	−	307.178i	−0.816347	−	0.508572i
$605$	27.9904	+	86.0941i	0.0462650	+	0.142304i
$606$	−76.8394	−	138.401i	−0.126798	−	0.228384i
$607$	−290.604	−	399.983i	−0.478755	−	0.658950i	0.499510	−	0.866308i	$-0.333513\pi$
$607$	−290.604	−	399.983i	−0.478755	−	0.658950i	−0.978265	+	0.207358i	$0.933513\pi$
$608$	−587.723	−	177.508i	−0.966649	−	0.291955i
$609$	18.3030	−	56.3308i	0.0300542	−	0.0924972i
$610$	115.464	+	14.0977i	0.189285	+	0.0231110i
$611$	−98.2505	+	135.230i	−0.160803	+	0.221326i
$612$	156.247	+	185.696i	0.255306	+	0.303425i
$613$	−252.174	−	776.112i	−0.411377	−	1.26609i	−0.915452	−	0.402428i	$-0.868166\pi$
$613$	−252.174	−	776.112i	−0.411377	−	1.26609i	0.504075	−	0.863660i	$-0.331834\pi$
$614$	957.509	+	445.704i	1.55946	+	0.725902i
$615$			45.1176i			0.0733619i
$616$	−318.884	−	121.632i	−0.517669	−	0.197455i
$617$	965.796			1.56531			0.782654	−	0.622457i	$-0.213865\pi$
$617$	965.796			1.56531			0.782654	+	0.622457i	$0.213865\pi$
$618$	−19.3354	+	41.5384i	−0.0312871	+	0.0672143i
$619$	−1.84967	+	0.600994i	−0.00298816	+	0.000970911i	−0.310511	−	0.950570i	$-0.600500\pi$
$619$	−1.84967	+	0.600994i	−0.00298816	+	0.000970911i	0.307523	+	0.951541i	$0.400500\pi$
$620$	−127.388	+	107.186i	−0.205465	+	0.172881i
$621$	222.934	+	161.971i	0.358992	+	0.260823i
$622$	77.2870	−	633.000i	0.124256	−	1.01769i
$623$	172.409	+	56.0190i	0.276740	+	0.0899182i
$624$	−41.9193	−	43.1738i	−0.0671784	−	0.0691888i
$625$	−471.924	+	342.873i	−0.755079	+	0.548597i
$626$	563.716	−	312.973i	0.900504	−	0.499956i
$627$	−219.304	+	71.2776i	−0.349768	+	0.113680i
$628$	187.743	−	301.360i	0.298953	−	0.479872i
$629$	230.624	−	167.558i	0.366652	−	0.266388i
$630$	−30.8734	+	33.1527i	−0.0490054	+	0.0526233i
$631$	−408.093	−	132.598i	−0.646740	−	0.210139i	−0.0327641	−	0.999463i	$-0.510431\pi$
$631$	−408.093	−	132.598i	−0.646740	−	0.210139i	−0.613976	+	0.789324i	$0.710431\pi$
$632$	471.083	+	379.891i	0.745384	+	0.601094i
$633$	−254.511	−	184.913i	−0.402071	−	0.292122i
$634$	−138.833	−	711.657i	−0.218979	−	1.12249i
$635$	−63.1877	+	20.5309i	−0.0995081	+	0.0323322i
$636$	402.932	−	28.7249i	0.633542	−	0.0451649i
$637$	116.889			0.183499
$638$	−149.281	−	268.825i	−0.233983	−	0.421355i
$639$			767.271i			1.20074i
$640$	48.9336	−	82.3216i	0.0764587	−	0.128628i
$641$	−86.8750	−	267.374i	−0.135530	−	0.417120i	0.860142	−	0.510055i	$-0.170375\pi$
$641$	−86.8750	−	267.374i	−0.135530	−	0.417120i	−0.995672	+	0.0929354i	$0.970375\pi$
$642$	10.9856	+	56.3123i	0.0171116	+	0.0877139i
$643$	367.425	−	505.717i	0.571422	−	0.786495i	−0.421300	−	0.906921i	$-0.638426\pi$
$643$	367.425	−	505.717i	0.571422	−	0.786495i	0.992722	+	0.120426i	$0.0384260\pi$
$644$	−215.726	+	87.4993i	−0.334978	+	0.135869i
$645$	−10.8740	+	33.4666i	−0.0168589	+	0.0518862i
$646$	−203.247	+	218.253i	−0.314624	+	0.337852i
$647$	−4.40525	−	6.06331i	−0.00680874	−	0.00937142i	0.805599	−	0.592461i	$-0.201844\pi$
$647$	−4.40525	−	6.06331i	−0.00680874	−	0.00937142i	−0.812408	+	0.583090i	$0.801844\pi$
$648$	−20.1984	+	401.014i	−0.0311704	+	0.618849i
$649$	713.992	+	518.650i	1.10014	+	0.799153i
$650$	147.101	−	81.6699i	0.226309	−	0.125646i
$651$	−138.564	−	190.717i	−0.212848	−	0.292960i
$652$	−21.8728	+	88.2366i	−0.0335473	+	0.135332i
$653$	338.138	−	1040.68i	0.517823	−	1.59369i	−0.260264	−	0.965538i	$-0.583810\pi$
$653$	338.138	−	1040.68i	0.517823	−	1.59369i	0.778087	−	0.628157i	$-0.216190\pi$
$654$	−21.0177	+	172.140i	−0.0321372	+	0.263212i
$655$	75.0487	−	103.296i	0.114578	−	0.157703i
$656$	−874.103	+	125.266i	−1.33247	+	0.190954i
$657$	180.492	+	555.497i	0.274721	+	0.845506i
$658$	158.958	−	341.492i	0.241578	−	0.518984i
$659$		−	690.561i		−	1.04789i	−0.851752	−	0.523946i	$-0.824459\pi$
$659$		−	690.561i		−	1.04789i	0.851752	−	0.523946i	$-0.175541\pi$
$660$	−2.56094	−	35.8788i	−0.00388022	−	0.0543618i
$661$	−981.006			−1.48412			−0.742062	−	0.670331i	$-0.766152\pi$
$661$	−981.006			−1.48412			−0.742062	+	0.670331i	$0.766152\pi$
$662$	−159.621	−	74.3008i	−0.241119	−	0.112237i
$663$	−27.8011	+	9.03312i	−0.0419322	+	0.0136246i
$664$	188.338	−	493.637i	0.283642	−	0.743429i
$665$	−45.0390	−	32.7227i	−0.0677278	−	0.0492071i
$666$	568.394	+	69.3989i	0.853445	+	0.104203i
$667$	−199.474	−	64.8132i	−0.299062	−	0.0971711i
$668$	288.140	−	1162.38i	0.431347	−	1.74009i
$669$	−135.990	+	98.8024i	−0.203273	+	0.147687i
$670$	41.9370	+	75.5355i	0.0625925	+	0.112739i
$671$	502.674	+	691.744i	0.749142	+	1.03092i
$672$	111.345	+	77.4032i	0.165691	+	0.115183i
$673$	173.221	−	125.852i	0.257386	−	0.187002i	−0.451608	−	0.892217i	$-0.649149\pi$
$673$	173.221	−	125.852i	0.257386	−	0.187002i	0.708994	+	0.705214i	$0.249149\pi$
$674$	16.9569	+	15.7911i	0.0251586	+	0.0234289i
$675$	426.836	+	138.687i	0.632349	+	0.205463i
$676$	582.515	−	236.271i	0.861708	−	0.349513i
$677$	909.036	+	660.454i	1.34274	+	0.975559i	0.999338	+	0.0363712i	$0.0115799\pi$
$677$	909.036	+	660.454i	1.34274	+	0.975559i	0.343404	+	0.939188i	$0.388420\pi$
$678$	−48.7920	+	9.51853i	−0.0719645	+	0.0140391i
$679$	−395.775	+	128.595i	−0.582879	+	0.189389i
$680$	−25.4162	−	38.9638i	−0.0373768	−	0.0572998i
$681$	−352.974			−0.518317
$682$	−1214.84	−	148.219i	−1.78129	−	0.217330i
$683$		−	87.6213i		−	0.128289i	−0.997941	−	0.0641445i	$-0.979568\pi$
$683$		−	87.6213i		−	0.128289i	0.997941	−	0.0641445i	$-0.0204318\pi$
$684$	−597.548	+	42.5990i	−0.873608	+	0.0622792i
$685$	−20.6160	−	63.4495i	−0.0300963	−	0.0926270i
$686$	−631.576	+	123.210i	−0.920665	+	0.179607i
$687$	183.125	−	252.050i	0.266558	−	0.366885i
$688$	−678.570	−	117.753i	−0.986293	−	0.171153i
$689$	98.3100	−	302.567i	0.142685	−	0.439140i
$690$	−17.9552	−	16.7207i	−0.0260220	−	0.0242329i
$691$	316.481	+	435.598i	0.458004	+	0.630388i	0.974093	−	0.226147i	$-0.0726129\pi$
$691$	316.481	+	435.598i	0.458004	+	0.630388i	−0.516090	+	0.856535i	$0.672613\pi$
$692$	−99.5389	+	159.777i	−0.143842	+	0.230892i
$693$	−333.022	+	0.0291682i	−0.480551	+	4.20898e-5i
$694$	−25.6960	−	46.2827i	−0.0370259	−	0.0666898i
$695$	78.7840	+	108.437i	0.113358	+	0.156024i
$696$	31.8613	+	117.948i	0.0457777	+	0.169465i
$697$	−132.553	+	407.955i	−0.190176	+	0.585301i
$698$	−575.244	−	70.2352i	−0.824132	−	0.100624i
$699$	125.257	−	172.401i	0.179195	−	0.246640i
$700$	−290.115	+	244.106i	−0.414450	+	0.348723i
$701$	253.827	+	781.200i	0.362093	+	1.11441i	0.951781	+	0.306777i	$0.0992506\pi$
$701$	253.827	+	781.200i	0.362093	+	1.11441i	−0.589688	+	0.807631i	$0.700749\pi$
$702$	−114.608	−	53.3482i	−0.163260	−	0.0759947i
$703$			703.683i			1.00097i
$704$	688.002	−	149.230i	0.977275	−	0.211975i
$705$	39.6991			0.0563107
$706$	183.178	−	393.522i	0.259459	−	0.557397i
$707$	267.191	−	86.8156i	0.377922	−	0.122794i
$708$	−225.749	−	268.298i	−0.318855	−	0.378951i
$709$	−574.514	−	417.409i	−0.810315	−	0.588729i	0.103607	−	0.994618i	$-0.466962\pi$
$709$	−574.514	−	417.409i	−0.810315	−	0.588729i	−0.913922	+	0.405890i	$0.866962\pi$
$710$	17.8254	−	145.995i	0.0251062	−	0.205626i
$711$	561.606	+	182.477i	0.789882	+	0.256648i
$712$	−360.997	+	97.5163i	−0.507018	+	0.136961i
$713$	−675.352	+	490.672i	−0.947198	+	0.688180i
$714$	57.5920	−	31.9748i	0.0806611	−	0.0447827i
$715$	−26.9428	−	8.75163i	−0.0376822	−	0.0122400i
$716$	309.809	+	193.007i	0.432695	+	0.269562i
$717$	−186.809	+	135.724i	−0.260542	+	0.189295i
$718$	−319.415	+	342.996i	−0.444867	+	0.477710i
$719$	878.206	+	285.347i	1.22143	+	0.396866i	0.847602	−	0.530633i	$-0.178046\pi$
$719$	878.206	+	285.347i	1.22143	+	0.396866i	0.373826	+	0.927499i	$0.378046\pi$
$720$	15.9771	−	92.0701i	0.0221904	−	0.127875i
$721$	−65.7852	−	47.7958i	−0.0912417	−	0.0662909i
$722$	−2.71624	−	13.9234i	−0.00376210	−	0.0192845i
$723$	341.147	−	110.845i	0.471849	−	0.153313i
$724$	−5.69117	−	79.8316i	−0.00786073	−	0.110265i
$725$	−341.599			−0.471172
$726$	180.170	−	193.540i	0.248168	−	0.266584i
$727$		−	824.285i		−	1.13382i	−0.823781	−	0.566909i	$-0.808139\pi$
$727$		−	824.285i		−	1.13382i	0.823781	−	0.566909i	$-0.191861\pi$
$728$	89.4492	−	58.3480i	0.122870	−	0.0801484i
$729$	65.2674	+	200.872i	0.0895300	+	0.275545i
$730$	−21.4382	−	109.892i	−0.0293674	−	0.150537i
$731$	−196.646	+	270.659i	−0.269009	+	0.370259i
$732$	−127.701	−	314.842i	−0.174455	−	0.430112i
$733$	−0.267616	+	0.823639i	−0.000365098	+	0.00112365i	−0.951239	−	0.308455i	$-0.900188\pi$
$733$	−0.267616	+	0.823639i	−0.000365098	+	0.00112365i	0.950874	+	0.309579i	$0.100188\pi$
$734$	−386.795	+	415.351i	−0.526968	+	0.565873i
$735$	−16.3176	−	22.4592i	−0.0222008	−	0.0305568i
$736$	274.094	−	394.285i	0.372411	−	0.535714i
$737$	−196.208	+	604.046i	−0.266225	+	0.819601i
$738$	−753.317	+	418.238i	−1.02075	+	0.566718i
$739$	247.106	+	340.112i	0.334378	+	0.460232i	0.942789	−	0.333390i	$-0.108193\pi$
$739$	247.106	+	340.112i	0.334378	+	0.460232i	−0.608411	+	0.793622i	$0.708193\pi$
$740$	−106.541	−	26.4102i	−0.143974	−	0.0356894i
$741$	22.2981	−	68.6265i	0.0300919	−	0.0926133i
$742$	−86.8872	+	711.628i	−0.117099	+	0.959068i
$743$	−814.385	+	1120.90i	−1.09608	+	1.50862i	−0.255591	+	0.966785i	$0.582270\pi$
$743$	−814.385	+	1120.90i	−1.09608	+	1.50862i	−0.840485	+	0.541835i	$0.817730\pi$
$744$	454.324	+	173.339i	0.610651	+	0.232983i
$745$	27.3905	+	84.2994i	0.0367658	+	0.113154i
$746$	318.366	−	683.948i	0.426764	−	0.916821i
$747$		−	515.540i		−	0.690148i
$748$	82.2535	−	331.941i	0.109965	−	0.443772i
$749$	−101.823			−0.135946
$750$	−73.2845	−	34.1126i	−0.0977126	−	0.0454835i
$751$	1243.83	−	404.146i	1.65624	−	0.538144i	0.676159	−	0.736756i	$-0.263643\pi$
$751$	1243.83	−	404.146i	1.65624	−	0.538144i	0.980078	+	0.198612i	$0.0636434\pi$
$752$	110.222	+	769.126i	0.146571	+	1.02277i
$753$	74.1534	+	53.8756i	0.0984773	+	0.0715479i
$754$	95.5110	+	11.6615i	0.126672	+	0.0154662i
$755$	103.342	+	33.5778i	0.136877	+	0.0444740i
$756$	276.507	+	68.5427i	0.365749	+	0.0906649i
$757$	27.1049	−	19.6929i	0.0358057	−	0.0260143i	−0.569738	−	0.821826i	$-0.692956\pi$
$757$	27.1049	−	19.6929i	0.0358057	−	0.0260143i	0.605544	+	0.795812i	$0.292956\pi$
$758$	393.017	+	707.890i	0.518493	+	0.933892i
$759$	−0.0157972	−	180.361i	−2.08132e−5	−	0.237630i
$760$	114.690	+	5.77674i	0.150908	+	0.00760097i
$761$	−53.4377	+	38.8247i	−0.0702203	+	0.0510181i	−0.622342	−	0.782746i	$-0.713819\pi$
$761$	−53.4377	+	38.8247i	−0.0702203	+	0.0510181i	0.552121	+	0.833764i	$0.313819\pi$
$762$	142.015	+	132.251i	0.186371	+	0.173558i
$763$	−292.709	−	95.1069i	−0.383629	−	0.124649i
$764$	330.389	+	814.560i	0.432447	+	1.06618i
$765$	−36.7238	−	26.6814i	−0.0480050	−	0.0348776i
$766$	−354.089	+	69.0771i	−0.462257	+	0.0901789i
$767$	−262.631	+	85.3341i	−0.342414	+	0.111257i
$768$	−279.597	−	8.24560i	−0.364059	−	0.0107365i
$769$	1115.14			1.45012			0.725062	−	0.688684i	$-0.241811\pi$
$769$	1115.14			1.45012			0.725062	+	0.688684i	$0.241811\pi$
$770$	63.3674	+	7.73130i	0.0822954	+	0.0100407i
$771$			176.917i			0.229465i
$772$	25.5458	+	358.339i	0.0330905	+	0.464170i
$773$	−52.6568	−	162.061i	−0.0681200	−	0.209652i	0.911202	−	0.411960i	$-0.135156\pi$
$773$	−52.6568	−	162.061i	−0.0681200	−	0.209652i	−0.979322	+	0.202308i	$0.935156\pi$
$774$	−659.585	+	128.675i	−0.852177	+	0.166246i
$775$	−799.149	+	1099.93i	−1.03116	+	1.41927i
$776$	538.847	−	668.195i	0.694390	−	0.861075i
$777$	48.0295	−	147.820i	0.0618141	−	0.190244i
$778$	−311.434	−	290.022i	−0.400301	−	0.372779i
$779$	−622.378	−	856.630i	−0.798945	−	1.09965i
$780$	9.55347	+	5.95167i	0.0122480	+	0.00763035i
$781$	874.655	−	635.591i	1.11992	−	0.813817i
$782$	−113.227	−	203.940i	−0.144791	−	0.260793i
$783$	150.862	+	207.644i	0.192672	+	0.265190i
$784$	389.818	−	378.492i	0.497217	−	0.482770i
$785$	−20.5223	+	63.1611i	−0.0261431	+	0.0804601i
$786$	−370.183	−	45.1980i	−0.470971	−	0.0575038i
$787$	306.107	−	421.320i	0.388954	−	0.535350i	−0.568975	−	0.822355i	$-0.692660\pi$
$787$	306.107	−	421.320i	0.388954	−	0.535350i	0.957929	+	0.287005i	$0.0926598\pi$
$788$	291.905	+	346.922i	0.370438	+	0.440257i
$789$	134.810	+	414.904i	0.170862	+	0.525860i
$790$	−102.622	−	47.7687i	−0.129901	−	0.0604667i
$791$		−	88.2252i		−	0.111536i
$792$	575.319	−	375.355i	0.726413	−	0.473933i
$793$	−267.576			−0.337423
$794$	−431.189	+	926.327i	−0.543059	+	1.16666i
$795$	−71.8598	+	23.3487i	−0.0903897	+	0.0293694i
$796$	392.421	−	330.189i	0.492992	−	0.414810i
$797$	−332.100	−	241.285i	−0.416688	−	0.302742i	0.359616	−	0.933100i	$-0.382908\pi$
$797$	−332.100	−	241.285i	−0.416688	−	0.302742i	−0.776304	+	0.630359i	$0.782908\pi$
$798$	−19.7072	+	161.407i	−0.0246958	+	0.202265i
$799$	358.960	+	116.633i	0.449262	+	0.145974i
$800$	226.123	−	748.685i	0.282654	−	0.935856i
$801$	−295.189	+	214.467i	−0.368525	+	0.267749i
$802$	47.9662	−	26.6306i	0.0598082	−	0.0332052i
$803$	483.727	−	665.915i	0.602399	−	0.829284i
$804$	133.434	−	214.185i	0.165963	−	0.266399i
$805$	35.2272	−	25.5941i	0.0437606	−	0.0317939i
$806$	260.991	−	280.259i	0.323810	−	0.347716i
$807$	66.2894	+	21.5387i	0.0821430	+	0.0266899i
$808$	−363.780	+	451.104i	−0.450222	+	0.558297i
$809$	−1064.09	−	773.105i	−1.31531	−	0.955630i	−0.999978	−	0.00664931i	$-0.997883\pi$
$809$	−1064.09	−	773.105i	−1.31531	−	0.955630i	−0.315334	−	0.948981i	$-0.602117\pi$
$810$	−14.3803	−	73.7133i	−0.0177535	−	0.0910041i
$811$	−967.742	+	314.438i	−1.19327	+	0.387717i	−0.837281	−	0.546773i	$-0.815856\pi$
$811$	−967.742	+	314.438i	−1.19327	+	0.387717i	−0.355989	+	0.934490i	$0.615856\pi$
$812$	−216.280	+	15.4185i	−0.266355	+	0.0189883i
$813$	−186.620			−0.229544
$814$	−391.734	−	705.433i	−0.481246	−	0.866625i
$815$		−	17.0038i		−	0.0208635i
$816$	−63.4655	+	120.146i	−0.0777763	+	0.147238i
$817$	−255.198	−	785.420i	−0.312360	−	0.961347i
$818$	51.0964	+	261.920i	0.0624650	+	0.320195i
$819$	61.2525	−	84.3068i	0.0747893	−	0.102939i
$820$	153.056	−	62.0803i	0.186654	−	0.0757077i
$821$	1.01822	−	3.13376i	0.00124022	−	0.00381700i	−0.950434	−	0.310925i	$-0.899361\pi$
$821$	1.01822	−	3.13376i	0.00124022	−	0.00381700i	0.951675	+	0.307108i	$0.0993612\pi$
$822$	−132.799	+	142.603i	−0.161556	+	0.173483i
$823$	−686.883	−	945.413i	−0.834608	−	1.14874i	−0.987048	−	0.160427i	$-0.948713\pi$
$823$	−686.883	−	945.413i	−0.834608	−	1.14874i	0.152440	−	0.988313i	$-0.451287\pi$
$824$	167.519	+	8.43767i	0.203300	+	0.0102399i
$825$	−90.7987	−	279.366i	−0.110059	−	0.338626i
$826$	544.060	−	302.060i	0.658668	−	0.365690i
$827$	−629.832	−	866.889i	−0.761586	−	1.04823i	−0.997080	−	0.0763576i	$-0.975671\pi$
$827$	−629.832	−	866.889i	−0.761586	−	1.04823i	0.235494	−	0.971876i	$-0.424329\pi$
$828$	112.738	−	454.793i	0.136157	−	0.549267i
$829$	74.0327	−	227.849i	0.0893036	−	0.274848i	−0.896424	−	0.443198i	$-0.853844\pi$
$829$	74.0327	−	227.849i	0.0893036	−	0.274848i	0.985727	+	0.168350i	$0.0538438\pi$
$830$	−11.9772	+	98.0960i	−0.0144303	+	0.118188i
$831$	−207.899	+	286.149i	−0.250180	+	0.344343i
$832$	−88.7826	+	201.612i	−0.106710	+	0.242323i
$833$	−81.5604	−	251.017i	−0.0979117	−	0.301341i
$834$	165.212	−	354.926i	0.198096	−	0.425571i
$835$			223.998i			0.268261i
$836$	543.557	+	645.890i	0.650188	+	0.772596i
$837$	1021.53			1.22047
$838$	548.311	+	255.229i	0.654309	+	0.304570i
$839$	−826.516	+	268.551i	−0.985120	+	0.320085i	−0.756904	−	0.653526i	$-0.773289\pi$
$839$	−826.516	+	268.551i	−0.985120	+	0.320085i	−0.228216	+	0.973611i	$0.573289\pi$
$840$	−23.6981	−	9.04159i	−0.0282121	−	0.0107638i
$841$	522.338	+	379.501i	0.621092	+	0.451249i
$842$	−206.614	−	25.2269i	−0.245385	−	0.0299607i
$843$	−397.416	−	129.128i	−0.471430	−	0.153177i
$844$	−277.098	+	1117.83i	−0.328315	+	1.32445i
$845$	−95.1226	+	69.1106i	−0.112571	+	0.0817877i
$846$	368.009	+	662.845i	0.434999	+	0.783505i
$847$	275.902	+	379.606i	0.325740	+	0.448177i
$848$	−651.868	−	1327.38i	−0.768712	−	1.56530i
$849$	389.688	−	283.125i	0.458996	−	0.333480i
$850$	−278.026	−	258.911i	−0.327090	−	0.304602i
$851$	−523.448	−	170.079i	−0.615098	−	0.199857i
$852$	−398.092	+	161.468i	−0.467244	+	0.189516i
$853$	1053.49	+	765.403i	1.23504	+	0.897307i	0.997257	−	0.0740115i	$-0.0235802\pi$
$853$	1053.49	+	765.403i	1.23504	+	0.897307i	0.237780	+	0.971319i	$0.423580\pi$
$854$	591.817	−	115.454i	0.692995	−	0.135192i
$855$	106.568	−	34.6260i	0.124641	−	0.0404982i
$856$	175.917	−	114.751i	0.205511	−	0.134055i
$857$	676.267			0.789110			0.394555	−	0.918872i	$-0.370899\pi$
$857$	676.267			0.789110			0.394555	+	0.918872i	$0.370899\pi$
$858$	15.8502	+	81.2103i	0.0184735	+	0.0946507i
$859$		−	745.506i		−	0.867877i	−0.900943	−	0.433938i	$-0.857124\pi$
$859$		−	745.506i		−	0.867877i	0.900943	−	0.433938i	$-0.142876\pi$
$860$	128.494	−	9.16028i	0.149412	−	0.0106515i
$861$	72.2715	+	222.429i	0.0839390	+	0.258338i
$862$	659.062	−	128.572i	0.764573	−	0.149156i
$863$	−783.896	+	1078.94i	−0.908338	+	1.25022i	0.0593926	+	0.998235i	$0.481084\pi$
$863$	−783.896	+	1078.94i	−0.908338	+	1.25022i	−0.967731	+	0.251986i	$0.918916\pi$
$864$	−554.957	+	193.194i	−0.642312	+	0.223604i
$865$	10.8807	−	33.4873i	0.0125788	−	0.0387136i
$866$	935.696	+	871.365i	1.08048	+	1.00620i
$867$	−146.812	−	202.069i	−0.169333	−	0.233067i
$868$	−456.326	+	732.483i	−0.525721	+	0.843874i
$869$	−257.207	−	791.366i	−0.295981	−	0.910663i
$870$	−11.0926	−	19.9796i	−0.0127501	−	0.0229650i
$871$	−116.816	−	160.783i	−0.134117	−	0.184596i
$872$	612.887	−	165.559i	0.702852	−	0.189862i
$873$	258.829	−	796.595i	0.296483	−	0.912480i
$874$	571.563	+	69.7858i	0.653963	+	0.0798465i
$875$	84.3240	−	116.062i	0.0963703	−	0.132642i
$876$	−250.232	+	210.548i	−0.285652	+	0.240352i
$877$	−122.743	−	377.764i	−0.139958	−	0.430746i	0.856370	−	0.516362i	$-0.172714\pi$
$877$	−122.743	−	377.764i	−0.139958	−	0.430746i	−0.996328	+	0.0856163i	$0.972714\pi$
$878$	−761.219	−	354.334i	−0.866992	−	0.403569i
$879$			571.204i			0.649834i
$880$	−118.191	+	58.0558i	−0.134308	+	0.0659725i
$881$	473.383			0.537325			0.268662	−	0.963234i	$-0.413418\pi$
$881$	473.383			0.537325			0.268662	+	0.963234i	$0.413418\pi$
$882$	223.733	−	480.647i	0.253665	−	0.544951i
$883$	1305.74	−	424.260i	1.47875	−	0.480475i	0.545011	−	0.838429i	$-0.316525\pi$
$883$	1305.74	−	424.260i	1.47875	−	0.480475i	0.933739	+	0.357954i	$0.116525\pi$
$884$	68.8972	+	81.8827i	0.0779380	+	0.0926275i
$885$	53.0593	+	38.5499i	0.0599540	+	0.0435592i
$886$	60.7138	−	497.261i	0.0685257	−	0.561243i
$887$	−266.937	−	86.7330i	−0.300943	−	0.0977824i	0.154653	−	0.987969i	$-0.450574\pi$
$887$	−266.937	−	86.7330i	−0.300943	−	0.0977824i	−0.455597	+	0.890186i	$0.650574\pi$
$888$	83.6084	+	309.511i	0.0941536	+	0.348549i
$889$	−278.627	+	202.434i	−0.313416	+	0.227710i
$890$	61.1505	−	33.9505i	0.0687084	−	0.0381466i
$891$	324.474	−	446.682i	0.364168	−	0.501326i
$892$	522.294	+	325.381i	0.585531	+	0.364777i
$893$	−753.751	+	547.632i	−0.844066	+	0.613250i
$894$	176.438	−	189.464i	0.197358	−	0.211928i
$895$	−64.9321	−	21.0977i	−0.0725498	−	0.0235729i
$896$	109.375	−	484.228i	0.122070	−	0.540433i
$897$	45.6597	+	33.1737i	0.0509027	+	0.0369830i
$898$	42.0351	+	215.472i	0.0468097	+	0.239946i
$899$	−739.472	+	240.269i	−0.822550	+	0.267263i
$900$	−54.2657	−	761.201i	−0.0602952	−	0.845778i
$901$	−718.356			−0.797287
$902$	1100.80	+	512.288i	1.22040	+	0.567947i
$903$			182.408i			0.202003i
$904$	99.4267	+	152.424i	0.109985	+	0.168611i
$905$	4.62599	+	14.2373i	0.00511159	+	0.0157319i
$906$	−60.7697	−	311.505i	−0.0670747	−	0.343825i
$907$	286.376	−	394.163i	0.315740	−	0.434578i	−0.621421	−	0.783477i	$-0.713444\pi$
$907$	286.376	−	394.163i	0.315740	−	0.434578i	0.937160	+	0.348899i	$0.113444\pi$
$908$	485.680	+	1197.42i	0.534890	+	1.31875i
$909$	−174.738	+	537.788i	−0.192231	+	0.591626i
$910$	−13.6136	+	14.6187i	−0.0149600	+	0.0160645i
$911$	627.748	+	864.021i	0.689076	+	0.948431i	0.999998	−	0.00200421i	$-0.000637960\pi$
$911$	627.748	+	864.021i	0.689076	+	0.948431i	−0.310922	+	0.950435i	$0.600638\pi$
$912$	−147.853	−	301.068i	−0.162119	−	0.330118i
$913$	−587.693	+	427.063i	−0.643695	+	0.467758i
$914$	−558.446	+	310.047i	−0.610991	+	0.339219i
$915$	37.3534	+	51.4126i	0.0408234	+	0.0561886i
$916$	−1107.03	−	274.419i	−1.20854	−	0.299584i
$917$	204.525	−	629.462i	0.223037	−	0.686436i
$918$	−34.5953	+	283.344i	−0.0376855	+	0.308654i
$919$	170.812	−	235.102i	0.185867	−	0.255824i	−0.705908	−	0.708304i	$-0.749461\pi$
$919$	170.812	−	235.102i	0.185867	−	0.255824i	0.891774	+	0.452480i	$0.149461\pi$
$920$	−32.0174	+	83.9180i	−0.0348015	+	0.0912152i
$921$	178.305	+	548.768i	0.193600	+	0.595839i
$922$	−536.066	+	1151.64i	−0.581417	+	1.24906i
$923$			338.328i			0.366553i
$924$	−70.0978	−	172.780i	−0.0758634	−	0.186991i
$925$	−896.403			−0.969085
$926$	−1333.80	−	620.859i	−1.44038	−	0.670474i
$927$	155.656	−	50.5757i	0.167914	−	0.0545585i
$928$	356.285	−	270.378i	0.383927	−	0.291356i
$929$	139.029	+	101.011i	0.149655	+	0.108731i	0.660093	−	0.751184i	$-0.270517\pi$
$929$	139.029	+	101.011i	0.149655	+	0.108731i	−0.510438	+	0.859914i	$0.670517\pi$
$930$	−90.2837	−	11.0233i	−0.0970792	−	0.0118530i
$931$	619.632	+	201.331i	0.665555	+	0.216252i
$932$	−757.202	−	187.701i	−0.812448	−	0.201396i
$933$	281.856	−	204.780i	0.302096	−	0.219486i
$934$	−284.772	−	512.921i	−0.304895	−	0.549166i
$935$	0.00560254	+	63.9658i	5.99202e−6	+	0.0684126i
$936$	−10.8133	+	214.684i	−0.0115526	+	0.229363i
$937$	−694.695	+	504.726i	−0.741404	+	0.538661i	−0.893150	−	0.449758i	$-0.851510\pi$
$937$	−694.695	+	504.726i	−0.741404	+	0.538661i	0.151747	+	0.988419i	$0.451510\pi$
$938$	327.745	+	305.212i	0.349408	+	0.325386i
$939$	335.014	+	108.853i	0.356777	+	0.115924i
$940$	−54.6246	−	134.675i	−0.0581113	−	0.143271i
$941$	−755.437	−	548.857i	−0.802802	−	0.583270i	0.108932	−	0.994049i	$-0.465257\pi$
$941$	−755.437	−	548.857i	−0.802802	−	0.583270i	−0.911735	+	0.410779i	$0.865257\pi$
$942$	190.387	−	37.1416i	0.202110	−	0.0394284i
$943$	787.648	−	255.922i	0.835258	−	0.271392i
$944$	−599.546	+	1135.00i	−0.635112	+	1.20233i
$945$	−53.2846			−0.0563858
$946$	693.070	+	645.307i	0.732632	+	0.682142i
$947$			588.592i			0.621533i	0.950486	+	0.310767i	$0.100586\pi$
$947$			588.592i			0.621533i	−0.950486	+	0.310767i	$0.899414\pi$
$948$	23.5103	+	329.786i	0.0247999	+	0.347875i
$949$	79.5881	+	244.947i	0.0838652	+	0.258110i
$950$	920.456	−	179.566i	0.968901	−	0.189017i
$951$	232.837	−	320.473i	0.244834	−	0.336985i
$952$	−187.716	−	151.378i	−0.197180	−	0.159011i
$953$	−4.59701	+	14.1481i	−0.00482373	+	0.0148459i	−0.953439	−	0.301585i	$-0.902484\pi$
$953$	−4.59701	+	14.1481i	−0.00482373	+	0.0148459i	0.948616	+	0.316431i	$0.102484\pi$
$954$	−1055.98	−	983.384i	−1.10690	−	1.03080i
$955$	−96.6409	−	133.015i	−0.101195	−	0.139282i
$956$	717.473	+	446.975i	0.750494	+	0.467547i
$957$	51.8982	−	159.774i	0.0542300	−	0.166953i
$958$	−97.6240	−	175.837i	−0.101904	−	0.183546i
$959$	−203.273	−	279.781i	−0.211963	−	0.291743i
$960$	51.1321	−	11.0861i	0.0532626	−	0.0115480i
$961$	−659.325	+	2029.19i	−0.686083	+	2.11155i
$962$	250.634	+	30.6015i	0.260534	+	0.0318103i
$963$	120.464	−	165.804i	0.125092	−	0.172174i
$964$	−845.437	−	1004.78i	−0.877009	−	1.04231i
$965$	−20.7646	−	63.9069i	−0.0215177	−	0.0662248i
$966$	−115.303	−	53.6714i	−0.119361	−	0.0555604i
$967$			974.002i			1.00724i	0.863925	+	0.503621i	$0.167999\pi$
$967$			974.002i			1.00724i	−0.863925	+	0.503621i	$0.832001\pi$
$968$	−904.470	−	344.903i	−0.934370	−	0.356305i
$969$	−162.933			−0.168146
$970$	−67.7562	+	145.561i	−0.0698518	+	0.150063i
$971$	−408.637	+	132.774i	−0.420841	+	0.136740i	−0.511779	−	0.859117i	$-0.671013\pi$
$971$	−408.637	+	132.774i	−0.420841	+	0.136740i	0.0909380	+	0.995857i	$0.471013\pi$
$972$	−673.687	+	566.849i	−0.693094	+	0.583178i
$973$	562.103	+	408.392i	0.577701	+	0.419725i
$974$	−29.0011	+	237.526i	−0.0297752	+	0.243867i
$975$	87.4215	+	28.4050i	0.0896631	+	0.0291333i
$976$	−892.353	+	866.424i	−0.914296	+	0.887730i
$977$	258.647	−	187.918i	0.264736	−	0.192342i	−0.447496	−	0.894286i	$-0.647684\pi$
$977$	258.647	−	187.918i	0.264736	−	0.192342i	0.712232	+	0.701944i	$0.247684\pi$
$978$	−43.4217	+	24.1075i	−0.0443984	+	0.0246498i
$979$	489.011	+	158.842i	0.499501	+	0.162249i
$980$	−53.7379	+	86.2587i	−0.0548346	+	0.0880191i
$981$	501.160	−	364.114i	0.510866	−	0.371166i
$982$	380.480	−	408.570i	0.387454	−	0.416059i
$983$	281.950	+	91.6112i	0.286826	+	0.0931955i	0.448897	−	0.893584i	$-0.351817\pi$
$983$	281.950	+	91.6112i	0.286826	+	0.0931955i	−0.162070	+	0.986779i	$0.551817\pi$
$984$	−375.531	−	302.836i	−0.381637	−	0.307760i
$985$	−68.6084	−	49.8469i	−0.0696532	−	0.0506060i
$986$	−41.6008	−	213.245i	−0.0421915	−	0.216273i
$987$	195.716	−	63.5919i	0.198293	−	0.0644295i
$988$	−263.489	+	18.7840i	−0.266689	+	0.0190122i
$989$	645.931			0.653115
$990$	−87.5569	+	94.0375i	−0.0884413	+	0.0949874i
$991$			418.812i			0.422616i	0.977420	+	0.211308i	$0.0677723\pi$
$991$			418.812i			0.422616i	−0.977420	+	0.211308i	$0.932228\pi$
$992$	−37.1014	−	1779.75i	−0.0374006	−	1.79410i
$993$	−29.7243	−	91.4820i	−0.0299338	−	0.0921269i
$994$	−145.982	−	748.305i	−0.146864	−	0.752822i
$995$	−56.3844	+	77.6065i	−0.0566677	+	0.0779964i
$996$	267.484	−	108.493i	0.268558	−	0.108928i
$997$	−474.883	+	1461.54i	−0.476312	+	1.46594i	0.367868	+	0.929878i	$0.380088\pi$
$997$	−474.883	+	1461.54i	−0.476312	+	1.46594i	−0.844180	+	0.536059i	$0.819912\pi$
$998$	230.481	−	247.496i	0.230943	−	0.247992i
$999$	395.882	+	544.886i	0.396279	+	0.545431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	44.3.h.a.3.7	✓	40
3.2	odd	2		396.3.s.a.91.4		40
4.3	odd	2	inner	44.3.h.a.3.10	yes	40
11.2	odd	10		484.3.b.k.243.17		20
11.4	even	5	inner	44.3.h.a.15.10	yes	40
11.9	even	5		484.3.b.j.243.4		20
12.11	even	2		396.3.s.a.91.1		40
33.26	odd	10		396.3.s.a.235.1		40
44.15	odd	10	inner	44.3.h.a.15.7	yes	40
44.31	odd	10		484.3.b.j.243.3		20
44.35	even	10		484.3.b.k.243.18		20
132.59	even	10		396.3.s.a.235.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.3.h.a.3.7	✓	40	1.1	even	1	trivial
44.3.h.a.3.10	yes	40	4.3	odd	2	inner
44.3.h.a.15.7	yes	40	44.15	odd	10	inner
44.3.h.a.15.10	yes	40	11.4	even	5	inner
396.3.s.a.91.1		40	12.11	even	2
396.3.s.a.91.4		40	3.2	odd	2
396.3.s.a.235.1		40	33.26	odd	10
396.3.s.a.235.4		40	132.59	even	10
484.3.b.j.243.3		20	44.31	odd	10
484.3.b.j.243.4		20	11.9	even	5
484.3.b.k.243.17		20	11.2	odd	10
484.3.b.k.243.18		20	44.35	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:	\( N \)	\(=\)	\( 44 = 2^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	44.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.844007 - 1.81319i) q^{2} +(1.03917 - 0.337648i) q^{3} +(-2.57530 - 3.06069i) q^{4} +(0.605291 + 0.439770i) q^{5} +(0.264851 - 2.16920i) q^{6} +(3.68852 + 1.19847i) q^{7} +(-7.72318 + 2.08627i) q^{8} +(-6.31528 + 4.58832i) q^{9} +O(q^{10})\)	\(q+(0.844007 - 1.81319i) q^{2} +(1.03917 - 0.337648i) q^{3} +(-2.57530 - 3.06069i) q^{4} +(0.605291 + 0.439770i) q^{5} +(0.264851 - 2.16920i) q^{6} +(3.68852 + 1.19847i) q^{7} +(-7.72318 + 2.08627i) q^{8} +(-6.31528 + 4.58832i) q^{9} +(1.30826 - 0.726338i) q^{10} +(10.4619 + 3.39827i) q^{11} +(-3.70962 - 2.31104i) q^{12} +(-2.78472 + 2.02322i) q^{13} +(5.28619 - 5.67646i) q^{14} +(0.777490 + 0.252622i) q^{15} +(-2.73563 + 15.7644i) q^{16} +(6.28791 + 4.56843i) q^{17} +(2.98934 + 15.3234i) q^{18} +(-18.2467 + 5.92872i) q^{19} +(-0.212810 - 2.98515i) q^{20} +4.23767 q^{21} +(14.9916 - 16.1013i) q^{22} -15.0061i q^{23} +(-7.32131 + 4.77571i) q^{24} +(-7.55245 - 23.2440i) q^{25} +(1.31815 + 6.75684i) q^{26} +(-10.7936 + 14.8562i) q^{27} +(-5.83090 - 14.3758i) q^{28} +(4.31911 - 13.2929i) q^{29} +(1.11426 - 1.19652i) q^{30} +(-32.6981 - 45.0051i) q^{31} +(26.2749 + 18.2655i) q^{32} +(12.0192 - 0.00105272i) q^{33} +(13.5905 - 7.54537i) q^{34} +(1.70557 + 2.34752i) q^{35} +(30.3072 + 7.51279i) q^{36} +(11.3339 - 34.8823i) q^{37} +(-4.65049 + 38.0886i) q^{38} +(-2.21068 + 3.04274i) q^{39} +(-5.59225 - 2.13362i) q^{40} +(17.0545 + 52.4884i) q^{41} +(3.57663 - 7.68370i) q^{42} +43.0444i q^{43} +(-16.5416 - 40.7723i) q^{44} -5.84038 q^{45} +(-27.2090 - 12.6653i) q^{46} +(46.1847 - 15.0063i) q^{47} +(2.48003 + 17.3056i) q^{48} +(-27.4730 - 19.9603i) q^{49} +(-48.5201 - 5.92413i) q^{50} +(8.07676 + 2.62430i) q^{51} +(13.3640 + 3.31277i) q^{52} +(-74.7736 + 54.3262i) q^{53} +(17.8271 + 32.1096i) q^{54} +(4.83805 + 6.65778i) q^{55} +(-30.9874 - 1.56078i) q^{56} +(-16.9597 + 12.3220i) q^{57} +(-20.4571 - 19.0506i) q^{58} +(76.2995 + 24.7912i) q^{59} +(-1.22908 - 3.03023i) q^{60} +(62.8898 + 45.6921i) q^{61} +(-109.200 + 21.3032i) q^{62} +(-28.7930 + 9.35541i) q^{63} +(55.2950 - 32.2252i) q^{64} -2.57532 q^{65} +(10.1424 - 21.7939i) q^{66} +57.7376i q^{67} +(-2.21072 - 31.0104i) q^{68} +(-5.06680 - 15.5940i) q^{69} +(5.69602 - 1.11120i) q^{70} +(57.7740 - 79.5191i) q^{71} +(39.2016 - 48.6117i) q^{72} +(23.1219 - 71.1618i) q^{73} +(-53.6822 - 49.9914i) q^{74} +(-15.6966 - 21.6045i) q^{75} +(65.1368 + 40.5793i) q^{76} +(34.5162 + 25.0729i) q^{77} +(3.65123 + 6.57647i) q^{78} +(-44.4641 - 61.1996i) q^{79} +(-8.58856 + 8.33900i) q^{80} +(15.5097 - 47.7339i) q^{81} +(109.565 + 13.3775i) q^{82} +(-38.8192 + 53.4301i) q^{83} +(-10.9133 - 12.9702i) q^{84} +(1.79696 + 5.53046i) q^{85} +(78.0477 + 36.3298i) q^{86} -15.2719i q^{87} +(-87.8890 - 4.41910i) q^{88} +46.7420 q^{89} +(-4.92933 + 10.5897i) q^{90} +(-12.6963 + 4.12527i) q^{91} +(-45.9291 + 38.6454i) q^{92} +(-49.1749 - 35.7277i) q^{93} +(11.7709 - 96.4070i) q^{94} +(-13.6519 - 4.43576i) q^{95} +(33.4715 + 10.1093i) q^{96} +(-86.8069 + 63.0689i) q^{97} +(-59.3792 + 32.9671i) q^{98} +(-81.6622 + 26.5416i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} - 9 q^{4} - 6 q^{5} - 11 q^{6} + 7 q^{8} + 20 q^{9}+O(q^{10}) \) 40 * q - 5 * q^2 - 9 * q^4 - 6 * q^5 - 11 * q^6 + 7 * q^8 + 20 * q^9	\( 40 q - 5 q^{2} - 9 q^{4} - 6 q^{5} - 11 q^{6} + 7 q^{8} + 20 q^{9} - 8 q^{10} - 50 q^{12} - 6 q^{13} - 36 q^{14} - 65 q^{16} - 30 q^{17} - 58 q^{18} + 34 q^{20} - 52 q^{21} + 25 q^{22} + 49 q^{24} + 156 q^{26} + 130 q^{28} - 38 q^{29} + 94 q^{30} + 20 q^{32} - 110 q^{33} + 258 q^{34} + 324 q^{36} - 150 q^{37} + 80 q^{38} + 112 q^{40} - 150 q^{41} - 230 q^{42} + 4 q^{44} + 144 q^{45} + 40 q^{46} - 304 q^{48} + 132 q^{49} - 177 q^{50} - 314 q^{52} + 290 q^{53} - 540 q^{54} - 856 q^{56} + 242 q^{57} - 476 q^{58} - 344 q^{60} + 42 q^{61} - 364 q^{62} + 303 q^{64} + 164 q^{65} - 50 q^{66} + 14 q^{68} - 104 q^{69} + 576 q^{70} + 535 q^{72} + 186 q^{73} + 588 q^{74} + 366 q^{76} + 190 q^{77} + 1412 q^{78} + 1100 q^{80} - 160 q^{81} + 365 q^{82} + 380 q^{84} + 286 q^{85} - 501 q^{86} + 47 q^{88} - 88 q^{89} - 150 q^{90} - 702 q^{92} - 178 q^{93} - 678 q^{94} - 616 q^{96} - 130 q^{97} - 652 q^{98}+O(q^{100}) \) 40 * q - 5 * q^2 - 9 * q^4 - 6 * q^5 - 11 * q^6 + 7 * q^8 + 20 * q^9 - 8 * q^10 - 50 * q^12 - 6 * q^13 - 36 * q^14 - 65 * q^16 - 30 * q^17 - 58 * q^18 + 34 * q^20 - 52 * q^21 + 25 * q^22 + 49 * q^24 + 156 * q^26 + 130 * q^28 - 38 * q^29 + 94 * q^30 + 20 * q^32 - 110 * q^33 + 258 * q^34 + 324 * q^36 - 150 * q^37 + 80 * q^38 + 112 * q^40 - 150 * q^41 - 230 * q^42 + 4 * q^44 + 144 * q^45 + 40 * q^46 - 304 * q^48 + 132 * q^49 - 177 * q^50 - 314 * q^52 + 290 * q^53 - 540 * q^54 - 856 * q^56 + 242 * q^57 - 476 * q^58 - 344 * q^60 + 42 * q^61 - 364 * q^62 + 303 * q^64 + 164 * q^65 - 50 * q^66 + 14 * q^68 - 104 * q^69 + 576 * q^70 + 535 * q^72 + 186 * q^73 + 588 * q^74 + 366 * q^76 + 190 * q^77 + 1412 * q^78 + 1100 * q^80 - 160 * q^81 + 365 * q^82 + 380 * q^84 + 286 * q^85 - 501 * q^86 + 47 * q^88 - 88 * q^89 - 150 * q^90 - 702 * q^92 - 178 * q^93 - 678 * q^94 - 616 * q^96 - 130 * q^97 - 652 * q^98

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