LMFDB - Embedded newform 105.4.i.d.46.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(16,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("105.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.i (of order $3$, degree $2$, 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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} + 34 x^{8} + 16 x^{7} + 791 x^{6} - 132 x^{5} + 4906 x^{4} - 1674 x^{3} + 25257 x^{2} + \cdots + 7056 $ x^10 - 2x^9 + 34x^8 + 16x^7 + 791x^6 - 132x^5 + 4906x^4 - 1674x^3 + 25257x^2 - 12852*x + 7056
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.5
Root			$2.90324 + 5.02855i$ of defining polynomial
Character	$\chi$	$=$	105.46
Dual form			105.4.i.d.16.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.40324 + 4.16253i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-7.55109 + 13.0789i) q^{4} +(-2.50000 - 4.33013i) q^{5} -14.4194 q^{6} +(-18.4976 + 0.916253i) q^{7} -34.1365 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(2.40324 + 4.16253i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-7.55109 + 13.0789i) q^{4} +(-2.50000 - 4.33013i) q^{5} -14.4194 q^{6} +(-18.4976 + 0.916253i) q^{7} -34.1365 q^{8} +(-4.50000 - 7.79423i) q^{9} +(12.0162 - 20.8126i) q^{10} +(-26.6281 + 46.1213i) q^{11} +(-22.6533 - 39.2366i) q^{12} +60.9548 q^{13} +(-48.2680 - 74.7947i) q^{14} +15.0000 q^{15} +(-21.6293 - 37.4630i) q^{16} +(-15.5599 + 26.9505i) q^{17} +(21.6291 - 37.4628i) q^{18} +(8.95663 + 15.5133i) q^{19} +75.5109 q^{20} +(25.3659 - 49.4325i) q^{21} -255.975 q^{22} +(17.4112 + 30.1570i) q^{23} +(51.2047 - 88.6892i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(146.489 + 253.726i) q^{26} +27.0000 q^{27} +(127.693 - 248.846i) q^{28} +141.423 q^{29} +(36.0486 + 62.4379i) q^{30} +(-58.8697 + 101.965i) q^{31} +(-32.5853 + 56.4394i) q^{32} +(-79.8844 - 138.364i) q^{33} -149.576 q^{34} +(50.2114 + 77.8062i) q^{35} +135.920 q^{36} +(-87.6595 - 151.831i) q^{37} +(-43.0498 + 74.5644i) q^{38} +(-91.4322 + 158.365i) q^{39} +(85.3412 + 147.815i) q^{40} +411.157 q^{41} +(266.724 - 13.2118i) q^{42} -498.509 q^{43} +(-402.143 - 696.532i) q^{44} +(-22.5000 + 38.9711i) q^{45} +(-83.6863 + 144.949i) q^{46} +(145.131 + 251.375i) q^{47} +129.776 q^{48} +(341.321 - 33.8969i) q^{49} -120.162 q^{50} +(-46.6797 - 80.8516i) q^{51} +(-460.275 + 797.220i) q^{52} +(-291.316 + 504.575i) q^{53} +(64.8874 + 112.388i) q^{54} +266.281 q^{55} +(631.442 - 31.2777i) q^{56} -53.7398 q^{57} +(339.873 + 588.677i) q^{58} +(328.855 - 569.594i) q^{59} +(-113.266 + 196.183i) q^{60} +(208.583 + 361.277i) q^{61} -565.911 q^{62} +(90.3806 + 140.051i) q^{63} -659.310 q^{64} +(-152.387 - 263.942i) q^{65} +(383.962 - 665.042i) q^{66} +(283.955 - 491.825i) q^{67} +(-234.989 - 407.012i) q^{68} -104.467 q^{69} +(-203.201 + 395.993i) q^{70} +887.933 q^{71} +(153.614 + 266.068i) q^{72} +(546.253 - 946.138i) q^{73} +(421.333 - 729.770i) q^{74} +(-37.5000 - 64.9519i) q^{75} -270.529 q^{76} +(450.297 - 877.530i) q^{77} -878.933 q^{78} +(-67.7126 - 117.282i) q^{79} +(-108.146 + 187.315i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(988.108 + 1711.45i) q^{82} -464.523 q^{83} +(454.982 + 705.027i) q^{84} +155.599 q^{85} +(-1198.04 - 2075.06i) q^{86} +(-212.134 + 367.427i) q^{87} +(908.991 - 1574.42i) q^{88} +(-15.9399 - 27.6088i) q^{89} -216.291 q^{90} +(-1127.52 + 55.8500i) q^{91} -525.894 q^{92} +(-176.609 - 305.896i) q^{93} +(-697.569 + 1208.23i) q^{94} +(44.7831 - 77.5667i) q^{95} +(-97.7560 - 169.318i) q^{96} -254.781 q^{97} +(961.372 + 1339.30i) q^{98} +479.306 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{2} - 15 q^{3} - 25 q^{4} - 25 q^{5} + 18 q^{6} - 32 q^{7} + 42 q^{8} - 45 q^{9}+O(q^{10}) $ 10 * q - 3 * q^2 - 15 * q^3 - 25 * q^4 - 25 * q^5 + 18 * q^6 - 32 * q^7 + 42 * q^8 - 45 * q^9	\( 10 q - 3 q^{2} - 15 q^{3} - 25 q^{4} - 25 q^{5} + 18 q^{6} - 32 q^{7} + 42 q^{8} - 45 q^{9} - 15 q^{10} - 43 q^{11} - 75 q^{12} + 246 q^{13} - 23 q^{14} + 150 q^{15} - 161 q^{16} - 124 q^{17} - 27 q^{18} - 37 q^{19} + 250 q^{20} + 3 q^{21} - 442 q^{22} - 77 q^{23} - 63 q^{24} - 125 q^{25} + 79 q^{26} + 270 q^{27} - 71 q^{28} + 720 q^{29} - 45 q^{30} - 314 q^{31} + 59 q^{32} - 129 q^{33} + 352 q^{34} + 155 q^{35} + 450 q^{36} - 225 q^{37} - 759 q^{38} - 369 q^{39} - 105 q^{40} + 682 q^{41} + 354 q^{42} + 64 q^{43} - 679 q^{44} - 225 q^{45} + 331 q^{46} - 25 q^{47} + 966 q^{48} + 710 q^{49} + 150 q^{50} - 372 q^{51} - 2299 q^{52} + 317 q^{53} - 81 q^{54} + 430 q^{55} + 1884 q^{56} + 222 q^{57} - 8 q^{58} - 676 q^{59} - 375 q^{60} + 188 q^{61} - 696 q^{62} + 279 q^{63} - 2206 q^{64} - 615 q^{65} + 663 q^{66} + 1776 q^{67} - 1280 q^{68} + 462 q^{69} - 475 q^{70} - 12 q^{71} - 189 q^{72} - 2006 q^{73} + 2729 q^{74} - 375 q^{75} + 2834 q^{76} + 3731 q^{77} - 474 q^{78} - 200 q^{79} - 805 q^{80} - 405 q^{81} + 539 q^{82} - 664 q^{83} + 1821 q^{84} + 1240 q^{85} - 4262 q^{86} - 1080 q^{87} + 4529 q^{88} - 894 q^{89} + 270 q^{90} + 2016 q^{91} - 7374 q^{92} - 942 q^{93} - 4233 q^{94} - 185 q^{95} + 177 q^{96} - 1152 q^{97} + 2539 q^{98} + 774 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 - 15 * q^3 - 25 * q^4 - 25 * q^5 + 18 * q^6 - 32 * q^7 + 42 * q^8 - 45 * q^9 - 15 * q^10 - 43 * q^11 - 75 * q^12 + 246 * q^13 - 23 * q^14 + 150 * q^15 - 161 * q^16 - 124 * q^17 - 27 * q^18 - 37 * q^19 + 250 * q^20 + 3 * q^21 - 442 * q^22 - 77 * q^23 - 63 * q^24 - 125 * q^25 + 79 * q^26 + 270 * q^27 - 71 * q^28 + 720 * q^29 - 45 * q^30 - 314 * q^31 + 59 * q^32 - 129 * q^33 + 352 * q^34 + 155 * q^35 + 450 * q^36 - 225 * q^37 - 759 * q^38 - 369 * q^39 - 105 * q^40 + 682 * q^41 + 354 * q^42 + 64 * q^43 - 679 * q^44 - 225 * q^45 + 331 * q^46 - 25 * q^47 + 966 * q^48 + 710 * q^49 + 150 * q^50 - 372 * q^51 - 2299 * q^52 + 317 * q^53 - 81 * q^54 + 430 * q^55 + 1884 * q^56 + 222 * q^57 - 8 * q^58 - 676 * q^59 - 375 * q^60 + 188 * q^61 - 696 * q^62 + 279 * q^63 - 2206 * q^64 - 615 * q^65 + 663 * q^66 + 1776 * q^67 - 1280 * q^68 + 462 * q^69 - 475 * q^70 - 12 * q^71 - 189 * q^72 - 2006 * q^73 + 2729 * q^74 - 375 * q^75 + 2834 * q^76 + 3731 * q^77 - 474 * q^78 - 200 * q^79 - 805 * q^80 - 405 * q^81 + 539 * q^82 - 664 * q^83 + 1821 * q^84 + 1240 * q^85 - 4262 * q^86 - 1080 * q^87 + 4529 * q^88 - 894 * q^89 + 270 * q^90 + 2016 * q^91 - 7374 * q^92 - 942 * q^93 - 4233 * q^94 - 185 * q^95 + 177 * q^96 - 1152 * q^97 + 2539 * q^98 + 774 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	2.40324	+	4.16253i	0.849673	+	1.47168i	0.881501	+	0.472183i	$0.156534\pi$
$2$	2.40324	+	4.16253i	0.849673	+	1.47168i	−0.0318283	+	0.999493i	$0.510133\pi$
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$4$	−7.55109	+	13.0789i	−0.943887	+	1.63486i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$	−14.4194			−0.981117
$7$	−18.4976	+	0.916253i	−0.998775	+	0.0494730i
$7$	−18.4976	+	0.916253i	−0.998775	+	0.0494730i
$8$	−34.1365			−1.50863
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	12.0162	−	20.8126i	0.379985	−	0.658153i
$11$	−26.6281	+	46.1213i	−0.729881	+	1.26419i	0.227053	+	0.973882i	$0.427091\pi$
$11$	−26.6281	+	46.1213i	−0.729881	+	1.26419i	−0.956933	+	0.290308i	$0.906242\pi$
$12$	−22.6533	−	39.2366i	−0.544953	−	0.943887i
$13$	60.9548			1.30045			0.650224	−	0.759743i	$-0.274675\pi$
$13$	60.9548			1.30045			0.650224	+	0.759743i	$0.274675\pi$
$14$	−48.2680	−	74.7947i	−0.921440	−	1.42784i
$15$	15.0000			0.258199
$16$	−21.6293	−	37.4630i	−0.337958	−	0.585360i
$17$	−15.5599	+	26.9505i	−0.221990	+	0.384498i	−0.955412	−	0.295276i	$-0.904589\pi$
$17$	−15.5599	+	26.9505i	−0.221990	+	0.384498i	0.733422	+	0.679773i	$0.237922\pi$
$18$	21.6291	−	37.4628i	0.283224	−	0.490559i
$19$	8.95663	+	15.5133i	0.108147	+	0.187316i	0.915020	−	0.403409i	$-0.132175\pi$
$19$	8.95663	+	15.5133i	0.108147	+	0.187316i	−0.806873	+	0.590725i	$0.798842\pi$
$20$	75.5109			0.844238
$21$	25.3659	−	49.4325i	0.263585	−	0.513669i
$22$	−255.975			−2.48064
$23$	17.4112	+	30.1570i	0.157847	+	0.273399i	0.934092	−	0.357032i	$-0.116211\pi$
$23$	17.4112	+	30.1570i	0.157847	+	0.273399i	−0.776245	+	0.630431i	$0.782878\pi$
$24$	51.2047	−	88.6892i	0.435505	−	0.754317i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	146.489	+	253.726i	1.10495	+	1.91384i
$27$	27.0000			0.192450
$28$	127.693	−	248.846i	0.861849	−	1.67955i
$29$	141.423			0.905571			0.452786	−	0.891619i	$-0.350430\pi$
$29$	141.423			0.905571			0.452786	+	0.891619i	$0.350430\pi$
$30$	36.0486	+	62.4379i	0.219384	+	0.379985i
$31$	−58.8697	+	101.965i	−0.341075	+	0.590759i	−0.984633	−	0.174639i	$-0.944124\pi$
$31$	−58.8697	+	101.965i	−0.341075	+	0.590759i	0.643558	+	0.765397i	$0.277458\pi$
$32$	−32.5853	+	56.4394i	−0.180010	+	0.311787i
$33$	−79.8844	−	138.364i	−0.421397	−	0.729881i
$34$	−149.576			−0.754475
$35$	50.2114	+	77.8062i	0.242494	+	0.375762i
$36$	135.920			0.629258
$37$	−87.6595	−	151.831i	−0.389490	−	0.674617i	0.602891	−	0.797824i	$-0.294015\pi$
$37$	−87.6595	−	151.831i	−0.389490	−	0.674617i	−0.992381	+	0.123207i	$0.960682\pi$
$38$	−43.0498	+	74.5644i	−0.183779	+	0.318314i
$39$	−91.4322	+	158.365i	−0.375407	+	0.650224i
$40$	85.3412	+	147.815i	0.337341	+	0.584291i
$41$	411.157			1.56615			0.783073	−	0.621930i	$-0.213651\pi$
$41$	411.157			1.56615			0.783073	+	0.621930i	$0.213651\pi$
$42$	266.724	−	13.2118i	0.979916	−	0.0485388i
$43$	−498.509			−1.76795			−0.883976	−	0.467532i	$-0.845143\pi$
$43$	−498.509			−1.76795			−0.883976	+	0.467532i	$0.845143\pi$
$44$	−402.143	−	696.532i	−1.37785	−	2.38650i
$45$	−22.5000	+	38.9711i	−0.0745356	+	0.129099i
$46$	−83.6863	+	144.949i	−0.268236	+	0.464599i
$47$	145.131	+	251.375i	0.450416	+	0.780144i	0.998412	−	0.0563376i	$-0.0179423\pi$
$47$	145.131	+	251.375i	0.450416	+	0.780144i	−0.547996	+	0.836481i	$0.684609\pi$
$48$	129.776			0.390240
$49$	341.321	−	33.8969i	0.995105	−	0.0988249i
$50$	−120.162			−0.339869
$51$	−46.6797	−	80.8516i	−0.128166	−	0.221990i
$52$	−460.275	+	797.220i	−1.22748	+	2.12605i
$53$	−291.316	+	504.575i	−0.755007	+	1.30771i	0.190364	+	0.981714i	$0.439033\pi$
$53$	−291.316	+	504.575i	−0.755007	+	1.30771i	−0.945371	+	0.325997i	$0.894300\pi$
$54$	64.8874	+	112.388i	0.163520	+	0.283224i
$55$	266.281			0.652825
$56$	631.442	−	31.2777i	1.50679	−	0.0746367i
$57$	−53.7398			−0.124877
$58$	339.873	+	588.677i	0.769439	+	1.33271i
$59$	328.855	−	569.594i	0.725649	−	1.25686i	−0.233058	−	0.972463i	$-0.574873\pi$
$59$	328.855	−	569.594i	0.725649	−	1.25686i	0.958706	−	0.284397i	$-0.0917935\pi$
$60$	−113.266	+	196.183i	−0.243711	+	0.422119i
$61$	208.583	+	361.277i	0.437809	+	0.758308i	0.997520	−	0.0703801i	$-0.0224212\pi$
$61$	208.583	+	361.277i	0.437809	+	0.758308i	−0.559711	+	0.828688i	$0.689088\pi$
$62$	−565.911			−1.15921
$63$	90.3806	+	140.051i	0.180744	+	0.280076i
$64$	−659.310			−1.28771
$65$	−152.387	−	263.942i	−0.290789	−	0.503661i
$66$	383.962	−	665.042i	0.716098	−	1.24032i
$67$	283.955	−	491.825i	0.517771	−	0.896806i	−0.482016	−	0.876163i	$-0.660095\pi$
$67$	283.955	−	491.825i	0.517771	−	0.896806i	0.999787	−	0.0206433i	$-0.00657143\pi$
$68$	−234.989	−	407.012i	−0.419067	−	0.725845i
$69$	−104.467			−0.182266
$70$	−203.201	+	395.993i	−0.346959	+	0.676147i
$71$	887.933			1.48420			0.742100	−	0.670289i	$-0.233830\pi$
$71$	887.933			1.48420			0.742100	+	0.670289i	$0.233830\pi$
$72$	153.614	+	266.068i	0.251439	+	0.435505i
$73$	546.253	−	946.138i	0.875809	−	1.51695i	0.0199113	−	0.999802i	$-0.493662\pi$
$73$	546.253	−	946.138i	0.875809	−	1.51695i	0.855898	−	0.517145i	$-0.173005\pi$
$74$	421.333	−	729.770i	0.661878	−	1.14641i
$75$	−37.5000	−	64.9519i	−0.0577350	−	0.100000i
$76$	−270.529			−0.408314
$77$	450.297	−	877.530i	0.666443	−	1.29875i
$78$	−878.933			−1.27589
$79$	−67.7126	−	117.282i	−0.0964337	−	0.167028i	0.813772	−	0.581184i	$-0.197410\pi$
$79$	−67.7126	−	117.282i	−0.0964337	−	0.167028i	−0.910206	+	0.414156i	$0.864077\pi$
$80$	−108.146	+	187.315i	−0.151139	+	0.261781i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	988.108	+	1711.45i	1.33071	+	2.30486i
$83$	−464.523			−0.614313			−0.307157	−	0.951659i	$-0.599378\pi$
$83$	−464.523			−0.614313			−0.307157	+	0.951659i	$0.599378\pi$
$84$	454.982	+	705.027i	0.590983	+	0.915770i
$85$	155.599			0.198554
$86$	−1198.04	−	2075.06i	−1.50218	−	2.60185i
$87$	−212.134	+	367.427i	−0.261416	+	0.452786i
$88$	908.991	−	1574.42i	1.10112	−	1.90720i
$89$	−15.9399	−	27.6088i	−0.0189846	−	0.0328823i	0.856377	−	0.516351i	$-0.172710\pi$
$89$	−15.9399	−	27.6088i	−0.0189846	−	0.0328823i	−0.875362	+	0.483469i	$0.839377\pi$
$90$	−216.291			−0.253323
$91$	−1127.52	+	55.8500i	−1.29886	+	0.0643371i
$92$	−525.894			−0.595959
$93$	−176.609	−	305.896i	−0.196920	−	0.341075i
$94$	−697.569	+	1208.23i	−0.765412	+	1.32573i
$95$	44.7831	−	77.5667i	0.0483648	−	0.0837702i
$96$	−97.7560	−	169.318i	−0.103929	−	0.180010i
$97$	−254.781			−0.266691			−0.133346	−	0.991070i	$-0.542572\pi$
$97$	−254.781			−0.266691			−0.133346	+	0.991070i	$0.542572\pi$
$98$	961.372	+	1339.30i	0.990951	+	1.38050i
$99$	479.306			0.486587
$100$	−188.777	−	326.972i	−0.188777	−	0.326972i
$101$	−679.764	+	1177.39i	−0.669694	+	1.15994i	0.308296	+	0.951291i	$0.400241\pi$
$101$	−679.764	+	1177.39i	−0.669694	+	1.15994i	−0.977990	+	0.208653i	$0.933092\pi$
$102$	224.365	−	388.611i	0.217798	−	0.377238i
$103$	−724.029	−	1254.06i	−0.692629	−	1.19967i	−0.970974	−	0.239187i	$-0.923119\pi$
$103$	−724.029	−	1254.06i	−0.692629	−	1.19967i	0.278345	−	0.960481i	$-0.410214\pi$
$104$	−2080.78			−1.96190
$105$	−277.464	+	13.7438i	−0.257883	+	0.0127739i
$106$	−2800.41			−2.56603
$107$	833.227	+	1443.19i	0.752814	+	1.30391i	0.946454	+	0.322839i	$0.104637\pi$
$107$	833.227	+	1443.19i	0.752814	+	1.30391i	−0.193640	+	0.981073i	$0.562029\pi$
$108$	−203.880	+	353.130i	−0.181651	+	0.314629i
$109$	559.198	−	968.560i	0.491390	−	0.851112i	−0.508561	−	0.861026i	$-0.669822\pi$
$109$	559.198	−	968.560i	0.491390	−	0.851112i	0.999951	+	0.00991369i	$0.00315568\pi$
$110$	639.937	+	1108.40i	0.554687	+	0.960747i
$111$	525.957			0.449745
$112$	434.415	+	673.157i	0.366503	+	0.567923i
$113$	806.732			0.671602			0.335801	−	0.941933i	$-0.390993\pi$
$113$	806.732			0.671602			0.335801	+	0.941933i	$0.390993\pi$
$114$	−129.149	−	223.693i	−0.106105	−	0.183779i
$115$	87.0559	−	150.785i	0.0705913	−	0.122268i
$116$	−1067.90	+	1849.65i	−0.854757	+	1.48048i
$117$	−274.297	−	475.096i	−0.216741	−	0.375407i
$118$	3161.27			2.46625
$119$	263.127	−	512.777i	0.202696	−	0.395010i
$120$	−512.047			−0.389527
$121$	−752.615	−	1303.57i	−0.565451	−	0.979390i
$122$	−1002.55	+	1736.47i	−0.743989	+	1.28863i
$123$	−616.736	+	1068.22i	−0.452107	+	0.783073i
$124$	−889.062	−	1539.90i	−0.643872	−	1.11522i
$125$	125.000			0.0894427
$126$	−365.761	+	712.788i	−0.258608	+	0.503970i
$127$	−1433.92			−1.00189			−0.500945	−	0.865479i	$-0.667014\pi$
$127$	−1433.92			−1.00189			−0.500945	+	0.865479i	$0.667014\pi$
$128$	−1323.79	−	2292.88i	−0.914125	−	1.58331i
$129$	747.764	−	1295.17i	0.510364	−	0.883976i
$130$	732.444	−	1268.63i	0.494151	−	0.855894i
$131$	−325.467	−	563.725i	−0.217070	−	0.375976i	0.736841	−	0.676066i	$-0.236317\pi$
$131$	−325.467	−	563.725i	−0.217070	−	0.375976i	−0.953911	+	0.300090i	$0.902983\pi$
$132$	2412.86			1.59100
$133$	−179.890	−	278.753i	−0.117282	−	0.181736i
$134$	2729.65			1.75974
$135$	−67.5000	−	116.913i	−0.0430331	−	0.0745356i
$136$	531.160	−	919.996i	0.334902	−	0.580066i
$137$	308.891	−	535.015i	0.192630	−	0.333645i	−0.753491	−	0.657458i	$-0.771632\pi$
$137$	308.891	−	535.015i	0.192630	−	0.333645i	0.946121	+	0.323813i	$0.104965\pi$
$138$	−251.059	−	434.847i	−0.154866	−	0.268236i
$139$	1525.08			0.930614			0.465307	−	0.885149i	$-0.345944\pi$
$139$	1525.08			0.930614			0.465307	+	0.885149i	$0.345944\pi$
$140$	−1396.77	+	69.1871i	−0.843204	+	0.0417670i
$141$	−870.787			−0.520096
$142$	2133.91	+	3696.04i	1.26108	+	2.18426i
$143$	−1623.11	+	2811.31i	−0.949171	+	1.64401i
$144$	−194.664	+	337.167i	−0.112653	+	0.195120i
$145$	−353.557	−	612.379i	−0.202492	−	0.350726i
$146$	5251.10			2.97660
$147$	−423.915	+	937.623i	−0.237850	+	0.526081i
$148$	2647.70			1.47054
$149$	693.909	+	1201.89i	0.381525	+	0.660821i	0.991281	−	0.131769i	$-0.0420656\pi$
$149$	693.909	+	1201.89i	0.381525	+	0.660821i	−0.609755	+	0.792590i	$0.708732\pi$
$150$	180.243	−	312.190i	0.0981117	−	0.169935i
$151$	−1142.17	+	1978.30i	−0.615554	+	1.06617i	0.374733	+	0.927133i	$0.377734\pi$
$151$	−1142.17	+	1978.30i	−0.615554	+	1.06617i	−0.990287	+	0.139038i	$0.955599\pi$
$152$	−305.748	−	529.571i	−0.163154	−	0.282591i
$153$	280.078			0.147993
$154$	4734.92	−	234.538i	2.47760	−	0.122725i
$155$	588.697			0.305066
$156$	−1380.83	−	2391.66i	−0.708683	−	1.22748i
$157$	−134.154	+	232.362i	−0.0681953	+	0.118118i	−0.898107	−	0.439777i	$-0.855057\pi$
$157$	−134.154	+	232.362i	−0.0681953	+	0.118118i	0.829912	+	0.557895i	$0.188391\pi$
$158$	325.459	−	563.711i	0.163874	−	0.283838i
$159$	−873.949	−	1513.72i	−0.435903	−	0.755007i
$160$	325.853			0.161006
$161$	−349.696	−	541.879i	−0.171180	−	0.265255i
$162$	−389.324			−0.188816
$163$	1363.79	+	2362.16i	0.655340	+	1.13508i	0.981808	+	0.189874i	$0.0608081\pi$
$163$	1363.79	+	2362.16i	0.655340	+	1.13508i	−0.326468	+	0.945208i	$0.605859\pi$
$164$	−3104.69	+	5377.47i	−1.47826	+	2.56043i
$165$	−399.422	+	691.819i	−0.188454	+	0.326412i
$166$	−1116.36	−	1933.59i	−0.521965	−	0.904070i
$167$	2234.41			1.03535			0.517675	−	0.855577i	$-0.326798\pi$
$167$	2234.41			1.03535			0.517675	+	0.855577i	$0.326798\pi$
$168$	−865.902	+	1687.45i	−0.397653	+	0.774939i
$169$	1518.49			0.691164
$170$	373.941	+	647.685i	0.168706	+	0.292207i
$171$	80.6096	−	139.620i	0.0360490	−	0.0624386i
$172$	3764.29	−	6519.94i	1.66875	−	2.89035i
$173$	−1169.83	−	2026.21i	−0.514108	−	0.890462i	−0.999866	−	0.0163681i	$-0.994790\pi$
$173$	−1169.83	−	2026.21i	−0.514108	−	0.890462i	0.485758	−	0.874093i	$-0.338544\pi$
$174$	−2039.24			−0.888472
$175$	211.382	−	411.938i	0.0913086	−	0.177940i
$176$	2303.79			0.986675
$177$	986.565	+	1708.78i	0.418953	+	0.725649i
$178$	76.6148	−	132.701i	0.0322614	−	0.0558783i
$179$	−1222.88	+	2118.08i	−0.510626	+	0.884430i	0.489298	+	0.872116i	$0.337253\pi$
$179$	−1222.88	+	2118.08i	−0.510626	+	0.884430i	−0.999924	+	0.0123133i	$0.996080\pi$
$180$	−339.799	−	588.550i	−0.140706	−	0.243711i
$181$	1178.45			0.483944			0.241972	−	0.970283i	$-0.422206\pi$
$181$	1178.45			0.483944			0.241972	+	0.970283i	$0.422206\pi$
$182$	−2942.17	−	4559.10i	−1.19828	−	1.85683i
$183$	−1251.50			−0.505539
$184$	−594.356	−	1029.45i	−0.238133	−	0.412459i
$185$	−438.298	+	759.154i	−0.174185	+	0.301698i
$186$	848.867	−	1470.28i	0.334634	−	0.579603i
$187$	−828.662	−	1435.29i	−0.324052	−	0.561275i
$188$	−4383.60			−1.70057
$189$	−499.435	+	24.7388i	−0.192214	+	0.00952109i
$190$	430.498			0.164377
$191$	1137.64	+	1970.46i	0.430979	+	0.746478i	0.996958	−	0.0779421i	$-0.0248349\pi$
$191$	1137.64	+	1970.46i	0.430979	+	0.746478i	−0.565979	+	0.824420i	$0.691502\pi$
$192$	988.964	−	1712.94i	0.371731	−	0.643857i
$193$	−2205.52	+	3820.07i	−0.822574	+	1.42474i	0.0811857	+	0.996699i	$0.474129\pi$
$193$	−2205.52	+	3820.07i	−0.822574	+	1.42474i	−0.903760	+	0.428041i	$0.859204\pi$
$194$	−612.298	−	1060.53i	−0.226600	−	0.392483i
$195$	914.322			0.335774
$196$	−2134.01	+	4720.05i	−0.777701	+	1.72014i
$197$	−2011.41			−0.727447			−0.363723	−	0.931507i	$-0.618495\pi$
$197$	−2011.41			−0.727447			−0.363723	+	0.931507i	$0.618495\pi$
$198$	1151.89	+	1995.13i	0.413440	+	0.716098i
$199$	−555.618	+	962.358i	−0.197923	+	0.342813i	−0.947855	−	0.318702i	$-0.896753\pi$
$199$	−555.618	+	962.358i	−0.197923	+	0.342813i	0.749932	+	0.661515i	$0.230086\pi$
$200$	426.706	−	739.076i	0.150863	−	0.261303i
$201$	851.866	+	1475.48i	0.298935	+	0.517771i
$202$	−6534.54			−2.27608
$203$	−2615.98	+	129.579i	−0.904463	+	0.0448014i
$204$	1409.93			0.483897
$205$	−1027.89	−	1780.36i	−0.350201	−	0.606565i
$206$	3480.03	−	6027.59i	1.17701	−	2.03865i
$207$	156.701	−	271.413i	0.0526157	−	0.0911330i
$208$	−1318.41	−	2283.55i	−0.439496	−	0.761230i
$209$	−953.993			−0.315737
$210$	−724.020	−	1121.92i	−0.237915	−	0.368666i
$211$	3031.04			0.988936			0.494468	−	0.869196i	$-0.335363\pi$
$211$	3031.04			0.988936			0.494468	+	0.869196i	$0.335363\pi$
$212$	−4399.51	−	7620.18i	−1.42528	−	2.46866i
$213$	−1331.90	+	2306.92i	−0.428452	+	0.742100i
$214$	−4004.88	+	6936.66i	−1.27929	+	2.21580i
$215$	1246.27	+	2158.61i	0.395326	+	0.684725i
$216$	−921.685			−0.290337
$217$	995.521	−	1940.05i	0.311430	−	0.606909i
$218$	5375.55			1.67008
$219$	1638.76	+	2838.41i	0.505649	+	0.875809i
$220$	−2010.72	+	3482.66i	−0.616193	+	1.06728i
$221$	−948.450	+	1642.76i	−0.288686	+	0.500019i
$222$	1264.00	+	2189.31i	0.382136	+	0.661878i
$223$	−3789.93			−1.13808			−0.569042	−	0.822309i	$-0.692686\pi$
$223$	−3789.93			−1.13808			−0.569042	+	0.822309i	$0.692686\pi$
$224$	551.037	−	1073.85i	0.164365	−	0.320311i
$225$	225.000			0.0666667
$226$	1938.77	+	3358.05i	0.570641	+	0.988380i
$227$	−1938.16	+	3356.98i	−0.566696	+	0.981546i	0.430194	+	0.902736i	$0.358445\pi$
$227$	−1938.16	+	3356.98i	−0.566696	+	0.981546i	−0.996890	+	0.0788091i	$0.974888\pi$
$228$	405.794	−	702.856i	0.117870	−	0.204157i
$229$	−2963.22	−	5132.45i	−0.855088	−	1.48106i	−0.876564	−	0.481286i	$-0.840170\pi$
$229$	−2963.22	−	5132.45i	−0.855088	−	1.48106i	0.0214758	−	0.999769i	$-0.493164\pi$
$230$	836.863			0.239918
$231$	1604.44	+	2486.20i	0.456990	+	0.708139i
$232$	−4827.68			−1.36618
$233$	−2321.52	−	4020.99i	−0.652737	−	1.13057i	−0.982456	−	0.186494i	$-0.940287\pi$
$233$	−2321.52	−	4020.99i	−0.652737	−	1.13057i	0.329719	−	0.944079i	$-0.393046\pi$
$234$	1318.40	−	2283.53i	0.368318	−	0.637946i
$235$	725.656	−	1256.87i	0.201432	−	0.348891i
$236$	4966.43	+	8602.11i	1.36986	+	2.37267i
$237$	406.276			0.111352
$238$	2766.80	−	137.050i	0.753551	−	0.0373262i
$239$	944.025			0.255497			0.127749	−	0.991807i	$-0.459225\pi$
$239$	944.025			0.255497			0.127749	+	0.991807i	$0.459225\pi$
$240$	−324.439	−	561.945i	−0.0872603	−	0.151139i
$241$	−757.505	+	1312.04i	−0.202470	+	0.350688i	−0.949324	−	0.314301i	$-0.898230\pi$
$241$	−757.505	+	1312.04i	−0.202470	+	0.350688i	0.746854	+	0.664988i	$0.231563\pi$
$242$	3617.43	−	6265.57i	0.960897	−	1.66432i
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$	−6300.13			−1.65297
$245$	−1000.08	−	1393.22i	−0.260787	−	0.363305i
$246$	−5928.65			−1.53657
$247$	545.949	+	945.612i	0.140639	+	0.243595i
$248$	2009.60	−	3480.74i	0.514557	−	0.891238i
$249$	696.784	−	1206.87i	0.177337	−	0.307157i
$250$	300.405	+	520.316i	0.0759970	+	0.131631i
$251$	3219.82			0.809695			0.404847	−	0.914384i	$-0.367325\pi$
$251$	3219.82			0.809695			0.404847	+	0.914384i	$0.367325\pi$
$252$	−2514.19	+	124.537i	−0.628487	+	0.0311313i
$253$	−1854.51			−0.460838
$254$	−3446.05	−	5968.74i	−0.851278	−	1.47446i
$255$	−233.398	+	404.258i	−0.0573176	+	0.0992769i
$256$	3725.54	−	6452.83i	0.909557	−	1.57540i
$257$	−1107.27	−	1917.85i	−0.268754	−	0.465496i	0.699786	−	0.714352i	$-0.253279\pi$
$257$	−1107.27	−	1917.85i	−0.268754	−	0.465496i	−0.968540	+	0.248856i	$0.919945\pi$
$258$	7188.21			1.73457
$259$	1760.60	+	2728.18i	0.422389	+	0.654521i
$260$	4602.75			1.09789
$261$	−636.403	−	1102.28i	−0.150929	−	0.261416i
$262$	1564.35	−	2709.53i	0.368877	−	0.638913i
$263$	2728.51	−	4725.92i	0.639723	−	1.10803i	−0.345770	−	0.938319i	$-0.612382\pi$
$263$	2728.51	−	4725.92i	0.639723	−	1.10803i	0.985493	−	0.169714i	$-0.0542844\pi$
$264$	2726.97	+	4723.25i	0.635733	+	1.10112i
$265$	2913.16			0.675299
$266$	727.997	−	1418.71i	0.167806	−	0.327017i
$267$	95.6396			0.0219215
$268$	4288.35	+	7427.63i	0.977434	+	1.69297i
$269$	2910.38	−	5040.92i	0.659661	−	1.14257i	−0.321042	−	0.947065i	$-0.604033\pi$
$269$	2910.38	−	5040.92i	0.659661	−	1.14257i	0.980703	−	0.195502i	$-0.0626337\pi$
$270$	324.437	−	561.941i	0.0731282	−	0.126662i
$271$	−1650.37	−	2858.53i	−0.369937	−	0.640750i	0.619618	−	0.784903i	$-0.287287\pi$
$271$	−1650.37	−	2858.53i	−0.369937	−	0.640750i	−0.989555	+	0.144154i	$0.953954\pi$
$272$	1346.20			0.300093
$273$	1546.17	−	3013.15i	0.342779	−	0.668000i
$274$	2969.35			0.654690
$275$	−665.703	−	1153.03i	−0.145976	−	0.252838i
$276$	788.840	−	1366.31i	0.172038	−	0.297979i
$277$	1935.63	−	3352.60i	0.419857	−	0.727214i	−0.576068	−	0.817402i	$-0.695413\pi$
$277$	1935.63	−	3352.60i	0.419857	−	0.727214i	0.995925	+	0.0901881i	$0.0287468\pi$
$278$	3665.12	+	6348.18i	0.790717	+	1.36956i
$279$	1059.65			0.227383
$280$	−1714.04	−	2656.03i	−0.365834	−	0.566886i
$281$	−1411.40			−0.299634			−0.149817	−	0.988714i	$-0.547869\pi$
$281$	−1411.40			−0.299634			−0.149817	+	0.988714i	$0.547869\pi$
$282$	−2092.71	−	3624.68i	−0.441911	−	0.765412i
$283$	2376.25	−	4115.79i	0.499129	−	0.864517i	−0.500870	−	0.865522i	$-0.666987\pi$
$283$	2376.25	−	4115.79i	0.499129	−	0.864517i	0.999999	+	0.00100512i	$0.000319941\pi$
$284$	−6704.86	+	11613.2i	−1.40092	+	2.42646i
$285$	134.349	+	232.700i	0.0279234	+	0.0483648i
$286$	−15602.9			−3.22594
$287$	−7605.41	+	376.724i	−1.56423	+	0.0774820i
$288$	586.536			0.120007
$289$	1972.28	+	3416.09i	0.401441	+	0.695316i
$290$	1699.36	−	2943.38i	0.344104	−	0.596005i
$291$	382.171	−	661.939i	0.0769871	−	0.133346i
$292$	8249.62	+	14288.8i	1.65333	+	2.86365i
$293$	−1301.32			−0.259468			−0.129734	−	0.991549i	$-0.541412\pi$
$293$	−1301.32			−0.259468			−0.129734	+	0.991549i	$0.541412\pi$
$294$	−4921.65	+	488.774i	−0.976315	+	0.0969588i
$295$	−3288.55			−0.649040
$296$	2992.39	+	5182.97i	0.587598	+	1.01775i
$297$	−718.960	+	1245.27i	−0.140466	+	0.243294i
$298$	−3335.26	+	5776.83i	−0.648343	+	1.12296i
$299$	1061.29	+	1838.22i	0.205272	+	0.355541i
$300$	1132.66			0.217981
$301$	9221.21	−	456.761i	1.76579	−	0.0874660i
$302$	−10979.6			−2.09208
$303$	−2039.29	−	3532.16i	−0.386648	−	0.669694i
$304$	387.451	−	671.085i	0.0730981	−	0.126610i
$305$	1042.92	−	1806.38i	0.195794	−	0.339126i
$306$	673.094	+	1165.83i	0.125746	+	0.217798i
$307$	6138.12			1.14111			0.570555	−	0.821259i	$-0.306728\pi$
$307$	6138.12			1.14111			0.570555	+	0.821259i	$0.306728\pi$
$308$	8076.87	+	12515.7i	1.49423	+	2.31542i
$309$	4344.18			0.799779
$310$	1414.78	+	2450.47i	0.259207	+	0.448959i
$311$	−2041.02	+	3535.15i	−0.372140	+	0.644566i	−0.989895	−	0.141805i	$-0.954709\pi$
$311$	−2041.02	+	3535.15i	−0.372140	+	0.644566i	0.617754	+	0.786371i	$0.288043\pi$
$312$	3121.17	−	5406.03i	0.566351	−	0.980949i
$313$	−3571.60	−	6186.19i	−0.644979	−	1.11714i	−0.984306	−	0.176469i	$-0.943533\pi$
$313$	−3571.60	−	6186.19i	−0.644979	−	1.11714i	0.339327	−	0.940669i	$-0.389801\pi$
$314$	−1289.62			−0.231775
$315$	380.488	−	741.488i	0.0680574	−	0.132629i
$316$	2045.22			0.364090
$317$	3740.81	+	6479.27i	0.662791	+	1.14799i	0.979879	+	0.199592i	$0.0639615\pi$
$317$	3740.81	+	6479.27i	0.662791	+	1.14799i	−0.317088	+	0.948396i	$0.602705\pi$
$318$	4200.61	−	7275.67i	0.740750	−	1.28302i
$319$	−3765.83	+	6522.61i	−0.660959	+	1.14481i
$320$	1648.27	+	2854.89i	0.287942	+	0.498729i
$321$	−4999.36			−0.869275
$322$	1415.18	−	2757.88i	0.244923	−	0.477301i
$323$	−557.457			−0.0960301
$324$	−611.639	−	1059.39i	−0.104876	−	0.181651i
$325$	−761.935	+	1319.71i	−0.130045	+	0.225244i
$326$	−6555.03	+	11353.6i	−1.11365	+	1.92890i
$327$	1677.60	+	2905.68i	0.283704	+	0.491390i
$328$	−14035.5			−2.36274
$329$	−2914.90	−	4516.84i	−0.488461	−	0.756905i
$330$	−3839.62			−0.640498
$331$	972.059	+	1683.65i	0.161417	+	0.279583i	0.935377	−	0.353652i	$-0.115060\pi$
$331$	972.059	+	1683.65i	0.161417	+	0.279583i	−0.773960	+	0.633235i	$0.781727\pi$
$332$	3507.65	−	6075.44i	0.579842	−	1.00432i
$333$	−788.936	+	1366.48i	−0.129830	+	0.224872i
$334$	5369.81	+	9300.78i	0.879709	+	1.52370i
$335$	−2839.55			−0.463109
$336$	−2400.54	+	118.907i	−0.389762	+	0.0193063i
$337$	−1920.36			−0.310411			−0.155205	−	0.987882i	$-0.549604\pi$
$337$	−1920.36			−0.310411			−0.155205	+	0.987882i	$0.549604\pi$
$338$	3649.28	+	6320.75i	0.587263	+	1.01717i
$339$	−1210.10	+	2095.95i	−0.193875	+	0.335801i
$340$	−1174.94	+	2035.06i	−0.187412	+	0.324608i
$341$	−3135.18	−	5430.29i	−0.497887	−	0.862366i
$342$	774.896			0.122519
$343$	−6282.55	+	939.748i	−0.988997	+	0.147935i
$344$	17017.3			2.66719
$345$	261.168	+	452.355i	0.0407559	+	0.0705913i
$346$	5622.77	−	9738.92i	0.873647	−	1.51320i
$347$	−1046.72	+	1812.98i	−0.161934	+	0.280478i	−0.935562	−	0.353162i	$-0.885106\pi$
$347$	−1046.72	+	1812.98i	−0.161934	+	0.280478i	0.773628	+	0.633640i	$0.218440\pi$
$348$	−3203.69	−	5548.96i	−0.493494	−	0.854757i
$349$	2199.00			0.337277			0.168638	−	0.985678i	$-0.446063\pi$
$349$	2199.00			0.337277			0.168638	+	0.985678i	$0.446063\pi$
$350$	2222.70	−	110.099i	0.339453	−	0.0168143i
$351$	1645.78			0.250271
$352$	−1735.37	−	3005.75i	−0.262772	−	0.455134i
$353$	2930.58	−	5075.92i	0.441867	−	0.765337i	−0.555961	−	0.831209i	$-0.687650\pi$
$353$	2930.58	−	5075.92i	0.441867	−	0.765337i	0.997828	+	0.0658719i	$0.0209829\pi$
$354$	−4741.90	+	8213.21i	−0.711946	+	1.23313i
$355$	−2219.83	−	3844.86i	−0.331877	−	0.574828i
$356$	481.456			0.0716772
$357$	937.542	+	1452.79i	0.138992	+	0.215377i
$358$	−11755.4			−1.73546
$359$	−3635.72	−	6297.25i	−0.534502	−	0.925784i	−0.999187	−	0.0403082i	$-0.987166\pi$
$359$	−3635.72	−	6297.25i	−0.534502	−	0.925784i	0.464686	−	0.885476i	$-0.346167\pi$
$360$	768.071	−	1330.34i	0.112447	−	0.194764i
$361$	3269.06	−	5662.17i	0.476608	−	0.825510i
$362$	2832.10	+	4905.35i	0.411194	+	0.712208i
$363$	4515.69			0.652927
$364$	7783.53	−	15168.4i	1.12079	−	2.18417i
$365$	−5462.53			−0.783348
$366$	−3007.65	−	5209.40i	−0.429542	−	0.743989i
$367$	6318.98	−	10944.8i	0.898768	−	1.55671i	0.0696971	−	0.997568i	$-0.477797\pi$
$367$	6318.98	−	10944.8i	0.898768	−	1.55671i	0.829071	−	0.559144i	$-0.188870\pi$
$368$	753.182	−	1304.55i	0.106691	−	0.184795i
$369$	−1850.21	−	3204.65i	−0.261024	−	0.452107i
$370$	−4213.33			−0.592002
$371$	4926.33	−	9600.33i	0.689386	−	1.34346i
$372$	5334.37			0.743479
$373$	3106.40	+	5380.45i	0.431216	+	0.746888i	0.996978	−	0.0776807i	$-0.0247515\pi$
$373$	3106.40	+	5380.45i	0.431216	+	0.746888i	−0.565763	+	0.824568i	$0.691418\pi$
$374$	3982.94	−	6898.66i	0.550677	−	0.953800i
$375$	−187.500	+	324.760i	−0.0258199	+	0.0447214i
$376$	−4954.27	−	8581.04i	−0.679513	−	1.17695i
$377$	8620.40			1.17765
$378$	−1303.24	−	2019.46i	−0.177331	−	0.274788i
$379$	5075.53			0.687896			0.343948	−	0.938989i	$-0.388236\pi$
$379$	5075.53			0.687896			0.343948	+	0.938989i	$0.388236\pi$
$380$	676.323	+	1171.43i	0.0913017	+	0.158139i
$381$	2150.88	−	3725.44i	0.289221	−	0.500945i
$382$	−5468.05	+	9470.95i	−0.732382	+	1.26852i
$383$	4206.85	+	7286.49i	0.561254	+	0.972120i	0.997387	+	0.0722383i	$0.0230142\pi$
$383$	4206.85	+	7286.49i	0.561254	+	0.972120i	−0.436134	+	0.899882i	$0.643652\pi$
$384$	7942.77			1.05554
$385$	−4925.56	+	243.981i	−0.652026	+	0.0322972i
$386$	−21201.5			−2.79567
$387$	2243.29	+	3885.50i	0.294659	+	0.510364i
$388$	1923.87	−	3332.24i	0.251726	−	0.436003i
$389$	−1854.35	+	3211.82i	−0.241694	+	0.418627i	−0.961197	−	0.275863i	$-0.911036\pi$
$389$	−1854.35	+	3211.82i	−0.241694	+	0.418627i	0.719503	+	0.694490i	$0.244370\pi$
$390$	2197.33	+	3805.89i	0.285298	+	0.494151i
$391$	−1083.66			−0.140162
$392$	−11651.5	+	1157.12i	−1.50125	+	0.149091i
$393$	1952.80			0.250651
$394$	−4833.90	−	8372.55i	−0.618092	−	1.07057i
$395$	−338.563	+	586.408i	−0.0431265	+	0.0746972i
$396$	−3619.29	+	6268.79i	−0.459283	+	0.795502i
$397$	2260.02	+	3914.48i	0.285711	+	0.494866i	0.972781	−	0.231725i	$-0.0744369\pi$
$397$	2260.02	+	3914.48i	0.285711	+	0.494866i	−0.687070	+	0.726591i	$0.741104\pi$
$398$	−5341.12			−0.672679
$399$	994.056	−	49.2392i	0.124724	−	0.00617806i
$400$	1081.46			0.135183
$401$	6295.88	+	10904.8i	0.784043	+	1.35800i	0.929569	+	0.368648i	$0.120179\pi$
$401$	6295.88	+	10904.8i	0.784043	+	1.35800i	−0.145526	+	0.989354i	$0.546488\pi$
$402$	−4094.47	+	7091.83i	−0.507994	+	0.879872i
$403$	−3588.39	+	6215.28i	−0.443550	+	0.768251i
$404$	−10265.9	−	17781.1i	−1.26423	−	2.18971i
$405$	405.000			0.0496904
$406$	−6826.20	−	10577.7i	−0.834430	−	1.29301i
$407$	9336.84			1.13713
$408$	1593.48	+	2759.99i	0.193355	+	0.334902i
$409$	−4508.81	+	7809.49i	−0.545101	+	0.944143i	0.453499	+	0.891257i	$0.350175\pi$
$409$	−4508.81	+	7809.49i	−0.545101	+	0.944143i	−0.998601	+	0.0528864i	$0.983158\pi$
$410$	4940.54	−	8557.27i	0.595112	−	1.03076i
$411$	926.673	+	1605.04i	0.111215	+	0.192630i
$412$	21868.9			2.61505
$413$	−5561.13	+	10837.4i	−0.662579	+	1.29122i
$414$	1506.35			0.178824
$415$	1161.31	+	2011.44i	0.137365	+	0.237922i
$416$	−1986.23	+	3440.25i	−0.234094	+	0.405462i
$417$	−2287.62	+	3962.27i	−0.268645	+	0.465307i
$418$	−2292.67	−	3971.02i	−0.268273	−	0.464663i
$419$	3.80670			0.000443842			0.000221921	−	1.00000i	$-0.499929\pi$
$419$	3.80670			0.000443842			0.000221921		1.00000i	$0.499929\pi$
$420$	1915.40	−	3732.69i	0.222529	−	0.433659i
$421$	12076.0			1.39798			0.698989	−	0.715132i	$-0.253633\pi$
$421$	12076.0			1.39798			0.698989	+	0.715132i	$0.253633\pi$
$422$	7284.31	+	12616.8i	0.840271	+	1.45539i
$423$	1306.18	−	2262.37i	0.150139	−	0.260048i
$424$	9944.51	−	17224.4i	1.13903	−	1.97286i
$425$	−388.997	−	673.763i	−0.0443980	−	0.0768996i
$426$	−12803.5			−1.45617
$427$	−4189.31	−	6491.63i	−0.474789	−	0.735719i
$428$	−25167.1			−2.84228
$429$	−4869.34	−	8433.94i	−0.548004	−	0.949171i
$430$	−5990.18	+	10375.3i	−0.671796	+	1.16358i
$431$	5158.85	−	8935.40i	0.576551	−	0.998615i	−0.419321	−	0.907838i	$-0.637732\pi$
$431$	5158.85	−	8935.40i	0.576551	−	0.998615i	0.995871	−	0.0907767i	$-0.0289349\pi$
$432$	−583.991	−	1011.50i	−0.0650400	−	0.112653i
$433$	12728.4			1.41267			0.706334	−	0.707878i	$-0.250347\pi$
$433$	12728.4			1.41267			0.706334	+	0.707878i	$0.250347\pi$
$434$	10468.0	−	518.518i	1.15779	−	0.0573495i
$435$	2121.34			0.233818
$436$	8445.12	+	14627.4i	0.927633	+	1.60671i
$437$	−311.891	+	540.211i	−0.0341413	+	0.0591345i
$438$	−7876.65	+	13642.8i	−0.859272	+	1.48830i
$439$	4986.29	+	8636.51i	0.542102	+	0.938948i	0.998783	+	0.0493175i	$0.0157046\pi$
$439$	4986.29	+	8636.51i	0.542102	+	0.938948i	−0.456681	+	0.889630i	$0.650962\pi$
$440$	−9089.91			−0.984874
$441$	−1800.14	−	2507.80i	−0.194379	−	0.270791i
$442$	−9117.40			−0.981155
$443$	−5231.39	−	9061.03i	−0.561063	−	0.971789i	−0.997404	−	0.0720080i	$-0.977059\pi$
$443$	−5231.39	−	9061.03i	−0.561063	−	0.971789i	0.436341	−	0.899781i	$-0.356274\pi$
$444$	−3971.55	+	6878.93i	−0.424508	+	0.735269i
$445$	−79.6996	+	138.044i	−0.00849017	+	0.0147054i
$446$	−9108.11	−	15775.7i	−0.966998	−	1.67489i
$447$	−4163.46			−0.440547
$448$	12195.6	−	604.095i	1.28614	−	0.0637071i
$449$	−11664.7			−1.22604			−0.613019	−	0.790068i	$-0.710045\pi$
$449$	−11664.7			−1.22604			−0.613019	+	0.790068i	$0.710045\pi$
$450$	540.728	+	936.569i	0.0566448	+	0.0981117i
$451$	−10948.3	+	18963.1i	−1.14310	+	1.97991i
$452$	−6091.71	+	10551.2i	−0.633916	+	1.09797i
$453$	−3426.51	−	5934.90i	−0.355390	−	0.615554i
$454$	−18631.4			−1.92602
$455$	3060.63	+	4742.66i	0.315350	+	0.488658i
$456$	1834.49			0.188394
$457$	−2271.26	−	3933.95i	−0.232484	−	0.402674i	0.726054	−	0.687637i	$-0.241352\pi$
$457$	−2271.26	−	3933.95i	−0.232484	−	0.402674i	−0.958539	+	0.284963i	$0.908019\pi$
$458$	14242.6	−	24669.0i	1.45309	−	2.51682i
$459$	−420.117	+	727.664i	−0.0427220	+	0.0739967i
$460$	1314.73	+	2277.19i	0.133260	+	0.230814i
$461$	7887.54			0.796875			0.398437	−	0.917195i	$-0.369553\pi$
$461$	7887.54			0.796875			0.398437	+	0.917195i	$0.369553\pi$
$462$	−6493.03	+	12653.5i	−0.653859	+	1.27423i
$463$	−5444.15			−0.546460			−0.273230	−	0.961949i	$-0.588092\pi$
$463$	−5444.15			−0.546460			−0.273230	+	0.961949i	$0.588092\pi$
$464$	−3058.88	−	5298.13i	−0.306045	−	0.530085i
$465$	−883.046	+	1529.48i	−0.0880651	+	0.152533i
$466$	11158.3	−	19326.8i	1.10922	−	1.92123i
$467$	5289.01	+	9160.83i	0.524082	+	0.907736i	0.999607	+	0.0280342i	$0.00892472\pi$
$467$	5289.01	+	9160.83i	0.524082	+	0.907736i	−0.475525	+	0.879702i	$0.657742\pi$
$468$	8284.96			0.818317
$469$	−4801.85	+	9357.75i	−0.472769	+	0.921323i
$470$	6975.69			0.684606
$471$	−402.463	−	697.086i	−0.0393726	−	0.0681953i
$472$	−11226.0	+	19443.9i	−1.09474	+	1.89614i
$473$	13274.4	−	22991.9i	1.29039	−	2.23503i
$474$	976.376	+	1691.13i	0.0946128	+	0.163874i
$475$	−447.831			−0.0432588
$476$	4719.65	+	7313.43i	0.454463	+	0.704224i
$477$	5243.69			0.503338
$478$	2268.71	+	3929.53i	0.217089	+	0.376009i
$479$	−5822.35	+	10084.6i	−0.555386	+	0.961957i	0.442487	+	0.896775i	$0.354096\pi$
$479$	−5822.35	+	10084.6i	−0.555386	+	0.961957i	−0.997873	+	0.0651825i	$0.979237\pi$
$480$	−488.780	+	846.591i	−0.0464784	+	0.0805030i
$481$	−5343.27	−	9254.81i	−0.506512	−	0.877304i
$482$	−7281.85			−0.688131
$483$	1932.39	−	95.7183i	0.182043	−	0.00901725i
$484$	22732.3			2.13489
$485$	636.952	+	1103.23i	0.0596340	+	0.103289i
$486$	583.987	−	1011.49i	0.0545065	−	0.0944081i
$487$	4618.61	−	7999.67i	0.429752	−	0.744353i	−0.567099	−	0.823650i	$-0.691934\pi$
$487$	4618.61	−	7999.67i	0.429752	−	0.744353i	0.996851	+	0.0792971i	$0.0252676\pi$
$488$	−7120.30	−	12332.7i	−0.660494	−	1.14401i
$489$	−8182.75			−0.756722
$490$	3395.89	−	7511.10i	0.313083	−	0.692484i
$491$	−2704.47			−0.248576			−0.124288	−	0.992246i	$-0.539665\pi$
$491$	−2704.47			−0.248576			−0.124288	+	0.992246i	$0.539665\pi$
$492$	−9314.06	−	16132.4i	−0.853476	−	1.47826i
$493$	−2200.53	+	3811.42i	−0.201028	+	0.348190i
$494$	−2624.09	+	4545.06i	−0.238995	+	0.413951i
$495$	−1198.27	−	2075.46i	−0.108804	−	0.188454i
$496$	5093.24			0.461075
$497$	−16424.6	+	813.571i	−1.48238	+	0.0734279i
$498$	6698.15			0.602713
$499$	381.675	+	661.081i	0.0342408	+	0.0593067i	0.882638	−	0.470053i	$-0.155765\pi$
$499$	381.675	+	661.081i	0.0342408	+	0.0593067i	−0.848397	+	0.529360i	$0.822432\pi$
$500$	−943.887	+	1634.86i	−0.0844238	+	0.146226i
$501$	−3351.61	+	5805.16i	−0.298880	+	0.517675i
$502$	7738.00	+	13402.6i	0.687976	+	1.19161i
$503$	5902.36			0.523207			0.261604	−	0.965175i	$-0.415749\pi$
$503$	5902.36			0.523207			0.261604	+	0.965175i	$0.415749\pi$
$504$	−3085.28	−	4780.86i	−0.272677	−	0.422532i
$505$	6797.64			0.598993
$506$	−4456.82	−	7719.44i	−0.391561	−	0.678204i
$507$	−2277.73	+	3945.15i	−0.199522	+	0.345582i
$508$	10827.7	−	18754.1i	0.945670	−	1.63795i
$509$	−1100.15	−	1905.51i	−0.0958020	−	0.165934i	0.814141	−	0.580667i	$-0.197208\pi$
$509$	−1100.15	−	1905.51i	−0.0958020	−	0.165934i	−0.909943	+	0.414733i	$0.863875\pi$
$510$	−2243.65			−0.194805
$511$	−9237.46	+	18001.8i	−0.799689	+	1.55842i
$512$	14632.8			1.26305
$513$	241.829	+	418.860i	0.0208129	+	0.0360490i
$514$	5322.08	−	9218.12i	0.456706	−	0.791038i
$515$	−3620.15	+	6270.28i	−0.309753	+	0.536508i
$516$	11292.9	+	19559.8i	0.963451	+	1.66875i
$517$	−15458.3			−1.31500
$518$	−7124.99	+	13885.0i	−0.604351	+	1.17775i
$519$	7018.99			0.593641
$520$	5201.95	+	9010.05i	0.438694	+	0.759840i
$521$	606.846	−	1051.09i	0.0510296	−	0.0883858i	−0.839382	−	0.543541i	$-0.817083\pi$
$521$	606.846	−	1051.09i	0.0510296	−	0.0883858i	0.890412	+	0.455156i	$0.150416\pi$
$522$	3058.85	−	5298.09i	0.256480	−	0.444236i
$523$	4432.09	+	7676.61i	0.370558	+	0.641825i	0.989651	−	0.143492i	$-0.0458332\pi$
$523$	4432.09	+	7676.61i	0.370558	+	0.641825i	−0.619094	+	0.785317i	$0.712500\pi$
$524$	9830.52			0.819558
$525$	753.172	+	1167.09i	0.0626116	+	0.0970212i
$526$	26229.0			2.17422
$527$	−1832.01	−	3173.14i	−0.151430	−	0.262285i
$528$	−3455.69	+	5985.42i	−0.284828	+	0.493337i
$529$	5477.20	−	9486.79i	0.450169	−	0.779715i
$530$	7001.02	+	12126.1i	0.573783	+	0.993821i
$531$	−5919.39			−0.483766
$532$	5004.14	−	247.873i	0.407814	−	0.0202005i
$533$	25062.0			2.03669
$534$	229.845	+	398.102i	0.0186261	+	0.0322614i
$535$	4166.13	−	7215.96i	0.336669	−	0.583127i
$536$	−9693.23	+	16789.2i	−0.781127	+	1.35295i
$537$	−3668.63	−	6354.25i	−0.294810	−	0.510626i
$538$	27977.3			2.24198
$539$	−7525.37	+	16644.8i	−0.601374	+	1.33013i
$540$	2038.80			0.162474
$541$	5792.83	+	10033.5i	0.460357	+	0.797362i	0.998979	−	0.0451859i	$-0.0143880\pi$
$541$	5792.83	+	10033.5i	0.460357	+	0.797362i	−0.538621	+	0.842548i	$0.681055\pi$
$542$	7932.47	−	13739.4i	0.628651	−	1.08885i
$543$	−1767.68	+	3061.71i	−0.139702	+	0.241972i
$544$	−1014.05	−	1756.38i	−0.0799209	−	0.138427i
$545$	−5591.98			−0.439513
$546$	16258.1	−	805.325i	1.27433	−	0.0631222i
$547$	4233.45			0.330913			0.165456	−	0.986217i	$-0.447090\pi$
$547$	4233.45			0.330913			0.165456	+	0.986217i	$0.447090\pi$
$548$	4664.93	+	8079.89i	0.363642	+	0.629847i
$549$	1877.25	−	3251.49i	0.145936	−	0.252769i
$550$	3199.69	−	5542.02i	0.248064	−	0.429659i
$551$	1266.67	+	2193.94i	0.0979347	+	0.169628i
$552$	3566.14			0.274973
$553$	1359.98	+	2107.38i	0.104579	+	0.162053i
$554$	18607.1			1.42696
$555$	−1314.89	−	2277.46i	−0.100566	−	0.174185i
$556$	−11516.0	+	19946.3i	−0.878395	+	1.52142i
$557$	−1099.12	+	1903.73i	−0.0836106	+	0.144818i	−0.904798	−	0.425840i	$-0.859979\pi$
$557$	−1099.12	+	1903.73i	−0.0836106	+	0.144818i	0.821188	+	0.570658i	$0.193312\pi$
$558$	2546.60	+	4410.84i	0.193201	+	0.334634i
$559$	−30386.5			−2.29913
$560$	1828.82	−	3563.97i	0.138003	−	0.268938i
$561$	4971.97			0.374183
$562$	−3391.94	−	5875.01i	−0.254591	−	0.440965i
$563$	2959.33	−	5125.72i	0.221529	−	0.383700i	−0.733743	−	0.679427i	$-0.762228\pi$
$563$	2959.33	−	5125.72i	0.221529	−	0.383700i	0.955273	+	0.295727i	$0.0955618\pi$
$564$	6575.39	−	11388.9i	0.490911	−	0.850284i
$565$	−2016.83	−	3493.25i	−0.150175	−	0.260110i
$566$	22842.8			1.69639
$567$	684.879	−	1334.68i	0.0507270	−	0.0988557i
$568$	−30310.9			−2.23911
$569$	1280.48	+	2217.86i	0.0943422	+	0.163405i	0.909334	−	0.416067i	$-0.136592\pi$
$569$	1280.48	+	2217.86i	0.0943422	+	0.163405i	−0.814992	+	0.579473i	$0.803259\pi$
$570$	−645.747	+	1118.47i	−0.0474515	+	0.0821884i
$571$	12341.9	−	21376.8i	0.904540	−	1.56671i	0.0830067	−	0.996549i	$-0.473548\pi$
$571$	12341.9	−	21376.8i	0.904540	−	1.56671i	0.821533	−	0.570160i	$-0.193119\pi$
$572$	−24512.6	−	42457.0i	−1.79182	−	3.10352i
$573$	−6825.86			−0.497652
$574$	−19845.7	−	30752.4i	−1.44311	−	2.23620i
$575$	−870.559			−0.0631388
$576$	2966.89	+	5138.81i	0.214619	+	0.371731i
$577$	−5072.29	+	8785.47i	−0.365966	+	0.633871i	−0.988931	−	0.148378i	$-0.952595\pi$
$577$	−5072.29	+	8785.47i	−0.365966	+	0.633871i	0.622965	+	0.782250i	$0.285928\pi$
$578$	−9479.71	+	16419.3i	−0.682187	+	1.18158i
$579$	−6616.56	−	11460.2i	−0.474913	−	0.822574i
$580$	10679.0			0.764518
$581$	8592.55	−	425.620i	0.613561	−	0.0303919i
$582$	3673.79			0.261655
$583$	−15514.4	−	26871.8i	−1.10213	−	1.90894i
$584$	−18647.2	+	32297.8i	−1.32128	+	2.28852i
$585$	−1371.48	+	2375.48i	−0.0969296	+	0.167887i
$586$	−3127.39	−	5416.80i	−0.220463	−	0.381853i
$587$	12204.6			0.858158			0.429079	−	0.903267i	$-0.358838\pi$
$587$	12204.6			0.858158			0.429079	+	0.903267i	$0.358838\pi$
$588$	−9062.04	−	12624.4i	−0.635565	−	0.885411i
$589$	−2109.10			−0.147545
$590$	−7903.16	−	13688.7i	−0.551471	−	0.955176i
$591$	3017.12	−	5225.80i	0.209996	−	0.363723i
$592$	−3792.03	+	6567.98i	−0.263262	+	0.455984i
$593$	−5185.98	−	8982.38i	−0.359128	−	0.622027i	0.628688	−	0.777658i	$-0.283592\pi$
$593$	−5185.98	−	8982.38i	−0.359128	−	0.622027i	−0.987815	+	0.155631i	$0.950259\pi$
$594$	−6911.32			−0.477399
$595$	−2878.20	+	142.568i	−0.198311	+	0.00982306i
$596$	−20959.1			−1.44047
$597$	−1666.85	−	2887.07i	−0.114271	−	0.197923i
$598$	−5101.08	+	8835.34i	−0.348827	+	0.604187i
$599$	10454.1	−	18107.0i	0.713091	−	1.23511i	−0.250600	−	0.968091i	$-0.580628\pi$
$599$	10454.1	−	18107.0i	0.713091	−	1.23511i	0.963691	−	0.267019i	$-0.0860387\pi$
$600$	1280.12	+	2217.23i	0.0871010	+	0.150863i
$601$	−758.785			−0.0515000			−0.0257500	−	0.999668i	$-0.508197\pi$
$601$	−758.785			−0.0515000			−0.0257500	+	0.999668i	$0.508197\pi$
$602$	24062.0	+	37285.9i	1.62906	+	2.52435i
$603$	−5111.20			−0.345181
$604$	−17249.3	−	29876.6i	−1.16203	−	2.01269i
$605$	−3763.08	+	6517.84i	−0.252877	+	0.437997i
$606$	9801.81	−	16977.2i	0.657048	−	1.13804i
$607$	−9390.42	−	16264.7i	−0.627917	−	1.08758i	−0.987969	−	0.154652i	$-0.950575\pi$
$607$	−9390.42	−	16264.7i	−0.627917	−	1.08758i	0.360052	−	0.932932i	$-0.382759\pi$
$608$	−1167.42			−0.0778702
$609$	3587.32	−	6990.89i	0.238695	−	0.465164i
$610$	10025.5			0.665444
$611$	8846.44	+	15322.5i	0.585743	+	1.01454i
$612$	−2114.90	+	3663.11i	−0.139689	+	0.241948i
$613$	−13673.0	+	23682.3i	−0.900893	+	1.56039i	−0.0745568	+	0.997217i	$0.523754\pi$
$613$	−13673.0	+	23682.3i	−0.900893	+	1.56039i	−0.826337	+	0.563176i	$0.809579\pi$
$614$	14751.3	+	25550.1i	0.969570	+	1.67934i
$615$	6167.36			0.404377
$616$	−15371.6	+	29955.8i	−1.00542	+	1.95934i
$617$	−16384.9			−1.06910			−0.534548	−	0.845138i	$-0.679518\pi$
$617$	−16384.9			−1.06910			−0.534548	+	0.845138i	$0.679518\pi$
$618$	10440.1	+	18082.8i	0.679550	+	1.17701i
$619$	4768.23	−	8258.81i	0.309614	−	0.536268i	−0.668664	−	0.743565i	$-0.733133\pi$
$619$	4768.23	−	8258.81i	0.309614	−	0.536268i	0.978278	+	0.207297i	$0.0664667\pi$
$620$	−4445.31	+	7699.50i	−0.287948	+	0.498741i
$621$	470.102	+	814.240i	0.0303777	+	0.0526157i
$622$	−19620.2			−1.26479
$623$	320.147	+	496.090i	0.0205881	+	0.0319028i
$624$	7910.45			0.507486
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	17166.8	−	29733.7i	1.09604	−	1.89840i
$627$	1430.99	−	2478.55i	0.0911455	−	0.157869i
$628$	−2026.02	−	3509.17i	−0.128737	−	0.222980i
$629$	5455.89			0.345852
$630$	4000.87	−	198.178i	0.253013	−	0.0125327i
$631$	−20656.2			−1.30318			−0.651592	−	0.758570i	$-0.725899\pi$
$631$	−20656.2			−1.30318			−0.651592	+	0.758570i	$0.725899\pi$
$632$	2311.47	+	4003.58i	0.145483	+	0.251984i
$633$	−4546.56	+	7874.87i	−0.285481	+	0.494468i
$634$	−17980.1	+	31142.4i	−1.12631	+	1.95083i
$635$	3584.80	+	6209.06i	0.224029	+	0.388030i
$636$	26397.1			1.64577
$637$	20805.1	−	2066.18i	1.29408	−	0.128517i
$638$	−36200.7			−2.24639
$639$	−3995.70	−	6920.75i	−0.247367	−	0.428452i
$640$	−6618.97	+	11464.4i	−0.408809	+	0.708078i
$641$	8952.27	−	15505.8i	0.551628	−	0.955447i	−0.446530	−	0.894769i	$-0.647340\pi$
$641$	8952.27	−	15505.8i	0.551628	−	0.955447i	0.998157	−	0.0606782i	$-0.0193263\pi$
$642$	−12014.6	−	20810.0i	−0.738599	−	1.27929i
$643$	−4497.56			−0.275842			−0.137921	−	0.990443i	$-0.544042\pi$
$643$	−4497.56			−0.275842			−0.137921	+	0.990443i	$0.544042\pi$
$644$	9727.76	−	481.852i	0.595229	−	0.0294839i
$645$	−7477.64			−0.456483
$646$	−1339.70	−	2320.43i	−0.0815942	−	0.141325i
$647$	−130.657	+	226.305i	−0.00793922	+	0.0137511i	−0.869968	−	0.493109i	$-0.835860\pi$
$647$	−130.657	+	226.305i	−0.00793922	+	0.0137511i	0.862029	+	0.506860i	$0.169194\pi$
$648$	1382.53	−	2394.61i	0.0838130	−	0.145168i
$649$	17513.6	+	30334.4i	1.05927	+	1.83472i
$650$	−7324.44			−0.441982
$651$	3547.12	+	5496.52i	0.213552	+	0.330915i
$652$	−41192.5			−2.47427
$653$	−1895.57	−	3283.22i	−0.113598	−	0.196757i	0.803621	−	0.595142i	$-0.202904\pi$
$653$	−1895.57	−	3283.22i	−0.113598	−	0.196757i	−0.917218	+	0.398385i	$0.869571\pi$
$654$	−8063.32	+	13966.1i	−0.482111	+	0.835041i
$655$	−1627.33	+	2818.62i	−0.0970766	+	0.168142i
$656$	−8893.04	−	15403.2i	−0.529291	−	0.916758i
$657$	−9832.55			−0.583873
$658$	11796.3	−	22988.4i	0.698887	−	1.36198i
$659$	1149.18			0.0679298			0.0339649	−	0.999423i	$-0.489187\pi$
$659$	1149.18			0.0679298			0.0339649	+	0.999423i	$0.489187\pi$
$660$	−6032.15	−	10448.0i	−0.355759	−	0.616193i
$661$	−971.548	+	1682.77i	−0.0571692	+	0.0990200i	−0.893194	−	0.449672i	$-0.851541\pi$
$661$	−971.548	+	1682.77i	−0.0571692	+	0.0990200i	0.836024	+	0.548692i	$0.184874\pi$
$662$	−4672.17	+	8092.44i	−0.274304	+	0.475108i
$663$	−2845.35	−	4928.29i	−0.166673	−	0.288686i
$664$	15857.2			0.926773
$665$	−757.309	+	1475.83i	−0.0441612	+	0.0860604i
$666$	−7584.00			−0.441252
$667$	2462.34	+	4264.89i	0.142942	+	0.247582i
$668$	−16872.2	+	29223.5i	−0.977253	+	1.69265i
$669$	5684.90	−	9846.53i	0.328536	−	0.569042i
$670$	−6824.12	−	11819.7i	−0.393491	−	0.681546i
$671$	−22216.7			−1.27819
$672$	1963.39	+	3042.41i	0.112707	+	0.174648i
$673$	31546.2			1.80686			0.903431	−	0.428734i	$-0.141040\pi$
$673$	31546.2			1.80686			0.903431	+	0.428734i	$0.141040\pi$
$674$	−4615.07	−	7993.53i	−0.263748	−	0.456824i
$675$	−337.500	+	584.567i	−0.0192450	+	0.0333333i
$676$	−11466.2	+	19860.1i	−0.652380	+	1.12996i
$677$	1704.78	+	2952.76i	0.0967798	+	0.167627i	0.910350	−	0.413839i	$-0.135812\pi$
$677$	1704.78	+	2952.76i	0.0967798	+	0.167627i	−0.813570	+	0.581467i	$0.802479\pi$
$678$	−11632.6			−0.658920
$679$	4712.82	−	233.444i	0.266365	−	0.0131940i
$680$	−5311.60			−0.299545
$681$	−5814.47	−	10071.0i	−0.327182	−	0.566696i
$682$	15069.2	−	26100.6i	0.846083	−	1.46546i
$683$	−1316.43	+	2280.12i	−0.0737508	+	0.127740i	−0.900542	−	0.434768i	$-0.856830\pi$
$683$	−1316.43	+	2280.12i	−0.0737508	+	0.127740i	0.826792	+	0.562508i	$0.190164\pi$
$684$	1217.38	+	2108.57i	0.0680523	+	0.117870i
$685$	−3088.91			−0.172294
$686$	−19010.2	−	23892.9i	−1.05804	−	1.32979i
$687$	17779.3			0.987370
$688$	10782.4	+	18675.7i	0.597493	+	1.03489i
$689$	−17757.1	+	30756.2i	−0.981847	+	1.70061i
$690$	−1255.29	+	2174.23i	−0.0692584	+	0.119959i
$691$	−12625.5	−	21868.1i	−0.695076	−	1.20391i	−0.970155	−	0.242486i	$-0.922037\pi$
$691$	−12625.5	−	21868.1i	−0.695076	−	1.20391i	0.275079	−	0.961422i	$-0.411296\pi$
$692$	35334.1			1.94104
$693$	−8866.01	+	439.166i	−0.485991	+	0.0240729i
$694$	−10062.1			−0.550363
$695$	−3812.69	−	6603.78i	−0.208092	−	0.360425i
$696$	7241.52	−	12542.7i	0.394381	−	0.683088i
$697$	−6397.56	+	11080.9i	−0.347669	+	0.602180i
$698$	5284.71	+	9153.38i	0.286575	+	0.496362i
$699$	13929.1			0.753715
$700$	3791.51	+	5875.22i	0.204722	+	0.317232i
$701$	−18046.3			−0.972325			−0.486162	−	0.873869i	$-0.661604\pi$
$701$	−18046.3			−0.972325			−0.486162	+	0.873869i	$0.661604\pi$
$702$	3955.20	+	6850.60i	0.212649	+	0.368318i
$703$	1570.27	−	2719.78i	0.0842443	−	0.145915i
$704$	17556.2	−	30408.2i	0.939877	−	1.62792i
$705$	2176.97	+	3770.62i	0.116297	+	0.201432i
$706$	28171.5			1.50177
$707$	11495.2	−	22401.6i	0.611488	−	1.19166i
$708$	−29798.6			−1.58178
$709$	10868.3	+	18824.4i	0.575693	+	0.997130i	0.995966	+	0.0897324i	$0.0286012\pi$
$709$	10868.3	+	18824.4i	0.575693	+	0.997130i	−0.420272	+	0.907398i	$0.638065\pi$
$710$	10669.6	−	18480.2i	0.563974	−	0.976832i
$711$	−609.413	+	1055.53i	−0.0321446	+	0.0556760i
$712$	544.133	+	942.466i	0.0286408	+	0.0496073i
$713$	−4099.96			−0.215350
$714$	−3794.14	+	7393.94i	−0.198868	+	0.387551i
$715$	16231.1			0.848965
$716$	−18468.1	−	31987.7i	−0.963946	−	1.66960i
$717$	−1416.04	+	2452.65i	−0.0737557	+	0.127749i
$718$	17475.0	−	30267.6i	0.908303	−	1.57323i
$719$	−5460.57	−	9457.98i	−0.283233	−	0.490575i	0.688946	−	0.724813i	$-0.258074\pi$
$719$	−5460.57	−	9457.98i	−0.283233	−	0.490575i	−0.972179	+	0.234238i	$0.924740\pi$
$720$	1946.64			0.100759
$721$	14541.8	+	22533.6i	0.751132	+	1.16393i
$722$	31425.3			1.61984
$723$	−2272.51	−	3936.11i	−0.116896	−	0.202470i
$724$	−8898.62	+	15412.9i	−0.456788	+	0.791180i
$725$	−1767.79	+	3061.90i	−0.0905571	+	0.156850i
$726$	10852.3	+	18796.7i	0.554774	+	0.960897i
$727$	−15670.3			−0.799420			−0.399710	−	0.916642i	$-0.630889\pi$
$727$	−15670.3			−0.799420			−0.399710	+	0.916642i	$0.630889\pi$
$728$	38489.4	−	1906.52i	1.95950	−	0.0970611i
$729$	729.000			0.0370370
$730$	−13127.8	−	22737.9i	−0.665589	−	1.15283i
$731$	7756.75	−	13435.1i	0.392468	−	0.679774i
$732$	9450.19	−	16368.2i	0.477171	−	0.826485i
$733$	4016.08	+	6956.05i	0.202370	+	0.350515i	0.949292	−	0.314397i	$-0.101802\pi$
$733$	4016.08	+	6956.05i	0.202370	+	0.350515i	−0.746922	+	0.664912i	$0.768469\pi$
$734$	60744.0			3.05463
$735$	5119.81	−	508.454i	0.256935	−	0.0255165i
$736$	−2269.39			−0.113656
$737$	15122.4	+	26192.8i	0.755822	+	1.30912i
$738$	8892.97	−	15403.1i	0.443570	−	0.768286i
$739$	−4801.25	+	8316.01i	−0.238994	+	0.413950i	−0.960426	−	0.278535i	$-0.910151\pi$
$739$	−4801.25	+	8316.01i	−0.238994	+	0.413950i	0.721432	+	0.692486i	$0.243484\pi$
$740$	−6619.25	−	11464.9i	−0.328822	−	0.569537i
$741$	−3275.70			−0.162396
$742$	51800.8	−	2565.88i	2.56289	−	0.126949i
$743$	−17641.7			−0.871078			−0.435539	−	0.900170i	$-0.643442\pi$
$743$	−17641.7			−0.871078			−0.435539	+	0.900170i	$0.643442\pi$
$744$	6028.81	+	10442.2i	0.297079	+	0.514557i
$745$	3469.55	−	6009.43i	0.170623	−	0.295528i
$746$	−14930.8	+	25861.0i	−0.732784	+	1.26922i
$747$	2090.35	+	3620.60i	0.102386	+	0.177337i
$748$	25029.2			1.22347
$749$	−16735.0	−	25932.1i	−0.816400	−	1.26507i
$750$	−1802.43			−0.0877538
$751$	−2844.47	−	4926.76i	−0.138211	−	0.239388i	0.788609	−	0.614895i	$-0.210802\pi$
$751$	−2844.47	−	4926.76i	−0.138211	−	0.239388i	−0.926819	+	0.375508i	$0.877468\pi$
$752$	6278.17	−	10874.1i	0.304443	−	0.527311i
$753$	−4829.73	+	8365.35i	−0.233739	+	0.404847i
$754$	20716.9	+	35882.7i	1.00062	+	1.73312i
$755$	11421.7			0.550568
$756$	3447.72	−	6718.85i	0.165863	−	0.323230i
$757$	−18939.2			−0.909324			−0.454662	−	0.890664i	$-0.650240\pi$
$757$	−18939.2			−0.909324			−0.454662	+	0.890664i	$0.650240\pi$
$758$	12197.7	+	21127.1i	0.584486	+	1.01236i
$759$	2781.76	−	4818.15i	0.133032	−	0.230419i
$760$	−1528.74	+	2647.85i	−0.0729647	+	0.126379i
$761$	8050.78	+	13944.4i	0.383496	+	0.664235i	0.991559	−	0.129654i	$-0.0413866\pi$
$761$	8050.78	+	13944.4i	0.383496	+	0.664235i	−0.608063	+	0.793889i	$0.708053\pi$
$762$	20676.3			0.982971
$763$	−9456.37	+	18428.4i	−0.448681	+	0.874381i
$764$	−34361.8			−1.62718
$765$	−700.195	−	1212.77i	−0.0330923	−	0.0573176i
$766$	−20220.1	+	35022.3i	−0.953764	+	1.65197i
$767$	20045.3	−	34719.5i	0.943668	−	1.63448i
$768$	11176.6	+	19358.5i	0.525133	+	0.909557i
$769$	10781.2			0.505568			0.252784	−	0.967523i	$-0.418654\pi$
$769$	10781.2			0.505568			0.252784	+	0.967523i	$0.418654\pi$
$770$	−12852.9	−	19916.4i	−0.601539	−	0.932128i
$771$	6643.64			0.310331
$772$	−33308.2	−	57691.4i	−1.55283	−	2.68959i
$773$	5112.38	−	8854.89i	0.237878	−	0.412016i	−0.722227	−	0.691656i	$-0.756882\pi$
$773$	5112.38	−	8854.89i	0.237878	−	0.412016i	0.960105	+	0.279640i	$0.0902150\pi$
$774$	−10782.3	+	18675.5i	−0.500727	+	0.867284i
$775$	−1471.74	−	2549.13i	−0.0682149	−	0.118152i
$776$	8697.31			0.402339
$777$	−9728.93	+	481.910i	−0.449194	+	0.0222502i
$778$	−17825.7			−0.821444
$779$	3682.58	+	6378.42i	0.169374	+	0.293364i
$780$	−6904.13	+	11958.3i	−0.316933	+	0.548944i
$781$	−23644.0	+	40952.6i	−1.08329	+	1.87631i
$782$	−2604.30	−	4510.78i	−0.119092	−	0.206273i
$783$	3818.42			0.174277
$784$	−8652.41	−	12053.7i	−0.394151	−	0.549096i
$785$	1341.54			0.0609958
$786$	4693.04	+	8128.59i	0.212971	+	0.368877i
$787$	6411.68	−	11105.4i	0.290409	−	0.503003i	−0.683498	−	0.729953i	$-0.739542\pi$
$787$	6411.68	−	11105.4i	0.290409	−	0.503003i	0.973906	+	0.226950i	$0.0728754\pi$
$788$	15188.3	−	26307.0i	0.686628	−	1.18927i
$789$	8185.54	+	14177.8i	0.369344	+	0.639723i
$790$	−3254.59			−0.146573
$791$	−14922.6	+	739.171i	−0.670779	+	0.0332262i
$792$	−16361.8			−0.734081
$793$	12714.2	+	22021.6i	0.569348	+	0.986140i
$794$	−10862.7	+	18814.8i	−0.485522	+	0.840948i
$795$	−4369.74	+	7568.62i	−0.194942	+	0.337649i
$796$	−8391.04	−	14533.7i	−0.373634	−	0.647153i
$797$	−28745.8			−1.27758			−0.638789	−	0.769382i	$-0.720564\pi$
$797$	−28745.8			−1.27758			−0.638789	+	0.769382i	$0.720564\pi$
$798$	2593.91	+	4019.45i	0.115067	+	0.178305i
$799$	−9032.91			−0.399951
$800$	−814.633	−	1410.99i	−0.0360020	−	0.0623573i
$801$	−143.459	+	248.479i	−0.00632820	+	0.0109608i
$802$	−30261.0	+	52413.5i	−1.33236	+	2.30771i
$803$	29091.4	+	50387.8i	1.27847	+	2.21438i
$804$	−25730.1			−1.12864
$805$	−1472.17	+	2868.93i	−0.0644559	+	0.125610i
$806$	−34495.0			−1.50749
$807$	8731.14	+	15122.8i	0.380856	+	0.659661i
$808$	23204.8	−	40191.8i	1.01032	−	1.74993i
$809$	15879.4	−	27503.9i	0.690099	−	1.19529i	−0.281706	−	0.959501i	$-0.590900\pi$
$809$	15879.4	−	27503.9i	0.690099	−	1.19529i	0.971805	−	0.235786i	$-0.0757664\pi$
$810$	973.311	+	1685.82i	0.0422206	+	0.0731282i
$811$	−3269.28			−0.141554			−0.0707769	−	0.997492i	$-0.522548\pi$
$811$	−3269.28			−0.141554			−0.0707769	+	0.997492i	$0.522548\pi$
$812$	18058.8	−	35192.6i	0.780466	−	1.52096i
$813$	9902.23			0.427167
$814$	22438.6	+	38864.9i	0.966184	+	1.67348i
$815$	6818.96	−	11810.8i	0.293077	−	0.507624i
$816$	−2019.30	+	3497.53i	−0.0866293	+	0.150046i
$817$	−4464.96	−	7733.54i	−0.191199	−	0.331166i
$818$	−43343.0			−1.85263
$819$	5509.13	+	8536.79i	0.235048	+	0.364224i
$820$	31046.9			1.32220
$821$	−8979.67	−	15553.2i	−0.381720	−	0.661159i	0.609588	−	0.792719i	$-0.291335\pi$
$821$	−8979.67	−	15553.2i	−0.381720	−	0.661159i	−0.991308	+	0.131559i	$0.958002\pi$
$822$	−4454.03	+	7714.60i	−0.188993	+	0.327345i
$823$	11408.1	−	19759.5i	0.483187	−	0.836904i	−0.516627	−	0.856211i	$-0.672813\pi$
$823$	11408.1	−	19759.5i	0.483187	−	0.836904i	0.999814	+	0.0193069i	$0.00614597\pi$
$824$	24715.8	+	42809.0i	1.04492	+	1.80986i
$825$	3994.22			0.168559
$826$	−58475.8	+	2896.52i	−2.46323	+	0.122013i
$827$	38776.6			1.63047			0.815233	−	0.579133i	$-0.196609\pi$
$827$	38776.6			1.63047			0.815233	+	0.579133i	$0.196609\pi$
$828$	2366.52	+	4098.93i	0.0993264	+	0.172038i
$829$	21619.5	−	37446.1i	0.905761	−	1.56882i	0.0858689	−	0.996306i	$-0.472633\pi$
$829$	21619.5	−	37446.1i	0.905761	−	1.56882i	0.819892	−	0.572518i	$-0.194033\pi$
$830$	−5581.79	+	9667.94i	−0.233430	+	0.404312i
$831$	5806.88	+	10057.8i	0.242405	+	0.419857i
$832$	−40188.1			−1.67460
$833$	−4397.38	+	9726.22i	−0.182905	+	0.404554i
$834$	−21990.7			−0.913042
$835$	−5586.01	−	9675.26i	−0.231511	−	0.400989i
$836$	7203.69	−	12477.2i	0.298020	−	0.516186i
$837$	−1589.48	+	2753.06i	−0.0656398	+	0.113692i
$838$	9.14841	+	15.8455i	0.000377120	+	0.000653191i
$839$	−38639.2			−1.58996			−0.794978	−	0.606638i	$-0.792518\pi$
$839$	−38639.2			−1.58996			−0.794978	+	0.606638i	$0.792518\pi$
$840$	9471.63	−	469.165i	0.389050	−	0.0192711i
$841$	−4388.57			−0.179940
$842$	29021.5	+	50266.8i	1.18782	+	2.05737i
$843$	2117.11	−	3666.93i	0.0864970	−	0.149817i
$844$	−22887.7	+	39642.6i	−0.933443	+	1.61677i
$845$	−3796.22	−	6575.24i	−0.154549	−	0.267687i
$846$	12556.2			0.510275
$847$	15116.0	+	23423.3i	0.613212	+	0.950216i
$848$	25203.9			1.02064
$849$	7128.76	+	12347.4i	0.288172	+	0.499129i
$850$	1869.71	−	3238.43i	0.0754475	−	0.130679i
$851$	3052.51	−	5287.10i	0.122960	−	0.212972i
$852$	−20114.6	−	34839.5i	−0.808820	−	1.40092i
$853$	21024.3			0.843914			0.421957	−	0.906616i	$-0.361343\pi$
$853$	21024.3			0.843914			0.421957	+	0.906616i	$0.361343\pi$
$854$	16953.7	−	33039.0i	0.679326	−	1.32386i
$855$	−806.096			−0.0322432
$856$	−28443.4	−	49265.5i	−1.13572	−	1.96712i
$857$	−20070.4	+	34763.0i	−0.799991	+	1.38563i	0.119629	+	0.992819i	$0.461829\pi$
$857$	−20070.4	+	34763.0i	−0.799991	+	1.38563i	−0.919621	+	0.392807i	$0.871504\pi$
$858$	23404.3	−	40537.5i	0.931248	−	1.61297i
$859$	−8485.00	−	14696.4i	−0.337025	−	0.583744i	0.646847	−	0.762620i	$-0.276087\pi$
$859$	−8485.00	−	14696.4i	−0.337025	−	0.583744i	−0.983872	+	0.178876i	$0.942754\pi$
$860$	−37642.9			−1.49257
$861$	10429.4	−	20324.5i	0.412813	−	0.804481i
$862$	49591.8			1.95952
$863$	−14319.4	−	24802.0i	−0.564819	−	0.978296i	−0.997066	−	0.0765405i	$-0.975613\pi$
$863$	−14319.4	−	24802.0i	−0.564819	−	0.978296i	0.432247	−	0.901755i	$-0.357721\pi$
$864$	−879.804	+	1523.86i	−0.0346430	+	0.0600034i
$865$	−5849.16	+	10131.0i	−0.229916	+	0.398226i
$866$	30589.2	+	52982.1i	1.20031	+	2.07899i
$867$	−11833.7			−0.463544
$868$	17856.4	+	27669.8i	0.698256	+	1.08200i
$869$	7212.24			0.281540
$870$	5098.09	+	8830.15i	0.198668	+	0.344104i
$871$	17308.4	−	29979.1i	0.673334	−	1.16625i
$872$	−19089.1	+	33063.2i	−0.741327	+	1.28402i
$873$	1146.51	+	1985.82i	0.0444485	+	0.0769871i
$874$	−2998.19			−0.116036
$875$	−2312.20	+	114.532i	−0.0893332	+	0.00442500i
$876$	−49497.7			−1.90910
$877$	−729.837	−	1264.12i	−0.0281013	−	0.0486729i	0.851633	−	0.524139i	$-0.175613\pi$
$877$	−729.837	−	1264.12i	−0.0281013	−	0.0486729i	−0.879734	+	0.475466i	$0.842279\pi$
$878$	−23966.5	+	41511.2i	−0.921218	+	1.59560i
$879$	1951.99	−	3380.94i	0.0749020	−	0.129734i
$880$	−5759.48	−	9975.71i	−0.220627	−	0.382137i
$881$	−34268.7			−1.31049			−0.655246	−	0.755416i	$-0.727435\pi$
$881$	−34268.7			−1.31049			−0.655246	+	0.755416i	$0.727435\pi$
$882$	6112.60	−	13520.0i	0.233358	−	0.516147i
$883$	−23106.9			−0.880645			−0.440322	−	0.897840i	$-0.645136\pi$
$883$	−23106.9			−0.880645			−0.440322	+	0.897840i	$0.645136\pi$
$884$	−14323.7	−	24809.3i	−0.544974	−	0.943923i
$885$	4932.82	−	8543.90i	0.187362	−	0.324520i
$886$	25144.5	−	43551.6i	0.953439	−	1.65141i
$887$	−11429.1	−	19795.8i	−0.432640	−	0.749354i	0.564460	−	0.825461i	$-0.309085\pi$
$887$	−11429.1	−	19795.8i	−0.432640	−	0.749354i	−0.997100	+	0.0761062i	$0.975751\pi$
$888$	−17954.3			−0.678500
$889$	26524.1	−	1313.84i	1.00066	−	0.0495665i
$890$	−766.148			−0.0288555
$891$	−2156.88	−	3735.82i	−0.0810978	−	0.140466i
$892$	28618.1	−	49568.1i	1.07422	−	1.86061i
$893$	−2599.77	+	4502.94i	−0.0974222	+	0.168740i
$894$	−10005.8	−	17330.5i	−0.374321	−	0.648343i
$895$	12228.8			0.456718
$896$	26587.8	+	41199.8i	0.991337	+	1.53615i
$897$	−6367.77			−0.237027
$898$	−28033.0	−	48554.6i	−1.04173	−	1.80433i
$899$	−8325.53	+	14420.2i	−0.308867	+	0.534974i
$900$	−1699.00	+	2942.75i	−0.0629258	+	0.108991i
$901$	−9065.70	−	15702.3i	−0.335208	−	0.580597i
$902$	−105246.			−3.88504
$903$	−12645.1	+	24642.6i	−0.466006	+	0.908143i
$904$	−27539.0			−1.01320
$905$	−2946.13	−	5102.85i	−0.108213	−	0.187431i
$906$	16469.5	−	28525.9i	0.603930	−	1.04604i
$907$	2210.38	−	3828.49i	0.0809199	−	0.140157i	−0.822725	−	0.568439i	$-0.807548\pi$
$907$	2210.38	−	3828.49i	0.0809199	−	0.140157i	0.903645	+	0.428282i	$0.140881\pi$
$908$	−29270.4	−	50697.8i	−1.06979	−	1.85294i
$909$	12235.8			0.446463
$910$	−12386.1	+	24137.7i	−0.451202	+	0.879293i
$911$	31813.3			1.15699			0.578496	−	0.815685i	$-0.303640\pi$
$911$	31813.3			1.15699			0.578496	+	0.815685i	$0.303640\pi$
$912$	1162.35	+	2013.25i	0.0422032	+	0.0730981i
$913$	12369.4	−	21424.4i	0.448375	−	0.776609i
$914$	10916.8	−	18908.4i	0.395071	−	0.684283i
$915$	3128.75	+	5419.15i	0.113042	+	0.195794i
$916$	89502.2			3.22842
$917$	6536.86	+	10129.3i	0.235405	+	0.364777i
$918$	−4038.57			−0.145199
$919$	−11018.3	−	19084.2i	−0.395494	−	0.685015i	0.597670	−	0.801742i	$-0.296093\pi$
$919$	−11018.3	−	19084.2i	−0.395494	−	0.685015i	−0.993164	+	0.116727i	$0.962760\pi$
$920$	−2971.78	+	5147.27i	−0.106496	+	0.184457i
$921$	−9207.17	+	15947.3i	−0.329410	+	0.570555i
$922$	18955.6	+	32832.1i	0.677083	+	1.17274i
$923$	54123.8			1.93012
$924$	−44632.0	+	2210.79i	−1.58905	+	0.0787117i
$925$	4382.98			0.155796
$926$	−13083.6	−	22661.4i	−0.464312	−	0.804212i
$927$	−6516.27	+	11286.5i	−0.230876	+	0.399889i
$928$	−4608.31	+	7981.83i	−0.163012	+	0.282345i
$929$	13507.7	+	23396.0i	0.477043	+	0.826263i	0.999654	−	0.0263087i	$-0.00837529\pi$
$929$	13507.7	+	23396.0i	0.477043	+	0.826263i	−0.522611	+	0.852571i	$0.675042\pi$
$930$	−8488.67			−0.299306
$931$	3582.94	+	4991.42i	0.126129	+	0.175711i
$932$	70120.0			2.46444
$933$	−6123.06	−	10605.5i	−0.214855	−	0.372140i
$934$	−25421.5	+	44031.3i	−0.890596	+	1.54256i
$935$	−4143.31	+	7176.43i	−0.144921	+	0.251010i
$936$	9363.52	+	16218.1i	0.326983	+	0.566351i
$937$	33711.1			1.17534			0.587670	−	0.809101i	$-0.300046\pi$
$937$	33711.1			1.17534			0.587670	+	0.809101i	$0.300046\pi$
$938$	−50491.9	+	2501.05i	−1.75759	+	0.0870598i
$939$	21429.6			0.744758
$940$	10959.0	+	18981.5i	0.380258	+	0.658627i
$941$	−11584.4	+	20064.8i	−0.401319	+	0.695105i	−0.993885	−	0.110417i	$-0.964782\pi$
$941$	−11584.4	+	20064.8i	−0.401319	+	0.695105i	0.592566	+	0.805522i	$0.298115\pi$
$942$	1934.43	−	3350.52i	0.0669076	−	0.115887i
$943$	7158.73	+	12399.3i	0.247211	+	0.428182i
$944$	−28451.6			−0.980954
$945$	1355.71	+	2100.77i	0.0466680	+	0.0723153i
$946$	127606.			4.38565
$947$	−19966.1	−	34582.3i	−0.685122	−	1.18667i	−0.973398	−	0.229120i	$-0.926415\pi$
$947$	−19966.1	−	34582.3i	−0.685122	−	1.18667i	0.288276	−	0.957547i	$-0.406918\pi$
$948$	−3067.82	+	5313.63i	−0.105104	+	0.182045i
$949$	33296.7	−	57671.6i	1.13894	−	1.97271i
$950$	−1076.24	−	1864.11i	−0.0367558	−	0.0636629i
$951$	−22444.9			−0.765325
$952$	−8982.23	+	17504.4i	−0.305794	+	0.595925i
$953$	−31125.8			−1.05799			−0.528995	−	0.848625i	$-0.677431\pi$
$953$	−31125.8			−1.05799			−0.528995	+	0.848625i	$0.677431\pi$
$954$	12601.8	+	21827.0i	0.427672	+	0.740750i
$955$	5688.22	−	9852.28i	0.192740	−	0.333835i
$956$	−7128.42	+	12346.8i	−0.241161	+	0.417702i
$957$	−11297.5	−	19567.8i	−0.381605	−	0.660959i
$958$	−55970.0			−1.88759
$959$	−5223.53	+	10179.5i	−0.175888	+	0.342767i
$960$	−9889.64			−0.332486
$961$	7964.21	+	13794.4i	0.267336	+	0.463040i
$962$	25682.3	−	44483.0i	0.860738	−	1.49084i
$963$	7499.04	−	12988.7i	0.250938	−	0.434637i
$964$	−11440.0	−	19814.6i	−0.382217	−	0.662019i
$965$	22055.2			0.735732
$966$	5042.41	+	7813.58i	0.167947	+	0.260246i
$967$	−35679.1			−1.18652			−0.593259	−	0.805011i	$-0.702159\pi$
$967$	−35679.1			−1.18652			−0.593259	+	0.805011i	$0.702159\pi$
$968$	25691.6	+	44499.2i	0.853058	+	1.47754i
$969$	836.185	−	1448.32i	0.0277215	−	0.0480151i
$970$	−3061.49	+	5302.66i	−0.101339	+	0.175524i
$971$	2068.82	+	3583.30i	0.0683744	+	0.118428i	0.898186	−	0.439616i	$-0.144885\pi$
$971$	2068.82	+	3583.30i	0.0683744	+	0.118428i	−0.829811	+	0.558044i	$0.811552\pi$
$972$	3669.83			0.121101
$973$	−28210.2	+	1397.36i	−0.929475	+	0.0460403i
$974$	44398.5			1.46059
$975$	−2285.80	−	3959.13i	−0.0750814	−	0.130045i
$976$	9023.02	−	15628.3i	0.295922	−	0.512552i
$977$	−15202.8	+	26332.1i	−0.497832	+	0.862270i	−0.999997	−	0.00250155i	$-0.999204\pi$
$977$	−15202.8	+	26332.1i	−0.497832	+	0.862270i	0.502165	+	0.864772i	$0.332537\pi$
$978$	−19665.1	−	34060.9i	−0.642966	−	1.11365i
$979$	1697.80			0.0554259
$980$	25773.5	−	2559.59i	0.840105	−	0.0834317i
$981$	−10065.6			−0.327593
$982$	−6499.47	−	11257.4i	−0.211208	−	0.365823i
$983$	−5005.64	+	8670.01i	−0.162416	+	0.281313i	−0.935735	−	0.352705i	$-0.885262\pi$
$983$	−5005.64	+	8670.01i	−0.162416	+	0.281313i	0.773319	+	0.634018i	$0.218595\pi$
$984$	21053.2	−	36465.2i	0.682064	−	1.18137i
$985$	5028.53	+	8709.66i	0.162662	+	0.281739i
$986$	−21153.5			−0.683231
$987$	16107.5	−	797.862i	0.519459	−	0.0257307i
$988$	−16490.1			−0.530991
$989$	−8679.63	−	15033.6i	−0.279066	−	0.483356i
$990$	5759.43	−	9975.63i	0.184896	−	0.320249i
$991$	1444.75	−	2502.39i	0.0463110	−	0.0802129i	−0.841941	−	0.539570i	$-0.818587\pi$
$991$	1444.75	−	2502.39i	0.0463110	−	0.0802129i	0.888252	+	0.459357i	$0.151920\pi$
$992$	−3836.58	−	6645.15i	−0.122794	−	0.212685i
$993$	−5832.35			−0.186389
$994$	−42858.7	−	66412.7i	−1.36760	−	2.11920i
$995$	5556.18			0.177028
$996$	10523.0	+	18226.3i	0.334772	+	0.579842i
$997$	3002.81	−	5201.03i	0.0953862	−	0.165214i	−0.814383	−	0.580327i	$-0.802925\pi$
$997$	3002.81	−	5201.03i	0.0953862	−	0.165214i	0.909770	+	0.415113i	$0.136258\pi$
$998$	−1834.51	+	3177.47i	−0.0581869	+	0.100783i
$999$	−2366.81	−	4099.43i	−0.0749574	−	0.129830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.i.d.46.5	yes	10
3.2	odd	2		315.4.j.h.46.1		10
7.2	even	3	inner	105.4.i.d.16.5	✓	10
7.3	odd	6		735.4.a.z.1.1		5
7.4	even	3		735.4.a.ba.1.1		5
21.2	odd	6		315.4.j.h.226.1		10
21.11	odd	6		2205.4.a.br.1.5		5
21.17	even	6		2205.4.a.bs.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.i.d.16.5	✓	10	7.2	even	3	inner
105.4.i.d.46.5	yes	10	1.1	even	1	trivial
315.4.j.h.46.1		10	3.2	odd	2
315.4.j.h.226.1		10	21.2	odd	6
735.4.a.z.1.1		5	7.3	odd	6
735.4.a.ba.1.1		5	7.4	even	3
2205.4.a.br.1.5		5	21.11	odd	6
2205.4.a.bs.1.5		5	21.17	even	6

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.40324 + 4.16253i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-7.55109 + 13.0789i) q^{4} +(-2.50000 - 4.33013i) q^{5} -14.4194 q^{6} +(-18.4976 + 0.916253i) q^{7} -34.1365 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(2.40324 + 4.16253i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-7.55109 + 13.0789i) q^{4} +(-2.50000 - 4.33013i) q^{5} -14.4194 q^{6} +(-18.4976 + 0.916253i) q^{7} -34.1365 q^{8} +(-4.50000 - 7.79423i) q^{9} +(12.0162 - 20.8126i) q^{10} +(-26.6281 + 46.1213i) q^{11} +(-22.6533 - 39.2366i) q^{12} +60.9548 q^{13} +(-48.2680 - 74.7947i) q^{14} +15.0000 q^{15} +(-21.6293 - 37.4630i) q^{16} +(-15.5599 + 26.9505i) q^{17} +(21.6291 - 37.4628i) q^{18} +(8.95663 + 15.5133i) q^{19} +75.5109 q^{20} +(25.3659 - 49.4325i) q^{21} -255.975 q^{22} +(17.4112 + 30.1570i) q^{23} +(51.2047 - 88.6892i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(146.489 + 253.726i) q^{26} +27.0000 q^{27} +(127.693 - 248.846i) q^{28} +141.423 q^{29} +(36.0486 + 62.4379i) q^{30} +(-58.8697 + 101.965i) q^{31} +(-32.5853 + 56.4394i) q^{32} +(-79.8844 - 138.364i) q^{33} -149.576 q^{34} +(50.2114 + 77.8062i) q^{35} +135.920 q^{36} +(-87.6595 - 151.831i) q^{37} +(-43.0498 + 74.5644i) q^{38} +(-91.4322 + 158.365i) q^{39} +(85.3412 + 147.815i) q^{40} +411.157 q^{41} +(266.724 - 13.2118i) q^{42} -498.509 q^{43} +(-402.143 - 696.532i) q^{44} +(-22.5000 + 38.9711i) q^{45} +(-83.6863 + 144.949i) q^{46} +(145.131 + 251.375i) q^{47} +129.776 q^{48} +(341.321 - 33.8969i) q^{49} -120.162 q^{50} +(-46.6797 - 80.8516i) q^{51} +(-460.275 + 797.220i) q^{52} +(-291.316 + 504.575i) q^{53} +(64.8874 + 112.388i) q^{54} +266.281 q^{55} +(631.442 - 31.2777i) q^{56} -53.7398 q^{57} +(339.873 + 588.677i) q^{58} +(328.855 - 569.594i) q^{59} +(-113.266 + 196.183i) q^{60} +(208.583 + 361.277i) q^{61} -565.911 q^{62} +(90.3806 + 140.051i) q^{63} -659.310 q^{64} +(-152.387 - 263.942i) q^{65} +(383.962 - 665.042i) q^{66} +(283.955 - 491.825i) q^{67} +(-234.989 - 407.012i) q^{68} -104.467 q^{69} +(-203.201 + 395.993i) q^{70} +887.933 q^{71} +(153.614 + 266.068i) q^{72} +(546.253 - 946.138i) q^{73} +(421.333 - 729.770i) q^{74} +(-37.5000 - 64.9519i) q^{75} -270.529 q^{76} +(450.297 - 877.530i) q^{77} -878.933 q^{78} +(-67.7126 - 117.282i) q^{79} +(-108.146 + 187.315i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(988.108 + 1711.45i) q^{82} -464.523 q^{83} +(454.982 + 705.027i) q^{84} +155.599 q^{85} +(-1198.04 - 2075.06i) q^{86} +(-212.134 + 367.427i) q^{87} +(908.991 - 1574.42i) q^{88} +(-15.9399 - 27.6088i) q^{89} -216.291 q^{90} +(-1127.52 + 55.8500i) q^{91} -525.894 q^{92} +(-176.609 - 305.896i) q^{93} +(-697.569 + 1208.23i) q^{94} +(44.7831 - 77.5667i) q^{95} +(-97.7560 - 169.318i) q^{96} -254.781 q^{97} +(961.372 + 1339.30i) q^{98} +479.306 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} - 15 q^{3} - 25 q^{4} - 25 q^{5} + 18 q^{6} - 32 q^{7} + 42 q^{8} - 45 q^{9}+O(q^{10}) \) 10 * q - 3 * q^2 - 15 * q^3 - 25 * q^4 - 25 * q^5 + 18 * q^6 - 32 * q^7 + 42 * q^8 - 45 * q^9	\( 10 q - 3 q^{2} - 15 q^{3} - 25 q^{4} - 25 q^{5} + 18 q^{6} - 32 q^{7} + 42 q^{8} - 45 q^{9} - 15 q^{10} - 43 q^{11} - 75 q^{12} + 246 q^{13} - 23 q^{14} + 150 q^{15} - 161 q^{16} - 124 q^{17} - 27 q^{18} - 37 q^{19} + 250 q^{20} + 3 q^{21} - 442 q^{22} - 77 q^{23} - 63 q^{24} - 125 q^{25} + 79 q^{26} + 270 q^{27} - 71 q^{28} + 720 q^{29} - 45 q^{30} - 314 q^{31} + 59 q^{32} - 129 q^{33} + 352 q^{34} + 155 q^{35} + 450 q^{36} - 225 q^{37} - 759 q^{38} - 369 q^{39} - 105 q^{40} + 682 q^{41} + 354 q^{42} + 64 q^{43} - 679 q^{44} - 225 q^{45} + 331 q^{46} - 25 q^{47} + 966 q^{48} + 710 q^{49} + 150 q^{50} - 372 q^{51} - 2299 q^{52} + 317 q^{53} - 81 q^{54} + 430 q^{55} + 1884 q^{56} + 222 q^{57} - 8 q^{58} - 676 q^{59} - 375 q^{60} + 188 q^{61} - 696 q^{62} + 279 q^{63} - 2206 q^{64} - 615 q^{65} + 663 q^{66} + 1776 q^{67} - 1280 q^{68} + 462 q^{69} - 475 q^{70} - 12 q^{71} - 189 q^{72} - 2006 q^{73} + 2729 q^{74} - 375 q^{75} + 2834 q^{76} + 3731 q^{77} - 474 q^{78} - 200 q^{79} - 805 q^{80} - 405 q^{81} + 539 q^{82} - 664 q^{83} + 1821 q^{84} + 1240 q^{85} - 4262 q^{86} - 1080 q^{87} + 4529 q^{88} - 894 q^{89} + 270 q^{90} + 2016 q^{91} - 7374 q^{92} - 942 q^{93} - 4233 q^{94} - 185 q^{95} + 177 q^{96} - 1152 q^{97} + 2539 q^{98} + 774 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 - 15 * q^3 - 25 * q^4 - 25 * q^5 + 18 * q^6 - 32 * q^7 + 42 * q^8 - 45 * q^9 - 15 * q^10 - 43 * q^11 - 75 * q^12 + 246 * q^13 - 23 * q^14 + 150 * q^15 - 161 * q^16 - 124 * q^17 - 27 * q^18 - 37 * q^19 + 250 * q^20 + 3 * q^21 - 442 * q^22 - 77 * q^23 - 63 * q^24 - 125 * q^25 + 79 * q^26 + 270 * q^27 - 71 * q^28 + 720 * q^29 - 45 * q^30 - 314 * q^31 + 59 * q^32 - 129 * q^33 + 352 * q^34 + 155 * q^35 + 450 * q^36 - 225 * q^37 - 759 * q^38 - 369 * q^39 - 105 * q^40 + 682 * q^41 + 354 * q^42 + 64 * q^43 - 679 * q^44 - 225 * q^45 + 331 * q^46 - 25 * q^47 + 966 * q^48 + 710 * q^49 + 150 * q^50 - 372 * q^51 - 2299 * q^52 + 317 * q^53 - 81 * q^54 + 430 * q^55 + 1884 * q^56 + 222 * q^57 - 8 * q^58 - 676 * q^59 - 375 * q^60 + 188 * q^61 - 696 * q^62 + 279 * q^63 - 2206 * q^64 - 615 * q^65 + 663 * q^66 + 1776 * q^67 - 1280 * q^68 + 462 * q^69 - 475 * q^70 - 12 * q^71 - 189 * q^72 - 2006 * q^73 + 2729 * q^74 - 375 * q^75 + 2834 * q^76 + 3731 * q^77 - 474 * q^78 - 200 * q^79 - 805 * q^80 - 405 * q^81 + 539 * q^82 - 664 * q^83 + 1821 * q^84 + 1240 * q^85 - 4262 * q^86 - 1080 * q^87 + 4529 * q^88 - 894 * q^89 + 270 * q^90 + 2016 * q^91 - 7374 * q^92 - 942 * q^93 - 4233 * q^94 - 185 * q^95 + 177 * q^96 - 1152 * q^97 + 2539 * q^98 + 774 * q^99

Introduction

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