LMFDB - Embedded newform 242.4.c.f.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [242,4,Mod(3,242)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(242, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("242.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 242 = 2 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	242.c (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.2784622214$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	242.81
Dual form			242.4.c.f.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61803 - 1.17557i) q^{2} +(-0.972136 + 2.99193i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-0.500000 + 0.363271i) q^{5} +(5.09017 - 3.69822i) q^{6} +(-3.02786 - 9.31881i) q^{7} +(2.47214 - 7.60845i) q^{8} +(13.8369 + 10.0531i) q^{9} +O(q^{10})$	\(q+(-1.61803 - 1.17557i) q^{2} +(-0.972136 + 2.99193i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-0.500000 + 0.363271i) q^{5} +(5.09017 - 3.69822i) q^{6} +(-3.02786 - 9.31881i) q^{7} +(2.47214 - 7.60845i) q^{8} +(13.8369 + 10.0531i) q^{9} +1.23607 q^{10} -12.5836 q^{12} +(-11.2639 - 8.18373i) q^{13} +(-6.05573 + 18.6376i) q^{14} +(-0.600813 - 1.84911i) q^{15} +(-12.9443 + 9.40456i) q^{16} +(97.6378 - 70.9380i) q^{17} +(-10.5704 - 32.5325i) q^{18} +(-14.3885 + 44.2834i) q^{19} +(-2.00000 - 1.45309i) q^{20} +30.8247 q^{21} -82.8328 q^{23} +(20.3607 + 14.7929i) q^{24} +(-38.5091 + 118.519i) q^{25} +(8.60488 + 26.4831i) q^{26} +(-112.247 + 81.5520i) q^{27} +(31.7082 - 23.0374i) q^{28} +(63.4311 + 195.221i) q^{29} +(-1.20163 + 3.69822i) q^{30} +(234.921 + 170.680i) q^{31} +32.0000 q^{32} -241.374 q^{34} +(4.89919 + 3.55947i) q^{35} +(-21.1409 + 65.0649i) q^{36} +(-14.8870 - 45.8174i) q^{37} +(75.3394 - 54.7373i) q^{38} +(35.4352 - 25.7452i) q^{39} +(1.52786 + 4.70228i) q^{40} +(-52.1393 + 160.468i) q^{41} +(-49.8754 - 36.2366i) q^{42} +366.026 q^{43} -10.5704 q^{45} +(134.026 + 97.3758i) q^{46} +(-68.5952 + 211.114i) q^{47} +(-15.5542 - 47.8708i) q^{48} +(199.821 - 145.178i) q^{49} +(201.636 - 146.497i) q^{50} +(117.324 + 361.086i) q^{51} +(17.2098 - 52.9662i) q^{52} +(454.523 + 330.230i) q^{53} +277.489 q^{54} -78.3870 q^{56} +(-118.505 - 86.0989i) q^{57} +(126.862 - 390.442i) q^{58} +(127.015 + 390.911i) q^{59} +(6.29180 - 4.57126i) q^{60} +(-245.916 + 178.669i) q^{61} +(-179.464 - 552.333i) q^{62} +(51.7865 - 159.383i) q^{63} +(-51.7771 - 37.6183i) q^{64} +8.60488 q^{65} +107.692 q^{67} +(390.551 + 283.752i) q^{68} +(80.5248 - 247.830i) q^{69} +(-3.74265 - 11.5187i) q^{70} +(-56.1838 + 40.8199i) q^{71} +(110.695 - 80.4247i) q^{72} +(25.5000 + 78.4809i) q^{73} +(-29.7740 + 91.6349i) q^{74} +(-317.163 - 230.433i) q^{75} -186.249 q^{76} -87.6006 q^{78} +(-1024.12 - 744.068i) q^{79} +(3.05573 - 9.40456i) q^{80} +(7.82231 + 24.0746i) q^{81} +(273.005 - 198.350i) q^{82} +(-672.751 + 488.782i) q^{83} +(38.1014 + 117.264i) q^{84} +(-23.0492 + 70.9380i) q^{85} +(-592.243 - 430.290i) q^{86} -645.750 q^{87} +1482.95 q^{89} +(17.1033 + 12.4263i) q^{90} +(-42.1569 + 129.746i) q^{91} +(-102.387 - 315.115i) q^{92} +(-739.039 + 536.943i) q^{93} +(359.169 - 260.952i) q^{94} +(-8.89261 - 27.3686i) q^{95} +(-31.1084 + 95.7417i) q^{96} +(-313.084 - 227.469i) q^{97} -493.984 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 14 q^{3} - 4 q^{4} - 2 q^{5} - 2 q^{6} - 30 q^{7} - 8 q^{8} + 71 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 14 * q^3 - 4 * q^4 - 2 * q^5 - 2 * q^6 - 30 * q^7 - 8 * q^8 + 71 * q^9	\( 4 q - 2 q^{2} + 14 q^{3} - 4 q^{4} - 2 q^{5} - 2 q^{6} - 30 q^{7} - 8 q^{8} + 71 q^{9} - 4 q^{10} - 104 q^{12} - 54 q^{13} - 60 q^{14} - 27 q^{15} - 16 q^{16} + 158 q^{17} - 248 q^{18} + 14 q^{19} - 8 q^{20} - 230 q^{21} - 224 q^{23} - 8 q^{24} + 121 q^{25} + 182 q^{26} - 487 q^{27} + 100 q^{28} + 370 q^{29} - 54 q^{30} + 488 q^{31} + 128 q^{32} - 724 q^{34} - 5 q^{35} - 496 q^{36} + 334 q^{37} + 118 q^{38} + 381 q^{39} + 24 q^{40} - 298 q^{41} - 280 q^{42} + 1160 q^{43} - 248 q^{45} + 232 q^{46} + 146 q^{47} + 224 q^{48} + 323 q^{49} + 252 q^{50} - 727 q^{51} + 364 q^{52} + 870 q^{53} - 1144 q^{54} + 80 q^{56} - 76 q^{57} + 740 q^{58} + 678 q^{59} + 52 q^{60} - 930 q^{61} - 454 q^{62} - 1575 q^{63} - 64 q^{64} + 182 q^{65} - 88 q^{67} + 632 q^{68} - 304 q^{69} + 70 q^{70} + 540 q^{71} + 568 q^{72} + 102 q^{73} + 668 q^{74} + 111 q^{75} - 584 q^{76} + 1832 q^{78} - 2008 q^{79} + 48 q^{80} - 3694 q^{81} + 694 q^{82} - 1488 q^{83} + 1020 q^{84} - 204 q^{85} - 920 q^{86} + 1670 q^{87} + 1728 q^{89} - 106 q^{90} + 1135 q^{91} - 16 q^{92} - 1657 q^{93} + 502 q^{94} - 87 q^{95} + 448 q^{96} - 1306 q^{97} - 1484 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 14 * q^3 - 4 * q^4 - 2 * q^5 - 2 * q^6 - 30 * q^7 - 8 * q^8 + 71 * q^9 - 4 * q^10 - 104 * q^12 - 54 * q^13 - 60 * q^14 - 27 * q^15 - 16 * q^16 + 158 * q^17 - 248 * q^18 + 14 * q^19 - 8 * q^20 - 230 * q^21 - 224 * q^23 - 8 * q^24 + 121 * q^25 + 182 * q^26 - 487 * q^27 + 100 * q^28 + 370 * q^29 - 54 * q^30 + 488 * q^31 + 128 * q^32 - 724 * q^34 - 5 * q^35 - 496 * q^36 + 334 * q^37 + 118 * q^38 + 381 * q^39 + 24 * q^40 - 298 * q^41 - 280 * q^42 + 1160 * q^43 - 248 * q^45 + 232 * q^46 + 146 * q^47 + 224 * q^48 + 323 * q^49 + 252 * q^50 - 727 * q^51 + 364 * q^52 + 870 * q^53 - 1144 * q^54 + 80 * q^56 - 76 * q^57 + 740 * q^58 + 678 * q^59 + 52 * q^60 - 930 * q^61 - 454 * q^62 - 1575 * q^63 - 64 * q^64 + 182 * q^65 - 88 * q^67 + 632 * q^68 - 304 * q^69 + 70 * q^70 + 540 * q^71 + 568 * q^72 + 102 * q^73 + 668 * q^74 + 111 * q^75 - 584 * q^76 + 1832 * q^78 - 2008 * q^79 + 48 * q^80 - 3694 * q^81 + 694 * q^82 - 1488 * q^83 + 1020 * q^84 - 204 * q^85 - 920 * q^86 + 1670 * q^87 + 1728 * q^89 - 106 * q^90 + 1135 * q^91 - 16 * q^92 - 1657 * q^93 + 502 * q^94 - 87 * q^95 + 448 * q^96 - 1306 * q^97 - 1484 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/242\mathbb{Z}\right)^\times$.

$n$	$123$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.61803	−	1.17557i	−0.572061	−	0.415627i
$2$	−1.61803	−	1.17557i	−0.572061	−	0.415627i
$3$	−0.972136	+	2.99193i	−0.187088	+	0.575797i	−0.999978	−	0.00662005i	$-0.997893\pi$
$3$	−0.972136	+	2.99193i	−0.187088	+	0.575797i	0.812890	+	0.582417i	$0.197893\pi$
$4$	1.23607	+	3.80423i	0.154508	+	0.475528i
$5$	−0.500000	+	0.363271i	−0.0447214	+	0.0324920i	−0.609921	−	0.792462i	$-0.708799\pi$
$5$	−0.500000	+	0.363271i	−0.0447214	+	0.0324920i	0.565200	+	0.824954i	$0.308799\pi$
$6$	5.09017	−	3.69822i	0.346342	−	0.251632i
$7$	−3.02786	−	9.31881i	−0.163489	−	0.503168i	0.835432	−	0.549593i	$-0.185217\pi$
$7$	−3.02786	−	9.31881i	−0.163489	−	0.503168i	−0.998922	+	0.0464248i	$0.985217\pi$
$8$	2.47214	−	7.60845i	0.109254	−	0.336249i
$9$	13.8369	+	10.0531i	0.512477	+	0.372336i
$10$	1.23607			0.0390879
$11$		0			0
$11$		0			0
$12$	−12.5836			−0.302714
$13$	−11.2639	−	8.18373i	−0.240312	−	0.174597i	0.461110	−	0.887343i	$-0.347451\pi$
$13$	−11.2639	−	8.18373i	−0.240312	−	0.174597i	−0.701422	+	0.712746i	$0.747451\pi$
$14$	−6.05573	+	18.6376i	−0.115604	+	0.355794i
$15$	−0.600813	−	1.84911i	−0.0103420	−	0.0318293i
$16$	−12.9443	+	9.40456i	−0.202254	+	0.146946i
$17$	97.6378	−	70.9380i	1.39298	−	1.01206i	0.397447	−	0.917625i	$-0.369896\pi$
$17$	97.6378	−	70.9380i	1.39298	−	1.01206i	0.995531	−	0.0944333i	$-0.0301039\pi$
$18$	−10.5704	−	32.5325i	−0.138415	−	0.425999i
$19$	−14.3885	+	44.2834i	−0.173735	+	0.534700i	−0.999573	−	0.0292060i	$-0.990702\pi$
$19$	−14.3885	+	44.2834i	−0.173735	+	0.534700i	0.825839	+	0.563906i	$0.190702\pi$
$20$	−2.00000	−	1.45309i	−0.0223607	−	0.0162460i
$21$	30.8247			0.320309
$22$		0			0
$23$	−82.8328			−0.750949			−0.375475	−	0.926833i	$-0.622520\pi$
$23$	−82.8328			−0.750949			−0.375475	+	0.926833i	$0.622520\pi$
$24$	20.3607	+	14.7929i	0.173171	+	0.125816i
$25$	−38.5091	+	118.519i	−0.308073	+	0.948150i
$26$	8.60488	+	26.4831i	0.0649060	+	0.199760i
$27$	−112.247	+	81.5520i	−0.800070	+	0.581285i
$28$	31.7082	−	23.0374i	0.214010	−	0.155488i
$29$	63.4311	+	195.221i	0.406168	+	1.25006i	0.919916	+	0.392115i	$0.128256\pi$
$29$	63.4311	+	195.221i	0.406168	+	1.25006i	−0.513749	+	0.857941i	$0.671744\pi$
$30$	−1.20163	+	3.69822i	−0.00731286	+	0.0225067i
$31$	234.921	+	170.680i	1.36107	+	0.988874i	0.998376	+	0.0569656i	$0.0181425\pi$
$31$	234.921	+	170.680i	1.36107	+	0.988874i	0.362693	+	0.931909i	$0.381857\pi$
$32$	32.0000			0.176777
$33$		0			0
$34$	−241.374			−1.21751
$35$	4.89919	+	3.55947i	0.0236604	+	0.0171903i
$36$	−21.1409	+	65.0649i	−0.0978744	+	0.301226i
$37$	−14.8870	−	45.8174i	−0.0661461	−	0.203577i	0.912521	−	0.409030i	$-0.134133\pi$
$37$	−14.8870	−	45.8174i	−0.0661461	−	0.203577i	−0.978667	+	0.205454i	$0.934133\pi$
$38$	75.3394	−	54.7373i	0.321623	−	0.233673i
$39$	35.4352	−	25.7452i	0.145492	−	0.105706i
$40$	1.52786	+	4.70228i	0.00603941	+	0.0185874i
$41$	−52.1393	+	160.468i	−0.198605	+	0.611242i	0.801311	+	0.598248i	$0.204136\pi$
$41$	−52.1393	+	160.468i	−0.198605	+	0.611242i	−0.999916	+	0.0129943i	$0.995864\pi$
$42$	−49.8754	−	36.2366i	−0.183237	−	0.133129i
$43$	366.026			1.29810			0.649052	−	0.760744i	$-0.275166\pi$
$43$	366.026			1.29810			0.649052	+	0.760744i	$0.275166\pi$
$44$		0			0
$45$	−10.5704			−0.0350166
$46$	134.026	+	97.3758i	0.429589	+	0.312115i
$47$	−68.5952	+	211.114i	−0.212886	+	0.655195i	0.786411	+	0.617704i	$0.211937\pi$
$47$	−68.5952	+	211.114i	−0.212886	+	0.655195i	−0.999297	+	0.0374919i	$0.988063\pi$
$48$	−15.5542	−	47.8708i	−0.0467719	−	0.143949i
$49$	199.821	−	145.178i	0.582567	−	0.423260i
$50$	201.636	−	146.497i	0.570313	−	0.414357i
$51$	117.324	+	361.086i	0.322131	+	0.991416i
$52$	17.2098	−	52.9662i	0.0458955	−	0.141252i
$53$	454.523	+	330.230i	1.17799	+	0.855861i	0.991944	−	0.126680i	$-0.0404320\pi$
$53$	454.523	+	330.230i	1.17799	+	0.855861i	0.186048	+	0.982541i	$0.440432\pi$
$54$	277.489			0.699287
$55$		0			0
$56$	−78.3870			−0.187052
$57$	−118.505	−	86.0989i	−0.275375	−	0.200072i
$58$	126.862	−	390.442i	0.287204	−	0.883923i
$59$	127.015	+	390.911i	0.280270	+	0.862581i	0.987777	+	0.155875i	$0.0498197\pi$
$59$	127.015	+	390.911i	0.280270	+	0.862581i	−0.707507	+	0.706706i	$0.750180\pi$
$60$	6.29180	−	4.57126i	0.0135378	−	0.00983578i
$61$	−245.916	+	178.669i	−0.516170	+	0.375019i	−0.815159	−	0.579237i	$-0.803351\pi$
$61$	−245.916	+	178.669i	−0.516170	+	0.375019i	0.298989	+	0.954257i	$0.403351\pi$
$62$	−179.464	−	552.333i	−0.367612	−	1.13139i
$63$	51.7865	−	159.383i	0.103563	−	0.318735i
$64$	−51.7771	−	37.6183i	−0.101127	−	0.0734732i
$65$	8.60488			0.0164201
$66$		0			0
$67$	107.692			0.196368			0.0981841	−	0.995168i	$-0.468697\pi$
$67$	107.692			0.196368			0.0981841	+	0.995168i	$0.468697\pi$
$68$	390.551	+	283.752i	0.696489	+	0.506029i
$69$	80.5248	−	247.830i	0.140493	−	0.432394i
$70$	−3.74265	−	11.5187i	−0.00639045	−	0.0196678i
$71$	−56.1838	+	40.8199i	−0.0939126	+	0.0682315i	−0.633751	−	0.773537i	$-0.718485\pi$
$71$	−56.1838	+	40.8199i	−0.0939126	+	0.0682315i	0.539838	+	0.841769i	$0.318485\pi$
$72$	110.695	−	80.4247i	0.181188	−	0.131641i
$73$	25.5000	+	78.4809i	0.0408842	+	0.125829i	0.969415	−	0.245426i	$-0.0789277\pi$
$73$	25.5000	+	78.4809i	0.0408842	+	0.125829i	−0.928531	+	0.371254i	$0.878928\pi$
$74$	−29.7740	+	91.6349i	−0.0467724	+	0.143951i
$75$	−317.163	−	230.433i	−0.488305	−	0.354774i
$76$	−186.249			−0.281109
$77$		0			0
$78$	−87.6006			−0.127164
$79$	−1024.12	−	744.068i	−1.45852	−	1.05967i	−0.983746	−	0.179563i	$-0.942532\pi$
$79$	−1024.12	−	744.068i	−1.45852	−	1.05967i	−0.474769	−	0.880111i	$-0.657468\pi$
$80$	3.05573	−	9.40456i	0.00427051	−	0.0131433i
$81$	7.82231	+	24.0746i	0.0107302	+	0.0330241i
$82$	273.005	−	198.350i	0.367663	−	0.267123i
$83$	−672.751	+	488.782i	−0.889687	+	0.646396i	−0.935796	−	0.352541i	$-0.885318\pi$
$83$	−672.751	+	488.782i	−0.889687	+	0.646396i	0.0461093	+	0.998936i	$0.485318\pi$
$84$	38.1014	+	117.264i	0.0494905	+	0.152316i
$85$	−23.0492	+	70.9380i	−0.0294121	+	0.0905212i
$86$	−592.243	−	430.290i	−0.742595	−	0.539527i
$87$	−645.750			−0.795767
$88$		0			0
$89$	1482.95			1.76621			0.883104	−	0.469176i	$-0.155449\pi$
$89$	1482.95			1.76621			0.883104	+	0.469176i	$0.155449\pi$
$90$	17.1033	+	12.4263i	0.0200317	+	0.0145538i
$91$	−42.1569	+	129.746i	−0.0485631	+	0.149462i
$92$	−102.387	−	315.115i	−0.116028	−	0.357098i
$93$	−739.039	+	536.943i	−0.824030	+	0.598693i
$94$	359.169	−	260.952i	0.394101	−	0.286331i
$95$	−8.89261	−	27.3686i	−0.00960382	−	0.0295575i
$96$	−31.1084	+	95.7417i	−0.0330727	+	0.101787i
$97$	−313.084	−	227.469i	−0.327720	−	0.238102i	0.411743	−	0.911300i	$-0.364920\pi$
$97$	−313.084	−	227.469i	−0.327720	−	0.238102i	−0.739462	+	0.673198i	$0.764920\pi$
$98$	−493.984			−0.509183
$99$		0			0
$100$	−498.472			−0.498472
$101$	882.051	+	640.848i	0.868984	+	0.631354i	0.930314	−	0.366764i	$-0.119534\pi$
$101$	882.051	+	640.848i	0.868984	+	0.631354i	−0.0613303	+	0.998118i	$0.519534\pi$
$102$	234.648	−	722.173i	0.227781	−	0.701037i
$103$	−270.166	−	831.487i	−0.258449	−	0.795425i	−0.993130	−	0.117013i	$-0.962668\pi$
$103$	−270.166	−	831.487i	−0.258449	−	0.795425i	0.734681	−	0.678413i	$-0.237332\pi$
$104$	−90.1115	+	65.4698i	−0.0849630	+	0.0617293i
$105$	−15.4123	+	11.1977i	−0.0143247	+	0.0104075i
$106$	−347.225	−	1068.65i	−0.318165	−	0.979210i
$107$	267.358	−	822.845i	0.241556	−	0.743433i	−0.754628	−	0.656153i	$-0.772182\pi$
$107$	267.358	−	822.845i	0.241556	−	0.743433i	0.996184	−	0.0872802i	$-0.0278175\pi$
$108$	−448.987	−	326.208i	−0.400035	−	0.290642i
$109$	−1852.09			−1.62750			−0.813751	−	0.581214i	$-0.802578\pi$
$109$	−1852.09			−1.62750			−0.813751	+	0.581214i	$0.802578\pi$
$110$		0			0
$111$	151.555			0.129594
$112$	126.833	+	92.1494i	0.107005	+	0.0777438i
$113$	−97.7098	+	300.720i	−0.0813430	+	0.250348i	−0.983455	−	0.181155i	$-0.942017\pi$
$113$	−97.7098	+	300.720i	−0.0813430	+	0.250348i	0.902112	+	0.431503i	$0.142017\pi$
$114$	90.5298	+	278.622i	0.0743762	+	0.228907i
$115$	41.4164	−	30.0908i	0.0335835	−	0.0243998i
$116$	−664.259	+	482.613i	−0.531680	+	0.386288i
$117$	−73.5860	−	226.474i	−0.0581456	−	0.178954i
$118$	254.029	−	781.822i	0.198181	−	0.609937i
$119$	−956.691	−	695.077i	−0.736973	−	0.535442i
$120$	−15.5542			−0.0118325
$121$		0			0
$122$	607.939			0.451149
$123$	−429.423	−	311.994i	−0.314795	−	0.228712i
$124$	−358.928	+	1104.67i	−0.259941	+	0.800016i
$125$	−47.6728	−	146.722i	−0.0341119	−	0.104986i
$126$	−271.158	+	197.008i	−0.191720	+	0.139292i
$127$	−666.119	+	483.964i	−0.465421	+	0.338148i	−0.795654	−	0.605751i	$-0.792873\pi$
$127$	−666.119	+	483.964i	−0.465421	+	0.338148i	0.330233	+	0.943899i	$0.392873\pi$
$128$	39.5542	+	121.735i	0.0273135	+	0.0840623i
$129$	−355.827	+	1095.12i	−0.242859	+	0.747444i
$130$	−13.9230	−	10.1156i	−0.00939328	−	0.00682462i
$131$	−313.483			−0.209077			−0.104539	−	0.994521i	$-0.533337\pi$
$131$	−313.483			−0.209077			−0.104539	+	0.994521i	$0.533337\pi$
$132$		0			0
$133$	456.235			0.297448
$134$	−174.249	−	126.599i	−0.112335	−	0.0816159i
$135$	26.4979	−	81.5520i	0.0168931	−	0.0519917i
$136$	−298.354	−	918.241i	−0.188115	−	0.578959i
$137$	1517.83	−	1102.77i	0.946548	−	0.687708i	−0.00343955	−	0.999994i	$-0.501095\pi$
$137$	1517.83	−	1102.77i	0.946548	−	0.687708i	0.949988	+	0.312286i	$0.101095\pi$
$138$	−421.633	+	306.334i	−0.260085	+	0.188963i
$139$	−263.080	−	809.678i	−0.160534	−	0.494072i	0.838146	−	0.545446i	$-0.183640\pi$
$139$	−263.080	−	809.678i	−0.160534	−	0.494072i	−0.998679	+	0.0513742i	$0.983640\pi$
$140$	−7.48529	+	23.0374i	−0.00451873	+	0.0139072i
$141$	−564.955	−	410.464i	−0.337431	−	0.245158i
$142$	138.894			0.0820826
$143$		0			0
$144$	−273.653			−0.158364
$145$	−102.634	−	74.5677i	−0.0587811	−	0.0427070i
$146$	51.0000	−	156.962i	0.0289095	−	0.0889744i
$147$	240.110	+	738.982i	0.134720	+	0.414627i
$148$	155.899	−	113.267i	0.0865864	−	0.0629087i
$149$	700.458	−	508.913i	0.385126	−	0.279810i	−0.378329	−	0.925671i	$-0.623501\pi$
$149$	700.458	−	508.913i	0.385126	−	0.279810i	0.763455	+	0.645861i	$0.223501\pi$
$150$	242.291	+	745.696i	0.131887	+	0.405906i
$151$	496.738	−	1528.80i	0.267708	−	0.823921i	−0.723349	−	0.690483i	$-0.757398\pi$
$151$	496.738	−	1528.80i	0.267708	−	0.823921i	0.991057	−	0.133438i	$-0.0426018\pi$
$152$	301.358	+	218.949i	0.160811	+	0.116836i
$153$	2064.15			1.09070
$154$		0			0
$155$	−179.464			−0.0929993
$156$	141.741	+	102.981i	0.0727458	+	0.0528529i
$157$	914.394	−	2814.22i	0.464819	−	1.43057i	−0.394391	−	0.918943i	$-0.629044\pi$
$157$	914.394	−	2814.22i	0.464819	−	1.43057i	0.859210	−	0.511623i	$-0.170956\pi$
$158$	782.359	+	2407.85i	0.393932	+	1.21240i
$159$	−1429.88	+	1038.87i	−0.713190	+	0.518163i
$160$	−16.0000	+	11.6247i	−0.00790569	+	0.00574382i
$161$	250.807	+	771.903i	0.122772	+	0.377854i
$162$	15.6446	−	48.1492i	0.00758739	−	0.0233516i
$163$	1965.93	+	1428.33i	0.944685	+	0.686354i	0.949544	−	0.313634i	$-0.101547\pi$
$163$	1965.93	+	1428.33i	0.944685	+	0.686354i	−0.00485864	+	0.999988i	$0.501547\pi$
$164$	−674.906			−0.321349
$165$		0			0
$166$	1663.13			0.777615
$167$	912.423	+	662.914i	0.422787	+	0.307173i	0.778758	−	0.627324i	$-0.215850\pi$
$167$	912.423	+	662.914i	0.422787	+	0.307173i	−0.355971	+	0.934497i	$0.615850\pi$
$168$	76.2028	−	234.528i	0.0349951	−	0.107704i
$169$	−619.008	−	1905.11i	−0.281751	−	0.867141i
$170$	120.687	−	87.6842i	0.0544486	−	0.0395592i
$171$	−644.277	+	468.095i	−0.288123	+	0.209334i
$172$	452.433	+	1392.45i	0.200568	+	0.617285i
$173$	−824.044	+	2536.15i	−0.362144	+	1.11456i	0.589606	+	0.807691i	$0.299283\pi$
$173$	−824.044	+	2536.15i	−0.362144	+	1.11456i	−0.951750	+	0.306874i	$0.900717\pi$
$174$	1044.85	+	759.125i	0.455227	+	0.330742i
$175$	1221.05			0.527446
$176$		0			0
$177$	−1293.05			−0.549106
$178$	−2399.47	−	1743.31i	−1.01038	−	0.734084i
$179$	−90.8855	+	279.717i	−0.0379503	+	0.116799i	−0.968237	−	0.250034i	$-0.919558\pi$
$179$	−90.8855	+	279.717i	−0.0379503	+	0.116799i	0.930287	+	0.366833i	$0.119558\pi$
$180$	−13.0658	−	40.2123i	−0.00541036	−	0.0166514i
$181$	1000.94	−	727.227i	0.411047	−	0.298643i	−0.362979	−	0.931797i	$-0.618240\pi$
$181$	1000.94	−	727.227i	0.411047	−	0.298643i	0.774025	+	0.633154i	$0.218240\pi$
$182$	220.736	−	160.374i	0.0899015	−	0.0653173i
$183$	−295.500	−	909.454i	−0.119366	−	0.367370i
$184$	−204.774	+	630.230i	−0.0820442	+	0.252506i
$185$	24.0877	+	17.5007i	0.00957276	+	0.00695501i
$186$	1827.00			0.720228
$187$		0			0
$188$	−887.915			−0.344457
$189$	1099.84	+	799.077i	0.423287	+	0.307536i
$190$	−17.7852	+	54.7373i	−0.00679092	+	0.0209003i
$191$	1179.09	+	3628.88i	0.446682	+	1.37475i	0.880629	+	0.473807i	$0.157120\pi$
$191$	1179.09	+	3628.88i	0.446682	+	1.37475i	−0.433947	+	0.900938i	$0.642880\pi$
$192$	162.885	−	118.343i	0.0612252	−	0.0444827i
$193$	3807.84	−	2766.55i	1.42018	−	1.03182i	0.428434	−	0.903573i	$-0.359066\pi$
$193$	3807.84	−	2766.55i	1.42018	−	1.03182i	0.991742	−	0.128245i	$-0.0409345\pi$
$194$	239.175	+	736.104i	0.0885141	+	0.272418i
$195$	−8.36511	+	25.7452i	−0.00307199	+	0.00945461i
$196$	799.282	+	580.713i	0.291284	+	0.211630i
$197$	2794.25			1.01057			0.505284	−	0.862953i	$-0.331388\pi$
$197$	2794.25			1.01057			0.505284	+	0.862953i	$0.331388\pi$
$198$		0			0
$199$	−4188.70			−1.49211			−0.746053	−	0.665886i	$-0.768054\pi$
$199$	−4188.70			−1.49211			−0.746053	+	0.665886i	$0.768054\pi$
$200$	806.545	+	585.989i	0.285157	+	0.207178i
$201$	−104.691	+	322.206i	−0.0367381	+	0.113068i
$202$	−673.827	−	2073.83i	−0.234704	−	0.722346i
$203$	1627.17	−	1182.20i	0.562584	−	0.408741i
$204$	−1228.63	+	892.655i	−0.421674	+	0.306364i
$205$	−32.2239	−	99.1749i	−0.0109786	−	0.0337887i
$206$	−540.333	+	1662.97i	−0.182751	+	0.562451i
$207$	−1146.15	−	832.725i	−0.384844	−	0.279606i
$208$	222.768			0.0742604
$209$		0			0
$210$	38.1014			0.0125202
$211$	−679.921	−	493.992i	−0.221838	−	0.161174i	0.471316	−	0.881964i	$-0.343779\pi$
$211$	−679.921	−	493.992i	−0.221838	−	0.161174i	−0.693153	+	0.720790i	$0.743779\pi$
$212$	−694.450	+	2137.30i	−0.224976	+	0.692406i
$213$	−67.5119	−	207.780i	−0.0217176	−	0.0668398i
$214$	−1399.91	+	1017.09i	−0.447176	+	0.324892i
$215$	−183.013	+	132.967i	−0.0580530	+	0.0421780i
$216$	342.995	+	1055.63i	0.108046	+	0.332531i
$217$	879.228	−	2705.98i	0.275050	−	0.846517i
$218$	2996.74	+	2177.26i	0.931031	+	0.676434i
$219$	−259.599			−0.0801007
$220$		0			0
$221$	−1680.32			−0.511451
$222$	−245.221	−	178.163i	−0.0741357	−	0.0538627i
$223$	−1608.89	+	4951.65i	−0.483135	+	1.48694i	0.351530	+	0.936177i	$0.385662\pi$
$223$	−1608.89	+	4951.65i	−0.483135	+	1.48694i	−0.834664	+	0.550759i	$0.814338\pi$
$224$	−96.8916	−	298.202i	−0.0289011	−	0.0889484i
$225$	−1724.32	+	1252.80i	−0.510911	+	0.371199i
$226$	511.615	−	371.710i	0.150585	−	0.109406i
$227$	283.409	+	872.244i	0.0828658	+	0.255035i	0.983902	−	0.178709i	$-0.0571922\pi$
$227$	283.409	+	872.244i	0.0828658	+	0.255035i	−0.901036	+	0.433744i	$0.857192\pi$
$228$	181.060	−	557.244i	0.0525919	−	0.161861i
$229$	4093.02	+	2973.75i	1.18111	+	0.858127i	0.992297	−	0.123885i	$-0.0395355\pi$
$229$	4093.02	+	2973.75i	1.18111	+	0.858127i	0.188814	+	0.982013i	$0.439536\pi$
$230$	−102.387			−0.0293530
$231$		0			0
$232$	1642.14			0.464706
$233$	4000.64	+	2906.63i	1.12485	+	0.817252i	0.984937	−	0.172911i	$-0.0553174\pi$
$233$	4000.64	+	2906.63i	1.12485	+	0.817252i	0.139914	+	0.990164i	$0.455317\pi$
$234$	−147.172	+	452.949i	−0.0411151	+	0.126539i
$235$	−42.3942	−	130.476i	−0.0117680	−	0.0362183i
$236$	−1330.12	+	966.385i	−0.366878	+	0.266552i
$237$	3221.78	−	2340.76i	0.883027	−	0.641556i
$238$	730.847	+	2249.32i	0.199050	+	0.612611i
$239$	90.5658	−	278.733i	0.0245114	−	0.0754382i	−0.938053	−	0.346493i	$-0.887372\pi$
$239$	90.5658	−	278.733i	0.0245114	−	0.0754382i	0.962564	+	0.271055i	$0.0873725\pi$
$240$	25.1672	+	18.2850i	0.00676889	+	0.00491789i
$241$	−1254.72			−0.335369			−0.167684	−	0.985841i	$-0.553629\pi$
$241$	−1254.72			−0.335369			−0.167684	+	0.985841i	$0.553629\pi$
$242$		0			0
$243$	−3825.74			−1.00996
$244$	−983.666	−	714.675i	−0.258085	−	0.187510i
$245$	−47.1712	+	145.178i	−0.0123007	+	0.0378575i
$246$	328.050	+	1009.63i	0.0850232	+	0.261674i
$247$	524.475	−	381.053i	0.135107	−	0.0981613i
$248$	1879.37	−	1365.44i	0.481211	−	0.349620i
$249$	−808.395	−	2487.99i	−0.205743	−	0.633211i
$250$	−95.3456	+	293.444i	−0.0241207	+	0.0742360i
$251$	−4083.59	−	2966.91i	−1.02691	−	0.746093i	−0.0592215	−	0.998245i	$-0.518862\pi$
$251$	−4083.59	−	2966.91i	−1.02691	−	0.746093i	−0.967688	+	0.252152i	$0.918862\pi$
$252$	670.339			0.167569
$253$		0			0
$254$	1646.74			0.406793
$255$	−189.834	−	137.923i	−0.0466192	−	0.0338708i
$256$	79.1084	−	243.470i	0.0193136	−	0.0594410i
$257$	−1648.39	−	5073.23i	−0.400093	−	1.23136i	−0.924924	−	0.380152i	$-0.875872\pi$
$257$	−1648.39	−	5073.23i	−0.400093	−	1.23136i	0.524831	−	0.851206i	$-0.324128\pi$
$258$	1863.14	−	1353.65i	0.449588	−	0.326645i
$259$	−381.888	+	277.458i	−0.0916192	+	0.0665653i
$260$	10.6362	+	32.7349i	0.00253704	+	0.00780820i
$261$	−1084.88	+	3338.93i	−0.257290	+	0.791856i
$262$	507.226	+	368.521i	0.119605	+	0.0868982i
$263$	724.100			0.169772			0.0848858	−	0.996391i	$-0.472947\pi$
$263$	724.100			0.169772			0.0848858	+	0.996391i	$0.472947\pi$
$264$		0			0
$265$	−347.225			−0.0804900
$266$	−738.204	−	536.336i	−0.170159	−	0.123627i
$267$	−1441.63	+	4436.88i	−0.330436	+	1.01698i
$268$	133.115	+	409.684i	0.0303405	+	0.0933786i
$269$	−3267.59	+	2374.04i	−0.740626	+	0.538096i	−0.892907	−	0.450241i	$-0.851338\pi$
$269$	−3267.59	+	2374.04i	−0.740626	+	0.538096i	0.152281	+	0.988337i	$0.451338\pi$
$270$	−138.745	+	100.804i	−0.0312731	+	0.0227212i
$271$	−748.437	−	2303.45i	−0.167765	−	0.516328i	0.831464	−	0.555578i	$-0.187503\pi$
$271$	−748.437	−	2303.45i	−0.167765	−	0.516328i	−0.999229	+	0.0392504i	$0.987503\pi$
$272$	−596.709	+	1836.48i	−0.133018	+	0.409386i
$273$	−347.207	−	252.261i	−0.0769741	−	0.0559250i
$274$	−3752.29			−0.827314
$275$		0			0
$276$	1042.33			0.227323
$277$	−3549.78	−	2579.07i	−0.769985	−	0.559427i	0.131972	−	0.991253i	$-0.457869\pi$
$277$	−3549.78	−	2579.07i	−0.769985	−	0.559427i	−0.901957	+	0.431827i	$0.857869\pi$
$278$	−526.161	+	1619.36i	−0.113515	+	0.349362i
$279$	1534.72	+	4723.37i	0.329323	+	1.01355i
$280$	39.1935	−	28.4757i	0.00836521	−	0.00607768i
$281$	−35.1176	+	25.5144i	−0.00745530	+	0.00541659i	−0.591507	−	0.806300i	$-0.701467\pi$
$281$	−35.1176	+	25.5144i	−0.00745530	+	0.00541659i	0.584051	+	0.811717i	$0.301467\pi$
$282$	431.587	+	1328.29i	0.0911370	+	0.280491i
$283$	548.005	−	1686.59i	0.115108	−	0.354266i	−0.876862	−	0.480743i	$-0.840367\pi$
$283$	548.005	−	1686.59i	0.115108	−	0.354266i	0.991970	+	0.126477i	$0.0403671\pi$
$284$	−224.735	−	163.280i	−0.0469563	−	0.0341157i
$285$	90.5298			0.0188159
$286$		0			0
$287$	1653.24			0.340028
$288$	442.780	+	321.699i	0.0905940	+	0.0658204i
$289$	2982.73	−	9179.91i	0.607111	−	1.86849i
$290$	78.4052	+	241.306i	0.0158762	+	0.0488620i
$291$	984.929	−	715.593i	0.198411	−	0.144154i
$292$	−267.039	+	194.016i	−0.0535182	+	0.0388832i
$293$	−650.450	−	2001.88i	−0.129692	−	0.399150i	0.865035	−	0.501712i	$-0.167296\pi$
$293$	−650.450	−	2001.88i	−0.129692	−	0.399150i	−0.994727	+	0.102562i	$0.967296\pi$
$294$	480.219	−	1477.96i	0.0952618	−	0.293186i
$295$	−205.514	−	149.315i	−0.0405610	−	0.0294693i
$296$	−385.403			−0.0756793
$297$		0			0
$298$	−1731.63			−0.336612
$299$	933.023	+	677.881i	0.180462	+	0.131113i
$300$	484.583	−	1491.39i	0.0932580	−	0.287019i
$301$	−1108.28	−	3410.93i	−0.212226	−	0.653165i
$302$	−2600.95	+	1889.70i	−0.495589	+	0.360067i
$303$	−2774.84	+	2016.04i	−0.526107	+	0.382239i
$304$	−230.217	−	708.534i	−0.0434337	−	0.133675i
$305$	58.0530	−	178.669i	0.0108987	−	0.0335428i
$306$	−3339.86	−	2426.55i	−0.623945	−	0.453323i
$307$	−7670.26			−1.42594			−0.712972	−	0.701193i	$-0.752651\pi$
$307$	−7670.26			−1.42594			−0.712972	+	0.701193i	$0.752651\pi$
$308$		0			0
$309$	2750.39			0.506356
$310$	290.379	+	210.973i	0.0532013	+	0.0386530i
$311$	1479.94	−	4554.79i	0.269838	−	0.830477i	−0.720701	−	0.693246i	$-0.756180\pi$
$311$	1479.94	−	4554.79i	0.269838	−	0.830477i	0.990539	−	0.137230i	$-0.0438201\pi$
$312$	−108.280	−	333.252i	−0.0196480	−	0.0604702i
$313$	3234.20	−	2349.79i	0.584051	−	0.424338i	−0.256131	−	0.966642i	$-0.582448\pi$
$313$	3234.20	−	2349.79i	0.584051	−	0.424338i	0.840182	+	0.542304i	$0.182448\pi$
$314$	−4787.83	+	3478.56i	−0.860487	+	0.625180i
$315$	32.0058	+	98.5039i	0.00572484	+	0.0176193i
$316$	1564.72	−	4815.71i	0.278552	−	0.857294i
$317$	−5383.08	−	3911.04i	−0.953766	−	0.692951i	−0.00207132	−	0.999998i	$-0.500659\pi$
$317$	−5383.08	−	3911.04i	−0.953766	−	0.692951i	−0.951695	+	0.307046i	$0.900659\pi$
$318$	3534.87			0.623351
$319$		0			0
$320$	39.5542			0.00690983
$321$	2201.98	+	1599.83i	0.382874	+	0.278174i
$322$	501.613	−	1543.81i	0.0868130	−	0.267183i
$323$	1736.51	+	5344.43i	0.299139	+	0.920656i
$324$	−81.9163	+	59.5157i	−0.0140460	+	0.0102050i
$325$	1403.69	−	1019.84i	0.239577	−	0.174063i
$326$	−1501.84	−	4622.18i	−0.255151	−	0.785273i
$327$	1800.48	−	5541.31i	0.304486	−	0.937110i
$328$	1092.02	+	793.399i	0.183831	+	0.133561i
$329$	2175.03			0.364478
$330$		0			0
$331$	10258.7			1.70352			0.851762	−	0.523929i	$-0.175534\pi$
$331$	10258.7			1.70352			0.851762	+	0.523929i	$0.175534\pi$
$332$	−2691.00	−	1955.13i	−0.444844	−	0.323198i
$333$	254.617	−	783.631i	0.0419007	−	0.128957i
$334$	−697.029	−	2145.24i	−0.114191	−	0.351443i
$335$	−53.8460	+	39.1214i	−0.00878185	+	0.00638039i
$336$	−399.003	+	289.893i	−0.0647839	+	0.0470683i
$337$	1171.66	+	3605.99i	0.189390	+	0.582881i	0.999996	−	0.00270954i	$-0.000862476\pi$
$337$	1171.66	+	3605.99i	0.189390	+	0.582881i	−0.810607	+	0.585591i	$0.800862\pi$
$338$	−1238.02	+	3810.22i	−0.199228	+	0.613161i
$339$	−804.744	−	584.681i	−0.128931	−	0.0936741i
$340$	−298.354			−0.0475898
$341$		0			0
$342$	1592.74			0.251829
$343$	−4676.90	−	3397.96i	−0.736235	−	0.534906i
$344$	904.867	−	2784.89i	0.141823	−	0.436487i
$345$	49.7670	+	153.167i	0.00776628	+	0.0239022i
$346$	4314.75	−	3134.85i	0.670412	−	0.487083i
$347$	−7788.98	+	5659.03i	−1.20500	+	0.875483i	−0.994767	−	0.102169i	$-0.967422\pi$
$347$	−7788.98	+	5659.03i	−1.20500	+	0.875483i	−0.210232	+	0.977652i	$0.567422\pi$
$348$	−798.191	−	2456.58i	−0.122953	−	0.378410i
$349$	−3056.55	+	9407.08i	−0.468806	+	1.44284i	0.385327	+	0.922780i	$0.374089\pi$
$349$	−3056.55	+	9407.08i	−0.468806	+	1.44284i	−0.854133	+	0.520055i	$0.825911\pi$
$350$	−1975.71	−	1435.44i	−0.301731	−	0.219221i
$351$	1931.74			0.293757
$352$		0			0
$353$	4714.45			0.710836			0.355418	−	0.934708i	$-0.384339\pi$
$353$	4714.45			0.710836			0.355418	+	0.934708i	$0.384339\pi$
$354$	2092.20	+	1520.07i	0.314122	+	0.228223i
$355$	13.2632	−	40.8199i	0.00198292	−	0.00610281i
$356$	1833.03	+	5641.48i	0.272894	+	0.839882i
$357$	3009.65	−	2186.64i	0.446184	−	0.324172i
$358$	475.883	−	345.749i	0.0702547	−	0.0510430i
$359$	1329.97	+	4093.21i	0.195523	+	0.601759i	0.999970	+	0.00773419i	$0.00246189\pi$
$359$	1329.97	+	4093.21i	0.195523	+	0.601759i	−0.804447	+	0.594025i	$0.797538\pi$
$360$	−26.1316	+	80.4247i	−0.00382571	+	0.0117743i
$361$	3795.06	+	2757.27i	0.553296	+	0.401993i
$362$	−2474.47			−0.359268
$363$		0			0
$364$	−545.690			−0.0785768
$365$	−41.2599	−	29.9770i	−0.00591682	−	0.00429882i
$366$	−590.999	+	1818.91i	−0.0844044	+	0.259770i
$367$	−2900.21	−	8925.92i	−0.412506	−	1.26956i	−0.914463	−	0.404670i	$-0.867387\pi$
$367$	−2900.21	−	8925.92i	−0.412506	−	1.26956i	0.501957	−	0.864892i	$-0.332613\pi$
$368$	1072.21	−	779.007i	0.151883	−	0.110349i
$369$	−2334.65	+	1696.22i	−0.329368	+	0.239300i
$370$	−18.4013	−	56.6335i	−0.00258551	−	0.00795739i
$371$	1701.12	−	5235.51i	0.238053	−	0.732652i
$372$	−2956.16	−	2147.77i	−0.412015	−	0.299346i
$373$	−4540.37			−0.630272			−0.315136	−	0.949047i	$-0.602050\pi$
$373$	−4540.37			−0.630272			−0.315136	+	0.949047i	$0.602050\pi$
$374$		0			0
$375$	485.325			0.0668322
$376$	1436.68	+	1043.81i	0.197050	+	0.143165i
$377$	883.151	−	2718.06i	0.120649	−	0.371319i
$378$	−840.199	−	2585.87i	−0.114326	−	0.351859i
$379$	−336.516	+	244.493i	−0.0456086	+	0.0331366i	−0.610356	−	0.792127i	$-0.708974\pi$
$379$	−336.516	+	244.493i	−0.0456086	+	0.0331366i	0.564747	+	0.825264i	$0.308974\pi$
$380$	93.1246	−	67.6590i	0.0125716	−	0.00913377i
$381$	−800.426	−	2463.46i	−0.107630	−	0.331251i
$382$	2358.19	−	7257.75i	0.315852	−	0.972092i
$383$	528.109	+	383.693i	0.0704572	+	0.0511901i	0.622456	−	0.782655i	$-0.286135\pi$
$383$	528.109	+	383.693i	0.0704572	+	0.0511901i	−0.551999	+	0.833845i	$0.686135\pi$
$384$	−402.675			−0.0535128
$385$		0			0
$386$	−9413.49			−1.24128
$387$	5064.66	+	3679.69i	0.665249	+	0.483332i
$388$	478.349	−	1472.21i	0.0625889	−	0.192629i
$389$	−136.858	−	421.207i	−0.0178380	−	0.0548998i	0.941741	−	0.336338i	$-0.109189\pi$
$389$	−136.858	−	421.207i	−0.0178380	−	0.0548998i	−0.959579	+	0.281438i	$0.909189\pi$
$390$	43.8003	−	31.8228i	0.00568696	−	0.00413182i
$391$	−8087.61	+	5875.99i	−1.04606	+	0.760005i
$392$	−610.597	−	1879.23i	−0.0786730	−	0.242131i
$393$	304.748	−	937.918i	0.0391158	−	0.120386i
$394$	−4521.18	−	3284.83i	−0.578107	−	0.420019i
$395$	782.359			0.0996577
$396$		0			0
$397$	3516.62			0.444570			0.222285	−	0.974982i	$-0.428649\pi$
$397$	3516.62			0.444570			0.222285	+	0.974982i	$0.428649\pi$
$398$	6777.46	+	4924.11i	0.853576	+	0.620160i
$399$	−443.522	+	1365.02i	−0.0556488	+	0.171270i
$400$	−616.145	−	1896.30i	−0.0770182	−	0.237038i
$401$	−3612.42	+	2624.58i	−0.449864	+	0.326846i	−0.789542	−	0.613696i	$-0.789682\pi$
$401$	−3612.42	+	2624.58i	−0.449864	+	0.326846i	0.339678	+	0.940542i	$0.389682\pi$
$402$	548.170	−	398.269i	0.0680106	−	0.0494126i
$403$	−1249.34	−	3845.07i	−0.154427	−	0.475276i
$404$	−1347.65	+	4147.65i	−0.165961	+	0.510776i
$405$	−12.6568	−	9.19568i	−0.00155289	−	0.00112824i
$406$	−4022.57			−0.491717
$407$		0			0
$408$	3037.35			0.368557
$409$	−4438.79	−	3224.97i	−0.536635	−	0.389888i	0.286199	−	0.958170i	$-0.407608\pi$
$409$	−4438.79	−	3224.97i	−0.536635	−	0.389888i	−0.822834	+	0.568282i	$0.807608\pi$
$410$	−64.4477	+	198.350i	−0.00776304	+	0.0238922i
$411$	1823.87	+	5613.28i	0.218892	+	0.673681i
$412$	2829.22	−	2055.55i	0.338315	−	0.245800i
$413$	3258.24	−	2367.25i	0.388202	−	0.282046i
$414$	875.579	+	2694.76i	0.103943	+	0.319903i
$415$	158.815	−	488.782i	0.0187854	−	0.0578154i
$416$	−360.446	−	261.879i	−0.0424815	−	0.0308646i
$417$	2678.25			0.314519
$418$		0			0
$419$	−5133.78			−0.598571			−0.299286	−	0.954164i	$-0.596748\pi$
$419$	−5133.78			−0.598571			−0.299286	+	0.954164i	$0.596748\pi$
$420$	−61.6494	−	44.7909i	−0.00716234	−	0.00520374i
$421$	−1860.10	+	5724.80i	−0.215334	+	0.662730i	0.783796	+	0.621019i	$0.213281\pi$
$421$	−1860.10	+	5724.80i	−0.215334	+	0.662730i	−0.999130	+	0.0417114i	$0.986719\pi$
$422$	519.414	+	1598.59i	0.0599163	+	0.184403i
$423$	−3071.49	+	2231.57i	−0.353052	+	0.256507i
$424$	3636.19	−	2641.84i	0.416483	−	0.302593i
$425$	4647.54	+	14303.7i	0.530445	+	1.63254i
$426$	−135.024	+	415.561i	−0.0153566	+	0.0472629i
$427$	2409.58	+	1750.66i	0.273086	+	0.198409i
$428$	3460.76			0.390846
$429$		0			0
$430$	452.433			0.0507402
$431$	−10664.6	−	7748.29i	−1.19187	−	0.865945i	−0.198410	−	0.980119i	$-0.563578\pi$
$431$	−10664.6	−	7748.29i	−1.19187	−	0.865945i	−0.993461	+	0.114175i	$0.963578\pi$
$432$	685.991	−	2111.26i	0.0763999	−	0.235135i
$433$	−1139.45	−	3506.86i	−0.126463	−	0.389212i	0.867702	−	0.497085i	$-0.165596\pi$
$433$	−1139.45	−	3506.86i	−0.126463	−	0.389212i	−0.994165	+	0.107872i	$0.965596\pi$
$434$	−4603.70	+	3344.78i	−0.509181	+	0.369942i
$435$	322.875	−	234.583i	0.0355878	−	0.0258560i
$436$	−2289.30	−	7045.76i	−0.251463	−	0.773923i
$437$	1191.84	−	3668.12i	0.130466	−	0.401533i
$438$	420.039	+	305.177i	0.0458225	+	0.0332920i
$439$	−10680.8			−1.16120			−0.580600	−	0.814189i	$-0.697182\pi$
$439$	−10680.8			−1.16120			−0.580600	+	0.814189i	$0.697182\pi$
$440$		0			0
$441$	4224.38			0.456148
$442$	2718.82	+	1975.34i	0.292581	+	0.212573i
$443$	−3722.94	+	11458.0i	−0.399283	+	1.22887i	0.526293	+	0.850303i	$0.323582\pi$
$443$	−3722.94	+	11458.0i	−0.399283	+	1.22887i	−0.925576	+	0.378563i	$0.876418\pi$
$444$	187.332	+	576.548i	0.0200234	+	0.0616256i
$445$	−741.476	+	538.714i	−0.0789873	+	0.0573876i
$446$	8424.24	−	6120.57i	0.894393	−	0.649815i
$447$	841.689	+	2590.45i	0.0890616	+	0.274103i
$448$	−193.783	+	596.404i	−0.0204362	+	0.0628960i
$449$	−5080.77	−	3691.40i	−0.534023	−	0.387991i	0.287837	−	0.957679i	$-0.407064\pi$
$449$	−5080.77	−	3691.40i	−0.534023	−	0.387991i	−0.821861	+	0.569689i	$0.807064\pi$
$450$	4262.77			0.446553
$451$		0			0
$452$	−1264.78			−0.131616
$453$	4091.16	+	2972.40i	0.424326	+	0.308291i
$454$	566.819	−	1744.49i	0.0585950	−	0.180337i
$455$	−26.0544	−	80.1872i	−0.00268450	−	0.00826205i
$456$	−948.040	+	688.792i	−0.0973598	+	0.0707360i
$457$	6274.24	−	4558.50i	0.642224	−	0.466603i	−0.218390	−	0.975862i	$-0.570080\pi$
$457$	6274.24	−	4558.50i	0.642224	−	0.466603i	0.860614	+	0.509259i	$0.170080\pi$
$458$	−3126.79	−	9623.27i	−0.319007	−	0.981803i
$459$	−5174.38	+	15925.1i	−0.526186	+	1.61943i
$460$	165.666	+	120.363i	0.0167917	+	0.0121999i
$461$	5774.66			0.583411			0.291706	−	0.956508i	$-0.405777\pi$
$461$	5774.66			0.583411			0.291706	+	0.956508i	$0.405777\pi$
$462$		0			0
$463$	−10005.7			−1.00433			−0.502164	−	0.864773i	$-0.667462\pi$
$463$	−10005.7			−1.00433			−0.502164	+	0.864773i	$0.667462\pi$
$464$	−2657.04	−	1930.45i	−0.265840	−	0.193144i
$465$	174.463	−	536.943i	0.0173990	−	0.0535487i
$466$	−3056.21	−	9406.06i	−0.303812	−	0.935037i
$467$	−982.275	+	713.665i	−0.0973325	+	0.0707162i	−0.635387	−	0.772194i	$-0.719159\pi$
$467$	−982.275	+	713.665i	−0.0973325	+	0.0707162i	0.538055	+	0.842910i	$0.319159\pi$
$468$	770.603	−	559.876i	0.0761135	−	0.0552997i
$469$	−326.077	−	1003.56i	−0.0321041	−	0.0988062i
$470$	−84.7883	+	260.952i	−0.00832126	+	0.0256102i
$471$	7531.01	+	5471.60i	0.736753	+	0.535282i
$472$	3288.23			0.320663
$473$		0			0
$474$	−7964.69			−0.771794
$475$	−4694.32	−	3410.63i	−0.453453	−	0.329453i
$476$	1461.69	−	4498.63i	0.140749	−	0.433182i
$477$	2969.35	+	9138.72i	0.285026	+	0.877218i
$478$	−474.209	+	344.533i	−0.0453761	+	0.0329677i
$479$	7400.94	−	5377.10i	0.705966	−	0.512914i	−0.175904	−	0.984407i	$-0.556285\pi$
$479$	7400.94	−	5377.10i	0.705966	−	0.512914i	0.881870	+	0.471493i	$0.156285\pi$
$480$	−19.2260	−	59.1716i	−0.00182822	−	0.00562667i
$481$	−207.271	+	637.916i	−0.0196482	+	0.0604708i
$482$	2030.19	+	1475.02i	0.191852	+	0.139388i
$483$	−2553.30			−0.240536
$484$		0			0
$485$	239.175			0.0223925
$486$	6190.17	+	4497.42i	0.577761	+	0.419768i
$487$	−1020.31	+	3140.19i	−0.0949376	+	0.292188i	−0.987237	−	0.159255i	$-0.949091\pi$
$487$	−1020.31	+	3140.19i	−0.0949376	+	0.292188i	0.892300	+	0.451443i	$0.149091\pi$
$488$	751.454	+	2312.74i	0.0697064	+	0.214534i
$489$	−6184.62	+	4493.39i	−0.571939	+	0.415538i
$490$	246.992	−	179.450i	0.0227713	−	0.0165443i
$491$	1219.36	+	3752.79i	0.112075	+	0.344931i	0.991326	−	0.131428i	$-0.0419563\pi$
$491$	1219.36	+	3752.79i	0.112075	+	0.344931i	−0.879251	+	0.476359i	$0.841956\pi$
$492$	656.100	−	2019.27i	0.0601205	−	0.185032i
$493$	20041.9	+	14561.3i	1.83091	+	1.33024i
$494$	−1296.57			−0.118088
$495$		0			0
$496$	−4646.06			−0.420593
$497$	550.510	+	399.969i	0.0496856	+	0.0360987i
$498$	−1616.79	+	4975.97i	−0.145482	+	0.447748i
$499$	3218.78	+	9906.39i	0.288762	+	0.888719i	0.985246	+	0.171146i	$0.0547470\pi$
$499$	3218.78	+	9906.39i	0.288762	+	0.888719i	−0.696483	+	0.717573i	$0.745253\pi$
$500$	499.236	−	362.716i	0.0446530	−	0.0324423i
$501$	−2870.39	+	2085.46i	−0.255967	+	0.185971i
$502$	3119.59	+	9601.11i	0.277359	+	0.853622i
$503$	4328.56	−	13321.9i	0.383700	−	1.18091i	−0.553720	−	0.832703i	$-0.686792\pi$
$503$	4328.56	−	13321.9i	0.383700	−	1.18091i	0.937419	−	0.348203i	$-0.113208\pi$
$504$	−1084.63	−	788.031i	−0.0958598	−	0.0696462i
$505$	−673.827			−0.0593761
$506$		0			0
$507$	6301.71			0.552009
$508$	−2664.48	−	1935.85i	−0.232711	−	0.169074i
$509$	180.489	−	555.489i	0.0157172	−	0.0483725i	−0.942890	−	0.333103i	$-0.891904\pi$
$509$	180.489	−	555.489i	0.0157172	−	0.0483725i	0.958608	+	0.284731i	$0.0919042\pi$
$510$	145.021	+	446.327i	0.0125914	+	0.0387524i
$511$	654.138	−	475.259i	0.0566289	−	0.0411433i
$512$	−414.217	+	300.946i	−0.0357538	+	0.0259767i
$513$	−1996.33	−	6144.08i	−0.171813	−	0.528787i
$514$	−3296.78	+	10146.5i	−0.282908	+	0.870702i
$515$	437.138	+	317.600i	0.0374031	+	0.0271750i
$516$	−4605.93			−0.392955
$517$		0			0
$518$	944.079			0.0800781
$519$	−6786.88	−	4930.96i	−0.574010	−	0.417043i
$520$	21.2724	−	65.4698i	0.00179396	−	0.00552123i
$521$	−3295.48	−	10142.5i	−0.277117	−	0.852877i	−0.988652	−	0.150226i	$-0.952000\pi$
$521$	−3295.48	−	10142.5i	−0.277117	−	0.852877i	0.711535	−	0.702651i	$-0.248000\pi$
$522$	5680.52	−	4127.14i	0.476302	−	0.346054i
$523$	8909.45	−	6473.09i	0.744901	−	0.541202i	−0.149341	−	0.988786i	$-0.547715\pi$
$523$	8909.45	−	6473.09i	0.744901	−	0.541202i	0.894242	+	0.447584i	$0.147715\pi$
$524$	−387.486	−	1192.56i	−0.0323042	−	0.0994222i
$525$	−1187.03	+	3653.30i	−0.0986786	+	0.303701i
$526$	−1171.62	−	851.231i	−0.0971198	−	0.0705617i
$527$	35044.9			2.89674
$528$		0			0
$529$	−5305.72			−0.436075
$530$	561.822	+	408.187i	0.0460452	+	0.0334538i
$531$	−2172.37	+	6685.88i	−0.177539	+	0.546408i
$532$	563.937	+	1735.62i	0.0459582	+	0.141445i
$533$	1900.52	−	1380.81i	0.154448	−	0.112213i
$534$	7548.48	−	5484.29i	0.611713	−	0.444435i
$535$	165.237	+	508.546i	0.0133529	+	0.0410960i
$536$	266.229	−	819.369i	0.0214540	−	0.0660286i
$537$	−748.539	−	543.846i	−0.0601524	−	0.0437033i
$538$	8077.92			0.647331
$539$		0			0
$540$	342.995			0.0273337
$541$	7473.04	+	5429.48i	0.593884	+	0.431482i	0.843703	−	0.536811i	$-0.180371\pi$
$541$	7473.04	+	5429.48i	0.593884	+	0.431482i	−0.249819	+	0.968293i	$0.580371\pi$
$542$	−1496.87	+	4606.91i	−0.118628	+	0.365099i
$543$	1202.76	+	3701.71i	0.0950558	+	0.292552i
$544$	3124.41	−	2270.02i	0.246246	−	0.178908i
$545$	926.043	−	672.810i	0.0727841	−	0.0528807i
$546$	265.243	+	816.333i	0.0207900	+	0.0639850i
$547$	1003.96	−	3089.87i	0.0784758	−	0.241524i	−0.904120	−	0.427278i	$-0.859473\pi$
$547$	1003.96	−	3089.87i	0.0784758	−	0.241524i	0.982596	+	0.185754i	$0.0594727\pi$
$548$	6071.33	+	4411.08i	0.473274	+	0.343854i
$549$	−5198.89			−0.404159
$550$		0			0
$551$	−9557.72			−0.738970
$552$	−1686.53	−	1225.34i	−0.130043	−	0.0944816i
$553$	−3832.93	+	11796.5i	−0.294742	+	0.907124i
$554$	2711.79	+	8346.04i	0.207966	+	0.640053i
$555$	−75.7773	+	55.0554i	−0.00579562	+	0.00421076i
$556$	2755.01	−	2001.64i	0.210141	−	0.152677i
$557$	257.331	+	791.982i	0.0195753	+	0.0602466i	0.960367	−	0.278739i	$-0.0899163\pi$
$557$	257.331	+	791.982i	0.0195753	+	0.0602466i	−0.940792	+	0.338985i	$0.889916\pi$
$558$	3069.43	−	9446.74i	0.232866	−	0.716689i
$559$	−4122.90	−	2995.46i	−0.311950	−	0.226645i
$560$	−96.8916			−0.00731146
$561$		0			0
$562$	86.8154			0.00651617
$563$	9502.94	+	6904.29i	0.711370	+	0.516841i	0.883615	−	0.468214i	$-0.155102\pi$
$563$	9502.94	+	6904.29i	0.711370	+	0.516841i	−0.172245	+	0.985054i	$0.555102\pi$
$564$	863.174	−	2656.58i	0.0644436	−	0.198337i
$565$	−60.3880	−	185.855i	−0.00449653	−	0.0138389i
$566$	−2869.39	+	2084.74i	−0.213091	+	0.154820i
$567$	200.662	−	145.789i	0.0148624	−	0.0107982i
$568$	171.682	+	528.384i	0.0126825	+	0.0390326i
$569$	−2065.03	+	6355.51i	−0.152145	+	0.468254i	−0.997860	−	0.0653800i	$-0.979174\pi$
$569$	−2065.03	+	6355.51i	−0.152145	+	0.468254i	0.845715	+	0.533634i	$0.179174\pi$
$570$	−146.480	−	106.424i	−0.0107638	−	0.00782038i
$571$	−2066.18			−0.151431			−0.0757153	−	0.997129i	$-0.524124\pi$
$571$	−2066.18			−0.151431			−0.0757153	+	0.997129i	$0.524124\pi$
$572$		0			0
$573$	−12003.6			−0.875142
$574$	−2675.01	−	1943.51i	−0.194517	−	0.141325i
$575$	3189.82	−	9817.25i	0.231347	−	0.712013i
$576$	−338.254	−	1041.04i	−0.0244686	−	0.0753066i
$577$	14168.3	−	10293.9i	1.02224	−	0.742702i	0.0555002	−	0.998459i	$-0.482325\pi$
$577$	14168.3	−	10293.9i	1.02224	−	0.742702i	0.966741	+	0.255757i	$0.0823247\pi$
$578$	−15617.8	+	11347.0i	−1.12390	+	0.816562i
$579$	4575.60	+	14082.2i	0.328420	+	1.01077i
$580$	156.810	−	482.613i	0.0112262	−	0.0345507i
$581$	6591.87	+	4789.27i	0.470700	+	0.341984i
$582$	−2434.88			−0.173417
$583$		0			0
$584$	660.158			0.0467766
$585$	119.065	+	86.5056i	0.00841490	+	0.00611379i
$586$	−1300.90	+	4003.76i	−0.0917059	+	0.282242i
$587$	−4865.24	−	14973.7i	−0.342095	−	1.05286i	−0.963120	−	0.269071i	$-0.913283\pi$
$587$	−4865.24	−	14973.7i	−0.342095	−	1.05286i	0.621025	−	0.783791i	$-0.286717\pi$
$588$	−2514.46	+	1826.86i	−0.176351	+	0.128127i
$589$	−10938.5	+	7947.27i	−0.765216	+	0.555962i
$590$	156.999	+	483.193i	0.0109552	+	0.0337165i
$591$	−2716.39	+	8360.18i	−0.189065	+	0.581881i
$592$	623.594	+	453.068i	0.0432932	+	0.0314543i
$593$	−714.295			−0.0494647			−0.0247324	−	0.999694i	$-0.507873\pi$
$593$	−714.295			−0.0494647			−0.0247324	+	0.999694i	$0.507873\pi$
$594$		0			0
$595$	730.847			0.0503560
$596$	2801.83	+	2035.65i	0.192563	+	0.139905i
$597$	4071.99	−	12532.3i	0.279155	−	0.859150i
$598$	−712.766	−	2193.67i	−0.0487411	−	0.150010i
$599$	−11670.6	+	8479.20i	−0.796074	+	0.578382i	−0.909760	−	0.415135i	$-0.863734\pi$
$599$	−11670.6	+	8479.20i	−0.796074	+	0.578382i	0.113685	+	0.993517i	$0.463734\pi$
$600$	−2537.31	+	1843.46i	−0.172642	+	0.125432i
$601$	892.865	+	2747.95i	0.0606002	+	0.186508i	0.976774	−	0.214274i	$-0.0687385\pi$
$601$	892.865	+	2747.95i	0.0606002	+	0.186508i	−0.916173	+	0.400782i	$0.868738\pi$
$602$	−2216.56	+	6821.86i	−0.150067	+	0.461857i
$603$	1490.12	+	1082.64i	0.100634	+	0.0731150i
$604$	6429.91			0.433161
$605$		0			0
$606$	6859.79			0.459835
$607$	7404.53	+	5379.71i	0.495125	+	0.359729i	0.807152	−	0.590344i	$-0.201008\pi$
$607$	7404.53	+	5379.71i	0.495125	+	0.359729i	−0.312027	+	0.950073i	$0.601008\pi$
$608$	−460.433	+	1417.07i	−0.0307122	+	0.0945225i
$609$	1955.24	+	6017.62i	0.130099	+	0.400405i
$610$	−303.969	+	220.847i	−0.0201760	+	0.0146587i
$611$	2500.35	−	1816.61i	0.165554	−	0.120282i
$612$	2551.43	+	7852.48i	0.168522	+	0.518657i
$613$	391.971	−	1206.36i	0.0258264	−	0.0794854i	−0.937313	−	0.348490i	$-0.886695\pi$
$613$	391.971	−	1206.36i	0.0258264	−	0.0794854i	0.963139	+	0.269004i	$0.0866946\pi$
$614$	12410.7	+	9016.93i	0.815727	+	0.592661i
$615$	328.050			0.0215094
$616$		0			0
$617$	2961.74			0.193250			0.0966250	−	0.995321i	$-0.469195\pi$
$617$	2961.74			0.193250			0.0966250	+	0.995321i	$0.469195\pi$
$618$	−4450.22	−	3233.27i	−0.289667	−	0.210455i
$619$	7476.14	−	23009.2i	0.485447	−	1.49405i	−0.345886	−	0.938276i	$-0.612422\pi$
$619$	7476.14	−	23009.2i	0.485447	−	1.49405i	0.831333	−	0.555775i	$-0.187578\pi$
$620$	−221.830	−	682.722i	−0.0143692	−	0.0442238i
$621$	9297.71	−	6755.18i	0.600812	−	0.436516i
$622$	−7749.06	+	5630.02i	−0.499532	+	0.362932i
$623$	−4490.18	−	13819.3i	−0.288756	−	0.888700i
$624$	−216.561	+	666.505i	−0.0138932	+	0.0427589i
$625$	−12525.1	−	9100.04i	−0.801608	−	0.582402i
$626$	−7995.39			−0.510479
$627$		0			0
$628$	11836.2			0.752093
$629$	−4703.73	−	3417.46i	−0.298172	−	0.216634i
$630$	64.0117	−	197.008i	0.00404807	−	0.0124587i
$631$	−812.525	−	2500.69i	−0.0512617	−	0.157767i	0.922149	−	0.386836i	$-0.126432\pi$
$631$	−812.525	−	2500.69i	−0.0512617	−	0.157767i	−0.973410	+	0.229069i	$0.926432\pi$
$632$	−8192.97	+	5952.54i	−0.515663	+	0.374651i
$633$	2138.96	−	1554.05i	0.134307	−	0.0975796i
$634$	4112.31	+	12656.4i	0.257603	+	0.792822i
$635$	157.249	−	483.964i	0.00982716	−	0.0302449i
$636$	−5719.53	−	4155.49i	−0.356595	−	0.259081i
$637$	−3438.86			−0.213898
$638$		0			0
$639$	−1187.77			−0.0735331
$640$	−64.0000	−	46.4987i	−0.00395285	−	0.00287191i
$641$	−2602.23	+	8008.83i	−0.160346	+	0.493494i	−0.998663	−	0.0516885i	$-0.983540\pi$
$641$	−2602.23	+	8008.83i	−0.160346	+	0.493494i	0.838317	+	0.545183i	$0.183540\pi$
$642$	−1682.16	−	5177.17i	−0.103411	−	0.318266i
$643$	12321.5	−	8952.13i	0.755699	−	0.549047i	−0.141889	−	0.989883i	$-0.545318\pi$
$643$	12321.5	−	8952.13i	0.755699	−	0.549047i	0.897588	+	0.440835i	$0.145318\pi$
$644$	−2626.48	+	1908.25i	−0.160711	+	0.116763i
$645$	−219.913	−	676.824i	−0.0134249	−	0.0413177i
$646$	3473.02	−	10688.9i	0.211523	−	0.651002i
$647$	−16679.0	−	12118.0i	−1.01347	−	0.736332i	−0.0485391	−	0.998821i	$-0.515457\pi$
$647$	−16679.0	−	12118.0i	−1.01347	−	0.736332i	−0.964935	+	0.262489i	$0.915457\pi$
$648$	202.508			0.0122767
$649$		0			0
$650$	−3470.11			−0.209398
$651$	7241.38	+	5261.17i	0.435963	+	0.316746i
$652$	−3003.68	+	9244.37i	−0.180419	+	0.555272i
$653$	1792.45	+	5516.58i	0.107418	+	0.330598i	0.990290	−	0.139015i	$-0.0443935\pi$
$653$	1792.45	+	5516.58i	0.107418	+	0.330598i	−0.882873	+	0.469613i	$0.844394\pi$
$654$	−9427.44	+	6849.43i	−0.563673	+	0.409532i
$655$	156.741	−	113.879i	0.00935022	−	0.00679333i
$656$	−834.229	−	2567.49i	−0.0496512	−	0.152811i
$657$	−436.135	+	1342.28i	−0.0258984	+	0.0797070i
$658$	−3519.27	−	2556.90i	−0.208504	−	0.151487i
$659$	−14795.0			−0.874552			−0.437276	−	0.899327i	$-0.644057\pi$
$659$	−14795.0			−0.874552			−0.437276	+	0.899327i	$0.644057\pi$
$660$		0			0
$661$	12343.7			0.726344			0.363172	−	0.931722i	$-0.381694\pi$
$661$	12343.7			0.726344			0.363172	+	0.931722i	$0.381694\pi$
$662$	−16598.8	−	12059.8i	−0.974521	−	0.708031i
$663$	1633.50	−	5027.40i	0.0956862	−	0.294492i
$664$	2055.74	+	6326.93i	0.120148	+	0.369778i
$665$	−228.117	+	165.737i	−0.0133023	+	0.00966467i
$666$	−1333.19	+	968.621i	−0.0775678	+	0.0563563i
$667$	−5254.18	−	16170.7i	−0.305011	−	0.938728i
$668$	−1394.06	+	4290.47i	−0.0807451	+	0.248508i
$669$	−13250.9	−	9627.34i	−0.765784	−	0.556375i
$670$	133.115			0.00767562
$671$		0			0
$672$	986.390			0.0566232
$673$	773.888	+	562.262i	0.0443257	+	0.0322045i	0.609727	−	0.792611i	$-0.291279\pi$
$673$	773.888	+	562.262i	0.0443257	+	0.0322045i	−0.565402	+	0.824816i	$0.691279\pi$
$674$	2343.32	−	7211.99i	0.133919	−	0.412159i
$675$	−5342.93	−	16443.8i	−0.304666	−	0.937665i
$676$	6482.33	−	4709.69i	0.368817	−	0.267961i
$677$	3351.33	−	2434.89i	0.190254	−	0.138228i	−0.488581	−	0.872519i	$-0.662485\pi$
$677$	3351.33	−	2434.89i	0.190254	−	0.138228i	0.678835	+	0.734291i	$0.262485\pi$
$678$	614.770	+	1892.07i	0.0348231	+	0.107175i
$679$	−1171.76	+	3606.31i	−0.0662269	+	0.203825i
$680$	482.748	+	350.737i	0.0272243	+	0.0197796i
$681$	−2885.20			−0.162351
$682$		0			0
$683$	18776.7			1.05193			0.525967	−	0.850505i	$-0.323704\pi$
$683$	18776.7			1.05193			0.525967	+	0.850505i	$0.323704\pi$
$684$	−2577.11	−	1872.38i	−0.144062	−	0.104667i
$685$	−358.312	+	1102.77i	−0.0199860	+	0.0615104i
$686$	3572.83	+	10996.0i	0.198850	+	0.611998i
$687$	−12876.2	+	9355.13i	−0.715078	+	0.519535i
$688$	−4737.94	+	3442.32i	−0.262547	+	0.190752i
$689$	−2417.20	−	7439.39i	−0.133655	−	0.411347i
$690$	99.5341	−	306.334i	0.00549159	−	0.0169014i
$691$	2814.08	+	2044.55i	0.154924	+	0.112559i	0.662547	−	0.749021i	$-0.269476\pi$
$691$	2814.08	+	2044.55i	0.154924	+	0.112559i	−0.507623	+	0.861579i	$0.669476\pi$
$692$	−10666.7			−0.585961
$693$		0			0
$694$	19255.4			1.05321
$695$	425.673	+	309.270i	0.0232327	+	0.0168795i
$696$	−1596.38	+	4913.16i	−0.0869407	+	0.267576i
$697$	6292.53	+	19366.4i	0.341961	+	1.05245i
$698$	16004.3	−	11627.8i	0.867867	−	0.630542i
$699$	−12585.6	+	9143.97i	−0.681017	+	0.494788i
$700$	1509.31	+	4645.17i	0.0814949	+	0.250815i
$701$	11077.8	−	34094.1i	0.596868	−	1.83697i	0.0516695	−	0.998664i	$-0.483546\pi$
$701$	11077.8	−	34094.1i	0.596868	−	1.83697i	0.545199	−	0.838307i	$-0.316454\pi$
$702$	−3125.62	−	2270.89i	−0.168047	−	0.122093i
$703$	2243.15			0.120344
$704$		0			0
$705$	431.587			0.0230560
$706$	−7628.15	−	5542.17i	−0.406642	−	0.295443i
$707$	3301.20	−	10160.1i	0.175608	−	0.540465i
$708$	−1598.30	−	4919.07i	−0.0848416	−	0.261116i
$709$	−28058.8	+	20385.9i	−1.48628	+	1.07984i	−0.510809	+	0.859694i	$0.670654\pi$
$709$	−28058.8	+	20385.9i	−1.48628	+	1.07984i	−0.975467	+	0.220148i	$0.929346\pi$
$710$	−69.4470	+	50.4562i	−0.00367084	+	0.00266702i
$711$	−6690.47	−	20591.2i	−0.352901	−	1.08612i
$712$	3666.06	−	11283.0i	0.192965	−	0.593886i
$713$	−19459.2	−	14137.9i	−1.02209	−	0.742595i
$714$	−7440.27			−0.389979
$715$		0			0
$716$	−1176.45			−0.0614049
$717$	745.906	+	541.932i	0.0388513	+	0.0282271i
$718$	2659.93	−	8186.42i	0.138256	−	0.425508i
$719$	−6943.93	−	21371.2i	−0.360173	−	1.10850i	−0.952949	−	0.303132i	$-0.901968\pi$
$719$	−6943.93	−	21371.2i	−0.360173	−	1.10850i	0.592775	−	0.805368i	$-0.298032\pi$
$720$	136.827	−	99.4103i	0.00708226	−	0.00514556i
$721$	−6930.44	+	5035.26i	−0.357979	+	0.260087i
$722$	−2899.17	−	8922.72i	−0.149440	−	0.459930i
$723$	1219.76	−	3754.04i	0.0627434	−	0.193104i
$724$	4003.77	+	2908.91i	0.205523	+	0.149322i
$725$	−25580.0			−1.31037
$726$		0			0
$727$	−16477.2			−0.840585			−0.420293	−	0.907389i	$-0.638073\pi$
$727$	−16477.2			−0.840585			−0.420293	+	0.907389i	$0.638073\pi$
$728$	882.946	+	641.498i	0.0449508	+	0.0326586i
$729$	3507.93	−	10796.3i	0.178222	−	0.548509i
$730$	31.5197	+	97.0078i	0.00159808	+	0.00491838i
$731$	35738.0	−	25965.2i	1.80823	−	1.31376i
$732$	3094.51	−	2248.29i	0.156252	−	0.113524i
$733$	−11764.5	−	36207.3i	−0.592811	−	1.82449i	−0.565333	−	0.824863i	$-0.691252\pi$
$733$	−11764.5	−	36207.3i	−0.592811	−	1.82449i	−0.0274784	−	0.999622i	$-0.508748\pi$
$734$	−5800.41	+	17851.8i	−0.291686	+	0.897716i
$735$	−388.506	−	282.266i	−0.0194969	−	0.0141654i
$736$	−2650.65			−0.132750
$737$		0			0
$738$	5771.56			0.287878
$739$	15768.7	+	11456.6i	0.784925	+	0.570282i	0.906453	−	0.422306i	$-0.138779\pi$
$739$	15768.7	+	11456.6i	0.784925	+	0.570282i	−0.121528	+	0.992588i	$0.538779\pi$
$740$	−36.8027	+	113.267i	−0.00182823	+	0.00562672i
$741$	630.222	+	1939.63i	0.0312440	+	0.0961591i
$742$	−8907.18	+	6471.44i	−0.440691	+	0.320181i
$743$	13866.8	−	10074.9i	0.684691	−	0.497457i	−0.190220	−	0.981742i	$-0.560920\pi$
$743$	13866.8	−	10074.9i	0.684691	−	0.497457i	0.874910	+	0.484285i	$0.160920\pi$
$744$	2258.30	+	6950.34i	0.111281	+	0.342489i
$745$	−165.356	+	508.913i	−0.00813177	+	0.0250270i
$746$	7346.47	+	5337.52i	0.360554	+	0.261958i
$747$	−14222.5			−0.696621
$748$		0			0
$749$	−8477.45			−0.413564
$750$	−785.273	−	570.534i	−0.0382321	−	0.0277773i
$751$	374.620	−	1152.96i	0.0182025	−	0.0560216i	−0.941543	−	0.336894i	$-0.890624\pi$
$751$	374.620	−	1152.96i	0.0182025	−	0.0560216i	0.959745	+	0.280872i	$0.0906237\pi$
$752$	−1097.52	−	3377.83i	−0.0532215	−	0.163799i
$753$	12846.6	−	9333.58i	0.621720	−	0.451706i
$754$	−4624.24	+	3359.70i	−0.223348	+	0.162272i
$755$	307.001	+	944.851i	0.0147985	+	0.0455452i
$756$	−1680.40	+	5171.74i	−0.0808406	+	0.248802i
$757$	−22036.2	−	16010.3i	−1.05802	−	0.768696i	−0.0842979	−	0.996441i	$-0.526865\pi$
$757$	−22036.2	−	16010.3i	−1.05802	−	0.768696i	−0.973721	+	0.227745i	$0.926865\pi$
$758$	831.913			0.0398634
$759$		0			0
$760$	−230.217			−0.0109879
$761$	−13020.0	−	9459.61i	−0.620205	−	0.450605i	0.232788	−	0.972527i	$-0.425215\pi$
$761$	−13020.0	−	9459.61i	−0.620205	−	0.450605i	−0.852993	+	0.521922i	$0.825215\pi$
$762$	−1600.85	+	4926.91i	−0.0761059	+	0.234230i
$763$	5607.87	+	17259.2i	0.266079	+	0.818907i
$764$	−12347.6	+	8971.08i	−0.584714	+	0.424820i
$765$	−1032.07	+	749.846i	−0.0487774	+	0.0354389i
$766$	−403.439	−	1241.66i	−0.0190298	−	0.0585678i
$767$	1768.42	−	5442.65i	0.0832517	−	0.256223i
$768$	651.542	+	473.373i	0.0306126	+	0.0222414i
$769$	4026.65			0.188823			0.0944113	−	0.995533i	$-0.469903\pi$
$769$	4026.65			0.188823			0.0944113	+	0.995533i	$0.469903\pi$
$770$		0			0
$771$	16781.2			0.783864
$772$	15231.3	+	11066.2i	0.710088	+	0.515909i
$773$	−6336.13	+	19500.6i	−0.294819	+	0.907358i	0.688464	+	0.725271i	$0.258285\pi$
$773$	−6336.13	+	19500.6i	−0.294819	+	0.907358i	−0.983282	+	0.182087i	$0.941715\pi$
$774$	−3869.06	−	11907.7i	−0.179678	−	0.552991i
$775$	−29275.4	+	21269.9i	−1.35691	+	0.985853i
$776$	−2504.67	+	1819.75i	−0.115866	+	0.0841819i
$777$	−458.887	−	1412.31i	−0.0211872	−	0.0652076i
$778$	−273.717	+	842.413i	−0.0126134	+	0.0388200i
$779$	−6355.87	−	4617.81i	−0.292327	−	0.212388i
$780$	−108.280			−0.00497058
$781$		0			0
$782$	19993.7			0.914287
$783$	−23040.6	−	16740.0i	−1.05160	−	0.764033i
$784$	−1221.19	+	3758.45i	−0.0556302	+	0.171212i
$785$	565.127	+	1739.28i	0.0256946	+	0.0790797i
$786$	−1595.68	+	1159.33i	−0.0724123	+	0.0526106i
$787$	19425.3	−	14113.3i	0.879844	−	0.639244i	−0.0533663	−	0.998575i	$-0.516995\pi$
$787$	19425.3	−	14113.3i	0.879844	−	0.639244i	0.933210	+	0.359331i	$0.116995\pi$
$788$	3453.88	+	10629.9i	0.156141	+	0.480553i
$789$	−703.924	+	2166.46i	−0.0317622	+	0.0977539i
$790$	−1265.88	−	919.719i	−0.0570103	−	0.0414204i
$791$	3098.20			0.139266
$792$		0			0
$793$	4232.16			0.189519
$794$	−5690.01	−	4134.04i	−0.254321	−	0.184775i
$795$	337.550	−	1038.87i	0.0150587	−	0.0463459i
$796$	−5177.52	−	15934.8i	−0.230543	−	0.709539i
$797$	12251.4	−	8901.14i	0.544499	−	0.395602i	−0.281254	−	0.959633i	$-0.590750\pi$
$797$	12251.4	−	8901.14i	0.544499	−	0.395602i	0.825753	+	0.564032i	$0.190750\pi$
$798$	2322.31	−	1687.26i	0.103019	−	0.0748475i
$799$	8278.54	+	25478.7i	0.366550	+	1.12813i
$800$	−1232.29	+	3792.60i	−0.0544601	+	0.167611i
$801$	20519.4	+	14908.2i	0.905142	+	0.657624i
$802$	8930.39			0.393196
$803$		0			0
$804$	−1355.15			−0.0594434
$805$	−405.813	−	294.841i	−0.0177678	−	0.0129090i
$806$	−2498.67	+	7690.13i	−0.109196	+	0.336071i
$807$	−3926.42	−	12084.3i	−0.171272	−	0.527121i
$808$	7056.41	−	5126.78i	0.307232	−	0.223217i
$809$	−23438.8	+	17029.3i	−1.01862	+	0.740070i	−0.965999	−	0.258544i	$-0.916757\pi$
$809$	−23438.8	+	17029.3i	−1.01862	+	0.740070i	−0.0526200	+	0.998615i	$0.516757\pi$
$810$	9.66891	+	29.7578i	0.000419421	+	0.00129084i
$811$	−10313.3	+	31741.2i	−0.446548	+	1.37433i	0.434228	+	0.900803i	$0.357021\pi$
$811$	−10313.3	+	31741.2i	−0.446548	+	1.37433i	−0.880777	+	0.473532i	$0.842979\pi$
$812$	6508.66	+	4728.82i	0.281292	+	0.204371i
$813$	7619.34			0.328686
$814$		0			0
$815$	−1501.84			−0.0645486
$816$	−4914.54	−	3570.62i	−0.210837	−	0.153182i
$817$	−5266.59	+	16208.9i	−0.225526	+	0.694097i
$818$	3390.93	+	10436.2i	0.144940	+	0.446080i
$819$	−1887.66	+	1371.47i	−0.0805376	+	0.0585140i
$820$	337.453	−	245.174i	0.0143712	−	0.0104413i
$821$	9881.72	+	30412.8i	0.420066	+	1.29283i	0.907640	+	0.419749i	$0.137882\pi$
$821$	9881.72	+	30412.8i	0.420066	+	1.29283i	−0.487574	+	0.873082i	$0.662118\pi$
$822$	3647.73	−	11226.6i	0.154780	−	0.476364i
$823$	−2151.54	−	1563.18i	−0.0911275	−	0.0662080i	0.541289	−	0.840837i	$-0.317937\pi$
$823$	−2151.54	−	1563.18i	−0.0911275	−	0.0662080i	−0.632416	+	0.774629i	$0.717937\pi$
$824$	−6994.21			−0.295698
$825$		0			0
$826$	−8054.82			−0.339301
$827$	32355.8	+	23507.9i	1.36049	+	0.988451i	0.998414	+	0.0563013i	$0.0179307\pi$
$827$	32355.8	+	23507.9i	1.36049	+	0.988451i	0.362073	+	0.932150i	$0.382069\pi$
$828$	1751.16	−	5389.51i	0.0734987	−	0.226206i
$829$	286.177	+	880.763i	0.0119896	+	0.0369001i	0.956872	−	0.290509i	$-0.0938246\pi$
$829$	286.177	+	880.763i	0.0119896	+	0.0369001i	−0.944883	+	0.327409i	$0.893825\pi$
$830$	−831.566	+	604.168i	−0.0347760	+	0.0252662i
$831$	11167.3	−	8113.48i	0.466171	−	0.338693i
$832$	275.356	+	847.459i	0.0114739	+	0.0353129i
$833$	9211.39	−	28349.7i	0.383140	−	1.17918i
$834$	−4333.50	−	3148.47i	−0.179924	−	0.130723i
$835$	−697.029			−0.0288882
$836$		0			0
$837$	−40288.5			−1.66377
$838$	8306.63	+	6035.12i	0.342420	+	0.248782i
$839$	6314.88	−	19435.2i	0.259849	−	0.799734i	−0.732986	−	0.680244i	$-0.761874\pi$
$839$	6314.88	−	19435.2i	0.259849	−	0.799734i	0.992835	−	0.119491i	$-0.0381261\pi$
$840$	47.0959	+	144.946i	0.00193448	+	0.00595372i
$841$	−14356.6	+	10430.7i	−0.588650	+	0.427679i
$842$	9739.60	−	7076.24i	0.398633	−	0.289624i
$843$	−42.1982	−	129.873i	−0.00172406	−	0.00530611i
$844$	1038.83	−	3197.18i	0.0423672	−	0.130393i
$845$	1001.58	+	727.687i	0.0407754	+	0.0296251i
$846$	7593.15			0.308579
$847$		0			0
$848$	−8989.15			−0.364019
$849$	4513.41	+	3279.18i	0.182450	+	0.132557i
$850$	9295.09	−	28607.3i	0.375081	−	1.15438i
$851$	1233.13	+	3795.19i	0.0496724	+	0.152876i
$852$	706.994	−	513.661i	0.0284287	−	0.0206546i
$853$	−32175.7	+	23377.0i	−1.29153	+	0.938351i	−0.999835	−	0.0181612i	$-0.994219\pi$
$853$	−32175.7	+	23377.0i	−1.29153	+	0.938351i	−0.291694	+	0.956512i	$0.594219\pi$
$854$	−1840.76	−	5665.26i	−0.0737580	−	0.227004i
$855$	152.093	−	468.095i	0.00608360	−	0.0187234i
$856$	−5599.63	−	4068.37i	−0.223588	−	0.162446i
$857$	3490.30			0.139121			0.0695604	−	0.997578i	$-0.477840\pi$
$857$	3490.30			0.139121			0.0695604	+	0.997578i	$0.477840\pi$
$858$		0			0
$859$	2730.16			0.108442			0.0542210	−	0.998529i	$-0.482732\pi$
$859$	2730.16			0.108442			0.0542210	+	0.998529i	$0.482732\pi$
$860$	−732.053	−	531.867i	−0.0290265	−	0.0210890i
$861$	−1607.18	+	4946.39i	−0.0636150	+	0.195787i
$862$	8147.04	+	25074.0i	0.321913	+	0.990747i
$863$	16170.9	−	11748.9i	0.637850	−	0.463425i	−0.221261	−	0.975215i	$-0.571017\pi$
$863$	16170.9	−	11748.9i	0.637850	−	0.463425i	0.859111	+	0.511789i	$0.171017\pi$
$864$	−3591.89	+	2609.66i	−0.141434	+	0.102758i
$865$	−509.287	−	1567.43i	−0.0200188	−	0.0616116i
$866$	−2278.90	+	7013.72i	−0.0894227	+	0.275215i
$867$	24566.0	+	17848.2i	0.962290	+	0.699144i
$868$	11381.0			0.445040
$869$		0			0
$870$	−798.191			−0.0311048
$871$	−1213.03	−	881.321i	−0.0471896	−	0.0342852i
$872$	−4578.61	+	14091.5i	−0.177811	+	0.547246i
$873$	−2045.34	−	6294.91i	−0.0792947	−	0.244044i
$874$	−6240.57	+	4534.04i	−0.241522	+	0.175476i
$875$	−1222.93	+	888.507i	−0.0472485	+	0.0343280i
$876$	−320.882	−	987.572i	−0.0123762	−	0.0380901i
$877$	−1932.05	+	5946.23i	−0.0743907	+	0.228951i	−0.981337	−	0.192295i	$-0.938407\pi$
$877$	−1932.05	+	5946.23i	−0.0743907	+	0.228951i	0.906947	+	0.421246i	$0.138407\pi$
$878$	17281.9	+	12556.0i	0.664278	+	0.482626i
$879$	6621.80			0.254093
$880$		0			0
$881$	−22948.7			−0.877595			−0.438797	−	0.898586i	$-0.644595\pi$
$881$	−22948.7			−0.877595			−0.438797	+	0.898586i	$0.644595\pi$
$882$	−6835.19	−	4966.06i	−0.260944	−	0.189587i
$883$	−8952.27	+	27552.2i	−0.341187	+	1.05006i	0.622407	+	0.782694i	$0.286155\pi$
$883$	−8952.27	+	27552.2i	−0.341187	+	1.05006i	−0.963594	+	0.267371i	$0.913845\pi$
$884$	−2076.99	−	6392.33i	−0.0790235	−	0.243209i
$885$	646.526	−	469.729i	0.0245568	−	0.0178415i
$886$	19493.6	−	14162.9i	0.739164	−	0.537034i
$887$	2616.31	+	8052.16i	0.0990383	+	0.304809i	0.988285	−	0.152619i	$-0.0487708\pi$
$887$	2616.31	+	8052.16i	0.0990383	+	0.304809i	−0.889247	+	0.457428i	$0.848771\pi$
$888$	374.664	−	1153.10i	0.0141587	−	0.0435759i
$889$	6526.88	+	4742.06i	0.246237	+	0.178902i
$890$	1833.03			0.0690374
$891$		0			0
$892$	−20825.9			−0.781728
$893$	−8361.87	−	6075.25i	−0.313348	−	0.227660i
$894$	1683.38	−	5180.90i	0.0629760	−	0.193820i
$895$	−56.1703	−	172.875i	−0.00209784	−	0.00645649i
$896$	1014.66	−	737.195i	0.0378320	−	0.0274866i
$897$	−2935.20	+	2132.54i	−0.109257	+	0.0793797i
$898$	3881.37	+	11945.6i	0.144235	+	0.443909i
$899$	−18419.1	+	56688.0i	−0.683326	+	2.10306i
$900$	−6897.30	−	5011.18i	−0.255456	−	0.185599i
$901$	67804.5			2.50710
$902$		0			0
$903$	11282.6			0.415795
$904$	2046.46	+	1486.84i	0.0752923	+	0.0547031i
$905$	−236.291	+	727.227i	−0.00867907	+	0.0267114i
$906$	−3125.37	−	9618.90i	−0.114607	−	0.352723i
$907$	15571.7	−	11313.5i	0.570068	−	0.414178i	−0.265062	−	0.964231i	$-0.585392\pi$
$907$	15571.7	−	11313.5i	0.570068	−	0.414178i	0.835130	+	0.550053i	$0.185392\pi$
$908$	−2967.90	+	2156.31i	−0.108473	+	0.0788101i
$909$	5762.34	+	17734.7i	0.210258	+	0.647109i
$910$	−52.1088	+	160.374i	−0.00189823	+	0.00584215i
$911$	37369.2	+	27150.3i	1.35905	+	0.987410i	0.998505	+	0.0546689i	$0.0174103\pi$
$911$	37369.2	+	27150.3i	1.35905	+	0.987410i	0.360548	+	0.932741i	$0.382590\pi$
$912$	2343.68			0.0850955
$913$		0			0
$914$	−15510.8			−0.561324
$915$	478.128	+	347.381i	0.0172748	+	0.0125509i
$916$	−6253.58	+	19246.5i	−0.225572	+	0.694240i
$917$	949.184	+	2921.29i	0.0341819	+	0.105201i
$918$	27093.4	−	19684.5i	0.974092	−	0.707719i
$919$	40315.0	−	29290.6i	1.44708	−	1.05137i	0.460580	−	0.887618i	$-0.347641\pi$
$919$	40315.0	−	29290.6i	1.44708	−	1.05137i	0.986502	−	0.163749i	$-0.0523587\pi$
$920$	−126.557	−	389.503i	−0.00453529	−	0.0139582i
$921$	7456.53	−	22948.8i	0.266776	−	0.821053i
$922$	−9343.59	−	6788.52i	−0.333747	−	0.242481i
$923$	966.910			0.0344813
$924$		0			0
$925$	6003.51			0.213399
$926$	16189.5	+	11762.4i	0.574537	+	0.417425i
$927$	4620.74	−	14221.2i	0.163716	−	0.503867i
$928$	2029.80	+	6247.07i	0.0718010	+	0.220981i
$929$	−26151.1	+	18999.9i	−0.923561	+	0.671007i	−0.944408	−	0.328776i	$-0.893364\pi$
$929$	−26151.1	+	18999.9i	−0.923561	+	0.671007i	0.0208466	+	0.999783i	$0.493364\pi$
$930$	−913.502	+	663.698i	−0.0322096	+	0.0234016i
$931$	3553.85	+	10937.6i	0.125105	+	0.385034i
$932$	−6112.43	+	18812.1i	−0.214828	+	0.661171i
$933$	12188.9	+	8855.74i	0.427702	+	0.310744i
$934$	2428.32			0.0850717
$935$		0			0
$936$	−1905.03			−0.0665257
$937$	−10102.2	−	7339.69i	−0.352215	−	0.255899i	0.397583	−	0.917566i	$-0.369849\pi$
$937$	−10102.2	−	7339.69i	−0.352215	−	0.255899i	−0.749797	+	0.661667i	$0.769849\pi$
$938$	−652.153	+	2007.12i	−0.0227010	+	0.0698665i
$939$	3886.30	+	11960.8i	0.135064	+	0.415683i
$940$	443.957	−	322.554i	0.0154046	−	0.0111921i
$941$	23598.2	−	17145.1i	0.817514	−	0.593959i	−0.0984854	−	0.995138i	$-0.531400\pi$
$941$	23598.2	−	17145.1i	0.817514	−	0.593959i	0.915999	+	0.401180i	$0.131400\pi$
$942$	−5753.18	−	17706.5i	−0.198990	−	0.612429i
$943$	4318.85	−	13292.0i	0.149142	−	0.459012i
$944$	−5320.46	−	3865.54i	−0.183439	−	0.133276i
$945$	−840.199			−0.0289224
$946$		0			0
$947$	41085.7			1.40983			0.704913	−	0.709294i	$-0.250986\pi$
$947$	41085.7			1.40983			0.704913	+	0.709294i	$0.250986\pi$
$948$	12887.1	+	9363.05i	0.441513	+	0.320778i
$949$	355.036	−	1092.69i	0.0121443	−	0.0373764i
$950$	3586.14	+	11037.0i	0.122474	+	0.376935i
$951$	16934.6	−	12303.7i	0.577437	−	0.419532i
$952$	−7653.53	+	5560.62i	−0.260559	+	0.189307i
$953$	−5383.87	−	16569.8i	−0.183002	−	0.563221i	0.816906	−	0.576770i	$-0.195687\pi$
$953$	−5383.87	−	16569.8i	−0.183002	−	0.563221i	−0.999908	+	0.0135487i	$0.995687\pi$
$954$	5938.70	−	18277.4i	0.201543	−	0.620287i
$955$	−1907.81	−	1386.11i	−0.0646444	−	0.0469669i
$956$	1172.31			0.0396602
$957$		0			0
$958$	−18296.1			−0.617037
$959$	−14872.3	−	10805.3i	−0.500783	−	0.363840i
$960$	−38.4520	+	118.343i	−0.00129274	+	0.00397866i
$961$	16850.4	+	51860.0i	0.565619	+	1.74080i
$962$	1085.29	−	788.507i	0.0363732	−	0.0264267i
$963$	11971.5	−	8697.83i	0.400599	−	0.291052i
$964$	−1550.92	−	4773.25i	−0.0518173	−	0.159477i
$965$	−898.908	+	2766.55i	−0.0299864	+	0.0922886i
$966$	4131.32	+	3001.58i	0.137601	+	0.0999733i
$967$	39352.0			1.30866			0.654330	−	0.756209i	$-0.272951\pi$
$967$	39352.0			1.30866			0.654330	+	0.756209i	$0.272951\pi$
$968$		0			0
$969$	−17678.3			−0.586076
$970$	−386.993	−	281.167i	−0.0128099	−	0.00930692i
$971$	4841.14	−	14899.5i	0.160000	−	0.492428i	−0.838633	−	0.544696i	$-0.816645\pi$
$971$	4841.14	−	14899.5i	0.160000	−	0.492428i	0.998633	+	0.0522678i	$0.0166449\pi$
$972$	−4728.87	−	14554.0i	−0.156048	−	0.480266i
$973$	−6748.67	+	4903.19i	−0.222356	+	0.161551i
$974$	5342.41	−	3881.48i	0.175751	−	0.127691i
$975$	1686.71	+	5191.16i	0.0554030	+	0.170513i
$976$	1502.91	−	4625.47i	0.0492898	−	0.151699i
$977$	40008.2	+	29067.7i	1.31011	+	0.951849i	0.999999	+	0.00114792i	$0.000365393\pi$
$977$	40008.2	+	29067.7i	1.31011	+	0.951849i	0.310109	+	0.950701i	$0.399635\pi$
$978$	15289.2			0.499893
$979$		0			0
$980$	−610.597			−0.0199029
$981$	−25627.1	−	18619.2i	−0.834057	−	0.605978i
$982$	2438.71	−	7505.58i	0.0792489	−	0.243903i
$983$	−15589.3	−	47979.1i	−0.505822	−	1.55676i	−0.799385	−	0.600820i	$-0.794841\pi$
$983$	−15589.3	−	47979.1i	−0.505822	−	1.55676i	0.293563	−	0.955940i	$-0.405159\pi$
$984$	−3435.38	+	2495.95i	−0.111297	+	0.0808618i
$985$	−1397.12	+	1015.07i	−0.0451939	+	0.0328353i
$986$	−15310.6	−	47121.2i	−0.494512	−	1.52195i
$987$	−2114.43	+	6507.53i	−0.0681894	+	0.209865i
$988$	2097.90	+	1524.21i	0.0675537	+	0.0490806i
$989$	−30319.0			−0.974811
$990$		0			0
$991$	−37174.1			−1.19160			−0.595799	−	0.803134i	$-0.703164\pi$
$991$	−37174.1			−1.19160			−0.595799	+	0.803134i	$0.703164\pi$
$992$	7517.49	+	5461.77i	0.240605	+	0.174810i
$993$	−9972.81	+	30693.1i	−0.318708	+	0.980884i
$994$	−420.552	−	1294.33i	−0.0134196	−	0.0413014i
$995$	2094.35	−	1521.63i	0.0667290	−	0.0484815i
$996$	8465.63	−	6150.64i	0.269321	−	0.195673i
$997$	11853.4	+	36481.0i	0.376531	+	1.15884i	0.942440	+	0.334375i	$0.108525\pi$
$997$	11853.4	+	36481.0i	0.376531	+	1.15884i	−0.565910	+	0.824467i	$0.691475\pi$
$998$	6437.56	−	19812.8i	0.204186	−	0.628419i
$999$	5407.52	+	3928.79i	0.171258	+	0.124426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.4.c.f.81.1		4
11.2	odd	10		242.4.c.j.27.1		4
11.3	even	5	inner	242.4.c.f.3.1		4
11.4	even	5		22.4.c.a.9.1	yes	4
11.5	even	5		242.4.a.k.1.2		2
11.6	odd	10		242.4.a.h.1.2		2
11.7	odd	10		242.4.c.j.9.1		4
11.8	odd	10		242.4.c.m.3.1		4
11.9	even	5		22.4.c.a.5.1	✓	4
11.10	odd	2		242.4.c.m.81.1		4
33.5	odd	10		2178.4.a.z.1.1		2
33.17	even	10		2178.4.a.bi.1.1		2
33.20	odd	10		198.4.f.b.181.1		4
33.26	odd	10		198.4.f.b.163.1		4
44.15	odd	10		176.4.m.a.97.1		4
44.27	odd	10		1936.4.a.bb.1.1		2
44.31	odd	10		176.4.m.a.49.1		4
44.39	even	10		1936.4.a.bc.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.4.c.a.5.1	✓	4	11.9	even	5
22.4.c.a.9.1	yes	4	11.4	even	5
176.4.m.a.49.1		4	44.31	odd	10
176.4.m.a.97.1		4	44.15	odd	10
198.4.f.b.163.1		4	33.26	odd	10
198.4.f.b.181.1		4	33.20	odd	10
242.4.a.h.1.2		2	11.6	odd	10
242.4.a.k.1.2		2	11.5	even	5
242.4.c.f.3.1		4	11.3	even	5	inner
242.4.c.f.81.1		4	1.1	even	1	trivial
242.4.c.j.9.1		4	11.7	odd	10
242.4.c.j.27.1		4	11.2	odd	10
242.4.c.m.3.1		4	11.8	odd	10
242.4.c.m.81.1		4	11.10	odd	2
1936.4.a.bb.1.1		2	44.27	odd	10
1936.4.a.bc.1.1		2	44.39	even	10
2178.4.a.z.1.1		2	33.5	odd	10
2178.4.a.bi.1.1		2	33.17	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:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	242.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.61803 - 1.17557i) q^{2} +(-0.972136 + 2.99193i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-0.500000 + 0.363271i) q^{5} +(5.09017 - 3.69822i) q^{6} +(-3.02786 - 9.31881i) q^{7} +(2.47214 - 7.60845i) q^{8} +(13.8369 + 10.0531i) q^{9} +O(q^{10})\)	\(q+(-1.61803 - 1.17557i) q^{2} +(-0.972136 + 2.99193i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-0.500000 + 0.363271i) q^{5} +(5.09017 - 3.69822i) q^{6} +(-3.02786 - 9.31881i) q^{7} +(2.47214 - 7.60845i) q^{8} +(13.8369 + 10.0531i) q^{9} +1.23607 q^{10} -12.5836 q^{12} +(-11.2639 - 8.18373i) q^{13} +(-6.05573 + 18.6376i) q^{14} +(-0.600813 - 1.84911i) q^{15} +(-12.9443 + 9.40456i) q^{16} +(97.6378 - 70.9380i) q^{17} +(-10.5704 - 32.5325i) q^{18} +(-14.3885 + 44.2834i) q^{19} +(-2.00000 - 1.45309i) q^{20} +30.8247 q^{21} -82.8328 q^{23} +(20.3607 + 14.7929i) q^{24} +(-38.5091 + 118.519i) q^{25} +(8.60488 + 26.4831i) q^{26} +(-112.247 + 81.5520i) q^{27} +(31.7082 - 23.0374i) q^{28} +(63.4311 + 195.221i) q^{29} +(-1.20163 + 3.69822i) q^{30} +(234.921 + 170.680i) q^{31} +32.0000 q^{32} -241.374 q^{34} +(4.89919 + 3.55947i) q^{35} +(-21.1409 + 65.0649i) q^{36} +(-14.8870 - 45.8174i) q^{37} +(75.3394 - 54.7373i) q^{38} +(35.4352 - 25.7452i) q^{39} +(1.52786 + 4.70228i) q^{40} +(-52.1393 + 160.468i) q^{41} +(-49.8754 - 36.2366i) q^{42} +366.026 q^{43} -10.5704 q^{45} +(134.026 + 97.3758i) q^{46} +(-68.5952 + 211.114i) q^{47} +(-15.5542 - 47.8708i) q^{48} +(199.821 - 145.178i) q^{49} +(201.636 - 146.497i) q^{50} +(117.324 + 361.086i) q^{51} +(17.2098 - 52.9662i) q^{52} +(454.523 + 330.230i) q^{53} +277.489 q^{54} -78.3870 q^{56} +(-118.505 - 86.0989i) q^{57} +(126.862 - 390.442i) q^{58} +(127.015 + 390.911i) q^{59} +(6.29180 - 4.57126i) q^{60} +(-245.916 + 178.669i) q^{61} +(-179.464 - 552.333i) q^{62} +(51.7865 - 159.383i) q^{63} +(-51.7771 - 37.6183i) q^{64} +8.60488 q^{65} +107.692 q^{67} +(390.551 + 283.752i) q^{68} +(80.5248 - 247.830i) q^{69} +(-3.74265 - 11.5187i) q^{70} +(-56.1838 + 40.8199i) q^{71} +(110.695 - 80.4247i) q^{72} +(25.5000 + 78.4809i) q^{73} +(-29.7740 + 91.6349i) q^{74} +(-317.163 - 230.433i) q^{75} -186.249 q^{76} -87.6006 q^{78} +(-1024.12 - 744.068i) q^{79} +(3.05573 - 9.40456i) q^{80} +(7.82231 + 24.0746i) q^{81} +(273.005 - 198.350i) q^{82} +(-672.751 + 488.782i) q^{83} +(38.1014 + 117.264i) q^{84} +(-23.0492 + 70.9380i) q^{85} +(-592.243 - 430.290i) q^{86} -645.750 q^{87} +1482.95 q^{89} +(17.1033 + 12.4263i) q^{90} +(-42.1569 + 129.746i) q^{91} +(-102.387 - 315.115i) q^{92} +(-739.039 + 536.943i) q^{93} +(359.169 - 260.952i) q^{94} +(-8.89261 - 27.3686i) q^{95} +(-31.1084 + 95.7417i) q^{96} +(-313.084 - 227.469i) q^{97} -493.984 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 14 q^{3} - 4 q^{4} - 2 q^{5} - 2 q^{6} - 30 q^{7} - 8 q^{8} + 71 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 14 * q^3 - 4 * q^4 - 2 * q^5 - 2 * q^6 - 30 * q^7 - 8 * q^8 + 71 * q^9	\( 4 q - 2 q^{2} + 14 q^{3} - 4 q^{4} - 2 q^{5} - 2 q^{6} - 30 q^{7} - 8 q^{8} + 71 q^{9} - 4 q^{10} - 104 q^{12} - 54 q^{13} - 60 q^{14} - 27 q^{15} - 16 q^{16} + 158 q^{17} - 248 q^{18} + 14 q^{19} - 8 q^{20} - 230 q^{21} - 224 q^{23} - 8 q^{24} + 121 q^{25} + 182 q^{26} - 487 q^{27} + 100 q^{28} + 370 q^{29} - 54 q^{30} + 488 q^{31} + 128 q^{32} - 724 q^{34} - 5 q^{35} - 496 q^{36} + 334 q^{37} + 118 q^{38} + 381 q^{39} + 24 q^{40} - 298 q^{41} - 280 q^{42} + 1160 q^{43} - 248 q^{45} + 232 q^{46} + 146 q^{47} + 224 q^{48} + 323 q^{49} + 252 q^{50} - 727 q^{51} + 364 q^{52} + 870 q^{53} - 1144 q^{54} + 80 q^{56} - 76 q^{57} + 740 q^{58} + 678 q^{59} + 52 q^{60} - 930 q^{61} - 454 q^{62} - 1575 q^{63} - 64 q^{64} + 182 q^{65} - 88 q^{67} + 632 q^{68} - 304 q^{69} + 70 q^{70} + 540 q^{71} + 568 q^{72} + 102 q^{73} + 668 q^{74} + 111 q^{75} - 584 q^{76} + 1832 q^{78} - 2008 q^{79} + 48 q^{80} - 3694 q^{81} + 694 q^{82} - 1488 q^{83} + 1020 q^{84} - 204 q^{85} - 920 q^{86} + 1670 q^{87} + 1728 q^{89} - 106 q^{90} + 1135 q^{91} - 16 q^{92} - 1657 q^{93} + 502 q^{94} - 87 q^{95} + 448 q^{96} - 1306 q^{97} - 1484 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 14 * q^3 - 4 * q^4 - 2 * q^5 - 2 * q^6 - 30 * q^7 - 8 * q^8 + 71 * q^9 - 4 * q^10 - 104 * q^12 - 54 * q^13 - 60 * q^14 - 27 * q^15 - 16 * q^16 + 158 * q^17 - 248 * q^18 + 14 * q^19 - 8 * q^20 - 230 * q^21 - 224 * q^23 - 8 * q^24 + 121 * q^25 + 182 * q^26 - 487 * q^27 + 100 * q^28 + 370 * q^29 - 54 * q^30 + 488 * q^31 + 128 * q^32 - 724 * q^34 - 5 * q^35 - 496 * q^36 + 334 * q^37 + 118 * q^38 + 381 * q^39 + 24 * q^40 - 298 * q^41 - 280 * q^42 + 1160 * q^43 - 248 * q^45 + 232 * q^46 + 146 * q^47 + 224 * q^48 + 323 * q^49 + 252 * q^50 - 727 * q^51 + 364 * q^52 + 870 * q^53 - 1144 * q^54 + 80 * q^56 - 76 * q^57 + 740 * q^58 + 678 * q^59 + 52 * q^60 - 930 * q^61 - 454 * q^62 - 1575 * q^63 - 64 * q^64 + 182 * q^65 - 88 * q^67 + 632 * q^68 - 304 * q^69 + 70 * q^70 + 540 * q^71 + 568 * q^72 + 102 * q^73 + 668 * q^74 + 111 * q^75 - 584 * q^76 + 1832 * q^78 - 2008 * q^79 + 48 * q^80 - 3694 * q^81 + 694 * q^82 - 1488 * q^83 + 1020 * q^84 - 204 * q^85 - 920 * q^86 + 1670 * q^87 + 1728 * q^89 - 106 * q^90 + 1135 * q^91 - 16 * q^92 - 1657 * q^93 + 502 * q^94 - 87 * q^95 + 448 * q^96 - 1306 * q^97 - 1484 * q^98

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