LMFDB - Embedded newform 250.3.f.b.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,3,Mod(7,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([17]))

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

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

chi := DirichletCharacter("250.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	250.f (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.81200660901$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 30x^{14} + 351x^{12} + 2130x^{10} + 7341x^{8} + 14480x^{6} + 15196x^{4} + 6560x^{2} + 16 $ x^16 + 30x^14 + 351x^12 + 2130x^10 + 7341x^8 + 14480x^6 + 15196x^4 + 6560*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			107.2
Root			$-2.26402i$ of defining polynomial
Character	$\chi$	$=$	250.107
Dual form			250.3.f.b.243.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642040 - 1.26007i) q^{2} +(0.711697 - 4.49348i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-5.20517 - 3.78178i) q^{6} +(-3.58690 - 3.58690i) q^{7} +(-2.79360 + 0.442463i) q^{8} +(-11.1253 - 3.61484i) q^{9} +O(q^{10})$	\(q+(0.642040 - 1.26007i) q^{2} +(0.711697 - 4.49348i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-5.20517 - 3.78178i) q^{6} +(-3.58690 - 3.58690i) q^{7} +(-2.79360 + 0.442463i) q^{8} +(-11.1253 - 3.61484i) q^{9} +(3.53728 + 10.8866i) q^{11} +(-8.10725 + 4.13085i) q^{12} +(-10.0537 - 19.7315i) q^{13} +(-6.82270 + 2.21683i) q^{14} +(-1.23607 + 3.80423i) q^{16} +(3.10698 + 19.6167i) q^{17} +(-11.6979 + 11.6979i) q^{18} +(15.8404 - 21.8024i) q^{19} +(-18.6705 + 13.5649i) q^{21} +(15.9890 + 2.53241i) q^{22} +(0.476846 + 0.242965i) q^{23} +12.8679i q^{24} -31.3180 q^{26} +(-5.57222 + 10.9361i) q^{27} +(-1.58707 + 10.0204i) q^{28} +(-3.67470 - 5.05779i) q^{29} +(5.42369 + 3.94054i) q^{31} +(4.00000 + 4.00000i) q^{32} +(51.4362 - 8.14670i) q^{33} +(26.7133 + 8.67968i) q^{34} +(7.22967 + 22.2506i) q^{36} +(5.24626 - 2.67310i) q^{37} +(-17.3025 - 33.9580i) q^{38} +(-95.8181 + 31.1332i) q^{39} +(7.33457 - 22.5735i) q^{41} +(5.10558 + 32.2354i) q^{42} +(-44.7386 + 44.7386i) q^{43} +(13.4566 - 18.5214i) q^{44} +(0.612308 - 0.444868i) q^{46} +(27.2676 + 4.31877i) q^{47} +(16.2145 + 8.26170i) q^{48} -23.2682i q^{49} +90.3585 q^{51} +(-20.1074 + 39.4630i) q^{52} +(13.6315 - 86.0658i) q^{53} +(10.2027 + 14.0428i) q^{54} +(11.6075 + 8.43332i) q^{56} +(-86.6950 - 86.6950i) q^{57} +(-8.73248 + 1.38309i) q^{58} +(20.7422 + 6.73954i) q^{59} +(-21.3293 - 65.6449i) q^{61} +(8.44760 - 4.30427i) q^{62} +(26.9394 + 52.8715i) q^{63} +(7.60845 - 2.47214i) q^{64} +(22.7587 - 70.0439i) q^{66} +(-14.4421 - 91.1840i) q^{67} +(28.0880 - 28.0880i) q^{68} +(1.43113 - 1.96978i) q^{69} +(12.7283 - 9.24768i) q^{71} +(32.6792 + 5.17587i) q^{72} +(60.4466 + 30.7991i) q^{73} -8.32691i q^{74} -53.8984 q^{76} +(26.3614 - 51.7371i) q^{77} +(-22.2889 + 140.727i) q^{78} +(71.8966 + 98.9571i) q^{79} +(-39.9985 - 29.0606i) q^{81} +(-23.7352 - 23.7352i) q^{82} +(-60.8973 + 9.64518i) q^{83} +(43.8969 + 14.2630i) q^{84} +(27.6500 + 85.0979i) q^{86} +(-25.3423 + 12.9126i) q^{87} +(-14.6987 - 28.8478i) q^{88} +(75.7710 - 24.6195i) q^{89} +(-34.7133 + 106.837i) q^{91} +(-0.167440 - 1.05718i) q^{92} +(21.5668 - 21.5668i) q^{93} +(22.9488 - 31.5864i) q^{94} +(20.8207 - 15.1271i) q^{96} +(134.309 + 21.2725i) q^{97} +(-29.3197 - 14.9391i) q^{98} -133.904i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 2 q^{3} + 4 q^{6} + 2 q^{7} - 8 q^{8} - 40 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 2 * q^3 + 4 * q^6 + 2 * q^7 - 8 * q^8 - 40 * q^9	$ 16 q + 4 q^{2} - 2 q^{3} + 4 q^{6} + 2 q^{7} - 8 q^{8} - 40 q^{9} + 32 q^{11} - 4 q^{12} + 8 q^{13} - 30 q^{14} + 16 q^{16} + 62 q^{17} + 16 q^{18} + 30 q^{19} - 68 q^{21} + 48 q^{22} + 18 q^{23} - 56 q^{26} + 40 q^{27} - 44 q^{28} + 100 q^{29} + 132 q^{31} + 64 q^{32} + 36 q^{33} + 100 q^{34} + 48 q^{36} - 138 q^{37} - 20 q^{38} - 320 q^{39} - 88 q^{41} + 8 q^{42} + 78 q^{43} + 40 q^{44} - 26 q^{46} + 22 q^{47} + 8 q^{48} - 168 q^{51} + 16 q^{52} - 182 q^{53} + 80 q^{54} + 48 q^{56} - 280 q^{57} + 120 q^{58} - 350 q^{59} + 372 q^{61} + 158 q^{62} - 22 q^{63} - 202 q^{66} + 112 q^{67} + 196 q^{68} - 30 q^{69} + 122 q^{71} + 132 q^{72} + 248 q^{73} + 40 q^{76} - 16 q^{77} - 438 q^{78} + 760 q^{79} - 144 q^{81} - 352 q^{82} - 132 q^{83} - 20 q^{84} + 264 q^{86} - 770 q^{87} - 116 q^{88} + 550 q^{89} - 798 q^{91} - 384 q^{92} - 54 q^{93} + 190 q^{94} - 16 q^{96} + 292 q^{97} + 24 q^{98}+O(q^{100}) $ 16 * q + 4 * q^2 - 2 * q^3 + 4 * q^6 + 2 * q^7 - 8 * q^8 - 40 * q^9 + 32 * q^11 - 4 * q^12 + 8 * q^13 - 30 * q^14 + 16 * q^16 + 62 * q^17 + 16 * q^18 + 30 * q^19 - 68 * q^21 + 48 * q^22 + 18 * q^23 - 56 * q^26 + 40 * q^27 - 44 * q^28 + 100 * q^29 + 132 * q^31 + 64 * q^32 + 36 * q^33 + 100 * q^34 + 48 * q^36 - 138 * q^37 - 20 * q^38 - 320 * q^39 - 88 * q^41 + 8 * q^42 + 78 * q^43 + 40 * q^44 - 26 * q^46 + 22 * q^47 + 8 * q^48 - 168 * q^51 + 16 * q^52 - 182 * q^53 + 80 * q^54 + 48 * q^56 - 280 * q^57 + 120 * q^58 - 350 * q^59 + 372 * q^61 + 158 * q^62 - 22 * q^63 - 202 * q^66 + 112 * q^67 + 196 * q^68 - 30 * q^69 + 122 * q^71 + 132 * q^72 + 248 * q^73 + 40 * q^76 - 16 * q^77 - 438 * q^78 + 760 * q^79 - 144 * q^81 - 352 * q^82 - 132 * q^83 - 20 * q^84 + 264 * q^86 - 770 * q^87 - 116 * q^88 + 550 * q^89 - 798 * q^91 - 384 * q^92 - 54 * q^93 + 190 * q^94 - 16 * q^96 + 292 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{13}{20}\right)$

Coefficient data

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

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

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

$2$	0.642040	−	1.26007i	0.321020	−	0.630037i
$2$	0.642040	−	1.26007i	0.321020	−	0.630037i
$3$	0.711697	−	4.49348i	0.237232	−	1.49783i	−0.525323	−	0.850903i	$-0.676055\pi$
$3$	0.711697	−	4.49348i	0.237232	−	1.49783i	0.762555	−	0.646923i	$-0.223945\pi$
$4$	−1.17557	−	1.61803i	−0.293893	−	0.404508i
$5$		0			0
$5$		0			0
$6$	−5.20517	−	3.78178i	−0.867529	−	0.630297i
$7$	−3.58690	−	3.58690i	−0.512415	−	0.512415i	0.402851	−	0.915266i	$-0.368019\pi$
$7$	−3.58690	−	3.58690i	−0.512415	−	0.512415i	−0.915266	+	0.402851i	$0.868019\pi$
$8$	−2.79360	+	0.442463i	−0.349201	+	0.0553079i
$9$	−11.1253	−	3.61484i	−1.23615	−	0.401648i
$10$		0			0
$11$	3.53728	+	10.8866i	0.321571	+	0.989692i	0.972965	+	0.230953i	$0.0741844\pi$
$11$	3.53728	+	10.8866i	0.321571	+	0.989692i	−0.651394	+	0.758739i	$0.725816\pi$
$12$	−8.10725	+	4.13085i	−0.675604	+	0.344238i
$13$	−10.0537	−	19.7315i	−0.773361	−	1.51781i	−0.853541	−	0.521025i	$-0.825550\pi$
$13$	−10.0537	−	19.7315i	−0.773361	−	1.51781i	0.0801805	−	0.996780i	$-0.474450\pi$
$14$	−6.82270	+	2.21683i	−0.487336	+	0.158345i
$15$		0			0
$16$	−1.23607	+	3.80423i	−0.0772542	+	0.237764i
$17$	3.10698	+	19.6167i	0.182764	+	1.15392i	0.893032	+	0.449994i	$0.148574\pi$
$17$	3.10698	+	19.6167i	0.182764	+	1.15392i	−0.710268	+	0.703931i	$0.751426\pi$
$18$	−11.6979	+	11.6979i	−0.649881	+	0.649881i
$19$	15.8404	−	21.8024i	0.833703	−	1.14749i	−0.153520	−	0.988146i	$-0.549061\pi$
$19$	15.8404	−	21.8024i	0.833703	−	1.14749i	0.987222	−	0.159348i	$-0.0509392\pi$
$20$		0			0
$21$	−18.6705	+	13.5649i	−0.889070	+	0.645947i
$22$	15.9890	+	2.53241i	0.726773	+	0.115110i
$23$	0.476846	+	0.242965i	0.0207324	+	0.0105637i	0.464326	−	0.885664i	$-0.346297\pi$
$23$	0.476846	+	0.242965i	0.0207324	+	0.0105637i	−0.443594	+	0.896228i	$0.646297\pi$
$24$			12.8679i			0.536162i
$25$		0			0
$26$	−31.3180			−1.20454
$27$	−5.57222	+	10.9361i	−0.206378	+	0.405041i
$28$	−1.58707	+	10.0204i	−0.0566812	+	0.357871i
$29$	−3.67470	−	5.05779i	−0.126714	−	0.174406i	0.740947	−	0.671564i	$-0.234377\pi$
$29$	−3.67470	−	5.05779i	−0.126714	−	0.174406i	−0.867660	+	0.497157i	$0.834377\pi$
$30$		0			0
$31$	5.42369	+	3.94054i	0.174958	+	0.127114i	0.671818	−	0.740716i	$-0.265514\pi$
$31$	5.42369	+	3.94054i	0.174958	+	0.127114i	−0.496860	+	0.867831i	$0.665514\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	51.4362	−	8.14670i	1.55867	−	0.246870i
$34$	26.7133	+	8.67968i	0.785686	+	0.255285i
$35$		0			0
$36$	7.22967	+	22.2506i	0.200824	+	0.618073i
$37$	5.24626	−	2.67310i	0.141791	−	0.0722460i	−0.381656	−	0.924305i	$-0.624646\pi$
$37$	5.24626	−	2.67310i	0.141791	−	0.0722460i	0.523446	+	0.852059i	$0.324646\pi$
$38$	−17.3025	−	33.9580i	−0.455328	−	0.893632i
$39$	−95.8181	+	31.1332i	−2.45688	+	0.798287i
$40$		0			0
$41$	7.33457	−	22.5735i	0.178892	−	0.550573i	−0.820898	−	0.571075i	$-0.806526\pi$
$41$	7.33457	−	22.5735i	0.178892	−	0.550573i	0.999790	+	0.0205022i	$0.00652650\pi$
$42$	5.10558	+	32.2354i	0.121561	+	0.767508i
$43$	−44.7386	+	44.7386i	−1.04043	+	1.04043i	−0.0412854	+	0.999147i	$0.513145\pi$
$43$	−44.7386	+	44.7386i	−1.04043	+	1.04043i	−0.999147	+	0.0412854i	$0.986855\pi$
$44$	13.4566	−	18.5214i	0.305832	−	0.420941i
$45$		0			0
$46$	0.612308	−	0.444868i	0.0133110	−	0.00967104i
$47$	27.2676	+	4.31877i	0.580162	+	0.0918886i	0.439616	−	0.898186i	$-0.355114\pi$
$47$	27.2676	+	4.31877i	0.580162	+	0.0918886i	0.140545	+	0.990074i	$0.455114\pi$
$48$	16.2145	+	8.26170i	0.337802	+	0.172119i
$49$		−	23.2682i		−	0.474862i
$50$		0			0
$51$	90.3585			1.77174
$52$	−20.1074	+	39.4630i	−0.386680	+	0.758903i
$53$	13.6315	−	86.0658i	0.257198	−	1.62388i	−0.433788	−	0.901015i	$-0.642823\pi$
$53$	13.6315	−	86.0658i	0.257198	−	1.62388i	0.690986	−	0.722868i	$-0.257177\pi$
$54$	10.2027	+	14.0428i	0.188939	+	0.260052i
$55$		0			0
$56$	11.6075	+	8.43332i	0.207276	+	0.150595i
$57$	−86.6950	−	86.6950i	−1.52096	−	1.52096i
$58$	−8.73248	+	1.38309i	−0.150560	+	0.0238464i
$59$	20.7422	+	6.73954i	0.351562	+	0.114229i	0.479474	−	0.877556i	$-0.340827\pi$
$59$	20.7422	+	6.73954i	0.351562	+	0.114229i	−0.127912	+	0.991786i	$0.540827\pi$
$60$		0			0
$61$	−21.3293	−	65.6449i	−0.349661	−	1.07615i	−0.959041	−	0.283267i	$-0.908582\pi$
$61$	−21.3293	−	65.6449i	−0.349661	−	1.07615i	0.609380	−	0.792878i	$-0.291418\pi$
$62$	8.44760	−	4.30427i	0.136252	−	0.0694237i
$63$	26.9394	+	52.8715i	0.427609	+	0.839231i
$64$	7.60845	−	2.47214i	0.118882	−	0.0386271i
$65$		0			0
$66$	22.7587	−	70.0439i	0.344828	−	1.06127i
$67$	−14.4421	−	91.1840i	−0.215554	−	1.36096i	−0.823653	−	0.567094i	$-0.808068\pi$
$67$	−14.4421	−	91.1840i	−0.215554	−	1.36096i	0.608099	−	0.793861i	$-0.291932\pi$
$68$	28.0880	−	28.0880i	0.413060	−	0.413060i
$69$	1.43113	−	1.96978i	0.0207410	−	0.0285475i
$70$		0			0
$71$	12.7283	−	9.24768i	0.179272	−	0.130249i	−0.494530	−	0.869161i	$-0.664660\pi$
$71$	12.7283	−	9.24768i	0.179272	−	0.130249i	0.673803	+	0.738911i	$0.264660\pi$
$72$	32.6792	+	5.17587i	0.453878	+	0.0718871i
$73$	60.4466	+	30.7991i	0.828036	+	0.421905i	0.816021	−	0.578022i	$-0.196175\pi$
$73$	60.4466	+	30.7991i	0.828036	+	0.421905i	0.0120152	+	0.999928i	$0.496175\pi$
$74$		−	8.32691i		−	0.112526i
$75$		0			0
$76$	−53.8984			−0.709190
$77$	26.3614	−	51.7371i	0.342356	−	0.671911i
$78$	−22.2889	+	140.727i	−0.285755	+	1.80419i
$79$	71.8966	+	98.9571i	0.910083	+	1.25262i	0.967138	+	0.254251i	$0.0818289\pi$
$79$	71.8966	+	98.9571i	0.910083	+	1.25262i	−0.0570551	+	0.998371i	$0.518171\pi$
$80$		0			0
$81$	−39.9985	−	29.0606i	−0.493809	−	0.358773i
$82$	−23.7352	−	23.7352i	−0.289453	−	0.289453i
$83$	−60.8973	+	9.64518i	−0.733702	+	0.116207i	−0.512095	−	0.858929i	$-0.671130\pi$
$83$	−60.8973	+	9.64518i	−0.733702	+	0.116207i	−0.221607	+	0.975136i	$0.571130\pi$
$84$	43.8969	+	14.2630i	0.522582	+	0.169797i
$85$		0			0
$86$	27.6500	+	85.0979i	0.321511	+	0.989510i
$87$	−25.3423	+	12.9126i	−0.291291	+	0.148420i
$88$	−14.6987	−	28.8478i	−0.167030	−	0.327816i
$89$	75.7710	−	24.6195i	0.851359	−	0.276623i	0.149344	−	0.988785i	$-0.452284\pi$
$89$	75.7710	−	24.6195i	0.851359	−	0.276623i	0.702015	+	0.712162i	$0.252284\pi$
$90$		0			0
$91$	−34.7133	+	106.837i	−0.381465	+	1.17403i
$92$	−0.167440	−	1.05718i	−0.00182000	−	0.0114910i
$93$	21.5668	−	21.5668i	0.231901	−	0.231901i
$94$	22.9488	−	31.5864i	0.244137	−	0.336025i
$95$		0			0
$96$	20.8207	−	15.1271i	0.216882	−	0.157574i
$97$	134.309	+	21.2725i	1.38463	+	0.219304i	0.803886	−	0.594783i	$-0.202762\pi$
$97$	134.309	+	21.2725i	1.38463	+	0.219304i	0.580743	+	0.814087i	$0.302762\pi$
$98$	−29.3197	−	14.9391i	−0.299180	−	0.152440i
$99$		−	133.904i		−	1.35256i
$100$		0			0
$101$	60.2160			0.596198			0.298099	−	0.954535i	$-0.403648\pi$
$101$	60.2160			0.596198			0.298099	+	0.954535i	$0.403648\pi$
$102$	58.0138	−	113.858i	0.568762	−	1.11626i
$103$	−11.2435	+	70.9888i	−0.109160	+	0.689211i	0.871041	+	0.491210i	$0.163445\pi$
$103$	−11.2435	+	70.9888i	−0.109160	+	0.689211i	−0.980202	+	0.198002i	$0.936555\pi$
$104$	36.8165	+	50.6735i	0.354005	+	0.487246i
$105$		0			0
$106$	−99.6973	−	72.4343i	−0.940540	−	0.683342i
$107$	9.22591	+	9.22591i	0.0862234	+	0.0862234i	0.748903	−	0.662680i	$-0.230581\pi$
$107$	9.22591	+	9.22591i	0.0862234	+	0.0862234i	−0.662680	+	0.748903i	$0.730581\pi$
$108$	24.2455	−	3.84011i	0.224495	−	0.0355566i
$109$	4.89779	+	1.59139i	0.0449339	+	0.0145999i	0.331398	−	0.943491i	$-0.392480\pi$
$109$	4.89779	+	1.59139i	0.0449339	+	0.0145999i	−0.286464	+	0.958091i	$0.592480\pi$
$110$		0			0
$111$	−8.27778	−	25.4764i	−0.0745746	−	0.229517i
$112$	18.0791	−	9.21174i	0.161420	−	0.0822477i
$113$	47.9858	+	94.1774i	0.424653	+	0.833428i	0.999881	+	0.0154352i	$0.00491339\pi$
$113$	47.9858	+	94.1774i	0.424653	+	0.833428i	−0.575228	+	0.817993i	$0.695087\pi$
$114$	−164.904	+	53.5804i	−1.44652	+	0.470004i
$115$		0			0
$116$	−3.86380	+	11.8916i	−0.0333087	+	0.102514i
$117$	40.5245	+	255.861i	0.346363	+	2.18685i
$118$	21.8096	−	21.8096i	0.184827	−	0.184827i
$119$	59.2189	−	81.5078i	0.497638	−	0.684939i
$120$		0			0
$121$	−8.11501	+	5.89590i	−0.0670662	+	0.0487265i
$122$	−96.4116	−	15.2701i	−0.790259	−	0.125165i
$123$	−96.2135	−	49.0232i	−0.782223	−	0.398563i
$124$		−	13.4081i		−	0.108130i
$125$		0			0
$126$	83.9182			0.666017
$127$	27.8658	−	54.6898i	0.219416	−	0.430628i	−0.754892	−	0.655850i	$-0.772311\pi$
$127$	27.8658	−	54.6898i	0.219416	−	0.430628i	0.974308	+	0.225221i	$0.0723105\pi$
$128$	1.76985	−	11.1744i	0.0138270	−	0.0873001i
$129$	169.192	+	232.872i	1.31156	+	1.80521i
$130$		0			0
$131$	58.9504	+	42.8300i	0.450003	+	0.326947i	0.789597	−	0.613626i	$-0.210290\pi$
$131$	58.9504	+	42.8300i	0.450003	+	0.326947i	−0.339594	+	0.940572i	$0.610290\pi$
$132$	−73.6486	−	73.6486i	−0.557944	−	0.557944i
$133$	−135.021	+	21.3852i	−1.01519	+	0.160791i
$134$	−124.171	−	40.3456i	−0.926649	−	0.301087i
$135$		0			0
$136$	−17.3594	−	53.4266i	−0.127642	−	0.392843i
$137$	−140.901	+	71.7926i	−1.02847	+	0.524033i	−0.884985	−	0.465619i	$-0.845832\pi$
$137$	−140.901	+	71.7926i	−1.02847	+	0.524033i	−0.143488	+	0.989652i	$0.545832\pi$
$138$	−1.56323	−	3.06800i	−0.0113277	−	0.0222319i
$139$	−112.170	+	36.4463i	−0.806981	+	0.262204i	−0.683318	−	0.730120i	$-0.739464\pi$
$139$	−112.170	+	36.4463i	−0.806981	+	0.262204i	−0.123662	+	0.992324i	$0.539464\pi$
$140$		0			0
$141$	38.8126	−	119.453i	0.275266	−	0.847183i
$142$	−3.48066	−	21.9760i	−0.0245117	−	0.154761i
$143$	179.246	−	179.246i	1.25347	−	1.25347i
$144$	27.5033	−	37.8551i	0.190995	−	0.262882i
$145$		0			0
$146$	77.6183	−	56.3930i	0.531632	−	0.386253i
$147$	−104.555	−	16.5599i	−0.711260	−	0.112653i
$148$	−10.4925	−	5.34620i	−0.0708954	−	0.0361230i
$149$		−	127.548i		−	0.856024i	−0.903773	−	0.428012i	$-0.859214\pi$
$149$		−	127.548i		−	0.856024i	0.903773	−	0.428012i	$-0.140786\pi$
$150$		0			0
$151$	−89.8058			−0.594741			−0.297370	−	0.954762i	$-0.596110\pi$
$151$	−89.8058			−0.594741			−0.297370	+	0.954762i	$0.596110\pi$
$152$	−34.6049	+	67.9160i	−0.227664	+	0.446816i
$153$	36.3450	−	229.474i	0.237549	−	1.49983i
$154$	−48.2675	−	66.4346i	−0.313426	−	0.431393i
$155$		0			0
$156$	163.016	+	118.438i	1.04497	+	0.759216i
$157$	58.6460	+	58.6460i	0.373541	+	0.373541i	0.868765	−	0.495224i	$-0.164914\pi$
$157$	58.6460	+	58.6460i	0.373541	+	0.373541i	−0.495224	+	0.868765i	$0.664914\pi$
$158$	170.854	−	27.0606i	1.08135	−	0.171269i
$159$	−377.033	−	122.506i	−2.37128	−	0.770475i
$160$		0			0
$161$	−0.838909	−	2.58190i	−0.00521061	−	0.0160366i
$162$	−62.2991	+	31.7430i	−0.384563	+	0.195944i
$163$	86.5547	+	169.873i	0.531011	+	1.04217i	0.988253	+	0.152825i	$0.0488371\pi$
$163$	86.5547	+	169.873i	0.531011	+	1.04217i	−0.457243	+	0.889342i	$0.651163\pi$
$164$	−45.1470	+	14.6691i	−0.275286	+	0.0894460i
$165$		0			0
$166$	−26.9448	+	82.9276i	−0.162318	+	0.499564i
$167$	20.9891	+	132.520i	0.125683	+	0.793532i	0.967333	+	0.253509i	$0.0815847\pi$
$167$	20.9891	+	132.520i	0.125683	+	0.793532i	−0.841650	+	0.540024i	$0.818415\pi$
$168$	46.1559	−	46.1559i	0.274738	−	0.274738i
$169$	−188.919	+	260.024i	−1.11786	+	1.53861i
$170$		0			0
$171$	−255.041	+	185.298i	−1.49147	+	1.08362i
$172$	124.982	+	19.7952i	0.726639	+	0.115088i
$173$	−111.098	−	56.6075i	−0.642187	−	0.327211i	0.102393	−	0.994744i	$-0.467350\pi$
$173$	−111.098	−	56.6075i	−0.642187	−	0.327211i	−0.744580	+	0.667533i	$0.767350\pi$
$174$			40.2236i			0.231170i
$175$		0			0
$176$	−45.7875			−0.260156
$177$	45.0461	−	88.4080i	0.254498	−	0.499480i
$178$	17.6256	−	111.284i	0.0990203	−	0.625189i
$179$	103.351	+	142.251i	0.577381	+	0.794697i	0.993405	−	0.114656i	$-0.0365767\pi$
$179$	103.351	+	142.251i	0.577381	+	0.794697i	−0.416024	+	0.909354i	$0.636577\pi$
$180$		0			0
$181$	4.01656	+	2.91820i	0.0221909	+	0.0161227i	0.598825	−	0.800880i	$-0.295634\pi$
$181$	4.01656	+	2.91820i	0.0221909	+	0.0161227i	−0.576635	+	0.817002i	$0.695634\pi$
$182$	112.335	+	112.335i	0.617223	+	0.617223i
$183$	−310.154	+	49.1235i	−1.69483	+	0.268435i
$184$	−1.43962	−	0.467762i	−0.00782404	−	0.00254218i
$185$		0			0
$186$	−13.3290	−	41.0224i	−0.0716613	−	0.220551i
$187$	−202.569	+	103.214i	−1.08326	+	0.551948i
$188$	−25.0671	−	49.1969i	−0.133336	−	0.261686i
$189$	59.2138	−	19.2397i	0.313300	−	0.101797i
$190$		0			0
$191$	−57.5605	+	177.153i	−0.301364	+	0.927503i	0.679645	+	0.733541i	$0.262134\pi$
$191$	−57.5605	+	177.153i	−0.301364	+	0.927503i	−0.981009	+	0.193962i	$0.937866\pi$
$192$	−5.69358	−	35.9478i	−0.0296540	−	0.187228i
$193$	−149.932	+	149.932i	−0.776850	+	0.776850i	−0.979294	−	0.202444i	$-0.935112\pi$
$193$	−149.932	+	149.932i	−0.776850	+	0.776850i	0.202444	+	0.979294i	$0.435112\pi$
$194$	113.037	−	155.581i	0.582663	−	0.801966i
$195$		0			0
$196$	−37.6488	+	27.3534i	−0.192086	+	0.139558i
$197$	297.815	+	47.1692i	1.51175	+	0.239437i	0.856568	−	0.516034i	$-0.172592\pi$
$197$	297.815	+	47.1692i	1.51175	+	0.239437i	0.655181	+	0.755472i	$0.272592\pi$
$198$	−168.729	−	85.9715i	−0.852165	−	0.434200i
$199$		−	137.629i		−	0.691604i	−0.938307	−	0.345802i	$-0.887607\pi$
$199$		−	137.629i		−	0.691604i	0.938307	−	0.345802i	$-0.112393\pi$
$200$		0			0
$201$	−420.012			−2.08961
$202$	38.6610	−	75.8765i	0.191391	−	0.375626i
$203$	−4.96101	+	31.3226i	−0.0244385	+	0.154298i
$204$	−106.223	−	146.203i	−0.520700	−	0.716682i
$205$		0			0
$206$	82.2323	+	59.7453i	0.399186	+	0.290026i
$207$	−4.42679	−	4.42679i	−0.0213854	−	0.0213854i
$208$	87.4900	−	13.8571i	0.420625	−	0.0666205i
$209$	293.386	+	95.3268i	1.40376	+	0.456109i
$210$		0			0
$211$	34.9377	+	107.527i	0.165582	+	0.509608i	0.999079	−	0.0429161i	$-0.0136648\pi$
$211$	34.9377	+	107.527i	0.165582	+	0.509608i	−0.833497	+	0.552524i	$0.813665\pi$
$212$	−155.282	+	79.1202i	−0.732463	+	0.373208i
$213$	−32.4955	−	63.7761i	−0.152561	−	0.299418i
$214$	17.5487	−	5.70192i	0.0820034	−	0.0266445i
$215$		0			0
$216$	10.7278	−	33.0166i	0.0496655	−	0.152855i
$217$	−5.31992	−	33.5886i	−0.0245157	−	0.154786i
$218$	5.14985	−	5.14985i	0.0236231	−	0.0236231i
$219$	181.415	−	249.696i	0.828378	−	1.14016i
$220$		0			0
$221$	355.830	−	258.526i	1.61009	−	1.16980i
$222$	−37.4168	−	5.92624i	−0.168544	−	0.0266948i
$223$	213.575	+	108.822i	0.957738	+	0.487992i	0.861718	−	0.507388i	$-0.169389\pi$
$223$	213.575	+	108.822i	0.957738	+	0.487992i	0.0960197	+	0.995379i	$0.469389\pi$
$224$		−	28.6952i		−	0.128104i
$225$		0			0
$226$	149.479			0.661413
$227$	−55.9856	+	109.878i	−0.246633	+	0.484044i	−0.980823	−	0.194900i	$-0.937562\pi$
$227$	−55.9856	+	109.878i	−0.246633	+	0.484044i	0.734190	+	0.678944i	$0.237562\pi$
$228$	−38.3594	+	242.191i	−0.168243	+	1.06224i
$229$	−150.862	−	207.644i	−0.658787	−	0.906742i	0.340654	−	0.940189i	$-0.389352\pi$
$229$	−150.862	−	207.644i	−0.658787	−	0.906742i	−0.999440	+	0.0334469i	$0.989352\pi$
$230$		0			0
$231$	−213.718	−	155.275i	−0.925187	−	0.672188i
$232$	12.5035	+	12.5035i	0.0538945	+	0.0538945i
$233$	−10.2744	+	1.62731i	−0.0440962	+	0.00698416i	−0.178444	−	0.983950i	$-0.557106\pi$
$233$	−10.2744	+	1.62731i	−0.0440962	+	0.00698416i	0.134347	+	0.990934i	$0.457106\pi$
$234$	348.423	+	113.209i	1.48899	+	0.483801i
$235$		0			0
$236$	−13.4791	−	41.4843i	−0.0571147	−	0.175781i
$237$	495.830	−	252.638i	2.09211	−	1.06598i
$238$	−64.6849	−	126.951i	−0.271785	−	0.533409i
$239$	69.6575	−	22.6331i	0.291454	−	0.0946992i	−0.159641	−	0.987175i	$-0.551034\pi$
$239$	69.6575	−	22.6331i	0.291454	−	0.0946992i	0.451095	+	0.892476i	$0.351034\pi$
$240$		0			0
$241$	−20.2934	+	62.4568i	−0.0842052	+	0.259157i	−0.984290	−	0.176557i	$-0.943504\pi$
$241$	−20.2934	+	62.4568i	−0.0842052	+	0.259157i	0.900085	+	0.435714i	$0.143504\pi$
$242$	2.21911	+	14.0109i	0.00916988	+	0.0578964i
$243$	−237.160	+	237.160i	−0.975969	+	0.975969i
$244$	−81.1415	+	111.682i	−0.332547	+	0.457712i
$245$		0			0
$246$	−123.546	+	89.7612i	−0.502218	+	0.364883i
$247$	−589.447	−	93.3593i	−2.38643	−	0.377973i
$248$	−16.8952	−	8.60854i	−0.0681258	−	0.0347118i
$249$			280.505i			1.12653i
$250$		0			0
$251$	−47.1625			−0.187898			−0.0939492	−	0.995577i	$-0.529949\pi$
$251$	−47.1625			−0.187898			−0.0939492	+	0.995577i	$0.529949\pi$
$252$	53.8788	−	105.743i	0.213805	−	0.419615i
$253$	−0.958333	+	6.05068i	−0.00378788	+	0.0239157i
$254$	−51.0222	−	70.2260i	−0.200875	−	0.276480i
$255$		0			0
$256$	−12.9443	−	9.40456i	−0.0505636	−	0.0367366i
$257$	85.1375	+	85.1375i	0.331274	+	0.331274i	0.853070	−	0.521796i	$-0.174738\pi$
$257$	85.1375	+	85.1375i	0.331274	+	0.331274i	−0.521796	+	0.853070i	$0.674738\pi$
$258$	402.064	−	63.6807i	1.55839	−	0.246824i
$259$	−28.4060	−	9.22967i	−0.109676	−	0.0356358i
$260$		0			0
$261$	22.5991	+	69.5529i	0.0865866	+	0.266486i
$262$	91.8175	−	46.7833i	0.350448	−	0.178562i
$263$	−157.397	−	308.908i	−0.598467	−	1.17456i	−0.969305	−	0.245860i	$-0.920930\pi$
$263$	−157.397	−	308.908i	−0.598467	−	1.17456i	0.370839	−	0.928697i	$-0.379070\pi$
$264$	−140.088	+	45.5173i	−0.530636	+	0.172414i
$265$		0			0
$266$	−59.7418	+	183.866i	−0.224593	+	0.691227i
$267$	−56.7011	−	357.997i	−0.212364	−	1.34081i
$268$	−130.561	+	130.561i	−0.487168	+	0.487168i
$269$	−114.651	+	157.804i	−0.426212	+	0.586631i	−0.967079	−	0.254478i	$-0.918097\pi$
$269$	−114.651	+	157.804i	−0.426212	+	0.586631i	0.540866	+	0.841109i	$0.318097\pi$
$270$		0			0
$271$	295.640	−	214.795i	1.09092	−	0.792602i	0.111368	−	0.993779i	$-0.464477\pi$
$271$	295.640	−	214.795i	1.09092	−	0.792602i	0.979555	+	0.201177i	$0.0644768\pi$
$272$	−78.4669	−	12.4279i	−0.288481	−	0.0456909i
$273$	455.362	+	232.019i	1.66799	+	0.849885i
$274$			223.639i			0.816201i
$275$		0			0
$276$	−4.86956			−0.0176433
$277$	46.0601	−	90.3980i	0.166282	−	0.326346i	−0.792797	−	0.609486i	$-0.791376\pi$
$277$	46.0601	−	90.3980i	0.166282	−	0.326346i	0.959079	+	0.283139i	$0.0913759\pi$
$278$	−26.0927	+	164.743i	−0.0938586	+	0.592600i
$279$	−46.0959	−	63.4456i	−0.165218	−	0.227404i
$280$		0			0
$281$	324.001	+	235.401i	1.15303	+	0.837725i	0.988881	−	0.148710i	$-0.0475121\pi$
$281$	324.001	+	235.401i	1.15303	+	0.837725i	0.164149	+	0.986436i	$0.447512\pi$
$282$	−125.600	−	125.600i	−0.445390	−	0.445390i
$283$	246.358	−	39.0193i	0.870523	−	0.137877i	0.294837	−	0.955548i	$-0.404735\pi$
$283$	246.358	−	39.0193i	0.870523	−	0.137877i	0.575687	+	0.817670i	$0.304735\pi$
$284$	−29.9261	−	9.72359i	−0.105374	−	0.0342380i
$285$		0			0
$286$	−110.780	−	340.947i	−0.387344	−	1.19212i
$287$	−107.277	+	54.6606i	−0.373789	+	0.190455i
$288$	−30.0419	−	58.9606i	−0.104312	−	0.204724i
$289$	−100.307	+	32.5918i	−0.347084	+	0.112774i
$290$		0			0
$291$	191.175	−	588.375i	0.656957	−	2.02191i
$292$	−21.2253	−	134.011i	−0.0726894	−	0.458943i
$293$	353.989	−	353.989i	1.20815	−	1.20815i	0.236529	−	0.971624i	$-0.423990\pi$
$293$	353.989	−	353.989i	1.20815	−	1.20815i	0.971624	−	0.236529i	$-0.0760099\pi$
$294$	−87.9953	+	121.115i	−0.299304	+	0.411956i
$295$		0			0
$296$	−13.4732	+	9.78887i	−0.0455176	+	0.0330705i
$297$	−138.768	−	21.9786i	−0.467231	−	0.0740021i
$298$	−160.719	−	81.8906i	−0.539326	−	0.274801i
$299$		−	11.8516i		−	0.0396374i
$300$		0			0
$301$	320.946			1.06627
$302$	−57.6589	+	113.162i	−0.190923	+	0.374708i
$303$	42.8555	−	270.579i	0.141437	−	0.893000i
$304$	63.3614	+	87.2095i	0.208426	+	0.286873i
$305$		0			0
$306$	−265.819	−	193.129i	−0.868688	−	0.631139i
$307$	235.076	+	235.076i	0.765718	+	0.765718i	0.977350	−	0.211631i	$-0.0678776\pi$
$307$	235.076	+	235.076i	0.765718	+	0.765718i	−0.211631	+	0.977350i	$0.567878\pi$
$308$	−114.702	+	18.1670i	−0.372409	+	0.0589839i
$309$	310.985	+	101.045i	1.00642	+	0.327006i
$310$		0			0
$311$	73.4853	+	226.164i	0.236287	+	0.727217i	0.996948	+	0.0780676i	$0.0248750\pi$
$311$	73.4853	+	226.164i	0.236287	+	0.727217i	−0.760661	+	0.649149i	$0.775125\pi$
$312$	253.903	−	129.370i	0.813791	−	0.414647i
$313$	17.1378	+	33.6349i	0.0547535	+	0.107460i	0.916762	−	0.399434i	$-0.130793\pi$
$313$	17.1378	+	33.6349i	0.0547535	+	0.107460i	−0.862008	+	0.506894i	$0.830793\pi$
$314$	111.551	−	36.2452i	0.355259	−	0.115431i
$315$		0			0
$316$	75.5965	−	232.662i	0.239230	−	0.736273i
$317$	−30.3237	−	191.456i	−0.0956583	−	0.603963i	−0.988220	−	0.153038i	$-0.951094\pi$
$317$	−30.3237	−	191.456i	−0.0956583	−	0.603963i	0.892562	−	0.450925i	$-0.148906\pi$
$318$	−396.436	+	396.436i	−1.24665	+	1.24665i
$319$	42.0638	−	57.8958i	0.131861	−	0.181492i
$320$		0			0
$321$	48.0225	−	34.8904i	0.149603	−	0.108693i
$322$	−3.79199	−	0.600592i	−0.0117764	−	0.00186519i
$323$	476.907	+	242.996i	1.47649	+	0.752310i
$324$			98.8817i			0.305191i
$325$		0			0
$326$	269.624			0.827068
$327$	10.6366	−	20.8755i	0.0325279	−	0.0638396i
$328$	−10.5019	+	66.3067i	−0.0320181	+	0.202155i
$329$	−82.3153	−	113.297i	−0.250199	−	0.344369i
$330$		0			0
$331$	206.636	+	150.130i	0.624279	+	0.453566i	0.854414	−	0.519593i	$-0.173917\pi$
$331$	206.636	+	150.130i	0.624279	+	0.453566i	−0.230134	+	0.973159i	$0.573917\pi$
$332$	87.1953	+	87.1953i	0.262636	+	0.262636i
$333$	−68.0291	+	10.7748i	−0.204292	+	0.0323566i
$334$	180.461	+	58.6352i	0.540301	+	0.175555i
$335$		0			0
$336$	−28.5259	−	87.7938i	−0.0848986	−	0.261291i
$337$	−326.020	+	166.116i	−0.967419	+	0.492925i	−0.864975	−	0.501814i	$-0.832666\pi$
$337$	−326.020	+	166.116i	−0.967419	+	0.492925i	−0.102444	+	0.994739i	$0.532666\pi$
$338$	206.356	+	404.997i	0.610522	+	1.19822i
$339$	457.335	−	148.597i	1.34907	−	0.438340i
$340$		0			0
$341$	−23.7141	+	72.9845i	−0.0695428	+	0.214031i
$342$	69.7429	+	440.339i	0.203927	+	1.28754i
$343$	−259.219	+	259.219i	−0.755741	+	0.755741i
$344$	105.187	−	144.777i	0.305776	−	0.420864i
$345$		0			0
$346$	−142.659	+	103.648i	−0.412310	+	0.299560i
$347$	452.474	+	71.6649i	1.30396	+	0.206527i	0.769489	−	0.638660i	$-0.220511\pi$
$347$	452.474	+	71.6649i	1.30396	+	0.206527i	0.534471	+	0.845187i	$0.320511\pi$
$348$	50.6846	+	25.8251i	0.145646	+	0.0742101i
$349$			98.1992i			0.281373i	0.990054	+	0.140686i	$0.0449310\pi$
$349$			98.1992i			0.281373i	−0.990054	+	0.140686i	$0.955069\pi$
$350$		0			0
$351$	271.807			0.774378
$352$	−29.3974	+	57.6956i	−0.0835152	+	0.163908i
$353$	−22.0875	+	139.455i	−0.0625710	+	0.395058i	0.936449	+	0.350803i	$0.114091\pi$
$353$	−22.0875	+	139.455i	−0.0625710	+	0.395058i	−0.999020	+	0.0442546i	$0.985909\pi$
$354$	−82.4792	−	113.523i	−0.232992	−	0.320686i
$355$		0			0
$356$	−128.909	−	93.6581i	−0.362105	−	0.263085i
$357$	−324.108	−	324.108i	−0.907864	−	0.907864i
$358$	245.602	−	38.8996i	0.686039	−	0.108658i
$359$	−419.653	−	136.354i	−1.16895	−	0.379815i	−0.340699	−	0.940172i	$-0.610664\pi$
$359$	−419.653	−	136.354i	−1.16895	−	0.379815i	−0.828251	+	0.560358i	$0.810664\pi$
$360$		0			0
$361$	−112.872	−	347.383i	−0.312664	−	0.962281i
$362$	6.25594	−	3.18756i	0.0172816	−	0.00880541i
$363$	20.7177	+	40.6607i	0.0570735	+	0.112013i
$364$	213.673	−	69.4266i	0.587014	−	0.190732i
$365$		0			0
$366$	−137.232	+	422.356i	−0.374950	+	1.15398i
$367$	−53.9032	−	340.331i	−0.146875	−	0.927333i	−0.945528	−	0.325541i	$-0.894454\pi$
$367$	−53.9032	−	340.331i	−0.146875	−	0.927333i	0.798653	−	0.601792i	$-0.205546\pi$
$368$	−1.51371	+	1.51371i	−0.00411334	+	0.00411334i
$369$	−163.199	+	224.624i	−0.442274	+	0.608737i
$370$		0			0
$371$	−357.605	+	259.815i	−0.963894	+	0.700310i
$372$	−60.2490	−	9.54251i	−0.161960	−	0.0256519i
$373$	−316.871	−	161.454i	−0.849520	−	0.432852i	−0.0256771	−	0.999670i	$-0.508174\pi$
$373$	−316.871	−	161.454i	−0.849520	−	0.432852i	−0.823843	+	0.566818i	$0.808174\pi$
$374$			321.520i			0.859679i
$375$		0			0
$376$	−78.0858			−0.207675
$377$	−62.8533	+	123.357i	−0.166720	+	0.327206i
$378$	13.7741	−	86.9663i	0.0364395	−	0.230070i
$379$	−155.812	−	214.457i	−0.411115	−	0.565851i	0.552375	−	0.833596i	$-0.313722\pi$
$379$	−155.812	−	214.457i	−0.411115	−	0.565851i	−0.963490	+	0.267745i	$0.913722\pi$
$380$		0			0
$381$	−225.915	−	164.137i	−0.592954	−	0.430806i
$382$	186.270	+	186.270i	0.487617	+	0.487617i
$383$	−380.286	+	60.2315i	−0.992915	+	0.157262i	−0.631694	−	0.775218i	$-0.717640\pi$
$383$	−380.286	+	60.2315i	−0.992915	+	0.157262i	−0.361221	+	0.932480i	$0.617640\pi$
$384$	−48.9524	−	15.9056i	−0.127480	−	0.0414208i
$385$		0			0
$386$	92.6631	+	285.188i	0.240060	+	0.738828i
$387$	659.454	−	336.009i	1.70402	−	0.868239i
$388$	−123.470	−	242.324i	−0.318222	−	0.624546i
$389$	607.465	−	197.377i	1.56161	−	0.507397i	0.604370	−	0.796704i	$-0.293425\pi$
$389$	607.465	−	197.377i	1.56161	−	0.507397i	0.957236	+	0.289307i	$0.0934250\pi$
$390$		0			0
$391$	−3.28463	+	10.1090i	−0.00840059	+	0.0258543i
$392$	10.2953	+	65.0022i	0.0262636	+	0.165822i
$393$	234.411	−	234.411i	0.596464	−	0.596464i
$394$	250.645	−	344.984i	0.636156	−	0.875593i
$395$		0			0
$396$	−216.661	+	157.413i	−0.547123	+	0.397508i
$397$	19.7208	+	3.12348i	0.0496747	+	0.00786770i	0.181222	−	0.983442i	$-0.441995\pi$
$397$	19.7208	+	3.12348i	0.0496747	+	0.00786770i	−0.131548	+	0.991310i	$0.541995\pi$
$398$	−173.423	−	88.3634i	−0.435736	−	0.222019i
$399$			621.933i			1.55873i
$400$		0			0
$401$	−546.371			−1.36252			−0.681261	−	0.732041i	$-0.738568\pi$
$401$	−546.371			−1.36252			−0.681261	+	0.732041i	$0.738568\pi$
$402$	−269.664	+	529.246i	−0.670806	+	1.31653i
$403$	23.2246	−	146.634i	0.0576293	−	0.363857i
$404$	−70.7881	−	97.4315i	−0.175218	−	0.241167i
$405$		0			0
$406$	36.2836	+	26.3616i	0.0893685	+	0.0649300i
$407$	47.6585	+	47.6585i	0.117097	+	0.117097i
$408$	−252.426	+	39.9804i	−0.618691	+	0.0979911i
$409$	−396.232	−	128.743i	−0.968782	−	0.314776i	−0.218458	−	0.975846i	$-0.570103\pi$
$409$	−396.232	−	128.743i	−0.968782	−	0.314776i	−0.750324	+	0.661070i	$0.770103\pi$
$410$		0			0
$411$	222.320	+	684.229i	0.540924	+	1.66479i
$412$	128.080	−	65.2599i	0.310873	−	0.158398i
$413$	−50.2261	−	98.5743i	−0.121613	−	0.238679i
$414$	−8.42025	+	2.73591i	−0.0203388	+	0.00660847i
$415$		0			0
$416$	38.7111	−	119.141i	0.0930556	−	0.286396i
$417$	83.9396	+	529.974i	0.201294	+	1.27092i
$418$	308.484	−	308.484i	0.738000	−	0.738000i
$419$	−245.790	+	338.302i	−0.586612	+	0.807402i	−0.994401	−	0.105674i	$-0.966300\pi$
$419$	−245.790	+	338.302i	−0.586612	+	0.807402i	0.407789	+	0.913076i	$0.366300\pi$
$420$		0			0
$421$	−240.021	+	174.386i	−0.570122	+	0.414218i	−0.835149	−	0.550023i	$-0.814619\pi$
$421$	−240.021	+	174.386i	−0.570122	+	0.414218i	0.265028	+	0.964241i	$0.414619\pi$
$422$	157.924	+	25.0126i	0.374227	+	0.0592717i
$423$	−287.749	−	146.616i	−0.680258	−	0.346609i
$424$			246.465i			0.581286i
$425$		0			0
$426$	−101.226			−0.237620
$427$	−158.956	+	311.968i	−0.372262	+	0.730605i
$428$	4.08213	−	25.7735i	0.00953768	−	0.0602185i
$429$	−677.870	−	933.008i	−1.58012	−	2.17484i
$430$		0			0
$431$	−319.131	−	231.862i	−0.740442	−	0.537963i	0.152408	−	0.988318i	$-0.451297\pi$
$431$	−319.131	−	231.862i	−0.740442	−	0.537963i	−0.892850	+	0.450355i	$0.851297\pi$
$432$	−34.7157	−	34.7157i	−0.0803605	−	0.0803605i
$433$	112.334	−	17.7920i	0.259432	−	0.0410901i	−0.0253633	−	0.999678i	$-0.508074\pi$
$433$	112.334	−	17.7920i	0.259432	−	0.0410901i	0.284796	+	0.958588i	$0.408074\pi$
$434$	−45.7397	−	14.8617i	−0.105391	−	0.0342436i
$435$		0			0
$436$	−3.18278	−	9.79559i	−0.00729995	−	0.0224669i
$437$	12.8506	−	6.54773i	0.0294065	−	0.0149834i
$438$	−198.160	−	388.911i	−0.452420	−	0.887924i
$439$	−541.776	+	176.034i	−1.23411	+	0.400988i	−0.852203	−	0.523211i	$-0.824734\pi$
$439$	−541.776	+	176.034i	−1.23411	+	0.400988i	−0.381911	+	0.924199i	$0.624734\pi$
$440$		0			0
$441$	−84.1108	+	258.867i	−0.190728	+	0.586999i
$442$	−97.3044	−	614.356i	−0.220146	−	1.38995i
$443$	277.860	−	277.860i	0.627222	−	0.627222i	−0.320146	−	0.947368i	$-0.603732\pi$
$443$	277.860	−	277.860i	0.627222	−	0.627222i	0.947368	+	0.320146i	$0.103732\pi$
$444$	−31.4905	+	43.3430i	−0.0709246	+	0.0976194i
$445$		0			0
$446$	274.248	−	199.253i	0.614905	−	0.446755i
$447$	−573.132	−	90.7752i	−1.28217	−	0.203077i
$448$	−36.1581	−	18.4235i	−0.0807101	−	0.0411238i
$449$		−	733.358i		−	1.63331i	−0.577124	−	0.816657i	$-0.695825\pi$
$449$		−	733.358i		−	1.63331i	0.577124	−	0.816657i	$-0.304175\pi$
$450$		0			0
$451$	271.693			0.602424
$452$	95.9716	−	188.355i	0.212327	−	0.416714i
$453$	−63.9145	+	403.540i	−0.141092	+	0.890818i
$454$	102.509	+	141.092i	0.225792	+	0.310775i
$455$		0			0
$456$	280.551	+	203.832i	0.615243	+	0.447000i
$457$	−637.278	−	637.278i	−1.39448	−	1.39448i	−0.814948	−	0.579535i	$-0.803234\pi$
$457$	−637.278	−	637.278i	−1.39448	−	1.39448i	−0.579535	−	0.814948i	$-0.696766\pi$
$458$	−358.506	+	56.7818i	−0.782764	+	0.123978i
$459$	−231.843	−	75.3304i	−0.505105	−	0.164119i
$460$		0			0
$461$	−199.771	−	614.831i	−0.433342	−	1.33369i	−0.894776	−	0.446515i	$-0.852665\pi$
$461$	−199.771	−	614.831i	−0.433342	−	1.33369i	0.461434	−	0.887175i	$-0.347335\pi$
$462$	−332.874	+	169.608i	−0.720507	+	0.367116i
$463$	152.915	+	300.113i	0.330271	+	0.648192i	0.995108	−	0.0987958i	$-0.0314991\pi$
$463$	152.915	+	300.113i	0.330271	+	0.648192i	−0.664837	+	0.746988i	$0.731499\pi$
$464$	23.7831	−	7.72761i	0.0512568	−	0.0166543i
$465$		0			0
$466$	−4.54606	+	13.9913i	−0.00975549	+	0.0300243i
$467$	−88.2096	−	556.933i	−0.188886	−	1.19258i	−0.881824	−	0.471579i	$-0.843684\pi$
$467$	−88.2096	−	556.933i	−0.188886	−	1.19258i	0.692938	−	0.720997i	$-0.256316\pi$
$468$	366.353	−	366.353i	0.782806	−	0.782806i
$469$	−275.266	+	378.871i	−0.586921	+	0.807827i
$470$		0			0
$471$	305.263	−	221.786i	0.648116	−	0.470884i
$472$	−60.9274	−	9.64996i	−0.129084	−	0.0204448i
$473$	−645.305	−	328.799i	−1.36428	−	0.695136i
$474$		−	786.986i		−	1.66031i
$475$		0			0
$476$	−201.498			−0.423316
$477$	−462.768	+	908.234i	−0.970164	+	1.90405i
$478$	16.2035	−	102.305i	0.0338986	−	0.214027i
$479$	478.041	+	657.967i	0.997998	+	1.37363i	0.926546	+	0.376182i	$0.122763\pi$
$479$	478.041	+	657.967i	0.997998	+	1.37363i	0.0714519	+	0.997444i	$0.477237\pi$
$480$		0			0
$481$	−105.489	−	76.6419i	−0.219311	−	0.159339i
$482$	65.6710	+	65.6710i	0.136247	+	0.136247i
$483$	−12.1987	+	1.93209i	−0.0252562	+	0.00400019i
$484$	19.0795	+	6.19932i	0.0394205	+	0.0128085i
$485$		0			0
$486$	146.573	+	451.106i	0.301591	+	0.928202i
$487$	106.854	−	54.4449i	0.219413	−	0.111796i	−0.340830	−	0.940125i	$-0.610708\pi$
$487$	106.854	−	54.4449i	0.219413	−	0.111796i	0.560243	+	0.828329i	$0.310708\pi$
$488$	88.6311	+	173.948i	0.181621	+	0.356452i
$489$	824.922	−	268.033i	1.68696	−	0.548126i
$490$		0			0
$491$	−47.2164	+	145.317i	−0.0961637	+	0.295962i	−0.987555	−	0.157273i	$-0.949730\pi$
$491$	−47.2164	+	145.317i	−0.0961637	+	0.295962i	0.891391	+	0.453234i	$0.149730\pi$
$492$	33.7845	+	213.307i	0.0686677	+	0.433551i
$493$	87.8000	−	87.8000i	0.178093	−	0.178093i
$494$	−496.088	+	682.806i	−1.00423	+	1.38220i
$495$		0			0
$496$	−21.6948	+	15.7622i	−0.0437395	+	0.0317786i
$497$	−78.8259	−	12.4848i	−0.158603	−	0.0251203i
$498$	353.457	+	180.095i	0.709753	+	0.361637i
$499$		−	424.984i		−	0.851671i	−0.904801	−	0.425836i	$-0.859980\pi$
$499$		−	424.984i		−	0.851671i	0.904801	−	0.425836i	$-0.140020\pi$
$500$		0			0
$501$	610.413			1.21839
$502$	−30.2802	+	59.4282i	−0.0603191	+	0.118383i
$503$	93.9909	−	593.435i	0.186861	−	1.17979i	−0.698751	−	0.715365i	$-0.746260\pi$
$503$	93.9909	−	593.435i	0.186861	−	1.17979i	0.885611	−	0.464427i	$-0.153740\pi$
$504$	−98.6518	−	135.782i	−0.195738	−	0.269410i
$505$		0			0
$506$	7.00901	+	5.09234i	0.0138518	+	0.0100639i
$507$	1033.96	+	1033.96i	2.03937	+	2.03937i
$508$	−121.248	+	19.2038i	−0.238678	+	0.0378028i
$509$	−103.142	−	33.5130i	−0.202637	−	0.0658408i	0.205940	−	0.978565i	$-0.433975\pi$
$509$	−103.142	−	33.5130i	−0.202637	−	0.0658408i	−0.408577	+	0.912724i	$0.633975\pi$
$510$		0			0
$511$	−106.343	−	327.290i	−0.208107	−	0.640489i
$512$	−20.1612	+	10.2726i	−0.0393773	+	0.0200637i
$513$	150.167	+	294.719i	0.292723	+	0.574501i
$514$	161.941	−	52.6179i	0.315061	−	0.102369i
$515$		0			0
$516$	177.899	−	547.516i	0.344765	−	1.06108i
$517$	49.4363	+	312.129i	0.0956215	+	0.603730i
$518$	−29.8678	+	29.8678i	−0.0576599	+	0.0576599i
$519$	−333.433	+	458.931i	−0.642452	+	0.884260i
$520$		0			0
$521$	−161.044	+	117.005i	−0.309105	+	0.224578i	−0.731512	−	0.681828i	$-0.761185\pi$
$521$	−161.044	+	117.005i	−0.309105	+	0.224578i	0.422407	+	0.906406i	$0.361185\pi$
$522$	102.151	+	16.1792i	0.195692	+	0.0309946i
$523$	−565.327	−	288.049i	−1.08093	−	0.550762i	−0.179533	−	0.983752i	$-0.557459\pi$
$523$	−565.327	−	288.049i	−1.08093	−	0.550762i	−0.901399	+	0.432990i	$0.857459\pi$
$524$		−	145.734i		−	0.278117i
$525$		0			0
$526$	−490.302			−0.932134
$527$	−60.4492	+	118.638i	−0.114704	+	0.225120i
$528$	−32.5868	+	205.745i	−0.0617174	+	0.389668i
$529$	−310.770	−	427.738i	−0.587467	−	0.808579i
$530$		0			0
$531$	−206.401	−	149.959i	−0.388702	−	0.282409i
$532$	193.329	+	193.329i	0.363400	+	0.363400i
$533$	−519.148	+	82.2249i	−0.974011	+	0.154268i
$534$	−487.507	−	158.401i	−0.912934	−	0.296630i
$535$		0			0
$536$	80.6912	+	248.342i	0.150543	+	0.463325i
$537$	712.756	−	363.167i	1.32729	−	0.676289i
$538$	125.234	+	245.785i	0.232777	+	0.456850i
$539$	253.312	−	82.3061i	0.469967	−	0.152702i
$540$		0			0
$541$	−287.608	+	885.166i	−0.531622	+	1.63617i	0.219214	+	0.975677i	$0.429651\pi$
$541$	−287.608	+	885.166i	−0.531622	+	1.63617i	−0.750836	+	0.660489i	$0.770349\pi$
$542$	−80.8450	−	510.435i	−0.149161	−	0.941762i
$543$	15.9714	−	15.9714i	0.0294133	−	0.0294133i
$544$	−66.0390	+	90.8948i	−0.121395	+	0.167086i
$545$		0			0
$546$	584.721	−	424.825i	1.07092	−	0.778067i
$547$	674.591	+	106.845i	1.23326	+	0.195328i	0.738830	−	0.673892i	$-0.235379\pi$
$547$	674.591	+	106.845i	1.23326	+	0.195328i	0.494425	+	0.869220i	$0.335379\pi$
$548$	281.802	+	143.585i	0.514237	+	0.262017i
$549$			807.422i			1.47071i
$550$		0			0
$551$	−168.480			−0.305772
$552$	−3.12645	+	6.13601i	−0.00566386	+	0.0111160i
$553$	97.0637	−	612.836i	0.175522	−	1.10820i
$554$	−84.3357	−	116.078i	−0.152231	−	0.209527i
$555$		0			0
$556$	190.836	+	138.650i	0.343229	+	0.249371i
$557$	−18.5591	−	18.5591i	−0.0333198	−	0.0333198i	0.690251	−	0.723570i	$-0.257500\pi$
$557$	−18.5591	−	18.5591i	−0.0333198	−	0.0333198i	−0.723570	+	0.690251i	$0.757500\pi$
$558$	−109.542	+	17.3497i	−0.196311	+	0.0310926i
$559$	1332.55	+	432.971i	2.38380	+	0.774545i
$560$		0			0
$561$	319.623	+	983.699i	0.569738	+	1.75347i
$562$	504.644	−	257.129i	0.897943	−	0.457525i
$563$	428.520	+	841.019i	0.761138	+	1.49382i	0.866388	+	0.499371i	$0.166435\pi$
$563$	428.520	+	841.019i	0.761138	+	1.49382i	−0.105251	+	0.994446i	$0.533565\pi$
$564$	−238.906	+	77.6251i	−0.423591	+	0.137633i
$565$		0			0
$566$	109.004	−	335.481i	0.192587	−	0.592723i
$567$	39.2332	+	247.709i	0.0691943	+	0.436876i
$568$	−31.4662	+	31.4662i	−0.0553982	+	0.0553982i
$569$	212.998	−	293.167i	0.374337	−	0.515231i	−0.579736	−	0.814804i	$-0.696844\pi$
$569$	212.998	−	293.167i	0.374337	−	0.515231i	0.954073	+	0.299573i	$0.0968443\pi$
$570$		0			0
$571$	−908.751	+	660.246i	−1.59151	+	1.15630i	−0.689758	+	0.724040i	$0.742283\pi$
$571$	−908.751	+	660.246i	−1.59151	+	1.15630i	−0.901750	+	0.432258i	$0.857717\pi$
$572$	−500.743	−	79.3099i	−0.875425	−	0.138654i
$573$	755.067	+	384.726i	1.31774	+	0.671424i
$574$			170.272i			0.296640i
$575$		0			0
$576$	−93.5828			−0.162470
$577$	−42.7144	+	83.8317i	−0.0740284	+	0.145289i	−0.925054	−	0.379835i	$-0.875981\pi$
$577$	−42.7144	+	83.8317i	−0.0740284	+	0.145289i	0.851026	+	0.525124i	$0.175981\pi$
$578$	−23.3331	+	147.320i	−0.0403688	+	0.254878i
$579$	567.010	+	780.423i	0.979292	+	1.34788i
$580$		0			0
$581$	253.029	+	183.836i	0.435506	+	0.316414i
$582$	−618.654	−	618.654i	−1.06298	−	1.06298i
$583$	985.183	−	156.038i	1.68985	−	0.267646i
$584$	−182.491	−	59.2951i	−0.312485	−	0.101533i
$585$		0			0
$586$	−218.777	−	673.327i	−0.373340	−	1.14902i
$587$	−349.794	+	178.229i	−0.595901	+	0.303627i	−0.725806	−	0.687900i	$-0.758533\pi$
$587$	−349.794	+	178.229i	−0.595901	+	0.303627i	0.129905	+	0.991526i	$0.458533\pi$
$588$	96.1176	+	188.641i	0.163465	+	0.320819i
$589$	171.826	−	55.8298i	0.291726	−	0.0947875i
$590$		0			0
$591$	423.907	−	1304.65i	0.717271	−	2.20753i
$592$	3.68435	+	23.2621i	0.00622357	+	0.0392941i
$593$	−730.554	+	730.554i	−1.23196	+	1.23196i	−0.268754	+	0.963209i	$0.586612\pi$
$593$	−730.554	+	730.554i	−1.23196	+	1.23196i	−0.963209	+	0.268754i	$0.913388\pi$
$594$	−116.789	+	160.746i	−0.196614	+	0.270616i
$595$		0			0
$596$	−206.376	+	149.941i	−0.346269	+	0.251579i
$597$	−618.434	−	97.9503i	−1.03590	−	0.164071i
$598$	−14.9339	−	7.60918i	−0.0249730	−	0.0127244i
$599$			287.501i			0.479968i	0.970777	+	0.239984i	$0.0771422\pi$
$599$			287.501i			0.479968i	−0.970777	+	0.239984i	$0.922858\pi$
$600$		0			0
$601$	481.352			0.800919			0.400459	−	0.916314i	$-0.368851\pi$
$601$	481.352			0.800919			0.400459	+	0.916314i	$0.368851\pi$
$602$	206.060	−	404.416i	0.342293	−	0.671787i
$603$	−168.942	+	1066.66i	−0.280169	+	1.76892i
$604$	105.573	+	145.309i	0.174790	+	0.240578i
$605$		0			0
$606$	−313.435	−	227.724i	−0.517219	−	0.375781i
$607$	431.854	+	431.854i	0.711456	+	0.711456i	0.966840	−	0.255383i	$-0.0822017\pi$
$607$	431.854	+	431.854i	0.711456	+	0.711456i	−0.255383	+	0.966840i	$0.582202\pi$
$608$	150.571	−	23.8481i	0.247650	−	0.0392238i
$609$	137.217	+	44.5844i	0.225315	+	0.0732092i
$610$		0			0
$611$	−188.924	−	581.450i	−0.309205	−	0.951636i
$612$	−414.022	+	210.955i	−0.676507	+	0.344698i
$613$	136.550	+	267.994i	0.222757	+	0.437185i	0.975155	−	0.221524i	$-0.0711030\pi$
$613$	136.550	+	267.994i	0.222757	+	0.437185i	−0.752398	+	0.658709i	$0.771103\pi$
$614$	447.140	−	145.285i	0.728242	−	0.236620i
$615$		0			0
$616$	−50.7515	+	156.197i	−0.0823888	+	0.253567i
$617$	−6.55430	−	41.3822i	−0.0106228	−	0.0670700i	0.981807	−	0.189879i	$-0.0608097\pi$
$617$	−6.55430	−	41.3822i	−0.0106228	−	0.0670700i	−0.992430	+	0.122809i	$0.960810\pi$
$618$	326.988	−	326.988i	0.529108	−	0.529108i
$619$	491.415	−	676.375i	0.793885	−	1.09269i	−0.199728	−	0.979851i	$-0.564006\pi$
$619$	491.415	−	676.375i	0.793885	−	1.09269i	0.993613	−	0.112838i	$-0.0359941\pi$
$620$		0			0
$621$	−5.31418	+	3.86098i	−0.00855746	+	0.00621736i
$622$	332.164	+	52.6097i	0.534026	+	0.0845814i
$623$	−360.091	−	183.476i	−0.577995	−	0.294503i
$624$		−	402.997i		−	0.645828i
$625$		0			0
$626$	53.3856			0.0852805
$627$	637.151	−	1250.48i	1.01619	−	1.99438i
$628$	25.9487	−	163.834i	0.0413196	−	0.260882i
$629$	68.7376	+	94.6091i	0.109281	+	0.150412i
$630$		0			0
$631$	559.824	+	406.736i	0.887201	+	0.644589i	0.935147	−	0.354261i	$-0.115268\pi$
$631$	559.824	+	406.736i	0.887201	+	0.644589i	−0.0479460	+	0.998850i	$0.515268\pi$
$632$	−244.635	−	244.635i	−0.387081	−	0.387081i
$633$	508.036	−	80.4651i	0.802585	−	0.127117i
$634$	−260.718	−	84.7124i	−0.411227	−	0.133616i
$635$		0			0
$636$	245.011	+	754.066i	0.385237	+	1.18564i
$637$	−459.116	+	233.932i	−0.720748	+	0.367239i
$638$	−45.9464	−	90.1748i	−0.0720162	−	0.141340i
$639$	−175.036	+	56.8726i	−0.273921	+	0.0890025i
$640$		0			0
$641$	353.774	−	1088.81i	0.551910	−	1.69860i	−0.152057	−	0.988372i	$-0.548590\pi$
$641$	353.774	−	1088.81i	0.551910	−	1.69860i	0.703967	−	0.710233i	$-0.251410\pi$
$642$	−13.1321	−	82.9128i	−0.0204550	−	0.129148i
$643$	−160.690	+	160.690i	−0.249906	+	0.249906i	−0.820932	−	0.571026i	$-0.806546\pi$
$643$	−160.690	+	160.690i	−0.249906	+	0.249906i	0.571026	+	0.820932i	$0.306546\pi$
$644$	−3.19140	+	4.39258i	−0.00495559	+	0.00682078i
$645$		0			0
$646$	612.386	−	444.925i	0.947966	−	0.688738i
$647$	−197.406	−	31.2660i	−0.305110	−	0.0483246i	0.00200241	−	0.999998i	$-0.499363\pi$
$647$	−197.406	−	31.2660i	−0.305110	−	0.0483246i	−0.307112	+	0.951673i	$0.599363\pi$
$648$	124.598	+	63.4860i	0.192281	+	0.0979722i
$649$			249.652i			0.384671i
$650$		0			0
$651$	−154.716			−0.237659
$652$	173.109	−	339.746i	0.265505	−	0.521083i
$653$	−123.333	+	778.694i	−0.188871	+	1.19249i	0.692979	+	0.720958i	$0.256298\pi$
$653$	−123.333	+	778.694i	−0.188871	+	1.19249i	−0.881850	+	0.471529i	$0.843702\pi$
$654$	−19.4756	−	26.8058i	−0.0297792	−	0.0409875i
$655$		0			0
$656$	76.8086	+	55.8047i	0.117086	+	0.0850682i
$657$	−561.155	−	561.155i	−0.854117	−	0.854117i
$658$	−195.613	+	30.9820i	−0.297284	+	0.0470851i
$659$	119.459	+	38.8147i	0.181274	+	0.0588994i	0.398247	−	0.917278i	$-0.369619\pi$
$659$	119.459	+	38.8147i	0.181274	+	0.0588994i	−0.216974	+	0.976177i	$0.569619\pi$
$660$		0			0
$661$	−358.442	−	1103.17i	−0.542272	−	1.66894i	−0.727390	−	0.686224i	$-0.759267\pi$
$661$	−358.442	−	1103.17i	−0.542272	−	1.66894i	0.185118	−	0.982716i	$-0.440733\pi$
$662$	321.844	−	163.988i	0.486169	−	0.247715i
$663$	−908.437	−	1782.91i	−1.37019	−	2.68915i
$664$	165.855	−	53.8897i	0.249782	−	0.0811591i
$665$		0			0
$666$	−30.1004	+	92.6395i	−0.0451958	+	0.139098i
$667$	−0.523399	−	3.30461i	−0.000784706	−	0.00495444i
$668$	189.748	−	189.748i	0.284053	−	0.284053i
$669$	640.991	−	882.248i	0.958133	−	1.31876i
$670$		0			0
$671$	639.203	−	464.408i	0.952612	−	0.692113i
$672$	−128.941	−	20.4223i	−0.191877	−	0.0303903i
$673$	−210.697	−	107.355i	−0.313071	−	0.159517i	0.290394	−	0.956907i	$-0.406214\pi$
$673$	−210.697	−	107.355i	−0.313071	−	0.159517i	−0.603465	+	0.797390i	$0.706214\pi$
$674$			517.462i			0.767748i
$675$		0			0
$676$	642.816			0.950911
$677$	349.807	−	686.535i	0.516701	−	1.01408i	−0.474317	−	0.880354i	$-0.657305\pi$
$677$	349.807	−	686.535i	0.516701	−	1.01408i	0.991018	−	0.133729i	$-0.0426952\pi$
$678$	106.384	−	671.682i	0.156908	−	0.990681i
$679$	−405.451	−	558.056i	−0.597130	−	0.821879i
$680$		0			0
$681$	453.890	+	329.770i	0.666504	+	0.484244i
$682$	76.7404	+	76.7404i	0.112523	+	0.112523i
$683$	442.682	−	70.1140i	0.648144	−	0.102656i	0.176298	−	0.984337i	$-0.443588\pi$
$683$	442.682	−	70.1140i	0.648144	−	0.102656i	0.471846	+	0.881681i	$0.343588\pi$
$684$	599.638	+	194.834i	0.876663	+	0.284845i
$685$		0			0
$686$	160.206	+	493.064i	0.233537	+	0.718753i
$687$	−1040.41	+	530.116i	−1.51443	+	0.771639i
$688$	−114.896	−	225.496i	−0.167000	−	0.327755i
$689$	−1835.25	+	596.309i	−2.66365	+	0.865471i
$690$		0			0
$691$	−316.495	+	974.071i	−0.458024	+	1.40965i	0.409523	+	0.912300i	$0.365695\pi$
$691$	−316.495	+	974.071i	−0.458024	+	1.40965i	−0.867547	+	0.497355i	$0.834305\pi$
$692$	39.0112	+	246.307i	0.0563746	+	0.355935i
$693$	−480.300	+	480.300i	−0.693074	+	0.693074i
$694$	380.809	−	524.139i	0.548717	−	0.755244i
$695$		0			0
$696$	65.0831	−	47.2856i	0.0935102	−	0.0679391i
$697$	465.606	+	73.7448i	0.668015	+	0.105803i
$698$	123.738	+	63.0477i	0.177275	+	0.0903263i
$699$			47.3260i			0.0677054i
$700$		0			0
$701$	−1352.58			−1.92951			−0.964753	−	0.263156i	$-0.915237\pi$
$701$	−1352.58			−1.92951			−0.964753	+	0.263156i	$0.915237\pi$
$702$	174.511	−	342.496i	0.248591	−	0.487887i
$703$	24.8226	−	156.724i	0.0353095	−	0.222936i
$704$	53.8264	+	74.0857i	0.0764579	+	0.105235i
$705$		0			0
$706$	161.543	+	117.368i	0.228814	+	0.166243i
$707$	−215.989	−	215.989i	−0.305501	−	0.305501i
$708$	−196.002	+	31.0437i	−0.276839	+	0.0438470i
$709$	−131.683	−	42.7865i	−0.185731	−	0.0603477i	0.214675	−	0.976686i	$-0.431131\pi$
$709$	−131.683	−	42.7865i	−0.185731	−	0.0603477i	−0.400406	+	0.916338i	$0.631131\pi$
$710$		0			0
$711$	−442.159	−	1360.82i	−0.621883	−	1.91396i
$712$	−200.781	+	102.303i	−0.281996	+	0.143684i
$713$	1.62885	+	3.19680i	0.00228451	+	0.00448359i
$714$	−616.489	+	200.309i	−0.863430	+	0.280545i
$715$		0			0
$716$	108.670	−	334.452i	0.151774	−	0.467111i
$717$	−52.1263	−	329.112i	−0.0727005	−	0.459013i
$718$	−441.249	+	441.249i	−0.614553	+	0.614553i
$719$	165.133	−	227.286i	0.229670	−	0.316114i	−0.678592	−	0.734515i	$-0.737410\pi$
$719$	165.133	−	227.286i	0.229670	−	0.316114i	0.908262	+	0.418402i	$0.137410\pi$
$720$		0			0
$721$	294.959	−	214.301i	0.409098	−	0.297227i
$722$	−510.197	−	80.8072i	−0.706644	−	0.111921i
$723$	266.205	+	135.638i	0.368196	+	0.187605i
$724$		−	9.92948i		−	0.0137147i
$725$		0			0
$726$	64.5371			0.0888940
$727$	83.8826	−	164.629i	0.115382	−	0.226449i	−0.826092	−	0.563535i	$-0.809441\pi$
$727$	83.8826	−	164.629i	0.115382	−	0.226449i	0.941474	+	0.337085i	$0.109441\pi$
$728$	49.7040	−	313.818i	0.0682747	−	0.431069i
$729$	635.343	+	874.475i	0.871527	+	1.19955i
$730$		0			0
$731$	−1016.63	−	738.623i	−1.39073	−	1.01043i
$732$	444.091	+	444.091i	0.606682	+	0.606682i
$733$	−91.4234	+	14.4800i	−0.124725	+	0.0197545i	−0.218485	−	0.975840i	$-0.570111\pi$
$733$	−91.4234	+	14.4800i	−0.124725	+	0.0197545i	0.0937599	+	0.995595i	$0.470111\pi$
$734$	−463.450	−	150.584i	−0.631404	−	0.205155i
$735$		0			0
$736$	0.935524	+	2.87925i	0.00127109	+	0.00391202i
$737$	941.600	−	479.769i	1.27761	−	0.650975i
$738$	178.263	+	349.860i	0.241548	+	0.474065i
$739$	146.136	−	47.4824i	0.197748	−	0.0642523i	−0.208468	−	0.978029i	$-0.566848\pi$
$739$	146.136	−	47.4824i	0.197748	−	0.0642523i	0.406217	+	0.913777i	$0.366848\pi$
$740$		0			0
$741$	−839.015	+	2582.22i	−1.13227	+	3.48478i
$742$	97.7897	+	617.420i	0.131792	+	0.832102i
$743$	379.385	−	379.385i	0.510613	−	0.510613i	−0.404101	−	0.914714i	$-0.632416\pi$
$743$	379.385	−	379.385i	0.510613	−	0.510613i	0.914714	+	0.404101i	$0.132416\pi$
$744$	−50.7065	+	69.7916i	−0.0681539	+	0.0938058i
$745$		0			0
$746$	−406.887	+	295.621i	−0.545425	+	0.396275i
$747$	712.368	+	112.828i	0.953638	+	0.151041i
$748$	405.139	+	206.429i	0.541630	+	0.275974i
$749$		−	66.1849i		−	0.0883644i
$750$		0			0
$751$	1091.70			1.45366			0.726829	−	0.686819i	$-0.240993\pi$
$751$	1091.70			1.45366			0.726829	+	0.686819i	$0.240993\pi$
$752$	−50.1342	+	98.3939i	−0.0666678	+	0.130843i
$753$	−33.5654	+	211.924i	−0.0445756	+	0.281439i
$754$	115.084	+	158.400i	0.152631	+	0.210079i
$755$		0			0
$756$	−100.740	−	73.1922i	−0.133255	−	0.0968151i
$757$	−167.215	−	167.215i	−0.220892	−	0.220892i	0.587982	−	0.808874i	$-0.299923\pi$
$757$	−167.215	−	167.215i	−0.220892	−	0.220892i	−0.808874	+	0.587982i	$0.799923\pi$
$758$	−370.270	+	58.6450i	−0.488483	+	0.0773681i
$759$	26.5065	+	8.61250i	0.0349230	+	0.0113472i
$760$		0			0
$761$	274.175	+	843.824i	0.360283	+	1.10884i	0.952883	+	0.303339i	$0.0981015\pi$
$761$	274.175	+	843.824i	0.360283	+	1.10884i	−0.592600	+	0.805497i	$0.701899\pi$
$762$	−351.871	+	179.287i	−0.461774	+	0.235285i
$763$	−11.8598	−	23.2761i	−0.0155436	−	0.0305060i
$764$	354.306	−	115.121i	0.463751	−	0.150682i
$765$		0			0
$766$	−168.263	+	517.860i	−0.219664	+	0.676057i
$767$	−75.5543	−	477.031i	−0.0985062	−	0.621944i
$768$	−51.4716	+	51.4716i	−0.0670203	+	0.0670203i
$769$	259.529	−	357.212i	0.337489	−	0.464514i	−0.606217	−	0.795300i	$-0.707314\pi$
$769$	259.529	−	357.212i	0.337489	−	0.464514i	0.943706	+	0.330785i	$0.107314\pi$
$770$		0			0
$771$	443.156	−	321.971i	0.574780	−	0.417602i
$772$	418.851	+	66.3395i	0.542553	+	0.0859320i
$773$	674.908	+	343.883i	0.873102	+	0.444868i	0.832317	−	0.554300i	$-0.187014\pi$
$773$	674.908	+	343.883i	0.873102	+	0.444868i	0.0407854	+	0.999168i	$0.487014\pi$
$774$		−	1046.69i		−	1.35231i
$775$		0			0
$776$	−384.618			−0.495642
$777$	−61.6898	+	121.073i	−0.0793948	+	0.155821i
$778$	141.307	−	892.174i	0.181628	−	1.14675i
$779$	−375.974	−	517.483i	−0.482636	−	0.664292i
$780$		0			0
$781$	145.700	+	105.857i	0.186555	+	0.135540i
$782$	10.6293	+	10.6293i	0.0135924	+	0.0135924i
$783$	75.7886	−	12.0037i	0.0967926	−	0.0153304i
$784$	88.5176	+	28.7611i	0.112905	+	0.0366851i
$785$		0			0
$786$	−144.874	−	445.875i	−0.184318	−	0.567271i
$787$	−987.772	+	503.295i	−1.25511	+	0.639511i	−0.949834	−	0.312753i	$-0.898749\pi$
$787$	−987.772	+	503.295i	−1.25511	+	0.639511i	−0.305276	+	0.952264i	$0.598749\pi$
$788$	−273.781	−	537.325i	−0.347437	−	0.681884i
$789$	−1500.09	+	487.409i	−1.90126	+	0.617756i
$790$		0			0
$791$	165.685	−	509.926i	0.209463	−	0.644660i
$792$	59.2475	+	374.074i	0.0748075	+	0.472316i
$793$	−1080.83	+	1080.83i	−1.36297	+	1.36297i
$794$	16.5974	−	22.8443i	0.0209035	−	0.0287712i
$795$		0			0
$796$	−222.689	+	161.793i	−0.279760	+	0.203257i
$797$	−292.105	−	46.2648i	−0.366505	−	0.0580487i	−0.0295343	−	0.999564i	$-0.509402\pi$
$797$	−292.105	−	46.2648i	−0.366505	−	0.0580487i	−0.336971	+	0.941515i	$0.609402\pi$
$798$	783.682	+	399.306i	0.982057	+	0.500383i
$799$			548.320i			0.686257i
$800$		0			0
$801$	−931.972			−1.16351
$802$	−350.792	+	688.468i	−0.437396	+	0.858439i
$803$	−121.482	+	767.004i	−0.151285	+	0.955173i
$804$	493.753	+	679.593i	0.614121	+	0.845265i
$805$		0			0
$806$	−169.859	−	123.410i	−0.210743	−	0.153114i
$807$	627.491	+	627.491i	0.777560	+	0.777560i
$808$	−168.220	+	26.6434i	−0.208193	+	0.0329745i
$809$	−173.388	−	56.3370i	−0.214323	−	0.0696378i	0.199887	−	0.979819i	$-0.435942\pi$
$809$	−173.388	−	56.3370i	−0.214323	−	0.0696378i	−0.414211	+	0.910181i	$0.635942\pi$
$810$		0			0
$811$	368.062	+	1132.78i	0.453837	+	1.39677i	0.872495	+	0.488622i	$0.162500\pi$
$811$	368.062	+	1132.78i	0.453837	+	1.39677i	−0.418659	+	0.908144i	$0.637500\pi$
$812$	56.5130	−	28.7948i	0.0695973	−	0.0354616i
$813$	−754.771	−	1481.32i	−0.928377	−	1.82204i
$814$	90.6519	−	29.4546i	0.111366	−	0.0361850i
$815$		0			0
$816$	−111.689	+	343.744i	−0.136874	+	0.421255i
$817$	266.733	+	1684.08i	0.326478	+	2.06130i
$818$	−416.623	+	416.623i	−0.509319	+	0.509319i
$819$	772.393	−	1063.11i	0.943093	−	1.29806i
$820$		0			0
$821$	388.310	−	282.124i	0.472972	−	0.343634i	−0.325626	−	0.945499i	$-0.605575\pi$
$821$	388.310	−	282.124i	0.472972	−	0.343634i	0.798598	+	0.601864i	$0.205575\pi$
$822$	1004.92	+	159.163i	1.22253	+	0.193629i
$823$	156.554	+	79.7683i	0.190224	+	0.0969238i	0.546508	−	0.837454i	$-0.315957\pi$
$823$	156.554	+	79.7683i	0.190224	+	0.0969238i	−0.356285	+	0.934377i	$0.615957\pi$
$824$		−	203.289i		−	0.246710i
$825$		0			0
$826$	−156.458			−0.189416
$827$	73.1995	−	143.662i	0.0885121	−	0.173715i	−0.842507	−	0.538686i	$-0.818921\pi$
$827$	73.1995	−	143.662i	0.0885121	−	0.173715i	0.931019	+	0.364971i	$0.118921\pi$
$828$	−1.95869	+	12.3667i	−0.00236557	+	0.0149356i
$829$	920.375	+	1266.79i	1.11022	+	1.52809i	0.821087	+	0.570803i	$0.193368\pi$
$829$	920.375	+	1266.79i	1.11022	+	1.52809i	0.289136	+	0.957288i	$0.406632\pi$
$830$		0			0
$831$	−373.420	−	271.306i	−0.449363	−	0.326481i
$832$	−125.272	−	125.272i	−0.150567	−	0.150567i
$833$	456.446	−	72.2940i	0.547955	−	0.0867875i
$834$	721.698	+	234.494i	0.865346	+	0.281168i
$835$		0			0
$836$	−190.654	−	586.772i	−0.228055	−	0.701880i
$837$	−73.3162	+	37.3565i	−0.0875940	+	0.0446314i
$838$	268.478	+	526.917i	0.320379	+	0.628779i
$839$	−1047.63	+	340.396i	−1.24867	+	0.405717i	−0.857443	−	0.514579i	$-0.827948\pi$
$839$	−1047.63	+	340.396i	−1.24867	+	0.405717i	−0.391224	+	0.920295i	$0.627948\pi$
$840$		0			0
$841$	247.805	−	762.667i	0.294656	−	0.906857i
$842$	65.6356	+	414.407i	0.0779520	+	0.492170i
$843$	1288.36	−	1288.36i	1.52830	−	1.52830i
$844$	132.911	−	182.936i	0.157477	−	0.216749i
$845$		0			0
$846$	−369.493	+	268.452i	−0.436753	+	0.317319i
$847$	50.2558	+	7.95974i	0.0593339	+	0.00939757i
$848$	310.564	+	158.240i	0.366231	+	0.186604i
$849$		−	1134.77i		−	1.33660i
$850$		0			0
$851$	3.15113			0.00370285
$852$	−64.9911	+	127.552i	−0.0762806	+	0.149709i
$853$	−69.4424	+	438.442i	−0.0814096	+	0.514000i	0.912961	+	0.408046i	$0.133790\pi$
$853$	−69.4424	+	438.442i	−0.0814096	+	0.514000i	−0.994371	+	0.105954i	$0.966210\pi$
$854$	291.047	+	400.592i	0.340804	+	0.469077i
$855$		0			0
$856$	−29.8557	−	21.6914i	−0.0348781	−	0.0253404i
$857$	−155.970	−	155.970i	−0.181996	−	0.181996i	0.610229	−	0.792225i	$-0.291077\pi$
$857$	−155.970	−	155.970i	−0.181996	−	0.181996i	−0.792225	+	0.610229i	$0.791077\pi$
$858$	−1610.88	+	255.138i	−1.87748	+	0.297364i
$859$	391.117	+	127.082i	0.455316	+	0.147941i	0.527691	−	0.849436i	$-0.323058\pi$
$859$	391.117	+	127.082i	0.455316	+	0.147941i	−0.0723749	+	0.997377i	$0.523058\pi$
$860$		0			0
$861$	169.267	+	520.950i	0.196593	+	0.605053i
$862$	−497.057	+	253.263i	−0.576633	+	0.293809i
$863$	−140.246	−	275.247i	−0.162509	−	0.318943i	0.795365	−	0.606131i	$-0.207279\pi$
$863$	−140.246	−	275.247i	−0.162509	−	0.318943i	−0.957874	+	0.287189i	$0.907279\pi$
$864$	−66.0333	+	21.4555i	−0.0764274	+	0.0248328i
$865$		0			0
$866$	49.7038	−	152.973i	0.0573947	−	0.176643i
$867$	75.0621	+	473.924i	0.0865769	+	0.546625i
$868$	−48.0936	+	48.0936i	−0.0554074	+	0.0554074i
$869$	−822.990	+	1132.75i	−0.947054	+	1.30351i
$870$		0			0
$871$	−1654.00	+	1201.70i	−1.89897	+	1.37968i
$872$	−14.3866	−	2.27862i	−0.0164984	−	0.00261309i
$873$	−1417.33	−	722.168i	−1.62352	−	0.827225i
$874$		−	20.3966i		−	0.0233371i
$875$		0			0
$876$	−617.282			−0.704660
$877$	−160.555	+	315.106i	−0.183073	+	0.359300i	−0.964244	−	0.265016i	$-0.914623\pi$
$877$	−160.555	+	315.106i	−0.183073	+	0.359300i	0.781171	+	0.624317i	$0.214623\pi$
$878$	−126.026	+	795.699i	−0.143538	+	0.906263i
$879$	−1338.71	−	1842.57i	−1.52299	−	2.09622i
$880$		0			0
$881$	1399.81	+	1017.02i	1.58889	+	1.15440i	0.905503	+	0.424340i	$0.139494\pi$
$881$	1399.81	+	1017.02i	1.58889	+	1.15440i	0.683387	+	0.730056i	$0.260506\pi$
$882$	272.188	+	272.188i	0.308604	+	0.308604i
$883$	1262.49	−	199.959i	1.42978	−	0.226454i	0.606947	−	0.794742i	$-0.292394\pi$
$883$	1262.49	−	199.959i	1.42978	−	0.226454i	0.822830	+	0.568288i	$0.192394\pi$
$884$	−836.607	−	271.830i	−0.946388	−	0.307500i
$885$		0			0
$886$	−171.727	−	528.520i	−0.193822	−	0.596524i
$887$	−1492.83	+	760.633i	−1.68301	+	0.857534i	−0.692284	+	0.721625i	$0.743395\pi$
$887$	−1492.83	+	760.633i	−1.68301	+	0.857534i	−0.990721	+	0.135909i	$0.956605\pi$
$888$	34.3972	+	67.5083i	0.0387356	+	0.0760229i
$889$	−296.119	+	96.2150i	−0.333092	+	0.108228i
$890$		0			0
$891$	174.886	−	538.244i	0.196281	−	0.604090i
$892$	−74.9951	−	473.500i	−0.0840752	−	0.530830i
$893$	526.088	−	526.088i	0.589124	−	0.589124i
$894$	−482.357	+	663.907i	−0.539549	+	0.742626i
$895$		0			0
$896$	−46.4299	+	33.7333i	−0.0518191	+	0.0376487i
$897$	−53.2548	−	8.43473i	−0.0593699	−	0.00940327i
$898$	−924.085	−	470.845i	−1.02905	−	0.524326i
$899$		−	41.9122i		−	0.0466209i
$900$		0			0
$901$	1730.68			1.92085
$902$	174.438	−	342.354i	0.193390	−	0.379549i
$903$	228.416	−	1442.16i	0.252953	−	1.59708i
$904$	−175.723	−	241.862i	−0.194384	−	0.267547i
$905$		0			0
$906$	467.455	+	339.626i	0.515955	+	0.374863i
$907$	−324.628	−	324.628i	−0.357914	−	0.357914i	0.505129	−	0.863044i	$-0.331445\pi$
$907$	−324.628	−	324.628i	−0.357914	−	0.357914i	−0.863044	+	0.505129i	$0.831445\pi$
$908$	243.601	−	38.5827i	0.268283	−	0.0424919i
$909$	−669.922	−	217.671i	−0.736988	−	0.239462i
$910$		0			0
$911$	184.738	+	568.566i	0.202786	+	0.624112i	0.999797	+	0.0201467i	$0.00641332\pi$
$911$	184.738	+	568.566i	0.202786	+	0.624112i	−0.797011	+	0.603965i	$0.793587\pi$
$912$	436.968	−	222.646i	0.479132	−	0.244130i
$913$	−320.414	−	628.848i	−0.350946	−	0.688771i
$914$	−1212.18	+	393.860i	−1.32623	+	0.430919i
$915$		0			0
$916$	−158.626	+	488.200i	−0.173172	+	0.532970i
$917$	−57.8225	−	365.077i	−0.0630561	−	0.398121i
$918$	−243.774	+	243.774i	−0.265549	+	0.265549i
$919$	−432.747	+	595.625i	−0.470889	+	0.648123i	−0.976722	−	0.214508i	$-0.931185\pi$
$919$	−432.747	+	595.625i	−0.470889	+	0.648123i	0.505833	+	0.862631i	$0.331185\pi$
$920$		0			0
$921$	1223.61	−	889.004i	1.32857	−	0.965260i
$922$	−902.993	−	143.020i	−0.979385	−	0.155119i
$923$	−310.437	−	158.176i	−0.336335	−	0.171371i
$924$			528.341i			0.571797i
$925$		0			0
$926$	476.342			0.514408
$927$	381.701	−	749.130i	0.411759	−	0.808122i
$928$	5.53236	−	34.9299i	0.00596159	−	0.0376400i
$929$	−469.300	−	645.936i	−0.505167	−	0.695303i	0.477928	−	0.878399i	$-0.341388\pi$
$929$	−469.300	−	645.936i	−0.505167	−	0.695303i	−0.983095	+	0.183096i	$0.941388\pi$
$930$		0			0
$931$	−507.303	−	368.577i	−0.544901	−	0.395894i
$932$	14.7114	+	14.7114i	0.0157847	+	0.0157847i
$933$	1068.56	−	169.244i	1.14530	−	0.181398i
$934$	−758.411	−	246.423i	−0.812003	−	0.263836i
$935$		0			0
$936$	−226.419	−	696.845i	−0.241900	−	0.744493i
$937$	1258.08	−	641.022i	1.34266	−	0.684122i	0.372833	−	0.927898i	$-0.378386\pi$
$937$	1258.08	−	641.022i	1.34266	−	0.684122i	0.969831	+	0.243776i	$0.0783863\pi$
$938$	300.674	+	590.105i	0.320548	+	0.629110i
$939$	163.335	−	53.0706i	0.173945	−	0.0565182i
$940$		0			0
$941$	−135.437	+	416.831i	−0.143928	+	0.442966i	−0.996872	−	0.0790378i	$-0.974815\pi$
$941$	−135.437	+	416.831i	−0.143928	+	0.442966i	0.852943	+	0.522004i	$0.174815\pi$
$942$	−83.4764	−	527.049i	−0.0886161	−	0.559500i
$943$	8.98204	−	8.98204i	0.00952496	−	0.00952496i
$944$	−51.2775	+	70.5774i	−0.0543194	+	0.0747642i
$945$		0			0
$946$	−828.622	+	602.029i	−0.875922	+	0.636395i
$947$	941.730	+	149.155i	0.994435	+	0.157503i	0.632384	−	0.774655i	$-0.282077\pi$
$947$	941.730	+	149.155i	0.994435	+	0.157503i	0.362051	+	0.932158i	$0.382077\pi$
$948$	−991.661	−	505.276i	−1.04606	−	0.532992i
$949$		−	1502.35i		−	1.58308i
$950$		0			0
$951$	−881.886			−0.927325
$952$	−129.370	+	253.903i	−0.135893	+	0.266705i
$953$	−7.52363	+	47.5024i	−0.00789468	+	0.0498451i	−0.991321	−	0.131462i	$-0.958033\pi$
$953$	−7.52363	+	47.5024i	−0.00789468	+	0.0498451i	0.983427	+	0.181307i	$0.0580328\pi$
$954$	847.326	+	1166.24i	0.888182	+	1.22248i
$955$		0			0
$956$	−118.508	−	86.1014i	−0.123963	−	0.0900642i
$957$	−230.217	−	230.217i	−0.240561	−	0.240561i
$958$	1136.01	−	179.926i	1.18581	−	0.187814i
$959$	762.911	+	247.885i	0.795528	+	0.258483i
$960$		0			0
$961$	−283.077	−	871.221i	−0.294565	−	0.906577i
$962$	−164.302	+	83.7162i	−0.170792	+	0.0870230i
$963$	−69.2910	−	135.991i	−0.0719533	−	0.141216i
$964$	124.914	−	40.5869i	0.129578	−	0.0421026i
$965$		0			0
$966$	−5.39750	+	16.6118i	−0.00558747	+	0.0171965i
$967$	157.289	+	993.084i	0.162657	+	1.02697i	0.925046	+	0.379856i	$0.124026\pi$
$967$	157.289	+	993.084i	0.162657	+	1.02697i	−0.762389	+	0.647119i	$0.775974\pi$
$968$	20.0614	−	20.0614i	0.0207246	−	0.0207246i
$969$	1431.31	−	1970.03i	1.47710	−	2.03306i
$970$		0			0
$971$	722.828	−	525.165i	0.744416	−	0.540850i	−0.149675	−	0.988735i	$-0.547823\pi$
$971$	722.828	−	525.165i	0.744416	−	0.540850i	0.894091	+	0.447885i	$0.147823\pi$
$972$	662.533	+	104.935i	0.681618	+	0.107958i
$973$	533.074	+	271.615i	0.547866	+	0.279152i
$974$		−	169.600i		−	0.174127i
$975$		0			0
$976$	276.092			0.282882
$977$	−319.212	+	626.489i	−0.326727	+	0.641237i	−0.994685	−	0.102961i	$-0.967168\pi$
$977$	−319.212	+	626.489i	−0.326727	+	0.641237i	0.667959	+	0.744198i	$0.267168\pi$
$978$	191.891	−	1211.55i	0.196207	−	1.23880i
$979$	536.046	+	737.804i	0.547544	+	0.753630i
$980$		0			0
$981$	−48.7369	−	35.4094i	−0.0496809	−	0.0360953i
$982$	152.795	+	152.795i	0.155596	+	0.155596i
$983$	−1496.27	+	236.985i	−1.52214	+	0.241084i	−0.860777	−	0.508981i	$-0.830022\pi$
$983$	−1496.27	+	236.985i	−1.52214	+	0.241084i	−0.661364	+	0.750065i	$0.730022\pi$
$984$	290.473	+	94.3805i	0.295197	+	0.0959152i
$985$		0			0
$986$	−54.2634	−	167.005i	−0.0550338	−	0.169377i
$987$	−567.683	+	289.249i	−0.575160	+	0.293058i
$988$	541.878	+	1063.50i	0.548460	+	1.07641i
$989$	−32.2034	+	10.4635i	−0.0325615	+	0.0105799i
$990$		0			0
$991$	349.037	−	1074.23i	0.352207	−	1.08398i	−0.605404	−	0.795918i	$-0.706989\pi$
$991$	349.037	−	1074.23i	0.352207	−	1.08398i	0.957611	−	0.288063i	$-0.0930114\pi$
$992$	5.93260	+	37.4570i	0.00598044	+	0.0377590i
$993$	821.669	−	821.669i	0.827461	−	0.827461i
$994$	−66.3411	+	91.3107i	−0.0667416	+	0.0918619i
$995$		0			0
$996$	453.867	−	329.753i	0.455689	−	0.331078i
$997$	−1358.50	−	215.165i	−1.36259	−	0.215813i	−0.568033	−	0.823006i	$-0.692295\pi$
$997$	−1358.50	−	215.165i	−1.36259	−	0.215813i	−0.794554	+	0.607194i	$0.792295\pi$
$998$	−535.511	−	272.857i	−0.536584	−	0.273403i
$999$			72.2687i			0.0723410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.3.f.b.107.2		16
5.2	odd	4		250.3.f.a.143.1		16
5.3	odd	4		250.3.f.c.143.2		16
5.4	even	2		50.3.f.a.17.1	yes	16
20.19	odd	2		400.3.bg.a.17.2		16
25.3	odd	20	inner	250.3.f.b.243.2		16
25.4	even	10		250.3.f.a.7.1		16
25.21	even	5		250.3.f.c.7.2		16
25.22	odd	20		50.3.f.a.3.1	✓	16
100.47	even	20		400.3.bg.a.353.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.a.3.1	✓	16	25.22	odd	20
50.3.f.a.17.1	yes	16	5.4	even	2
250.3.f.a.7.1		16	25.4	even	10
250.3.f.a.143.1		16	5.2	odd	4
250.3.f.b.107.2		16	1.1	even	1	trivial
250.3.f.b.243.2		16	25.3	odd	20	inner
250.3.f.c.7.2		16	25.21	even	5
250.3.f.c.143.2		16	5.3	odd	4
400.3.bg.a.17.2		16	20.19	odd	2
400.3.bg.a.353.2		16	100.47	even	20

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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	250.f (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.642040 - 1.26007i) q^{2} +(0.711697 - 4.49348i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-5.20517 - 3.78178i) q^{6} +(-3.58690 - 3.58690i) q^{7} +(-2.79360 + 0.442463i) q^{8} +(-11.1253 - 3.61484i) q^{9} +O(q^{10})\)	\(q+(0.642040 - 1.26007i) q^{2} +(0.711697 - 4.49348i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-5.20517 - 3.78178i) q^{6} +(-3.58690 - 3.58690i) q^{7} +(-2.79360 + 0.442463i) q^{8} +(-11.1253 - 3.61484i) q^{9} +(3.53728 + 10.8866i) q^{11} +(-8.10725 + 4.13085i) q^{12} +(-10.0537 - 19.7315i) q^{13} +(-6.82270 + 2.21683i) q^{14} +(-1.23607 + 3.80423i) q^{16} +(3.10698 + 19.6167i) q^{17} +(-11.6979 + 11.6979i) q^{18} +(15.8404 - 21.8024i) q^{19} +(-18.6705 + 13.5649i) q^{21} +(15.9890 + 2.53241i) q^{22} +(0.476846 + 0.242965i) q^{23} +12.8679i q^{24} -31.3180 q^{26} +(-5.57222 + 10.9361i) q^{27} +(-1.58707 + 10.0204i) q^{28} +(-3.67470 - 5.05779i) q^{29} +(5.42369 + 3.94054i) q^{31} +(4.00000 + 4.00000i) q^{32} +(51.4362 - 8.14670i) q^{33} +(26.7133 + 8.67968i) q^{34} +(7.22967 + 22.2506i) q^{36} +(5.24626 - 2.67310i) q^{37} +(-17.3025 - 33.9580i) q^{38} +(-95.8181 + 31.1332i) q^{39} +(7.33457 - 22.5735i) q^{41} +(5.10558 + 32.2354i) q^{42} +(-44.7386 + 44.7386i) q^{43} +(13.4566 - 18.5214i) q^{44} +(0.612308 - 0.444868i) q^{46} +(27.2676 + 4.31877i) q^{47} +(16.2145 + 8.26170i) q^{48} -23.2682i q^{49} +90.3585 q^{51} +(-20.1074 + 39.4630i) q^{52} +(13.6315 - 86.0658i) q^{53} +(10.2027 + 14.0428i) q^{54} +(11.6075 + 8.43332i) q^{56} +(-86.6950 - 86.6950i) q^{57} +(-8.73248 + 1.38309i) q^{58} +(20.7422 + 6.73954i) q^{59} +(-21.3293 - 65.6449i) q^{61} +(8.44760 - 4.30427i) q^{62} +(26.9394 + 52.8715i) q^{63} +(7.60845 - 2.47214i) q^{64} +(22.7587 - 70.0439i) q^{66} +(-14.4421 - 91.1840i) q^{67} +(28.0880 - 28.0880i) q^{68} +(1.43113 - 1.96978i) q^{69} +(12.7283 - 9.24768i) q^{71} +(32.6792 + 5.17587i) q^{72} +(60.4466 + 30.7991i) q^{73} -8.32691i q^{74} -53.8984 q^{76} +(26.3614 - 51.7371i) q^{77} +(-22.2889 + 140.727i) q^{78} +(71.8966 + 98.9571i) q^{79} +(-39.9985 - 29.0606i) q^{81} +(-23.7352 - 23.7352i) q^{82} +(-60.8973 + 9.64518i) q^{83} +(43.8969 + 14.2630i) q^{84} +(27.6500 + 85.0979i) q^{86} +(-25.3423 + 12.9126i) q^{87} +(-14.6987 - 28.8478i) q^{88} +(75.7710 - 24.6195i) q^{89} +(-34.7133 + 106.837i) q^{91} +(-0.167440 - 1.05718i) q^{92} +(21.5668 - 21.5668i) q^{93} +(22.9488 - 31.5864i) q^{94} +(20.8207 - 15.1271i) q^{96} +(134.309 + 21.2725i) q^{97} +(-29.3197 - 14.9391i) q^{98} -133.904i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 2 q^{3} + 4 q^{6} + 2 q^{7} - 8 q^{8} - 40 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 2 * q^3 + 4 * q^6 + 2 * q^7 - 8 * q^8 - 40 * q^9	\( 16 q + 4 q^{2} - 2 q^{3} + 4 q^{6} + 2 q^{7} - 8 q^{8} - 40 q^{9} + 32 q^{11} - 4 q^{12} + 8 q^{13} - 30 q^{14} + 16 q^{16} + 62 q^{17} + 16 q^{18} + 30 q^{19} - 68 q^{21} + 48 q^{22} + 18 q^{23} - 56 q^{26} + 40 q^{27} - 44 q^{28} + 100 q^{29} + 132 q^{31} + 64 q^{32} + 36 q^{33} + 100 q^{34} + 48 q^{36} - 138 q^{37} - 20 q^{38} - 320 q^{39} - 88 q^{41} + 8 q^{42} + 78 q^{43} + 40 q^{44} - 26 q^{46} + 22 q^{47} + 8 q^{48} - 168 q^{51} + 16 q^{52} - 182 q^{53} + 80 q^{54} + 48 q^{56} - 280 q^{57} + 120 q^{58} - 350 q^{59} + 372 q^{61} + 158 q^{62} - 22 q^{63} - 202 q^{66} + 112 q^{67} + 196 q^{68} - 30 q^{69} + 122 q^{71} + 132 q^{72} + 248 q^{73} + 40 q^{76} - 16 q^{77} - 438 q^{78} + 760 q^{79} - 144 q^{81} - 352 q^{82} - 132 q^{83} - 20 q^{84} + 264 q^{86} - 770 q^{87} - 116 q^{88} + 550 q^{89} - 798 q^{91} - 384 q^{92} - 54 q^{93} + 190 q^{94} - 16 q^{96} + 292 q^{97} + 24 q^{98}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 + 4 * q^6 + 2 * q^7 - 8 * q^8 - 40 * q^9 + 32 * q^11 - 4 * q^12 + 8 * q^13 - 30 * q^14 + 16 * q^16 + 62 * q^17 + 16 * q^18 + 30 * q^19 - 68 * q^21 + 48 * q^22 + 18 * q^23 - 56 * q^26 + 40 * q^27 - 44 * q^28 + 100 * q^29 + 132 * q^31 + 64 * q^32 + 36 * q^33 + 100 * q^34 + 48 * q^36 - 138 * q^37 - 20 * q^38 - 320 * q^39 - 88 * q^41 + 8 * q^42 + 78 * q^43 + 40 * q^44 - 26 * q^46 + 22 * q^47 + 8 * q^48 - 168 * q^51 + 16 * q^52 - 182 * q^53 + 80 * q^54 + 48 * q^56 - 280 * q^57 + 120 * q^58 - 350 * q^59 + 372 * q^61 + 158 * q^62 - 22 * q^63 - 202 * q^66 + 112 * q^67 + 196 * q^68 - 30 * q^69 + 122 * q^71 + 132 * q^72 + 248 * q^73 + 40 * q^76 - 16 * q^77 - 438 * q^78 + 760 * q^79 - 144 * q^81 - 352 * q^82 - 132 * q^83 - 20 * q^84 + 264 * q^86 - 770 * q^87 - 116 * q^88 + 550 * q^89 - 798 * q^91 - 384 * q^92 - 54 * q^93 + 190 * q^94 - 16 * q^96 + 292 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

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