LMFDB - Embedded newform 242.4.c.r.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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 71x^{6} - 141x^{5} + 2911x^{4} + 2710x^{3} + 75340x^{2} + 169400x + 5856400 $ x^8 - x^7 + 71x^6 - 141x^5 + 2911x^4 + 2710x^3 + 75340x^2 + 169400x + 5856400
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			$2.22300 + 6.84169i$ of defining polynomial
Character	$\chi$	$=$	242.81
Dual form			242.4.c.r.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61803 + 1.17557i) q^{2} +(-2.41398 + 7.42948i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-12.0690 + 8.76866i) q^{5} +(-12.6398 + 9.18334i) q^{6} +(6.72664 + 20.7025i) q^{7} +(-2.47214 + 7.60845i) q^{8} +(-27.5264 - 19.9991i) q^{9} +O(q^{10})$	\(q+(1.61803 + 1.17557i) q^{2} +(-2.41398 + 7.42948i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-12.0690 + 8.76866i) q^{5} +(-12.6398 + 9.18334i) q^{6} +(6.72664 + 20.7025i) q^{7} +(-2.47214 + 7.60845i) q^{8} +(-27.5264 - 19.9991i) q^{9} -29.8363 q^{10} -31.2473 q^{12} +(35.6199 + 25.8793i) q^{13} +(-13.4533 + 41.4049i) q^{14} +(-36.0121 - 110.834i) q^{15} +(-12.9443 + 9.40456i) q^{16} +(20.1563 - 14.6444i) q^{17} +(-21.0283 - 64.7184i) q^{18} +(6.78516 - 20.8826i) q^{19} +(-48.2761 - 35.0746i) q^{20} -170.046 q^{21} +177.749 q^{23} +(-50.5591 - 36.7334i) q^{24} +(30.1449 - 92.7763i) q^{25} +(27.2111 + 83.7473i) q^{26} +(44.3938 - 32.2540i) q^{27} +(-70.4423 + 51.1793i) q^{28} +(-46.1660 - 142.084i) q^{29} +(72.0243 - 221.668i) q^{30} +(-60.7925 - 44.1683i) q^{31} -32.0000 q^{32} +49.8290 q^{34} +(-262.717 - 190.875i) q^{35} +(42.0565 - 129.437i) q^{36} +(68.7057 + 211.455i) q^{37} +(35.5276 - 25.8123i) q^{38} +(-278.256 + 202.165i) q^{39} +(-36.8797 - 113.504i) q^{40} +(-78.2188 + 240.733i) q^{41} +(-275.141 - 199.902i) q^{42} +130.623 q^{43} +507.582 q^{45} +(287.604 + 208.957i) q^{46} +(154.228 - 474.666i) q^{47} +(-38.6237 - 118.872i) q^{48} +(-105.851 + 76.9055i) q^{49} +(157.841 - 114.678i) q^{50} +(60.1432 + 185.102i) q^{51} +(-54.4223 + 167.495i) q^{52} +(-10.4704 - 7.60718i) q^{53} +109.748 q^{54} -174.143 q^{56} +(138.767 + 100.820i) q^{57} +(92.3320 - 284.169i) q^{58} +(10.9891 + 33.8209i) q^{59} +(377.124 - 273.997i) q^{60} +(-435.529 + 316.430i) q^{61} +(-46.4413 - 142.932i) q^{62} +(228.870 - 704.390i) q^{63} +(-51.7771 - 37.6183i) q^{64} -656.824 q^{65} -519.621 q^{67} +(80.6250 + 58.5775i) q^{68} +(-429.083 + 1320.58i) q^{69} +(-200.698 - 617.684i) q^{70} +(-63.4663 + 46.1109i) q^{71} +(220.211 - 159.993i) q^{72} +(353.537 + 1088.07i) q^{73} +(-137.411 + 422.909i) q^{74} +(616.511 + 447.921i) q^{75} +87.8290 q^{76} -687.886 q^{78} +(-625.003 - 454.091i) q^{79} +(73.7593 - 227.008i) q^{80} +(-151.417 - 466.014i) q^{81} +(-409.559 + 297.562i) q^{82} +(-434.638 + 315.783i) q^{83} +(-210.189 - 646.895i) q^{84} +(-114.855 + 353.487i) q^{85} +(211.353 + 153.557i) q^{86} +1167.06 q^{87} +667.089 q^{89} +(821.284 + 596.698i) q^{90} +(-296.164 + 911.499i) q^{91} +(219.710 + 676.198i) q^{92} +(474.899 - 345.035i) q^{93} +(807.550 - 586.720i) q^{94} +(101.222 + 311.529i) q^{95} +(77.2475 - 237.743i) q^{96} +(145.343 + 105.598i) q^{97} -261.679 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 7 q^{3} - 8 q^{4} - 30 q^{5} - 6 q^{6} + 4 q^{7} + 16 q^{8} - 81 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 - 7 * q^3 - 8 * q^4 - 30 * q^5 - 6 * q^6 + 4 * q^7 + 16 * q^8 - 81 * q^9	\( 8 q + 4 q^{2} - 7 q^{3} - 8 q^{4} - 30 q^{5} - 6 q^{6} + 4 q^{7} + 16 q^{8} - 81 q^{9} - 100 q^{10} + 32 q^{12} - 48 q^{13} - 8 q^{14} - 279 q^{15} - 32 q^{16} - 109 q^{17} + 42 q^{18} + 288 q^{19} - 120 q^{20} - 50 q^{21} + 628 q^{23} - 24 q^{24} + 38 q^{25} - 14 q^{26} + 242 q^{27} - 4 q^{28} + 528 q^{29} + 558 q^{30} - 522 q^{31} - 256 q^{32} + 208 q^{34} - 17 q^{35} - 84 q^{36} - 406 q^{37} + 544 q^{38} - 1429 q^{39} - 40 q^{40} - 329 q^{41} - 1480 q^{42} + 1442 q^{43} + 2652 q^{45} + 1044 q^{46} + 666 q^{47} - 112 q^{48} - 114 q^{49} + 34 q^{50} + 1158 q^{51} + 28 q^{52} + 414 q^{53} - 1144 q^{54} + 48 q^{56} - 593 q^{57} - 1056 q^{58} - 888 q^{59} + 844 q^{60} - 302 q^{61} - 646 q^{62} - 2061 q^{63} - 128 q^{64} - 138 q^{65} + 578 q^{67} - 436 q^{68} + 1930 q^{69} + 1394 q^{70} + 1090 q^{71} + 648 q^{72} + 253 q^{73} + 812 q^{74} + 2763 q^{75} - 128 q^{76} - 4152 q^{78} - 674 q^{79} + 80 q^{80} - 230 q^{81} - 722 q^{82} - 428 q^{83} - 2860 q^{84} + 1046 q^{85} - 984 q^{86} + 2122 q^{87} - 2202 q^{89} + 1366 q^{90} - 2217 q^{91} + 832 q^{92} - 3721 q^{93} + 2138 q^{94} - 973 q^{95} + 224 q^{96} + 3012 q^{97} - 3292 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 7 * q^3 - 8 * q^4 - 30 * q^5 - 6 * q^6 + 4 * q^7 + 16 * q^8 - 81 * q^9 - 100 * q^10 + 32 * q^12 - 48 * q^13 - 8 * q^14 - 279 * q^15 - 32 * q^16 - 109 * q^17 + 42 * q^18 + 288 * q^19 - 120 * q^20 - 50 * q^21 + 628 * q^23 - 24 * q^24 + 38 * q^25 - 14 * q^26 + 242 * q^27 - 4 * q^28 + 528 * q^29 + 558 * q^30 - 522 * q^31 - 256 * q^32 + 208 * q^34 - 17 * q^35 - 84 * q^36 - 406 * q^37 + 544 * q^38 - 1429 * q^39 - 40 * q^40 - 329 * q^41 - 1480 * q^42 + 1442 * q^43 + 2652 * q^45 + 1044 * q^46 + 666 * q^47 - 112 * q^48 - 114 * q^49 + 34 * q^50 + 1158 * q^51 + 28 * q^52 + 414 * q^53 - 1144 * q^54 + 48 * q^56 - 593 * q^57 - 1056 * q^58 - 888 * q^59 + 844 * q^60 - 302 * q^61 - 646 * q^62 - 2061 * q^63 - 128 * q^64 - 138 * q^65 + 578 * q^67 - 436 * q^68 + 1930 * q^69 + 1394 * q^70 + 1090 * q^71 + 648 * q^72 + 253 * q^73 + 812 * q^74 + 2763 * q^75 - 128 * q^76 - 4152 * q^78 - 674 * q^79 + 80 * q^80 - 230 * q^81 - 722 * q^82 - 428 * q^83 - 2860 * q^84 + 1046 * q^85 - 984 * q^86 + 2122 * q^87 - 2202 * q^89 + 1366 * q^90 - 2217 * q^91 + 832 * q^92 - 3721 * q^93 + 2138 * q^94 - 973 * q^95 + 224 * q^96 + 3012 * q^97 - 3292 * 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
$3$	−2.41398	+	7.42948i	−0.464571	+	1.42980i	0.394949	+	0.918703i	$0.370762\pi$
$3$	−2.41398	+	7.42948i	−0.464571	+	1.42980i	−0.859521	+	0.511101i	$0.829238\pi$
$4$	1.23607	+	3.80423i	0.154508	+	0.475528i
$5$	−12.0690	+	8.76866i	−1.07949	+	0.784293i	−0.977593	−	0.210502i	$-0.932490\pi$
$5$	−12.0690	+	8.76866i	−1.07949	+	0.784293i	−0.101893	+	0.994795i	$0.532490\pi$
$6$	−12.6398	+	9.18334i	−0.860028	+	0.624847i
$7$	6.72664	+	20.7025i	0.363204	+	1.11783i	0.951098	+	0.308890i	$0.0999573\pi$
$7$	6.72664	+	20.7025i	0.363204	+	1.11783i	−0.587894	+	0.808938i	$0.700043\pi$
$8$	−2.47214	+	7.60845i	−0.109254	+	0.336249i
$9$	−27.5264	−	19.9991i	−1.01950	−	0.740706i
$10$	−29.8363			−0.943506
$11$		0			0
$11$		0			0
$12$	−31.2473			−0.751692
$13$	35.6199	+	25.8793i	0.759936	+	0.552126i	0.898891	−	0.438173i	$-0.144374\pi$
$13$	35.6199	+	25.8793i	0.759936	+	0.552126i	−0.138955	+	0.990299i	$0.544374\pi$
$14$	−13.4533	+	41.4049i	−0.256824	+	0.790424i
$15$	−36.0121	−	110.834i	−0.619886	−	1.90781i
$16$	−12.9443	+	9.40456i	−0.202254	+	0.146946i
$17$	20.1563	−	14.6444i	0.287565	−	0.208928i	−0.434645	−	0.900602i	$-0.643126\pi$
$17$	20.1563	−	14.6444i	0.287565	−	0.208928i	0.722210	+	0.691673i	$0.243126\pi$
$18$	−21.0283	−	64.7184i	−0.275356	−	0.847459i
$19$	6.78516	−	20.8826i	0.0819275	−	0.252147i	−0.901699	−	0.432363i	$-0.857680\pi$
$19$	6.78516	−	20.8826i	0.0819275	−	0.252147i	0.983627	+	0.180216i	$0.0576798\pi$
$20$	−48.2761	−	35.0746i	−0.539743	−	0.392146i
$21$	−170.046			−1.76701
$22$		0			0
$23$	177.749			1.61145			0.805723	−	0.592293i	$-0.201777\pi$
$23$	177.749			1.61145			0.805723	+	0.592293i	$0.201777\pi$
$24$	−50.5591	−	36.7334i	−0.430014	−	0.312424i
$25$	30.1449	−	92.7763i	0.241159	−	0.742211i
$26$	27.2111	+	83.7473i	0.205252	+	0.631700i
$27$	44.3938	−	32.2540i	0.316429	−	0.229899i
$28$	−70.4423	+	51.1793i	−0.475441	+	0.345428i
$29$	−46.1660	−	142.084i	−0.295614	−	0.909807i	−0.983014	−	0.183528i	$-0.941248\pi$
$29$	−46.1660	−	142.084i	−0.295614	−	0.909807i	0.687400	−	0.726279i	$-0.258752\pi$
$30$	72.0243	−	221.668i	0.438326	−	1.34903i
$31$	−60.7925	−	44.1683i	−0.352214	−	0.255899i	0.397583	−	0.917566i	$-0.369849\pi$
$31$	−60.7925	−	44.1683i	−0.352214	−	0.255899i	−0.749797	+	0.661667i	$0.769849\pi$
$32$	−32.0000			−0.176777
$33$		0			0
$34$	49.8290			0.251341
$35$	−262.717	−	190.875i	−1.26878	−	0.921821i
$36$	42.0565	−	129.437i	0.194706	−	0.599244i
$37$	68.7057	+	211.455i	0.305274	+	0.939538i	0.979575	+	0.201081i	$0.0644454\pi$
$37$	68.7057	+	211.455i	0.305274	+	0.939538i	−0.674300	+	0.738457i	$0.735555\pi$
$38$	35.5276	−	25.8123i	0.151667	−	0.110192i
$39$	−278.256	+	202.165i	−1.14248	+	0.830058i
$40$	−36.8797	−	113.504i	−0.145780	−	0.448664i
$41$	−78.2188	+	240.733i	−0.297944	+	0.916979i	0.684272	+	0.729227i	$0.260120\pi$
$41$	−78.2188	+	240.733i	−0.297944	+	0.916979i	−0.982217	+	0.187752i	$0.939880\pi$
$42$	−275.141	−	199.902i	−1.01084	−	0.734416i
$43$	130.623			0.463253			0.231626	−	0.972805i	$-0.425595\pi$
$43$	130.623			0.463253			0.231626	+	0.972805i	$0.425595\pi$
$44$		0			0
$45$	507.582			1.68146
$46$	287.604	+	208.957i	0.921846	+	0.669760i
$47$	154.228	−	474.666i	0.478649	−	1.47313i	−0.362323	−	0.932053i	$-0.618016\pi$
$47$	154.228	−	474.666i	0.478649	−	1.47313i	0.840972	−	0.541079i	$-0.181984\pi$
$48$	−38.6237	−	118.872i	−0.116143	−	0.357451i
$49$	−105.851	+	76.9055i	−0.308604	+	0.224214i
$50$	157.841	−	114.678i	0.446440	−	0.324358i
$51$	60.1432	+	185.102i	0.165132	+	0.508224i
$52$	−54.4223	+	167.495i	−0.145135	+	0.446679i
$53$	−10.4704	−	7.60718i	−0.0271362	−	0.0197156i	0.574134	−	0.818761i	$-0.305339\pi$
$53$	−10.4704	−	7.60718i	−0.0271362	−	0.0197156i	−0.601271	+	0.799045i	$0.705339\pi$
$54$	109.748			0.276569
$55$		0			0
$56$	−174.143			−0.415550
$57$	138.767	+	100.820i	0.322460	+	0.234281i
$58$	92.3320	−	284.169i	0.209031	−	0.643331i
$59$	10.9891	+	33.8209i	0.0242484	+	0.0746288i	0.962448	−	0.271465i	$-0.0875080\pi$
$59$	10.9891	+	33.8209i	0.0242484	+	0.0746288i	−0.938200	+	0.346093i	$0.887508\pi$
$60$	377.124	−	273.997i	0.811442	−	0.589547i
$61$	−435.529	+	316.430i	−0.914160	+	0.664176i	−0.942064	−	0.335435i	$-0.891117\pi$
$61$	−435.529	+	316.430i	−0.914160	+	0.664176i	0.0279035	+	0.999611i	$0.491117\pi$
$62$	−46.4413	−	142.932i	−0.0951299	−	0.292780i
$63$	228.870	−	704.390i	0.457697	−	1.40865i
$64$	−51.7771	−	37.6183i	−0.101127	−	0.0734732i
$65$	−656.824			−1.25337
$66$		0			0
$67$	−519.621			−0.947491			−0.473745	−	0.880662i	$-0.657098\pi$
$67$	−519.621			−0.947491			−0.473745	+	0.880662i	$0.657098\pi$
$68$	80.6250	+	58.5775i	0.143783	+	0.104464i
$69$	−429.083	+	1320.58i	−0.748631	+	2.30405i
$70$	−200.698	−	617.684i	−0.342685	−	1.05468i
$71$	−63.4663	+	46.1109i	−0.106085	+	0.0770755i	−0.639563	−	0.768739i	$-0.720885\pi$
$71$	−63.4663	+	46.1109i	−0.106085	+	0.0770755i	0.533478	+	0.845814i	$0.320885\pi$
$72$	220.211	−	159.993i	0.360446	−	0.261879i
$73$	353.537	+	1088.07i	0.566827	+	1.74451i	0.662460	+	0.749097i	$0.269512\pi$
$73$	353.537	+	1088.07i	0.566827	+	1.74451i	−0.0956336	+	0.995417i	$0.530488\pi$
$74$	−137.411	+	422.909i	−0.215862	+	0.664354i
$75$	616.511	+	447.921i	0.949180	+	0.689620i
$76$	87.8290			0.132562
$77$		0			0
$78$	−687.886			−0.998561
$79$	−625.003	−	454.091i	−0.890105	−	0.646699i	0.0458005	−	0.998951i	$-0.485416\pi$
$79$	−625.003	−	454.091i	−0.890105	−	0.646699i	−0.935905	+	0.352252i	$0.885416\pi$
$80$	73.7593	−	227.008i	0.103082	−	0.317253i
$81$	−151.417	−	466.014i	−0.207705	−	0.639252i
$82$	−409.559	+	297.562i	−0.551563	+	0.400734i
$83$	−434.638	+	315.783i	−0.574791	+	0.417610i	−0.836843	−	0.547444i	$-0.815601\pi$
$83$	−434.638	+	315.783i	−0.574791	+	0.417610i	0.262051	+	0.965054i	$0.415601\pi$
$84$	−210.189	−	646.895i	−0.273018	−	0.840262i
$85$	−114.855	+	353.487i	−0.146562	+	0.451071i
$86$	211.353	+	153.557i	0.265009	+	0.192540i
$87$	1167.06			1.43818
$88$		0			0
$89$	667.089			0.794509			0.397255	−	0.917708i	$-0.369963\pi$
$89$	667.089			0.794509			0.397255	+	0.917708i	$0.369963\pi$
$90$	821.284	+	596.698i	0.961900	+	0.698861i
$91$	−296.164	+	911.499i	−0.341170	+	1.05001i
$92$	219.710	+	676.198i	0.248982	+	0.766288i
$93$	474.899	−	345.035i	0.529514	−	0.384714i
$94$	807.550	−	586.720i	0.886090	−	0.643782i
$95$	101.222	+	311.529i	0.109317	+	0.336445i
$96$	77.2475	−	237.743i	0.0821254	−	0.252756i
$97$	145.343	+	105.598i	0.152138	+	0.110534i	0.661250	−	0.750166i	$-0.270026\pi$
$97$	145.343	+	105.598i	0.152138	+	0.110534i	−0.509112	+	0.860700i	$0.670026\pi$
$98$	−261.679			−0.269730
$99$		0			0
$100$	390.203			0.390203
$101$	332.292	+	241.424i	0.327369	+	0.237848i	0.739314	−	0.673361i	$-0.235150\pi$
$101$	332.292	+	241.424i	0.327369	+	0.237848i	−0.411944	+	0.911209i	$0.635150\pi$
$102$	−120.286	+	370.203i	−0.116766	+	0.359369i
$103$	422.630	+	1300.72i	0.404301	+	1.24431i	0.921478	+	0.388431i	$0.126983\pi$
$103$	422.630	+	1300.72i	0.404301	+	1.24431i	−0.517177	+	0.855879i	$0.673017\pi$
$104$	−284.959	+	207.035i	−0.268678	+	0.195206i
$105$	2052.30	−	1491.08i	1.90746	−	1.38585i
$106$	−7.99866	−	24.6173i	−0.00732923	−	0.0225571i
$107$	−122.136	+	375.896i	−0.110349	+	0.339619i	−0.990949	−	0.134242i	$-0.957140\pi$
$107$	−122.136	+	375.896i	−0.110349	+	0.339619i	0.880600	+	0.473861i	$0.157140\pi$
$108$	177.575	+	129.016i	0.158215	+	0.114950i
$109$	505.826			0.444490			0.222245	−	0.974991i	$-0.428662\pi$
$109$	505.826			0.444490			0.222245	+	0.974991i	$0.428662\pi$
$110$		0			0
$111$	−1736.85			−1.48518
$112$	−281.769	−	204.717i	−0.237720	−	0.172714i
$113$	475.152	−	1462.37i	0.395562	−	1.21742i	−0.532961	−	0.846140i	$-0.678921\pi$
$113$	475.152	−	1462.37i	0.395562	−	1.21742i	0.928523	−	0.371275i	$-0.121079\pi$
$114$	106.009	+	326.262i	0.0870934	+	0.268046i
$115$	−2145.26	+	1558.62i	−1.73953	+	1.26385i
$116$	483.457	−	351.252i	0.386964	−	0.281146i
$117$	−462.922	−	1424.73i	−0.365788	−	1.12578i
$118$	−21.9781	+	67.6417i	−0.0171462	+	0.0527706i
$119$	438.758	+	318.777i	0.337991	+	0.245565i
$120$	932.302			0.709226
$121$		0			0
$122$	−1076.69			−0.799005
$123$	−1599.70	−	1162.25i	−1.17268	−	0.852004i
$124$	92.8826	−	285.863i	0.0672670	−	0.207026i
$125$	−126.540	−	389.449i	−0.0905443	−	0.278667i
$126$	1198.38	−	870.674i	0.847303	−	0.615602i
$127$	564.153	−	409.881i	0.394177	−	0.286387i	−0.372988	−	0.927836i	$-0.621667\pi$
$127$	564.153	−	409.881i	0.394177	−	0.286387i	0.767165	+	0.641450i	$0.221667\pi$
$128$	−39.5542	−	121.735i	−0.0273135	−	0.0840623i
$129$	−315.322	+	970.463i	−0.215214	+	0.662360i
$130$	−1062.76	−	772.143i	−0.717004	−	0.520934i
$131$	−259.910			−0.173347			−0.0866735	−	0.996237i	$-0.527624\pi$
$131$	−259.910			−0.173347			−0.0866735	+	0.996237i	$0.527624\pi$
$132$		0			0
$133$	477.962			0.311613
$134$	−840.765	−	610.852i	−0.542023	−	0.393803i
$135$	−252.966	+	778.549i	−0.161273	+	0.496347i
$136$	61.5920	+	189.561i	0.0388344	+	0.119520i
$137$	1685.64	−	1224.69i	1.05119	−	0.763737i	0.0787550	−	0.996894i	$-0.474906\pi$
$137$	1685.64	−	1224.69i	1.05119	−	0.763737i	0.972439	+	0.233157i	$0.0749055\pi$
$138$	−2246.71	+	1632.33i	−1.38589	+	1.00691i
$139$	53.5924	+	164.940i	0.0327025	+	0.100648i	0.966075	−	0.258260i	$-0.0831492\pi$
$139$	53.5924	+	164.940i	0.0327025	+	0.100648i	−0.933373	+	0.358908i	$0.883149\pi$
$140$	401.396	−	1235.37i	0.242315	−	0.745769i
$141$	3154.22	+	2291.67i	1.88392	+	1.36875i
$142$	−156.897			−0.0927220
$143$		0			0
$144$	544.391			0.315041
$145$	1803.07	+	1310.01i	1.03267	+	0.750276i
$146$	−707.074	+	2176.15i	−0.400807	+	1.23356i
$147$	−315.844	−	972.069i	−0.177214	−	0.545407i
$148$	−719.496	+	522.744i	−0.399609	+	0.290333i
$149$	363.293	−	263.948i	0.199746	−	0.145124i	−0.483416	−	0.875391i	$-0.660604\pi$
$149$	363.293	−	263.948i	0.199746	−	0.145124i	0.683162	+	0.730267i	$0.260604\pi$
$150$	470.972	+	1449.50i	0.256365	+	0.789010i
$151$	8.81804	−	27.1391i	0.00475233	−	0.0146262i	−0.948652	−	0.316321i	$-0.897552\pi$
$151$	8.81804	−	27.1391i	0.00475233	−	0.0146262i	0.953405	+	0.301695i	$0.0975524\pi$
$152$	142.110	+	103.249i	0.0758333	+	0.0550962i
$153$	−847.702			−0.447926
$154$		0			0
$155$	1121.00			0.580910
$156$	−1113.02	−	808.658i	−0.571238	−	0.415029i
$157$	532.702	−	1639.49i	0.270791	−	0.833411i	−0.719511	−	0.694481i	$-0.755634\pi$
$157$	532.702	−	1639.49i	0.270791	−	0.833411i	0.990302	−	0.138929i	$-0.0443661\pi$
$158$	−477.459	−	1469.47i	−0.240409	−	0.739903i
$159$	81.7927	−	59.4259i	0.0407961	−	0.0296401i
$160$	386.209	−	280.597i	0.190828	−	0.138645i
$161$	1195.65	+	3679.84i	0.585284	+	1.80132i
$162$	302.835	−	932.029i	0.146870	−	0.452019i
$163$	−2684.50	−	1950.40i	−1.28998	−	0.937222i	−0.290171	−	0.956975i	$-0.593712\pi$
$163$	−2684.50	−	1950.40i	−1.28998	−	0.937222i	−0.999805	+	0.0197528i	$0.993712\pi$
$164$	−1012.49			−0.482084
$165$		0			0
$166$	−1074.48			−0.502386
$167$	2439.67	+	1772.52i	1.13046	+	0.821330i	0.985762	−	0.168146i	$-0.0537779\pi$
$167$	2439.67	+	1772.52i	1.13046	+	0.821330i	0.144701	+	0.989475i	$0.453778\pi$
$168$	420.378	−	1293.79i	0.193053	−	0.594155i
$169$	−79.8766	−	245.835i	−0.0363571	−	0.111896i
$170$	−601.388	+	436.934i	−0.271320	+	0.197125i
$171$	−604.403	+	439.125i	−0.270292	+	0.196378i
$172$	161.459	+	496.920i	0.0715765	+	0.220290i
$173$	−682.745	+	2101.27i	−0.300047	+	0.923450i	0.681432	+	0.731881i	$0.261357\pi$
$173$	−682.745	+	2101.27i	−0.300047	+	0.923450i	−0.981479	+	0.191569i	$0.938643\pi$
$174$	1888.34	+	1371.96i	0.822727	+	0.597746i
$175$	2123.47			0.917254
$176$		0			0
$177$	−277.799			−0.117970
$178$	1079.37	+	784.210i	0.454508	+	0.330219i
$179$	−702.034	+	2160.64i	−0.293143	+	0.902200i	0.690696	+	0.723145i	$0.257304\pi$
$179$	−702.034	+	2160.64i	−0.293143	+	0.902200i	−0.983839	+	0.179055i	$0.942696\pi$
$180$	627.405	+	1930.95i	0.259800	+	0.799583i
$181$	505.179	−	367.034i	0.207457	−	0.150726i	−0.479206	−	0.877703i	$-0.659075\pi$
$181$	505.179	−	367.034i	0.207457	−	0.150726i	0.686662	+	0.726977i	$0.259075\pi$
$182$	−1550.74	+	1126.68i	−0.631583	+	0.458872i
$183$	−1299.55	−	3999.61i	−0.524949	−	1.61563i
$184$	−439.420	+	1352.40i	−0.176057	+	0.541847i
$185$	−2683.38	−	1949.59i	−1.06641	−	0.774794i
$186$	1174.02			0.462812
$187$		0			0
$188$	1996.37			0.774471
$189$	966.358	+	702.100i	0.371916	+	0.270213i
$190$	−202.444	+	623.059i	−0.0772991	+	0.237902i
$191$	−415.380	−	1278.41i	−0.157360	−	0.484306i	0.841032	−	0.540985i	$-0.181949\pi$
$191$	−415.380	−	1278.41i	−0.157360	−	0.484306i	−0.998392	+	0.0566797i	$0.981949\pi$
$192$	404.473	−	293.867i	0.152033	−	0.110458i
$193$	−3740.70	+	2717.78i	−1.39514	+	1.01363i	−0.399858	+	0.916577i	$0.630941\pi$
$193$	−3740.70	+	2717.78i	−1.39514	+	1.01363i	−0.995280	+	0.0970499i	$0.969059\pi$
$194$	111.032	+	341.722i	0.0410910	+	0.126465i
$195$	1585.56	−	4879.86i	0.582279	−	1.79207i
$196$	−423.405	−	307.622i	−0.154302	−	0.112107i
$197$	664.691			0.240392			0.120196	−	0.992750i	$-0.461648\pi$
$197$	664.691			0.240392			0.120196	+	0.992750i	$0.461648\pi$
$198$		0			0
$199$	−3042.82			−1.08392			−0.541959	−	0.840405i	$-0.682317\pi$
$199$	−3042.82			−1.08392			−0.541959	+	0.840405i	$0.682317\pi$
$200$	631.362	+	458.711i	0.223220	+	0.162179i
$201$	1254.36	−	3860.52i	0.440177	−	1.35473i
$202$	253.849	+	781.265i	0.0884194	+	0.272127i
$203$	2630.95	−	1911.50i	0.909639	−	0.660892i
$204$	−629.828	+	457.597i	−0.216161	+	0.157050i
$205$	−1166.88	−	3591.28i	−0.397553	−	1.22354i
$206$	−845.260	+	2601.44i	−0.285884	+	0.879860i
$207$	−4892.79	−	3554.82i	−1.64286	−	1.19361i
$208$	−704.457			−0.234833
$209$		0			0
$210$	5073.55			1.66718
$211$	−2096.66	−	1523.31i	−0.684075	−	0.497009i	0.190632	−	0.981662i	$-0.438946\pi$
$211$	−2096.66	−	1523.31i	−0.684075	−	0.497009i	−0.874707	+	0.484652i	$0.838946\pi$
$212$	15.9973	−	49.2347i	0.00518255	−	0.0159502i
$213$	−189.374	−	582.832i	−0.0609187	−	0.187488i
$214$	−639.513	+	464.633i	−0.204281	+	0.148419i
$215$	−1576.50	+	1145.39i	−0.500075	+	0.363326i
$216$	135.655	+	417.505i	0.0427323	+	0.131517i
$217$	505.464	−	1555.66i	0.158125	−	0.486659i
$218$	818.444	+	594.634i	0.254275	+	0.184742i
$219$	−8937.26			−2.75764
$220$		0			0
$221$	1096.95			0.333886
$222$	−2810.28	−	2041.79i	−0.849612	−	0.617280i
$223$	814.941	−	2508.13i	0.244720	−	0.753170i	−0.750963	−	0.660345i	$-0.770410\pi$
$223$	814.941	−	2508.13i	0.244720	−	0.753170i	0.995682	−	0.0928251i	$-0.0295897\pi$
$224$	−215.252	−	662.479i	−0.0642060	−	0.197606i
$225$	−2685.22	+	1950.93i	−0.795621	+	0.578052i
$226$	2487.93	−	1807.59i	0.732276	−	0.532030i
$227$	77.4613	+	238.401i	0.0226488	+	0.0697059i	0.961742	−	0.273956i	$-0.0883324\pi$
$227$	77.4613	+	238.401i	0.0226488	+	0.0697059i	−0.939093	+	0.343662i	$0.888332\pi$
$228$	−212.018	+	652.524i	−0.0615843	+	0.189537i
$229$	−1455.67	−	1057.61i	−0.420060	−	0.305191i	0.357602	−	0.933874i	$-0.383594\pi$
$229$	−1455.67	−	1057.61i	−0.420060	−	0.305191i	−0.777662	+	0.628683i	$0.783594\pi$
$230$	−5303.37			−1.52041
$231$		0			0
$232$	1195.17			0.338219
$233$	−2573.06	−	1869.44i	−0.723462	−	0.525626i	0.164026	−	0.986456i	$-0.447552\pi$
$233$	−2573.06	−	1869.44i	−0.723462	−	0.525626i	−0.887488	+	0.460830i	$0.847552\pi$
$234$	925.844	−	2849.46i	0.258651	−	0.796046i
$235$	2300.80	+	7081.13i	0.638671	+	1.96563i
$236$	−115.079	+	83.6098i	−0.0317415	+	0.0230616i
$237$	4882.40	−	3547.27i	1.33817	−	0.972237i
$238$	335.182	+	1031.58i	0.0912882	+	0.280956i
$239$	1549.35	−	4768.41i	0.419327	−	1.29056i	−0.488996	−	0.872286i	$-0.662637\pi$
$239$	1549.35	−	4768.41i	0.419327	−	1.29056i	0.908323	−	0.418270i	$-0.137363\pi$
$240$	1508.50	+	1095.99i	0.405721	+	0.294773i
$241$	6074.13			1.62352			0.811761	−	0.583990i	$-0.198509\pi$
$241$	6074.13			1.62352			0.811761	+	0.583990i	$0.198509\pi$
$242$		0			0
$243$	5309.35			1.40163
$244$	−1742.12	−	1265.72i	−0.457080	−	0.332088i
$245$	603.164	−	1856.35i	0.157285	−	0.484073i
$246$	−1222.06	−	3761.12i	−0.316731	−	0.974797i
$247$	782.114	−	568.239i	0.201477	−	0.146381i
$248$	486.340	−	353.346i	0.124527	−	0.0904739i
$249$	−1296.89	−	3991.43i	−0.330069	−	1.01585i
$250$	253.079	−	778.897i	0.0640245	−	0.197047i
$251$	4505.98	+	3273.78i	1.13313	+	0.823264i	0.986147	−	0.165875i	$-0.0530449\pi$
$251$	4505.98	+	3273.78i	1.13313	+	0.823264i	0.146979	+	0.989140i	$0.453045\pi$
$252$	2962.56			0.740570
$253$		0			0
$254$	1394.66			0.344524
$255$	−2348.96	−	1706.62i	−0.576854	−	0.419109i
$256$	79.1084	−	243.470i	0.0193136	−	0.0594410i
$257$	−1825.38	−	5617.94i	−0.443051	−	1.36357i	−0.884607	−	0.466336i	$-0.845574\pi$
$257$	−1825.38	−	5617.94i	−0.443051	−	1.36357i	0.441557	−	0.897233i	$-0.354426\pi$
$258$	−1651.05	+	1199.56i	−0.398410	+	0.289462i
$259$	−3915.47	+	2844.76i	−0.939365	+	0.682488i
$260$	−811.879	−	2498.71i	−0.193656	−	0.596012i
$261$	−1570.77	+	4834.34i	−0.372523	+	1.14651i
$262$	−420.543	−	305.543i	−0.0991651	−	0.0720477i
$263$	−6853.74			−1.60692			−0.803459	−	0.595360i	$-0.797009\pi$
$263$	−6853.74			−1.60692			−0.803459	+	0.595360i	$0.797009\pi$
$264$		0			0
$265$	193.072			0.0447559
$266$	773.359	+	561.878i	0.178262	+	0.129515i
$267$	−1610.34	+	4956.12i	−0.369106	+	1.13599i
$268$	−642.287	−	1976.76i	−0.146395	−	0.450559i
$269$	−891.022	+	647.366i	−0.201958	+	0.146731i	−0.684167	−	0.729325i	$-0.739834\pi$
$269$	−891.022	+	647.366i	−0.201958	+	0.146731i	0.482210	+	0.876056i	$0.339834\pi$
$270$	−1324.55	+	962.339i	−0.298553	+	0.216911i
$271$	−794.697	−	2445.83i	−0.178134	−	0.548241i	0.821628	−	0.570024i	$-0.193066\pi$
$271$	−794.697	−	2445.83i	−0.178134	−	0.548241i	−0.999763	+	0.0217823i	$0.993066\pi$
$272$	−123.184	+	379.122i	−0.0274600	+	0.0845133i
$273$	−6057.03	−	4400.69i	−1.34281	−	0.975611i
$274$	4167.12			0.918777
$275$		0			0
$276$	−5554.17			−1.21131
$277$	5938.27	+	4314.40i	1.28807	+	0.935839i	0.999765	−	0.0216990i	$-0.00690756\pi$
$277$	5938.27	+	4314.40i	1.28807	+	0.935839i	0.288307	+	0.957538i	$0.406908\pi$
$278$	−107.185	+	329.881i	−0.0231242	+	0.0711689i
$279$	790.070	+	2431.59i	0.169535	+	0.521775i
$280$	2101.73	−	1527.00i	0.448581	−	0.325913i
$281$	6061.92	−	4404.24i	1.28692	−	0.935000i	0.287179	−	0.957877i	$-0.407282\pi$
$281$	6061.92	−	4404.24i	1.28692	−	0.935000i	0.999738	+	0.0228766i	$0.00728249\pi$
$282$	2409.61	+	7416.01i	0.508830	+	1.56602i
$283$	−2006.79	+	6176.26i	−0.421523	+	1.29732i	0.484761	+	0.874647i	$0.338907\pi$
$283$	−2006.79	+	6176.26i	−0.421523	+	1.29732i	−0.906284	+	0.422669i	$0.861093\pi$
$284$	−253.865	−	184.444i	−0.0530427	−	0.0385378i
$285$	−2558.85			−0.531835
$286$		0			0
$287$	−5509.91			−1.13324
$288$	880.844	+	639.970i	0.180223	+	0.130940i
$289$	−1326.38	+	4082.19i	−0.269974	+	0.830895i
$290$	1377.42	+	4239.27i	0.278914	+	0.858408i
$291$	−1135.39	+	824.911i	−0.228721	+	0.166176i
$292$	−3702.29	+	2689.87i	−0.741986	+	0.539084i
$293$	−829.672	−	2553.47i	−0.165426	−	0.509130i	0.833641	−	0.552307i	$-0.186252\pi$
$293$	−829.672	−	2553.47i	−0.165426	−	0.509130i	−0.999067	+	0.0431764i	$0.986252\pi$
$294$	631.689	−	1944.14i	0.125309	−	0.385661i
$295$	−429.191	−	311.826i	−0.0847067	−	0.0615430i
$296$	−1778.69			−0.349271
$297$		0			0
$298$	898.110			0.174584
$299$	6331.39	+	4600.03i	1.22460	+	0.889721i
$300$	−941.944	+	2899.01i	−0.181277	+	0.557914i
$301$	878.655	+	2704.22i	0.168255	+	0.517837i
$302$	46.1719	−	33.5458i	0.00879766	−	0.00639187i
$303$	−2595.80	+	1885.96i	−0.492162	+	0.357576i
$304$	108.563	+	334.121i	0.0204819	+	0.0630368i
$305$	2481.74	−	7638.01i	0.465915	−	1.43394i
$306$	−1371.61	−	996.534i	−0.256241	−	0.186170i
$307$	8331.66			1.54890			0.774451	−	0.632633i	$-0.218026\pi$
$307$	8331.66			1.54890			0.774451	+	0.632633i	$0.218026\pi$
$308$		0			0
$309$	−10683.9			−1.96695
$310$	1813.82	+	1317.82i	0.332316	+	0.241442i
$311$	−1551.37	+	4774.64i	−0.282863	+	0.870562i	0.704168	+	0.710033i	$0.251320\pi$
$311$	−1551.37	+	4774.64i	−0.282863	+	0.870562i	−0.987031	+	0.160529i	$0.948680\pi$
$312$	−850.274	−	2616.87i	−0.154286	−	0.474844i
$313$	−2444.91	+	1776.33i	−0.441516	+	0.320780i	−0.786237	−	0.617925i	$-0.787974\pi$
$313$	−2444.91	+	1776.33i	−0.441516	+	0.320780i	0.344721	+	0.938705i	$0.387974\pi$
$314$	2789.26	−	2026.52i	0.501297	−	0.364214i
$315$	3414.32	+	10508.2i	0.610714	+	1.87958i
$316$	954.919	−	2938.94i	0.169995	−	0.523191i
$317$	8527.16	+	6195.34i	1.51083	+	1.09768i	0.965808	+	0.259259i	$0.0834784\pi$
$317$	8527.16	+	6195.34i	1.51083	+	1.09768i	0.545021	+	0.838422i	$0.316522\pi$
$318$	202.203			0.0356571
$319$		0			0
$320$	954.761			0.166790
$321$	−2497.88	−	1814.81i	−0.434324	−	0.315555i
$322$	−2391.31	+	7359.69i	−0.413858	+	1.27372i
$323$	−169.049	−	520.279i	−0.0291212	−	0.0896257i
$324$	1585.66	−	1152.05i	0.271890	−	0.197540i
$325$	3474.75	−	2524.55i	0.593059	−	0.430883i
$326$	−2050.77	−	6311.63i	−0.348410	−	1.07230i
$327$	−1221.06	+	3758.02i	−0.206497	+	0.635533i
$328$	−1638.24	−	1190.25i	−0.275782	−	0.200367i
$329$	10864.2			1.82055
$330$		0			0
$331$	309.871			0.0514563			0.0257281	−	0.999669i	$-0.491810\pi$
$331$	309.871			0.0514563			0.0257281	+	0.999669i	$0.491810\pi$
$332$	−1738.55	−	1263.13i	−0.287396	−	0.208805i
$333$	2337.68	−	7194.63i	0.384696	−	1.18397i
$334$	1863.74	+	5736.01i	0.305328	+	0.939702i
$335$	6271.33	−	4556.38i	1.02280	−	0.743110i
$336$	2201.13	−	1599.21i	0.357385	−	0.259655i
$337$	3450.07	+	10618.2i	0.557677	+	1.71635i	0.688767	+	0.724983i	$0.258152\pi$
$337$	3450.07	+	10618.2i	0.557677	+	1.71635i	−0.131090	+	0.991371i	$0.541848\pi$
$338$	159.753	−	491.670i	0.0257084	−	0.0791223i
$339$	9717.61	+	7060.26i	1.55690	+	1.13115i
$340$	−1486.71			−0.237142
$341$		0			0
$342$	−1494.17			−0.236244
$343$	3736.27	+	2714.56i	0.588162	+	0.427324i
$344$	−322.918	+	993.841i	−0.0506122	+	0.155768i
$345$	−6401.12	−	19700.6i	−0.998913	−	3.07434i
$346$	−3574.90	+	2597.32i	−0.555456	+	0.403562i
$347$	−2035.07	+	1478.56i	−0.314836	+	0.228742i	−0.733969	−	0.679183i	$-0.762334\pi$
$347$	−2035.07	+	1478.56i	−0.314836	+	0.228742i	0.419133	+	0.907925i	$0.362334\pi$
$348$	1442.56	+	4439.75i	0.222211	+	0.683895i
$349$	−3515.56	+	10819.8i	−0.539208	+	1.65951i	0.195169	+	0.980770i	$0.437474\pi$
$349$	−3515.56	+	10819.8i	−0.539208	+	1.65951i	−0.734377	+	0.678742i	$0.762526\pi$
$350$	3435.85	+	2496.29i	0.524725	+	0.381235i
$351$	2416.01			0.367400
$352$		0			0
$353$	6210.08			0.936343			0.468172	−	0.883638i	$-0.344913\pi$
$353$	6210.08			0.936343			0.468172	+	0.883638i	$0.344913\pi$
$354$	−449.488	−	326.572i	−0.0674859	−	0.0490314i
$355$	361.645	−	1113.03i	0.0540679	−	0.166404i
$356$	824.568	+	2537.76i	0.122758	+	0.377812i
$357$	−3427.50	+	2490.22i	−0.508130	+	0.369178i
$358$	−3675.90	+	2670.70i	−0.542674	+	0.394276i
$359$	−768.682	−	2365.76i	−0.113007	−	0.347799i	0.878519	−	0.477707i	$-0.158532\pi$
$359$	−768.682	−	2365.76i	−0.113007	−	0.347799i	−0.991526	+	0.129908i	$0.958532\pi$
$360$	−1254.81	+	3861.91i	−0.183706	+	0.565390i
$361$	5159.00	+	3748.24i	0.752151	+	0.546470i
$362$	1248.87			0.181324
$363$		0			0
$364$	−3833.63			−0.552024
$365$	−13807.8	−	10032.0i	−1.98009	−	1.43862i
$366$	2599.10	−	7999.22i	0.371195	−	1.14242i
$367$	2076.45	+	6390.65i	0.295340	+	0.908962i	0.983107	+	0.183031i	$0.0585909\pi$
$367$	2076.45	+	6390.65i	0.295340	+	0.908962i	−0.687767	+	0.725931i	$0.741409\pi$
$368$	−2300.83	+	1671.65i	−0.325922	+	0.236796i
$369$	6967.51	−	5062.19i	0.982965	−	0.714166i
$370$	−2049.92	−	6309.02i	−0.288028	−	0.886460i
$371$	87.0568	−	267.933i	0.0121827	−	0.0374944i
$372$	1899.60	+	1380.14i	0.264757	+	0.192357i
$373$	−8614.37			−1.19580			−0.597902	−	0.801569i	$-0.703999\pi$
$373$	−8614.37			−1.19580			−0.597902	+	0.801569i	$0.703999\pi$
$374$		0			0
$375$	3198.87			0.440503
$376$	3230.20	+	2346.88i	0.443045	+	0.321891i
$377$	2032.62	−	6255.77i	0.277680	−	0.854611i
$378$	738.232	+	2272.04i	0.100451	+	0.309157i
$379$	6479.49	−	4707.63i	0.878178	−	0.638033i	−0.0545912	−	0.998509i	$-0.517386\pi$
$379$	6479.49	−	4707.63i	0.878178	−	0.638033i	0.932769	+	0.360475i	$0.117386\pi$
$380$	−1060.01	+	770.143i	−0.143098	+	0.103967i
$381$	1683.35	+	5180.81i	0.226353	+	0.696643i
$382$	830.760	−	2556.82i	0.111271	−	0.342456i
$383$	−6481.80	−	4709.31i	−0.864764	−	0.628288i	0.0644128	−	0.997923i	$-0.479483\pi$
$383$	−6481.80	−	4709.31i	−0.864764	−	0.628288i	−0.929177	+	0.369635i	$0.879483\pi$
$384$	999.912			0.132882
$385$		0			0
$386$	−9247.52			−1.21940
$387$	−3595.58	−	2612.34i	−0.472284	−	0.343134i
$388$	−222.064	+	683.444i	−0.0290557	+	0.0894242i
$389$	2481.28	+	7636.61i	0.323409	+	0.995350i	0.972154	+	0.234344i	$0.0752943\pi$
$389$	2481.28	+	7636.61i	0.323409	+	0.995350i	−0.648745	+	0.761006i	$0.724706\pi$
$390$	8302.11	−	6031.84i	1.07793	−	0.783164i
$391$	3582.76	−	2603.02i	0.463396	−	0.336677i
$392$	−323.453	−	995.486i	−0.0416756	−	0.128264i
$393$	627.419	−	1931.00i	0.0805321	−	0.247852i
$394$	1075.49	+	781.391i	0.137519	+	0.0999135i
$395$	11524.9			1.46806
$396$		0			0
$397$	4435.00			0.560670			0.280335	−	0.959902i	$-0.409554\pi$
$397$	4435.00			0.560670			0.280335	+	0.959902i	$0.409554\pi$
$398$	−4923.39	−	3577.05i	−0.620068	−	0.450506i
$399$	−1153.79	+	3551.01i	−0.144767	+	0.445546i
$400$	482.318	+	1484.42i	0.0602897	+	0.185553i
$401$	3178.79	−	2309.53i	0.395864	−	0.287612i	−0.371990	−	0.928237i	$-0.621325\pi$
$401$	3178.79	−	2309.53i	0.395864	−	0.287612i	0.767854	+	0.640625i	$0.221325\pi$
$402$	6567.90	−	4771.86i	0.814869	−	0.592037i
$403$	−1022.37	−	3146.54i	−0.126372	−	0.388933i
$404$	−507.697	+	1562.53i	−0.0625220	+	0.192423i
$405$	5913.78	+	4296.61i	0.725576	+	0.527162i
$406$	6504.07			0.795054
$407$		0			0
$408$	−1557.02			−0.188931
$409$	11782.7	+	8560.63i	1.42449	+	1.03495i	0.991010	+	0.133791i	$0.0427152\pi$
$409$	11782.7	+	8560.63i	1.42449	+	1.03495i	0.433482	+	0.901162i	$0.357285\pi$
$410$	2333.76	−	7182.56i	0.281112	−	0.865175i
$411$	5029.68	+	15479.8i	0.603640	+	1.85781i
$412$	−4425.84	+	3215.56i	−0.529237	+	0.384513i
$413$	−626.256	+	455.001i	−0.0746151	+	0.0542110i
$414$	−3737.76	−	11503.6i	−0.443721	−	1.36563i
$415$	2476.66	−	7622.38i	0.292951	−	0.901610i
$416$	−1139.84	−	828.139i	−0.134339	−	0.0976030i
$417$	−1354.79			−0.159099
$418$		0			0
$419$	4028.77			0.469734			0.234867	−	0.972028i	$-0.424535\pi$
$419$	4028.77			0.469734			0.234867	+	0.972028i	$0.424535\pi$
$420$	8209.18	+	5964.32i	0.953731	+	0.692926i
$421$	−2635.17	+	8110.23i	−0.305061	+	0.938880i	0.674594	+	0.738189i	$0.264319\pi$
$421$	−2635.17	+	8110.23i	−0.305061	+	0.938880i	−0.979655	+	0.200691i	$0.935681\pi$
$422$	−1601.70	−	4929.53i	−0.184762	−	0.568640i
$423$	−13738.2	+	9981.41i	−1.57914	+	1.14731i
$424$	83.7631	−	60.8574i	0.00959409	−	0.00697051i
$425$	−751.044	−	2311.48i	−0.0857200	−	0.263819i
$426$	378.747	−	1165.66i	0.0430760	−	0.132574i
$427$	−9480.53	−	6888.01i	−1.07446	−	0.780642i
$428$	−1580.96			−0.178548
$429$		0			0
$430$	−3897.31			−0.437082
$431$	−10853.1	−	7885.27i	−1.21294	−	0.881253i	−0.217446	−	0.976072i	$-0.569773\pi$
$431$	−10853.1	−	7885.27i	−1.21294	−	0.881253i	−0.995495	+	0.0948191i	$0.969773\pi$
$432$	−271.311	+	835.009i	−0.0302163	+	0.0929963i
$433$	1276.95	+	3930.06i	0.141724	+	0.436182i	0.996575	−	0.0826917i	$-0.0263517\pi$
$433$	1276.95	+	3930.06i	0.141724	+	0.436182i	−0.854851	+	0.518873i	$0.826352\pi$
$434$	2646.64	−	1922.90i	0.292726	−	0.212678i
$435$	−14085.2	+	10233.5i	−1.55250	+	1.12795i
$436$	625.236	+	1924.28i	0.0686774	+	0.211367i
$437$	1206.06	−	3711.86i	0.132022	−	0.406321i
$438$	−14460.8	−	10506.4i	−1.57754	−	1.14615i
$439$	3358.46			0.365126			0.182563	−	0.983194i	$-0.441561\pi$
$439$	3358.46			0.365126			0.182563	+	0.983194i	$0.441561\pi$
$440$		0			0
$441$	4451.74			0.480698
$442$	1774.90	+	1289.54i	0.191003	+	0.138772i
$443$	−136.508	+	420.129i	−0.0146404	+	0.0450585i	−0.958110	−	0.286401i	$-0.907541\pi$
$443$	−136.508	+	420.129i	−0.0146404	+	0.0450585i	0.943469	+	0.331460i	$0.107541\pi$
$444$	−2146.87	−	6607.38i	−0.229472	−	0.706244i
$445$	−8051.12	+	5849.48i	−0.857662	+	0.623128i
$446$	4267.09	−	3100.22i	0.453032	−	0.329147i
$447$	1084.01	+	3336.24i	0.114702	+	0.353018i
$448$	430.505	−	1324.96i	0.0454005	−	0.139728i
$449$	330.466	+	240.098i	0.0347342	+	0.0252359i	0.605017	−	0.796213i	$-0.293166\pi$
$449$	330.466	+	240.098i	0.0347342	+	0.0252359i	−0.570283	+	0.821448i	$0.693166\pi$
$450$	−6638.23			−0.695398
$451$		0			0
$452$	6150.49			0.640033
$453$	180.343	+	131.027i	0.0187048	+	0.0135898i
$454$	−154.923	+	476.802i	−0.0160151	+	0.0492895i
$455$	−4418.22	−	13597.9i	−0.455229	−	1.40105i
$456$	−1110.14	+	806.564i	−0.114007	+	0.0828307i
$457$	−1232.01	+	895.106i	−0.126107	+	0.0916221i	−0.649051	−	0.760745i	$-0.724834\pi$
$457$	−1232.01	+	895.106i	−0.126107	+	0.0916221i	0.522944	+	0.852367i	$0.324834\pi$
$458$	−1112.04	−	3422.50i	−0.113454	−	0.349176i
$459$	422.473	−	1300.24i	0.0429616	−	0.132222i
$460$	−8581.03	−	6234.49i	−0.869767	−	0.631923i
$461$	−13861.4			−1.40041			−0.700203	−	0.713944i	$-0.746907\pi$
$461$	−13861.4			−1.40041			−0.700203	+	0.713944i	$0.746907\pi$
$462$		0			0
$463$	−6502.26			−0.652669			−0.326334	−	0.945254i	$-0.605814\pi$
$463$	−6502.26			−0.652669			−0.326334	+	0.945254i	$0.605814\pi$
$464$	1933.83	+	1405.01i	0.193482	+	0.140573i
$465$	−2706.08	+	8328.46i	−0.269874	+	0.830588i
$466$	−1965.64	−	6049.62i	−0.195400	−	0.601381i
$467$	−343.002	+	249.205i	−0.0339876	+	0.0246935i	−0.604649	−	0.796492i	$-0.706687\pi$
$467$	−343.002	+	249.205i	−0.0339876	+	0.0246935i	0.570662	+	0.821185i	$0.306687\pi$
$468$	4847.78	−	3522.12i	0.478822	−	0.347885i
$469$	−3495.30	−	10757.4i	−0.344133	−	1.05913i
$470$	−4601.60	+	14162.3i	−0.451608	+	1.38991i
$471$	10894.6	+	7915.40i	1.06581	+	0.774357i
$472$	−284.491			−0.0277431
$473$		0			0
$474$	12070.0			1.16960
$475$	−1732.87	−	1259.01i	−0.167389	−	0.121615i
$476$	−670.363	+	2063.17i	−0.0645505	+	0.198666i
$477$	136.075	+	418.796i	0.0130617	+	0.0401999i
$478$	8112.51	−	5894.08i	0.776271	−	0.563994i
$479$	−3686.96	+	2678.74i	−0.351695	+	0.255521i	−0.749580	−	0.661914i	$-0.769744\pi$
$479$	−3686.96	+	2678.74i	−0.351695	+	0.255521i	0.397885	+	0.917435i	$0.369744\pi$
$480$	1152.39	+	3546.69i	0.109581	+	0.337257i
$481$	−3025.01	+	9310.04i	−0.286754	+	0.882539i
$482$	9828.14	+	7140.56i	0.928754	+	0.674779i
$483$	−30225.6			−2.84744
$484$		0			0
$485$	−2680.10			−0.250922
$486$	8590.72	+	6241.52i	0.801816	+	0.582554i
$487$	−2073.17	+	6380.56i	−0.192904	+	0.593698i	0.807090	+	0.590428i	$0.201041\pi$
$487$	−2073.17	+	6380.56i	−0.192904	+	0.593698i	−0.999995	+	0.00327027i	$0.998959\pi$
$488$	−1330.86	−	4095.96i	−0.123453	−	0.379950i
$489$	20970.8	−	15236.2i	1.93933	−	1.40901i
$490$	3158.21	−	2294.57i	0.291170	−	0.211547i
$491$	4489.29	+	13816.6i	0.412625	+	1.26993i	0.914358	+	0.404907i	$0.132696\pi$
$491$	4489.29	+	13816.6i	0.412625	+	1.26993i	−0.501733	+	0.865023i	$0.667304\pi$
$492$	2444.12	−	7522.24i	0.223962	−	0.689286i
$493$	−3011.27	−	2187.82i	−0.275093	−	0.199867i
$494$	1933.49			0.176097
$495$		0			0
$496$	1202.30			0.108840
$497$	−1381.52	−	1003.74i	−0.124688	−	0.0905910i
$498$	2593.79	−	7982.85i	0.233394	−	0.718313i
$499$	−2997.32	−	9224.80i	−0.268895	−	0.827573i	−0.990770	−	0.135550i	$-0.956720\pi$
$499$	−2997.32	−	9224.80i	−0.268895	−	0.827573i	0.721876	−	0.692023i	$-0.243280\pi$
$500$	1325.14	−	962.770i	0.118524	−	0.0861128i
$501$	−19058.3	+	13846.6i	−1.69952	+	1.23477i
$502$	3442.26	+	10594.2i	0.306047	+	0.941915i
$503$	4853.78	−	14938.4i	0.430257	−	1.32419i	−0.467613	−	0.883933i	$-0.654886\pi$
$503$	4853.78	−	14938.4i	0.430257	−	1.32419i	0.897870	−	0.440261i	$-0.145114\pi$
$504$	4793.52	+	3482.70i	0.423651	+	0.307801i
$505$	−6127.41			−0.539933
$506$		0			0
$507$	2019.25			0.176879
$508$	2256.61	+	1639.53i	0.197089	+	0.143193i
$509$	−455.516	+	1401.93i	−0.0396668	+	0.122082i	−0.968929	−	0.247339i	$-0.920444\pi$
$509$	−455.516	+	1401.93i	−0.0396668	+	0.122082i	0.929262	+	0.369421i	$0.120444\pi$
$510$	−1794.45	−	5522.75i	−0.155803	−	0.479512i
$511$	−20147.7	+	14638.2i	−1.74419	+	1.26723i
$512$	414.217	−	300.946i	0.0357538	−	0.0259767i
$513$	−372.328	−	1145.91i	−0.0320442	−	0.0986218i
$514$	3650.76	−	11235.9i	0.313284	−	0.964189i
$515$	−16506.3	−	11992.5i	−1.41234	−	1.02613i
$516$	−4081.62			−0.348223
$517$		0			0
$518$	−9679.57			−0.821035
$519$	−13963.2	−	10144.9i	−1.18096	−	0.858017i
$520$	1623.76	−	4997.41i	0.136936	−	0.421444i
$521$	−2865.47	−	8819.00i	−0.240956	−	0.741588i	−0.996275	−	0.0862302i	$-0.972518\pi$
$521$	−2865.47	−	8819.00i	−0.240956	−	0.741588i	0.755319	−	0.655358i	$-0.227482\pi$
$522$	−8224.68	+	5975.58i	−0.689625	+	0.501042i
$523$	3432.26	−	2493.68i	0.286964	−	0.208491i	−0.434985	−	0.900438i	$-0.643246\pi$
$523$	3432.26	−	2493.68i	0.286964	−	0.208491i	0.721949	+	0.691946i	$0.243246\pi$
$524$	−321.267	−	988.757i	−0.0267836	−	0.0824314i
$525$	−5126.03	+	15776.3i	−0.426130	+	1.31149i
$526$	−11089.6	−	8057.05i	−0.919256	−	0.667879i
$527$	−1872.17			−0.154749
$528$		0			0
$529$	19427.7			1.59676
$530$	312.397	+	226.970i	0.0256031	+	0.0186018i
$531$	373.897	−	1150.74i	0.0305570	−	0.0940447i
$532$	590.794	+	1818.28i	0.0481469	+	0.148181i
$533$	−9016.14	+	6550.61i	−0.732706	+	0.532342i
$534$	−8431.86	+	6126.11i	−0.683300	+	0.496447i
$535$	−1822.04	−	5607.67i	−0.147241	−	0.453160i
$536$	1284.57	−	3953.52i	0.103517	−	0.318593i
$537$	−14357.7	−	10431.5i	−1.15378	−	0.838273i
$538$	−2202.73			−0.176517
$539$		0			0
$540$	−3274.46			−0.260945
$541$	5275.00	+	3832.51i	0.419205	+	0.304570i	0.777318	−	0.629108i	$-0.216580\pi$
$541$	5275.00	+	3832.51i	0.419205	+	0.304570i	−0.358113	+	0.933678i	$0.616580\pi$
$542$	1589.39	−	4891.65i	0.125960	−	0.387665i
$543$	1507.38	+	4639.23i	0.119130	+	0.366645i
$544$	−645.000	+	468.620i	−0.0508348	+	0.0369337i
$545$	−6104.83	+	4435.42i	−0.479821	+	0.348610i
$546$	−4627.16	−	14240.9i	−0.362682	−	1.11622i
$547$	1968.68	−	6058.97i	0.153884	−	0.473607i	−0.844162	−	0.536088i	$-0.819901\pi$
$547$	1968.68	−	6058.97i	0.153884	−	0.473607i	0.998046	+	0.0624813i	$0.0199014\pi$
$548$	6742.54	+	4898.74i	0.525597	+	0.381869i
$549$	18316.8			1.42394
$550$		0			0
$551$	−3280.33			−0.253624
$552$	−8986.84	−	6529.32i	−0.692944	−	0.503453i
$553$	5196.63	−	15993.6i	0.399608	−	1.22987i
$554$	4536.43	+	13961.7i	0.347896	+	1.07071i
$555$	20962.1	−	15229.9i	1.60323	−	1.16481i
$556$	−561.227	+	407.755i	−0.0428081	+	0.0311019i
$557$	1886.24	+	5805.24i	0.143487	+	0.441609i	0.996813	−	0.0797691i	$-0.0254183\pi$
$557$	1886.24	+	5805.24i	0.143487	+	0.441609i	−0.853326	+	0.521378i	$0.825418\pi$
$558$	−1580.14	+	4863.17i	−0.119879	+	0.368951i
$559$	4652.78	+	3380.44i	0.352042	+	0.255774i
$560$	5195.77			0.392074
$561$		0			0
$562$	14985.9			1.12481
$563$	10996.6	+	7989.52i	0.823185	+	0.598079i	0.917623	−	0.397452i	$-0.130106\pi$
$563$	10996.6	+	7989.52i	0.823185	+	0.598079i	−0.0944384	+	0.995531i	$0.530106\pi$
$564$	−4819.21	+	14832.0i	−0.359797	+	1.10734i
$565$	7088.38	+	21815.8i	0.527806	+	1.62442i
$566$	−10507.7	+	7634.27i	−0.780337	+	0.566948i
$567$	8629.12	−	6269.42i	0.639134	−	0.464358i
$568$	−193.936	−	596.873i	−0.0143263	−	0.0440919i
$569$	5314.34	−	16355.9i	0.391544	−	1.20505i	−0.540076	−	0.841616i	$-0.681605\pi$
$569$	5314.34	−	16355.9i	0.391544	−	1.20505i	0.931620	−	0.363433i	$-0.118395\pi$
$570$	−4140.30	−	3008.11i	−0.304243	−	0.221045i
$571$	2475.65			0.181441			0.0907203	−	0.995876i	$-0.471083\pi$
$571$	2475.65			0.181441			0.0907203	+	0.995876i	$0.471083\pi$
$572$		0			0
$573$	10500.6			0.765567
$574$	−8915.22	−	6477.28i	−0.648282	−	0.471005i
$575$	5358.22	−	16490.9i	0.388614	−	1.19603i
$576$	672.905	+	2070.99i	0.0486766	+	0.149811i
$577$	16455.2	−	11955.4i	1.18724	−	0.862581i	0.194270	−	0.980948i	$-0.437766\pi$
$577$	16455.2	−	11955.4i	1.18724	−	0.862581i	0.992970	+	0.118367i	$0.0377661\pi$
$578$	−6945.04	+	5045.86i	−0.499784	+	0.363115i
$579$	−11161.7	−	34352.1i	−0.801146	−	2.46568i
$580$	−2754.84	+	8478.54i	−0.197222	+	0.606986i
$581$	−9461.13	−	6873.91i	−0.675583	−	0.490840i
$582$	−2806.85			−0.199910
$583$		0			0
$584$	−9152.55			−0.648519
$585$	18080.0	+	13135.9i	1.27780	+	0.928379i
$586$	1659.34	−	5106.94i	0.116974	−	0.360009i
$587$	−4579.15	−	14093.2i	−0.321979	−	0.990950i	−0.972786	−	0.231707i	$-0.925569\pi$
$587$	−4579.15	−	14093.2i	−0.321979	−	0.990950i	0.650806	−	0.759244i	$-0.274431\pi$
$588$	3307.56	−	2403.09i	0.231976	−	0.168540i
$589$	−1334.84	+	969.815i	−0.0933802	+	0.0678447i
$590$	−327.873	−	1009.09i	−0.0228785	−	0.0704127i
$591$	−1604.55	+	4938.31i	−0.111679	+	0.343714i
$592$	−2877.98	−	2090.98i	−0.199805	−	0.145167i
$593$	11123.2			0.770281			0.385140	−	0.922858i	$-0.374153\pi$
$593$	11123.2			0.770281			0.385140	+	0.922858i	$0.374153\pi$
$594$		0			0
$595$	−8090.63			−0.557451
$596$	1453.17	+	1055.79i	0.0998729	+	0.0725619i
$597$	7345.32	−	22606.6i	0.503558	−	1.54979i
$598$	4836.76	+	14886.0i	0.330752	+	1.01795i
$599$	−6702.85	+	4869.91i	−0.457214	+	0.332185i	−0.792437	−	0.609953i	$-0.791188\pi$
$599$	−6702.85	+	4869.91i	−0.457214	+	0.332185i	0.335224	+	0.942139i	$0.391188\pi$
$600$	−4932.08	+	3583.37i	−0.335586	+	0.243817i
$601$	8441.82	+	25981.3i	0.572960	+	1.76339i	0.643022	+	0.765848i	$0.277680\pi$
$601$	8441.82	+	25981.3i	0.572960	+	1.76339i	−0.0700619	+	0.997543i	$0.522320\pi$
$602$	−1757.31	+	5408.45i	−0.118974	+	0.366166i
$603$	14303.3	+	10391.9i	0.965962	+	0.701812i
$604$	114.143			0.00768944
$605$		0			0
$606$	−6417.18			−0.430165
$607$	−13209.4	−	9597.18i	−0.883282	−	0.641742i	0.0508356	−	0.998707i	$-0.483812\pi$
$607$	−13209.4	−	9597.18i	−0.883282	−	0.641742i	−0.934118	+	0.356965i	$0.883812\pi$
$608$	−217.125	+	668.243i	−0.0144829	+	0.0445737i
$609$	7850.37	+	24160.9i	0.522353	+	1.60764i
$610$	12994.6	−	9441.10i	0.862515	−	0.626654i
$611$	17777.6	−	12916.2i	1.17710	−	0.855211i
$612$	−1047.82	−	3224.85i	−0.0692084	−	0.213001i
$613$	−6497.18	+	19996.3i	−0.428089	+	1.31752i	0.471916	+	0.881644i	$0.343563\pi$
$613$	−6497.18	+	19996.3i	−0.428089	+	1.31752i	−0.900005	+	0.435879i	$0.856437\pi$
$614$	13480.9	+	9794.46i	0.886068	+	0.643766i
$615$	29498.2			1.93412
$616$		0			0
$617$	871.824			0.0568854			0.0284427	−	0.999595i	$-0.490945\pi$
$617$	871.824			0.0568854			0.0284427	+	0.999595i	$0.490945\pi$
$618$	−17286.9	−	12559.7i	−1.12521	−	0.817515i
$619$	2903.99	−	8937.57i	0.188564	−	0.580342i	−0.811427	−	0.584454i	$-0.801309\pi$
$619$	2903.99	−	8937.57i	0.188564	−	0.580342i	0.999992	+	0.00411206i	$0.00130891\pi$
$620$	1385.64	+	4264.55i	0.0897556	+	0.276239i
$621$	7890.96	−	5733.12i	0.509909	−	0.370470i
$622$	−8123.10	+	5901.78i	−0.523644	+	0.380450i
$623$	4487.27	+	13810.4i	0.288569	+	0.888124i
$624$	1700.55	−	5233.75i	0.109097	−	0.335765i
$625$	14807.2	+	10758.1i	0.947660	+	0.688515i
$626$	−6044.15			−0.385899
$627$		0			0
$628$	6895.44			0.438150
$629$	4481.47	+	3255.98i	0.284083	+	0.206398i
$630$	−6828.63	+	21016.4i	−0.431840	+	1.32907i
$631$	−4491.85	−	13824.5i	−0.283388	−	0.872178i	−0.986877	−	0.161472i	$-0.948376\pi$
$631$	−4491.85	−	13824.5i	−0.283388	−	0.872178i	0.703489	−	0.710706i	$-0.251624\pi$
$632$	5000.02	−	3632.73i	0.314700	−	0.228643i
$633$	16378.7	−	11899.8i	1.02843	−	0.747196i
$634$	6514.17	+	20048.5i	0.408061	+	1.25588i
$635$	−3214.67	+	9893.74i	−0.200898	+	0.618301i
$636$	327.171	+	237.703i	0.0203981	+	0.0148201i
$637$	−5760.67			−0.358314
$638$		0			0
$639$	2669.17			0.165244
$640$	1544.84	+	1122.39i	0.0954140	+	0.0693224i
$641$	−3528.87	+	10860.7i	−0.217445	+	0.669226i	0.781526	+	0.623872i	$0.214441\pi$
$641$	−3528.87	+	10860.7i	−0.217445	+	0.669226i	−0.998971	+	0.0453536i	$0.985559\pi$
$642$	−1908.21	−	5872.86i	−0.117307	−	0.361033i
$643$	−19392.1	+	14089.2i	−1.18934	+	0.864109i	−0.993195	−	0.116465i	$-0.962844\pi$
$643$	−19392.1	+	14089.2i	−1.18934	+	0.864109i	−0.196150	+	0.980574i	$0.562844\pi$
$644$	−12521.0	+	9097.07i	−0.766146	+	0.556638i
$645$	−4704.02	−	14477.5i	−0.287164	−	0.883800i
$646$	338.098	−	1040.56i	0.0205918	−	0.0633750i
$647$	−6726.37	−	4886.99i	−0.408719	−	0.296951i	0.364364	−	0.931257i	$-0.381286\pi$
$647$	−6726.37	−	4886.99i	−0.408719	−	0.296951i	−0.773083	+	0.634305i	$0.781286\pi$
$648$	3919.97			0.237641
$649$		0			0
$650$	8590.04			0.518353
$651$	10337.5	+	7510.66i	0.622366	+	0.452175i
$652$	4101.55	−	12623.3i	0.246363	−	0.758229i
$653$	−9295.02	−	28607.1i	−0.557033	−	1.71437i	−0.690514	−	0.723319i	$-0.742616\pi$
$653$	−9295.02	−	28607.1i	−0.557033	−	1.71437i	0.133482	−	0.991051i	$-0.457384\pi$
$654$	−6393.53	+	4645.17i	−0.382274	+	0.277738i
$655$	3136.86	−	2279.06i	0.187126	−	0.135955i
$656$	−1251.50	−	3851.72i	−0.0744861	−	0.229245i
$657$	12028.9	−	37021.1i	0.714295	−	2.19838i
$658$	17578.6	+	12771.6i	1.04147	+	0.756671i
$659$	−10041.6			−0.593572			−0.296786	−	0.954944i	$-0.595915\pi$
$659$	−10041.6			−0.593572			−0.296786	+	0.954944i	$0.595915\pi$
$660$		0			0
$661$	1402.50			0.0825281			0.0412640	−	0.999148i	$-0.486862\pi$
$661$	1402.50			0.0825281			0.0412640	+	0.999148i	$0.486862\pi$
$662$	501.381	+	364.275i	0.0294362	+	0.0213866i
$663$	−2648.02	+	8149.76i	−0.155114	+	0.477391i
$664$	−1328.13	−	4087.58i	−0.0776229	−	0.238899i
$665$	−5768.54	+	4191.09i	−0.336382	+	0.244396i
$666$	12240.2	−	8893.05i	0.712161	−	0.517415i
$667$	−8205.96	−	25255.4i	−0.476366	−	1.46610i
$668$	−3727.48	+	11472.0i	−0.215899	+	0.664470i
$669$	16666.8	+	12109.2i	0.963195	+	0.699802i
$670$	15503.6			0.893963
$671$		0			0
$672$	5441.49			0.312366
$673$	−16492.1	−	11982.2i	−0.944614	−	0.686302i	0.00491314	−	0.999988i	$-0.498436\pi$
$673$	−16492.1	−	11982.2i	−0.944614	−	0.686302i	−0.949527	+	0.313686i	$0.898436\pi$
$674$	−6900.14	+	21236.4i	−0.394337	+	1.21365i
$675$	−1654.16	−	5090.99i	−0.0943241	−	0.290300i
$676$	836.479	−	607.738i	0.0475921	−	0.0345777i
$677$	5974.59	−	4340.79i	0.339176	−	0.246426i	−0.405138	−	0.914256i	$-0.632777\pi$
$677$	5974.59	−	4340.79i	0.339176	−	0.246426i	0.744314	+	0.667830i	$0.232777\pi$
$678$	7423.60	+	22847.5i	0.420504	+	1.29418i
$679$	−1208.47	+	3719.28i	−0.0683014	+	0.210210i
$680$	−2405.55	−	1747.73i	−0.135660	−	0.0985626i
$681$	−1958.19			−0.110188
$682$		0			0
$683$	−25844.0			−1.44787			−0.723935	−	0.689868i	$-0.757668\pi$
$683$	−25844.0			−1.44787			−0.723935	+	0.689868i	$0.757668\pi$
$684$	−2417.61	−	1756.50i	−0.135146	−	0.0981892i
$685$	−9605.13	+	29561.5i	−0.535756	+	1.64889i
$686$	2854.25	+	8784.49i	0.158857	+	0.488912i
$687$	11371.5	−	8261.85i	0.631511	−	0.458820i
$688$	−1690.82	+	1228.45i	−0.0936948	+	0.0680733i
$689$	−176.085	−	541.933i	−0.00973628	−	0.0299652i
$690$	12802.2	−	39401.3i	0.706338	−	2.17389i
$691$	−6827.13	−	4960.20i	−0.375856	−	0.273075i	0.383779	−	0.923425i	$-0.374622\pi$
$691$	−6827.13	−	4960.20i	−0.375856	−	0.273075i	−0.759635	+	0.650350i	$0.774622\pi$
$692$	−8837.64			−0.485486
$693$		0			0
$694$	−5030.97			−0.275177
$695$	−2093.11	−	1520.74i	−0.114239	−	0.0829998i
$696$	−2885.12	+	8879.49i	−0.157127	+	0.483587i
$697$	1948.78	+	5997.73i	0.105904	+	0.325940i
$698$	−18407.7	+	13374.0i	−0.998198	+	0.725233i
$699$	20100.3	−	14603.7i	1.08764	−	0.790218i
$700$	2624.76	+	8078.17i	0.141723	+	0.436180i
$701$	−4012.08	+	12347.9i	−0.216169	+	0.665298i	0.782900	+	0.622148i	$0.213740\pi$
$701$	−4012.08	+	12347.9i	−0.216169	+	0.665298i	−0.999069	+	0.0431509i	$0.986260\pi$
$702$	3909.19	+	2840.19i	0.210175	+	0.152701i
$703$	4881.90			0.261912
$704$		0			0
$705$	−58163.2			−3.10717
$706$	10048.1	+	7300.39i	0.535646	+	0.389169i
$707$	−2762.87	+	8503.23i	−0.146971	+	0.452330i
$708$	−343.378	−	1056.81i	−0.0182273	−	0.0560979i
$709$	14496.4	−	10532.3i	0.767878	−	0.557896i	−0.133438	−	0.991057i	$-0.542602\pi$
$709$	14496.4	−	10532.3i	0.767878	−	0.557896i	0.901317	+	0.433161i	$0.142602\pi$
$710$	1893.60	−	1375.78i	0.100092	−	0.0727212i
$711$	8122.65	+	24998.9i	0.428443	+	1.31861i
$712$	−1649.14	+	5075.52i	−0.0868033	+	0.267153i
$713$	−10805.8	−	7850.87i	−0.567574	−	0.412367i
$714$	−8473.24			−0.444122
$715$		0			0
$716$	−9087.33			−0.474315
$717$	31686.7	+	23021.7i	1.65043	+	1.19911i
$718$	1537.36	−	4731.52i	0.0799079	−	0.245931i
$719$	1086.92	+	3345.20i	0.0563773	+	0.173512i	0.975280	−	0.220973i	$-0.0709232\pi$
$719$	1086.92	+	3345.20i	0.0563773	+	0.173512i	−0.918903	+	0.394484i	$0.870923\pi$
$720$	−6570.27	+	4773.58i	−0.340083	+	0.247085i
$721$	−24085.3	+	17499.0i	−1.24408	+	0.903877i
$722$	3941.13	+	12129.5i	0.203149	+	0.625228i
$723$	−14662.8	+	45127.6i	−0.754242	+	2.32132i
$724$	2020.71	+	1468.14i	0.103728	+	0.0753630i
$725$	−14573.7			−0.746559
$726$		0			0
$727$	−29438.9			−1.50183			−0.750913	−	0.660401i	$-0.770386\pi$
$727$	−29438.9			−1.50183			−0.750913	+	0.660401i	$0.770386\pi$
$728$	−6202.94	−	4506.70i	−0.315792	−	0.229436i
$729$	−8728.43	+	26863.3i	−0.443450	+	1.36480i
$730$	−10548.2	−	32464.1i	−0.534804	−	1.64596i
$731$	2632.88	−	1912.90i	0.133215	−	0.0967866i
$732$	13609.1	−	9887.58i	0.687167	−	0.499256i
$733$	1061.75	+	3267.73i	0.0535015	+	0.164661i	0.974237	−	0.225527i	$-0.0724102\pi$
$733$	1061.75	+	3267.73i	0.0535015	+	0.164661i	−0.920735	+	0.390187i	$0.872410\pi$
$734$	−4152.90	+	12781.3i	−0.208837	+	0.642733i
$735$	12335.7	+	8962.39i	0.619059	+	0.449773i
$736$	−5687.97			−0.284866
$737$		0			0
$738$	17224.6			0.859143
$739$	27184.4	+	19750.6i	1.35317	+	0.983137i	0.998847	+	0.0480154i	$0.0152896\pi$
$739$	27184.4	+	19750.6i	1.35317	+	0.983137i	0.354326	+	0.935122i	$0.384710\pi$
$740$	4099.85	−	12618.0i	0.203667	−	0.626822i
$741$	2333.71	+	7182.42i	0.115696	+	0.356077i
$742$	455.835	−	331.184i	0.0225529	−	0.0163856i
$743$	965.726	−	701.641i	0.0476838	−	0.0346443i	−0.563688	−	0.825988i	$-0.690618\pi$
$743$	965.726	−	701.641i	0.0476838	−	0.0346443i	0.611372	+	0.791343i	$0.290618\pi$
$744$	1451.16	+	4466.22i	0.0715084	+	0.220080i
$745$	−2070.12	+	6371.19i	−0.101803	+	0.313318i
$746$	−13938.3	−	10126.8i	−0.684074	−	0.497009i
$747$	18279.4			0.895324
$748$		0			0
$749$	−8603.54			−0.419715
$750$	5175.87	+	3760.49i	0.251995	+	0.183085i
$751$	7573.81	−	23309.8i	0.368006	−	1.13260i	−0.580072	−	0.814565i	$-0.696976\pi$
$751$	7573.81	−	23309.8i	0.368006	−	1.13260i	0.948077	−	0.318040i	$-0.103024\pi$
$752$	2467.65	+	7594.66i	0.119662	+	0.368283i
$753$	−35199.8	+	25574.2i	−1.70352	+	1.23768i
$754$	10642.9	−	7732.56i	0.514050	−	0.373479i
$755$	131.549	+	404.866i	0.00634113	+	0.0195160i
$756$	−1476.46	+	4544.09i	−0.0710297	+	0.218607i
$757$	−8740.48	−	6350.33i	−0.419654	−	0.304897i	0.357845	−	0.933781i	$-0.383512\pi$
$757$	−8740.48	−	6350.33i	−0.419654	−	0.304897i	−0.777499	+	0.628885i	$0.783512\pi$
$758$	16018.2			0.767555
$759$		0			0
$760$	−2620.49			−0.125073
$761$	−6614.45	−	4805.68i	−0.315077	−	0.228917i	0.418995	−	0.907989i	$-0.362383\pi$
$761$	−6614.45	−	4805.68i	−0.315077	−	0.228917i	−0.734072	+	0.679072i	$0.762383\pi$
$762$	−3366.70	+	10361.6i	−0.160056	+	0.492601i
$763$	3402.51	+	10471.8i	0.161440	+	0.496863i
$764$	4349.92	−	3160.40i	0.205988	−	0.149659i
$765$	10230.9	−	7433.22i	0.483530	−	0.351305i
$766$	−4951.66	−	15239.6i	−0.233565	−	0.718838i
$767$	−483.833	+	1489.08i	−0.0227773	+	0.0701013i
$768$	1617.89	+	1175.47i	0.0760165	+	0.0552292i
$769$	−28895.9			−1.35502			−0.677511	−	0.735513i	$-0.736941\pi$
$769$	−28895.9			−1.35502			−0.677511	+	0.735513i	$0.736941\pi$
$770$		0			0
$771$	46144.8			2.15547
$772$	−14962.8	−	10871.1i	−0.697569	−	0.506813i
$773$	−5561.32	+	17116.0i	−0.258767	+	0.796402i	0.734297	+	0.678828i	$0.237512\pi$
$773$	−5561.32	+	17116.0i	−0.258767	+	0.796402i	−0.993064	+	0.117574i	$0.962488\pi$
$774$	−2746.78	−	8453.72i	−0.127559	−	0.392588i
$775$	−5930.35	+	4308.65i	−0.274870	+	0.199705i
$776$	−1162.74	+	844.783i	−0.0537888	+	0.0390798i
$777$	−11683.2	−	35957.1i	−0.539423	−	1.66017i
$778$	−4962.57	+	15273.2i	−0.228685	+	0.703819i
$779$	4496.39	+	3266.82i	0.206804	+	0.150252i
$780$	20524.0			0.942148
$781$		0			0
$782$	8857.06			0.405023
$783$	−6632.27	−	4818.63i	−0.302705	−	0.219928i
$784$	646.906	−	1990.97i	0.0294691	−	0.0906966i
$785$	7946.92	+	24458.1i	0.361322	+	1.11204i
$786$	3285.21	−	2386.84i	0.149083	−	0.108315i
$787$	12844.5	−	9332.09i	0.581776	−	0.422685i	−0.257588	−	0.966255i	$-0.582928\pi$
$787$	12844.5	−	9332.09i	0.581776	−	0.422685i	0.839364	+	0.543570i	$0.182928\pi$
$788$	821.603	+	2528.63i	0.0371426	+	0.114313i
$789$	16544.8	−	50919.7i	0.746528	−	2.29758i
$790$	18647.7	+	13548.4i	0.839819	+	0.610164i
$791$	33470.8			1.50453
$792$		0			0
$793$	−23702.5			−1.06141
$794$	7175.97	+	5213.65i	0.320738	+	0.233030i
$795$	−466.073	+	1434.42i	−0.0207923	+	0.0639922i
$796$	−3761.13	−	11575.6i	−0.167475	−	0.515434i
$797$	−13346.9	+	9697.11i	−0.593190	+	0.430978i	−0.843455	−	0.537200i	$-0.819482\pi$
$797$	−13346.9	+	9697.11i	−0.593190	+	0.430978i	0.250265	+	0.968177i	$0.419482\pi$
$798$	−6041.34	+	4389.29i	−0.267996	+	0.194711i
$799$	−3842.52	−	11826.1i	−0.170136	−	0.523625i
$800$	−964.636	+	2968.84i	−0.0426313	+	0.131206i
$801$	−18362.5	−	13341.2i	−0.809998	−	0.588498i
$802$	7858.41			0.345998
$803$		0			0
$804$	16236.7			0.712221
$805$	−46697.7	−	33927.8i	−2.04457	−	1.48546i
$806$	2044.74	−	6293.07i	0.0893586	−	0.275017i
$807$	−2658.67	−	8182.56i	−0.115972	−	0.356927i
$808$	−2658.34	+	1931.39i	−0.115742	+	0.0840918i
$809$	7364.44	−	5350.58i	0.320049	−	0.232529i	−0.416147	−	0.909297i	$-0.636620\pi$
$809$	7364.44	−	5350.58i	0.320049	−	0.232529i	0.736197	+	0.676768i	$0.236620\pi$
$810$	4517.73	+	13904.1i	0.195971	+	0.603138i
$811$	11302.7	−	34786.1i	0.489384	−	1.50617i	−0.336144	−	0.941811i	$-0.609123\pi$
$811$	11302.7	−	34786.1i	0.489384	−	1.50617i	0.825529	−	0.564360i	$-0.190877\pi$
$812$	10523.8	+	7646.00i	0.454820	+	0.330446i
$813$	20089.6			0.866633
$814$		0			0
$815$	49501.7			2.12757
$816$	−2519.31	−	1830.39i	−0.108080	−	0.0785249i
$817$	886.300	−	2727.75i	0.0379531	−	0.116808i
$818$	9001.18	+	27702.8i	0.384742	+	1.18411i
$819$	26381.5	−	19167.3i	1.12557	−	0.817776i
$820$	12219.7	−	8878.14i	0.520403	−	0.378095i
$821$	−1126.12	−	3465.85i	−0.0478709	−	0.147331i	0.924264	−	0.381754i	$-0.124680\pi$
$821$	−1126.12	−	3465.85i	−0.0478709	−	0.147331i	−0.972135	+	0.234423i	$0.924680\pi$
$822$	−10059.4	+	30959.5i	−0.426838	+	1.31367i
$823$	13669.1	+	9931.15i	0.578947	+	0.420630i	0.838344	−	0.545141i	$-0.183524\pi$
$823$	13669.1	+	9931.15i	0.578947	+	0.420630i	−0.259397	+	0.965771i	$0.583524\pi$
$824$	−10941.3			−0.462570
$825$		0			0
$826$	−1548.19			−0.0652160
$827$	31372.1	+	22793.2i	1.31912	+	0.958400i	0.999943	+	0.0107058i	$0.00340784\pi$
$827$	31372.1	+	22793.2i	1.31912	+	0.958400i	0.319181	+	0.947694i	$0.396592\pi$
$828$	7475.51	−	23007.3i	0.313758	−	0.965649i
$829$	−3830.06	−	11787.7i	−0.160462	−	0.493853i	0.838211	−	0.545346i	$-0.183602\pi$
$829$	−3830.06	−	11787.7i	−0.160462	−	0.493853i	−0.998673	+	0.0514936i	$0.983602\pi$
$830$	12968.0	−	9421.78i	0.542319	−	0.394018i
$831$	−46388.6	+	33703.3i	−1.93647	+	1.40693i
$832$	−870.757	−	2679.91i	−0.0362837	−	0.111670i
$833$	−1007.33	+	3100.25i	−0.0418992	+	0.128952i
$834$	−2192.10	−	1592.65i	−0.0910147	−	0.0661260i
$835$	−44987.1			−1.86448
$836$		0			0
$837$	−4123.41			−0.170282
$838$	6518.69	+	4736.11i	0.268717	+	0.195234i
$839$	7590.65	−	23361.6i	0.312346	−	0.961302i	−0.664487	−	0.747300i	$-0.731350\pi$
$839$	7590.65	−	23361.6i	0.312346	−	0.961302i	0.976833	−	0.214002i	$-0.0686500\pi$
$840$	6271.26	+	19300.9i	0.257594	+	0.792793i
$841$	1674.45	−	1216.56i	0.0686560	−	0.0498815i
$842$	−13798.0	+	10024.8i	−0.564737	+	0.410306i
$843$	18087.8	+	55668.7i	0.739002	+	2.27441i
$844$	3203.41	−	9859.07i	0.130647	−	0.402089i
$845$	3119.68	+	2266.58i	0.127006	+	0.0922753i
$846$	−33962.8			−1.38022
$847$		0			0
$848$	207.074			0.00838554
$849$	−41042.0	−	29818.8i	−1.65908	−	1.20539i
$850$	1502.09	−	4622.95i	0.0606132	−	0.186548i
$851$	12212.4	+	37585.8i	0.491933	+	1.51401i
$852$	1983.15	−	1440.84i	0.0797436	−	0.0579371i
$853$	9876.18	−	7175.47i	0.396429	−	0.288023i	−0.371656	−	0.928371i	$-0.621210\pi$
$853$	9876.18	−	7175.47i	0.396429	−	0.288023i	0.768085	+	0.640348i	$0.221210\pi$
$854$	−7242.48	−	22290.1i	−0.290202	−	0.893150i
$855$	3444.02	−	10599.6i	0.137758	−	0.423976i
$856$	−2558.05	−	1858.53i	−0.102141	−	0.0742095i
$857$	7281.72			0.290244			0.145122	−	0.989414i	$-0.453643\pi$
$857$	7281.72			0.290244			0.145122	+	0.989414i	$0.453643\pi$
$858$		0			0
$859$	5927.39			0.235437			0.117718	−	0.993047i	$-0.462442\pi$
$859$	5927.39			0.235437			0.117718	+	0.993047i	$0.462442\pi$
$860$	−6305.98	−	4581.56i	−0.250037	−	0.181663i
$861$	13300.8	−	40935.7i	0.526470	−	1.62031i
$862$	−8291.06	−	25517.3i	−0.327604	−	1.00826i
$863$	31197.2	−	22666.1i	1.23055	−	0.894047i	0.233619	−	0.972328i	$-0.424943\pi$
$863$	31197.2	−	22666.1i	1.23055	−	0.894047i	0.996931	+	0.0782811i	$0.0249432\pi$
$864$	−1420.60	+	1032.13i	−0.0559373	+	0.0406409i
$865$	−10185.3	−	31347.1i	−0.400358	−	1.23218i
$866$	−2553.91	+	7860.12i	−0.100214	+	0.308427i
$867$	−27126.7	−	19708.7i	−1.06259	−	0.772020i
$868$	6542.86			0.255852
$869$		0			0
$870$	−34820.6			−1.35693
$871$	−18508.8	−	13447.5i	−0.720032	−	0.523134i
$872$	−1250.47	+	3848.55i	−0.0485623	+	0.149459i
$873$	−1888.91	−	5813.45i	−0.0732300	−	0.225379i
$874$	6314.99	−	4588.11i	0.244403	−	0.177569i
$875$	7211.36	−	5239.36i	0.278615	−	0.202426i
$876$	−11047.1	−	33999.3i	−0.426079	−	1.31134i
$877$	8810.90	−	27117.2i	0.339251	−	1.04411i	−0.625339	−	0.780353i	$-0.715039\pi$
$877$	8810.90	−	27117.2i	0.339251	−	1.04411i	0.964590	−	0.263754i	$-0.0849606\pi$
$878$	5434.10	+	3948.10i	0.208875	+	0.151756i
$879$	20973.7			0.804809
$880$		0			0
$881$	40747.6			1.55826			0.779128	−	0.626865i	$-0.215662\pi$
$881$	40747.6			1.55826			0.779128	+	0.626865i	$0.215662\pi$
$882$	7203.07	+	5233.34i	0.274989	+	0.199791i
$883$	−1111.10	+	3419.61i	−0.0423459	+	0.130327i	−0.969994	−	0.243127i	$-0.921827\pi$
$883$	−1111.10	+	3419.61i	−0.0423459	+	0.130327i	0.927649	+	0.373454i	$0.121827\pi$
$884$	1355.90	+	4173.04i	0.0515882	+	0.158772i
$885$	3352.76	−	2435.92i	0.127347	−	0.0925228i
$886$	−714.765	+	519.307i	−0.0271027	+	0.0196913i
$887$	−2384.16	−	7337.69i	−0.0902506	−	0.277763i	0.895736	−	0.444586i	$-0.146649\pi$
$887$	−2384.16	−	7337.69i	−0.0902506	−	0.277763i	−0.985987	+	0.166823i	$0.946649\pi$
$888$	4293.73	−	13214.8i	0.162262	−	0.499390i
$889$	12280.4	+	8922.24i	0.463298	+	0.336605i
$890$	−19903.5			−0.749624
$891$		0			0
$892$	10548.8			0.395965
$893$	−8865.79	−	6441.37i	−0.332231	−	0.241380i
$894$	−2168.02	+	6672.49i	−0.0811069	+	0.249621i
$895$	−10473.0	−	32232.7i	−0.391146	−	1.20382i
$896$	2254.15	−	1637.74i	0.0840468	−	0.0610636i
$897$	−49459.7	+	35934.6i	−1.84104	+	1.33759i
$898$	252.454	+	776.972i	0.00938138	+	0.0288729i
$899$	−3469.08	+	10676.7i	−0.128699	+	0.396094i
$900$	−10740.9	−	7803.70i	−0.397810	−	0.289026i
$901$	−322.446			−0.0119226
$902$		0			0
$903$	−22212.0			−0.818571
$904$	9951.71	+	7230.34i	0.366138	+	0.266015i
$905$	−2878.62	+	8859.48i	−0.105733	+	0.325413i
$906$	137.770	+	424.012i	0.00505198	+	0.0155484i
$907$	27275.0	−	19816.4i	0.998512	−	0.725461i	0.0367432	−	0.999325i	$-0.488302\pi$
$907$	27275.0	−	19816.4i	0.998512	−	0.725461i	0.961769	+	0.273863i	$0.0883016\pi$
$908$	−811.185	+	589.360i	−0.0296477	+	0.0215403i
$909$	−4318.53	−	13291.1i	−0.157576	−	0.484969i
$910$	8836.43	−	27195.7i	0.321896	−	0.990693i
$911$	−12160.1	−	8834.84i	−0.442242	−	0.321308i	0.344283	−	0.938866i	$-0.388122\pi$
$911$	−12160.1	−	8834.84i	−0.442242	−	0.321308i	−0.786525	+	0.617558i	$0.788122\pi$
$912$	−2744.42			−0.0996455
$913$		0			0
$914$	−3045.69			−0.110222
$915$	50755.5	+	36876.1i	1.83380	+	1.33233i
$916$	2224.07	−	6844.99i	0.0802243	−	0.246905i
$917$	−1748.32	−	5380.78i	−0.0629604	−	0.193772i
$918$	2212.10	−	1607.18i	0.0795318	−	0.0577832i
$919$	13826.7	−	10045.7i	0.496300	−	0.360583i	−0.311302	−	0.950311i	$-0.600765\pi$
$919$	13826.7	−	10045.7i	0.496300	−	0.360583i	0.807602	+	0.589728i	$0.200765\pi$
$920$	−6555.33	−	20175.2i	−0.234916	−	0.722997i
$921$	−20112.5	+	61899.9i	−0.719576	+	2.21463i
$922$	−22428.1	−	16295.0i	−0.801119	−	0.582047i
$923$	−3453.98			−0.123173
$924$		0			0
$925$	21689.1			0.770955
$926$	−10520.9	−	7643.86i	−0.373367	−	0.271267i
$927$	14379.8	−	44256.4i	0.509486	−	1.56804i
$928$	1477.31	+	4546.70i	0.0522577	+	0.160833i
$929$	−10646.9	+	7735.40i	−0.376009	+	0.273187i	−0.759698	−	0.650276i	$-0.774653\pi$
$929$	−10646.9	+	7735.40i	−0.376009	+	0.273187i	0.383689	+	0.923462i	$0.374653\pi$
$930$	−14169.2	+	10294.5i	−0.499599	+	0.362980i
$931$	887.767	+	2732.27i	0.0312518	+	0.0961830i
$932$	3931.28	−	12099.2i	0.138169	−	0.425240i
$933$	−31728.1	−	23051.8i	−1.11332	−	0.808877i
$934$	−847.946			−0.0297063
$935$		0			0
$936$	11984.4			0.418506
$937$	−3281.61	−	2384.23i	−0.114413	−	0.0831263i	0.529107	−	0.848555i	$-0.322527\pi$
$937$	−3281.61	−	2384.23i	−0.114413	−	0.0831263i	−0.643521	+	0.765429i	$0.722527\pi$
$938$	6990.61	−	21514.9i	0.243338	−	0.748919i
$939$	−7295.24	−	22452.4i	−0.253537	−	0.780306i
$940$	−24094.3	+	17505.5i	−0.836031	+	0.607412i
$941$	−27019.3	+	19630.6i	−0.936028	+	0.680064i	−0.947461	−	0.319870i	$-0.896361\pi$
$941$	−27019.3	+	19630.6i	−0.936028	+	0.680064i	0.0114331	+	0.999935i	$0.496361\pi$
$942$	8322.74	+	25614.8i	0.287866	+	0.885960i
$943$	−13903.3	+	42790.0i	−0.480121	+	1.47766i
$944$	−460.316	−	334.439i	−0.0158708	−	0.0115308i
$945$	−17819.5			−0.613405
$946$		0			0
$947$	25660.8			0.880533			0.440267	−	0.897867i	$-0.354884\pi$
$947$	25660.8			0.880533			0.440267	+	0.897867i	$0.354884\pi$
$948$	19529.6	+	14189.1i	0.669085	+	0.486119i
$949$	−15565.7	+	47906.3i	−0.532439	+	1.63868i
$950$	−1323.80	−	4074.23i	−0.0452101	−	0.139143i
$951$	−66612.6	+	48396.9i	−2.27136	+	1.65024i
$952$	−3510.07	+	2550.21i	−0.119498	+	0.0868203i
$953$	15096.3	+	46461.8i	0.513136	+	1.57927i	0.786648	+	0.617401i	$0.211815\pi$
$953$	15096.3	+	46461.8i	0.513136	+	1.57927i	−0.273512	+	0.961868i	$0.588185\pi$
$954$	−272.150	+	837.592i	−0.00923604	+	0.0284256i
$955$	16223.2	+	11786.8i	0.549706	+	0.399385i
$956$	20055.2			0.678485
$957$		0			0
$958$	−9114.68			−0.307392
$959$	36692.7	+	26658.8i	1.23552	+	0.897661i
$960$	−2304.78	+	7093.37i	−0.0774858	+	0.238477i
$961$	−7461.04	−	22962.7i	−0.250446	−	0.770794i
$962$	−15839.2	+	11507.8i	−0.530848	+	0.385684i
$963$	10879.5	−	7904.45i	0.364058	−	0.264504i
$964$	7508.03	+	23107.3i	0.250848	+	0.772031i
$965$	21315.3	−	65601.9i	0.711052	−	2.18839i
$966$	−48906.0	−	35532.3i	−1.62891	−	1.18347i
$967$	−48861.8			−1.62491			−0.812456	−	0.583023i	$-0.801870\pi$
$967$	−48861.8			−1.62491			−0.812456	+	0.583023i	$0.801870\pi$
$968$		0			0
$969$	4273.48			0.141676
$970$	−4336.49	−	3150.65i	−0.143543	−	0.104290i
$971$	10780.8	−	33180.0i	0.356306	−	1.09660i	−0.598942	−	0.800792i	$-0.704412\pi$
$971$	10780.8	−	33180.0i	0.356306	−	1.09660i	0.955248	−	0.295805i	$-0.0955880\pi$
$972$	6562.72	+	20198.0i	0.216563	+	0.666513i
$973$	−3054.18	+	2218.99i	−0.100629	+	0.0731115i
$974$	−10855.3	+	7886.81i	−0.357110	+	0.259456i
$975$	10368.1	+	31909.8i	0.340559	+	1.04813i
$976$	2661.72	−	8191.92i	0.0872945	−	0.268665i
$977$	15381.4	+	11175.2i	0.503678	+	0.365944i	0.810420	−	0.585849i	$-0.199239\pi$
$977$	15381.4	+	11175.2i	0.503678	+	0.365944i	−0.306742	+	0.951793i	$0.599239\pi$
$978$	51842.7			1.69504
$979$		0			0
$980$	7807.52			0.254492
$981$	−13923.6	−	10116.1i	−0.453155	−	0.329236i
$982$	−8978.58	+	27633.2i	−0.291770	+	0.897975i
$983$	−2301.52	−	7083.36i	−0.0746767	−	0.229831i	0.906750	−	0.421669i	$-0.138555\pi$
$983$	−2301.52	−	7083.36i	−0.0746767	−	0.229831i	−0.981427	+	0.191837i	$0.938555\pi$
$984$	12797.6	−	9297.99i	0.414606	−	0.301229i
$985$	−8022.17	+	5828.45i	−0.259500	+	0.188538i
$986$	−2300.41	−	7079.92i	−0.0743000	−	0.228672i
$987$	−26226.0	+	80715.3i	−0.845777	+	2.60304i
$988$	3128.46	+	2272.96i	0.100738	+	0.0731907i
$989$	23218.2			0.746506
$990$		0			0
$991$	5313.37			0.170318			0.0851588	−	0.996367i	$-0.472860\pi$
$991$	5313.37			0.170318			0.0851588	+	0.996367i	$0.472860\pi$
$992$	1945.36	+	1413.39i	0.0622633	+	0.0452369i
$993$	−748.023	+	2302.18i	−0.0239051	+	0.0735724i
$994$	−1055.39	−	3248.16i	−0.0336770	−	0.103647i
$995$	36723.9	−	26681.5i	1.17008	−	0.850110i
$996$	13581.2	−	9867.35i	0.432066	−	0.313914i
$997$	16539.8	+	50904.3i	0.525397	+	1.61701i	0.763529	+	0.645773i	$0.223465\pi$
$997$	16539.8	+	50904.3i	0.525397	+	1.61701i	−0.238132	+	0.971233i	$0.576535\pi$
$998$	5994.64	−	18449.6i	0.190137	−	0.585182i
$999$	9870.36	+	7171.24i	0.312597	+	0.227115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.4.c.r.81.1		8
11.2	odd	10		242.4.c.q.27.2		8
11.3	even	5	inner	242.4.c.r.3.1		8
11.4	even	5		22.4.c.b.9.2	yes	8
11.5	even	5		242.4.a.n.1.1		4
11.6	odd	10		242.4.a.o.1.1		4
11.7	odd	10		242.4.c.q.9.2		8
11.8	odd	10		242.4.c.n.3.1		8
11.9	even	5		22.4.c.b.5.2	✓	8
11.10	odd	2		242.4.c.n.81.1		8
33.5	odd	10		2178.4.a.by.1.1		4
33.17	even	10		2178.4.a.bt.1.1		4
33.20	odd	10		198.4.f.d.181.1		8
33.26	odd	10		198.4.f.d.163.1		8
44.15	odd	10		176.4.m.b.97.1		8
44.27	odd	10		1936.4.a.bn.1.4		4
44.31	odd	10		176.4.m.b.49.1		8
44.39	even	10		1936.4.a.bm.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.4.c.b.5.2	✓	8	11.9	even	5
22.4.c.b.9.2	yes	8	11.4	even	5
176.4.m.b.49.1		8	44.31	odd	10
176.4.m.b.97.1		8	44.15	odd	10
198.4.f.d.163.1		8	33.26	odd	10
198.4.f.d.181.1		8	33.20	odd	10
242.4.a.n.1.1		4	11.5	even	5
242.4.a.o.1.1		4	11.6	odd	10
242.4.c.n.3.1		8	11.8	odd	10
242.4.c.n.81.1		8	11.10	odd	2
242.4.c.q.9.2		8	11.7	odd	10
242.4.c.q.27.2		8	11.2	odd	10
242.4.c.r.3.1		8	11.3	even	5	inner
242.4.c.r.81.1		8	1.1	even	1	trivial
1936.4.a.bm.1.4		4	44.39	even	10
1936.4.a.bn.1.4		4	44.27	odd	10
2178.4.a.bt.1.1		4	33.17	even	10
2178.4.a.by.1.1		4	33.5	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.61803 + 1.17557i) q^{2} +(-2.41398 + 7.42948i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-12.0690 + 8.76866i) q^{5} +(-12.6398 + 9.18334i) q^{6} +(6.72664 + 20.7025i) q^{7} +(-2.47214 + 7.60845i) q^{8} +(-27.5264 - 19.9991i) q^{9} +O(q^{10})\)	\(q+(1.61803 + 1.17557i) q^{2} +(-2.41398 + 7.42948i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-12.0690 + 8.76866i) q^{5} +(-12.6398 + 9.18334i) q^{6} +(6.72664 + 20.7025i) q^{7} +(-2.47214 + 7.60845i) q^{8} +(-27.5264 - 19.9991i) q^{9} -29.8363 q^{10} -31.2473 q^{12} +(35.6199 + 25.8793i) q^{13} +(-13.4533 + 41.4049i) q^{14} +(-36.0121 - 110.834i) q^{15} +(-12.9443 + 9.40456i) q^{16} +(20.1563 - 14.6444i) q^{17} +(-21.0283 - 64.7184i) q^{18} +(6.78516 - 20.8826i) q^{19} +(-48.2761 - 35.0746i) q^{20} -170.046 q^{21} +177.749 q^{23} +(-50.5591 - 36.7334i) q^{24} +(30.1449 - 92.7763i) q^{25} +(27.2111 + 83.7473i) q^{26} +(44.3938 - 32.2540i) q^{27} +(-70.4423 + 51.1793i) q^{28} +(-46.1660 - 142.084i) q^{29} +(72.0243 - 221.668i) q^{30} +(-60.7925 - 44.1683i) q^{31} -32.0000 q^{32} +49.8290 q^{34} +(-262.717 - 190.875i) q^{35} +(42.0565 - 129.437i) q^{36} +(68.7057 + 211.455i) q^{37} +(35.5276 - 25.8123i) q^{38} +(-278.256 + 202.165i) q^{39} +(-36.8797 - 113.504i) q^{40} +(-78.2188 + 240.733i) q^{41} +(-275.141 - 199.902i) q^{42} +130.623 q^{43} +507.582 q^{45} +(287.604 + 208.957i) q^{46} +(154.228 - 474.666i) q^{47} +(-38.6237 - 118.872i) q^{48} +(-105.851 + 76.9055i) q^{49} +(157.841 - 114.678i) q^{50} +(60.1432 + 185.102i) q^{51} +(-54.4223 + 167.495i) q^{52} +(-10.4704 - 7.60718i) q^{53} +109.748 q^{54} -174.143 q^{56} +(138.767 + 100.820i) q^{57} +(92.3320 - 284.169i) q^{58} +(10.9891 + 33.8209i) q^{59} +(377.124 - 273.997i) q^{60} +(-435.529 + 316.430i) q^{61} +(-46.4413 - 142.932i) q^{62} +(228.870 - 704.390i) q^{63} +(-51.7771 - 37.6183i) q^{64} -656.824 q^{65} -519.621 q^{67} +(80.6250 + 58.5775i) q^{68} +(-429.083 + 1320.58i) q^{69} +(-200.698 - 617.684i) q^{70} +(-63.4663 + 46.1109i) q^{71} +(220.211 - 159.993i) q^{72} +(353.537 + 1088.07i) q^{73} +(-137.411 + 422.909i) q^{74} +(616.511 + 447.921i) q^{75} +87.8290 q^{76} -687.886 q^{78} +(-625.003 - 454.091i) q^{79} +(73.7593 - 227.008i) q^{80} +(-151.417 - 466.014i) q^{81} +(-409.559 + 297.562i) q^{82} +(-434.638 + 315.783i) q^{83} +(-210.189 - 646.895i) q^{84} +(-114.855 + 353.487i) q^{85} +(211.353 + 153.557i) q^{86} +1167.06 q^{87} +667.089 q^{89} +(821.284 + 596.698i) q^{90} +(-296.164 + 911.499i) q^{91} +(219.710 + 676.198i) q^{92} +(474.899 - 345.035i) q^{93} +(807.550 - 586.720i) q^{94} +(101.222 + 311.529i) q^{95} +(77.2475 - 237.743i) q^{96} +(145.343 + 105.598i) q^{97} -261.679 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 7 q^{3} - 8 q^{4} - 30 q^{5} - 6 q^{6} + 4 q^{7} + 16 q^{8} - 81 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 - 7 * q^3 - 8 * q^4 - 30 * q^5 - 6 * q^6 + 4 * q^7 + 16 * q^8 - 81 * q^9	\( 8 q + 4 q^{2} - 7 q^{3} - 8 q^{4} - 30 q^{5} - 6 q^{6} + 4 q^{7} + 16 q^{8} - 81 q^{9} - 100 q^{10} + 32 q^{12} - 48 q^{13} - 8 q^{14} - 279 q^{15} - 32 q^{16} - 109 q^{17} + 42 q^{18} + 288 q^{19} - 120 q^{20} - 50 q^{21} + 628 q^{23} - 24 q^{24} + 38 q^{25} - 14 q^{26} + 242 q^{27} - 4 q^{28} + 528 q^{29} + 558 q^{30} - 522 q^{31} - 256 q^{32} + 208 q^{34} - 17 q^{35} - 84 q^{36} - 406 q^{37} + 544 q^{38} - 1429 q^{39} - 40 q^{40} - 329 q^{41} - 1480 q^{42} + 1442 q^{43} + 2652 q^{45} + 1044 q^{46} + 666 q^{47} - 112 q^{48} - 114 q^{49} + 34 q^{50} + 1158 q^{51} + 28 q^{52} + 414 q^{53} - 1144 q^{54} + 48 q^{56} - 593 q^{57} - 1056 q^{58} - 888 q^{59} + 844 q^{60} - 302 q^{61} - 646 q^{62} - 2061 q^{63} - 128 q^{64} - 138 q^{65} + 578 q^{67} - 436 q^{68} + 1930 q^{69} + 1394 q^{70} + 1090 q^{71} + 648 q^{72} + 253 q^{73} + 812 q^{74} + 2763 q^{75} - 128 q^{76} - 4152 q^{78} - 674 q^{79} + 80 q^{80} - 230 q^{81} - 722 q^{82} - 428 q^{83} - 2860 q^{84} + 1046 q^{85} - 984 q^{86} + 2122 q^{87} - 2202 q^{89} + 1366 q^{90} - 2217 q^{91} + 832 q^{92} - 3721 q^{93} + 2138 q^{94} - 973 q^{95} + 224 q^{96} + 3012 q^{97} - 3292 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 7 * q^3 - 8 * q^4 - 30 * q^5 - 6 * q^6 + 4 * q^7 + 16 * q^8 - 81 * q^9 - 100 * q^10 + 32 * q^12 - 48 * q^13 - 8 * q^14 - 279 * q^15 - 32 * q^16 - 109 * q^17 + 42 * q^18 + 288 * q^19 - 120 * q^20 - 50 * q^21 + 628 * q^23 - 24 * q^24 + 38 * q^25 - 14 * q^26 + 242 * q^27 - 4 * q^28 + 528 * q^29 + 558 * q^30 - 522 * q^31 - 256 * q^32 + 208 * q^34 - 17 * q^35 - 84 * q^36 - 406 * q^37 + 544 * q^38 - 1429 * q^39 - 40 * q^40 - 329 * q^41 - 1480 * q^42 + 1442 * q^43 + 2652 * q^45 + 1044 * q^46 + 666 * q^47 - 112 * q^48 - 114 * q^49 + 34 * q^50 + 1158 * q^51 + 28 * q^52 + 414 * q^53 - 1144 * q^54 + 48 * q^56 - 593 * q^57 - 1056 * q^58 - 888 * q^59 + 844 * q^60 - 302 * q^61 - 646 * q^62 - 2061 * q^63 - 128 * q^64 - 138 * q^65 + 578 * q^67 - 436 * q^68 + 1930 * q^69 + 1394 * q^70 + 1090 * q^71 + 648 * q^72 + 253 * q^73 + 812 * q^74 + 2763 * q^75 - 128 * q^76 - 4152 * q^78 - 674 * q^79 + 80 * q^80 - 230 * q^81 - 722 * q^82 - 428 * q^83 - 2860 * q^84 + 1046 * q^85 - 984 * q^86 + 2122 * q^87 - 2202 * q^89 + 1366 * q^90 - 2217 * q^91 + 832 * q^92 - 3721 * q^93 + 2138 * q^94 - 973 * q^95 + 224 * q^96 + 3012 * q^97 - 3292 * q^98

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