LMFDB - Embedded newform 11.5.d.a.8.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,5,Mod(2,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(10))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("11.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	11.d (of order $10$, degree $4$, 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:	$1.13706959392$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 115x^{10} + 5030x^{8} + 102975x^{6} + 953170x^{4} + 2910655x^{2} + 73205 $ x^12 + 115x^10 + 5030x^8 + 102975x^6 + 953170x^4 + 2910655*x^2 + 73205
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			8.2
Root			$-0.159251i$ of defining polynomial
Character	$\chi$	$=$	11.8
Dual form			11.5.d.a.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02443 + 1.41001i) q^{2} +(2.68168 + 8.25338i) q^{3} +(4.00561 - 12.3280i) q^{4} +(-8.06057 - 5.85635i) q^{5} +(-8.89011 + 12.2362i) q^{6} +(-56.0338 - 18.2065i) q^{7} +(48.0070 - 15.5984i) q^{8} +(4.60358 - 3.34469i) q^{9} +O(q^{10})$	\(q+(1.02443 + 1.41001i) q^{2} +(2.68168 + 8.25338i) q^{3} +(4.00561 - 12.3280i) q^{4} +(-8.06057 - 5.85635i) q^{5} +(-8.89011 + 12.2362i) q^{6} +(-56.0338 - 18.2065i) q^{7} +(48.0070 - 15.5984i) q^{8} +(4.60358 - 3.34469i) q^{9} -17.3649i q^{10} +(-16.1117 + 119.923i) q^{11} +112.489 q^{12} +(75.0662 + 103.320i) q^{13} +(-31.7314 - 97.6593i) q^{14} +(26.7187 - 82.2318i) q^{15} +(-96.6156 - 70.1954i) q^{16} +(22.8472 - 31.4465i) q^{17} +(9.43207 + 3.06467i) q^{18} +(-560.182 + 182.014i) q^{19} +(-104.485 + 75.9125i) q^{20} -511.293i q^{21} +(-185.597 + 100.135i) q^{22} +973.600 q^{23} +(257.479 + 354.390i) q^{24} +(-162.460 - 499.999i) q^{25} +(-68.7814 + 211.687i) q^{26} +(608.630 + 442.196i) q^{27} +(-448.900 + 617.857i) q^{28} +(-141.677 - 46.0337i) q^{29} +(143.319 - 46.5671i) q^{30} +(140.685 - 102.214i) q^{31} -1015.78i q^{32} +(-1032.97 + 188.618i) q^{33} +67.7450 q^{34} +(345.041 + 474.909i) q^{35} +(-22.7933 - 70.1504i) q^{36} +(442.232 - 1361.05i) q^{37} +(-830.507 - 603.399i) q^{38} +(-651.433 + 896.620i) q^{39} +(-478.314 - 155.414i) q^{40} +(-561.211 + 182.349i) q^{41} +(720.925 - 523.783i) q^{42} +1171.41i q^{43} +(1413.87 + 678.988i) q^{44} -56.6952 q^{45} +(997.384 + 1372.78i) q^{46} +(-151.299 - 465.650i) q^{47} +(320.256 - 985.647i) q^{48} +(865.865 + 629.088i) q^{49} +(538.573 - 741.283i) q^{50} +(320.808 + 104.237i) q^{51} +(1574.41 - 511.557i) q^{52} +(-1804.69 + 1311.18i) q^{53} +1311.17i q^{54} +(832.178 - 872.289i) q^{55} -2974.01 q^{56} +(-3004.46 - 4135.29i) q^{57} +(-80.2304 - 246.924i) q^{58} +(-1488.77 + 4581.97i) q^{59} +(-906.729 - 658.778i) q^{60} +(2838.11 - 3906.32i) q^{61} +(288.243 + 93.6559i) q^{62} +(-318.851 + 103.601i) q^{63} +(-113.596 + 82.5323i) q^{64} -1272.43i q^{65} +(-1324.16 - 1263.27i) q^{66} +187.188 q^{67} +(-296.155 - 407.623i) q^{68} +(2610.89 + 8035.49i) q^{69} +(-316.153 + 973.020i) q^{70} +(-537.618 - 390.602i) q^{71} +(168.832 - 232.377i) q^{72} +(5025.08 + 1632.75i) q^{73} +(2372.13 - 770.750i) q^{74} +(3691.02 - 2681.68i) q^{75} +7635.00i q^{76} +(3086.17 - 6426.38i) q^{77} -1931.59 q^{78} +(-5015.11 - 6902.71i) q^{79} +(367.689 + 1131.63i) q^{80} +(-1875.02 + 5770.73i) q^{81} +(-832.034 - 604.508i) q^{82} +(-136.132 + 187.370i) q^{83} +(-6303.22 - 2048.04i) q^{84} +(-368.323 + 119.675i) q^{85} +(-1651.69 + 1200.02i) q^{86} -1292.76i q^{87} +(1097.13 + 6008.44i) q^{88} -6640.75 q^{89} +(-58.0802 - 79.9405i) q^{90} +(-2325.16 - 7156.09i) q^{91} +(3899.86 - 12002.5i) q^{92} +(1220.88 + 887.020i) q^{93} +(501.574 - 690.357i) q^{94} +(5581.33 + 1813.48i) q^{95} +(8383.61 - 2724.00i) q^{96} +(-5913.27 + 4296.24i) q^{97} +1865.33i q^{98} +(326.933 + 605.961i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 5 q^{2} - 6 q^{3} + 7 q^{4} - 18 q^{5} + 75 q^{6} - 80 q^{7} - 245 q^{8} + q^{9}+O(q^{10}) $ 12 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 - 18 * q^5 + 75 * q^6 - 80 * q^7 - 245 * q^8 + q^9	\( 12 q - 5 q^{2} - 6 q^{3} + 7 q^{4} - 18 q^{5} + 75 q^{6} - 80 q^{7} - 245 q^{8} + q^{9} - 43 q^{11} + 594 q^{12} + 250 q^{13} + 610 q^{14} + 1134 q^{15} - 633 q^{16} - 1250 q^{17} - 3150 q^{18} - 1025 q^{19} + 752 q^{20} - 35 q^{22} + 1684 q^{23} + 5345 q^{24} + 197 q^{25} + 3490 q^{26} - 687 q^{27} - 3580 q^{28} - 2690 q^{29} - 6740 q^{30} - 1136 q^{31} + 5939 q^{33} + 2370 q^{34} + 3610 q^{35} - 514 q^{36} - 336 q^{37} + 1900 q^{38} - 6880 q^{39} - 2340 q^{40} - 4550 q^{41} + 1310 q^{42} - 6268 q^{44} + 5136 q^{45} + 4150 q^{46} + 24 q^{47} + 344 q^{48} + 827 q^{49} + 8895 q^{50} + 13155 q^{51} + 14070 q^{52} + 414 q^{53} - 2738 q^{55} - 21340 q^{56} - 26925 q^{57} + 2980 q^{58} - 10011 q^{59} - 6856 q^{60} + 9460 q^{61} - 6200 q^{62} + 9150 q^{63} - 2633 q^{64} - 3210 q^{66} + 12154 q^{67} - 9400 q^{68} - 9022 q^{69} - 9380 q^{70} + 17574 q^{71} + 43045 q^{72} + 27950 q^{73} + 43270 q^{74} - 1761 q^{75} + 4090 q^{77} - 42920 q^{78} - 41540 q^{79} - 2308 q^{80} - 21080 q^{81} - 28175 q^{82} - 18665 q^{83} + 26250 q^{84} - 4230 q^{85} - 10125 q^{86} - 15125 q^{88} + 5554 q^{89} + 18400 q^{90} + 7390 q^{91} + 3904 q^{92} + 36898 q^{93} + 18920 q^{94} + 14110 q^{95} - 21140 q^{96} + 20769 q^{97} - 3269 q^{99}+O(q^{100}) \) 12 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 - 18 * q^5 + 75 * q^6 - 80 * q^7 - 245 * q^8 + q^9 - 43 * q^11 + 594 * q^12 + 250 * q^13 + 610 * q^14 + 1134 * q^15 - 633 * q^16 - 1250 * q^17 - 3150 * q^18 - 1025 * q^19 + 752 * q^20 - 35 * q^22 + 1684 * q^23 + 5345 * q^24 + 197 * q^25 + 3490 * q^26 - 687 * q^27 - 3580 * q^28 - 2690 * q^29 - 6740 * q^30 - 1136 * q^31 + 5939 * q^33 + 2370 * q^34 + 3610 * q^35 - 514 * q^36 - 336 * q^37 + 1900 * q^38 - 6880 * q^39 - 2340 * q^40 - 4550 * q^41 + 1310 * q^42 - 6268 * q^44 + 5136 * q^45 + 4150 * q^46 + 24 * q^47 + 344 * q^48 + 827 * q^49 + 8895 * q^50 + 13155 * q^51 + 14070 * q^52 + 414 * q^53 - 2738 * q^55 - 21340 * q^56 - 26925 * q^57 + 2980 * q^58 - 10011 * q^59 - 6856 * q^60 + 9460 * q^61 - 6200 * q^62 + 9150 * q^63 - 2633 * q^64 - 3210 * q^66 + 12154 * q^67 - 9400 * q^68 - 9022 * q^69 - 9380 * q^70 + 17574 * q^71 + 43045 * q^72 + 27950 * q^73 + 43270 * q^74 - 1761 * q^75 + 4090 * q^77 - 42920 * q^78 - 41540 * q^79 - 2308 * q^80 - 21080 * q^81 - 28175 * q^82 - 18665 * q^83 + 26250 * q^84 - 4230 * q^85 - 10125 * q^86 - 15125 * q^88 + 5554 * q^89 + 18400 * q^90 + 7390 * q^91 + 3904 * q^92 + 36898 * q^93 + 18920 * q^94 + 14110 * q^95 - 21140 * q^96 + 20769 * q^97 - 3269 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	1.02443	+	1.41001i	0.256107	+	0.352501i	0.917638	−	0.397416i	$-0.130093\pi$
$2$	1.02443	+	1.41001i	0.256107	+	0.352501i	−0.661531	+	0.749918i	$0.730093\pi$
$3$	2.68168	+	8.25338i	0.297965	+	0.917042i	0.982209	+	0.187789i	$0.0601322\pi$
$3$	2.68168	+	8.25338i	0.297965	+	0.917042i	−0.684244	+	0.729253i	$0.739868\pi$
$4$	4.00561	−	12.3280i	0.250351	−	0.770500i
$5$	−8.06057	−	5.85635i	−0.322423	−	0.234254i	0.414786	−	0.909919i	$-0.363857\pi$
$5$	−8.06057	−	5.85635i	−0.322423	−	0.234254i	−0.737209	+	0.675665i	$0.763857\pi$
$6$	−8.89011	+	12.2362i	−0.246948	+	0.339894i
$7$	−56.0338	−	18.2065i	−1.14355	−	0.371561i	−0.324839	−	0.945769i	$-0.605310\pi$
$7$	−56.0338	−	18.2065i	−1.14355	−	0.371561i	−0.818709	+	0.574208i	$0.805310\pi$
$8$	48.0070	−	15.5984i	0.750109	−	0.243725i
$9$	4.60358	−	3.34469i	0.0568343	−	0.0412925i
$10$		−	17.3649i		−	0.173649i
$11$	−16.1117	+	119.923i	−0.133155	+	0.991095i
$11$	−16.1117	+	119.923i	−0.133155	+	0.991095i
$12$	112.489			0.781177
$13$	75.0662	+	103.320i	0.444178	+	0.611359i	0.971134	−	0.238533i	$-0.0766667\pi$
$13$	75.0662	+	103.320i	0.444178	+	0.611359i	−0.526956	+	0.849893i	$0.676667\pi$
$14$	−31.7314	−	97.6593i	−0.161895	−	0.498262i
$15$	26.7187	−	82.2318i	0.118750	−	0.365475i
$16$	−96.6156	−	70.1954i	−0.377405	−	0.274201i
$17$	22.8472	−	31.4465i	0.0790560	−	0.108811i	−0.767658	−	0.640860i	$-0.778578\pi$
$17$	22.8472	−	31.4465i	0.0790560	−	0.108811i	0.846714	+	0.532049i	$0.178578\pi$
$18$	9.43207	+	3.06467i	0.0291113	+	0.00945885i
$19$	−560.182	+	182.014i	−1.55175	+	0.504194i	−0.954589	−	0.297927i	$-0.903705\pi$
$19$	−560.182	+	182.014i	−1.55175	+	0.504194i	−0.597162	+	0.802121i	$0.703705\pi$
$20$	−104.485	+	75.9125i	−0.261212	+	0.189781i
$21$		−	511.293i		−	1.15939i
$22$	−185.597	+	100.135i	−0.383464	+	0.206889i
$23$	973.600			1.84045			0.920227	−	0.391386i	$-0.128004\pi$
$23$	973.600			1.84045			0.920227	+	0.391386i	$0.128004\pi$
$24$	257.479	+	354.390i	0.447013	+	0.615260i
$25$	−162.460	−	499.999i	−0.259935	−	0.799999i
$26$	−68.7814	+	211.687i	−0.101748	+	0.313147i
$27$	608.630	+	442.196i	0.834884	+	0.606579i
$28$	−448.900	+	617.857i	−0.572576	+	0.788083i
$29$	−141.677	−	46.0337i	−0.168463	−	0.0547369i	0.223571	−	0.974688i	$-0.428228\pi$
$29$	−141.677	−	46.0337i	−0.168463	−	0.0547369i	−0.392034	+	0.919951i	$0.628228\pi$
$30$	143.319	−	46.5671i	0.159243	−	0.0517412i
$31$	140.685	−	102.214i	0.146394	−	0.106362i	−0.512177	−	0.858880i	$-0.671161\pi$
$31$	140.685	−	102.214i	0.146394	−	0.106362i	0.658572	+	0.752518i	$0.271161\pi$
$32$		−	1015.78i		−	0.991972i
$33$	−1032.97	+	188.618i	−0.948551	+	0.173203i
$34$	67.7450			0.0586029
$35$	345.041	+	474.909i	0.281666	+	0.387680i
$36$	−22.7933	−	70.1504i	−0.0175874	−	0.0541284i
$37$	442.232	−	1361.05i	0.323033	−	0.994194i	−0.649287	−	0.760543i	$-0.724933\pi$
$37$	442.232	−	1361.05i	0.323033	−	0.994194i	0.972321	−	0.233651i	$-0.0750672\pi$
$38$	−830.507	−	603.399i	−0.575144	−	0.417866i
$39$	−651.433	+	896.620i	−0.428292	+	0.589494i
$40$	−478.314	−	155.414i	−0.298946	−	0.0971334i
$41$	−561.211	+	182.349i	−0.333856	+	0.108476i	−0.471148	−	0.882054i	$-0.656160\pi$
$41$	−561.211	+	182.349i	−0.333856	+	0.108476i	0.137292	+	0.990531i	$0.456160\pi$
$42$	720.925	−	523.783i	0.408688	−	0.296929i
$43$			1171.41i			0.633535i	0.948503	+	0.316767i	$0.102597\pi$
$43$			1171.41i			0.633535i	−0.948503	+	0.316767i	$0.897403\pi$
$44$	1413.87	+	678.988i	0.730304	+	0.350717i
$45$	−56.6952			−0.0279976
$46$	997.384	+	1372.78i	0.471353	+	0.648762i
$47$	−151.299	−	465.650i	−0.0684920	−	0.210797i	0.910952	−	0.412512i	$-0.135348\pi$
$47$	−151.299	−	465.650i	−0.0684920	−	0.210797i	−0.979444	+	0.201715i	$0.935348\pi$
$48$	320.256	−	985.647i	0.139000	−	0.427798i
$49$	865.865	+	629.088i	0.360627	+	0.262011i
$50$	538.573	−	741.283i	0.215429	−	0.296513i
$51$	320.808	+	104.237i	0.123340	+	0.0400757i
$52$	1574.41	−	511.557i	0.582253	−	0.189185i
$53$	−1804.69	+	1311.18i	−0.642467	+	0.466780i	−0.860697	−	0.509118i	$-0.829972\pi$
$53$	−1804.69	+	1311.18i	−0.642467	+	0.466780i	0.218230	+	0.975897i	$0.429972\pi$
$54$			1311.17i			0.449647i
$55$	832.178	−	872.289i	0.275100	−	0.288360i
$56$	−2974.01			−0.948345
$57$	−3004.46	−	4135.29i	−0.924734	−	1.27279i
$58$	−80.2304	−	246.924i	−0.0238497	−	0.0734019i
$59$	−1488.77	+	4581.97i	−0.427685	+	1.31628i	0.472715	+	0.881215i	$0.343274\pi$
$59$	−1488.77	+	4581.97i	−0.427685	+	1.31628i	−0.900400	+	0.435063i	$0.856726\pi$
$60$	−906.729	−	658.778i	−0.251869	−	0.182994i
$61$	2838.11	−	3906.32i	0.762727	−	1.04980i	−0.234255	−	0.972175i	$-0.575265\pi$
$61$	2838.11	−	3906.32i	0.762727	−	1.04980i	0.996982	−	0.0776287i	$-0.0247349\pi$
$62$	288.243	+	93.6559i	0.0749852	+	0.0243642i
$63$	−318.851	+	103.601i	−0.0803354	+	0.0261026i
$64$	−113.596	+	82.5323i	−0.0277334	+	0.0201495i
$65$		−	1272.43i		−	0.301167i
$66$	−1324.16	−	1263.27i	−0.303985	−	0.290007i
$67$	187.188			0.0416992			0.0208496	−	0.999783i	$-0.493363\pi$
$67$	187.188			0.0416992			0.0208496	+	0.999783i	$0.493363\pi$
$68$	−296.155	−	407.623i	−0.0640474	−	0.0881537i
$69$	2610.89	+	8035.49i	0.548391	+	1.68777i
$70$	−316.153	+	973.020i	−0.0645211	+	0.198576i
$71$	−537.618	−	390.602i	−0.106649	−	0.0774850i	0.533183	−	0.846000i	$-0.320996\pi$
$71$	−537.618	−	390.602i	−0.106649	−	0.0774850i	−0.639832	+	0.768515i	$0.720996\pi$
$72$	168.832	−	232.377i	0.0325679	−	0.0448258i
$73$	5025.08	+	1632.75i	0.942969	+	0.306389i	0.739855	−	0.672766i	$-0.234894\pi$
$73$	5025.08	+	1632.75i	0.942969	+	0.306389i	0.203113	+	0.979155i	$0.434894\pi$
$74$	2372.13	−	770.750i	0.433186	−	0.140751i
$75$	3691.02	−	2681.68i	0.656181	−	0.476743i
$76$			7635.00i			1.32185i
$77$	3086.17	−	6426.38i	0.520521	−	1.08389i
$78$	−1931.59			−0.317486
$79$	−5015.11	−	6902.71i	−0.803575	−	1.10603i	−0.992283	−	0.123993i	$-0.960430\pi$
$79$	−5015.11	−	6902.71i	−0.803575	−	1.10603i	0.188708	−	0.982033i	$-0.439570\pi$
$80$	367.689	+	1131.63i	0.0574514	+	0.176817i
$81$	−1875.02	+	5770.73i	−0.285783	+	0.879550i
$82$	−832.034	−	604.508i	−0.123741	−	0.0899030i
$83$	−136.132	+	187.370i	−0.0197608	+	0.0271985i	−0.818783	−	0.574103i	$-0.805351\pi$
$83$	−136.132	+	187.370i	−0.0197608	+	0.0271985i	0.799022	+	0.601301i	$0.205351\pi$
$84$	−6303.22	−	2048.04i	−0.893313	−	0.290255i
$85$	−368.323	+	119.675i	−0.0509789	+	0.0165641i
$86$	−1651.69	+	1200.02i	−0.223322	+	0.162253i
$87$		−	1292.76i		−	0.170797i
$88$	1097.13	+	6008.44i	0.141674	+	0.775883i
$89$	−6640.75			−0.838372			−0.419186	−	0.907900i	$-0.637685\pi$
$89$	−6640.75			−0.838372			−0.419186	+	0.907900i	$0.637685\pi$
$90$	−58.0802	−	79.9405i	−0.00717039	−	0.00986919i
$91$	−2325.16	−	7156.09i	−0.280782	−	0.864158i
$92$	3899.86	−	12002.5i	0.460759	−	1.41807i
$93$	1220.88	+	887.020i	0.141158	+	0.102558i
$94$	501.574	−	690.357i	0.0567648	−	0.0781301i
$95$	5581.33	+	1813.48i	0.618429	+	0.200940i
$96$	8383.61	−	2724.00i	0.909680	−	0.295573i
$97$	−5913.27	+	4296.24i	−0.628470	+	0.456610i	−0.855870	−	0.517191i	$-0.826978\pi$
$97$	−5913.27	+	4296.24i	−0.628470	+	0.456610i	0.227400	+	0.973801i	$0.426978\pi$
$98$			1865.33i			0.194224i
$99$	326.933	+	605.961i	0.0333571	+	0.0618265i
$100$	−6814.74			−0.681474
$101$	9028.83	+	12427.1i	0.885092	+	1.21823i	0.974984	+	0.222274i	$0.0713478\pi$
$101$	9028.83	+	12427.1i	0.885092	+	1.21823i	−0.0898920	+	0.995952i	$0.528652\pi$
$102$	181.671	+	559.125i	0.0174616	+	0.0537413i
$103$	−282.605	+	869.770i	−0.0266383	+	0.0819841i	−0.963492	−	0.267738i	$-0.913724\pi$
$103$	−282.605	+	869.770i	−0.0266383	+	0.0819841i	0.936854	+	0.349722i	$0.113724\pi$
$104$	5215.32	+	3789.15i	0.482186	+	0.350329i
$105$	−2994.31	+	4121.31i	−0.271593	+	0.373815i
$106$	−3697.55	−	1201.41i	−0.329081	−	0.106925i
$107$	−7928.10	+	2576.00i	−0.692471	+	0.224998i	−0.634047	−	0.773294i	$-0.718608\pi$
$107$	−7928.10	+	2576.00i	−0.692471	+	0.224998i	−0.0584239	+	0.998292i	$0.518608\pi$
$108$	7889.33	−	5731.93i	0.676383	−	0.491421i
$109$		−	3099.23i		−	0.260856i	−0.991458	−	0.130428i	$-0.958365\pi$
$109$		−	3099.23i		−	0.260856i	0.991458	−	0.130428i	$-0.0416351\pi$
$110$	2082.44	+	279.778i	0.172102	+	0.0231221i
$111$	12419.2			1.00797
$112$	4135.73	+	5692.35i	0.329698	+	0.453791i
$113$	−1541.47	−	4744.16i	−0.120720	−	0.371538i	0.872377	−	0.488833i	$-0.162577\pi$
$113$	−1541.47	−	4744.16i	−0.120720	−	0.371538i	−0.993097	+	0.117296i	$0.962577\pi$
$114$	2752.92	−	8472.62i	0.211828	−	0.651940i
$115$	−7847.77	−	5701.74i	−0.593404	−	0.431134i
$116$	−1135.01	+	1562.20i	−0.0843496	+	0.116097i
$117$	691.145	+	224.567i	0.0504891	+	0.0164049i
$118$	−7985.74	+	2594.72i	−0.573523	+	0.186349i
$119$	−1852.75	+	1346.10i	−0.130834	+	0.0950567i
$120$		−	4364.47i		−	0.303088i
$121$	−14121.8	−	3864.31i	−0.964540	−	0.263938i
$122$	8415.37			0.565397
$123$	−3009.98	−	4142.89i	−0.198955	−	0.273837i
$124$	−696.560	−	2143.79i	−0.0453018	−	0.139424i
$125$	−3542.94	+	10904.1i	−0.226748	+	0.697860i
$126$	−472.718	−	343.450i	−0.0297757	−	0.0216333i
$127$	−6612.92	+	9101.91i	−0.410002	+	0.564319i	−0.963219	−	0.268718i	$-0.913400\pi$
$127$	−6612.92	+	9101.91i	−0.410002	+	0.564319i	0.553217	+	0.833037i	$0.313400\pi$
$128$	−15689.8	−	5097.91i	−0.957627	−	0.311152i
$129$	−9668.06	+	3141.34i	−0.580978	+	0.188771i
$130$	1794.13	−	1303.51i	0.106162	−	0.0771310i
$131$		−	27358.8i		−	1.59424i	−0.603818	−	0.797122i	$-0.706355\pi$
$131$		−	27358.8i		−	1.59424i	0.603818	−	0.797122i	$-0.293645\pi$
$132$	−1812.40	+	13490.0i	−0.104017	+	0.774221i
$133$	34703.0			1.96184
$134$	191.760	+	263.935i	0.0106795	+	0.0146990i
$135$	−2316.26	−	7128.71i	−0.127092	−	0.391150i
$136$	606.310	−	1866.03i	0.0327806	−	0.100888i
$137$	20807.3	+	15117.4i	1.10860	+	0.805445i	0.982443	−	0.186565i	$-0.0597355\pi$
$137$	20807.3	+	15117.4i	1.10860	+	0.805445i	0.126158	+	0.992010i	$0.459736\pi$
$138$	−8655.41	+	11913.2i	−0.454495	+	0.625559i
$139$	20596.8	+	6692.32i	1.06603	+	0.346375i	0.788942	−	0.614468i	$-0.210629\pi$
$139$	20596.8	+	6692.32i	1.06603	+	0.346375i	0.277092	+	0.960843i	$0.410629\pi$
$140$	7236.78	−	2351.37i	0.369223	−	0.119968i
$141$	3437.45	−	2497.45i	0.172901	−	0.125620i
$142$		−	1158.19i		−	0.0574384i
$143$	−13599.8	+	7337.47i	−0.665060	+	0.358818i
$144$	−679.559			−0.0327720
$145$	872.410	+	1200.77i	0.0414939	+	0.0571115i
$146$	2845.65	+	8758.02i	0.133498	+	0.410866i
$147$	−2870.12	+	8833.32i	−0.132821	+	0.408780i
$148$	−15007.6	−	10903.7i	−0.685155	−	0.497794i
$149$	21517.4	−	29616.2i	0.969211	−	1.33400i	0.0267658	−	0.999642i	$-0.491479\pi$
$149$	21517.4	−	29616.2i	0.969211	−	1.33400i	0.942445	−	0.334362i	$-0.108521\pi$
$150$	7562.37	+	2457.16i	0.336105	+	0.109207i
$151$	−8685.35	+	2822.04i	−0.380920	+	0.123768i	−0.493217	−	0.869906i	$-0.664179\pi$
$151$	−8685.35	+	2822.04i	−0.380920	+	0.123768i	0.112297	+	0.993675i	$0.464179\pi$
$152$	−24053.5	+	17475.9i	−1.04110	+	0.756401i
$153$		−	221.183i		−	0.00944863i
$154$	12222.8	−	2231.86i	0.515382	−	0.0941076i
$155$	−1732.60			−0.0721165
$156$	8444.15	+	11622.4i	0.346982	+	0.477580i
$157$	−2087.92	−	6425.96i	−0.0847061	−	0.260699i	0.899728	−	0.436450i	$-0.143764\pi$
$157$	−2087.92	−	6425.96i	−0.0847061	−	0.260699i	−0.984435	+	0.175752i	$0.943764\pi$
$158$	4595.23	−	14142.7i	0.184074	−	0.566522i
$159$	−15661.3	−	11378.6i	−0.619489	−	0.450085i
$160$	−5948.76	+	8187.76i	−0.232373	+	0.319834i
$161$	−54554.5	−	17725.8i	−2.10465	−	0.683841i
$162$	−10057.6	+	3267.91i	−0.383234	+	0.124520i
$163$	19475.3	−	14149.6i	0.733009	−	0.532562i	−0.157505	−	0.987518i	$-0.550345\pi$
$163$	19475.3	−	14149.6i	0.733009	−	0.532562i	0.890514	+	0.454956i	$0.150345\pi$
$164$			7649.03i			0.284393i
$165$	9430.97	+	4529.07i	0.346408	+	0.166357i
$166$	−403.651			−0.0146484
$167$	12349.4	+	16997.5i	0.442805	+	0.609469i	0.970833	−	0.239758i	$-0.0770683\pi$
$167$	12349.4	+	16997.5i	0.442805	+	0.609469i	−0.528028	+	0.849227i	$0.677068\pi$
$168$	−7975.35	−	24545.6i	−0.282573	−	0.869672i
$169$	3785.80	−	11651.5i	0.132551	−	0.407951i
$170$	−546.063	−	396.738i	−0.0188949	−	0.0137280i
$171$	−1970.06	+	2711.55i	−0.0673731	+	0.0927312i
$172$	14441.1	+	4692.20i	0.488139	+	0.158606i
$173$	6450.49	−	2095.89i	0.215526	−	0.0700288i	−0.199264	−	0.979946i	$-0.563855\pi$
$173$	6450.49	−	2095.89i	0.215526	−	0.0700288i	0.414790	+	0.909917i	$0.363855\pi$
$174$	1822.80	−	1324.34i	0.0602062	−	0.0437424i
$175$			30974.7i			1.01142i
$176$	9974.65	−	10455.4i	0.322012	−	0.337533i
$177$	−41809.1			−1.33452
$178$	−6802.97	−	9363.49i	−0.214713	−	0.295527i
$179$	11829.4	+	36407.2i	0.369196	+	1.13627i	0.947312	+	0.320313i	$0.103788\pi$
$179$	11829.4	+	36407.2i	0.369196	+	1.13627i	−0.578116	+	0.815955i	$0.696212\pi$
$180$	−227.099	+	698.938i	−0.00700922	+	0.0215722i
$181$	17836.1	+	12958.7i	0.544430	+	0.395551i	0.825727	−	0.564069i	$-0.190765\pi$
$181$	17836.1	+	12958.7i	0.544430	+	0.395551i	−0.281298	+	0.959620i	$0.590765\pi$
$182$	7708.17	−	10609.4i	0.232707	−	0.320293i
$183$	39851.2	+	12948.5i	1.18998	+	0.386648i
$184$	46739.6	−	15186.6i	1.38054	−	0.448565i
$185$	−11535.4	+	8380.99i	−0.337047	+	0.244879i
$186$			2630.14i			0.0760243i
$187$	3403.03	+	3246.55i	0.0973157	+	0.0928408i
$188$	−6346.58			−0.179566
$189$	−26053.1	−	35859.0i	−0.729349	−	1.00386i
$190$	3160.65	+	9727.48i	0.0875526	+	0.269459i
$191$	−1356.85	+	4175.95i	−0.0371933	+	0.114469i	−0.967929	−	0.251222i	$-0.919167\pi$
$191$	−1356.85	+	4175.95i	−0.0371933	+	0.114469i	0.930736	+	0.365691i	$0.119167\pi$
$192$	−985.799	−	716.225i	−0.0267415	−	0.0194288i
$193$	−11047.4	+	15205.4i	−0.296582	+	0.408210i	−0.931138	−	0.364666i	$-0.881183\pi$
$193$	−11047.4	+	15205.4i	−0.296582	+	0.408210i	0.634556	+	0.772877i	$0.281183\pi$
$194$	−12115.5	−	3936.55i	−0.321911	−	0.104595i
$195$	10501.8	−	3412.26i	0.276183	−	0.0897372i
$196$	11223.7	−	8154.51i	0.292162	−	0.212268i
$197$			13912.0i			0.358474i	0.983806	+	0.179237i	$0.0573629\pi$
$197$			13912.0i			0.358474i	−0.983806	+	0.179237i	$0.942637\pi$
$198$	−519.489	+	1081.74i	−0.0132509	+	0.0275926i
$199$	−42834.8			−1.08166			−0.540830	−	0.841132i	$-0.681890\pi$
$199$	−42834.8			−1.08166			−0.540830	+	0.841132i	$0.681890\pi$
$200$	−15598.4	−	21469.3i	−0.389960	−	0.536734i
$201$	501.978	+	1544.93i	0.0124249	+	0.0382399i
$202$	−8272.91	+	25461.4i	−0.202747	+	0.623992i
$203$	7100.61	+	5158.89i	0.172307	+	0.125188i
$204$	2570.07	−	3537.39i	0.0617567	−	0.0850008i
$205$	5591.58	+	1816.82i	0.133054	+	0.0432318i
$206$	−1515.89	+	492.542i	−0.0357218	+	0.0116067i
$207$	4482.04	−	3256.39i	0.104601	−	0.0759970i
$208$		−	15251.6i		−	0.352524i
$209$	−12802.1	−	70111.0i	−0.293082	−	1.60507i
$210$	−8878.53			−0.201327
$211$	−25464.9	−	35049.5i	−0.571975	−	0.787257i	0.420812	−	0.907148i	$-0.361745\pi$
$211$	−25464.9	−	35049.5i	−0.571975	−	0.787257i	−0.992787	+	0.119891i	$0.961745\pi$
$212$	8935.40	+	27500.3i	0.198812	+	0.611880i
$213$	1782.07	−	5484.63i	0.0392794	−	0.120889i
$214$	−11753.9	−	8539.74i	−0.256659	−	0.186474i
$215$	6860.16	−	9442.20i	0.148408	−	0.204266i
$216$	36116.1	+	11734.8i	0.774093	+	0.251518i
$217$	−9744.06	+	3166.04i	−0.206929	+	0.0672352i
$218$	4369.93	−	3174.94i	0.0919521	−	0.0668071i
$219$			45852.4i			0.956035i
$220$	−7420.20	−	13753.1i	−0.153310	−	0.284156i
$221$	4964.09			0.101638
$222$	12722.6	+	17511.1i	0.258148	+	0.355311i
$223$	945.780	+	2910.81i	0.0190187	+	0.0585335i	0.960115	−	0.279604i	$-0.0902031\pi$
$223$	945.780	+	2910.81i	0.0190187	+	0.0585335i	−0.941097	+	0.338137i	$0.890203\pi$
$224$	−18493.8	+	56918.0i	−0.368578	+	1.13437i
$225$	−2420.24	−	1758.41i	−0.0478072	−	0.0347340i
$226$	5110.17	−	7033.54i	0.100050	−	0.137707i
$227$	64.7787	+	21.0479i	0.00125713	+	0.000408467i	0.309645	−	0.950852i	$-0.399790\pi$
$227$	64.7787	+	21.0479i	0.00125713	+	0.000408467i	−0.308388	+	0.951261i	$0.599790\pi$
$228$	−63014.6	+	20474.7i	−1.21219	+	0.393865i
$229$	11009.2	−	7998.63i	0.209934	−	0.152526i	−0.477850	−	0.878442i	$-0.658584\pi$
$229$	11009.2	−	7998.63i	0.209934	−	0.152526i	0.687784	+	0.725915i	$0.258584\pi$
$230$		−	16906.4i		−	0.319592i
$231$	61315.5	+	8237.79i	1.14907	+	0.154379i
$232$	−7519.55			−0.139706
$233$	30700.4	+	42255.4i	0.565499	+	0.778343i	0.992013	−	0.126138i	$-0.0402584\pi$
$233$	30700.4	+	42255.4i	0.565499	+	0.778343i	−0.426514	+	0.904481i	$0.640258\pi$
$234$	391.389	+	1204.57i	0.00714787	+	0.0219989i
$235$	−1507.45	+	4639.46i	−0.0272966	+	0.0840102i
$236$	50523.1	+	36707.2i	0.907122	+	0.659063i
$237$	43521.7	−	59902.5i	0.774835	−	1.06647i
$238$	−3796.01	−	1233.40i	−0.0670153	−	0.0217746i
$239$	78576.7	−	25531.1i	1.37562	−	0.446965i	0.474392	−	0.880314i	$-0.342668\pi$
$239$	78576.7	−	25531.1i	1.37562	−	0.446965i	0.901226	+	0.433348i	$0.142668\pi$
$240$	−8353.74	+	6069.35i	−0.145030	+	0.105371i
$241$			24514.3i			0.422070i	0.977478	+	0.211035i	$0.0676835\pi$
$241$			24514.3i			0.422070i	−0.977478	+	0.211035i	$0.932317\pi$
$242$	−9018.11	−	23870.6i	−0.153987	−	0.407598i
$243$	8280.78			0.140236
$244$	−36788.8	−	50635.4i	−0.617925	−	0.850501i
$245$	−3295.21	−	10141.6i	−0.0548973	−	0.168957i
$246$	2757.98	−	8488.19i	0.0455744	−	0.140264i
$247$	−60856.3	−	44214.7i	−0.997498	−	0.724725i
$248$	5159.49	−	7101.42i	0.0838886	−	0.115463i
$249$	−1911.50	−	621.085i	−0.0308302	−	0.0100173i
$250$	−19004.3	+	6174.86i	−0.304068	+	0.0987978i
$251$	−86430.5	+	62795.5i	−1.37189	+	0.996737i	−0.374305	+	0.927306i	$0.622119\pi$
$251$	−86430.5	+	62795.5i	−1.37189	+	0.996737i	−0.997587	+	0.0694317i	$0.977881\pi$
$252$			4345.78i			0.0684332i
$253$	−15686.4	+	116757.i	−0.245065	+	1.82406i
$254$	−19608.2			−0.303928
$255$	−1975.45	−	2718.98i	−0.0303799	−	0.0418143i
$256$	−8190.72	−	25208.4i	−0.124980	−	0.384650i
$257$	27704.0	−	85264.0i	0.419446	−	1.29092i	−0.488768	−	0.872414i	$-0.662554\pi$
$257$	27704.0	−	85264.0i	0.419446	−	1.29092i	0.908214	−	0.418507i	$-0.137446\pi$
$258$	−14333.5	−	10413.9i	−0.215335	−	0.156450i
$259$	−49560.0	+	68213.4i	−0.738808	+	1.01688i
$260$	−15686.5	−	5096.86i	−0.232049	−	0.0753973i
$261$	−806.191	+	261.947i	−0.0118347	+	0.00384532i
$262$	38576.1	−	28027.2i	0.561973	−	0.408297i
$263$		−	109118.i		−	1.57756i	−0.614675	−	0.788781i	$-0.710713\pi$
$263$		−	109118.i		−	1.57756i	0.614675	−	0.788781i	$-0.289287\pi$
$264$	−46647.7	+	25167.7i	−0.669303	+	0.361107i
$265$	22225.6			0.316491
$266$	35550.7	+	48931.4i	0.502441	+	0.691551i
$267$	−17808.4	−	54808.6i	−0.249806	−	0.768822i
$268$	749.801	−	2307.65i	0.0104394	−	0.0321292i
$269$	7596.38	+	5519.09i	0.104979	+	0.0762716i	0.639036	−	0.769177i	$-0.279333\pi$
$269$	7596.38	+	5519.09i	0.104979	+	0.0762716i	−0.534057	+	0.845448i	$0.679333\pi$
$270$	7678.67	−	10568.8i	0.105332	−	0.144976i
$271$	−77397.0	−	25147.8i	−1.05387	−	0.342422i	−0.269682	−	0.962949i	$-0.586919\pi$
$271$	−77397.0	−	25147.8i	−1.05387	−	0.342422i	−0.784185	+	0.620527i	$0.786919\pi$
$272$	−4414.79	+	1434.45i	−0.0596722	+	0.0193887i
$273$	52826.6	−	38380.8i	0.708806	−	0.514978i
$274$			44825.1i			0.597063i
$275$	62578.7	−	11426.7i	0.827487	−	0.151097i
$276$	109520.			1.43772
$277$	28294.2	+	38943.7i	0.368755	+	0.507548i	0.952562	−	0.304344i	$-0.0984374\pi$
$277$	28294.2	+	38943.7i	0.368755	+	0.507548i	−0.583807	+	0.811893i	$0.698437\pi$
$278$	11663.8	+	35897.5i	0.150921	+	0.464488i
$279$	305.780	−	941.095i	0.00392827	−	0.0120900i
$280$	23972.2	+	17416.8i	0.305768	+	0.222153i
$281$	−51179.9	+	70443.1i	−0.648167	+	0.892126i	−0.999018	−	0.0443056i	$-0.985892\pi$
$281$	−51179.9	+	70443.1i	−0.648167	+	0.892126i	0.350851	+	0.936431i	$0.385892\pi$
$282$	7042.84	+	2288.36i	0.0885625	+	0.0287757i
$283$	8915.84	−	2896.93i	0.111324	−	0.0361714i	−0.252825	−	0.967512i	$-0.581360\pi$
$283$	8915.84	−	2896.93i	0.111324	−	0.0361714i	0.364149	+	0.931341i	$0.381360\pi$
$284$	−6968.83	+	5063.15i	−0.0864019	+	0.0627747i
$285$			50928.0i			0.626999i
$286$	−24277.9	−	11659.1i	−0.296810	−	0.142539i
$287$	34766.8			0.422085
$288$	−3397.47	−	4676.22i	−0.0409610	−	0.0563780i
$289$	25342.5	+	77996.3i	0.303427	+	0.933852i
$290$	−799.369	+	2460.21i	−0.00950499	+	0.0292533i
$291$	−51316.1	−	37283.3i	−0.605993	−	0.440279i
$292$	40257.0	−	55409.0i	0.472146	−	0.649853i
$293$	−74010.8	−	24047.6i	−0.862105	−	0.280115i	−0.155597	−	0.987821i	$-0.549730\pi$
$293$	−74010.8	−	24047.6i	−0.862105	−	0.280115i	−0.706507	+	0.707706i	$0.749730\pi$
$294$	−15395.3	+	5002.23i	−0.178112	+	0.0578720i
$295$	38833.9	−	28214.5i	0.446239	−	0.324212i
$296$		−	72238.1i		−	0.824485i
$297$	−62835.3	+	65864.0i	−0.712346	+	0.746681i
$298$	63802.1			0.718460
$299$	73084.4	+	100592.i	0.817490	+	1.12518i
$300$	−18275.0	−	56244.6i	−0.203055	−	0.624940i
$301$	21327.2	−	65638.4i	0.235397	−	0.724477i
$302$	−12876.6	−	9355.41i	−0.141185	−	0.102577i
$303$	−78353.2	+	107844.i	−0.853437	+	1.17466i
$304$	66898.9	+	21736.8i	0.723888	+	0.235206i
$305$	−45753.5	+	14866.2i	−0.491841	+	0.159809i
$306$	311.869	−	226.586i	0.00333065	−	0.00241986i
$307$		−	153965.i		−	1.63360i	−0.576921	−	0.816800i	$-0.695746\pi$
$307$		−	153965.i		−	1.63360i	0.576921	−	0.816800i	$-0.304254\pi$
$308$	−66862.5	−	63787.9i	−0.704824	−	0.672414i
$309$	−7936.40			−0.0831202
$310$	−1774.92	−	2442.97i	−0.0184695	−	0.0254212i
$311$	−25689.2	−	79063.2i	−0.265601	−	0.817436i	−0.991554	−	0.129692i	$-0.958601\pi$
$311$	−25689.2	−	79063.2i	−0.265601	−	0.817436i	0.725953	−	0.687744i	$-0.241399\pi$
$312$	−17287.5	+	53205.3i	−0.177591	+	0.546570i
$313$	82353.8	+	59833.6i	0.840611	+	0.610740i	0.922541	−	0.385898i	$-0.126108\pi$
$313$	82353.8	+	59833.6i	0.840611	+	0.610740i	−0.0819302	+	0.996638i	$0.526108\pi$
$314$	6921.71	−	9526.92i	0.0702027	−	0.0966258i
$315$	3176.85	+	1032.22i	0.0320166	+	0.0104028i
$316$	−105185.	+	34176.7i	−1.05337	+	0.342260i
$317$	−92619.0	+	67291.6i	−0.921683	+	0.669642i	−0.943942	−	0.330110i	$-0.892914\pi$
$317$	−92619.0	+	67291.6i	−0.921683	+	0.669642i	0.0222593	+	0.999752i	$0.492914\pi$
$318$		−	33739.1i		−	0.333641i
$319$	7803.14	−	16248.6i	0.0766811	−	0.159674i
$320$	1398.99			0.0136620
$321$	−42521.3	−	58525.6i	−0.412664	−	0.567984i
$322$	−30893.7	−	95081.1i	−0.297960	−	0.917027i
$323$	−7074.88	+	21774.2i	−0.0678132	+	0.208708i
$324$	63631.0	+	46230.6i	0.606148	+	0.440392i
$325$	39464.6	−	54318.3i	0.373629	−	0.514256i
$326$	39902.2	+	12965.0i	0.375458	+	0.121994i
$327$	25579.1	−	8311.16i	0.239216	−	0.0777259i
$328$	−24097.7	+	17508.0i	−0.223990	+	0.162738i
$329$			28846.8i			0.266505i
$330$	3275.33	+	17937.4i	0.0300765	+	0.164715i
$331$	3500.96			0.0319545			0.0159772	−	0.999872i	$-0.494914\pi$
$331$	3500.96			0.0319545			0.0159772	+	0.999872i	$0.494914\pi$
$332$	1764.61	+	2428.77i	0.0160093	+	0.0220349i
$333$	−2516.45	−	7744.84i	−0.0226934	−	0.0698431i
$334$	−11315.5	+	34825.4i	−0.101433	+	0.312179i
$335$	−1508.84	−	1096.24i	−0.0134448	−	0.00976820i
$336$	−35890.4	+	49398.8i	−0.317906	+	0.437561i
$337$	128354.	+	41704.6i	1.13018	+	0.367218i	0.813645	−	0.581362i	$-0.197480\pi$
$337$	128354.	+	41704.6i	1.13018	+	0.367218i	0.316536	+	0.948580i	$0.397480\pi$
$338$	20307.0	−	6598.13i	0.177751	−	0.0577547i
$339$	35021.6	−	25444.7i	0.304745	−	0.221410i
$340$			5020.06i			0.0434261i
$341$	9991.03	+	18518.1i	0.0859214	+	0.159253i
$342$	−5841.49			−0.0499426
$343$	46084.3	+	63429.7i	0.391710	+	0.539143i
$344$	18272.1	+	56235.7i	0.154408	+	0.475220i
$345$	26013.4	−	80060.9i	0.218554	−	0.672639i
$346$	9563.29	+	6948.13i	0.0798831	+	0.0580385i
$347$	54879.0	−	75534.5i	0.455772	−	0.627316i	−0.517853	−	0.855469i	$-0.673269\pi$
$347$	54879.0	−	75534.5i	0.455772	−	0.627316i	0.973625	+	0.228153i	$0.0732687\pi$
$348$	−15937.2	−	5178.31i	−0.131599	−	0.0427592i
$349$	−52327.1	+	17002.1i	−0.429612	+	0.139589i	−0.515838	−	0.856686i	$-0.672519\pi$
$349$	−52327.1	+	17002.1i	−0.429612	+	0.139589i	0.0862261	+	0.996276i	$0.472519\pi$
$350$	−43674.5	+	31731.4i	−0.356526	+	0.259032i
$351$			96077.5i			0.779843i
$352$	121815.	+	16365.9i	0.983139	+	0.132086i
$353$	−3735.78			−0.0299801			−0.0149900	−	0.999888i	$-0.504772\pi$
$353$	−3735.78			−0.0299801			−0.0149900	+	0.999888i	$0.504772\pi$
$354$	−42830.5	−	58951.1i	−0.341780	−	0.470419i
$355$	2046.00	+	6296.95i	0.0162349	+	0.0499659i
$356$	−26600.2	+	81867.1i	−0.209887	+	0.645966i
$357$	−16078.3	−	11681.6i	−0.126155	−	0.0916570i
$358$	−39215.9	+	53976.1i	−0.305982	+	0.421148i
$359$	−81956.4	−	26629.2i	−0.635907	−	0.206619i	−0.0267172	−	0.999643i	$-0.508505\pi$
$359$	−81956.4	−	26629.2i	−0.635907	−	0.206619i	−0.609190	+	0.793024i	$0.708505\pi$
$360$	−2721.76	+	884.355i	−0.0210013	+	0.00682372i
$361$	175243.	−	127321.i	1.34470	−	0.976982i
$362$			38424.2i			0.293216i
$363$	−5976.66	−	126916.i	−0.0453571	−	0.963168i
$364$	−97534.0			−0.736128
$365$	−30943.1	−	42589.5i	−0.232262	−	0.319681i
$366$	22567.4	+	69455.2i	0.168469	+	0.518493i
$367$	7826.17	−	24086.5i	0.0581055	−	0.178830i	−0.917791	−	0.397063i	$-0.870029\pi$
$367$	7826.17	−	24086.5i	0.0581055	−	0.178830i	0.975897	+	0.218233i	$0.0700293\pi$
$368$	−94065.0	−	68342.2i	−0.694596	−	0.504654i
$369$	−1973.68	+	2716.54i	−0.0144952	+	0.0199509i
$370$	−23634.5	−	7679.31i	−0.172640	−	0.0560943i
$371$	124996.	−	40613.6i	0.908129	−	0.295069i
$372$	15825.6	−	11497.9i	0.114360	−	0.0830872i
$373$			192208.i			1.38151i	0.723089	+	0.690755i	$0.242722\pi$
$373$			192208.i			1.38151i	−0.723089	+	0.690755i	$0.757278\pi$
$374$	−1091.49	+	8124.15i	−0.00780325	+	0.0580811i
$375$	−99496.4			−0.707530
$376$	−14526.8	−	19994.4i	−0.102753	−	0.141427i
$377$	−5878.97	−	18093.6i	−0.0413637	−	0.127304i
$378$	23871.8	−	73469.9i	0.167071	−	0.514193i
$379$	−106632.	−	77472.8i	−0.742352	−	0.539350i	0.151095	−	0.988519i	$-0.451720\pi$
$379$	−106632.	−	77472.8i	−0.742352	−	0.539350i	−0.893447	+	0.449169i	$0.851720\pi$
$380$	44713.2	−	61542.5i	0.309648	−	0.426195i
$381$	−92855.2	−	30170.5i	−0.639671	−	0.207842i
$382$	−7278.10	+	2364.80i	−0.0498760	+	0.0162057i
$383$	−142062.	+	103214.i	−0.968454	+	0.703623i	−0.955099	−	0.296288i	$-0.904251\pi$
$383$	−142062.	+	103214.i	−0.968454	+	0.703623i	−0.0133552	+	0.999911i	$0.504251\pi$
$384$		−	143164.i		−	0.970896i
$385$	−62511.4	+	33726.6i	−0.421733	+	0.227537i
$386$	−32757.0			−0.219852
$387$	3917.99	+	5392.66i	0.0261602	+	0.0360065i
$388$	29277.8	+	90108.0i	0.194480	+	0.598549i
$389$	7643.41	−	23524.0i	0.0505112	−	0.155458i	−0.922619	−	0.385712i	$-0.873956\pi$
$389$	7643.41	−	23524.0i	0.0505112	−	0.155458i	0.973130	+	0.230254i	$0.0739558\pi$
$390$	15569.7	+	11312.0i	0.102365	+	0.0743724i
$391$	22244.0	−	30616.3i	0.145499	−	0.200262i
$392$	51380.3	+	16694.5i	0.334368	+	0.108643i
$393$	225803.	−	73367.7i	1.46199	−	0.475029i
$394$	−19616.0	+	14251.9i	−0.126363	+	0.0918078i
$395$			85010.0i			0.544849i
$396$	8779.86	−	1603.18i	0.0559883	−	0.0102233i
$397$	−191822.			−1.21708			−0.608539	−	0.793524i	$-0.708244\pi$
$397$	−191822.			−1.21708			−0.608539	+	0.793524i	$0.708244\pi$
$398$	−43881.2	−	60397.3i	−0.277021	−	0.381286i
$399$	93062.5	+	286417.i	0.584559	+	1.79909i
$400$	−19401.5	+	59711.7i	−0.121259	+	0.373198i
$401$	91171.9	+	66240.3i	0.566986	+	0.411939i	0.834009	−	0.551751i	$-0.186040\pi$
$401$	91171.9	+	66240.3i	0.566986	+	0.411939i	−0.267023	+	0.963690i	$0.586040\pi$
$402$	−1664.12	+	2290.46i	−0.0102975	+	0.0141733i
$403$	21121.3	+	6862.74i	0.130050	+	0.0422559i
$404$	189367.	−	61529.2i	1.16023	−	0.376980i
$405$	48909.2	−	35534.6i	0.298181	−	0.216641i
$406$			15296.8i			0.0928002i
$407$	156096.	+	74962.5i	0.942328	+	0.452538i
$408$	17027.0			0.102286
$409$	−159737.	−	219859.i	−0.954902	−	1.31431i	−0.949315	−	0.314325i	$-0.898222\pi$
$409$	−159737.	−	219859.i	−0.954902	−	1.31431i	−0.00558643	−	0.999984i	$-0.501778\pi$
$410$	3166.46	+	9745.36i	0.0188368	+	0.0579736i
$411$	−68970.9	+	212271.i	−0.408303	+	1.25663i
$412$	9590.52	+	6967.92i	0.0564999	+	0.0410496i
$413$	166843.	−	229640.i	0.978156	−	1.34632i
$414$	9183.06	+	2983.76i	0.0535781	+	0.0174086i
$415$	2194.61	−	713.072i	0.0127427	−	0.00414035i
$416$	104950.	−	76250.6i	0.606451	−	0.440613i
$417$			187940.i			1.08081i
$418$	85742.0	−	89874.8i	0.490728	−	0.514381i
$419$	36389.5			0.207275			0.103638	−	0.994615i	$-0.466952\pi$
$419$	36389.5			0.207275			0.103638	+	0.994615i	$0.466952\pi$
$420$	38813.5	+	53422.2i	0.220031	+	0.302847i
$421$	−44837.8	−	137997.i	−0.252976	−	0.778581i	−0.994222	−	0.107347i	$-0.965764\pi$
$421$	−44837.8	−	137997.i	−0.252976	−	0.778581i	0.741245	−	0.671234i	$-0.234236\pi$
$422$	23332.9	−	71811.3i	0.131022	−	0.403244i
$423$	−2253.97	−	1637.61i	−0.0125970	−	0.00915227i
$424$	−66185.3	+	91096.3i	−0.368155	+	0.506721i
$425$	−19435.0	−	6314.80i	−0.107598	−	0.0349608i
$426$	9558.96	−	3105.89i	0.0526734	−	0.0171146i
$427$	−230150.	+	167214.i	−1.26228	+	0.917101i
$428$			108056.i			0.589877i
$429$	−97029.3	−	92567.5i	−0.527216	−	0.502972i
$430$	20341.3			0.110012
$431$	487.457	+	670.927i	0.00262411	+	0.00361178i	0.810327	−	0.585978i	$-0.199289\pi$
$431$	487.457	+	670.927i	0.00262411	+	0.00361178i	−0.807703	+	0.589590i	$0.799289\pi$
$432$	−27763.1	−	85446.1i	−0.148765	−	0.457851i
$433$	−45127.5	+	138888.i	−0.240694	+	0.740781i	0.755621	+	0.655009i	$0.227335\pi$
$433$	−45127.5	+	138888.i	−0.240694	+	0.740781i	−0.996315	+	0.0857711i	$0.972665\pi$
$434$	−14446.2	−	10495.8i	−0.0766964	−	0.0557232i
$435$	−7570.87	+	10420.4i	−0.0400099	+	0.0550689i
$436$	−38207.3	−	12414.3i	−0.200990	−	0.0653055i
$437$	−545393.	+	177209.i	−2.85592	+	0.927946i
$438$	−64652.1	+	46972.5i	−0.337004	+	0.244847i
$439$		−	325054.i		−	1.68666i	−0.537398	−	0.843329i	$-0.680593\pi$
$439$		−	325054.i		−	1.68666i	0.537398	−	0.843329i	$-0.319407\pi$
$440$	26344.0	−	54856.6i	0.136075	−	0.283350i
$441$	6090.18			0.0313150
$442$	5085.36	+	6999.39i	0.0260302	+	0.0358274i
$443$	−3613.23	−	11120.4i	−0.0184115	−	0.0566647i	0.941429	−	0.337212i	$-0.109484\pi$
$443$	−3613.23	−	11120.4i	−0.0184115	−	0.0566647i	−0.959840	+	0.280548i	$0.909484\pi$
$444$	49746.5	−	153104.i	0.252346	−	0.776641i
$445$	53528.2	+	38890.5i	0.270310	+	0.196392i
$446$	−3135.38	+	4315.48i	−0.0157623	+	0.0216950i
$447$	302137.	+	98170.2i	1.51213	+	0.491320i
$448$	7867.84	−	2556.42i	0.0392012	−	0.0127372i
$449$	284422.	−	206645.i	1.41082	−	1.02502i	0.417615	−	0.908624i	$-0.362866\pi$
$449$	284422.	−	206645.i	1.41082	−	1.02502i	0.993203	−	0.116395i	$-0.0371340\pi$
$450$		−	5213.91i		−	0.0257477i
$451$	−12825.6	−	70239.8i	−0.0630559	−	0.345327i
$452$	−64660.6			−0.316492
$453$	−46582.8	−	64115.7i	−0.227002	−	0.312441i
$454$	36.6836	+	112.900i	0.000177975	+	0.000547752i
$455$	−23166.5	+	71299.1i	−0.111902	+	0.344399i
$456$	−208739.	−	151658.i	−1.00386	−	0.729349i
$457$	90965.8	−	125204.i	0.435558	−	0.599494i	−0.533660	−	0.845699i	$-0.679184\pi$
$457$	90965.8	−	125204.i	0.435558	−	0.599494i	0.969218	+	0.246205i	$0.0791837\pi$
$458$	22556.2	+	7328.96i	0.107531	+	0.0349391i
$459$	27811.0	−	9036.34i	0.132005	−	0.0428911i
$460$	−101726.	+	73908.4i	−0.480748	+	0.349284i
$461$			116794.i			0.549564i	0.961507	+	0.274782i	$0.0886057\pi$
$461$			116794.i			0.549564i	−0.961507	+	0.274782i	$0.911394\pi$
$462$	51198.0	+	94894.2i	0.239866	+	0.444586i
$463$	39611.3			0.184781			0.0923904	−	0.995723i	$-0.470549\pi$
$463$	39611.3			0.184781			0.0923904	+	0.995723i	$0.470549\pi$
$464$	10456.9	+	14392.7i	0.0485698	+	0.0668506i
$465$	−4646.28	−	14299.8i	−0.0214882	−	0.0661338i
$466$	−28130.1	+	86575.4i	−0.129538	+	0.398678i
$467$	77040.8	+	55973.4i	0.353254	+	0.256654i	0.750233	−	0.661174i	$-0.229941\pi$
$467$	77040.8	+	55973.4i	0.353254	+	0.256654i	−0.396979	+	0.917828i	$0.629941\pi$
$468$	5536.92	−	7620.92i	0.0252800	−	0.0347949i
$469$	−10488.8	−	3408.03i	−0.0476850	−	0.0154938i
$470$	−8085.95	+	2627.28i	−0.0366046	+	0.0118935i
$471$	47436.7	−	34464.8i	0.213832	−	0.155358i
$472$			243189.i			1.09159i
$473$	−140478.	−	18873.3i	−0.627893	−	0.0843581i
$474$	129048.			0.574372
$475$	182014.	+	250521.i	0.806710	+	1.11034i
$476$	9173.33	+	28232.6i	0.0404868	+	0.124605i
$477$	−3922.52	+	12072.3i	−0.0172396	+	0.0530582i
$478$	116495.	+	84638.7i	0.509862	+	0.370436i
$479$	−206359.	+	284028.i	−0.899398	+	1.23791i	0.0712622	+	0.997458i	$0.477297\pi$
$479$	−206359.	+	284028.i	−0.899398	+	1.23791i	−0.970660	+	0.240457i	$0.922703\pi$
$480$	−83529.4	−	27140.3i	−0.362541	−	0.117797i
$481$	173820.	−	56477.6i	0.751294	−	0.244110i
$482$	−34565.2	+	25113.1i	−0.148780	+	0.108095i
$483$		−	497794.i		−	2.13381i
$484$	−104206.	+	158615.i	−0.444837	+	0.677101i
$485$	72824.7			0.309596
$486$	8483.07	+	11675.9i	0.0359154	+	0.0494333i
$487$	−50720.6	−	156102.i	−0.213858	−	0.658189i	−0.999233	−	0.0391673i	$-0.987529\pi$
$487$	−50720.6	−	156102.i	−0.213858	−	0.658189i	0.785374	−	0.619021i	$-0.212471\pi$
$488$	75316.6	−	231801.i	0.316265	−	0.973363i
$489$	169009.	+	122792.i	0.706793	+	0.513515i
$490$	10924.0	−	15035.6i	0.0454978	−	0.0626224i
$491$	172324.	+	55991.5i	0.714797	+	0.232252i	0.643766	−	0.765222i	$-0.277371\pi$
$491$	172324.	+	55991.5i	0.714797	+	0.232252i	0.0710312	+	0.997474i	$0.477371\pi$
$492$	−63130.4	+	20512.3i	−0.260800	+	0.0847391i
$493$	−4684.52	+	3403.51i	−0.0192740	+	0.0140034i
$494$		−	131103.i		−	0.537227i
$495$	913.455	−	6799.03i	0.00372801	−	0.0277483i
$496$	−20767.3			−0.0844143
$497$	23013.3	+	31675.1i	0.0931678	+	0.128234i
$498$	−1082.47	−	3331.48i	−0.00436471	−	0.0134332i
$499$	35889.1	−	110455.i	0.144132	−	0.443594i	−0.852766	−	0.522293i	$-0.825077\pi$
$499$	35889.1	−	110455.i	0.144132	−	0.443594i	0.996898	+	0.0786994i	$0.0250767\pi$
$500$	120234.	+	87354.8i	0.480934	+	0.349419i
$501$	−107169.	+	147506.i	−0.426968	+	0.587671i
$502$	−177084.	−	57538.0i	−0.702703	−	0.228322i
$503$	61308.6	−	19920.4i	0.242318	−	0.0787339i	−0.185340	−	0.982674i	$-0.559339\pi$
$503$	61308.6	−	19920.4i	0.242318	−	0.0787339i	0.427658	+	0.903941i	$0.359339\pi$
$504$	−13691.1	+	9947.15i	−0.0538985	+	0.0391595i
$505$		−	153046.i		−	0.600120i
$506$	−180697.	+	97491.0i	−0.705748	+	0.380771i
$507$	106317.			0.413604
$508$	85719.5	+	117983.i	0.332164	+	0.457184i
$509$	−44701.3	−	137576.i	−0.172538	−	0.531017i	0.826975	−	0.562239i	$-0.190060\pi$
$509$	−44701.3	−	137576.i	−0.172538	−	0.531017i	−0.999512	+	0.0312225i	$0.990060\pi$
$510$	1810.06	−	5570.79i	0.00695910	−	0.0214179i
$511$	−251848.	−	182978.i	−0.964487	−	0.700741i
$512$	−127996.	+	176171.i	−0.488265	+	0.672038i
$513$	−421430.	−	136931.i	−1.60137	−	0.520315i
$514$	148603.	−	48284.2i	0.562474	−	0.182759i
$515$	7371.64	−	5355.81i	0.0277939	−	0.0201934i
$516$			131771.i			0.494903i
$517$	58279.6	−	10641.7i	0.218040	−	0.0398135i
$518$	−146952.			−0.547666
$519$	34596.4	+	47617.8i	0.128439	+	0.176781i
$520$	−19847.9	−	61085.5i	−0.0734019	−	0.225908i
$521$	33121.1	−	101936.i	0.122020	−	0.375538i	−0.871327	−	0.490703i	$-0.836740\pi$
$521$	33121.1	−	101936.i	0.122020	−	0.375538i	0.993346	+	0.115166i	$0.0367399\pi$
$522$	−1195.23	−	868.387i	−0.00438643	−	0.00318693i
$523$	−118355.	+	162901.i	−0.432695	+	0.595554i	−0.968569	−	0.248744i	$-0.919982\pi$
$523$	−118355.	+	162901.i	−0.432695	+	0.595554i	0.535874	+	0.844298i	$0.319982\pi$
$524$	−337280.	−	109589.i	−1.22837	−	0.399120i
$525$	−255646.	+	83064.4i	−0.927513	+	0.301367i
$526$	153857.	−	111784.i	0.556093	−	0.404025i
$527$		−	6759.33i		−	0.0243379i
$528$	113041.	+	54286.4i	0.405480	+	0.194726i
$529$	668056.			2.38727
$530$	22768.5	+	31338.2i	0.0810557	+	0.111564i
$531$	8471.60	+	26072.9i	0.0300453	+	0.0924699i
$532$	139007.	−	427818.i	0.491148	−	1.51160i
$533$	−60968.2	−	44296.0i	−0.214609	−	0.155923i
$534$	59037.0	−	81257.4i	0.207034	−	0.284958i
$535$	78991.0	+	25665.7i	0.275975	+	0.0896698i
$536$	8986.31	−	2919.83i	0.0312789	−	0.0101631i
$537$	−268759.	+	195265.i	−0.931998	+	0.677136i
$538$			16364.8i			0.0565389i
$539$	−89392.3	+	93701.0i	−0.307697	+	0.322528i
$540$	−97160.7			−0.333199
$541$	90406.1	+	124433.i	0.308890	+	0.425150i	0.935035	−	0.354557i	$-0.115368\pi$
$541$	90406.1	+	124433.i	0.308890	+	0.425150i	−0.626145	+	0.779707i	$0.715368\pi$
$542$	−43829.2	−	134892.i	−0.149199	−	0.459186i
$543$	−59122.0	+	181959.i	−0.200516	+	0.617125i
$544$	−31942.7	−	23207.7i	−0.107938	−	0.0784213i
$545$	−18150.2	+	24981.6i	−0.0611065	+	0.0841059i
$546$	108234.	+	35167.4i	0.363061	+	0.117966i
$547$	−150147.	+	48785.9i	−0.501815	+	0.163049i	−0.548976	−	0.835838i	$-0.684982\pi$
$547$	−150147.	+	48785.9i	−0.501815	+	0.163049i	0.0471619	+	0.998887i	$0.484982\pi$
$548$	269713.	−	195958.i	0.898134	−	0.652533i
$549$		−	27475.6i		−	0.0911598i
$550$	80219.1	+	76530.4i	0.265187	+	0.252993i
$551$	87743.8			0.289010
$552$	250682.	+	345034.i	0.822706	+	1.13236i
$553$	155342.	+	478093.i	0.507970	+	1.56337i
$554$	−25925.4	+	79790.0i	−0.0844705	+	0.259974i
$555$	−100106.	−	72731.2i	−0.324993	−	0.236121i
$556$	165006.	−	227111.i	0.533765	−	0.734664i
$557$	553427.	+	179819.i	1.78382	+	0.579597i	0.999185	−	0.0403674i	$-0.0128528\pi$
$557$	553427.	+	179819.i	1.78382	+	0.579597i	0.784630	+	0.619964i	$0.212853\pi$
$558$	1640.20	−	532.933i	0.00526779	−	0.00171161i
$559$	−121029.	+	87932.9i	−0.387317	+	0.281403i
$560$		−	70103.9i		−	0.223546i
$561$	−17669.1	+	36792.7i	−0.0561422	+	0.116906i
$562$	−151755.			−0.480476
$563$	−228448.	−	314432.i	−0.720728	−	0.991997i	−0.999499	−	0.0316397i	$-0.989927\pi$
$563$	−228448.	−	314432.i	−0.720728	−	0.991997i	0.278771	−	0.960358i	$-0.410073\pi$
$564$	−17019.5	−	52380.7i	−0.0535043	−	0.164669i
$565$	−15358.3	+	47268.1i	−0.0481113	+	0.148071i
$566$	13218.3	+	9603.68i	0.0412614	+	0.0299781i
$567$	210130.	−	289218.i	0.653613	−	0.899622i
$568$	−31902.2	−	10365.6i	−0.0988835	−	0.0321292i
$569$	−194357.	+	63150.3i	−0.600309	+	0.195052i	−0.593378	−	0.804924i	$-0.702206\pi$
$569$	−194357.	+	63150.3i	−0.600309	+	0.195052i	−0.00693101	+	0.999976i	$0.502206\pi$
$570$	−71808.7	+	52172.1i	−0.221018	+	0.160579i
$571$		−	68721.2i		−	0.210775i	−0.994431	−	0.105387i	$-0.966392\pi$
$571$		−	68721.2i		−	0.210775i	0.994431	−	0.105387i	$-0.0336083\pi$
$572$	35980.8	+	197049.i	0.109971	+	0.602259i
$573$	−38104.3			−0.116055
$574$	35616.1	+	49021.3i	0.108099	+	0.148786i
$575$	−158171.	−	486799.i	−0.478399	−	1.47236i
$576$	−246.902	+	759.887i	−0.000744184	+	0.00229036i
$577$	194489.	+	141305.i	0.584177	+	0.424429i	0.840227	−	0.542234i	$-0.182421\pi$
$577$	194489.	+	141305.i	0.584177	+	0.424429i	−0.256051	+	0.966663i	$0.582421\pi$
$578$	−84013.5	+	115635.i	−0.251474	+	0.346125i
$579$	−155122.	−	50402.1i	−0.462717	−	0.150346i
$580$	18297.6	−	5945.26i	0.0543925	−	0.0176732i
$581$	11039.4	−	8020.58i	0.0327034	−	0.0237604i
$582$		−	110550.i		−	0.326372i
$583$	−128164.	−	237548.i	−0.377076	−	0.698900i
$584$	266707.			0.782004
$585$	−4255.89	−	5857.73i	−0.0124359	−	0.0171166i
$586$	−41911.6	−	128991.i	−0.122050	−	0.375633i
$587$	−143863.	+	442766.i	−0.417517	+	1.28499i	0.492463	+	0.870334i	$0.336097\pi$
$587$	−143863.	+	442766.i	−0.417517	+	1.28499i	−0.909980	+	0.414652i	$0.863903\pi$
$588$	97400.7	+	70765.7i	0.281713	+	0.204677i
$589$	−60204.8	+	82864.8i	−0.173540	+	0.238858i
$590$	79565.2	+	25852.3i	0.228570	+	0.0742669i
$591$	−114821.	+	37307.6i	−0.328736	+	0.106813i
$592$	−138266.	+	100456.i	−0.394523	+	0.286638i
$593$			54204.4i			0.154143i	0.997026	+	0.0770717i	$0.0245570\pi$
$593$			54204.4i			0.154143i	−0.997026	+	0.0770717i	$0.975443\pi$
$594$	−157239.	−	21125.2i	−0.445643	−	0.0598725i
$595$	22817.4			0.0644514
$596$	−278918.	−	383898.i	−0.785208	−	1.08075i
$597$	−114869.	−	353532.i	−0.322297	−	0.991927i
$598$	−66965.6	+	206099.i	−0.187262	+	0.576332i
$599$	−344600.	−	250367.i	−0.960421	−	0.697787i	−0.00717284	−	0.999974i	$-0.502283\pi$
$599$	−344600.	−	250367.i	−0.960421	−	0.697787i	−0.953249	+	0.302187i	$0.902283\pi$
$600$	135365.	−	186313.i	0.376013	−	0.517537i
$601$	−178462.	−	57985.7i	−0.494078	−	0.160536i	0.0513708	−	0.998680i	$-0.483641\pi$
$601$	−178462.	−	57985.7i	−0.494078	−	0.160536i	−0.545449	+	0.838144i	$0.683641\pi$
$602$	114399.	−	37170.4i	0.315666	−	0.102566i
$603$	861.732	−	626.085i	0.00236994	−	0.00172186i
$604$			118377.i			0.324484i
$605$	91199.3	+	113851.i	0.249161	+	0.311047i
$606$	−232328.			−0.632639
$607$	−197925.	−	272420.i	−0.537183	−	0.739369i	0.451021	−	0.892513i	$-0.351060\pi$
$607$	−197925.	−	272420.i	−0.537183	−	0.739369i	−0.988204	+	0.153144i	$0.951060\pi$
$608$	184886.	+	569021.i	0.500147	+	1.53929i
$609$	−23536.7	+	72438.5i	−0.0634616	+	0.195315i
$610$	−67832.7	−	49283.4i	−0.182297	−	0.132447i
$611$	36753.4	−	50586.7i	0.0984498	−	0.135505i
$612$	−2726.74	−	885.973i	−0.00728017	−	0.00236547i
$613$	253103.	−	82238.3i	0.673561	−	0.218853i	0.0477869	−	0.998858i	$-0.484783\pi$
$613$	253103.	−	82238.3i	0.673561	−	0.218853i	0.625774	+	0.780004i	$0.284783\pi$
$614$	217092.	−	157726.i	0.575846	−	0.418377i
$615$			51021.6i			0.134897i
$616$	47916.3	−	356651.i	0.126276	−	0.939900i
$617$	−266633.			−0.700396			−0.350198	−	0.936676i	$-0.613886\pi$
$617$	−266633.			−0.700396			−0.350198	+	0.936676i	$0.613886\pi$
$618$	−8130.27	−	11190.4i	−0.0212877	−	0.0293000i
$619$	190706.	+	586932.i	0.497717	+	1.53182i	0.812679	+	0.582711i	$0.198008\pi$
$619$	190706.	+	586932.i	0.497717	+	1.53182i	−0.314962	+	0.949104i	$0.601992\pi$
$620$	−6940.12	+	21359.5i	−0.0180544	+	0.0555658i
$621$	592563.	+	430522.i	1.53657	+	1.11638i
$622$	85162.8	−	117217.i	0.220125	−	0.302976i
$623$	372106.	+	120905.i	0.958719	+	0.311507i
$624$	125877.	−	40900.0i	0.323279	−	0.105040i
$625$	−173412.	+	125991.i	−0.443934	+	0.322537i
$626$			177415.i			0.452731i
$627$	544321.	−	293676.i	1.38459	−	0.747022i
$628$	−87582.6			−0.222075
$629$	−32696.5	−	45002.8i	−0.0826418	−	0.113747i
$630$	1799.02	+	5536.81i	0.00453267	+	0.0139501i
$631$	24299.7	−	74786.9i	0.0610299	−	0.187831i	−0.915893	−	0.401422i	$-0.868516\pi$
$631$	24299.7	−	74786.9i	0.0610299	−	0.187831i	0.976923	+	0.213591i	$0.0685161\pi$
$632$	−348432.	−	253150.i	−0.872335	−	0.633789i
$633$	220987.	−	304163.i	0.551519	−	0.759100i
$634$	−189763.	−	61657.8i	−0.472099	−	0.153394i
$635$	106608.	−	34639.0i	0.264388	−	0.0859049i
$636$	−203009.	+	147494.i	−0.501880	+	0.364637i
$637$			136684.i			0.336852i
$638$	30904.4	−	5643.07i	0.0759240	−	0.0138635i
$639$	−3781.41			−0.00926087
$640$	96613.3	+	132977.i	0.235872	+	0.324650i
$641$	169464.	+	521557.i	0.412441	+	1.26936i	0.914520	+	0.404541i	$0.132569\pi$
$641$	169464.	+	521557.i	0.412441	+	1.26936i	−0.502079	+	0.864822i	$0.667431\pi$
$642$	38961.3	−	119911.i	0.0945287	−	0.290929i
$643$	103495.	+	75193.8i	0.250322	+	0.181870i	0.705870	−	0.708342i	$-0.250556\pi$
$643$	103495.	+	75193.8i	0.250322	+	0.181870i	−0.455548	+	0.890211i	$0.650556\pi$
$644$	−437049.	+	601546.i	−1.05380	+	1.45043i
$645$	96326.9	+	31298.5i	0.231541	+	0.0752323i
$646$	−37949.5	+	12330.5i	−0.0909371	+	0.0295473i
$647$	575751.	−	418308.i	1.37539	−	0.999281i	0.378098	−	0.925766i	$-0.376578\pi$
$647$	575751.	−	418308.i	1.37539	−	0.999281i	0.997294	−	0.0735150i	$-0.0234217\pi$
$648$			306283.i			0.729411i
$649$	−525494.	−	252360.i	−1.24761	−	0.599145i
$650$	117018.			0.276965
$651$	−52261.0	−	71931.1i	−0.123315	−	0.169728i
$652$	−96426.4	−	296770.i	−0.226830	−	0.698111i
$653$	74638.0	−	229712.i	0.175039	−	0.538713i	−0.824597	−	0.565721i	$-0.808598\pi$
$653$	74638.0	−	229712.i	0.175039	−	0.538713i	0.999635	+	0.0270077i	$0.00859788\pi$
$654$	37922.8	+	27552.5i	0.0886634	+	0.0644177i
$655$	−160223.	+	220528.i	−0.373458	+	0.514021i
$656$	67021.8	+	21776.7i	0.155743	+	0.0506040i
$657$	28594.4	−	9290.88i	0.0662445	−	0.0215241i
$658$	−40674.1	+	29551.5i	−0.0939434	+	0.0682539i
$659$			165208.i			0.380418i	0.981744	+	0.190209i	$0.0609165\pi$
$659$			165208.i			0.380418i	−0.981744	+	0.190209i	$0.939084\pi$
$660$	93611.2	−	98123.3i	0.214902	−	0.225260i
$661$	−782672.			−1.79133			−0.895667	−	0.444725i	$-0.853302\pi$
$661$	−782672.			−1.79133			−0.895667	+	0.444725i	$0.853302\pi$
$662$	3586.49	+	4936.38i	0.00818377	+	0.0112640i
$663$	13312.1	+	40970.5i	0.0302845	+	0.0932061i
$664$	−3612.63	+	11118.5i	−0.00819384	+	0.0252180i
$665$	−279726.	−	203233.i	−0.632542	−	0.459569i
$666$	8342.34	−	11482.2i	0.0188079	−	0.0258868i
$667$	−137937.	−	44818.4i	−0.310048	−	0.100741i
$668$	259012.	−	84158.0i	0.580452	−	0.188600i
$669$	−21487.7	+	15611.8i	−0.0480108	+	0.0348819i
$670$		−	3250.49i		−	0.00724100i
$671$	422729.	+	403291.i	0.938895	+	0.895721i
$672$	−519360.			−1.15009
$673$	−198195.	−	272792.i	−0.437586	−	0.602285i	0.532088	−	0.846689i	$-0.321408\pi$
$673$	−198195.	−	272792.i	−0.437586	−	0.602285i	−0.969673	+	0.244404i	$0.921408\pi$
$674$	72685.4	+	223703.i	0.160003	+	0.492437i
$675$	122220.	−	376154.i	0.268246	−	0.825577i
$676$	−128475.	−	93342.8i	−0.281142	−	0.204262i
$677$	439699.	−	605194.i	0.959353	−	1.32044i	0.0121078	−	0.999927i	$-0.496146\pi$
$677$	439699.	−	605194.i	0.959353	−	1.32044i	0.947245	−	0.320510i	$-0.103854\pi$
$678$	71754.3	+	23314.4i	0.156095	+	0.0507183i
$679$	409563.	−	133075.i	0.888344	−	0.288640i
$680$	−15815.3	+	11490.5i	−0.0342027	+	0.0248497i
$681$			591.087i			0.00127455i
$682$	−15875.5	+	33057.9i	−0.0341318	+	0.0710733i
$683$	−591342.			−1.26764			−0.633822	−	0.773479i	$-0.718515\pi$
$683$	−591342.			−1.26764			−0.633822	+	0.773479i	$0.718515\pi$
$684$	25536.7	+	35148.3i	0.0545825	+	0.0751263i
$685$	−79186.1	−	243710.i	−0.168759	−	0.519388i
$686$	−42226.0	+	129958.i	−0.0897288	+	0.276157i
$687$	95538.9	+	69413.1i	0.202426	+	0.147071i
$688$	82227.3	−	113176.i	0.173716	−	0.239099i
$689$	−270942.	−	88034.5i	−0.570740	−	0.185445i
$690$	139535.	−	45337.7i	0.293080	−	0.0952273i
$691$	−187294.	+	136077.i	−0.392253	+	0.284989i	−0.766378	−	0.642390i	$-0.777943\pi$
$691$	−187294.	+	136077.i	−0.392253	+	0.284989i	0.374125	+	0.927378i	$0.377943\pi$
$692$		−	87917.0i		−	0.183595i
$693$	−7286.86	−	39906.6i	−0.0151731	−	0.0830957i
$694$	162724.			0.337856
$695$	−126830.	−	174566.i	−0.262574	−	0.361402i
$696$	−20165.1	−	62061.7i	−0.0416276	−	0.128116i
$697$	−7087.88	+	21814.3i	−0.0145899	+	0.0449030i
$698$	−77578.5	−	56364.1i	−0.159232	−	0.115689i
$699$	−266421.	+	366698.i	−0.545274	+	0.750505i
$700$	381856.	+	124073.i	0.779298	+	0.253209i
$701$	46147.3	−	14994.2i	0.0939097	−	0.0305131i	−0.261685	−	0.965153i	$-0.584278\pi$
$701$	46147.3	−	14994.2i	0.0939097	−	0.0305131i	0.355595	+	0.934640i	$0.384278\pi$
$702$	−135470.	+	98424.5i	−0.274896	+	0.199723i
$703$			842929.i			1.70561i
$704$	−8067.26	−	14952.4i	−0.0162772	−	0.0301694i
$705$	−42333.8			−0.0851743
$706$	−3827.05	−	5267.48i	−0.00767811	−	0.0105680i
$707$	−279666.	−	860722.i	−0.559500	−	1.72196i
$708$	−167471.	+	515423.i	−0.334098	+	1.02825i
$709$	472771.	+	343488.i	0.940499	+	0.683313i	0.948541	−	0.316655i	$-0.102560\pi$
$709$	472771.	+	343488.i	0.940499	+	0.683313i	−0.00804160	+	0.999968i	$0.502560\pi$
$710$	−6782.75	+	9335.66i	−0.0134552	+	0.0185195i
$711$	−46174.9	−	15003.1i	−0.0913412	−	0.0296785i
$712$	−318802.	+	103585.i	−0.628871	+	0.204332i
$713$	136971.	−	99515.1i	0.269432	−	0.195754i
$714$		−	34637.5i		−	0.0679439i
$715$	152593.	+	20501.0i	0.298485	+	0.0401017i
$716$	496212.			0.967923
$717$	421436.	+	580057.i	0.819772	+	1.12832i
$718$	−46411.1	−	142839.i	−0.0900270	−	0.277075i
$719$	−81167.1	+	249807.i	−0.157008	+	0.483221i	−0.998359	−	0.0572683i	$-0.981761\pi$
$719$	−81167.1	+	249807.i	−0.157008	+	0.483221i	0.841351	+	0.540490i	$0.181761\pi$
$720$	5477.64	+	3979.74i	0.0105664	+	0.00767696i
$721$	31670.9	−	43591.3i	0.0609242	−	0.0838550i
$722$	359047.	+	116662.i	0.688775	+	0.223797i
$723$	−202325.	+	65739.5i	−0.387056	+	0.125762i
$724$	231199.	−	167976.i	0.441071	−	0.320457i
$725$			78317.1i			0.148998i
$726$	172829.	−	138443.i	0.327902	−	0.262663i
$727$	172573.			0.326516			0.163258	−	0.986583i	$-0.447800\pi$
$727$	172573.			0.326516			0.163258	+	0.986583i	$0.447800\pi$
$728$	−223247.	−	307274.i	−0.421234	−	0.579779i
$729$	174083.	+	535773.i	0.327568	+	1.00815i
$730$	28352.4	−	87259.8i	0.0532040	−	0.163745i
$731$	36836.6	+	26763.3i	0.0689357	+	0.0500847i
$732$	319257.	−	439420.i	0.595825	−	0.820082i
$733$	−174118.	−	56574.4i	−0.324068	−	0.105296i	0.142465	−	0.989800i	$-0.454497\pi$
$733$	−174118.	−	56574.4i	−0.324068	−	0.105296i	−0.466533	+	0.884504i	$0.654497\pi$
$734$	41979.4	−	13639.9i	0.0779191	−	0.0253175i
$735$	74865.9	−	54393.2i	0.138583	−	0.100686i
$736$		−	988963.i		−	1.82568i
$737$	−3015.91	+	22448.0i	−0.00555243	+	0.0413279i
$738$	−5852.22			−0.0107450
$739$	177886.	+	244839.i	0.325726	+	0.448323i	0.940205	−	0.340610i	$-0.110634\pi$
$739$	177886.	+	244839.i	0.325726	+	0.448323i	−0.614479	+	0.788933i	$0.710634\pi$
$740$	57114.4	+	175780.i	0.104299	+	0.321001i
$741$	201723.	−	620840.i	0.367383	−	1.13069i
$742$	185315.	+	134639.i	0.336591	+	0.244547i
$743$	−271424.	+	373583.i	−0.491666	+	0.676721i	−0.980694	−	0.195547i	$-0.937352\pi$
$743$	−271424.	+	373583.i	−0.491666	+	0.676721i	0.489028	+	0.872268i	$0.337352\pi$
$744$	72446.8	+	23539.4i	0.130880	+	0.0425255i
$745$	−346886.	+	112710.i	−0.624991	+	0.203072i
$746$	−271014.	+	196904.i	−0.486984	+	0.353815i
$747$			1317.89i			0.00236178i
$748$	53654.7	−	28948.2i	0.0958969	−	0.0517390i
$749$	491142.			0.875474
$750$	−101927.	−	140290.i	−0.181203	−	0.249405i
$751$	185329.	+	570383.i	0.328596	+	1.01132i	0.969791	+	0.243937i	$0.0784390\pi$
$751$	185329.	+	570383.i	0.328596	+	1.01132i	−0.641195	+	0.767378i	$0.721561\pi$
$752$	−18068.6	+	55609.5i	−0.0319514	+	0.0983362i
$753$	−750054.	−	544946.i	−1.32283	−	0.961089i
$754$	19489.5	−	26825.0i	0.0342814	−	0.0471843i
$755$	86535.8	+	28117.2i	0.151811	+	0.0493262i
$756$	−546428.	+	177545.i	−0.956069	+	0.310646i
$757$	−506946.	+	368318.i	−0.884647	+	0.642734i	−0.934477	−	0.356024i	$-0.884132\pi$
$757$	−506946.	+	368318.i	−0.884647	+	0.642734i	0.0498296	+	0.998758i	$0.484132\pi$
$758$		−	229717.i		−	0.399812i
$759$	−1.00570e6	+	183639.i	−1.74576	+	0.318773i
$760$	296230.			0.512864
$761$	23646.8	+	32547.1i	0.0408323	+	0.0562008i	0.828945	−	0.559330i	$-0.188942\pi$
$761$	23646.8	+	32547.1i	0.0408323	+	0.0562008i	−0.788113	+	0.615531i	$0.788942\pi$
$762$	−52583.0	−	161834.i	−0.0905598	−	0.278715i
$763$	−56426.1	+	173662.i	−0.0969240	+	0.298301i
$764$	46046.1	+	33454.5i	0.0788871	+	0.0573149i
$765$	−1295.32	+	1782.86i	−0.00221338	+	0.00304646i
$766$	−291064.	−	94572.4i	−0.496056	−	0.161178i
$767$	−585164.	+	190131.i	−0.994688	+	0.323194i
$768$	186090.	−	135202.i	0.315501	−	0.229225i
$769$		−	816302.i		−	1.38038i	−0.723629	−	0.690189i	$-0.757527\pi$
$769$		−	816302.i		−	1.38038i	0.723629	−	0.690189i	$-0.242473\pi$
$770$	−111593.	−	53590.9i	−0.188216	−	0.0903878i
$771$	778009.			1.30881
$772$	143201.	+	197099.i	0.240277	+	0.330712i
$773$	−131828.	−	405724.i	−0.220621	−	0.679002i	−0.998707	−	0.0508439i	$-0.983809\pi$
$773$	−131828.	−	405724.i	−0.220621	−	0.679002i	0.778085	−	0.628159i	$-0.216191\pi$
$774$	−3589.97	+	11048.8i	−0.00599251	+	0.0184430i
$775$	−73962.3	−	53736.7i	−0.123142	−	0.0894680i
$776$	−216864.	+	298487.i	−0.360134	+	0.495681i
$777$	−695895.	−	226110.i	−1.15266	−	0.374523i
$778$	40999.1	−	13321.4i	0.0677353	−	0.0220085i
$779$	281190.	−	204297.i	0.463367	−	0.336656i
$780$		−	143135.i		−	0.235264i
$781$	55503.9	−	58179.2i	0.0909959	−	0.0953818i
$782$	65956.5			0.107856
$783$	−65873.1	−	90666.6i	−0.107445	−	0.147885i
$784$	−39497.0	−	121559.i	−0.0642588	−	0.197768i
$785$	−20802.8	+	64024.5i	−0.0337585	+	0.103898i
$786$	334768.	+	243223.i	0.541874	+	0.393695i
$787$	459337.	−	632224.i	0.741621	−	1.02075i	−0.256902	−	0.966437i	$-0.582702\pi$
$787$	459337.	−	632224.i	0.741621	−	1.02075i	0.998524	−	0.0543170i	$-0.0172982\pi$
$788$	171507.	+	55726.1i	0.276204	+	0.0897442i
$789$	900595.	−	292621.i	1.44669	−	0.470058i
$790$	−119865.	+	87086.7i	−0.192060	+	0.139540i
$791$			293899.i			0.469726i
$792$	25147.1	+	23990.7i	0.0400901	+	0.0382466i
$793$	616646.			0.980594
$794$	−196508.	−	270471.i	−0.311703	−	0.429022i
$795$	59602.0	+	183436.i	0.0943033	+	0.290236i
$796$	−171580.	+	528067.i	−0.270794	+	0.833419i
$797$	−246599.	−	179164.i	−0.388217	−	0.282056i	0.376508	−	0.926414i	$-0.377125\pi$
$797$	−246599.	−	179164.i	−0.388217	−	0.282056i	−0.764724	+	0.644358i	$0.777125\pi$
$798$	−308513.	+	424632.i	−0.484471	+	0.666818i
$799$	−18099.8	−	5880.98i	−0.0283518	−	0.00921204i
$800$	−507889.	+	165023.i	−0.793576	+	0.257849i
$801$	−30571.2	+	22211.3i	−0.0476483	+	0.0346185i
$802$			196411.i			0.305364i
$803$	−276766.	+	576314.i	−0.429221	+	0.893775i
$804$	21056.6			0.0325744
$805$	335932.	+	462371.i	0.518394	+	0.713508i
$806$	11960.8	+	36811.6i	0.0184116	+	0.0566649i
$807$	−25180.0	+	77496.2i	−0.0386642	+	0.118996i
$808$	627290.	+	455753.i	0.960828	+	0.698082i
$809$	−427633.	+	588586.i	−0.653392	+	0.899317i	−0.999240	−	0.0389736i	$-0.987591\pi$
$809$	−427633.	+	588586.i	−0.653392	+	0.899317i	0.345848	+	0.938290i	$0.387591\pi$
$810$	100208.	+	32559.5i	0.152733	+	0.0496259i
$811$	924592.	−	300418.i	1.40575	−	0.456756i	0.494706	−	0.869061i	$-0.335276\pi$
$811$	924592.	−	300418.i	1.40575	−	0.456756i	0.911046	+	0.412304i	$0.135276\pi$
$812$	92041.1	−	66871.8i	0.139595	−	0.101422i
$813$		−	706225.i		−	1.06847i
$814$	54211.3	+	296889.i	0.0818166	+	0.448070i
$815$	−239848.			−0.361094
$816$	−23678.2	−	32590.2i	−0.0355605	−	0.0489448i
$817$	−213212.	−	656200.i	−0.319425	−	0.983088i
$818$	146363.	−	450460.i	0.218739	−	0.673208i
$819$	−34639.0	−	25166.7i	−0.0516413	−	0.0375196i
$820$	44795.4	−	61655.6i	0.0666202	−	0.0916948i
$821$	120294.	+	39086.0i	0.178468	+	0.0579876i	0.396888	−	0.917867i	$-0.370090\pi$
$821$	120294.	+	39086.0i	0.178468	+	0.0579876i	−0.218420	+	0.975855i	$0.570090\pi$
$822$	−369959.	+	120207.i	−0.547532	+	0.177904i
$823$	671667.	−	487995.i	0.991641	−	0.720469i	0.0313612	−	0.999508i	$-0.490016\pi$
$823$	671667.	−	487995.i	0.991641	−	0.720469i	0.960280	+	0.279039i	$0.0900158\pi$
$824$			46163.2i			0.0679895i
$825$	262125.	+	485843.i	0.385125	+	0.713818i
$826$	494712.			0.725091
$827$	736162.	+	1.01324e6i	1.07637	+	1.48150i	0.863453	+	0.504429i	$0.168297\pi$
$827$	736162.	+	1.01324e6i	1.07637	+	1.48150i	0.212919	+	0.977070i	$0.431703\pi$
$828$	−22191.5	−	68298.5i	−0.0323688	−	0.0996209i
$829$	164951.	−	507668.i	0.240020	−	0.738705i	−0.756396	−	0.654114i	$-0.773042\pi$
$829$	164951.	−	507668.i	0.240020	−	0.738705i	0.996416	−	0.0845907i	$-0.0269583\pi$
$830$	3253.66	+	2363.92i	0.00472298	+	0.00343144i
$831$	−245541.	+	337958.i	−0.355567	+	0.489396i
$832$	−17054.4	−	5541.32i	−0.0246371	−	0.00800509i
$833$	39565.2	−	12855.5i	0.0570194	−	0.0185267i
$834$	−264997.	+	192531.i	−0.380985	+	0.276802i
$835$		−	209332.i		−	0.300236i
$836$	−915609.	−	123013.i	−1.31008	−	0.176010i
$837$	130823.			0.186739
$838$	37278.4	+	51309.4i	0.0530847	+	0.0730649i
$839$	−247517.	−	761779.i	−0.351626	−	1.08219i	−0.957940	−	0.286968i	$-0.907353\pi$
$839$	−247517.	−	761779.i	−0.351626	−	1.08219i	0.606314	−	0.795225i	$-0.292647\pi$
$840$	−79461.8	+	244558.i	−0.112616	+	0.346596i
$841$	−554249.	−	402685.i	−0.783633	−	0.569343i
$842$	148643.	−	204589.i	0.209662	−	0.288575i
$843$	−718642.	−	233501.i	−1.01125	−	0.328574i
$844$	−534092.	+	173537.i	−0.749776	+	0.243617i
$845$	−98751.0	+	71746.8i	−0.138302	+	0.100482i
$846$		−	4855.72i		−	0.00678443i
$847$	720945.	+	473641.i	1.00493	+	0.660211i
$848$	266400.			0.370461
$849$	47818.9	+	65817.1i	0.0663414	+	0.0913111i
$850$	−11005.8	−	33872.4i	−0.0152330	−	0.0468823i
$851$	430557.	−	1.32512e6i	0.594528	−	1.82977i
$852$	−60476.3	−	43938.6i	−0.0833117	−	0.0605295i
$853$	−441124.	+	607155.i	−0.606265	+	0.834453i	−0.996264	−	0.0863629i	$-0.972476\pi$
$853$	−441124.	+	607155.i	−0.606265	+	0.834453i	0.389998	+	0.920816i	$0.372476\pi$
$854$	−471546.	−	153214.i	−0.646559	−	0.210080i
$855$	31759.6	−	10319.3i	0.0434453	−	0.0141162i
$856$	−340423.	+	247332.i	−0.464591	+	0.337545i
$857$			918487.i			1.25058i	0.780392	+	0.625290i	$0.215019\pi$
$857$			918487.i			1.25058i	−0.780392	+	0.625290i	$0.784981\pi$
$858$	31121.1	−	231641.i	0.0422747	−	0.314659i
$859$	−997172.			−1.35140			−0.675700	−	0.737177i	$-0.736158\pi$
$859$	−997172.			−1.35140			−0.675700	+	0.737177i	$0.736158\pi$
$860$	−88924.4	−	122394.i	−0.120233	−	0.165487i
$861$	93233.5	+	286943.i	0.125767	+	0.387070i
$862$	−446.646	+	1374.63i	−0.000601103	+	0.00185000i
$863$	141638.	+	102906.i	0.190178	+	0.138172i	0.678800	−	0.734323i	$-0.262500\pi$
$863$	141638.	+	102906.i	0.190178	+	0.138172i	−0.488622	+	0.872495i	$0.662500\pi$
$864$	449173.	−	618234.i	0.601709	−	0.828182i
$865$	−64268.9	−	20882.2i	−0.0858952	−	0.0279090i
$866$	−242063.	+	78651.0i	−0.322770	+	0.104874i
$867$	−575772.	+	418323.i	−0.765971	+	0.556510i
$868$			132807.i			0.176271i
$869$	908592.	−	490210.i	1.20318	−	0.649147i
$870$	−22448.7			−0.0296587
$871$	14051.5	+	19340.2i	0.0185219	+	0.0254932i
$872$	−48343.1	−	148785.i	−0.0635772	−	0.195670i
$873$	−12852.6	+	39556.2i	−0.0168641	+	0.0519022i
$874$	−808582.	−	587469.i	−1.05853	−	0.769063i
$875$	397049.	−	546492.i	0.518595	−	0.713785i
$876$	565268.	+	183667.i	0.736625	+	0.239344i
$877$	−637584.	+	207164.i	−0.828969	+	0.269348i	−0.692611	−	0.721311i	$-0.743540\pi$
$877$	−637584.	+	207164.i	−0.828969	+	0.269348i	−0.136358	+	0.990660i	$0.543540\pi$
$878$	458328.	−	332995.i	0.594549	−	0.431965i
$879$		−	675327.i		−	0.874051i
$880$	−141632.	+	25861.7i	−0.182893	+	0.0333958i
$881$	−1.11426e6			−1.43561			−0.717805	−	0.696244i	$-0.754853\pi$
$881$	−1.11426e6			−1.43561			−0.717805	+	0.696244i	$0.754853\pi$
$882$	6238.96	+	8587.19i	0.00802001	+	0.0110386i
$883$	135169.	+	416006.i	0.173362	+	0.533554i	0.999555	−	0.0298335i	$-0.00949771\pi$
$883$	135169.	+	416006.i	0.173362	+	0.533554i	−0.826193	+	0.563388i	$0.809498\pi$
$884$	19884.2	−	61197.3i	0.0254451	−	0.0783119i
$885$	337005.	+	244849.i	0.430279	+	0.312616i
$886$	11978.3	−	16486.7i	0.0152591	−	0.0210023i
$887$	733230.	+	238241.i	0.931950	+	0.302809i	0.735360	−	0.677677i	$-0.237013\pi$
$887$	733230.	+	238241.i	0.931950	+	0.302809i	0.196590	+	0.980486i	$0.437013\pi$
$888$	596208.	−	193720.i	0.756088	−	0.245668i
$889$	536261.	−	389617.i	0.678536	−	0.492985i
$890$			115316.i			0.145582i
$891$	−661831.	−	317834.i	−0.833665	−	0.400354i
$892$	39672.9			0.0498614
$893$	169510.	+	233310.i	0.212565	+	0.292571i
$894$	171097.	+	526583.i	0.214076	+	0.658858i
$895$	117861.	−	362740.i	0.147138	−	0.452844i
$896$	786342.	+	571311.i	0.979480	+	0.711634i
$897$	−634235.	+	872949.i	−0.788252	+	1.08494i
$898$	582741.	+	189344.i	0.722641	+	0.234800i
$899$	−24637.1	+	8005.08i	−0.0304839	+	0.00990481i
$900$	−31372.2	+	22793.2i	−0.0387311	+	0.0281398i
$901$			86708.0i			0.106809i
$902$	85899.6	−	90039.9i	0.105579	−	0.110668i
$903$	598931.			0.734516
$904$	−148003.	−	203708.i	−0.181106	−	0.249271i
$905$	−67878.4	−	208908.i	−0.0828771	−	0.255070i
$906$	42682.7	−	131364.i	0.0519991	−	0.160037i
$907$	241833.	+	175702.i	0.293969	+	0.213581i	0.724987	−	0.688762i	$-0.241846\pi$
$907$	241833.	+	175702.i	0.293969	+	0.213581i	−0.431018	+	0.902343i	$0.641846\pi$
$908$	518.957	−	714.283i	0.000629447	−	0.000866360i
$909$	83129.8	+	27010.5i	0.100607	+	0.0326892i
$910$	−124265.	+	40376.0i	−0.150060	+	0.0487574i
$911$	−763082.	+	554411.i	−0.919463	+	0.668029i	−0.943390	−	0.331685i	$-0.892383\pi$
$911$	−763082.	+	554411.i	−0.919463	+	0.668029i	0.0239274	+	0.999714i	$0.492383\pi$
$912$			610433.i			0.733919i
$913$	−20276.6	−	19344.2i	−0.0243250	−	0.0232065i
$914$	269726.			0.322872
$915$	−245393.	−	337755.i	−0.293103	−	0.403422i
$916$	−54508.7	−	167761.i	−0.0649643	−	0.199940i
$917$	−498108.	+	1.53302e6i	−0.592359	+	1.82309i
$918$	41231.7	+	29956.6i	0.0489267	+	0.0355473i
$919$	23459.5	−	32289.3i	0.0277772	−	0.0382320i	−0.794903	−	0.606737i	$-0.792478\pi$
$919$	23459.5	−	32289.3i	0.0277772	−	0.0382320i	0.822680	+	0.568505i	$0.192478\pi$
$920$	−465686.	−	151311.i	−0.550196	−	0.178770i
$921$	1.27073e6	−	412886.i	1.49808	−	0.486756i
$922$	−164680.	+	119647.i	−0.193722	+	0.140747i
$923$		−	84867.5i		−	0.0996180i
$924$	347162.	−	722900.i	0.406619	−	0.846709i
$925$	−752370.			−0.879322
$926$	40578.9	+	55852.1i	0.0473237	+	0.0651355i
$927$	1608.12	+	4949.28i	0.00187136	+	0.00575947i
$928$	−46760.1	+	143913.i	−0.0542975	+	0.167110i
$929$	602349.	+	437632.i	0.697938	+	0.507082i	0.879260	−	0.476342i	$-0.158038\pi$
$929$	602349.	+	437632.i	0.697938	+	0.507082i	−0.181322	+	0.983424i	$0.558038\pi$
$930$	15403.0	−	21200.4i	0.0178090	−	0.0245120i
$931$	−599545.	−	194804.i	−0.691707	−	0.224749i
$932$	643899.	−	209215.i	0.741286	−	0.240859i
$933$	583648.	−	424045.i	0.670483	−	0.487134i
$934$			165969.i			0.190253i
$935$	−8417.46	−	46098.4i	−0.00962849	−	0.0527306i
$936$	36682.7			0.0418706
$937$	−447603.	−	616073.i	−0.509816	−	0.701702i	0.474072	−	0.880486i	$-0.342784\pi$
$937$	−447603.	−	616073.i	−0.509816	−	0.701702i	−0.983888	+	0.178784i	$0.942784\pi$
$938$	−5939.73	−	18280.6i	−0.00675089	−	0.0207771i
$939$	−272982.	+	840152.i	−0.309601	+	0.952855i
$940$	51157.1	+	37167.8i	0.0578962	+	0.0420640i
$941$	745350.	−	1.02589e6i	0.841746	−	1.15856i	−0.143875	−	0.989596i	$-0.545956\pi$
$941$	745350.	−	1.02589e6i	0.841746	−	1.15856i	0.985621	−	0.168968i	$-0.0540435\pi$
$942$	97191.1	+	31579.3i	0.109528	+	0.0355878i
$943$	−546395.	+	177535.i	−0.614446	+	0.199646i
$944$	465471.	−	338185.i	0.522335	−	0.379498i
$945$			441620.i			0.494521i
$946$	−117298.	−	217409.i	−0.131072	−	0.242938i
$947$	−334276.			−0.372740			−0.186370	−	0.982480i	$-0.559672\pi$
$947$	−334276.			−0.372740			−0.186370	+	0.982480i	$0.559672\pi$
$948$	−564147.	−	776482.i	−0.627734	−	0.864002i
$949$	208518.	+	641754.i	0.231533	+	0.712584i
$950$	−166775.	+	513281.i	−0.184792	+	0.568732i
$951$	−803758.	−	583965.i	−0.888719	−	0.645692i
$952$	−67947.7	+	93522.0i	−0.0749723	+	0.103191i
$953$	593076.	+	192702.i	0.653017	+	0.212178i	0.616744	−	0.787164i	$-0.288451\pi$
$953$	593076.	+	192702.i	0.653017	+	0.212178i	0.0362728	+	0.999342i	$0.488451\pi$
$954$	−21040.3	+	6836.41i	−0.0231183	+	0.00751158i
$955$	35392.8	−	25714.4i	0.0388068	−	0.0281948i
$956$		−	1.07096e6i		−	1.17181i
$957$	155031.	+	20828.6i	0.169276	+	0.0227424i
$958$	−611881.			−0.666709
$959$	−890679.	−	1.22591e6i	−0.968465	−	1.33298i
$960$	3751.64	+	11546.4i	0.00407079	+	0.0125286i
$961$	−276039.	+	849561.i	−0.298899	+	0.919915i
$962$	257700.	+	187230.i	0.278461	+	0.202314i
$963$	−27881.7	+	38375.9i	−0.0300654	+	0.0413814i
$964$	302212.	+	98194.6i	0.325205	+	0.105666i
$965$	178097.	−	57867.1i	0.191250	−	0.0621408i
$966$	701893.	−	509955.i	0.752171	−	0.546484i
$967$			183055.i			0.195762i	0.995198	+	0.0978809i	$0.0312064\pi$
$967$			183055.i			0.195762i	−0.995198	+	0.0978809i	$0.968794\pi$
$968$	−738223.	+	34764.1i	−0.787838	+	0.0371006i
$969$	−198684.			−0.211599
$970$	74603.7	+	102683.i	0.0792897	+	0.109133i
$971$	254131.	+	782134.i	0.269537	+	0.829551i	0.990613	+	0.136695i	$0.0436479\pi$
$971$	254131.	+	782134.i	0.269537	+	0.829551i	−0.721076	+	0.692856i	$0.756352\pi$
$972$	33169.6	−	102085.i	0.0351081	−	0.108052i
$973$	−1.03228e6	−	749993.i	−1.09036	−	0.792194i
$974$	168145.	−	231432.i	0.177242	−	0.243952i
$975$	554141.	+	180051.i	0.582923	+	0.189403i
$976$	−548411.	+	178190.i	−0.575714	+	0.187061i
$977$	−1.07719e6	+	782623.i	−1.12850	+	0.819905i	−0.985476	−	0.169814i	$-0.945683\pi$
$977$	−1.07719e6	+	782623.i	−1.12850	+	0.819905i	−0.143027	+	0.989719i	$0.545683\pi$
$978$			364096.i			0.380660i
$979$	106994.	−	796375.i	0.111633	−	0.830907i
$980$	−138225.			−0.143925
$981$	−10366.0	−	14267.5i	−0.0107714	−	0.0148256i
$982$	97585.4	+	300337.i	0.101196	+	0.311448i
$983$	443474.	−	1.36487e6i	0.458945	−	1.41249i	−0.407495	−	0.913207i	$-0.633598\pi$
$983$	443474.	−	1.36487e6i	0.458945	−	1.41249i	0.866440	−	0.499281i	$-0.166402\pi$
$984$	−209123.	−	151937.i	−0.215979	−	0.156918i
$985$	81473.6	−	112139.i	0.0839739	−	0.115580i
$986$	−9597.92	−	3118.55i	−0.00987241	−	0.00320774i
$987$	−238083.	+	77357.9i	−0.244396	+	0.0794092i
$988$	−788846.	+	573130.i	−0.808125	+	0.587137i
$989$			1.14048e6i			1.16599i
$990$	10522.4	−	5677.14i	0.0107361	−	0.00579241i
$991$	−519599.			−0.529079			−0.264540	−	0.964375i	$-0.585220\pi$
$991$	−519599.			−0.529079			−0.264540	+	0.964375i	$0.585220\pi$
$992$	−103826.	−	142905.i	−0.105508	−	0.145219i
$993$	9388.48	+	28894.8i	0.00952131	+	0.0293036i
$994$	−21086.5	+	64897.7i	−0.0213419	+	0.0656835i
$995$	345273.	+	250855.i	0.348752	+	0.253383i
$996$	−15313.5	+	21077.2i	−0.0154367	+	0.0212468i
$997$	356006.	+	115673.i	0.358152	+	0.116370i	0.482565	−	0.875860i	$-0.339705\pi$
$997$	356006.	+	115673.i	0.358152	+	0.116370i	−0.124414	+	0.992230i	$0.539705\pi$
$998$	192508.	−	62549.7i	0.193281	−	0.0628007i
$999$	871008.	−	632824.i	0.872752	−	0.634092i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.5.d.a.8.2	yes	12
3.2	odd	2		99.5.k.a.19.2		12
4.3	odd	2		176.5.n.a.129.1		12
11.2	odd	10		121.5.b.b.120.7		12
11.3	even	5		121.5.d.e.94.2		12
11.4	even	5		121.5.d.d.40.2		12
11.5	even	5		121.5.d.c.112.2		12
11.6	odd	10		121.5.d.e.112.2		12
11.7	odd	10	inner	11.5.d.a.7.2	✓	12
11.8	odd	10		121.5.d.c.94.2		12
11.9	even	5		121.5.b.b.120.6		12
11.10	odd	2		121.5.d.d.118.2		12
33.29	even	10		99.5.k.a.73.2		12
44.7	even	10		176.5.n.a.161.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.5.d.a.7.2	✓	12	11.7	odd	10	inner
11.5.d.a.8.2	yes	12	1.1	even	1	trivial
99.5.k.a.19.2		12	3.2	odd	2
99.5.k.a.73.2		12	33.29	even	10
121.5.b.b.120.6		12	11.9	even	5
121.5.b.b.120.7		12	11.2	odd	10
121.5.d.c.94.2		12	11.8	odd	10
121.5.d.c.112.2		12	11.5	even	5
121.5.d.d.40.2		12	11.4	even	5
121.5.d.d.118.2		12	11.10	odd	2
121.5.d.e.94.2		12	11.3	even	5
121.5.d.e.112.2		12	11.6	odd	10
176.5.n.a.129.1		12	4.3	odd	2
176.5.n.a.161.1		12	44.7	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	11.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02443 + 1.41001i) q^{2} +(2.68168 + 8.25338i) q^{3} +(4.00561 - 12.3280i) q^{4} +(-8.06057 - 5.85635i) q^{5} +(-8.89011 + 12.2362i) q^{6} +(-56.0338 - 18.2065i) q^{7} +(48.0070 - 15.5984i) q^{8} +(4.60358 - 3.34469i) q^{9} +O(q^{10})\)	\(q+(1.02443 + 1.41001i) q^{2} +(2.68168 + 8.25338i) q^{3} +(4.00561 - 12.3280i) q^{4} +(-8.06057 - 5.85635i) q^{5} +(-8.89011 + 12.2362i) q^{6} +(-56.0338 - 18.2065i) q^{7} +(48.0070 - 15.5984i) q^{8} +(4.60358 - 3.34469i) q^{9} -17.3649i q^{10} +(-16.1117 + 119.923i) q^{11} +112.489 q^{12} +(75.0662 + 103.320i) q^{13} +(-31.7314 - 97.6593i) q^{14} +(26.7187 - 82.2318i) q^{15} +(-96.6156 - 70.1954i) q^{16} +(22.8472 - 31.4465i) q^{17} +(9.43207 + 3.06467i) q^{18} +(-560.182 + 182.014i) q^{19} +(-104.485 + 75.9125i) q^{20} -511.293i q^{21} +(-185.597 + 100.135i) q^{22} +973.600 q^{23} +(257.479 + 354.390i) q^{24} +(-162.460 - 499.999i) q^{25} +(-68.7814 + 211.687i) q^{26} +(608.630 + 442.196i) q^{27} +(-448.900 + 617.857i) q^{28} +(-141.677 - 46.0337i) q^{29} +(143.319 - 46.5671i) q^{30} +(140.685 - 102.214i) q^{31} -1015.78i q^{32} +(-1032.97 + 188.618i) q^{33} +67.7450 q^{34} +(345.041 + 474.909i) q^{35} +(-22.7933 - 70.1504i) q^{36} +(442.232 - 1361.05i) q^{37} +(-830.507 - 603.399i) q^{38} +(-651.433 + 896.620i) q^{39} +(-478.314 - 155.414i) q^{40} +(-561.211 + 182.349i) q^{41} +(720.925 - 523.783i) q^{42} +1171.41i q^{43} +(1413.87 + 678.988i) q^{44} -56.6952 q^{45} +(997.384 + 1372.78i) q^{46} +(-151.299 - 465.650i) q^{47} +(320.256 - 985.647i) q^{48} +(865.865 + 629.088i) q^{49} +(538.573 - 741.283i) q^{50} +(320.808 + 104.237i) q^{51} +(1574.41 - 511.557i) q^{52} +(-1804.69 + 1311.18i) q^{53} +1311.17i q^{54} +(832.178 - 872.289i) q^{55} -2974.01 q^{56} +(-3004.46 - 4135.29i) q^{57} +(-80.2304 - 246.924i) q^{58} +(-1488.77 + 4581.97i) q^{59} +(-906.729 - 658.778i) q^{60} +(2838.11 - 3906.32i) q^{61} +(288.243 + 93.6559i) q^{62} +(-318.851 + 103.601i) q^{63} +(-113.596 + 82.5323i) q^{64} -1272.43i q^{65} +(-1324.16 - 1263.27i) q^{66} +187.188 q^{67} +(-296.155 - 407.623i) q^{68} +(2610.89 + 8035.49i) q^{69} +(-316.153 + 973.020i) q^{70} +(-537.618 - 390.602i) q^{71} +(168.832 - 232.377i) q^{72} +(5025.08 + 1632.75i) q^{73} +(2372.13 - 770.750i) q^{74} +(3691.02 - 2681.68i) q^{75} +7635.00i q^{76} +(3086.17 - 6426.38i) q^{77} -1931.59 q^{78} +(-5015.11 - 6902.71i) q^{79} +(367.689 + 1131.63i) q^{80} +(-1875.02 + 5770.73i) q^{81} +(-832.034 - 604.508i) q^{82} +(-136.132 + 187.370i) q^{83} +(-6303.22 - 2048.04i) q^{84} +(-368.323 + 119.675i) q^{85} +(-1651.69 + 1200.02i) q^{86} -1292.76i q^{87} +(1097.13 + 6008.44i) q^{88} -6640.75 q^{89} +(-58.0802 - 79.9405i) q^{90} +(-2325.16 - 7156.09i) q^{91} +(3899.86 - 12002.5i) q^{92} +(1220.88 + 887.020i) q^{93} +(501.574 - 690.357i) q^{94} +(5581.33 + 1813.48i) q^{95} +(8383.61 - 2724.00i) q^{96} +(-5913.27 + 4296.24i) q^{97} +1865.33i q^{98} +(326.933 + 605.961i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 5 q^{2} - 6 q^{3} + 7 q^{4} - 18 q^{5} + 75 q^{6} - 80 q^{7} - 245 q^{8} + q^{9}+O(q^{10}) \) 12 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 - 18 * q^5 + 75 * q^6 - 80 * q^7 - 245 * q^8 + q^9	\( 12 q - 5 q^{2} - 6 q^{3} + 7 q^{4} - 18 q^{5} + 75 q^{6} - 80 q^{7} - 245 q^{8} + q^{9} - 43 q^{11} + 594 q^{12} + 250 q^{13} + 610 q^{14} + 1134 q^{15} - 633 q^{16} - 1250 q^{17} - 3150 q^{18} - 1025 q^{19} + 752 q^{20} - 35 q^{22} + 1684 q^{23} + 5345 q^{24} + 197 q^{25} + 3490 q^{26} - 687 q^{27} - 3580 q^{28} - 2690 q^{29} - 6740 q^{30} - 1136 q^{31} + 5939 q^{33} + 2370 q^{34} + 3610 q^{35} - 514 q^{36} - 336 q^{37} + 1900 q^{38} - 6880 q^{39} - 2340 q^{40} - 4550 q^{41} + 1310 q^{42} - 6268 q^{44} + 5136 q^{45} + 4150 q^{46} + 24 q^{47} + 344 q^{48} + 827 q^{49} + 8895 q^{50} + 13155 q^{51} + 14070 q^{52} + 414 q^{53} - 2738 q^{55} - 21340 q^{56} - 26925 q^{57} + 2980 q^{58} - 10011 q^{59} - 6856 q^{60} + 9460 q^{61} - 6200 q^{62} + 9150 q^{63} - 2633 q^{64} - 3210 q^{66} + 12154 q^{67} - 9400 q^{68} - 9022 q^{69} - 9380 q^{70} + 17574 q^{71} + 43045 q^{72} + 27950 q^{73} + 43270 q^{74} - 1761 q^{75} + 4090 q^{77} - 42920 q^{78} - 41540 q^{79} - 2308 q^{80} - 21080 q^{81} - 28175 q^{82} - 18665 q^{83} + 26250 q^{84} - 4230 q^{85} - 10125 q^{86} - 15125 q^{88} + 5554 q^{89} + 18400 q^{90} + 7390 q^{91} + 3904 q^{92} + 36898 q^{93} + 18920 q^{94} + 14110 q^{95} - 21140 q^{96} + 20769 q^{97} - 3269 q^{99}+O(q^{100}) \) 12 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 - 18 * q^5 + 75 * q^6 - 80 * q^7 - 245 * q^8 + q^9 - 43 * q^11 + 594 * q^12 + 250 * q^13 + 610 * q^14 + 1134 * q^15 - 633 * q^16 - 1250 * q^17 - 3150 * q^18 - 1025 * q^19 + 752 * q^20 - 35 * q^22 + 1684 * q^23 + 5345 * q^24 + 197 * q^25 + 3490 * q^26 - 687 * q^27 - 3580 * q^28 - 2690 * q^29 - 6740 * q^30 - 1136 * q^31 + 5939 * q^33 + 2370 * q^34 + 3610 * q^35 - 514 * q^36 - 336 * q^37 + 1900 * q^38 - 6880 * q^39 - 2340 * q^40 - 4550 * q^41 + 1310 * q^42 - 6268 * q^44 + 5136 * q^45 + 4150 * q^46 + 24 * q^47 + 344 * q^48 + 827 * q^49 + 8895 * q^50 + 13155 * q^51 + 14070 * q^52 + 414 * q^53 - 2738 * q^55 - 21340 * q^56 - 26925 * q^57 + 2980 * q^58 - 10011 * q^59 - 6856 * q^60 + 9460 * q^61 - 6200 * q^62 + 9150 * q^63 - 2633 * q^64 - 3210 * q^66 + 12154 * q^67 - 9400 * q^68 - 9022 * q^69 - 9380 * q^70 + 17574 * q^71 + 43045 * q^72 + 27950 * q^73 + 43270 * q^74 - 1761 * q^75 + 4090 * q^77 - 42920 * q^78 - 41540 * q^79 - 2308 * q^80 - 21080 * q^81 - 28175 * q^82 - 18665 * q^83 + 26250 * q^84 - 4230 * q^85 - 10125 * q^86 - 15125 * q^88 + 5554 * q^89 + 18400 * q^90 + 7390 * q^91 + 3904 * q^92 + 36898 * q^93 + 18920 * q^94 + 14110 * q^95 - 21140 * q^96 + 20769 * q^97 - 3269 * q^99

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