LMFDB - Embedded newform 361.3.f.e.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,3,Mod(116,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("361.116");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	361.f (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.83653754341$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
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} + 24x^{10} + 216x^{8} + 905x^{6} + 1770x^{4} + 1395x^{2} + 361 $ x^12 + 24x^10 + 216x^8 + 905x^6 + 1770x^4 + 1395*x^2 + 361
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			127.2
Root			$-2.57727i$ of defining polynomial
Character	$\chi$	$=$	361.127
Dual form			361.3.f.e.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.21695 + 1.45030i) q^{2} +(0.664575 - 1.82591i) q^{3} +(0.0721792 - 0.409349i) q^{4} +(-0.485005 - 2.75060i) q^{5} +(3.45687 - 1.25820i) q^{6} +(-1.20796 + 2.09224i) q^{7} +(7.23987 - 4.17994i) q^{8} +(4.00213 + 3.35818i) q^{9} +O(q^{10})$	\(q+(1.21695 + 1.45030i) q^{2} +(0.664575 - 1.82591i) q^{3} +(0.0721792 - 0.409349i) q^{4} +(-0.485005 - 2.75060i) q^{5} +(3.45687 - 1.25820i) q^{6} +(-1.20796 + 2.09224i) q^{7} +(7.23987 - 4.17994i) q^{8} +(4.00213 + 3.35818i) q^{9} +(3.39898 - 4.05074i) q^{10} +(-9.60360 - 16.6339i) q^{11} +(-0.699463 - 0.403835i) q^{12} +(-4.96498 - 13.6412i) q^{13} +(-4.50440 + 0.794247i) q^{14} +(-5.34466 - 0.942409i) q^{15} +(13.3103 + 4.84457i) q^{16} +(-13.1432 + 11.0285i) q^{17} +9.89103i q^{18} -1.16096 q^{20} +(3.01746 + 3.59607i) q^{21} +(12.4371 - 34.1707i) q^{22} +(-1.32476 + 7.51307i) q^{23} +(-2.82074 - 15.9972i) q^{24} +(16.1617 - 5.88239i) q^{25} +(13.7417 - 23.8013i) q^{26} +(23.9363 - 13.8196i) q^{27} +(0.769267 + 0.645491i) q^{28} +(5.29504 - 6.31038i) q^{29} +(-5.13740 - 8.89824i) q^{30} +(5.19837 + 3.00128i) q^{31} +(-2.26509 - 6.22329i) q^{32} +(-36.7543 + 6.48078i) q^{33} +(-31.9893 - 5.64057i) q^{34} +(6.34079 + 2.30786i) q^{35} +(1.66354 - 1.39587i) q^{36} -59.5153i q^{37} -28.2071 q^{39} +(-15.0087 - 17.8867i) q^{40} +(10.5649 - 29.0269i) q^{41} +(-1.54329 + 8.75245i) q^{42} +(4.26712 + 24.2001i) q^{43} +(-7.50225 + 2.73060i) q^{44} +(7.29598 - 12.6370i) q^{45} +(-12.5084 + 7.22171i) q^{46} +(56.0539 + 47.0348i) q^{47} +(17.6915 - 21.0839i) q^{48} +(21.5817 + 37.3806i) q^{49} +(28.1992 + 16.2808i) q^{50} +(11.4023 + 31.3276i) q^{51} +(-5.94236 + 1.04780i) q^{52} +(27.6039 + 4.86732i) q^{53} +(49.1719 + 17.8971i) q^{54} +(-41.0955 + 34.4832i) q^{55} +20.1968i q^{56} +15.5957 q^{58} +(5.92334 + 7.05916i) q^{59} +(-0.771547 + 2.11981i) q^{60} +(-10.7063 + 60.7186i) q^{61} +(1.97338 + 11.1916i) q^{62} +(-11.8605 + 4.31688i) q^{63} +(34.5983 - 59.9260i) q^{64} +(-35.1134 + 20.2727i) q^{65} +(-54.1272 - 45.4181i) q^{66} +(-7.74429 + 9.22929i) q^{67} +(3.56583 + 6.17619i) q^{68} +(12.8378 + 7.41188i) q^{69} +(4.36932 + 12.0046i) q^{70} +(-37.8747 + 6.67833i) q^{71} +(43.0119 + 7.58416i) q^{72} +(-47.7593 - 17.3830i) q^{73} +(86.3151 - 72.4269i) q^{74} -33.4191i q^{75} +46.4029 q^{77} +(-34.3266 - 40.9088i) q^{78} +(-36.7556 + 100.985i) q^{79} +(6.86989 - 38.9611i) q^{80} +(-1.16100 - 6.58434i) q^{81} +(54.9548 - 20.0019i) q^{82} +(-35.6336 + 61.7192i) q^{83} +(1.68984 - 0.975631i) q^{84} +(36.7095 + 30.8030i) q^{85} +(-29.9045 + 35.6388i) q^{86} +(-8.00321 - 13.8620i) q^{87} +(-139.058 - 80.2850i) q^{88} +(-2.77264 - 7.61778i) q^{89} +(27.2063 - 4.79720i) q^{90} +(34.5381 + 6.09000i) q^{91} +(2.97984 + 1.08457i) q^{92} +(8.93476 - 7.49716i) q^{93} +138.534i q^{94} -12.8685 q^{96} +(76.5684 + 91.2507i) q^{97} +(-27.9493 + 76.7902i) q^{98} +(17.4249 - 98.8218i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 9 q^{3} - 9 q^{4} + 3 q^{5} + 9 q^{6} + 6 q^{7} - 9 q^{8} + 39 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 - 9 * q^3 - 9 * q^4 + 3 * q^5 + 9 * q^6 + 6 * q^7 - 9 * q^8 + 39 * q^9	\( 12 q + 3 q^{2} - 9 q^{3} - 9 q^{4} + 3 q^{5} + 9 q^{6} + 6 q^{7} - 9 q^{8} + 39 q^{9} - 30 q^{10} - 18 q^{11} + 63 q^{12} - 51 q^{13} - 90 q^{14} - 54 q^{15} + 51 q^{16} - 75 q^{17} - 90 q^{20} + 48 q^{21} - 33 q^{22} - 66 q^{23} - 66 q^{24} + 123 q^{25} + 21 q^{26} - 27 q^{27} - 6 q^{28} - 78 q^{29} + 24 q^{30} + 99 q^{31} - 222 q^{32} - 15 q^{33} - 66 q^{34} - 66 q^{35} - 225 q^{36} - 108 q^{39} + 141 q^{40} - 171 q^{41} + 123 q^{42} + 54 q^{43} - 51 q^{44} - 3 q^{45} - 54 q^{46} - 81 q^{47} - 24 q^{48} - 24 q^{49} + 72 q^{50} + 48 q^{51} - 123 q^{52} - 96 q^{53} + 210 q^{54} - 153 q^{55} - 132 q^{58} + 111 q^{59} + 231 q^{60} - 120 q^{61} - 171 q^{62} + 171 q^{63} + 27 q^{64} + 126 q^{65} + 69 q^{66} - 18 q^{67} - 30 q^{68} + 72 q^{69} - 126 q^{70} + 138 q^{71} + 114 q^{72} - 135 q^{73} + 471 q^{74} + 246 q^{77} - 99 q^{78} + 132 q^{79} + 264 q^{80} + 390 q^{81} - 126 q^{82} - 156 q^{83} + 99 q^{84} + 15 q^{85} + 72 q^{86} + 69 q^{87} - 405 q^{88} + 531 q^{89} - 93 q^{90} + 393 q^{91} + 12 q^{92} + 384 q^{93} + 558 q^{96} - 588 q^{97} - 159 q^{98} - 366 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 9 * q^3 - 9 * q^4 + 3 * q^5 + 9 * q^6 + 6 * q^7 - 9 * q^8 + 39 * q^9 - 30 * q^10 - 18 * q^11 + 63 * q^12 - 51 * q^13 - 90 * q^14 - 54 * q^15 + 51 * q^16 - 75 * q^17 - 90 * q^20 + 48 * q^21 - 33 * q^22 - 66 * q^23 - 66 * q^24 + 123 * q^25 + 21 * q^26 - 27 * q^27 - 6 * q^28 - 78 * q^29 + 24 * q^30 + 99 * q^31 - 222 * q^32 - 15 * q^33 - 66 * q^34 - 66 * q^35 - 225 * q^36 - 108 * q^39 + 141 * q^40 - 171 * q^41 + 123 * q^42 + 54 * q^43 - 51 * q^44 - 3 * q^45 - 54 * q^46 - 81 * q^47 - 24 * q^48 - 24 * q^49 + 72 * q^50 + 48 * q^51 - 123 * q^52 - 96 * q^53 + 210 * q^54 - 153 * q^55 - 132 * q^58 + 111 * q^59 + 231 * q^60 - 120 * q^61 - 171 * q^62 + 171 * q^63 + 27 * q^64 + 126 * q^65 + 69 * q^66 - 18 * q^67 - 30 * q^68 + 72 * q^69 - 126 * q^70 + 138 * q^71 + 114 * q^72 - 135 * q^73 + 471 * q^74 + 246 * q^77 - 99 * q^78 + 132 * q^79 + 264 * q^80 + 390 * q^81 - 126 * q^82 - 156 * q^83 + 99 * q^84 + 15 * q^85 + 72 * q^86 + 69 * q^87 - 405 * q^88 + 531 * q^89 - 93 * q^90 + 393 * q^91 + 12 * q^92 + 384 * q^93 + 558 * q^96 - 588 * q^97 - 159 * q^98 - 366 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	1.21695	+	1.45030i	0.608474	+	0.725151i	0.979043	−	0.203654i	$-0.0652818\pi$
$2$	1.21695	+	1.45030i	0.608474	+	0.725151i	−0.370569	+	0.928805i	$0.620837\pi$
$3$	0.664575	−	1.82591i	0.221525	−	0.608635i	−0.778289	−	0.627906i	$-0.783912\pi$
$3$	0.664575	−	1.82591i	0.221525	−	0.608635i	0.999814	+	0.0192707i	$0.00613443\pi$
$4$	0.0721792	−	0.409349i	0.0180448	−	0.102337i
$5$	−0.485005	−	2.75060i	−0.0970011	−	0.550121i	−0.994116	−	0.108323i	$-0.965452\pi$
$5$	−0.485005	−	2.75060i	−0.0970011	−	0.550121i	0.897115	−	0.441798i	$-0.145659\pi$
$6$	3.45687	−	1.25820i	0.576145	−	0.209700i
$7$	−1.20796	+	2.09224i	−0.172565	+	0.298892i	−0.939316	−	0.343053i	$-0.888539\pi$
$7$	−1.20796	+	2.09224i	−0.172565	+	0.298892i	0.766751	+	0.641945i	$0.221872\pi$
$8$	7.23987	−	4.17994i	0.904984	−	0.522493i
$9$	4.00213	+	3.35818i	0.444681	+	0.373132i
$10$	3.39898	−	4.05074i	0.339898	−	0.405074i
$11$	−9.60360	−	16.6339i	−0.873055	−	1.51218i	−0.858821	−	0.512277i	$-0.828802\pi$
$11$	−9.60360	−	16.6339i	−0.873055	−	1.51218i	−0.0142343	−	0.999899i	$-0.504531\pi$
$12$	−0.699463	−	0.403835i	−0.0582886	−	0.0336529i
$13$	−4.96498	−	13.6412i	−0.381921	−	1.04932i	−0.970546	−	0.240914i	$-0.922553\pi$
$13$	−4.96498	−	13.6412i	−0.381921	−	1.04932i	0.588625	−	0.808406i	$-0.299670\pi$
$14$	−4.50440	+	0.794247i	−0.321743	+	0.0567320i
$15$	−5.34466	−	0.942409i	−0.356311	−	0.0628272i
$16$	13.3103	+	4.84457i	0.831896	+	0.302786i
$17$	−13.1432	+	11.0285i	−0.773132	+	0.648735i	−0.941509	−	0.336988i	$-0.890592\pi$
$17$	−13.1432	+	11.0285i	−0.773132	+	0.648735i	0.168377	+	0.985723i	$0.446147\pi$
$18$			9.89103i			0.549501i
$19$		0			0
$19$		0			0
$20$	−1.16096			−0.0580481
$21$	3.01746	+	3.59607i	0.143688	+	0.171241i
$22$	12.4371	−	34.1707i	0.565324	−	1.55322i
$23$	−1.32476	+	7.51307i	−0.0575981	+	0.326655i	−0.999969	−	0.00791590i	$-0.997480\pi$
$23$	−1.32476	+	7.51307i	−0.0575981	+	0.326655i	0.942371	+	0.334571i	$0.108591\pi$
$24$	−2.82074	−	15.9972i	−0.117531	−	0.666551i
$25$	16.1617	−	5.88239i	0.646469	−	0.235296i
$26$	13.7417	−	23.8013i	0.528527	−	0.915435i
$27$	23.9363	−	13.8196i	0.886530	−	0.511839i
$28$	0.769267	+	0.645491i	0.0274738	+	0.0230533i
$29$	5.29504	−	6.31038i	0.182587	−	0.217599i	−0.666985	−	0.745071i	$-0.732416\pi$
$29$	5.29504	−	6.31038i	0.182587	−	0.217599i	0.849573	+	0.527472i	$0.176860\pi$
$30$	−5.13740	−	8.89824i	−0.171247	−	0.296608i
$31$	5.19837	+	3.00128i	0.167689	+	0.0968155i	0.581496	−	0.813549i	$-0.302468\pi$
$31$	5.19837	+	3.00128i	0.167689	+	0.0968155i	−0.413806	+	0.910365i	$0.635801\pi$
$32$	−2.26509	−	6.22329i	−0.0707842	−	0.194478i
$33$	−36.7543	+	6.48078i	−1.11377	+	0.196387i
$34$	−31.9893	−	5.64057i	−0.940861	−	0.165899i
$35$	6.34079	+	2.30786i	0.181165	+	0.0659388i
$36$	1.66354	−	1.39587i	0.0462094	−	0.0387743i
$37$		−	59.5153i		−	1.60852i	−0.594277	−	0.804260i	$-0.702562\pi$
$37$		−	59.5153i		−	1.60852i	0.594277	−	0.804260i	$-0.297438\pi$
$38$		0			0
$39$	−28.2071			−0.723259
$40$	−15.0087	−	17.8867i	−0.375219	−	0.447168i
$41$	10.5649	−	29.0269i	0.257681	−	0.707974i	−0.741628	−	0.670811i	$-0.765946\pi$
$41$	10.5649	−	29.0269i	0.257681	−	0.707974i	0.999309	−	0.0371621i	$-0.0118318\pi$
$42$	−1.54329	+	8.75245i	−0.0367451	+	0.208392i
$43$	4.26712	+	24.2001i	0.0992354	+	0.562792i	0.993367	+	0.114988i	$0.0366828\pi$
$43$	4.26712	+	24.2001i	0.0992354	+	0.562792i	−0.894131	+	0.447805i	$0.852206\pi$
$44$	−7.50225	+	2.73060i	−0.170506	+	0.0620590i
$45$	7.29598	−	12.6370i	0.162133	−	0.280822i
$46$	−12.5084	+	7.22171i	−0.271921	+	0.156994i
$47$	56.0539	+	47.0348i	1.19264	+	1.00074i	0.999810	+	0.0195069i	$0.00620964\pi$
$47$	56.0539	+	47.0348i	1.19264	+	1.00074i	0.192826	+	0.981233i	$0.438235\pi$
$48$	17.6915	−	21.0839i	0.368572	−	0.439247i
$49$	21.5817	+	37.3806i	0.440443	+	0.762869i
$50$	28.1992	+	16.2808i	0.563984	+	0.325617i
$51$	11.4023	+	31.3276i	0.223575	+	0.614266i
$52$	−5.94236	+	1.04780i	−0.114276	+	0.0201500i
$53$	27.6039	+	4.86732i	0.520829	+	0.0918362i	0.427882	−	0.903835i	$-0.359260\pi$
$53$	27.6039	+	4.86732i	0.520829	+	0.0918362i	0.0929475	+	0.995671i	$0.470371\pi$
$54$	49.1719	+	17.8971i	0.910591	+	0.331428i
$55$	−41.0955	+	34.4832i	−0.747191	+	0.626968i
$56$			20.1968i			0.360656i
$57$		0			0
$58$	15.5957			0.268892
$59$	5.92334	+	7.05916i	0.100396	+	0.119647i	0.813903	−	0.581001i	$-0.197339\pi$
$59$	5.92334	+	7.05916i	0.100396	+	0.119647i	−0.713507	+	0.700648i	$0.752894\pi$
$60$	−0.771547	+	2.11981i	−0.0128591	+	0.0353301i
$61$	−10.7063	+	60.7186i	−0.175513	+	0.995386i	0.762036	+	0.647535i	$0.224200\pi$
$61$	−10.7063	+	60.7186i	−0.175513	+	0.995386i	−0.937550	+	0.347852i	$0.886911\pi$
$62$	1.97338	+	11.1916i	0.0318287	+	0.180510i
$63$	−11.8605	+	4.31688i	−0.188262	+	0.0685219i
$64$	34.5983	−	59.9260i	0.540598	−	0.936344i
$65$	−35.1134	+	20.2727i	−0.540206	+	0.311888i
$66$	−54.1272	−	45.4181i	−0.820108	−	0.688153i
$67$	−7.74429	+	9.22929i	−0.115586	+	0.137751i	−0.820735	−	0.571309i	$-0.806436\pi$
$67$	−7.74429	+	9.22929i	−0.115586	+	0.137751i	0.705149	+	0.709060i	$0.250880\pi$
$68$	3.56583	+	6.17619i	0.0524386	+	0.0908264i
$69$	12.8378	+	7.41188i	0.186054	+	0.107419i
$70$	4.36932	+	12.0046i	0.0624188	+	0.171494i
$71$	−37.8747	+	6.67833i	−0.533446	+	0.0940610i	−0.433881	−	0.900970i	$-0.642856\pi$
$71$	−37.8747	+	6.67833i	−0.533446	+	0.0940610i	−0.0995651	+	0.995031i	$0.531745\pi$
$72$	43.0119	+	7.58416i	0.597388	+	0.105336i
$73$	−47.7593	−	17.3830i	−0.654237	−	0.238123i	−0.00649085	−	0.999979i	$-0.502066\pi$
$73$	−47.7593	−	17.3830i	−0.654237	−	0.238123i	−0.647746	+	0.761856i	$0.724288\pi$
$74$	86.3151	−	72.4269i	1.16642	−	0.978743i
$75$		−	33.4191i		−	0.445588i
$76$		0			0
$77$	46.4029			0.602635
$78$	−34.3266	−	40.9088i	−0.440084	−	0.524472i
$79$	−36.7556	+	100.985i	−0.465261	+	1.27829i	0.456219	+	0.889868i	$0.349203\pi$
$79$	−36.7556	+	100.985i	−0.465261	+	1.27829i	−0.921480	+	0.388426i	$0.873019\pi$
$80$	6.86989	−	38.9611i	0.0858737	−	0.487014i
$81$	−1.16100	−	6.58434i	−0.0143333	−	0.0812882i
$82$	54.9548	−	20.0019i	0.670180	−	0.243926i
$83$	−35.6336	+	61.7192i	−0.429321	+	0.743605i	−0.996813	−	0.0797735i	$-0.974580\pi$
$83$	−35.6336	+	61.7192i	−0.429321	+	0.743605i	0.567492	+	0.823379i	$0.307914\pi$
$84$	1.68984	−	0.975631i	0.0201172	−	0.0116147i
$85$	36.7095	+	30.8030i	0.431877	+	0.362388i
$86$	−29.9045	+	35.6388i	−0.347727	+	0.414405i
$87$	−8.00321	−	13.8620i	−0.0919909	−	0.159333i
$88$	−139.058	−	80.2850i	−1.58020	−	0.912330i
$89$	−2.77264	−	7.61778i	−0.0311533	−	0.0855930i	0.923141	−	0.384462i	$-0.125613\pi$
$89$	−2.77264	−	7.61778i	−0.0311533	−	0.0855930i	−0.954294	+	0.298869i	$0.903391\pi$
$90$	27.2063	−	4.79720i	0.302292	−	0.0533022i
$91$	34.5381	+	6.09000i	0.379539	+	0.0669231i
$92$	2.97984	+	1.08457i	0.0323896	+	0.0117888i
$93$	8.93476	−	7.49716i	0.0960727	−	0.0806146i
$94$			138.534i			1.47376i
$95$		0			0
$96$	−12.8685			−0.134047
$97$	76.5684	+	91.2507i	0.789365	+	0.940729i	0.999316	−	0.0369830i	$-0.0117747\pi$
$97$	76.5684	+	91.2507i	0.789365	+	0.940729i	−0.209950	+	0.977712i	$0.567330\pi$
$98$	−27.9493	+	76.7902i	−0.285197	+	0.783573i
$99$	17.4249	−	98.8218i	0.176010	−	0.998200i
$100$	−1.24141	−	7.04037i	−0.0124141	−	0.0704037i
$101$	−123.482	+	44.9438i	−1.22260	+	0.444988i	−0.871055	−	0.491185i	$-0.836564\pi$
$101$	−123.482	+	44.9438i	−1.22260	+	0.444988i	−0.351540	+	0.936173i	$0.614342\pi$
$102$	−31.5584	+	54.6608i	−0.309396	+	0.535890i
$103$	11.4431	−	6.60670i	0.111098	−	0.0641427i	−0.443421	−	0.896313i	$-0.646235\pi$
$103$	11.4431	−	6.60670i	0.111098	−	0.0641427i	0.554520	+	0.832171i	$0.312902\pi$
$104$	−92.9651	−	78.0070i	−0.893895	−	0.750067i
$105$	8.42787	−	10.0439i	0.0802654	−	0.0956566i
$106$	26.5335	+	45.9573i	0.250316	+	0.433560i
$107$	94.8683	+	54.7722i	0.886620	+	0.511890i	0.872835	−	0.488015i	$-0.162279\pi$
$107$	94.8683	+	54.7722i	0.886620	+	0.511890i	0.0137844	+	0.999905i	$0.495612\pi$
$108$	−3.92935	−	10.7958i	−0.0363828	−	0.0999610i
$109$	202.969	−	35.7890i	1.86210	−	0.328339i	0.874466	−	0.485088i	$-0.161212\pi$
$109$	202.969	−	35.7890i	1.86210	−	0.328339i	0.987639	+	0.156748i	$0.0501012\pi$
$110$	−100.022	−	17.6366i	−0.909293	−	0.160333i
$111$	−108.669	−	39.5524i	−0.979002	−	0.356328i
$112$	−26.2143	+	21.9964i	−0.234056	+	0.196397i
$113$			18.3671i			0.162541i	0.996692	+	0.0812705i	$0.0258978\pi$
$113$			18.3671i			0.162541i	−0.996692	+	0.0812705i	$0.974102\pi$
$114$		0			0
$115$	21.3080			0.185287
$116$	−2.20095	−	2.62299i	−0.0189737	−	0.0226120i
$117$	25.9391	−	71.2670i	0.221701	−	0.609120i
$118$	−3.02952	+	17.1813i	−0.0256739	+	0.145604i
$119$	−7.19780	−	40.8208i	−0.0604857	−	0.343032i
$120$	−42.6339	+	15.5175i	−0.355283	+	0.129312i
$121$	−123.958	+	214.702i	−1.02445	+	1.77440i
$122$	−101.089	+	58.3639i	−0.828601	+	0.478393i
$123$	−45.9792	−	38.5812i	−0.373815	−	0.313668i
$124$	1.60378	−	1.91132i	0.0129337	−	0.0154138i
$125$	−58.9316	−	102.072i	−0.471453	−	0.816580i
$126$	−20.6944	−	11.9479i	−0.164241	−	0.0948248i
$127$	3.87536	+	10.6475i	0.0305146	+	0.0838383i	0.954014	−	0.299761i	$-0.0969068\pi$
$127$	3.87536	+	10.6475i	0.0305146	+	0.0838383i	−0.923500	+	0.383599i	$0.874685\pi$
$128$	102.927	−	18.1488i	0.804116	−	0.141787i
$129$	47.0229	+	8.29140i	0.364518	+	0.0642744i
$130$	−72.1327	−	26.2542i	−0.554867	−	0.201955i
$131$	8.59823	−	7.21477i	0.0656353	−	0.0550746i	−0.609380	−	0.792878i	$-0.708582\pi$
$131$	8.59823	−	7.21477i	0.0656353	−	0.0550746i	0.675015	+	0.737804i	$0.264137\pi$
$132$			15.5131i			0.117523i
$133$		0			0
$134$	−22.8097			−0.170221
$135$	−49.6216	−	59.1367i	−0.367567	−	0.438050i
$136$	−49.0569	+	134.783i	−0.360713	+	0.991050i
$137$	28.0857	−	159.282i	0.205005	−	1.16264i	−0.692427	−	0.721488i	$-0.743459\pi$
$137$	28.0857	−	159.282i	0.205005	−	1.16264i	0.897432	−	0.441153i	$-0.145430\pi$
$138$	4.87341	+	27.6385i	0.0353146	+	0.200279i
$139$	180.475	−	65.6874i	1.29838	−	0.472571i	0.401910	−	0.915679i	$-0.368346\pi$
$139$	180.475	−	65.6874i	1.29838	−	0.472571i	0.896468	+	0.443108i	$0.146124\pi$
$140$	1.40239	−	2.42901i	0.0100171	−	0.0173501i
$141$	123.133	−	71.0909i	0.873284	−	0.504191i
$142$	−55.7771	−	46.8026i	−0.392797	−	0.329595i
$143$	−179.225	+	213.591i	−1.25332	+	1.49365i
$144$	37.0007	+	64.0872i	0.256950	+	0.445050i
$145$	−19.9255	−	11.5040i	−0.137417	−	0.0793378i
$146$	−32.9100	−	90.4196i	−0.225411	−	0.619312i
$147$	82.5961	−	14.5639i	0.561878	−	0.0990743i
$148$	−24.3625	−	4.29576i	−0.164611	−	0.0290254i
$149$	−132.089	−	48.0764i	−0.886502	−	0.322660i	−0.141671	−	0.989914i	$-0.545247\pi$
$149$	−132.089	−	48.0764i	−0.886502	−	0.322660i	−0.744831	+	0.667254i	$0.767470\pi$
$150$	48.4678	−	40.6693i	0.323118	−	0.271129i
$151$		−	101.605i		−	0.672880i	−0.941705	−	0.336440i	$-0.890777\pi$
$151$		−	101.605i		−	0.672880i	0.941705	−	0.336440i	$-0.109223\pi$
$152$		0			0
$153$	−89.6366			−0.585860
$154$	56.4699	+	67.2982i	0.366688	+	0.437002i
$155$	5.73409	−	15.7543i	0.0369941	−	0.101641i
$156$	−2.03597	+	11.5465i	−0.0130511	+	0.0740162i
$157$	29.0602	+	164.809i	0.185097	+	1.04974i	0.925831	+	0.377939i	$0.123367\pi$
$157$	29.0602	+	164.809i	0.185097	+	1.04974i	−0.740734	+	0.671799i	$0.765522\pi$
$158$	−191.189	+	69.5870i	−1.21005	+	0.440424i
$159$	27.2322	−	47.1675i	0.171272	−	0.296651i
$160$	−16.0192	+	9.24871i	−0.100120	+	0.0578044i
$161$	−14.1189	−	11.8472i	−0.0876950	−	0.0735849i
$162$	8.13641	−	9.69660i	0.0502248	−	0.0598555i
$163$	16.9195	+	29.3054i	0.103801	+	0.179788i	0.913248	−	0.407405i	$-0.133566\pi$
$163$	16.9195	+	29.3054i	0.103801	+	0.179788i	−0.809447	+	0.587193i	$0.800233\pi$
$164$	−11.1196	−	6.41988i	−0.0678022	−	0.0391456i
$165$	35.6521	+	97.9533i	0.216073	+	0.593656i
$166$	−132.876	+	23.4296i	−0.800456	+	0.141142i
$167$	47.5443	+	8.38334i	0.284696	+	0.0501996i	0.314173	−	0.949366i	$-0.398273\pi$
$167$	47.5443	+	8.38334i	0.284696	+	0.0501996i	−0.0294764	+	0.999565i	$0.509384\pi$
$168$	36.8774	+	13.4223i	0.219508	+	0.0798944i
$169$	−31.9689	+	26.8251i	−0.189165	+	0.158729i
$170$			90.7255i			0.533679i
$171$		0			0
$172$	10.2143			0.0593852
$173$	33.2452	+	39.6201i	0.192169	+	0.229018i	0.853522	−	0.521057i	$-0.174462\pi$
$173$	33.2452	+	39.6201i	0.192169	+	0.229018i	−0.661353	+	0.750075i	$0.730018\pi$
$174$	10.3645	−	28.4763i	0.0595663	−	0.163657i
$175$	−7.21528	+	40.9199i	−0.0412302	+	0.233828i
$176$	−47.2430	−	267.929i	−0.268426	−	1.52232i
$177$	16.8259	−	6.12412i	0.0950614	−	0.0345995i
$178$	7.67391	−	13.2916i	0.0431119	−	0.0746719i
$179$	−200.919	+	116.001i	−1.12245	+	0.648048i	−0.942026	−	0.335541i	$-0.891081\pi$
$179$	−200.919	+	116.001i	−1.12245	+	0.648048i	−0.180426	+	0.983589i	$0.557748\pi$
$180$	−4.64632	−	3.89873i	−0.0258129	−	0.0216596i
$181$	173.808	−	207.137i	0.960268	−	1.14440i	−0.0291889	−	0.999574i	$-0.509292\pi$
$181$	173.808	−	207.137i	0.960268	−	1.14440i	0.989457	−	0.144829i	$-0.0462631\pi$
$182$	33.1987	+	57.5019i	0.182411	+	0.315944i
$183$	103.751	+	59.9008i	0.566947	+	0.327327i
$184$	21.8131	+	59.9310i	0.118550	+	0.325712i
$185$	−163.703	+	28.8652i	−0.884880	+	0.156028i
$186$	21.7463	+	3.83446i	0.116915	+	0.0206154i
$187$	309.670	+	112.710i	1.65599	+	0.602730i
$188$	23.2995	−	19.5506i	0.123934	−	0.103993i
$189$			66.7741i			0.353302i
$190$		0			0
$191$	81.4552			0.426467			0.213233	−	0.977001i	$-0.431601\pi$
$191$	81.4552			0.426467			0.213233	+	0.977001i	$0.431601\pi$
$192$	−86.4261	−	102.999i	−0.450136	−	0.536451i
$193$	10.2027	−	28.0316i	0.0528635	−	0.145241i	−0.910451	−	0.413618i	$-0.864265\pi$
$193$	10.2027	−	28.0316i	0.0528635	−	0.145241i	0.963314	+	0.268377i	$0.0864872\pi$
$194$	−39.1613	+	222.095i	−0.201862	+	1.14482i
$195$	13.6806	+	77.5865i	0.0701569	+	0.397880i
$196$	16.8594	−	6.13633i	0.0860175	−	0.0313078i
$197$	90.0191	−	155.918i	0.456950	−	0.791461i	−0.541848	−	0.840476i	$-0.682275\pi$
$197$	90.0191	−	155.918i	0.456950	−	0.791461i	0.998798	+	0.0490159i	$0.0156085\pi$
$198$	164.527	−	94.9895i	0.830943	−	0.479745i
$199$	84.3626	+	70.7886i	0.423933	+	0.355722i	0.829657	−	0.558274i	$-0.188536\pi$
$199$	84.3626	+	70.7886i	0.423933	+	0.355722i	−0.405724	+	0.913996i	$0.632981\pi$
$200$	92.4208	−	110.143i	0.462104	−	0.550714i
$201$	11.7051	+	20.2739i	0.0582346	+	0.100865i
$202$	−215.453	−	124.392i	−1.06660	−	0.615802i
$203$	6.80666	+	18.7012i	0.0335304	+	0.0921239i
$204$	13.6469	−	2.40632i	0.0668966	−	0.0117957i
$205$	−84.9656	−	14.9817i	−0.414466	−	0.0730816i
$206$	23.5074	+	8.55600i	0.114114	+	0.0415340i
$207$	−30.5321	+	25.6195i	−0.147498	+	0.123766i
$208$		−	205.622i		−	0.988566i
$209$		0			0
$210$	24.8230			0.118205
$211$	−98.9315	−	117.902i	−0.468870	−	0.558777i	0.478843	−	0.877900i	$-0.341056\pi$
$211$	−98.9315	−	117.902i	−0.468870	−	0.558777i	−0.947713	+	0.319123i	$0.896612\pi$
$212$	3.98486	−	10.9483i	0.0187965	−	0.0516430i
$213$	−12.9766	+	73.5939i	−0.0609229	+	0.345511i
$214$	36.0135	+	204.243i	0.168287	+	0.954405i
$215$	64.4952	−	23.4743i	0.299978	−	0.109183i
$216$	115.531	−	200.105i	0.534864	−	0.926412i
$217$	−12.5588	+	7.25083i	−0.0578747	+	0.0334140i
$218$	298.908	+	250.813i	1.37114	+	1.15052i
$219$	−63.4793	+	75.6517i	−0.289860	+	0.345442i
$220$	11.1494	+	19.3114i	0.0506792	+	0.0877789i
$221$	215.697	+	124.533i	0.976006	+	0.563497i
$222$	−74.8819	−	205.736i	−0.337306	−	0.926741i
$223$	−153.268	+	27.0252i	−0.687298	+	0.121189i	−0.506382	−	0.862309i	$-0.669017\pi$
$223$	−153.268	+	27.0252i	−0.687298	+	0.121189i	−0.180916	+	0.983498i	$0.557906\pi$
$224$	15.7568	+	2.77834i	0.0703427	+	0.0124033i
$225$	84.4354	+	30.7320i	0.375269	+	0.136587i
$226$	−26.6379	+	22.3519i	−0.117867	+	0.0989020i
$227$		−	67.0830i		−	0.295520i	−0.989023	−	0.147760i	$-0.952794\pi$
$227$		−	67.0830i		−	0.295520i	0.989023	−	0.147760i	$-0.0472063\pi$
$228$		0			0
$229$	69.2740			0.302506			0.151253	−	0.988495i	$-0.451669\pi$
$229$	69.2740			0.302506			0.151253	+	0.988495i	$0.451669\pi$
$230$	25.9307	+	30.9030i	0.112742	+	0.134361i
$231$	30.8382	−	84.7274i	0.133499	−	0.366785i
$232$	11.9584	−	67.8193i	0.0515447	−	0.292325i
$233$	−28.3415	−	160.733i	−0.121637	−	0.689840i	−0.983248	−	0.182271i	$-0.941655\pi$
$233$	−28.3415	−	160.733i	−0.121637	−	0.689840i	0.861611	−	0.507569i	$-0.169456\pi$
$234$	134.925	−	49.1087i	0.576603	−	0.209866i
$235$	102.188	−	176.994i	0.434841	−	0.753166i
$236$	3.31720	−	1.91519i	0.0140559	−	0.00811519i
$237$	159.963	+	134.225i	0.674948	+	0.566348i
$238$	50.4431	−	60.1157i	0.211946	−	0.252587i
$239$	−152.816	−	264.685i	−0.639397	−	1.10747i	−0.985565	−	0.169296i	$-0.945851\pi$
$239$	−152.816	−	264.685i	−0.639397	−	1.10747i	0.346168	−	0.938172i	$-0.387483\pi$
$240$	−66.5738	−	38.4364i	−0.277391	−	0.160152i
$241$	82.1018	+	225.573i	0.340672	+	0.935987i	0.985200	+	0.171407i	$0.0548314\pi$
$241$	82.1018	+	225.573i	0.340672	+	0.935987i	−0.644529	+	0.764580i	$0.722946\pi$
$242$	−462.234	+	81.5043i	−1.91006	+	0.336795i
$243$	232.180	+	40.9397i	0.955475	+	0.168476i
$244$	24.0823	+	8.76523i	0.0986979	+	0.0359231i
$245$	92.3519	−	77.4924i	0.376946	−	0.316296i
$246$		−	113.635i		−	0.461931i
$247$		0			0
$248$	50.1807			0.202342
$249$	89.0123	+	106.081i	0.357479	+	0.426027i
$250$	76.3193	−	209.685i	0.305277	−	0.838742i
$251$	−55.4581	+	314.518i	−0.220948	+	1.25306i	0.649332	+	0.760505i	$0.275048\pi$
$251$	−55.4581	+	314.518i	−0.220948	+	1.25306i	−0.870281	+	0.492556i	$0.836063\pi$
$252$	0.911025	+	5.16668i	0.00361518	+	0.0205027i
$253$	137.694	−	50.1166i	0.544246	−	0.198089i
$254$	−10.7259	+	18.5778i	−0.0422280	+	0.0731411i
$255$	80.6396	−	46.5573i	0.316234	−	0.182578i
$256$	−60.4529	−	50.7260i	−0.236144	−	0.198149i
$257$	74.0054	−	88.1963i	0.287959	−	0.343176i	−0.602600	−	0.798043i	$-0.705869\pi$
$257$	74.0054	−	88.1963i	0.287959	−	0.343176i	0.890559	+	0.454867i	$0.150313\pi$
$258$	45.1993	+	78.2875i	0.175191	+	0.303440i
$259$	124.520	+	71.8918i	0.480773	+	0.277575i
$260$	5.76415	+	15.8369i	0.0221698	+	0.0609111i
$261$	42.3828	−	7.47324i	0.162386	−	0.0286331i
$262$	20.9272	+	3.69003i	0.0798748	+	0.0140841i
$263$	21.3498	+	7.77068i	0.0811778	+	0.0295463i	0.382290	−	0.924042i	$-0.375136\pi$
$263$	21.3498	+	7.77068i	0.0811778	+	0.0295463i	−0.301112	+	0.953589i	$0.597358\pi$
$264$	−239.007	+	200.551i	−0.905331	+	0.759663i
$265$		−	78.2882i		−	0.295427i
$266$		0			0
$267$	−15.7520			−0.0589962
$268$	3.21902	+	3.83628i	0.0120113	+	0.0143145i
$269$	95.0197	−	261.064i	0.353233	−	0.970500i	−0.628091	−	0.778140i	$-0.716164\pi$
$269$	95.0197	−	261.064i	0.353233	−	0.970500i	0.981324	−	0.192360i	$-0.0616142\pi$
$270$	25.3792	−	143.933i	0.0939970	−	0.533084i
$271$	0.587579	+	3.33232i	0.00216819	+	0.0122964i	0.985873	−	0.167497i	$-0.0535683\pi$
$271$	0.587579	+	3.33232i	0.00216819	+	0.0122964i	−0.983704	+	0.179793i	$0.942457\pi$
$272$	−228.369	+	83.1196i	−0.839593	+	0.305587i
$273$	34.0729	−	59.0161i	0.124809	−	0.216176i
$274$	265.185	−	153.105i	0.967830	−	0.558777i
$275$	−253.058	−	212.341i	−0.920211	−	0.772149i
$276$	3.96066	−	4.72013i	0.0143502	−	0.0171019i
$277$	67.8848	+	117.580i	0.245072	+	0.424476i	0.962152	−	0.272514i	$-0.0878552\pi$
$277$	67.8848	+	117.580i	0.245072	+	0.424476i	−0.717080	+	0.696991i	$0.754522\pi$
$278$	314.895	+	181.804i	1.13271	+	0.653973i
$279$	10.7257	+	29.4686i	0.0384433	+	0.105622i
$280$	55.5532	−	9.79553i	0.198404	−	0.0349841i
$281$	−485.734	−	85.6480i	−1.72859	−	0.304797i	−0.781059	−	0.624458i	$-0.785320\pi$
$281$	−485.734	−	85.6480i	−1.72859	−	0.304797i	−0.947532	+	0.319660i	$0.896431\pi$
$282$	252.950	+	92.0662i	0.896985	+	0.326476i
$283$	−287.011	+	240.831i	−1.01417	+	0.850993i	−0.988884	−	0.148687i	$-0.952495\pi$
$283$	−287.011	+	240.831i	−1.01417	+	0.850993i	−0.0252901	+	0.999680i	$0.508051\pi$
$284$			15.9860i			0.0562887i
$285$		0			0
$286$	−527.879			−1.84573
$287$	47.9693	+	57.1676i	0.167141	+	0.199190i
$288$	11.8338	−	32.5130i	0.0410895	−	0.112892i
$289$	0.932891	−	5.29069i	0.00322800	−	0.0183069i
$290$	−7.56402	−	42.8977i	−0.0260828	−	0.147923i
$291$	217.501	−	79.1638i	0.747425	−	0.272041i
$292$	−10.5629	+	18.2955i	−0.0361744	+	0.0626559i
$293$	−63.5500	+	36.6906i	−0.216894	+	0.125224i	−0.604511	−	0.796597i	$-0.706632\pi$
$293$	−63.5500	+	36.6906i	−0.216894	+	0.125224i	0.387617	+	0.921820i	$0.373298\pi$
$294$	121.637	+	102.066i	0.413732	+	0.347162i
$295$	16.5441	−	19.7165i	0.0560817	−	0.0668356i
$296$	−248.770	−	430.883i	−0.840440	−	1.45569i
$297$	−459.750	−	265.437i	−1.54798	−	0.893726i
$298$	−91.0198	−	250.075i	−0.305436	−	0.839178i
$299$	109.064	−	19.2310i	0.364764	−	0.0643177i
$300$	−13.6801	−	2.41216i	−0.0456002	−	0.00804054i
$301$	−55.7869	−	20.3048i	−0.185338	−	0.0674577i
$302$	147.358	−	123.648i	0.487940	−	0.409430i
$303$			255.335i			0.842691i
$304$		0			0
$305$	172.205			0.564607
$306$	−109.083	−	130.000i	−0.356481	−	0.424837i
$307$	31.6140	−	86.8587i	0.102977	−	0.282927i	−0.877495	−	0.479586i	$-0.840787\pi$
$307$	31.6140	−	86.8587i	0.102977	−	0.282927i	0.980472	+	0.196659i	$0.0630091\pi$
$308$	3.34933	−	18.9950i	0.0108744	−	0.0616720i
$309$	−4.45838	−	25.2848i	−0.0144284	−	0.0818277i
$310$	29.8266	−	10.8560i	0.0962147	−	0.0350193i
$311$	−99.6155	+	172.539i	−0.320307	+	0.554788i	−0.980551	−	0.196263i	$-0.937119\pi$
$311$	−99.6155	+	172.539i	−0.320307	+	0.554788i	0.660244	+	0.751051i	$0.270453\pi$
$312$	−204.216	+	117.904i	−0.654538	+	0.377898i
$313$	23.4391	+	19.6678i	0.0748854	+	0.0628363i	0.679462	−	0.733711i	$-0.262213\pi$
$313$	23.4391	+	19.6678i	0.0748854	+	0.0628363i	−0.604577	+	0.796547i	$0.706658\pi$
$314$	−203.658	+	242.710i	−0.648591	+	0.772961i
$315$	17.6264	+	30.5299i	0.0559569	+	0.0969203i
$316$	38.6852	+	22.3349i	0.122421	+	0.0706800i
$317$	−194.919	−	535.536i	−0.614887	−	1.68939i	−0.719164	−	0.694840i	$-0.755475\pi$
$317$	−194.919	−	535.536i	−0.614887	−	1.68939i	0.104277	−	0.994548i	$-0.466747\pi$
$318$	101.547	−	17.9055i	0.319331	−	0.0563067i
$319$	−155.818	−	27.4749i	−0.488457	−	0.0861282i
$320$	−181.613	−	66.1017i	−0.567541	−	0.206568i
$321$	163.056	−	136.820i	0.507963	−	0.426232i
$322$		−	34.8940i		−	0.108367i
$323$		0			0
$324$	−2.77909			−0.00857744
$325$	−160.485	−	191.259i	−0.493801	−	0.588489i
$326$	−21.9116	+	60.2015i	−0.0672134	+	0.184667i
$327$	69.5411	−	394.387i	0.212664	−	1.20608i
$328$	−44.8421	−	254.312i	−0.136714	−	0.775342i
$329$	−166.119	+	60.4623i	−0.504920	+	0.183776i
$330$	−98.6751	+	170.910i	−0.299015	+	0.517910i
$331$	383.016	−	221.134i	1.15715	−	0.668079i	0.206529	−	0.978441i	$-0.433783\pi$
$331$	383.016	−	221.134i	1.15715	−	0.668079i	0.950619	+	0.310361i	$0.100450\pi$
$332$	22.6927	+	19.0414i	0.0683514	+	0.0573536i
$333$	199.863	−	238.188i	0.600190	−	0.715278i
$334$	45.7005	+	79.1556i	0.136828	+	0.236993i
$335$	29.1421	+	16.8252i	0.0869915	+	0.0502245i
$336$	22.7420	+	62.4832i	0.0676846	+	0.185962i
$337$	435.527	−	76.7951i	1.29236	−	0.227879i	0.515142	−	0.857105i	$-0.327739\pi$
$337$	435.527	−	76.7951i	1.29236	−	0.227879i	0.777222	+	0.629226i	$0.216628\pi$
$338$	−77.8090	−	13.7198i	−0.230204	−	0.0405912i
$339$	33.5367	+	12.2064i	0.0989283	+	0.0360069i
$340$	15.2588	−	12.8037i	0.0448788	−	0.0376578i
$341$		−	115.292i		−	0.338101i
$342$		0			0
$343$	−222.659			−0.649150
$344$	132.048	+	157.369i	0.383861	+	0.457468i
$345$	14.1608	−	38.9064i	0.0410457	−	0.112772i
$346$	−17.0034	+	96.4312i	−0.0491428	+	0.278703i
$347$	0.608746	+	3.45237i	0.00175431	+	0.00994919i	0.985672	−	0.168671i	$-0.0539477\pi$
$347$	0.608746	+	3.45237i	0.00175431	+	0.00994919i	−0.983918	+	0.178621i	$0.942837\pi$
$348$	−6.25204	+	2.27556i	−0.0179656	+	0.00653895i
$349$	−44.1774	+	76.5174i	−0.126583	+	0.219248i	−0.922350	−	0.386354i	$-0.873734\pi$
$349$	−44.1774	+	76.5174i	−0.126583	+	0.219248i	0.795768	+	0.605602i	$0.207068\pi$
$350$	−68.1268	+	39.3330i	−0.194648	+	0.112380i
$351$	−307.359	−	257.905i	−0.875668	−	0.734772i
$352$	−81.7648	+	97.4435i	−0.232286	+	0.276828i
$353$	62.9423	+	109.019i	0.178307	+	0.308837i	0.941301	−	0.337569i	$-0.109605\pi$
$353$	62.9423	+	109.019i	0.178307	+	0.308837i	−0.762994	+	0.646406i	$0.776271\pi$
$354$	29.3580	+	16.9499i	0.0829323	+	0.0478810i
$355$	36.7389	+	100.939i	0.103490	+	0.284336i
$356$	−3.31845	+	0.585133i	−0.00932150	+	0.00164363i
$357$	−79.3184	−	13.9860i	−0.222180	−	0.0391764i
$358$	−412.743	−	150.226i	−1.15291	−	0.419627i
$359$	−46.1064	+	38.6879i	−0.128430	+	0.107766i	−0.704740	−	0.709465i	$-0.748936\pi$
$359$	−46.1064	+	38.6879i	−0.128430	+	0.107766i	0.576310	+	0.817231i	$0.304492\pi$
$360$		−	121.987i		−	0.338853i
$361$		0			0
$362$	511.927			1.41416
$363$	309.646	+	369.022i	0.853020	+	1.01659i
$364$	4.98586	−	13.6985i	0.0136974	−	0.0376334i
$365$	−24.6501	+	139.798i	−0.0675346	+	0.383008i
$366$	39.3856	+	223.367i	0.107611	+	0.610292i
$367$	−144.131	+	52.4592i	−0.392726	+	0.142941i	−0.530833	−	0.847477i	$-0.678121\pi$
$367$	−144.131	+	52.4592i	−0.392726	+	0.142941i	0.138106	+	0.990417i	$0.455898\pi$
$368$	−54.0305	+	93.5836i	−0.146822	+	0.254303i
$369$	139.760	−	80.6904i	0.378753	−	0.218673i
$370$	−241.081	−	202.291i	−0.651570	−	0.546732i
$371$	−43.5280	+	51.8746i	−0.117326	+	0.139824i
$372$	−2.42405	−	4.19857i	−0.00651625	−	0.0112865i
$373$	−230.727	−	133.210i	−0.618571	−	0.357132i	0.157741	−	0.987480i	$-0.449579\pi$
$373$	−230.727	−	133.210i	−0.618571	−	0.357132i	−0.776313	+	0.630348i	$0.782912\pi$
$374$	213.387	+	586.277i	0.570555	+	1.56759i
$375$	−225.539	+	39.7687i	−0.601438	+	0.106050i
$376$	602.426	+	106.224i	1.60220	+	0.282510i
$377$	−112.371	−	40.8996i	−0.298065	−	0.108487i
$378$	−96.8426	+	81.2606i	−0.256197	+	0.214975i
$379$			670.093i			1.76806i	0.467435	+	0.884028i	$0.345178\pi$
$379$			670.093i			1.76806i	−0.467435	+	0.884028i	$0.654822\pi$
$380$		0			0
$381$	22.0167			0.0577867
$382$	99.1267	+	118.135i	0.259494	+	0.309253i
$383$	−235.958	+	648.289i	−0.616078	+	1.69266i	0.100307	+	0.994957i	$0.468017\pi$
$383$	−235.958	+	648.289i	−0.616078	+	1.69266i	−0.716386	+	0.697705i	$0.754205\pi$
$384$	35.2647	−	199.996i	0.0918351	−	0.520823i
$385$	−22.5057	−	127.636i	−0.0584563	−	0.331522i
$386$	53.0703	−	19.3160i	0.137488	−	0.0500415i
$387$	−64.1907	+	111.182i	−0.165867	+	0.287291i
$388$	42.8800	−	24.7568i	0.110515	−	0.0638061i
$389$	172.996	+	145.161i	0.444719	+	0.373163i	0.837472	−	0.546481i	$-0.184033\pi$
$389$	172.996	+	145.161i	0.444719	+	0.373163i	−0.392753	+	0.919644i	$0.628477\pi$
$390$	−95.8753	+	114.260i	−0.245834	+	0.292974i
$391$	−65.4462	−	113.356i	−0.167381	−	0.289913i
$392$	312.497	+	180.420i	0.797187	+	0.460256i
$393$	−7.45932	−	20.4943i	−0.0189805	−	0.0521484i
$394$	335.676	−	59.1888i	0.851970	−	0.150225i
$395$	295.597	+	52.1217i	0.748346	+	0.131954i
$396$	−39.1948	−	14.2658i	−0.0989768	−	0.0360246i
$397$	463.140	−	388.621i	1.16660	−	0.978893i	0.166625	−	0.986020i	$-0.446713\pi$
$397$	463.140	−	388.621i	1.16660	−	0.978893i	0.999975	+	0.00712690i	$0.00226858\pi$
$398$			208.497i			0.523862i
$399$		0			0
$400$	243.616			0.609039
$401$	−208.376	−	248.333i	−0.519641	−	0.619284i	0.440855	−	0.897579i	$-0.354675\pi$
$401$	−208.376	−	248.333i	−0.519641	−	0.619284i	−0.960496	+	0.278294i	$0.910231\pi$
$402$	−15.1587	+	41.6483i	−0.0377083	+	0.103603i
$403$	15.1312	−	85.8131i	0.0375463	−	0.212936i
$404$	9.48484	+	53.7912i	0.0234773	+	0.133147i
$405$	−17.5478	+	6.38689i	−0.0433280	+	0.0157701i
$406$	−18.8390	+	32.6300i	−0.0464014	+	0.0803696i
$407$	−989.972	+	571.561i	−2.43236	+	1.40433i
$408$	213.499	+	179.147i	0.523281	+	0.439085i
$409$	−168.048	+	200.272i	−0.410876	+	0.489663i	−0.931304	−	0.364243i	$-0.881328\pi$
$409$	−168.048	+	200.272i	−0.410876	+	0.489663i	0.520428	+	0.853905i	$0.325772\pi$
$410$	−81.6706	−	141.458i	−0.199197	−	0.345019i
$411$	−272.168	−	157.137i	−0.662210	−	0.382327i
$412$	−1.87849	−	5.16110i	−0.00455943	−	0.0125269i
$413$	−21.9246	+	3.86590i	−0.0530862	+	0.00936053i
$414$	−74.3119	−	13.1032i	−0.179497	−	0.0316502i
$415$	187.048	+	68.0798i	0.450717	+	0.164048i
$416$	−73.6469	+	61.7971i	−0.177036	+	0.148551i
$417$		−	373.184i		−	0.894925i
$418$		0			0
$419$	−242.808			−0.579495			−0.289747	−	0.957103i	$-0.593571\pi$
$419$	−242.808			−0.579495			−0.289747	+	0.957103i	$0.593571\pi$
$420$	−3.50316	−	4.17490i	−0.00834085	−	0.00994023i
$421$	−190.093	+	522.275i	−0.451526	+	1.24056i	0.480123	+	0.877201i	$0.340592\pi$
$421$	−190.093	+	522.275i	−0.451526	+	1.24056i	−0.931650	+	0.363358i	$0.881630\pi$
$422$	50.5990	−	286.961i	0.119903	−	0.680003i
$423$	66.3833	+	376.478i	0.156934	+	0.890020i
$424$	220.194	−	80.1441i	0.519326	−	0.189019i
$425$	−147.544	+	255.553i	−0.347162	+	0.601301i
$426$	−122.525	+	70.7399i	−0.287618	+	0.166056i
$427$	−114.105	−	95.7456i	−0.267225	−	0.224229i
$428$	29.2685	−	34.8808i	0.0683842	−	0.0814972i
$429$	270.890	+	469.195i	0.631445	+	1.09369i
$430$	112.532	+	64.9704i	0.261703	+	0.151094i
$431$	−2.19041	−	6.01809i	−0.00508215	−	0.0139631i	0.937126	−	0.348992i	$-0.113476\pi$
$431$	−2.19041	−	6.01809i	−0.00508215	−	0.0139631i	−0.942208	+	0.335029i	$0.891254\pi$
$432$	385.551	−	67.9830i	0.892479	−	0.157368i
$433$	56.3966	+	9.94424i	0.130246	+	0.0229659i	0.238391	−	0.971169i	$-0.423380\pi$
$433$	56.3966	+	9.94424i	0.130246	+	0.0229659i	−0.108145	+	0.994135i	$0.534491\pi$
$434$	−25.7993	−	9.39018i	−0.0594454	−	0.0216364i
$435$	−34.2472	+	28.7368i	−0.0787291	+	0.0660616i
$436$		−	85.6684i		−	0.196487i
$437$		0			0
$438$	−186.969			−0.426870
$439$	−336.539	−	401.071i	−0.766603	−	0.913602i	0.231643	−	0.972801i	$-0.425590\pi$
$439$	−336.539	−	401.071i	−0.766603	−	0.913602i	−0.998246	+	0.0591989i	$0.981145\pi$
$440$	−153.388	+	421.431i	−0.348610	+	0.957798i
$441$	−39.1582	+	222.077i	−0.0887941	+	0.503576i
$442$	81.8821	+	464.376i	0.185254	+	1.05063i
$443$	−408.324	+	148.618i	−0.921726	+	0.335481i	−0.758925	−	0.651178i	$-0.774275\pi$
$443$	−408.324	+	148.618i	−0.921726	+	0.335481i	−0.162801	+	0.986659i	$0.552053\pi$
$444$	−24.0344	+	41.6287i	−0.0541315	+	0.0937584i
$445$	−19.6087	+	11.3211i	−0.0440646	+	0.0254407i
$446$	−225.713	−	189.396i	−0.506083	−	0.424654i
$447$	−175.566	+	209.231i	−0.392765	+	0.468079i
$448$	83.5864	+	144.776i	0.186577	+	0.323161i
$449$	−272.280	−	157.201i	−0.606415	−	0.350114i	0.165146	−	0.986269i	$-0.447190\pi$
$449$	−272.280	−	157.201i	−0.606415	−	0.350114i	−0.771561	+	0.636155i	$0.780524\pi$
$450$	58.1829	+	159.856i	0.129295	+	0.355236i
$451$	−584.293	+	103.027i	−1.29555	+	0.228440i
$452$	7.51856	+	1.32573i	0.0166340	+	0.00293302i
$453$	−185.521	−	67.5241i	−0.409539	−	0.149060i
$454$	97.2906	−	81.6365i	0.214296	−	0.179816i
$455$		−	97.9543i		−	0.215284i
$456$		0			0
$457$	525.189			1.14921			0.574606	−	0.818431i	$-0.305155\pi$
$457$	525.189			1.14921			0.574606	+	0.818431i	$0.305155\pi$
$458$	84.3028	+	100.468i	0.184067	+	0.219363i
$459$	−162.191	+	445.616i	−0.353357	+	0.970842i
$460$	1.53799	−	8.72239i	0.00334346	−	0.0189617i
$461$	−105.856	−	600.341i	−0.229623	−	1.30226i	−0.853647	−	0.520852i	$-0.825614\pi$
$461$	−105.856	−	600.341i	−0.229623	−	1.30226i	0.624024	−	0.781405i	$-0.285497\pi$
$462$	160.409	−	58.3840i	0.347205	−	0.126372i
$463$	381.720	−	661.158i	0.824449	−	1.42799i	−0.0778909	−	0.996962i	$-0.524819\pi$
$463$	381.720	−	661.158i	0.824449	−	1.42799i	0.902340	−	0.431025i	$-0.141848\pi$
$464$	101.050	−	58.3411i	0.217780	−	0.125735i
$465$	−24.9551	−	20.9398i	−0.0536669	−	0.0450319i
$466$	198.621	−	236.707i	0.426225	−	0.507955i
$467$	224.311	+	388.519i	0.480324	+	0.831946i	0.999745	−	0.0225724i	$-0.00718563\pi$
$467$	224.311	+	388.519i	0.480324	+	0.831946i	−0.519421	+	0.854519i	$0.673852\pi$
$468$	−27.3008	−	15.7621i	−0.0583350	−	0.0336797i
$469$	−9.95514	−	27.3515i	−0.0212263	−	0.0583188i
$470$	381.052	−	67.1897i	0.810748	−	0.142957i
$471$	320.238	+	56.4666i	0.679911	+	0.119887i
$472$	72.3911	+	26.3482i	0.153371	+	0.0558225i
$473$	361.562	−	303.387i	0.764402	−	0.641410i
$474$			395.338i			0.834047i
$475$		0			0
$476$	−17.2294			−0.0361963
$477$	94.1292	+	112.179i	0.197336	+	0.235176i
$478$	197.904	−	543.737i	0.414025	−	1.13752i
$479$	−120.974	+	686.080i	−0.252556	+	1.43232i	0.549712	+	0.835354i	$0.314737\pi$
$479$	−120.974	+	686.080i	−0.252556	+	1.43232i	−0.802268	+	0.596964i	$0.796374\pi$
$480$	6.24128	+	35.3961i	0.0130027	+	0.0737418i
$481$	−811.858	+	295.492i	−1.68785	+	0.614328i
$482$	−227.235	+	393.583i	−0.471442	+	0.816562i
$483$	−31.0149	+	17.9064i	−0.0642130	+	0.0370734i
$484$	78.9408	+	66.2392i	0.163101	+	0.136858i
$485$	213.858	−	254.866i	0.440945	−	0.525498i
$486$	223.177	+	386.553i	0.459211	+	0.795377i
$487$	16.8247	+	9.71373i	0.0345476	+	0.0199461i	0.517174	−	0.855880i	$-0.326984\pi$
$487$	16.8247	+	9.71373i	0.0345476	+	0.0199461i	−0.482627	+	0.875826i	$0.660317\pi$
$488$	176.288	+	484.347i	0.361245	+	0.992513i
$489$	64.7532	−	11.4177i	0.132420	−	0.0233492i
$490$	224.775	+	39.6339i	0.458724	+	0.0808854i
$491$	−622.404	−	226.537i	−1.26763	−	0.461378i	−0.381305	−	0.924449i	$-0.624525\pi$
$491$	−622.404	−	226.537i	−1.26763	−	0.461378i	−0.886321	+	0.463072i	$0.846747\pi$
$492$	−19.1119	+	16.0368i	−0.0388453	+	0.0325951i
$493$			141.335i			0.286684i
$494$		0			0
$495$	−280.271			−0.566203
$496$	54.6522	+	65.1319i	0.110186	+	0.131314i
$497$	31.7783	−	87.3101i	0.0639402	−	0.175674i
$498$	−45.5257	+	258.189i	−0.0914172	+	0.518453i
$499$	−23.2000	−	131.574i	−0.0464929	−	0.263674i	0.952697	−	0.303922i	$-0.0982963\pi$
$499$	−23.2000	−	131.574i	−0.0464929	−	0.263674i	−0.999190	+	0.0402479i	$0.987185\pi$
$500$	−46.0369	+	16.7560i	−0.0920737	+	0.0335121i
$501$	46.9040	−	81.2400i	0.0936207	−	0.162156i
$502$	−523.636	+	302.321i	−1.04310	+	0.602234i
$503$	−248.770	−	208.743i	−0.494572	−	0.414995i	0.361089	−	0.932531i	$-0.382405\pi$
$503$	−248.770	−	208.743i	−0.494572	−	0.414995i	−0.855661	+	0.517536i	$0.826849\pi$
$504$	−67.8244	+	80.8300i	−0.134572	+	0.160377i
$505$	183.512	+	317.852i	0.363390	+	0.629410i
$506$	240.251	+	138.709i	0.474804	+	0.274128i
$507$	27.7344	+	76.1996i	0.0547029	+	0.150295i
$508$	4.63824	−	0.817847i	0.00913040	−	0.00160994i
$509$	−481.130	−	84.8363i	−0.945246	−	0.166672i	−0.320279	−	0.947323i	$-0.603777\pi$
$509$	−481.130	−	84.8363i	−0.945246	−	0.166672i	−0.624967	+	0.780651i	$0.714888\pi$
$510$	165.656	+	60.2939i	0.324816	+	0.118223i
$511$	94.0605	−	78.9262i	0.184071	−	0.154454i
$512$		−	567.464i		−	1.10833i
$513$		0			0
$514$	217.972			0.424070
$515$	−23.7224	−	28.2713i	−0.0460629	−	0.0548956i
$516$	6.78815	−	18.6503i	0.0131553	−	0.0361439i
$517$	244.054	−	1384.10i	0.472058	−	2.67717i
$518$	47.2698	+	268.081i	0.0912545	+	0.517530i
$519$	94.4366	−	34.3721i	0.181959	−	0.0662275i
$520$	−169.478	+	293.544i	−0.325919	+	0.564508i
$521$	539.718	−	311.606i	1.03593	−	0.598093i	0.117250	−	0.993102i	$-0.462592\pi$
$521$	539.718	−	311.606i	1.03593	−	0.598093i	0.918677	+	0.395010i	$0.129259\pi$
$522$	62.4161	+	52.3733i	0.119571	+	0.100332i
$523$	−422.510	+	503.528i	−0.807858	+	0.962768i	−0.999826	−	0.0186330i	$-0.994069\pi$
$523$	−422.510	+	503.528i	−0.807858	+	0.962768i	0.191968	+	0.981401i	$0.438513\pi$
$524$	−2.33274	−	4.04043i	−0.00445180	−	0.00771074i
$525$	69.9208	+	40.3688i	0.133182	+	0.0768929i
$526$	14.7117	+	40.4201i	0.0279690	+	0.0768443i
$527$	−101.423	+	17.8836i	−0.192454	+	0.0339347i
$528$	−520.609	−	91.7974i	−0.986002	−	0.173859i
$529$	442.406	+	161.023i	0.836307	+	0.304391i
$530$	113.541	−	95.2726i	0.214229	−	0.179760i
$531$			48.1433i			0.0906654i
$532$		0			0
$533$	−448.416			−0.841305
$534$	−19.1693	−	22.8451i	−0.0358976	−	0.0427811i
$535$	104.645	−	287.510i	0.195598	−	0.537402i
$536$	−17.4898	+	99.1896i	−0.0326302	+	0.185055i
$537$	78.2804	+	443.950i	0.145773	+	0.826723i
$538$	494.256	−	179.895i	0.918692	−	0.334376i
$539$	414.524	−	717.976i	0.769061	−	1.33205i
$540$	−27.7892	+	16.0441i	−0.0514614	+	0.0297113i
$541$	68.4827	+	57.4638i	0.126585	+	0.106218i	0.703883	−	0.710316i	$-0.251448\pi$
$541$	68.4827	+	57.4638i	0.126585	+	0.106218i	−0.577297	+	0.816534i	$0.695893\pi$
$542$	−4.11782	+	4.90743i	−0.00759746	+	0.00905430i
$543$	−262.704	−	455.016i	−0.483800	−	0.837967i
$544$	98.4042	+	56.8137i	0.180890	+	0.104437i
$545$	−196.882	−	540.930i	−0.361252	−	0.992532i
$546$	127.056	−	22.4034i	0.232703	−	0.0410319i
$547$	690.166	+	121.695i	1.26173	+	0.222477i	0.764205	−	0.644973i	$-0.223132\pi$
$547$	690.166	+	121.695i	1.26173	+	0.222477i	0.497524	+	0.867450i	$0.334243\pi$
$548$	−63.1745	−	22.9937i	−0.115282	−	0.0419592i
$549$	−246.752	+	207.050i	−0.449457	+	0.377140i
$550$		−	625.418i		−	1.13712i
$551$		0			0
$552$	123.925			0.224502
$553$	−166.886	−	198.887i	−0.301783	−	0.359652i
$554$	−87.9142	+	241.542i	−0.158690	+	0.435997i
$555$	−56.0877	+	318.089i	−0.101059	+	0.573134i
$556$	−13.8625	−	78.6183i	−0.0249326	−	0.141400i
$557$	197.952	−	72.0486i	0.355390	−	0.129351i	−0.158155	−	0.987414i	$-0.550554\pi$
$557$	197.952	−	72.0486i	0.355390	−	0.129351i	0.513544	+	0.858063i	$0.328332\pi$
$558$	−29.6857	+	51.4172i	−0.0532003	+	0.0921455i
$559$	308.931	−	178.361i	0.552649	−	0.319072i
$560$	73.2175	+	61.4368i	0.130746	+	0.109709i
$561$	411.598	−	490.523i	0.733685	−	0.874372i
$562$	−466.897	−	808.690i	−0.830778	−	1.43895i
$563$	−461.855	−	266.652i	−0.820347	−	0.473627i	0.0301894	−	0.999544i	$-0.490389\pi$
$563$	−461.855	−	266.652i	−0.820347	−	0.473627i	−0.850536	+	0.525917i	$0.823722\pi$
$564$	−20.2133	−	55.5356i	−0.0358392	−	0.0984674i
$565$	50.5207	−	8.90816i	0.0894172	−	0.0157667i
$566$	−698.556	−	123.174i	−1.23420	−	0.217622i
$567$	15.1785	+	5.52451i	0.0267698	+	0.00974341i
$568$	−246.293	+	206.664i	−0.433614	+	0.363846i
$569$			610.046i			1.07214i	0.844174	+	0.536068i	$0.180091\pi$
$569$			610.046i			1.07214i	−0.844174	+	0.536068i	$0.819909\pi$
$570$		0			0
$571$	−678.976			−1.18910			−0.594550	−	0.804059i	$-0.702670\pi$
$571$	−678.976			−1.18910			−0.594550	+	0.804059i	$0.702670\pi$
$572$	74.4971	+	88.7822i	0.130240	+	0.155214i
$573$	54.1331	−	148.729i	0.0944731	−	0.259563i
$574$	−24.5341	+	139.140i	−0.0427424	+	0.242404i
$575$	22.7844	+	129.217i	0.0396251	+	0.224725i
$576$	339.709	−	123.644i	0.589773	−	0.214660i
$577$	−363.669	+	629.894i	−0.630276	+	1.09167i	0.357219	+	0.934021i	$0.383725\pi$
$577$	−363.669	+	629.894i	−0.630276	+	1.09167i	−0.987495	+	0.157649i	$0.949608\pi$
$578$	8.80838	−	5.08552i	0.0152394	−	0.00879847i
$579$	−44.4025	−	37.2582i	−0.0766883	−	0.0643492i
$580$	−6.14734	+	7.32611i	−0.0105989	+	0.0126312i
$581$	−86.0877	−	149.108i	−0.148172	−	0.256641i
$582$	379.498	+	219.104i	0.652059	+	0.376467i
$583$	−184.135	−	505.906i	−0.315840	−	0.867763i
$584$	−418.431	+	73.7807i	−0.716492	+	0.126337i
$585$	−208.608	−	36.7832i	−0.356595	−	0.0628772i
$586$	−130.549	−	47.5161i	−0.222781	−	0.0810855i
$587$	−750.571	+	629.804i	−1.27866	+	1.07292i	−0.285229	+	0.958459i	$0.592070\pi$
$587$	−750.571	+	629.804i	−1.27866	+	1.07292i	−0.993428	+	0.114461i	$0.963486\pi$
$588$		−	34.8618i		−	0.0592888i
$589$		0			0
$590$	48.7282			0.0825901
$591$	−224.867	−	267.986i	−0.380485	−	0.453444i
$592$	288.326	−	792.168i	0.487037	−	1.33812i
$593$	−60.5272	+	343.267i	−0.102069	+	0.578864i	0.890281	+	0.455412i	$0.150508\pi$
$593$	−60.5272	+	343.267i	−0.102069	+	0.578864i	−0.992350	+	0.123453i	$0.960603\pi$
$594$	−174.528	−	989.799i	−0.293819	−	1.66633i
$595$	−108.791	+	39.5966i	−0.182842	+	0.0665489i
$596$	−29.2140	+	50.6002i	−0.0490169	+	0.0848997i
$597$	185.319	−	106.994i	0.310417	−	0.179219i
$598$	160.616	+	134.773i	0.268589	+	0.225373i
$599$	−272.099	+	324.275i	−0.454256	+	0.541361i	−0.943756	−	0.330642i	$-0.892735\pi$
$599$	−272.099	+	324.275i	−0.454256	+	0.541361i	0.489500	+	0.872003i	$0.337179\pi$
$600$	−139.690	−	241.950i	−0.232817	−	0.403250i
$601$	437.051	+	252.331i	0.727206	+	0.419853i	0.817399	−	0.576072i	$-0.195415\pi$
$601$	437.051	+	252.331i	0.727206	+	0.419853i	−0.0901931	+	0.995924i	$0.528748\pi$
$602$	−38.4417	−	105.618i	−0.0638566	−	0.175445i
$603$	−61.9873	+	10.9300i	−0.102798	+	0.0181261i
$604$	−41.5918	−	7.33376i	−0.0688606	−	0.0121420i
$605$	650.681	+	236.829i	1.07551	+	0.391452i
$606$	−370.313	+	310.730i	−0.611078	+	0.512755i
$607$		−	73.0072i		−	0.120275i	−0.998190	−	0.0601377i	$-0.980846\pi$
$607$		−	73.0072i		−	0.120275i	0.998190	−	0.0601377i	$-0.0191540\pi$
$608$		0			0
$609$	38.6701			0.0634977
$610$	209.565	+	249.750i	0.343549	+	0.409426i
$611$	363.303	−	998.167i	0.594604	−	1.63366i
$612$	−6.46990	+	36.6926i	−0.0105717	+	0.0599553i
$613$	−178.365	−	1011.56i	−0.290971	−	1.65018i	−0.683141	−	0.730287i	$-0.739387\pi$
$613$	−178.365	−	1011.56i	−0.290971	−	1.65018i	0.392170	−	0.919893i	$-0.371725\pi$
$614$	164.444	−	59.8527i	0.267824	−	0.0974799i
$615$	−83.8212	+	145.183i	−0.136295	+	0.236069i
$616$	335.951	−	193.962i	0.545376	−	0.314873i
$617$	324.931	+	272.649i	0.526630	+	0.441895i	0.866936	−	0.498420i	$-0.166086\pi$
$617$	324.931	+	272.649i	0.526630	+	0.441895i	−0.340306	+	0.940315i	$0.610531\pi$
$618$	31.2449	−	37.2362i	0.0505581	−	0.0602528i
$619$	−164.352	−	284.665i	−0.265512	−	0.459879i	0.702186	−	0.711994i	$-0.252208\pi$
$619$	−164.352	−	284.665i	−0.265512	−	0.459879i	−0.967698	+	0.252114i	$0.918874\pi$
$620$	−6.03511	−	3.48437i	−0.00973405	−	0.00561996i
$621$	72.1181	+	198.143i	0.116132	+	0.319071i
$622$	−371.461	+	65.4985i	−0.597204	+	0.105303i
$623$	19.2875	+	3.40090i	0.0309590	+	0.00545891i
$624$	−375.446	−	136.651i	−0.601676	−	0.218992i
$625$	77.2003	−	64.7788i	0.123521	−	0.103646i
$626$			57.9284i			0.0925375i
$627$		0			0
$628$	69.5618			0.110767
$629$	656.363	+	782.223i	1.04350	+	1.24360i
$630$	−22.8271	+	62.7169i	−0.0362335	+	0.0995507i
$631$	20.4522	−	115.990i	0.0324123	−	0.183819i	−0.964303	−	0.264800i	$-0.914694\pi$
$631$	20.4522	−	115.990i	0.0324123	−	0.183819i	0.996716	+	0.0809806i	$0.0258052\pi$
$632$	156.006	+	884.756i	0.246846	+	1.39993i
$633$	−281.025	+	102.285i	−0.443958	+	0.161588i
$634$	539.483	−	934.411i	0.850919	−	1.47383i
$635$	27.4074	−	15.8236i	0.0431612	−	0.0249191i
$636$	−17.3424	−	14.5520i	−0.0272679	−	0.0228804i
$637$	402.762	−	479.993i	0.632280	−	0.753521i
$638$	−149.775	−	259.418i	−0.234757	−	0.406612i
$639$	−174.006	−	100.463i	−0.272310	−	0.157219i
$640$	−99.8401	−	274.308i	−0.156000	−	0.428607i
$641$	−73.2824	+	12.9217i	−0.114325	+	0.0201586i	−0.230518	−	0.973068i	$-0.574042\pi$
$641$	−73.2824	+	12.9217i	−0.114325	+	0.0201586i	0.116193	+	0.993227i	$0.462931\pi$
$642$	396.862	+	69.9774i	0.618164	+	0.108999i
$643$	463.236	+	168.604i	0.720429	+	0.262215i	0.676108	−	0.736802i	$-0.263665\pi$
$643$	463.236	+	168.604i	0.720429	+	0.262215i	0.0443214	+	0.999017i	$0.485887\pi$
$644$	−5.86871	+	4.92443i	−0.00911290	+	0.00764663i
$645$		−	133.363i		−	0.206764i
$646$		0			0
$647$	989.083			1.52872			0.764361	−	0.644789i	$-0.223055\pi$
$647$	989.083			1.52872			0.764361	+	0.644789i	$0.223055\pi$
$648$	−35.9277	−	42.8169i	−0.0554439	−	0.0660755i
$649$	60.5362	−	166.322i	0.0932761	−	0.256274i
$650$	82.0810	−	465.504i	0.126278	−	0.716160i
$651$	4.89306	+	27.7499i	0.00751622	+	0.0426266i
$652$	13.2174	−	4.81073i	0.0202720	−	0.00737842i
$653$	79.5099	−	137.715i	0.121761	−	0.210896i	−0.798701	−	0.601728i	$-0.794479\pi$
$653$	79.5099	−	137.715i	0.121761	−	0.210896i	0.920462	+	0.390832i	$0.127813\pi$
$654$	656.609	−	379.093i	1.00399	−	0.579653i
$655$	−24.0152	−	20.1511i	−0.0366644	−	0.0307651i
$656$	281.246	−	335.176i	0.428728	−	0.510939i
$657$	−132.764	−	229.953i	−0.202076	−	0.350005i
$658$	−289.846	−	167.343i	−0.440496	−	0.254320i
$659$	−254.578	−	699.446i	−0.386309	−	1.06137i	−0.968650	−	0.248430i	$-0.920085\pi$
$659$	−254.578	−	699.446i	−0.386309	−	1.06137i	0.582341	−	0.812945i	$-0.302137\pi$
$660$	42.6704	−	7.52394i	0.0646521	−	0.0113999i
$661$	−754.889	−	133.107i	−1.14204	−	0.201373i	−0.429543	−	0.903046i	$-0.641325\pi$
$661$	−754.889	−	133.107i	−1.14204	−	0.201373i	−0.712498	+	0.701674i	$0.752436\pi$
$662$	786.821	+	286.380i	1.18855	+	0.432598i
$663$	370.733	−	311.082i	0.559174	−	0.469203i
$664$			595.786i			0.897268i
$665$		0			0
$666$	588.667			0.883884
$667$	40.3957	+	48.1417i	0.0605632	+	0.0721764i
$668$	6.86342	−	18.8571i	0.0102746	−	0.0282292i
$669$	−52.5124	+	297.812i	−0.0784938	+	0.445161i
$670$	11.0628	+	62.7403i	0.0165117	+	0.0936422i
$671$	1112.81	−	405.029i	1.65843	−	0.603620i
$672$	15.5446	−	26.9240i	0.0231318	−	0.0400654i
$673$	695.119	−	401.327i	1.03287	−	0.596326i	0.115062	−	0.993358i	$-0.463293\pi$
$673$	695.119	−	401.327i	1.03287	−	0.596326i	0.917804	+	0.397033i	$0.129960\pi$
$674$	641.390	+	538.190i	0.951617	+	0.798501i
$675$	305.560	−	364.152i	0.452681	−	0.539485i
$676$	8.67333	+	15.0227i	0.0128304	+	0.0222229i
$677$	−432.884	−	249.926i	−0.639415	−	0.369166i	0.144974	−	0.989435i	$-0.453690\pi$
$677$	−432.884	−	249.926i	−0.639415	−	0.369166i	−0.784389	+	0.620269i	$0.787023\pi$
$678$	23.1095	+	63.4928i	0.0340848	+	0.0936472i
$679$	−283.410	+	49.9728i	−0.417393	+	0.0735976i
$680$	394.527	+	69.5657i	0.580187	+	0.102303i
$681$	−122.487	−	44.5817i	−0.179864	−	0.0654651i
$682$	167.209	−	140.305i	0.245174	−	0.205726i
$683$			52.2603i			0.0765159i	0.999268	+	0.0382579i	$0.0121808\pi$
$683$			52.2603i			0.0765159i	−0.999268	+	0.0382579i	$0.987819\pi$
$684$		0			0
$685$	−451.742			−0.659478
$686$	−270.964	−	322.922i	−0.394991	−	0.470732i
$687$	46.0378	−	126.488i	0.0670128	−	0.184116i
$688$	−60.4420	+	342.784i	−0.0878517	+	0.498232i
$689$	−70.6571	−	400.716i	−0.102550	−	0.581591i
$690$	73.6589	−	26.8096i	0.106752	−	0.0388545i
$691$	130.083	−	225.311i	0.188253	−	0.326065i	−0.756415	−	0.654093i	$-0.773051\pi$
$691$	130.083	−	225.311i	0.188253	−	0.326065i	0.944668	+	0.328028i	$0.106384\pi$
$692$	18.6180	−	10.7491i	0.0269047	−	0.0155334i
$693$	185.710	+	155.830i	0.267980	+	0.224862i
$694$	−4.26617	+	5.08422i	−0.00614721	+	0.00732596i
$695$	−268.211	−	464.555i	−0.385915	−	0.668425i
$696$	−115.884	−	66.9059i	−0.166501	−	0.0961292i
$697$	181.266	+	498.023i	0.260065	+	0.714524i
$698$	−164.735	+	29.0472i	−0.236010	+	0.0416149i
$699$	−312.318	−	55.0701i	−0.446807	−	0.0787841i
$700$	16.2297	+	5.90713i	0.0231853	+	0.00843876i
$701$	367.741	−	308.571i	0.524595	−	0.440187i	−0.341635	−	0.939833i	$-0.610981\pi$
$701$	367.741	−	308.571i	0.524595	−	0.440187i	0.866230	+	0.499645i	$0.166536\pi$
$702$		−	759.621i		−	1.08208i
$703$		0			0
$704$	−1329.07			−1.88789
$705$	−255.263	−	304.211i	−0.362075	−	0.431505i
$706$	−81.5134	+	223.956i	−0.115458	+	0.317218i
$707$	55.1277	−	312.645i	0.0779741	−	0.442213i
$708$	−1.29242	−	7.32968i	−0.00182545	−	0.0103527i
$709$	−400.096	+	145.623i	−0.564310	+	0.205392i	−0.608393	−	0.793636i	$-0.708186\pi$
$709$	−400.096	+	145.623i	−0.564310	+	0.205392i	0.0440832	+	0.999028i	$0.485963\pi$
$710$	−101.683	+	176.120i	−0.143216	+	0.248057i
$711$	−486.227	+	280.724i	−0.683864	+	0.394829i
$712$	−51.9155	−	43.5622i	−0.0729150	−	0.0611829i
$713$	−29.4354	+	35.0797i	−0.0412839	+	0.0492002i
$714$	−76.2424	−	132.056i	−0.106782	−	0.184952i
$715$	674.430	+	389.382i	0.943259	+	0.544591i
$716$	32.9825	+	90.6186i	0.0460649	+	0.126562i
$717$	−584.847	+	103.124i	−0.815687	+	0.143828i
$718$	−112.218	−	19.7871i	−0.156293	−	0.0275586i
$719$	−528.176	−	192.240i	−0.734598	−	0.267372i	−0.0524881	−	0.998622i	$-0.516715\pi$
$719$	−528.176	−	192.240i	−0.734598	−	0.267372i	−0.682110	+	0.731250i	$0.738937\pi$
$720$	158.333	−	132.857i	0.219907	−	0.184524i
$721$			31.9224i			0.0442752i
$722$		0			0
$723$	466.438			0.645142
$724$	−72.2458	−	86.0992i	−0.0997870	−	0.118922i
$725$	48.4569	−	133.134i	0.0668370	−	0.183633i
$726$	−158.370	+	898.161i	−0.218141	+	1.23714i
$727$	46.1543	+	261.754i	0.0634859	+	0.360047i	0.999957	+	0.00930111i	$0.00296068\pi$
$727$	46.1543	+	261.754i	0.0634859	+	0.360047i	−0.936471	+	0.350746i	$0.885928\pi$
$728$	275.507	−	100.276i	0.378444	−	0.137742i
$729$	259.140	−	448.844i	0.355473	−	0.615698i
$730$	−232.747	+	134.376i	−0.318831	+	0.184077i
$731$	−322.974	−	271.007i	−0.441825	−	0.370735i
$732$	32.0090	−	38.1468i	0.0437281	−	0.0521131i
$733$	354.455	+	613.934i	0.483567	+	0.837563i	0.999822	−	0.0188721i	$-0.00600753\pi$
$733$	354.455	+	613.934i	0.483567	+	0.837563i	−0.516255	+	0.856435i	$0.672674\pi$
$734$	−251.481	−	145.193i	−0.342617	−	0.197810i
$735$	−80.1191	−	220.125i	−0.109006	−	0.299490i
$736$	49.7567	−	8.77345i	0.0676042	−	0.0119204i
$737$	227.892	+	40.1836i	0.309216	+	0.0545232i
$738$	287.106	+	104.498i	0.389033	+	0.141596i
$739$	−476.469	+	399.805i	−0.644748	+	0.541008i	−0.905472	−	0.424405i	$-0.860483\pi$
$739$	−476.469	+	399.805i	−0.644748	+	0.541008i	0.260724	+	0.965413i	$0.416039\pi$
$740$			69.0950i			0.0933716i
$741$		0			0
$742$	−128.205			−0.172783
$743$	−327.193	−	389.934i	−0.440368	−	0.524810i	0.499516	−	0.866305i	$-0.333511\pi$
$743$	−327.193	−	389.934i	−0.440368	−	0.524810i	−0.939884	+	0.341495i	$0.889067\pi$
$744$	33.3489	−	91.6253i	0.0448238	−	0.123152i
$745$	−68.1752	+	386.641i	−0.0915104	+	0.518981i
$746$	−87.5876	−	496.734i	−0.117410	−	0.665863i
$747$	−349.875	+	127.344i	−0.468373	+	0.170474i
$748$	68.4896	−	118.627i	0.0915636	−	0.158593i
$749$	−229.194	+	132.325i	−0.305999	+	0.176669i
$750$	−332.146	−	278.704i	−0.442861	−	0.371605i
$751$	−349.082	+	416.020i	−0.464823	+	0.553954i	−0.946630	−	0.322323i	$-0.895536\pi$
$751$	−349.082	+	416.020i	−0.464823	+	0.553954i	0.481807	+	0.876277i	$0.339981\pi$
$752$	518.233	+	897.606i	0.689140	+	1.19362i
$753$	537.425	+	310.282i	0.713712	+	0.412062i
$754$	−77.4325	−	212.744i	−0.102696	−	0.282154i
$755$	−279.475	+	49.2789i	−0.370165	+	0.0652701i
$756$	27.3339	+	4.81970i	0.0361559	+	0.00637526i
$757$	578.580	+	210.586i	0.764306	+	0.278185i	0.694613	−	0.719384i	$-0.255576\pi$
$757$	578.580	+	210.586i	0.764306	+	0.278185i	0.0696933	+	0.997568i	$0.477798\pi$
$758$	−971.837	+	815.468i	−1.28211	+	1.07582i
$759$		−	284.723i		−	0.375129i
$760$		0			0
$761$	841.391			1.10564			0.552819	−	0.833301i	$-0.313552\pi$
$761$	841.391			1.10564			0.552819	+	0.833301i	$0.313552\pi$
$762$	26.7932	+	31.9309i	0.0351617	+	0.0419041i
$763$	−170.299	+	467.892i	−0.223196	+	0.613227i
$764$	5.87937	−	33.3436i	0.00769551	−	0.0436434i
$765$	43.4742	+	246.555i	0.0568291	+	0.322294i
$766$	−1227.36	+	446.724i	−1.60230	+	0.583190i
$767$	66.8860	−	115.850i	0.0872046	−	0.151043i
$768$	−132.797	+	76.6701i	−0.172912	+	0.0998309i
$769$	599.583	+	503.110i	0.779692	+	0.654239i	0.943171	−	0.332308i	$-0.107827\pi$
$769$	599.583	+	503.110i	0.779692	+	0.654239i	−0.163479	+	0.986547i	$0.552272\pi$
$770$	157.723	−	187.966i	0.204834	−	0.244112i
$771$	−111.856	−	193.740i	−0.145079	−	0.251284i
$772$	−10.7383	−	6.19973i	−0.0139097	−	0.00803074i
$773$	330.028	+	906.745i	0.426945	+	1.17302i	0.947657	+	0.319289i	$0.103444\pi$
$773$	330.028	+	906.745i	0.426945	+	1.17302i	−0.520713	+	0.853732i	$0.674334\pi$
$774$	−239.363	+	42.2062i	−0.309255	+	0.0545300i
$775$	101.669	+	17.9270i	0.131186	+	0.0231317i
$776$	935.769	+	340.592i	1.20589	+	0.438907i
$777$	214.021	−	179.585i	0.275445	−	0.231126i
$778$			427.549i			0.549548i
$779$		0			0
$780$	32.7474			0.0419838
$781$	474.820	+	565.869i	0.607965	+	0.724544i
$782$	84.7560	−	232.865i	0.108384	−	0.297781i
$783$	39.5365	−	224.223i	0.0504936	−	0.286364i
$784$	106.167	+	602.102i	0.135417	+	0.767987i
$785$	439.229	−	159.866i	0.559527	−	0.203651i
$786$	20.6453	−	35.7588i	0.0262663	−	0.0454946i
$787$	−1163.29	+	671.627i	−1.47814	+	0.853402i	−0.999694	−	0.0247177i	$-0.992131\pi$
$787$	−1163.29	+	671.627i	−1.47814	+	0.853402i	−0.478441	+	0.878120i	$0.658798\pi$
$788$	−57.3272	−	48.1032i	−0.0727502	−	0.0610447i
$789$	28.3771	−	33.8185i	0.0359658	−	0.0428624i
$790$	284.134	+	492.134i	0.359663	+	0.622954i
$791$	−38.4285	−	22.1867i	−0.0485822	−	0.0280489i
$792$	−286.915	−	788.292i	−0.362266	−	0.995319i
$793$	881.429	−	155.420i	1.11151	−	0.195990i
$794$	1127.23	+	198.762i	1.41969	+	0.250330i
$795$	−142.947	−	52.0284i	−0.179807	−	0.0654445i
$796$	35.0664	−	29.4242i	0.0440533	−	0.0369651i
$797$		−	1393.79i		−	1.74880i	−0.485209	−	0.874398i	$-0.661257\pi$
$797$		−	1393.79i		−	1.74880i	0.485209	−	0.874398i	$-0.338743\pi$
$798$		0			0
$799$	−1255.45			−1.57128
$800$	−73.2157	−	87.2550i	−0.0915196	−	0.109069i
$801$	14.4854	−	39.7984i	0.0180842	−	0.0496858i
$802$	106.575	−	604.417i	0.132886	−	0.753637i
$803$	169.514	+	961.364i	0.211101	+	1.19722i
$804$	9.14396	−	3.32813i	0.0113731	−	0.00413947i
$805$	−25.7391	+	44.5814i	−0.0319740	+	0.0553806i
$806$	142.869	−	82.4853i	0.177257	−	0.102339i
$807$	−413.531	−	346.994i	−0.512430	−	0.429980i
$808$	−706.132	+	841.536i	−0.873926	+	1.04150i
$809$	650.512	+	1126.72i	0.804095	+	1.39273i	0.916901	+	0.399116i	$0.130683\pi$
$809$	650.512	+	1126.72i	0.804095	+	1.39273i	−0.112806	+	0.993617i	$0.535984\pi$
$810$	−30.6177	−	17.6771i	−0.0377996	−	0.0218236i
$811$	505.128	+	1387.83i	0.622846	+	1.71126i	0.699912	+	0.714229i	$0.253223\pi$
$811$	505.128	+	1387.83i	0.622846	+	1.71126i	−0.0770660	+	0.997026i	$0.524555\pi$
$812$	8.14659	−	1.43646i	0.0100327	−	0.00176904i
$813$	6.47500	+	1.14172i	0.00796433	+	0.00140433i
$814$	−2033.68	−	740.199i	−2.49838	−	0.909336i
$815$	72.4015	−	60.7521i	0.0888362	−	0.0745425i
$816$			472.220i			0.578701i
$817$		0			0
$818$	−494.961			−0.605087
$819$	117.775	+	140.358i	0.143803	+	0.171378i
$820$	−12.2655	+	33.6992i	−0.0149579	+	0.0410965i
$821$	−20.6551	+	117.141i	−0.0251585	+	0.142681i	−0.994800	−	0.101852i	$-0.967523\pi$
$821$	−20.6551	+	117.141i	−0.0251585	+	0.142681i	0.969641	+	0.244532i	$0.0786344\pi$
$822$	−103.319	−	585.953i	−0.125693	−	0.712838i
$823$	986.551	−	359.075i	1.19873	−	0.436300i	0.335946	−	0.941881i	$-0.390944\pi$
$823$	986.551	−	359.075i	1.19873	−	0.436300i	0.862779	+	0.505581i	$0.168722\pi$
$824$	55.2313	−	95.6634i	0.0670282	−	0.116096i
$825$	−555.891	+	320.944i	−0.673807	+	0.389023i
$826$	−32.2878	−	27.0927i	−0.0390894	−	0.0327999i
$827$	235.825	−	281.046i	0.285158	−	0.339838i	−0.604383	−	0.796694i	$-0.706580\pi$
$827$	235.825	−	281.046i	0.285158	−	0.339838i	0.889541	+	0.456856i	$0.151025\pi$
$828$	8.28351	+	14.3475i	0.0100042	+	0.0173279i
$829$	290.861	+	167.929i	0.350858	+	0.202568i	0.665063	−	0.746787i	$-0.268405\pi$
$829$	290.861	+	167.929i	0.350858	+	0.202568i	−0.314205	+	0.949355i	$0.601738\pi$
$830$	128.891	+	354.125i	0.155290	+	0.426657i
$831$	259.805	−	45.8106i	0.312641	−	0.0551270i
$832$	−989.240	−	174.430i	−1.18899	−	0.209651i
$833$	−695.904	−	253.289i	−0.835420	−	0.304068i
$834$	541.229	−	454.145i	0.648956	−	0.544539i
$835$		−	134.841i		−	0.161487i
$836$		0			0
$837$	165.906			0.198216
$838$	−295.485	−	352.145i	−0.352607	−	0.420221i
$839$	−360.812	+	991.323i	−0.430050	+	1.18155i	0.515732	+	0.856750i	$0.327520\pi$
$839$	−360.812	+	991.323i	−0.430050	+	1.18155i	−0.945782	+	0.324803i	$0.894702\pi$
$840$	19.0336	−	107.945i	0.0226590	−	0.128506i
$841$	134.255	+	761.396i	0.159637	+	0.905346i
$842$	−988.789	+	359.890i	−1.17433	+	0.427423i
$843$	−479.192	+	829.985i	−0.568437	+	0.984561i
$844$	−55.4038	+	31.9874i	−0.0656443	+	0.0378998i
$845$	89.2904	+	74.9235i	0.105669	+	0.0886669i
$846$	−465.222	+	554.430i	−0.549908	+	0.655355i
$847$	−299.473	−	518.702i	−0.353569	−	0.612399i
$848$	343.838	+	198.515i	0.405469	+	0.234098i
$849$	248.994	+	684.106i	0.293280	+	0.805779i
$850$	−550.182	+	97.0119i	−0.647273	+	0.114132i
$851$	447.142	+	78.8432i	0.525431	+	0.0926477i
$852$	29.1889	+	10.6239i	0.0342593	+	0.0124694i
$853$	411.254	−	345.083i	0.482127	−	0.404553i	−0.369068	−	0.929403i	$-0.620323\pi$
$853$	411.254	−	345.083i	0.482127	−	0.404553i	0.851195	+	0.524850i	$0.175879\pi$
$854$		−	282.004i		−	0.330216i
$855$		0			0
$856$	915.780			1.06984
$857$	−802.321	−	956.168i	−0.936197	−	1.11572i	−0.993092	−	0.117336i	$-0.962565\pi$
$857$	−802.321	−	956.168i	−0.936197	−	1.11572i	0.0568956	−	0.998380i	$-0.481880\pi$
$858$	−350.815	+	963.857i	−0.408876	+	1.12338i
$859$	−87.9162	+	498.598i	−0.102347	+	0.580440i	0.889900	+	0.456156i	$0.150774\pi$
$859$	−87.9162	+	498.598i	−0.102347	+	0.580440i	−0.992247	+	0.124283i	$0.960337\pi$
$860$	−4.95397	−	28.0954i	−0.00576043	−	0.0326690i
$861$	136.262	−	49.5953i	0.158260	−	0.0576020i
$862$	6.06244	−	10.5005i	0.00703299	−	0.0121815i
$863$	1102.47	−	636.511i	1.27748	−	0.737556i	0.301099	−	0.953593i	$-0.402646\pi$
$863$	1102.47	−	636.511i	1.27748	−	0.737556i	0.976385	+	0.216037i	$0.0693131\pi$
$864$	−140.222	−	117.660i	−0.162294	−	0.136181i
$865$	92.8551	−	110.660i	0.107347	−	0.127931i
$866$	54.2095	+	93.8937i	0.0625976	+	0.108422i
$867$	−9.04032	−	5.21943i	−0.0104271	−	0.00602011i
$868$	2.06163	+	5.66429i	0.00237515	+	0.00652568i
$869$	2032.77	−	358.432i	2.33920	−	0.412464i
$870$	−83.3540	−	14.6976i	−0.0958092	−	0.0168937i
$871$	164.349	+	59.8180i	0.188690	+	0.0686774i
$872$	1319.88	−	1107.51i	1.51362	−	1.27008i
$873$			622.328i			0.712861i
$874$		0			0
$875$	284.747			0.325425
$876$	26.3860	+	31.4457i	0.0301210	+	0.0358969i
$877$	−105.282	+	289.260i	−0.120048	+	0.329829i	−0.985132	−	0.171797i	$-0.945043\pi$
$877$	−105.282	+	289.260i	−0.120048	+	0.329829i	0.865084	+	0.501627i	$0.167265\pi$
$878$	172.124	−	976.165i	0.196041	−	1.11181i
$879$	24.7598	+	140.420i	0.0281682	+	0.159750i
$880$	−714.052	+	259.894i	−0.811423	+	0.295334i
$881$	−117.273	+	203.123i	−0.133113	+	0.230559i	−0.924875	−	0.380271i	$-0.875831\pi$
$881$	−117.273	+	203.123i	−0.133113	+	0.230559i	0.791762	+	0.610830i	$0.209164\pi$
$882$	−369.732	+	213.465i	−0.419198	+	0.242024i
$883$	−210.989	−	177.040i	−0.238945	−	0.200499i	0.515449	−	0.856920i	$-0.327625\pi$
$883$	−210.989	−	177.040i	−0.238945	−	0.200499i	−0.754395	+	0.656421i	$0.772069\pi$
$884$	66.5462	−	79.3067i	0.0752785	−	0.0897135i
$885$	−25.0057	−	43.3111i	−0.0282550	−	0.0489391i
$886$	−712.450	−	411.333i	−0.804120	−	0.464259i
$887$	−115.367	−	316.969i	−0.130065	−	0.357350i	0.857517	−	0.514455i	$-0.172006\pi$
$887$	−115.367	−	316.969i	−0.130065	−	0.357350i	−0.987582	+	0.157106i	$0.949784\pi$
$888$	−952.078	+	167.877i	−1.07216	+	0.189051i
$889$	−26.9583	−	4.75348i	−0.0303243	−	0.00534699i
$890$	−40.2818	−	14.6614i	−0.0452605	−	0.0164735i
$891$	−98.3737	+	82.5454i	−0.110408	+	0.0926435i
$892$			64.6905i			0.0725230i
$893$		0			0
$894$	−517.103			−0.578415
$895$	416.518	+	496.387i	0.465383	+	0.554622i
$896$	−86.3594	+	237.271i	−0.0963833	+	0.264811i
$897$	37.3675	−	211.922i	0.0416583	−	0.236256i
$898$	−103.362	−	586.194i	−0.115102	−	0.652777i
$899$	46.4648	−	16.9118i	0.0516850	−	0.0188118i
$900$	18.6746	−	32.3453i	0.0207495	−	0.0359392i
$901$	−416.485	+	240.457i	−0.462247	+	0.266878i
$902$	−860.474	−	722.023i	−0.953962	−	0.800469i
$903$	−74.1492	+	88.3675i	−0.0821143	+	0.0978600i
$904$	76.7736	+	132.976i	0.0849266	+	0.147097i
$905$	−654.049	−	377.616i	−0.722706	−	0.417255i
$906$	−127.839	−	351.235i	−0.141103	−	0.387676i
$907$	251.658	−	44.3740i	0.277462	−	0.0489240i	−0.0331858	−	0.999449i	$-0.510565\pi$
$907$	251.658	−	44.3740i	0.277462	−	0.0489240i	0.310647	+	0.950525i	$0.399454\pi$
$908$	−27.4603	−	4.84200i	−0.0302426	−	0.00533259i
$909$	−645.121	−	234.805i	−0.709704	−	0.258311i
$910$	142.063	−	119.205i	0.156113	−	0.130995i
$911$			598.961i			0.657477i	0.944421	+	0.328738i	$0.106623\pi$
$911$			598.961i			0.657477i	−0.944421	+	0.328738i	$0.893377\pi$
$912$		0			0
$913$	1368.84			1.49928
$914$	639.128	+	761.683i	0.699265	+	0.833351i
$915$	114.443	−	314.431i	0.125075	−	0.343640i
$916$	5.00014	−	28.3572i	0.00545867	−	0.0309576i
$917$	4.70876	+	26.7047i	0.00513496	+	0.0291218i
$918$	−843.656	+	307.066i	−0.919015	+	0.334494i
$919$	−724.843	+	1255.46i	−0.788730	+	1.36612i	0.138015	+	0.990430i	$0.455928\pi$
$919$	−724.843	+	1255.46i	−0.788730	+	1.36612i	−0.926745	+	0.375691i	$0.877406\pi$
$920$	154.267	−	89.0661i	0.167682	−	0.0968110i
$921$	−137.586	−	115.448i	−0.149388	−	0.125351i
$922$	741.854	−	884.107i	0.804614	−	0.958901i
$923$	279.147	+	483.497i	0.302435	+	0.523832i
$924$	−32.4571	−	18.7391i	−0.0351268	−	0.0202805i
$925$	−350.092	−	961.869i	−0.378478	−	1.03986i
$926$	1423.41	−	250.986i	1.53716	−	0.271043i
$927$	67.9834	+	11.9873i	0.0733370	+	0.0129313i
$928$	−51.2651	−	18.6590i	−0.0552426	−	0.0201067i
$929$	−1356.63	+	1138.35i	−1.46031	+	1.22535i	−0.535720	+	0.844396i	$0.679960\pi$
$929$	−1356.63	+	1138.35i	−1.46031	+	1.22535i	−0.924594	+	0.380953i	$0.875596\pi$
$930$		−	61.6751i		−	0.0663173i
$931$		0			0
$932$	−67.8414			−0.0727912
$933$	248.838	+	296.554i	0.266708	+	0.317850i
$934$	−290.494	+	798.126i	−0.311022	+	0.854525i
$935$	159.830	−	906.443i	0.170942	−	0.969458i
$936$	−110.096	−	624.388i	−0.117624	−	0.667081i
$937$	608.577	−	221.504i	0.649496	−	0.236397i	0.00380095	−	0.999993i	$-0.498790\pi$
$937$	608.577	−	221.504i	0.649496	−	0.236397i	0.645695	+	0.763596i	$0.276568\pi$
$938$	27.5531	−	47.7233i	0.0293743	−	0.0508777i
$939$	51.4886	−	29.7269i	0.0548334	−	0.0316581i
$940$	−65.0764	−	54.6056i	−0.0692302	−	0.0580911i
$941$	−871.098	+	1038.13i	−0.925715	+	1.10322i	0.0686946	+	0.997638i	$0.478117\pi$
$941$	−871.098	+	1038.13i	−0.925715	+	1.10322i	−0.994410	+	0.105587i	$0.966328\pi$
$942$	307.819	+	533.159i	0.326772	+	0.565986i
$943$	204.085	+	117.829i	0.216421	+	0.124951i
$944$	44.6431	+	122.656i	0.0472914	+	0.129932i
$945$	183.669	−	32.3858i	0.194359	−	0.0342707i
$946$	880.005	+	155.169i	0.930238	+	0.164026i
$947$	298.912	+	108.795i	0.315641	+	0.114884i	0.494982	−	0.868903i	$-0.335175\pi$
$947$	298.912	+	108.795i	0.315641	+	0.114884i	−0.179342	+	0.983787i	$0.557397\pi$
$948$	66.4906	−	55.7922i	0.0701378	−	0.0588526i
$949$			737.799i			0.777449i
$950$		0			0
$951$	−1107.38			−1.16443
$952$	−222.740	−	265.451i	−0.233970	−	0.278835i
$953$	313.993	−	862.688i	0.329478	−	0.905234i	−0.658766	−	0.752348i	$-0.728921\pi$
$953$	313.993	−	862.688i	0.329478	−	0.905234i	0.988244	−	0.152886i	$-0.0488566\pi$
$954$	−48.1428	+	273.031i	−0.0504641	+	0.286196i
$955$	−39.5062	−	224.051i	−0.0413678	−	0.234608i
$956$	−119.378	+	43.4502i	−0.124873	+	0.0454500i
$957$	−153.719	+	266.250i	−0.160626	+	0.278213i
$958$	−1142.24	+	659.474i	−1.19232	+	0.688387i
$959$	299.330	+	251.167i	0.312127	+	0.261905i
$960$	−241.391	+	287.679i	−0.251449	+	0.299665i
$961$	−462.485	−	801.047i	−0.481254	−	0.833556i
$962$	−1416.54	−	817.840i	−1.47250	−	0.850146i
$963$	195.740	+	537.791i	0.203260	+	0.558454i
$964$	98.2640	−	17.3266i	0.101934	−	0.0179736i
$965$	−82.0520	−	14.4680i	−0.0850280	−	0.0149927i
$966$	−63.7132	−	23.1897i	−0.0659557	−	0.0240059i
$967$	300.590	−	252.225i	0.310847	−	0.260832i	−0.473995	−	0.880528i	$-0.657188\pi$
$967$	300.590	−	252.225i	0.310847	−	0.260832i	0.784842	+	0.619696i	$0.212744\pi$
$968$			2072.56i			2.14107i
$969$		0			0
$970$	629.888			0.649369
$971$	302.795	+	360.857i	0.311838	+	0.371634i	0.899085	−	0.437773i	$-0.144233\pi$
$971$	302.795	+	360.857i	0.311838	+	0.371634i	−0.587247	+	0.809408i	$0.699788\pi$
$972$	33.5172	−	92.0877i	0.0344827	−	0.0947405i
$973$	−80.5715	+	456.944i	−0.0828073	+	0.469624i
$974$	6.38691	+	36.2220i	0.00655740	+	0.0371889i
$975$	−455.875	+	165.925i	−0.467565	+	0.170180i
$976$	−436.660	+	756.317i	−0.447398	+	0.774915i
$977$	170.882	−	98.6590i	0.174905	−	0.100982i	−0.409991	−	0.912089i	$-0.634468\pi$
$977$	170.882	−	98.6590i	0.174905	−	0.100982i	0.584897	+	0.811108i	$0.301135\pi$
$978$	95.3605	+	80.0169i	0.0975056	+	0.0818169i
$979$	−100.086	+	119.278i	−0.102233	+	0.121837i
$980$	−25.0555	−	43.3974i	−0.0255669	−	0.0442831i
$981$	932.495	+	538.376i	0.950556	+	0.548804i
$982$	−428.887	−	1178.36i	−0.436748	−	1.19996i
$983$	757.250	−	133.524i	0.770346	−	0.135833i	0.225357	−	0.974276i	$-0.427645\pi$
$983$	757.250	−	133.524i	0.770346	−	0.135833i	0.544989	+	0.838443i	$0.316534\pi$
$984$	−494.151	−	87.1321i	−0.502186	−	0.0885489i
$985$	−472.528	−	171.986i	−0.479723	−	0.174605i
$986$	−204.979	+	171.997i	−0.207889	+	0.174440i
$987$			343.499i			0.348023i
$988$		0			0
$989$	−187.470			−0.189555
$990$	−341.075	−	406.477i	−0.344520	−	0.410583i
$991$	−596.900	+	1639.97i	−0.602321	+	1.65486i	0.144237	+	0.989543i	$0.453927\pi$
$991$	−596.900	+	1639.97i	−0.602321	+	1.65486i	−0.746558	+	0.665320i	$0.768295\pi$
$992$	6.90305	−	39.1492i	0.00695872	−	0.0394649i
$993$	−149.227	−	846.311i	−0.150279	−	0.852277i
$994$	165.299	−	60.1637i	0.166296	−	0.0605269i
$995$	153.795	−	266.381i	0.154568	−	0.267719i
$996$	49.8488	−	28.7802i	0.0500490	−	0.0288958i
$997$	−944.648	−	792.654i	−0.947490	−	0.795039i	0.0313827	−	0.999507i	$-0.490009\pi$
$997$	−944.648	−	792.654i	−0.947490	−	0.795039i	−0.978873	+	0.204469i	$0.934453\pi$
$998$	162.588	−	193.765i	0.162914	−	0.194153i
$999$	−822.479	−	1424.58i	−0.823303	−	1.42600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.3.f.e.127.2		12
19.2	odd	18		19.3.f.a.14.2	✓	12
19.3	odd	18	inner	361.3.f.e.307.2		12
19.4	even	9		361.3.b.c.360.9		12
19.5	even	9		361.3.f.b.116.2		12
19.6	even	9		361.3.d.f.69.5		12
19.7	even	3		361.3.f.f.333.1		12
19.8	odd	6		361.3.f.g.262.1		12
19.9	even	9		361.3.d.d.293.2		12
19.10	odd	18		361.3.d.f.293.5		12
19.11	even	3		19.3.f.a.15.2	yes	12
19.12	odd	6		361.3.f.b.333.2		12
19.13	odd	18		361.3.d.d.69.2		12
19.14	odd	18		361.3.f.f.116.1		12
19.15	odd	18		361.3.b.c.360.4		12
19.16	even	9		361.3.f.c.307.1		12
19.17	even	9		361.3.f.g.299.1		12
19.18	odd	2		361.3.f.c.127.1		12
57.2	even	18		171.3.ba.b.109.1		12
57.11	odd	6		171.3.ba.b.91.1		12
76.11	odd	6		304.3.z.a.129.2		12
76.59	even	18		304.3.z.a.33.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.f.a.14.2	✓	12	19.2	odd	18
19.3.f.a.15.2	yes	12	19.11	even	3
171.3.ba.b.91.1		12	57.11	odd	6
171.3.ba.b.109.1		12	57.2	even	18
304.3.z.a.33.2		12	76.59	even	18
304.3.z.a.129.2		12	76.11	odd	6
361.3.b.c.360.4		12	19.15	odd	18
361.3.b.c.360.9		12	19.4	even	9
361.3.d.d.69.2		12	19.13	odd	18
361.3.d.d.293.2		12	19.9	even	9
361.3.d.f.69.5		12	19.6	even	9
361.3.d.f.293.5		12	19.10	odd	18
361.3.f.b.116.2		12	19.5	even	9
361.3.f.b.333.2		12	19.12	odd	6
361.3.f.c.127.1		12	19.18	odd	2
361.3.f.c.307.1		12	19.16	even	9
361.3.f.e.127.2		12	1.1	even	1	trivial
361.3.f.e.307.2		12	19.3	odd	18	inner
361.3.f.f.116.1		12	19.14	odd	18
361.3.f.f.333.1		12	19.7	even	3
361.3.f.g.262.1		12	19.8	odd	6
361.3.f.g.299.1		12	19.17	even	9

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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	361.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.21695 + 1.45030i) q^{2} +(0.664575 - 1.82591i) q^{3} +(0.0721792 - 0.409349i) q^{4} +(-0.485005 - 2.75060i) q^{5} +(3.45687 - 1.25820i) q^{6} +(-1.20796 + 2.09224i) q^{7} +(7.23987 - 4.17994i) q^{8} +(4.00213 + 3.35818i) q^{9} +O(q^{10})\)	\(q+(1.21695 + 1.45030i) q^{2} +(0.664575 - 1.82591i) q^{3} +(0.0721792 - 0.409349i) q^{4} +(-0.485005 - 2.75060i) q^{5} +(3.45687 - 1.25820i) q^{6} +(-1.20796 + 2.09224i) q^{7} +(7.23987 - 4.17994i) q^{8} +(4.00213 + 3.35818i) q^{9} +(3.39898 - 4.05074i) q^{10} +(-9.60360 - 16.6339i) q^{11} +(-0.699463 - 0.403835i) q^{12} +(-4.96498 - 13.6412i) q^{13} +(-4.50440 + 0.794247i) q^{14} +(-5.34466 - 0.942409i) q^{15} +(13.3103 + 4.84457i) q^{16} +(-13.1432 + 11.0285i) q^{17} +9.89103i q^{18} -1.16096 q^{20} +(3.01746 + 3.59607i) q^{21} +(12.4371 - 34.1707i) q^{22} +(-1.32476 + 7.51307i) q^{23} +(-2.82074 - 15.9972i) q^{24} +(16.1617 - 5.88239i) q^{25} +(13.7417 - 23.8013i) q^{26} +(23.9363 - 13.8196i) q^{27} +(0.769267 + 0.645491i) q^{28} +(5.29504 - 6.31038i) q^{29} +(-5.13740 - 8.89824i) q^{30} +(5.19837 + 3.00128i) q^{31} +(-2.26509 - 6.22329i) q^{32} +(-36.7543 + 6.48078i) q^{33} +(-31.9893 - 5.64057i) q^{34} +(6.34079 + 2.30786i) q^{35} +(1.66354 - 1.39587i) q^{36} -59.5153i q^{37} -28.2071 q^{39} +(-15.0087 - 17.8867i) q^{40} +(10.5649 - 29.0269i) q^{41} +(-1.54329 + 8.75245i) q^{42} +(4.26712 + 24.2001i) q^{43} +(-7.50225 + 2.73060i) q^{44} +(7.29598 - 12.6370i) q^{45} +(-12.5084 + 7.22171i) q^{46} +(56.0539 + 47.0348i) q^{47} +(17.6915 - 21.0839i) q^{48} +(21.5817 + 37.3806i) q^{49} +(28.1992 + 16.2808i) q^{50} +(11.4023 + 31.3276i) q^{51} +(-5.94236 + 1.04780i) q^{52} +(27.6039 + 4.86732i) q^{53} +(49.1719 + 17.8971i) q^{54} +(-41.0955 + 34.4832i) q^{55} +20.1968i q^{56} +15.5957 q^{58} +(5.92334 + 7.05916i) q^{59} +(-0.771547 + 2.11981i) q^{60} +(-10.7063 + 60.7186i) q^{61} +(1.97338 + 11.1916i) q^{62} +(-11.8605 + 4.31688i) q^{63} +(34.5983 - 59.9260i) q^{64} +(-35.1134 + 20.2727i) q^{65} +(-54.1272 - 45.4181i) q^{66} +(-7.74429 + 9.22929i) q^{67} +(3.56583 + 6.17619i) q^{68} +(12.8378 + 7.41188i) q^{69} +(4.36932 + 12.0046i) q^{70} +(-37.8747 + 6.67833i) q^{71} +(43.0119 + 7.58416i) q^{72} +(-47.7593 - 17.3830i) q^{73} +(86.3151 - 72.4269i) q^{74} -33.4191i q^{75} +46.4029 q^{77} +(-34.3266 - 40.9088i) q^{78} +(-36.7556 + 100.985i) q^{79} +(6.86989 - 38.9611i) q^{80} +(-1.16100 - 6.58434i) q^{81} +(54.9548 - 20.0019i) q^{82} +(-35.6336 + 61.7192i) q^{83} +(1.68984 - 0.975631i) q^{84} +(36.7095 + 30.8030i) q^{85} +(-29.9045 + 35.6388i) q^{86} +(-8.00321 - 13.8620i) q^{87} +(-139.058 - 80.2850i) q^{88} +(-2.77264 - 7.61778i) q^{89} +(27.2063 - 4.79720i) q^{90} +(34.5381 + 6.09000i) q^{91} +(2.97984 + 1.08457i) q^{92} +(8.93476 - 7.49716i) q^{93} +138.534i q^{94} -12.8685 q^{96} +(76.5684 + 91.2507i) q^{97} +(-27.9493 + 76.7902i) q^{98} +(17.4249 - 98.8218i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 9 q^{3} - 9 q^{4} + 3 q^{5} + 9 q^{6} + 6 q^{7} - 9 q^{8} + 39 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 - 9 * q^3 - 9 * q^4 + 3 * q^5 + 9 * q^6 + 6 * q^7 - 9 * q^8 + 39 * q^9	\( 12 q + 3 q^{2} - 9 q^{3} - 9 q^{4} + 3 q^{5} + 9 q^{6} + 6 q^{7} - 9 q^{8} + 39 q^{9} - 30 q^{10} - 18 q^{11} + 63 q^{12} - 51 q^{13} - 90 q^{14} - 54 q^{15} + 51 q^{16} - 75 q^{17} - 90 q^{20} + 48 q^{21} - 33 q^{22} - 66 q^{23} - 66 q^{24} + 123 q^{25} + 21 q^{26} - 27 q^{27} - 6 q^{28} - 78 q^{29} + 24 q^{30} + 99 q^{31} - 222 q^{32} - 15 q^{33} - 66 q^{34} - 66 q^{35} - 225 q^{36} - 108 q^{39} + 141 q^{40} - 171 q^{41} + 123 q^{42} + 54 q^{43} - 51 q^{44} - 3 q^{45} - 54 q^{46} - 81 q^{47} - 24 q^{48} - 24 q^{49} + 72 q^{50} + 48 q^{51} - 123 q^{52} - 96 q^{53} + 210 q^{54} - 153 q^{55} - 132 q^{58} + 111 q^{59} + 231 q^{60} - 120 q^{61} - 171 q^{62} + 171 q^{63} + 27 q^{64} + 126 q^{65} + 69 q^{66} - 18 q^{67} - 30 q^{68} + 72 q^{69} - 126 q^{70} + 138 q^{71} + 114 q^{72} - 135 q^{73} + 471 q^{74} + 246 q^{77} - 99 q^{78} + 132 q^{79} + 264 q^{80} + 390 q^{81} - 126 q^{82} - 156 q^{83} + 99 q^{84} + 15 q^{85} + 72 q^{86} + 69 q^{87} - 405 q^{88} + 531 q^{89} - 93 q^{90} + 393 q^{91} + 12 q^{92} + 384 q^{93} + 558 q^{96} - 588 q^{97} - 159 q^{98} - 366 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 9 * q^3 - 9 * q^4 + 3 * q^5 + 9 * q^6 + 6 * q^7 - 9 * q^8 + 39 * q^9 - 30 * q^10 - 18 * q^11 + 63 * q^12 - 51 * q^13 - 90 * q^14 - 54 * q^15 + 51 * q^16 - 75 * q^17 - 90 * q^20 + 48 * q^21 - 33 * q^22 - 66 * q^23 - 66 * q^24 + 123 * q^25 + 21 * q^26 - 27 * q^27 - 6 * q^28 - 78 * q^29 + 24 * q^30 + 99 * q^31 - 222 * q^32 - 15 * q^33 - 66 * q^34 - 66 * q^35 - 225 * q^36 - 108 * q^39 + 141 * q^40 - 171 * q^41 + 123 * q^42 + 54 * q^43 - 51 * q^44 - 3 * q^45 - 54 * q^46 - 81 * q^47 - 24 * q^48 - 24 * q^49 + 72 * q^50 + 48 * q^51 - 123 * q^52 - 96 * q^53 + 210 * q^54 - 153 * q^55 - 132 * q^58 + 111 * q^59 + 231 * q^60 - 120 * q^61 - 171 * q^62 + 171 * q^63 + 27 * q^64 + 126 * q^65 + 69 * q^66 - 18 * q^67 - 30 * q^68 + 72 * q^69 - 126 * q^70 + 138 * q^71 + 114 * q^72 - 135 * q^73 + 471 * q^74 + 246 * q^77 - 99 * q^78 + 132 * q^79 + 264 * q^80 + 390 * q^81 - 126 * q^82 - 156 * q^83 + 99 * q^84 + 15 * q^85 + 72 * q^86 + 69 * q^87 - 405 * q^88 + 531 * q^89 - 93 * q^90 + 393 * q^91 + 12 * q^92 + 384 * q^93 + 558 * q^96 - 588 * q^97 - 159 * q^98 - 366 * q^99

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