LMFDB - Embedded newform 201.3.c.a.68.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(68,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("201.68");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.c (of order $2$, degree $1$, 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:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			68.17
Character	$\chi$	$=$	201.68
Dual form			201.3.c.a.68.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.01079i q^{2} +(-0.770133 + 2.89946i) q^{3} +2.97831 q^{4} -8.93347i q^{5} +(2.93075 + 0.778442i) q^{6} -6.17840 q^{7} -7.05360i q^{8} +(-7.81379 - 4.46595i) q^{9} +O(q^{10})$	\(q-1.01079i q^{2} +(-0.770133 + 2.89946i) q^{3} +2.97831 q^{4} -8.93347i q^{5} +(2.93075 + 0.778442i) q^{6} -6.17840 q^{7} -7.05360i q^{8} +(-7.81379 - 4.46595i) q^{9} -9.02986 q^{10} -2.41977i q^{11} +(-2.29369 + 8.63549i) q^{12} -5.04754 q^{13} +6.24506i q^{14} +(25.9023 + 6.87996i) q^{15} +4.78352 q^{16} -12.1945i q^{17} +(-4.51413 + 7.89809i) q^{18} +10.7964 q^{19} -26.6066i q^{20} +(4.75819 - 17.9141i) q^{21} -2.44588 q^{22} -28.0620i q^{23} +(20.4516 + 5.43221i) q^{24} -54.8069 q^{25} +5.10200i q^{26} +(18.9665 - 19.2164i) q^{27} -18.4012 q^{28} +26.8551i q^{29} +(6.95419 - 26.1818i) q^{30} +21.7537 q^{31} -33.0495i q^{32} +(7.01605 + 1.86355i) q^{33} -12.3261 q^{34} +55.1946i q^{35} +(-23.2719 - 13.3010i) q^{36} +42.5343 q^{37} -10.9129i q^{38} +(3.88728 - 14.6352i) q^{39} -63.0131 q^{40} +69.7097i q^{41} +(-18.1073 - 4.80953i) q^{42} +28.5053 q^{43} -7.20683i q^{44} +(-39.8964 + 69.8043i) q^{45} -28.3648 q^{46} -64.0131i q^{47} +(-3.68395 + 13.8697i) q^{48} -10.8274 q^{49} +55.3983i q^{50} +(35.3575 + 9.39138i) q^{51} -15.0331 q^{52} +4.09922i q^{53} +(-19.4238 - 19.1711i) q^{54} -21.6170 q^{55} +43.5799i q^{56} +(-8.31467 + 31.3038i) q^{57} +27.1448 q^{58} +39.4419i q^{59} +(77.1449 + 20.4906i) q^{60} -48.4301 q^{61} -21.9884i q^{62} +(48.2767 + 27.5924i) q^{63} -14.2720 q^{64} +45.0921i q^{65} +(1.88365 - 7.09175i) q^{66} +8.18535 q^{67} -36.3189i q^{68} +(81.3648 + 21.6115i) q^{69} +55.7901 q^{70} -17.9173i q^{71} +(-31.5010 + 55.1153i) q^{72} +105.468 q^{73} -42.9932i q^{74} +(42.2086 - 158.911i) q^{75} +32.1550 q^{76} +14.9503i q^{77} +(-14.7931 - 3.92922i) q^{78} +57.9921 q^{79} -42.7335i q^{80} +(41.1106 + 69.7919i) q^{81} +70.4618 q^{82} +104.770i q^{83} +(14.1713 - 53.3535i) q^{84} -108.939 q^{85} -28.8129i q^{86} +(-77.8653 - 20.6820i) q^{87} -17.0681 q^{88} +145.725i q^{89} +(70.5574 + 40.3269i) q^{90} +31.1857 q^{91} -83.5772i q^{92} +(-16.7532 + 63.0740i) q^{93} -64.7038 q^{94} -96.4494i q^{95} +(95.8259 + 25.4525i) q^{96} -159.821 q^{97} +10.9442i q^{98} +(-10.8066 + 18.9076i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.01079i		−	0.505395i	−0.967545	−	0.252697i	$-0.918682\pi$
$2$		−	1.01079i		−	0.505395i	0.967545	−	0.252697i	$-0.0813177\pi$
$3$	−0.770133	+	2.89946i	−0.256711	+	0.966488i
$3$	−0.770133	+	2.89946i	−0.256711	+	0.966488i
$4$	2.97831			0.744576
$5$		−	8.93347i		−	1.78669i	−0.449367	−	0.893347i	$-0.648350\pi$
$5$		−	8.93347i		−	1.78669i	0.449367	−	0.893347i	$-0.351650\pi$
$6$	2.93075	+	0.778442i	0.488458	+	0.129740i
$7$	−6.17840			−0.882629			−0.441314	−	0.897353i	$-0.645488\pi$
$7$	−6.17840			−0.882629			−0.441314	+	0.897353i	$0.645488\pi$
$8$		−	7.05360i		−	0.881699i
$9$	−7.81379	−	4.46595i	−0.868199	−	0.496216i
$10$	−9.02986			−0.902986
$11$		−	2.41977i		−	0.219980i	−0.993933	−	0.109990i	$-0.964918\pi$
$11$		−	2.41977i		−	0.219980i	0.993933	−	0.109990i	$-0.0350818\pi$
$12$	−2.29369	+	8.63549i	−0.191141	+	0.719624i
$13$	−5.04754			−0.388273			−0.194136	−	0.980975i	$-0.562190\pi$
$13$	−5.04754			−0.388273			−0.194136	+	0.980975i	$0.562190\pi$
$14$			6.24506i			0.446076i
$15$	25.9023	+	6.87996i	1.72682	+	0.458664i
$16$	4.78352			0.298970
$17$		−	12.1945i		−	0.717323i	−0.933468	−	0.358662i	$-0.883233\pi$
$17$		−	12.1945i		−	0.717323i	0.933468	−	0.358662i	$-0.116767\pi$
$18$	−4.51413	+	7.89809i	−0.250785	+	0.438783i
$19$	10.7964			0.568232			0.284116	−	0.958790i	$-0.408300\pi$
$19$	10.7964			0.568232			0.284116	+	0.958790i	$0.408300\pi$
$20$		−	26.6066i		−	1.33033i
$21$	4.75819	−	17.9141i	0.226580	−	0.853050i
$22$	−2.44588			−0.111176
$23$		−	28.0620i		−	1.22009i	−0.792368	−	0.610044i	$-0.791152\pi$
$23$		−	28.0620i		−	1.22009i	0.792368	−	0.610044i	$-0.208848\pi$
$24$	20.4516	+	5.43221i	0.852152	+	0.226342i
$25$	−54.8069			−2.19228
$26$			5.10200i			0.196231i
$27$	18.9665	−	19.2164i	0.702463	−	0.711720i
$28$	−18.4012			−0.657184
$29$			26.8551i			0.926036i	0.886349	+	0.463018i	$0.153234\pi$
$29$			26.8551i			0.926036i	−0.886349	+	0.463018i	$0.846766\pi$
$30$	6.95419	−	26.1818i	0.231806	−	0.872725i
$31$	21.7537			0.701731			0.350866	−	0.936426i	$-0.385887\pi$
$31$	21.7537			0.701731			0.350866	+	0.936426i	$0.385887\pi$
$32$		−	33.0495i		−	1.03280i
$33$	7.01605	+	1.86355i	0.212608	+	0.0564712i
$34$	−12.3261			−0.362531
$35$			55.1946i			1.57699i
$36$	−23.2719	−	13.3010i	−0.646440	−	0.369471i
$37$	42.5343			1.14958			0.574788	−	0.818303i	$-0.305085\pi$
$37$	42.5343			1.14958			0.574788	+	0.818303i	$0.305085\pi$
$38$		−	10.9129i		−	0.287181i
$39$	3.88728	−	14.6352i	0.0996738	−	0.375261i
$40$	−63.0131			−1.57533
$41$			69.7097i			1.70024i	0.526591	+	0.850119i	$0.323470\pi$
$41$			69.7097i			1.70024i	−0.526591	+	0.850119i	$0.676530\pi$
$42$	−18.1073	−	4.80953i	−0.431127	−	0.114513i
$43$	28.5053			0.662914			0.331457	−	0.943470i	$-0.392460\pi$
$43$	28.5053			0.662914			0.331457	+	0.943470i	$0.392460\pi$
$44$		−	7.20683i		−	0.163792i
$45$	−39.8964	+	69.8043i	−0.886587	+	1.55121i
$46$	−28.3648			−0.616625
$47$		−	64.0131i		−	1.36198i	−0.732292	−	0.680991i	$-0.761549\pi$
$47$		−	64.0131i		−	1.36198i	0.732292	−	0.680991i	$-0.238451\pi$
$48$	−3.68395	+	13.8697i	−0.0767489	+	0.288951i
$49$	−10.8274			−0.220967
$50$			55.3983i			1.10797i
$51$	35.3575	+	9.39138i	0.693284	+	0.184145i
$52$	−15.0331			−0.289099
$53$			4.09922i			0.0773437i	0.999252	+	0.0386719i	$0.0123127\pi$
$53$			4.09922i			0.0773437i	−0.999252	+	0.0386719i	$0.987687\pi$
$54$	−19.4238	−	19.1711i	−0.359699	−	0.355021i
$55$	−21.6170			−0.393036
$56$			43.5799i			0.778213i
$57$	−8.31467	+	31.3038i	−0.145871	+	0.549190i
$58$	27.1448			0.468014
$59$			39.4419i			0.668506i	0.942483	+	0.334253i	$0.108484\pi$
$59$			39.4419i			0.668506i	−0.942483	+	0.334253i	$0.891516\pi$
$60$	77.1449	+	20.4906i	1.28575	+	0.341510i
$61$	−48.4301			−0.793936			−0.396968	−	0.917832i	$-0.629938\pi$
$61$	−48.4301			−0.793936			−0.396968	+	0.917832i	$0.629938\pi$
$62$		−	21.9884i		−	0.354651i
$63$	48.2767	+	27.5924i	0.766297	+	0.437975i
$64$	−14.2720			−0.223000
$65$			45.0921i			0.693725i
$66$	1.88365	−	7.09175i	0.0285402	−	0.107451i
$67$	8.18535			0.122169
$67$	8.18535			0.122169
$68$		−	36.3189i		−	0.534102i
$69$	81.3648	+	21.6115i	1.17920	+	0.313210i
$70$	55.7901			0.797001
$71$		−	17.9173i		−	0.252357i	−0.992008	−	0.126178i	$-0.959729\pi$
$71$		−	17.9173i		−	0.252357i	0.992008	−	0.126178i	$-0.0402712\pi$
$72$	−31.5010	+	55.1153i	−0.437514	+	0.765490i
$73$	105.468			1.44477			0.722384	−	0.691492i	$-0.243046\pi$
$73$	105.468			1.44477			0.722384	+	0.691492i	$0.243046\pi$
$74$		−	42.9932i		−	0.580989i
$75$	42.2086	−	158.911i	0.562782	−	2.11881i
$76$	32.1550			0.423092
$77$			14.9503i			0.194160i
$78$	−14.7931	−	3.92922i	−0.189655	−	0.0503746i
$79$	57.9921			0.734077			0.367038	−	0.930206i	$-0.380372\pi$
$79$	57.9921			0.734077			0.367038	+	0.930206i	$0.380372\pi$
$80$		−	42.7335i		−	0.534169i
$81$	41.1106	+	69.7919i	0.507539	+	0.861629i
$82$	70.4618			0.859291
$83$			104.770i			1.26229i	0.775665	+	0.631145i	$0.217415\pi$
$83$			104.770i			1.26229i	−0.775665	+	0.631145i	$0.782585\pi$
$84$	14.1713	−	53.3535i	0.168706	−	0.635161i
$85$	−108.939			−1.28164
$86$		−	28.8129i		−	0.335033i
$87$	−77.8653	−	20.6820i	−0.895003	−	0.237724i
$88$	−17.0681			−0.193956
$89$			145.725i			1.63736i	0.574253	+	0.818678i	$0.305293\pi$
$89$			145.725i			1.63736i	−0.574253	+	0.818678i	$0.694707\pi$
$90$	70.5574	+	40.3269i	0.783971	+	0.448076i
$91$	31.1857			0.342700
$92$		−	83.5772i		−	0.908448i
$93$	−16.7532	+	63.0740i	−0.180142	+	0.678215i
$94$	−64.7038			−0.688338
$95$		−	96.4494i		−	1.01526i
$96$	95.8259	+	25.4525i	0.998186	+	0.265130i
$97$	−159.821			−1.64764			−0.823820	−	0.566851i	$-0.808161\pi$
$97$	−159.821			−1.64764			−0.823820	+	0.566851i	$0.808161\pi$
$98$			10.9442i			0.111675i
$99$	−10.8066	+	18.9076i	−0.109157	+	0.190986i
$100$	−163.232			−1.63232
$101$		−	120.682i		−	1.19487i	−0.801916	−	0.597437i	$-0.796186\pi$
$101$		−	120.682i		−	1.19487i	0.801916	−	0.597437i	$-0.203814\pi$
$102$	9.49270	−	35.7390i	0.0930657	−	0.350382i
$103$	100.089			0.971734			0.485867	−	0.874033i	$-0.338504\pi$
$103$	100.089			0.971734			0.485867	+	0.874033i	$0.338504\pi$
$104$			35.6033i			0.342340i
$105$	−160.035	−	42.5072i	−1.52414	−	0.404830i
$106$	4.14344			0.0390891
$107$			67.1942i			0.627984i	0.949426	+	0.313992i	$0.101666\pi$
$107$			67.1942i			0.627984i	−0.949426	+	0.313992i	$0.898334\pi$
$108$	56.4881	−	57.2324i	0.523038	−	0.529930i
$109$	−182.239			−1.67192			−0.835958	−	0.548793i	$-0.815087\pi$
$109$	−182.239			−1.67192			−0.835958	+	0.548793i	$0.815087\pi$
$110$			21.8502i			0.198638i
$111$	−32.7571	+	123.327i	−0.295109	+	1.11105i
$112$	−29.5545			−0.263880
$113$		−	167.644i		−	1.48358i	−0.670633	−	0.741789i	$-0.733977\pi$
$113$		−	167.644i		−	1.48358i	0.670633	−	0.741789i	$-0.266023\pi$
$114$	31.6416	+	8.40438i	0.277557	+	0.0737226i
$115$	−250.691			−2.17992
$116$			79.9826i			0.689505i
$117$	39.4405	+	22.5421i	0.337098	+	0.192667i
$118$	39.8674			0.337859
$119$			75.3424i			0.633130i
$120$	48.5285	−	182.704i	0.404404	−	1.52254i
$121$	115.145			0.951609
$122$			48.9526i			0.401251i
$123$	−202.121	−	53.6858i	−1.64326	−	0.436470i
$124$	64.7891			0.522493
$125$			266.279i			2.13024i
$126$	27.8901	−	48.7976i	0.221350	−	0.387282i
$127$	193.849			1.52637			0.763183	−	0.646182i	$-0.223635\pi$
$127$	193.849			1.52637			0.763183	+	0.646182i	$0.223635\pi$
$128$		−	117.772i		−	0.920094i
$129$	−21.9529	+	82.6501i	−0.170177	+	0.640699i
$130$	45.5786			0.350605
$131$		−	121.925i		−	0.930728i	−0.885119	−	0.465364i	$-0.845923\pi$
$131$		−	121.925i		−	0.930728i	0.885119	−	0.465364i	$-0.154077\pi$
$132$	20.8959	+	5.55022i	0.158303	+	0.0420471i
$133$	−66.7045			−0.501538
$134$		−	8.27367i		−	0.0617438i
$135$	−171.670	−	169.437i	−1.27163	−	1.25509i
$136$	−86.0150			−0.632463
$137$		−	139.206i		−	1.01610i	−0.861327	−	0.508051i	$-0.830366\pi$
$137$		−	139.206i		−	1.01610i	0.861327	−	0.508051i	$-0.169634\pi$
$138$	21.8446	−	82.2426i	0.158295	−	0.595961i
$139$	121.165			0.871694			0.435847	−	0.900021i	$-0.356449\pi$
$139$	121.165			0.871694			0.435847	+	0.900021i	$0.356449\pi$
$140$			164.386i			1.17419i
$141$	185.604	+	49.2986i	1.31634	+	0.349636i
$142$	−18.1107			−0.127540
$143$			12.2139i			0.0854120i
$144$	−37.3775	−	21.3630i	−0.259566	−	0.148354i
$145$	239.909			1.65454
$146$		−	106.606i		−	0.730178i
$147$	8.33852	−	31.3936i	0.0567246	−	0.213562i
$148$	126.680			0.855947
$149$		−	149.735i		−	1.00493i	−0.864597	−	0.502466i	$-0.832426\pi$
$149$		−	149.735i		−	1.00493i	0.864597	−	0.502466i	$-0.167574\pi$
$150$	−160.625	−	42.6640i	−1.07084	−	0.284427i
$151$	122.341			0.810207			0.405104	−	0.914271i	$-0.367235\pi$
$151$	122.341			0.810207			0.405104	+	0.914271i	$0.367235\pi$
$152$		−	76.1535i		−	0.501010i
$153$	−54.4599	+	95.2852i	−0.355947	+	0.622779i
$154$	15.1116			0.0981275
$155$		−	194.336i		−	1.25378i
$156$	11.5775	−	43.5880i	0.0742148	−	0.279410i
$157$	−154.695			−0.985319			−0.492660	−	0.870222i	$-0.663975\pi$
$157$	−154.695			−0.985319			−0.492660	+	0.870222i	$0.663975\pi$
$158$		−	58.6178i		−	0.370998i
$159$	−11.8855	−	3.15694i	−0.0747518	−	0.0198550i
$160$	−295.247			−1.84529
$161$			173.378i			1.07688i
$162$	70.5449	−	41.5542i	0.435463	−	0.256507i
$163$	60.5033			0.371186			0.185593	−	0.982627i	$-0.440579\pi$
$163$	60.5033			0.371186			0.185593	+	0.982627i	$0.440579\pi$
$164$			207.617i			1.26596i
$165$	16.6480	−	62.6777i	0.100897	−	0.379865i
$166$	105.900			0.637955
$167$			50.7628i			0.303969i	0.988383	+	0.151984i	$0.0485663\pi$
$167$			50.7628i			0.303969i	−0.988383	+	0.151984i	$0.951434\pi$
$168$	−126.358	−	33.5623i	−0.752134	−	0.199776i
$169$	−143.522			−0.849244
$170$			110.115i			0.647732i
$171$	−84.3609	−	48.2162i	−0.493339	−	0.281966i
$172$	84.8975			0.493590
$173$			7.71263i			0.0445816i	0.999752	+	0.0222908i	$0.00709598\pi$
$173$			7.71263i			0.0445816i	−0.999752	+	0.0222908i	$0.992904\pi$
$174$	−20.9051	+	78.7054i	−0.120144	+	0.452330i
$175$	338.619			1.93497
$176$		−	11.5750i		−	0.0657673i
$177$	−114.360	−	30.3755i	−0.646103	−	0.171613i
$178$	147.297			0.827511
$179$		−	82.8799i		−	0.463016i	−0.972833	−	0.231508i	$-0.925634\pi$
$179$		−	82.8799i		−	0.463016i	0.972833	−	0.231508i	$-0.0743659\pi$
$180$	−118.824	+	207.898i	−0.660132	+	1.15499i
$181$	319.001			1.76244			0.881219	−	0.472708i	$-0.156724\pi$
$181$	319.001			1.76244			0.881219	+	0.472708i	$0.156724\pi$
$182$		−	31.5222i		−	0.173199i
$183$	37.2976	−	140.421i	0.203812	−	0.767330i
$184$	−197.938			−1.07575
$185$		−	379.979i		−	2.05394i
$186$	63.7545	+	16.9340i	0.342766	+	0.0910429i
$187$	−29.5079			−0.157796
$188$		−	190.651i		−	1.01410i
$189$	−117.183	+	118.727i	−0.620014	+	0.628184i
$190$	−97.4900			−0.513106
$191$			90.6821i			0.474775i	0.971415	+	0.237388i	$0.0762912\pi$
$191$			90.6821i			0.474775i	−0.971415	+	0.237388i	$0.923709\pi$
$192$	10.9913	−	41.3811i	0.0572465	−	0.215527i
$193$	165.204			0.855980			0.427990	−	0.903784i	$-0.359222\pi$
$193$	165.204			0.855980			0.427990	+	0.903784i	$0.359222\pi$
$194$			161.545i			0.832708i
$195$	−130.743	−	34.7269i	−0.670477	−	0.178087i
$196$	−32.2472			−0.164527
$197$		−	294.854i		−	1.49672i	−0.663293	−	0.748360i	$-0.730842\pi$
$197$		−	294.854i		−	1.49672i	0.663293	−	0.748360i	$-0.269158\pi$
$198$	19.1116	+	10.9232i	0.0965233	+	0.0551676i
$199$	−321.398			−1.61507			−0.807533	−	0.589823i	$-0.799198\pi$
$199$	−321.398			−1.61507			−0.807533	+	0.589823i	$0.799198\pi$
$200$			386.586i			1.93293i
$201$	−6.30381	+	23.7331i	−0.0313622	+	0.118075i
$202$	−121.984			−0.603883
$203$		−	165.921i		−	0.817346i
$204$	105.305	+	27.9704i	0.516203	+	0.137110i
$205$	622.750			3.03780
$206$		−	101.168i		−	0.491109i
$207$	−125.323	+	219.271i	−0.605427	+	1.05928i
$208$	−24.1450			−0.116082
$209$		−	26.1249i		−	0.124999i
$210$	−42.9658	+	161.761i	−0.204599	+	0.770292i
$211$	295.953			1.40262			0.701309	−	0.712857i	$-0.252599\pi$
$211$	295.953			1.40262			0.701309	+	0.712857i	$0.252599\pi$
$212$			12.2087i			0.0575883i
$213$	51.9507	+	13.7987i	0.243900	+	0.0647828i
$214$	67.9192			0.317379
$215$		−	254.651i		−	1.18443i
$216$	−135.545	−	133.782i	−0.627523	−	0.619362i
$217$	−134.403			−0.619368
$218$			184.205i			0.844977i
$219$	−81.2244	+	305.801i	−0.370888	+	1.39635i
$220$	−64.3820			−0.292645
$221$			61.5522i			0.278517i
$222$	124.657	+	33.1105i	0.561519	+	0.149146i
$223$	119.451			0.535656			0.267828	−	0.963467i	$-0.413694\pi$
$223$	119.451			0.535656			0.267828	+	0.963467i	$0.413694\pi$
$224$			204.193i			0.911576i
$225$	428.250	+	244.765i	1.90333	+	1.08784i
$226$	−169.453			−0.749793
$227$			413.614i			1.82209i	0.412310	+	0.911044i	$0.364722\pi$
$227$			413.614i			1.82209i	−0.412310	+	0.911044i	$0.635278\pi$
$228$	−24.7636	+	93.2323i	−0.108612	+	0.408914i
$229$	390.202			1.70394			0.851969	−	0.523593i	$-0.175409\pi$
$229$	390.202			1.70394			0.851969	+	0.523593i	$0.175409\pi$
$230$			253.396i			1.10172i
$231$	−43.3480	−	11.5137i	−0.187654	−	0.0498431i
$232$	189.425			0.816486
$233$			109.232i			0.468805i	0.972140	+	0.234403i	$0.0753134\pi$
$233$			109.232i			0.468805i	−0.972140	+	0.234403i	$0.924687\pi$
$234$	22.7853	−	39.8660i	0.0973730	−	0.170367i
$235$	−571.860			−2.43345
$236$			117.470i			0.497754i
$237$	−44.6616	+	168.146i	−0.188446	+	0.709477i
$238$	76.1553			0.319980
$239$			50.5577i			0.211539i	0.994391	+	0.105769i	$0.0337305\pi$
$239$			50.5577i			0.211539i	−0.994391	+	0.105769i	$0.966269\pi$
$240$	123.904	+	32.9105i	0.516268	+	0.137127i
$241$	−240.974			−0.999894			−0.499947	−	0.866056i	$-0.666647\pi$
$241$	−240.974			−0.999894			−0.499947	+	0.866056i	$0.666647\pi$
$242$		−	116.387i		−	0.480938i
$243$	−234.020	+	65.4498i	−0.963045	+	0.269341i
$244$	−144.240			−0.591146
$245$			96.7261i			0.394800i
$246$	−54.2650	+	204.302i	−0.220589	+	0.830494i
$247$	−54.4954			−0.220629
$248$		−	153.442i		−	0.618716i
$249$	−303.777	−	80.6869i	−1.21999	−	0.324044i
$250$	269.152			1.07661
$251$		−	308.923i		−	1.23077i	−0.788227	−	0.615384i	$-0.789001\pi$
$251$		−	308.923i		−	1.23077i	0.788227	−	0.615384i	$-0.210999\pi$
$252$	143.783	+	82.1786i	0.570567	+	0.326106i
$253$	−67.9037			−0.268394
$254$		−	195.940i		−	0.771417i
$255$	83.8976	−	315.865i	0.329010	−	1.23869i
$256$	−176.131			−0.688011
$257$		−	198.268i		−	0.771471i	−0.922609	−	0.385735i	$-0.873948\pi$
$257$		−	198.268i		−	0.771471i	0.922609	−	0.385735i	$-0.126052\pi$
$258$	83.5419	+	22.1897i	0.323806	+	0.0860067i
$259$	−262.794			−1.01465
$260$			134.298i			0.516531i
$261$	119.933	−	209.840i	0.459514	−	0.803984i
$262$	−123.241			−0.470385
$263$			265.066i			1.00786i	0.863745	+	0.503929i	$0.168113\pi$
$263$			265.066i			1.00786i	−0.863745	+	0.503929i	$0.831887\pi$
$264$	13.1447	−	49.4884i	0.0497906	−	0.187456i
$265$	36.6203			0.138190
$266$			67.4242i			0.253475i
$267$	−422.524	−	112.227i	−1.58249	−	0.420327i
$268$	24.3785			0.0909645
$269$			249.943i			0.929156i	0.885532	+	0.464578i	$0.153794\pi$
$269$			249.943i			0.929156i	−0.885532	+	0.464578i	$0.846206\pi$
$270$	−171.265	+	173.522i	−0.634314	+	0.642673i
$271$	−69.6626			−0.257058			−0.128529	−	0.991706i	$-0.541025\pi$
$271$	−69.6626			−0.257058			−0.128529	+	0.991706i	$0.541025\pi$
$272$		−	58.3326i		−	0.214458i
$273$	−24.0172	+	90.4220i	−0.0879750	+	0.331216i
$274$	−140.708			−0.513533
$275$			132.620i			0.482256i
$276$	242.329	+	64.3656i	0.878004	+	0.233209i
$277$	7.39428			0.0266941			0.0133471	−	0.999911i	$-0.495751\pi$
$277$	7.39428			0.0266941			0.0133471	+	0.999911i	$0.495751\pi$
$278$		−	122.473i		−	0.440549i
$279$	−169.979	−	97.1508i	−0.609243	−	0.348211i
$280$	389.320			1.39043
$281$			19.6646i			0.0699808i	0.999388	+	0.0349904i	$0.0111401\pi$
$281$			19.6646i			0.0699808i	−0.999388	+	0.0349904i	$0.988860\pi$
$282$	49.8305	−	187.606i	0.176704	−	0.665271i
$283$	−38.1968			−0.134971			−0.0674856	−	0.997720i	$-0.521498\pi$
$283$	−38.1968			−0.134971			−0.0674856	+	0.997720i	$0.521498\pi$
$284$		−	53.3633i		−	0.187899i
$285$	279.652	+	74.2789i	0.981234	+	0.260628i
$286$	12.3457			0.0431668
$287$		−	430.695i		−	1.50068i
$288$	−147.597	+	258.242i	−0.512491	+	0.896674i
$289$	140.294			0.485448
$290$		−	242.497i		−	0.836198i
$291$	123.083	−	463.396i	0.422967	−	1.59242i
$292$	314.116			1.07574
$293$			168.011i			0.573416i	0.958018	+	0.286708i	$0.0925610\pi$
$293$			168.011i			0.573416i	−0.958018	+	0.286708i	$0.907439\pi$
$294$	−31.7323	−	8.42849i	−0.107933	−	0.0286683i
$295$	352.353			1.19442
$296$		−	300.020i		−	1.01358i
$297$	−46.4994	−	45.8947i	−0.156564	−	0.154528i
$298$	−151.351			−0.507888
$299$			141.644i			0.473726i
$300$	125.710	−	473.285i	0.419034	−	1.57762i
$301$	−176.117			−0.585107
$302$		−	123.661i		−	0.409474i
$303$	349.914	+	92.9414i	1.15483	+	0.306737i
$304$	51.6449			0.169885
$305$			432.649i			1.41852i
$306$	96.3132	+	55.0475i	0.314749	+	0.179894i
$307$	−342.217			−1.11471			−0.557357	−	0.830273i	$-0.688184\pi$
$307$	−342.217			−1.11471			−0.557357	+	0.830273i	$0.688184\pi$
$308$			44.5267i			0.144567i
$309$	−77.0815	+	290.203i	−0.249455	+	0.939169i
$310$	−196.433			−0.633654
$311$		−	55.0061i		−	0.176869i	−0.996082	−	0.0884343i	$-0.971814\pi$
$311$		−	55.0061i		−	0.176869i	0.996082	−	0.0884343i	$-0.0281863\pi$
$312$	−103.231	−	27.4193i	−0.330867	−	0.0878824i
$313$	−483.360			−1.54428			−0.772141	−	0.635452i	$-0.780814\pi$
$313$	−483.360			−1.54428			−0.772141	+	0.635452i	$0.780814\pi$
$314$			156.364i			0.497975i
$315$	246.496	−	431.279i	0.782527	−	1.36914i
$316$	172.718			0.546576
$317$			380.613i			1.20067i	0.799747	+	0.600337i	$0.204967\pi$
$317$			380.613i			1.20067i	−0.799747	+	0.600337i	$0.795033\pi$
$318$	−3.19100	+	12.0138i	−0.0100346	+	0.0377792i
$319$	64.9832			0.203709
$320$			127.498i			0.398433i
$321$	−194.827	−	51.7485i	−0.606939	−	0.161210i
$322$	175.249			0.544251
$323$		−	131.657i		−	0.407606i
$324$	122.440	+	207.862i	0.377901	+	0.641548i
$325$	276.640			0.851201
$326$		−	61.1561i		−	0.187595i
$327$	140.348	−	528.395i	0.429199	−	1.61589i
$328$	491.704			1.49910
$329$			395.499i			1.20212i
$330$	−63.3539	−	16.8276i	−0.191982	−	0.0509926i
$331$	57.8785			0.174859			0.0874297	−	0.996171i	$-0.472135\pi$
$331$	57.8785			0.174859			0.0874297	+	0.996171i	$0.472135\pi$
$332$			312.037i			0.939871i
$333$	−332.354	−	189.956i	−0.998060	−	0.570438i
$334$	51.3105			0.153624
$335$		−	73.1236i		−	0.218279i
$336$	22.7609	−	85.6923i	0.0677408	−	0.255037i
$337$	96.2228			0.285528			0.142764	−	0.989757i	$-0.454401\pi$
$337$	96.2228			0.285528			0.142764	+	0.989757i	$0.454401\pi$
$338$			145.071i			0.429203i
$339$	486.079	+	129.108i	1.43386	+	0.380851i
$340$	−324.454			−0.954277
$341$		−	52.6390i		−	0.154367i
$342$	−48.7364	+	85.2711i	−0.142504	+	0.249331i
$343$	369.637			1.07766
$344$		−	201.065i		−	0.584491i
$345$	193.066	−	726.870i	0.559610	−	2.10687i
$346$	7.79584			0.0225313
$347$		−	382.695i		−	1.10287i	−0.834219	−	0.551433i	$-0.814081\pi$
$347$		−	382.695i		−	1.10287i	0.834219	−	0.551433i	$-0.185919\pi$
$348$	−231.907	−	61.5972i	−0.666398	−	0.177003i
$349$	203.183			0.582187			0.291094	−	0.956695i	$-0.405981\pi$
$349$	203.183			0.582187			0.291094	+	0.956695i	$0.405981\pi$
$350$		−	342.273i		−	0.977922i
$351$	−95.7343	+	96.9958i	−0.272747	+	0.276341i
$352$	−79.9724			−0.227194
$353$			450.579i			1.27643i	0.769859	+	0.638214i	$0.220326\pi$
$353$			450.579i			1.27643i	−0.769859	+	0.638214i	$0.779674\pi$
$354$	−30.7032	+	115.594i	−0.0867322	+	0.326537i
$355$	−160.064			−0.450885
$356$			434.013i			1.21914i
$357$	−218.453	−	58.0237i	−0.611912	−	0.162531i
$358$	−83.7741			−0.234006
$359$		−	54.2490i		−	0.151111i	−0.997142	−	0.0755557i	$-0.975927\pi$
$359$		−	54.2490i		−	0.151111i	0.997142	−	0.0755557i	$-0.0240731\pi$
$360$	492.371	+	281.413i	1.36770	+	0.781703i
$361$	−244.438			−0.677112
$362$		−	322.443i		−	0.890727i
$363$	−88.6767	+	333.858i	−0.244288	+	0.919719i
$364$	92.8807			0.255167
$365$		−	942.196i		−	2.58136i
$366$	−141.936	−	37.7000i	−0.387804	−	0.103006i
$367$	−453.693			−1.23622			−0.618111	−	0.786091i	$-0.712102\pi$
$367$	−453.693			−1.23622			−0.618111	+	0.786091i	$0.712102\pi$
$368$		−	134.235i		−	0.364770i
$369$	311.320	−	544.697i	0.843685	−	1.47614i
$370$	−384.079			−1.03805
$371$		−	25.3266i		−	0.0682658i
$372$	−49.8962	+	187.854i	−0.134130	+	0.504983i
$373$	11.2663			0.0302047			0.0151023	−	0.999886i	$-0.495193\pi$
$373$	11.2663			0.0302047			0.0151023	+	0.999886i	$0.495193\pi$
$374$			29.8263i			0.0797494i
$375$	−772.068	−	205.071i	−2.05885	−	0.546855i
$376$	−451.523			−1.20086
$377$		−	135.552i		−	0.359555i
$378$	120.008	+	118.447i	0.317481	+	0.313352i
$379$	−389.962			−1.02892			−0.514461	−	0.857514i	$-0.672008\pi$
$379$	−389.962			−1.02892			−0.514461	+	0.857514i	$0.672008\pi$
$380$		−	287.256i		−	0.755937i
$381$	−149.289	+	562.057i	−0.391835	+	1.47522i
$382$	91.6605			0.239949
$383$			492.468i			1.28582i	0.765943	+	0.642909i	$0.222273\pi$
$383$			492.468i			1.28582i	−0.765943	+	0.642909i	$0.777727\pi$
$384$	341.476	+	90.7002i	0.889260	+	0.236198i
$385$	133.558			0.346905
$386$		−	166.986i		−	0.432607i
$387$	−222.735	−	127.303i	−0.575541	−	0.328949i
$388$	−475.996			−1.22679
$389$		−	194.270i		−	0.499410i	−0.968322	−	0.249705i	$-0.919666\pi$
$389$		−	194.270i		−	0.499410i	0.968322	−	0.249705i	$-0.0803336\pi$
$390$	−35.1016	+	132.154i	−0.0900041	+	0.338855i
$391$	−342.202			−0.875197
$392$			76.3719i			0.194826i
$393$	353.518	+	93.8987i	0.899538	+	0.238928i
$394$	−298.035			−0.756434
$395$		−	518.071i		−	1.31157i
$396$	−32.1853	+	56.3126i	−0.0812760	+	0.142204i
$397$	−388.847			−0.979462			−0.489731	−	0.871873i	$-0.662905\pi$
$397$	−388.847			−0.979462			−0.489731	+	0.871873i	$0.662905\pi$
$398$			324.866i			0.816245i
$399$	51.3714	−	193.407i	0.128750	−	0.484730i
$400$	−262.170			−0.655426
$401$			202.445i			0.504851i	0.967616	+	0.252425i	$0.0812282\pi$
$401$			202.445i			0.504851i	−0.967616	+	0.252425i	$0.918772\pi$
$402$	23.9892	+	6.37182i	0.0596746	+	0.0158503i
$403$	−109.803			−0.272463
$404$		−	359.429i		−	0.889675i
$405$	623.484	−	367.261i	1.53947	−	0.906817i
$406$	−167.711			−0.413082
$407$		−	102.923i		−	0.252883i
$408$	66.2430	−	249.397i	0.162360	−	0.611268i
$409$	−57.6346			−0.140916			−0.0704579	−	0.997515i	$-0.522446\pi$
$409$	−57.6346			−0.140916			−0.0704579	+	0.997515i	$0.522446\pi$
$410$		−	629.469i		−	1.53529i
$411$	403.623	+	107.207i	0.982051	+	0.260845i
$412$	298.094			0.723530
$413$		−	243.688i		−	0.590043i
$414$	221.636	+	126.676i	0.535354	+	0.305980i
$415$	935.961			2.25533
$416$			166.819i			0.401007i
$417$	−93.3135	+	351.315i	−0.223773	+	0.842482i
$418$	−26.4067			−0.0631740
$419$			441.619i			1.05398i	0.849870	+	0.526992i	$0.176680\pi$
$419$			441.619i			1.05398i	−0.849870	+	0.526992i	$0.823320\pi$
$420$	−476.632	−	126.599i	−1.13484	−	0.301427i
$421$	119.514			0.283881			0.141941	−	0.989875i	$-0.454666\pi$
$421$	119.514			0.283881			0.141941	+	0.989875i	$0.454666\pi$
$422$		−	299.146i		−	0.708876i
$423$	−285.879	+	500.185i	−0.675838	+	1.18247i
$424$	28.9142			0.0681939
$425$			668.343i			1.57257i
$426$	13.9476	−	52.5112i	0.0327409	−	0.123266i
$427$	299.221			0.700751
$428$			200.125i			0.467582i
$429$	−35.4138	−	9.40634i	−0.0825497	−	0.0219262i
$430$	−257.399			−0.598602
$431$			84.0534i			0.195020i	0.995235	+	0.0975098i	$0.0310877\pi$
$431$			84.0534i			0.195020i	−0.995235	+	0.0975098i	$0.968912\pi$
$432$	90.7268	−	91.9223i	0.210016	−	0.212783i
$433$	−693.855			−1.60244			−0.801218	−	0.598373i	$-0.795814\pi$
$433$	−693.855			−1.60244			−0.801218	+	0.598373i	$0.795814\pi$
$434$			135.853i			0.313025i
$435$	−184.762	+	695.607i	−0.424740	+	1.59910i
$436$	−542.763			−1.24487
$437$		−	302.969i		−	0.693293i
$438$	309.100	+	82.1007i	0.705708	+	0.187445i
$439$	587.670			1.33866			0.669328	−	0.742967i	$-0.266582\pi$
$439$	587.670			1.33866			0.669328	+	0.742967i	$0.266582\pi$
$440$			152.477i			0.346540i
$441$	84.6029	+	48.3545i	0.191843	+	0.109647i
$442$	62.2163			0.140761
$443$			47.7910i			0.107880i	0.998544	+	0.0539402i	$0.0171780\pi$
$443$			47.7910i			0.107880i	−0.998544	+	0.0539402i	$0.982822\pi$
$444$	−97.5605	+	367.304i	−0.219731	+	0.827262i
$445$	1301.83			2.92545
$446$		−	120.740i		−	0.270717i
$447$	434.151	+	115.316i	0.971256	+	0.257977i
$448$	88.1781			0.196826
$449$		−	566.170i		−	1.26096i	−0.776206	−	0.630479i	$-0.782859\pi$
$449$		−	566.170i		−	1.26096i	0.776206	−	0.630479i	$-0.217141\pi$
$450$	247.406	−	432.870i	0.549790	−	0.961934i
$451$	168.682			0.374017
$452$		−	499.296i		−	1.10464i
$453$	−94.2191	+	354.724i	−0.207989	+	0.783056i
$454$	418.076			0.920873
$455$		−	278.597i		−	0.612301i
$456$	220.804	+	58.6483i	0.484220	+	0.128615i
$457$	−730.508			−1.59849			−0.799243	−	0.601008i	$-0.794766\pi$
$457$	−730.508			−1.59849			−0.799243	+	0.601008i	$0.794766\pi$
$458$		−	394.412i		−	0.861161i
$459$	−234.335	−	231.287i	−0.510533	−	0.503893i
$460$	−746.635			−1.62312
$461$		−	51.4723i		−	0.111654i	−0.998440	−	0.0558268i	$-0.982221\pi$
$461$		−	51.4723i		−	0.111654i	0.998440	−	0.0558268i	$-0.0177795\pi$
$462$	−11.6380	+	43.8157i	−0.0251904	+	0.0948391i
$463$	656.086			1.41703			0.708516	−	0.705695i	$-0.249365\pi$
$463$	656.086			1.41703			0.708516	+	0.705695i	$0.249365\pi$
$464$			128.462i			0.276857i
$465$	563.470	+	149.664i	1.21176	+	0.321859i
$466$	110.410			0.236932
$467$		−	317.335i		−	0.679519i	−0.940512	−	0.339760i	$-0.889654\pi$
$467$		−	317.335i		−	0.679519i	0.940512	−	0.339760i	$-0.110346\pi$
$468$	117.466	+	67.1371i	0.250995	+	0.143455i
$469$	−50.5724			−0.107830
$470$			578.030i			1.22985i
$471$	119.136	−	448.533i	0.252942	−	0.952300i
$472$	278.207			0.589421
$473$		−	68.9764i		−	0.145828i
$474$	169.960	+	45.1435i	0.358566	+	0.0952394i
$475$	−591.718			−1.24572
$476$			224.393i			0.471413i
$477$	18.3069	−	32.0304i	0.0383792	−	0.0671497i
$478$	51.1032			0.106910
$479$			675.064i			1.40932i	0.709545	+	0.704660i	$0.248901\pi$
$479$			675.064i			1.40932i	−0.709545	+	0.704660i	$0.751099\pi$
$480$	227.379	−	856.058i	0.473707	−	1.78345i
$481$	−214.694			−0.446349
$482$			243.574i			0.505341i
$483$	−502.704	−	133.524i	−1.04080	−	0.276448i
$484$	342.936			0.708546
$485$			1427.76i			2.94383i
$486$	66.1559	+	236.545i	0.136123	+	0.486718i
$487$	−223.648			−0.459236			−0.229618	−	0.973281i	$-0.573748\pi$
$487$	−223.648			−0.459236			−0.229618	+	0.973281i	$0.573748\pi$
$488$			341.606i			0.700013i
$489$	−46.5956	+	175.427i	−0.0952875	+	0.358747i
$490$	97.7697			0.199530
$491$		−	370.463i		−	0.754508i	−0.926110	−	0.377254i	$-0.876868\pi$
$491$		−	370.463i		−	0.754508i	0.926110	−	0.377254i	$-0.123132\pi$
$492$	−601.978	−	159.893i	−1.22353	−	0.324985i
$493$	327.484			0.664267
$494$			55.0833i			0.111505i
$495$	168.911	+	96.5403i	0.341234	+	0.195031i
$496$	104.059			0.209797
$497$			110.701i			0.222737i
$498$	−81.5574	+	307.055i	−0.163770	+	0.616576i
$499$	401.158			0.803923			0.401962	−	0.915656i	$-0.368328\pi$
$499$	401.158			0.803923			0.401962	+	0.915656i	$0.368328\pi$
$500$			793.062i			1.58612i
$501$	−147.185	−	39.0941i	−0.293782	−	0.0780321i
$502$	−312.256			−0.622024
$503$			904.714i			1.79864i	0.437294	+	0.899318i	$0.355937\pi$
$503$			904.714i			1.79864i	−0.437294	+	0.899318i	$0.644063\pi$
$504$	194.626	−	340.524i	0.386162	−	0.675644i
$505$	−1078.11			−2.13488
$506$			68.6363i			0.135645i
$507$	110.531	−	416.138i	0.218010	−	0.820785i
$508$	577.340			1.13650
$509$			204.696i			0.402153i	0.979576	+	0.201077i	$0.0644440\pi$
$509$			204.696i			0.402153i	−0.979576	+	0.201077i	$0.935556\pi$
$510$	−319.273	−	84.8028i	−0.626026	−	0.166280i
$511$	−651.624			−1.27519
$512$		−	293.057i		−	0.572378i
$513$	204.770	−	207.469i	0.399162	−	0.404422i
$514$	−200.407			−0.389897
$515$		−	894.139i		−	1.73619i
$516$	−65.3824	+	246.157i	−0.126710	+	0.477049i
$517$	−154.897			−0.299608
$518$			265.629i			0.512798i
$519$	−22.3625	−	5.93975i	−0.0430876	−	0.0114446i
$520$	318.061			0.611657
$521$			608.868i			1.16865i	0.811519	+	0.584326i	$0.198641\pi$
$521$			608.868i			1.16865i	−0.811519	+	0.584326i	$0.801359\pi$
$522$	−212.104	−	121.227i	−0.406329	−	0.232236i
$523$	−463.095			−0.885459			−0.442730	−	0.896655i	$-0.645990\pi$
$523$	−463.095			−0.885459			−0.442730	+	0.896655i	$0.645990\pi$
$524$		−	363.131i		−	0.692998i
$525$	−260.782	+	981.814i	−0.496727	+	1.87012i
$526$	267.926			0.509365
$527$		−	265.275i		−	0.503368i
$528$	33.5614	+	8.91433i	0.0635633	+	0.0168832i
$529$	−258.476			−0.488613
$530$		−	37.0154i		−	0.0698403i
$531$	176.145	−	308.190i	0.331724	−	0.580396i
$532$	−198.666			−0.373433
$533$		−	351.863i		−	0.660156i
$534$	−113.438	+	427.082i	−0.212431	+	0.799779i
$535$	600.278			1.12201
$536$		−	57.7362i		−	0.107717i
$537$	240.307	+	63.8285i	0.447499	+	0.118861i
$538$	252.640			0.469590
$539$			26.1998i			0.0486082i
$540$	−511.284	−	504.635i	−0.946823	−	0.934508i
$541$	177.148			0.327445			0.163722	−	0.986506i	$-0.447650\pi$
$541$	177.148			0.327445			0.163722	+	0.986506i	$0.447650\pi$
$542$			70.4142i			0.129916i
$543$	−245.673	+	924.933i	−0.452437	+	1.70338i
$544$	−403.022			−0.740849
$545$			1628.03i			2.98720i
$546$	91.3975	+	24.2763i	0.167395	+	0.0444621i
$547$	177.112			0.323789			0.161894	−	0.986808i	$-0.448240\pi$
$547$	177.112			0.323789			0.161894	+	0.986808i	$0.448240\pi$
$548$		−	414.598i		−	0.756566i
$549$	378.423	+	216.286i	0.689295	+	0.393964i
$550$	134.051			0.243730
$551$			289.938i			0.526204i
$552$	152.439	−	573.914i	0.276157	−	1.03970i
$553$	−358.298			−0.647917
$554$		−	7.47406i		−	0.0134911i
$555$	1101.74	+	292.634i	1.98511	+	0.527269i
$556$	360.868			0.649042
$557$		−	792.510i		−	1.42282i	−0.702778	−	0.711409i	$-0.748057\pi$
$557$		−	792.510i		−	1.42282i	0.702778	−	0.711409i	$-0.251943\pi$
$558$	−98.1989	+	171.813i	−0.175984	+	0.307908i
$559$	−143.882			−0.257391
$560$			264.025i			0.471472i
$561$	22.7250	−	85.5572i	0.0405081	−	0.152508i
$562$	19.8768			0.0353679
$563$		−	304.222i		−	0.540359i	−0.962810	−	0.270179i	$-0.912917\pi$
$563$		−	304.222i		−	0.540359i	0.962810	−	0.270179i	$-0.0870830\pi$
$564$	552.785	+	146.826i	0.980115	+	0.260330i
$565$	−1497.65			−2.65070
$566$			38.6089i			0.0682137i
$567$	−253.998	−	431.202i	−0.447968	−	0.760498i
$568$	−126.382			−0.222503
$569$			381.327i			0.670171i	0.942188	+	0.335086i	$0.108765\pi$
$569$			381.327i			0.670171i	−0.942188	+	0.335086i	$0.891235\pi$
$570$	75.0803	−	282.669i	0.131720	−	0.495910i
$571$	−267.814			−0.469026			−0.234513	−	0.972113i	$-0.575350\pi$
$571$	−267.814			−0.469026			−0.234513	+	0.972113i	$0.575350\pi$
$572$			36.3768i			0.0635958i
$573$	−262.930	−	69.8373i	−0.458865	−	0.121880i
$574$	−435.341			−0.758434
$575$			1537.99i			2.67477i
$576$	111.518	+	63.7380i	0.193608	+	0.110656i
$577$	438.881			0.760625			0.380312	−	0.924858i	$-0.375816\pi$
$577$	438.881			0.760625			0.380312	+	0.924858i	$0.375816\pi$
$578$		−	141.808i		−	0.245343i
$579$	−127.229	+	479.003i	−0.219739	+	0.827294i
$580$	714.522			1.23193
$581$		−	647.312i		−	1.11413i
$582$	−468.395	−	124.411i	−0.804803	−	0.213765i
$583$	9.91918			0.0170140
$584$		−	743.929i		−	1.27385i
$585$	201.379	−	352.340i	0.344237	−	0.602291i
$586$	169.824			0.289802
$587$		−	304.708i		−	0.519094i	−0.965730	−	0.259547i	$-0.916427\pi$
$587$		−	304.708i		−	0.519094i	0.965730	−	0.259547i	$-0.0835733\pi$
$588$	24.8347	−	93.4997i	0.0422358	−	0.159013i
$589$	234.862			0.398746
$590$		−	356.154i		−	0.603651i
$591$	854.918	+	227.077i	1.44656	+	0.384224i
$592$	203.464			0.343689
$593$		−	322.352i		−	0.543595i	−0.962355	−	0.271797i	$-0.912382\pi$
$593$		−	322.352i		−	0.543595i	0.962355	−	0.271797i	$-0.0876180\pi$
$594$	−46.3898	+	47.0011i	−0.0780974	+	0.0791265i
$595$	673.070			1.13121
$596$		−	445.957i		−	0.748249i
$597$	247.519	−	931.882i	0.414605	−	1.56094i
$598$	143.172			0.239419
$599$		−	95.9797i		−	0.160233i	−0.996785	−	0.0801166i	$-0.974471\pi$
$599$		−	95.9797i		−	0.160233i	0.996785	−	0.0801166i	$-0.0255293\pi$
$600$	−1120.89	−	297.723i	−1.86815	−	0.496204i
$601$	998.553			1.66149			0.830743	−	0.556657i	$-0.187916\pi$
$601$	998.553			1.66149			0.830743	+	0.556657i	$0.187916\pi$
$602$			178.017i			0.295710i
$603$	−63.9586	−	36.5553i	−0.106067	−	0.0606225i
$604$	364.370			0.603261
$605$		−	1028.64i		−	1.70023i
$606$	93.9442	−	353.689i	0.155023	−	0.583646i
$607$	−575.629			−0.948319			−0.474159	−	0.880439i	$-0.657248\pi$
$607$	−575.629			−0.948319			−0.474159	+	0.880439i	$0.657248\pi$
$608$		−	356.816i		−	0.586869i
$609$	481.083	+	127.781i	0.789955	+	0.209822i
$610$	437.317			0.716913
$611$			323.109i			0.528820i
$612$	−162.198	+	283.788i	−0.265030	+	0.463707i
$613$	−247.197			−0.403259			−0.201629	−	0.979462i	$-0.564624\pi$
$613$	−247.197			−0.403259			−0.201629	+	0.979462i	$0.564624\pi$
$614$			345.909i			0.563370i
$615$	−479.600	+	1805.64i	−0.779838	+	2.93600i
$616$	105.454			0.171191
$617$			515.586i			0.835634i	0.908531	+	0.417817i	$0.137205\pi$
$617$			515.586i			0.835634i	−0.908531	+	0.417817i	$0.862795\pi$
$618$	293.334	+	77.9132i	0.474651	+	0.126073i
$619$	460.666			0.744210			0.372105	−	0.928191i	$-0.378636\pi$
$619$	460.666			0.744210			0.372105	+	0.928191i	$0.378636\pi$
$620$		−	578.792i		−	0.933535i
$621$	−539.252	−	532.238i	−0.868360	−	0.857067i
$622$	−55.5996			−0.0893884
$623$		−	900.345i		−	1.44518i
$624$	18.5949	−	70.0077i	0.0297995	−	0.112192i
$625$	1008.63			1.61380
$626$			488.575i			0.780471i
$627$	75.7482	+	20.1196i	0.120810	+	0.0320887i
$628$	−460.729			−0.733645
$629$		−	518.684i		−	0.824617i
$630$	−435.932	−	249.155i	−0.691955	−	0.395485i
$631$	574.622			0.910653			0.455327	−	0.890324i	$-0.349522\pi$
$631$	574.622			0.910653			0.455327	+	0.890324i	$0.349522\pi$
$632$		−	409.053i		−	0.647235i
$633$	−227.923	+	858.104i	−0.360068	+	1.35561i
$634$	384.720			0.606814
$635$		−	1731.74i		−	2.72715i
$636$	−35.3988	−	9.40234i	−0.0556584	−	0.0147836i
$637$	54.6517			0.0857954
$638$		−	65.6843i		−	0.102953i
$639$	−80.0179	+	140.002i	−0.125224	+	0.219096i
$640$	−1052.11			−1.64393
$641$			666.692i			1.04008i	0.854141	+	0.520041i	$0.174083\pi$
$641$			666.692i			1.04008i	−0.854141	+	0.520041i	$0.825917\pi$
$642$	−52.3068	+	196.929i	−0.0814748	+	0.306744i
$643$	−737.329			−1.14670			−0.573351	−	0.819310i	$-0.694357\pi$
$643$	−737.329			−1.14670			−0.573351	+	0.819310i	$0.694357\pi$
$644$			516.373i			0.801822i
$645$	738.353	+	196.115i	1.14473	+	0.304055i
$646$	−133.077			−0.206002
$647$		−	212.272i		−	0.328086i	−0.986453	−	0.164043i	$-0.947546\pi$
$647$		−	212.272i		−	0.328086i	0.986453	−	0.164043i	$-0.0524536\pi$
$648$	492.284	−	289.978i	0.759698	−	0.447497i
$649$	95.4404			0.147058
$650$		−	279.625i		−	0.430193i
$651$	103.508	−	389.696i	0.158999	−	0.598612i
$652$	180.197			0.276376
$653$		−	321.827i		−	0.492843i	−0.969163	−	0.246422i	$-0.920745\pi$
$653$		−	321.827i		−	0.492843i	0.969163	−	0.246422i	$-0.0792548\pi$
$654$	−534.096	−	141.862i	−0.816661	−	0.216915i
$655$	−1089.22			−1.66293
$656$			333.458i			0.508320i
$657$	−824.105	−	471.015i	−1.25435	−	0.716917i
$658$	399.766			0.607547
$659$		−	974.758i		−	1.47915i	−0.673075	−	0.739574i	$-0.735027\pi$
$659$		−	974.758i		−	1.47915i	0.673075	−	0.739574i	$-0.264973\pi$
$660$	49.5827	−	186.673i	0.0751253	−	0.282838i
$661$	−238.219			−0.360392			−0.180196	−	0.983631i	$-0.557673\pi$
$661$	−238.219			−0.360392			−0.180196	+	0.983631i	$0.557673\pi$
$662$		−	58.5029i		−	0.0883730i
$663$	−178.469	−	47.4034i	−0.269183	−	0.0714983i
$664$	739.006			1.11296
$665$			595.903i			0.896095i
$666$	−192.005	+	335.940i	−0.288296	+	0.504414i
$667$	753.607			1.12985
$668$			151.187i			0.226328i
$669$	−91.9933	+	346.345i	−0.137509	+	0.517705i
$670$	−73.9126			−0.110317
$671$			117.190i			0.174650i
$672$	−592.051	−	157.256i	−0.881028	−	0.234012i
$673$	−294.633			−0.437791			−0.218896	−	0.975748i	$-0.570245\pi$
$673$	−294.633			−0.437791			−0.218896	+	0.975748i	$0.570245\pi$
$674$		−	97.2610i		−	0.144304i
$675$	−1039.50	+	1053.19i	−1.53999	+	1.56029i
$676$	−427.453			−0.632327
$677$			271.648i			0.401252i	0.979668	+	0.200626i	$0.0642977\pi$
$677$			271.648i			0.401252i	−0.979668	+	0.200626i	$0.935702\pi$
$678$	130.501	−	491.323i	0.192480	−	0.724666i
$679$	987.439			1.45425
$680$			768.413i			1.13002i
$681$	−1199.26	−	318.538i	−1.76103	−	0.467750i
$682$	−53.2069			−0.0780160
$683$			1182.17i			1.73084i	0.501044	+	0.865422i	$0.332950\pi$
$683$			1182.17i			1.73084i	−0.501044	+	0.865422i	$0.667050\pi$
$684$	−251.252	−	143.603i	−0.367328	−	0.209945i
$685$	−1243.59			−1.81547
$686$		−	373.626i		−	0.544644i
$687$	−300.507	+	1131.38i	−0.437419	+	1.64684i
$688$	136.356			0.198192
$689$		−	20.6910i		−	0.0300305i
$690$	−734.712	−	195.149i	−1.06480	−	0.282824i
$691$	−246.427			−0.356623			−0.178312	−	0.983974i	$-0.557064\pi$
$691$	−246.427			−0.356623			−0.178312	+	0.983974i	$0.557064\pi$
$692$			22.9706i			0.0331944i
$693$	66.7674	−	116.819i	0.0963454	−	0.168570i
$694$	−386.823			−0.557382
$695$		−	1082.43i		−	1.55745i
$696$	−145.882	+	549.230i	−0.209601	+	0.789124i
$697$	850.075			1.21962
$698$		−	205.376i		−	0.294234i
$699$	−316.713	−	84.1229i	−0.453095	−	0.120347i
$700$	1008.51			1.44073
$701$			341.770i			0.487547i	0.969832	+	0.243773i	$0.0783853\pi$
$701$			341.770i			0.487547i	−0.969832	+	0.243773i	$0.921615\pi$
$702$	98.0423	+	96.7672i	0.139661	+	0.137845i
$703$	459.218			0.653226
$704$			34.5350i			0.0490554i
$705$	440.408	−	1658.09i	0.624692	−	2.35190i
$706$	455.440			0.645099
$707$			745.624i			1.05463i
$708$	−340.600	−	90.4674i	−0.481073	−	0.127779i
$709$	402.800			0.568124			0.284062	−	0.958806i	$-0.408318\pi$
$709$	402.800			0.568124			0.284062	+	0.958806i	$0.408318\pi$
$710$			161.791i			0.227875i
$711$	−453.138	−	258.989i	−0.637325	−	0.364261i
$712$	1027.88			1.44366
$713$		−	610.452i		−	0.856174i
$714$	−58.6497	+	220.810i	−0.0821425	+	0.309257i
$715$	109.113			0.152605
$716$		−	246.842i		−	0.344751i
$717$	−146.590	−	38.9362i	−0.204450	−	0.0543043i
$718$	−54.8343			−0.0763708
$719$			153.355i			0.213289i	0.994297	+	0.106644i	$0.0340106\pi$
$719$			153.355i			0.213289i	−0.994297	+	0.106644i	$0.965989\pi$
$720$	−190.845	+	333.910i	−0.265063	+	0.463765i
$721$	−618.387			−0.857680
$722$			247.075i			0.342209i
$723$	185.582	−	698.697i	0.256684	−	0.966386i
$724$	950.083			1.31227
$725$		−	1471.84i		−	2.03013i
$726$	337.460	+	89.6335i	0.464821	+	0.123462i
$727$	620.768			0.853876			0.426938	−	0.904281i	$-0.359592\pi$
$727$	620.768			0.853876			0.426938	+	0.904281i	$0.359592\pi$
$728$		−	219.972i		−	0.302159i
$729$	−9.54288	−	728.938i	−0.0130904	−	0.999914i
$730$	−952.361			−1.30460
$731$		−	347.608i		−	0.475524i
$732$	111.084	−	418.218i	0.151754	−	0.571336i
$733$	−808.097			−1.10245			−0.551226	−	0.834356i	$-0.685840\pi$
$733$	−808.097			−1.10245			−0.551226	+	0.834356i	$0.685840\pi$
$734$			458.588i			0.624780i
$735$	−280.454	−	74.4920i	−0.381570	−	0.101350i
$736$	−927.436			−1.26010
$737$		−	19.8067i		−	0.0268748i
$738$	−550.574	−	314.679i	−0.746035	−	0.426394i
$739$	893.483			1.20904			0.604522	−	0.796589i	$-0.293364\pi$
$739$	893.483			1.20904			0.604522	+	0.796589i	$0.293364\pi$
$740$		−	1131.69i		−	1.52932i
$741$	41.9687	−	158.007i	0.0566379	−	0.213235i
$742$	−25.5999			−0.0345012
$743$			536.034i			0.721445i	0.932673	+	0.360722i	$0.117470\pi$
$743$			536.034i			0.721445i	−0.932673	+	0.360722i	$0.882530\pi$
$744$	444.899	+	118.170i	0.597982	+	0.158831i
$745$	−1337.65			−1.79551
$746$		−	11.3879i		−	0.0152653i
$747$	467.898	−	818.652i	0.626369	−	1.09592i
$748$	−87.8836			−0.117491
$749$		−	415.153i		−	0.554276i
$750$	−207.283	+	780.398i	−0.276378	+	1.04053i
$751$	−413.727			−0.550902			−0.275451	−	0.961315i	$-0.588827\pi$
$751$	−413.727			−0.550902			−0.275451	+	0.961315i	$0.588827\pi$
$752$		−	306.208i		−	0.407192i
$753$	895.711	+	237.912i	1.18952	+	0.315952i
$754$	−137.015			−0.181717
$755$		−	1092.93i		−	1.44759i
$756$	−349.006	+	353.605i	−0.461648	+	0.467731i
$757$	388.186			0.512796			0.256398	−	0.966571i	$-0.417464\pi$
$757$	388.186			0.512796			0.256398	+	0.966571i	$0.417464\pi$
$758$			394.169i			0.520012i
$759$	52.2949	−	196.884i	0.0688997	−	0.259400i
$760$	−680.315			−0.895152
$761$			730.566i			0.960008i	0.877266	+	0.480004i	$0.159365\pi$
$761$			730.566i			0.960008i	−0.877266	+	0.480004i	$0.840635\pi$
$762$	568.121	+	150.900i	0.745566	+	0.198031i
$763$	1125.94			1.47568
$764$			270.079i			0.353506i
$765$	851.228	+	486.516i	1.11272	+	0.635969i
$766$	497.782			0.649845
$767$		−	199.085i		−	0.259563i
$768$	135.644	−	510.685i	0.176620	−	0.664954i
$769$	217.799			0.283224			0.141612	−	0.989922i	$-0.454771\pi$
$769$	217.799			0.283224			0.141612	+	0.989922i	$0.454771\pi$
$770$		−	134.999i		−	0.175324i
$771$	574.871	+	152.693i	0.745617	+	0.198045i
$772$	492.028			0.637342
$773$			235.591i			0.304775i	0.988321	+	0.152387i	$0.0486961\pi$
$773$			235.591i			0.304775i	−0.988321	+	0.152387i	$0.951304\pi$
$774$	−128.677	+	225.138i	−0.166249	+	0.290875i
$775$	−1192.25			−1.53839
$776$			1127.31i			1.45272i
$777$	202.386	−	761.961i	0.260471	−	0.980645i
$778$	−196.366			−0.252399
$779$			752.615i			0.966129i
$780$	−389.392	−	103.427i	−0.499221	−	0.132599i
$781$	−43.3559			−0.0555134
$782$			345.894i			0.442320i
$783$	516.058	+	509.347i	0.659079	+	0.650507i
$784$	−51.7930			−0.0660625
$785$			1381.96i			1.76046i
$786$	94.9118	−	357.332i	0.120753	−	0.454621i
$787$	1110.23			1.41072			0.705358	−	0.708852i	$-0.250786\pi$
$787$	1110.23			1.41072			0.705358	+	0.708852i	$0.250786\pi$
$788$		−	878.164i		−	1.11442i
$789$	−768.551	−	204.136i	−0.974082	−	0.258728i
$790$	−523.660			−0.662861
$791$			1035.77i			1.30945i
$792$	133.367	+	76.2253i	0.168392	+	0.0962440i
$793$	244.453			0.308264
$794$			393.042i			0.495015i
$795$	−28.2025	+	106.179i	−0.0354748	+	0.133559i
$796$	−957.221			−1.20254
$797$			10.2893i			0.0129101i	0.999979	+	0.00645503i	$0.00205471\pi$
$797$			10.2893i			0.0129101i	−0.999979	+	0.00645503i	$0.997945\pi$
$798$	−195.494	−	51.9256i	−0.244980	−	0.0650697i
$799$	−780.608			−0.976981
$800$			1811.34i			2.26418i
$801$	650.799	−	1138.66i	0.812483	−	1.42155i
$802$	204.629			0.255149
$803$		−	255.209i		−	0.317819i
$804$	−18.7747	+	70.6845i	−0.0233516	+	0.0879161i
$805$	1548.87			1.92406
$806$			110.987i			0.137701i
$807$	−724.701	−	192.489i	−0.898018	−	0.238525i
$808$	−851.244			−1.05352
$809$			765.063i			0.945690i	0.881146	+	0.472845i	$0.156773\pi$
$809$			765.063i			0.945690i	−0.881146	+	0.472845i	$0.843227\pi$
$810$	−371.223	−	630.211i	−0.458300	−	0.778039i
$811$	−1231.02			−1.51791			−0.758954	−	0.651145i	$-0.774289\pi$
$811$	−1231.02			−1.51791			−0.758954	+	0.651145i	$0.774289\pi$
$812$		−	494.164i		−	0.608577i
$813$	53.6495	−	201.984i	0.0659895	−	0.248443i
$814$	−104.034			−0.127806
$815$		−	540.505i		−	0.663196i
$816$	169.133	+	44.9239i	0.207271	+	0.0550538i
$817$	307.755			0.376689
$818$			58.2564i			0.0712181i
$819$	−243.679	−	139.274i	−0.297532	−	0.170054i
$820$	1854.74			2.26188
$821$		−	24.2528i		−	0.0295406i	−0.999891	−	0.0147703i	$-0.995298\pi$
$821$		−	24.2528i		−	0.0295406i	0.999891	−	0.0147703i	$-0.00470170\pi$
$822$	108.364	−	407.978i	0.131830	−	0.496323i
$823$	88.4434			0.107465			0.0537323	−	0.998555i	$-0.482888\pi$
$823$	88.4434			0.107465			0.0537323	+	0.998555i	$0.482888\pi$
$824$		−	705.984i		−	0.856777i
$825$	−384.528	−	102.135i	−0.466095	−	0.123800i
$826$	−246.317			−0.298204
$827$			988.087i			1.19479i	0.801949	+	0.597393i	$0.203797\pi$
$827$			988.087i			1.19479i	−0.801949	+	0.597393i	$0.796203\pi$
$828$	−373.251	+	653.055i	−0.450787	+	0.788714i
$829$	−825.297			−0.995533			−0.497767	−	0.867311i	$-0.665846\pi$
$829$	−825.297			−0.995533			−0.497767	+	0.867311i	$0.665846\pi$
$830$		−	946.059i		−	1.13983i
$831$	−5.69458	+	21.4394i	−0.00685268	+	0.0257996i
$832$	72.0385			0.0865848
$833$			132.034i			0.158505i
$834$	355.105	+	94.3203i	0.425786	+	0.113094i
$835$	453.488			0.543099
$836$		−	77.8079i		−	0.0930716i
$837$	412.591	−	418.028i	0.492941	−	0.499436i
$838$	446.384			0.532678
$839$			1621.64i			1.93283i	0.256989	+	0.966414i	$0.417270\pi$
$839$			1621.64i			1.93283i	−0.256989	+	0.966414i	$0.582730\pi$
$840$	−299.828	+	1128.82i	−0.356938	+	1.34383i
$841$	119.806			0.142457
$842$		−	120.803i		−	0.143472i
$843$	−57.0168	−	15.1444i	−0.0676356	−	0.0179648i
$844$	881.437			1.04436
$845$			1282.15i			1.51734i
$846$	505.582	+	288.964i	0.597615	+	0.341565i
$847$	−711.410			−0.839917
$848$			19.6087i			0.0231235i
$849$	29.4166	−	110.750i	0.0346486	−	0.130448i
$850$	675.554			0.794769
$851$		−	1193.60i		−	1.40258i
$852$	154.725	+	41.0969i	0.181602	+	0.0482357i
$853$	460.822			0.540237			0.270118	−	0.962827i	$-0.412937\pi$
$853$	460.822			0.540237			0.270118	+	0.962827i	$0.412937\pi$
$854$		−	302.449i		−	0.354156i
$855$	−430.738	+	753.636i	−0.503787	+	0.881445i
$856$	473.961			0.553693
$857$			1387.48i			1.61900i	0.587121	+	0.809499i	$0.300261\pi$
$857$			1387.48i			1.61900i	−0.587121	+	0.809499i	$0.699739\pi$
$858$	−9.50783	+	35.7959i	−0.0110814	+	0.0417202i
$859$	573.729			0.667904			0.333952	−	0.942590i	$-0.391618\pi$
$859$	573.729			0.667904			0.333952	+	0.942590i	$0.391618\pi$
$860$		−	758.430i		−	0.881895i
$861$	1248.78	+	331.692i	1.45039	+	0.385240i
$862$	84.9603			0.0985618
$863$			157.930i			0.183001i	0.995805	+	0.0915004i	$0.0291663\pi$
$863$			157.930i			0.183001i	−0.995805	+	0.0915004i	$0.970834\pi$
$864$	−635.094	−	626.834i	−0.735062	−	0.725502i
$865$	68.9005			0.0796538
$866$			701.341i			0.809862i
$867$	−108.045	+	406.779i	−0.124620	+	0.469179i
$868$	−400.293			−0.461167
$869$		−	140.328i		−	0.161482i
$870$	703.112	+	186.755i	0.808175	+	0.214661i
$871$	−41.3159			−0.0474351
$872$			1285.44i			1.47413i
$873$	1248.81	+	713.753i	1.43048	+	0.817586i
$874$	−306.238			−0.350386
$875$		−	1645.18i		−	1.88021i
$876$	−241.911	+	910.768i	−0.276154	+	1.03969i
$877$	−149.217			−0.170144			−0.0850722	−	0.996375i	$-0.527112\pi$
$877$	−149.217			−0.170144			−0.0850722	+	0.996375i	$0.527112\pi$
$878$		−	594.010i		−	0.676549i
$879$	−487.142	−	129.391i	−0.554200	−	0.147202i
$880$	−103.405			−0.117506
$881$		−	242.487i		−	0.275241i	−0.990485	−	0.137620i	$-0.956055\pi$
$881$		−	242.487i		−	0.275241i	0.990485	−	0.137620i	$-0.0439454\pi$
$882$	48.8762	−	85.5157i	0.0554152	−	0.0969565i
$883$	−936.449			−1.06053			−0.530265	−	0.847832i	$-0.677908\pi$
$883$	−936.449			−1.06053			−0.530265	+	0.847832i	$0.677908\pi$
$884$			183.321i			0.207377i
$885$	−271.358	+	1021.63i	−0.306620	+	1.15439i
$886$	48.3066			0.0545222
$887$			794.872i			0.896135i	0.894000	+	0.448068i	$0.147888\pi$
$887$			794.872i			0.896135i	−0.894000	+	0.448068i	$0.852112\pi$
$888$	869.896	+	231.055i	0.979613	+	0.260197i
$889$	−1197.67			−1.34721
$890$		−	1315.87i		−	1.47851i
$891$	168.881	−	99.4785i	0.189541	−	0.111648i
$892$	355.762			0.398837
$893$		−	691.112i		−	0.773922i
$894$	116.560	−	438.835i	0.130380	−	0.490867i
$895$	−740.405			−0.827268
$896$			727.643i			0.812102i
$897$	−410.692	−	109.085i	−0.457851	−	0.121611i
$898$	−572.279			−0.637281
$899$			584.196i			0.649829i
$900$	1275.46	+	728.984i	1.41718	+	0.809983i
$901$	49.9879			0.0554804
$902$		−	170.502i		−	0.189026i
$903$	135.634	−	510.646i	0.150203	−	0.565499i
$904$	−1182.50			−1.30807
$905$		−	2849.79i		−	3.14894i
$906$	358.552	+	95.2356i	0.395752	+	0.105117i
$907$	1675.39			1.84718			0.923590	−	0.383383i	$-0.125241\pi$
$907$	1675.39			1.84718			0.923590	+	0.383383i	$0.125241\pi$
$908$			1231.87i			1.35668i
$909$	−538.961	+	942.986i	−0.592916	+	1.03739i
$910$	−281.603			−0.309454
$911$		−	1549.41i		−	1.70078i	−0.526152	−	0.850390i	$-0.676366\pi$
$911$		−	1549.41i		−	1.70078i	0.526152	−	0.850390i	$-0.323634\pi$
$912$	−39.7734	+	149.743i	−0.0436112	+	0.164191i
$913$	253.520			0.277678
$914$			738.390i			0.807866i
$915$	−1254.45	−	333.197i	−1.37098	−	0.364150i
$916$	1162.14			1.26871
$917$			753.304i			0.821487i
$918$	−233.782	+	236.863i	−0.254665	+	0.258021i
$919$	1521.28			1.65537			0.827683	−	0.561197i	$-0.189659\pi$
$919$	1521.28			1.65537			0.827683	+	0.561197i	$0.189659\pi$
$920$			1768.27i			1.92204i
$921$	263.553	−	992.246i	0.286159	−	1.07736i
$922$	−52.0277			−0.0564291
$923$			90.4386i			0.0979833i
$924$	−129.103	−	34.2914i	−0.139722	−	0.0371120i
$925$	−2331.17			−2.52019
$926$		−	663.164i		−	0.716160i
$927$	−782.071	−	446.990i	−0.843658	−	0.482190i
$928$	887.547			0.956408
$929$		−	235.103i		−	0.253071i	−0.991962	−	0.126535i	$-0.959614\pi$
$929$		−	235.103i		−	0.253071i	0.991962	−	0.126535i	$-0.0403858\pi$
$930$	151.279	−	569.549i	0.162666	−	0.612419i
$931$	−116.897			−0.125561
$932$			325.325i			0.349061i
$933$	159.488	+	42.3620i	0.170941	+	0.0454041i
$934$	−320.759			−0.343425
$935$			263.608i			0.281934i
$936$	159.003	−	278.197i	0.169875	−	0.297219i
$937$	1627.59			1.73702			0.868510	−	0.495671i	$-0.165078\pi$
$937$	1627.59			1.73702			0.868510	+	0.495671i	$0.165078\pi$
$938$			51.1180i			0.0544968i
$939$	372.251	−	1401.49i	0.396434	−	1.49253i
$940$	−1703.17			−1.81189
$941$			1120.01i			1.19023i	0.803639	+	0.595117i	$0.202894\pi$
$941$			1120.01i			1.19023i	−0.803639	+	0.595117i	$0.797106\pi$
$942$	−453.372	−	120.421i	−0.481287	−	0.127836i
$943$	1956.19			2.07444
$944$			188.671i			0.199863i
$945$	1060.64	+	1046.85i	1.12237	+	1.10778i
$946$	−69.7206			−0.0737004
$947$		−	140.599i		−	0.148468i	−0.997241	−	0.0742341i	$-0.976349\pi$
$947$		−	140.599i		−	0.148468i	0.997241	−	0.0742341i	$-0.0236512\pi$
$948$	−133.016	+	500.790i	−0.140312	+	0.528259i
$949$	−532.355			−0.560964
$950$			598.102i			0.629581i
$951$	−1103.58	−	293.123i	−1.16044	−	0.308226i
$952$	531.435			0.558230
$953$		−	1074.10i		−	1.12707i	−0.826091	−	0.563537i	$-0.809440\pi$
$953$		−	1074.10i		−	1.12707i	0.826091	−	0.563537i	$-0.190560\pi$
$954$	−32.3760	−	18.5044i	−0.0339371	−	0.0193966i
$955$	810.106			0.848278
$956$			150.576i			0.157507i
$957$	−50.0457	+	188.416i	−0.0522943	+	0.196882i
$958$	682.348			0.712263
$959$			860.071i			0.896841i
$960$	−369.677	−	98.1908i	−0.385081	−	0.102282i
$961$	−487.778			−0.507573
$962$			217.010i			0.225582i
$963$	300.086	−	525.042i	0.311616	−	0.545215i
$964$	−717.695			−0.744497
$965$		−	1475.85i		−	1.52937i
$966$	−134.965	+	508.128i	−0.139715	+	0.526012i
$967$	−1443.75			−1.49301			−0.746507	−	0.665377i	$-0.768271\pi$
$967$	−1443.75			−1.49301			−0.746507	+	0.665377i	$0.768271\pi$
$968$		−	812.184i		−	0.839033i
$969$	381.734	+	101.393i	0.393946	+	0.104637i
$970$	1443.16			1.48780
$971$		−	2.84820i		−	0.00293327i	−0.999999	−	0.00146663i	$-0.999533\pi$
$971$		−	2.84820i		−	0.00293327i	0.999999	−	0.00146663i	$-0.000466844\pi$
$972$	−696.983	+	194.929i	−0.717060	+	0.200545i
$973$	−748.608			−0.769382
$974$			226.061i			0.232095i
$975$	−213.050	+	802.109i	−0.218513	+	0.822676i
$976$	−231.667			−0.237363
$977$		−	1579.16i		−	1.61633i	−0.588955	−	0.808166i	$-0.700461\pi$
$977$		−	1579.16i		−	1.61633i	0.588955	−	0.808166i	$-0.299539\pi$
$978$	177.320	+	47.0983i	0.181309	+	0.0481578i
$979$	352.621			0.360185
$980$			288.080i			0.293959i
$981$	1423.98	+	813.869i	1.45156	+	0.829632i
$982$	−374.460			−0.381324
$983$			133.080i			0.135381i	0.997706	+	0.0676905i	$0.0215630\pi$
$983$			133.080i			0.135381i	−0.997706	+	0.0676905i	$0.978437\pi$
$984$	−378.678	+	1425.68i	−0.384835	+	1.44886i
$985$	−2634.07			−2.67418
$986$		−	331.017i		−	0.335717i
$987$	−1146.73	−	304.587i	−1.16184	−	0.308598i
$988$	−162.304			−0.164275
$989$		−	799.916i		−	0.808813i
$990$	97.5819	−	170.733i	0.0985676	−	0.172458i
$991$	−1284.35			−1.29602			−0.648009	−	0.761632i	$-0.724398\pi$
$991$	−1284.35			−1.29602			−0.648009	+	0.761632i	$0.724398\pi$
$992$		−	718.948i		−	0.724746i
$993$	−44.5741	+	167.817i	−0.0448883	+	0.169000i
$994$	111.895			0.112570
$995$			2871.20i			2.88563i
$996$	−904.741	−	240.310i	−0.908375	−	0.241275i
$997$	−215.042			−0.215689			−0.107844	−	0.994168i	$-0.534395\pi$
$997$	−215.042			−0.215689			−0.107844	+	0.994168i	$0.534395\pi$
$998$		−	405.486i		−	0.406299i
$999$	806.727	−	817.357i	0.807535	−	0.818176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.c.a.68.17	✓	44
3.2	odd	2	inner	201.3.c.a.68.28	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.c.a.68.17	✓	44	1.1	even	1	trivial
201.3.c.a.68.28	yes	44	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.01079i q^{2} +(-0.770133 + 2.89946i) q^{3} +2.97831 q^{4} -8.93347i q^{5} +(2.93075 + 0.778442i) q^{6} -6.17840 q^{7} -7.05360i q^{8} +(-7.81379 - 4.46595i) q^{9} +O(q^{10})\)	\(q-1.01079i q^{2} +(-0.770133 + 2.89946i) q^{3} +2.97831 q^{4} -8.93347i q^{5} +(2.93075 + 0.778442i) q^{6} -6.17840 q^{7} -7.05360i q^{8} +(-7.81379 - 4.46595i) q^{9} -9.02986 q^{10} -2.41977i q^{11} +(-2.29369 + 8.63549i) q^{12} -5.04754 q^{13} +6.24506i q^{14} +(25.9023 + 6.87996i) q^{15} +4.78352 q^{16} -12.1945i q^{17} +(-4.51413 + 7.89809i) q^{18} +10.7964 q^{19} -26.6066i q^{20} +(4.75819 - 17.9141i) q^{21} -2.44588 q^{22} -28.0620i q^{23} +(20.4516 + 5.43221i) q^{24} -54.8069 q^{25} +5.10200i q^{26} +(18.9665 - 19.2164i) q^{27} -18.4012 q^{28} +26.8551i q^{29} +(6.95419 - 26.1818i) q^{30} +21.7537 q^{31} -33.0495i q^{32} +(7.01605 + 1.86355i) q^{33} -12.3261 q^{34} +55.1946i q^{35} +(-23.2719 - 13.3010i) q^{36} +42.5343 q^{37} -10.9129i q^{38} +(3.88728 - 14.6352i) q^{39} -63.0131 q^{40} +69.7097i q^{41} +(-18.1073 - 4.80953i) q^{42} +28.5053 q^{43} -7.20683i q^{44} +(-39.8964 + 69.8043i) q^{45} -28.3648 q^{46} -64.0131i q^{47} +(-3.68395 + 13.8697i) q^{48} -10.8274 q^{49} +55.3983i q^{50} +(35.3575 + 9.39138i) q^{51} -15.0331 q^{52} +4.09922i q^{53} +(-19.4238 - 19.1711i) q^{54} -21.6170 q^{55} +43.5799i q^{56} +(-8.31467 + 31.3038i) q^{57} +27.1448 q^{58} +39.4419i q^{59} +(77.1449 + 20.4906i) q^{60} -48.4301 q^{61} -21.9884i q^{62} +(48.2767 + 27.5924i) q^{63} -14.2720 q^{64} +45.0921i q^{65} +(1.88365 - 7.09175i) q^{66} +8.18535 q^{67} -36.3189i q^{68} +(81.3648 + 21.6115i) q^{69} +55.7901 q^{70} -17.9173i q^{71} +(-31.5010 + 55.1153i) q^{72} +105.468 q^{73} -42.9932i q^{74} +(42.2086 - 158.911i) q^{75} +32.1550 q^{76} +14.9503i q^{77} +(-14.7931 - 3.92922i) q^{78} +57.9921 q^{79} -42.7335i q^{80} +(41.1106 + 69.7919i) q^{81} +70.4618 q^{82} +104.770i q^{83} +(14.1713 - 53.3535i) q^{84} -108.939 q^{85} -28.8129i q^{86} +(-77.8653 - 20.6820i) q^{87} -17.0681 q^{88} +145.725i q^{89} +(70.5574 + 40.3269i) q^{90} +31.1857 q^{91} -83.5772i q^{92} +(-16.7532 + 63.0740i) q^{93} -64.7038 q^{94} -96.4494i q^{95} +(95.8259 + 25.4525i) q^{96} -159.821 q^{97} +10.9442i q^{98} +(-10.8066 + 18.9076i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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