LMFDB - Embedded newform 11.5.d.a.2.2

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			2.2
Root			$2.38108i$ of defining polynomial
Character	$\chi$	$=$	11.2
Dual form			11.5.d.a.6.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.38257 - 1.09906i) q^{2} +(12.7857 - 9.28936i) q^{3} +(-2.71041 - 1.96923i) q^{4} +(5.48545 + 16.8825i) q^{5} +(-53.4582 + 17.3696i) q^{6} +(-19.6356 + 27.0262i) q^{7} +(40.4526 + 55.6782i) q^{8} +(52.1517 - 160.506i) q^{9} +O(q^{10})$	\(q+(-3.38257 - 1.09906i) q^{2} +(12.7857 - 9.28936i) q^{3} +(-2.71041 - 1.96923i) q^{4} +(5.48545 + 16.8825i) q^{5} +(-53.4582 + 17.3696i) q^{6} +(-19.6356 + 27.0262i) q^{7} +(40.4526 + 55.6782i) q^{8} +(52.1517 - 160.506i) q^{9} -63.1351i q^{10} +(44.7432 + 112.423i) q^{11} -52.9474 q^{12} +(-133.670 - 43.4321i) q^{13} +(96.1225 - 69.8371i) q^{14} +(226.963 + 164.898i) q^{15} +(-59.0753 - 181.815i) q^{16} +(84.2066 - 27.3604i) q^{17} +(-352.814 + 485.607i) q^{18} +(-192.513 - 264.971i) q^{19} +(18.3776 - 56.5605i) q^{20} +527.951i q^{21} +(-27.7866 - 429.457i) q^{22} -527.616 q^{23} +(1034.43 + 336.107i) q^{24} +(250.708 - 182.150i) q^{25} +(404.415 + 293.825i) q^{26} +(-428.625 - 1319.17i) q^{27} +(106.441 - 34.5849i) q^{28} +(-100.856 + 138.816i) q^{29} +(-586.484 - 807.227i) q^{30} +(-318.892 + 981.449i) q^{31} -421.222i q^{32} +(1616.42 + 1021.78i) q^{33} -314.906 q^{34} +(-563.979 - 183.248i) q^{35} +(-457.426 + 332.339i) q^{36} +(238.981 + 173.630i) q^{37} +(359.968 + 1107.87i) q^{38} +(-2112.53 + 686.401i) q^{39} +(-718.085 + 988.360i) q^{40} +(16.1331 + 22.2053i) q^{41} +(580.252 - 1785.83i) q^{42} -2508.66i q^{43} +(100.115 - 392.823i) q^{44} +2995.82 q^{45} +(1784.70 + 579.884i) q^{46} +(1080.95 - 785.358i) q^{47} +(-2444.27 - 1775.86i) q^{48} +(397.096 + 1222.13i) q^{49} +(-1048.23 + 340.591i) q^{50} +(822.480 - 1132.05i) q^{51} +(276.773 + 380.946i) q^{52} +(159.574 - 491.117i) q^{53} +4933.29i q^{54} +(-1652.55 + 1372.07i) q^{55} -2299.08 q^{56} +(-4922.82 - 1599.52i) q^{57} +(493.720 - 358.709i) q^{58} +(1796.54 + 1305.27i) q^{59} +(-290.440 - 893.882i) q^{60} +(5069.82 - 1647.29i) q^{61} +(2157.35 - 2969.34i) q^{62} +(3313.84 + 4561.11i) q^{63} +(-1408.16 + 4333.86i) q^{64} -2494.93i q^{65} +(-4344.65 - 5232.78i) q^{66} -4026.91 q^{67} +(-282.113 - 91.6641i) q^{68} +(-6745.95 + 4901.22i) q^{69} +(1706.30 + 1239.70i) q^{70} +(538.898 + 1658.56i) q^{71} +(11046.4 - 3589.19i) q^{72} +(1326.54 - 1825.82i) q^{73} +(-617.540 - 849.971i) q^{74} +(1513.42 - 4657.83i) q^{75} +1097.28i q^{76} +(-3916.94 - 998.271i) q^{77} +7900.17 q^{78} +(3331.84 + 1082.58i) q^{79} +(2745.44 - 1994.68i) q^{80} +(-6675.22 - 4849.83i) q^{81} +(-30.1663 - 92.8423i) q^{82} +(-10550.4 + 3428.04i) q^{83} +(1039.66 - 1430.96i) q^{84} +(923.822 + 1271.53i) q^{85} +(-2757.18 + 8485.74i) q^{86} +2711.75i q^{87} +(-4449.56 + 7039.04i) q^{88} +2775.39 q^{89} +(-10133.6 - 3292.60i) q^{90} +(3798.51 - 2759.78i) q^{91} +(1430.06 + 1039.00i) q^{92} +(5039.77 + 15510.8i) q^{93} +(-4519.56 + 1468.49i) q^{94} +(3417.34 - 4703.57i) q^{95} +(-3912.88 - 5385.62i) q^{96} +(3047.94 - 9380.60i) q^{97} -4570.39i q^{98} +(20378.1 - 1318.50i) 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 $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−3.38257	−	1.09906i	−0.845643	−	0.274766i	−0.146023	−	0.989281i	$-0.546647\pi$
$2$	−3.38257	−	1.09906i	−0.845643	−	0.274766i	−0.699620	+	0.714515i	$0.746647\pi$
$3$	12.7857	−	9.28936i	1.42063	−	1.03215i	0.428967	−	0.903320i	$-0.358878\pi$
$3$	12.7857	−	9.28936i	1.42063	−	1.03215i	0.991667	−	0.128831i	$-0.0411224\pi$
$4$	−2.71041	−	1.96923i	−0.169401	−	0.123077i
$5$	5.48545	+	16.8825i	0.219418	+	0.675299i	0.998810	+	0.0487629i	$0.0155279\pi$
$5$	5.48545	+	16.8825i	0.219418	+	0.675299i	−0.779392	+	0.626536i	$0.784472\pi$
$6$	−53.4582	+	17.3696i	−1.48495	+	0.482489i
$7$	−19.6356	+	27.0262i	−0.400728	+	0.551554i	−0.960926	−	0.276804i	$-0.910725\pi$
$7$	−19.6356	+	27.0262i	−0.400728	+	0.551554i	0.560199	+	0.828358i	$0.310725\pi$
$8$	40.4526	+	55.6782i	0.632072	+	0.869972i
$9$	52.1517	−	160.506i	0.643848	−	1.98156i
$10$		−	63.1351i		−	0.631351i
$11$	44.7432	+	112.423i	0.369779	+	0.929120i
$11$	44.7432	+	112.423i	0.369779	+	0.929120i
$12$	−52.9474			−0.367690
$13$	−133.670	−	43.4321i	−0.790948	−	0.256995i	−0.114441	−	0.993430i	$-0.536508\pi$
$13$	−133.670	−	43.4321i	−0.790948	−	0.256995i	−0.676508	+	0.736435i	$0.736508\pi$
$14$	96.1225	−	69.8371i	0.490421	−	0.356312i
$15$	226.963	+	164.898i	1.00872	+	0.732880i
$16$	−59.0753	−	181.815i	−0.230763	−	0.710216i
$17$	84.2066	−	27.3604i	0.291372	−	0.0946726i	−0.159684	−	0.987168i	$-0.551047\pi$
$17$	84.2066	−	27.3604i	0.291372	−	0.0946726i	0.451056	+	0.892496i	$0.351047\pi$
$18$	−352.814	+	485.607i	−1.08893	+	1.49879i
$19$	−192.513	−	264.971i	−0.533276	−	0.733991i	0.454350	−	0.890824i	$-0.349872\pi$
$19$	−192.513	−	264.971i	−0.533276	−	0.733991i	−0.987625	+	0.156832i	$0.949872\pi$
$20$	18.3776	−	56.5605i	0.0459441	−	0.141401i
$21$			527.951i			1.19717i
$22$	−27.7866	−	429.457i	−0.0574103	−	0.887307i
$23$	−527.616			−0.997384			−0.498692	−	0.866779i	$-0.666186\pi$
$23$	−527.616			−0.997384			−0.498692	+	0.866779i	$0.666186\pi$
$24$	1034.43	+	336.107i	1.79588	+	0.583518i
$25$	250.708	−	182.150i	0.401132	−	0.291440i
$26$	404.415	+	293.825i	0.598247	+	0.434652i
$27$	−428.625	−	1319.17i	−0.587963	−	1.80957i
$28$	106.441	−	34.5849i	0.135767	−	0.0441134i
$29$	−100.856	+	138.816i	−0.119924	+	0.165061i	−0.864758	−	0.502188i	$-0.832528\pi$
$29$	−100.856	+	138.816i	−0.119924	+	0.165061i	0.744835	+	0.667249i	$0.232528\pi$
$30$	−586.484	−	807.227i	−0.651649	−	0.896918i
$31$	−318.892	+	981.449i	−0.331834	+	1.02128i	0.636427	+	0.771337i	$0.280412\pi$
$31$	−318.892	+	981.449i	−0.331834	+	1.02128i	−0.968261	+	0.249942i	$0.919588\pi$
$32$		−	421.222i		−	0.411349i
$33$	1616.42	+	1021.78i	1.48431	+	0.938272i
$34$	−314.906			−0.272410
$35$	−563.979	−	183.248i	−0.460391	−	0.149590i
$36$	−457.426	+	332.339i	−0.352952	+	0.256435i
$37$	238.981	+	173.630i	0.174566	+	0.126830i	0.671637	−	0.740880i	$-0.265591\pi$
$37$	238.981	+	173.630i	0.174566	+	0.126830i	−0.497071	+	0.867710i	$0.665591\pi$
$38$	359.968	+	1107.87i	0.249285	+	0.767221i
$39$	−2112.53	+	686.401i	−1.38891	+	0.451283i
$40$	−718.085	+	988.360i	−0.448803	+	0.617725i
$41$	16.1331	+	22.2053i	0.00959731	+	0.0132096i	0.813789	−	0.581161i	$-0.197401\pi$
$41$	16.1331	+	22.2053i	0.00959731	+	0.0132096i	−0.804191	+	0.594370i	$0.797401\pi$
$42$	580.252	−	1785.83i	0.328941	−	1.01238i
$43$		−	2508.66i		−	1.35677i	−0.734708	−	0.678384i	$-0.762681\pi$
$43$		−	2508.66i		−	1.35677i	0.734708	−	0.678384i	$-0.237319\pi$
$44$	100.115	−	392.823i	0.0517123	−	0.202905i
$45$	2995.82			1.47942
$46$	1784.70	+	579.884i	0.843431	+	0.274047i
$47$	1080.95	−	785.358i	0.489340	−	0.355526i	−0.315590	−	0.948896i	$-0.602203\pi$
$47$	1080.95	−	785.358i	0.489340	−	0.355526i	0.804931	+	0.593369i	$0.202203\pi$
$48$	−2444.27	−	1775.86i	−1.06088	−	0.770774i
$49$	397.096	+	1222.13i	0.165388	+	0.509011i
$50$	−1048.23	+	340.591i	−0.419293	+	0.136237i
$51$	822.480	−	1132.05i	0.316217	−	0.435235i
$52$	276.773	+	380.946i	0.102357	+	0.140882i
$53$	159.574	−	491.117i	0.0568080	−	0.174837i	−0.918626	−	0.395127i	$-0.870700\pi$
$53$	159.574	−	491.117i	0.0568080	−	0.174837i	0.975434	+	0.220290i	$0.0707005\pi$
$54$			4933.29i			1.69180i
$55$	−1652.55	+	1372.07i	−0.546298	+	0.453577i
$56$	−2299.08			−0.733125
$57$	−4922.82	−	1599.52i	−1.51518	−	0.492312i
$58$	493.720	−	358.709i	0.146766	−	0.106632i
$59$	1796.54	+	1305.27i	0.516100	+	0.374969i	0.815133	−	0.579274i	$-0.196664\pi$
$59$	1796.54	+	1305.27i	0.516100	+	0.374969i	−0.299033	+	0.954243i	$0.596664\pi$
$60$	−290.440	−	893.882i	−0.0806778	−	0.248301i
$61$	5069.82	−	1647.29i	1.36249	−	0.442700i	0.465616	−	0.884987i	$-0.345833\pi$
$61$	5069.82	−	1647.29i	1.36249	−	0.442700i	0.896874	+	0.442287i	$0.145833\pi$
$62$	2157.35	−	2969.34i	0.561226	−	0.772461i
$63$	3313.84	+	4561.11i	0.834930	+	1.14918i
$64$	−1408.16	+	4333.86i	−0.343788	+	1.05807i
$65$		−	2494.93i		−	0.590516i
$66$	−4344.65	−	5232.78i	−0.997394	−	1.20128i
$67$	−4026.91			−0.897062			−0.448531	−	0.893767i	$-0.648053\pi$
$67$	−4026.91			−0.897062			−0.448531	+	0.893767i	$0.648053\pi$
$68$	−282.113	−	91.6641i	−0.0610106	−	0.0198236i
$69$	−6745.95	+	4901.22i	−1.41692	+	1.02945i
$70$	1706.30	+	1239.70i	0.348224	+	0.253000i
$71$	538.898	+	1658.56i	0.106903	+	0.329014i	0.990172	−	0.139852i	$-0.0446627\pi$
$71$	538.898	+	1658.56i	0.106903	+	0.329014i	−0.883269	+	0.468866i	$0.844663\pi$
$72$	11046.4	−	3589.19i	2.13086	−	0.692358i
$73$	1326.54	−	1825.82i	0.248928	−	0.342620i	−0.666207	−	0.745766i	$-0.732083\pi$
$73$	1326.54	−	1825.82i	0.248928	−	0.342620i	0.915135	+	0.403146i	$0.132083\pi$
$74$	−617.540	−	849.971i	−0.112772	−	0.155217i
$75$	1513.42	−	4657.83i	0.269053	−	0.828059i
$76$			1097.28i			0.189972i
$77$	−3916.94	−	998.271i	−0.660640	−	0.168371i
$78$	7900.17			1.29852
$79$	3331.84	+	1082.58i	0.533863	+	0.173463i	0.563527	−	0.826097i	$-0.309444\pi$
$79$	3331.84	+	1082.58i	0.533863	+	0.173463i	−0.0296646	+	0.999560i	$0.509444\pi$
$80$	2745.44	−	1994.68i	0.428974	−	0.311668i
$81$	−6675.22	−	4849.83i	−1.01741	−	0.739191i
$82$	−30.1663	−	92.8423i	−0.00448636	−	0.0138076i
$83$	−10550.4	+	3428.04i	−1.53149	+	0.497610i	−0.949012	−	0.315239i	$-0.897915\pi$
$83$	−10550.4	+	3428.04i	−1.53149	+	0.497610i	−0.582474	+	0.812849i	$0.697915\pi$
$84$	1039.66	−	1430.96i	0.147343	−	0.202801i
$85$	923.822	+	1271.53i	0.127865	+	0.175991i
$86$	−2757.18	+	8485.74i	−0.372794	+	1.14734i
$87$			2711.75i			0.358270i
$88$	−4449.56	+	7039.04i	−0.574581	+	0.908967i
$89$	2775.39			0.350383			0.175192	−	0.984534i	$-0.443945\pi$
$89$	2775.39			0.350383			0.175192	+	0.984534i	$0.443945\pi$
$90$	−10133.6	−	3292.60i	−1.25106	−	0.406494i
$91$	3798.51	−	2759.78i	0.458701	−	0.333266i
$92$	1430.06	+	1039.00i	0.168957	+	0.122755i
$93$	5039.77	+	15510.8i	0.582700	+	1.79337i
$94$	−4519.56	+	1468.49i	−0.511494	+	0.166194i
$95$	3417.34	−	4703.57i	0.378653	−	0.521171i
$96$	−3912.88	−	5385.62i	−0.424575	−	0.584377i
$97$	3047.94	−	9380.60i	0.323939	−	0.996982i	−0.647978	−	0.761659i	$-0.724385\pi$
$97$	3047.94	−	9380.60i	0.323939	−	0.996982i	0.971917	−	0.235323i	$-0.0756147\pi$
$98$		−	4570.39i		−	0.475884i
$99$	20378.1	−	1318.50i	2.07919	−	0.134527i
$100$	−1038.22			−0.103822
$101$	8247.05	+	2679.63i	0.808455	+	0.262683i	0.683943	−	0.729535i	$-0.260264\pi$
$101$	8247.05	+	2679.63i	0.808455	+	0.262683i	0.124512	+	0.992218i	$0.460264\pi$
$102$	−4026.29	+	2925.27i	−0.386995	+	0.281168i
$103$	−13839.0	−	10054.6i	−1.30445	−	0.947741i	−0.304466	−	0.952523i	$-0.598478\pi$
$103$	−13839.0	−	10054.6i	−1.30445	−	0.947741i	−0.999989	+	0.00478190i	$0.998478\pi$
$104$	−2989.09	−	9199.46i	−0.276358	−	0.850542i
$105$	−8913.12	+	2896.05i	−0.808446	+	0.262680i
$106$	−1079.54	+	1485.86i	−0.0960786	+	0.132241i
$107$	7525.74	+	10358.3i	0.657327	+	0.904734i	0.999389	−	0.0349438i	$-0.0111252\pi$
$107$	7525.74	+	10358.3i	0.657327	+	0.904734i	−0.342062	+	0.939677i	$0.611125\pi$
$108$	−1436.00	+	4419.56i	−0.123114	+	0.378906i
$109$		−	21394.0i		−	1.80069i	−0.435173	−	0.900347i	$-0.643313\pi$
$109$		−	21394.0i		−	1.80069i	0.435173	−	0.900347i	$-0.356687\pi$
$110$	7097.87	−	2824.87i	0.586601	−	0.233460i
$111$	4668.45			0.378902
$112$	6073.75	+	1973.48i	0.484195	+	0.157325i
$113$	−2614.92	+	1899.85i	−0.204786	+	0.148786i	−0.685452	−	0.728118i	$-0.740395\pi$
$113$	−2614.92	+	1899.85i	−0.204786	+	0.148786i	0.480665	+	0.876904i	$0.340395\pi$
$114$	14893.8	+	10821.0i	1.14603	+	0.832640i
$115$	−2894.21	−	8907.47i	−0.218844	−	0.673533i
$116$	546.721	−	177.640i	0.0406303	−	0.0132016i
$117$	−13942.3	+	19189.9i	−1.01850	+	1.40185i
$118$	−4642.37	−	6389.68i	−0.333408	−	0.458897i
$119$	−914.005	+	2813.02i	−0.0645438	+	0.198645i
$120$			19307.4i			1.34079i
$121$	−10637.1	+	10060.4i	−0.726527	+	0.687138i
$122$	−18959.5			−1.27382
$123$	412.545	+	134.044i	0.0272685	+	0.00886008i
$124$	2797.03	−	2032.16i	0.181909	−	0.132164i
$125$	13426.1	+	9754.61i	0.859268	+	0.624295i
$126$	−6196.35	−	19070.4i	−0.390297	−	1.20121i
$127$	3645.45	−	1184.48i	0.226018	−	0.0734378i	−0.193818	−	0.981037i	$-0.562087\pi$
$127$	3645.45	−	1184.48i	0.226018	−	0.0734378i	0.419837	+	0.907600i	$0.362087\pi$
$128$	5564.97	−	7659.53i	0.339659	−	0.467501i
$129$	−23303.9	−	32075.0i	−1.40039	−	1.92747i
$130$	−2742.09	+	8439.28i	−0.162254	+	0.499366i
$131$			24843.5i			1.44767i	0.689971	+	0.723837i	$0.257623\pi$
$131$			24843.5i			1.44767i	−0.689971	+	0.723837i	$0.742377\pi$
$132$	−2369.04	−	5952.53i	−0.135964	−	0.341628i
$133$	10941.2			0.618534
$134$	13621.3	+	4425.84i	0.758595	+	0.246482i
$135$	19919.7	−	14472.5i	1.09299	−	0.794102i
$136$	4929.75	+	3581.67i	0.266531	+	0.193646i
$137$	−133.385	−	410.518i	−0.00710668	−	0.0218721i	0.947440	−	0.319933i	$-0.103660\pi$
$137$	−133.385	−	410.518i	−0.00710668	−	0.0218721i	−0.954547	+	0.298061i	$0.903660\pi$
$138$	28205.4	−	9164.49i	1.48107	−	0.481227i
$139$	−17520.3	+	24114.6i	−0.906801	+	1.24810i	0.0614464	+	0.998110i	$0.480429\pi$
$139$	−17520.3	+	24114.6i	−0.906801	+	1.24810i	−0.968247	+	0.249994i	$0.919571\pi$
$140$	1167.76	+	1607.28i	0.0595794	+	0.0820040i
$141$	6525.27	−	20082.7i	0.328216	−	1.01015i
$142$		−	6202.48i		−	0.307602i
$143$	−1098.05	−	16971.0i	−0.0536971	−	0.829917i
$144$	−32263.4			−1.55591
$145$	−2896.80	−	941.227i	−0.137779	−	0.0447671i
$146$	−6493.81	+	4718.03i	−0.304645	+	0.221337i
$147$	16430.0	+	11937.1i	0.760331	+	0.552413i
$148$	−305.819	−	941.215i	−0.0139618	−	0.0429700i
$149$	−16775.4	+	5450.66i	−0.755615	+	0.245514i	−0.661396	−	0.750037i	$-0.730036\pi$
$149$	−16775.4	+	5450.66i	−0.755615	+	0.245514i	−0.0942196	+	0.995551i	$0.530036\pi$
$150$	−10238.5	+	14092.1i	−0.455045	+	0.626316i
$151$	13739.9	+	18911.4i	0.602602	+	0.829410i	0.995943	−	0.0899823i	$-0.0286810\pi$
$151$	13739.9	+	18911.4i	0.602602	+	0.829410i	−0.393342	+	0.919392i	$0.628681\pi$
$152$	6965.47	−	21437.5i	0.301483	−	0.927870i
$153$		−	14942.6i		−	0.638327i
$154$	12152.2	+	7681.69i	0.512404	+	0.323903i
$155$	−18318.6			−0.762479
$156$	7077.49	+	2299.62i	0.290824	+	0.0944944i
$157$	5550.70	−	4032.82i	0.225190	−	0.163610i	−0.469470	−	0.882948i	$-0.655555\pi$
$157$	5550.70	−	4032.82i	0.225190	−	0.163610i	0.694660	+	0.719339i	$0.255555\pi$
$158$	−10080.4	−	7323.81i	−0.403796	−	0.293375i
$159$	−2521.90	−	7761.62i	−0.0997548	−	0.307014i
$160$	7111.26	−	2310.59i	0.277784	−	0.0902574i
$161$	10360.1	−	14259.4i	0.399679	−	0.550111i
$162$	17249.1	+	23741.4i	0.657261	+	0.904642i
$163$	−3206.11	+	9867.40i	−0.120671	+	0.371388i	−0.993088	−	0.117376i	$-0.962552\pi$
$163$	−3206.11	+	9867.40i	−0.120671	+	0.371388i	0.872416	+	0.488763i	$0.162552\pi$
$164$		−	91.9551i		−	0.00341891i
$165$	−8383.37	+	32894.0i	−0.307929	+	1.20823i
$166$	39455.2			1.43182
$167$	−50732.0	−	16483.8i	−1.81907	−	0.591051i	−0.999846	−	0.0175744i	$-0.994406\pi$
$167$	−50732.0	−	16483.8i	−1.81907	−	0.591051i	−0.819222	−	0.573477i	$-0.805594\pi$
$168$	−29395.4	+	21357.0i	−1.04150	+	0.756696i
$169$	−7124.94	−	5176.57i	−0.249464	−	0.181246i
$170$	−1727.40	−	5316.39i	−0.0597716	−	0.183958i
$171$	−52569.4	+	17080.8i	−1.79780	+	0.584139i
$172$	−4940.13	+	6799.50i	−0.166986	+	0.229837i
$173$	11127.9	+	15316.2i	0.371809	+	0.511752i	0.953392	−	0.301736i	$-0.0975661\pi$
$173$	11127.9	+	15316.2i	0.371809	+	0.511752i	−0.581582	+	0.813488i	$0.697566\pi$
$174$	2980.39	−	9172.69i	0.0984406	−	0.302969i
$175$			10352.3i			0.338034i
$176$	17797.1	−	14776.5i	0.574544	−	0.477029i
$177$	35095.2			1.12021
$178$	−9387.95	−	3050.33i	−0.296299	−	0.0962735i
$179$	49361.8	−	35863.5i	1.54058	−	1.11930i	0.590616	−	0.806953i	$-0.298885\pi$
$179$	49361.8	−	35863.5i	1.54058	−	1.11930i	0.949968	−	0.312347i	$-0.101115\pi$
$180$	−8119.90	−	5899.45i	−0.250614	−	0.182082i
$181$	13152.2	+	40478.2i	0.401458	+	1.23556i	0.923817	+	0.382835i	$0.125052\pi$
$181$	13152.2	+	40478.2i	0.401458	+	1.23556i	−0.522359	+	0.852726i	$0.674948\pi$
$182$	−15881.9	+	5160.34i	−0.479468	+	0.155789i
$183$	49519.1	−	68157.1i	1.47867	−	2.03521i
$184$	−21343.4	−	29376.7i	−0.630418	−	0.867696i
$185$	−1620.38	+	4987.03i	−0.0473450	+	0.145713i
$186$		−	58005.5i		−	1.67665i
$187$	6843.62	+	8242.61i	0.195705	+	0.235712i
$188$	−4476.37			−0.126652
$189$	44068.5	+	14318.7i	1.23369	+	0.400849i
$190$	−16729.0	+	12154.3i	−0.463406	+	0.336684i
$191$	−40407.2	−	29357.6i	−1.10762	−	0.804736i	−0.125336	−	0.992114i	$-0.540001\pi$
$191$	−40407.2	−	29357.6i	−1.10762	−	0.804736i	−0.982288	+	0.187378i	$0.940001\pi$
$192$	22254.5	+	68492.3i	0.603692	+	1.85797i
$193$	62374.8	−	20266.8i	1.67454	−	0.544090i	0.690697	−	0.723145i	$-0.257304\pi$
$193$	62374.8	−	20266.8i	1.67454	−	0.544090i	0.983839	+	0.179055i	$0.0573040\pi$
$194$	−20619.8	+	28380.7i	−0.547874	+	0.754084i
$195$	−23176.3	−	31899.4i	−0.609502	−	0.838907i
$196$	1330.37	−	4094.46i	0.0346306	−	0.106582i
$197$			35687.2i			0.919559i	0.888033	+	0.459779i	$0.152072\pi$
$197$			35687.2i			0.919559i	−0.888033	+	0.459779i	$0.847928\pi$
$198$	−70379.6	−	17937.0i	−1.79522	−	0.457529i
$199$	−10569.8			−0.266907			−0.133453	−	0.991055i	$-0.542607\pi$
$199$	−10569.8			−0.266907			−0.133453	+	0.991055i	$0.542607\pi$
$200$	20283.6	+	6590.53i	0.507089	+	0.164763i
$201$	−51486.9	+	37407.4i	−1.27440	+	0.925903i
$202$	−24951.2	−	18128.1i	−0.611488	−	0.444272i
$203$	−1771.30	−	5451.49i	−0.0429832	−	0.132289i
$204$	−4458.52	+	1448.66i	−0.107135	+	0.0348102i
$205$	−286.383	+	394.172i	−0.00681458	+	0.00937947i
$206$	35760.6	+	49220.3i	0.842696	+	1.15987i
$207$	−27516.1	+	84685.8i	−0.642164	+	1.97638i
$208$			26869.1i			0.621049i
$209$	21175.3	−	33498.6i	0.484772	−	0.766891i
$210$	33332.2			0.755833
$211$	−22961.2	−	7460.53i	−0.515738	−	0.167573i	0.0395724	−	0.999217i	$-0.487400\pi$
$211$	−22961.2	−	7460.53i	−0.515738	−	0.167573i	−0.555310	+	0.831643i	$0.687400\pi$
$212$	−1399.63	+	1016.89i	−0.0311417	+	0.0226258i
$213$	22297.1	+	16199.8i	0.491462	+	0.357068i
$214$	−14071.9	−	43309.0i	−0.307274	−	0.945693i
$215$	42352.4	−	13761.1i	0.916224	−	0.297699i
$216$	56110.2	−	77229.0i	1.20264	−	1.65529i
$217$	−20263.1	−	27889.8i	−0.430316	−	0.592279i
$218$	−23513.4	+	72366.9i	−0.494770	+	1.52274i
$219$		−	35667.1i		−	0.743669i
$220$	7181.01	−	464.623i	0.148368	−	0.00959966i
$221$	−12444.2			−0.254791
$222$	−15791.4	−	5130.93i	−0.320416	−	0.104109i
$223$	−56598.8	+	41121.5i	−1.13815	+	0.826911i	−0.986860	−	0.161579i	$-0.948341\pi$
$223$	−56598.8	+	41121.5i	−1.13815	+	0.826911i	−0.151286	+	0.988490i	$0.548341\pi$
$224$	11384.0	+	8270.96i	0.226881	+	0.164839i
$225$	−16161.4	−	49739.6i	−0.319237	−	0.982511i
$226$	10933.2	−	3552.41i	0.214058	−	0.0695515i
$227$	26594.8	−	36604.7i	0.516114	−	0.710370i	−0.468821	−	0.883293i	$-0.655321\pi$
$227$	26594.8	−	36604.7i	0.516114	−	0.710370i	0.984935	+	0.172923i	$0.0553211\pi$
$228$	10193.0	+	14029.5i	0.196080	+	0.269881i
$229$	10716.1	−	32980.7i	0.204345	−	0.628910i	−0.795394	−	0.606092i	$-0.792736\pi$
$229$	10716.1	−	32980.7i	0.204345	−	0.628910i	0.999740	−	0.0228179i	$-0.00726379\pi$
$230$			33311.1i			0.629699i
$231$	−59354.1	+	23622.2i	−1.11231	+	0.442687i
$232$	−11808.9			−0.219399
$233$	−6091.22	−	1979.16i	−0.112200	−	0.0364559i	0.252379	−	0.967628i	$-0.418787\pi$
$233$	−6091.22	−	1979.16i	−0.112200	−	0.0364559i	−0.364579	+	0.931173i	$0.618787\pi$
$234$	68251.7	−	49587.7i	1.24647	−	0.905613i
$235$	19188.3	+	13941.1i	0.347457	+	0.252442i
$236$	−2299.00	−	7075.61i	−0.0412777	−	0.127040i
$237$	52656.4	−	17109.1i	0.937463	−	0.304600i
$238$	6183.38	−	8510.69i	0.109162	−	0.150249i
$239$	46589.7	+	64125.3i	0.815632	+	1.12262i	0.990430	+	0.138017i	$0.0440729\pi$
$239$	46589.7	+	64125.3i	0.815632	+	1.12262i	−0.174798	+	0.984604i	$0.555927\pi$
$240$	16573.1	−	51006.7i	0.287727	−	0.885533i
$241$			17413.4i			0.299813i	0.988700	+	0.149907i	$0.0478973\pi$
$241$			17413.4i			0.299813i	−0.988700	+	0.149907i	$0.952103\pi$
$242$	47037.7	−	22339.1i	0.803185	−	0.381448i
$243$	−18047.3			−0.305633
$244$	−16985.2	−	5518.82i	−0.285293	−	0.0926972i
$245$	−18454.4	+	13407.9i	−0.307445	+	0.223372i
$246$	−1248.14	−	906.828i	−0.0206250	−	0.0149849i
$247$	14225.0	+	43779.9i	0.233162	+	0.717598i
$248$	−67545.3	+	21946.8i	−1.09823	+	0.356836i
$249$	−103050.	+	141836.i	−1.66207	+	2.28765i
$250$	−34693.7	−	47751.8i	−0.555099	−	0.764029i
$251$	11753.2	−	36172.7i	0.186556	−	0.574160i	−0.813416	−	0.581683i	$-0.802394\pi$
$251$	11753.2	−	36172.7i	0.186556	−	0.574160i	0.999972	+	0.00752246i	$0.00239450\pi$
$252$		−	18888.2i		−	0.297433i
$253$	−23607.3	−	59316.5i	−0.368812	−	0.926689i
$254$	−13632.8			−0.211309
$255$	23623.4	+	7675.72i	0.363298	+	0.118043i
$256$	31743.3	−	23062.9i	0.484365	−	0.351912i
$257$	−71189.9	−	51722.5i	−1.07783	−	0.783092i	−0.100530	−	0.994934i	$-0.532054\pi$
$257$	−71189.9	−	51722.5i	−1.07783	−	0.783092i	−0.977304	+	0.211841i	$0.932054\pi$
$258$	43574.5	+	134109.i	0.654626	+	2.01473i
$259$	−9385.09	+	3049.40i	−0.139907	+	0.0454585i
$260$	−4913.08	+	6762.28i	−0.0726788	+	0.100034i
$261$	17021.1	+	23427.5i	0.249865	+	0.343910i
$262$	27304.7	−	84035.1i	0.397772	−	1.22422i
$263$			1908.11i			0.0275863i	0.999905	+	0.0137931i	$0.00439063\pi$
$263$			1908.11i			0.0275863i	−0.999905	+	0.0137931i	$0.995609\pi$
$264$	8497.45	+	131333.i	0.121922	+	1.88436i
$265$	9166.61			0.130532
$266$	−37009.6	−	12025.1i	−0.523059	−	0.169952i
$267$	35485.3	−	25781.6i	0.497766	−	0.361649i
$268$	10914.6	+	7929.90i	0.151963	+	0.110407i
$269$	−18872.3	−	58082.9i	−0.260807	−	0.802683i	−0.992630	−	0.121187i	$-0.961330\pi$
$269$	−18872.3	−	58082.9i	−0.260807	−	0.802683i	0.731822	−	0.681496i	$-0.238670\pi$
$270$	−83286.1	+	27061.3i	−1.14247	+	0.371211i
$271$	4245.02	−	5842.77i	0.0578018	−	0.0795573i	−0.779138	−	0.626853i	$-0.784343\pi$
$271$	4245.02	−	5842.77i	0.0578018	−	0.0795573i	0.836939	+	0.547296i	$0.184343\pi$
$272$	−9949.07	−	13693.7i	−0.134476	−	0.185090i
$273$	22930.0	−	70571.4i	0.307666	−	0.946898i
$274$			1535.21i			0.0204487i
$275$	31695.4	+	20035.5i	0.419113	+	0.264932i
$276$	27935.9			0.366728
$277$	19321.0	+	6277.77i	0.251808	+	0.0818174i	0.432201	−	0.901777i	$-0.357737\pi$
$277$	19321.0	+	6277.77i	0.251808	+	0.0818174i	−0.180393	+	0.983595i	$0.557737\pi$
$278$	85767.3	−	62313.6i	1.10977	−	0.806293i
$279$	140898.	+	102368.i	1.81008	+	1.31510i
$280$	−12611.5	−	38814.2i	−0.160861	−	0.495079i
$281$	−63587.0	+	20660.7i	−0.805296	+	0.261656i	−0.682604	−	0.730788i	$-0.739153\pi$
$281$	−63587.0	+	20660.7i	−0.805296	+	0.261656i	−0.122692	+	0.992445i	$0.539153\pi$
$282$	−44144.4	+	60759.6i	−0.555108	+	0.764040i
$283$	−7848.36	−	10802.3i	−0.0979955	−	0.134879i	0.757203	−	0.653179i	$-0.226565\pi$
$283$	−7848.36	−	10802.3i	−0.0979955	−	0.134879i	−0.855199	+	0.518300i	$0.826565\pi$
$284$	1805.44	−	5556.59i	0.0223845	−	0.0688924i
$285$		−	91883.4i		−	1.13122i
$286$	−14938.0	+	58612.4i	−0.182625	+	0.716568i
$287$	−916.906			−0.0111317
$288$	−67608.8	−	21967.4i	−0.815113	−	0.264846i
$289$	−61227.7	+	44484.6i	−0.733082	+	0.532615i
$290$	8764.17	+	6367.54i	0.104211	+	0.0757139i
$291$	−48169.7	−	148251.i	−0.568837	−	1.75070i
$292$	−7190.92	+	2336.47i	−0.0843371	+	0.0274028i
$293$	20572.5	−	28315.6i	0.239635	−	0.329830i	−0.672212	−	0.740358i	$-0.734656\pi$
$293$	20572.5	−	28315.6i	0.239635	−	0.329830i	0.911848	+	0.410529i	$0.134656\pi$
$294$	−42456.0	−	58435.7i	−0.491185	−	0.676058i
$295$	−12181.3	+	37490.1i	−0.139974	+	0.430797i
$296$			20329.8i			0.232033i
$297$	129128.	−	107212.i	1.46389	−	1.21543i
$298$	62734.7			0.706440
$299$	70526.6	+	22915.5i	0.788879	+	0.256322i
$300$	−13274.3	+	9644.35i	−0.147492	+	0.107159i
$301$	67799.5	+	49259.2i	0.748331	+	0.543694i
$302$	−25691.5	−	79070.2i	−0.281692	−	0.866960i
$303$	130336.	−	42348.8i	1.41965	−	0.461271i
$304$	−36803.0	+	50654.9i	−0.398232	+	0.548119i
$305$	55620.5	+	76555.1i	0.597909	+	0.822952i
$306$	−16422.9	+	50544.4i	−0.175391	+	0.539797i
$307$			41183.9i			0.436969i	0.975840	+	0.218484i	$0.0701113\pi$
$307$			41183.9i			0.436969i	−0.975840	+	0.218484i	$0.929889\pi$
$308$	8650.68	+	10419.1i	0.0911903	+	0.109832i
$309$	−270341.			−2.83136
$310$	61963.9	+	20133.3i	0.644785	+	0.209503i
$311$	−26765.2	+	19446.0i	−0.276725	+	0.201053i	−0.717488	−	0.696571i	$-0.754708\pi$
$311$	−26765.2	+	19446.0i	−0.276725	+	0.201053i	0.440762	+	0.897624i	$0.354708\pi$
$312$	−123675.	−	89854.9i	−1.27049	−	0.923066i
$313$	22727.2	+	69947.3i	0.231984	+	0.713974i	0.997507	+	0.0705652i	$0.0224803\pi$
$313$	22727.2	+	69947.3i	0.231984	+	0.713974i	−0.765523	+	0.643408i	$0.777520\pi$
$314$	−23208.0	+	7540.73i	−0.235384	+	0.0764811i
$315$	−58824.9	+	80965.5i	−0.592843	+	0.815979i
$316$	−6898.80	−	9495.38i	−0.0690875	−	0.0950907i
$317$	−49628.0	+	152739.i	−0.493865	+	1.51996i	0.324854	+	0.945764i	$0.394685\pi$
$317$	−49628.0	+	152739.i	−0.493865	+	1.51996i	−0.818719	+	0.574195i	$0.805315\pi$
$318$			29026.0i			0.287034i
$319$	−20118.8	−	5127.48i	−0.197707	−	0.0503875i
$320$	−80890.6			−0.789947
$321$	192444.	+	62528.8i	1.86764	+	0.606834i
$322$	−50715.8	+	36847.2i	−0.489138	+	0.355380i
$323$	−23460.5	−	17045.1i	−0.224871	−	0.163378i
$324$	8542.16	+	26290.1i	0.0813725	+	0.250439i
$325$	−41423.3	+	13459.3i	−0.392174	+	0.127425i
$326$	21689.8	−	29853.5i	0.204090	−	0.280905i
$327$	−198737.	−	273538.i	−1.85859	−	2.55813i
$328$	−583.725	+	1796.52i	−0.00542576	+	0.0166988i
$329$			44635.0i			0.412367i
$330$	64510.0	−	102053.i	0.592379	−	0.937122i
$331$	135669.			1.23829			0.619147	−	0.785275i	$-0.287478\pi$
$331$	135669.			1.23829			0.619147	+	0.785275i	$0.287478\pi$
$332$	35346.5	+	11484.8i	0.320679	+	0.104195i
$333$	40331.9	−	29302.9i	0.363715	−	0.264254i
$334$	153488.	+	111515.i	1.37588	+	0.999637i
$335$	−22089.4	−	67984.2i	−0.196832	−	0.605785i
$336$	95989.5	−	31188.9i	0.850247	−	0.276262i
$337$	57084.0	−	78569.4i	0.502637	−	0.691821i	−0.480019	−	0.877258i	$-0.659370\pi$
$337$	57084.0	−	78569.4i	0.502637	−	0.691821i	0.982656	+	0.185437i	$0.0593702\pi$
$338$	18411.2	+	25340.9i	0.161157	+	0.221814i
$339$	−15785.2	+	48581.8i	−0.137357	+	0.422741i
$340$		−	5265.59i		−	0.0455501i
$341$	−124606.	+	8062.24i	−1.07160	+	0.0693341i
$342$	196593.			1.68080
$343$	−117109.	−	38051.1i	−0.995413	−	0.323429i
$344$	139678.	−	101482.i	1.18035	−	0.857574i
$345$	−119749.	−	87002.9i	−1.00608	−	0.730963i
$346$	−20807.4	−	64038.5i	−0.173806	−	0.534920i
$347$	91169.0	−	29622.6i	0.757161	−	0.246016i	0.0951010	−	0.995468i	$-0.469683\pi$
$347$	91169.0	−	29622.6i	0.757161	−	0.246016i	0.662060	+	0.749451i	$0.269683\pi$
$348$	5340.05	−	7349.95i	0.0440947	−	0.0606912i
$349$	−32669.6	−	44965.8i	−0.268221	−	0.369174i	0.653567	−	0.756868i	$-0.273272\pi$
$349$	−32669.6	−	44965.8i	−0.268221	−	0.369174i	−0.921788	+	0.387694i	$0.873272\pi$
$350$	11377.8	−	35017.4i	0.0928804	−	0.285856i
$351$			194950.i			1.58238i
$352$	47355.2	−	18846.8i	0.382193	−	0.152108i
$353$	−56919.5			−0.456785			−0.228392	−	0.973569i	$-0.573347\pi$
$353$	−56919.5			−0.456785			−0.228392	+	0.973569i	$0.573347\pi$
$354$	−118712.	−	38571.9i	−0.947301	−	0.307797i
$355$	−25044.5	+	18195.9i	−0.198726	+	0.144383i
$356$	−7522.43	−	5465.37i	−0.0593551	−	0.0431240i
$357$	14444.9	+	44456.9i	0.113339	+	0.348821i
$358$	−206386.	+	67059.0i	−1.61033	+	0.523228i
$359$	29878.4	−	41124.1i	0.231830	−	0.319086i	−0.677215	−	0.735785i	$-0.736813\pi$
$359$	29878.4	−	41124.1i	0.231830	−	0.319086i	0.909044	+	0.416699i	$0.136813\pi$
$360$	121189.	+	166802.i	0.935098	+	1.28705i
$361$	7122.97	−	21922.3i	0.0546571	−	0.168217i
$362$		−	151376.i		−	1.15515i
$363$	−42548.2	+	227441.i	−0.322900	+	1.72606i
$364$	−15730.1			−0.118722
$365$	38101.0	+	12379.8i	0.285990	+	0.0929239i
$366$	−242411.	+	176122.i	−1.80963	+	1.31477i
$367$	20488.1	+	14885.4i	0.152114	+	0.110517i	0.661239	−	0.750175i	$-0.270031\pi$
$367$	20488.1	+	14885.4i	0.152114	+	0.110517i	−0.509125	+	0.860693i	$0.670031\pi$
$368$	31169.1	+	95928.7i	0.230159	+	0.708358i
$369$	4405.46	−	1431.42i	0.0323548	−	0.0105127i
$370$	10962.1	−	15088.1i	0.0800740	−	0.110212i
$371$	10139.7	+	13956.1i	0.0736676	+	0.101395i
$372$	16884.5	−	51965.1i	0.122012	−	0.375514i
$373$		−	246121.i		−	1.76901i	−0.466527	−	0.884507i	$-0.654495\pi$
$373$		−	246121.i		−	1.76901i	0.466527	−	0.884507i	$-0.345505\pi$
$374$	−14089.9	−	35402.8i	−0.100731	−	0.253101i
$375$	262276.			1.86507
$376$	87454.6	+	28415.7i	0.618596	+	0.200994i
$377$	19510.5	−	14175.2i	0.137273	−	0.0997348i
$378$	−133328.	−	96868.3i	−0.933119	−	0.677951i
$379$	67854.3	+	208834.i	0.472388	+	1.45386i	0.849448	+	0.527673i	$0.176935\pi$
$379$	67854.3	+	208834.i	0.472388	+	1.45386i	−0.377059	+	0.926189i	$0.623065\pi$
$380$	−18524.8	+	6019.07i	−0.128288	+	0.0416833i
$381$	35606.6	−	49008.3i	0.245290	−	0.337613i
$382$	104415.	+	143714.i	0.715541	+	0.984857i
$383$	16737.3	−	51512.2i	0.114101	−	0.351166i	−0.877658	−	0.479288i	$-0.840895\pi$
$383$	16737.3	−	51512.2i	0.114101	−	0.351166i	0.991758	+	0.128122i	$0.0408950\pi$
$384$		−	149628.i		−	1.01473i
$385$	−4632.87	−	71603.6i	−0.0312557	−	0.483073i
$386$	−233262.			−1.56556
$387$	−402656.	−	130831.i	−2.68852	−	0.873552i
$388$	−26733.7	+	19423.2i	−0.177581	+	0.129020i
$389$	−4944.93	−	3592.70i	−0.0326784	−	0.0237423i	0.571326	−	0.820723i	$-0.306429\pi$
$389$	−4944.93	−	3592.70i	−0.0326784	−	0.0237423i	−0.604005	+	0.796981i	$0.706429\pi$
$390$	43336.0	+	133374.i	0.284918	+	0.876887i
$391$	−44428.8	+	14435.8i	−0.290610	+	0.0944249i
$392$	−51982.7	+	71548.1i	−0.338288	+	0.465614i
$393$	230780.	+	317642.i	1.49422	+	2.05661i
$394$	39222.5	−	120714.i	0.252664	−	0.777619i
$395$			62188.1i			0.398578i
$396$	−57829.5	−	36555.5i	−0.368773	−	0.233111i
$397$	−121993.			−0.774022			−0.387011	−	0.922075i	$-0.626493\pi$
$397$	−121993.			−0.774022			−0.387011	+	0.922075i	$0.626493\pi$
$398$	35753.1	+	11616.9i	0.225708	+	0.0733370i
$399$	139892.	−	101637.i	0.878710	−	0.638420i
$400$	−47928.3	−	34821.9i	−0.299552	−	0.217637i
$401$	30.6968	+	94.4752i	0.000190900	+	0.000587529i	0.951152	−	0.308723i	$-0.0999017\pi$
$401$	30.6968	+	94.4752i	0.000190900	+	0.000587529i	−0.950961	+	0.309311i	$0.899902\pi$
$402$	215271.	−	69945.9i	1.33209	−	0.432823i
$403$	85252.8	−	117340.i	0.524927	−	0.722500i
$404$	−17076.1	−	23503.2i	−0.104623	−	0.144001i
$405$	45260.6	−	139298.i	0.275937	−	0.849247i
$406$			20386.8i			0.123680i
$407$	−8827.29	+	34635.8i	−0.0532891	+	0.209092i
$408$	96301.8			0.578514
$409$	−37657.4	−	12235.6i	−0.225115	−	0.0731441i	0.194288	−	0.980945i	$-0.437760\pi$
$409$	−37657.4	−	12235.6i	−0.225115	−	0.0731441i	−0.419402	+	0.907800i	$0.637760\pi$
$410$	1401.93	−	1018.56i	0.00833987	−	0.00605927i
$411$	−5518.87	−	4009.70i	−0.0326713	−	0.0237371i
$412$	17709.5	+	54504.1i	0.104330	+	0.321096i
$413$	−70552.6	+	22923.9i	−0.413631	+	0.134397i
$414$	186150.	−	256214.i	1.08608	−	1.49487i
$415$	−115747.	−	159313.i	−0.672071	−	0.925027i
$416$	−18294.5	+	56304.8i	−0.105715	+	0.325356i
$417$			471075.i			2.70905i
$418$	−108444.	+	90038.4i	−0.620660	+	0.515318i
$419$	167355.			0.953256			0.476628	−	0.879105i	$-0.341859\pi$
$419$	167355.			0.953256			0.476628	+	0.879105i	$0.341859\pi$
$420$	29861.2	+	9702.48i	0.169281	+	0.0550027i
$421$	230240.	−	167279.i	1.29902	−	0.943794i	0.299075	−	0.954230i	$-0.403322\pi$
$421$	230240.	−	167279.i	1.29902	−	0.943794i	0.999946	+	0.0104357i	$0.00332184\pi$
$422$	69468.2	+	50471.6i	0.390087	+	0.283415i
$423$	−69681.5	−	214458.i	−0.389436	−	1.19856i
$424$	33799.7	−	10982.2i	0.188010	−	0.0610882i
$425$	16127.6	−	22197.7i	0.0892875	−	0.122894i
$426$	−57617.1	−	79303.1i	−0.317491	−	0.436990i
$427$	−55029.5	+	169363.i	−0.301814	+	0.928889i
$428$		−	42895.1i		−	0.234164i
$429$	−171689.	−	206786.i	−0.932884	−	1.12358i
$430$	−158385.			−0.856596
$431$	−84558.1	−	27474.6i	−0.455198	−	0.147903i	0.0724387	−	0.997373i	$-0.476922\pi$
$431$	−84558.1	−	27474.6i	−0.455198	−	0.147903i	−0.527637	+	0.849470i	$0.676922\pi$
$432$	−214525.	+	155861.i	−1.14950	+	0.835162i
$433$	−48997.4	−	35598.7i	−0.261335	−	0.189871i	0.449401	−	0.893330i	$-0.351638\pi$
$433$	−48997.4	−	35598.7i	−0.261335	−	0.189871i	−0.710735	+	0.703460i	$0.751638\pi$
$434$	37888.8	+	116610.i	0.201156	+	0.619093i
$435$	−45781.0	+	14875.2i	−0.241940	+	0.0786110i
$436$	−42129.7	+	57986.6i	−0.221623	+	0.305038i
$437$	101573.	+	139803.i	0.531881	+	0.732071i
$438$	−39200.5	+	120647.i	−0.204335	+	0.628879i
$439$		−	158687.i		−	0.823401i	−0.911319	−	0.411701i	$-0.864935\pi$
$439$		−	158687.i		−	0.823401i	0.911319	−	0.411701i	$-0.135065\pi$
$440$	−143244.	−	36507.3i	−0.739898	−	0.188571i
$441$	216870.			1.11512
$442$	42093.6	+	13677.0i	0.215462	+	0.0700079i
$443$	−57293.4	+	41626.1i	−0.291943	+	0.212109i	−0.724110	−	0.689685i	$-0.757749\pi$
$443$	−57293.4	+	41626.1i	−0.291943	+	0.212109i	0.432167	+	0.901794i	$0.357749\pi$
$444$	−12653.4	−	9193.24i	−0.0641862	−	0.0466340i
$445$	15224.2	+	46855.4i	0.0768804	+	0.236614i
$446$	236645.	−	76890.6i	1.18967	−	0.386548i
$447$	−163852.	+	225523.i	−0.820045	+	1.12870i
$448$	−89477.4	−	123155.i	−0.445818	−	0.613616i
$449$	−56221.7	+	173033.i	−0.278876	+	0.858292i	0.709292	+	0.704915i	$0.249015\pi$
$449$	−56221.7	+	173033.i	−0.278876	+	0.858292i	−0.988168	+	0.153377i	$0.950985\pi$
$450$			186010.i			0.918570i
$451$	−1774.55	+	2807.27i	−0.00872438	+	0.0138017i
$452$	10828.7			0.0530030
$453$	351349.	+	114160.i	1.71215	+	0.556312i
$454$	−130190.	+	94588.5i	−0.631634	+	0.458909i
$455$	67428.4	+	48989.6i	0.325702	+	0.236636i
$456$	−110082.	−	338798.i	−0.529404	−	1.62934i
$457$	227035.	−	73768.1i	1.08708	−	0.353213i	0.289960	−	0.957039i	$-0.406358\pi$
$457$	227035.	−	73768.1i	1.08708	−	0.353213i	0.797116	+	0.603826i	$0.206358\pi$
$458$	−72495.8	+	99781.9i	−0.345607	+	0.475687i
$459$	−72186.1	−	99355.7i	−0.342632	−	0.471593i
$460$	−9696.33	+	29842.2i	−0.0458239	+	0.141031i
$461$		−	229797.i		−	1.08129i	−0.841251	−	0.540645i	$-0.818180\pi$
$461$		−	229797.i		−	1.08129i	0.841251	−	0.540645i	$-0.181820\pi$
$462$	226732.	−	14670.0i	1.06226	−	0.0687297i
$463$	−273524.			−1.27595			−0.637976	−	0.770057i	$-0.720228\pi$
$463$	−273524.			−1.27595			−0.637976	+	0.770057i	$0.720228\pi$
$464$	31197.0	+	10136.5i	0.144903	+	0.0470818i
$465$	−234216.	+	170168.i	−1.08320	+	0.786993i
$466$	18428.8	+	13389.3i	0.0848642	+	0.0616575i
$467$	45298.9	+	139416.i	0.207708	+	0.639260i	0.999591	+	0.0285876i	$0.00910094\pi$
$467$	45298.9	+	139416.i	0.207708	+	0.639260i	−0.791883	+	0.610673i	$0.790899\pi$
$468$	75578.5	−	24556.9i	0.345069	−	0.112120i
$469$	79071.0	−	108832.i	0.359477	−	0.494778i
$470$	−49583.6	−	68246.0i	−0.224462	−	0.308945i
$471$	33507.3	−	103125.i	0.151042	−	0.464859i
$472$			152830.i			0.686000i
$473$	282033.	−	112246.i	1.26060	−	0.501704i
$474$	−196918.			−0.876453
$475$	−96528.8	−	31364.1i	−0.427828	−	0.139010i
$476$	8016.80	−	5824.55i	0.0353824	−	0.0257068i
$477$	−70505.4	−	51225.2i	−0.309874	−	0.225137i
$478$	−87115.4	−	268114.i	−0.381276	−	1.17345i
$479$	−150250.	+	48819.1i	−0.654851	+	0.212774i	−0.617552	−	0.786530i	$-0.711875\pi$
$479$	−150250.	+	48819.1i	−0.654851	+	0.212774i	−0.0372992	+	0.999304i	$0.511875\pi$
$480$	69458.6	−	95601.6i	0.301470	−	0.414937i
$481$	−24403.5	−	33588.6i	−0.105478	−	0.145178i
$482$	19138.5	−	58902.3i	0.0823785	−	0.253535i
$483$		−	278555.i		−	1.19404i
$484$	48642.0	−	6320.91i	0.207645	−	0.0269829i
$485$	175087.			0.744339
$486$	61046.3	+	19835.2i	0.258456	+	0.0839775i
$487$	146114.	−	106158.i	0.616075	−	0.447605i	−0.235473	−	0.971881i	$-0.575664\pi$
$487$	146114.	−	106158.i	0.616075	−	0.447605i	0.851548	+	0.524276i	$0.175664\pi$
$488$	296805.	+	215642.i	1.24633	+	0.905510i
$489$	50669.4	+	155944.i	0.211899	+	0.652157i
$490$	77159.6	−	25070.7i	0.321364	−	0.104418i
$491$	51972.2	−	71533.6i	0.215580	−	0.296720i	−0.687507	−	0.726177i	$-0.741295\pi$
$491$	51972.2	−	71533.6i	0.215580	−	0.296720i	0.903087	+	0.429457i	$0.141295\pi$
$492$	−854.203	−	1175.71i	−0.00352883	−	0.00485702i
$493$	−4694.66	+	14448.7i	−0.0193157	+	0.0594476i
$494$		−	163723.i		−	0.670897i
$495$	134043.	+	336801.i	0.547057	+	1.37456i
$496$	197281.			0.801903
$497$	−55406.1	−	18002.5i	−0.224308	−	0.0728821i
$498$	504462.	−	366513.i	2.03409	−	1.47785i
$499$	−58425.2	−	42448.4i	−0.234638	−	0.170475i	0.464253	−	0.885703i	$-0.346323\pi$
$499$	−58425.2	−	42448.4i	−0.234638	−	0.170475i	−0.698891	+	0.715228i	$0.746323\pi$
$500$	−17181.1	−	52878.0i	−0.0687244	−	0.211512i
$501$	−801768.	+	260510.i	−3.19428	+	1.03789i
$502$	−79512.2	+	109439.i	−0.315520	+	0.434276i
$503$	−262146.	−	360812.i	−1.03611	−	1.42609i	−0.900258	−	0.435356i	$-0.856622\pi$
$503$	−262146.	−	360812.i	−1.03611	−	1.42609i	−0.135853	−	0.990729i	$-0.543378\pi$
$504$	−119901.	+	369017.i	−0.472021	+	1.45273i
$505$			153930.i			0.603586i
$506$	14660.6	+	226588.i	0.0572601	+	0.884986i
$507$	−139184.			−0.541470
$508$	−12213.2	−	3968.30i	−0.0473261	−	0.0153772i
$509$	−274741.	+	199611.i	−1.06044	+	0.770457i	−0.974170	−	0.225814i	$-0.927496\pi$
$509$	−274741.	+	199611.i	−1.06044	+	0.770457i	−0.0862731	+	0.996272i	$0.527496\pi$
$510$	−71471.9	−	51927.4i	−0.274786	−	0.199644i
$511$	23297.5	+	71702.4i	0.0892212	+	0.274595i
$512$	−276791.	+	89934.8i	−1.05587	+	0.343074i
$513$	−267027.	+	367531.i	−1.01466	+	1.39656i
$514$	183959.	+	253197.i	0.696296	+	0.958370i
$515$	93833.5	−	288790.i	0.353788	−	1.08885i
$516$			132827.i			0.498870i
$517$	136658.	+	86385.0i	0.511274	+	0.323190i
$518$	35097.2			0.130802
$519$	284556.	+	92457.7i	1.05641	+	0.343248i
$520$	138913.	−	100926.i	0.513732	−	0.373248i
$521$	−314293.	−	228348.i	−1.15787	−	0.841242i	−0.168363	−	0.985725i	$-0.553848\pi$
$521$	−314293.	−	228348.i	−1.15787	−	0.841242i	−0.989507	+	0.144483i	$0.953848\pi$
$522$	−31826.7	−	97952.5i	−0.116802	−	0.359480i
$523$	−136425.	+	44327.1i	−0.498758	+	0.162056i	−0.547584	−	0.836751i	$-0.684452\pi$
$523$	−136425.	+	44327.1i	−0.498758	+	0.162056i	0.0488254	+	0.998807i	$0.484452\pi$
$524$	48922.6	−	67336.1i	0.178175	−	0.245237i
$525$	96166.2	+	132361.i	0.348902	+	0.480223i
$526$	2097.14	−	6454.34i	0.00757978	−	0.0233282i
$527$			91369.5i			0.328988i
$528$	90284.4	−	354251.i	0.323851	−	1.27070i
$529$	−1462.13			−0.00522487
$530$	−31006.7	−	10074.7i	−0.110384	−	0.0358658i
$531$	303196.	−	220285.i	1.07531	−	0.781261i
$532$	−29655.3	−	21545.8i	−0.104780	−	0.0761271i
$533$	−1192.09	−	3668.88i	−0.00419619	−	0.0129145i
$534$	−148367.	+	48207.4i	−0.520302	+	0.169056i
$535$	−133592.	+	183873.i	−0.466736	+	0.642407i
$536$	−162899.	−	224211.i	−0.567007	−	0.780419i
$537$	297977.	−	917080.i	1.03332	−	3.18023i
$538$			217212.i			0.750445i
$539$	−119629.	+	99325.1i	−0.411775	+	0.341886i
$540$	−82490.2			−0.282888
$541$	342946.	+	111430.i	1.17174	+	0.380721i	0.829292	−	0.558815i	$-0.188744\pi$
$541$	342946.	+	111430.i	1.17174	+	0.380721i	0.342448	+	0.939537i	$0.388744\pi$
$542$	−20780.7	+	15098.0i	−0.0707394	+	0.0513952i
$543$	544176.	+	395367.i	1.84561	+	1.34091i
$544$	−11524.8	−	35469.6i	−0.0389435	−	0.119856i
$545$	361184.	−	117356.i	1.21601	−	0.395104i
$546$	−155125.	+	213511.i	−0.520351	+	0.716202i
$547$	345895.	+	476084.i	1.15603	+	1.59114i	0.724900	+	0.688854i	$0.241886\pi$
$547$	345895.	+	476084.i	1.15603	+	1.59114i	0.431133	+	0.902289i	$0.358114\pi$
$548$	−446.874	+	1375.34i	−0.00148807	+	0.00457982i
$549$		−	899648.i		−	2.98489i
$550$	−85191.8	−	102607.i	−0.281626	−	0.339196i
$551$	56198.2			0.185106
$552$	−545782.	−	177335.i	−1.79119	−	0.581992i
$553$	−94680.8	+	68789.6i	−0.309608	+	0.224943i
$554$	−58455.0	−	42470.0i	−0.190459	−	0.138377i
$555$	25608.5	+	78814.9i	0.0831378	+	0.255872i
$556$	94974.4	−	30859.0i	0.307225	−	0.0998235i
$557$	−227035.	+	312486.i	−0.731782	+	1.00721i	0.267267	+	0.963622i	$0.413879\pi$
$557$	−227035.	+	312486.i	−0.731782	+	1.00721i	−0.999050	+	0.0435893i	$0.986121\pi$
$558$	−364089.	−	501125.i	−1.16933	−	1.60945i
$559$	−108957.	+	335334.i	−0.348682	+	1.07313i
$560$			113365.i			0.361497i
$561$	164069.	+	41814.7i	0.521316	+	0.132863i
$562$	237795.			0.752887
$563$	37883.9	+	12309.2i	0.119519	+	0.0388342i	0.368166	−	0.929760i	$-0.379986\pi$
$563$	37883.9	+	12309.2i	0.119519	+	0.0388342i	−0.248647	+	0.968594i	$0.579986\pi$
$564$	−57233.6	+	41582.6i	−0.179925	+	0.130724i
$565$	−46418.1	−	33724.7i	−0.145409	−	0.105646i
$566$	14675.2	+	45165.6i	0.0458090	+	0.140986i
$567$	262145.	−	85175.9i	0.815408	−	0.264942i
$568$	−70545.7	+	97097.9i	−0.218662	+	0.300963i
$569$	−35162.0	−	48396.4i	−0.108605	−	0.149482i	0.751255	−	0.660012i	$-0.229449\pi$
$569$	−35162.0	−	48396.4i	−0.108605	−	0.149482i	−0.859860	+	0.510531i	$0.829449\pi$
$570$	−100986.	+	310802.i	−0.310821	+	0.956610i
$571$			54543.1i			0.167289i	0.996496	+	0.0836445i	$0.0266560\pi$
$571$			54543.1i			0.167289i	−0.996496	+	0.0836445i	$0.973344\pi$
$572$	−30443.5	+	48160.6i	−0.0930472	+	0.147197i
$573$	−789348.			−2.40414
$574$	3101.50	+	1007.74i	0.00941344	+	0.00305861i
$575$	−132277.	+	96105.2i	−0.400083	+	0.290677i
$576$	622174.	+	452036.i	1.87528	+	1.36247i
$577$	−143516.	−	441697.i	−0.431071	−	1.32670i	−0.897059	−	0.441910i	$-0.854301\pi$
$577$	−143516.	−	441697.i	−0.431071	−	1.32670i	0.465988	−	0.884791i	$-0.345699\pi$
$578$	255999.	−	83179.1i	0.766271	−	0.248976i
$579$	609240.	−	838547.i	1.81732	−	2.50133i
$580$	5998.02	+	8255.57i	0.0178300	+	0.0245409i
$581$	114518.	−	352449.i	0.339250	−	1.04410i
$582$			554412.i			1.63677i
$583$	62353.0	−	4034.34i	0.183451	−	0.0118696i
$584$	155320.			0.455410
$585$	−400452.	−	130115.i	−1.17014	−	0.380203i
$586$	−100709.	+	73169.0i	−0.293272	+	0.213075i
$587$	−97704.5	−	70986.5i	−0.283556	−	0.206015i	0.436911	−	0.899505i	$-0.356072\pi$
$587$	−97704.5	−	70986.5i	−0.283556	−	0.206015i	−0.720467	+	0.693489i	$0.756072\pi$
$588$	−21025.2	−	64708.8i	−0.0608114	−	0.187158i
$589$	321446.	−	104444.i	0.926569	−	0.301060i
$590$	82408.1	−	113425.i	0.236737	−	0.325840i
$591$	331511.	+	456286.i	0.949124	+	1.30636i
$592$	17450.7	−	53707.6i	0.0497930	−	0.153247i
$593$			567951.i			1.61511i	0.589794	+	0.807554i	$0.299209\pi$
$593$			567951.i			1.61511i	−0.589794	+	0.807554i	$0.700791\pi$
$594$	−554617.	+	220731.i	−1.57188	+	0.625592i
$595$	−52504.4			−0.148307
$596$	56201.8	+	18261.1i	0.158219	+	0.0514084i
$597$	−135142.	+	98186.5i	−0.379177	+	0.275488i
$598$	−213376.	−	155027.i	−0.596682	−	0.433515i
$599$	−31518.1	−	97002.7i	−0.0878428	−	0.270352i	0.897480	−	0.441056i	$-0.145396\pi$
$599$	−31518.1	−	97002.7i	−0.0878428	−	0.270352i	−0.985322	+	0.170704i	$0.945396\pi$
$600$	320561.	−	104157.i	0.890448	−	0.289324i
$601$	−235833.	+	324596.i	−0.652912	+	0.898657i	−0.999221	−	0.0394638i	$-0.987435\pi$
$601$	−235833.	+	324596.i	−0.652912	+	0.898657i	0.346309	+	0.938121i	$0.387435\pi$
$602$	−175198.	−	241139.i	−0.483432	−	0.665387i
$603$	−210010.	+	646345.i	−0.577572	+	1.77758i
$604$		−	78314.6i		−	0.214669i
$605$	−228193.	−	124395.i	−0.623436	−	0.339853i
$606$	−487416.			−1.32726
$607$	−249048.	−	80920.5i	−0.675935	−	0.219625i	−0.0491203	−	0.998793i	$-0.515642\pi$
$607$	−249048.	−	80920.5i	−0.675935	−	0.219625i	−0.626815	+	0.779168i	$0.715642\pi$
$608$	−111611.	+	81090.4i	−0.301927	+	0.219363i
$609$	−73288.1	−	53246.9i	−0.197605	−	0.143569i
$610$	−104002.	−	320084.i	−0.279499	−	0.860209i
$611$	−178601.	+	58031.0i	−0.478411	+	0.155445i
$612$	−29425.4	+	40500.5i	−0.0785631	+	0.108133i
$613$	−49274.5	−	67820.6i	−0.131130	−	0.180485i	0.738403	−	0.674359i	$-0.235580\pi$
$613$	−49274.5	−	67820.6i	−0.131130	−	0.180485i	−0.869533	+	0.493875i	$0.835580\pi$
$614$	45263.7	−	139307.i	0.120064	−	0.369520i
$615$			7700.08i			0.0203585i
$616$	−102868.	−	258471.i	−0.271094	−	0.681161i
$617$	699485.			1.83742			0.918709	−	0.394936i	$-0.129233\pi$
$617$	699485.			1.83742			0.918709	+	0.394936i	$0.129233\pi$
$618$	914450.	+	297123.i	2.39432	+	0.777963i
$619$	261946.	−	190315.i	0.683645	−	0.496697i	−0.190920	−	0.981606i	$-0.561147\pi$
$619$	261946.	−	190315.i	0.683645	−	0.496697i	0.874565	+	0.484909i	$0.161147\pi$
$620$	49650.8	+	36073.4i	0.129164	+	0.0938434i
$621$	226150.	+	696017.i	0.586425	+	1.80483i
$622$	111908.	−	36361.0i	0.289254	−	0.0939842i
$623$	−54496.5	+	75008.0i	−0.140408	+	0.193255i
$624$	249596.	+	343540.i	0.641016	+	0.882283i
$625$	−31182.8	+	95970.7i	−0.0798279	+	0.245685i
$626$		−	261581.i		−	0.667509i
$627$	−40439.1	−	625008.i	−0.102865	−	1.58983i
$628$	−22986.2			−0.0582838
$629$	24874.3	+	8082.16i	0.0628710	+	0.0204280i
$630$	287966.	−	209219.i	0.725538	−	0.527134i
$631$	−378867.	−	275263.i	−0.951541	−	0.691335i	−0.000370493	−	1.00000i	$-0.500118\pi$
$631$	−378867.	−	275263.i	−0.951541	−	0.691335i	−0.951171	+	0.308665i	$0.900118\pi$
$632$	74505.3	+	229304.i	0.186532	+	0.574086i
$633$	−362878.	+	117906.i	−0.905635	+	0.294259i
$634$	335741.	−	462107.i	0.835267	−	1.14965i
$635$	39993.9	+	55046.8i	0.0991850	+	0.136516i
$636$	−8449.00	+	26003.4i	−0.0208877	+	0.0642858i
$637$		−	180610.i		−	0.445105i
$638$	62417.9	+	39456.0i	0.153344	+	0.0969329i
$639$	294314.			0.720790
$640$	159838.	+	51934.6i	0.390230	+	0.126793i
$641$	−249904.	+	181566.i	−0.608216	+	0.441895i	−0.848786	−	0.528737i	$-0.822666\pi$
$641$	−249904.	+	181566.i	−0.608216	+	0.441895i	0.240570	+	0.970632i	$0.422666\pi$
$642$	−582232.	−	423017.i	−1.41262	−	1.02633i
$643$	−68532.0	−	210920.i	−0.165757	−	0.510147i	0.833334	−	0.552769i	$-0.186429\pi$
$643$	−68532.0	−	210920.i	−0.165757	−	0.510147i	−0.999091	+	0.0426219i	$0.986429\pi$
$644$	−56160.1	+	18247.5i	−0.135412	+	0.0439980i
$645$	413674.	−	569373.i	0.994348	−	1.36860i
$646$	60623.3	+	83440.8i	0.145270	+	0.199946i
$647$	87456.3	−	269163.i	0.208921	−	0.642994i	−0.790608	−	0.612322i	$-0.790236\pi$
$647$	87456.3	−	269163.i	0.208921	−	0.642994i	0.999530	−	0.0306713i	$-0.00976449\pi$
$648$		−	567852.i		−	1.35234i
$649$	−66359.3	+	260376.i	−0.157548	+	0.618174i
$650$	154910.			0.366651
$651$	−518157.	−	168359.i	−1.22264	−	0.397261i
$652$	28121.0	−	20431.1i	0.0661509	−	0.0480615i
$653$	530719.	+	385590.i	1.24462	+	0.904273i	0.997897	−	0.0648122i	$-0.0206448\pi$
$653$	530719.	+	385590.i	1.24462	+	0.904273i	0.246727	+	0.969085i	$0.420645\pi$
$654$	371606.	+	1.14369e6i	0.868816	+	2.67394i
$655$	−419420.	+	136278.i	−0.977613	+	0.317646i
$656$	3084.19	−	4245.02i	0.00716693	−	0.00986444i
$657$	−223875.	−	308137.i	−0.518650	−	0.713861i
$658$	49056.8	−	150981.i	0.113304	−	0.348715i
$659$			266782.i			0.614307i	0.951660	+	0.307154i	$0.0993765\pi$
$659$			266782.i			0.614307i	−0.951660	+	0.307154i	$0.900623\pi$
$660$	87498.2	−	72647.5i	0.200868	−	0.166776i
$661$	121616.			0.278349			0.139174	−	0.990268i	$-0.455555\pi$
$661$	121616.			0.278349			0.139174	+	0.990268i	$0.455555\pi$
$662$	−458910.	−	149109.i	−1.04716	−	0.340241i
$663$	−159108.	+	115599.i	−0.361964	+	0.262983i
$664$	−617658.	−	448755.i	−1.40092	−	1.01783i
$665$	60017.7	+	184715.i	0.135717	+	0.417695i
$666$	−168632.	+	54791.7i	−0.380181	+	0.123528i
$667$	53213.2	−	73241.7i	0.119610	−	0.164629i
$668$	105044.	+	144581.i	0.235406	+	0.324009i
$669$	−341664.	+	1.05153e6i	−0.763391	+	2.34948i
$670$			254239.i			0.566361i
$671$	412034.	+	496263.i	0.915141	+	1.10222i
$672$	222384.			0.492454
$673$	−424599.	−	137961.i	−0.937452	−	0.304596i	−0.199845	−	0.979827i	$-0.564044\pi$
$673$	−424599.	−	137961.i	−0.937452	−	0.304596i	−0.737606	+	0.675231i	$0.764044\pi$
$674$	−279444.	+	203028.i	−0.615141	+	0.446926i
$675$	−347747.	−	252653.i	−0.763231	−	0.554519i
$676$	9117.65	+	28061.2i	0.0199521	+	0.0614064i
$677$	443664.	−	144155.i	0.968002	−	0.314523i	0.217993	−	0.975950i	$-0.430049\pi$
$677$	443664.	−	144155.i	0.968002	−	0.314523i	0.750009	+	0.661427i	$0.230049\pi$
$678$	106789.	−	146983.i	0.232310	−	0.319747i
$679$	193673.	+	266568.i	0.420078	+	0.578188i
$680$	−33425.6	+	102873.i	−0.0722872	+	0.222477i
$681$		−	715066.i		−	1.54188i
$682$	430351.	+	109679.i	0.925239	+	0.235806i
$683$	468573.			1.00447			0.502233	−	0.864732i	$-0.332512\pi$
$683$	468573.			1.00447			0.502233	+	0.864732i	$0.332512\pi$
$684$	176120.	+	57225.0i	0.376442	+	0.122313i
$685$	6198.88	−	4503.75i	0.0132109	−	0.00959827i
$686$	354310.	+	257422.i	0.752897	+	0.547012i
$687$	−169357.	−	521227.i	−0.358830	−	1.10437i
$688$	−456113.	+	148200.i	−0.963597	+	0.313092i
$689$	−42660.5	+	58717.2i	−0.0898644	+	0.123688i
$690$	309439.	+	425906.i	0.649945	+	0.894572i
$691$	14366.7	−	44216.1i	0.0300885	−	0.0926029i	−0.934885	−	0.354952i	$-0.884497\pi$
$691$	14366.7	−	44216.1i	0.0300885	−	0.0926029i	0.964973	+	0.262349i	$0.0844972\pi$
$692$		−	63426.5i		−	0.132452i
$693$	−364504.	+	576632.i	−0.758989	+	1.20069i
$694$	−340943.			−0.707885
$695$	−503221.	−	163507.i	−1.04181	−	0.338505i
$696$	−150985.	+	109697.i	−0.311685	+	0.226453i
$697$	1966.06	+	1428.42i	0.00404697	+	0.00294030i
$698$	61086.9	+	188006.i	0.125383	+	0.385888i
$699$	−96265.6	+	31278.6i	−0.197023	+	0.0640166i
$700$	20386.0	−	28059.0i	0.0416041	−	0.0572632i
$701$	−551414.	−	758956.i	−1.12213	−	1.54447i	−0.802224	−	0.597023i	$-0.796350\pi$
$701$	−551414.	−	758956.i	−1.12213	−	1.54447i	−0.319902	−	0.947451i	$-0.603650\pi$
$702$	214263.	−	659434.i	0.434784	−	1.33813i
$703$		−	96748.8i		−	0.195765i
$704$	−550233.	+	35601.0i	−1.11020	+	0.0718318i
$705$	374840.			0.754167
$706$	192534.	+	62558.2i	0.386277	+	0.125509i
$707$	−234356.	+	170270.i	−0.468854	+	0.340642i
$708$	−95122.3	−	69110.4i	−0.189765	−	0.137872i
$709$	159258.	+	490145.i	0.316816	+	0.975061i	0.975000	+	0.222204i	$0.0713250\pi$
$709$	159258.	+	490145.i	0.316816	+	0.975061i	−0.658184	+	0.752857i	$0.728675\pi$
$710$	104713.	−	34023.4i	0.207723	−	0.0674934i
$711$	347522.	−	478323.i	0.687453	−	0.946198i
$712$	112272.	+	154529.i	0.221467	+	0.304824i
$713$	168253.	−	517829.i	0.330966	−	1.01861i
$714$		−	166255.i		−	0.326120i
$715$	280489.	−	111631.i	0.548660	−	0.218360i
$716$	−204414.			−0.398736
$717$	1.19136e6	+	387098.i	2.31743	+	0.752978i
$718$	−146264.	+	106267.i	−0.283719	+	0.206134i
$719$	−232894.	−	169208.i	−0.450507	−	0.327312i	0.339289	−	0.940682i	$-0.389814\pi$
$719$	−232894.	−	169208.i	−0.450507	−	0.327312i	−0.789796	+	0.613370i	$0.789814\pi$
$720$	−176979.	−	544686.i	−0.341395	−	1.05071i
$721$	543474.	−	176585.i	1.04546	−	0.339691i
$722$	−48188.0	+	66325.0i	−0.0924409	+	0.127234i
$723$	161760.	+	222643.i	0.309452	+	0.425925i
$724$	44063.1	−	135612.i	0.0840616	−	0.258715i
$725$			53173.2i			0.101162i
$726$	393894.	−	722572.i	0.747320	−	1.37091i
$727$	−263581.			−0.498706			−0.249353	−	0.968413i	$-0.580218\pi$
$727$	−263581.			−0.498706			−0.249353	+	0.968413i	$0.580218\pi$
$728$	307319.	+	99853.9i	0.579864	+	0.188409i
$729$	309945.	−	225188.i	0.583217	−	0.423732i
$730$	−115273.	−	83751.0i	−0.216313	−	0.157161i
$731$	−68638.0	−	211246.i	−0.128449	−	0.395324i
$732$	−268434.	+	87219.4i	−0.500974	+	0.162776i
$733$	−83867.7	+	115434.i	−0.156094	+	0.214845i	−0.879900	−	0.475158i	$-0.842391\pi$
$733$	−83867.7	+	115434.i	−0.156094	+	0.214845i	0.723806	+	0.690003i	$0.242391\pi$
$734$	−52942.3	−	72868.8i	−0.0982677	−	0.135254i
$735$	−111402.	+	342859.i	−0.206214	+	0.634660i
$736$			222243.i			0.410273i
$737$	−180177.	−	452719.i	−0.331715	−	0.833478i
$738$	−16475.0			−0.0302491
$739$	229806.	+	74668.6i	0.420798	+	0.136725i	0.511759	−	0.859129i	$-0.328994\pi$
$739$	229806.	+	74668.6i	0.420798	+	0.136725i	−0.0909615	+	0.995854i	$0.528994\pi$
$740$	14212.5	−	10326.0i	0.0259541	−	0.0188568i
$741$	588564.	+	427617.i	1.07191	+	0.778786i
$742$	−18959.6	−	58351.6i	−0.0344367	−	0.105985i
$743$	368874.	−	119854.i	0.668191	−	0.217108i	0.0447731	−	0.998997i	$-0.485744\pi$
$743$	368874.	−	119854.i	0.668191	−	0.217108i	0.623418	+	0.781889i	$0.285744\pi$
$744$	−659743.	+	908058.i	−1.19187	+	1.64047i
$745$	−184041.	−	253311.i	−0.331591	−	0.456396i
$746$	−270503.	+	832523.i	−0.486065	+	1.49596i
$747$			1.87219e6i			3.35512i
$748$	−2317.45	−	35817.5i	−0.00414198	−	0.0640165i
$749$	−427718.			−0.762419
$750$	−887167.	−	288258.i	−1.57719	−	0.512459i
$751$	716843.	−	520817.i	1.27100	−	0.923432i	0.271753	−	0.962367i	$-0.412396\pi$
$751$	716843.	−	520817.i	1.27100	−	0.923432i	0.999242	+	0.0389349i	$0.0123965\pi$
$752$	−206648.	−	150138.i	−0.365422	−	0.265495i
$753$	−185748.	−	571673.i	−0.327592	−	1.00823i
$754$	−81575.2	+	26505.4i	−0.143488	+	0.0466221i
$755$	−243901.	+	335701.i	−0.427878	+	0.588924i
$756$	−91246.9	−	125591.i	−0.159652	−	0.219742i
$757$	−115343.	+	354989.i	−0.201279	+	0.619475i	0.798566	+	0.601907i	$0.205592\pi$
$757$	−115343.	+	354989.i	−0.201279	+	0.619475i	−0.999846	+	0.0175675i	$0.994408\pi$
$758$		−	780973.i		−	1.35925i
$759$	−852847.	−	539106.i	−1.48043	−	0.935817i
$760$	400127.			0.692740
$761$	−244306.	−	79379.9i	−0.421857	−	0.137070i	0.0903927	−	0.995906i	$-0.471188\pi$
$761$	−244306.	−	79379.9i	−0.421857	−	0.137070i	−0.512250	+	0.858837i	$0.671188\pi$
$762$	−174305.	+	126640.i	−0.300193	+	0.218103i
$763$	578199.	+	420086.i	0.993180	+	0.721587i
$764$	51708.4	+	159142.i	0.0885879	+	0.272645i
$765$	252268.	−	81966.8i	0.431061	−	0.140060i
$766$	−113230.	+	155848.i	−0.192977	+	0.265610i
$767$	−183454.	−	252503.i	−0.311844	−	0.429216i
$768$	191621.	−	589750.i	0.324879	−	0.999875i
$769$			337919.i			0.571426i	0.958315	+	0.285713i	$0.0922304\pi$
$769$			337919.i			0.571426i	−0.958315	+	0.285713i	$0.907770\pi$
$770$	−63025.9	+	247296.i	−0.106301	+	0.417096i
$771$	−1.39068e6			−2.33948
$772$	−208971.	−	67898.8i	−0.350632	−	0.113927i
$773$	529625.	−	384795.i	0.886359	−	0.643978i	−0.0485670	−	0.998820i	$-0.515465\pi$
$773$	529625.	−	384795.i	0.886359	−	0.643978i	0.934926	+	0.354842i	$0.115465\pi$
$774$	1.21822e6	+	885091.i	2.03350	+	1.47743i
$775$	98822.1	+	304143.i	0.164532	+	0.506378i
$776$	645592.	−	209766.i	1.07210	−	0.348346i
$777$	−91668.0	+	126170.i	−0.151836	+	0.208985i
$778$	12778.0	+	17587.4i	0.0211107	+	0.0290564i
$779$	2777.93	−	8549.59i	0.00457769	−	0.0140887i
$780$			132100.i			0.217127i
$781$	−162349.	+	134794.i	−0.266163	+	0.220988i
$782$	166149.			0.271697
$783$	226352.	+	73546.2i	0.369199	+	0.119960i
$784$	198744.	−	144396.i	0.323342	−	0.234922i
$785$	98532.0	+	71587.7i	0.159896	+	0.116171i
$786$	−431523.	−	1.32809e6i	−0.698487	−	2.14972i
$787$	−158385.	+	51462.3i	−0.255719	+	0.0830883i	−0.434071	−	0.900878i	$-0.642923\pi$
$787$	−158385.	+	51462.3i	−0.255719	+	0.0830883i	0.178352	+	0.983967i	$0.442923\pi$
$788$	70276.1	−	96726.8i	0.113176	−	0.155774i
$789$	17725.2	+	24396.6i	0.0284732	+	0.0391900i
$790$	68348.8	−	210356.i	0.109516	−	0.337055i
$791$		−	107976.i		−	0.172573i
$792$	897760.	+	1.08128e6i	1.43123	+	1.72380i
$793$	−749230.			−1.19143
$794$	412650.	+	134078.i	0.654547	+	0.212675i
$795$	117202.	−	85151.9i	0.185438	−	0.134729i
$796$	28648.4	+	20814.3i	0.0452142	+	0.0328500i
$797$	−221413.	−	681440.i	−0.348568	−	1.07278i	−0.959646	−	0.281211i	$-0.909264\pi$
$797$	−221413.	−	681440.i	−0.348568	−	1.07278i	0.611078	−	0.791570i	$-0.290736\pi$
$798$	−584899.	+	190045.i	−0.918492	+	0.298436i
$799$	69535.6	−	95707.6i	0.108922	−	0.149918i
$800$	−76725.5	−	105604.i	−0.119884	−	0.165006i
$801$	144741.	−	445467.i	0.225594	−	0.694306i
$802$		−	353.307i		−	0.000549293i
$803$	264619.	+	67440.8i	0.410383	+	0.104590i
$804$	213214.			0.329841
$805$	297564.	+	96684.5i	0.459186	+	0.149199i
$806$	−417339.	+	303214.i	−0.642419	+	0.466745i
$807$	−780849.	−	567320.i	−1.19900	−	0.871126i
$808$	184417.	+	567579.i	0.282475	+	0.869367i
$809$	16380.3	−	5322.29i	0.0250280	−	0.00813208i	−0.296476	−	0.955040i	$-0.595812\pi$
$809$	16380.3	−	5322.29i	0.0250280	−	0.00813208i	0.321504	+	0.946908i	$0.395812\pi$
$810$	−306195.	+	421441.i	−0.466689	+	0.642342i
$811$	187890.	+	258608.i	0.285668	+	0.393188i	0.927601	−	0.373573i	$-0.121867\pi$
$811$	187890.	+	258608.i	0.285668	+	0.393188i	−0.641933	+	0.766761i	$0.721867\pi$
$812$	−5934.29	+	18263.9i	−0.00900029	+	0.0277000i
$813$		−	114137.i		−	0.172682i
$814$	67926.0	−	107456.i	0.102515	−	0.162175i
$815$	−184173.			−0.277275
$816$	−254412.	−	82663.4i	−0.382082	−	0.124146i
$817$	−664722.	+	482949.i	−0.995855	+	0.723531i
$818$	113931.	+	82775.8i	0.170269	+	0.123708i
$819$	−244863.	−	753611.i	−0.365053	−	1.12352i
$820$	1552.43	−	504.415i	0.00230879	−	0.000750171i
$821$	−518136.	+	713153.i	−0.768701	+	1.05803i	0.227739	+	0.973722i	$0.426867\pi$
$821$	−518136.	+	713153.i	−0.768701	+	1.05803i	−0.996440	+	0.0843039i	$0.973133\pi$
$822$	14261.1	+	19628.7i	0.0211061	+	0.0290501i
$823$	204339.	−	628890.i	0.301683	−	0.928486i	−0.679211	−	0.733943i	$-0.737678\pi$
$823$	204339.	−	628890.i	0.301683	−	0.928486i	0.980894	−	0.194543i	$-0.0623222\pi$
$824$		−	1.17726e6i		−	1.73388i
$825$	591365.	−	38262.3i	0.868855	−	0.0562164i
$826$	263844.			0.386712
$827$	848404.	+	275663.i	1.24049	+	0.403058i	0.854502	−	0.519448i	$-0.173862\pi$
$827$	848404.	+	275663.i	1.24049	+	0.403058i	0.385983	+	0.922506i	$0.373862\pi$
$828$	241345.	−	175348.i	0.352029	−	0.255764i
$829$	862880.	+	626919.i	1.25557	+	0.912226i	0.998531	−	0.0541744i	$-0.0172527\pi$
$829$	862880.	+	626919.i	1.25557	+	0.912226i	0.257040	+	0.966401i	$0.417253\pi$
$830$	216429.	+	666101.i	0.314167	+	0.966905i
$831$	305349.	−	99213.9i	0.442175	−	0.143671i
$832$	376457.	−	518149.i	0.543837	−	0.748528i
$833$	66876.1	+	92047.1i	0.0963787	+	0.132654i
$834$	517742.	−	1.59345e6i	0.744357	−	2.29089i
$835$		−	946902.i		−	1.35810i
$836$	−123360.	+	49095.9i	−0.176507	+	0.0702477i
$837$	1.43139e6			2.04318
$838$	−566089.	−	183934.i	−0.806115	−	0.261923i
$839$	−4381.47	+	3183.33i	−0.00622438	+	0.00452228i	−0.590893	−	0.806750i	$-0.701225\pi$
$839$	−4381.47	+	3183.33i	−0.00622438	+	0.00452228i	0.584669	+	0.811272i	$0.301225\pi$
$840$	−521805.	−	379114.i	−0.739520	−	0.537293i
$841$	209464.	+	644663.i	0.296154	+	0.911467i
$842$	−962653.	+	312785.i	−1.35783	+	0.441186i
$843$	−621080.	+	854843.i	−0.873962	+	1.20290i
$844$	47542.6	+	65436.8i	0.0667419	+	0.0918623i
$845$	48309.8	−	148682.i	0.0676585	−	0.208231i
$846$			802003.i			1.12056i
$847$	−63027.3	−	485022.i	−0.0878541	−	0.676074i
$848$	−98719.5			−0.137281
$849$	−200694.	−	65209.3i	−0.278431	−	0.0904678i
$850$	−78949.3	+	57360.1i	−0.109272	+	0.0793911i
$851$	−126090.	−	91609.9i	−0.174109	−	0.126498i
$852$	−28533.2	−	87816.3i	−0.0393072	−	0.120975i
$853$	−1.12579e6	+	365793.i	−1.54725	+	0.502732i	−0.953366	−	0.301818i	$-0.902407\pi$
$853$	−1.12579e6	+	365793.i	−1.54725	+	0.502732i	−0.593885	+	0.804550i	$0.702407\pi$
$854$	372283.	−	512403.i	0.510455	−	0.702580i
$855$	−576733.	−	793805.i	−0.788938	−	1.08588i
$856$	−272296.	+	838040.i	−0.371615	+	1.14371i
$857$			649083.i			0.883769i	0.897072	+	0.441884i	$0.145690\pi$
$857$			649083.i			0.883769i	−0.897072	+	0.441884i	$0.854310\pi$
$858$	353479.	+	888165.i	0.480164	+	1.20648i
$859$	−919174.			−1.24569			−0.622847	−	0.782344i	$-0.714024\pi$
$859$	−919174.			−1.24569			−0.622847	+	0.782344i	$0.714024\pi$
$860$	−141891.	−	46103.3i	−0.191849	−	0.0623354i
$861$	−11723.3	+	8517.47i	−0.0158141	+	0.0114896i
$862$	255828.	+	185870.i	0.344297	+	0.250146i
$863$	316845.	+	975149.i	0.425427	+	1.30933i	0.902585	+	0.430513i	$0.141667\pi$
$863$	316845.	+	975149.i	0.425427	+	1.30933i	−0.477157	+	0.878818i	$0.658333\pi$
$864$	−555664.	+	180546.i	−0.744363	+	0.241858i
$865$	−197534.	+	271882.i	−0.264004	+	0.363370i
$866$	126612.	+	174267.i	0.168826	+	0.232369i
$867$	−369607.	+	1.13753e6i	−0.491702	+	1.51330i
$868$			115496.i			0.153294i
$869$	27369.8	+	423015.i	0.0362437	+	0.560165i
$870$	171206.			0.226194
$871$	538278.	+	174897.i	0.709530	+	0.230540i
$872$	1.19118e6	−	865444.i	1.56655	−	1.13817i
$873$	−1.34669e6	−	978428.i	−1.76701	−	1.28381i
$874$	−189925.	−	584529.i	−0.248633	−	0.765214i
$875$	−527259.	+	171317.i	−0.688665	+	0.223761i
$876$	−70236.6	+	96672.4i	−0.0915283	+	0.125978i
$877$	−229763.	−	316242.i	−0.298731	−	0.411169i	0.633094	−	0.774075i	$-0.281785\pi$
$877$	−229763.	−	316242.i	−0.298731	−	0.411169i	−0.931826	+	0.362906i	$0.881785\pi$
$878$	−174407.	+	536769.i	−0.226243	+	0.696304i
$879$		−	553139.i		−	0.715907i
$880$	347088.	+	219403.i	0.448203	+	0.283320i
$881$	657104.			0.846608			0.423304	−	0.905988i	$-0.360870\pi$
$881$	657104.			0.846608			0.423304	+	0.905988i	$0.360870\pi$
$882$	−733578.	−	238354.i	−0.942994	−	0.306397i
$883$	178221.	−	129485.i	0.228579	−	0.166073i	−0.467601	−	0.883940i	$-0.654882\pi$
$883$	178221.	−	129485.i	0.228579	−	0.166073i	0.696180	+	0.717867i	$0.254882\pi$
$884$	33729.0	+	24505.5i	0.0431617	+	0.0313588i
$885$	192513.	+	592493.i	0.245795	+	0.756479i
$886$	239549.	−	77834.2i	0.305160	−	0.0991524i
$887$	−49959.7	+	68763.6i	−0.0634998	+	0.0874000i	−0.839586	−	0.543227i	$-0.817202\pi$
$887$	−49959.7	+	68763.6i	−0.0634998	+	0.0874000i	0.776086	+	0.630627i	$0.217202\pi$
$888$	188851.	+	259931.i	0.239493	+	0.329634i
$889$	−39568.9	+	121781.i	−0.0500669	+	0.154090i
$890$		−	175224.i		−	0.221215i
$891$	246564.	−	967449.i	0.310581	−	1.21863i
$892$	234384.			0.294576
$893$	−416194.	−	135230.i	−0.521906	−	0.169578i
$894$	802108.	−	582765.i	1.00359	−	0.729153i
$895$	876236.	+	636623.i	1.09389	+	0.794760i
$896$	97735.7	+	300800.i	0.121741	+	0.374681i
$897$	1.11460e6	−	362156.i	1.38527	−	0.450102i
$898$	380348.	−	523504.i	0.471659	−	0.649183i
$899$	−104079.	−	143252.i	−0.128778	−	0.177248i
$900$	−54144.7	+	166640.i	−0.0668453	+	0.205729i
$901$		−	45721.3i		−	0.0563208i
$902$	9087.91	−	7545.46i	0.0111699	−	0.00927412i
$903$	1.32445e6			1.62428
$904$	−211560.	−	68740.1i	−0.258879	−	0.0841150i
$905$	−611227.	+	444082.i	−0.746286	+	0.542209i
$906$	−1.06299e6	−	772311.i	−1.29502	−	0.940884i
$907$	−365587.	−	1.12516e6i	−0.444402	−	1.36773i	−0.883139	−	0.469112i	$-0.844574\pi$
$907$	−365587.	−	1.12516e6i	−0.444402	−	1.36773i	0.438737	−	0.898616i	$-0.355426\pi$
$908$	−144166.	+	46842.3i	−0.174860	+	0.0568155i
$909$	860195.	−	1.18396e6i	1.04104	−	1.43287i
$910$	−174239.	−	239819.i	−0.210408	−	0.289601i
$911$	21470.1	−	66078.1i	0.0258700	−	0.0796198i	−0.937288	−	0.348556i	$-0.886672\pi$
$911$	21470.1	−	66078.1i	0.0258700	−	0.0796198i	0.963158	+	0.268936i	$0.0866721\pi$
$912$			989535.i			1.18971i
$913$	−857451.	−	1.03273e6i	−1.02865	−	1.23893i
$914$	−849038.			−1.01633
$915$	1.42230e6	+	462132.i	1.69882	+	0.551980i
$916$	−93991.4	+	68288.7i	−0.112020	+	0.0813876i
$917$	−671425.	−	487819.i	−0.798470	−	0.580123i
$918$	134977.	+	415415.i	0.160167	+	0.492943i
$919$	188172.	−	61141.0i	0.222805	−	0.0723938i	−0.195487	−	0.980706i	$-0.562629\pi$
$919$	188172.	−	61141.0i	0.222805	−	0.0723938i	0.418292	+	0.908312i	$0.362629\pi$
$920$	378873.	−	521475.i	0.447629	−	0.616109i
$921$	382572.	+	526565.i	0.451018	+	0.620773i
$922$	−252562.	+	777304.i	−0.297102	+	0.914385i
$923$		−	245106.i		−	0.287707i
$924$	207391.	+	52855.8i	0.242911	+	0.0619083i
$925$	91541.0			0.106987
$926$	925216.	+	300621.i	1.07900	+	0.350588i
$927$	−2.33555e6	+	1.69688e6i	−2.71788	+	1.97465i
$928$	58472.4	+	42482.7i	0.0678977	+	0.0493305i
$929$	−502833.	−	1.54756e6i	−0.582629	−	1.79315i	−0.608589	−	0.793485i	$-0.708264\pi$
$929$	−502833.	−	1.54756e6i	−0.582629	−	1.79315i	0.0259601	−	0.999663i	$-0.491736\pi$
$930$	979277.	−	318186.i	1.13224	−	0.367888i
$931$	247384.	−	340495.i	0.285412	−	0.392836i
$932$	12612.3	+	17359.3i	0.0145198	+	0.0199848i
$933$	−161570.	+	497262.i	−0.185609	+	0.571245i
$934$		−	521370.i		−	0.597658i
$935$	−101615.	+	160752.i	−0.116235	+	0.183879i
$936$	−1.63246e6			−1.86333
$937$	210048.	+	68248.7i	0.239243	+	0.0777347i	0.426184	−	0.904636i	$-0.359857\pi$
$937$	210048.	+	68248.7i	0.239243	+	0.0777347i	−0.186941	+	0.982371i	$0.559857\pi$
$938$	−387077.	+	281228.i	−0.439938	+	0.319634i
$939$	940349.	+	683204.i	1.06649	+	0.774852i
$940$	−24554.9	−	75572.2i	−0.0277896	−	0.0855277i
$941$	908843.	−	295301.i	1.02638	−	0.333492i	0.253024	−	0.967460i	$-0.418575\pi$
$941$	908843.	−	295301.i	1.02638	−	0.333492i	0.773359	+	0.633968i	$0.218575\pi$
$942$	−226682.	+	312001.i	−0.255455	+	0.351604i
$943$	−8512.07	−	11715.9i	−0.00957220	−	0.0131750i
$944$	131186.	−	403748.i	0.147212	−	0.453071i
$945$			822530.i			0.921061i
$946$	−1.07736e6	+	69707.2i	−1.20387	+	0.0778924i
$947$	−376410.			−0.419722			−0.209861	−	0.977731i	$-0.567301\pi$
$947$	−376410.			−0.419722			−0.209861	+	0.977731i	$0.567301\pi$
$948$	−176412.	−	57319.7i	−0.196296	−	0.0637804i
$949$	−256618.	+	186444.i	−0.284941	+	0.207022i
$950$	292045.	+	212183.i	0.323595	+	0.235106i
$951$	784320.	+	2.41389e6i	0.867226	+	2.66905i
$952$	−193598.	+	62903.7i	−0.213612	+	0.0694068i
$953$	550907.	−	758259.i	0.606586	−	0.834895i	−0.389705	−	0.920940i	$-0.627423\pi$
$953$	550907.	−	758259.i	0.606586	−	0.834895i	0.996291	+	0.0860452i	$0.0274229\pi$
$954$	182190.	+	250763.i	0.200183	+	0.275529i
$955$	273977.	−	843214.i	0.300405	−	0.924551i
$956$		−	265551.i		−	0.290558i
$957$	−304864.	+	121332.i	−0.332876	+	0.132481i
$958$	561886.			0.612234
$959$	13713.8	+	4455.89i	0.0149115	+	0.00484504i
$960$	−1.03424e6	+	751422.i	−1.12223	+	0.815345i
$961$	−114406.	−	83120.9i	−0.123880	−	0.0900044i
$962$	45630.7	+	140437.i	0.0493068	+	0.151751i
$963$	2.05505e6	−	667727.i	2.21600	−	0.720023i
$964$	34291.0	−	47197.6i	0.0369000	−	0.0507885i
$965$	684307.	+	941868.i	0.734846	+	1.01143i
$966$	−306151.	+	942235.i	−0.328081	+	1.00973i
$967$		−	352770.i		−	0.377258i	−0.982048	−	0.188629i	$-0.939596\pi$
$967$		−	352770.i		−	0.377258i	0.982048	−	0.188629i	$-0.0604044\pi$
$968$	−990442.	−	185285.i	−1.05701	−	0.197738i
$969$	−458297.			−0.488090
$970$	−592245.	−	192432.i	−0.629445	−	0.204519i
$971$	1.01472e6	−	737240.i	1.07624	−	0.781934i	0.0992167	−	0.995066i	$-0.468366\pi$
$971$	1.01472e6	−	737240.i	1.07624	−	0.781934i	0.977024	+	0.213132i	$0.0683663\pi$
$972$	48915.6	+	35539.3i	0.0517744	+	0.0376163i
$973$	−307703.	−	947013.i	−0.325017	−	1.00030i
$974$	−610915.	+	198498.i	−0.643966	+	0.209237i
$975$	−404599.	+	556882.i	−0.425613	+	0.585806i
$976$	−599003.	−	824457.i	−0.628825	−	0.865503i
$977$	−343151.	+	1.05611e6i	−0.359498	+	1.10642i	0.593858	+	0.804570i	$0.297604\pi$
$977$	−343151.	+	1.05611e6i	−0.359498	+	1.10642i	−0.953355	+	0.301850i	$0.902396\pi$
$978$		−	583182.i		−	0.609715i
$979$	124180.	+	312019.i	0.129564	+	0.325548i
$980$	76422.2			0.0795733
$981$	−3.43388e6	−	1.11574e6i	−3.56818	−	1.15937i
$982$	−254420.	+	184847.i	−0.263832	+	0.191685i
$983$	−136040.	−	98839.0i	−0.140786	−	0.102287i	0.515163	−	0.857092i	$-0.327731\pi$
$983$	−136040.	−	98839.0i	−0.140786	−	0.102287i	−0.655949	+	0.754805i	$0.727731\pi$
$984$	9225.19	+	28392.2i	0.00952764	+	0.0293230i
$985$	−602488.	+	195760.i	−0.620977	+	0.201768i
$986$	31760.1	−	43714.0i	0.0326684	−	0.0449642i
$987$	414630.	+	570690.i	0.425625	+	0.585822i
$988$	47657.2	−	146674.i	0.0488219	−	0.150258i
$989$			1.32361e6i			1.35322i
$990$	−83243.6	−	1.28657e6i	−0.0849338	−	1.31270i
$991$	931437.			0.948432			0.474216	−	0.880409i	$-0.342732\pi$
$991$	931437.			0.948432			0.474216	+	0.880409i	$0.342732\pi$
$992$	413408.	+	134324.i	0.420102	+	0.136500i
$993$	1.73462e6	−	1.26028e6i	1.75916	−	1.27811i
$994$	167629.	+	121790.i	0.169659	+	0.123265i
$995$	−57980.0	−	178444.i	−0.0585642	−	0.180242i
$996$	558616.	−	181505.i	0.563112	−	0.182966i
$997$	378584.	−	521076.i	0.380865	−	0.524216i	−0.574948	−	0.818190i	$-0.694978\pi$
$997$	378584.	−	521076.i	0.380865	−	0.524216i	0.955814	+	0.293974i	$0.0949778\pi$
$998$	150974.	+	207798.i	0.151580	+	0.208632i
$999$	126614.	−	389679.i	0.126868	−	0.390460i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.5.d.a.2.2	✓	12
3.2	odd	2		99.5.k.a.46.2		12
4.3	odd	2		176.5.n.a.145.1		12
11.2	odd	10		121.5.d.c.118.2		12
11.3	even	5		121.5.d.c.40.2		12
11.4	even	5		121.5.b.b.120.5		12
11.5	even	5		121.5.d.d.94.2		12
11.6	odd	10	inner	11.5.d.a.6.2	yes	12
11.7	odd	10		121.5.b.b.120.8		12
11.8	odd	10		121.5.d.e.40.2		12
11.9	even	5		121.5.d.e.118.2		12
11.10	odd	2		121.5.d.d.112.2		12
33.17	even	10		99.5.k.a.28.2		12
44.39	even	10		176.5.n.a.17.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.5.d.a.2.2	✓	12	1.1	even	1	trivial
11.5.d.a.6.2	yes	12	11.6	odd	10	inner
99.5.k.a.28.2		12	33.17	even	10
99.5.k.a.46.2		12	3.2	odd	2
121.5.b.b.120.5		12	11.4	even	5
121.5.b.b.120.8		12	11.7	odd	10
121.5.d.c.40.2		12	11.3	even	5
121.5.d.c.118.2		12	11.2	odd	10
121.5.d.d.94.2		12	11.5	even	5
121.5.d.d.112.2		12	11.10	odd	2
121.5.d.e.40.2		12	11.8	odd	10
121.5.d.e.118.2		12	11.9	even	5
176.5.n.a.17.1		12	44.39	even	10
176.5.n.a.145.1		12	4.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-3.38257 - 1.09906i) q^{2} +(12.7857 - 9.28936i) q^{3} +(-2.71041 - 1.96923i) q^{4} +(5.48545 + 16.8825i) q^{5} +(-53.4582 + 17.3696i) q^{6} +(-19.6356 + 27.0262i) q^{7} +(40.4526 + 55.6782i) q^{8} +(52.1517 - 160.506i) q^{9} +O(q^{10})\)	\(q+(-3.38257 - 1.09906i) q^{2} +(12.7857 - 9.28936i) q^{3} +(-2.71041 - 1.96923i) q^{4} +(5.48545 + 16.8825i) q^{5} +(-53.4582 + 17.3696i) q^{6} +(-19.6356 + 27.0262i) q^{7} +(40.4526 + 55.6782i) q^{8} +(52.1517 - 160.506i) q^{9} -63.1351i q^{10} +(44.7432 + 112.423i) q^{11} -52.9474 q^{12} +(-133.670 - 43.4321i) q^{13} +(96.1225 - 69.8371i) q^{14} +(226.963 + 164.898i) q^{15} +(-59.0753 - 181.815i) q^{16} +(84.2066 - 27.3604i) q^{17} +(-352.814 + 485.607i) q^{18} +(-192.513 - 264.971i) q^{19} +(18.3776 - 56.5605i) q^{20} +527.951i q^{21} +(-27.7866 - 429.457i) q^{22} -527.616 q^{23} +(1034.43 + 336.107i) q^{24} +(250.708 - 182.150i) q^{25} +(404.415 + 293.825i) q^{26} +(-428.625 - 1319.17i) q^{27} +(106.441 - 34.5849i) q^{28} +(-100.856 + 138.816i) q^{29} +(-586.484 - 807.227i) q^{30} +(-318.892 + 981.449i) q^{31} -421.222i q^{32} +(1616.42 + 1021.78i) q^{33} -314.906 q^{34} +(-563.979 - 183.248i) q^{35} +(-457.426 + 332.339i) q^{36} +(238.981 + 173.630i) q^{37} +(359.968 + 1107.87i) q^{38} +(-2112.53 + 686.401i) q^{39} +(-718.085 + 988.360i) q^{40} +(16.1331 + 22.2053i) q^{41} +(580.252 - 1785.83i) q^{42} -2508.66i q^{43} +(100.115 - 392.823i) q^{44} +2995.82 q^{45} +(1784.70 + 579.884i) q^{46} +(1080.95 - 785.358i) q^{47} +(-2444.27 - 1775.86i) q^{48} +(397.096 + 1222.13i) q^{49} +(-1048.23 + 340.591i) q^{50} +(822.480 - 1132.05i) q^{51} +(276.773 + 380.946i) q^{52} +(159.574 - 491.117i) q^{53} +4933.29i q^{54} +(-1652.55 + 1372.07i) q^{55} -2299.08 q^{56} +(-4922.82 - 1599.52i) q^{57} +(493.720 - 358.709i) q^{58} +(1796.54 + 1305.27i) q^{59} +(-290.440 - 893.882i) q^{60} +(5069.82 - 1647.29i) q^{61} +(2157.35 - 2969.34i) q^{62} +(3313.84 + 4561.11i) q^{63} +(-1408.16 + 4333.86i) q^{64} -2494.93i q^{65} +(-4344.65 - 5232.78i) q^{66} -4026.91 q^{67} +(-282.113 - 91.6641i) q^{68} +(-6745.95 + 4901.22i) q^{69} +(1706.30 + 1239.70i) q^{70} +(538.898 + 1658.56i) q^{71} +(11046.4 - 3589.19i) q^{72} +(1326.54 - 1825.82i) q^{73} +(-617.540 - 849.971i) q^{74} +(1513.42 - 4657.83i) q^{75} +1097.28i q^{76} +(-3916.94 - 998.271i) q^{77} +7900.17 q^{78} +(3331.84 + 1082.58i) q^{79} +(2745.44 - 1994.68i) q^{80} +(-6675.22 - 4849.83i) q^{81} +(-30.1663 - 92.8423i) q^{82} +(-10550.4 + 3428.04i) q^{83} +(1039.66 - 1430.96i) q^{84} +(923.822 + 1271.53i) q^{85} +(-2757.18 + 8485.74i) q^{86} +2711.75i q^{87} +(-4449.56 + 7039.04i) q^{88} +2775.39 q^{89} +(-10133.6 - 3292.60i) q^{90} +(3798.51 - 2759.78i) q^{91} +(1430.06 + 1039.00i) q^{92} +(5039.77 + 15510.8i) q^{93} +(-4519.56 + 1468.49i) q^{94} +(3417.34 - 4703.57i) q^{95} +(-3912.88 - 5385.62i) q^{96} +(3047.94 - 9380.60i) q^{97} -4570.39i q^{98} +(20378.1 - 1318.50i) 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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