LMFDB - Embedded newform 70.4.e.e.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [70,4,Mod(11,70)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(70, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("70.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	70.e (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:	$4.13013370040$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.362560708800.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 67x^{4} - 114x^{3} + 4446x^{2} - 5940x + 8100 $ x^6 - x^5 + 67x^4 - 114x^3 + 4446x^2 - 5940x + 8100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.1
Root			$3.95365 - 6.84792i$ of defining polynomial
Character	$\chi$	$=$	70.11
Dual form			70.4.e.e.51.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(-4.45365 + 7.71395i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.50000 - 4.33013i) q^{5} +17.8146 q^{6} +(-1.45365 - 18.4631i) q^{7} +8.00000 q^{8} +(-26.1700 - 45.3278i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(-4.45365 + 7.71395i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.50000 - 4.33013i) q^{5} +17.8146 q^{6} +(-1.45365 - 18.4631i) q^{7} +8.00000 q^{8} +(-26.1700 - 45.3278i) q^{9} +(-5.00000 + 8.66025i) q^{10} +(24.9846 - 43.2746i) q^{11} +(-17.8146 - 30.8558i) q^{12} -18.5254 q^{13} +(-30.5254 + 20.9809i) q^{14} +44.5365 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-50.4438 + 87.3712i) q^{17} +(-52.3400 + 90.6556i) q^{18} +(-50.6027 - 87.6465i) q^{19} +20.0000 q^{20} +(148.898 + 71.0149i) q^{21} -99.9384 q^{22} +(-46.1093 - 79.8637i) q^{23} +(-35.6292 + 61.7116i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(18.5254 + 32.0870i) q^{26} +225.711 q^{27} +(66.8654 + 31.8907i) q^{28} +37.8740 q^{29} +(-44.5365 - 77.1395i) q^{30} +(63.7727 - 110.458i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(222.545 + 385.460i) q^{33} +201.775 q^{34} +(-76.3135 + 52.4523i) q^{35} +209.360 q^{36} +(-141.552 - 245.175i) q^{37} +(-101.205 + 175.293i) q^{38} +(82.5057 - 142.904i) q^{39} +(-20.0000 - 34.6410i) q^{40} -250.157 q^{41} +(-25.8962 - 328.913i) q^{42} -260.330 q^{43} +(99.9384 + 173.098i) q^{44} +(-130.850 + 226.639i) q^{45} +(-92.2187 + 159.727i) q^{46} +(302.173 + 523.378i) q^{47} +142.517 q^{48} +(-338.774 + 53.6779i) q^{49} +50.0000 q^{50} +(-449.318 - 778.242i) q^{51} +(37.0508 - 64.1739i) q^{52} +(-205.755 + 356.378i) q^{53} +(-225.711 - 390.943i) q^{54} -249.846 q^{55} +(-11.6292 - 147.705i) q^{56} +901.467 q^{57} +(-37.8740 - 65.5997i) q^{58} +(190.724 - 330.344i) q^{59} +(-89.0730 + 154.279i) q^{60} +(-37.5666 - 65.0672i) q^{61} -255.091 q^{62} +(-798.850 + 549.071i) q^{63} +64.0000 q^{64} +(46.3135 + 80.2174i) q^{65} +(445.091 - 770.920i) q^{66} +(315.474 - 546.417i) q^{67} +(-201.775 - 349.485i) q^{68} +821.419 q^{69} +(167.164 + 79.7266i) q^{70} -214.755 q^{71} +(-209.360 - 362.622i) q^{72} +(524.520 - 908.495i) q^{73} +(-283.104 + 490.350i) q^{74} +(-111.341 - 192.849i) q^{75} +404.822 q^{76} +(-835.303 - 398.388i) q^{77} -330.023 q^{78} +(530.385 + 918.654i) q^{79} +(-40.0000 + 69.2820i) q^{80} +(-298.649 + 517.274i) q^{81} +(250.157 + 433.285i) q^{82} -289.875 q^{83} +(-543.798 + 373.767i) q^{84} +504.438 q^{85} +(260.330 + 450.904i) q^{86} +(-168.678 + 292.158i) q^{87} +(199.877 - 346.197i) q^{88} +(497.079 + 860.966i) q^{89} +523.400 q^{90} +(26.9295 + 342.037i) q^{91} +368.875 q^{92} +(568.043 + 983.879i) q^{93} +(604.345 - 1046.76i) q^{94} +(-253.014 + 438.232i) q^{95} +(-142.517 - 246.846i) q^{96} -281.931 q^{97} +(431.747 + 533.096i) q^{98} -2615.39 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 4 q^{3} - 12 q^{4} - 15 q^{5} + 16 q^{6} + 14 q^{7} + 48 q^{8} - 57 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 4 * q^3 - 12 * q^4 - 15 * q^5 + 16 * q^6 + 14 * q^7 + 48 * q^8 - 57 * q^9	\( 6 q - 6 q^{2} - 4 q^{3} - 12 q^{4} - 15 q^{5} + 16 q^{6} + 14 q^{7} + 48 q^{8} - 57 q^{9} - 30 q^{10} - 41 q^{11} - 16 q^{12} - 2 q^{13} - 74 q^{14} + 40 q^{15} - 48 q^{16} - 30 q^{17} - 114 q^{18} - 49 q^{19} + 120 q^{20} + 48 q^{21} + 164 q^{22} - 145 q^{23} - 32 q^{24} - 75 q^{25} + 2 q^{26} + 236 q^{27} + 92 q^{28} + 536 q^{29} - 40 q^{30} + 28 q^{31} - 96 q^{32} + 626 q^{33} + 120 q^{34} - 185 q^{35} + 456 q^{36} - 813 q^{37} - 98 q^{38} - 114 q^{39} - 120 q^{40} + 626 q^{41} - 228 q^{42} + 720 q^{43} - 164 q^{44} - 285 q^{45} - 290 q^{46} + 977 q^{47} + 128 q^{48} - 1860 q^{49} + 300 q^{50} - 1632 q^{51} + 4 q^{52} - 325 q^{53} - 236 q^{54} + 410 q^{55} + 112 q^{56} + 500 q^{57} - 536 q^{58} + 272 q^{59} - 80 q^{60} + 902 q^{61} - 112 q^{62} - 3193 q^{63} + 384 q^{64} + 5 q^{65} + 1252 q^{66} + 170 q^{67} - 120 q^{68} + 4528 q^{69} + 230 q^{70} - 2160 q^{71} - 456 q^{72} + 584 q^{73} - 1626 q^{74} - 100 q^{75} + 392 q^{76} - 2395 q^{77} + 456 q^{78} + 310 q^{79} - 240 q^{80} - 147 q^{81} - 626 q^{82} + 1252 q^{83} + 264 q^{84} + 300 q^{85} - 720 q^{86} + 1846 q^{87} - 328 q^{88} + 400 q^{89} + 1140 q^{90} - 120 q^{91} + 1160 q^{92} + 372 q^{93} + 1954 q^{94} - 245 q^{95} - 128 q^{96} + 3252 q^{97} + 1482 q^{98} - 5222 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 4 * q^3 - 12 * q^4 - 15 * q^5 + 16 * q^6 + 14 * q^7 + 48 * q^8 - 57 * q^9 - 30 * q^10 - 41 * q^11 - 16 * q^12 - 2 * q^13 - 74 * q^14 + 40 * q^15 - 48 * q^16 - 30 * q^17 - 114 * q^18 - 49 * q^19 + 120 * q^20 + 48 * q^21 + 164 * q^22 - 145 * q^23 - 32 * q^24 - 75 * q^25 + 2 * q^26 + 236 * q^27 + 92 * q^28 + 536 * q^29 - 40 * q^30 + 28 * q^31 - 96 * q^32 + 626 * q^33 + 120 * q^34 - 185 * q^35 + 456 * q^36 - 813 * q^37 - 98 * q^38 - 114 * q^39 - 120 * q^40 + 626 * q^41 - 228 * q^42 + 720 * q^43 - 164 * q^44 - 285 * q^45 - 290 * q^46 + 977 * q^47 + 128 * q^48 - 1860 * q^49 + 300 * q^50 - 1632 * q^51 + 4 * q^52 - 325 * q^53 - 236 * q^54 + 410 * q^55 + 112 * q^56 + 500 * q^57 - 536 * q^58 + 272 * q^59 - 80 * q^60 + 902 * q^61 - 112 * q^62 - 3193 * q^63 + 384 * q^64 + 5 * q^65 + 1252 * q^66 + 170 * q^67 - 120 * q^68 + 4528 * q^69 + 230 * q^70 - 2160 * q^71 - 456 * q^72 + 584 * q^73 - 1626 * q^74 - 100 * q^75 + 392 * q^76 - 2395 * q^77 + 456 * q^78 + 310 * q^79 - 240 * q^80 - 147 * q^81 - 626 * q^82 + 1252 * q^83 + 264 * q^84 + 300 * q^85 - 720 * q^86 + 1846 * q^87 - 328 * q^88 + 400 * q^89 + 1140 * q^90 - 120 * q^91 + 1160 * q^92 + 372 * q^93 + 1954 * q^94 - 245 * q^95 - 128 * q^96 + 3252 * q^97 + 1482 * q^98 - 5222 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$	−4.45365	+	7.71395i	−0.857105	+	1.48455i	0.0175724	+	0.999846i	$0.494406\pi$
$3$	−4.45365	+	7.71395i	−0.857105	+	1.48455i	−0.874678	+	0.484705i	$0.838927\pi$
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$	17.8146			1.21213
$7$	−1.45365	−	18.4631i	−0.0784898	−	0.996915i
$7$	−1.45365	−	18.4631i	−0.0784898	−	0.996915i
$8$	8.00000			0.353553
$9$	−26.1700	−	45.3278i	−0.969260	−	1.67881i
$10$	−5.00000	+	8.66025i	−0.158114	+	0.273861i
$11$	24.9846	−	43.2746i	0.684831	−	1.18616i	−0.288659	−	0.957432i	$-0.593209\pi$
$11$	24.9846	−	43.2746i	0.684831	−	1.18616i	0.973490	−	0.228730i	$-0.0734574\pi$
$12$	−17.8146	−	30.8558i	−0.428553	−	0.742275i
$13$	−18.5254			−0.395233			−0.197616	−	0.980279i	$-0.563320\pi$
$13$	−18.5254			−0.395233			−0.197616	+	0.980279i	$0.563320\pi$
$14$	−30.5254	+	20.9809i	−0.582733	+	0.400528i
$15$	44.5365			0.766618
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−50.4438	+	87.3712i	−0.719672	+	1.24651i	0.241458	+	0.970411i	$0.422374\pi$
$17$	−50.4438	+	87.3712i	−0.719672	+	1.24651i	−0.961130	+	0.276097i	$0.910959\pi$
$18$	−52.3400	+	90.6556i	−0.685370	+	1.18710i
$19$	−50.6027	−	87.6465i	−0.611003	−	1.05829i	−0.991072	−	0.133330i	$-0.957433\pi$
$19$	−50.6027	−	87.6465i	−0.611003	−	1.05829i	0.380068	−	0.924958i	$-0.375900\pi$
$20$	20.0000			0.223607
$21$	148.898	+	71.0149i	1.54724	+	0.737939i
$22$	−99.9384			−0.968498
$23$	−46.1093	−	79.8637i	−0.418020	−	0.724032i	0.577720	−	0.816235i	$-0.303942\pi$
$23$	−46.1093	−	79.8637i	−0.418020	−	0.724032i	−0.995740	+	0.0922029i	$0.970609\pi$
$24$	−35.6292	+	61.7116i	−0.303033	+	0.524868i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	18.5254	+	32.0870i	0.139736	+	0.242030i
$27$	225.711			1.60882
$28$	66.8654	+	31.8907i	0.451299	+	0.215242i
$29$	37.8740			0.242518			0.121259	−	0.992621i	$-0.461307\pi$
$29$	37.8740			0.242518			0.121259	+	0.992621i	$0.461307\pi$
$30$	−44.5365	−	77.1395i	−0.271041	−	0.469456i
$31$	63.7727	−	110.458i	0.369481	−	0.639960i	−0.620003	−	0.784599i	$-0.712869\pi$
$31$	63.7727	−	110.458i	0.369481	−	0.639960i	0.989485	+	0.144639i	$0.0462020\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$	222.545	+	385.460i	1.17395	+	2.03333i
$34$	201.775			1.01777
$35$	−76.3135	+	52.4523i	−0.368553	+	0.253316i
$36$	209.360			0.969260
$37$	−141.552	−	245.175i	−0.628946	−	1.08937i	−0.987764	−	0.155958i	$-0.950153\pi$
$37$	−141.552	−	245.175i	−0.628946	−	1.08937i	0.358818	−	0.933408i	$-0.383180\pi$
$38$	−101.205	+	175.293i	−0.432045	+	0.748323i
$39$	82.5057	−	142.904i	0.338756	−	0.586743i
$40$	−20.0000	−	34.6410i	−0.0790569	−	0.136931i
$41$	−250.157			−0.952879			−0.476439	−	0.879207i	$-0.658073\pi$
$41$	−250.157			−0.952879			−0.476439	+	0.879207i	$0.658073\pi$
$42$	−25.8962	−	328.913i	−0.0951398	−	1.20839i
$43$	−260.330			−0.923254			−0.461627	−	0.887074i	$-0.652734\pi$
$43$	−260.330			−0.923254			−0.461627	+	0.887074i	$0.652734\pi$
$44$	99.9384	+	173.098i	0.342416	+	0.593081i
$45$	−130.850	+	226.639i	−0.433466	+	0.750785i
$46$	−92.2187	+	159.727i	−0.295585	+	0.511968i
$47$	302.173	+	523.378i	0.937796	+	1.62431i	0.769571	+	0.638561i	$0.220470\pi$
$47$	302.173	+	523.378i	0.937796	+	1.62431i	0.168224	+	0.985749i	$0.446197\pi$
$48$	142.517			0.428553
$49$	−338.774	+	53.6779i	−0.987679	+	0.156495i
$50$	50.0000			0.141421
$51$	−449.318	−	778.242i	−1.23367	−	2.13678i
$52$	37.0508	−	64.1739i	0.0988082	−	0.171141i
$53$	−205.755	+	356.378i	−0.533258	+	0.923629i	0.465988	+	0.884791i	$0.345699\pi$
$53$	−205.755	+	356.378i	−0.533258	+	0.923629i	−0.999246	+	0.0388382i	$0.987634\pi$
$54$	−225.711	−	390.943i	−0.568804	−	0.985197i
$55$	−249.846			−0.612532
$56$	−11.6292	−	147.705i	−0.0277503	−	0.352463i
$57$	901.467			2.09478
$58$	−37.8740	−	65.5997i	−0.0857432	−	0.148512i
$59$	190.724	−	330.344i	0.420851	−	0.728935i	−0.575172	−	0.818032i	$-0.695065\pi$
$59$	190.724	−	330.344i	0.420851	−	0.728935i	0.996023	+	0.0890974i	$0.0283982\pi$
$60$	−89.0730	+	154.279i	−0.191655	+	0.331956i
$61$	−37.5666	−	65.0672i	−0.0788510	−	0.136574i	0.823903	−	0.566730i	$-0.191792\pi$
$61$	−37.5666	−	65.0672i	−0.0788510	−	0.136574i	−0.902754	+	0.430156i	$0.858458\pi$
$62$	−255.091			−0.522526
$63$	−798.850	+	549.071i	−1.59755	+	1.09804i
$64$	64.0000			0.125000
$65$	46.3135	+	80.2174i	0.0883767	+	0.153073i
$66$	445.091	−	770.920i	0.830105	−	1.43778i
$67$	315.474	−	546.417i	0.575243	−	0.996350i	−0.420772	−	0.907166i	$-0.638241\pi$
$67$	315.474	−	546.417i	0.575243	−	0.996350i	0.996015	−	0.0891840i	$-0.0284259\pi$
$68$	−201.775	−	349.485i	−0.359836	−	0.623254i
$69$	821.419			1.43315
$70$	167.164	+	79.7266i	0.285427	+	0.136131i
$71$	−214.755			−0.358967			−0.179484	−	0.983761i	$-0.557443\pi$
$71$	−214.755			−0.358967			−0.179484	+	0.983761i	$0.557443\pi$
$72$	−209.360	−	362.622i	−0.342685	−	0.593548i
$73$	524.520	−	908.495i	0.840964	−	1.45659i	−0.0481162	−	0.998842i	$-0.515322\pi$
$73$	524.520	−	908.495i	0.840964	−	1.45659i	0.889080	−	0.457751i	$-0.151345\pi$
$74$	−283.104	+	490.350i	−0.444732	+	0.770298i
$75$	−111.341	−	192.849i	−0.171421	−	0.296910i
$76$	404.822			0.611003
$77$	−835.303	−	398.388i	−1.23626	−	0.589617i
$78$	−330.023			−0.479074
$79$	530.385	+	918.654i	0.755354	+	1.30831i	0.945198	+	0.326498i	$0.105869\pi$
$79$	530.385	+	918.654i	0.755354	+	1.30831i	−0.189844	+	0.981814i	$0.560798\pi$
$80$	−40.0000	+	69.2820i	−0.0559017	+	0.0968246i
$81$	−298.649	+	517.274i	−0.409669	+	0.709567i
$82$	250.157	+	433.285i	0.336894	+	0.583517i
$83$	−289.875			−0.383349			−0.191674	−	0.981459i	$-0.561392\pi$
$83$	−289.875			−0.383349			−0.191674	+	0.981459i	$0.561392\pi$
$84$	−543.798	+	373.767i	−0.706348	+	0.485492i
$85$	504.438			0.643694
$86$	260.330	+	450.904i	0.326419	+	0.565375i
$87$	−168.678	+	292.158i	−0.207864	+	0.360031i
$88$	199.877	−	346.197i	0.242124	−	0.419372i
$89$	497.079	+	860.966i	0.592026	+	1.02542i	0.993959	+	0.109750i	$0.0350049\pi$
$89$	497.079	+	860.966i	0.592026	+	1.02542i	−0.401934	+	0.915669i	$0.631662\pi$
$90$	523.400			0.613014
$91$	26.9295	+	342.037i	0.0310217	+	0.394013i
$92$	368.875			0.418020
$93$	568.043	+	983.879i	0.633369	+	1.09703i
$94$	604.345	−	1046.76i	0.663122	−	1.14856i
$95$	−253.014	+	438.232i	−0.273249	+	0.473281i
$96$	−142.517	−	246.846i	−0.151516	−	0.262434i
$97$	−281.931			−0.295111			−0.147556	−	0.989054i	$-0.547141\pi$
$97$	−281.931			−0.295111			−0.147556	+	0.989054i	$0.547141\pi$
$98$	431.747	+	533.096i	0.445031	+	0.549498i
$99$	−2615.39			−2.65512
$100$	−50.0000	−	86.6025i	−0.0500000	−	0.0866025i
$101$	−119.125	+	206.330i	−0.117360	+	0.203273i	−0.918721	−	0.394908i	$-0.870776\pi$
$101$	−119.125	+	206.330i	−0.117360	+	0.203273i	0.801361	+	0.598181i	$0.204110\pi$
$102$	−898.636	+	1556.48i	−0.872336	+	1.51093i
$103$	−478.090	−	828.076i	−0.457355	−	0.792162i	0.541465	−	0.840723i	$-0.317870\pi$
$103$	−478.090	−	828.076i	−0.457355	−	0.792162i	−0.998820	+	0.0485609i	$0.984536\pi$
$104$	−148.203			−0.139736
$105$	−64.7405	−	822.283i	−0.0601717	−	0.764253i
$106$	823.021			0.754140
$107$	−763.605	−	1322.60i	−0.689911	−	1.19496i	−0.971866	−	0.235534i	$-0.924316\pi$
$107$	−763.605	−	1322.60i	−0.689911	−	1.19496i	0.281955	−	0.959428i	$-0.409017\pi$
$108$	−451.422	+	781.886i	−0.402205	+	0.696639i
$109$	5.11632	−	8.86172i	0.00449591	−	0.00778714i	−0.863769	−	0.503889i	$-0.831902\pi$
$109$	5.11632	−	8.86172i	0.00449591	−	0.00778714i	0.868265	+	0.496101i	$0.165236\pi$
$110$	249.846	+	432.746i	0.216563	+	0.375098i
$111$	2521.69			2.15629
$112$	−244.203	+	167.847i	−0.206027	+	0.141608i
$113$	1287.33			1.07170			0.535849	−	0.844314i	$-0.319992\pi$
$113$	1287.33			1.07170			0.535849	+	0.844314i	$0.319992\pi$
$114$	−901.467	−	1561.39i	−0.740615	−	1.28278i
$115$	−230.547	+	399.319i	−0.186944	+	0.323797i
$116$	−75.7481	+	131.199i	−0.0606296	+	0.105013i
$117$	484.810	+	839.716i	0.383083	+	0.663519i
$118$	−762.898			−0.595173
$119$	1686.47	+	804.343i	1.29915	+	0.619613i
$120$	356.292			0.271041
$121$	−582.962	−	1009.72i	−0.437988	−	0.758617i
$122$	−75.1332	+	130.134i	−0.0557561	+	0.0965723i
$123$	1114.11	−	1929.70i	0.816718	−	1.41460i
$124$	255.091	+	441.830i	0.184741	+	0.319980i
$125$	125.000			0.0894427
$126$	1749.87	+	834.579i	1.23723	+	0.590081i
$127$	1243.53			0.868859			0.434430	−	0.900706i	$-0.356950\pi$
$127$	1243.53			0.868859			0.434430	+	0.900706i	$0.356950\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$	1159.42	−	2008.17i	0.791326	−	1.37062i
$130$	92.6271	−	160.435i	0.0624918	−	0.108239i
$131$	278.942	+	483.142i	0.186040	+	0.322231i	0.943927	−	0.330155i	$-0.107101\pi$
$131$	278.942	+	483.142i	0.186040	+	0.322231i	−0.757886	+	0.652387i	$0.773768\pi$
$132$	−1780.36			−1.17395
$133$	−1544.67	+	1061.69i	−1.00707	+	0.692183i
$134$	−1261.90			−0.813517
$135$	−564.278	−	977.358i	−0.359743	−	0.623093i
$136$	−403.550	+	698.970i	−0.254442	+	0.440707i
$137$	−381.966	+	661.584i	−0.238201	+	0.412576i	−0.960198	−	0.279320i	$-0.909891\pi$
$137$	−381.966	+	661.584i	−0.238201	+	0.412576i	0.721997	+	0.691896i	$0.243224\pi$
$138$	−821.419	−	1422.74i	−0.506695	−	0.877621i
$139$	551.104			0.336288			0.168144	−	0.985762i	$-0.446223\pi$
$139$	551.104			0.336288			0.168144	+	0.985762i	$0.446223\pi$
$140$	−29.0730	−	369.262i	−0.0175508	−	0.222917i
$141$	−5383.08			−3.21516
$142$	214.755	+	371.966i	0.126914	+	0.219822i
$143$	−462.850	+	801.680i	−0.270668	+	0.468810i
$144$	−418.720	+	725.245i	−0.242315	+	0.419702i
$145$	−94.6851	−	163.999i	−0.0542287	−	0.0939269i
$146$	−2098.08			−1.18930
$147$	1094.71	−	2852.35i	0.614220	−	1.60039i
$148$	1132.42			0.628946
$149$	1278.61	+	2214.61i	0.703003	+	1.21764i	0.967407	+	0.253225i	$0.0814914\pi$
$149$	1278.61	+	2214.61i	0.703003	+	1.21764i	−0.264404	+	0.964412i	$0.585175\pi$
$150$	−222.683	+	385.697i	−0.121213	+	0.209947i
$151$	378.828	−	656.149i	0.204163	−	0.353620i	−0.745703	−	0.666279i	$-0.767886\pi$
$151$	378.828	−	656.149i	0.204163	−	0.353620i	0.949866	+	0.312658i	$0.101220\pi$
$152$	−404.822	−	701.172i	−0.216022	−	0.374162i
$153$	5280.46			2.79020
$154$	145.276	+	1845.18i	0.0760172	+	0.965510i
$155$	−637.727			−0.330474
$156$	330.023	+	571.616i	0.169378	+	0.293371i
$157$	−491.194	+	850.773i	−0.249691	+	0.432478i	−0.963440	−	0.267924i	$-0.913663\pi$
$157$	−491.194	+	850.773i	−0.249691	+	0.432478i	0.713749	+	0.700402i	$0.246996\pi$
$158$	1060.77	−	1837.31i	0.534116	−	0.925116i
$159$	−1832.72	−	3174.37i	−0.914116	−	1.58330i
$160$	160.000			0.0790569
$161$	−1407.51	+	967.416i	−0.688988	+	0.473560i
$162$	1194.59			0.579359
$163$	−1133.76	−	1963.73i	−0.544802	−	0.943625i	−0.998619	−	0.0525305i	$-0.983271\pi$
$163$	−1133.76	−	1963.73i	−0.544802	−	0.943625i	0.453817	−	0.891095i	$-0.350062\pi$
$164$	500.315	−	866.571i	0.238220	−	0.412609i
$165$	1112.73	−	1927.30i	0.525004	−	0.909334i
$166$	289.875	+	502.078i	0.135534	+	0.234752i
$167$	−1079.84			−0.500364			−0.250182	−	0.968199i	$-0.580491\pi$
$167$	−1079.84			−0.500364			−0.250182	+	0.968199i	$0.580491\pi$
$168$	1191.18	+	568.119i	0.547033	+	0.260901i
$169$	−1853.81			−0.843791
$170$	−504.438	−	873.712i	−0.227580	−	0.394180i
$171$	−2648.55	+	4587.42i	−1.18444	+	2.05151i
$172$	520.659	−	901.808i	0.230813	−	0.399781i
$173$	−1298.71	−	2249.43i	−0.570746	−	0.988562i	−0.996490	−	0.0837175i	$-0.973321\pi$
$173$	−1298.71	−	2249.43i	−0.570746	−	0.988562i	0.425743	−	0.904844i	$-0.360013\pi$
$174$	674.711			0.293964
$175$	417.909	+	199.317i	0.180520	+	0.0860967i
$176$	−799.508			−0.342416
$177$	1698.84	+	2942.48i	0.721427	+	1.24955i
$178$	994.158	−	1721.93i	0.418625	−	0.725080i
$179$	1043.85	−	1808.00i	0.435870	−	0.754949i	−0.561496	−	0.827479i	$-0.689774\pi$
$179$	1043.85	−	1808.00i	0.435870	−	0.754949i	0.997366	+	0.0725302i	$0.0231074\pi$
$180$	−523.400	−	906.556i	−0.216733	−	0.375393i
$181$	−1911.11			−0.784815			−0.392408	−	0.919791i	$-0.628358\pi$
$181$	−1911.11			−0.784815			−0.392408	+	0.919791i	$0.628358\pi$
$182$	565.496	−	388.680i	0.230315	−	0.158302i
$183$	669.234			0.270334
$184$	−368.875	−	638.910i	−0.147792	−	0.255984i
$185$	−707.759	+	1225.88i	−0.281273	+	0.487179i
$186$	1136.09	−	1967.76i	0.447859	−	0.775715i
$187$	2520.64	+	4365.87i	0.985708	+	1.70730i
$188$	−2417.38			−0.937796
$189$	−328.105	−	4167.33i	−0.126276	−	1.60386i
$190$	1012.05			0.386432
$191$	−229.495	−	397.497i	−0.0869407	−	0.150586i	0.819276	−	0.573400i	$-0.194376\pi$
$191$	−229.495	−	397.497i	−0.0869407	−	0.150586i	−0.906217	+	0.422814i	$0.861042\pi$
$192$	−285.034	+	493.693i	−0.107138	+	0.185569i
$193$	−873.162	+	1512.36i	−0.325656	+	0.564052i	−0.981645	−	0.190718i	$-0.938918\pi$
$193$	−873.162	+	1512.36i	−0.325656	+	0.564052i	0.655989	+	0.754770i	$0.272252\pi$
$194$	281.931	+	488.319i	0.104338	+	0.180718i
$195$	−825.057			−0.302993
$196$	491.602	−	1280.90i	0.179155	−	0.466801i
$197$	4099.78			1.48273			0.741363	−	0.671105i	$-0.234180\pi$
$197$	4099.78			1.48273			0.741363	+	0.671105i	$0.234180\pi$
$198$	2615.39	+	4529.99i	0.938726	+	1.62592i
$199$	−2151.65	+	3726.77i	−0.766466	+	1.32756i	0.173002	+	0.984921i	$0.444653\pi$
$199$	−2151.65	+	3726.77i	−0.766466	+	1.32756i	−0.939468	+	0.342636i	$0.888680\pi$
$200$	−100.000	+	173.205i	−0.0353553	+	0.0612372i
$201$	2810.02	+	4867.10i	0.986088	+	1.70795i
$202$	476.498			0.165972
$203$	−55.0556	−	699.273i	−0.0190352	−	0.241770i
$204$	3594.55			1.23367
$205$	625.394	+	1083.21i	0.213070	+	0.369048i
$206$	−956.179	+	1656.15i	−0.323399	+	0.560143i
$207$	−2413.36	+	4180.07i	−0.810340	+	1.40355i
$208$	148.203	+	256.696i	0.0494041	+	0.0855704i
$209$	−5057.16			−1.67374
$210$	−1359.50	+	934.417i	−0.446734	+	0.307052i
$211$	812.214			0.265000			0.132500	−	0.991183i	$-0.457699\pi$
$211$	812.214			0.265000			0.132500	+	0.991183i	$0.457699\pi$
$212$	−823.021	−	1425.51i	−0.266629	−	0.461815i
$213$	956.442	−	1656.61i	0.307673	−	0.532905i
$214$	−1527.21	+	2645.21i	−0.487841	+	0.844965i
$215$	650.824	+	1127.26i	0.206446	+	0.357575i
$216$	1805.69			0.568804
$217$	−2132.10	−	1016.88i	−0.666987	−	0.318111i
$218$	−20.4653			−0.00635818
$219$	4672.06	+	8092.24i	1.44159	+	2.49691i
$220$	499.692	−	865.492i	0.153133	−	0.265234i
$221$	934.493	−	1618.59i	0.284438	−	0.492661i
$222$	−2521.69	−	4367.70i	−0.762364	−	1.32045i
$223$	−1293.12			−0.388313			−0.194156	−	0.980971i	$-0.562197\pi$
$223$	−1293.12			−0.388313			−0.194156	+	0.980971i	$0.562197\pi$
$224$	534.923	+	255.125i	0.159558	+	0.0760994i
$225$	1308.50			0.387704
$226$	−1287.33	−	2229.72i	−0.378902	−	0.656278i
$227$	2536.19	−	4392.81i	0.741555	−	1.28441i	−0.210232	−	0.977651i	$-0.567422\pi$
$227$	2536.19	−	4392.81i	0.741555	−	1.28441i	0.951787	−	0.306759i	$-0.0992446\pi$
$228$	−1802.93	+	3122.77i	−0.523694	+	0.907065i
$229$	−972.592	−	1684.58i	−0.280658	−	0.486114i	0.690889	−	0.722961i	$-0.257219\pi$
$229$	−972.592	−	1684.58i	−0.280658	−	0.486114i	−0.971547	+	0.236847i	$0.923886\pi$
$230$	922.187			0.264379
$231$	6793.29	−	4669.21i	1.93492	−	1.32992i
$232$	302.992			0.0857432
$233$	341.724	+	591.883i	0.0960818	+	0.166419i	0.910060	−	0.414477i	$-0.136036\pi$
$233$	341.724	+	591.883i	0.0960818	+	0.166419i	−0.813978	+	0.580896i	$0.802702\pi$
$234$	969.621	−	1679.43i	0.270881	−	0.469179i
$235$	1510.86	−	2616.89i	0.419395	−	0.726413i
$236$	762.898	+	1321.38i	0.210425	+	0.364468i
$237$	−9448.60			−2.58967
$238$	−293.311	−	3725.40i	−0.0798845	−	1.01463i
$239$	4579.46			1.23942			0.619708	−	0.784832i	$-0.287251\pi$
$239$	4579.46			1.23942			0.619708	+	0.784832i	$0.287251\pi$
$240$	−356.292	−	617.116i	−0.0958273	−	0.165978i
$241$	2534.03	−	4389.07i	0.677309	−	1.17313i	−0.298479	−	0.954416i	$-0.596479\pi$
$241$	2534.03	−	4389.07i	0.677309	−	1.17313i	0.975788	−	0.218717i	$-0.0701872\pi$
$242$	−1165.92	+	2019.44i	−0.309704	+	0.536423i
$243$	386.949	+	670.215i	0.102151	+	0.176931i
$244$	300.533			0.0788510
$245$	1079.37	+	1332.74i	0.281462	+	0.347533i
$246$	−4456.46			−1.15501
$247$	937.437	+	1623.69i	0.241489	+	0.418270i
$248$	510.182	−	883.661i	0.130631	−	0.226260i
$249$	1291.00	−	2236.08i	0.328570	−	0.569100i
$250$	−125.000	−	216.506i	−0.0316228	−	0.0547723i
$251$	1416.11			0.356112			0.178056	−	0.984020i	$-0.443019\pi$
$251$	1416.11			0.356112			0.178056	+	0.984020i	$0.443019\pi$
$252$	−304.336	−	3865.44i	−0.0760770	−	0.966269i
$253$	−4608.10			−1.14509
$254$	−1243.53	−	2153.85i	−0.307188	−	0.532065i
$255$	−2246.59	+	3891.21i	−0.551714	+	0.955596i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−1761.16	−	3050.42i	−0.427464	−	0.740390i	0.569183	−	0.822211i	$-0.307260\pi$
$257$	−1761.16	−	3050.42i	−0.427464	−	0.740390i	−0.996647	+	0.0818212i	$0.973926\pi$
$258$	−4637.67			−1.11910
$259$	−4320.93	+	2969.89i	−1.03664	+	0.712509i
$260$	−370.508			−0.0883767
$261$	−991.164	−	1716.75i	−0.235063	−	0.407141i
$262$	557.884	−	966.283i	0.131550	−	0.227852i
$263$	1581.80	−	2739.77i	0.370868	−	0.642362i	−0.618831	−	0.785524i	$-0.712394\pi$
$263$	1581.80	−	2739.77i	0.370868	−	0.642362i	0.989699	+	0.143162i	$0.0457269\pi$
$264$	1780.36	+	3083.68i	0.415052	+	0.718892i
$265$	2057.55			0.476960
$266$	3383.57	+	1613.75i	0.779926	+	0.371976i
$267$	−8855.27			−2.02971
$268$	1261.90	+	2185.67i	0.287622	+	0.498175i
$269$	1951.69	−	3380.42i	0.442366	−	0.766200i	−0.555499	−	0.831517i	$-0.687473\pi$
$269$	1951.69	−	3380.42i	0.442366	−	0.766200i	0.997865	+	0.0653175i	$0.0208060\pi$
$270$	−1128.56	+	1954.72i	−0.254377	+	0.440593i
$271$	−1484.56	−	2571.33i	−0.332769	−	0.576373i	0.650285	−	0.759691i	$-0.274650\pi$
$271$	−1484.56	−	2571.33i	−0.332769	−	0.576373i	−0.983054	+	0.183318i	$0.941316\pi$
$272$	1614.20			0.359836
$273$	−2758.39	−	1315.58i	−0.611522	−	0.291658i
$274$	1527.86			0.336867
$275$	624.615	+	1081.87i	0.136966	+	0.237233i
$276$	−1642.84	+	2845.48i	−0.358287	+	0.620572i
$277$	2154.25	−	3731.27i	0.467279	−	0.809351i	−0.532022	−	0.846731i	$-0.678568\pi$
$277$	2154.25	−	3731.27i	0.467279	−	0.809351i	0.999301	+	0.0373793i	$0.0119010\pi$
$278$	−551.104	−	954.541i	−0.118896	−	0.205934i
$279$	−6675.73			−1.43249
$280$	−610.508	+	419.618i	−0.130303	+	0.0895607i
$281$	3116.17			0.661550			0.330775	−	0.943710i	$-0.392690\pi$
$281$	3116.17			0.661550			0.330775	+	0.943710i	$0.392690\pi$
$282$	5383.08	+	9323.77i	1.13673	+	1.96887i
$283$	−3805.58	+	6591.47i	−0.799359	+	1.38453i	0.120676	+	0.992692i	$0.461494\pi$
$283$	−3805.58	+	6591.47i	−0.799359	+	1.38453i	−0.920034	+	0.391838i	$0.871839\pi$
$284$	429.509	−	743.931i	0.0897418	−	0.155437i
$285$	−2253.67	−	3903.47i	−0.468406	−	0.811304i
$286$	1851.40			0.382782
$287$	363.642	+	4618.69i	0.0747912	+	0.949939i
$288$	1674.88			0.342685
$289$	−2632.66	−	4559.89i	−0.535855	−	0.928128i
$290$	−189.370	+	327.999i	−0.0383455	+	0.0664164i
$291$	1255.62	−	2174.80i	0.252941	−	0.438107i
$292$	2098.08	+	3633.98i	0.420482	+	0.728296i
$293$	−2351.74			−0.468908			−0.234454	−	0.972127i	$-0.575330\pi$
$293$	−2351.74			−0.468908			−0.234454	+	0.972127i	$0.575330\pi$
$294$	−6035.12	+	956.250i	−1.19720	+	0.189693i
$295$	−1907.24			−0.376420
$296$	−1132.42	−	1961.40i	−0.222366	−	0.385149i
$297$	5639.31	−	9767.57i	1.10177	−	1.90832i
$298$	2557.21	−	4429.22i	0.497098	−	0.861000i
$299$	854.195	+	1479.51i	0.165215	+	0.286161i
$300$	890.730			0.171421
$301$	378.428	+	4806.50i	0.0724660	+	0.920405i
$302$	−1515.31			−0.288730
$303$	−1061.08	−	1837.84i	−0.201180	−	0.348453i
$304$	−809.644	+	1402.34i	−0.152751	+	0.264572i
$305$	−187.833	+	325.336i	−0.0352632	+	0.0610777i
$306$	−5280.46	−	9146.02i	−0.986483	−	1.70864i
$307$	2261.80			0.420480			0.210240	−	0.977650i	$-0.432575\pi$
$307$	2261.80			0.420480			0.210240	+	0.977650i	$0.432575\pi$
$308$	3050.66	−	2096.80i	0.564375	−	0.387910i
$309$	8516.98			1.56801
$310$	637.727	+	1104.58i	0.116840	+	0.202373i
$311$	−738.111	+	1278.44i	−0.134580	+	0.233100i	−0.925437	−	0.378902i	$-0.876302\pi$
$311$	−738.111	+	1278.44i	−0.134580	+	0.233100i	0.790857	+	0.612001i	$0.209635\pi$
$312$	660.046	−	1143.23i	0.119768	−	0.207445i
$313$	3014.07	+	5220.53i	0.544299	+	0.942753i	0.998651	+	0.0519309i	$0.0165376\pi$
$313$	3014.07	+	5220.53i	0.544299	+	0.942753i	−0.454352	+	0.890822i	$0.650129\pi$
$314$	1964.78			0.353117
$315$	4374.67	+	2086.45i	0.782492	+	0.373200i
$316$	−4243.08			−0.755354
$317$	−983.166	−	1702.89i	−0.174196	−	0.301716i	0.765687	−	0.643214i	$-0.222399\pi$
$317$	−983.166	−	1702.89i	−0.174196	−	0.301716i	−0.939883	+	0.341497i	$0.889066\pi$
$318$	−3665.45	+	6348.74i	−0.646378	+	1.11956i
$319$	946.268	−	1638.98i	0.166084	−	0.287666i
$320$	−160.000	−	277.128i	−0.0279508	−	0.0484123i
$321$	13603.3			2.36531
$322$	3083.12	+	1470.46i	0.533589	+	0.254489i
$323$	10210.4			1.75889
$324$	−1194.59	−	2069.10i	−0.204834	−	0.354784i
$325$	231.568	−	401.087i	0.0395233	−	0.0684563i
$326$	−2267.52	+	3927.45i	−0.385233	+	0.667244i
$327$	45.5726	+	78.9340i	0.00770694	+	0.0133488i
$328$	−2001.26			−0.336894
$329$	9223.94	−	6339.86i	1.54569	−	1.06239i
$330$	−4450.91			−0.742468
$331$	−3876.71	−	6714.67i	−0.643757	−	1.11502i	−0.984587	−	0.174895i	$-0.944042\pi$
$331$	−3876.71	−	6714.67i	−0.643757	−	1.11502i	0.340830	−	0.940125i	$-0.389292\pi$
$332$	579.750	−	1004.16i	0.0958371	−	0.165995i
$333$	−7408.83	+	12832.5i	−1.21922	+	2.11176i
$334$	1079.84	+	1870.34i	0.176906	+	0.306409i
$335$	−3154.74			−0.514513
$336$	−207.170	−	2631.31i	−0.0336370	−	0.427231i
$337$	3258.06			0.526640			0.263320	−	0.964709i	$-0.415182\pi$
$337$	3258.06			0.526640			0.263320	+	0.964709i	$0.415182\pi$
$338$	1853.81	+	3210.89i	0.298325	+	0.516714i
$339$	−5733.32	+	9930.40i	−0.918558	+	1.59099i
$340$	−1008.88	+	1747.42i	−0.160924	+	0.278728i
$341$	−3186.67	−	5519.48i	−0.506065	−	0.876530i
$342$	10594.2			1.67505
$343$	1483.52	+	6176.79i	0.233535	+	0.972348i
$344$	−2082.64			−0.326419
$345$	−2053.55	−	3556.85i	−0.320462	−	0.555056i
$346$	−2597.42	+	4498.86i	−0.403579	+	0.699019i
$347$	5474.53	−	9482.16i	0.846940	−	1.46694i	−0.0369862	−	0.999316i	$-0.511776\pi$
$347$	5474.53	−	9482.16i	0.846940	−	1.46694i	0.883926	−	0.467627i	$-0.154891\pi$
$348$	−674.711	−	1168.63i	−0.103932	−	0.180015i
$349$	−2498.45			−0.383206			−0.191603	−	0.981473i	$-0.561369\pi$
$349$	−2498.45			−0.383206			−0.191603	+	0.981473i	$0.561369\pi$
$350$	−72.6825	−	923.156i	−0.0111001	−	0.140985i
$351$	−4181.39			−0.635858
$352$	799.508	+	1384.79i	0.121062	+	0.209686i
$353$	−4394.79	+	7612.00i	−0.662637	+	1.14772i	0.317283	+	0.948331i	$0.397230\pi$
$353$	−4394.79	+	7612.00i	−0.662637	+	1.14772i	−0.979920	+	0.199391i	$0.936104\pi$
$354$	3397.68	−	5884.95i	0.510126	−	0.883564i
$355$	536.886	+	929.914i	0.0802675	+	0.139027i
$356$	−3976.63			−0.592026
$357$	−13715.6	+	9427.11i	−2.03336	+	1.39758i
$358$	−4175.39			−0.616413
$359$	1084.67	+	1878.70i	0.159462	+	0.276196i	0.934675	−	0.355504i	$-0.115691\pi$
$359$	1084.67	+	1878.70i	0.159462	+	0.276196i	−0.775213	+	0.631700i	$0.782358\pi$
$360$	−1046.80	+	1813.11i	−0.153253	+	0.265443i
$361$	−1691.77	+	2930.23i	−0.246650	+	0.427210i
$362$	1911.11	+	3310.14i	0.277474	+	0.480599i
$363$	10385.2			1.50161
$364$	−1238.71	−	590.788i	−0.178368	−	0.0850706i
$365$	−5245.20			−0.752181
$366$	−669.234	−	1159.15i	−0.0955776	−	0.165545i
$367$	6501.24	−	11260.5i	0.924692	−	1.60161i	0.132637	−	0.991165i	$-0.457656\pi$
$367$	6501.24	−	11260.5i	0.924692	−	1.60161i	0.792055	−	0.610449i	$-0.209011\pi$
$368$	−737.749	+	1277.82i	−0.104505	+	0.181008i
$369$	6546.62	+	11339.1i	0.923587	+	1.59970i
$370$	2831.04			0.397780
$371$	6878.96	+	3280.83i	0.962635	+	0.459117i
$372$	−4544.34			−0.633369
$373$	−2553.75	−	4423.22i	−0.354499	−	0.614010i	0.632533	−	0.774533i	$-0.282015\pi$
$373$	−2553.75	−	4423.22i	−0.354499	−	0.614010i	−0.987032	+	0.160523i	$0.948682\pi$
$374$	5041.28	−	8731.75i	0.697000	−	1.20724i
$375$	−556.706	+	964.244i	−0.0766618	+	0.132782i
$376$	2417.38	+	4187.03i	0.331561	+	0.574280i
$377$	−701.632			−0.0958512
$378$	−6889.93	+	4735.63i	−0.937512	+	0.644377i
$379$	−12391.9			−1.67950			−0.839749	−	0.542975i	$-0.817298\pi$
$379$	−12391.9			−1.67950			−0.839749	+	0.542975i	$0.817298\pi$
$380$	−1012.05	−	1752.93i	−0.136624	−	0.236641i
$381$	−5538.23	+	9592.50i	−0.744704	+	1.28986i
$382$	−458.990	+	794.994i	−0.0614763	+	0.106480i
$383$	−4565.10	−	7906.99i	−0.609049	−	1.05490i	−0.991397	−	0.130886i	$-0.958218\pi$
$383$	−4565.10	−	7906.99i	−0.609049	−	1.05490i	0.382348	−	0.924018i	$-0.375116\pi$
$384$	1140.13			0.151516
$385$	363.189	+	4612.94i	0.0480775	+	0.610642i
$386$	3492.65			0.460547
$387$	6812.83	+	11800.2i	0.894872	+	1.54996i
$388$	563.863	−	976.639i	0.0737778	−	0.127787i
$389$	−6156.12	+	10662.7i	−0.802385	+	1.38977i	0.115657	+	0.993289i	$0.463103\pi$
$389$	−6156.12	+	10662.7i	−0.802385	+	1.38977i	−0.918042	+	0.396483i	$0.870231\pi$
$390$	825.057	+	1429.04i	0.107124	+	0.185544i
$391$	9303.72			1.20335
$392$	−2710.19	+	429.423i	−0.349197	+	0.0553294i
$393$	−4969.24			−0.637825
$394$	−4099.78	−	7101.02i	−0.524223	−	0.907980i
$395$	2651.93	−	4593.27i	0.337805	−	0.585095i
$396$	5230.78	−	9059.98i	0.663779	−	1.14970i
$397$	679.697	+	1177.27i	0.0859270	+	0.148830i	0.905786	−	0.423736i	$-0.139281\pi$
$397$	679.697	+	1177.27i	0.0859270	+	0.148830i	−0.819859	+	0.572566i	$0.805948\pi$
$398$	8606.62			1.08395
$399$	−1310.42	−	16643.9i	−0.164419	−	2.08831i
$400$	400.000			0.0500000
$401$	−5571.15	−	9649.51i	−0.693790	−	1.20168i	−0.970587	−	0.240751i	$-0.922606\pi$
$401$	−5571.15	−	9649.51i	−0.693790	−	1.20168i	0.276796	−	0.960929i	$-0.410727\pi$
$402$	5620.05	−	9734.20i	0.697270	−	1.20771i
$403$	−1181.42	+	2046.27i	−0.146031	+	0.252933i
$404$	−476.498	−	825.320i	−0.0586799	−	0.101637i
$405$	2986.49			0.366419
$406$	−1156.12	+	794.632i	−0.141323	+	0.0971353i
$407$	−14146.5			−1.72289
$408$	−3594.55	−	6225.94i	−0.436168	−	0.755465i
$409$	5188.98	−	8987.57i	0.627331	−	1.08657i	−0.360754	−	0.932661i	$-0.617481\pi$
$409$	5188.98	−	8987.57i	0.627331	−	1.08657i	0.988085	−	0.153908i	$-0.0491859\pi$
$410$	1250.79	−	2166.43i	0.150663	−	0.260957i
$411$	−3402.28	−	5892.93i	−0.408327	−	0.707242i
$412$	3824.72			0.457355
$413$	−6376.44	−	3041.16i	−0.759719	−	0.362339i
$414$	9653.45			1.14599
$415$	724.688	+	1255.20i	0.0857193	+	0.148470i
$416$	296.407	−	513.391i	0.0349340	−	0.0605074i
$417$	−2454.43	+	4251.19i	−0.288235	+	0.499237i
$418$	5057.16	+	8759.25i	0.591755	+	1.02495i
$419$	−477.650			−0.0556915			−0.0278458	−	0.999612i	$-0.508865\pi$
$419$	−477.650			−0.0556915			−0.0278458	+	0.999612i	$0.508865\pi$
$420$	2977.95	+	1420.30i	0.345974	+	0.165008i
$421$	7877.72			0.911963			0.455981	−	0.889989i	$-0.349288\pi$
$421$	7877.72			0.911963			0.455981	+	0.889989i	$0.349288\pi$
$422$	−812.214	−	1406.80i	−0.0936918	−	0.162279i
$423$	15815.7	−	27393.6i	1.81793	−	3.14876i
$424$	−1646.04	+	2851.03i	−0.188535	+	0.326552i
$425$	−1261.10	−	2184.28i	−0.143934	−	0.249302i
$426$	−3825.77			−0.435115
$427$	−1146.74	+	788.182i	−0.129964	+	0.0893274i
$428$	6108.84			0.689911
$429$	−4122.75	−	7140.81i	−0.463982	−	0.803640i
$430$	1301.65	−	2254.52i	0.145979	−	0.252843i
$431$	−4712.55	+	8162.38i	−0.526672	+	0.912223i	0.472845	+	0.881146i	$0.343227\pi$
$431$	−4712.55	+	8162.38i	−0.526672	+	0.912223i	−0.999517	+	0.0310774i	$0.990106\pi$
$432$	−1805.69	−	3127.55i	−0.201102	−	0.348320i
$433$	−2438.58			−0.270648			−0.135324	−	0.990801i	$-0.543208\pi$
$433$	−2438.58			−0.270648			−0.135324	+	0.990801i	$0.543208\pi$
$434$	370.813	+	4709.78i	0.0410129	+	0.520913i
$435$	1686.78			0.185919
$436$	20.4653	+	35.4469i	0.00224796	+	0.00389357i
$437$	−4666.52	+	8082.64i	−0.510823	+	0.884772i
$438$	9344.11	−	16184.5i	1.01936	−	1.76558i
$439$	−3392.76	−	5876.43i	−0.368856	−	0.638877i	0.620531	−	0.784182i	$-0.286917\pi$
$439$	−3392.76	−	5876.43i	−0.368856	−	0.638877i	−0.989387	+	0.145305i	$0.953584\pi$
$440$	−1998.77			−0.216563
$441$	11298.8	+	13951.1i	1.22004	+	1.50644i
$442$	−3737.97			−0.402256
$443$	3658.70	+	6337.06i	0.392393	+	0.679645i	0.992765	−	0.120076i	$-0.0383138\pi$
$443$	3658.70	+	6337.06i	0.392393	+	0.679645i	−0.600371	+	0.799721i	$0.704981\pi$
$444$	−5043.38	+	8735.39i	−0.539073	+	0.933701i
$445$	2485.40	−	4304.83i	0.264762	−	0.458581i
$446$	1293.12	+	2239.75i	0.137289	+	0.237792i
$447$	−22777.9			−2.41019
$448$	−93.0336	−	1181.64i	−0.00981122	−	0.124614i
$449$	5411.83			0.568820			0.284410	−	0.958703i	$-0.408202\pi$
$449$	5411.83			0.568820			0.284410	+	0.958703i	$0.408202\pi$
$450$	−1308.50	−	2266.39i	−0.137074	−	0.237419i
$451$	−6250.09	+	10825.5i	−0.652561	+	1.13027i
$452$	−2574.66	+	4459.44i	−0.267924	+	0.464059i
$453$	3374.33	+	5844.52i	0.349978	+	0.606179i
$454$	−10144.8			−1.04872
$455$	1413.74	−	971.701i	0.145664	−	0.100119i
$456$	7211.74			0.740615
$457$	2037.18	+	3528.49i	0.208523	+	0.361173i	0.951250	−	0.308422i	$-0.0998010\pi$
$457$	2037.18	+	3528.49i	0.208523	+	0.361173i	−0.742726	+	0.669595i	$0.766468\pi$
$458$	−1945.18	+	3369.16i	−0.198455	+	0.343735i
$459$	−11385.7	+	19720.7i	−1.15782	+	2.00541i
$460$	−922.187	−	1597.27i	−0.0934721	−	0.161898i
$461$	2259.32			0.228258			0.114129	−	0.993466i	$-0.463592\pi$
$461$	2259.32			0.228258			0.114129	+	0.993466i	$0.463592\pi$
$462$	−14880.6	−	7097.12i	−1.49850	−	0.714692i
$463$	11153.8			1.11957			0.559786	−	0.828637i	$-0.310883\pi$
$463$	11153.8			1.11957			0.559786	+	0.828637i	$0.310883\pi$
$464$	−302.992	−	524.798i	−0.0303148	−	0.0525067i
$465$	2840.21	−	4919.40i	0.283251	−	0.490605i
$466$	683.447	−	1183.77i	0.0679401	−	0.117676i
$467$	−7652.25	−	13254.1i	−0.758253	−	1.31333i	−0.943741	−	0.330685i	$-0.892720\pi$
$467$	−7652.25	−	13254.1i	−0.758253	−	1.31333i	0.185488	−	0.982646i	$-0.440613\pi$
$468$	−3878.48			−0.383083
$469$	−10547.2	−	5030.34i	−1.03843	−	0.495265i
$470$	−6043.45			−0.593114
$471$	−4375.21	−	7578.09i	−0.428024	−	0.741359i
$472$	1525.80	−	2642.75i	0.148793	−	0.257717i
$473$	−6504.24	+	11265.7i	−0.632273	+	1.09513i
$474$	9448.60	+	16365.5i	0.915588	+	1.58584i
$475$	2530.14			0.244401
$476$	−6159.27	+	4233.43i	−0.593088	+	0.407645i
$477$	21538.5			2.06746
$478$	−4579.46	−	7931.85i	−0.438200	−	0.758984i
$479$	1226.08	−	2123.64i	0.116954	−	0.202571i	−0.801605	−	0.597854i	$-0.796020\pi$
$479$	1226.08	−	2123.64i	0.116954	−	0.202571i	0.918559	+	0.395283i	$0.129354\pi$
$480$	−712.584	+	1234.23i	−0.0677601	+	0.117364i
$481$	2622.31	+	4541.97i	0.248580	+	0.430553i
$482$	−10136.1			−0.957859
$483$	−1194.06	−	15166.0i	−0.112488	−	1.42873i
$484$	4663.69			0.437988
$485$	704.828	+	1220.80i	0.0659889	+	0.114296i
$486$	773.897	−	1340.43i	0.0722319	−	0.125109i
$487$	−7124.27	+	12339.6i	−0.662899	+	1.14817i	0.316952	+	0.948442i	$0.397341\pi$
$487$	−7124.27	+	12339.6i	−0.662899	+	1.14817i	−0.979850	+	0.199732i	$0.935993\pi$
$488$	−300.533	−	520.538i	−0.0278780	−	0.0482862i
$489$	20197.5			1.86781
$490$	1229.01	−	3202.26i	0.113308	−	0.295231i
$491$	10764.1			0.989364			0.494682	−	0.869074i	$-0.335285\pi$
$491$	10764.1			0.989364			0.494682	+	0.869074i	$0.335285\pi$
$492$	4456.46	+	7718.81i	0.408359	+	0.707298i
$493$	−1910.51	+	3309.10i	−0.174534	+	0.302301i
$494$	1874.87	−	3247.38i	0.170758	−	0.295762i
$495$	6538.48	+	11325.0i	0.593702	+	1.02832i
$496$	−2040.73			−0.184741
$497$	312.178	+	3965.04i	0.0281753	+	0.357860i
$498$	−5164.01			−0.464668
$499$	3647.41	+	6317.50i	0.327216	+	0.566754i	0.981958	−	0.189098i	$-0.0605563\pi$
$499$	3647.41	+	6317.50i	0.327216	+	0.566754i	−0.654743	+	0.755852i	$0.727223\pi$
$500$	−250.000	+	433.013i	−0.0223607	+	0.0387298i
$501$	4809.25	−	8329.86i	0.428865	−	0.742816i
$502$	−1416.11	−	2452.78i	−0.125905	−	0.218073i
$503$	−11064.2			−0.980774			−0.490387	−	0.871505i	$-0.663145\pi$
$503$	−11064.2			−0.980774			−0.490387	+	0.871505i	$0.663145\pi$
$504$	−6390.80	+	4392.57i	−0.564819	+	0.388215i
$505$	1191.25			0.104970
$506$	4608.10	+	7981.46i	0.404851	+	0.701223i
$507$	8256.22	−	14300.2i	0.723218	−	1.25265i
$508$	−2487.05	+	4307.70i	−0.217215	+	0.376227i
$509$	−7445.33	−	12895.7i	−0.648347	−	1.12297i	−0.983518	−	0.180812i	$-0.942127\pi$
$509$	−7445.33	−	12895.7i	−0.648347	−	1.12297i	0.335171	−	0.942157i	$-0.391206\pi$
$510$	8986.36			0.780241
$511$	−17536.1	−	8363.64i	−1.51811	−	0.724042i
$512$	512.000			0.0441942
$513$	−11421.6	−	19782.8i	−0.982994	−	1.70260i
$514$	−3522.33	+	6100.85i	−0.302263	+	0.523535i
$515$	−2390.45	+	4140.38i	−0.204535	+	0.354266i
$516$	4637.67	+	8032.68i	0.395663	+	0.685308i
$517$	30198.7			2.56893
$518$	9464.93	+	4514.18i	0.802828	+	0.382899i
$519$	23136.0			1.95676
$520$	370.508	+	641.739i	0.0312459	+	0.0541195i
$521$	−3180.13	+	5508.15i	−0.267417	+	0.463180i	−0.968194	−	0.250201i	$-0.919503\pi$
$521$	−3180.13	+	5508.15i	−0.267417	+	0.463180i	0.700777	+	0.713380i	$0.252837\pi$
$522$	−1982.33	+	3433.49i	−0.166215	+	0.287892i
$523$	21.4136	+	37.0894i	0.00179034	+	0.00310096i	0.866919	−	0.498449i	$-0.166097\pi$
$523$	21.4136	+	37.0894i	0.00179034	+	0.00310096i	−0.865129	+	0.501550i	$0.832763\pi$
$524$	−2231.54			−0.186040
$525$	−3398.74	+	2336.04i	−0.282539	+	0.194197i
$526$	−6327.22			−0.524486
$527$	6433.88	+	11143.8i	0.531811	+	0.921123i
$528$	3560.73	−	6167.36i	0.293486	−	0.508333i
$529$	1831.36	−	3172.01i	0.150518	−	0.260706i
$530$	−2057.55	−	3563.78i	−0.168631	−	0.292077i
$531$	−19965.0			−1.63166
$532$	−588.470	−	7474.27i	−0.0479575	−	0.609118i
$533$	4634.27			0.376609
$534$	8855.27	+	15337.8i	0.717612	+	1.24294i
$535$	−3818.03	+	6613.02i	−0.308538	+	0.534403i
$536$	2523.79	−	4371.34i	0.203379	−	0.352263i
$537$	9297.85	+	16104.4i	0.747173	+	1.29414i
$538$	−7806.74			−0.625600
$539$	−6141.24	+	16001.4i	−0.490764	+	1.27872i
$540$	4514.22			0.359743
$541$	1646.87	+	2852.47i	0.130877	+	0.226686i	0.924015	−	0.382356i	$-0.124887\pi$
$541$	1646.87	+	2852.47i	0.130877	+	0.226686i	−0.793138	+	0.609042i	$0.791554\pi$
$542$	−2969.11	+	5142.66i	−0.235303	+	0.407557i
$543$	8511.41	−	14742.2i	0.672670	−	1.16510i
$544$	−1614.20	−	2795.88i	−0.127221	−	0.220354i
$545$	−51.1632			−0.00402126
$546$	479.738	+	6093.25i	0.0376024	+	0.477596i
$547$	12786.8			0.999492			0.499746	−	0.866172i	$-0.333427\pi$
$547$	12786.8			0.999492			0.499746	+	0.866172i	$0.333427\pi$
$548$	−1527.86	−	2646.34i	−0.119100	−	0.206288i
$549$	−1966.24	+	3405.62i	−0.152854	+	0.264751i
$550$	1249.23	−	2163.73i	0.0968498	−	0.167749i
$551$	−1916.53	−	3319.53i	−0.148179	−	0.256654i
$552$	6571.36			0.506695
$553$	16190.2	−	11128.0i	1.24499	−	0.855713i
$554$	−8617.00			−0.660833
$555$	−6304.23	−	10919.2i	−0.482161	−	0.835128i
$556$	−1102.21	+	1909.08i	−0.0840721	+	0.145617i
$557$	−8456.55	+	14647.2i	−0.643295	+	1.11422i	0.341397	+	0.939919i	$0.389100\pi$
$557$	−8456.55	+	14647.2i	−0.643295	+	1.11422i	−0.984692	+	0.174301i	$0.944233\pi$
$558$	6675.73	+	11562.7i	0.506463	+	0.877219i
$559$	4822.72			0.364900
$560$	1337.31	+	637.813i	0.100914	+	0.0481295i
$561$	−44904.2			−3.37942
$562$	−3116.17	−	5397.37i	−0.233893	−	0.405115i
$563$	8668.12	−	15013.6i	0.648877	−	1.12389i	−0.334514	−	0.942391i	$-0.608572\pi$
$563$	8668.12	−	15013.6i	0.648877	−	1.12389i	0.983391	−	0.181498i	$-0.0580944\pi$
$564$	10766.2	−	18647.5i	0.803790	−	1.39220i
$565$	−3218.33	−	5574.30i	−0.239639	−	0.415067i
$566$	15222.3			1.13046
$567$	9984.63	+	4762.05i	0.739533	+	0.352711i
$568$	−1718.04			−0.126914
$569$	1571.89	+	2722.60i	0.115812	+	0.200593i	0.918104	−	0.396339i	$-0.129720\pi$
$569$	1571.89	+	2722.60i	0.115812	+	0.200593i	−0.802292	+	0.596932i	$0.796386\pi$
$570$	−4507.34	+	7806.94i	−0.331213	+	0.573678i
$571$	4897.41	−	8482.57i	0.358932	−	0.621689i	−0.628850	−	0.777526i	$-0.716474\pi$
$571$	4897.41	−	8482.57i	0.358932	−	0.621689i	0.987783	+	0.155837i	$0.0498076\pi$
$572$	−1851.40	−	3206.72i	−0.135334	−	0.234405i
$573$	4088.36			0.298069
$574$	7636.16	−	5248.53i	0.555274	−	0.381654i
$575$	2305.47			0.167208
$576$	−1674.88	−	2900.98i	−0.121157	−	0.209851i
$577$	4193.15	−	7262.74i	0.302536	−	0.524007i	−0.674174	−	0.738573i	$-0.735500\pi$
$577$	4193.15	−	7262.74i	0.302536	−	0.524007i	0.976710	+	0.214566i	$0.0688336\pi$
$578$	−5265.31	+	9119.79i	−0.378907	+	0.656286i
$579$	−7777.52	−	13471.1i	−0.558243	−	0.966905i
$580$	757.481			0.0542287
$581$	421.377	+	5352.00i	0.0300889	+	0.382166i
$582$	−5022.49			−0.357713
$583$	10281.4	+	17808.0i	0.730383	+	1.26506i
$584$	4196.16	−	7267.96i	0.297326	−	0.514983i
$585$	2424.05	−	4198.58i	0.171320	−	0.296735i
$586$	2351.74	+	4073.33i	0.165784	+	0.287146i
$587$	−21032.1			−1.47886			−0.739428	−	0.673236i	$-0.764904\pi$
$587$	−21032.1			−1.47886			−0.739428	+	0.673236i	$0.764904\pi$
$588$	7691.39	+	9496.89i	0.539435	+	0.666063i
$589$	−12908.3			−0.903017
$590$	1907.24	+	3303.44i	0.133085	+	0.230510i
$591$	−18259.0	+	31625.5i	−1.27085	+	2.20118i
$592$	−2264.83	+	3922.80i	−0.157236	+	0.272341i
$593$	5409.20	+	9369.00i	0.374585	+	0.648801i	0.990265	−	0.139196i	$-0.0444518\pi$
$593$	5409.20	+	9369.00i	0.374585	+	0.648801i	−0.615680	+	0.787997i	$0.711118\pi$
$594$	−22557.2			−1.55814
$595$	−733.277	−	9313.50i	−0.0505234	−	0.641708i
$596$	−10228.8			−0.703003
$597$	−19165.4	−	33195.5i	−1.31388	−	2.27571i
$598$	1708.39	−	2959.02i	0.116825	−	0.202346i
$599$	−4297.70	+	7443.83i	−0.293154	+	0.507757i	−0.974554	−	0.224154i	$-0.928038\pi$
$599$	−4297.70	+	7443.83i	−0.293154	+	0.507757i	0.681400	+	0.731911i	$0.261371\pi$
$600$	−890.730	−	1542.79i	−0.0606065	−	0.104974i
$601$	18316.3			1.24316			0.621579	−	0.783351i	$-0.286491\pi$
$601$	18316.3			1.24316			0.621579	+	0.783351i	$0.286491\pi$
$602$	7946.67	−	5461.96i	0.538010	−	0.369789i
$603$	−33023.8			−2.23024
$604$	1515.31	+	2624.60i	0.102081	+	0.176810i
$605$	−2914.81	+	5048.60i	−0.195874	+	0.339264i
$606$	−2122.16	+	3675.69i	−0.142255	+	0.246394i
$607$	6784.36	+	11750.8i	0.453655	+	0.785753i	0.998610	−	0.0527121i	$-0.0167866\pi$
$607$	6784.36	+	11750.8i	0.453655	+	0.785753i	−0.544955	+	0.838465i	$0.683453\pi$
$608$	3238.57			0.216022
$609$	5639.35	+	2689.62i	0.375235	+	0.178964i
$610$	751.332			0.0498697
$611$	−5597.87	−	9695.80i	−0.370648	−	0.641980i
$612$	−10560.9	+	18292.0i	−0.697549	+	1.20819i
$613$	6173.14	−	10692.2i	0.406739	−	0.704492i	−0.587783	−	0.809018i	$-0.699999\pi$
$613$	6173.14	−	10692.2i	0.406739	−	0.704492i	0.994522	+	0.104526i	$0.0333326\pi$
$614$	−2261.80	−	3917.54i	−0.148662	−	0.257491i
$615$	−11141.1			−0.730495
$616$	−6682.43	−	3187.10i	−0.437082	−	0.208461i
$617$	17639.2			1.15094			0.575469	−	0.817824i	$-0.304820\pi$
$617$	17639.2			1.15094			0.575469	+	0.817824i	$0.304820\pi$
$618$	−8516.98	−	14751.8i	−0.554374	−	0.960204i
$619$	345.460	−	598.354i	0.0224317	−	0.0388528i	−0.854592	−	0.519301i	$-0.826193\pi$
$619$	345.460	−	598.354i	0.0224317	−	0.0388528i	0.877023	+	0.480448i	$0.159526\pi$
$620$	1275.45	−	2209.15i	0.0826185	−	0.143100i
$621$	−10407.4	−	18026.1i	−0.672519	−	1.16484i
$622$	2952.44			0.190325
$623$	15173.5	−	10429.2i	0.975787	−	0.670684i
$624$	−2640.18			−0.169378
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	6028.15	−	10441.1i	0.384877	−	0.666627i
$627$	22522.8	−	39010.7i	1.43457	−	2.48475i
$628$	−1964.78	−	3403.09i	−0.124846	−	0.216239i
$629$	28561.7			1.81054
$630$	−760.841	−	9663.60i	−0.0481153	−	0.611122i
$631$	7403.38			0.467074			0.233537	−	0.972348i	$-0.424970\pi$
$631$	7403.38			0.467074			0.233537	+	0.972348i	$0.424970\pi$
$632$	4243.08	+	7349.23i	0.267058	+	0.462558i
$633$	−3617.32	+	6265.37i	−0.227133	+	0.393406i
$634$	−1966.33	+	3405.79i	−0.123175	+	0.213346i
$635$	−3108.82	−	5384.63i	−0.194283	−	0.336508i
$636$	14661.8			0.914116
$637$	6275.93	−	994.405i	0.390363	−	0.0618520i
$638$	−3785.07			−0.234878
$639$	5620.13	+	9734.35i	0.347932	+	0.602637i
$640$	−320.000	+	554.256i	−0.0197642	+	0.0342327i
$641$	−6640.22	+	11501.2i	−0.409162	+	0.708690i	−0.994796	−	0.101886i	$-0.967512\pi$
$641$	−6640.22	+	11501.2i	−0.409162	+	0.708690i	0.585634	+	0.810576i	$0.300846\pi$
$642$	−13603.3	−	23561.7i	−0.836262	−	1.44845i
$643$	−13586.5			−0.833279			−0.416640	−	0.909072i	$-0.636792\pi$
$643$	−13586.5			−0.833279			−0.416640	+	0.909072i	$0.636792\pi$
$644$	−536.215	−	6810.58i	−0.0328103	−	0.416730i
$645$	−11594.2			−0.707783
$646$	−10210.4	−	17684.9i	−0.621861	−	1.07709i
$647$	−8194.55	+	14193.4i	−0.497931	+	0.862441i	−0.999997	−	0.00238796i	$-0.999240\pi$
$647$	−8194.55	+	14193.4i	−0.497931	+	0.862441i	0.502067	+	0.864829i	$0.332573\pi$
$648$	−2389.19	+	4138.20i	−0.144840	+	0.250870i
$649$	−9530.35	−	16507.1i	−0.576424	−	0.998395i
$650$	−926.271			−0.0558944
$651$	17339.7	−	11918.1i	1.04393	−	0.717520i
$652$	9070.07			0.544802
$653$	9141.24	+	15833.1i	0.547817	+	0.948846i	0.998424	+	0.0561238i	$0.0178741\pi$
$653$	9141.24	+	15833.1i	0.547817	+	0.948846i	−0.450607	+	0.892722i	$0.648793\pi$
$654$	91.1451	−	157.868i	0.00544963	−	0.00943903i
$655$	1394.71	−	2415.71i	0.0831997	−	0.144106i
$656$	2001.26	+	3466.28i	0.119110	+	0.206304i
$657$	−54906.7			−3.26045
$658$	−20204.9	−	9636.48i	−1.19707	−	0.570926i
$659$	−3419.09			−0.202108			−0.101054	−	0.994881i	$-0.532221\pi$
$659$	−3419.09			−0.202108			−0.101054	+	0.994881i	$0.532221\pi$
$660$	4450.91	+	7709.20i	0.262502	+	0.454667i
$661$	4975.38	−	8617.61i	0.292768	−	0.507089i	−0.681695	−	0.731636i	$-0.738757\pi$
$661$	4975.38	−	8617.61i	0.292768	−	0.507089i	0.974463	+	0.224547i	$0.0720903\pi$
$662$	−7753.43	+	13429.3i	−0.455205	+	0.788438i
$663$	8323.81	+	14417.3i	0.487587	+	0.844525i
$664$	−2319.00			−0.135534
$665$	8458.93	+	4034.38i	0.493268	+	0.235258i
$666$	29635.3			1.72424
$667$	−1746.35	−	3024.76i	−0.101378	−	0.175591i
$668$	2159.69	−	3740.69i	0.125091	−	0.216664i
$669$	5759.10	−	9975.06i	0.332825	−	0.576469i
$670$	3154.74	+	5464.17i	0.181908	+	0.315074i
$671$	−3754.35			−0.215998
$672$	−4350.39	+	2990.13i	−0.249732	+	0.171647i
$673$	−15363.3			−0.879957			−0.439978	−	0.898008i	$-0.645014\pi$
$673$	−15363.3			−0.879957			−0.439978	+	0.898008i	$0.645014\pi$
$674$	−3258.06	−	5643.12i	−0.186195	−	0.322500i
$675$	−2821.39	+	4886.79i	−0.160882	+	0.278656i
$676$	3707.62	−	6421.78i	0.210948	−	0.365372i
$677$	1843.64	+	3193.28i	0.104663	+	0.181282i	0.913601	−	0.406613i	$-0.133290\pi$
$677$	1843.64	+	3193.28i	0.104663	+	0.181282i	−0.808937	+	0.587895i	$0.799957\pi$
$678$	22933.3			1.29904
$679$	409.830	+	5205.33i	0.0231632	+	0.294201i
$680$	4035.50			0.227580
$681$	22590.6	+	39128.1i	1.27118	+	2.20175i
$682$	−6373.35	+	11039.0i	−0.357842	+	0.619800i
$683$	−7558.04	+	13090.9i	−0.423427	+	0.733397i	−0.996272	−	0.0862667i	$-0.972506\pi$
$683$	−7558.04	+	13090.9i	−0.423427	+	0.733397i	0.572845	+	0.819664i	$0.305840\pi$
$684$	−10594.2	−	18349.7i	−0.592221	−	1.02576i
$685$	3819.66			0.213053
$686$	9215.00	−	8746.32i	0.512872	−	0.486788i
$687$	17326.3			0.962214
$688$	2082.64	+	3607.23i	0.115407	+	0.199890i
$689$	3811.70	−	6602.06i	0.210761	−	0.365049i
$690$	−4107.10	+	7113.70i	−0.226601	+	0.392484i
$691$	2713.56	+	4700.02i	0.149390	+	0.258751i	0.931002	−	0.365014i	$-0.118936\pi$
$691$	2713.56	+	4700.02i	0.149390	+	0.258751i	−0.781612	+	0.623765i	$0.785602\pi$
$692$	10389.7			0.570746
$693$	3801.86	+	48288.3i	0.208400	+	2.64693i
$694$	−21898.1			−1.19775
$695$	−1377.76	−	2386.35i	−0.0751963	−	0.130244i
$696$	−1349.42	+	2337.27i	−0.0734909	+	0.127290i
$697$	12618.9	−	21856.6i	0.685760	−	1.18777i
$698$	2498.45	+	4327.44i	0.135484	+	0.234665i
$699$	−6087.67			−0.329409
$700$	−1526.27	+	1049.05i	−0.0824109	+	0.0566432i
$701$	1857.26			0.100068			0.0500340	−	0.998748i	$-0.484067\pi$
$701$	1857.26			0.100068			0.0500340	+	0.998748i	$0.484067\pi$
$702$	4181.39	+	7242.39i	0.224810	+	0.389382i
$703$	−14325.8	+	24813.1i	−0.768576	+	1.33121i
$704$	1599.02	−	2769.58i	0.0856039	−	0.148270i
$705$	13457.7	+	23309.4i	0.718931	+	1.24523i
$706$	17579.2			0.937111
$707$	3982.66	+	1899.48i	0.211858	+	0.101043i
$708$	−13590.7			−0.721427
$709$	2296.11	+	3976.99i	0.121625	+	0.210661i	0.920409	−	0.390957i	$-0.127856\pi$
$709$	2296.11	+	3976.99i	0.121625	+	0.210661i	−0.798783	+	0.601619i	$0.794523\pi$
$710$	1073.77	−	1859.83i	0.0567577	−	0.0983072i
$711$	27760.4	−	48082.4i	1.46427	−	2.53619i
$712$	3976.63	+	6887.73i	0.209313	+	0.362540i
$713$	−11762.1			−0.617802
$714$	30043.9	+	14329.1i	1.57474	+	0.751052i
$715$	4628.50			0.242093
$716$	4175.39	+	7231.98i	0.217935	+	0.377475i
$717$	−20395.3	+	35325.7i	−1.06231	+	1.83998i
$718$	2169.34	−	3757.41i	0.112756	−	0.195300i
$719$	7493.47	+	12979.1i	0.388678	+	0.673209i	0.992272	−	0.124082i	$-0.0395987\pi$
$719$	7493.47	+	12979.1i	0.388678	+	0.673209i	−0.603594	+	0.797292i	$0.706265\pi$
$720$	4187.20			0.216733
$721$	−14593.9	+	10030.8i	−0.753821	+	0.518121i
$722$	6767.09			0.348816
$723$	22571.4	+	39094.8i	1.16105	+	2.01100i
$724$	3822.22	−	6620.27i	0.196204	−	0.339835i
$725$	−473.425	+	819.997i	−0.0242518	+	0.0420054i
$726$	−10385.2	−	17987.7i	−0.530898	−	0.919543i
$727$	−8473.49			−0.432276			−0.216138	−	0.976363i	$-0.569346\pi$
$727$	−8473.49			−0.432276			−0.216138	+	0.976363i	$0.569346\pi$
$728$	215.436	+	2736.30i	0.0109678	+	0.139305i
$729$	−23020.4			−1.16956
$730$	5245.20	+	9084.95i	0.265936	+	0.460615i
$731$	13132.0	−	22745.3i	0.664440	−	1.15084i
$732$	−1338.47	+	2318.29i	−0.0675836	+	0.117058i
$733$	−15731.4	−	27247.6i	−0.792706	−	1.37301i	−0.924286	−	0.381701i	$-0.875338\pi$
$733$	−15731.4	−	27247.6i	−0.792706	−	1.37301i	0.131580	−	0.991306i	$-0.457995\pi$
$734$	−26005.0			−1.30771
$735$	−15087.8	+	2390.62i	−0.757173	+	0.119972i
$736$	2951.00			0.147792
$737$	−15764.0	−	27304.0i	−0.787889	−	1.36466i
$738$	13093.2	−	22678.2i	0.653075	−	1.13116i
$739$	−192.385	+	333.221i	−0.00957645	+	0.0165869i	−0.870774	−	0.491684i	$-0.836382\pi$
$739$	−192.385	+	333.221i	−0.00957645	+	0.0165869i	0.861197	+	0.508271i	$0.169715\pi$
$740$	−2831.04	−	4903.50i	−0.140637	−	0.243590i
$741$	−16700.1			−0.827924
$742$	−1196.38	−	15195.5i	−0.0591923	−	0.751814i
$743$	−13573.4			−0.670201			−0.335100	−	0.942182i	$-0.608770\pi$
$743$	−13573.4			−0.670201			−0.335100	+	0.942182i	$0.608770\pi$
$744$	4544.34	+	7871.03i	0.223930	+	0.387858i
$745$	6393.03	−	11073.1i	0.314393	−	0.544544i
$746$	−5107.50	+	8846.45i	−0.250669	+	0.434171i
$747$	7586.04	+	13139.4i	0.371564	+	0.643568i
$748$	−20165.1			−0.985708
$749$	−23309.4	+	16021.1i	−1.13712	+	0.781575i
$750$	2226.83			0.108416
$751$	17133.4	+	29676.0i	0.832501	+	1.44193i	0.896049	+	0.443955i	$0.146425\pi$
$751$	17133.4	+	29676.0i	0.832501	+	1.44193i	−0.0635477	+	0.997979i	$0.520242\pi$
$752$	4834.76	−	8374.05i	0.234449	−	0.406077i
$753$	−6306.86	+	10923.8i	−0.305226	+	0.528666i
$754$	701.632	+	1215.26i	0.0338885	+	0.0586966i
$755$	−3788.28			−0.182609
$756$	15092.3	+	7198.08i	0.726059	+	0.346285i
$757$	9605.37			0.461180			0.230590	−	0.973051i	$-0.425934\pi$
$757$	9605.37			0.461180			0.230590	+	0.973051i	$0.425934\pi$
$758$	12391.9	+	21463.4i	0.593792	+	1.02848i
$759$	20522.8	−	35546.6i	0.981465	−	1.69995i
$760$	−2024.11	+	3505.86i	−0.0966081	+	0.167330i
$761$	−10464.1	−	18124.4i	−0.498455	−	0.863350i	0.501543	−	0.865133i	$-0.332766\pi$
$761$	−10464.1	−	18124.4i	−0.498455	−	0.863350i	−0.999998	+	0.00178253i	$0.999433\pi$
$762$	22152.9			1.05317
$763$	−171.052	−	81.5813i	−0.00811600	−	0.00387083i
$764$	1835.96			0.0869407
$765$	−13201.1	−	22865.1i	−0.623907	−	1.08064i
$766$	−9130.21	+	15814.0i	−0.430663	+	0.745930i
$767$	−3533.25	+	6119.77i	−0.166334	+	0.288099i
$768$	−1140.13	−	1974.77i	−0.0535691	−	0.0927844i
$769$	18338.3			0.859940			0.429970	−	0.902843i	$-0.358524\pi$
$769$	18338.3			0.859940			0.429970	+	0.902843i	$0.358524\pi$
$770$	7626.66	−	5242.00i	0.356942	−	0.245336i
$771$	31374.4			1.46553
$772$	−3492.65	−	6049.44i	−0.162828	−	0.282026i
$773$	−2823.51	+	4890.46i	−0.131377	+	0.227552i	−0.924208	−	0.381890i	$-0.875273\pi$
$773$	−2823.51	+	4890.46i	−0.131377	+	0.227552i	0.792830	+	0.609442i	$0.208607\pi$
$774$	13625.7	−	23600.3i	0.632770	−	1.09599i
$775$	1594.32	+	2761.44i	0.0738963	+	0.127992i
$776$	−2255.45			−0.104338
$777$	−3665.66	−	46558.3i	−0.169247	−	2.14964i
$778$	24624.5			1.13474
$779$	12658.7	+	21925.4i	0.582212	+	1.00842i
$780$	1650.11	−	2858.08i	0.0757482	−	0.131200i
$781$	−5365.56	+	9293.42i	−0.245832	+	0.425793i
$782$	−9303.72	−	16114.5i	−0.425448	−	0.736898i
$783$	8548.59			0.390168
$784$	3453.97	+	4264.76i	0.157342	+	0.194277i
$785$	4911.94			0.223331
$786$	4969.24	+	8606.98i	0.225505	+	0.390586i
$787$	14203.6	−	24601.4i	0.643336	−	1.11429i	−0.341347	−	0.939937i	$-0.610883\pi$
$787$	14203.6	−	24601.4i	0.643336	−	1.11429i	0.984683	−	0.174353i	$-0.0557835\pi$
$788$	−8199.55	+	14202.0i	−0.370681	+	0.642039i
$789$	14089.6	+	24403.9i	0.635746	+	1.10114i
$790$	−10607.7			−0.477728
$791$	−1871.33	−	23768.1i	−0.0841173	−	1.06839i
$792$	−20923.1			−0.938726
$793$	695.937	+	1205.40i	0.0311645	+	0.0539785i
$794$	1359.39	−	2354.54i	0.0607596	−	0.105239i
$795$	−9163.62	+	15871.9i	−0.408805	+	0.708071i
$796$	−8606.62	−	14907.1i	−0.383233	−	0.663779i
$797$	5120.09			0.227557			0.113778	−	0.993506i	$-0.463705\pi$
$797$	5120.09			0.227557			0.113778	+	0.993506i	$0.463705\pi$
$798$	−27517.7	+	18913.6i	−1.22070	+	0.839016i
$799$	−60970.9			−2.69962
$800$	−400.000	−	692.820i	−0.0176777	−	0.0306186i
$801$	26017.1	−	45063.0i	1.14765	−	1.98779i
$802$	−11142.3	+	19299.0i	−0.490584	+	0.849716i
$803$	−26209.8	−	45396.8i	−1.15184	−	1.99504i
$804$	−22480.2			−0.986088
$805$	7707.80	+	3676.14i	0.337471	+	0.160953i
$806$	4725.67			0.206519
$807$	17384.3	+	30110.4i	0.758308	+	1.31343i
$808$	−952.997	+	1650.64i	−0.0414930	+	0.0718679i
$809$	−13193.8	+	22852.3i	−0.573386	+	0.993134i	0.422829	+	0.906210i	$0.361037\pi$
$809$	−13193.8	+	22852.3i	−0.573386	+	0.993134i	−0.996215	+	0.0869245i	$0.972296\pi$
$810$	−2986.49	−	5172.74i	−0.129549	−	0.224385i
$811$	−43383.4			−1.87842			−0.939210	−	0.343343i	$-0.888441\pi$
$811$	−43383.4			−1.87842			−0.939210	+	0.343343i	$0.888441\pi$
$812$	2532.46	+	1207.83i	0.109448	+	0.0522000i
$813$	26446.8			1.14087
$814$	14146.5	+	24502.4i	0.609132	+	1.05505i
$815$	−5668.79	+	9818.63i	−0.243643	+	0.422002i
$816$	−7189.09	+	12451.9i	−0.308417	+	0.534194i
$817$	13173.4	+	22817.0i	0.564111	+	0.977069i
$818$	−20755.9			−0.887180
$819$	14799.0	−	10171.8i	0.631404	−	0.433981i
$820$	−5003.15			−0.213070
$821$	−14779.4	−	25598.6i	−0.628263	−	1.08818i	−0.987900	−	0.155091i	$-0.950433\pi$
$821$	−14779.4	−	25598.6i	−0.628263	−	1.08818i	0.359637	−	0.933092i	$-0.382900\pi$
$822$	−6804.57	+	11785.9i	−0.288731	+	0.500096i
$823$	14507.7	−	25128.1i	0.614468	−	1.06429i	−0.376009	−	0.926616i	$-0.622704\pi$
$823$	14507.7	−	25128.1i	0.614468	−	1.06429i	0.990478	−	0.137674i	$-0.0439627\pi$
$824$	−3824.72	−	6624.61i	−0.161699	−	0.280072i
$825$	−11127.3			−0.469578
$826$	1108.99	+	14085.5i	0.0467150	+	0.593337i
$827$	425.416			0.0178878			0.00894388	−	0.999960i	$-0.497153\pi$
$827$	425.416			0.0178878			0.00894388	+	0.999960i	$0.497153\pi$
$828$	−9653.45	−	16720.3i	−0.405170	−	0.701775i
$829$	4056.88	−	7026.73i	0.169965	−	0.294389i	−0.768442	−	0.639919i	$-0.778968\pi$
$829$	4056.88	−	7026.73i	0.169965	−	0.294389i	0.938407	+	0.345531i	$0.112301\pi$
$830$	1449.38	−	2510.39i	0.0606127	−	0.104984i
$831$	19188.6	+	33235.5i	0.801015	+	1.38740i
$832$	−1185.63			−0.0494041
$833$	12399.1	−	32306.8i	0.515732	−	1.34377i
$834$	9817.71			0.407625
$835$	2699.61	+	4675.86i	0.111885	+	0.193790i
$836$	10114.3	−	17518.5i	0.418434	−	0.724749i
$837$	14394.2	−	24931.5i	0.594429	−	1.02958i
$838$	477.650	+	827.315i	0.0196899	+	0.0341040i
$839$	17633.8			0.725609			0.362804	−	0.931865i	$-0.381819\pi$
$839$	17633.8			0.725609			0.362804	+	0.931865i	$0.381819\pi$
$840$	−517.924	−	6578.26i	−0.0212739	−	0.270204i
$841$	−22954.6			−0.941185
$842$	−7877.72	−	13644.6i	−0.322428	−	0.558461i
$843$	−13878.4	+	24038.0i	−0.567018	+	0.982103i
$844$	−1624.43	+	2813.59i	−0.0662501	+	0.114749i
$845$	4634.52	+	8027.23i	0.188677	+	0.326799i
$846$	−63262.9			−2.57095
$847$	−17795.1	+	12231.1i	−0.721899	+	0.496180i
$848$	6584.17			0.266629
$849$	−33897.5	−	58712.2i	−1.37027	−	2.37338i
$850$	−2522.19	+	4368.56i	−0.101777	+	0.176283i
$851$	−13053.7	+	22609.7i	−0.525824	+	0.910753i
$852$	3825.77	+	6626.42i	0.153836	+	0.266452i
$853$	33769.2			1.35549			0.677746	−	0.735296i	$-0.262957\pi$
$853$	33769.2			1.35549			0.677746	+	0.735296i	$0.262957\pi$
$854$	2511.91	+	1198.02i	0.100651	+	0.0480041i
$855$	26485.5			1.05940
$856$	−6108.84	−	10580.8i	−0.243921	−	0.422483i
$857$	−9707.00	+	16813.0i	−0.386914	+	0.670154i	−0.992033	−	0.125981i	$-0.959792\pi$
$857$	−9707.00	+	16813.0i	−0.386914	+	0.670154i	0.605119	+	0.796135i	$0.293126\pi$
$858$	−8245.49	+	14281.6i	−0.328085	+	0.568259i
$859$	11412.1	+	19766.3i	0.453290	+	0.785121i	0.998588	−	0.0531209i	$-0.0169169\pi$
$859$	11412.1	+	19766.3i	0.453290	+	0.785121i	−0.545298	+	0.838242i	$0.683584\pi$
$860$	−5206.59			−0.206446
$861$	−37247.9	−	17764.9i	−1.47434	−	0.703167i
$862$	18850.2			0.744827
$863$	−15435.9	−	26735.7i	−0.608856	−	1.05457i	−0.991429	−	0.130644i	$-0.958295\pi$
$863$	−15435.9	−	26735.7i	−0.608856	−	1.05457i	0.382573	−	0.923925i	$-0.375038\pi$
$864$	−3611.38	+	6255.09i	−0.142201	+	0.246299i
$865$	−6493.55	+	11247.2i	−0.255245	+	0.442098i
$866$	2438.58	+	4223.75i	0.0956886	+	0.165738i
$867$	46899.7			1.83714
$868$	7786.76	−	5352.04i	0.304493	−	0.209286i
$869$	53005.9			2.06916
$870$	−1686.78	−	2921.58i	−0.0657323	−	0.113852i
$871$	−5844.29	+	10122.6i	−0.227355	+	0.393790i
$872$	40.9305	−	70.8938i	0.00158954	−	0.00275317i
$873$	7378.14	+	12779.3i	0.286039	+	0.495435i
$874$	18666.1			0.722413
$875$	−181.706	−	2307.89i	−0.00702034	−	0.0891668i
$876$	−37376.4			−1.44159
$877$	19581.0	+	33915.4i	0.753939	+	1.30586i	0.945900	+	0.324459i	$0.105182\pi$
$877$	19581.0	+	33915.4i	0.753939	+	1.30586i	−0.191961	+	0.981403i	$0.561485\pi$
$878$	−6785.52	+	11752.9i	−0.260820	+	0.451754i
$879$	10473.8	−	18141.2i	0.401903	−	0.696117i
$880$	1998.77	+	3461.97i	0.0765665	+	0.132617i
$881$	7446.38			0.284762			0.142381	−	0.989812i	$-0.454524\pi$
$881$	7446.38			0.284762			0.142381	+	0.989812i	$0.454524\pi$
$882$	12865.2	−	33521.2i	0.491151	−	1.27973i
$883$	−43961.2			−1.67544			−0.837720	−	0.546100i	$-0.816112\pi$
$883$	−43961.2			−1.67544			−0.837720	+	0.546100i	$0.816112\pi$
$884$	3737.97	+	6474.35i	0.142219	+	0.246330i
$885$	8494.20	−	14712.4i	0.322632	−	0.558815i
$886$	7317.41	−	12674.1i	0.277464	−	0.480582i
$887$	−9664.60	−	16739.6i	−0.365846	−	0.633664i	0.623066	−	0.782170i	$-0.285887\pi$
$887$	−9664.60	−	16739.6i	−0.365846	−	0.633664i	−0.988912	+	0.148506i	$0.952554\pi$
$888$	20173.5			0.762364
$889$	−1807.65	−	22959.4i	−0.0681965	−	0.866179i
$890$	−9941.58			−0.374430
$891$	14923.2	+	25847.8i	0.561108	+	0.971867i
$892$	2586.24	−	4479.50i	0.0970781	−	0.168144i
$893$	30581.5	−	52968.7i	1.14599	−	1.98492i
$894$	22777.9	+	39452.4i	0.852131	+	1.47593i
$895$	−10438.5			−0.389854
$896$	−1953.63	+	1342.78i	−0.0728416	+	0.0500660i
$897$	−15217.1			−0.566427
$898$	−5411.83	−	9373.57i	−0.201108	−	0.348330i
$899$	2415.33	−	4183.47i	0.0896060	−	0.155202i
$900$	−2617.00	+	4532.78i	−0.0969260	+	0.167881i
$901$	−20758.2	−	35954.2i	−0.767541	−	1.32942i
$902$	25000.4			0.922861
$903$	−38762.5	−	18487.3i	−1.42850	−	0.681305i
$904$	10298.6			0.378902
$905$	4777.77	+	8275.34i	0.175490	+	0.303958i
$906$	6748.67	−	11689.0i	0.247472	−	0.428634i
$907$	13665.4	−	23669.2i	0.500278	−	0.866507i	−0.499722	−	0.866186i	$-0.666564\pi$
$907$	13665.4	−	23669.2i	0.500278	−	0.866507i	1.00000		0.000321244i	$-0.000102255\pi$
$908$	10144.8	+	17571.2i	0.370777	+	0.642205i
$909$	12470.0			0.455009
$910$	−3096.77	−	1476.97i	−0.112810	−	0.0538033i
$911$	35141.2			1.27803			0.639013	−	0.769196i	$-0.279343\pi$
$911$	35141.2			1.27803			0.639013	+	0.769196i	$0.279343\pi$
$912$	−7211.74	−	12491.1i	−0.261847	−	0.453533i
$913$	−7242.42	+	12544.2i	−0.262529	+	0.454714i
$914$	4074.35	−	7056.99i	0.147448	−	0.255388i
$915$	−1673.08	−	2897.87i	−0.0604486	−	0.104700i
$916$	7780.74			0.280658
$917$	8514.82	−	5852.46i	0.306635	−	0.210758i
$918$	45542.9			1.63741
$919$	−1428.53	−	2474.29i	−0.0512763	−	0.0888131i	0.839248	−	0.543749i	$-0.182996\pi$
$919$	−1428.53	−	2474.29i	−0.0512763	−	0.0888131i	−0.890524	+	0.454936i	$0.849662\pi$
$920$	−1844.37	+	3194.55i	−0.0660948	+	0.114480i
$921$	−10073.2	+	17447.4i	−0.360396	+	0.624224i
$922$	−2259.32	−	3913.25i	−0.0807013	−	0.139779i
$923$	3978.42			0.141876
$924$	2588.03	+	32871.1i	0.0921427	+	1.17032i
$925$	7077.59			0.251578
$926$	−11153.8	−	19319.0i	−0.395829	−	0.685595i
$927$	−25023.2	+	43341.5i	−0.886592	+	1.53562i
$928$	−605.984	+	1049.60i	−0.0214358	+	0.0371279i
$929$	−5437.71	−	9418.39i	−0.192040	−	0.332624i	0.753886	−	0.657005i	$-0.228177\pi$
$929$	−5437.71	−	9418.39i	−0.192040	−	0.332624i	−0.945926	+	0.324382i	$0.894844\pi$
$930$	−11360.9			−0.400578
$931$	21847.6	+	26976.1i	0.769092	+	0.949630i
$932$	−2733.79			−0.0960818
$933$	−6574.57	−	11387.5i	−0.230699	−	0.399582i
$934$	−15304.5	+	26508.2i	−0.536166	+	0.928666i
$935$	12603.2	−	21829.4i	0.440822	−	0.763526i
$936$	3878.48	+	6717.73i	0.135440	+	0.234590i
$937$	−31754.7			−1.10713			−0.553566	−	0.832805i	$-0.686733\pi$
$937$	−31754.7			−1.10713			−0.553566	+	0.832805i	$0.686733\pi$
$938$	1834.36	+	23298.5i	0.0638527	+	0.811007i
$939$	−53694.5			−1.86609
$940$	6043.45	+	10467.6i	0.209697	+	0.363207i
$941$	16648.4	−	28836.0i	0.576752	−	0.998964i	−0.419097	−	0.907942i	$-0.637653\pi$
$941$	16648.4	−	28836.0i	0.576752	−	0.998964i	0.995849	−	0.0910225i	$-0.0290135\pi$
$942$	−8750.43	+	15156.2i	−0.302659	+	0.524220i
$943$	11534.6	+	19978.5i	0.398322	+	0.689915i
$944$	−6103.18			−0.210425
$945$	−17224.8	+	11839.1i	−0.592935	+	0.407540i
$946$	26016.9			0.894169
$947$	−28558.0	−	49463.9i	−0.979948	−	1.69732i	−0.662533	−	0.749033i	$-0.730518\pi$
$947$	−28558.0	−	49463.9i	−0.979948	−	1.69732i	−0.317415	−	0.948287i	$-0.602815\pi$
$948$	18897.2	−	32730.9i	0.647418	−	1.12136i
$949$	−9716.95	+	16830.2i	−0.332377	+	0.575693i
$950$	−2530.14	−	4382.32i	−0.0864089	−	0.149665i
$951$	17514.7			0.597217
$952$	13491.8	+	6434.74i	0.459319	+	0.219066i
$953$	−15228.5			−0.517630			−0.258815	−	0.965927i	$-0.583332\pi$
$953$	−15228.5			−0.517630			−0.258815	+	0.965927i	$0.583332\pi$
$954$	−21538.5	−	37305.7i	−0.730958	−	1.26606i
$955$	−1147.47	+	1987.48i	−0.0388811	+	0.0673440i
$956$	−9158.92	+	15863.7i	−0.309854	+	0.536683i
$957$	8428.69	+	14598.9i	0.284703	+	0.493120i
$958$	−4904.33			−0.165398
$959$	12770.1	+	6090.57i	0.430000	+	0.205083i
$960$	2850.34			0.0958273
$961$	6761.58	+	11711.4i	0.226967	+	0.393119i
$962$	5244.62	−	9083.94i	0.175773	−	0.304447i
$963$	−39967.1	+	69225.1i	−1.33741	+	2.31646i
$964$	10136.1	+	17556.3i	0.338654	+	0.586567i
$965$	8731.62			0.291275
$966$	−25074.2	+	17234.1i	−0.835143	+	0.574016i
$967$	−52050.8			−1.73096			−0.865481	−	0.500942i	$-0.832987\pi$
$967$	−52050.8			−1.73096			−0.865481	+	0.500942i	$0.832987\pi$
$968$	−4663.69	−	8077.75i	−0.154852	−	0.268212i
$969$	−45473.5	+	78762.3i	−1.50755	+	2.61116i
$970$	1409.66	−	2441.60i	0.0466612	−	0.0808195i
$971$	16128.1	+	27934.7i	0.533034	+	0.923242i	0.999256	+	0.0385743i	$0.0122816\pi$
$971$	16128.1	+	27934.7i	0.533034	+	0.923242i	−0.466222	+	0.884668i	$0.654385\pi$
$972$	−3095.59			−0.102151
$973$	−801.113	−	10175.1i	−0.0263952	−	0.335251i
$974$	28497.1			0.937480
$975$	2062.64	+	3572.60i	0.0677512	+	0.117349i
$976$	−601.065	+	1041.08i	−0.0197127	+	0.0341435i
$977$	−23866.8	+	41338.5i	−0.781542	+	1.35367i	0.149501	+	0.988761i	$0.452233\pi$
$977$	−23866.8	+	41338.5i	−0.781542	+	1.35367i	−0.931043	+	0.364909i	$0.881100\pi$
$978$	−20197.5	−	34983.0i	−0.660371	−	1.14380i
$979$	49677.3			1.62175
$980$	−6775.48	+	1073.56i	−0.220852	+	0.0349934i
$981$	−535.576			−0.0174308
$982$	−10764.1	−	18644.0i	−0.349793	−	0.605859i
$983$	7023.12	−	12164.4i	0.227877	−	0.394694i	−0.729302	−	0.684192i	$-0.760155\pi$
$983$	7023.12	−	12164.4i	0.227877	−	0.394694i	0.957179	+	0.289498i	$0.0934884\pi$
$984$	8912.91	−	15437.6i	0.288753	−	0.500135i
$985$	−10249.4	−	17752.5i	−0.331547	−	0.574257i
$986$	7642.04			0.246828
$987$	7825.12	+	99388.5i	0.252357	+	3.20524i
$988$	−7499.49			−0.241489
$989$	12003.6	+	20790.9i	0.385938	+	0.668465i
$990$	13077.0	−	22649.9i	0.419811	−	0.727134i
$991$	−25325.4	+	43864.8i	−0.811793	+	1.40607i	0.0998144	+	0.995006i	$0.468175\pi$
$991$	−25325.4	+	43864.8i	−0.811793	+	1.40607i	−0.911608	+	0.411061i	$0.865158\pi$
$992$	2040.73	+	3534.64i	0.0653157	+	0.113130i
$993$	69062.1			2.20707
$994$	6555.47	−	4505.75i	0.209182	−	0.143776i
$995$	21516.5			0.685548
$996$	5164.01	+	8944.33i	0.164285	+	0.284550i
$997$	−12924.8	+	22386.4i	−0.410564	+	0.711117i	−0.994951	−	0.100357i	$-0.968001\pi$
$997$	−12924.8	+	22386.4i	−0.410564	+	0.711117i	0.584388	+	0.811475i	$0.301335\pi$
$998$	7294.82	−	12635.0i	0.231376	−	0.400756i
$999$	−31949.8	−	55338.8i	−1.01186	−	1.75259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.4.e.e.11.1	✓	6
3.2	odd	2		630.4.k.r.361.1		6
4.3	odd	2		560.4.q.m.81.3		6
5.2	odd	4		350.4.j.i.249.6		12
5.3	odd	4		350.4.j.i.249.1		12
5.4	even	2		350.4.e.k.151.3		6
7.2	even	3	inner	70.4.e.e.51.1	yes	6
7.3	odd	6		490.4.a.v.1.1		3
7.4	even	3		490.4.a.w.1.3		3
7.5	odd	6		490.4.e.y.471.3		6
7.6	odd	2		490.4.e.y.361.3		6
21.2	odd	6		630.4.k.r.541.1		6
28.23	odd	6		560.4.q.m.401.3		6
35.2	odd	12		350.4.j.i.149.1		12
35.4	even	6		2450.4.a.cb.1.1		3
35.9	even	6		350.4.e.k.51.3		6
35.23	odd	12		350.4.j.i.149.6		12
35.24	odd	6		2450.4.a.ce.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.e.e.11.1	✓	6	1.1	even	1	trivial
70.4.e.e.51.1	yes	6	7.2	even	3	inner
350.4.e.k.51.3		6	35.9	even	6
350.4.e.k.151.3		6	5.4	even	2
350.4.j.i.149.1		12	35.2	odd	12
350.4.j.i.149.6		12	35.23	odd	12
350.4.j.i.249.1		12	5.3	odd	4
350.4.j.i.249.6		12	5.2	odd	4
490.4.a.v.1.1		3	7.3	odd	6
490.4.a.w.1.3		3	7.4	even	3
490.4.e.y.361.3		6	7.6	odd	2
490.4.e.y.471.3		6	7.5	odd	6
560.4.q.m.81.3		6	4.3	odd	2
560.4.q.m.401.3		6	28.23	odd	6
630.4.k.r.361.1		6	3.2	odd	2
630.4.k.r.541.1		6	21.2	odd	6
2450.4.a.cb.1.1		3	35.4	even	6
2450.4.a.ce.1.3		3	35.24	odd	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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	70.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-4.45365 + 7.71395i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.50000 - 4.33013i) q^{5} +17.8146 q^{6} +(-1.45365 - 18.4631i) q^{7} +8.00000 q^{8} +(-26.1700 - 45.3278i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-4.45365 + 7.71395i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.50000 - 4.33013i) q^{5} +17.8146 q^{6} +(-1.45365 - 18.4631i) q^{7} +8.00000 q^{8} +(-26.1700 - 45.3278i) q^{9} +(-5.00000 + 8.66025i) q^{10} +(24.9846 - 43.2746i) q^{11} +(-17.8146 - 30.8558i) q^{12} -18.5254 q^{13} +(-30.5254 + 20.9809i) q^{14} +44.5365 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-50.4438 + 87.3712i) q^{17} +(-52.3400 + 90.6556i) q^{18} +(-50.6027 - 87.6465i) q^{19} +20.0000 q^{20} +(148.898 + 71.0149i) q^{21} -99.9384 q^{22} +(-46.1093 - 79.8637i) q^{23} +(-35.6292 + 61.7116i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(18.5254 + 32.0870i) q^{26} +225.711 q^{27} +(66.8654 + 31.8907i) q^{28} +37.8740 q^{29} +(-44.5365 - 77.1395i) q^{30} +(63.7727 - 110.458i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(222.545 + 385.460i) q^{33} +201.775 q^{34} +(-76.3135 + 52.4523i) q^{35} +209.360 q^{36} +(-141.552 - 245.175i) q^{37} +(-101.205 + 175.293i) q^{38} +(82.5057 - 142.904i) q^{39} +(-20.0000 - 34.6410i) q^{40} -250.157 q^{41} +(-25.8962 - 328.913i) q^{42} -260.330 q^{43} +(99.9384 + 173.098i) q^{44} +(-130.850 + 226.639i) q^{45} +(-92.2187 + 159.727i) q^{46} +(302.173 + 523.378i) q^{47} +142.517 q^{48} +(-338.774 + 53.6779i) q^{49} +50.0000 q^{50} +(-449.318 - 778.242i) q^{51} +(37.0508 - 64.1739i) q^{52} +(-205.755 + 356.378i) q^{53} +(-225.711 - 390.943i) q^{54} -249.846 q^{55} +(-11.6292 - 147.705i) q^{56} +901.467 q^{57} +(-37.8740 - 65.5997i) q^{58} +(190.724 - 330.344i) q^{59} +(-89.0730 + 154.279i) q^{60} +(-37.5666 - 65.0672i) q^{61} -255.091 q^{62} +(-798.850 + 549.071i) q^{63} +64.0000 q^{64} +(46.3135 + 80.2174i) q^{65} +(445.091 - 770.920i) q^{66} +(315.474 - 546.417i) q^{67} +(-201.775 - 349.485i) q^{68} +821.419 q^{69} +(167.164 + 79.7266i) q^{70} -214.755 q^{71} +(-209.360 - 362.622i) q^{72} +(524.520 - 908.495i) q^{73} +(-283.104 + 490.350i) q^{74} +(-111.341 - 192.849i) q^{75} +404.822 q^{76} +(-835.303 - 398.388i) q^{77} -330.023 q^{78} +(530.385 + 918.654i) q^{79} +(-40.0000 + 69.2820i) q^{80} +(-298.649 + 517.274i) q^{81} +(250.157 + 433.285i) q^{82} -289.875 q^{83} +(-543.798 + 373.767i) q^{84} +504.438 q^{85} +(260.330 + 450.904i) q^{86} +(-168.678 + 292.158i) q^{87} +(199.877 - 346.197i) q^{88} +(497.079 + 860.966i) q^{89} +523.400 q^{90} +(26.9295 + 342.037i) q^{91} +368.875 q^{92} +(568.043 + 983.879i) q^{93} +(604.345 - 1046.76i) q^{94} +(-253.014 + 438.232i) q^{95} +(-142.517 - 246.846i) q^{96} -281.931 q^{97} +(431.747 + 533.096i) q^{98} -2615.39 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 4 q^{3} - 12 q^{4} - 15 q^{5} + 16 q^{6} + 14 q^{7} + 48 q^{8} - 57 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 4 * q^3 - 12 * q^4 - 15 * q^5 + 16 * q^6 + 14 * q^7 + 48 * q^8 - 57 * q^9	\( 6 q - 6 q^{2} - 4 q^{3} - 12 q^{4} - 15 q^{5} + 16 q^{6} + 14 q^{7} + 48 q^{8} - 57 q^{9} - 30 q^{10} - 41 q^{11} - 16 q^{12} - 2 q^{13} - 74 q^{14} + 40 q^{15} - 48 q^{16} - 30 q^{17} - 114 q^{18} - 49 q^{19} + 120 q^{20} + 48 q^{21} + 164 q^{22} - 145 q^{23} - 32 q^{24} - 75 q^{25} + 2 q^{26} + 236 q^{27} + 92 q^{28} + 536 q^{29} - 40 q^{30} + 28 q^{31} - 96 q^{32} + 626 q^{33} + 120 q^{34} - 185 q^{35} + 456 q^{36} - 813 q^{37} - 98 q^{38} - 114 q^{39} - 120 q^{40} + 626 q^{41} - 228 q^{42} + 720 q^{43} - 164 q^{44} - 285 q^{45} - 290 q^{46} + 977 q^{47} + 128 q^{48} - 1860 q^{49} + 300 q^{50} - 1632 q^{51} + 4 q^{52} - 325 q^{53} - 236 q^{54} + 410 q^{55} + 112 q^{56} + 500 q^{57} - 536 q^{58} + 272 q^{59} - 80 q^{60} + 902 q^{61} - 112 q^{62} - 3193 q^{63} + 384 q^{64} + 5 q^{65} + 1252 q^{66} + 170 q^{67} - 120 q^{68} + 4528 q^{69} + 230 q^{70} - 2160 q^{71} - 456 q^{72} + 584 q^{73} - 1626 q^{74} - 100 q^{75} + 392 q^{76} - 2395 q^{77} + 456 q^{78} + 310 q^{79} - 240 q^{80} - 147 q^{81} - 626 q^{82} + 1252 q^{83} + 264 q^{84} + 300 q^{85} - 720 q^{86} + 1846 q^{87} - 328 q^{88} + 400 q^{89} + 1140 q^{90} - 120 q^{91} + 1160 q^{92} + 372 q^{93} + 1954 q^{94} - 245 q^{95} - 128 q^{96} + 3252 q^{97} + 1482 q^{98} - 5222 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 4 * q^3 - 12 * q^4 - 15 * q^5 + 16 * q^6 + 14 * q^7 + 48 * q^8 - 57 * q^9 - 30 * q^10 - 41 * q^11 - 16 * q^12 - 2 * q^13 - 74 * q^14 + 40 * q^15 - 48 * q^16 - 30 * q^17 - 114 * q^18 - 49 * q^19 + 120 * q^20 + 48 * q^21 + 164 * q^22 - 145 * q^23 - 32 * q^24 - 75 * q^25 + 2 * q^26 + 236 * q^27 + 92 * q^28 + 536 * q^29 - 40 * q^30 + 28 * q^31 - 96 * q^32 + 626 * q^33 + 120 * q^34 - 185 * q^35 + 456 * q^36 - 813 * q^37 - 98 * q^38 - 114 * q^39 - 120 * q^40 + 626 * q^41 - 228 * q^42 + 720 * q^43 - 164 * q^44 - 285 * q^45 - 290 * q^46 + 977 * q^47 + 128 * q^48 - 1860 * q^49 + 300 * q^50 - 1632 * q^51 + 4 * q^52 - 325 * q^53 - 236 * q^54 + 410 * q^55 + 112 * q^56 + 500 * q^57 - 536 * q^58 + 272 * q^59 - 80 * q^60 + 902 * q^61 - 112 * q^62 - 3193 * q^63 + 384 * q^64 + 5 * q^65 + 1252 * q^66 + 170 * q^67 - 120 * q^68 + 4528 * q^69 + 230 * q^70 - 2160 * q^71 - 456 * q^72 + 584 * q^73 - 1626 * q^74 - 100 * q^75 + 392 * q^76 - 2395 * q^77 + 456 * q^78 + 310 * q^79 - 240 * q^80 - 147 * q^81 - 626 * q^82 + 1252 * q^83 + 264 * q^84 + 300 * q^85 - 720 * q^86 + 1846 * q^87 - 328 * q^88 + 400 * q^89 + 1140 * q^90 - 120 * q^91 + 1160 * q^92 + 372 * q^93 + 1954 * q^94 - 245 * q^95 - 128 * q^96 + 3252 * q^97 + 1482 * q^98 - 5222 * q^99

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