LMFDB - Embedded newform 242.4.c.r.3.1

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			3.1
Root			$2.22300 - 6.84169i$ of defining polynomial
Character	$\chi$	$=$	242.3
Dual form			242.4.c.r.81.1

$q$-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 $\left(\mathbb{Z}/242\mathbb{Z}\right)^\times$.

$n$	$123$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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	−0.859521	−	0.511101i	$-0.829238\pi$
$3$	−2.41398	−	7.42948i	−0.464571	−	1.42980i	0.394949	−	0.918703i	$-0.370762\pi$
$4$	1.23607	−	3.80423i	0.154508	−	0.475528i
$5$	−12.0690	−	8.76866i	−1.07949	−	0.784293i	−0.101893	−	0.994795i	$-0.532490\pi$
$5$	−12.0690	−	8.76866i	−1.07949	−	0.784293i	−0.977593	+	0.210502i	$0.932490\pi$
$6$	−12.6398	−	9.18334i	−0.860028	−	0.624847i
$7$	6.72664	−	20.7025i	0.363204	−	1.11783i	−0.587894	−	0.808938i	$-0.700043\pi$
$7$	6.72664	−	20.7025i	0.363204	−	1.11783i	0.951098	−	0.308890i	$-0.0999573\pi$
$8$	−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	−0.138955	−	0.990299i	$-0.544374\pi$
$13$	35.6199	−	25.8793i	0.759936	−	0.552126i	0.898891	+	0.438173i	$0.144374\pi$
$14$	−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	0.722210	−	0.691673i	$-0.243126\pi$
$17$	20.1563	+	14.6444i	0.287565	+	0.208928i	−0.434645	+	0.900602i	$0.643126\pi$
$18$	−21.0283	+	64.7184i	−0.275356	+	0.847459i
$19$	6.78516	+	20.8826i	0.0819275	+	0.252147i	0.983627	−	0.180216i	$-0.0576798\pi$
$19$	6.78516	+	20.8826i	0.0819275	+	0.252147i	−0.901699	+	0.432363i	$0.857680\pi$
$20$	−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	0.687400	+	0.726279i	$0.258752\pi$
$29$	−46.1660	+	142.084i	−0.295614	+	0.909807i	−0.983014	+	0.183528i	$0.941248\pi$
$30$	72.0243	+	221.668i	0.438326	+	1.34903i
$31$	−60.7925	+	44.1683i	−0.352214	+	0.255899i	−0.749797	−	0.661667i	$-0.769849\pi$
$31$	−60.7925	+	44.1683i	−0.352214	+	0.255899i	0.397583	+	0.917566i	$0.369849\pi$
$32$	−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	−0.674300	−	0.738457i	$-0.735555\pi$
$37$	68.7057	−	211.455i	0.305274	−	0.939538i	0.979575	−	0.201081i	$-0.0644454\pi$
$38$	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	−0.982217	−	0.187752i	$-0.939880\pi$
$41$	−78.2188	−	240.733i	−0.297944	−	0.916979i	0.684272	−	0.729227i	$-0.260120\pi$
$42$	−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	0.840972	+	0.541079i	$0.181984\pi$
$47$	154.228	+	474.666i	0.478649	+	1.47313i	−0.362323	+	0.932053i	$0.618016\pi$
$48$	−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	−0.601271	−	0.799045i	$-0.705339\pi$
$53$	−10.4704	+	7.60718i	−0.0271362	+	0.0197156i	0.574134	+	0.818761i	$0.305339\pi$
$54$	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	−0.938200	−	0.346093i	$-0.887508\pi$
$59$	10.9891	−	33.8209i	0.0242484	−	0.0746288i	0.962448	+	0.271465i	$0.0875080\pi$
$60$	377.124	+	273.997i	0.811442	+	0.589547i
$61$	−435.529	−	316.430i	−0.914160	−	0.664176i	0.0279035	−	0.999611i	$-0.491117\pi$
$61$	−435.529	−	316.430i	−0.914160	−	0.664176i	−0.942064	+	0.335435i	$0.891117\pi$
$62$	−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	0.533478	−	0.845814i	$-0.320885\pi$
$71$	−63.4663	−	46.1109i	−0.106085	−	0.0770755i	−0.639563	+	0.768739i	$0.720885\pi$
$72$	220.211	+	159.993i	0.360446	+	0.261879i
$73$	353.537	−	1088.07i	0.566827	−	1.74451i	−0.0956336	−	0.995417i	$-0.530488\pi$
$73$	353.537	−	1088.07i	0.566827	−	1.74451i	0.662460	−	0.749097i	$-0.269512\pi$
$74$	−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	−0.935905	−	0.352252i	$-0.885416\pi$
$79$	−625.003	+	454.091i	−0.890105	+	0.646699i	0.0458005	+	0.998951i	$0.485416\pi$
$80$	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	0.262051	−	0.965054i	$-0.415601\pi$
$83$	−434.638	−	315.783i	−0.574791	−	0.417610i	−0.836843	+	0.547444i	$0.815601\pi$
$84$	−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	−0.509112	−	0.860700i	$-0.670026\pi$
$97$	145.343	−	105.598i	0.152138	−	0.110534i	0.661250	+	0.750166i	$0.270026\pi$
$98$	−261.679			−0.269730
$99$		0			0
$100$	390.203			0.390203
$101$	332.292	−	241.424i	0.327369	−	0.237848i	−0.411944	−	0.911209i	$-0.635150\pi$
$101$	332.292	−	241.424i	0.327369	−	0.237848i	0.739314	+	0.673361i	$0.235150\pi$
$102$	−120.286	−	370.203i	−0.116766	−	0.359369i
$103$	422.630	−	1300.72i	0.404301	−	1.24431i	−0.517177	−	0.855879i	$-0.673017\pi$
$103$	422.630	−	1300.72i	0.404301	−	1.24431i	0.921478	−	0.388431i	$-0.126983\pi$
$104$	−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	0.880600	−	0.473861i	$-0.157140\pi$
$107$	−122.136	−	375.896i	−0.110349	−	0.339619i	−0.990949	+	0.134242i	$0.957140\pi$
$108$	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	0.928523	+	0.371275i	$0.121079\pi$
$113$	475.152	+	1462.37i	0.395562	+	1.21742i	−0.532961	+	0.846140i	$0.678921\pi$
$114$	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	0.767165	−	0.641450i	$-0.221667\pi$
$127$	564.153	+	409.881i	0.394177	+	0.286387i	−0.372988	+	0.927836i	$0.621667\pi$
$128$	−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	0.972439	−	0.233157i	$-0.0749055\pi$
$137$	1685.64	+	1224.69i	1.05119	+	0.763737i	0.0787550	+	0.996894i	$0.474906\pi$
$138$	−2246.71	−	1632.33i	−1.38589	−	1.00691i
$139$	53.5924	−	164.940i	0.0327025	−	0.100648i	−0.933373	−	0.358908i	$-0.883149\pi$
$139$	53.5924	−	164.940i	0.0327025	−	0.100648i	0.966075	+	0.258260i	$0.0831492\pi$
$140$	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	0.683162	−	0.730267i	$-0.260604\pi$
$149$	363.293	+	263.948i	0.199746	+	0.145124i	−0.483416	+	0.875391i	$0.660604\pi$
$150$	470.972	−	1449.50i	0.256365	−	0.789010i
$151$	8.81804	+	27.1391i	0.00475233	+	0.0146262i	0.953405	−	0.301695i	$-0.0975524\pi$
$151$	8.81804	+	27.1391i	0.00475233	+	0.0146262i	−0.948652	+	0.316321i	$0.897552\pi$
$152$	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	0.990302	+	0.138929i	$0.0443661\pi$
$157$	532.702	+	1639.49i	0.270791	+	0.833411i	−0.719511	+	0.694481i	$0.755634\pi$
$158$	−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	−0.999805	−	0.0197528i	$-0.993712\pi$
$163$	−2684.50	+	1950.40i	−1.28998	+	0.937222i	−0.290171	+	0.956975i	$0.593712\pi$
$164$	−1012.49			−0.482084
$165$		0			0
$166$	−1074.48			−0.502386
$167$	2439.67	−	1772.52i	1.13046	−	0.821330i	0.144701	−	0.989475i	$-0.453778\pi$
$167$	2439.67	−	1772.52i	1.13046	−	0.821330i	0.985762	+	0.168146i	$0.0537779\pi$
$168$	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	−0.981479	−	0.191569i	$-0.938643\pi$
$173$	−682.745	−	2101.27i	−0.300047	−	0.923450i	0.681432	−	0.731881i	$-0.261357\pi$
$174$	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	−0.983839	−	0.179055i	$-0.942696\pi$
$179$	−702.034	−	2160.64i	−0.293143	−	0.902200i	0.690696	−	0.723145i	$-0.257304\pi$
$180$	627.405	−	1930.95i	0.259800	−	0.799583i
$181$	505.179	+	367.034i	0.207457	+	0.150726i	0.686662	−	0.726977i	$-0.259075\pi$
$181$	505.179	+	367.034i	0.207457	+	0.150726i	−0.479206	+	0.877703i	$0.659075\pi$
$182$	−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	−0.998392	−	0.0566797i	$-0.981949\pi$
$191$	−415.380	+	1278.41i	−0.157360	+	0.484306i	0.841032	+	0.540985i	$0.181949\pi$
$192$	404.473	+	293.867i	0.152033	+	0.110458i
$193$	−3740.70	−	2717.78i	−1.39514	−	1.01363i	−0.995280	−	0.0970499i	$-0.969059\pi$
$193$	−3740.70	−	2717.78i	−1.39514	−	1.01363i	−0.399858	−	0.916577i	$-0.630941\pi$
$194$	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	−0.874707	−	0.484652i	$-0.838946\pi$
$211$	−2096.66	+	1523.31i	−0.684075	+	0.497009i	0.190632	+	0.981662i	$0.438946\pi$
$212$	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	0.995682	+	0.0928251i	$0.0295897\pi$
$223$	814.941	+	2508.13i	0.244720	+	0.753170i	−0.750963	+	0.660345i	$0.770410\pi$
$224$	−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	−0.939093	−	0.343662i	$-0.888332\pi$
$227$	77.4613	−	238.401i	0.0226488	−	0.0697059i	0.961742	+	0.273956i	$0.0883324\pi$
$228$	−212.018	−	652.524i	−0.0615843	−	0.189537i
$229$	−1455.67	+	1057.61i	−0.420060	+	0.305191i	−0.777662	−	0.628683i	$-0.783594\pi$
$229$	−1455.67	+	1057.61i	−0.420060	+	0.305191i	0.357602	+	0.933874i	$0.383594\pi$
$230$	−5303.37			−1.52041
$231$		0			0
$232$	1195.17			0.338219
$233$	−2573.06	+	1869.44i	−0.723462	+	0.525626i	−0.887488	−	0.460830i	$-0.847552\pi$
$233$	−2573.06	+	1869.44i	−0.723462	+	0.525626i	0.164026	+	0.986456i	$0.447552\pi$
$234$	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	0.908323	+	0.418270i	$0.137363\pi$
$239$	1549.35	+	4768.41i	0.419327	+	1.29056i	−0.488996	+	0.872286i	$0.662637\pi$
$240$	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	0.146979	−	0.989140i	$-0.453045\pi$
$251$	4505.98	−	3273.78i	1.13313	−	0.823264i	0.986147	+	0.165875i	$0.0530449\pi$
$252$	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	0.441557	+	0.897233i	$0.354426\pi$
$257$	−1825.38	+	5617.94i	−0.443051	+	1.36357i	−0.884607	+	0.466336i	$0.845574\pi$
$258$	−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	0.482210	−	0.876056i	$-0.339834\pi$
$269$	−891.022	−	647.366i	−0.201958	−	0.146731i	−0.684167	+	0.729325i	$0.739834\pi$
$270$	−1324.55	−	962.339i	−0.298553	−	0.216911i
$271$	−794.697	+	2445.83i	−0.178134	+	0.548241i	−0.999763	−	0.0217823i	$-0.993066\pi$
$271$	−794.697	+	2445.83i	−0.178134	+	0.548241i	0.821628	+	0.570024i	$0.193066\pi$
$272$	−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	0.288307	−	0.957538i	$-0.406908\pi$
$277$	5938.27	−	4314.40i	1.28807	−	0.935839i	0.999765	+	0.0216990i	$0.00690756\pi$
$278$	−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	0.999738	−	0.0228766i	$-0.00728249\pi$
$281$	6061.92	+	4404.24i	1.28692	+	0.935000i	0.287179	+	0.957877i	$0.407282\pi$
$282$	2409.61	−	7416.01i	0.508830	−	1.56602i
$283$	−2006.79	−	6176.26i	−0.421523	−	1.29732i	−0.906284	−	0.422669i	$-0.861093\pi$
$283$	−2006.79	−	6176.26i	−0.421523	−	1.29732i	0.484761	−	0.874647i	$-0.338907\pi$
$284$	−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	−0.999067	−	0.0431764i	$-0.986252\pi$
$293$	−829.672	+	2553.47i	−0.165426	+	0.509130i	0.833641	+	0.552307i	$0.186252\pi$
$294$	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	−0.987031	−	0.160529i	$-0.948680\pi$
$311$	−1551.37	−	4774.64i	−0.282863	−	0.870562i	0.704168	−	0.710033i	$-0.251320\pi$
$312$	−850.274	+	2616.87i	−0.154286	+	0.474844i
$313$	−2444.91	−	1776.33i	−0.441516	−	0.320780i	0.344721	−	0.938705i	$-0.387974\pi$
$313$	−2444.91	−	1776.33i	−0.441516	−	0.320780i	−0.786237	+	0.617925i	$0.787974\pi$
$314$	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	0.545021	−	0.838422i	$-0.316522\pi$
$317$	8527.16	−	6195.34i	1.51083	−	1.09768i	0.965808	−	0.259259i	$-0.0834784\pi$
$318$	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	−0.131090	−	0.991371i	$-0.541848\pi$
$337$	3450.07	−	10618.2i	0.557677	−	1.71635i	0.688767	−	0.724983i	$-0.258152\pi$
$338$	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	0.419133	−	0.907925i	$-0.362334\pi$
$347$	−2035.07	−	1478.56i	−0.314836	−	0.228742i	−0.733969	+	0.679183i	$0.762334\pi$
$348$	1442.56	−	4439.75i	0.222211	−	0.683895i
$349$	−3515.56	−	10819.8i	−0.539208	−	1.65951i	−0.734377	−	0.678742i	$-0.762526\pi$
$349$	−3515.56	−	10819.8i	−0.539208	−	1.65951i	0.195169	−	0.980770i	$-0.437474\pi$
$350$	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	−0.991526	−	0.129908i	$-0.958532\pi$
$359$	−768.682	+	2365.76i	−0.113007	+	0.347799i	0.878519	+	0.477707i	$0.158532\pi$
$360$	−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	−0.687767	−	0.725931i	$-0.741409\pi$
$367$	2076.45	−	6390.65i	0.295340	−	0.908962i	0.983107	−	0.183031i	$-0.0585909\pi$
$368$	−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	0.932769	−	0.360475i	$-0.117386\pi$
$379$	6479.49	+	4707.63i	0.878178	+	0.638033i	−0.0545912	+	0.998509i	$0.517386\pi$
$380$	−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	−0.929177	−	0.369635i	$-0.879483\pi$
$383$	−6481.80	+	4709.31i	−0.864764	+	0.628288i	0.0644128	+	0.997923i	$0.479483\pi$
$384$	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	−0.648745	−	0.761006i	$-0.724706\pi$
$389$	2481.28	−	7636.61i	0.323409	−	0.995350i	0.972154	−	0.234344i	$-0.0752943\pi$
$390$	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	0.767854	−	0.640625i	$-0.221325\pi$
$401$	3178.79	+	2309.53i	0.395864	+	0.287612i	−0.371990	+	0.928237i	$0.621325\pi$
$402$	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	0.433482	−	0.901162i	$-0.357285\pi$
$409$	11782.7	−	8560.63i	1.42449	−	1.03495i	0.991010	−	0.133791i	$-0.0427152\pi$
$410$	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	−0.979655	−	0.200691i	$-0.935681\pi$
$421$	−2635.17	−	8110.23i	−0.305061	−	0.938880i	0.674594	−	0.738189i	$-0.264319\pi$
$422$	−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	−0.995495	−	0.0948191i	$-0.969773\pi$
$431$	−10853.1	+	7885.27i	−1.21294	+	0.881253i	−0.217446	+	0.976072i	$0.569773\pi$
$432$	−271.311	−	835.009i	−0.0302163	−	0.0929963i
$433$	1276.95	−	3930.06i	0.141724	−	0.436182i	−0.854851	−	0.518873i	$-0.826352\pi$
$433$	1276.95	−	3930.06i	0.141724	−	0.436182i	0.996575	+	0.0826917i	$0.0263517\pi$
$434$	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	0.943469	−	0.331460i	$-0.107541\pi$
$443$	−136.508	−	420.129i	−0.0146404	−	0.0450585i	−0.958110	+	0.286401i	$0.907541\pi$
$444$	−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	−0.570283	−	0.821448i	$-0.693166\pi$
$449$	330.466	−	240.098i	0.0347342	−	0.0252359i	0.605017	+	0.796213i	$0.293166\pi$
$450$	−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	0.522944	−	0.852367i	$-0.324834\pi$
$457$	−1232.01	−	895.106i	−0.126107	−	0.0916221i	−0.649051	+	0.760745i	$0.724834\pi$
$458$	−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	0.570662	−	0.821185i	$-0.306687\pi$
$467$	−343.002	−	249.205i	−0.0339876	−	0.0246935i	−0.604649	+	0.796492i	$0.706687\pi$
$468$	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	0.397885	−	0.917435i	$-0.369744\pi$
$479$	−3686.96	−	2678.74i	−0.351695	−	0.255521i	−0.749580	+	0.661914i	$0.769744\pi$
$480$	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	−0.999995	−	0.00327027i	$-0.998959\pi$
$487$	−2073.17	−	6380.56i	−0.192904	−	0.593698i	0.807090	−	0.590428i	$-0.201041\pi$
$488$	−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	−0.501733	−	0.865023i	$-0.667304\pi$
$491$	4489.29	−	13816.6i	0.412625	−	1.26993i	0.914358	−	0.404907i	$-0.132696\pi$
$492$	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	0.721876	+	0.692023i	$0.243280\pi$
$499$	−2997.32	+	9224.80i	−0.268895	+	0.827573i	−0.990770	+	0.135550i	$0.956720\pi$
$500$	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	0.897870	+	0.440261i	$0.145114\pi$
$503$	4853.78	+	14938.4i	0.430257	+	1.32419i	−0.467613	+	0.883933i	$0.654886\pi$
$504$	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	0.929262	−	0.369421i	$-0.120444\pi$
$509$	−455.516	−	1401.93i	−0.0396668	−	0.122082i	−0.968929	+	0.247339i	$0.920444\pi$
$510$	−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	0.755319	+	0.655358i	$0.227482\pi$
$521$	−2865.47	+	8819.00i	−0.240956	+	0.741588i	−0.996275	+	0.0862302i	$0.972518\pi$
$522$	−8224.68	−	5975.58i	−0.689625	−	0.501042i
$523$	3432.26	+	2493.68i	0.286964	+	0.208491i	0.721949	−	0.691946i	$-0.243246\pi$
$523$	3432.26	+	2493.68i	0.286964	+	0.208491i	−0.434985	+	0.900438i	$0.643246\pi$
$524$	−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	−0.358113	−	0.933678i	$-0.616580\pi$
$541$	5275.00	−	3832.51i	0.419205	−	0.304570i	0.777318	+	0.629108i	$0.216580\pi$
$542$	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	0.998046	−	0.0624813i	$-0.0199014\pi$
$547$	1968.68	+	6058.97i	0.153884	+	0.473607i	−0.844162	+	0.536088i	$0.819901\pi$
$548$	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	−0.853326	−	0.521378i	$-0.825418\pi$
$557$	1886.24	−	5805.24i	0.143487	−	0.441609i	0.996813	+	0.0797691i	$0.0254183\pi$
$558$	−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	−0.0944384	−	0.995531i	$-0.530106\pi$
$563$	10996.6	−	7989.52i	0.823185	−	0.598079i	0.917623	+	0.397452i	$0.130106\pi$
$564$	−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	0.931620	+	0.363433i	$0.118395\pi$
$569$	5314.34	+	16355.9i	0.391544	+	1.20505i	−0.540076	+	0.841616i	$0.681605\pi$
$570$	−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	0.992970	−	0.118367i	$-0.0377661\pi$
$577$	16455.2	+	11955.4i	1.18724	+	0.862581i	0.194270	+	0.980948i	$0.437766\pi$
$578$	−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	0.650806	+	0.759244i	$0.274431\pi$
$587$	−4579.15	+	14093.2i	−0.321979	+	0.990950i	−0.972786	+	0.231707i	$0.925569\pi$
$588$	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	0.335224	−	0.942139i	$-0.391188\pi$
$599$	−6702.85	−	4869.91i	−0.457214	−	0.332185i	−0.792437	+	0.609953i	$0.791188\pi$
$600$	−4932.08	−	3583.37i	−0.335586	−	0.243817i
$601$	8441.82	−	25981.3i	0.572960	−	1.76339i	−0.0700619	−	0.997543i	$-0.522320\pi$
$601$	8441.82	−	25981.3i	0.572960	−	1.76339i	0.643022	−	0.765848i	$-0.277680\pi$
$602$	−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	−0.934118	−	0.356965i	$-0.883812\pi$
$607$	−13209.4	+	9597.18i	−0.883282	+	0.641742i	0.0508356	+	0.998707i	$0.483812\pi$
$608$	−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	−0.900005	−	0.435879i	$-0.856437\pi$
$613$	−6497.18	−	19996.3i	−0.428089	−	1.31752i	0.471916	−	0.881644i	$-0.343563\pi$
$614$	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	0.999992	−	0.00411206i	$-0.00130891\pi$
$619$	2903.99	+	8937.57i	0.188564	+	0.580342i	−0.811427	+	0.584454i	$0.801309\pi$
$620$	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	0.703489	+	0.710706i	$0.251624\pi$
$631$	−4491.85	+	13824.5i	−0.283388	+	0.872178i	−0.986877	+	0.161472i	$0.948376\pi$
$632$	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	−0.998971	−	0.0453536i	$-0.985559\pi$
$641$	−3528.87	−	10860.7i	−0.217445	−	0.669226i	0.781526	−	0.623872i	$-0.214441\pi$
$642$	−1908.21	+	5872.86i	−0.117307	+	0.361033i
$643$	−19392.1	−	14089.2i	−1.18934	−	0.864109i	−0.196150	−	0.980574i	$-0.562844\pi$
$643$	−19392.1	−	14089.2i	−1.18934	−	0.864109i	−0.993195	+	0.116465i	$0.962844\pi$
$644$	−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	−0.773083	−	0.634305i	$-0.781286\pi$
$647$	−6726.37	+	4886.99i	−0.408719	+	0.296951i	0.364364	+	0.931257i	$0.381286\pi$
$648$	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	0.133482	+	0.991051i	$0.457384\pi$
$653$	−9295.02	+	28607.1i	−0.557033	+	1.71437i	−0.690514	+	0.723319i	$0.742616\pi$
$654$	−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	−0.949527	−	0.313686i	$-0.898436\pi$
$673$	−16492.1	+	11982.2i	−0.944614	+	0.686302i	0.00491314	+	0.999988i	$0.498436\pi$
$674$	−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	0.744314	−	0.667830i	$-0.232777\pi$
$677$	5974.59	+	4340.79i	0.339176	+	0.246426i	−0.405138	+	0.914256i	$0.632777\pi$
$678$	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	−0.759635	−	0.650350i	$-0.774622\pi$
$691$	−6827.13	+	4960.20i	−0.375856	+	0.273075i	0.383779	+	0.923425i	$0.374622\pi$
$692$	−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	−0.999069	−	0.0431509i	$-0.986260\pi$
$701$	−4012.08	−	12347.9i	−0.216169	−	0.665298i	0.782900	−	0.622148i	$-0.213740\pi$
$702$	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	0.901317	−	0.433161i	$-0.142602\pi$
$709$	14496.4	+	10532.3i	0.767878	+	0.557896i	−0.133438	+	0.991057i	$0.542602\pi$
$710$	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	−0.918903	−	0.394484i	$-0.870923\pi$
$719$	1086.92	−	3345.20i	0.0563773	−	0.173512i	0.975280	+	0.220973i	$0.0709232\pi$
$720$	−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	−0.920735	−	0.390187i	$-0.872410\pi$
$733$	1061.75	−	3267.73i	0.0535015	−	0.164661i	0.974237	+	0.225527i	$0.0724102\pi$
$734$	−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	0.354326	−	0.935122i	$-0.384710\pi$
$739$	27184.4	−	19750.6i	1.35317	−	0.983137i	0.998847	−	0.0480154i	$-0.0152896\pi$
$740$	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	0.611372	−	0.791343i	$-0.290618\pi$
$743$	965.726	+	701.641i	0.0476838	+	0.0346443i	−0.563688	+	0.825988i	$0.690618\pi$
$744$	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	0.948077	+	0.318040i	$0.103024\pi$
$751$	7573.81	+	23309.8i	0.368006	+	1.13260i	−0.580072	+	0.814565i	$0.696976\pi$
$752$	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	−0.777499	−	0.628885i	$-0.783512\pi$
$757$	−8740.48	+	6350.33i	−0.419654	+	0.304897i	0.357845	+	0.933781i	$0.383512\pi$
$758$	16018.2			0.767555
$759$		0			0
$760$	−2620.49			−0.125073
$761$	−6614.45	+	4805.68i	−0.315077	+	0.228917i	−0.734072	−	0.679072i	$-0.762383\pi$
$761$	−6614.45	+	4805.68i	−0.315077	+	0.228917i	0.418995	+	0.907989i	$0.362383\pi$
$762$	−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	−0.993064	−	0.117574i	$-0.962488\pi$
$773$	−5561.32	−	17116.0i	−0.258767	−	0.796402i	0.734297	−	0.678828i	$-0.237512\pi$
$774$	−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	0.839364	−	0.543570i	$-0.182928\pi$
$787$	12844.5	+	9332.09i	0.581776	+	0.422685i	−0.257588	+	0.966255i	$0.582928\pi$
$788$	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	0.250265	−	0.968177i	$-0.419482\pi$
$797$	−13346.9	−	9697.11i	−0.593190	−	0.430978i	−0.843455	+	0.537200i	$0.819482\pi$
$798$	−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	0.736197	−	0.676768i	$-0.236620\pi$
$809$	7364.44	+	5350.58i	0.320049	+	0.232529i	−0.416147	+	0.909297i	$0.636620\pi$
$810$	4517.73	−	13904.1i	0.195971	−	0.603138i
$811$	11302.7	+	34786.1i	0.489384	+	1.50617i	0.825529	+	0.564360i	$0.190877\pi$
$811$	11302.7	+	34786.1i	0.489384	+	1.50617i	−0.336144	+	0.941811i	$0.609123\pi$
$812$	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	−0.972135	−	0.234423i	$-0.924680\pi$
$821$	−1126.12	+	3465.85i	−0.0478709	+	0.147331i	0.924264	+	0.381754i	$0.124680\pi$
$822$	−10059.4	−	30959.5i	−0.426838	−	1.31367i
$823$	13669.1	−	9931.15i	0.578947	−	0.420630i	−0.259397	−	0.965771i	$-0.583524\pi$
$823$	13669.1	−	9931.15i	0.578947	−	0.420630i	0.838344	+	0.545141i	$0.183524\pi$
$824$	−10941.3			−0.462570
$825$		0			0
$826$	−1548.19			−0.0652160
$827$	31372.1	−	22793.2i	1.31912	−	0.958400i	0.319181	−	0.947694i	$-0.396592\pi$
$827$	31372.1	−	22793.2i	1.31912	−	0.958400i	0.999943	−	0.0107058i	$-0.00340784\pi$
$828$	7475.51	+	23007.3i	0.313758	+	0.965649i
$829$	−3830.06	+	11787.7i	−0.160462	+	0.493853i	−0.998673	−	0.0514936i	$-0.983602\pi$
$829$	−3830.06	+	11787.7i	−0.160462	+	0.493853i	0.838211	+	0.545346i	$0.183602\pi$
$830$	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	0.976833	+	0.214002i	$0.0686500\pi$
$839$	7590.65	+	23361.6i	0.312346	+	0.961302i	−0.664487	+	0.747300i	$0.731350\pi$
$840$	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	0.768085	−	0.640348i	$-0.221210\pi$
$853$	9876.18	+	7175.47i	0.396429	+	0.288023i	−0.371656	+	0.928371i	$0.621210\pi$
$854$	−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	0.996931	−	0.0782811i	$-0.0249432\pi$
$863$	31197.2	+	22666.1i	1.23055	+	0.894047i	0.233619	+	0.972328i	$0.424943\pi$
$864$	−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	0.964590	+	0.263754i	$0.0849606\pi$
$877$	8810.90	+	27117.2i	0.339251	+	1.04411i	−0.625339	+	0.780353i	$0.715039\pi$
$878$	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	0.927649	−	0.373454i	$-0.121827\pi$
$883$	−1111.10	−	3419.61i	−0.0423459	−	0.130327i	−0.969994	+	0.243127i	$0.921827\pi$
$884$	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	−0.985987	−	0.166823i	$-0.946649\pi$
$887$	−2384.16	+	7337.69i	−0.0902506	+	0.277763i	0.895736	+	0.444586i	$0.146649\pi$
$888$	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	0.961769	−	0.273863i	$-0.0883016\pi$
$907$	27275.0	+	19816.4i	0.998512	+	0.725461i	0.0367432	+	0.999325i	$0.488302\pi$
$908$	−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	−0.786525	−	0.617558i	$-0.788122\pi$
$911$	−12160.1	+	8834.84i	−0.442242	+	0.321308i	0.344283	+	0.938866i	$0.388122\pi$
$912$	−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	0.807602	−	0.589728i	$-0.200765\pi$
$919$	13826.7	+	10045.7i	0.496300	+	0.360583i	−0.311302	+	0.950311i	$0.600765\pi$
$920$	−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	0.383689	−	0.923462i	$-0.374653\pi$
$929$	−10646.9	−	7735.40i	−0.376009	−	0.273187i	−0.759698	+	0.650276i	$0.774653\pi$
$930$	−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	−0.643521	−	0.765429i	$-0.722527\pi$
$937$	−3281.61	+	2384.23i	−0.114413	+	0.0831263i	0.529107	+	0.848555i	$0.322527\pi$
$938$	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	0.0114331	−	0.999935i	$-0.496361\pi$
$941$	−27019.3	−	19630.6i	−0.936028	−	0.680064i	−0.947461	+	0.319870i	$0.896361\pi$
$942$	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	−0.273512	−	0.961868i	$-0.588185\pi$
$953$	15096.3	−	46461.8i	0.513136	−	1.57927i	0.786648	−	0.617401i	$-0.211815\pi$
$954$	−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	0.955248	+	0.295805i	$0.0955880\pi$
$971$	10780.8	+	33180.0i	0.356306	+	1.09660i	−0.598942	+	0.800792i	$0.704412\pi$
$972$	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	−0.306742	−	0.951793i	$-0.599239\pi$
$977$	15381.4	−	11175.2i	0.503678	−	0.365944i	0.810420	+	0.585849i	$0.199239\pi$
$978$	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	−0.981427	−	0.191837i	$-0.938555\pi$
$983$	−2301.52	+	7083.36i	−0.0746767	+	0.229831i	0.906750	+	0.421669i	$0.138555\pi$
$984$	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	−0.238132	−	0.971233i	$-0.576535\pi$
$997$	16539.8	−	50904.3i	0.525397	−	1.61701i	0.763529	−	0.645773i	$-0.223465\pi$
$998$	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.3.1		8
11.2	odd	10		242.4.a.o.1.1		4
11.3	even	5		22.4.c.b.5.2	✓	8
11.4	even	5	inner	242.4.c.r.81.1		8
11.5	even	5		22.4.c.b.9.2	yes	8
11.6	odd	10		242.4.c.q.9.2		8
11.7	odd	10		242.4.c.n.81.1		8
11.8	odd	10		242.4.c.q.27.2		8
11.9	even	5		242.4.a.n.1.1		4
11.10	odd	2		242.4.c.n.3.1		8
33.2	even	10		2178.4.a.bt.1.1		4
33.5	odd	10		198.4.f.d.163.1		8
33.14	odd	10		198.4.f.d.181.1		8
33.20	odd	10		2178.4.a.by.1.1		4
44.3	odd	10		176.4.m.b.49.1		8
44.27	odd	10		176.4.m.b.97.1		8
44.31	odd	10		1936.4.a.bn.1.4		4
44.35	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	11.3	even	5
22.4.c.b.9.2	yes	8	11.5	even	5
176.4.m.b.49.1		8	44.3	odd	10
176.4.m.b.97.1		8	44.27	odd	10
198.4.f.d.163.1		8	33.5	odd	10
198.4.f.d.181.1		8	33.14	odd	10
242.4.a.n.1.1		4	11.9	even	5
242.4.a.o.1.1		4	11.2	odd	10
242.4.c.n.3.1		8	11.10	odd	2
242.4.c.n.81.1		8	11.7	odd	10
242.4.c.q.9.2		8	11.6	odd	10
242.4.c.q.27.2		8	11.8	odd	10
242.4.c.r.3.1		8	1.1	even	1	trivial
242.4.c.r.81.1		8	11.4	even	5	inner
1936.4.a.bm.1.4		4	44.35	even	10
1936.4.a.bn.1.4		4	44.31	odd	10
2178.4.a.bt.1.1		4	33.2	even	10
2178.4.a.by.1.1		4	33.20	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
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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